premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is curious or tall then paul is either patient or creative.
If alice is strong or not funny then john is both rich and not kind.
Everyone who is kind or not rich is both not tall and not quiet.
Everyone who is either not humble or strong is kind or brave and vice versa.
If someone is not kind or quiet then paul is both tall and not tall and vice versa.
If paul is both humble and not tall then john is humble or not calm and vice versa.
If someone is brave then someone is both not wise and calm and vice versa.
Everyone who is either funny or old is not tall and vice versa.
Everyone who is not humble is not creative or generous and vice versa.
If someone is not tall then someone is calm and vice versa.
If someone is either old or wise then mary is either tall or not calm.
Everyone who is not humble or generous is both kind and not patient.
If alice is both not old and not curious then susan is not quiet.
Everyone who is not happy or not quiet is both not happy and not wise and vice versa.
Everyone who is not tall or not brave is not quiet or not rich and vice versa.
Everyone who is not generous or calm is both not creative and generous.
Mary is either not creative or curious.
Mary is either not generous or rich.
Someone is not rich or not curious. | Alice is not brave. | neutral | ((?[X]:((curious(X)|tall(X))))=>((patient(paul)<~>creative(paul))))&
(((strong(alice)|~funny(alice)))=>((rich(john)&~kind(john))))&
(![X]:((kind(X)|~rich(X))=>(~tall(X)&~quiet(X))))&
(![X]:((~humble(X)<~>strong(X))<=>(kind(X)|brave(X))))&
((?[X]:((~kind(X)|quiet(X))))<=>((tall(paul)&~tall(paul))))&
(((humble(paul)&~tall(paul)))<=>((humble(john)|~calm(john))))&
((?[X]:(brave(X)))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:((funny(X)<~>old(X))<=>~tall(X)))&
(![X]:(~humble(X)<=>(~creative(X)|generous(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(calm(X))))&
((?[X]:((old(X)<~>wise(X))))=>((tall(mary)<~>~calm(mary))))&
(![X]:((~humble(X)|generous(X))=>(kind(X)&~patient(X))))&
(((~old(alice)&~curious(alice)))=>(~quiet(susan)))&
(![X]:((~happy(X)|~quiet(X))<=>(~happy(X)&~wise(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~quiet(X)|~rich(X))))&
(![X]:((~generous(X)|calm(X))=>(~creative(X)&generous(X))))&
((~creative(mary)<~>curious(mary)))&
((~generous(mary)<~>rich(mary)))&
(?[X]:((~rich(X)|~curious(X)))) | ~brave(alice) | [] | null | 0 |
If fred is either happy or wise then susan is either rich or happy and vice versa. If someone is both not old and happy then someone is both strong and not rich and vice versa. Everyone who is quiet or strong is either rich or not strong. If someone is quiet then john is either quiet or not humble and vice versa. If someone is both kind and strong then someone is either not tall or not wise. If someone is either patient or kind then someone is both tall and calm and vice versa. Everyone who is either rich or not generous is strong or generous. If susan is happy then someone is patient. Everyone who is both humble and quiet is both not generous and humble and vice versa. If someone is not kind or happy then someone is strong and vice versa. If john is not kind then fred is either funny or calm and vice versa. If mary is either creative or quiet then lucy is both not humble and not rich and vice versa. If john is curious or not quiet then someone is both not patient and humble. Everyone who is either not wise or not quiet is either not funny or not rich. Everyone who is not old or generous is brave and vice versa. If someone is tall then mary is either creative or funny and vice versa. Mary is curious. Someone is not old. Mary is happy or not calm. Lucy is curious or wise. Lucy is not wise. Someone is either not funny or not wise. Paul is both rich and not kind. Susan is both calm and creative. | Lucy is curious. | entailment | (((happy(fred)<~>wise(fred)))<=>((rich(susan)<~>happy(susan))))&
((?[X]:((~old(X)&happy(X))))<=>(?[X]:((strong(X)&~rich(X)))))&
(![X]:((quiet(X)|strong(X))=>(rich(X)<~>~strong(X))))&
((?[X]:(quiet(X)))<=>((quiet(john)<~>~humble(john))))&
((?[X]:((kind(X)&strong(X))))=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((patient(X)<~>kind(X))))<=>(?[X]:((tall(X)&calm(X)))))&
(![X]:((rich(X)<~>~generous(X))=>(strong(X)|generous(X))))&
((happy(susan))=>(?[X]:(patient(X))))&
(![X]:((humble(X)&quiet(X))<=>(~generous(X)&humble(X))))&
((?[X]:((~kind(X)|happy(X))))<=>(?[X]:(strong(X))))&
((~kind(john))<=>((funny(fred)<~>calm(fred))))&
(((creative(mary)<~>quiet(mary)))<=>((~humble(lucy)&~rich(lucy))))&
(((curious(john)|~quiet(john)))=>(?[X]:((~patient(X)&humble(X)))))&
(![X]:((~wise(X)<~>~quiet(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((~old(X)|generous(X))<=>brave(X)))&
((?[X]:(tall(X)))<=>((creative(mary)<~>funny(mary))))&
(curious(mary))&
(?[X]:(~old(X)))&
((happy(mary)|~calm(mary)))&
((curious(lucy)|wise(lucy)))&
(~wise(lucy))&
(?[X]:((~funny(X)<~>~wise(X))))&
((rich(paul)&~kind(paul)))&
((calm(susan)&creative(susan))) | curious(lucy) | [
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 745131152495611164421678
% SZS output start Proof for 745131152495611164421678
20. wise(lucy) | curious(lucy) [input p19]
21. ~wise(lucy) [input p20]
25. ~curious(lucy) [input hypothesis]
145. wise(lucy) | curious(lucy) [cnf transformation 20]
146. ~wise(lucy) [cnf transformation 21]
153. ~curious(lucy) [cnf transformation 25]
378. 47 <=> curious(lucy) [avatar definition]
382. 48 <=> wise(lucy) [avatar definition]
385. 47 | 48 [avatar split clause 145,382,378]
386. ~48 [avatar split clause 146,382]
397. ~47 [avatar split clause 153,378]
398. $false [avatar sat refutation 385,386,397]
% SZS output end Proof for 745131152495611164421678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not curious is both not wise and not creative. If paul is either not creative or not patient then someone is either not wise or old and vice versa. If someone is either not generous or not happy then someone is both creative and humble and vice versa. If alice is not kind then susan is not humble. If lucy is quiet or not wise then someone is not brave or kind. Everyone who is not creative or quiet is both not creative and quiet and vice versa. Everyone who is brave or not wise is both not rich and creative and vice versa. Everyone who is curious is either curious or humble and vice versa. If alice is either not creative or curious then mary is quiet. If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa. Everyone who is both calm and strong is both quiet and wise. If lucy is both rich and not generous then paul is either creative or not tall and vice versa. If someone is rich then paul is both not old and strong. If someone is not creative or wise then fred is humble. Everyone who is not kind or funny is either patient or tall and vice versa. If alice is not patient then someone is brave. Paul is either creative or not brave. Lucy is both not funny and patient. Lucy is not happy or creative. Mary is both not humble and creative. Lucy is strong. Susan is happy or generous. | Paul is not patient. | entailment | (![X]:((old(X)&~curious(X))=>(~wise(X)&~creative(X))))&
(((~creative(paul)<~>~patient(paul)))<=>(?[X]:((~wise(X)<~>old(X)))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((creative(X)&humble(X)))))&
((~kind(alice))=>(~humble(susan)))&
(((quiet(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
((~patient(alice))=>(?[X]:(brave(X))))&
((creative(paul)<~>~brave(paul)))&
((~funny(lucy)&patient(lucy)))&
((~happy(lucy)|creative(lucy)))&
((~humble(mary)&creative(mary)))&
(strong(lucy))&
((happy(susan)|generous(susan))) | ~patient(paul) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3964670941589603681533288
% SZS output start Proof for 3964670941589603681533288
1. ! [X0] : ((~curious(X0) & old(X0)) => (~creative(X0) & ~wise(X0))) [input p0]
2. (~creative(paul) <~> ~patient(paul)) <=> ? [X0] : (~wise(X0) <~> old(X0)) [input p1]
6. ! [X0] : ((quiet(X0) | ~creative(X0)) <=> (quiet(X0) & ~creative(X0))) [input p5]
7. ! [X0] : ((~wise(X0) | brave(X0)) <=> (creative(X0) & ~rich(X0))) [input p6]
8. ! [X0] : (curious(X0) <=> (curious(X0) <~> humble(X0))) [input p7]
9. (~creative(alice) <~> curious(alice)) => quiet(mary) [input p8]
14. ? [X0] : (wise(X0) | ~creative(X0)) => humble(fred) [input p13]
23. patient(paul) [input hypothesis]
28. ! [X0] : ((~creative(X0) & ~wise(X0)) | (curious(X0) | ~old(X0))) [ennf transformation 1]
29. ! [X0] : ((~creative(X0) & ~wise(X0)) | curious(X0) | ~old(X0)) [flattening 28]
32. quiet(mary) | (~creative(alice) <=> curious(alice)) [ennf transformation 9]
34. humble(fred) | ! [X0] : (~wise(X0) & creative(X0)) [ennf transformation 14]
36. (((patient(paul) | creative(paul)) & (~patient(paul) | ~creative(paul))) | ! [X0] : ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (? [X0] : ((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | ((~creative(paul) | patient(paul)) & (~patient(paul) | creative(paul)))) [nnf transformation 2]
37. (((patient(paul) | creative(paul)) & (~patient(paul) | ~creative(paul))) | ! [X0] : ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (? [X1] : ((~old(X1) | wise(X1)) & (old(X1) | ~wise(X1))) | ((~creative(paul) | patient(paul)) & (~patient(paul) | creative(paul)))) [rectify 36]
38. ? [X1] : ((~old(X1) | wise(X1)) & (old(X1) | ~wise(X1))) => ((~old(sK0) | wise(sK0)) & (old(sK0) | ~wise(sK0))) [choice axiom]
39. (((patient(paul) | creative(paul)) & (~patient(paul) | ~creative(paul))) | ! [X0] : ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (((~old(sK0) | wise(sK0)) & (old(sK0) | ~wise(sK0))) | ((~creative(paul) | patient(paul)) & (~patient(paul) | creative(paul)))) [skolemisation 37,38]
47. ! [X0] : (((quiet(X0) | ~creative(X0)) | (~quiet(X0) | creative(X0))) & ((quiet(X0) & ~creative(X0)) | (~quiet(X0) & creative(X0)))) [nnf transformation 6]
48. ! [X0] : ((quiet(X0) | ~creative(X0) | ~quiet(X0) | creative(X0)) & ((quiet(X0) & ~creative(X0)) | (~quiet(X0) & creative(X0)))) [flattening 47]
49. ! [X0] : (((~wise(X0) | brave(X0)) | (~creative(X0) | rich(X0))) & ((creative(X0) & ~rich(X0)) | (wise(X0) & ~brave(X0)))) [nnf transformation 7]
50. ! [X0] : ((~wise(X0) | brave(X0) | ~creative(X0) | rich(X0)) & ((creative(X0) & ~rich(X0)) | (wise(X0) & ~brave(X0)))) [flattening 49]
51. ! [X0] : ((curious(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ~curious(X0))) [nnf transformation 8]
52. quiet(mary) | ((~creative(alice) | ~curious(alice)) & (curious(alice) | creative(alice))) [nnf transformation 32]
66. ~creative(X0) | curious(X0) | ~old(X0) [cnf transformation 29]
71. ~patient(paul) | ~creative(paul) | old(X0) | wise(X0) [cnf transformation 39]
85. ~quiet(X0) | ~creative(X0) [cnf transformation 48]
92. creative(X0) | wise(X0) [cnf transformation 50]
95. ~humble(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 51]
97. curious(X0) | curious(X0) | ~humble(X0) [cnf transformation 51]
99. quiet(mary) | ~creative(alice) | ~curious(alice) [cnf transformation 52]
113. humble(fred) | creative(X0) [cnf transformation 34]
114. humble(fred) | ~wise(X0) [cnf transformation 34]
130. patient(paul) [cnf transformation 23]
131. ~humble(X0) | ~curious(X0) [duplicate literal removal 95]
132. ~humble(X0) | curious(X0) [duplicate literal removal 97]
137. 2 <=> creative(paul) [avatar definition]
138. ~creative(paul) <- (~2) [avatar component clause 137]
141. 3 <=> patient(paul) [avatar definition]
146. 4 <=> ! [X0] : (old(X0) | wise(X0)) [avatar definition]
147. old(X0) | wise(X0) <- (4) [avatar component clause 146]
150. 4 | ~2 | ~3 [avatar split clause 71,141,137,146]
221. ~humble(X0) [subsumption resolution 131,132]
223. 20 <=> curious(alice) [avatar definition]
225. ~curious(alice) <- (~20) [avatar component clause 223]
227. 21 <=> creative(alice) [avatar definition]
229. ~creative(alice) <- (~21) [avatar component clause 227]
231. 22 <=> quiet(mary) [avatar definition]
233. quiet(mary) <- (22) [avatar component clause 231]
234. ~20 | ~21 | 22 [avatar split clause 99,231,227,223]
275. ~wise(X0) [subsumption resolution 114,221]
276. creative(X0) [subsumption resolution 113,221]
296. 3 [avatar split clause 130,141]
297. $false <- (~21) [subsumption resolution 229,276]
298. 21 [avatar contradiction clause 297]
299. $false <- (~2) [subsumption resolution 138,276]
300. 2 [avatar contradiction clause 299]
301. old(X0) <- (4) [subsumption resolution 147,275]
317. curious(X0) | ~old(X0) | wise(X0) [resolution 66,92]
319. curious(X0) | wise(X0) <- (4) [subsumption resolution 317,301]
320. curious(X0) <- (4) [subsumption resolution 319,275]
322. $false <- (4, ~20) [resolution 320,225]
323. ~4 | 20 [avatar contradiction clause 322]
324. ~creative(mary) <- (22) [resolution 233,85]
325. $false <- (22) [subsumption resolution 324,276]
326. ~22 [avatar contradiction clause 325]
327. $false [avatar sat refutation 150,234,296,298,300,323,326]
% SZS output end Proof for 3964670941589603681533288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and old then mary is both old and strong and vice versa. Everyone who is not wise or not old is curious and vice versa. Everyone who is either calm or humble is both not generous and kind and vice versa. If someone is either brave or patient then someone is both not curious and not tall and vice versa. Everyone who is either not tall or not generous is humble and vice versa. If paul is patient then someone is both not tall and not generous and vice versa. Everyone who is both not tall and creative is humble or not wise and vice versa. Everyone who is not wise or kind is patient and vice versa. If mary is both tall and not rich then lucy is either creative or funny. If alice is both not brave and kind then someone is old. Everyone who is either not humble or not calm is quiet or not generous and vice versa. If john is both not tall and not calm then susan is not happy. Everyone who is not tall or not quiet is generous and vice versa. Everyone who is either not happy or generous is either happy or not strong. If fred is strong or not patient then fred is curious and vice versa. Someone is either strong or patient. Someone is either brave or creative. Someone is tall. Someone is not rich or calm. John is both not quiet and wise. Paul is either happy or humble. | Mary is not strong. | neutral | ((?[X]:((~brave(X)&old(X))))<=>((old(mary)&strong(mary))))&
(![X]:((~wise(X)|~old(X))<=>curious(X)))&
(![X]:((calm(X)<~>humble(X))<=>(~generous(X)&kind(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>humble(X)))&
((patient(paul))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~tall(X)&creative(X))<=>(humble(X)|~wise(X))))&
(![X]:((~wise(X)|kind(X))<=>patient(X)))&
(((tall(mary)&~rich(mary)))=>((creative(lucy)<~>funny(lucy))))&
(((~brave(alice)&kind(alice)))=>(?[X]:(old(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(quiet(X)|~generous(X))))&
(((~tall(john)&~calm(john)))=>(~happy(susan)))&
(![X]:((~tall(X)|~quiet(X))<=>generous(X)))&
(![X]:((~happy(X)<~>generous(X))=>(happy(X)<~>~strong(X))))&
(((strong(fred)|~patient(fred)))<=>(curious(fred)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)|calm(X))))&
((~quiet(john)&wise(john)))&
((happy(paul)<~>humble(paul))) | ~strong(mary) | [] | null | 0 |
If someone is either strong or not kind then mary is humble and vice versa. Everyone who is either brave or not curious is not brave and vice versa. If someone is either tall or not kind then someone is both rich and not patient. Everyone who is not kind is either not patient or not tall. If someone is either quiet or not quiet then someone is both tall and strong and vice versa. If someone is creative or not happy then someone is curious or not creative and vice versa. If someone is strong or not funny then alice is both not rich and not funny. Everyone who is wise or humble is patient. Everyone who is not curious is either patient or not generous and vice versa. Everyone who is not humble is generous or not patient and vice versa. Everyone who is both patient and wise is both not happy and not curious and vice versa. If alice is either curious or not funny then someone is not happy and vice versa. Everyone who is not patient is both not calm and not humble and vice versa. If john is both wise and creative then someone is both calm and not patient and vice versa. If mary is both old and quiet then mary is not generous. Someone is both old and not wise. Susan is either not quiet or old. Someone is either curious or rich. Susan is both happy and generous. Someone is not curious or humble. Susan is rich or not old. Someone is not creative. Someone is either not strong or rich. | Susan is humble. | contradiction | ((?[X]:((strong(X)<~>~kind(X))))<=>(humble(mary)))&
(![X]:((brave(X)<~>~curious(X))<=>~brave(X)))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>~tall(X))))&
((?[X]:((quiet(X)<~>~quiet(X))))<=>(?[X]:((tall(X)&strong(X)))))&
((?[X]:((creative(X)|~happy(X))))<=>(?[X]:((curious(X)|~creative(X)))))&
((?[X]:((strong(X)|~funny(X))))=>((~rich(alice)&~funny(alice))))&
(![X]:((wise(X)|humble(X))=>patient(X)))&
(![X]:(~curious(X)<=>(patient(X)<~>~generous(X))))&
(![X]:(~humble(X)<=>(generous(X)|~patient(X))))&
(![X]:((patient(X)&wise(X))<=>(~happy(X)&~curious(X))))&
(((curious(alice)<~>~funny(alice)))<=>(?[X]:(~happy(X))))&
(![X]:(~patient(X)<=>(~calm(X)&~humble(X))))&
(((wise(john)&creative(john)))<=>(?[X]:((calm(X)&~patient(X)))))&
(((old(mary)&quiet(mary)))=>(~generous(mary)))&
(?[X]:((old(X)&~wise(X))))&
((~quiet(susan)<~>old(susan)))&
(?[X]:((curious(X)<~>rich(X))))&
((happy(susan)&generous(susan)))&
(?[X]:((~curious(X)|humble(X))))&
((rich(susan)|~old(susan)))&
(?[X]:(~creative(X)))&
(?[X]:((~strong(X)<~>rich(X)))) | humble(susan) | [
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9187527342754644984752564
% SZS output start Proof for 9187527342754644984752564
10. ! [X0] : (~humble(X0) <=> (~patient(X0) | generous(X0))) [input p9]
19. generous(susan) & happy(susan) [input p18]
24. humble(susan) [input hypothesis]
55. ! [X0] : ((~humble(X0) | (patient(X0) & ~generous(X0))) & ((~patient(X0) | generous(X0)) | humble(X0))) [nnf transformation 10]
56. ! [X0] : ((~humble(X0) | (patient(X0) & ~generous(X0))) & (~patient(X0) | generous(X0) | humble(X0))) [flattening 55]
118. ~generous(X0) | ~humble(X0) [cnf transformation 56]
143. generous(susan) [cnf transformation 19]
149. humble(susan) [cnf transformation 24]
334. ~humble(susan) [resolution 118,143]
335. $false [subsumption resolution 334,149]
% SZS output end Proof for 9187527342754644984752564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not curious then someone is both not rich and not quiet.
Everyone who is not generous or not funny is funny.
Everyone who is quiet or creative is not happy or not humble.
If susan is either not tall or creative then paul is both old and not wise.
Everyone who is not generous is either not strong or patient and vice versa.
Everyone who is both rich and not old is patient or not generous.
Everyone who is both quiet and calm is both not strong and humble and vice versa.
If susan is either not creative or not tall then fred is not quiet.
Everyone who is both not kind and tall is not rich or not strong and vice versa.
Everyone who is not kind is both not strong and strong.
Everyone who is not quiet or not creative is not tall or not curious and vice versa.
Everyone who is creative is both humble and not wise and vice versa.
If lucy is patient or not humble then susan is either happy or funny.
If someone is both not wise and not strong then someone is both not brave and not generous and vice versa.
If someone is either not wise or wise then alice is brave or not funny.
Someone is either funny or not quiet.
Mary is either not curious or generous.
Paul is calm or not quiet.
Someone is not rich or brave.
Someone is either strong or not strong. | Mary is kind. | entailment | ((~curious(susan))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((~generous(X)|~funny(X))=>funny(X)))&
(![X]:((quiet(X)|creative(X))=>(~happy(X)|~humble(X))))&
(((~tall(susan)<~>creative(susan)))=>((old(paul)&~wise(paul))))&
(![X]:(~generous(X)<=>(~strong(X)<~>patient(X))))&
(![X]:((rich(X)&~old(X))=>(patient(X)|~generous(X))))&
(![X]:((quiet(X)&calm(X))<=>(~strong(X)&humble(X))))&
(((~creative(susan)<~>~tall(susan)))=>(~quiet(fred)))&
(![X]:((~kind(X)&tall(X))<=>(~rich(X)|~strong(X))))&
(![X]:(~kind(X)=>(~strong(X)&strong(X))))&
(![X]:((~quiet(X)|~creative(X))<=>(~tall(X)|~curious(X))))&
(![X]:(creative(X)<=>(humble(X)&~wise(X))))&
(((patient(lucy)|~humble(lucy)))=>((happy(susan)<~>funny(susan))))&
((?[X]:((~wise(X)&~strong(X))))<=>(?[X]:((~brave(X)&~generous(X)))))&
((?[X]:((~wise(X)<~>wise(X))))=>((brave(alice)|~funny(alice))))&
(?[X]:((funny(X)<~>~quiet(X))))&
((~curious(mary)<~>generous(mary)))&
((calm(paul)|~quiet(paul)))&
(?[X]:((~rich(X)|brave(X))))&
(?[X]:((strong(X)<~>~strong(X)))) | kind(mary) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3881486393238003333293462
% SZS output start Proof for 3881486393238003333293462
9. ! [X0] : ((tall(X0) & ~kind(X0)) <=> (~strong(X0) | ~rich(X0))) [input p8]
10. ! [X0] : (~kind(X0) => (strong(X0) & ~strong(X0))) [input p9]
21. ~kind(mary) [input hypothesis]
31. ! [X0] : ((strong(X0) & ~strong(X0)) | kind(X0)) [ennf transformation 10]
42. ! [X0] : (((tall(X0) & ~kind(X0)) | (strong(X0) & rich(X0))) & ((~strong(X0) | ~rich(X0)) | (~tall(X0) | kind(X0)))) [nnf transformation 9]
43. ! [X0] : (((tall(X0) & ~kind(X0)) | (strong(X0) & rich(X0))) & (~strong(X0) | ~rich(X0) | ~tall(X0) | kind(X0))) [flattening 42]
84. ~kind(X0) | strong(X0) [cnf transformation 43]
87. ~strong(X0) | kind(X0) [cnf transformation 31]
88. strong(X0) | kind(X0) [cnf transformation 31]
114. ~kind(mary) [cnf transformation 21]
152. strong(X0) [subsumption resolution 88,84]
153. kind(X0) [subsumption resolution 87,152]
214. $false [subsumption resolution 114,153]
% SZS output end Proof for 3881486393238003333293462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or not calm then someone is either quiet or not quiet and vice versa. Everyone who is both not creative and strong is either not strong or not happy. Everyone who is either not strong or not funny is not wise and vice versa. If alice is either not happy or not brave then alice is both kind and calm and vice versa. Everyone who is either not wise or not funny is both not funny and wise and vice versa. If mary is strong or humble then lucy is both strong and happy and vice versa. Everyone who is not strong is kind. Everyone who is either not kind or wise is both curious and not wise. If someone is either brave or kind then susan is either generous or patient and vice versa. Everyone who is both not creative and old is not humble and vice versa. If someone is both generous and not wise then someone is not happy or curious and vice versa. Everyone who is not patient or not quiet is not patient or not wise and vice versa. If john is brave or not kind then john is calm and vice versa. Everyone who is both humble and calm is either quiet or not creative. If fred is curious or patient then someone is both tall and generous. Fred is not creative. Fred is wise or not old. Alice is both not quiet and patient. Alice is not happy. Someone is both generous and not creative. Susan is not creative. Someone is either not patient or not creative. | John is wise. | neutral | ((?[X]:((~strong(X)|~calm(X))))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~creative(X)&strong(X))=>(~strong(X)<~>~happy(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>~wise(X)))&
(((~happy(alice)<~>~brave(alice)))<=>((kind(alice)&calm(alice))))&
(![X]:((~wise(X)<~>~funny(X))<=>(~funny(X)&wise(X))))&
(((strong(mary)|humble(mary)))<=>((strong(lucy)&happy(lucy))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((~kind(X)<~>wise(X))=>(curious(X)&~wise(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>((generous(susan)<~>patient(susan))))&
(![X]:((~creative(X)&old(X))<=>~humble(X)))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(~patient(X)|~wise(X))))&
(((brave(john)|~kind(john)))<=>(calm(john)))&
(![X]:((humble(X)&calm(X))=>(quiet(X)<~>~creative(X))))&
(((curious(fred)|patient(fred)))=>(?[X]:((tall(X)&generous(X)))))&
(~creative(fred))&
((wise(fred)|~old(fred)))&
((~quiet(alice)&patient(alice)))&
(~happy(alice))&
(?[X]:((generous(X)&~creative(X))))&
(~creative(susan))&
(?[X]:((~patient(X)<~>~creative(X)))) | wise(john) | [] | null | 0 |
Everyone who is both not quiet and generous is not happy or creative and vice versa.
Everyone who is calm is quiet and vice versa.
Everyone who is tall is either not happy or funny.
Everyone who is either brave or not patient is patient.
Everyone who is both quiet and humble is not creative or generous.
Everyone who is tall is not humble and vice versa.
Everyone who is generous is either wise or happy and vice versa.
Everyone who is creative or not happy is either kind or not generous.
Everyone who is not brave is not creative and vice versa.
Everyone who is either not calm or happy is brave and vice versa.
If mary is not patient or not creative then someone is both not curious and not humble.
If alice is not brave or not funny then lucy is either not patient or curious.
Everyone who is creative or funny is both humble and strong and vice versa.
If someone is calm then someone is both not curious and not calm.
If someone is both wise and generous then someone is either happy or not strong.
Paul is either not strong or not patient.
Fred is both not generous and curious.
Fred is tall or not funny.
Fred is patient or not brave.
Someone is both kind and humble.
Susan is rich or not funny.
John is both happy and rich.
Fred is either humble or not happy. | Mary is not happy. | entailment | (![X]:((~quiet(X)&generous(X))<=>(~happy(X)|creative(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(tall(X)=>(~happy(X)<~>funny(X))))&
(![X]:((brave(X)<~>~patient(X))=>patient(X)))&
(![X]:((quiet(X)&humble(X))=>(~creative(X)|generous(X))))&
(![X]:(tall(X)<=>~humble(X)))&
(![X]:(generous(X)<=>(wise(X)<~>happy(X))))&
(![X]:((creative(X)|~happy(X))=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
((~strong(paul)<~>~patient(paul)))&
((~generous(fred)&curious(fred)))&
((tall(fred)|~funny(fred)))&
((patient(fred)|~brave(fred)))&
(?[X]:((kind(X)&humble(X))))&
((rich(susan)|~funny(susan)))&
((happy(john)&rich(john)))&
((humble(fred)<~>~happy(fred))) | ~happy(mary) | [
"p0",
"p1",
"p2",
"p5",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2774545753700911195231384
% SZS output start Proof for 2774545753700911195231384
1. ! [X0] : ((generous(X0) & ~quiet(X0)) <=> (creative(X0) | ~happy(X0))) [input p0]
2. ! [X0] : (calm(X0) <=> quiet(X0)) [input p1]
3. ! [X0] : (tall(X0) => (~happy(X0) <~> funny(X0))) [input p2]
6. ! [X0] : (tall(X0) <=> ~humble(X0)) [input p5]
9. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> brave(X0)) [input p9]
11. (~creative(mary) | ~patient(mary)) => ? [X0] : (~humble(X0) & ~curious(X0)) [input p10]
13. ! [X0] : ((funny(X0) | creative(X0)) <=> (strong(X0) & humble(X0))) [input p12]
24. happy(mary) [input hypothesis]
29. ! [X0] : ((~happy(X0) <~> funny(X0)) | ~tall(X0)) [ennf transformation 3]
34. ? [X0] : (~humble(X0) & ~curious(X0)) | (creative(mary) & patient(mary)) [ennf transformation 11]
38. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~generous(X0) | quiet(X0)))) [nnf transformation 1]
39. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~generous(X0) | quiet(X0))) [flattening 38]
40. ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))) [nnf transformation 2]
41. ! [X0] : (((~funny(X0) | happy(X0)) & (funny(X0) | ~happy(X0))) | ~tall(X0)) [nnf transformation 29]
43. ! [X0] : ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))) [nnf transformation 6]
46. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 9]
47. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 10]
48. ? [X0] : (~humble(X0) & ~curious(X0)) => (~humble(sK0) & ~curious(sK0)) [choice axiom]
49. (~humble(sK0) & ~curious(sK0)) | (creative(mary) & patient(mary)) [skolemisation 34,48]
51. ! [X0] : (((funny(X0) | creative(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~funny(X0) & ~creative(X0)))) [nnf transformation 13]
52. ! [X0] : ((funny(X0) | creative(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~funny(X0) & ~creative(X0)))) [flattening 51]
65. ~quiet(X0) | happy(X0) [cnf transformation 39]
66. ~creative(X0) | ~quiet(X0) [cnf transformation 39]
69. ~calm(X0) | quiet(X0) [cnf transformation 40]
71. ~tall(X0) | ~happy(X0) | funny(X0) [cnf transformation 41]
77. humble(X0) | tall(X0) [cnf transformation 43]
86. ~creative(X0) | brave(X0) [cnf transformation 46]
87. ~brave(X0) | creative(X0) [cnf transformation 46]
88. brave(X0) | happy(X0) | calm(X0) [cnf transformation 47]
91. ~brave(X0) | calm(X0) | ~happy(X0) [cnf transformation 47]
95. ~humble(sK0) | creative(mary) [cnf transformation 49]
100. ~creative(X0) | humble(X0) [cnf transformation 52]
101. ~funny(X0) | humble(X0) [cnf transformation 52]
120. happy(mary) [cnf transformation 24]
127. 1 <=> creative(mary) [avatar definition]
129. creative(mary) <- (1) [avatar component clause 127]
131. 2 <=> humble(sK0) [avatar definition]
133. ~humble(sK0) <- (~2) [avatar component clause 131]
134. 1 | ~2 [avatar split clause 95,131,127]
229. tall(sK0) <- (~2) [resolution 77,133]
247. ~happy(sK0) | funny(sK0) <- (~2) [resolution 71,229]
249. 21 <=> funny(sK0) [avatar definition]
251. funny(sK0) <- (21) [avatar component clause 249]
253. 22 <=> happy(sK0) [avatar definition]
256. 21 | ~22 | 2 [avatar split clause 247,131,253,249]
261. calm(X0) | happy(X0) | creative(X0) [resolution 88,87]
298. 27 <=> quiet(mary) [avatar definition]
299. ~quiet(mary) <- (~27) [avatar component clause 298]
323. happy(X1) | creative(X1) | quiet(X1) [resolution 261,69]
334. creative(X1) | happy(X1) [subsumption resolution 323,65]
345. humble(X2) | happy(X2) [resolution 334,100]
427. happy(sK0) <- (~2) [resolution 345,133]
431. 22 | 2 [avatar split clause 427,131,253]
434. humble(sK0) <- (21) [resolution 251,101]
435. $false <- (~2, 21) [subsumption resolution 434,133]
436. 2 | ~21 [avatar contradiction clause 435]
440. brave(mary) <- (1) [resolution 129,86]
442. ~quiet(mary) <- (1) [resolution 129,66]
445. ~27 | ~1 [avatar split clause 442,127,298]
450. calm(mary) | ~happy(mary) <- (1) [resolution 440,91]
453. calm(mary) <- (1) [subsumption resolution 450,120]
469. quiet(mary) <- (1) [resolution 453,69]
470. $false <- (1, ~27) [subsumption resolution 469,299]
471. ~1 | 27 [avatar contradiction clause 470]
472. $false [avatar sat refutation 134,256,431,436,445,471]
% SZS output end Proof for 2774545753700911195231384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not wise or not quiet then someone is tall. If someone is not old then someone is not kind. If someone is curious then someone is not generous and vice versa. If lucy is not creative or not brave then someone is both not strong and not tall and vice versa. If someone is either not kind or not quiet then fred is either kind or not old and vice versa. Everyone who is both happy and not happy is generous. Everyone who is creative or not patient is kind. Everyone who is both curious and not funny is both not generous and brave. If lucy is not happy or humble then paul is wise. If someone is not rich or not brave then fred is both not creative and not happy and vice versa. If susan is curious then someone is either curious or humble and vice versa. Everyone who is either not patient or not old is not happy or not humble. Everyone who is happy or tall is either creative or not kind and vice versa. Everyone who is both calm and not curious is not happy or not generous and vice versa. If paul is strong or brave then lucy is tall and vice versa. Everyone who is wise or not strong is not calm or not humble. Paul is either not rich or not creative. Lucy is either not tall or patient. Someone is both not happy and not curious. Someone is both not patient and quiet. Someone is patient or not quiet. Someone is either not curious or not quiet. Someone is not wise or rich. Lucy is both creative and not curious. | Lucy is not happy. | neutral | (((~wise(paul)|~quiet(paul)))=>(?[X]:(tall(X))))&
((?[X]:(~old(X)))=>(?[X]:(~kind(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~generous(X))))&
(((~creative(lucy)|~brave(lucy)))<=>(?[X]:((~strong(X)&~tall(X)))))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>((kind(fred)<~>~old(fred))))&
(![X]:((happy(X)&~happy(X))=>generous(X)))&
(![X]:((creative(X)|~patient(X))=>kind(X)))&
(![X]:((curious(X)&~funny(X))=>(~generous(X)&brave(X))))&
(((~happy(lucy)|humble(lucy)))=>(wise(paul)))&
((?[X]:((~rich(X)|~brave(X))))<=>((~creative(fred)&~happy(fred))))&
((curious(susan))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~patient(X)<~>~old(X))=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|tall(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((calm(X)&~curious(X))<=>(~happy(X)|~generous(X))))&
(((strong(paul)|brave(paul)))<=>(tall(lucy)))&
(![X]:((wise(X)|~strong(X))=>(~calm(X)|~humble(X))))&
((~rich(paul)<~>~creative(paul)))&
((~tall(lucy)<~>patient(lucy)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((patient(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~wise(X)|rich(X))))&
((creative(lucy)&~curious(lucy))) | ~happy(lucy) | [] | null | 0 |
Everyone who is either quiet or not calm is not creative.
If paul is both generous and creative then someone is not funny or happy and vice versa.
Everyone who is patient or not wise is not curious.
If someone is either old or not wise then someone is both not calm and not strong and vice versa.
Everyone who is patient or strong is both kind and happy and vice versa.
Everyone who is both not calm and rich is both quiet and humble and vice versa.
If someone is kind or not old then mary is not rich.
Everyone who is both strong and patient is not rich or wise.
Everyone who is either not kind or not generous is either wise or not funny.
Everyone who is both not brave and curious is strong or brave and vice versa.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Everyone who is both strong and not patient is not wise or not calm and vice versa.
If john is either tall or not funny then someone is either tall or not humble.
Everyone who is not curious is either not brave or creative and vice versa.
Someone is either not generous or not happy.
Someone is not generous or strong.
Susan is not quiet or not strong.
Someone is patient or not strong.
Susan is both funny and not humble.
Someone is not tall or brave. | Lucy is not calm. | contradiction | (![X]:((quiet(X)<~>~calm(X))=>~creative(X)))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((patient(X)|~wise(X))=>~curious(X)))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((patient(X)|strong(X))<=>(kind(X)&happy(X))))&
(![X]:((~calm(X)&rich(X))<=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
(((tall(john)<~>~funny(john)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:(~curious(X)<=>(~brave(X)<~>creative(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((~generous(X)|strong(X))))&
((~quiet(susan)|~strong(susan)))&
(?[X]:((patient(X)|~strong(X))))&
((funny(susan)&~humble(susan)))&
(?[X]:((~tall(X)|brave(X)))) | ~calm(lucy) | [
"p2",
"p4",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2241919464701378929878971
% SZS output start Proof for 2241919464701378929878971
3. ! [X0] : ((~wise(X0) | patient(X0)) => ~curious(X0)) [input p2]
5. ! [X0] : ((strong(X0) | patient(X0)) <=> (happy(X0) & kind(X0))) [input p4]
10. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (brave(X0) | strong(X0))) [input p9]
13. ? [X0] : happy(X0) <=> (curious(lucy) & ~wise(lucy)) [input p12]
14. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~calm(X0) | ~wise(X0))) [input p13]
23. ~calm(lucy) [input hypothesis]
27. ! [X0] : (~curious(X0) | (wise(X0) & ~patient(X0))) [ennf transformation 3]
44. ! [X0] : (((strong(X0) | patient(X0)) | (~happy(X0) | ~kind(X0))) & ((happy(X0) & kind(X0)) | (~strong(X0) & ~patient(X0)))) [nnf transformation 5]
45. ! [X0] : ((strong(X0) | patient(X0) | ~happy(X0) | ~kind(X0)) & ((happy(X0) & kind(X0)) | (~strong(X0) & ~patient(X0)))) [flattening 44]
49. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (~curious(X0) | brave(X0)))) [nnf transformation 10]
50. ! [X0] : (((curious(X0) & ~brave(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | ~curious(X0) | brave(X0))) [flattening 49]
60. (? [X0] : happy(X0) | (~curious(lucy) | wise(lucy))) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [nnf transformation 13]
61. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [flattening 60]
62. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [rectify 61]
63. ? [X0] : happy(X0) => happy(sK6) [choice axiom]
64. (happy(sK6) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [skolemisation 62,63]
65. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 14]
66. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | patient(X0) | ~strong(X0))) [flattening 65]
88. ~curious(X0) | wise(X0) [cnf transformation 27]
98. ~strong(X0) | happy(X0) [cnf transformation 45]
114. ~strong(X0) | curious(X0) [cnf transformation 50]
126. ~wise(lucy) | ~happy(X1) [cnf transformation 64]
130. strong(X0) | wise(X0) [cnf transformation 66]
131. strong(X0) | calm(X0) [cnf transformation 66]
150. ~calm(lucy) [cnf transformation 23]
154. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
155. ~happy(X0) <- (1) [avatar component clause 154]
181. 7 <=> ! [X1] : (strong(X1) | calm(X1)) [avatar definition]
182. strong(X1) | calm(X1) <- (7) [avatar component clause 181]
243. 21 <=> ! [X1] : calm(X1) [avatar definition]
244. calm(X1) <- (21) [avatar component clause 243]
284. 30 <=> wise(lucy) [avatar definition]
286. ~wise(lucy) <- (~30) [avatar component clause 284]
287. 1 | ~30 [avatar split clause 126,284,154]
288. 7 [avatar split clause 131,181]
353. wise(X0) | curious(X0) [resolution 130,114]
359. wise(X0) [subsumption resolution 353,88]
360. $false <- (~30) [resolution 359,286]
361. 30 [avatar contradiction clause 360]
363. calm(X1) | happy(X1) <- (7) [resolution 182,98]
368. calm(X1) <- (1, 7) [subsumption resolution 363,155]
369. 21 | ~1 | ~7 [avatar split clause 368,181,154,243]
380. $false <- (21) [resolution 244,150]
383. ~21 [avatar contradiction clause 380]
384. $false [avatar sat refutation 287,288,361,369,383]
% SZS output end Proof for 2241919464701378929878971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not wise then mary is not happy and vice versa.
If someone is happy then paul is either kind or wise.
If paul is either strong or creative then someone is not funny and vice versa.
If someone is not curious or happy then someone is not wise.
If alice is kind then someone is rich.
If someone is not curious then someone is both patient and not old.
Everyone who is not curious is not kind and vice versa.
Everyone who is rich or not quiet is either patient or kind and vice versa.
Everyone who is not humble is happy or patient and vice versa.
Everyone who is either not curious or not happy is not old and vice versa.
Everyone who is either not brave or not creative is not funny.
If susan is not funny then someone is either not calm or brave.
If lucy is both creative and not humble then fred is not humble and vice versa.
Everyone who is either not brave or not calm is not strong.
If lucy is either strong or not kind then fred is both funny and old and vice versa.
If someone is both not creative and not old then paul is kind.
Someone is quiet.
Someone is either not humble or humble.
Susan is not rich.
Fred is both calm and not quiet.
Paul is either curious or brave.
Someone is both generous and curious.
Alice is both old and not kind.
Someone is not curious or funny. | Alice is curious. | contradiction | ((?[X]:((~strong(X)&~wise(X))))<=>(~happy(mary)))&
((?[X]:(happy(X)))=>((kind(paul)<~>wise(paul))))&
(((strong(paul)<~>creative(paul)))<=>(?[X]:(~funny(X))))&
((?[X]:((~curious(X)|happy(X))))=>(?[X]:(~wise(X))))&
((kind(alice))=>(?[X]:(rich(X))))&
((?[X]:(~curious(X)))=>(?[X]:((patient(X)&~old(X)))))&
(![X]:(~curious(X)<=>~kind(X)))&
(![X]:((rich(X)|~quiet(X))<=>(patient(X)<~>kind(X))))&
(![X]:(~humble(X)<=>(happy(X)|patient(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>~old(X)))&
(![X]:((~brave(X)<~>~creative(X))=>~funny(X)))&
((~funny(susan))=>(?[X]:((~calm(X)<~>brave(X)))))&
(((creative(lucy)&~humble(lucy)))<=>(~humble(fred)))&
(![X]:((~brave(X)<~>~calm(X))=>~strong(X)))&
(((strong(lucy)<~>~kind(lucy)))<=>((funny(fred)&old(fred))))&
((?[X]:((~creative(X)&~old(X))))=>(kind(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((~humble(X)<~>humble(X))))&
(~rich(susan))&
((calm(fred)&~quiet(fred)))&
((curious(paul)<~>brave(paul)))&
(?[X]:((generous(X)&curious(X))))&
((old(alice)&~kind(alice)))&
(?[X]:((~curious(X)|funny(X)))) | curious(alice) | [
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8886414761436056190381970
% SZS output start Proof for 8886414761436056190381970
7. ! [X0] : (~curious(X0) <=> ~kind(X0)) [input p6]
23. ~kind(alice) & old(alice) [input p22]
25. curious(alice) [input hypothesis]
54. ! [X0] : ((~curious(X0) | kind(X0)) & (~kind(X0) | curious(X0))) [nnf transformation 7]
94. ~curious(X0) | kind(X0) [cnf transformation 54]
134. ~kind(alice) [cnf transformation 23]
136. curious(alice) [cnf transformation 25]
197. 14 <=> kind(alice) [avatar definition]
199. ~kind(alice) <- (~14) [avatar component clause 197]
280. ~14 [avatar split clause 134,197]
294. kind(alice) [resolution 94,136]
296. $false <- (~14) [subsumption resolution 294,199]
297. 14 [avatar contradiction clause 296]
298. $false [avatar sat refutation 280,297]
% SZS output end Proof for 8886414761436056190381970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not creative or not strong then fred is not strong. Everyone who is not creative is happy or calm and vice versa. Everyone who is both strong and not curious is tall and vice versa. Everyone who is tall or strong is quiet and vice versa. Everyone who is both not calm and not happy is strong and vice versa. Everyone who is old or not generous is both not quiet and not calm and vice versa. Everyone who is not kind or brave is either not strong or not tall and vice versa. If someone is rich or not calm then someone is not rich. Everyone who is quiet is both rich and brave. Everyone who is calm is not kind or humble. Everyone who is strong or not curious is funny and vice versa. Everyone who is both patient and not quiet is either humble or not humble. If someone is not humble or not calm then mary is strong and vice versa. Everyone who is either not patient or not old is both not old and not quiet and vice versa. Someone is either curious or humble. Someone is funny or not tall. Paul is either generous or wise. Someone is either not rich or humble. Paul is not old or not wise. | Paul is not generous. | neutral | (((~creative(mary)|~strong(mary)))=>(~strong(fred)))&
(![X]:(~creative(X)<=>(happy(X)|calm(X))))&
(![X]:((strong(X)&~curious(X))<=>tall(X)))&
(![X]:((tall(X)|strong(X))<=>quiet(X)))&
(![X]:((~calm(X)&~happy(X))<=>strong(X)))&
(![X]:((old(X)|~generous(X))<=>(~quiet(X)&~calm(X))))&
(![X]:((~kind(X)|brave(X))<=>(~strong(X)<~>~tall(X))))&
((?[X]:((rich(X)|~calm(X))))=>(?[X]:(~rich(X))))&
(![X]:(quiet(X)=>(rich(X)&brave(X))))&
(![X]:(calm(X)=>(~kind(X)|humble(X))))&
(![X]:((strong(X)|~curious(X))<=>funny(X)))&
(![X]:((patient(X)&~quiet(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((~humble(X)|~calm(X))))<=>(strong(mary)))&
(![X]:((~patient(X)<~>~old(X))<=>(~old(X)&~quiet(X))))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((funny(X)|~tall(X))))&
((generous(paul)<~>wise(paul)))&
(?[X]:((~rich(X)<~>humble(X))))&
((~old(paul)|~wise(paul))) | ~generous(paul) | [] | null | 0 |
Everyone who is either happy or not humble is both not quiet and brave and vice versa. If someone is both calm and humble then someone is creative and vice versa. If someone is quiet then fred is calm or not quiet. Everyone who is not creative is either creative or humble. If fred is funny or generous then someone is not curious. If john is both not calm and not tall then susan is either strong or humble and vice versa. If susan is both not quiet and funny then someone is either strong or creative and vice versa. Everyone who is either curious or generous is not tall or not brave. If someone is both old and happy then someone is kind and vice versa. Everyone who is creative is not rich. If someone is not brave then someone is either not kind or kind. If paul is both humble and happy then susan is either kind or not generous. Everyone who is both not humble and rich is generous and vice versa. Everyone who is either funny or not brave is brave and vice versa. Lucy is not happy or not strong. Someone is not happy or not wise. Alice is both calm and not rich. Someone is either not tall or generous. Paul is both not quiet and tall. Someone is not wise or brave. Someone is calm or not generous. | Susan is not funny. | contradiction | (![X]:((happy(X)<~>~humble(X))<=>(~quiet(X)&brave(X))))&
((?[X]:((calm(X)&humble(X))))<=>(?[X]:(creative(X))))&
((?[X]:(quiet(X)))=>((calm(fred)|~quiet(fred))))&
(![X]:(~creative(X)=>(creative(X)<~>humble(X))))&
(((funny(fred)|generous(fred)))=>(?[X]:(~curious(X))))&
(((~calm(john)&~tall(john)))<=>((strong(susan)<~>humble(susan))))&
(((~quiet(susan)&funny(susan)))<=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((curious(X)<~>generous(X))=>(~tall(X)|~brave(X))))&
((?[X]:((old(X)&happy(X))))<=>(?[X]:(kind(X))))&
(![X]:(creative(X)=>~rich(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~kind(X)<~>kind(X)))))&
(((humble(paul)&happy(paul)))=>((kind(susan)<~>~generous(susan))))&
(![X]:((~humble(X)&rich(X))<=>generous(X)))&
(![X]:((funny(X)<~>~brave(X))<=>brave(X)))&
((~happy(lucy)|~strong(lucy)))&
(?[X]:((~happy(X)|~wise(X))))&
((calm(alice)&~rich(alice)))&
(?[X]:((~tall(X)<~>generous(X))))&
((~quiet(paul)&tall(paul)))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((calm(X)|~generous(X)))) | ~funny(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 61387697782881390951273
% SZS output start Proof for 61387697782881390951273
14. ! [X0] : ((funny(X0) <~> ~brave(X0)) <=> brave(X0)) [input p13]
22. ~funny(susan) [input hypothesis]
68. ! [X0] : ((((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | ~brave(X0)) & (brave(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))))) [nnf transformation 14]
114. brave(X0) | funny(X0) | brave(X0) [cnf transformation 68]
115. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 68]
125. ~funny(susan) [cnf transformation 22]
126. brave(X0) | funny(X0) [duplicate literal removal 114]
127. ~brave(X0) | funny(X0) [duplicate literal removal 115]
265. funny(X0) [subsumption resolution 126,127]
294. $false [subsumption resolution 125,265]
% SZS output end Proof for 61387697782881390951273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old then lucy is not creative or not calm and vice versa.
If mary is not tall then someone is brave and vice versa.
Everyone who is either wise or not wise is either not tall or rich.
If lucy is not rich or not patient then john is both generous and not creative.
If john is not quiet or not curious then mary is not quiet.
If mary is both old and not wise then someone is either not strong or curious.
Everyone who is both not patient and patient is happy or not brave and vice versa.
If someone is not patient then john is not happy.
If someone is both quiet and not curious then mary is not old.
Everyone who is either quiet or calm is not strong.
If mary is either not patient or generous then someone is either not humble or not curious and vice versa.
If lucy is rich or not happy then someone is either not creative or humble and vice versa.
Everyone who is both brave and not curious is either quiet or not curious and vice versa.
If someone is generous or not quiet then paul is not curious or not tall.
If lucy is either not humble or not quiet then someone is either not patient or old and vice versa.
Everyone who is strong or not rich is not curious.
Someone is not quiet.
Mary is not calm.
Mary is not wise.
Susan is not quiet.
Someone is either not strong or not calm.
Fred is calm.
Someone is tall or not quiet.
John is quiet or not kind. | Mary is wise. | contradiction | ((?[X]:(~old(X)))<=>((~creative(lucy)|~calm(lucy))))&
((~tall(mary))<=>(?[X]:(brave(X))))&
(![X]:((wise(X)<~>~wise(X))=>(~tall(X)<~>rich(X))))&
(((~rich(lucy)|~patient(lucy)))=>((generous(john)&~creative(john))))&
(((~quiet(john)|~curious(john)))=>(~quiet(mary)))&
(((old(mary)&~wise(mary)))=>(?[X]:((~strong(X)<~>curious(X)))))&
(![X]:((~patient(X)&patient(X))<=>(happy(X)|~brave(X))))&
((?[X]:(~patient(X)))=>(~happy(john)))&
((?[X]:((quiet(X)&~curious(X))))=>(~old(mary)))&
(![X]:((quiet(X)<~>calm(X))=>~strong(X)))&
(((~patient(mary)<~>generous(mary)))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(((rich(lucy)|~happy(lucy)))<=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((brave(X)&~curious(X))<=>(quiet(X)<~>~curious(X))))&
((?[X]:((generous(X)|~quiet(X))))=>((~curious(paul)|~tall(paul))))&
(((~humble(lucy)<~>~quiet(lucy)))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:((strong(X)|~rich(X))=>~curious(X)))&
(?[X]:(~quiet(X)))&
(~calm(mary))&
(~wise(mary))&
(~quiet(susan))&
(?[X]:((~strong(X)<~>~calm(X))))&
(calm(fred))&
(?[X]:((tall(X)|~quiet(X))))&
((quiet(john)|~kind(john))) | wise(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7709204664927470860500513
% SZS output start Proof for 7709204664927470860500513
19. ~wise(mary) [input p18]
25. wise(mary) [input hypothesis]
136. ~wise(mary) [cnf transformation 19]
142. wise(mary) [cnf transformation 25]
221. 16 <=> wise(mary) [avatar definition]
326. ~16 [avatar split clause 136,221]
337. 16 [avatar split clause 142,221]
338. $false [avatar sat refutation 326,337]
% SZS output end Proof for 7709204664927470860500513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not creative is either not rich or not generous and vice versa.
Everyone who is generous or not patient is not rich.
If lucy is creative or calm then someone is both happy and not calm.
Everyone who is not quiet or not humble is both not patient and brave.
If someone is either not quiet or not creative then someone is both old and calm and vice versa.
If alice is not wise or generous then someone is both humble and not creative and vice versa.
Everyone who is curious or wise is both not quiet and not funny and vice versa.
Everyone who is either not happy or not funny is generous.
Everyone who is both not curious and not funny is either not old or creative.
Everyone who is both happy and kind is both old and not tall.
Everyone who is either brave or not generous is both not generous and strong and vice versa.
Everyone who is tall or humble is not calm.
Everyone who is not calm is either not rich or brave and vice versa.
If someone is generous then someone is both kind and patient and vice versa.
Everyone who is kind is either tall or humble and vice versa.
Everyone who is both funny and not brave is both not tall and not happy and vice versa.
Alice is both not patient and tall.
Alice is either rich or not funny.
Susan is not happy.
Mary is kind.
Susan is not patient.
John is strong or tall.
Susan is not creative or not happy. | John is wise. | contradiction | (![X]:((~calm(X)|~creative(X))<=>(~rich(X)<~>~generous(X))))&
(![X]:((generous(X)|~patient(X))=>~rich(X)))&
(((creative(lucy)|calm(lucy)))=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((~quiet(X)|~humble(X))=>(~patient(X)&brave(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))<=>(?[X]:((old(X)&calm(X)))))&
(((~wise(alice)|generous(alice)))<=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:((curious(X)|wise(X))<=>(~quiet(X)&~funny(X))))&
(![X]:((~happy(X)<~>~funny(X))=>generous(X)))&
(![X]:((~curious(X)&~funny(X))=>(~old(X)<~>creative(X))))&
(![X]:((happy(X)&kind(X))=>(old(X)&~tall(X))))&
(![X]:((brave(X)<~>~generous(X))<=>(~generous(X)&strong(X))))&
(![X]:((tall(X)|humble(X))=>~calm(X)))&
(![X]:(~calm(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:(generous(X)))<=>(?[X]:((kind(X)&patient(X)))))&
(![X]:(kind(X)<=>(tall(X)<~>humble(X))))&
(![X]:((funny(X)&~brave(X))<=>(~tall(X)&~happy(X))))&
((~patient(alice)&tall(alice)))&
((rich(alice)<~>~funny(alice)))&
(~happy(susan))&
(kind(mary))&
(~patient(susan))&
((strong(john)|tall(john)))&
((~creative(susan)|~happy(susan))) | wise(john) | [
"p0",
"p1",
"p3",
"p6",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2385521627986613306842801
% SZS output start Proof for 2385521627986613306842801
1. ! [X0] : ((~creative(X0) | ~calm(X0)) <=> (~rich(X0) <~> ~generous(X0))) [input p0]
2. ! [X0] : ((~patient(X0) | generous(X0)) => ~rich(X0)) [input p1]
4. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (brave(X0) & ~patient(X0))) [input p3]
7. ! [X0] : ((wise(X0) | curious(X0)) <=> (~funny(X0) & ~quiet(X0))) [input p6]
11. ! [X0] : ((brave(X0) <~> ~generous(X0)) <=> (strong(X0) & ~generous(X0))) [input p10]
12. ! [X0] : ((humble(X0) | tall(X0)) => ~calm(X0)) [input p11]
22. tall(john) | strong(john) [input p21]
24. wise(john) [input hypothesis]
27. ! [X0] : (~rich(X0) | (patient(X0) & ~generous(X0))) [ennf transformation 2]
29. ! [X0] : ((brave(X0) & ~patient(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 4]
35. ! [X0] : (~calm(X0) | (~humble(X0) & ~tall(X0))) [ennf transformation 12]
36. ! [X0] : (((~creative(X0) | ~calm(X0)) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0)))) & (((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | (creative(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~calm(X0) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0)))) & (((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | (creative(X0) & calm(X0)))) [flattening 36]
50. ! [X0] : (((wise(X0) | curious(X0)) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | (~wise(X0) & ~curious(X0)))) [nnf transformation 7]
51. ! [X0] : ((wise(X0) | curious(X0) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | (~wise(X0) & ~curious(X0)))) [flattening 50]
54. ! [X0] : ((((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | (~strong(X0) | generous(X0))) & ((strong(X0) & ~generous(X0)) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))))) [nnf transformation 11]
55. ! [X0] : ((((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | ~strong(X0) | generous(X0)) & ((strong(X0) & ~generous(X0)) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))))) [flattening 54]
68. generous(X0) | rich(X0) | calm(X0) [cnf transformation 37]
73. ~rich(X0) | patient(X0) [cnf transformation 27]
78. ~patient(X0) | quiet(X0) [cnf transformation 29]
80. brave(X0) | quiet(X0) [cnf transformation 29]
94. ~wise(X0) | ~quiet(X0) [cnf transformation 51]
104. ~generous(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 55]
109. generous(X0) | ~brave(X0) | ~strong(X0) | generous(X0) [cnf transformation 55]
110. ~tall(X0) | ~calm(X0) [cnf transformation 35]
134. tall(john) | strong(john) [cnf transformation 22]
136. wise(john) [cnf transformation 24]
137. ~brave(X0) | ~generous(X0) [duplicate literal removal 104]
138. ~strong(X0) | ~brave(X0) | generous(X0) [duplicate literal removal 109]
246. 24 <=> strong(john) [avatar definition]
248. strong(john) <- (24) [avatar component clause 246]
250. 25 <=> tall(john) [avatar definition]
252. tall(john) <- (25) [avatar component clause 250]
253. 24 | 25 [avatar split clause 134,250,246]
254. ~quiet(john) [resolution 94,136]
258. ~generous(X1) | quiet(X1) [resolution 137,80]
423. ~brave(john) | generous(john) <- (24) [resolution 138,248]
426. ~brave(john) <- (24) [subsumption resolution 423,137]
428. quiet(john) <- (24) [resolution 426,80]
429. $false <- (24) [subsumption resolution 428,254]
430. ~24 [avatar contradiction clause 429]
433. 45 <=> generous(john) [avatar definition]
434. ~generous(john) <- (~45) [avatar component clause 433]
435. generous(john) <- (45) [avatar component clause 433]
445. ~calm(john) <- (25) [resolution 252,110]
484. 52 <=> rich(john) [avatar definition]
485. rich(john) <- (52) [avatar component clause 484]
514. quiet(john) <- (45) [resolution 258,435]
519. $false <- (45) [subsumption resolution 514,254]
520. ~45 [avatar contradiction clause 519]
540. rich(john) | calm(john) <- (~45) [resolution 434,68]
544. rich(john) <- (25, ~45) [subsumption resolution 540,445]
545. 52 | ~25 | 45 [avatar split clause 544,433,250,484]
568. patient(john) <- (52) [resolution 485,73]
632. quiet(john) <- (52) [resolution 568,78]
633. $false <- (52) [subsumption resolution 632,254]
634. ~52 [avatar contradiction clause 633]
635. $false [avatar sat refutation 253,430,520,545,634]
% SZS output end Proof for 2385521627986613306842801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or quiet then lucy is either not calm or calm.
Everyone who is both quiet and humble is brave or not humble and vice versa.
Everyone who is both happy and not curious is old or humble.
Everyone who is kind or not old is strong or not curious and vice versa.
If someone is not wise then someone is either funny or not creative and vice versa.
Everyone who is both old and not quiet is not wise or not calm and vice versa.
If lucy is either not happy or not funny then fred is either not happy or not strong and vice versa.
Everyone who is not calm or patient is quiet.
Everyone who is both not old and not creative is not happy.
If someone is not creative or strong then paul is not curious or patient and vice versa.
Everyone who is both not wise and humble is either patient or strong.
Everyone who is either not creative or not happy is not patient.
Everyone who is either rich or not strong is not patient.
Everyone who is quiet is both old and happy and vice versa.
Everyone who is not quiet or old is both not brave and creative and vice versa.
Fred is old or not brave.
Someone is both tall and not rich.
John is wise or patient.
Someone is strong or happy.
Someone is both not patient and not old.
Someone is kind or patient.
Someone is not wise or not rich. | Lucy is creative. | entailment | ((?[X]:((tall(X)<~>quiet(X))))=>((~calm(lucy)<~>calm(lucy))))&
(![X]:((quiet(X)&humble(X))<=>(brave(X)|~humble(X))))&
(![X]:((happy(X)&~curious(X))=>(old(X)|humble(X))))&
(![X]:((kind(X)|~old(X))<=>(strong(X)|~curious(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((old(X)&~quiet(X))<=>(~wise(X)|~calm(X))))&
(((~happy(lucy)<~>~funny(lucy)))<=>((~happy(fred)<~>~strong(fred))))&
(![X]:((~calm(X)|patient(X))=>quiet(X)))&
(![X]:((~old(X)&~creative(X))=>~happy(X)))&
((?[X]:((~creative(X)|strong(X))))<=>((~curious(paul)|patient(paul))))&
(![X]:((~wise(X)&humble(X))=>(patient(X)<~>strong(X))))&
(![X]:((~creative(X)<~>~happy(X))=>~patient(X)))&
(![X]:((rich(X)<~>~strong(X))=>~patient(X)))&
(![X]:(quiet(X)<=>(old(X)&happy(X))))&
(![X]:((~quiet(X)|old(X))<=>(~brave(X)&creative(X))))&
((old(fred)|~brave(fred)))&
(?[X]:((tall(X)&~rich(X))))&
((wise(john)|patient(john)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((~patient(X)&~old(X))))&
(?[X]:((kind(X)|patient(X))))&
(?[X]:((~wise(X)|~rich(X)))) | creative(lucy) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9097079242745299683205377
% SZS output start Proof for 9097079242745299683205377
14. ! [X0] : (quiet(X0) <=> (happy(X0) & old(X0))) [input p13]
15. ! [X0] : ((old(X0) | ~quiet(X0)) <=> (creative(X0) & ~brave(X0))) [input p14]
23. ~creative(lucy) [input hypothesis]
56. ! [X0] : ((quiet(X0) | (~happy(X0) | ~old(X0))) & ((happy(X0) & old(X0)) | ~quiet(X0))) [nnf transformation 14]
57. ! [X0] : ((quiet(X0) | ~happy(X0) | ~old(X0)) & ((happy(X0) & old(X0)) | ~quiet(X0))) [flattening 56]
58. ! [X0] : (((old(X0) | ~quiet(X0)) | (~creative(X0) | brave(X0))) & ((creative(X0) & ~brave(X0)) | (~old(X0) & quiet(X0)))) [nnf transformation 15]
59. ! [X0] : ((old(X0) | ~quiet(X0) | ~creative(X0) | brave(X0)) & ((creative(X0) & ~brave(X0)) | (~old(X0) & quiet(X0)))) [flattening 58]
114. ~quiet(X0) | old(X0) [cnf transformation 57]
119. creative(X0) | quiet(X0) [cnf transformation 59]
120. ~old(X0) | creative(X0) [cnf transformation 59]
131. ~creative(lucy) [cnf transformation 23]
256. quiet(lucy) [resolution 119,131]
260. old(lucy) [resolution 256,114]
347. creative(lucy) [resolution 260,120]
358. $false [subsumption resolution 347,131]
% SZS output end Proof for 9097079242745299683205377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and strong is either not generous or humble and vice versa.
If susan is not creative then someone is both not old and not brave.
Everyone who is curious or strong is either not quiet or generous.
If someone is not old then someone is curious and vice versa.
If lucy is brave then alice is either brave or funny and vice versa.
Everyone who is not tall or humble is either not generous or not patient and vice versa.
If mary is not quiet or happy then someone is either brave or curious.
Everyone who is not funny or not kind is either calm or not old and vice versa.
Everyone who is either creative or not calm is either not strong or patient and vice versa.
Everyone who is both not brave and strong is brave or generous and vice versa.
If alice is either not happy or not wise then someone is quiet or strong.
If someone is patient or not generous then someone is generous.
Everyone who is either strong or kind is calm and vice versa.
Everyone who is both funny and not tall is both happy and quiet.
Everyone who is not quiet is both not brave and not happy and vice versa.
Everyone who is patient or not kind is tall or not calm and vice versa.
Fred is both patient and curious.
Someone is not generous or not kind.
Paul is strong.
Someone is not curious or not generous.
John is either not funny or wise.
Someone is not kind or patient.
Fred is either not old or patient.
Lucy is generous. | Fred is not happy. | entailment | (![X]:((curious(X)&strong(X))<=>(~generous(X)<~>humble(X))))&
((~creative(susan))=>(?[X]:((~old(X)&~brave(X)))))&
(![X]:((curious(X)|strong(X))=>(~quiet(X)<~>generous(X))))&
((?[X]:(~old(X)))<=>(?[X]:(curious(X))))&
((brave(lucy))<=>((brave(alice)<~>funny(alice))))&
(![X]:((~tall(X)|humble(X))<=>(~generous(X)<~>~patient(X))))&
(((~quiet(mary)|happy(mary)))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(calm(X)<~>~old(X))))&
(![X]:((creative(X)<~>~calm(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((~brave(X)&strong(X))<=>(brave(X)|generous(X))))&
(((~happy(alice)<~>~wise(alice)))=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((patient(X)|~generous(X))))=>(?[X]:(generous(X))))&
(![X]:((strong(X)<~>kind(X))<=>calm(X)))&
(![X]:((funny(X)&~tall(X))=>(happy(X)&quiet(X))))&
(![X]:(~quiet(X)<=>(~brave(X)&~happy(X))))&
(![X]:((patient(X)|~kind(X))<=>(tall(X)|~calm(X))))&
((patient(fred)&curious(fred)))&
(?[X]:((~generous(X)|~kind(X))))&
(strong(paul))&
(?[X]:((~curious(X)|~generous(X))))&
((~funny(john)<~>wise(john)))&
(?[X]:((~kind(X)|patient(X))))&
((~old(fred)<~>patient(fred)))&
(generous(lucy)) | ~happy(fred) | [
"p0",
"p2",
"p5",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3293908205975539135744937
% SZS output start Proof for 3293908205975539135744937
1. ! [X0] : ((strong(X0) & curious(X0)) <=> (~generous(X0) <~> humble(X0))) [input p0]
3. ! [X0] : ((strong(X0) | curious(X0)) => (~quiet(X0) <~> generous(X0))) [input p2]
6. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (~generous(X0) <~> ~patient(X0))) [input p5]
10. ! [X0] : ((strong(X0) & ~brave(X0)) <=> (generous(X0) | brave(X0))) [input p9]
15. ! [X0] : (~quiet(X0) <=> (~happy(X0) & ~brave(X0))) [input p14]
17. curious(fred) & patient(fred) [input p16]
25. happy(fred) [input hypothesis]
29. ! [X0] : ((~quiet(X0) <~> generous(X0)) | (~strong(X0) & ~curious(X0))) [ennf transformation 3]
35. ! [X0] : (((strong(X0) & curious(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~strong(X0) | ~curious(X0)))) [nnf transformation 1]
36. ! [X0] : (((strong(X0) & curious(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ~strong(X0) | ~curious(X0))) [flattening 35]
39. ! [X0] : (((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~strong(X0) & ~curious(X0))) [nnf transformation 29]
46. ! [X0] : (((humble(X0) | ~tall(X0)) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (~humble(X0) & tall(X0)))) [nnf transformation 6]
47. ! [X0] : ((humble(X0) | ~tall(X0) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (~humble(X0) & tall(X0)))) [flattening 46]
54. ! [X0] : (((strong(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~strong(X0) | brave(X0)))) [nnf transformation 10]
55. ! [X0] : (((strong(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~strong(X0) | brave(X0))) [flattening 54]
63. ! [X0] : ((~quiet(X0) | (happy(X0) | brave(X0))) & ((~happy(X0) & ~brave(X0)) | quiet(X0))) [nnf transformation 15]
64. ! [X0] : ((~quiet(X0) | happy(X0) | brave(X0)) & ((~happy(X0) & ~brave(X0)) | quiet(X0))) [flattening 63]
75. ~generous(X0) | humble(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 36]
83. ~quiet(X0) | generous(X0) | ~curious(X0) [cnf transformation 39]
94. ~patient(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 47]
121. ~generous(X0) | strong(X0) [cnf transformation 55]
133. ~happy(X0) | quiet(X0) [cnf transformation 64]
139. patient(fred) [cnf transformation 17]
140. curious(fred) [cnf transformation 17]
150. happy(fred) [cnf transformation 25]
297. quiet(fred) [resolution 133,150]
309. generous(fred) | ~curious(fred) [resolution 83,297]
310. generous(fred) [subsumption resolution 309,140]
311. strong(fred) [resolution 310,121]
369. ~generous(fred) | ~humble(fred) [resolution 94,139]
370. ~humble(fred) [subsumption resolution 369,310]
452. humble(fred) | ~strong(fred) | ~curious(fred) [resolution 75,310]
552. ~strong(fred) | ~curious(fred) [subsumption resolution 452,370]
553. ~curious(fred) [subsumption resolution 552,311]
554. $false [subsumption resolution 553,140]
% SZS output end Proof for 3293908205975539135744937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or calm then paul is not tall or tall and vice versa.
If someone is kind or happy then lucy is not rich or kind and vice versa.
If lucy is kind then someone is either rich or not humble and vice versa.
Everyone who is either old or not curious is both not strong and patient.
Everyone who is happy is both kind and not old and vice versa.
Everyone who is either not funny or not tall is both patient and rich and vice versa.
If fred is either not humble or quiet then susan is both rich and wise and vice versa.
If susan is not happy or old then someone is both creative and rich and vice versa.
Everyone who is creative is either not kind or kind and vice versa.
If someone is both not brave and not tall then lucy is rich or not curious.
If alice is not generous then paul is both not rich and not tall.
If someone is both quiet and not funny then mary is not happy or strong.
If someone is rich or patient then someone is not curious or tall and vice versa.
Everyone who is both not kind and not funny is not funny.
If john is curious or not creative then someone is calm or curious and vice versa.
Everyone who is not tall or curious is either not curious or not creative and vice versa.
Someone is funny.
Someone is old or kind.
Paul is either not humble or calm.
Paul is both patient and not tall.
Lucy is kind or not tall.
Alice is both not curious and not wise.
Mary is not patient or not quiet. | Paul is humble. | contradiction | ((?[X]:((strong(X)|calm(X))))<=>((~tall(paul)|tall(paul))))&
((?[X]:((kind(X)|happy(X))))<=>((~rich(lucy)|kind(lucy))))&
((kind(lucy))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:((old(X)<~>~curious(X))=>(~strong(X)&patient(X))))&
(![X]:(happy(X)<=>(kind(X)&~old(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>(patient(X)&rich(X))))&
(((~humble(fred)<~>quiet(fred)))<=>((rich(susan)&wise(susan))))&
(((~happy(susan)|old(susan)))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:(creative(X)<=>(~kind(X)<~>kind(X))))&
((?[X]:((~brave(X)&~tall(X))))=>((rich(lucy)|~curious(lucy))))&
((~generous(alice))=>((~rich(paul)&~tall(paul))))&
((?[X]:((quiet(X)&~funny(X))))=>((~happy(mary)|strong(mary))))&
((?[X]:((rich(X)|patient(X))))<=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((~kind(X)&~funny(X))=>~funny(X)))&
(((curious(john)|~creative(john)))<=>(?[X]:((calm(X)|curious(X)))))&
(![X]:((~tall(X)|curious(X))<=>(~curious(X)<~>~creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((old(X)|kind(X))))&
((~humble(paul)<~>calm(paul)))&
((patient(paul)&~tall(paul)))&
((kind(lucy)|~tall(lucy)))&
((~curious(alice)&~wise(alice)))&
((~patient(mary)|~quiet(mary))) | humble(paul) | [
"p8",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 843302512555234788197926
% SZS output start Proof for 843302512555234788197926
9. ! [X0] : (creative(X0) <=> (~kind(X0) <~> kind(X0))) [input p8]
15. (~creative(john) | curious(john)) <=> ? [X0] : (curious(X0) | calm(X0)) [input p14]
16. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~curious(X0) <~> ~creative(X0))) [input p15]
19. ~humble(paul) <~> calm(paul) [input p18]
24. humble(paul) [input hypothesis]
59. ! [X0] : ((creative(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 9]
65. ((~creative(john) | curious(john)) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X0] : (curious(X0) | calm(X0)) | (creative(john) & ~curious(john))) [nnf transformation 15]
66. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X0] : (curious(X0) | calm(X0)) | (creative(john) & ~curious(john))) [flattening 65]
67. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & (? [X1] : (curious(X1) | calm(X1)) | (creative(john) & ~curious(john))) [rectify 66]
68. ? [X1] : (curious(X1) | calm(X1)) => (curious(sK6) | calm(sK6)) [choice axiom]
69. (~creative(john) | curious(john) | ! [X0] : (~curious(X0) & ~calm(X0))) & ((curious(sK6) | calm(sK6)) | (creative(john) & ~curious(john))) [skolemisation 67,68]
70. ! [X0] : (((curious(X0) | ~tall(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~curious(X0) & tall(X0)))) [nnf transformation 16]
71. ! [X0] : ((curious(X0) | ~tall(X0) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) & (((creative(X0) | curious(X0)) & (~creative(X0) | ~curious(X0))) | (~curious(X0) & tall(X0)))) [flattening 70]
76. (~calm(paul) | humble(paul)) & (calm(paul) | ~humble(paul)) [nnf transformation 19]
115. creative(X0) | kind(X0) | kind(X0) [cnf transformation 59]
116. creative(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 59]
125. ~creative(john) | curious(john) | ~calm(X0) [cnf transformation 69]
128. ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 71]
135. calm(paul) | ~humble(paul) [cnf transformation 76]
143. humble(paul) [cnf transformation 24]
144. ~creative(X0) | ~curious(X0) [duplicate literal removal 128]
146. creative(X0) | kind(X0) [duplicate literal removal 115]
147. creative(X0) | ~kind(X0) [duplicate literal removal 116]
253. creative(X0) [subsumption resolution 146,147]
300. 34 <=> ! [X0] : ~curious(X0) [avatar definition]
301. ~curious(X0) <- (34) [avatar component clause 300]
303. 35 <=> curious(john) [avatar definition]
305. curious(john) <- (35) [avatar component clause 303]
307. curious(john) | ~calm(X0) [subsumption resolution 125,253]
309. 36 <=> ! [X0] : ~calm(X0) [avatar definition]
310. ~calm(X0) <- (36) [avatar component clause 309]
311. 36 | 35 [avatar split clause 307,303,309]
322. ~curious(X0) [subsumption resolution 144,253]
323. 34 [avatar split clause 322,300]
335. 41 <=> humble(paul) [avatar definition]
339. 42 <=> calm(paul) [avatar definition]
340. calm(paul) <- (42) [avatar component clause 339]
343. ~41 | 42 [avatar split clause 135,339,335]
359. 41 [avatar split clause 143,335]
364. $false <- (34, 35) [subsumption resolution 305,301]
365. ~34 | ~35 [avatar contradiction clause 364]
368. $false <- (36, 42) [resolution 340,310]
369. ~36 | ~42 [avatar contradiction clause 368]
370. $false [avatar sat refutation 311,323,343,359,365,369]
% SZS output end Proof for 843302512555234788197926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not old is either humble or kind and vice versa.
Everyone who is not kind is both brave and creative and vice versa.
Everyone who is both strong and not strong is both not kind and not strong and vice versa.
Everyone who is either not funny or not curious is either strong or quiet and vice versa.
If someone is not old then lucy is humble.
If someone is funny then someone is either patient or kind and vice versa.
Everyone who is both brave and creative is not quiet or generous and vice versa.
Everyone who is both quiet and not brave is not creative and vice versa.
Everyone who is both happy and strong is patient.
Everyone who is calm or not rich is not humble and vice versa.
Everyone who is both not quiet and old is both not creative and not wise and vice versa.
If susan is either quiet or creative then susan is either not patient or rich and vice versa.
Everyone who is not happy is either not patient or patient.
Everyone who is old is either not strong or not old and vice versa.
Everyone who is not curious is either not generous or not creative.
Someone is not generous or humble.
Someone is not tall.
Someone is both not humble and not happy.
Lucy is not rich or not patient.
Alice is wise or not kind.
Lucy is not wise or wise. | Susan is not calm. | contradiction | (![X]:((old(X)<~>~old(X))<=>(humble(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~funny(X)<~>~curious(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:(~old(X)))=>(humble(lucy)))&
((?[X]:(funny(X)))<=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:((brave(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((quiet(X)&~brave(X))<=>~creative(X)))&
(![X]:((happy(X)&strong(X))=>patient(X)))&
(![X]:((calm(X)|~rich(X))<=>~humble(X)))&
(![X]:((~quiet(X)&old(X))<=>(~creative(X)&~wise(X))))&
(((quiet(susan)<~>creative(susan)))<=>((~patient(susan)<~>rich(susan))))&
(![X]:(~happy(X)=>(~patient(X)<~>patient(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~old(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~creative(X))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)&~happy(X))))&
((~rich(lucy)|~patient(lucy)))&
((wise(alice)|~kind(alice)))&
((~wise(lucy)|wise(lucy))) | ~calm(susan) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3092555933738909705730128
% SZS output start Proof for 3092555933738909705730128
1. ! [X0] : ((old(X0) <~> ~old(X0)) <=> (humble(X0) <~> kind(X0))) [input p0]
2. ! [X0] : (~kind(X0) <=> (creative(X0) & brave(X0))) [input p1]
3. ! [X0] : ((~strong(X0) & strong(X0)) <=> (~strong(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> ~curious(X0)) <=> (strong(X0) <~> quiet(X0))) [input p3]
5. ? [X0] : ~old(X0) => humble(lucy) [input p4]
6. ? [X0] : funny(X0) <=> ? [X0] : (patient(X0) <~> kind(X0)) [input p5]
7. ! [X0] : ((creative(X0) & brave(X0)) <=> (generous(X0) | ~quiet(X0))) [input p6]
8. ! [X0] : ((~brave(X0) & quiet(X0)) <=> ~creative(X0)) [input p7]
10. ! [X0] : ((~rich(X0) | calm(X0)) <=> ~humble(X0)) [input p9]
11. ! [X0] : ((old(X0) & ~quiet(X0)) <=> (~wise(X0) & ~creative(X0))) [input p10]
12. (quiet(susan) <~> creative(susan)) <=> (~patient(susan) <~> rich(susan)) [input p11]
14. ! [X0] : (old(X0) <=> (~strong(X0) <~> ~old(X0))) [input p13]
15. ! [X0] : (~curious(X0) => (~generous(X0) <~> ~creative(X0))) [input p14]
22. ~calm(susan) [input hypothesis]
23. ? [X0] : funny(X0) <=> ? [X1] : (patient(X1) <~> kind(X1)) [rectify 6]
25. humble(lucy) | ! [X0] : old(X0) [ennf transformation 5]
29. ! [X0] : ((~generous(X0) <~> ~creative(X0)) | curious(X0)) [ennf transformation 15]
30. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) & (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 1]
31. ! [X0] : ((~kind(X0) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | kind(X0))) [nnf transformation 2]
32. ! [X0] : ((~kind(X0) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | kind(X0))) [flattening 31]
33. ! [X0] : (((~strong(X0) & strong(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : (((~strong(X0) & strong(X0)) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | strong(X0) | ~strong(X0))) [flattening 33]
35. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) & (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [nnf transformation 4]
36. (? [X0] : funny(X0) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1)))) & (? [X1] : ((~kind(X1) | ~patient(X1)) & (kind(X1) | patient(X1))) | ! [X0] : ~funny(X0)) [nnf transformation 23]
37. (? [X0] : funny(X0) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1)))) & (? [X2] : ((~kind(X2) | ~patient(X2)) & (kind(X2) | patient(X2))) | ! [X3] : ~funny(X3)) [rectify 36]
38. ? [X0] : funny(X0) => funny(sK0) [choice axiom]
39. ? [X2] : ((~kind(X2) | ~patient(X2)) & (kind(X2) | patient(X2))) => ((~kind(sK1) | ~patient(sK1)) & (kind(sK1) | patient(sK1))) [choice axiom]
40. (funny(sK0) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1)))) & (((~kind(sK1) | ~patient(sK1)) & (kind(sK1) | patient(sK1))) | ! [X3] : ~funny(X3)) [skolemisation 37,39,38]
41. ! [X0] : (((creative(X0) & brave(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~creative(X0) | ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : (((creative(X0) & brave(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0) | ~brave(X0))) [flattening 41]
43. ! [X0] : (((~brave(X0) & quiet(X0)) | creative(X0)) & (~creative(X0) | (brave(X0) | ~quiet(X0)))) [nnf transformation 8]
44. ! [X0] : (((~brave(X0) & quiet(X0)) | creative(X0)) & (~creative(X0) | brave(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : (((~rich(X0) | calm(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) & ~calm(X0)))) [nnf transformation 10]
46. ! [X0] : ((~rich(X0) | calm(X0) | humble(X0)) & (~humble(X0) | (rich(X0) & ~calm(X0)))) [flattening 45]
47. ! [X0] : (((old(X0) & ~quiet(X0)) | (wise(X0) | creative(X0))) & ((~wise(X0) & ~creative(X0)) | (~old(X0) | quiet(X0)))) [nnf transformation 11]
48. ! [X0] : (((old(X0) & ~quiet(X0)) | wise(X0) | creative(X0)) & ((~wise(X0) & ~creative(X0)) | ~old(X0) | quiet(X0))) [flattening 47]
49. (((~creative(susan) | ~quiet(susan)) & (creative(susan) | quiet(susan))) | ((~patient(susan) | ~rich(susan)) & (rich(susan) | patient(susan)))) & (((~rich(susan) | patient(susan)) & (rich(susan) | ~patient(susan))) | ((quiet(susan) | ~creative(susan)) & (creative(susan) | ~quiet(susan)))) [nnf transformation 12]
51. ! [X0] : ((old(X0) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | ~old(X0))) [nnf transformation 14]
52. ! [X0] : (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | curious(X0)) [nnf transformation 29]
59. ~kind(X0) | ~humble(X0) | ~old(X0) | ~old(X0) [cnf transformation 30]
60. ~kind(X0) | ~humble(X0) | old(X0) | old(X0) [cnf transformation 30]
67. ~creative(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 32]
70. strong(X0) | strong(X0) | kind(X0) [cnf transformation 34]
77. ~quiet(X0) | ~funny(X0) | strong(X0) | ~curious(X0) [cnf transformation 35]
80. humble(lucy) | old(X0) [cnf transformation 25]
84. funny(sK0) | patient(X1) | ~kind(X1) [cnf transformation 40]
86. quiet(X0) | brave(X0) [cnf transformation 42]
88. quiet(X0) | creative(X0) [cnf transformation 42]
89. ~generous(X0) | creative(X0) [cnf transformation 42]
90. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 44]
96. ~rich(X0) | calm(X0) | humble(X0) [cnf transformation 46]
97. ~creative(X0) | ~old(X0) | quiet(X0) [cnf transformation 48]
101. rich(susan) | ~patient(susan) | creative(susan) | ~quiet(susan) [cnf transformation 49]
111. ~old(X0) | ~strong(X0) | ~old(X0) [cnf transformation 51]
114. old(X0) | ~strong(X0) | old(X0) [cnf transformation 51]
116. creative(X0) | generous(X0) | curious(X0) [cnf transformation 52]
123. ~calm(susan) [cnf transformation 22]
124. ~old(X0) | ~strong(X0) [duplicate literal removal 111]
125. ~strong(X0) | old(X0) [duplicate literal removal 114]
127. strong(X0) | kind(X0) [duplicate literal removal 70]
130. ~kind(X0) | ~humble(X0) | ~old(X0) [duplicate literal removal 59]
131. ~kind(X0) | ~humble(X0) | old(X0) [duplicate literal removal 60]
132. ~kind(X0) | ~humble(X0) [subsumption resolution 130,131]
135. 1 <=> ! [X0] : old(X0) [avatar definition]
136. old(X0) <- (1) [avatar component clause 135]
138. 2 <=> humble(lucy) [avatar definition]
140. humble(lucy) <- (2) [avatar component clause 138]
141. 1 | 2 [avatar split clause 80,138,135]
143. 3 <=> ! [X1] : (patient(X1) | ~kind(X1)) [avatar definition]
144. patient(X1) | ~kind(X1) <- (3) [avatar component clause 143]
146. 4 <=> funny(sK0) [avatar definition]
148. funny(sK0) <- (4) [avatar component clause 146]
149. 3 | 4 [avatar split clause 84,146,143]
167. ~creative(X0) | brave(X0) [subsumption resolution 90,86]
169. ~old(X0) | quiet(X0) [subsumption resolution 97,88]
171. 9 <=> rich(susan) [avatar definition]
172. rich(susan) <- (9) [avatar component clause 171]
175. 10 <=> patient(susan) [avatar definition]
177. ~patient(susan) <- (~10) [avatar component clause 175]
183. 12 <=> creative(susan) [avatar definition]
184. creative(susan) <- (12) [avatar component clause 183]
194. rich(susan) | ~patient(susan) | creative(susan) [subsumption resolution 101,88]
195. 12 | ~10 | 9 [avatar split clause 194,171,175,183]
196. ~strong(X0) [subsumption resolution 124,125]
197. curious(X0) | creative(X0) [subsumption resolution 116,89]
233. kind(X1) [resolution 127,196]
237. ~humble(X0) [resolution 233,132]
240. patient(X1) <- (3) [subsumption resolution 144,233]
241. $false <- (3, ~10) [resolution 240,177]
244. ~3 | 10 [avatar contradiction clause 241]
246. $false <- (2) [resolution 237,140]
247. ~2 [avatar contradiction clause 246]
249. quiet(X0) <- (1) [resolution 169,136]
275. ~funny(X0) | strong(X0) | ~curious(X0) <- (1) [resolution 77,249]
278. ~curious(X0) | ~funny(X0) <- (1) [subsumption resolution 275,196]
280. ~funny(X0) | creative(X0) <- (1) [resolution 278,197]
294. creative(sK0) <- (1, 4) [resolution 280,148]
295. ~kind(sK0) | ~brave(sK0) <- (1, 4) [resolution 294,67]
296. brave(sK0) <- (1, 4) [resolution 294,167]
297. ~brave(sK0) <- (1, 4) [subsumption resolution 295,233]
298. $false <- (1, 4) [subsumption resolution 296,297]
299. ~1 | ~4 [avatar contradiction clause 298]
301. calm(susan) | humble(susan) <- (9) [resolution 172,96]
302. humble(susan) <- (9) [subsumption resolution 301,123]
305. $false <- (9) [subsumption resolution 302,237]
306. ~9 [avatar contradiction clause 305]
309. ~kind(susan) | ~brave(susan) <- (12) [resolution 184,67]
310. brave(susan) <- (12) [resolution 184,167]
311. ~brave(susan) <- (12) [subsumption resolution 309,233]
312. $false <- (12) [subsumption resolution 310,311]
313. ~12 [avatar contradiction clause 312]
314. $false [avatar sat refutation 141,149,195,244,247,299,306,313]
% SZS output end Proof for 3092555933738909705730128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or humble is either not brave or not generous. Everyone who is not old or not rich is either not funny or generous. If someone is generous or not funny then someone is not old or not tall and vice versa. If someone is either not humble or not strong then someone is either not happy or calm. If lucy is both not rich and rich then someone is not old or not tall and vice versa. Everyone who is happy or calm is both quiet and happy and vice versa. Everyone who is both not creative and not old is calm and vice versa. Everyone who is both not happy and brave is brave or not quiet. Everyone who is both not generous and old is either not strong or not brave. Everyone who is either curious or not wise is both not generous and not wise and vice versa. If someone is curious or patient then paul is both quiet and not happy. Everyone who is patient is both funny and not wise and vice versa. Everyone who is both brave and not funny is kind. Everyone who is curious or old is either kind or tall. Someone is both humble and not kind. Lucy is patient or quiet. Someone is patient or generous. Lucy is either generous or not kind. Someone is funny. Mary is not wise. | Paul is brave. | entailment | (![X]:((~generous(X)|humble(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~old(X)|~rich(X))=>(~funny(X)<~>generous(X))))&
((?[X]:((generous(X)|~funny(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))=>(?[X]:((~happy(X)<~>calm(X)))))&
(((~rich(lucy)&rich(lucy)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((happy(X)|calm(X))<=>(quiet(X)&happy(X))))&
(![X]:((~creative(X)&~old(X))<=>calm(X)))&
(![X]:((~happy(X)&brave(X))=>(brave(X)|~quiet(X))))&
(![X]:((~generous(X)&old(X))=>(~strong(X)<~>~brave(X))))&
(![X]:((curious(X)<~>~wise(X))<=>(~generous(X)&~wise(X))))&
((?[X]:((curious(X)|patient(X))))=>((quiet(paul)&~happy(paul))))&
(![X]:(patient(X)<=>(funny(X)&~wise(X))))&
(![X]:((brave(X)&~funny(X))=>kind(X)))&
(![X]:((curious(X)|old(X))=>(kind(X)<~>tall(X))))&
(?[X]:((humble(X)&~kind(X))))&
((patient(lucy)|quiet(lucy)))&
(?[X]:((patient(X)|generous(X))))&
((generous(lucy)<~>~kind(lucy)))&
(?[X]:(funny(X)))&
(~wise(mary)) | brave(paul) | [
"p0",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5319298510110372460414223
% SZS output start Proof for 5319298510110372460414223
1. ! [X0] : ((humble(X0) | ~generous(X0)) => (~brave(X0) <~> ~generous(X0))) [input p0]
3. ? [X0] : (~funny(X0) | generous(X0)) <=> ? [X0] : (~tall(X0) | ~old(X0)) [input p2]
5. (rich(lucy) & ~rich(lucy)) <=> ? [X0] : (~tall(X0) | ~old(X0)) [input p4]
21. ~brave(paul) [input hypothesis]
22. ? [X0] : (~funny(X0) | generous(X0)) <=> ? [X1] : (~tall(X1) | ~old(X1)) [rectify 3]
24. ! [X0] : ((~brave(X0) <~> ~generous(X0)) | (~humble(X0) & generous(X0))) [ennf transformation 1]
35. ! [X0] : (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (~humble(X0) & generous(X0))) [nnf transformation 24]
37. (? [X0] : (~funny(X0) | generous(X0)) | ! [X1] : (tall(X1) & old(X1))) & (? [X1] : (~tall(X1) | ~old(X1)) | ! [X0] : (funny(X0) & ~generous(X0))) [nnf transformation 22]
38. (? [X0] : (~funny(X0) | generous(X0)) | ! [X1] : (tall(X1) & old(X1))) & (? [X2] : (~tall(X2) | ~old(X2)) | ! [X3] : (funny(X3) & ~generous(X3))) [rectify 37]
39. ? [X0] : (~funny(X0) | generous(X0)) => (~funny(sK0) | generous(sK0)) [choice axiom]
40. ? [X2] : (~tall(X2) | ~old(X2)) => (~tall(sK1) | ~old(sK1)) [choice axiom]
41. ((~funny(sK0) | generous(sK0)) | ! [X1] : (tall(X1) & old(X1))) & ((~tall(sK1) | ~old(sK1)) | ! [X3] : (funny(X3) & ~generous(X3))) [skolemisation 38,40,39]
46. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X0] : (~tall(X0) | ~old(X0)) | (~rich(lucy) | rich(lucy))) [nnf transformation 5]
47. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X0] : (~tall(X0) | ~old(X0)) | ~rich(lucy) | rich(lucy)) [flattening 46]
48. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X1] : (~tall(X1) | ~old(X1)) | ~rich(lucy) | rich(lucy)) [rectify 47]
49. ? [X1] : (~tall(X1) | ~old(X1)) => (~tall(sK3) | ~old(sK3)) [choice axiom]
50. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & ((~tall(sK3) | ~old(sK3)) | ~rich(lucy) | rich(lucy)) [skolemisation 48,49]
70. generous(X0) | brave(X0) | generous(X0) [cnf transformation 35]
76. ~tall(sK1) | ~old(sK1) | ~generous(X3) [cnf transformation 41]
85. ~rich(lucy) | old(X0) [cnf transformation 50]
86. ~rich(lucy) | tall(X0) [cnf transformation 50]
87. rich(lucy) | old(X0) [cnf transformation 50]
88. rich(lucy) | tall(X0) [cnf transformation 50]
126. ~brave(paul) [cnf transformation 21]
129. brave(X0) | generous(X0) [duplicate literal removal 70]
131. 1 <=> ! [X1] : tall(X1) [avatar definition]
132. tall(X1) <- (1) [avatar component clause 131]
143. 4 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (4) [avatar component clause 143]
150. 6 <=> old(sK1) [avatar definition]
152. ~old(sK1) <- (~6) [avatar component clause 150]
154. 7 <=> tall(sK1) [avatar definition]
156. ~tall(sK1) <- (~7) [avatar component clause 154]
159. 8 <=> ! [X3] : ~generous(X3) [avatar definition]
160. ~generous(X3) <- (8) [avatar component clause 159]
161. 8 | ~6 | ~7 [avatar split clause 76,154,150,159]
181. 13 <=> rich(lucy) [avatar definition]
184. 1 | 13 [avatar split clause 88,181,131]
185. 4 | 13 [avatar split clause 87,181,143]
186. 1 | ~13 [avatar split clause 86,181,131]
187. 4 | ~13 [avatar split clause 85,181,143]
235. $false <- (1, ~7) [resolution 156,132]
236. ~1 | 7 [avatar contradiction clause 235]
237. $false <- (4, ~6) [subsumption resolution 152,144]
238. ~4 | 6 [avatar contradiction clause 237]
245. generous(paul) [resolution 129,126]
246. $false <- (8) [subsumption resolution 245,160]
247. ~8 [avatar contradiction clause 246]
248. $false [avatar sat refutation 161,184,185,186,187,236,238,247]
% SZS output end Proof for 5319298510110372460414223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not quiet or not wise is either calm or not wise.
If someone is not curious then alice is either not kind or generous and vice versa.
If someone is both not old and funny then someone is both not kind and calm.
Everyone who is not humble is both calm and not creative.
Everyone who is either brave or humble is not wise or humble and vice versa.
Everyone who is either calm or not creative is either strong or funny and vice versa.
Everyone who is either calm or wise is both generous and funny and vice versa.
Everyone who is old is both strong and not rich and vice versa.
Everyone who is both not brave and kind is either not rich or creative and vice versa.
Everyone who is both not old and funny is not strong and vice versa.
Everyone who is both brave and happy is happy.
Everyone who is strong or not creative is either not kind or tall and vice versa.
Everyone who is rich is generous.
Everyone who is not calm or not brave is either tall or quiet and vice versa.
Everyone who is not brave or creative is not funny or tall.
Everyone who is not old is both not kind and calm and vice versa.
Someone is either not calm or funny.
Fred is not creative or generous.
Mary is both not wise and not brave.
Alice is both happy and humble.
Paul is both not happy and wise.
Someone is not funny or not happy.
Mary is tall or not patient.
John is either not curious or not funny. | Alice is not humble. | contradiction | (![X]:((~quiet(X)<~>~wise(X))=>(calm(X)<~>~wise(X))))&
((?[X]:(~curious(X)))<=>((~kind(alice)<~>generous(alice))))&
((?[X]:((~old(X)&funny(X))))=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:(~humble(X)=>(calm(X)&~creative(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~wise(X)|humble(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)<~>funny(X))))&
(![X]:((calm(X)<~>wise(X))<=>(generous(X)&funny(X))))&
(![X]:(old(X)<=>(strong(X)&~rich(X))))&
(![X]:((~brave(X)&kind(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~old(X)&funny(X))<=>~strong(X)))&
(![X]:((brave(X)&happy(X))=>happy(X)))&
(![X]:((strong(X)|~creative(X))<=>(~kind(X)<~>tall(X))))&
(![X]:(rich(X)=>generous(X)))&
(![X]:((~calm(X)|~brave(X))<=>(tall(X)<~>quiet(X))))&
(![X]:((~brave(X)|creative(X))=>(~funny(X)|tall(X))))&
(![X]:(~old(X)<=>(~kind(X)&calm(X))))&
(?[X]:((~calm(X)<~>funny(X))))&
((~creative(fred)|generous(fred)))&
((~wise(mary)&~brave(mary)))&
((happy(alice)&humble(alice)))&
((~happy(paul)&wise(paul)))&
(?[X]:((~funny(X)|~happy(X))))&
((tall(mary)|~patient(mary)))&
((~curious(john)<~>~funny(john))) | ~humble(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1728953925445463807487551
% SZS output start Proof for 1728953925445463807487551
20. humble(alice) & happy(alice) [input p19]
25. ~humble(alice) [input hypothesis]
136. humble(alice) [cnf transformation 20]
142. ~humble(alice) [cnf transformation 25]
218. $false [subsumption resolution 142,136]
% SZS output end Proof for 1728953925445463807487551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either strong or rich then john is humble.
Everyone who is old is both not wise and patient and vice versa.
Everyone who is not patient or not tall is calm and vice versa.
Everyone who is not quiet or not rich is both not quiet and strong and vice versa.
Everyone who is both not humble and quiet is not happy or kind and vice versa.
Everyone who is not creative or not calm is strong or not brave and vice versa.
Everyone who is either curious or not wise is not strong and vice versa.
Everyone who is either not rich or wise is either brave or not wise.
Everyone who is both strong and curious is quiet or not curious.
Everyone who is wise is not funny or generous.
Everyone who is wise is both patient and not wise.
Everyone who is either not tall or not strong is either not rich or calm.
Everyone who is both not humble and old is not generous or happy and vice versa.
Everyone who is both not kind and not generous is both happy and generous.
If someone is both not calm and happy then fred is both humble and not creative.
Everyone who is not generous is not wise or not patient.
Mary is both not wise and not calm.
Someone is brave or not happy.
Fred is either tall or strong.
Susan is generous.
Someone is quiet.
Susan is either old or rich.
Someone is both not tall and curious. | Susan is quiet. | entailment | (((strong(mary)<~>rich(mary)))=>(humble(john)))&
(![X]:(old(X)<=>(~wise(X)&patient(X))))&
(![X]:((~patient(X)|~tall(X))<=>calm(X)))&
(![X]:((~quiet(X)|~rich(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~humble(X)&quiet(X))<=>(~happy(X)|kind(X))))&
(![X]:((~creative(X)|~calm(X))<=>(strong(X)|~brave(X))))&
(![X]:((curious(X)<~>~wise(X))<=>~strong(X)))&
(![X]:((~rich(X)<~>wise(X))=>(brave(X)<~>~wise(X))))&
(![X]:((strong(X)&curious(X))=>(quiet(X)|~curious(X))))&
(![X]:(wise(X)=>(~funny(X)|generous(X))))&
(![X]:(wise(X)=>(patient(X)&~wise(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~rich(X)<~>calm(X))))&
(![X]:((~humble(X)&old(X))<=>(~generous(X)|happy(X))))&
(![X]:((~kind(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((~calm(X)&happy(X))))=>((humble(fred)&~creative(fred))))&
(![X]:(~generous(X)=>(~wise(X)|~patient(X))))&
((~wise(mary)&~calm(mary)))&
(?[X]:((brave(X)|~happy(X))))&
((tall(fred)<~>strong(fred)))&
(generous(susan))&
(?[X]:(quiet(X)))&
((old(susan)<~>rich(susan)))&
(?[X]:((~tall(X)&curious(X)))) | quiet(susan) | [
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2200176451666467543512661
% SZS output start Proof for 2200176451666467543512661
2. ! [X0] : (old(X0) <=> (patient(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((~tall(X0) | ~patient(X0)) <=> calm(X0)) [input p2]
4. ! [X0] : ((~rich(X0) | ~quiet(X0)) <=> (strong(X0) & ~quiet(X0))) [input p3]
5. ! [X0] : ((quiet(X0) & ~humble(X0)) <=> (kind(X0) | ~happy(X0))) [input p4]
12. ! [X0] : ((~tall(X0) <~> ~strong(X0)) => (~rich(X0) <~> calm(X0))) [input p11]
13. ! [X0] : ((old(X0) & ~humble(X0)) <=> (happy(X0) | ~generous(X0))) [input p12]
15. ? [X0] : (happy(X0) & ~calm(X0)) => (~creative(fred) & humble(fred)) [input p14]
22. old(susan) <~> rich(susan) [input p21]
24. ~quiet(susan) [input hypothesis]
31. ! [X0] : ((~rich(X0) <~> calm(X0)) | (~tall(X0) <=> ~strong(X0))) [ennf transformation 12]
34. (~creative(fred) & humble(fred)) | ! [X0] : (~happy(X0) | calm(X0)) [ennf transformation 15]
38. ! [X0] : ((old(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | ~old(X0))) [nnf transformation 2]
39. ! [X0] : ((old(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | ~old(X0))) [flattening 38]
40. ! [X0] : (((~tall(X0) | ~patient(X0)) | ~calm(X0)) & (calm(X0) | (tall(X0) & patient(X0)))) [nnf transformation 3]
41. ! [X0] : ((~tall(X0) | ~patient(X0) | ~calm(X0)) & (calm(X0) | (tall(X0) & patient(X0)))) [flattening 40]
42. ! [X0] : (((~rich(X0) | ~quiet(X0)) | (~strong(X0) | quiet(X0))) & ((strong(X0) & ~quiet(X0)) | (rich(X0) & quiet(X0)))) [nnf transformation 4]
43. ! [X0] : ((~rich(X0) | ~quiet(X0) | ~strong(X0) | quiet(X0)) & ((strong(X0) & ~quiet(X0)) | (rich(X0) & quiet(X0)))) [flattening 42]
44. ! [X0] : (((quiet(X0) & ~humble(X0)) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | (~quiet(X0) | humble(X0)))) [nnf transformation 5]
45. ! [X0] : (((quiet(X0) & ~humble(X0)) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | ~quiet(X0) | humble(X0))) [flattening 44]
50. ! [X0] : (((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 31]
51. ! [X0] : (((old(X0) & ~humble(X0)) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | (~old(X0) | humble(X0)))) [nnf transformation 13]
52. ! [X0] : (((old(X0) & ~humble(X0)) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | ~old(X0) | humble(X0))) [flattening 51]
58. (~rich(susan) | ~old(susan)) & (rich(susan) | old(susan)) [nnf transformation 22]
64. ~old(X0) | patient(X0) [cnf transformation 39]
67. calm(X0) | tall(X0) [cnf transformation 41]
68. ~calm(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 41]
72. rich(X0) | strong(X0) [cnf transformation 43]
75. ~humble(X0) | happy(X0) [cnf transformation 45]
77. happy(X0) | quiet(X0) [cnf transformation 45]
96. ~calm(X0) | rich(X0) | ~strong(X0) | tall(X0) [cnf transformation 50]
100. ~humble(X0) | ~happy(X0) [cnf transformation 52]
102. ~happy(X0) | old(X0) [cnf transformation 52]
105. humble(fred) | ~happy(X0) | calm(X0) [cnf transformation 34]
116. ~rich(susan) | ~old(susan) [cnf transformation 58]
119. ~quiet(susan) [cnf transformation 24]
140. rich(X0) | ~strong(X0) | tall(X0) [subsumption resolution 96,67]
141. tall(X0) | rich(X0) [subsumption resolution 140,72]
144. ~humble(X0) [subsumption resolution 100,75]
147. 4 <=> ! [X0] : (~happy(X0) | calm(X0)) [avatar definition]
148. ~happy(X0) | calm(X0) <- (4) [avatar component clause 147]
154. ~happy(X0) | calm(X0) [subsumption resolution 105,144]
155. 4 [avatar split clause 154,147]
176. 10 <=> old(susan) [avatar definition]
177. old(susan) <- (10) [avatar component clause 176]
180. 11 <=> rich(susan) [avatar definition]
182. ~rich(susan) <- (~11) [avatar component clause 180]
183. ~10 | ~11 [avatar split clause 116,180,176]
185. patient(susan) <- (10) [resolution 64,177]
199. quiet(X0) | old(X0) [resolution 102,77]
204. quiet(X0) | calm(X0) <- (4) [resolution 148,77]
205. old(susan) [resolution 199,119]
214. calm(susan) <- (4) [resolution 204,119]
216. ~patient(susan) | ~tall(susan) <- (4) [resolution 214,68]
217. ~tall(susan) <- (4, 10) [subsumption resolution 216,185]
218. rich(susan) <- (4, 10) [resolution 217,141]
219. $false <- (4, 10, ~11) [subsumption resolution 218,182]
220. ~4 | ~10 | 11 [avatar contradiction clause 219]
230. 10 [avatar split clause 205,176]
231. $false [avatar sat refutation 155,183,220,230]
% SZS output end Proof for 2200176451666467543512661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is not quiet.
If paul is not brave or not curious then someone is calm.
If someone is tall then fred is not humble or not happy.
If someone is curious or funny then susan is both not quiet and quiet.
Everyone who is not tall or rich is not happy.
If lucy is either kind or not creative then fred is either not generous or strong and vice versa.
If alice is humble or not strong then someone is either kind or happy.
If someone is old or curious then paul is both brave and wise.
If someone is both not tall and not happy then john is both strong and tall and vice versa.
If someone is both not humble and not creative then someone is both generous and wise.
If someone is either patient or not patient then susan is either calm or brave.
Everyone who is either old or not rich is tall or calm and vice versa.
If lucy is tall then alice is not strong or curious.
If fred is either not calm or happy then alice is both happy and not patient and vice versa.
Everyone who is either not quiet or not tall is both curious and quiet and vice versa.
If lucy is not brave or not strong then alice is both not kind and not funny.
John is not calm.
Someone is patient.
Lucy is not rich or tall.
Someone is not kind.
Someone is rich.
Someone is not curious or not happy.
Lucy is either not tall or funny.
Lucy is brave or generous. | Lucy is not quiet. | entailment | ((?[X]:(~strong(X)))=>(?[X]:(~quiet(X))))&
(((~brave(paul)|~curious(paul)))=>(?[X]:(calm(X))))&
((?[X]:(tall(X)))=>((~humble(fred)|~happy(fred))))&
((?[X]:((curious(X)|funny(X))))=>((~quiet(susan)&quiet(susan))))&
(![X]:((~tall(X)|rich(X))=>~happy(X)))&
(((kind(lucy)<~>~creative(lucy)))<=>((~generous(fred)<~>strong(fred))))&
(((humble(alice)|~strong(alice)))=>(?[X]:((kind(X)<~>happy(X)))))&
((?[X]:((old(X)|curious(X))))=>((brave(paul)&wise(paul))))&
((?[X]:((~tall(X)&~happy(X))))<=>((strong(john)&tall(john))))&
((?[X]:((~humble(X)&~creative(X))))=>(?[X]:((generous(X)&wise(X)))))&
((?[X]:((patient(X)<~>~patient(X))))=>((calm(susan)<~>brave(susan))))&
(![X]:((old(X)<~>~rich(X))<=>(tall(X)|calm(X))))&
((tall(lucy))=>((~strong(alice)|curious(alice))))&
(((~calm(fred)<~>happy(fred)))<=>((happy(alice)&~patient(alice))))&
(![X]:((~quiet(X)<~>~tall(X))<=>(curious(X)&quiet(X))))&
(((~brave(lucy)|~strong(lucy)))=>((~kind(alice)&~funny(alice))))&
(~calm(john))&
(?[X]:(patient(X)))&
((~rich(lucy)|tall(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:(rich(X)))&
(?[X]:((~curious(X)|~happy(X))))&
((~tall(lucy)<~>funny(lucy)))&
((brave(lucy)|generous(lucy))) | ~quiet(lucy) | [
"p3",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8298995506270326470323132
% SZS output start Proof for 8298995506270326470323132
4. ? [X0] : (funny(X0) | curious(X0)) => (quiet(susan) & ~quiet(susan)) [input p3]
15. ! [X0] : ((~quiet(X0) <~> ~tall(X0)) <=> (quiet(X0) & curious(X0))) [input p14]
23. ~tall(lucy) <~> funny(lucy) [input p22]
25. quiet(lucy) [input hypothesis]
34. (quiet(susan) & ~quiet(susan)) | ! [X0] : (~funny(X0) & ~curious(X0)) [ennf transformation 4]
65. ! [X0] : ((((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))))) [nnf transformation 15]
66. ! [X0] : ((((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))))) [flattening 65]
75. (~funny(lucy) | tall(lucy)) & (funny(lucy) | ~tall(lucy)) [nnf transformation 23]
80. ~quiet(susan) | ~curious(X0) [cnf transformation 34]
81. ~quiet(susan) | ~funny(X0) [cnf transformation 34]
82. quiet(susan) | ~curious(X0) [cnf transformation 34]
83. quiet(susan) | ~funny(X0) [cnf transformation 34]
123. ~quiet(X0) | curious(X0) | tall(X0) [cnf transformation 66]
138. funny(lucy) | ~tall(lucy) [cnf transformation 75]
141. quiet(lucy) [cnf transformation 25]
183. 9 <=> ! [X0] : ~funny(X0) [avatar definition]
184. ~funny(X0) <- (9) [avatar component clause 183]
186. 10 <=> quiet(susan) [avatar definition]
189. 9 | 10 [avatar split clause 83,186,183]
191. 11 <=> ! [X0] : ~curious(X0) [avatar definition]
192. ~curious(X0) <- (11) [avatar component clause 191]
193. 11 | 10 [avatar split clause 82,186,191]
194. 9 | ~10 [avatar split clause 81,186,183]
195. 11 | ~10 [avatar split clause 80,186,191]
297. 32 <=> tall(lucy) [avatar definition]
358. 44 <=> funny(lucy) [avatar definition]
359. funny(lucy) <- (44) [avatar component clause 358]
362. ~32 | 44 [avatar split clause 138,358,297]
391. curious(lucy) | tall(lucy) [resolution 123,141]
394. tall(lucy) <- (11) [subsumption resolution 391,192]
397. 32 | ~11 [avatar split clause 394,191,297]
398. $false <- (9, 44) [subsumption resolution 359,184]
399. ~9 | ~44 [avatar contradiction clause 398]
400. $false [avatar sat refutation 189,193,194,195,362,397,399]
% SZS output end Proof for 8298995506270326470323132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not rich then someone is both kind and patient and vice versa.
Everyone who is not happy or not rich is either not patient or patient.
Everyone who is both not calm and generous is not funny and vice versa.
Everyone who is either calm or not happy is calm and vice versa.
Everyone who is not calm is both not calm and not generous.
If fred is both not humble and not kind then someone is both rich and patient and vice versa.
Everyone who is either not tall or not brave is both not happy and strong and vice versa.
If someone is either not humble or strong then john is not kind.
If lucy is not creative then someone is either creative or not tall.
Everyone who is both not curious and not quiet is not tall and vice versa.
Everyone who is either not kind or not curious is humble.
If susan is patient then alice is generous or not rich and vice versa.
Everyone who is rich or not wise is not brave.
If susan is quiet or not calm then someone is not brave and vice versa.
Everyone who is either patient or brave is not brave or strong.
Everyone who is either rich or not tall is either not rich or patient and vice versa.
Someone is quiet or strong.
Someone is not strong.
Alice is not calm.
Someone is generous.
Someone is creative or kind.
Someone is either brave or generous.
Fred is kind or rich.
Someone is funny or creative. | Lucy is not funny. | contradiction | ((~rich(susan))<=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((~happy(X)|~rich(X))=>(~patient(X)<~>patient(X))))&
(![X]:((~calm(X)&generous(X))<=>~funny(X)))&
(![X]:((calm(X)<~>~happy(X))<=>calm(X)))&
(![X]:(~calm(X)=>(~calm(X)&~generous(X))))&
(((~humble(fred)&~kind(fred)))<=>(?[X]:((rich(X)&patient(X)))))&
(![X]:((~tall(X)<~>~brave(X))<=>(~happy(X)&strong(X))))&
((?[X]:((~humble(X)<~>strong(X))))=>(~kind(john)))&
((~creative(lucy))=>(?[X]:((creative(X)<~>~tall(X)))))&
(![X]:((~curious(X)&~quiet(X))<=>~tall(X)))&
(![X]:((~kind(X)<~>~curious(X))=>humble(X)))&
((patient(susan))<=>((generous(alice)|~rich(alice))))&
(![X]:((rich(X)|~wise(X))=>~brave(X)))&
(((quiet(susan)|~calm(susan)))<=>(?[X]:(~brave(X))))&
(![X]:((patient(X)<~>brave(X))=>(~brave(X)|strong(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(~rich(X)<~>patient(X))))&
(?[X]:((quiet(X)|strong(X))))&
(?[X]:(~strong(X)))&
(~calm(alice))&
(?[X]:(generous(X)))&
(?[X]:((creative(X)|kind(X))))&
(?[X]:((brave(X)<~>generous(X))))&
((kind(fred)|rich(fred)))&
(?[X]:((funny(X)|creative(X)))) | ~funny(lucy) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 153979694732504202422445
% SZS output start Proof for 153979694732504202422445
3. ! [X0] : ((generous(X0) & ~calm(X0)) <=> ~funny(X0)) [input p2]
5. ! [X0] : (~calm(X0) => (~generous(X0) & ~calm(X0))) [input p4]
25. ~funny(lucy) [input hypothesis]
28. ! [X0] : ((~generous(X0) & ~calm(X0)) | calm(X0)) [ennf transformation 5]
40. ! [X0] : (((generous(X0) & ~calm(X0)) | funny(X0)) & (~funny(X0) | (~generous(X0) | calm(X0)))) [nnf transformation 3]
41. ! [X0] : (((generous(X0) & ~calm(X0)) | funny(X0)) & (~funny(X0) | ~generous(X0) | calm(X0))) [flattening 40]
87. ~calm(X0) | funny(X0) [cnf transformation 41]
88. funny(X0) | generous(X0) [cnf transformation 41]
94. ~generous(X0) | calm(X0) [cnf transformation 28]
140. ~funny(lucy) [cnf transformation 25]
295. generous(lucy) [resolution 88,140]
297. calm(lucy) [resolution 94,295]
299. funny(lucy) [resolution 297,87]
300. $false [subsumption resolution 299,140]
% SZS output end Proof for 153979694732504202422445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not funny is either old or rich and vice versa.
Everyone who is either happy or not old is either brave or not happy.
If lucy is both not funny and kind then someone is either patient or wise.
If john is either not tall or not quiet then someone is not funny or curious and vice versa.
Everyone who is not brave is patient.
Everyone who is either not kind or generous is either not happy or wise.
Everyone who is both curious and not patient is generous or patient and vice versa.
Everyone who is either not funny or wise is not humble or humble.
Everyone who is not strong is either not generous or not kind and vice versa.
Everyone who is patient is not curious.
Everyone who is both not quiet and curious is not generous or humble and vice versa.
If mary is either happy or not brave then paul is not old.
Everyone who is quiet is not patient or not wise.
Everyone who is either not generous or calm is either patient or not brave and vice versa.
Everyone who is strong is either creative or rich.
Everyone who is strong is brave or calm.
Someone is not rich or creative.
Someone is old or not patient.
Someone is not quiet.
Someone is happy.
John is rich.
Someone is creative. | Lucy is not patient. | entailment | (![X]:((~rich(X)&~funny(X))<=>(old(X)<~>rich(X))))&
(![X]:((happy(X)<~>~old(X))=>(brave(X)<~>~happy(X))))&
(((~funny(lucy)&kind(lucy)))=>(?[X]:((patient(X)<~>wise(X)))))&
(((~tall(john)<~>~quiet(john)))<=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:(~brave(X)=>patient(X)))&
(![X]:((~kind(X)<~>generous(X))=>(~happy(X)<~>wise(X))))&
(![X]:((curious(X)&~patient(X))<=>(generous(X)|patient(X))))&
(![X]:((~funny(X)<~>wise(X))=>(~humble(X)|humble(X))))&
(![X]:(~strong(X)<=>(~generous(X)<~>~kind(X))))&
(![X]:(patient(X)=>~curious(X)))&
(![X]:((~quiet(X)&curious(X))<=>(~generous(X)|humble(X))))&
(((happy(mary)<~>~brave(mary)))=>(~old(paul)))&
(![X]:(quiet(X)=>(~patient(X)|~wise(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(patient(X)<~>~brave(X))))&
(![X]:(strong(X)=>(creative(X)<~>rich(X))))&
(![X]:(strong(X)=>(brave(X)|calm(X))))&
(?[X]:((~rich(X)|creative(X))))&
(?[X]:((old(X)|~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(happy(X)))&
(rich(john))&
(?[X]:(creative(X))) | ~patient(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3297724433812979432908767
% SZS output start Proof for 3297724433812979432908767
7. ! [X0] : ((~patient(X0) & curious(X0)) <=> (patient(X0) | generous(X0))) [input p6]
23. patient(lucy) [input hypothesis]
51. ! [X0] : (((~patient(X0) & curious(X0)) | (~patient(X0) & ~generous(X0))) & ((patient(X0) | generous(X0)) | (patient(X0) | ~curious(X0)))) [nnf transformation 7]
52. ! [X0] : (((~patient(X0) & curious(X0)) | (~patient(X0) & ~generous(X0))) & (patient(X0) | generous(X0) | patient(X0) | ~curious(X0))) [flattening 51]
97. ~patient(X0) | ~patient(X0) [cnf transformation 52]
128. patient(lucy) [cnf transformation 23]
130. ~patient(X0) [duplicate literal removal 97]
210. $false [subsumption resolution 128,130]
% SZS output end Proof for 3297724433812979432908767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or wise is not funny or tall and vice versa.
Everyone who is not calm or not kind is humble or not old and vice versa.
If someone is humble then alice is creative or not wise.
If someone is both funny and not calm then lucy is either wise or patient and vice versa.
Everyone who is either creative or not calm is either creative or not funny and vice versa.
If someone is not tall or not creative then someone is both generous and quiet and vice versa.
Everyone who is both happy and not generous is not calm or funny and vice versa.
Everyone who is either not old or not funny is not humble and vice versa.
If someone is calm then someone is not brave and vice versa.
Everyone who is either not kind or not generous is either humble or creative.
Everyone who is both wise and not curious is either not humble or not patient.
Everyone who is not funny or curious is either not strong or creative and vice versa.
If fred is old or not strong then someone is either not calm or not tall.
If someone is either not strong or not humble then alice is either old or funny and vice versa.
If paul is wise or not happy then someone is patient and vice versa.
Everyone who is either patient or not calm is not strong and vice versa.
Someone is either not quiet or not old.
John is either not wise or humble.
Alice is calm or not humble.
Alice is not funny or not quiet.
Someone is tall or strong. | John is old. | contradiction | (![X]:((creative(X)<~>wise(X))<=>(~funny(X)|tall(X))))&
(![X]:((~calm(X)|~kind(X))<=>(humble(X)|~old(X))))&
((?[X]:(humble(X)))=>((creative(alice)|~wise(alice))))&
((?[X]:((funny(X)&~calm(X))))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((creative(X)<~>~calm(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((happy(X)&~generous(X))<=>(~calm(X)|funny(X))))&
(![X]:((~old(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(humble(X)<~>creative(X))))&
(![X]:((wise(X)&~curious(X))=>(~humble(X)<~>~patient(X))))&
(![X]:((~funny(X)|curious(X))<=>(~strong(X)<~>creative(X))))&
(((old(fred)|~strong(fred)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>((old(alice)<~>funny(alice))))&
(((wise(paul)|~happy(paul)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)<~>~calm(X))<=>~strong(X)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~wise(john)<~>humble(john)))&
((calm(alice)|~humble(alice)))&
((~funny(alice)|~quiet(alice)))&
(?[X]:((tall(X)|strong(X)))) | old(john) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6379850981398954687944743
% SZS output start Proof for 6379850981398954687944743
1. ! [X0] : ((creative(X0) <~> wise(X0)) <=> (tall(X0) | ~funny(X0))) [input p0]
2. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> (~old(X0) | humble(X0))) [input p1]
5. ! [X0] : ((creative(X0) <~> ~calm(X0)) <=> (creative(X0) <~> ~funny(X0))) [input p4]
6. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X0] : (quiet(X0) & generous(X0)) [input p5]
7. ! [X0] : ((~generous(X0) & happy(X0)) <=> (funny(X0) | ~calm(X0))) [input p6]
8. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> ~humble(X0)) [input p7]
18. ~wise(john) <~> humble(john) [input p17]
22. old(john) [input hypothesis]
23. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X1] : (quiet(X1) & generous(X1)) [rectify 6]
31. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [nnf transformation 1]
32. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [flattening 31]
33. ! [X0] : (((~kind(X0) | ~calm(X0)) | (old(X0) & ~humble(X0))) & ((~old(X0) | humble(X0)) | (kind(X0) & calm(X0)))) [nnf transformation 2]
34. ! [X0] : ((~kind(X0) | ~calm(X0) | (old(X0) & ~humble(X0))) & (~old(X0) | humble(X0) | (kind(X0) & calm(X0)))) [flattening 33]
39. ! [X0] : ((((calm(X0) | ~creative(X0)) & (~calm(X0) | creative(X0))) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0)))) & (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))))) [nnf transformation 5]
40. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X1] : (quiet(X1) & generous(X1)) | ! [X0] : (creative(X0) & tall(X0))) [nnf transformation 23]
41. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X2] : (quiet(X2) & generous(X2)) | ! [X3] : (creative(X3) & tall(X3))) [rectify 40]
42. ? [X0] : (~creative(X0) | ~tall(X0)) => (~creative(sK1) | ~tall(sK1)) [choice axiom]
43. ? [X2] : (quiet(X2) & generous(X2)) => (quiet(sK2) & generous(sK2)) [choice axiom]
44. ((~creative(sK1) | ~tall(sK1)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & ((quiet(sK2) & generous(sK2)) | ! [X3] : (creative(X3) & tall(X3))) [skolemisation 41,43,42]
45. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & ((funny(X0) | ~calm(X0)) | (generous(X0) | ~happy(X0)))) [nnf transformation 7]
46. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & (funny(X0) | ~calm(X0) | generous(X0) | ~happy(X0))) [flattening 45]
47. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | humble(X0)) & (~humble(X0) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 8]
73. (~humble(john) | wise(john)) & (humble(john) | ~wise(john)) [nnf transformation 18]
81. ~tall(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 32]
82. ~old(X0) | humble(X0) | calm(X0) [cnf transformation 34]
95. funny(X0) | ~creative(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 39]
98. ~calm(X0) | creative(X0) | creative(X0) | funny(X0) [cnf transformation 39]
101. generous(sK2) | tall(X3) [cnf transformation 44]
102. generous(sK2) | creative(X3) [cnf transformation 44]
109. ~generous(X0) | calm(X0) [cnf transformation 46]
110. ~generous(X0) | ~funny(X0) [cnf transformation 46]
113. ~old(X0) | ~funny(X0) | humble(X0) [cnf transformation 47]
151. ~humble(john) | wise(john) [cnf transformation 73]
155. old(john) [cnf transformation 22]
157. funny(X0) | ~creative(X0) | ~calm(X0) [duplicate literal removal 95]
158. ~calm(X0) | creative(X0) | funny(X0) [duplicate literal removal 98]
197. ~calm(X0) | funny(X0) [subsumption resolution 157,158]
213. 12 <=> ! [X3] : creative(X3) [avatar definition]
214. creative(X3) <- (12) [avatar component clause 213]
221. 14 <=> ! [X3] : tall(X3) [avatar definition]
222. tall(X3) <- (14) [avatar component clause 221]
225. 15 <=> generous(sK2) [avatar definition]
227. generous(sK2) <- (15) [avatar component clause 225]
228. 12 | 15 [avatar split clause 102,225,213]
229. 14 | 15 [avatar split clause 101,225,221]
325. 36 <=> wise(john) [avatar definition]
327. wise(john) <- (36) [avatar component clause 325]
329. 37 <=> humble(john) [avatar definition]
331. ~humble(john) <- (~37) [avatar component clause 329]
332. 36 | ~37 [avatar split clause 151,329,325]
377. ~creative(X0) | ~wise(X0) <- (14) [resolution 81,222]
379. ~wise(X0) <- (12, 14) [subsumption resolution 377,214]
380. humble(john) | calm(john) [resolution 82,155]
381. calm(john) <- (~37) [subsumption resolution 380,331]
382. funny(john) <- (~37) [resolution 381,197]
389. ~funny(john) | humble(john) [resolution 113,155]
390. humble(john) <- (~37) [subsumption resolution 389,382]
391. $false <- (~37) [subsumption resolution 390,331]
392. 37 [avatar contradiction clause 391]
409. $false <- (12, 14, 36) [subsumption resolution 327,379]
410. ~12 | ~14 | ~36 [avatar contradiction clause 409]
424. ~funny(sK2) <- (15) [resolution 227,110]
425. calm(sK2) <- (15) [resolution 227,109]
496. funny(sK2) <- (15) [resolution 425,197]
497. $false <- (15) [subsumption resolution 496,424]
498. ~15 [avatar contradiction clause 497]
499. $false [avatar sat refutation 228,229,332,392,410,498]
% SZS output end Proof for 6379850981398954687944743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or strong is either not kind or old.
Everyone who is not happy is not old and vice versa.
Everyone who is rich is both old and patient and vice versa.
Everyone who is not patient or patient is not calm or not rich and vice versa.
If lucy is either not wise or quiet then someone is both generous and curious.
If mary is both funny and not funny then lucy is funny and vice versa.
Everyone who is funny is not brave or not happy.
If john is creative or not tall then someone is either quiet or not generous and vice versa.
If someone is creative or not kind then someone is patient or generous and vice versa.
Everyone who is either not calm or happy is both calm and wise and vice versa.
Everyone who is not happy is either not curious or not kind and vice versa.
Everyone who is calm is not calm or wise and vice versa.
If alice is brave or curious then someone is both creative and tall.
If someone is either old or wise then john is humble and vice versa.
Everyone who is both kind and not quiet is old or not patient and vice versa.
If someone is either tall or wise then someone is either not strong or not quiet.
Mary is brave or funny.
Someone is either not strong or not brave.
Susan is not brave or not kind.
Someone is not patient or strong.
Someone is both funny and not creative.
John is either not strong or creative.
Mary is not curious or funny. | John is wise. | entailment | (![X]:((humble(X)<~>strong(X))=>(~kind(X)<~>old(X))))&
(![X]:(~happy(X)<=>~old(X)))&
(![X]:(rich(X)<=>(old(X)&patient(X))))&
(![X]:((~patient(X)|patient(X))<=>(~calm(X)|~rich(X))))&
(((~wise(lucy)<~>quiet(lucy)))=>(?[X]:((generous(X)&curious(X)))))&
(((funny(mary)&~funny(mary)))<=>(funny(lucy)))&
(![X]:(funny(X)=>(~brave(X)|~happy(X))))&
(((creative(john)|~tall(john)))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~calm(X)<~>happy(X))<=>(calm(X)&wise(X))))&
(![X]:(~happy(X)<=>(~curious(X)<~>~kind(X))))&
(![X]:(calm(X)<=>(~calm(X)|wise(X))))&
(((brave(alice)|curious(alice)))=>(?[X]:((creative(X)&tall(X)))))&
((?[X]:((old(X)<~>wise(X))))<=>(humble(john)))&
(![X]:((kind(X)&~quiet(X))<=>(old(X)|~patient(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((brave(mary)|funny(mary)))&
(?[X]:((~strong(X)<~>~brave(X))))&
((~brave(susan)|~kind(susan)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((funny(X)&~creative(X))))&
((~strong(john)<~>creative(john)))&
((~curious(mary)|funny(mary))) | wise(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2163261846951619180343376
% SZS output start Proof for 2163261846951619180343376
12. ! [X0] : (calm(X0) <=> (wise(X0) | ~calm(X0))) [input p11]
24. ~wise(john) [input hypothesis]
57. ! [X0] : ((calm(X0) | (~wise(X0) & calm(X0))) & ((wise(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 12]
58. ! [X0] : ((calm(X0) | (~wise(X0) & calm(X0))) & (wise(X0) | ~calm(X0) | ~calm(X0))) [flattening 57]
120. wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 58]
121. calm(X0) | calm(X0) [cnf transformation 58]
150. ~wise(john) [cnf transformation 24]
151. wise(X0) | ~calm(X0) [duplicate literal removal 120]
152. calm(X0) [duplicate literal removal 121]
246. wise(X0) [subsumption resolution 151,152]
341. $false [subsumption resolution 150,246]
% SZS output end Proof for 2163261846951619180343376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or happy is not old or wise.
If paul is tall then someone is either not generous or not curious.
Everyone who is curious is both not old and not curious.
If someone is both not funny and not happy then susan is not happy or kind and vice versa.
Everyone who is not brave is either not strong or not humble and vice versa.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Susan is not creative or brave.
John is rich or kind.
Someone is not old or not tall.
Someone is wise.
Someone is not happy or not brave.
Lucy is rich.
John is either happy or not patient. | Susan is not humble. | entailment | (![X]:((curious(X)<~>happy(X))=>(~old(X)|wise(X))))&
((tall(paul))=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:(curious(X)=>(~old(X)&~curious(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>((~happy(susan)|kind(susan))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~humble(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
((~creative(susan)|brave(susan)))&
((rich(john)|kind(john)))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:(wise(X)))&
(?[X]:((~happy(X)|~brave(X))))&
(rich(lucy))&
((happy(john)<~>~patient(john))) | ~humble(susan) | [
"p2",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5992399839866691201604030
% SZS output start Proof for 5992399839866691201604030
3. ! [X0] : (curious(X0) => (~curious(X0) & ~old(X0))) [input p2]
10. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p9]
12. ! [X0] : ((~kind(X0) & patient(X0)) <=> (~generous(X0) | kind(X0))) [input p11]
13. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (curious(X0) <~> ~humble(X0))) [input p12]
23. humble(susan) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~old(X0)) | ~curious(X0)) [ennf transformation 3]
31. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 10]
61. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | (kind(X0) | ~patient(X0)))) [nnf transformation 12]
62. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | kind(X0) | ~patient(X0))) [flattening 61]
63. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (creative(X0) | kind(X0)))) [nnf transformation 13]
64. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | creative(X0) | kind(X0))) [flattening 63]
79. ~curious(X0) | ~curious(X0) [cnf transformation 29]
107. ~creative(X0) | ~creative(X0) [cnf transformation 31]
113. ~kind(X0) | ~kind(X0) [cnf transformation 62]
115. ~humble(X0) | curious(X0) | creative(X0) | kind(X0) [cnf transformation 64]
137. humble(susan) [cnf transformation 23]
139. ~kind(X0) [duplicate literal removal 113]
140. ~creative(X0) [duplicate literal removal 107]
141. ~curious(X0) [duplicate literal removal 79]
223. 18 <=> ! [X3] : ~humble(X3) [avatar definition]
224. ~humble(X3) <- (18) [avatar component clause 223]
249. ~humble(X0) | creative(X0) | kind(X0) [subsumption resolution 115,141]
250. ~humble(X0) | kind(X0) [subsumption resolution 249,140]
251. ~humble(X0) [subsumption resolution 250,139]
252. 18 [avatar split clause 251,223]
282. $false <- (18) [resolution 224,137]
283. ~18 [avatar contradiction clause 282]
284. $false [avatar sat refutation 252,283]
% SZS output end Proof for 5992399839866691201604030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong then susan is not strong or happy.
Everyone who is both not humble and not kind is not curious or humble and vice versa.
Everyone who is both not rich and not strong is both humble and not rich.
If fred is both not strong and not brave then lucy is either not wise or happy and vice versa.
If someone is strong then someone is not tall and vice versa.
Everyone who is either humble or wise is both patient and generous.
If someone is funny or wise then lucy is funny and vice versa.
If john is not patient or funny then fred is not patient or creative and vice versa.
If paul is both rich and not generous then someone is not old or calm.
Everyone who is not happy or not quiet is both curious and not kind and vice versa.
Everyone who is either humble or wise is both not funny and not tall.
Everyone who is old or kind is not funny and vice versa.
If john is rich then mary is both tall and funny.
Everyone who is either calm or creative is either not funny or not humble and vice versa.
If lucy is creative then someone is either patient or creative.
Everyone who is both kind and not quiet is wise or old and vice versa.
John is not old.
Susan is either tall or strong.
Someone is both patient and curious.
Someone is not funny.
Someone is not curious or not rich.
Susan is either strong or not wise. | John is happy. | entailment | ((?[X]:(~strong(X)))=>((~strong(susan)|happy(susan))))&
(![X]:((~humble(X)&~kind(X))<=>(~curious(X)|humble(X))))&
(![X]:((~rich(X)&~strong(X))=>(humble(X)&~rich(X))))&
(((~strong(fred)&~brave(fred)))<=>((~wise(lucy)<~>happy(lucy))))&
((?[X]:(strong(X)))<=>(?[X]:(~tall(X))))&
(![X]:((humble(X)<~>wise(X))=>(patient(X)&generous(X))))&
((?[X]:((funny(X)|wise(X))))<=>(funny(lucy)))&
(((~patient(john)|funny(john)))<=>((~patient(fred)|creative(fred))))&
(((rich(paul)&~generous(paul)))=>(?[X]:((~old(X)|calm(X)))))&
(![X]:((~happy(X)|~quiet(X))<=>(curious(X)&~kind(X))))&
(![X]:((humble(X)<~>wise(X))=>(~funny(X)&~tall(X))))&
(![X]:((old(X)|kind(X))<=>~funny(X)))&
((rich(john))=>((tall(mary)&funny(mary))))&
(![X]:((calm(X)<~>creative(X))<=>(~funny(X)<~>~humble(X))))&
((creative(lucy))=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((kind(X)&~quiet(X))<=>(wise(X)|old(X))))&
(~old(john))&
((tall(susan)<~>strong(susan)))&
(?[X]:((patient(X)&curious(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~curious(X)|~rich(X))))&
((strong(susan)<~>~wise(susan))) | happy(john) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6545671389213573691540872
% SZS output start Proof for 6545671389213573691540872
2. ! [X0] : ((~kind(X0) & ~humble(X0)) <=> (humble(X0) | ~curious(X0))) [input p1]
10. ! [X0] : ((~quiet(X0) | ~happy(X0)) <=> (~kind(X0) & curious(X0))) [input p9]
23. ~happy(john) [input hypothesis]
35. ! [X0] : (((~kind(X0) & ~humble(X0)) | (~humble(X0) & curious(X0))) & ((humble(X0) | ~curious(X0)) | (kind(X0) | humble(X0)))) [nnf transformation 2]
36. ! [X0] : (((~kind(X0) & ~humble(X0)) | (~humble(X0) & curious(X0))) & (humble(X0) | ~curious(X0) | kind(X0) | humble(X0))) [flattening 35]
51. ! [X0] : (((~quiet(X0) | ~happy(X0)) | (kind(X0) | ~curious(X0))) & ((~kind(X0) & curious(X0)) | (quiet(X0) & happy(X0)))) [nnf transformation 10]
52. ! [X0] : ((~quiet(X0) | ~happy(X0) | kind(X0) | ~curious(X0)) & ((~kind(X0) & curious(X0)) | (quiet(X0) & happy(X0)))) [flattening 51]
71. humble(X0) | ~curious(X0) | kind(X0) | humble(X0) [cnf transformation 36]
73. ~humble(X0) | ~humble(X0) [cnf transformation 36]
95. curious(X0) | happy(X0) [cnf transformation 52]
97. ~kind(X0) | happy(X0) [cnf transformation 52]
133. ~happy(john) [cnf transformation 23]
134. humble(X0) | ~curious(X0) | kind(X0) [duplicate literal removal 71]
135. ~humble(X0) [duplicate literal removal 73]
148. ~curious(X0) | kind(X0) [subsumption resolution 134,135]
293. kind(X0) | happy(X0) [resolution 148,95]
294. happy(X0) [subsumption resolution 293,97]
300. $false [resolution 294,133]
% SZS output end Proof for 6545671389213573691540872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not tall is not calm and vice versa.
Everyone who is not curious is both not happy and generous and vice versa.
Everyone who is not wise or not strong is either old or not curious and vice versa.
Everyone who is either happy or not generous is either not happy or not funny and vice versa.
If alice is creative or curious then paul is not old or funny.
Everyone who is either not rich or generous is happy or not old.
Everyone who is both tall and not brave is generous and vice versa.
If mary is both curious and old then someone is not brave or kind.
If someone is not calm then someone is creative and vice versa.
Everyone who is not funny or not humble is both creative and strong and vice versa.
Everyone who is calm or patient is not strong or funny and vice versa.
Everyone who is not patient is kind.
Everyone who is either strong or not strong is either not funny or patient and vice versa.
If someone is either not creative or not funny then someone is not brave or not happy and vice versa.
If someone is both not tall and not patient then someone is not calm and vice versa.
If mary is not kind or not creative then mary is not funny or strong and vice versa.
Someone is either not patient or tall.
Fred is either not strong or not funny.
Someone is either not wise or old.
Someone is both not old and not happy.
Lucy is tall. | Lucy is curious. | entailment | (![X]:((kind(X)<~>~tall(X))<=>~calm(X)))&
(![X]:(~curious(X)<=>(~happy(X)&generous(X))))&
(![X]:((~wise(X)|~strong(X))<=>(old(X)<~>~curious(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~happy(X)<~>~funny(X))))&
(((creative(alice)|curious(alice)))=>((~old(paul)|funny(paul))))&
(![X]:((~rich(X)<~>generous(X))=>(happy(X)|~old(X))))&
(![X]:((tall(X)&~brave(X))<=>generous(X)))&
(((curious(mary)&old(mary)))=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:(creative(X))))&
(![X]:((~funny(X)|~humble(X))<=>(creative(X)&strong(X))))&
(![X]:((calm(X)|patient(X))<=>(~strong(X)|funny(X))))&
(![X]:(~patient(X)=>kind(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:(~calm(X))))&
(((~kind(mary)|~creative(mary)))<=>((~funny(mary)|strong(mary))))&
(?[X]:((~patient(X)<~>tall(X))))&
((~strong(fred)<~>~funny(fred)))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~old(X)&~happy(X))))&
(tall(lucy)) | curious(lucy) | [
"p1",
"p3",
"p6",
"p8",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4457541952324563365616163
% SZS output start Proof for 4457541952324563365616163
2. ! [X0] : (~curious(X0) <=> (generous(X0) & ~happy(X0))) [input p1]
4. ! [X0] : ((happy(X0) <~> ~generous(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p3]
7. ! [X0] : ((~brave(X0) & tall(X0)) <=> generous(X0)) [input p6]
9. ? [X0] : ~calm(X0) <=> ? [X0] : creative(X0) [input p8]
10. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (strong(X0) & creative(X0))) [input p9]
13. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p12]
15. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X0] : ~calm(X0) [input p14]
22. ~curious(lucy) [input hypothesis]
23. ? [X0] : ~calm(X0) <=> ? [X1] : creative(X1) [rectify 9]
25. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X1] : ~calm(X1) [rectify 15]
34. ! [X0] : ((~curious(X0) | (~generous(X0) | happy(X0))) & ((generous(X0) & ~happy(X0)) | curious(X0))) [nnf transformation 2]
35. ! [X0] : ((~curious(X0) | ~generous(X0) | happy(X0)) & ((generous(X0) & ~happy(X0)) | curious(X0))) [flattening 34]
38. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [nnf transformation 4]
40. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 7]
41. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | brave(X0) | ~tall(X0))) [flattening 40]
44. (? [X0] : ~calm(X0) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : calm(X0)) [nnf transformation 23]
45. (? [X0] : ~calm(X0) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : calm(X3)) [rectify 44]
46. ? [X0] : ~calm(X0) => ~calm(sK1) [choice axiom]
47. ? [X2] : creative(X2) => creative(sK2) [choice axiom]
48. (~calm(sK1) | ! [X1] : ~creative(X1)) & (creative(sK2) | ! [X3] : calm(X3)) [skolemisation 45,47,46]
49. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 10]
50. ! [X0] : ((~humble(X0) | ~funny(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [flattening 49]
53. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 13]
59. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : (patient(X0) | tall(X0))) [nnf transformation 25]
60. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : (patient(X3) | tall(X3))) [rectify 59]
61. ? [X0] : (~patient(X0) & ~tall(X0)) => (~patient(sK5) & ~tall(sK5)) [choice axiom]
62. ? [X2] : ~calm(X2) => ~calm(sK6) [choice axiom]
63. ((~patient(sK5) & ~tall(sK5)) | ! [X1] : calm(X1)) & (~calm(sK6) | ! [X3] : (patient(X3) | tall(X3))) [skolemisation 60,62,61]
80. generous(X0) | curious(X0) [cnf transformation 35]
88. ~funny(X0) | ~happy(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 38]
91. funny(X0) | happy(X0) | happy(X0) | generous(X0) [cnf transformation 38]
92. ~generous(X0) | happy(X0) | ~funny(X0) | happy(X0) [cnf transformation 38]
95. generous(X0) | ~happy(X0) | ~happy(X0) | funny(X0) [cnf transformation 38]
101. ~generous(X0) | tall(X0) [cnf transformation 41]
105. ~calm(sK1) | ~creative(X1) [cnf transformation 48]
106. creative(X0) | funny(X0) [cnf transformation 50]
108. funny(X0) | strong(X0) [cnf transformation 50]
116. patient(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
117. patient(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 53]
131. ~tall(sK5) | calm(X1) [cnf transformation 63]
132. ~patient(sK5) | calm(X1) [cnf transformation 63]
146. ~curious(lucy) [cnf transformation 22]
147. patient(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 116]
148. patient(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 117]
151. ~funny(X0) | ~happy(X0) | ~generous(X0) [duplicate literal removal 88]
152. funny(X0) | happy(X0) | generous(X0) [duplicate literal removal 91]
153. ~funny(X0) | happy(X0) | ~generous(X0) [duplicate literal removal 92]
154. ~happy(X0) | generous(X0) | funny(X0) [duplicate literal removal 95]
155. funny(X0) | generous(X0) [subsumption resolution 152,154]
156. ~funny(X0) | ~generous(X0) [subsumption resolution 151,153]
193. 9 <=> ! [X1] : ~creative(X1) [avatar definition]
194. ~creative(X1) <- (9) [avatar component clause 193]
196. 10 <=> calm(sK1) [avatar definition]
198. ~calm(sK1) <- (~10) [avatar component clause 196]
199. 9 | ~10 [avatar split clause 105,196,193]
201. 11 <=> ! [X3] : calm(X3) [avatar definition]
202. calm(X3) <- (11) [avatar component clause 201]
210. patient(X0) | strong(X0) [subsumption resolution 148,108]
211. ~funny(X0) | patient(X0) [subsumption resolution 147,210]
230. 17 <=> ! [X3] : funny(X3) [avatar definition]
231. funny(X3) <- (17) [avatar component clause 230]
247. 21 <=> patient(sK5) [avatar definition]
249. ~patient(sK5) <- (~21) [avatar component clause 247]
250. 11 | ~21 [avatar split clause 132,247,201]
252. 22 <=> tall(sK5) [avatar definition]
255. 11 | ~22 [avatar split clause 131,252,201]
316. $false <- (~10, 11) [subsumption resolution 198,202]
317. 10 | ~11 [avatar contradiction clause 316]
340. patient(X0) | generous(X0) [resolution 211,155]
537. generous(sK5) <- (~21) [resolution 340,249]
542. tall(sK5) <- (~21) [resolution 537,101]
550. 22 | 21 [avatar split clause 542,247,252]
557. funny(X0) <- (9) [resolution 194,106]
559. 17 | ~9 [avatar split clause 557,193,230]
569. ~generous(X3) <- (17) [resolution 231,156]
587. curious(X0) <- (17) [resolution 569,80]
601. $false <- (17) [resolution 587,146]
606. ~17 [avatar contradiction clause 601]
607. $false [avatar sat refutation 199,250,255,317,550,559,606]
% SZS output end Proof for 4457541952324563365616163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious is both not rich and happy. Everyone who is not curious is generous and vice versa. If someone is both not humble and not curious then alice is rich or not calm. Everyone who is both not generous and brave is both not rich and happy and vice versa. If someone is both not brave and wise then someone is humble. Everyone who is not quiet is humble. Everyone who is both not curious and not humble is either not generous or rich. Everyone who is curious or creative is either curious or not wise. Everyone who is happy is either curious or not strong and vice versa. If someone is rich or not happy then someone is either tall or quiet. Everyone who is humble or not wise is generous and vice versa. If someone is not generous then someone is both strong and not funny. Everyone who is either not funny or old is either not funny or not tall. Everyone who is either not brave or patient is curious and vice versa. If fred is creative or strong then someone is either happy or kind. If someone is either not strong or funny then someone is not patient or brave. Mary is both not old and not humble. Someone is both quiet and not humble. Lucy is quiet or not humble. Someone is either not funny or not generous. Someone is either not generous or not strong. Fred is both happy and strong. | Alice is curious. | entailment | (![X]:(~curious(X)=>(~rich(X)&happy(X))))&
(![X]:(~curious(X)<=>generous(X)))&
((?[X]:((~humble(X)&~curious(X))))=>((rich(alice)|~calm(alice))))&
(![X]:((~generous(X)&brave(X))<=>(~rich(X)&happy(X))))&
((?[X]:((~brave(X)&wise(X))))=>(?[X]:(humble(X))))&
(![X]:(~quiet(X)=>humble(X)))&
(![X]:((~curious(X)&~humble(X))=>(~generous(X)<~>rich(X))))&
(![X]:((curious(X)|creative(X))=>(curious(X)<~>~wise(X))))&
(![X]:(happy(X)<=>(curious(X)<~>~strong(X))))&
((?[X]:((rich(X)|~happy(X))))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:((humble(X)|~wise(X))<=>generous(X)))&
((?[X]:(~generous(X)))=>(?[X]:((strong(X)&~funny(X)))))&
(![X]:((~funny(X)<~>old(X))=>(~funny(X)<~>~tall(X))))&
(![X]:((~brave(X)<~>patient(X))<=>curious(X)))&
(((creative(fred)|strong(fred)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:((~patient(X)|brave(X)))))&
((~old(mary)&~humble(mary)))&
(?[X]:((quiet(X)&~humble(X))))&
((quiet(lucy)|~humble(lucy)))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((~generous(X)<~>~strong(X))))&
((happy(fred)&strong(fred))) | curious(alice) | [
"p0",
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1555746498461787181477525
% SZS output start Proof for 1555746498461787181477525
1. ! [X0] : (~curious(X0) => (happy(X0) & ~rich(X0))) [input p0]
2. ! [X0] : (~curious(X0) <=> generous(X0)) [input p1]
4. ! [X0] : ((brave(X0) & ~generous(X0)) <=> (happy(X0) & ~rich(X0))) [input p3]
23. ~curious(alice) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~rich(X0)) | curious(X0)) [ennf transformation 1]
42. ! [X0] : ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))) [nnf transformation 2]
43. ! [X0] : (((brave(X0) & ~generous(X0)) | (~happy(X0) | rich(X0))) & ((happy(X0) & ~rich(X0)) | (~brave(X0) | generous(X0)))) [nnf transformation 4]
44. ! [X0] : (((brave(X0) & ~generous(X0)) | ~happy(X0) | rich(X0)) & ((happy(X0) & ~rich(X0)) | ~brave(X0) | generous(X0))) [flattening 43]
77. ~rich(X0) | curious(X0) [cnf transformation 31]
78. happy(X0) | curious(X0) [cnf transformation 31]
79. generous(X0) | curious(X0) [cnf transformation 42]
83. ~generous(X0) | ~happy(X0) | rich(X0) [cnf transformation 44]
127. ~curious(alice) [cnf transformation 23]
242. ~happy(X0) | rich(X0) | curious(X0) [resolution 83,79]
246. rich(X0) | curious(X0) [subsumption resolution 242,78]
247. curious(X0) [subsumption resolution 246,77]
276. $false [resolution 247,127]
% SZS output end Proof for 1555746498461787181477525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not happy and rich then someone is either not quiet or kind and vice versa.
Everyone who is calm or humble is not strong or patient.
Everyone who is either patient or not humble is not patient or not quiet.
Everyone who is either not curious or not brave is rich or not tall and vice versa.
If mary is both not creative and not humble then someone is rich.
Everyone who is both kind and quiet is tall or rich and vice versa.
If someone is both rich and calm then someone is either humble or brave and vice versa.
Everyone who is either not tall or not quiet is either not generous or not humble and vice versa.
Everyone who is both old and not strong is both not happy and not wise and vice versa.
If someone is either not brave or creative then lucy is not strong or not tall.
Everyone who is humble is patient.
Everyone who is both not wise and generous is both not generous and quiet and vice versa.
If paul is generous then someone is not strong.
If alice is not happy or not humble then someone is not happy or funny and vice versa.
If mary is strong then susan is both calm and not generous and vice versa.
Everyone who is both funny and not wise is not creative or generous and vice versa.
Someone is not brave or happy.
Alice is funny.
Someone is both not funny and patient.
Paul is both not generous and funny.
Someone is either not patient or not old. | Mary is kind. | entailment | (((~happy(mary)&rich(mary)))<=>(?[X]:((~quiet(X)<~>kind(X)))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)|patient(X))))&
(![X]:((patient(X)<~>~humble(X))=>(~patient(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(rich(X)|~tall(X))))&
(((~creative(mary)&~humble(mary)))=>(?[X]:(rich(X))))&
(![X]:((kind(X)&quiet(X))<=>(tall(X)|rich(X))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((old(X)&~strong(X))<=>(~happy(X)&~wise(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>((~strong(lucy)|~tall(lucy))))&
(![X]:(humble(X)=>patient(X)))&
(![X]:((~wise(X)&generous(X))<=>(~generous(X)&quiet(X))))&
((generous(paul))=>(?[X]:(~strong(X))))&
(((~happy(alice)|~humble(alice)))<=>(?[X]:((~happy(X)|funny(X)))))&
((strong(mary))<=>((calm(susan)&~generous(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~creative(X)|generous(X))))&
(?[X]:((~brave(X)|happy(X))))&
(funny(alice))&
(?[X]:((~funny(X)&patient(X))))&
((~generous(paul)&funny(paul)))&
(?[X]:((~patient(X)<~>~old(X)))) | kind(mary) | [
"p0",
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4496915129681725457144187
% SZS output start Proof for 4496915129681725457144187
1. (rich(mary) & ~happy(mary)) <=> ? [X0] : (~quiet(X0) <~> kind(X0)) [input p0]
6. ! [X0] : ((quiet(X0) & kind(X0)) <=> (rich(X0) | tall(X0))) [input p5]
12. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (quiet(X0) & ~generous(X0))) [input p11]
16. ! [X0] : ((~wise(X0) & funny(X0)) <=> (generous(X0) | ~creative(X0))) [input p15]
22. ~kind(mary) [input hypothesis]
34. ((rich(mary) & ~happy(mary)) | ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0)))) & (? [X0] : ((~kind(X0) | quiet(X0)) & (kind(X0) | ~quiet(X0))) | (~rich(mary) | happy(mary))) [nnf transformation 1]
35. ((rich(mary) & ~happy(mary)) | ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0)))) & (? [X0] : ((~kind(X0) | quiet(X0)) & (kind(X0) | ~quiet(X0))) | ~rich(mary) | happy(mary)) [flattening 34]
36. ((rich(mary) & ~happy(mary)) | ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0)))) & (? [X1] : ((~kind(X1) | quiet(X1)) & (kind(X1) | ~quiet(X1))) | ~rich(mary) | happy(mary)) [rectify 35]
37. ? [X1] : ((~kind(X1) | quiet(X1)) & (kind(X1) | ~quiet(X1))) => ((~kind(sK0) | quiet(sK0)) & (kind(sK0) | ~quiet(sK0))) [choice axiom]
38. ((rich(mary) & ~happy(mary)) | ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0)))) & (((~kind(sK0) | quiet(sK0)) & (kind(sK0) | ~quiet(sK0))) | ~rich(mary) | happy(mary)) [skolemisation 36,37]
44. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 6]
45. ! [X0] : (((quiet(X0) & kind(X0)) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | ~quiet(X0) | ~kind(X0))) [flattening 44]
55. ! [X0] : (((generous(X0) & ~wise(X0)) | (~quiet(X0) | generous(X0))) & ((quiet(X0) & ~generous(X0)) | (~generous(X0) | wise(X0)))) [nnf transformation 12]
56. ! [X0] : (((generous(X0) & ~wise(X0)) | ~quiet(X0) | generous(X0)) & ((quiet(X0) & ~generous(X0)) | ~generous(X0) | wise(X0))) [flattening 55]
66. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 16]
67. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | wise(X0) | ~funny(X0))) [flattening 66]
79. rich(mary) | kind(X0) | quiet(X0) [cnf transformation 38]
94. ~rich(X0) | kind(X0) [cnf transformation 45]
118. ~generous(X0) | ~generous(X0) | wise(X0) [cnf transformation 56]
121. generous(X0) | ~quiet(X0) | generous(X0) [cnf transformation 56]
134. ~wise(X0) | ~generous(X0) [cnf transformation 67]
143. ~kind(mary) [cnf transformation 22]
144. ~generous(X0) | wise(X0) [duplicate literal removal 118]
145. ~quiet(X0) | generous(X0) [duplicate literal removal 121]
151. 2 <=> rich(mary) [avatar definition]
153. rich(mary) <- (2) [avatar component clause 151]
156. 3 <=> ! [X0] : (kind(X0) | quiet(X0)) [avatar definition]
157. kind(X0) | quiet(X0) <- (3) [avatar component clause 156]
158. 3 | 2 [avatar split clause 79,151,156]
289. ~generous(X0) [subsumption resolution 134,144]
310. kind(mary) <- (2) [resolution 94,153]
311. $false <- (2) [subsumption resolution 310,143]
312. ~2 [avatar contradiction clause 311]
314. quiet(mary) <- (3) [resolution 157,143]
324. generous(mary) <- (3) [resolution 314,145]
325. $false <- (3) [subsumption resolution 324,289]
326. ~3 [avatar contradiction clause 325]
327. $false [avatar sat refutation 158,312,326]
% SZS output end Proof for 4496915129681725457144187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and strong then alice is not old or wise and vice versa.
If someone is both kind and calm then lucy is not rich or not wise and vice versa.
If someone is both rich and not curious then someone is not funny or not generous and vice versa.
If alice is both not creative and not kind then someone is happy and vice versa.
If someone is not wise or not curious then someone is both not creative and kind.
If someone is not curious or rich then paul is humble and vice versa.
If john is creative or curious then susan is either not calm or not strong.
Everyone who is strong or tall is not old.
If someone is generous then someone is both not calm and not creative.
Everyone who is generous is not happy.
Everyone who is humble or patient is old.
Everyone who is creative is both brave and not old.
Everyone who is either happy or rich is either quiet or brave.
Everyone who is not happy or funny is either not happy or not generous and vice versa.
Everyone who is both not kind and not old is both humble and not creative and vice versa.
If someone is both not wise and not kind then someone is kind.
John is either not tall or not kind.
Susan is both generous and strong.
Fred is either not brave or tall.
Susan is not funny or not happy.
Someone is both kind and not old.
Someone is not happy or not creative.
Someone is both not brave and generous.
Mary is tall. | Paul is happy. | contradiction | ((?[X]:((creative(X)&strong(X))))<=>((~old(alice)|wise(alice))))&
((?[X]:((kind(X)&calm(X))))<=>((~rich(lucy)|~wise(lucy))))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~creative(alice)&~kind(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((~curious(X)|rich(X))))<=>(humble(paul)))&
(((creative(john)|curious(john)))=>((~calm(susan)<~>~strong(susan))))&
(![X]:((strong(X)|tall(X))=>~old(X)))&
((?[X]:(generous(X)))=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:(generous(X)=>~happy(X)))&
(![X]:((humble(X)|patient(X))=>old(X)))&
(![X]:(creative(X)=>(brave(X)&~old(X))))&
(![X]:((happy(X)<~>rich(X))=>(quiet(X)<~>brave(X))))&
(![X]:((~happy(X)|funny(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((~kind(X)&~old(X))<=>(humble(X)&~creative(X))))&
((?[X]:((~wise(X)&~kind(X))))=>(?[X]:(kind(X))))&
((~tall(john)<~>~kind(john)))&
((generous(susan)&strong(susan)))&
((~brave(fred)<~>tall(fred)))&
((~funny(susan)|~happy(susan)))&
(?[X]:((kind(X)&~old(X))))&
(?[X]:((~happy(X)|~creative(X))))&
(?[X]:((~brave(X)&generous(X))))&
(tall(mary)) | happy(paul) | [
"p2",
"p5",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6017610380066206941729199
% SZS output start Proof for 6017610380066206941729199
3. ? [X0] : (~curious(X0) & rich(X0)) <=> ? [X0] : (~generous(X0) | ~funny(X0)) [input p2]
6. ? [X0] : (rich(X0) | ~curious(X0)) <=> humble(paul) [input p5]
10. ! [X0] : (generous(X0) => ~happy(X0)) [input p9]
11. ! [X0] : ((patient(X0) | humble(X0)) => old(X0)) [input p10]
12. ! [X0] : (creative(X0) => (~old(X0) & brave(X0))) [input p11]
15. ! [X0] : ((~old(X0) & ~kind(X0)) <=> (~creative(X0) & humble(X0))) [input p14]
25. happy(paul) [input hypothesis]
26. ? [X0] : (~curious(X0) & rich(X0)) <=> ? [X1] : (~generous(X1) | ~funny(X1)) [rectify 3]
30. ! [X0] : (humble(X0) => old(X0)) [pure predicate removal 11]
35. ! [X0] : (~happy(X0) | ~generous(X0)) [ennf transformation 10]
36. ! [X0] : (old(X0) | ~humble(X0)) [ennf transformation 30]
37. ! [X0] : ((~old(X0) & brave(X0)) | ~creative(X0)) [ennf transformation 12]
50. (? [X0] : (~curious(X0) & rich(X0)) | ! [X1] : (generous(X1) & funny(X1))) & (? [X1] : (~generous(X1) | ~funny(X1)) | ! [X0] : (curious(X0) | ~rich(X0))) [nnf transformation 26]
51. (? [X0] : (~curious(X0) & rich(X0)) | ! [X1] : (generous(X1) & funny(X1))) & (? [X2] : (~generous(X2) | ~funny(X2)) | ! [X3] : (curious(X3) | ~rich(X3))) [rectify 50]
52. ? [X0] : (~curious(X0) & rich(X0)) => (~curious(sK2) & rich(sK2)) [choice axiom]
53. ? [X2] : (~generous(X2) | ~funny(X2)) => (~generous(sK3) | ~funny(sK3)) [choice axiom]
54. ((~curious(sK2) & rich(sK2)) | ! [X1] : (generous(X1) & funny(X1))) & ((~generous(sK3) | ~funny(sK3)) | ! [X3] : (curious(X3) | ~rich(X3))) [skolemisation 51,53,52]
63. (? [X0] : (rich(X0) | ~curious(X0)) | ~humble(paul)) & (humble(paul) | ! [X0] : (~rich(X0) & curious(X0))) [nnf transformation 6]
64. (? [X0] : (rich(X0) | ~curious(X0)) | ~humble(paul)) & (humble(paul) | ! [X1] : (~rich(X1) & curious(X1))) [rectify 63]
65. ? [X0] : (rich(X0) | ~curious(X0)) => (rich(sK6) | ~curious(sK6)) [choice axiom]
66. ((rich(sK6) | ~curious(sK6)) | ~humble(paul)) & (humble(paul) | ! [X1] : (~rich(X1) & curious(X1))) [skolemisation 64,65]
74. ! [X0] : (((~old(X0) & ~kind(X0)) | (creative(X0) | ~humble(X0))) & ((~creative(X0) & humble(X0)) | (old(X0) | kind(X0)))) [nnf transformation 15]
75. ! [X0] : (((~old(X0) & ~kind(X0)) | creative(X0) | ~humble(X0)) & ((~creative(X0) & humble(X0)) | old(X0) | kind(X0))) [flattening 74]
101. ~curious(sK2) | generous(X1) [cnf transformation 54]
109. humble(paul) | curious(X1) [cnf transformation 66]
120. ~happy(X0) | ~generous(X0) [cnf transformation 35]
121. ~humble(X0) | old(X0) [cnf transformation 36]
123. ~old(X0) | ~creative(X0) [cnf transformation 37]
137. ~old(X0) | creative(X0) | ~humble(X0) [cnf transformation 75]
152. happy(paul) [cnf transformation 25]
204. 11 <=> ! [X1] : generous(X1) [avatar definition]
205. generous(X1) <- (11) [avatar component clause 204]
207. 12 <=> curious(sK2) [avatar definition]
209. ~curious(sK2) <- (~12) [avatar component clause 207]
210. 11 | ~12 [avatar split clause 101,207,204]
252. 22 <=> ! [X1] : curious(X1) [avatar definition]
253. curious(X1) <- (22) [avatar component clause 252]
270. 26 <=> humble(paul) [avatar definition]
271. humble(paul) <- (26) [avatar component clause 270]
286. 22 | 26 [avatar split clause 109,270,252]
321. ~humble(X0) | creative(X0) [subsumption resolution 137,121]
369. ~generous(paul) [resolution 120,152]
371. old(paul) <- (26) [resolution 121,271]
376. ~creative(paul) <- (26) [resolution 371,123]
381. creative(paul) <- (26) [resolution 321,271]
382. $false <- (26) [subsumption resolution 381,376]
383. ~26 [avatar contradiction clause 382]
384. $false <- (~12, 22) [resolution 253,209]
387. 12 | ~22 [avatar contradiction clause 384]
391. $false <- (11) [resolution 205,369]
392. ~11 [avatar contradiction clause 391]
394. $false [avatar sat refutation 210,286,383,387,392]
% SZS output end Proof for 6017610380066206941729199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or patient is generous and vice versa.
Everyone who is wise or not old is both not happy and wise and vice versa.
If fred is not calm or not old then susan is either rich or quiet.
If susan is generous or not generous then someone is either strong or not creative.
Everyone who is not brave or brave is both not strong and not humble.
If someone is either not brave or generous then someone is either generous or not wise.
Everyone who is not tall or happy is either generous or tall and vice versa.
Everyone who is both not brave and not curious is happy.
Everyone who is either not brave or curious is not tall and vice versa.
Everyone who is either not curious or not old is not old and vice versa.
If alice is brave then someone is both not kind and old and vice versa.
Everyone who is calm or not happy is not kind.
If paul is not strong then someone is not old or not kind.
If lucy is generous then alice is either not rich or humble and vice versa.
Everyone who is either not generous or not quiet is creative or not tall.
Everyone who is both quiet and brave is funny or not rich and vice versa.
Someone is not kind or humble.
Paul is either happy or wise.
Someone is not humble.
Someone is kind.
Paul is either tall or generous.
Someone is both tall and old. | Susan is not wise. | neutral | (![X]:((~calm(X)|patient(X))<=>generous(X)))&
(![X]:((wise(X)|~old(X))<=>(~happy(X)&wise(X))))&
(((~calm(fred)|~old(fred)))=>((rich(susan)<~>quiet(susan))))&
(((generous(susan)|~generous(susan)))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((~brave(X)|brave(X))=>(~strong(X)&~humble(X))))&
((?[X]:((~brave(X)<~>generous(X))))=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:((~tall(X)|happy(X))<=>(generous(X)<~>tall(X))))&
(![X]:((~brave(X)&~curious(X))=>happy(X)))&
(![X]:((~brave(X)<~>curious(X))<=>~tall(X)))&
(![X]:((~curious(X)<~>~old(X))<=>~old(X)))&
((brave(alice))<=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((calm(X)|~happy(X))=>~kind(X)))&
((~strong(paul))=>(?[X]:((~old(X)|~kind(X)))))&
((generous(lucy))<=>((~rich(alice)<~>humble(alice))))&
(![X]:((~generous(X)<~>~quiet(X))=>(creative(X)|~tall(X))))&
(![X]:((quiet(X)&brave(X))<=>(funny(X)|~rich(X))))&
(?[X]:((~kind(X)|humble(X))))&
((happy(paul)<~>wise(paul)))&
(?[X]:(~humble(X)))&
(?[X]:(kind(X)))&
((tall(paul)<~>generous(paul)))&
(?[X]:((tall(X)&old(X)))) | ~wise(susan) | [] | null | 0 |
Everyone who is not curious or kind is both not tall and not quiet and vice versa. If someone is curious then someone is both kind and curious. If paul is not funny or not creative then someone is either not strong or not calm and vice versa. If someone is both not strong and creative then someone is not brave or not creative and vice versa. Everyone who is both kind and not humble is either not funny or generous and vice versa. If susan is both rich and not wise then paul is either brave or rich and vice versa. Everyone who is both not happy and strong is both wise and not happy and vice versa. If mary is either not old or not curious then susan is not rich or quiet and vice versa. Everyone who is not funny is either not patient or funny and vice versa. Everyone who is both not humble and not generous is brave or not calm and vice versa. If mary is not brave then someone is both not curious and brave and vice versa. If alice is not quiet or tall then john is strong and vice versa. Everyone who is rich or strong is not wise or curious. Everyone who is not rich is both not rich and not creative. If lucy is both curious and not quiet then someone is not kind or creative. Susan is both not tall and quiet. Someone is both not calm and not patient. Someone is wise or not humble. Someone is funny. Someone is both funny and old. | Susan is not quiet. | contradiction | (![X]:((~curious(X)|kind(X))<=>(~tall(X)&~quiet(X))))&
((?[X]:(curious(X)))=>(?[X]:((kind(X)&curious(X)))))&
(((~funny(paul)|~creative(paul)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
((?[X]:((~strong(X)&creative(X))))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((kind(X)&~humble(X))<=>(~funny(X)<~>generous(X))))&
(((rich(susan)&~wise(susan)))<=>((brave(paul)<~>rich(paul))))&
(![X]:((~happy(X)&strong(X))<=>(wise(X)&~happy(X))))&
(((~old(mary)<~>~curious(mary)))<=>((~rich(susan)|quiet(susan))))&
(![X]:(~funny(X)<=>(~patient(X)<~>funny(X))))&
(![X]:((~humble(X)&~generous(X))<=>(brave(X)|~calm(X))))&
((~brave(mary))<=>(?[X]:((~curious(X)&brave(X)))))&
(((~quiet(alice)|tall(alice)))<=>(strong(john)))&
(![X]:((rich(X)|strong(X))=>(~wise(X)|curious(X))))&
(![X]:(~rich(X)=>(~rich(X)&~creative(X))))&
(((curious(lucy)&~quiet(lucy)))=>(?[X]:((~kind(X)|creative(X)))))&
((~tall(susan)&quiet(susan)))&
(?[X]:((~calm(X)&~patient(X))))&
(?[X]:((wise(X)|~humble(X))))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)&old(X)))) | ~quiet(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6428578291001150902213776
% SZS output start Proof for 6428578291001150902213776
16. quiet(susan) & ~tall(susan) [input p15]
21. ~quiet(susan) [input hypothesis]
133. quiet(susan) [cnf transformation 16]
140. ~quiet(susan) [cnf transformation 21]
237. 21 <=> quiet(susan) [avatar definition]
305. 21 [avatar split clause 133,237]
315. ~21 [avatar split clause 140,237]
316. $false [avatar sat refutation 305,315]
% SZS output end Proof for 6428578291001150902213776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or curious is tall or not generous.
If someone is both old and not calm then fred is calm.
Everyone who is not quiet is patient and vice versa.
If john is kind then someone is brave or curious and vice versa.
Everyone who is not generous or creative is rich or funny and vice versa.
Everyone who is rich is both calm and not kind.
Everyone who is rich is not funny or not creative and vice versa.
If someone is not happy or kind then john is not curious and vice versa.
If someone is either funny or not kind then someone is not old or humble and vice versa.
Everyone who is not tall is not funny.
Everyone who is either not curious or not rich is old.
If someone is both rich and not creative then someone is both rich and not wise.
Everyone who is both not strong and brave is both not happy and calm.
Everyone who is both creative and humble is both not rich and rich.
If someone is either quiet or wise then someone is either old or wise.
If someone is funny or generous then someone is not brave or calm.
John is humble or creative.
John is not wise or not curious.
Someone is either generous or curious.
Someone is both not rich and not happy.
John is both not happy and not tall.
Someone is either not strong or not quiet.
Someone is both patient and not humble.
Paul is rich or not kind. | Fred is not brave. | entailment | (![X]:((calm(X)|curious(X))=>(tall(X)|~generous(X))))&
((?[X]:((old(X)&~calm(X))))=>(calm(fred)))&
(![X]:(~quiet(X)<=>patient(X)))&
((kind(john))<=>(?[X]:((brave(X)|curious(X)))))&
(![X]:((~generous(X)|creative(X))<=>(rich(X)|funny(X))))&
(![X]:(rich(X)=>(calm(X)&~kind(X))))&
(![X]:(rich(X)<=>(~funny(X)|~creative(X))))&
((?[X]:((~happy(X)|kind(X))))<=>(~curious(john)))&
((?[X]:((funny(X)<~>~kind(X))))<=>(?[X]:((~old(X)|humble(X)))))&
(![X]:(~tall(X)=>~funny(X)))&
(![X]:((~curious(X)<~>~rich(X))=>old(X)))&
((?[X]:((rich(X)&~creative(X))))=>(?[X]:((rich(X)&~wise(X)))))&
(![X]:((~strong(X)&brave(X))=>(~happy(X)&calm(X))))&
(![X]:((creative(X)&humble(X))=>(~rich(X)&rich(X))))&
((?[X]:((quiet(X)<~>wise(X))))=>(?[X]:((old(X)<~>wise(X)))))&
((?[X]:((funny(X)|generous(X))))=>(?[X]:((~brave(X)|calm(X)))))&
((humble(john)|creative(john)))&
((~wise(john)|~curious(john)))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((~rich(X)&~happy(X))))&
((~happy(john)&~tall(john)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
(?[X]:((patient(X)&~humble(X))))&
((rich(paul)|~kind(paul))) | ~brave(fred) | [
"p3",
"p5",
"p6",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7661575420776824272954410
% SZS output start Proof for 7661575420776824272954410
4. kind(john) <=> ? [X0] : (curious(X0) | brave(X0)) [input p3]
6. ! [X0] : (rich(X0) => (~kind(X0) & calm(X0))) [input p5]
7. ! [X0] : (rich(X0) <=> (~creative(X0) | ~funny(X0))) [input p6]
10. ! [X0] : (~tall(X0) => ~funny(X0)) [input p9]
21. ~tall(john) & ~happy(john) [input p20]
25. brave(fred) [input hypothesis]
33. ! [X0] : ((~kind(X0) & calm(X0)) | ~rich(X0)) [ennf transformation 6]
34. ! [X0] : (~funny(X0) | tall(X0)) [ennf transformation 10]
44. (kind(john) | ! [X0] : (~curious(X0) & ~brave(X0))) & (? [X0] : (curious(X0) | brave(X0)) | ~kind(john)) [nnf transformation 4]
45. (kind(john) | ! [X0] : (~curious(X0) & ~brave(X0))) & (? [X1] : (curious(X1) | brave(X1)) | ~kind(john)) [rectify 44]
46. ? [X1] : (curious(X1) | brave(X1)) => (curious(sK0) | brave(sK0)) [choice axiom]
47. (kind(john) | ! [X0] : (~curious(X0) & ~brave(X0))) & ((curious(sK0) | brave(sK0)) | ~kind(john)) [skolemisation 45,46]
50. ! [X0] : ((rich(X0) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | ~rich(X0))) [nnf transformation 7]
51. ! [X0] : ((rich(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~rich(X0))) [flattening 50]
88. kind(john) | ~brave(X0) [cnf transformation 47]
95. ~rich(X0) | ~kind(X0) [cnf transformation 33]
97. funny(X0) | rich(X0) [cnf transformation 51]
108. ~funny(X0) | tall(X0) [cnf transformation 34]
130. ~tall(john) [cnf transformation 21]
136. brave(fred) [cnf transformation 25]
149. 4 <=> kind(john) [avatar definition]
151. kind(john) <- (4) [avatar component clause 149]
154. 5 <=> ! [X0] : ~brave(X0) [avatar definition]
155. ~brave(X0) <- (5) [avatar component clause 154]
156. 5 | 4 [avatar split clause 88,149,154]
307. $false <- (5) [resolution 155,136]
308. ~5 [avatar contradiction clause 307]
317. rich(X0) | tall(X0) [resolution 108,97]
363. ~kind(X2) | tall(X2) [resolution 317,95]
383. tall(john) <- (4) [resolution 363,151]
384. $false <- (4) [subsumption resolution 383,130]
385. ~4 [avatar contradiction clause 384]
386. $false [avatar sat refutation 156,308,385]
% SZS output end Proof for 7661575420776824272954410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not brave is strong or rich.
If someone is old or not humble then alice is both kind and not kind.
If alice is both calm and old then someone is both happy and old.
Everyone who is humble is not generous.
Everyone who is not strong or quiet is old.
If john is wise or curious then fred is not creative or curious.
If fred is either calm or not wise then someone is both brave and not wise and vice versa.
If someone is either patient or not humble then alice is humble and vice versa.
If mary is not funny then someone is both not quiet and calm and vice versa.
Everyone who is not old is not wise or rich.
Everyone who is either curious or wise is happy or not kind.
If someone is not wise or not tall then someone is both rich and not wise.
If someone is brave or humble then mary is not creative.
If someone is humble then lucy is either brave or generous and vice versa.
If someone is both not patient and old then alice is both tall and generous.
If alice is patient then fred is old or creative.
Someone is not quiet.
Someone is both not tall and not patient.
Mary is either not brave or not old.
Someone is both happy and not creative.
Someone is not happy.
Lucy is either tall or not funny. | Mary is not creative. | entailment | (![X]:((happy(X)|~brave(X))=>(strong(X)|rich(X))))&
((?[X]:((old(X)|~humble(X))))=>((kind(alice)&~kind(alice))))&
(((calm(alice)&old(alice)))=>(?[X]:((happy(X)&old(X)))))&
(![X]:(humble(X)=>~generous(X)))&
(![X]:((~strong(X)|quiet(X))=>old(X)))&
(((wise(john)|curious(john)))=>((~creative(fred)|curious(fred))))&
(((calm(fred)<~>~wise(fred)))<=>(?[X]:((brave(X)&~wise(X)))))&
((?[X]:((patient(X)<~>~humble(X))))<=>(humble(alice)))&
((~funny(mary))<=>(?[X]:((~quiet(X)&calm(X)))))&
(![X]:(~old(X)=>(~wise(X)|rich(X))))&
(![X]:((curious(X)<~>wise(X))=>(happy(X)|~kind(X))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((rich(X)&~wise(X)))))&
((?[X]:((brave(X)|humble(X))))=>(~creative(mary)))&
((?[X]:(humble(X)))<=>((brave(lucy)<~>generous(lucy))))&
((?[X]:((~patient(X)&old(X))))=>((tall(alice)&generous(alice))))&
((patient(alice))=>((old(fred)|creative(fred))))&
(?[X]:(~quiet(X)))&
(?[X]:((~tall(X)&~patient(X))))&
((~brave(mary)<~>~old(mary)))&
(?[X]:((happy(X)&~creative(X))))&
(?[X]:(~happy(X)))&
((tall(lucy)<~>~funny(lucy))) | ~creative(mary) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6046856107246957477583921
% SZS output start Proof for 6046856107246957477583921
2. ? [X0] : (~humble(X0) | old(X0)) => (~kind(alice) & kind(alice)) [input p1]
13. ? [X0] : (humble(X0) | brave(X0)) => ~creative(mary) [input p12]
23. creative(mary) [input hypothesis]
29. (~kind(alice) & kind(alice)) | ! [X0] : (humble(X0) & ~old(X0)) [ennf transformation 2]
39. ~creative(mary) | ! [X0] : (~humble(X0) & ~brave(X0)) [ennf transformation 13]
76. kind(alice) | humble(X0) [cnf transformation 29]
78. ~kind(alice) | humble(X0) [cnf transformation 29]
103. ~creative(mary) | ~humble(X0) [cnf transformation 39]
121. creative(mary) [cnf transformation 23]
123. 1 <=> ! [X0] : humble(X0) [avatar definition]
124. humble(X0) <- (1) [avatar component clause 123]
126. 2 <=> kind(alice) [avatar definition]
129. 1 | ~2 [avatar split clause 78,126,123]
134. 1 | 2 [avatar split clause 76,126,123]
250. 29 <=> ! [X0] : ~humble(X0) [avatar definition]
251. ~humble(X0) <- (29) [avatar component clause 250]
253. 30 <=> creative(mary) [avatar definition]
256. 29 | ~30 [avatar split clause 103,253,250]
319. 30 [avatar split clause 121,253]
322. $false <- (1, 29) [subsumption resolution 124,251]
323. ~1 | ~29 [avatar contradiction clause 322]
324. $false [avatar sat refutation 129,134,256,319,323]
% SZS output end Proof for 6046856107246957477583921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not humble or not rich then someone is not humble or not happy and vice versa.
If someone is not creative or not wise then lucy is brave and vice versa.
If someone is either not brave or rich then fred is humble.
If paul is both tall and not patient then someone is both rich and not patient.
If lucy is both not patient and tall then john is both not strong and not old and vice versa.
Everyone who is happy or quiet is either rich or generous.
If someone is happy or quiet then someone is not humble and vice versa.
Everyone who is not tall or happy is either humble or curious and vice versa.
Everyone who is not humble is not strong or not kind.
Everyone who is both happy and not wise is both not creative and humble and vice versa.
Everyone who is either patient or not wise is not creative or wise.
Everyone who is not kind is either not wise or funny.
If fred is old or kind then fred is not brave or not wise and vice versa.
If someone is both not tall and not happy then lucy is either quiet or not tall.
If paul is not old or generous then paul is both rich and curious and vice versa.
If paul is both rich and strong then fred is both creative and not brave.
Someone is either quiet or not strong.
Alice is both patient and curious.
Someone is not humble or kind.
Someone is not patient.
Someone is both not brave and tall.
Someone is curious.
Alice is not strong.
Someone is either not funny or generous. | Fred is old. | neutral | (((~humble(paul)|~rich(paul)))<=>(?[X]:((~humble(X)|~happy(X)))))&
((?[X]:((~creative(X)|~wise(X))))<=>(brave(lucy)))&
((?[X]:((~brave(X)<~>rich(X))))=>(humble(fred)))&
(((tall(paul)&~patient(paul)))=>(?[X]:((rich(X)&~patient(X)))))&
(((~patient(lucy)&tall(lucy)))<=>((~strong(john)&~old(john))))&
(![X]:((happy(X)|quiet(X))=>(rich(X)<~>generous(X))))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)|happy(X))<=>(humble(X)<~>curious(X))))&
(![X]:(~humble(X)=>(~strong(X)|~kind(X))))&
(![X]:((happy(X)&~wise(X))<=>(~creative(X)&humble(X))))&
(![X]:((patient(X)<~>~wise(X))=>(~creative(X)|wise(X))))&
(![X]:(~kind(X)=>(~wise(X)<~>funny(X))))&
(((old(fred)|kind(fred)))<=>((~brave(fred)|~wise(fred))))&
((?[X]:((~tall(X)&~happy(X))))=>((quiet(lucy)<~>~tall(lucy))))&
(((~old(paul)|generous(paul)))<=>((rich(paul)&curious(paul))))&
(((rich(paul)&strong(paul)))=>((creative(fred)&~brave(fred))))&
(?[X]:((quiet(X)<~>~strong(X))))&
((patient(alice)&curious(alice)))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)&tall(X))))&
(?[X]:(curious(X)))&
(~strong(alice))&
(?[X]:((~funny(X)<~>generous(X)))) | old(fred) | [] | null | 0 |
Everyone who is brave or not old is both not funny and wise.
If someone is brave then susan is quiet.
Everyone who is either curious or strong is not quiet and vice versa.
If someone is either old or not strong then alice is either humble or calm and vice versa.
If lucy is tall or not tall then someone is not strong or happy.
Everyone who is either wise or patient is either humble or calm and vice versa.
Everyone who is generous is either not strong or not tall.
Everyone who is either kind or not old is not patient or wise and vice versa.
If john is either not curious or not tall then someone is both funny and not strong.
Everyone who is funny or calm is not brave and vice versa.
If someone is either happy or not happy then susan is brave and vice versa.
Everyone who is both patient and happy is both rich and curious and vice versa.
Everyone who is not happy is not happy or humble.
Everyone who is old or tall is either not kind or not patient and vice versa.
Everyone who is both not brave and quiet is both not quiet and curious and vice versa.
Everyone who is not old is both kind and not wise.
Alice is both kind and tall.
Someone is both not calm and rich.
Someone is generous.
Someone is both not calm and patient.
John is tall or not happy.
Mary is generous.
Lucy is either humble or rich. | John is not kind. | neutral | (![X]:((brave(X)|~old(X))=>(~funny(X)&wise(X))))&
((?[X]:(brave(X)))=>(quiet(susan)))&
(![X]:((curious(X)<~>strong(X))<=>~quiet(X)))&
((?[X]:((old(X)<~>~strong(X))))<=>((humble(alice)<~>calm(alice))))&
(((tall(lucy)|~tall(lucy)))=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(humble(X)<~>calm(X))))&
(![X]:(generous(X)=>(~strong(X)<~>~tall(X))))&
(![X]:((kind(X)<~>~old(X))<=>(~patient(X)|wise(X))))&
(((~curious(john)<~>~tall(john)))=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((funny(X)|calm(X))<=>~brave(X)))&
((?[X]:((happy(X)<~>~happy(X))))<=>(brave(susan)))&
(![X]:((patient(X)&happy(X))<=>(rich(X)&curious(X))))&
(![X]:(~happy(X)=>(~happy(X)|humble(X))))&
(![X]:((old(X)|tall(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~brave(X)&quiet(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~old(X)=>(kind(X)&~wise(X))))&
((kind(alice)&tall(alice)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)&patient(X))))&
((tall(john)|~happy(john)))&
(generous(mary))&
((humble(lucy)<~>rich(lucy))) | ~kind(john) | [] | null | 0 |
Everyone who is both not rich and funny is either old or patient and vice versa.
Everyone who is humble is both wise and kind and vice versa.
If fred is either not patient or not generous then someone is not happy or kind.
Everyone who is not quiet or funny is both strong and not funny and vice versa.
Everyone who is either not quiet or funny is both not wise and not curious.
If someone is not tall then alice is not tall and vice versa.
Everyone who is wise or creative is both not creative and not patient and vice versa.
If lucy is generous or creative then alice is either not calm or strong and vice versa.
Everyone who is not wise or patient is both funny and not funny and vice versa.
If someone is either strong or patient then someone is both not old and not strong.
If alice is both creative and generous then someone is either not patient or not kind and vice versa.
If someone is either not old or not calm then alice is both not tall and quiet.
Everyone who is wise or not quiet is not brave or wise and vice versa.
Everyone who is generous is both quiet and curious.
Everyone who is not funny or strong is both calm and not rich.
Someone is generous or calm.
Someone is either funny or not rich.
Someone is patient or not humble.
Fred is brave.
Someone is either creative or not rich. | Alice is happy. | neutral | (![X]:((~rich(X)&funny(X))<=>(old(X)<~>patient(X))))&
(![X]:(humble(X)<=>(wise(X)&kind(X))))&
(((~patient(fred)<~>~generous(fred)))=>(?[X]:((~happy(X)|kind(X)))))&
(![X]:((~quiet(X)|funny(X))<=>(strong(X)&~funny(X))))&
(![X]:((~quiet(X)<~>funny(X))=>(~wise(X)&~curious(X))))&
((?[X]:(~tall(X)))<=>(~tall(alice)))&
(![X]:((wise(X)|creative(X))<=>(~creative(X)&~patient(X))))&
(((generous(lucy)|creative(lucy)))<=>((~calm(alice)<~>strong(alice))))&
(![X]:((~wise(X)|patient(X))<=>(funny(X)&~funny(X))))&
((?[X]:((strong(X)<~>patient(X))))=>(?[X]:((~old(X)&~strong(X)))))&
(((creative(alice)&generous(alice)))<=>(?[X]:((~patient(X)<~>~kind(X)))))&
((?[X]:((~old(X)<~>~calm(X))))=>((~tall(alice)&quiet(alice))))&
(![X]:((wise(X)|~quiet(X))<=>(~brave(X)|wise(X))))&
(![X]:(generous(X)=>(quiet(X)&curious(X))))&
(![X]:((~funny(X)|strong(X))=>(calm(X)&~rich(X))))&
(?[X]:((generous(X)|calm(X))))&
(?[X]:((funny(X)<~>~rich(X))))&
(?[X]:((patient(X)|~humble(X))))&
(brave(fred))&
(?[X]:((creative(X)<~>~rich(X)))) | happy(alice) | [] | null | 0 |
Everyone who is generous is not humble and vice versa. Everyone who is not brave is old. If fred is either creative or not wise then someone is not kind and vice versa. Everyone who is both brave and wise is both rich and tall. If someone is both not kind and tall then fred is old or curious. If lucy is not tall then someone is either not humble or kind and vice versa. Everyone who is either not strong or not tall is not quiet and vice versa. If alice is strong or not patient then someone is not happy. Everyone who is not tall or not old is not strong or not brave and vice versa. Everyone who is both rich and not happy is both not funny and not old and vice versa. If mary is either not quiet or generous then paul is both humble and not curious. If someone is humble or not curious then someone is both not generous and not brave and vice versa. Everyone who is not old or strong is both quiet and old. If fred is either not curious or happy then fred is not brave and vice versa. Everyone who is old is both creative and not funny and vice versa. Mary is either calm or patient. Someone is either not funny or wise. Someone is brave. Susan is not curious. John is generous. | Alice is quiet. | entailment | (![X]:(generous(X)<=>~humble(X)))&
(![X]:(~brave(X)=>old(X)))&
(((creative(fred)<~>~wise(fred)))<=>(?[X]:(~kind(X))))&
(![X]:((brave(X)&wise(X))=>(rich(X)&tall(X))))&
((?[X]:((~kind(X)&tall(X))))=>((old(fred)|curious(fred))))&
((~tall(lucy))<=>(?[X]:((~humble(X)<~>kind(X)))))&
(![X]:((~strong(X)<~>~tall(X))<=>~quiet(X)))&
(((strong(alice)|~patient(alice)))=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|~old(X))<=>(~strong(X)|~brave(X))))&
(![X]:((rich(X)&~happy(X))<=>(~funny(X)&~old(X))))&
(((~quiet(mary)<~>generous(mary)))=>((humble(paul)&~curious(paul))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:((~generous(X)&~brave(X)))))&
(![X]:((~old(X)|strong(X))=>(quiet(X)&old(X))))&
(((~curious(fred)<~>happy(fred)))<=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
((calm(mary)<~>patient(mary)))&
(?[X]:((~funny(X)<~>wise(X))))&
(?[X]:(brave(X)))&
(~curious(susan))&
(generous(john)) | quiet(alice) | [
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3827245268892515921251680
% SZS output start Proof for 3827245268892515921251680
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> ~quiet(X0)) [input p6]
9. ! [X0] : ((~old(X0) | ~tall(X0)) <=> (~brave(X0) | ~strong(X0))) [input p8]
13. ! [X0] : ((strong(X0) | ~old(X0)) => (old(X0) & quiet(X0))) [input p12]
21. ~quiet(alice) [input hypothesis]
30. ! [X0] : ((old(X0) & quiet(X0)) | (~strong(X0) & old(X0))) [ennf transformation 13]
40. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | quiet(X0)) & (~quiet(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 7]
43. ! [X0] : (((~old(X0) | ~tall(X0)) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | (old(X0) & tall(X0)))) [nnf transformation 9]
44. ! [X0] : ((~old(X0) | ~tall(X0) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | (old(X0) & tall(X0)))) [flattening 43]
79. quiet(X0) | strong(X0) | tall(X0) [cnf transformation 40]
84. ~tall(X0) | ~old(X0) | strong(X0) [cnf transformation 44]
100. ~strong(X0) | quiet(X0) [cnf transformation 30]
101. old(X0) | old(X0) [cnf transformation 30]
117. ~quiet(alice) [cnf transformation 21]
118. old(X0) [duplicate literal removal 101]
182. 15 <=> strong(alice) [avatar definition]
183. strong(alice) <- (15) [avatar component clause 182]
184. ~strong(alice) <- (~15) [avatar component clause 182]
269. strong(alice) | tall(alice) [resolution 79,117]
276. 31 <=> tall(alice) [avatar definition]
278. tall(alice) <- (31) [avatar component clause 276]
279. 31 | 15 [avatar split clause 269,182,276]
291. quiet(alice) <- (15) [resolution 183,100]
294. $false <- (15) [subsumption resolution 291,117]
295. ~15 [avatar contradiction clause 294]
302. ~old(alice) | strong(alice) <- (31) [resolution 84,278]
303. strong(alice) <- (31) [subsumption resolution 302,118]
304. $false <- (~15, 31) [subsumption resolution 303,184]
305. 15 | ~31 [avatar contradiction clause 304]
306. $false [avatar sat refutation 279,295,305]
% SZS output end Proof for 3827245268892515921251680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not patient or funny then someone is either not tall or not funny and vice versa.
If someone is tall then someone is quiet.
If lucy is either not creative or not wise then someone is either rich or not humble.
If lucy is humble then fred is curious.
If someone is either patient or strong then someone is both not strong and calm.
If someone is either strong or calm then someone is not wise.
Everyone who is either patient or not quiet is either not calm or not quiet.
Everyone who is generous is not happy or not generous.
Everyone who is not creative is not tall and vice versa.
Everyone who is not old is either not happy or not brave and vice versa.
If susan is quiet or not funny then paul is either not strong or not funny and vice versa.
If someone is strong or old then alice is not calm or patient and vice versa.
If susan is kind then someone is either not happy or tall.
If john is strong or not humble then someone is either not rich or not happy and vice versa.
If john is both calm and not humble then someone is both humble and generous.
Everyone who is not kind is curious and vice versa.
Paul is either patient or not creative.
Mary is not wise or not generous.
Paul is funny.
Someone is not tall.
Lucy is both old and quiet.
Someone is not funny or not calm.
Mary is both creative and generous. | Mary is not happy. | entailment | (((~patient(john)|funny(john)))<=>(?[X]:((~tall(X)<~>~funny(X)))))&
((?[X]:(tall(X)))=>(?[X]:(quiet(X))))&
(((~creative(lucy)<~>~wise(lucy)))=>(?[X]:((rich(X)<~>~humble(X)))))&
((humble(lucy))=>(curious(fred)))&
((?[X]:((patient(X)<~>strong(X))))=>(?[X]:((~strong(X)&calm(X)))))&
((?[X]:((strong(X)<~>calm(X))))=>(?[X]:(~wise(X))))&
(![X]:((patient(X)<~>~quiet(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:(generous(X)=>(~happy(X)|~generous(X))))&
(![X]:(~creative(X)<=>~tall(X)))&
(![X]:(~old(X)<=>(~happy(X)<~>~brave(X))))&
(((quiet(susan)|~funny(susan)))<=>((~strong(paul)<~>~funny(paul))))&
((?[X]:((strong(X)|old(X))))<=>((~calm(alice)|patient(alice))))&
((kind(susan))=>(?[X]:((~happy(X)<~>tall(X)))))&
(((strong(john)|~humble(john)))<=>(?[X]:((~rich(X)<~>~happy(X)))))&
(((calm(john)&~humble(john)))=>(?[X]:((humble(X)&generous(X)))))&
(![X]:(~kind(X)<=>curious(X)))&
((patient(paul)<~>~creative(paul)))&
((~wise(mary)|~generous(mary)))&
(funny(paul))&
(?[X]:(~tall(X)))&
((old(lucy)&quiet(lucy)))&
(?[X]:((~funny(X)|~calm(X))))&
((creative(mary)&generous(mary))) | ~happy(mary) | [
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8746306865115823362888842
% SZS output start Proof for 8746306865115823362888842
8. ! [X0] : (generous(X0) => (~generous(X0) | ~happy(X0))) [input p7]
23. generous(mary) & creative(mary) [input p22]
24. happy(mary) [input hypothesis]
37. ! [X0] : ((~generous(X0) | ~happy(X0)) | ~generous(X0)) [ennf transformation 8]
38. ! [X0] : (~generous(X0) | ~happy(X0) | ~generous(X0)) [flattening 37]
103. ~generous(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 38]
137. generous(mary) [cnf transformation 23]
138. happy(mary) [cnf transformation 24]
139. ~happy(X0) | ~generous(X0) [duplicate literal removal 103]
333. 42 <=> generous(mary) [avatar definition]
334. generous(mary) <- (42) [avatar component clause 333]
347. 42 [avatar split clause 137,333]
354. ~generous(mary) [resolution 139,138]
355. $false <- (42) [subsumption resolution 354,334]
356. ~42 [avatar contradiction clause 355]
357. $false [avatar sat refutation 347,356]
% SZS output end Proof for 8746306865115823362888842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either curious or tall and vice versa.
Everyone who is either not rich or not creative is either patient or not generous.
If fred is either not creative or creative then paul is both happy and strong and vice versa.
If john is rich or quiet then someone is both not strong and brave.
Everyone who is not creative is not calm or not generous.
Everyone who is not kind is either rich or old.
If lucy is wise then john is calm or not strong and vice versa.
Everyone who is not quiet is either wise or not rich and vice versa.
Everyone who is not tall or humble is both not old and not brave and vice versa.
If john is kind or patient then fred is both calm and kind.
If someone is both strong and not patient then someone is not creative or patient.
If susan is either humble or quiet then someone is both happy and not humble and vice versa.
If someone is humble then someone is either not rich or not kind and vice versa.
Everyone who is both not patient and curious is not calm or not generous and vice versa.
Everyone who is not brave is not old and vice versa.
If mary is either calm or not rich then someone is not funny or not kind.
Someone is either happy or not tall.
Lucy is patient or not old.
Someone is either not patient or not generous.
Someone is kind.
John is either brave or funny.
Someone is not patient or happy.
Lucy is not strong.
Mary is both not wise and tall. | Susan is not curious. | neutral | (![X]:(~patient(X)<=>(curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>~creative(X))=>(patient(X)<~>~generous(X))))&
(((~creative(fred)<~>creative(fred)))<=>((happy(paul)&strong(paul))))&
(((rich(john)|quiet(john)))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:(~creative(X)=>(~calm(X)|~generous(X))))&
(![X]:(~kind(X)=>(rich(X)<~>old(X))))&
((wise(lucy))<=>((calm(john)|~strong(john))))&
(![X]:(~quiet(X)<=>(wise(X)<~>~rich(X))))&
(![X]:((~tall(X)|humble(X))<=>(~old(X)&~brave(X))))&
(((kind(john)|patient(john)))=>((calm(fred)&kind(fred))))&
((?[X]:((strong(X)&~patient(X))))=>(?[X]:((~creative(X)|patient(X)))))&
(((humble(susan)<~>quiet(susan)))<=>(?[X]:((happy(X)&~humble(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((~patient(X)&curious(X))<=>(~calm(X)|~generous(X))))&
(![X]:(~brave(X)<=>~old(X)))&
(((calm(mary)<~>~rich(mary)))=>(?[X]:((~funny(X)|~kind(X)))))&
(?[X]:((happy(X)<~>~tall(X))))&
((patient(lucy)|~old(lucy)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
((brave(john)<~>funny(john)))&
(?[X]:((~patient(X)|happy(X))))&
(~strong(lucy))&
((~wise(mary)&tall(mary))) | ~curious(susan) | [] | null | 0 |
Everyone who is both not happy and not strong is kind or tall.
Everyone who is both not tall and kind is either not rich or happy and vice versa.
Everyone who is both tall and rich is both not rich and quiet and vice versa.
If paul is generous then someone is not strong or tall and vice versa.
Everyone who is not generous is not calm and vice versa.
If alice is strong then mary is not happy or not tall.
Everyone who is not funny or calm is both not old and strong.
Everyone who is happy is not strong and vice versa.
Everyone who is both generous and kind is either brave or humble.
Everyone who is not generous or rich is both brave and old and vice versa.
If someone is not old or not calm then someone is not funny and vice versa.
If someone is not calm or calm then someone is either tall or not rich.
If lucy is both not tall and generous then someone is both not brave and tall.
Everyone who is either strong or not rich is rich and vice versa.
If someone is not funny then someone is wise or quiet and vice versa.
Everyone who is patient is either funny or not curious.
Someone is not rich.
Someone is either not quiet or funny.
Someone is not calm or funny.
Susan is both brave and not happy.
Alice is either not tall or not generous.
Someone is not calm.
Mary is either not quiet or generous. | Lucy is not brave. | contradiction | (![X]:((~happy(X)&~strong(X))=>(kind(X)|tall(X))))&
(![X]:((~tall(X)&kind(X))<=>(~rich(X)<~>happy(X))))&
(![X]:((tall(X)&rich(X))<=>(~rich(X)&quiet(X))))&
((generous(paul))<=>(?[X]:((~strong(X)|tall(X)))))&
(![X]:(~generous(X)<=>~calm(X)))&
((strong(alice))=>((~happy(mary)|~tall(mary))))&
(![X]:((~funny(X)|calm(X))=>(~old(X)&strong(X))))&
(![X]:(happy(X)<=>~strong(X)))&
(![X]:((generous(X)&kind(X))=>(brave(X)<~>humble(X))))&
(![X]:((~generous(X)|rich(X))<=>(brave(X)&old(X))))&
((?[X]:((~old(X)|~calm(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((tall(X)<~>~rich(X)))))&
(((~tall(lucy)&generous(lucy)))=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:((strong(X)<~>~rich(X))<=>rich(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:(patient(X)=>(funny(X)<~>~curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~quiet(X)<~>funny(X))))&
(?[X]:((~calm(X)|funny(X))))&
((brave(susan)&~happy(susan)))&
((~tall(alice)<~>~generous(alice)))&
(?[X]:(~calm(X)))&
((~quiet(mary)<~>generous(mary))) | ~brave(lucy) | [
"p1",
"p2",
"p3",
"p7",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6772651774843263674150121
% SZS output start Proof for 6772651774843263674150121
2. ! [X0] : ((kind(X0) & ~tall(X0)) <=> (~rich(X0) <~> happy(X0))) [input p1]
3. ! [X0] : ((rich(X0) & tall(X0)) <=> (quiet(X0) & ~rich(X0))) [input p2]
4. generous(paul) <=> ? [X0] : (tall(X0) | ~strong(X0)) [input p3]
8. ! [X0] : (happy(X0) <=> ~strong(X0)) [input p7]
10. ! [X0] : ((rich(X0) | ~generous(X0)) <=> (old(X0) & brave(X0))) [input p9]
13. (generous(lucy) & ~tall(lucy)) => ? [X0] : (tall(X0) & ~brave(X0)) [input p12]
14. ! [X0] : ((strong(X0) <~> ~rich(X0)) <=> rich(X0)) [input p13]
24. ~brave(lucy) [input hypothesis]
37. ? [X0] : (tall(X0) & ~brave(X0)) | (~generous(lucy) | tall(lucy)) [ennf transformation 13]
38. ? [X0] : (tall(X0) & ~brave(X0)) | ~generous(lucy) | tall(lucy) [flattening 37]
39. ! [X0] : (((kind(X0) & ~tall(X0)) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0)))) & (((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | (~kind(X0) | tall(X0)))) [nnf transformation 2]
40. ! [X0] : (((kind(X0) & ~tall(X0)) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0)))) & (((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | ~kind(X0) | tall(X0))) [flattening 39]
41. ! [X0] : (((rich(X0) & tall(X0)) | (~quiet(X0) | rich(X0))) & ((quiet(X0) & ~rich(X0)) | (~rich(X0) | ~tall(X0)))) [nnf transformation 3]
42. ! [X0] : (((rich(X0) & tall(X0)) | ~quiet(X0) | rich(X0)) & ((quiet(X0) & ~rich(X0)) | ~rich(X0) | ~tall(X0))) [flattening 41]
43. (generous(paul) | ! [X0] : (~tall(X0) & strong(X0))) & (? [X0] : (tall(X0) | ~strong(X0)) | ~generous(paul)) [nnf transformation 4]
44. (generous(paul) | ! [X0] : (~tall(X0) & strong(X0))) & (? [X1] : (tall(X1) | ~strong(X1)) | ~generous(paul)) [rectify 43]
45. ? [X1] : (tall(X1) | ~strong(X1)) => (tall(sK0) | ~strong(sK0)) [choice axiom]
46. (generous(paul) | ! [X0] : (~tall(X0) & strong(X0))) & ((tall(sK0) | ~strong(sK0)) | ~generous(paul)) [skolemisation 44,45]
48. ! [X0] : ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))) [nnf transformation 8]
50. ! [X0] : (((rich(X0) | ~generous(X0)) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | (~rich(X0) & generous(X0)))) [nnf transformation 10]
51. ! [X0] : ((rich(X0) | ~generous(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | (~rich(X0) & generous(X0)))) [flattening 50]
61. ? [X0] : (tall(X0) & ~brave(X0)) => (tall(sK4) & ~brave(sK4)) [choice axiom]
62. (tall(sK4) & ~brave(sK4)) | ~generous(lucy) | tall(lucy) [skolemisation 38,61]
63. ! [X0] : ((((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | ~rich(X0)) & (rich(X0) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0))))) [nnf transformation 14]
83. ~tall(X0) | happy(X0) | rich(X0) [cnf transformation 40]
87. ~rich(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 42]
91. tall(sK0) | ~strong(sK0) | ~generous(paul) [cnf transformation 46]
93. generous(paul) | ~tall(X0) [cnf transformation 46]
101. ~strong(X0) | ~happy(X0) [cnf transformation 48]
105. brave(X0) | generous(X0) [cnf transformation 51]
118. tall(sK4) | ~generous(lucy) | tall(lucy) [cnf transformation 62]
120. rich(X0) | strong(X0) | rich(X0) [cnf transformation 63]
121. ~rich(X0) | strong(X0) | ~rich(X0) [cnf transformation 63]
137. ~brave(lucy) [cnf transformation 24]
138. rich(X0) | strong(X0) [duplicate literal removal 120]
139. ~rich(X0) | strong(X0) [duplicate literal removal 121]
140. ~rich(X0) | ~tall(X0) [duplicate literal removal 87]
143. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
144. ~tall(X0) <- (1) [avatar component clause 143]
146. 2 <=> generous(paul) [avatar definition]
149. 1 | 2 [avatar split clause 93,146,143]
151. 3 <=> ! [X0] : strong(X0) [avatar definition]
152. strong(X0) <- (3) [avatar component clause 151]
155. 4 <=> strong(sK0) [avatar definition]
157. ~strong(sK0) <- (~4) [avatar component clause 155]
159. 5 <=> tall(sK0) [avatar definition]
161. tall(sK0) <- (5) [avatar component clause 159]
162. ~2 | ~4 | 5 [avatar split clause 91,159,155,146]
208. 15 <=> tall(lucy) [avatar definition]
210. tall(lucy) <- (15) [avatar component clause 208]
212. 16 <=> generous(lucy) [avatar definition]
216. 17 <=> tall(sK4) [avatar definition]
218. tall(sK4) <- (17) [avatar component clause 216]
219. 15 | ~16 | 17 [avatar split clause 118,216,212,208]
225. strong(X0) [subsumption resolution 138,139]
226. 3 [avatar split clause 225,151]
294. $false <- (3, ~4) [resolution 157,152]
295. ~3 | 4 [avatar contradiction clause 294]
308. ~happy(X0) <- (3) [resolution 101,152]
310. generous(lucy) [resolution 105,137]
313. 16 [avatar split clause 310,212]
322. happy(sK0) | rich(sK0) <- (5) [resolution 83,161]
325. rich(sK0) <- (3, 5) [subsumption resolution 322,308]
328. ~tall(sK0) <- (3, 5) [resolution 325,140]
332. $false <- (3, 5) [subsumption resolution 328,161]
333. ~3 | ~5 [avatar contradiction clause 332]
334. $false <- (1, 15) [resolution 144,210]
337. ~1 | ~15 [avatar contradiction clause 334]
338. $false <- (1, 17) [subsumption resolution 218,144]
339. ~1 | ~17 [avatar contradiction clause 338]
340. $false [avatar sat refutation 149,162,219,226,295,313,333,337,339]
% SZS output end Proof for 6772651774843263674150121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not strong or not generous then fred is not patient and vice versa.
Everyone who is both not curious and humble is old or not rich and vice versa.
Everyone who is happy is not humble and vice versa.
Everyone who is generous or not creative is either not rich or calm.
If someone is either tall or not calm then someone is not generous or not tall.
Everyone who is creative or not humble is either not funny or old.
Everyone who is either quiet or not rich is both calm and patient and vice versa.
Everyone who is calm is not curious.
If fred is either calm or not curious then alice is both not humble and creative and vice versa.
If someone is not old or not calm then john is both not creative and old and vice versa.
Everyone who is generous or humble is creative.
Everyone who is both patient and rich is not curious or not rich and vice versa.
If someone is both old and funny then john is either kind or patient and vice versa.
If lucy is both not kind and not tall then someone is either not quiet or quiet.
Everyone who is kind or not rich is either curious or not strong.
Mary is calm or not funny.
Someone is not wise.
Someone is brave. | Alice is curious. | contradiction | (((~strong(paul)|~generous(paul)))<=>(~patient(fred)))&
(![X]:((~curious(X)&humble(X))<=>(old(X)|~rich(X))))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((generous(X)|~creative(X))=>(~rich(X)<~>calm(X))))&
((?[X]:((tall(X)<~>~calm(X))))=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:((creative(X)|~humble(X))=>(~funny(X)<~>old(X))))&
(![X]:((quiet(X)<~>~rich(X))<=>(calm(X)&patient(X))))&
(![X]:(calm(X)=>~curious(X)))&
(((calm(fred)<~>~curious(fred)))<=>((~humble(alice)&creative(alice))))&
((?[X]:((~old(X)|~calm(X))))<=>((~creative(john)&old(john))))&
(![X]:((generous(X)|humble(X))=>creative(X)))&
(![X]:((patient(X)&rich(X))<=>(~curious(X)|~rich(X))))&
((?[X]:((old(X)&funny(X))))<=>((kind(john)<~>patient(john))))&
(((~kind(lucy)&~tall(lucy)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((kind(X)|~rich(X))=>(curious(X)<~>~strong(X))))&
((calm(mary)|~funny(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X))) | curious(alice) | [
"p1",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5796348255572510042341286
% SZS output start Proof for 5796348255572510042341286
2. ! [X0] : ((humble(X0) & ~curious(X0)) <=> (~rich(X0) | old(X0))) [input p1]
8. ! [X0] : (calm(X0) => ~curious(X0)) [input p7]
10. ? [X0] : (~calm(X0) | ~old(X0)) <=> (old(john) & ~creative(john)) [input p9]
11. ! [X0] : ((humble(X0) | generous(X0)) => creative(X0)) [input p10]
19. curious(alice) [input hypothesis]
26. ! [X0] : (~curious(X0) | ~calm(X0)) [ennf transformation 8]
27. ! [X0] : (creative(X0) | (~humble(X0) & ~generous(X0))) [ennf transformation 11]
33. ! [X0] : (((humble(X0) & ~curious(X0)) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | (~humble(X0) | curious(X0)))) [nnf transformation 2]
34. ! [X0] : (((humble(X0) & ~curious(X0)) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | ~humble(X0) | curious(X0))) [flattening 33]
45. (? [X0] : (~calm(X0) | ~old(X0)) | (~old(john) | creative(john))) & ((old(john) & ~creative(john)) | ! [X0] : (calm(X0) & old(X0))) [nnf transformation 10]
46. (? [X0] : (~calm(X0) | ~old(X0)) | ~old(john) | creative(john)) & ((old(john) & ~creative(john)) | ! [X0] : (calm(X0) & old(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) | ~old(X0)) | ~old(john) | creative(john)) & ((old(john) & ~creative(john)) | ! [X1] : (calm(X1) & old(X1))) [rectify 46]
48. ? [X0] : (~calm(X0) | ~old(X0)) => (~calm(sK1) | ~old(sK1)) [choice axiom]
49. ((~calm(sK1) | ~old(sK1)) | ~old(john) | creative(john)) & ((old(john) & ~creative(john)) | ! [X1] : (calm(X1) & old(X1))) [skolemisation 47,48]
66. ~old(X0) | humble(X0) [cnf transformation 34]
84. ~calm(X0) | ~curious(X0) [cnf transformation 26]
92. ~creative(john) | calm(X1) [cnf transformation 49]
93. old(john) | old(X1) [cnf transformation 49]
97. ~humble(X0) | creative(X0) [cnf transformation 27]
116. curious(alice) [cnf transformation 19]
174. 12 <=> creative(john) [avatar definition]
175. ~creative(john) <- (~12) [avatar component clause 174]
178. 13 <=> old(john) [avatar definition]
179. old(john) <- (13) [avatar component clause 178]
180. ~old(john) <- (~13) [avatar component clause 178]
191. 16 <=> ! [X1] : calm(X1) [avatar definition]
192. calm(X1) <- (16) [avatar component clause 191]
195. 17 <=> ! [X1] : old(X1) [avatar definition]
196. old(X1) <- (17) [avatar component clause 195]
197. 17 | 13 [avatar split clause 93,178,195]
198. 16 | ~12 [avatar split clause 92,174,191]
238. humble(john) <- (13) [resolution 66,179]
242. creative(john) <- (13) [resolution 97,238]
244. $false <- (~12, 13) [subsumption resolution 242,175]
245. 12 | ~13 [avatar contradiction clause 244]
246. $false <- (~13, 17) [subsumption resolution 180,196]
247. 13 | ~17 [avatar contradiction clause 246]
249. ~curious(X0) <- (16) [resolution 192,84]
253. $false <- (16) [resolution 249,116]
254. ~16 [avatar contradiction clause 253]
255. $false [avatar sat refutation 197,198,245,247,254]
% SZS output end Proof for 5796348255572510042341286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not creative is kind or patient.
Everyone who is either not patient or not happy is not kind or not humble.
If alice is either not kind or not tall then paul is curious or not humble.
If lucy is not creative then someone is both old and not strong.
Everyone who is both strong and calm is either not tall or not old and vice versa.
If someone is not creative then someone is both not funny and not rich and vice versa.
If paul is either quiet or not old then someone is funny and vice versa.
Everyone who is either not curious or curious is not humble and vice versa.
Everyone who is not rich is not wise or creative and vice versa.
If susan is both not strong and not old then susan is not kind or not brave and vice versa.
Everyone who is both not generous and not happy is not kind or not tall.
If someone is either happy or old then someone is either creative or generous and vice versa.
Everyone who is both strong and curious is rich or kind and vice versa.
Everyone who is both old and not curious is calm.
Everyone who is quiet or not patient is rich or wise and vice versa.
John is creative or not happy.
Someone is both brave and strong.
Someone is both strong and old.
Fred is either curious or not generous.
Someone is not humble or not generous.
Someone is generous.
Someone is curious. | Lucy is quiet. | neutral | (![X]:((~kind(X)<~>~creative(X))=>(kind(X)|patient(X))))&
(![X]:((~patient(X)<~>~happy(X))=>(~kind(X)|~humble(X))))&
(((~kind(alice)<~>~tall(alice)))=>((curious(paul)|~humble(paul))))&
((~creative(lucy))=>(?[X]:((old(X)&~strong(X)))))&
(![X]:((strong(X)&calm(X))<=>(~tall(X)<~>~old(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&~rich(X)))))&
(((quiet(paul)<~>~old(paul)))<=>(?[X]:(funny(X))))&
(![X]:((~curious(X)<~>curious(X))<=>~humble(X)))&
(![X]:(~rich(X)<=>(~wise(X)|creative(X))))&
(((~strong(susan)&~old(susan)))<=>((~kind(susan)|~brave(susan))))&
(![X]:((~generous(X)&~happy(X))=>(~kind(X)|~tall(X))))&
((?[X]:((happy(X)<~>old(X))))<=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((strong(X)&curious(X))<=>(rich(X)|kind(X))))&
(![X]:((old(X)&~curious(X))=>calm(X)))&
(![X]:((quiet(X)|~patient(X))<=>(rich(X)|wise(X))))&
((creative(john)|~happy(john)))&
(?[X]:((brave(X)&strong(X))))&
(?[X]:((strong(X)&old(X))))&
((curious(fred)<~>~generous(fred)))&
(?[X]:((~humble(X)|~generous(X))))&
(?[X]:(generous(X)))&
(?[X]:(curious(X))) | quiet(lucy) | [] | null | 0 |
If someone is funny then someone is not curious or wise. Everyone who is both kind and calm is brave or strong and vice versa. Everyone who is either curious or happy is both calm and brave and vice versa. Everyone who is both kind and generous is kind and vice versa. Everyone who is not strong or creative is happy and vice versa. If alice is both not curious and tall then john is both not brave and not quiet. If john is rich then someone is both strong and curious and vice versa. If someone is both kind and rich then susan is either brave or not curious and vice versa. Everyone who is not strong or calm is both funny and not rich. Everyone who is quiet is both not rich and not humble and vice versa. Everyone who is not quiet is not humble or kind and vice versa. Everyone who is either not generous or calm is either not brave or tall. If alice is both happy and generous then lucy is both calm and not funny and vice versa. Everyone who is not strong is both not quiet and rich. If fred is not old or brave then someone is both creative and not tall. Everyone who is either not humble or not brave is either brave or not quiet. Paul is strong or old. Susan is kind. Someone is either not brave or not generous. Susan is either not rich or not creative. Susan is creative or quiet. Lucy is wise or curious. | Alice is not humble. | contradiction | ((?[X]:(funny(X)))=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((kind(X)&calm(X))<=>(brave(X)|strong(X))))&
(![X]:((curious(X)<~>happy(X))<=>(calm(X)&brave(X))))&
(![X]:((kind(X)&generous(X))<=>kind(X)))&
(![X]:((~strong(X)|creative(X))<=>happy(X)))&
(((~curious(alice)&tall(alice)))=>((~brave(john)&~quiet(john))))&
((rich(john))<=>(?[X]:((strong(X)&curious(X)))))&
((?[X]:((kind(X)&rich(X))))<=>((brave(susan)<~>~curious(susan))))&
(![X]:((~strong(X)|calm(X))=>(funny(X)&~rich(X))))&
(![X]:(quiet(X)<=>(~rich(X)&~humble(X))))&
(![X]:(~quiet(X)<=>(~humble(X)|kind(X))))&
(![X]:((~generous(X)<~>calm(X))=>(~brave(X)<~>tall(X))))&
(((happy(alice)&generous(alice)))<=>((calm(lucy)&~funny(lucy))))&
(![X]:(~strong(X)=>(~quiet(X)&rich(X))))&
(((~old(fred)|brave(fred)))=>(?[X]:((creative(X)&~tall(X)))))&
(![X]:((~humble(X)<~>~brave(X))=>(brave(X)<~>~quiet(X))))&
((strong(paul)|old(paul)))&
(kind(susan))&
(?[X]:((~brave(X)<~>~generous(X))))&
((~rich(susan)<~>~creative(susan)))&
((creative(susan)|quiet(susan)))&
((wise(lucy)|curious(lucy))) | ~humble(alice) | [
"p1",
"p7",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2281224704216430014171549
% SZS output start Proof for 2281224704216430014171549
2. ! [X0] : ((calm(X0) & kind(X0)) <=> (strong(X0) | brave(X0))) [input p1]
8. ? [X0] : (rich(X0) & kind(X0)) <=> (brave(susan) <~> ~curious(susan)) [input p7]
9. ! [X0] : ((calm(X0) | ~strong(X0)) => (~rich(X0) & funny(X0))) [input p8]
10. ! [X0] : (quiet(X0) <=> (~humble(X0) & ~rich(X0))) [input p9]
11. ! [X0] : (~quiet(X0) <=> (kind(X0) | ~humble(X0))) [input p10]
14. ! [X0] : (~strong(X0) => (rich(X0) & ~quiet(X0))) [input p13]
23. ~humble(alice) [input hypothesis]
31. ! [X0] : ((~rich(X0) & funny(X0)) | (~calm(X0) & strong(X0))) [ennf transformation 9]
33. ! [X0] : ((rich(X0) & ~quiet(X0)) | strong(X0)) [ennf transformation 14]
36. ! [X0] : (((calm(X0) & kind(X0)) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | (~calm(X0) | ~kind(X0)))) [nnf transformation 2]
37. ! [X0] : (((calm(X0) & kind(X0)) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | ~calm(X0) | ~kind(X0))) [flattening 36]
48. (? [X0] : (rich(X0) & kind(X0)) | ((brave(susan) | curious(susan)) & (~curious(susan) | ~brave(susan)))) & (((curious(susan) | ~brave(susan)) & (~curious(susan) | brave(susan))) | ! [X0] : (~rich(X0) | ~kind(X0))) [nnf transformation 8]
49. (? [X0] : (rich(X0) & kind(X0)) | ((brave(susan) | curious(susan)) & (~curious(susan) | ~brave(susan)))) & (((curious(susan) | ~brave(susan)) & (~curious(susan) | brave(susan))) | ! [X1] : (~rich(X1) | ~kind(X1))) [rectify 48]
50. ? [X0] : (rich(X0) & kind(X0)) => (rich(sK1) & kind(sK1)) [choice axiom]
51. ((rich(sK1) & kind(sK1)) | ((brave(susan) | curious(susan)) & (~curious(susan) | ~brave(susan)))) & (((curious(susan) | ~brave(susan)) & (~curious(susan) | brave(susan))) | ! [X1] : (~rich(X1) | ~kind(X1))) [skolemisation 49,50]
52. ! [X0] : ((quiet(X0) | (humble(X0) | rich(X0))) & ((~humble(X0) & ~rich(X0)) | ~quiet(X0))) [nnf transformation 10]
53. ! [X0] : ((quiet(X0) | humble(X0) | rich(X0)) & ((~humble(X0) & ~rich(X0)) | ~quiet(X0))) [flattening 52]
54. ! [X0] : ((~quiet(X0) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | quiet(X0))) [nnf transformation 11]
55. ! [X0] : ((~quiet(X0) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | quiet(X0))) [flattening 54]
68. ~strong(X0) | kind(X0) [cnf transformation 37]
70. ~strong(X0) | calm(X0) [cnf transformation 37]
88. ~curious(susan) | brave(susan) | ~rich(X1) | ~kind(X1) [cnf transformation 51]
89. curious(susan) | ~brave(susan) | ~rich(X1) | ~kind(X1) [cnf transformation 51]
92. rich(sK1) | ~curious(susan) | ~brave(susan) [cnf transformation 51]
93. rich(sK1) | brave(susan) | curious(susan) [cnf transformation 51]
96. ~rich(X0) | strong(X0) [cnf transformation 31]
97. ~rich(X0) | ~calm(X0) [cnf transformation 31]
99. ~humble(X0) | ~quiet(X0) [cnf transformation 53]
100. humble(X0) | quiet(X0) | rich(X0) [cnf transformation 53]
102. ~quiet(X0) | humble(X0) [cnf transformation 55]
113. rich(X0) | strong(X0) [cnf transformation 33]
126. ~humble(alice) [cnf transformation 23]
168. 9 <=> curious(susan) [avatar definition]
172. 10 <=> brave(susan) [avatar definition]
176. 11 <=> rich(sK1) [avatar definition]
178. rich(sK1) <- (11) [avatar component clause 176]
179. 9 | 10 | 11 [avatar split clause 93,176,172,168]
180. ~10 | ~9 | 11 [avatar split clause 92,176,168,172]
188. 13 <=> ! [X1] : (~rich(X1) | ~kind(X1)) [avatar definition]
189. ~rich(X1) | ~kind(X1) <- (13) [avatar component clause 188]
190. 13 | ~10 | 9 [avatar split clause 89,168,172,188]
191. 13 | 10 | ~9 [avatar split clause 88,168,172,188]
192. ~quiet(X0) [subsumption resolution 102,99]
214. strong(X0) [subsumption resolution 113,96]
254. kind(X0) [resolution 68,214]
256. calm(X0) [resolution 70,214]
269. ~calm(sK1) <- (11) [resolution 97,178]
270. $false <- (11) [subsumption resolution 269,256]
271. ~11 [avatar contradiction clause 270]
272. ~rich(X1) <- (13) [subsumption resolution 189,254]
284. quiet(alice) | rich(alice) [resolution 100,126]
287. rich(alice) [subsumption resolution 284,192]
288. $false <- (13) [subsumption resolution 287,272]
289. ~13 [avatar contradiction clause 288]
290. $false [avatar sat refutation 179,180,190,191,271,289]
% SZS output end Proof for 2281224704216430014171549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and funny then someone is brave and vice versa. Everyone who is not curious or tall is not quiet or not calm. Everyone who is not patient is not curious or not kind. Everyone who is not old or not brave is happy and vice versa. If fred is both not tall and not brave then mary is both happy and not funny. If someone is both happy and kind then someone is either not wise or rich. Everyone who is kind or old is not generous or patient and vice versa. Everyone who is both creative and not wise is either not quiet or not tall. If paul is old then someone is both old and not rich. Everyone who is not creative is tall or kind. If someone is happy or brave then mary is either brave or patient and vice versa. Everyone who is either not brave or not tall is brave and vice versa. Everyone who is humble or not generous is creative. Everyone who is either creative or rich is both not creative and quiet. Everyone who is rich or creative is not generous or wise and vice versa. If someone is old then alice is kind or old. Someone is not tall. Someone is not happy or not quiet. Paul is not kind or not creative. Someone is not brave. Lucy is either old or not tall. Someone is both not brave and strong. Someone is either not quiet or humble. Someone is brave or not quiet. | Lucy is happy. | entailment | ((?[X]:((~brave(X)&funny(X))))<=>(?[X]:(brave(X))))&
(![X]:((~curious(X)|tall(X))=>(~quiet(X)|~calm(X))))&
(![X]:(~patient(X)=>(~curious(X)|~kind(X))))&
(![X]:((~old(X)|~brave(X))<=>happy(X)))&
(((~tall(fred)&~brave(fred)))=>((happy(mary)&~funny(mary))))&
((?[X]:((happy(X)&kind(X))))=>(?[X]:((~wise(X)<~>rich(X)))))&
(![X]:((kind(X)|old(X))<=>(~generous(X)|patient(X))))&
(![X]:((creative(X)&~wise(X))=>(~quiet(X)<~>~tall(X))))&
((old(paul))=>(?[X]:((old(X)&~rich(X)))))&
(![X]:(~creative(X)=>(tall(X)|kind(X))))&
((?[X]:((happy(X)|brave(X))))<=>((brave(mary)<~>patient(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>brave(X)))&
(![X]:((humble(X)|~generous(X))=>creative(X)))&
(![X]:((creative(X)<~>rich(X))=>(~creative(X)&quiet(X))))&
(![X]:((rich(X)|creative(X))<=>(~generous(X)|wise(X))))&
((?[X]:(old(X)))=>((kind(alice)|old(alice))))&
(?[X]:(~tall(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
((~kind(paul)|~creative(paul)))&
(?[X]:(~brave(X)))&
((old(lucy)<~>~tall(lucy)))&
(?[X]:((~brave(X)&strong(X))))&
(?[X]:((~quiet(X)<~>humble(X))))&
(?[X]:((brave(X)|~quiet(X)))) | happy(lucy) | [
"p3",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2673771890235071156523363
% SZS output start Proof for 2673771890235071156523363
4. ! [X0] : ((~brave(X0) | ~old(X0)) <=> happy(X0)) [input p3]
12. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> brave(X0)) [input p11]
21. old(lucy) <~> ~tall(lucy) [input p20]
25. ~happy(lucy) [input hypothesis]
48. ! [X0] : (((~brave(X0) | ~old(X0)) | ~happy(X0)) & (happy(X0) | (brave(X0) & old(X0)))) [nnf transformation 4]
49. ! [X0] : ((~brave(X0) | ~old(X0) | ~happy(X0)) & (happy(X0) | (brave(X0) & old(X0)))) [flattening 48]
63. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | ~brave(X0)) & (brave(X0) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 12]
73. (tall(lucy) | ~old(lucy)) & (~tall(lucy) | old(lucy)) [nnf transformation 21]
84. happy(X0) | old(X0) [cnf transformation 49]
106. brave(X0) | ~tall(X0) | brave(X0) [cnf transformation 63]
108. ~tall(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 63]
126. tall(lucy) | ~old(lucy) [cnf transformation 73]
131. ~happy(lucy) [cnf transformation 25]
133. brave(X0) | ~tall(X0) [duplicate literal removal 106]
134. ~tall(X0) | ~brave(X0) [duplicate literal removal 108]
216. ~tall(X0) [subsumption resolution 133,134]
248. ~old(lucy) [subsumption resolution 126,216]
270. old(lucy) [resolution 84,131]
271. $false [subsumption resolution 270,248]
% SZS output end Proof for 2673771890235071156523363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either humble or not quiet then someone is patient or wise.
Everyone who is either not humble or not tall is not funny.
Everyone who is both not rich and not old is either not kind or not patient and vice versa.
Everyone who is old or patient is not calm or not kind and vice versa.
Everyone who is funny is not calm or old and vice versa.
Everyone who is calm is both not happy and not quiet.
If alice is either not calm or curious then someone is either calm or patient and vice versa.
Everyone who is not strong is both not patient and happy.
Everyone who is either old or brave is either not brave or not creative and vice versa.
If someone is both generous and not old then someone is both calm and not funny.
Everyone who is tall is both not quiet and humble and vice versa.
If someone is not happy or not creative then someone is both not tall and not rich and vice versa.
If fred is either not funny or not strong then someone is either not brave or old and vice versa.
Everyone who is not curious or wise is both not old and tall and vice versa.
Everyone who is both not tall and patient is old and vice versa.
Susan is not patient or not calm.
Paul is both brave and not wise.
John is both tall and not funny.
Someone is both brave and rich.
Someone is either calm or not kind.
Someone is not calm or rich. | Susan is not happy. | neutral | (((humble(susan)<~>~quiet(susan)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:((~humble(X)<~>~tall(X))=>~funny(X)))&
(![X]:((~rich(X)&~old(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((old(X)|patient(X))<=>(~calm(X)|~kind(X))))&
(![X]:(funny(X)<=>(~calm(X)|old(X))))&
(![X]:(calm(X)=>(~happy(X)&~quiet(X))))&
(((~calm(alice)<~>curious(alice)))<=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:(~strong(X)=>(~patient(X)&happy(X))))&
(![X]:((old(X)<~>brave(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((generous(X)&~old(X))))=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:(tall(X)<=>(~quiet(X)&humble(X))))&
((?[X]:((~happy(X)|~creative(X))))<=>(?[X]:((~tall(X)&~rich(X)))))&
(((~funny(fred)<~>~strong(fred)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~curious(X)|wise(X))<=>(~old(X)&tall(X))))&
(![X]:((~tall(X)&patient(X))<=>old(X)))&
((~patient(susan)|~calm(susan)))&
((brave(paul)&~wise(paul)))&
((tall(john)&~funny(john)))&
(?[X]:((brave(X)&rich(X))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~calm(X)|rich(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is tall is not calm.
Everyone who is calm is either calm or humble and vice versa.
If someone is not quiet then fred is wise or not calm and vice versa.
If someone is both kind and not rich then someone is either not funny or not rich.
If fred is both calm and wise then someone is not creative or not quiet.
Everyone who is brave or not wise is curious and vice versa.
Everyone who is either rich or not kind is not strong.
If lucy is not wise or funny then someone is curious.
If fred is either patient or not curious then someone is tall and vice versa.
If someone is not funny then someone is patient.
If someone is both rich and not wise then someone is not kind and vice versa.
Everyone who is not strong or brave is not patient and vice versa.
If fred is both not humble and strong then someone is not wise and vice versa.
Everyone who is either not strong or not humble is both tall and wise and vice versa.
If someone is both not generous and rich then paul is both not calm and not old and vice versa.
If someone is not brave or kind then someone is not humble or not curious.
Someone is either brave or funny.
Someone is quiet.
Someone is either not generous or not patient.
Alice is generous or not tall.
Someone is kind or not curious.
Paul is generous or patient. | Alice is not curious. | neutral | (![X]:(tall(X)=>~calm(X)))&
(![X]:(calm(X)<=>(calm(X)<~>humble(X))))&
((?[X]:(~quiet(X)))<=>((wise(fred)|~calm(fred))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(((calm(fred)&wise(fred)))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((brave(X)|~wise(X))<=>curious(X)))&
(![X]:((rich(X)<~>~kind(X))=>~strong(X)))&
(((~wise(lucy)|funny(lucy)))=>(?[X]:(curious(X))))&
(((patient(fred)<~>~curious(fred)))<=>(?[X]:(tall(X))))&
((?[X]:(~funny(X)))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)|brave(X))<=>~patient(X)))&
(((~humble(fred)&strong(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(tall(X)&wise(X))))&
((?[X]:((~generous(X)&rich(X))))<=>((~calm(paul)&~old(paul))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
((generous(alice)|~tall(alice)))&
(?[X]:((kind(X)|~curious(X))))&
((generous(paul)|patient(paul))) | ~curious(alice) | [] | null | 0 |
If someone is calm or not curious then mary is either wise or funny.
Everyone who is both not calm and calm is both not strong and quiet and vice versa.
If someone is not humble or happy then someone is either brave or wise and vice versa.
Everyone who is either funny or not happy is not kind.
Everyone who is not funny or brave is either strong or not brave and vice versa.
Everyone who is not creative or wise is funny or not generous and vice versa.
Everyone who is both not generous and kind is both patient and humble.
Everyone who is old or funny is either not brave or not quiet.
If someone is kind then fred is strong or not old.
Everyone who is either strong or not tall is either not rich or not strong.
Everyone who is either quiet or not calm is creative.
If someone is rich or not curious then someone is tall or old.
Everyone who is not kind or curious is either not strong or not humble.
Everyone who is not creative or happy is either not patient or calm and vice versa.
If someone is not humble or creative then someone is both not funny and not brave.
Everyone who is not funny or not creative is old or quiet.
Someone is not patient.
Lucy is both rich and not creative.
Susan is old or not humble.
Paul is either not old or creative.
Susan is both calm and funny. | Fred is kind. | entailment | ((?[X]:((calm(X)|~curious(X))))=>((wise(mary)<~>funny(mary))))&
(![X]:((~calm(X)&calm(X))<=>(~strong(X)&quiet(X))))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((funny(X)<~>~happy(X))=>~kind(X)))&
(![X]:((~funny(X)|brave(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((~creative(X)|wise(X))<=>(funny(X)|~generous(X))))&
(![X]:((~generous(X)&kind(X))=>(patient(X)&humble(X))))&
(![X]:((old(X)|funny(X))=>(~brave(X)<~>~quiet(X))))&
((?[X]:(kind(X)))=>((strong(fred)|~old(fred))))&
(![X]:((strong(X)<~>~tall(X))=>(~rich(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>~calm(X))=>creative(X)))&
((?[X]:((rich(X)|~curious(X))))=>(?[X]:((tall(X)|old(X)))))&
(![X]:((~kind(X)|curious(X))=>(~strong(X)<~>~humble(X))))&
(![X]:((~creative(X)|happy(X))<=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)|quiet(X))))&
(?[X]:(~patient(X)))&
((rich(lucy)&~creative(lucy)))&
((old(susan)|~humble(susan)))&
((~old(paul)<~>creative(paul)))&
((calm(susan)&funny(susan))) | kind(fred) | [
"p1",
"p4",
"p7",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6256644839006290019938390
% SZS output start Proof for 6256644839006290019938390
2. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (quiet(X0) & ~strong(X0))) [input p1]
5. ! [X0] : ((brave(X0) | ~funny(X0)) <=> (strong(X0) <~> ~brave(X0))) [input p4]
8. ! [X0] : ((funny(X0) | old(X0)) => (~brave(X0) <~> ~quiet(X0))) [input p7]
13. ! [X0] : ((curious(X0) | ~kind(X0)) => (~strong(X0) <~> ~humble(X0))) [input p12]
15. ? [X0] : (creative(X0) | ~humble(X0)) => ? [X0] : (~brave(X0) & ~funny(X0)) [input p14]
16. ! [X0] : ((~creative(X0) | ~funny(X0)) => (quiet(X0) | old(X0))) [input p15]
22. ~kind(fred) [input hypothesis]
25. ? [X0] : (creative(X0) | ~humble(X0)) => ? [X1] : (~brave(X1) & ~funny(X1)) [rectify 15]
30. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | (~funny(X0) & ~old(X0))) [ennf transformation 8]
36. ! [X0] : ((~strong(X0) <~> ~humble(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 13]
37. ? [X1] : (~brave(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) & humble(X0)) [ennf transformation 25]
38. ! [X0] : ((quiet(X0) | old(X0)) | (creative(X0) & funny(X0))) [ennf transformation 16]
39. ! [X0] : (quiet(X0) | old(X0) | (creative(X0) & funny(X0))) [flattening 38]
41. ! [X0] : (((calm(X0) & ~calm(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 2]
42. ! [X0] : (((calm(X0) & ~calm(X0)) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ~calm(X0) | calm(X0))) [flattening 41]
49. ! [X0] : (((brave(X0) | ~funny(X0)) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~brave(X0) & funny(X0)))) [nnf transformation 5]
50. ! [X0] : ((brave(X0) | ~funny(X0) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~brave(X0) & funny(X0)))) [flattening 49]
53. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~funny(X0) & ~old(X0))) [nnf transformation 30]
59. ! [X0] : (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~curious(X0) & kind(X0))) [nnf transformation 36]
62. ? [X0] : (~brave(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) & humble(X1)) [rectify 37]
63. ? [X0] : (~brave(X0) & ~funny(X0)) => (~brave(sK3) & ~funny(sK3)) [choice axiom]
64. (~brave(sK3) & ~funny(sK3)) | ! [X1] : (~creative(X1) & humble(X1)) [skolemisation 62,63]
74. ~calm(X0) | ~quiet(X0) | strong(X0) [cnf transformation 42]
75. ~quiet(X0) | calm(X0) | strong(X0) [cnf transformation 42]
85. ~brave(X0) | strong(X0) | ~brave(X0) [cnf transformation 50]
86. ~strong(X0) | brave(X0) | funny(X0) [cnf transformation 50]
98. ~old(X0) | brave(X0) | quiet(X0) [cnf transformation 53]
99. ~funny(X0) | brave(X0) | quiet(X0) [cnf transformation 53]
109. ~humble(X0) | ~strong(X0) | kind(X0) [cnf transformation 59]
119. ~funny(sK3) | humble(X1) [cnf transformation 64]
121. ~brave(sK3) | humble(X1) [cnf transformation 64]
123. old(X0) | quiet(X0) | funny(X0) [cnf transformation 39]
133. ~kind(fred) [cnf transformation 22]
136. ~brave(X0) | strong(X0) [duplicate literal removal 85]
156. ~quiet(X0) | strong(X0) [subsumption resolution 74,75]
186. 12 <=> ! [X3] : humble(X3) [avatar definition]
187. humble(X3) <- (12) [avatar component clause 186]
195. 14 <=> strong(fred) [avatar definition]
196. ~strong(fred) <- (~14) [avatar component clause 195]
220. 20 <=> brave(sK3) [avatar definition]
222. ~brave(sK3) <- (~20) [avatar component clause 220]
224. 12 | ~20 [avatar split clause 121,220,186]
226. 21 <=> funny(sK3) [avatar definition]
230. 12 | ~21 [avatar split clause 119,226,186]
315. 35 <=> humble(fred) [avatar definition]
316. ~humble(fred) <- (~35) [avatar component clause 315]
317. humble(fred) <- (35) [avatar component clause 315]
330. ~strong(fred) | kind(fred) <- (35) [resolution 317,109]
367. quiet(X0) | funny(X0) | brave(X0) | quiet(X0) [resolution 123,98]
370. quiet(X0) | funny(X0) | brave(X0) [duplicate literal removal 367]
376. brave(X0) | quiet(X0) [subsumption resolution 370,99]
382. ~strong(fred) <- (35) [subsumption resolution 330,133]
383. ~14 | ~35 [avatar split clause 382,315,195]
424. quiet(X1) | strong(X1) [resolution 376,136]
425. strong(X1) [subsumption resolution 424,156]
444. brave(X0) | funny(X0) [resolution 425,86]
462. funny(sK3) <- (~20) [resolution 444,222]
467. 21 | 20 [avatar split clause 462,220,226]
470. $false <- (12, ~35) [resolution 187,316]
475. ~12 | 35 [avatar contradiction clause 470]
478. $false <- (~14) [subsumption resolution 196,425]
479. 14 [avatar contradiction clause 478]
480. $false [avatar sat refutation 224,230,383,467,475,479]
% SZS output end Proof for 6256644839006290019938390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or curious then someone is either not funny or rich.
Everyone who is rich is not patient.
Everyone who is either tall or creative is both not curious and old and vice versa.
If mary is either not humble or tall then someone is wise or not kind.
Everyone who is either kind or rich is patient or not rich.
If someone is not curious or not patient then mary is both tall and brave and vice versa.
Everyone who is not kind or not tall is quiet and vice versa.
If someone is both humble and patient then alice is both curious and funny and vice versa.
If lucy is both generous and creative then paul is not tall or strong and vice versa.
Everyone who is tall or not happy is not strong or not tall.
Everyone who is not wise or funny is curious.
If someone is not kind or kind then mary is curious or wise and vice versa.
If someone is either not rich or not quiet then john is both curious and calm.
Everyone who is both old and wise is either not humble or not tall and vice versa.
Everyone who is generous is not patient or kind.
If someone is both generous and funny then someone is tall.
Someone is both wise and not kind.
Mary is either patient or generous.
Susan is quiet or tall.
John is not old.
Someone is tall.
Someone is tall or creative.
Paul is creative or not creative.
Susan is either not quiet or kind. | John is calm. | entailment | ((?[X]:((~brave(X)|curious(X))))=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:(rich(X)=>~patient(X)))&
(![X]:((tall(X)<~>creative(X))<=>(~curious(X)&old(X))))&
(((~humble(mary)<~>tall(mary)))=>(?[X]:((wise(X)|~kind(X)))))&
(![X]:((kind(X)<~>rich(X))=>(patient(X)|~rich(X))))&
((?[X]:((~curious(X)|~patient(X))))<=>((tall(mary)&brave(mary))))&
(![X]:((~kind(X)|~tall(X))<=>quiet(X)))&
((?[X]:((humble(X)&patient(X))))<=>((curious(alice)&funny(alice))))&
(((generous(lucy)&creative(lucy)))<=>((~tall(paul)|strong(paul))))&
(![X]:((tall(X)|~happy(X))=>(~strong(X)|~tall(X))))&
(![X]:((~wise(X)|funny(X))=>curious(X)))&
((?[X]:((~kind(X)|kind(X))))<=>((curious(mary)|wise(mary))))&
((?[X]:((~rich(X)<~>~quiet(X))))=>((curious(john)&calm(john))))&
(![X]:((old(X)&wise(X))<=>(~humble(X)<~>~tall(X))))&
(![X]:(generous(X)=>(~patient(X)|kind(X))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:(tall(X))))&
(?[X]:((wise(X)&~kind(X))))&
((patient(mary)<~>generous(mary)))&
((quiet(susan)|tall(susan)))&
(~old(john))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)|creative(X))))&
((creative(paul)|~creative(paul)))&
((~quiet(susan)<~>kind(susan))) | calm(john) | [
"p1",
"p4",
"p6",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5218772939783607493119382
% SZS output start Proof for 5218772939783607493119382
2. ! [X0] : (rich(X0) => ~patient(X0)) [input p1]
5. ! [X0] : ((kind(X0) <~> rich(X0)) => (~rich(X0) | patient(X0))) [input p4]
7. ! [X0] : ((~tall(X0) | ~kind(X0)) <=> quiet(X0)) [input p6]
13. ? [X0] : (~rich(X0) <~> ~quiet(X0)) => (calm(john) & curious(john)) [input p12]
17. ? [X0] : (~kind(X0) & wise(X0)) [input p16]
25. ~calm(john) [input hypothesis]
30. ! [X0] : (~patient(X0) | ~rich(X0)) [ennf transformation 2]
32. ! [X0] : ((~rich(X0) | patient(X0)) | (kind(X0) <=> rich(X0))) [ennf transformation 5]
33. ! [X0] : (~rich(X0) | patient(X0) | (kind(X0) <=> rich(X0))) [flattening 32]
37. (calm(john) & curious(john)) | ! [X0] : (~rich(X0) <=> ~quiet(X0)) [ennf transformation 13]
50. ! [X0] : (~rich(X0) | patient(X0) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) [nnf transformation 33]
56. ! [X0] : (((~tall(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (tall(X0) & kind(X0)))) [nnf transformation 7]
57. ! [X0] : ((~tall(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (tall(X0) & kind(X0)))) [flattening 56]
70. (calm(john) & curious(john)) | ! [X0] : ((~rich(X0) | quiet(X0)) & (~quiet(X0) | rich(X0))) [nnf transformation 37]
76. ? [X0] : (~kind(X0) & wise(X0)) => (~kind(sK6) & wise(sK6)) [choice axiom]
77. ~kind(sK6) & wise(sK6) [skolemisation 17,76]
88. ~patient(X0) | ~rich(X0) [cnf transformation 30]
98. ~rich(X0) | patient(X0) | kind(X0) | ~rich(X0) [cnf transformation 50]
104. quiet(X0) | kind(X0) [cnf transformation 57]
125. calm(john) | ~quiet(X0) | rich(X0) [cnf transformation 70]
136. ~kind(sK6) [cnf transformation 77]
146. ~calm(john) [cnf transformation 25]
148. ~rich(X0) | patient(X0) | kind(X0) [duplicate literal removal 98]
185. ~rich(X0) | kind(X0) [subsumption resolution 148,88]
257. 24 <=> calm(john) [avatar definition]
262. 25 <=> ! [X0] : (~quiet(X0) | rich(X0)) [avatar definition]
263. ~quiet(X0) | rich(X0) <- (25) [avatar component clause 262]
264. 25 | 24 [avatar split clause 125,257,262]
300. ~24 [avatar split clause 146,257]
306. rich(X1) | kind(X1) <- (25) [resolution 263,104]
307. kind(X1) <- (25) [subsumption resolution 306,185]
310. $false <- (25) [resolution 307,136]
313. ~25 [avatar contradiction clause 310]
314. $false [avatar sat refutation 264,300,313]
% SZS output end Proof for 5218772939783607493119382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both strong and tall.
If someone is tall then someone is either quiet or brave.
Everyone who is both calm and not curious is not funny or not happy and vice versa.
Everyone who is either not funny or wise is not quiet or wise and vice versa.
If mary is humble or not kind then susan is tall and vice versa.
Everyone who is not curious or calm is both not rich and brave and vice versa.
Everyone who is either funny or not old is both not old and funny and vice versa.
If mary is either happy or patient then alice is either brave or calm and vice versa.
Everyone who is both humble and brave is both old and not rich and vice versa.
Everyone who is either not curious or not rich is either strong or creative.
If susan is either happy or curious then someone is either not calm or not creative.
If someone is patient or not calm then someone is both not calm and not tall and vice versa.
Everyone who is not patient or not tall is either brave or generous.
Everyone who is either not quiet or humble is either not rich or not wise.
Alice is not generous or not curious.
Someone is either calm or quiet.
Someone is either not rich or wise.
Paul is either strong or not strong. | Susan is not creative. | neutral | (![X]:(creative(X)=>(strong(X)&tall(X))))&
((?[X]:(tall(X)))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:((calm(X)&~curious(X))<=>(~funny(X)|~happy(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(~quiet(X)|wise(X))))&
(((humble(mary)|~kind(mary)))<=>(tall(susan)))&
(![X]:((~curious(X)|calm(X))<=>(~rich(X)&brave(X))))&
(![X]:((funny(X)<~>~old(X))<=>(~old(X)&funny(X))))&
(((happy(mary)<~>patient(mary)))<=>((brave(alice)<~>calm(alice))))&
(![X]:((humble(X)&brave(X))<=>(old(X)&~rich(X))))&
(![X]:((~curious(X)<~>~rich(X))=>(strong(X)<~>creative(X))))&
(((happy(susan)<~>curious(susan)))=>(?[X]:((~calm(X)<~>~creative(X)))))&
((?[X]:((patient(X)|~calm(X))))<=>(?[X]:((~calm(X)&~tall(X)))))&
(![X]:((~patient(X)|~tall(X))=>(brave(X)<~>generous(X))))&
(![X]:((~quiet(X)<~>humble(X))=>(~rich(X)<~>~wise(X))))&
((~generous(alice)|~curious(alice)))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>wise(X))))&
((strong(paul)<~>~strong(paul))) | ~creative(susan) | [] | null | 0 |
Everyone who is not brave is not wise or generous and vice versa. Everyone who is curious is either not patient or tall. Everyone who is not strong is either rich or not old and vice versa. If john is both not curious and not humble then someone is not humble and vice versa. Everyone who is not patient or not creative is either not calm or not happy. If someone is patient then someone is either not happy or not calm and vice versa. Everyone who is not calm or kind is either not calm or not wise and vice versa. Everyone who is both strong and not generous is both rich and generous. Everyone who is not rich or not generous is both not calm and generous. Everyone who is not humble is both kind and tall. If someone is both kind and not old then someone is rich or tall. Everyone who is not brave or generous is both not wise and not funny and vice versa. Everyone who is not funny is not strong or not humble and vice versa. Everyone who is calm is old and vice versa. If someone is not quiet then someone is happy. Fred is both not funny and tall. Someone is not patient. John is either not patient or not curious. Someone is either humble or not happy. Someone is not strong. Someone is not tall or kind. | Fred is patient. | neutral | (![X]:(~brave(X)<=>(~wise(X)|generous(X))))&
(![X]:(curious(X)=>(~patient(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>~old(X))))&
(((~curious(john)&~humble(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)|~creative(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((~calm(X)|kind(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~generous(X))=>(rich(X)&generous(X))))&
(![X]:((~rich(X)|~generous(X))=>(~calm(X)&generous(X))))&
(![X]:(~humble(X)=>(kind(X)&tall(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(~funny(X)<=>(~strong(X)|~humble(X))))&
(![X]:(calm(X)<=>old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(happy(X))))&
((~funny(fred)&tall(fred)))&
(?[X]:(~patient(X)))&
((~patient(john)<~>~curious(john)))&
(?[X]:((humble(X)<~>~happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)|kind(X)))) | patient(fred) | [] | null | 0 |
Everyone who is either not calm or quiet is either not tall or not kind.
Everyone who is both not humble and rich is both wise and not tall and vice versa.
If someone is tall or not curious then fred is both not wise and kind and vice versa.
Everyone who is kind is either quiet or humble and vice versa.
If john is either humble or quiet then alice is both creative and not old and vice versa.
Everyone who is either brave or not patient is old or wise.
Everyone who is patient is not strong or not brave and vice versa.
Everyone who is both wise and happy is not old or kind and vice versa.
Everyone who is either not old or not curious is not wise or not funny and vice versa.
If someone is either not strong or not funny then alice is not kind or humble and vice versa.
Everyone who is either not funny or not generous is both funny and brave.
If lucy is not curious or old then someone is brave or not brave and vice versa.
Everyone who is either not happy or tall is both kind and not funny and vice versa.
If mary is not calm then someone is either not patient or curious and vice versa.
Everyone who is rich or funny is not quiet or old and vice versa.
Someone is not calm or happy.
Someone is either rich or brave.
John is creative or rich.
Lucy is not calm or patient. | John is not old. | neutral | (![X]:((~calm(X)<~>quiet(X))=>(~tall(X)<~>~kind(X))))&
(![X]:((~humble(X)&rich(X))<=>(wise(X)&~tall(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((~wise(fred)&kind(fred))))&
(![X]:(kind(X)<=>(quiet(X)<~>humble(X))))&
(((humble(john)<~>quiet(john)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((creative(john)|rich(john)))&
((~calm(lucy)|patient(lucy))) | ~old(john) | [] | null | 0 |
Everyone who is not humble is funny and vice versa.
If mary is brave or rich then someone is both old and curious.
Everyone who is both not kind and not rich is quiet or curious and vice versa.
Everyone who is brave is funny or not generous and vice versa.
Everyone who is either old or not creative is not rich and vice versa.
Everyone who is not creative is not brave and vice versa.
Everyone who is both not humble and not quiet is either not brave or creative.
Everyone who is both calm and not humble is not brave and vice versa.
If susan is curious then lucy is either not kind or quiet.
Everyone who is brave or patient is tall or quiet and vice versa.
If john is tall then someone is either happy or wise and vice versa.
If someone is not rich or not wise then fred is both calm and curious and vice versa.
If someone is either not rich or not wise then someone is both creative and curious and vice versa.
If someone is both wise and not funny then someone is both not happy and kind.
Everyone who is either not strong or not brave is old or not brave and vice versa.
If paul is not calm or creative then alice is either humble or not calm.
Someone is not quiet.
Alice is funny or not old.
Someone is both funny and wise.
Mary is not curious.
Someone is kind.
Paul is either funny or curious.
Lucy is not patient. | Fred is not calm. | contradiction | (![X]:(~humble(X)<=>funny(X)))&
(((brave(mary)|rich(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:(brave(X)<=>(funny(X)|~generous(X))))&
(![X]:((old(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:((~humble(X)&~quiet(X))=>(~brave(X)<~>creative(X))))&
(![X]:((calm(X)&~humble(X))<=>~brave(X)))&
((curious(susan))=>((~kind(lucy)<~>quiet(lucy))))&
(![X]:((brave(X)|patient(X))<=>(tall(X)|quiet(X))))&
((tall(john))<=>(?[X]:((happy(X)<~>wise(X)))))&
((?[X]:((~rich(X)|~wise(X))))<=>((calm(fred)&curious(fred))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(?[X]:((creative(X)&curious(X)))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((~strong(X)<~>~brave(X))<=>(old(X)|~brave(X))))&
(((~calm(paul)|creative(paul)))=>((humble(alice)<~>~calm(alice))))&
(?[X]:(~quiet(X)))&
((funny(alice)|~old(alice)))&
(?[X]:((funny(X)&wise(X))))&
(~curious(mary))&
(?[X]:(kind(X)))&
((funny(paul)<~>curious(paul)))&
(~patient(lucy)) | ~calm(fred) | [
"p1",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1375743112358653222103491
% SZS output start Proof for 1375743112358653222103491
2. (rich(mary) | brave(mary)) => ? [X0] : (curious(X0) & old(X0)) [input p1]
3. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (curious(X0) | quiet(X0))) [input p2]
12. ? [X0] : (~wise(X0) | ~rich(X0)) <=> (curious(fred) & calm(fred)) [input p11]
24. ~calm(fred) [input hypothesis]
27. ? [X0] : (curious(X0) & old(X0)) | (~rich(mary) & ~brave(mary)) [ennf transformation 2]
34. ? [X0] : (curious(X0) & old(X0)) => (curious(sK0) & old(sK0)) [choice axiom]
35. (curious(sK0) & old(sK0)) | (~rich(mary) & ~brave(mary)) [skolemisation 27,34]
36. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 3]
37. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | rich(X0) | kind(X0))) [flattening 36]
52. (? [X0] : (~wise(X0) | ~rich(X0)) | (~curious(fred) | ~calm(fred))) & ((curious(fred) & calm(fred)) | ! [X0] : (wise(X0) & rich(X0))) [nnf transformation 12]
53. (? [X0] : (~wise(X0) | ~rich(X0)) | ~curious(fred) | ~calm(fred)) & ((curious(fred) & calm(fred)) | ! [X0] : (wise(X0) & rich(X0))) [flattening 52]
54. (? [X0] : (~wise(X0) | ~rich(X0)) | ~curious(fred) | ~calm(fred)) & ((curious(fred) & calm(fred)) | ! [X1] : (wise(X1) & rich(X1))) [rectify 53]
55. ? [X0] : (~wise(X0) | ~rich(X0)) => (~wise(sK2) | ~rich(sK2)) [choice axiom]
56. ((~wise(sK2) | ~rich(sK2)) | ~curious(fred) | ~calm(fred)) & ((curious(fred) & calm(fred)) | ! [X1] : (wise(X1) & rich(X1))) [skolemisation 54,55]
80. curious(sK0) | ~rich(mary) [cnf transformation 35]
85. ~curious(X0) | ~rich(X0) [cnf transformation 37]
110. calm(fred) | rich(X1) [cnf transformation 56]
142. ~calm(fred) [cnf transformation 24]
146. 1 <=> rich(mary) [avatar definition]
148. ~rich(mary) <- (~1) [avatar component clause 146]
150. 2 <=> curious(sK0) [avatar definition]
152. curious(sK0) <- (2) [avatar component clause 150]
153. ~1 | 2 [avatar split clause 80,150,146]
204. 13 <=> calm(fred) [avatar definition]
225. 18 <=> ! [X1] : rich(X1) [avatar definition]
226. rich(X1) <- (18) [avatar component clause 225]
229. 18 | 13 [avatar split clause 110,204,225]
314. ~13 [avatar split clause 142,204]
316. $false <- (~1, 18) [subsumption resolution 148,226]
317. 1 | ~18 [avatar contradiction clause 316]
322. ~rich(sK0) <- (2) [resolution 85,152]
323. $false <- (2, 18) [subsumption resolution 322,226]
324. ~2 | ~18 [avatar contradiction clause 323]
325. $false [avatar sat refutation 153,229,314,317,324]
% SZS output end Proof for 1375743112358653222103491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not brave is both not kind and kind.
If someone is either calm or tall then someone is funny and vice versa.
Everyone who is not calm or quiet is both not wise and not generous.
If susan is not calm then someone is both not humble and not rich.
Everyone who is both not patient and not humble is not old or curious.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Someone is not rich or not funny.
Lucy is either rich or happy.
Mary is not quiet.
Fred is either rich or curious.
Mary is both tall and not humble.
Someone is either not quiet or not creative. | Susan is not generous. | entailment | (![X]:((brave(X)&~brave(X))=>(~kind(X)&kind(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|quiet(X))=>(~wise(X)&~generous(X))))&
((~calm(susan))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((~patient(X)&~humble(X))=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(?[X]:((~rich(X)|~funny(X))))&
((rich(lucy)<~>happy(lucy)))&
(~quiet(mary))&
((rich(fred)<~>curious(fred)))&
((tall(mary)&~humble(mary)))&
(?[X]:((~quiet(X)<~>~creative(X)))) | ~generous(susan) | [
"p2",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 881422894821036006638291
% SZS output start Proof for 881422894821036006638291
3. ! [X0] : ((quiet(X0) | ~calm(X0)) => (~generous(X0) & ~wise(X0))) [input p2]
11. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p10]
12. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p11]
14. ? [X0] : (curious(X0) & brave(X0)) <=> (curious(susan) | ~humble(susan)) [input p13]
23. generous(susan) [input hypothesis]
31. ! [X0] : ((~generous(X0) & ~wise(X0)) | (~quiet(X0) & calm(X0))) [ennf transformation 3]
53. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 11]
54. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 53]
55. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 12]
56. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 55]
59. (? [X0] : (curious(X0) & brave(X0)) | (~curious(susan) & humble(susan))) & ((curious(susan) | ~humble(susan)) | ! [X0] : (~curious(X0) | ~brave(X0))) [nnf transformation 14]
60. (? [X0] : (curious(X0) & brave(X0)) | (~curious(susan) & humble(susan))) & (curious(susan) | ~humble(susan) | ! [X0] : (~curious(X0) | ~brave(X0))) [flattening 59]
61. (? [X0] : (curious(X0) & brave(X0)) | (~curious(susan) & humble(susan))) & (curious(susan) | ~humble(susan) | ! [X1] : (~curious(X1) | ~brave(X1))) [rectify 60]
62. ? [X0] : (curious(X0) & brave(X0)) => (curious(sK5) & brave(sK5)) [choice axiom]
63. ((curious(sK5) & brave(sK5)) | (~curious(susan) & humble(susan))) & (curious(susan) | ~humble(susan) | ! [X1] : (~curious(X1) | ~brave(X1))) [skolemisation 61,62]
81. ~generous(X0) | calm(X0) [cnf transformation 31]
106. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 54]
110. ~calm(X0) | curious(X0) [cnf transformation 56]
121. brave(sK5) | ~curious(susan) [cnf transformation 63]
123. curious(sK5) | ~curious(susan) [cnf transformation 63]
137. generous(susan) [cnf transformation 23]
139. ~curious(X0) | ~brave(X0) [duplicate literal removal 106]
166. 7 <=> calm(susan) [avatar definition]
168. calm(susan) <- (7) [avatar component clause 166]
215. 17 <=> curious(susan) [avatar definition]
219. 18 <=> curious(sK5) [avatar definition]
221. curious(sK5) <- (18) [avatar component clause 219]
222. ~17 | 18 [avatar split clause 123,219,215]
229. 20 <=> brave(sK5) [avatar definition]
231. brave(sK5) <- (20) [avatar component clause 229]
232. ~17 | 20 [avatar split clause 121,229,215]
265. calm(susan) [resolution 81,137]
267. 7 [avatar split clause 265,166]
277. curious(susan) <- (7) [resolution 110,168]
280. 17 | ~7 [avatar split clause 277,166,215]
287. ~brave(sK5) <- (18) [resolution 139,221]
289. $false <- (18, 20) [subsumption resolution 287,231]
290. ~18 | ~20 [avatar contradiction clause 289]
291. $false [avatar sat refutation 222,232,267,280,290]
% SZS output end Proof for 881422894821036006638291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or tall is both funny and not brave and vice versa.
If someone is both not curious and patient then someone is not rich and vice versa.
If alice is curious or not quiet then paul is both not wise and humble.
Everyone who is both creative and funny is both not creative and not curious.
If someone is curious or not wise then someone is not rich or patient and vice versa.
If john is wise or not generous then lucy is both not kind and happy.
Everyone who is both generous and not rich is rich and vice versa.
If lucy is quiet then someone is not brave or happy and vice versa.
Everyone who is either not wise or creative is both rich and wise.
Everyone who is either humble or patient is not generous.
If someone is curious then lucy is both generous and old.
If someone is either old or not rich then someone is either not rich or not wise.
Everyone who is not patient is strong.
If susan is not brave or not wise then someone is not quiet.
If someone is not funny or rich then mary is not wise.
Everyone who is rich is not funny.
Susan is patient.
Someone is either creative or not kind.
Someone is either not kind or strong.
Paul is not quiet or not funny.
Paul is curious or humble.
Someone is brave. | Mary is wise. | contradiction | (![X]:((happy(X)|tall(X))<=>(funny(X)&~brave(X))))&
((?[X]:((~curious(X)&patient(X))))<=>(?[X]:(~rich(X))))&
(((curious(alice)|~quiet(alice)))=>((~wise(paul)&humble(paul))))&
(![X]:((creative(X)&funny(X))=>(~creative(X)&~curious(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~rich(X)|patient(X)))))&
(((wise(john)|~generous(john)))=>((~kind(lucy)&happy(lucy))))&
(![X]:((generous(X)&~rich(X))<=>rich(X)))&
((quiet(lucy))<=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:((~wise(X)<~>creative(X))=>(rich(X)&wise(X))))&
(![X]:((humble(X)<~>patient(X))=>~generous(X)))&
((?[X]:(curious(X)))=>((generous(lucy)&old(lucy))))&
((?[X]:((old(X)<~>~rich(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:(~patient(X)=>strong(X)))&
(((~brave(susan)|~wise(susan)))=>(?[X]:(~quiet(X))))&
((?[X]:((~funny(X)|rich(X))))=>(~wise(mary)))&
(![X]:(rich(X)=>~funny(X)))&
(patient(susan))&
(?[X]:((creative(X)<~>~kind(X))))&
(?[X]:((~kind(X)<~>strong(X))))&
((~quiet(paul)|~funny(paul)))&
((curious(paul)|humble(paul)))&
(?[X]:(brave(X))) | wise(mary) | [
"p3",
"p4",
"p6",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5488952745863162867546366
% SZS output start Proof for 5488952745863162867546366
4. ! [X0] : ((funny(X0) & creative(X0)) => (~curious(X0) & ~creative(X0))) [input p3]
5. ? [X0] : (~wise(X0) | curious(X0)) <=> ? [X0] : (patient(X0) | ~rich(X0)) [input p4]
7. ! [X0] : ((~rich(X0) & generous(X0)) <=> rich(X0)) [input p6]
9. ! [X0] : ((~wise(X0) <~> creative(X0)) => (wise(X0) & rich(X0))) [input p8]
11. ? [X0] : curious(X0) => (old(lucy) & generous(lucy)) [input p10]
15. ? [X0] : (rich(X0) | ~funny(X0)) => ~wise(mary) [input p14]
23. wise(mary) [input hypothesis]
25. ? [X0] : (~wise(X0) | curious(X0)) <=> ? [X1] : (patient(X1) | ~rich(X1)) [rectify 5]
28. ! [X0] : ((~curious(X0) & ~creative(X0)) | (~funny(X0) | ~creative(X0))) [ennf transformation 4]
29. ! [X0] : ((~curious(X0) & ~creative(X0)) | ~funny(X0) | ~creative(X0)) [flattening 28]
31. ! [X0] : ((wise(X0) & rich(X0)) | (~wise(X0) <=> creative(X0))) [ennf transformation 9]
33. (old(lucy) & generous(lucy)) | ! [X0] : ~curious(X0) [ennf transformation 11]
37. ~wise(mary) | ! [X0] : (~rich(X0) & funny(X0)) [ennf transformation 15]
46. (? [X0] : (~wise(X0) | curious(X0)) | ! [X1] : (~patient(X1) & rich(X1))) & (? [X1] : (patient(X1) | ~rich(X1)) | ! [X0] : (wise(X0) & ~curious(X0))) [nnf transformation 25]
47. (? [X0] : (~wise(X0) | curious(X0)) | ! [X1] : (~patient(X1) & rich(X1))) & (? [X2] : (patient(X2) | ~rich(X2)) | ! [X3] : (wise(X3) & ~curious(X3))) [rectify 46]
48. ? [X0] : (~wise(X0) | curious(X0)) => (~wise(sK2) | curious(sK2)) [choice axiom]
49. ? [X2] : (patient(X2) | ~rich(X2)) => (patient(sK3) | ~rich(sK3)) [choice axiom]
50. ((~wise(sK2) | curious(sK2)) | ! [X1] : (~patient(X1) & rich(X1))) & ((patient(sK3) | ~rich(sK3)) | ! [X3] : (wise(X3) & ~curious(X3))) [skolemisation 47,49,48]
51. ! [X0] : (((~rich(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) | ~generous(X0)))) [nnf transformation 7]
52. ! [X0] : (((~rich(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | rich(X0) | ~generous(X0))) [flattening 51]
57. ! [X0] : ((wise(X0) & rich(X0)) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0)))) [nnf transformation 31]
85. ~creative(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 29]
89. ~wise(sK2) | curious(sK2) | rich(X1) [cnf transformation 50]
95. rich(X0) | rich(X0) | ~generous(X0) [cnf transformation 52]
97. ~rich(X0) | ~rich(X0) [cnf transformation 52]
103. wise(X0) | creative(X0) | wise(X0) [cnf transformation 57]
107. generous(lucy) | ~curious(X0) [cnf transformation 33]
116. ~wise(mary) | funny(X0) [cnf transformation 37]
127. wise(mary) [cnf transformation 23]
128. creative(X0) | wise(X0) [duplicate literal removal 103]
129. rich(X0) | ~generous(X0) [duplicate literal removal 95]
130. ~rich(X0) [duplicate literal removal 97]
131. ~creative(X0) | ~funny(X0) [duplicate literal removal 85]
133. 1 <=> ! [X1] : rich(X1) [avatar definition]
134. rich(X1) <- (1) [avatar component clause 133]
177. 11 <=> curious(sK2) [avatar definition]
179. curious(sK2) <- (11) [avatar component clause 177]
181. 12 <=> wise(sK2) [avatar definition]
183. ~wise(sK2) <- (~12) [avatar component clause 181]
185. 1 | 11 | ~12 [avatar split clause 89,181,177,133]
187. 13 <=> ! [X3] : wise(X3) [avatar definition]
188. wise(X3) <- (13) [avatar component clause 187]
199. 16 <=> ! [X3] : ~curious(X3) [avatar definition]
200. ~curious(X3) <- (16) [avatar component clause 199]
222. ~generous(X0) [subsumption resolution 129,130]
247. ~curious(X0) [subsumption resolution 107,222]
248. 16 [avatar split clause 247,199]
274. 31 <=> ! [X0] : funny(X0) [avatar definition]
275. funny(X0) <- (31) [avatar component clause 274]
277. 32 <=> wise(mary) [avatar definition]
280. 31 | ~32 [avatar split clause 116,277,274]
315. 32 [avatar split clause 127,277]
325. ~funny(X0) | wise(X0) [resolution 131,128]
326. wise(X0) <- (31) [subsumption resolution 325,275]
327. 13 | ~31 [avatar split clause 326,274,187]
329. $false <- (~12, 13) [resolution 188,183]
332. 12 | ~13 [avatar contradiction clause 329]
334. $false <- (11, 16) [subsumption resolution 179,200]
335. ~11 | ~16 [avatar contradiction clause 334]
336. $false <- (1) [subsumption resolution 134,130]
337. ~1 [avatar contradiction clause 336]
338. $false [avatar sat refutation 185,248,280,315,327,332,335,337]
% SZS output end Proof for 5488952745863162867546366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not old is not quiet or humble and vice versa.
Everyone who is not strong or wise is not brave.
If lucy is not humble or not old then mary is both brave and kind and vice versa.
Everyone who is either not calm or calm is both not creative and not old and vice versa.
If someone is both not quiet and strong then someone is either not quiet or not creative.
Everyone who is both not quiet and not humble is either not rich or generous.
If susan is not rich or not calm then john is creative.
Everyone who is both patient and curious is not tall.
Everyone who is either not strong or not old is not tall.
If someone is calm or kind then someone is either not tall or kind.
Everyone who is not humble is either funny or not calm and vice versa.
If someone is either not wise or not calm then someone is either tall or not brave and vice versa.
Everyone who is patient or curious is both creative and not old and vice versa.
Everyone who is not calm or not quiet is either not patient or not creative.
If someone is either not generous or curious then lucy is not brave or funny.
Susan is happy.
Alice is both wise and humble.
Susan is both strong and not generous.
Alice is either happy or not strong.
Alice is either calm or rich.
Someone is not brave.
Mary is either patient or not patient. | Mary is not calm. | contradiction | (![X]:((~creative(X)&~old(X))<=>(~quiet(X)|humble(X))))&
(![X]:((~strong(X)|wise(X))=>~brave(X)))&
(((~humble(lucy)|~old(lucy)))<=>((brave(mary)&kind(mary))))&
(![X]:((~calm(X)<~>calm(X))<=>(~creative(X)&~old(X))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(![X]:((~quiet(X)&~humble(X))=>(~rich(X)<~>generous(X))))&
(((~rich(susan)|~calm(susan)))=>(creative(john)))&
(![X]:((patient(X)&curious(X))=>~tall(X)))&
(![X]:((~strong(X)<~>~old(X))=>~tall(X)))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:(~humble(X)<=>(funny(X)<~>~calm(X))))&
((?[X]:((~wise(X)<~>~calm(X))))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(![X]:((patient(X)|curious(X))<=>(creative(X)&~old(X))))&
(![X]:((~calm(X)|~quiet(X))=>(~patient(X)<~>~creative(X))))&
((?[X]:((~generous(X)<~>curious(X))))=>((~brave(lucy)|funny(lucy))))&
(happy(susan))&
((wise(alice)&humble(alice)))&
((strong(susan)&~generous(susan)))&
((happy(alice)<~>~strong(alice)))&
((calm(alice)<~>rich(alice)))&
(?[X]:(~brave(X)))&
((patient(mary)<~>~patient(mary))) | ~calm(mary) | [
"p3",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6057368994689009358301
% SZS output start Proof for 6057368994689009358301
4. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (~old(X0) & ~creative(X0))) [input p3]
13. ! [X0] : ((curious(X0) | patient(X0)) <=> (~old(X0) & creative(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (~patient(X0) <~> ~creative(X0))) [input p13]
23. ~calm(mary) [input hypothesis]
36. ! [X0] : ((~patient(X0) <~> ~creative(X0)) | (quiet(X0) & calm(X0))) [ennf transformation 14]
43. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [flattening 43]
61. ! [X0] : (((curious(X0) | patient(X0)) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | (~curious(X0) & ~patient(X0)))) [nnf transformation 13]
62. ! [X0] : ((curious(X0) | patient(X0) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | (~curious(X0) & ~patient(X0)))) [flattening 61]
63. ! [X0] : (((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | (quiet(X0) & calm(X0))) [nnf transformation 36]
82. ~creative(X0) | calm(X0) | calm(X0) [cnf transformation 44]
83. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 44]
113. creative(X0) | ~patient(X0) [cnf transformation 62]
120. creative(X0) | patient(X0) | calm(X0) [cnf transformation 63]
136. ~calm(mary) [cnf transformation 23]
137. ~creative(X0) | calm(X0) [duplicate literal removal 82]
138. ~creative(X0) | ~calm(X0) [duplicate literal removal 83]
162. ~creative(X0) [subsumption resolution 137,138]
230. ~patient(X0) [subsumption resolution 113,162]
233. patient(X0) | calm(X0) [subsumption resolution 120,162]
234. calm(X0) [subsumption resolution 233,230]
259. $false [subsumption resolution 136,234]
% SZS output end Proof for 6057368994689009358301
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not tall or quiet then fred is patient and vice versa.
If someone is not patient then lucy is funny or not kind.
If someone is not humble then paul is funny and vice versa.
Everyone who is both strong and quiet is both not tall and not rich.
If someone is happy then someone is both not happy and not humble.
Everyone who is patient is not brave or tall and vice versa.
Everyone who is either not strong or not brave is happy or not curious and vice versa.
If mary is not kind then susan is either not strong or tall.
If susan is either not funny or not kind then someone is either not tall or not old and vice versa.
If susan is creative or tall then someone is either not calm or not funny and vice versa.
Everyone who is not rich or brave is both strong and old and vice versa.
If someone is kind or brave then john is both quiet and calm and vice versa.
If someone is quiet then paul is both not quiet and patient and vice versa.
If someone is both old and not quiet then someone is either not wise or humble and vice versa.
Everyone who is either happy or not happy is both not funny and strong.
If someone is generous or brave then someone is both funny and brave.
Someone is creative.
Susan is strong.
Someone is quiet or brave.
Susan is both old and strong.
Someone is either funny or kind. | Paul is not happy. | entailment | ((?[X]:((~tall(X)<~>quiet(X))))<=>(patient(fred)))&
((?[X]:(~patient(X)))=>((funny(lucy)|~kind(lucy))))&
((?[X]:(~humble(X)))<=>(funny(paul)))&
(![X]:((strong(X)&quiet(X))=>(~tall(X)&~rich(X))))&
((?[X]:(happy(X)))=>(?[X]:((~happy(X)&~humble(X)))))&
(![X]:(patient(X)<=>(~brave(X)|tall(X))))&
(![X]:((~strong(X)<~>~brave(X))<=>(happy(X)|~curious(X))))&
((~kind(mary))=>((~strong(susan)<~>tall(susan))))&
(((~funny(susan)<~>~kind(susan)))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(((creative(susan)|tall(susan)))<=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((~rich(X)|brave(X))<=>(strong(X)&old(X))))&
((?[X]:((kind(X)|brave(X))))<=>((quiet(john)&calm(john))))&
((?[X]:(quiet(X)))<=>((~quiet(paul)&patient(paul))))&
((?[X]:((old(X)&~quiet(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((happy(X)<~>~happy(X))=>(~funny(X)&strong(X))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((funny(X)&brave(X)))))&
(?[X]:(creative(X)))&
(strong(susan))&
(?[X]:((quiet(X)|brave(X))))&
((old(susan)&strong(susan)))&
(?[X]:((funny(X)<~>kind(X)))) | ~happy(paul) | [
"p2",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4308613083706565994580890
% SZS output start Proof for 4308613083706565994580890
3. ? [X0] : ~humble(X0) <=> funny(paul) [input p2]
5. ? [X0] : happy(X0) => ? [X0] : (~humble(X0) & ~happy(X0)) [input p4]
15. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (strong(X0) & ~funny(X0))) [input p14]
22. happy(paul) [input hypothesis]
23. ? [X0] : happy(X0) => ? [X1] : (~humble(X1) & ~happy(X1)) [rectify 5]
31. ? [X1] : (~humble(X1) & ~happy(X1)) | ! [X0] : ~happy(X0) [ennf transformation 23]
33. ! [X0] : ((strong(X0) & ~funny(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 15]
39. (? [X0] : ~humble(X0) | ~funny(paul)) & (funny(paul) | ! [X0] : humble(X0)) [nnf transformation 3]
40. (? [X0] : ~humble(X0) | ~funny(paul)) & (funny(paul) | ! [X1] : humble(X1)) [rectify 39]
41. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
42. (~humble(sK1) | ~funny(paul)) & (funny(paul) | ! [X1] : humble(X1)) [skolemisation 40,41]
43. ? [X0] : (~humble(X0) & ~happy(X0)) | ! [X1] : ~happy(X1) [rectify 31]
44. ? [X0] : (~humble(X0) & ~happy(X0)) => (~humble(sK2) & ~happy(sK2)) [choice axiom]
45. (~humble(sK2) & ~happy(sK2)) | ! [X1] : ~happy(X1) [skolemisation 43,44]
77. ! [X0] : ((strong(X0) & ~funny(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 33]
93. funny(paul) | humble(X1) [cnf transformation 42]
98. ~humble(sK2) | ~happy(X1) [cnf transformation 45]
143. ~funny(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 77]
144. ~funny(X0) | happy(X0) | happy(X0) [cnf transformation 77]
156. happy(paul) [cnf transformation 22]
157. ~funny(X0) | ~happy(X0) [duplicate literal removal 143]
158. ~funny(X0) | happy(X0) [duplicate literal removal 144]
196. 9 <=> funny(paul) [avatar definition]
197. funny(paul) <- (9) [avatar component clause 196]
205. 11 <=> ! [X1] : humble(X1) [avatar definition]
206. humble(X1) <- (11) [avatar component clause 205]
207. 11 | 9 [avatar split clause 93,196,205]
209. 12 <=> ! [X1] : ~happy(X1) [avatar definition]
210. ~happy(X1) <- (12) [avatar component clause 209]
212. 13 <=> humble(sK2) [avatar definition]
214. ~humble(sK2) <- (~13) [avatar component clause 212]
215. 12 | ~13 [avatar split clause 98,212,209]
366. ~funny(X0) [subsumption resolution 157,158]
387. $false <- (9) [subsumption resolution 197,366]
388. ~9 [avatar contradiction clause 387]
391. $false <- (11, ~13) [resolution 214,206]
392. ~11 | 13 [avatar contradiction clause 391]
393. $false <- (12) [resolution 210,156]
394. ~12 [avatar contradiction clause 393]
395. $false [avatar sat refutation 207,215,388,392,394]
% SZS output end Proof for 4308613083706565994580890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not generous or not old then someone is not generous or humble.
Everyone who is both not tall and not quiet is not quiet and vice versa.
Everyone who is either creative or patient is either not tall or not happy.
Everyone who is curious is both not creative and funny.
If someone is not tall then alice is not generous and vice versa.
Everyone who is not patient or rich is wise.
Everyone who is both not quiet and old is either not creative or not old.
Everyone who is either not creative or humble is either not calm or not strong.
Everyone who is both not calm and patient is not brave and vice versa.
Everyone who is curious is not curious or old and vice versa.
Everyone who is either not funny or not old is not kind or not tall and vice versa.
If someone is tall or not kind then someone is curious or not curious and vice versa.
Everyone who is either tall or not kind is curious and vice versa.
Everyone who is either not strong or not rich is either not wise or not funny and vice versa.
Everyone who is not strong is calm or curious and vice versa.
Everyone who is both not curious and kind is both curious and not happy.
John is curious or not funny.
Someone is either wise or rich.
Mary is either kind or not brave.
Mary is both kind and not calm.
John is either not tall or not happy. | Mary is not humble. | contradiction | (((~generous(paul)<~>~old(paul)))=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~tall(X)&~quiet(X))<=>~quiet(X)))&
(![X]:((creative(X)<~>patient(X))=>(~tall(X)<~>~happy(X))))&
(![X]:(curious(X)=>(~creative(X)&funny(X))))&
((?[X]:(~tall(X)))<=>(~generous(alice)))&
(![X]:((~patient(X)|rich(X))=>wise(X)))&
(![X]:((~quiet(X)&old(X))=>(~creative(X)<~>~old(X))))&
(![X]:((~creative(X)<~>humble(X))=>(~calm(X)<~>~strong(X))))&
(![X]:((~calm(X)&patient(X))<=>~brave(X)))&
(![X]:(curious(X)<=>(~curious(X)|old(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(~kind(X)|~tall(X))))&
((?[X]:((tall(X)|~kind(X))))<=>(?[X]:((curious(X)|~curious(X)))))&
(![X]:((tall(X)<~>~kind(X))<=>curious(X)))&
(![X]:((~strong(X)<~>~rich(X))<=>(~wise(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(calm(X)|curious(X))))&
(![X]:((~curious(X)&kind(X))=>(curious(X)&~happy(X))))&
((curious(john)|~funny(john)))&
(?[X]:((wise(X)<~>rich(X))))&
((kind(mary)<~>~brave(mary)))&
((kind(mary)&~calm(mary)))&
((~tall(john)<~>~happy(john))) | ~humble(mary) | [
"p3",
"p7",
"p9",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1879905730175462546496398
% SZS output start Proof for 1879905730175462546496398
4. ! [X0] : (curious(X0) => (funny(X0) & ~creative(X0))) [input p3]
8. ! [X0] : ((~creative(X0) <~> humble(X0)) => (~calm(X0) <~> ~strong(X0))) [input p7]
10. ! [X0] : (curious(X0) <=> (old(X0) | ~curious(X0))) [input p9]
15. ! [X0] : (~strong(X0) <=> (curious(X0) | calm(X0))) [input p14]
20. ~calm(mary) & kind(mary) [input p19]
22. ~humble(mary) [input hypothesis]
26. ! [X0] : ((funny(X0) & ~creative(X0)) | ~curious(X0)) [ennf transformation 4]
30. ! [X0] : ((~calm(X0) <~> ~strong(X0)) | (~creative(X0) <=> humble(X0))) [ennf transformation 8]
44. ! [X0] : (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) [nnf transformation 30]
47. ! [X0] : ((curious(X0) | (~old(X0) & curious(X0))) & ((old(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 10]
48. ! [X0] : ((curious(X0) | (~old(X0) & curious(X0))) & (old(X0) | ~curious(X0) | ~curious(X0))) [flattening 47]
58. ! [X0] : ((~strong(X0) | (~curious(X0) & ~calm(X0))) & ((curious(X0) | calm(X0)) | strong(X0))) [nnf transformation 15]
59. ! [X0] : ((~strong(X0) | (~curious(X0) & ~calm(X0))) & (curious(X0) | calm(X0) | strong(X0))) [flattening 58]
74. ~curious(X0) | ~creative(X0) [cnf transformation 26]
84. strong(X0) | calm(X0) | humble(X0) | creative(X0) [cnf transformation 44]
90. curious(X0) | curious(X0) [cnf transformation 48]
116. ~strong(X0) | ~curious(X0) [cnf transformation 59]
125. ~calm(mary) [cnf transformation 20]
128. ~humble(mary) [cnf transformation 22]
131. curious(X0) [duplicate literal removal 90]
184. ~strong(X0) [subsumption resolution 116,131]
209. ~creative(X0) [resolution 74,131]
235. calm(X4) | humble(X4) | creative(X4) [resolution 84,184]
237. calm(X4) | humble(X4) [subsumption resolution 235,209]
238. humble(mary) [resolution 237,125]
240. $false [subsumption resolution 238,128]
% SZS output end Proof for 1879905730175462546496398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either generous or calm then someone is humble.
If alice is humble then someone is both not generous and funny.
If fred is either generous or not quiet then someone is brave.
Everyone who is not kind is both not wise and not strong and vice versa.
If mary is not calm then someone is not funny and vice versa.
Everyone who is either not funny or not wise is both not kind and happy and vice versa.
Everyone who is happy or strong is happy and vice versa.
Everyone who is kind or not generous is humble.
If someone is both old and not patient then someone is not humble or not creative.
If john is not calm or patient then susan is happy.
Everyone who is not wise or not tall is both not kind and not humble and vice versa.
If john is both calm and wise then fred is either quiet or brave and vice versa.
Everyone who is either not patient or not happy is patient and vice versa.
If someone is both kind and rich then susan is humble and vice versa.
Everyone who is rich is not patient and vice versa.
If someone is both tall and not quiet then someone is not creative or not strong and vice versa.
Someone is patient.
Someone is both not patient and not funny.
Someone is not quiet or not creative.
Someone is either not strong or tall.
Someone is either not tall or not humble.
Fred is both not quiet and not happy.
Someone is not strong or not patient.
Fred is both not rich and wise. | Mary is strong. | contradiction | ((?[X]:((generous(X)<~>calm(X))))=>(?[X]:(humble(X))))&
((humble(alice))=>(?[X]:((~generous(X)&funny(X)))))&
(((generous(fred)<~>~quiet(fred)))=>(?[X]:(brave(X))))&
(![X]:(~kind(X)<=>(~wise(X)&~strong(X))))&
((~calm(mary))<=>(?[X]:(~funny(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>(~kind(X)&happy(X))))&
(![X]:((happy(X)|strong(X))<=>happy(X)))&
(![X]:((kind(X)|~generous(X))=>humble(X)))&
((?[X]:((old(X)&~patient(X))))=>(?[X]:((~humble(X)|~creative(X)))))&
(((~calm(john)|patient(john)))=>(happy(susan)))&
(![X]:((~wise(X)|~tall(X))<=>(~kind(X)&~humble(X))))&
(((calm(john)&wise(john)))<=>((quiet(fred)<~>brave(fred))))&
(![X]:((~patient(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((kind(X)&rich(X))))<=>(humble(susan)))&
(![X]:(rich(X)<=>~patient(X)))&
((?[X]:((tall(X)&~quiet(X))))<=>(?[X]:((~creative(X)|~strong(X)))))&
(?[X]:(patient(X)))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((~quiet(X)|~creative(X))))&
(?[X]:((~strong(X)<~>tall(X))))&
(?[X]:((~tall(X)<~>~humble(X))))&
((~quiet(fred)&~happy(fred)))&
(?[X]:((~strong(X)|~patient(X))))&
((~rich(fred)&wise(fred))) | strong(mary) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 917631805456134757618846
% SZS output start Proof for 917631805456134757618846
7. ! [X0] : ((strong(X0) | happy(X0)) <=> happy(X0)) [input p6]
13. ! [X0] : ((~patient(X0) <~> ~happy(X0)) <=> patient(X0)) [input p12]
25. strong(mary) [input hypothesis]
52. ! [X0] : (((strong(X0) | happy(X0)) | ~happy(X0)) & (happy(X0) | (~strong(X0) & ~happy(X0)))) [nnf transformation 7]
53. ! [X0] : ((strong(X0) | happy(X0) | ~happy(X0)) & (happy(X0) | (~strong(X0) & ~happy(X0)))) [flattening 52]
58. ! [X0] : ((((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0))))) [nnf transformation 13]
101. ~strong(X0) | happy(X0) [cnf transformation 53]
118. patient(X0) | ~happy(X0) | patient(X0) [cnf transformation 58]
120. ~happy(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 58]
145. strong(mary) [cnf transformation 25]
146. patient(X0) | ~happy(X0) [duplicate literal removal 118]
147. ~happy(X0) | ~patient(X0) [duplicate literal removal 120]
231. ~happy(X0) [subsumption resolution 146,147]
319. happy(mary) [resolution 101,145]
320. $false [subsumption resolution 319,231]
% SZS output end Proof for 917631805456134757618846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both brave and wise and vice versa. If someone is calm then someone is either not humble or creative. If paul is both patient and not funny then someone is old or not old and vice versa. If john is not creative or not brave then someone is not patient. Everyone who is both happy and not brave is either not rich or not quiet. Everyone who is wise or not funny is both not kind and curious and vice versa. Everyone who is both humble and not generous is both not old and funny and vice versa. If john is not creative then susan is both old and kind and vice versa. If fred is either not strong or not generous then fred is either patient or not rich. Everyone who is both not funny and not brave is wise and vice versa. If lucy is both calm and not calm then someone is both wise and not funny. Everyone who is both old and not quiet is both not strong and not tall and vice versa. Everyone who is strong is either generous or strong. Everyone who is both calm and kind is either not curious or tall and vice versa. Everyone who is either not patient or not generous is happy or not tall and vice versa. If paul is quiet or happy then paul is not quiet. Someone is brave. Someone is curious or not funny. Someone is both not rich and old. Lucy is curious or not generous. John is both old and not generous. Someone is either happy or not rich. Someone is not patient. Someone is not happy or generous. | Fred is generous. | neutral | (![X]:(creative(X)<=>(brave(X)&wise(X))))&
((?[X]:(calm(X)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(((patient(paul)&~funny(paul)))<=>(?[X]:((old(X)|~old(X)))))&
(((~creative(john)|~brave(john)))=>(?[X]:(~patient(X))))&
(![X]:((happy(X)&~brave(X))=>(~rich(X)<~>~quiet(X))))&
(![X]:((wise(X)|~funny(X))<=>(~kind(X)&curious(X))))&
(![X]:((humble(X)&~generous(X))<=>(~old(X)&funny(X))))&
((~creative(john))<=>((old(susan)&kind(susan))))&
(((~strong(fred)<~>~generous(fred)))=>((patient(fred)<~>~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>wise(X)))&
(((calm(lucy)&~calm(lucy)))=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((old(X)&~quiet(X))<=>(~strong(X)&~tall(X))))&
(![X]:(strong(X)=>(generous(X)<~>strong(X))))&
(![X]:((calm(X)&kind(X))<=>(~curious(X)<~>tall(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>(happy(X)|~tall(X))))&
(((quiet(paul)|happy(paul)))=>(~quiet(paul)))&
(?[X]:(brave(X)))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:((~rich(X)&old(X))))&
((curious(lucy)|~generous(lucy)))&
((old(john)&~generous(john)))&
(?[X]:((happy(X)<~>~rich(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~happy(X)|generous(X)))) | generous(fred) | [] | null | 0 |
Everyone who is not generous or not rich is either generous or brave and vice versa.
If someone is both humble and not patient then susan is funny or generous and vice versa.
If alice is quiet then mary is calm.
Everyone who is not happy or not funny is either old or not tall and vice versa.
If john is not curious then john is both happy and not curious and vice versa.
Everyone who is not patient or not creative is not happy or strong and vice versa.
If someone is patient or not rich then alice is either brave or humble.
Everyone who is both not quiet and brave is funny and vice versa.
Everyone who is generous or patient is not generous and vice versa.
Everyone who is either wise or not tall is both old and generous and vice versa.
Everyone who is not generous is not funny.
If someone is both quiet and not humble then someone is happy.
If alice is either tall or funny then someone is either not wise or tall and vice versa.
If lucy is not creative then someone is quiet and vice versa.
Everyone who is not old or tall is both not generous and not creative and vice versa.
If someone is both humble and wise then someone is calm.
Mary is either creative or calm.
Someone is brave or not curious.
Someone is curious or not funny.
Fred is either not humble or not brave.
Susan is both not strong and humble.
Alice is happy.
Mary is not strong.
Someone is not generous or not tall. | Fred is not creative. | entailment | (![X]:((~generous(X)|~rich(X))<=>(generous(X)<~>brave(X))))&
((?[X]:((humble(X)&~patient(X))))<=>((funny(susan)|generous(susan))))&
((quiet(alice))=>(calm(mary)))&
(![X]:((~happy(X)|~funny(X))<=>(old(X)<~>~tall(X))))&
((~curious(john))<=>((happy(john)&~curious(john))))&
(![X]:((~patient(X)|~creative(X))<=>(~happy(X)|strong(X))))&
((?[X]:((patient(X)|~rich(X))))=>((brave(alice)<~>humble(alice))))&
(![X]:((~quiet(X)&brave(X))<=>funny(X)))&
(![X]:((generous(X)|patient(X))<=>~generous(X)))&
(![X]:((wise(X)<~>~tall(X))<=>(old(X)&generous(X))))&
(![X]:(~generous(X)=>~funny(X)))&
((?[X]:((quiet(X)&~humble(X))))=>(?[X]:(happy(X))))&
(((tall(alice)<~>funny(alice)))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((~creative(lucy))<=>(?[X]:(quiet(X))))&
(![X]:((~old(X)|tall(X))<=>(~generous(X)&~creative(X))))&
((?[X]:((humble(X)&wise(X))))=>(?[X]:(calm(X))))&
((creative(mary)<~>calm(mary)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((curious(X)|~funny(X))))&
((~humble(fred)<~>~brave(fred)))&
((~strong(susan)&humble(susan)))&
(happy(alice))&
(~strong(mary))&
(?[X]:((~generous(X)|~tall(X)))) | ~creative(fred) | [
"p3",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 478773404754583107237779
% SZS output start Proof for 478773404754583107237779
4. ! [X0] : ((~funny(X0) | ~happy(X0)) <=> (old(X0) <~> ~tall(X0))) [input p3]
9. ! [X0] : ((patient(X0) | generous(X0)) <=> ~generous(X0)) [input p8]
11. ! [X0] : (~generous(X0) => ~funny(X0)) [input p10]
15. ! [X0] : ((tall(X0) | ~old(X0)) <=> (~creative(X0) & ~generous(X0))) [input p14]
25. creative(fred) [input hypothesis]
30. ! [X0] : (~funny(X0) | generous(X0)) [ennf transformation 11]
40. ! [X0] : (((~funny(X0) | ~happy(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (funny(X0) & happy(X0)))) [nnf transformation 4]
41. ! [X0] : ((~funny(X0) | ~happy(X0) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (funny(X0) & happy(X0)))) [flattening 40]
49. ! [X0] : (((patient(X0) | generous(X0)) | generous(X0)) & (~generous(X0) | (~patient(X0) & ~generous(X0)))) [nnf transformation 9]
50. ! [X0] : ((patient(X0) | generous(X0) | generous(X0)) & (~generous(X0) | (~patient(X0) & ~generous(X0)))) [flattening 49]
64. ! [X0] : (((tall(X0) | ~old(X0)) | (creative(X0) | generous(X0))) & ((~creative(X0) & ~generous(X0)) | (~tall(X0) & old(X0)))) [nnf transformation 15]
65. ! [X0] : ((tall(X0) | ~old(X0) | creative(X0) | generous(X0)) & ((~creative(X0) & ~generous(X0)) | (~tall(X0) & old(X0)))) [flattening 64]
92. ~old(X0) | tall(X0) | funny(X0) [cnf transformation 41]
109. ~generous(X0) | ~generous(X0) [cnf transformation 50]
118. ~funny(X0) | generous(X0) [cnf transformation 30]
132. ~creative(X0) | old(X0) [cnf transformation 65]
133. ~creative(X0) | ~tall(X0) [cnf transformation 65]
147. creative(fred) [cnf transformation 25]
148. ~generous(X0) [duplicate literal removal 109]
214. ~funny(X0) [subsumption resolution 118,148]
286. old(fred) [resolution 132,147]
288. ~tall(fred) [resolution 133,147]
324. tall(fred) | funny(fred) [resolution 92,286]
326. funny(fred) [subsumption resolution 324,288]
327. $false [subsumption resolution 326,214]
% SZS output end Proof for 478773404754583107237779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or tall is not quiet.
Everyone who is either patient or brave is both not happy and wise.
If mary is tall then lucy is both not humble and happy.
If paul is both not happy and generous then someone is both not kind and wise.
Everyone who is quiet or tall is either rich or not funny.
Everyone who is wise or not funny is both happy and wise.
If alice is either not kind or wise then fred is both not calm and not strong.
Everyone who is either tall or strong is funny and vice versa.
Everyone who is either not wise or creative is not calm and vice versa.
If someone is not generous then someone is both curious and happy and vice versa.
Everyone who is not generous is either happy or not humble.
Everyone who is either not creative or old is either not creative or patient.
If someone is either happy or not calm then someone is either kind or funny.
Everyone who is either not creative or generous is not tall.
Everyone who is either calm or not happy is humble or quiet.
If someone is both funny and not humble then someone is both not kind and generous and vice versa.
Someone is either tall or funny.
Someone is not creative or rich.
Someone is either not kind or not calm.
Someone is both patient and happy.
Someone is both quiet and kind.
Someone is either not kind or not funny. | Mary is creative. | neutral | (![X]:((calm(X)<~>tall(X))=>~quiet(X)))&
(![X]:((patient(X)<~>brave(X))=>(~happy(X)&wise(X))))&
((tall(mary))=>((~humble(lucy)&happy(lucy))))&
(((~happy(paul)&generous(paul)))=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:((quiet(X)|tall(X))=>(rich(X)<~>~funny(X))))&
(![X]:((wise(X)|~funny(X))=>(happy(X)&wise(X))))&
(((~kind(alice)<~>wise(alice)))=>((~calm(fred)&~strong(fred))))&
(![X]:((tall(X)<~>strong(X))<=>funny(X)))&
(![X]:((~wise(X)<~>creative(X))<=>~calm(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((curious(X)&happy(X)))))&
(![X]:(~generous(X)=>(happy(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>old(X))=>(~creative(X)<~>patient(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:((~creative(X)<~>generous(X))=>~tall(X)))&
(![X]:((calm(X)<~>~happy(X))=>(humble(X)|quiet(X))))&
((?[X]:((funny(X)&~humble(X))))<=>(?[X]:((~kind(X)&generous(X)))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:((~kind(X)<~>~calm(X))))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:((quiet(X)&kind(X))))&
(?[X]:((~kind(X)<~>~funny(X)))) | creative(mary) | [] | null | 0 |
If someone is either not old or not strong then someone is both calm and old and vice versa.
Everyone who is both funny and not generous is not brave or curious and vice versa.
Everyone who is not quiet is both tall and calm.
Everyone who is both not wise and not kind is both calm and not kind and vice versa.
If someone is both rich and tall then someone is not creative or strong.
If lucy is both patient and not old then someone is not rich and vice versa.
If susan is both not curious and generous then lucy is either not curious or quiet and vice versa.
Everyone who is both not funny and strong is both not humble and humble and vice versa.
If someone is not creative or creative then someone is not funny and vice versa.
If someone is rich or not humble then alice is either not tall or not creative and vice versa.
If mary is both not happy and curious then susan is either not generous or not calm and vice versa.
Everyone who is patient is generous or not strong.
Everyone who is not old is both not calm and not strong.
Everyone who is either not generous or brave is both not old and not rich and vice versa.
Everyone who is not calm is not happy and vice versa.
Everyone who is humble is both tall and not rich.
Alice is patient.
Susan is both rich and not funny.
Susan is wise.
Paul is quiet or wise.
Someone is both not calm and rich.
John is not patient.
Alice is both quiet and generous.
Mary is either generous or not tall. | Alice is not happy. | entailment | ((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:((calm(X)&old(X)))))&
(![X]:((funny(X)&~generous(X))<=>(~brave(X)|curious(X))))&
(![X]:(~quiet(X)=>(tall(X)&calm(X))))&
(![X]:((~wise(X)&~kind(X))<=>(calm(X)&~kind(X))))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((~creative(X)|strong(X)))))&
(((patient(lucy)&~old(lucy)))<=>(?[X]:(~rich(X))))&
(((~curious(susan)&generous(susan)))<=>((~curious(lucy)<~>quiet(lucy))))&
(![X]:((~funny(X)&strong(X))<=>(~humble(X)&humble(X))))&
((?[X]:((~creative(X)|creative(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((rich(X)|~humble(X))))<=>((~tall(alice)<~>~creative(alice))))&
(((~happy(mary)&curious(mary)))<=>((~generous(susan)<~>~calm(susan))))&
(![X]:(patient(X)=>(generous(X)|~strong(X))))&
(![X]:(~old(X)=>(~calm(X)&~strong(X))))&
(![X]:((~generous(X)<~>brave(X))<=>(~old(X)&~rich(X))))&
(![X]:(~calm(X)<=>~happy(X)))&
(![X]:(humble(X)=>(tall(X)&~rich(X))))&
(patient(alice))&
((rich(susan)&~funny(susan)))&
(wise(susan))&
((quiet(paul)|wise(paul)))&
(?[X]:((~calm(X)&rich(X))))&
(~patient(john))&
((quiet(alice)&generous(alice)))&
((generous(mary)<~>~tall(mary))) | ~happy(alice) | [
"p1",
"p12",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3646590572514993524388120
% SZS output start Proof for 3646590572514993524388120
2. ! [X0] : ((~generous(X0) & funny(X0)) <=> (curious(X0) | ~brave(X0))) [input p1]
13. ! [X0] : (~old(X0) => (~strong(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> (~rich(X0) & ~old(X0))) [input p13]
15. ! [X0] : (~calm(X0) <=> ~happy(X0)) [input p14]
23. generous(alice) & quiet(alice) [input p22]
25. happy(alice) [input hypothesis]
33. ! [X0] : ((~strong(X0) & ~calm(X0)) | old(X0)) [ennf transformation 13]
40. ! [X0] : (((~generous(X0) & funny(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (generous(X0) | ~funny(X0)))) [nnf transformation 2]
41. ! [X0] : (((~generous(X0) & funny(X0)) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | generous(X0) | ~funny(X0))) [flattening 40]
67. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | (rich(X0) | old(X0))) & ((~rich(X0) & ~old(X0)) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 14]
68. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | rich(X0) | old(X0)) & ((~rich(X0) & ~old(X0)) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [flattening 67]
69. ! [X0] : ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))) [nnf transformation 15]
82. ~generous(X0) | brave(X0) [cnf transformation 41]
120. ~calm(X0) | old(X0) [cnf transformation 33]
123. ~old(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 68]
128. ~happy(X0) | calm(X0) [cnf transformation 69]
141. generous(alice) [cnf transformation 23]
144. happy(alice) [cnf transformation 25]
292. ~generous(X0) | ~old(X0) [subsumption resolution 123,82]
316. calm(alice) [resolution 128,144]
318. old(alice) [resolution 316,120]
332. ~old(alice) [resolution 292,141]
333. $false [subsumption resolution 332,318]
% SZS output end Proof for 3646590572514993524388120
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is wise then alice is either creative or not generous and vice versa.
Everyone who is either not old or not creative is either not calm or calm and vice versa.
Everyone who is rich is either not quiet or creative.
If someone is not curious or tall then fred is not old or not curious.
If lucy is not curious then someone is either not quiet or not strong and vice versa.
If someone is creative or not happy then fred is both brave and tall and vice versa.
Everyone who is rich or not patient is both curious and quiet.
Everyone who is both not wise and not generous is not brave or wise and vice versa.
If someone is both not creative and not funny then paul is not curious or not happy.
Everyone who is old or generous is not patient.
If someone is both not humble and happy then lucy is either not strong or creative and vice versa.
Everyone who is not old or happy is not tall.
If lucy is not curious then someone is strong.
If someone is not rich or old then alice is happy and vice versa.
If susan is not rich or quiet then someone is strong or not generous.
If someone is both creative and not funny then john is both funny and brave.
Mary is either not old or not tall.
Someone is calm or happy.
Lucy is not creative.
Mary is old or strong. | Paul is not humble. | contradiction | ((wise(paul))<=>((creative(alice)<~>~generous(alice))))&
(![X]:((~old(X)<~>~creative(X))<=>(~calm(X)<~>calm(X))))&
(![X]:(rich(X)=>(~quiet(X)<~>creative(X))))&
((?[X]:((~curious(X)|tall(X))))=>((~old(fred)|~curious(fred))))&
((~curious(lucy))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
((?[X]:((creative(X)|~happy(X))))<=>((brave(fred)&tall(fred))))&
(![X]:((rich(X)|~patient(X))=>(curious(X)&quiet(X))))&
(![X]:((~wise(X)&~generous(X))<=>(~brave(X)|wise(X))))&
((?[X]:((~creative(X)&~funny(X))))=>((~curious(paul)|~happy(paul))))&
(![X]:((old(X)|generous(X))=>~patient(X)))&
((?[X]:((~humble(X)&happy(X))))<=>((~strong(lucy)<~>creative(lucy))))&
(![X]:((~old(X)|happy(X))=>~tall(X)))&
((~curious(lucy))=>(?[X]:(strong(X))))&
((?[X]:((~rich(X)|old(X))))<=>(happy(alice)))&
(((~rich(susan)|quiet(susan)))=>(?[X]:((strong(X)|~generous(X)))))&
((?[X]:((creative(X)&~funny(X))))=>((funny(john)&brave(john))))&
((~old(mary)<~>~tall(mary)))&
(?[X]:((calm(X)|happy(X))))&
(~creative(lucy))&
((old(mary)|strong(mary))) | ~humble(paul) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7915708833009368676371075
% SZS output start Proof for 7915708833009368676371075
2. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> (~calm(X0) <~> calm(X0))) [input p1]
4. ? [X0] : (tall(X0) | ~curious(X0)) => (~curious(fred) | ~old(fred)) [input p3]
5. ~curious(lucy) <=> ? [X0] : (~quiet(X0) <~> ~strong(X0)) [input p4]
6. ? [X0] : (~happy(X0) | creative(X0)) <=> (tall(fred) & brave(fred)) [input p5]
7. ! [X0] : ((~patient(X0) | rich(X0)) => (quiet(X0) & curious(X0))) [input p6]
10. ! [X0] : ((generous(X0) | old(X0)) => ~patient(X0)) [input p9]
11. ? [X0] : (happy(X0) & ~humble(X0)) <=> (~strong(lucy) <~> creative(lucy)) [input p10]
12. ! [X0] : ((happy(X0) | ~old(X0)) => ~tall(X0)) [input p11]
19. ~creative(lucy) [input p18]
21. ~humble(paul) [input hypothesis]
25. (~curious(fred) | ~old(fred)) | ! [X0] : (~tall(X0) & curious(X0)) [ennf transformation 4]
26. ~curious(fred) | ~old(fred) | ! [X0] : (~tall(X0) & curious(X0)) [flattening 25]
27. ! [X0] : ((quiet(X0) & curious(X0)) | (patient(X0) & ~rich(X0))) [ennf transformation 7]
28. ! [X0] : (~patient(X0) | (~generous(X0) & ~old(X0))) [ennf transformation 10]
29. ! [X0] : (~tall(X0) | (~happy(X0) & old(X0))) [ennf transformation 12]
33. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 2]
35. (~curious(lucy) | ! [X0] : ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | curious(lucy)) [nnf transformation 5]
36. (~curious(lucy) | ! [X0] : ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (? [X1] : ((strong(X1) | quiet(X1)) & (~strong(X1) | ~quiet(X1))) | curious(lucy)) [rectify 35]
37. ? [X1] : ((strong(X1) | quiet(X1)) & (~strong(X1) | ~quiet(X1))) => ((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) [choice axiom]
38. (~curious(lucy) | ! [X0] : ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) | curious(lucy)) [skolemisation 36,37]
39. (? [X0] : (~happy(X0) | creative(X0)) | (~tall(fred) | ~brave(fred))) & ((tall(fred) & brave(fred)) | ! [X0] : (happy(X0) & ~creative(X0))) [nnf transformation 6]
40. (? [X0] : (~happy(X0) | creative(X0)) | ~tall(fred) | ~brave(fred)) & ((tall(fred) & brave(fred)) | ! [X0] : (happy(X0) & ~creative(X0))) [flattening 39]
41. (? [X0] : (~happy(X0) | creative(X0)) | ~tall(fred) | ~brave(fred)) & ((tall(fred) & brave(fred)) | ! [X1] : (happy(X1) & ~creative(X1))) [rectify 40]
42. ? [X0] : (~happy(X0) | creative(X0)) => (~happy(sK1) | creative(sK1)) [choice axiom]
43. ((~happy(sK1) | creative(sK1)) | ~tall(fred) | ~brave(fred)) & ((tall(fred) & brave(fred)) | ! [X1] : (happy(X1) & ~creative(X1))) [skolemisation 41,42]
46. (? [X0] : (happy(X0) & ~humble(X0)) | ((~strong(lucy) | ~creative(lucy)) & (creative(lucy) | strong(lucy)))) & (((~creative(lucy) | strong(lucy)) & (creative(lucy) | ~strong(lucy))) | ! [X0] : (~happy(X0) | humble(X0))) [nnf transformation 11]
47. (? [X0] : (happy(X0) & ~humble(X0)) | ((~strong(lucy) | ~creative(lucy)) & (creative(lucy) | strong(lucy)))) & (((~creative(lucy) | strong(lucy)) & (creative(lucy) | ~strong(lucy))) | ! [X1] : (~happy(X1) | humble(X1))) [rectify 46]
48. ? [X0] : (happy(X0) & ~humble(X0)) => (happy(sK2) & ~humble(sK2)) [choice axiom]
49. ((happy(sK2) & ~humble(sK2)) | ((~strong(lucy) | ~creative(lucy)) & (creative(lucy) | strong(lucy)))) & (((~creative(lucy) | strong(lucy)) & (creative(lucy) | ~strong(lucy))) | ! [X1] : (~happy(X1) | humble(X1))) [skolemisation 47,48]
71. creative(X0) | old(X0) | calm(X0) | calm(X0) [cnf transformation 33]
72. creative(X0) | old(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 33]
75. ~curious(fred) | ~old(fred) | curious(X0) [cnf transformation 26]
76. ~curious(fred) | ~old(fred) | ~tall(X0) [cnf transformation 26]
80. ~curious(lucy) | ~quiet(X0) | strong(X0) [cnf transformation 38]
83. tall(fred) | ~creative(X1) [cnf transformation 43]
84. tall(fred) | happy(X1) [cnf transformation 43]
87. patient(X0) | curious(X0) [cnf transformation 27]
89. patient(X0) | quiet(X0) [cnf transformation 27]
95. ~patient(X0) | ~old(X0) [cnf transformation 28]
97. creative(lucy) | ~strong(lucy) | ~happy(X1) | humble(X1) [cnf transformation 49]
103. ~tall(X0) | old(X0) [cnf transformation 29]
114. ~creative(lucy) [cnf transformation 19]
116. ~humble(paul) [cnf transformation 21]
121. creative(X0) | old(X0) | calm(X0) [duplicate literal removal 71]
122. ~calm(X0) | old(X0) | creative(X0) [duplicate literal removal 72]
139. old(X0) | creative(X0) [subsumption resolution 121,122]
142. 4 <=> ! [X0] : ~tall(X0) [avatar definition]
143. ~tall(X0) <- (4) [avatar component clause 142]
145. 5 <=> old(fred) [avatar definition]
146. old(fred) <- (5) [avatar component clause 145]
147. ~old(fred) <- (~5) [avatar component clause 145]
149. 6 <=> curious(fred) [avatar definition]
151. ~curious(fred) <- (~6) [avatar component clause 149]
152. 4 | ~5 | ~6 [avatar split clause 76,149,145,142]
154. 7 <=> ! [X0] : curious(X0) [avatar definition]
155. curious(X0) <- (7) [avatar component clause 154]
156. 7 | ~5 | ~6 [avatar split clause 75,149,145,154]
158. 8 <=> ! [X0] : (~quiet(X0) | strong(X0)) [avatar definition]
159. ~quiet(X0) | strong(X0) <- (8) [avatar component clause 158]
161. 9 <=> curious(lucy) [avatar definition]
163. ~curious(lucy) <- (~9) [avatar component clause 161]
164. 8 | ~9 [avatar split clause 80,161,158]
184. 14 <=> tall(fred) [avatar definition]
185. tall(fred) <- (14) [avatar component clause 184]
197. 17 <=> ! [X1] : happy(X1) [avatar definition]
198. happy(X1) <- (17) [avatar component clause 197]
199. 17 | 14 [avatar split clause 84,184,197]
201. 18 <=> ! [X1] : ~creative(X1) [avatar definition]
202. ~creative(X1) <- (18) [avatar component clause 201]
203. 18 | 14 [avatar split clause 83,184,201]
208. 19 <=> creative(lucy) [avatar definition]
212. 20 <=> strong(lucy) [avatar definition]
214. ~strong(lucy) <- (~20) [avatar component clause 212]
228. 23 <=> ! [X1] : (~happy(X1) | humble(X1)) [avatar definition]
229. ~happy(X1) | humble(X1) <- (23) [avatar component clause 228]
231. 23 | ~20 | 19 [avatar split clause 97,208,212,228]
287. ~19 [avatar split clause 114,208]
288. ~old(X0) | quiet(X0) [resolution 95,89]
289. ~old(X1) | curious(X1) [resolution 95,87]
292. old(fred) <- (14) [resolution 103,185]
295. 5 | ~14 [avatar split clause 292,184,145]
306. quiet(X0) | creative(X0) [resolution 288,139]
317. curious(fred) <- (5) [resolution 289,146]
319. $false <- (5, ~6) [subsumption resolution 317,151]
320. ~5 | 6 [avatar contradiction clause 319]
321. creative(fred) <- (~5) [resolution 147,139]
322. $false <- (~5, 18) [subsumption resolution 321,202]
323. 5 | ~18 [avatar contradiction clause 322]
348. creative(X1) | strong(X1) <- (8) [resolution 306,159]
351. strong(X1) <- (8, 18) [subsumption resolution 348,202]
354. $false <- (8, 18, ~20) [resolution 351,214]
356. ~8 | ~18 | 20 [avatar contradiction clause 354]
357. humble(X1) <- (17, 23) [subsumption resolution 229,198]
358. $false <- (17, 23) [resolution 357,116]
361. ~17 | ~23 [avatar contradiction clause 358]
362. $false <- (7, ~9) [subsumption resolution 163,155]
363. ~7 | 9 [avatar contradiction clause 362]
366. $false <- (4, 14) [subsumption resolution 185,143]
367. ~4 | ~14 [avatar contradiction clause 366]
368. $false [avatar sat refutation 152,156,164,199,203,231,287,295,320,323,356,361,363,367]
% SZS output end Proof for 7915708833009368676371075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not funny is strong or patient. If someone is either brave or not rich then mary is not humble or strong. If mary is not curious or calm then paul is not wise and vice versa. If someone is both creative and wise then mary is either wise or curious and vice versa. Everyone who is not happy or not rich is kind and vice versa. If fred is both happy and not patient then someone is wise. Everyone who is generous is not generous or not happy and vice versa. Everyone who is either not happy or quiet is not tall or brave and vice versa. Everyone who is generous or not curious is both not curious and not calm and vice versa. If someone is both wise and tall then alice is patient or not humble. If someone is both not happy and calm then alice is both not funny and not humble. If susan is not curious or calm then paul is both kind and not patient and vice versa. Everyone who is not rich or rich is rich or generous. Everyone who is not rich is either not wise or rich and vice versa. If someone is not humble then someone is both curious and humble. Fred is both humble and not funny. Paul is both not brave and strong. Susan is kind. Someone is tall. Someone is kind. Someone is not funny. | Susan is not tall. | neutral | (![X]:((old(X)|~funny(X))=>(strong(X)|patient(X))))&
((?[X]:((brave(X)<~>~rich(X))))=>((~humble(mary)|strong(mary))))&
(((~curious(mary)|calm(mary)))<=>(~wise(paul)))&
((?[X]:((creative(X)&wise(X))))<=>((wise(mary)<~>curious(mary))))&
(![X]:((~happy(X)|~rich(X))<=>kind(X)))&
(((happy(fred)&~patient(fred)))=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>(~generous(X)|~happy(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>(~tall(X)|brave(X))))&
(![X]:((generous(X)|~curious(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((wise(X)&tall(X))))=>((patient(alice)|~humble(alice))))&
((?[X]:((~happy(X)&calm(X))))=>((~funny(alice)&~humble(alice))))&
(((~curious(susan)|calm(susan)))<=>((kind(paul)&~patient(paul))))&
(![X]:((~rich(X)|rich(X))=>(rich(X)|generous(X))))&
(![X]:(~rich(X)<=>(~wise(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((curious(X)&humble(X)))))&
((humble(fred)&~funny(fred)))&
((~brave(paul)&strong(paul)))&
(kind(susan))&
(?[X]:(tall(X)))&
(?[X]:(kind(X)))&
(?[X]:(~funny(X))) | ~tall(susan) | [] | null | 0 |
If someone is either not rich or calm then someone is tall and vice versa.
Everyone who is not funny is creative and vice versa.
Everyone who is either brave or kind is not tall.
If mary is not calm or patient then someone is both not brave and not strong.
Everyone who is not curious is not generous or not old and vice versa.
If mary is both not happy and not brave then fred is not patient and vice versa.
Everyone who is not curious or not wise is both curious and not patient.
If john is not strong or rich then alice is creative or tall and vice versa.
Everyone who is both happy and wise is wise or not strong and vice versa.
Everyone who is both not funny and old is either brave or not generous and vice versa.
If someone is both creative and not happy then lucy is both not calm and rich.
Everyone who is rich is not calm and vice versa.
Everyone who is either not humble or not quiet is not kind or not old.
Lucy is not strong or not funny.
Someone is funny or not patient.
Someone is both kind and not tall.
Susan is not brave.
Susan is both old and not brave. | John is not curious. | contradiction | ((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:(tall(X))))&
(![X]:(~funny(X)<=>creative(X)))&
(![X]:((brave(X)<~>kind(X))=>~tall(X)))&
(((~calm(mary)|patient(mary)))=>(?[X]:((~brave(X)&~strong(X)))))&
(![X]:(~curious(X)<=>(~generous(X)|~old(X))))&
(((~happy(mary)&~brave(mary)))<=>(~patient(fred)))&
(![X]:((~curious(X)|~wise(X))=>(curious(X)&~patient(X))))&
(((~strong(john)|rich(john)))<=>((creative(alice)|tall(alice))))&
(![X]:((happy(X)&wise(X))<=>(wise(X)|~strong(X))))&
(![X]:((~funny(X)&old(X))<=>(brave(X)<~>~generous(X))))&
((?[X]:((creative(X)&~happy(X))))=>((~calm(lucy)&rich(lucy))))&
(![X]:(rich(X)<=>~calm(X)))&
(![X]:((~humble(X)<~>~quiet(X))=>(~kind(X)|~old(X))))&
((~strong(lucy)|~funny(lucy)))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:((kind(X)&~tall(X))))&
(~brave(susan))&
((old(susan)&~brave(susan))) | ~curious(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4709836925417309766371743
% SZS output start Proof for 4709836925417309766371743
7. ! [X0] : ((~wise(X0) | ~curious(X0)) => (~patient(X0) & curious(X0))) [input p6]
19. ~curious(john) [input hypothesis]
23. ! [X0] : ((~patient(X0) & curious(X0)) | (wise(X0) & curious(X0))) [ennf transformation 7]
70. curious(X0) | curious(X0) [cnf transformation 23]
102. ~curious(john) [cnf transformation 19]
103. curious(X0) [duplicate literal removal 70]
217. $false [subsumption resolution 102,103]
% SZS output end Proof for 4709836925417309766371743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is creative and vice versa.
Everyone who is either generous or calm is either rich or not calm.
If someone is either old or funny then someone is either old or not kind.
Everyone who is tall or not wise is both not humble and strong.
Everyone who is either curious or not brave is either not old or not kind.
Everyone who is either strong or generous is both not tall and not calm.
Everyone who is old or not generous is both calm and wise and vice versa.
Everyone who is either not quiet or generous is both wise and not calm and vice versa.
Everyone who is patient or calm is either curious or humble and vice versa.
If lucy is not happy then alice is either quiet or not patient.
Everyone who is calm or funny is not wise and vice versa.
If susan is both wise and brave then susan is both rich and not wise and vice versa.
Everyone who is both creative and quiet is patient or not calm and vice versa.
Everyone who is quiet or old is not funny and vice versa.
If fred is either generous or not humble then fred is curious or not tall and vice versa.
Everyone who is funny or not generous is patient and vice versa.
Someone is either not funny or not curious.
Someone is both not curious and generous.
Someone is not funny.
Fred is either not creative or brave.
Someone is not brave. | Susan is not strong. | neutral | (![X]:(~rich(X)<=>creative(X)))&
(![X]:((generous(X)<~>calm(X))=>(rich(X)<~>~calm(X))))&
((?[X]:((old(X)<~>funny(X))))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((tall(X)|~wise(X))=>(~humble(X)&strong(X))))&
(![X]:((curious(X)<~>~brave(X))=>(~old(X)<~>~kind(X))))&
(![X]:((strong(X)<~>generous(X))=>(~tall(X)&~calm(X))))&
(![X]:((old(X)|~generous(X))<=>(calm(X)&wise(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(wise(X)&~calm(X))))&
(![X]:((patient(X)|calm(X))<=>(curious(X)<~>humble(X))))&
((~happy(lucy))=>((quiet(alice)<~>~patient(alice))))&
(![X]:((calm(X)|funny(X))<=>~wise(X)))&
(((wise(susan)&brave(susan)))<=>((rich(susan)&~wise(susan))))&
(![X]:((creative(X)&quiet(X))<=>(patient(X)|~calm(X))))&
(![X]:((quiet(X)|old(X))<=>~funny(X)))&
(((generous(fred)<~>~humble(fred)))<=>((curious(fred)|~tall(fred))))&
(![X]:((funny(X)|~generous(X))<=>patient(X)))&
(?[X]:((~funny(X)<~>~curious(X))))&
(?[X]:((~curious(X)&generous(X))))&
(?[X]:(~funny(X)))&
((~creative(fred)<~>brave(fred)))&
(?[X]:(~brave(X))) | ~strong(susan) | [] | null | 0 |
Everyone who is either not happy or generous is not old or generous.
Everyone who is both not strong and not wise is not creative.
If someone is not tall then someone is not generous or not creative.
If someone is not patient or strong then someone is not tall or patient and vice versa.
If paul is curious then mary is either not brave or curious.
Everyone who is both calm and wise is either rich or wise and vice versa.
If paul is not humble then someone is both not curious and brave.
Everyone who is not brave or patient is both patient and not kind and vice versa.
If paul is calm or not old then alice is humble.
If mary is rich then susan is either not calm or brave and vice versa.
If someone is not wise or brave then someone is both kind and not rich and vice versa.
If paul is brave or happy then someone is either tall or not humble and vice versa.
Everyone who is either not old or strong is both not kind and not creative and vice versa.
Everyone who is both tall and not happy is both creative and not wise and vice versa.
Everyone who is either not wise or wise is wise.
Everyone who is not patient is both not happy and humble.
Someone is funny or not happy.
Susan is not creative or not curious.
Lucy is not wise or happy.
Someone is calm.
Someone is both strong and not funny.
Someone is either wise or not tall.
Someone is not brave or not old. | Susan is wise. | entailment | (![X]:((~happy(X)<~>generous(X))=>(~old(X)|generous(X))))&
(![X]:((~strong(X)&~wise(X))=>~creative(X)))&
((?[X]:(~tall(X)))=>(?[X]:((~generous(X)|~creative(X)))))&
((?[X]:((~patient(X)|strong(X))))<=>(?[X]:((~tall(X)|patient(X)))))&
((curious(paul))=>((~brave(mary)<~>curious(mary))))&
(![X]:((calm(X)&wise(X))<=>(rich(X)<~>wise(X))))&
((~humble(paul))=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:((~brave(X)|patient(X))<=>(patient(X)&~kind(X))))&
(((calm(paul)|~old(paul)))=>(humble(alice)))&
((rich(mary))<=>((~calm(susan)<~>brave(susan))))&
((?[X]:((~wise(X)|brave(X))))<=>(?[X]:((kind(X)&~rich(X)))))&
(((brave(paul)|happy(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:((~old(X)<~>strong(X))<=>(~kind(X)&~creative(X))))&
(![X]:((tall(X)&~happy(X))<=>(creative(X)&~wise(X))))&
(![X]:((~wise(X)<~>wise(X))=>wise(X)))&
(![X]:(~patient(X)=>(~happy(X)&humble(X))))&
(?[X]:((funny(X)|~happy(X))))&
((~creative(susan)|~curious(susan)))&
((~wise(lucy)|happy(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((strong(X)&~funny(X))))&
(?[X]:((wise(X)<~>~tall(X))))&
(?[X]:((~brave(X)|~old(X)))) | wise(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3263080398212245150825225
% SZS output start Proof for 3263080398212245150825225
15. ! [X0] : ((~wise(X0) <~> wise(X0)) => wise(X0)) [input p14]
24. ~wise(susan) [input hypothesis]
36. ! [X0] : (wise(X0) | (~wise(X0) <=> wise(X0))) [ennf transformation 15]
69. ! [X0] : (wise(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 36]
131. wise(X0) | wise(X0) | wise(X0) [cnf transformation 69]
144. ~wise(susan) [cnf transformation 24]
145. wise(X0) [duplicate literal removal 131]
271. 28 <=> ! [X3] : wise(X3) [avatar definition]
272. wise(X3) <- (28) [avatar component clause 271]
308. 28 [avatar split clause 145,271]
359. $false <- (28) [resolution 272,144]
360. ~28 [avatar contradiction clause 359]
361. $false [avatar sat refutation 308,360]
% SZS output end Proof for 3263080398212245150825225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or happy then someone is not generous and vice versa. Everyone who is not tall or rich is either creative or not curious. If someone is either not brave or not kind then alice is generous or not brave and vice versa. If someone is either not curious or rich then someone is either not curious or kind and vice versa. If someone is both not calm and not curious then lucy is not tall. Everyone who is not strong or strong is tall and vice versa. If someone is strong then someone is not kind and vice versa. If someone is either wise or not humble then someone is kind or tall and vice versa. If someone is either not generous or not calm then someone is either quiet or not patient. If fred is not curious then paul is not creative or tall and vice versa. Everyone who is both happy and not brave is not strong and vice versa. If someone is either not brave or humble then someone is either not humble or not rich. If someone is both not patient and not kind then lucy is either calm or patient. Everyone who is either not old or humble is both generous and not curious. Everyone who is wise is both brave and not old and vice versa. If susan is not tall or wise then someone is not humble or curious and vice versa. Lucy is wise. Someone is either wise or not wise. Someone is either not tall or not happy. Paul is not creative or not strong. Someone is either not kind or not rich. Fred is curious or not funny. Fred is both creative and not quiet. John is not quiet or funny. | Alice is tall. | entailment | ((?[X]:((brave(X)|happy(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)|rich(X))=>(creative(X)<~>~curious(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>((generous(alice)|~brave(alice))))&
((?[X]:((~curious(X)<~>rich(X))))<=>(?[X]:((~curious(X)<~>kind(X)))))&
((?[X]:((~calm(X)&~curious(X))))=>(~tall(lucy)))&
(![X]:((~strong(X)|strong(X))<=>tall(X)))&
((?[X]:(strong(X)))<=>(?[X]:(~kind(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:((kind(X)|tall(X)))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((quiet(X)<~>~patient(X)))))&
((~curious(fred))<=>((~creative(paul)|tall(paul))))&
(![X]:((happy(X)&~brave(X))<=>~strong(X)))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((~humble(X)<~>~rich(X)))))&
((?[X]:((~patient(X)&~kind(X))))=>((calm(lucy)<~>patient(lucy))))&
(![X]:((~old(X)<~>humble(X))=>(generous(X)&~curious(X))))&
(![X]:(wise(X)<=>(brave(X)&~old(X))))&
(((~tall(susan)|wise(susan)))<=>(?[X]:((~humble(X)|curious(X)))))&
(wise(lucy))&
(?[X]:((wise(X)<~>~wise(X))))&
(?[X]:((~tall(X)<~>~happy(X))))&
((~creative(paul)|~strong(paul)))&
(?[X]:((~kind(X)<~>~rich(X))))&
((curious(fred)|~funny(fred)))&
((creative(fred)&~quiet(fred)))&
((~quiet(john)|funny(john))) | tall(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6739266855752610316943367
% SZS output start Proof for 6739266855752610316943367
6. ! [X0] : ((strong(X0) | ~strong(X0)) <=> tall(X0)) [input p5]
25. ~tall(alice) [input hypothesis]
54. ! [X0] : (((strong(X0) | ~strong(X0)) | ~tall(X0)) & (tall(X0) | (~strong(X0) & strong(X0)))) [nnf transformation 6]
55. ! [X0] : ((strong(X0) | ~strong(X0) | ~tall(X0)) & (tall(X0) | (~strong(X0) & strong(X0)))) [flattening 54]
118. tall(X0) | strong(X0) [cnf transformation 55]
119. tall(X0) | ~strong(X0) [cnf transformation 55]
168. ~tall(alice) [cnf transformation 25]
265. tall(X0) [subsumption resolution 118,119]
402. $false [subsumption resolution 168,265]
% SZS output end Proof for 6739266855752610316943367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not strong is either not humble or not generous and vice versa.
Everyone who is funny is funny or not happy and vice versa.
Everyone who is not calm or brave is both not rich and not humble.
If mary is either not curious or tall then someone is both not patient and not old and vice versa.
If someone is not funny then lucy is either happy or funny.
Everyone who is wise or not happy is either old or brave.
Everyone who is not happy or not quiet is either curious or wise and vice versa.
If lucy is curious then john is calm and vice versa.
If lucy is not wise or funny then someone is not strong or happy and vice versa.
Everyone who is quiet or not calm is either not rich or happy and vice versa.
If alice is both not strong and generous then someone is either creative or not kind.
If someone is either not happy or not old then someone is either patient or not wise and vice versa.
If fred is both wise and not tall then someone is either not curious or not generous.
If someone is either strong or rich then susan is both wise and happy and vice versa.
Everyone who is not wise or happy is wise and vice versa.
If someone is either wise or not strong then someone is either creative or not calm and vice versa.
Someone is either not kind or generous.
Susan is not kind.
Someone is either not happy or tall.
Someone is either generous or brave.
John is not patient.
Paul is patient.
John is curious. | Mary is not creative. | neutral | (![X]:((humble(X)&~strong(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:(funny(X)<=>(funny(X)|~happy(X))))&
(![X]:((~calm(X)|brave(X))=>(~rich(X)&~humble(X))))&
(((~curious(mary)<~>tall(mary)))<=>(?[X]:((~patient(X)&~old(X)))))&
((?[X]:(~funny(X)))=>((happy(lucy)<~>funny(lucy))))&
(![X]:((wise(X)|~happy(X))=>(old(X)<~>brave(X))))&
(![X]:((~happy(X)|~quiet(X))<=>(curious(X)<~>wise(X))))&
((curious(lucy))<=>(calm(john)))&
(((~wise(lucy)|funny(lucy)))<=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((quiet(X)|~calm(X))<=>(~rich(X)<~>happy(X))))&
(((~strong(alice)&generous(alice)))=>(?[X]:((creative(X)<~>~kind(X)))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(?[X]:((patient(X)<~>~wise(X)))))&
(((wise(fred)&~tall(fred)))=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:((strong(X)<~>rich(X))))<=>((wise(susan)&happy(susan))))&
(![X]:((~wise(X)|happy(X))<=>wise(X)))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((creative(X)<~>~calm(X)))))&
(?[X]:((~kind(X)<~>generous(X))))&
(~kind(susan))&
(?[X]:((~happy(X)<~>tall(X))))&
(?[X]:((generous(X)<~>brave(X))))&
(~patient(john))&
(patient(paul))&
(curious(john)) | ~creative(mary) | [] | null | 0 |
Everyone who is either kind or happy is not kind or calm and vice versa.
Everyone who is both patient and funny is either not creative or not generous.
If someone is both quiet and funny then someone is not strong.
If alice is both not calm and not curious then john is creative.
If someone is generous then someone is both old and not curious and vice versa.
Everyone who is tall or not generous is both strong and not happy.
If someone is patient then someone is not brave or patient and vice versa.
If someone is creative or not kind then someone is not patient.
Everyone who is not calm is brave.
If john is both quiet and strong then someone is both quiet and not tall and vice versa.
Everyone who is both not rich and not kind is curious.
Everyone who is not curious is rich or not curious.
Everyone who is not kind or not wise is both not quiet and tall.
If someone is brave then someone is both humble and old and vice versa.
Everyone who is both not humble and not tall is either not humble or kind and vice versa.
Everyone who is not funny is not quiet or not rich.
Alice is not rich or quiet.
Alice is patient or curious.
Fred is wise or not brave.
Paul is either wise or not patient.
Someone is strong or tall.
Someone is both old and patient.
John is either not wise or patient. | Fred is quiet. | neutral | (![X]:((kind(X)<~>happy(X))<=>(~kind(X)|calm(X))))&
(![X]:((patient(X)&funny(X))=>(~creative(X)<~>~generous(X))))&
((?[X]:((quiet(X)&funny(X))))=>(?[X]:(~strong(X))))&
(((~calm(alice)&~curious(alice)))=>(creative(john)))&
((?[X]:(generous(X)))<=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((tall(X)|~generous(X))=>(strong(X)&~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:((creative(X)|~kind(X))))=>(?[X]:(~patient(X))))&
(![X]:(~calm(X)=>brave(X)))&
(((quiet(john)&strong(john)))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~rich(X)&~kind(X))=>curious(X)))&
(![X]:(~curious(X)=>(rich(X)|~curious(X))))&
(![X]:((~kind(X)|~wise(X))=>(~quiet(X)&tall(X))))&
((?[X]:(brave(X)))<=>(?[X]:((humble(X)&old(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(~humble(X)<~>kind(X))))&
(![X]:(~funny(X)=>(~quiet(X)|~rich(X))))&
((~rich(alice)|quiet(alice)))&
((patient(alice)|curious(alice)))&
((wise(fred)|~brave(fred)))&
((wise(paul)<~>~patient(paul)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:((old(X)&patient(X))))&
((~wise(john)<~>patient(john))) | quiet(fred) | [] | null | 0 |
If john is both not wise and not humble then alice is patient. If someone is both funny and not creative then susan is both not calm and not strong. Everyone who is not brave is kind. Everyone who is not funny is funny or not strong and vice versa. Everyone who is both patient and creative is both not kind and funny and vice versa. Everyone who is rich or tall is either generous or brave. Everyone who is not creative is not tall and vice versa. If susan is both not old and not rich then someone is both funny and patient and vice versa. Everyone who is both not humble and not tall is happy and vice versa. If someone is both generous and not tall then someone is happy. If paul is both brave and not funny then someone is both rich and not curious and vice versa. If mary is both not strong and not generous then someone is both wise and not rich. If someone is not humble then someone is both generous and not brave and vice versa. If someone is either humble or not wise then alice is both not tall and not patient. If someone is both humble and not curious then fred is old and vice versa. If someone is either not funny or not calm then someone is brave or not quiet and vice versa. Alice is both not wise and kind. Alice is not strong or brave. Fred is both rich and not brave. Susan is either old or happy. Mary is both not tall and generous. Someone is not strong. Someone is either funny or rich. Someone is not creative or not funny. | Alice is funny. | contradiction | (((~wise(john)&~humble(john)))=>(patient(alice)))&
((?[X]:((funny(X)&~creative(X))))=>((~calm(susan)&~strong(susan))))&
(![X]:(~brave(X)=>kind(X)))&
(![X]:(~funny(X)<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&creative(X))<=>(~kind(X)&funny(X))))&
(![X]:((rich(X)|tall(X))=>(generous(X)<~>brave(X))))&
(![X]:(~creative(X)<=>~tall(X)))&
(((~old(susan)&~rich(susan)))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:((~humble(X)&~tall(X))<=>happy(X)))&
((?[X]:((generous(X)&~tall(X))))=>(?[X]:(happy(X))))&
(((brave(paul)&~funny(paul)))<=>(?[X]:((rich(X)&~curious(X)))))&
(((~strong(mary)&~generous(mary)))=>(?[X]:((wise(X)&~rich(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((humble(X)<~>~wise(X))))=>((~tall(alice)&~patient(alice))))&
((?[X]:((humble(X)&~curious(X))))<=>(old(fred)))&
((?[X]:((~funny(X)<~>~calm(X))))<=>(?[X]:((brave(X)|~quiet(X)))))&
((~wise(alice)&kind(alice)))&
((~strong(alice)|brave(alice)))&
((rich(fred)&~brave(fred)))&
((old(susan)<~>happy(susan)))&
((~tall(mary)&generous(mary)))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)<~>rich(X))))&
(?[X]:((~creative(X)|~funny(X)))) | funny(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5832644035448757989209410
% SZS output start Proof for 5832644035448757989209410
4. ! [X0] : (~funny(X0) <=> (~strong(X0) | funny(X0))) [input p3]
25. funny(alice) [input hypothesis]
38. ! [X0] : ((~funny(X0) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | funny(X0))) [nnf transformation 4]
39. ! [X0] : ((~funny(X0) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | funny(X0))) [flattening 38]
89. ~funny(X0) | ~funny(X0) [cnf transformation 39]
144. funny(alice) [cnf transformation 25]
146. ~funny(X0) [duplicate literal removal 89]
322. $false [subsumption resolution 144,146]
% SZS output end Proof for 5832644035448757989209410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy then fred is either creative or patient.
Everyone who is not quiet or creative is not curious or happy.
Everyone who is both not tall and not generous is brave and vice versa.
If someone is both tall and quiet then paul is not creative or curious and vice versa.
If john is both patient and rich then someone is either funny or creative.
Everyone who is either not happy or happy is either old or not brave.
If someone is either tall or not humble then susan is not humble or not old and vice versa.
If someone is either not generous or curious then someone is not funny or calm.
If someone is old or happy then alice is curious or creative.
Everyone who is both not wise and not curious is not old or creative.
Everyone who is not quiet is not patient.
Everyone who is not wise is either not strong or old.
Everyone who is either not old or patient is either not brave or not humble.
Everyone who is either creative or calm is either calm or not old and vice versa.
If someone is either not quiet or not happy then lucy is not creative or rich.
Everyone who is either not strong or kind is kind and vice versa.
Someone is both happy and not generous.
Someone is rich.
Someone is both patient and rich.
Mary is either not wise or quiet.
Someone is not creative or not rich.
Alice is kind.
Paul is either kind or quiet. | Mary is wise. | neutral | ((?[X]:(~happy(X)))=>((creative(fred)<~>patient(fred))))&
(![X]:((~quiet(X)|creative(X))=>(~curious(X)|happy(X))))&
(![X]:((~tall(X)&~generous(X))<=>brave(X)))&
((?[X]:((tall(X)&quiet(X))))<=>((~creative(paul)|curious(paul))))&
(((patient(john)&rich(john)))=>(?[X]:((funny(X)<~>creative(X)))))&
(![X]:((~happy(X)<~>happy(X))=>(old(X)<~>~brave(X))))&
((?[X]:((tall(X)<~>~humble(X))))<=>((~humble(susan)|~old(susan))))&
((?[X]:((~generous(X)<~>curious(X))))=>(?[X]:((~funny(X)|calm(X)))))&
((?[X]:((old(X)|happy(X))))=>((curious(alice)|creative(alice))))&
(![X]:((~wise(X)&~curious(X))=>(~old(X)|creative(X))))&
(![X]:(~quiet(X)=>~patient(X)))&
(![X]:(~wise(X)=>(~strong(X)<~>old(X))))&
(![X]:((~old(X)<~>patient(X))=>(~brave(X)<~>~humble(X))))&
(![X]:((creative(X)<~>calm(X))<=>(calm(X)<~>~old(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))=>((~creative(lucy)|rich(lucy))))&
(![X]:((~strong(X)<~>kind(X))<=>kind(X)))&
(?[X]:((happy(X)&~generous(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)&rich(X))))&
((~wise(mary)<~>quiet(mary)))&
(?[X]:((~creative(X)|~rich(X))))&
(kind(alice))&
((kind(paul)<~>quiet(paul))) | wise(mary) | [] | null | 0 |
If someone is either old or not quiet then lucy is rich or not strong and vice versa.
If susan is both not strong and not patient then paul is both not curious and not humble and vice versa.
If lucy is both calm and not generous then someone is both strong and curious.
Everyone who is either creative or not tall is not creative and vice versa.
Everyone who is both brave and humble is either not calm or quiet.
If alice is either creative or quiet then someone is not curious or generous.
Everyone who is not humble or not kind is not patient and vice versa.
Everyone who is not humble or not creative is rich or wise and vice versa.
Everyone who is calm or not wise is both not patient and not calm and vice versa.
If paul is creative or brave then someone is not humble and vice versa.
Everyone who is both brave and tall is not rich.
Everyone who is either generous or not rich is both not kind and not humble and vice versa.
If someone is both strong and not old then john is quiet and vice versa.
Everyone who is both curious and not brave is quiet or tall.
If someone is not tall then lucy is either brave or tall.
Everyone who is happy or not old is both not happy and not funny.
Mary is both generous and brave.
Someone is both not curious and not calm.
Someone is rich.
Fred is not tall or funny.
Alice is either not rich or curious.
Someone is both not rich and generous.
Susan is not old. | Susan is not rich. | neutral | ((?[X]:((old(X)<~>~quiet(X))))<=>((rich(lucy)|~strong(lucy))))&
(((~strong(susan)&~patient(susan)))<=>((~curious(paul)&~humble(paul))))&
(((calm(lucy)&~generous(lucy)))=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((creative(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((brave(X)&humble(X))=>(~calm(X)<~>quiet(X))))&
(((creative(alice)<~>quiet(alice)))=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:((~humble(X)|~kind(X))<=>~patient(X)))&
(![X]:((~humble(X)|~creative(X))<=>(rich(X)|wise(X))))&
(![X]:((calm(X)|~wise(X))<=>(~patient(X)&~calm(X))))&
(((creative(paul)|brave(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)&tall(X))=>~rich(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((strong(X)&~old(X))))<=>(quiet(john)))&
(![X]:((curious(X)&~brave(X))=>(quiet(X)|tall(X))))&
((?[X]:(~tall(X)))=>((brave(lucy)<~>tall(lucy))))&
(![X]:((happy(X)|~old(X))=>(~happy(X)&~funny(X))))&
((generous(mary)&brave(mary)))&
(?[X]:((~curious(X)&~calm(X))))&
(?[X]:(rich(X)))&
((~tall(fred)|funny(fred)))&
((~rich(alice)<~>curious(alice)))&
(?[X]:((~rich(X)&generous(X))))&
(~old(susan)) | ~rich(susan) | [] | null | 0 |
If someone is not wise then lucy is strong or not happy.
If someone is both not generous and creative then lucy is not wise and vice versa.
Everyone who is either curious or brave is either not calm or kind and vice versa.
Everyone who is either not humble or not strong is either not creative or tall.
Everyone who is either not old or old is not creative or not curious and vice versa.
If someone is both calm and not quiet then paul is creative and vice versa.
Everyone who is tall or not happy is both not patient and not strong and vice versa.
Everyone who is both not brave and quiet is rich or not calm and vice versa.
Everyone who is either not patient or funny is not creative or tall.
Everyone who is either rich or calm is not brave and vice versa.
Everyone who is not generous or old is patient or curious.
Everyone who is strong or rich is kind or not rich.
If someone is not happy then alice is both curious and creative and vice versa.
If susan is rich or curious then lucy is both not kind and kind and vice versa.
If someone is both not generous and tall then lucy is kind or humble.
Everyone who is either calm or tall is either kind or old and vice versa.
Someone is not old or not happy.
Someone is funny or patient.
Someone is both not wise and not curious.
Fred is not humble.
Fred is both happy and creative.
Someone is either humble or brave.
Someone is not funny or curious.
Susan is not humble or creative. | Lucy is not creative. | neutral | ((?[X]:(~wise(X)))=>((strong(lucy)|~happy(lucy))))&
((?[X]:((~generous(X)&creative(X))))<=>(~wise(lucy)))&
(![X]:((curious(X)<~>brave(X))<=>(~calm(X)<~>kind(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(~creative(X)<~>tall(X))))&
(![X]:((~old(X)<~>old(X))<=>(~creative(X)|~curious(X))))&
((?[X]:((calm(X)&~quiet(X))))<=>(creative(paul)))&
(![X]:((tall(X)|~happy(X))<=>(~patient(X)&~strong(X))))&
(![X]:((~brave(X)&quiet(X))<=>(rich(X)|~calm(X))))&
(![X]:((~patient(X)<~>funny(X))=>(~creative(X)|tall(X))))&
(![X]:((rich(X)<~>calm(X))<=>~brave(X)))&
(![X]:((~generous(X)|old(X))=>(patient(X)|curious(X))))&
(![X]:((strong(X)|rich(X))=>(kind(X)|~rich(X))))&
((?[X]:(~happy(X)))<=>((curious(alice)&creative(alice))))&
(((rich(susan)|curious(susan)))<=>((~kind(lucy)&kind(lucy))))&
((?[X]:((~generous(X)&tall(X))))=>((kind(lucy)|humble(lucy))))&
(![X]:((calm(X)<~>tall(X))<=>(kind(X)<~>old(X))))&
(?[X]:((~old(X)|~happy(X))))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((~wise(X)&~curious(X))))&
(~humble(fred))&
((happy(fred)&creative(fred)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:((~funny(X)|curious(X))))&
((~humble(susan)|creative(susan))) | ~creative(lucy) | [] | null | 0 |
Everyone who is either strong or not patient is strong and vice versa. If someone is either not funny or curious then someone is not wise or tall and vice versa. If someone is either strong or not quiet then someone is both wise and not patient. If alice is curious then someone is not funny. If john is not old then lucy is not humble or patient. If john is either not kind or not calm then lucy is both not calm and not generous. Everyone who is both not tall and tall is either not kind or not humble and vice versa. Everyone who is either not generous or not quiet is either not quiet or strong. If paul is both creative and not strong then john is not quiet or tall and vice versa. If mary is either not strong or not curious then fred is either creative or kind and vice versa. Everyone who is either not brave or humble is both quiet and not calm and vice versa. If lucy is both not humble and quiet then alice is not tall or not happy and vice versa. If alice is not strong then someone is both rich and old and vice versa. Everyone who is not patient or kind is both not funny and not kind. Everyone who is both not quiet and not wise is not happy. If someone is curious or strong then someone is strong. Someone is either not brave or kind. Mary is not funny or curious. Someone is not old. Someone is wise. Fred is either not strong or old. Alice is not generous. Someone is both funny and not creative. Paul is either strong or brave. | Paul is not generous. | contradiction | (![X]:((strong(X)<~>~patient(X))<=>strong(X)))&
((?[X]:((~funny(X)<~>curious(X))))<=>(?[X]:((~wise(X)|tall(X)))))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:((wise(X)&~patient(X)))))&
((curious(alice))=>(?[X]:(~funny(X))))&
((~old(john))=>((~humble(lucy)|patient(lucy))))&
(((~kind(john)<~>~calm(john)))=>((~calm(lucy)&~generous(lucy))))&
(![X]:((~tall(X)&tall(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((~generous(X)<~>~quiet(X))=>(~quiet(X)<~>strong(X))))&
(((creative(paul)&~strong(paul)))<=>((~quiet(john)|tall(john))))&
(((~strong(mary)<~>~curious(mary)))<=>((creative(fred)<~>kind(fred))))&
(![X]:((~brave(X)<~>humble(X))<=>(quiet(X)&~calm(X))))&
(((~humble(lucy)&quiet(lucy)))<=>((~tall(alice)|~happy(alice))))&
((~strong(alice))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:((~patient(X)|kind(X))=>(~funny(X)&~kind(X))))&
(![X]:((~quiet(X)&~wise(X))=>~happy(X)))&
((?[X]:((curious(X)|strong(X))))=>(?[X]:(strong(X))))&
(?[X]:((~brave(X)<~>kind(X))))&
((~funny(mary)|curious(mary)))&
(?[X]:(~old(X)))&
(?[X]:(wise(X)))&
((~strong(fred)<~>old(fred)))&
(~generous(alice))&
(?[X]:((funny(X)&~creative(X))))&
((strong(paul)<~>brave(paul))) | ~generous(paul) | [
"p0",
"p2",
"p6",
"p7",
"p10",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1458114120693819921484480
% SZS output start Proof for 1458114120693819921484480
1. ! [X0] : ((strong(X0) <~> ~patient(X0)) <=> strong(X0)) [input p0]
3. ? [X0] : (strong(X0) <~> ~quiet(X0)) => ? [X0] : (~patient(X0) & wise(X0)) [input p2]
7. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~kind(X0) <~> ~humble(X0))) [input p6]
8. ! [X0] : ((~generous(X0) <~> ~quiet(X0)) => (~quiet(X0) <~> strong(X0))) [input p7]
11. ! [X0] : ((~brave(X0) <~> humble(X0)) <=> (~calm(X0) & quiet(X0))) [input p10]
14. ! [X0] : ((kind(X0) | ~patient(X0)) => (~kind(X0) & ~funny(X0))) [input p13]
24. strong(paul) <~> brave(paul) [input p23]
25. ~generous(paul) [input hypothesis]
27. ? [X0] : (strong(X0) <~> ~quiet(X0)) => ? [X1] : (~patient(X1) & wise(X1)) [rectify 3]
29. ? [X1] : (~patient(X1) & wise(X1)) | ! [X0] : (strong(X0) <=> ~quiet(X0)) [ennf transformation 27]
34. ! [X0] : ((~quiet(X0) <~> strong(X0)) | (~generous(X0) <=> ~quiet(X0))) [ennf transformation 8]
35. ! [X0] : ((~kind(X0) & ~funny(X0)) | (~kind(X0) & patient(X0))) [ennf transformation 14]
39. ! [X0] : ((((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | ~strong(X0)) & (strong(X0) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0))))) [nnf transformation 1]
45. ? [X1] : (~patient(X1) & wise(X1)) | ! [X0] : ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0))) [nnf transformation 29]
46. ? [X0] : (~patient(X0) & wise(X0)) | ! [X1] : ((strong(X1) | quiet(X1)) & (~quiet(X1) | ~strong(X1))) [rectify 45]
47. ? [X0] : (~patient(X0) & wise(X0)) => (~patient(sK2) & wise(sK2)) [choice axiom]
48. (~patient(sK2) & wise(sK2)) | ! [X1] : ((strong(X1) | quiet(X1)) & (~quiet(X1) | ~strong(X1))) [skolemisation 46,47]
52. ! [X0] : (((tall(X0) & ~tall(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (~tall(X0) | tall(X0)))) [nnf transformation 7]
53. ! [X0] : (((tall(X0) & ~tall(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | ~tall(X0) | tall(X0))) [flattening 52]
54. ! [X0] : (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) [nnf transformation 34]
58. ! [X0] : ((((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | (calm(X0) | ~quiet(X0))) & ((~calm(X0) & quiet(X0)) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0))))) [nnf transformation 11]
59. ! [X0] : ((((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | calm(X0) | ~quiet(X0)) & ((~calm(X0) & quiet(X0)) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0))))) [flattening 58]
79. (~brave(paul) | ~strong(paul)) & (brave(paul) | strong(paul)) [nnf transformation 24]
81. strong(X0) | strong(X0) | patient(X0) [cnf transformation 39]
83. patient(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 39]
92. ~patient(sK2) | ~quiet(X1) | ~strong(X1) [cnf transformation 48]
93. ~patient(sK2) | strong(X1) | quiet(X1) [cnf transformation 48]
102. ~tall(X0) | ~humble(X0) | kind(X0) [cnf transformation 53]
104. ~humble(X0) | tall(X0) | kind(X0) [cnf transformation 53]
106. strong(X0) | ~quiet(X0) | ~quiet(X0) | generous(X0) [cnf transformation 54]
123. brave(X0) | humble(X0) | quiet(X0) [cnf transformation 59]
140. ~kind(X0) | ~kind(X0) [cnf transformation 35]
155. ~brave(paul) | ~strong(paul) [cnf transformation 79]
156. ~generous(paul) [cnf transformation 25]
157. ~kind(X0) [duplicate literal removal 140]
158. strong(X0) | ~quiet(X0) | generous(X0) [duplicate literal removal 106]
160. strong(X0) | patient(X0) [duplicate literal removal 81]
161. ~strong(X0) | patient(X0) [duplicate literal removal 83]
162. patient(X0) [subsumption resolution 160,161]
197. quiet(X1) | strong(X1) [subsumption resolution 93,162]
198. ~quiet(X1) | ~strong(X1) [subsumption resolution 92,162]
229. ~humble(X0) | kind(X0) [subsumption resolution 102,104]
231. ~quiet(X0) | generous(X0) [subsumption resolution 158,198]
237. 16 <=> strong(paul) [avatar definition]
345. 37 <=> brave(paul) [avatar definition]
347. ~brave(paul) <- (~37) [avatar component clause 345]
348. ~16 | ~37 [avatar split clause 155,345,237]
358. generous(X0) | strong(X0) [resolution 231,197]
366. strong(paul) [resolution 358,156]
379. 40 <=> quiet(paul) [avatar definition]
381. quiet(paul) <- (40) [avatar component clause 379]
383. 41 <=> humble(paul) [avatar definition]
385. humble(paul) <- (41) [avatar component clause 383]
387. 16 [avatar split clause 366,237]
389. humble(paul) | quiet(paul) <- (~37) [resolution 347,123]
394. generous(paul) <- (40) [resolution 381,231]
396. $false <- (40) [subsumption resolution 394,156]
397. ~40 [avatar contradiction clause 396]
400. 40 | 41 | 37 [avatar split clause 389,345,383,379]
404. kind(paul) <- (41) [resolution 385,229]
406. $false <- (41) [subsumption resolution 404,157]
407. ~41 [avatar contradiction clause 406]
408. $false [avatar sat refutation 348,387,397,400,407]
% SZS output end Proof for 1458114120693819921484480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is either not wise or not kind and vice versa. Everyone who is either not wise or wise is both not patient and old and vice versa. Everyone who is humble is rich or creative. Everyone who is both not humble and generous is both not humble and not kind and vice versa. Everyone who is either not humble or not old is either happy or not funny and vice versa. If fred is either not strong or calm then fred is not calm or not rich. Everyone who is both old and calm is not kind. If someone is either not tall or kind then mary is both strong and rich and vice versa. If mary is not calm then someone is strong or not old. Everyone who is not brave or generous is either patient or not quiet. Everyone who is not happy is either not patient or not calm. Everyone who is not calm is either not generous or not curious. If alice is wise or old then mary is not rich or not generous. If susan is generous or not kind then alice is either wise or not generous and vice versa. Everyone who is not creative or brave is both humble and kind. Everyone who is either brave or not humble is not tall. Someone is both creative and not generous. Someone is either tall or calm. Mary is either humble or creative. Mary is both not patient and quiet. Someone is not calm. Someone is wise. Someone is not funny or rich. | Mary is not humble. | contradiction | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~patient(X)&old(X))))&
(![X]:(humble(X)=>(rich(X)|creative(X))))&
(![X]:((~humble(X)&generous(X))<=>(~humble(X)&~kind(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)<~>~funny(X))))&
(((~strong(fred)<~>calm(fred)))=>((~calm(fred)|~rich(fred))))&
(![X]:((old(X)&calm(X))=>~kind(X)))&
((?[X]:((~tall(X)<~>kind(X))))<=>((strong(mary)&rich(mary))))&
((~calm(mary))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((~brave(X)|generous(X))=>(patient(X)<~>~quiet(X))))&
(![X]:(~happy(X)=>(~patient(X)<~>~calm(X))))&
(![X]:(~calm(X)=>(~generous(X)<~>~curious(X))))&
(((wise(alice)|old(alice)))=>((~rich(mary)|~generous(mary))))&
(((generous(susan)|~kind(susan)))<=>((wise(alice)<~>~generous(alice))))&
(![X]:((~creative(X)|brave(X))=>(humble(X)&kind(X))))&
(![X]:((brave(X)<~>~humble(X))=>~tall(X)))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((humble(mary)<~>creative(mary)))&
((~patient(mary)&quiet(mary)))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
(?[X]:((~funny(X)|rich(X)))) | ~humble(mary) | [
"p1",
"p9",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4332694478874739895932819
% SZS output start Proof for 4332694478874739895932819
2. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (old(X0) & ~patient(X0))) [input p1]
10. ! [X0] : ((generous(X0) | ~brave(X0)) => (patient(X0) <~> ~quiet(X0))) [input p9]
15. ! [X0] : ((brave(X0) | ~creative(X0)) => (kind(X0) & humble(X0))) [input p14]
20. quiet(mary) & ~patient(mary) [input p19]
24. ~humble(mary) [input hypothesis]
32. ! [X0] : ((patient(X0) <~> ~quiet(X0)) | (~generous(X0) & brave(X0))) [ennf transformation 10]
37. ! [X0] : ((kind(X0) & humble(X0)) | (~brave(X0) & creative(X0))) [ennf transformation 15]
40. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~old(X0) | patient(X0))) & ((old(X0) & ~patient(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~old(X0) | patient(X0)) & ((old(X0) & ~patient(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 40]
53. ! [X0] : (((quiet(X0) | ~patient(X0)) & (~quiet(X0) | patient(X0))) | (~generous(X0) & brave(X0))) [nnf transformation 32]
75. ~patient(X0) | wise(X0) | wise(X0) [cnf transformation 41]
76. ~patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 41]
104. ~quiet(X0) | patient(X0) | brave(X0) [cnf transformation 53]
121. ~brave(X0) | humble(X0) [cnf transformation 37]
133. quiet(mary) [cnf transformation 20]
137. ~humble(mary) [cnf transformation 24]
139. ~patient(X0) | wise(X0) [duplicate literal removal 75]
140. ~patient(X0) | ~wise(X0) [duplicate literal removal 76]
144. ~patient(X0) [subsumption resolution 139,140]
202. ~quiet(X0) | brave(X0) [subsumption resolution 104,144]
246. 19 <=> humble(mary) [avatar definition]
248. ~humble(mary) <- (~19) [avatar component clause 246]
263. ~19 [avatar split clause 137,246]
267. brave(mary) [resolution 202,133]
272. humble(mary) [resolution 267,121]
275. $false <- (~19) [subsumption resolution 272,248]
276. 19 [avatar contradiction clause 275]
277. $false [avatar sat refutation 263,276]
% SZS output end Proof for 4332694478874739895932819
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either curious or not happy then someone is not kind or creative.
Everyone who is curious is either funny or calm and vice versa.
If mary is either kind or not old then mary is both not brave and not strong and vice versa.
If susan is either not brave or not rich then someone is calm.
Everyone who is either not quiet or not creative is funny or not creative and vice versa.
Everyone who is both strong and not creative is either not patient or not tall.
Everyone who is either not creative or quiet is either calm or not brave and vice versa.
If john is both strong and wise then someone is strong.
Everyone who is not creative is rich or not quiet and vice versa.
Everyone who is both calm and old is quiet or not curious and vice versa.
If lucy is not kind or not creative then someone is quiet and vice versa.
If someone is both funny and not kind then john is both wise and not old and vice versa.
Everyone who is both not calm and not brave is either humble or not funny and vice versa.
If someone is both kind and old then paul is either not kind or old and vice versa.
Everyone who is either old or not old is both quiet and creative.
If someone is both not curious and not tall then susan is not old.
Susan is humble.
Someone is generous.
Someone is both not kind and calm.
Someone is both not tall and patient.
Someone is rich or not happy. | Mary is not brave. | contradiction | (((curious(alice)<~>~happy(alice)))=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:(curious(X)<=>(funny(X)<~>calm(X))))&
(((kind(mary)<~>~old(mary)))<=>((~brave(mary)&~strong(mary))))&
(((~brave(susan)<~>~rich(susan)))=>(?[X]:(calm(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(funny(X)|~creative(X))))&
(![X]:((strong(X)&~creative(X))=>(~patient(X)<~>~tall(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>(calm(X)<~>~brave(X))))&
(((strong(john)&wise(john)))=>(?[X]:(strong(X))))&
(![X]:(~creative(X)<=>(rich(X)|~quiet(X))))&
(![X]:((calm(X)&old(X))<=>(quiet(X)|~curious(X))))&
(((~kind(lucy)|~creative(lucy)))<=>(?[X]:(quiet(X))))&
((?[X]:((funny(X)&~kind(X))))<=>((wise(john)&~old(john))))&
(![X]:((~calm(X)&~brave(X))<=>(humble(X)<~>~funny(X))))&
((?[X]:((kind(X)&old(X))))<=>((~kind(paul)<~>old(paul))))&
(![X]:((old(X)<~>~old(X))=>(quiet(X)&creative(X))))&
((?[X]:((~curious(X)&~tall(X))))=>(~old(susan)))&
(humble(susan))&
(?[X]:(generous(X)))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:((rich(X)|~happy(X)))) | ~brave(mary) | [
"p4",
"p6",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2099070585648728491480631
% SZS output start Proof for 2099070585648728491480631
5. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) <=> (~creative(X0) | funny(X0))) [input p4]
7. ! [X0] : ((~creative(X0) <~> quiet(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p6]
9. ! [X0] : (~creative(X0) <=> (~quiet(X0) | rich(X0))) [input p8]
10. ! [X0] : ((old(X0) & calm(X0)) <=> (~curious(X0) | quiet(X0))) [input p9]
15. ! [X0] : ((old(X0) <~> ~old(X0)) => (creative(X0) & quiet(X0))) [input p14]
22. ~brave(mary) [input hypothesis]
30. ! [X0] : ((creative(X0) & quiet(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 15]
41. ! [X0] : ((((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (creative(X0) & ~funny(X0))) & ((~creative(X0) | funny(X0)) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0))))) [nnf transformation 5]
42. ! [X0] : ((((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (creative(X0) & ~funny(X0))) & (~creative(X0) | funny(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0))))) [flattening 41]
44. ! [X0] : ((((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0))))) [nnf transformation 7]
47. ! [X0] : ((~creative(X0) | (quiet(X0) & ~rich(X0))) & ((~quiet(X0) | rich(X0)) | creative(X0))) [nnf transformation 9]
48. ! [X0] : ((~creative(X0) | (quiet(X0) & ~rich(X0))) & (~quiet(X0) | rich(X0) | creative(X0))) [flattening 47]
49. ! [X0] : (((old(X0) & calm(X0)) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | (~old(X0) | ~calm(X0)))) [nnf transformation 10]
50. ! [X0] : (((old(X0) & calm(X0)) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~old(X0) | ~calm(X0))) [flattening 49]
67. ! [X0] : ((creative(X0) & quiet(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 30]
88. ~creative(X0) | funny(X0) | ~creative(X0) | quiet(X0) [cnf transformation 42]
90. ~quiet(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 42]
93. creative(X0) | quiet(X0) | creative(X0) [cnf transformation 42]
99. ~quiet(X0) | ~calm(X0) | ~creative(X0) | brave(X0) [cnf transformation 44]
107. ~creative(X0) | quiet(X0) [cnf transformation 48]
109. calm(X0) | ~quiet(X0) [cnf transformation 50]
111. old(X0) | ~quiet(X0) [cnf transformation 50]
134. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 67]
143. ~brave(mary) [cnf transformation 22]
146. creative(X0) | ~old(X0) [duplicate literal removal 134]
148. ~creative(X0) | funny(X0) | quiet(X0) [duplicate literal removal 88]
149. quiet(X0) | creative(X0) [duplicate literal removal 93]
169. 5 <=> brave(mary) [avatar definition]
170. ~brave(mary) <- (~5) [avatar component clause 169]
204. quiet(X0) | funny(X0) [subsumption resolution 148,149]
222. quiet(X0) [subsumption resolution 107,149]
224. old(X0) [subsumption resolution 111,222]
225. calm(X0) [subsumption resolution 109,222]
255. creative(X0) [subsumption resolution 146,224]
266. ~5 [avatar split clause 143,169]
289. ~creative(X2) | ~funny(X2) [resolution 90,222]
290. ~funny(X2) [subsumption resolution 289,255]
315. ~calm(X1) | ~creative(X1) | brave(X1) | funny(X1) [resolution 99,204]
319. ~creative(X1) | brave(X1) | funny(X1) [subsumption resolution 315,225]
320. brave(X1) | funny(X1) [subsumption resolution 319,255]
321. brave(X1) [subsumption resolution 320,290]
322. $false <- (~5) [resolution 321,170]
328. 5 [avatar contradiction clause 322]
329. $false [avatar sat refutation 266,328]
% SZS output end Proof for 2099070585648728491480631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either not funny or not strong and vice versa. If someone is happy then alice is both quiet and calm. If mary is either not patient or not happy then fred is not wise or quiet and vice versa. If someone is either happy or not brave then someone is either patient or not brave. Everyone who is both generous and strong is curious or not kind. If someone is not brave then lucy is either humble or not curious. If fred is either not kind or not wise then someone is either not happy or curious. If someone is kind then fred is curious or not creative and vice versa. If someone is either quiet or brave then fred is either not humble or curious. Everyone who is both quiet and calm is not patient. If fred is both tall and not funny then alice is not old or not calm and vice versa. Everyone who is either not humble or tall is both quiet and not curious. If john is kind or not curious then someone is not kind or not generous. Everyone who is kind or curious is both happy and not calm and vice versa. If alice is either quiet or not quiet then mary is curious or not quiet. Everyone who is brave is not generous or curious and vice versa. Someone is not quiet or not patient. Mary is both strong and quiet. Someone is either not humble or wise. Fred is not happy. Someone is either not strong or quiet. Someone is humble or wise. Someone is funny or happy. Someone is not brave. | Alice is not patient. | entailment | (![X]:(~happy(X)<=>(~funny(X)<~>~strong(X))))&
((?[X]:(happy(X)))=>((quiet(alice)&calm(alice))))&
(((~patient(mary)<~>~happy(mary)))<=>((~wise(fred)|quiet(fred))))&
((?[X]:((happy(X)<~>~brave(X))))=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((generous(X)&strong(X))=>(curious(X)|~kind(X))))&
((?[X]:(~brave(X)))=>((humble(lucy)<~>~curious(lucy))))&
(((~kind(fred)<~>~wise(fred)))=>(?[X]:((~happy(X)<~>curious(X)))))&
((?[X]:(kind(X)))<=>((curious(fred)|~creative(fred))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~humble(fred)<~>curious(fred))))&
(![X]:((quiet(X)&calm(X))=>~patient(X)))&
(((tall(fred)&~funny(fred)))<=>((~old(alice)|~calm(alice))))&
(![X]:((~humble(X)<~>tall(X))=>(quiet(X)&~curious(X))))&
(((kind(john)|~curious(john)))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:((kind(X)|curious(X))<=>(happy(X)&~calm(X))))&
(((quiet(alice)<~>~quiet(alice)))=>((curious(mary)|~quiet(mary))))&
(![X]:(brave(X)<=>(~generous(X)|curious(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
((strong(mary)&quiet(mary)))&
(?[X]:((~humble(X)<~>wise(X))))&
(~happy(fred))&
(?[X]:((~strong(X)<~>quiet(X))))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((funny(X)|happy(X))))&
(?[X]:(~brave(X))) | ~patient(alice) | [
"p1",
"p9",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3017474871510964018149491
% SZS output start Proof for 3017474871510964018149491
2. ? [X0] : happy(X0) => (calm(alice) & quiet(alice)) [input p1]
10. ! [X0] : ((calm(X0) & quiet(X0)) => ~patient(X0)) [input p9]
14. ! [X0] : ((curious(X0) | kind(X0)) <=> (~calm(X0) & happy(X0))) [input p13]
15. (quiet(alice) <~> ~quiet(alice)) => (~quiet(mary) | curious(mary)) [input p14]
18. quiet(mary) & strong(mary) [input p17]
25. patient(alice) [input hypothesis]
27. (calm(alice) & quiet(alice)) | ! [X0] : ~happy(X0) [ennf transformation 2]
34. ! [X0] : (~patient(X0) | (~calm(X0) | ~quiet(X0))) [ennf transformation 10]
35. ! [X0] : (~patient(X0) | ~calm(X0) | ~quiet(X0)) [flattening 34]
38. (~quiet(mary) | curious(mary)) | (quiet(alice) <=> ~quiet(alice)) [ennf transformation 15]
39. ~quiet(mary) | curious(mary) | (quiet(alice) <=> ~quiet(alice)) [flattening 38]
62. ! [X0] : (((curious(X0) | kind(X0)) | (calm(X0) | ~happy(X0))) & ((~calm(X0) & happy(X0)) | (~curious(X0) & ~kind(X0)))) [nnf transformation 14]
63. ! [X0] : ((curious(X0) | kind(X0) | calm(X0) | ~happy(X0)) & ((~calm(X0) & happy(X0)) | (~curious(X0) & ~kind(X0)))) [flattening 62]
64. ~quiet(mary) | curious(mary) | ((quiet(alice) | quiet(alice)) & (~quiet(alice) | ~quiet(alice))) [nnf transformation 39]
85. quiet(alice) | ~happy(X0) [cnf transformation 27]
86. calm(alice) | ~happy(X0) [cnf transformation 27]
111. ~patient(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 35]
124. ~curious(X0) | happy(X0) [cnf transformation 63]
128. ~quiet(mary) | curious(mary) | ~quiet(alice) | ~quiet(alice) [cnf transformation 64]
129. ~quiet(mary) | curious(mary) | quiet(alice) | quiet(alice) [cnf transformation 64]
135. quiet(mary) [cnf transformation 18]
144. patient(alice) [cnf transformation 25]
145. ~quiet(mary) | curious(mary) | ~quiet(alice) [duplicate literal removal 128]
146. ~quiet(mary) | curious(mary) | quiet(alice) [duplicate literal removal 129]
148. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
149. ~happy(X0) <- (1) [avatar component clause 148]
151. 2 <=> calm(alice) [avatar definition]
153. calm(alice) <- (2) [avatar component clause 151]
154. 1 | 2 [avatar split clause 86,151,148]
156. 3 <=> quiet(alice) [avatar definition]
159. 1 | 3 [avatar split clause 85,156,148]
169. 6 <=> happy(mary) [avatar definition]
171. happy(mary) <- (6) [avatar component clause 169]
297. 32 <=> curious(mary) [avatar definition]
299. curious(mary) <- (32) [avatar component clause 297]
301. 33 <=> quiet(mary) [avatar definition]
304. 3 | 32 | ~33 [avatar split clause 146,301,297,156]
305. ~3 | 32 | ~33 [avatar split clause 145,301,297,156]
315. 33 [avatar split clause 135,301]
355. happy(mary) <- (32) [resolution 124,299]
358. 6 | ~32 [avatar split clause 355,297,169]
390. ~calm(alice) | ~quiet(alice) [resolution 111,144]
391. ~quiet(alice) <- (2) [subsumption resolution 390,153]
394. ~3 | ~2 [avatar split clause 391,151,156]
395. $false <- (1, 6) [resolution 149,171]
398. ~1 | ~6 [avatar contradiction clause 395]
399. $false [avatar sat refutation 154,159,304,305,315,358,394,398]
% SZS output end Proof for 3017474871510964018149491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both creative and not brave then someone is either not tall or humble. If lucy is either not patient or calm then someone is funny and vice versa. Everyone who is creative or quiet is either old or tall and vice versa. Everyone who is both not tall and not calm is generous and vice versa. Everyone who is not calm is tall or wise and vice versa. Everyone who is both not kind and quiet is not generous or kind and vice versa. Everyone who is not funny or humble is either not tall or not quiet. If someone is both not strong and not rich then john is both not funny and not curious and vice versa. Everyone who is either tall or humble is not tall and vice versa. If john is quiet or happy then fred is strong and vice versa. If mary is not patient or curious then someone is either tall or calm. Everyone who is both old and not strong is either not kind or creative. If someone is not calm or not brave then john is either not wise or brave and vice versa. Everyone who is either calm or tall is both not rich and not curious. If someone is not calm then someone is not creative or wise. Fred is not curious. Someone is humble or strong. Lucy is either tall or not rich. | Lucy is not creative. | neutral | (((creative(mary)&~brave(mary)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(((~patient(lucy)<~>calm(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)|quiet(X))<=>(old(X)<~>tall(X))))&
(![X]:((~tall(X)&~calm(X))<=>generous(X)))&
(![X]:(~calm(X)<=>(tall(X)|wise(X))))&
(![X]:((~kind(X)&quiet(X))<=>(~generous(X)|kind(X))))&
(![X]:((~funny(X)|humble(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~funny(john)&~curious(john))))&
(![X]:((tall(X)<~>humble(X))<=>~tall(X)))&
(((quiet(john)|happy(john)))<=>(strong(fred)))&
(((~patient(mary)|curious(mary)))=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((old(X)&~strong(X))=>(~kind(X)<~>creative(X))))&
((?[X]:((~calm(X)|~brave(X))))<=>((~wise(john)<~>brave(john))))&
(![X]:((calm(X)<~>tall(X))=>(~rich(X)&~curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~creative(X)|wise(X)))))&
(~curious(fred))&
(?[X]:((humble(X)|strong(X))))&
((tall(lucy)<~>~rich(lucy))) | ~creative(lucy) | [] | null | 0 |
Everyone who is both not generous and strong is either old or not funny.
If susan is not kind then someone is both happy and not rich.
Everyone who is either funny or kind is creative or not strong and vice versa.
Everyone who is both tall and not kind is curious.
If john is either not brave or rich then someone is not rich or patient.
Everyone who is wise or not patient is both curious and humble.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
If someone is not tall then fred is not wise or not rich and vice versa.
Everyone who is not strong is patient or happy and vice versa.
Fred is either not happy or not rich.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old.
Someone is either creative or strong.
Mary is either not patient or not wise.
Someone is not funny or kind. | Fred is not rich. | contradiction | (![X]:((~generous(X)&strong(X))=>(old(X)<~>~funny(X))))&
((~kind(susan))=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((funny(X)<~>kind(X))<=>(creative(X)|~strong(X))))&
(![X]:((tall(X)&~kind(X))=>curious(X)))&
(((~brave(john)<~>rich(john)))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:(~tall(X)))<=>((~wise(fred)|~rich(fred))))&
(![X]:(~strong(X)<=>(patient(X)|happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan)))&
(?[X]:((creative(X)<~>strong(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X)))) | ~rich(fred) | [
"p5",
"p6",
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5109349415796892712225187
% SZS output start Proof for 5109349415796892712225187
6. ! [X0] : ((~patient(X0) | wise(X0)) => (humble(X0) & curious(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p6]
12. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p11]
16. ! [X0] : (~strong(X0) <=> (happy(X0) | patient(X0))) [input p15]
17. ~happy(fred) <~> ~rich(fred) [input p16]
25. ~rich(fred) [input hypothesis]
32. ! [X0] : ((humble(X0) & curious(X0)) | (patient(X0) & ~wise(X0))) [ennf transformation 6]
33. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 7]
57. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 12]
58. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 57]
67. ! [X0] : ((~strong(X0) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | strong(X0))) [nnf transformation 16]
68. ! [X0] : ((~strong(X0) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | strong(X0))) [flattening 67]
69. (rich(fred) | happy(fred)) & (~rich(fred) | ~happy(fred)) [nnf transformation 17]
98. ~wise(X0) | humble(X0) [cnf transformation 32]
102. ~generous(X0) | wise(X0) [cnf transformation 33]
126. strong(X0) | generous(X0) [cnf transformation 58]
127. ~humble(X0) | strong(X0) [cnf transformation 58]
143. ~happy(X0) | ~strong(X0) [cnf transformation 68]
145. rich(fred) | happy(fred) [cnf transformation 69]
158. ~rich(fred) [cnf transformation 25]
239. 18 <=> rich(fred) [avatar definition]
248. 20 <=> wise(fred) [avatar definition]
250. wise(fred) <- (20) [avatar component clause 248]
257. 22 <=> happy(fred) [avatar definition]
259. happy(fred) <- (22) [avatar component clause 257]
260. 22 | 18 [avatar split clause 145,239,257]
321. ~18 [avatar split clause 158,239]
352. ~strong(fred) <- (22) [resolution 143,259]
373. generous(fred) <- (22) [resolution 352,126]
415. wise(fred) <- (22) [resolution 373,102]
416. 20 | ~22 [avatar split clause 415,257,248]
417. humble(fred) <- (20) [resolution 250,98]
419. strong(fred) <- (20) [resolution 417,127]
420. $false <- (20, 22) [subsumption resolution 419,352]
421. ~20 | ~22 [avatar contradiction clause 420]
422. $false [avatar sat refutation 260,321,416,421]
% SZS output end Proof for 5109349415796892712225187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then someone is both old and generous. If fred is both not curious and not rich then someone is quiet. Everyone who is both not humble and humble is either not funny or old and vice versa. Everyone who is happy or tall is either not curious or creative. Everyone who is both tall and creative is not humble. Everyone who is old or not wise is either not funny or patient. If someone is creative or not curious then someone is both old and wise and vice versa. If paul is rich then john is both not wise and old. Everyone who is either strong or not tall is strong. If paul is both not rich and not humble then mary is both not funny and not curious. Everyone who is both creative and tall is wise and vice versa. If someone is either not tall or calm then mary is quiet and vice versa. If someone is either not strong or brave then fred is either not humble or not brave and vice versa. Everyone who is not quiet or old is happy or calm. If susan is not patient or generous then someone is either kind or not curious. Everyone who is both calm and humble is not funny or wise and vice versa. Someone is not humble or not tall. Someone is not kind. Someone is both old and not generous. Mary is not rich or strong. Paul is both funny and not old. | Mary is generous. | neutral | ((?[X]:(patient(X)))=>(?[X]:((old(X)&generous(X)))))&
(((~curious(fred)&~rich(fred)))=>(?[X]:(quiet(X))))&
(![X]:((~humble(X)&humble(X))<=>(~funny(X)<~>old(X))))&
(![X]:((happy(X)|tall(X))=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)&creative(X))=>~humble(X)))&
(![X]:((old(X)|~wise(X))=>(~funny(X)<~>patient(X))))&
((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((old(X)&wise(X)))))&
((rich(paul))=>((~wise(john)&old(john))))&
(![X]:((strong(X)<~>~tall(X))=>strong(X)))&
(((~rich(paul)&~humble(paul)))=>((~funny(mary)&~curious(mary))))&
(![X]:((creative(X)&tall(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)&~generous(X))))&
((~rich(mary)|strong(mary)))&
((funny(paul)&~old(paul))) | generous(mary) | [] | null | 0 |
Everyone who is both funny and not tall is not tall.
Everyone who is strong or funny is either tall or strong.
Everyone who is both humble and not old is not rich.
Everyone who is not brave or rich is rich or happy and vice versa.
Everyone who is both not tall and not patient is generous and vice versa.
If fred is quiet then someone is tall.
If susan is not calm then someone is not creative or curious.
If someone is not old or not kind then john is not quiet or generous.
Everyone who is either not curious or not wise is both old and brave.
If someone is not generous or funny then someone is both not humble and not funny and vice versa.
If fred is both humble and creative then someone is either not creative or not funny and vice versa.
Everyone who is either not wise or happy is both not calm and not kind and vice versa.
If someone is either not patient or generous then susan is either not strong or not happy and vice versa.
Everyone who is both not humble and old is both not quiet and not humble and vice versa.
If someone is kind then someone is both kind and rich.
Everyone who is both not wise and humble is either not wise or not old and vice versa.
Someone is both not curious and not strong.
Susan is not tall.
Someone is not kind or tall.
Someone is not curious.
Someone is both old and calm.
Someone is not patient.
Someone is funny or not funny.
Lucy is either not tall or not funny. | Susan is not calm. | neutral | (![X]:((funny(X)&~tall(X))=>~tall(X)))&
(![X]:((strong(X)|funny(X))=>(tall(X)<~>strong(X))))&
(![X]:((humble(X)&~old(X))=>~rich(X)))&
(![X]:((~brave(X)|rich(X))<=>(rich(X)|happy(X))))&
(![X]:((~tall(X)&~patient(X))<=>generous(X)))&
((quiet(fred))=>(?[X]:(tall(X))))&
((~calm(susan))=>(?[X]:((~creative(X)|curious(X)))))&
((?[X]:((~old(X)|~kind(X))))=>((~quiet(john)|generous(john))))&
(![X]:((~curious(X)<~>~wise(X))=>(old(X)&brave(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:((~humble(X)&~funny(X)))))&
(((humble(fred)&creative(fred)))<=>(?[X]:((~creative(X)<~>~funny(X)))))&
(![X]:((~wise(X)<~>happy(X))<=>(~calm(X)&~kind(X))))&
((?[X]:((~patient(X)<~>generous(X))))<=>((~strong(susan)<~>~happy(susan))))&
(![X]:((~humble(X)&old(X))<=>(~quiet(X)&~humble(X))))&
((?[X]:(kind(X)))=>(?[X]:((kind(X)&rich(X)))))&
(![X]:((~wise(X)&humble(X))<=>(~wise(X)<~>~old(X))))&
(?[X]:((~curious(X)&~strong(X))))&
(~tall(susan))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)&calm(X))))&
(?[X]:(~patient(X)))&
(?[X]:((funny(X)|~funny(X))))&
((~tall(lucy)<~>~funny(lucy))) | ~calm(susan) | [] | null | 0 |
If lucy is either tall or not quiet then someone is not calm and vice versa.
Everyone who is both not old and creative is either not kind or strong and vice versa.
Everyone who is either not humble or not brave is both not curious and not kind.
If someone is both not curious and not brave then someone is not humble and vice versa.
If someone is quiet then someone is calm and vice versa.
If susan is funny then someone is either not wise or not humble and vice versa.
If someone is kind or rich then someone is both not funny and not creative.
Everyone who is strong is both curious and funny and vice versa.
Everyone who is not creative is both strong and not quiet and vice versa.
Everyone who is both strong and tall is both brave and tall and vice versa.
Everyone who is generous or strong is either happy or not brave and vice versa.
If alice is both not curious and humble then fred is not happy.
Everyone who is not strong or not calm is either tall or kind and vice versa.
Everyone who is wise is both not wise and not calm.
Everyone who is funny is quiet or not tall and vice versa.
If fred is not brave then mary is not brave and vice versa.
Susan is not wise.
Lucy is either creative or not brave.
Someone is both humble and not patient.
Fred is funny or not strong.
Someone is patient or not rich.
Mary is not generous or not happy.
Someone is not quiet or old.
Someone is generous. | Mary is not wise. | entailment | (((tall(lucy)<~>~quiet(lucy)))<=>(?[X]:(~calm(X))))&
(![X]:((~old(X)&creative(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(~curious(X)&~kind(X))))&
((?[X]:((~curious(X)&~brave(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(calm(X))))&
((funny(susan))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
((?[X]:((kind(X)|rich(X))))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:(strong(X)<=>(curious(X)&funny(X))))&
(![X]:(~creative(X)<=>(strong(X)&~quiet(X))))&
(![X]:((strong(X)&tall(X))<=>(brave(X)&tall(X))))&
(![X]:((generous(X)|strong(X))<=>(happy(X)<~>~brave(X))))&
(((~curious(alice)&humble(alice)))=>(~happy(fred)))&
(![X]:((~strong(X)|~calm(X))<=>(tall(X)<~>kind(X))))&
(![X]:(wise(X)=>(~wise(X)&~calm(X))))&
(![X]:(funny(X)<=>(quiet(X)|~tall(X))))&
((~brave(fred))<=>(~brave(mary)))&
(~wise(susan))&
((creative(lucy)<~>~brave(lucy)))&
(?[X]:((humble(X)&~patient(X))))&
((funny(fred)|~strong(fred)))&
(?[X]:((patient(X)|~rich(X))))&
((~generous(mary)|~happy(mary)))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:(generous(X))) | ~wise(mary) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 112447485649218575658097
% SZS output start Proof for 112447485649218575658097
14. ! [X0] : (wise(X0) => (~calm(X0) & ~wise(X0))) [input p13]
25. wise(mary) [input hypothesis]
36. ! [X0] : ((~calm(X0) & ~wise(X0)) | ~wise(X0)) [ennf transformation 14]
129. ~wise(X0) | ~wise(X0) [cnf transformation 36]
144. wise(mary) [cnf transformation 25]
145. ~wise(X0) [duplicate literal removal 129]
288. $false [subsumption resolution 144,145]
% SZS output end Proof for 112447485649218575658097
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not humble or not quiet and vice versa.
Everyone who is either brave or not brave is both creative and not patient and vice versa.
If lucy is curious then mary is old and vice versa.
Everyone who is both humble and tall is patient and vice versa.
Everyone who is not wise is not creative or not tall.
If someone is both rich and wise then someone is strong.
If lucy is not wise then someone is not happy.
If someone is not creative or quiet then paul is curious or not strong.
Everyone who is both not humble and not old is both not patient and not strong and vice versa.
If lucy is not rich then someone is not brave.
If someone is not brave or patient then mary is not tall and vice versa.
Everyone who is funny or happy is quiet.
If mary is both rich and old then someone is not quiet or funny and vice versa.
Everyone who is not kind is either not humble or rich.
Everyone who is either patient or not curious is not generous or not strong.
Everyone who is calm or not tall is creative and vice versa.
Paul is both not humble and kind.
John is wise or strong.
Someone is not curious.
Someone is either not calm or not strong.
Someone is tall.
Someone is either calm or quiet.
Someone is either not happy or rich. | Lucy is not patient. | entailment | (![X]:(strong(X)<=>(~humble(X)|~quiet(X))))&
(![X]:((brave(X)<~>~brave(X))<=>(creative(X)&~patient(X))))&
((curious(lucy))<=>(old(mary)))&
(![X]:((humble(X)&tall(X))<=>patient(X)))&
(![X]:(~wise(X)=>(~creative(X)|~tall(X))))&
((?[X]:((rich(X)&wise(X))))=>(?[X]:(strong(X))))&
((~wise(lucy))=>(?[X]:(~happy(X))))&
((?[X]:((~creative(X)|quiet(X))))=>((curious(paul)|~strong(paul))))&
(![X]:((~humble(X)&~old(X))<=>(~patient(X)&~strong(X))))&
((~rich(lucy))=>(?[X]:(~brave(X))))&
((?[X]:((~brave(X)|patient(X))))<=>(~tall(mary)))&
(![X]:((funny(X)|happy(X))=>quiet(X)))&
(((rich(mary)&old(mary)))<=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:(~kind(X)=>(~humble(X)<~>rich(X))))&
(![X]:((patient(X)<~>~curious(X))=>(~generous(X)|~strong(X))))&
(![X]:((calm(X)|~tall(X))<=>creative(X)))&
((~humble(paul)&kind(paul)))&
((wise(john)|strong(john)))&
(?[X]:(~curious(X)))&
(?[X]:((~calm(X)<~>~strong(X))))&
(?[X]:(tall(X)))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((~happy(X)<~>rich(X)))) | ~patient(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4366171538367179879422884
% SZS output start Proof for 4366171538367179879422884
2. ! [X0] : ((brave(X0) <~> ~brave(X0)) <=> (~patient(X0) & creative(X0))) [input p1]
24. patient(lucy) [input hypothesis]
39. ! [X0] : ((((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (patient(X0) | ~creative(X0))) & ((~patient(X0) & creative(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0))))) [nnf transformation 2]
40. ! [X0] : ((((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | patient(X0) | ~creative(X0)) & ((~patient(X0) & creative(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0))))) [flattening 39]
82. ~patient(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 40]
83. ~patient(X0) | brave(X0) | brave(X0) [cnf transformation 40]
124. patient(lucy) [cnf transformation 24]
127. ~patient(X0) | ~brave(X0) [duplicate literal removal 82]
128. ~patient(X0) | brave(X0) [duplicate literal removal 83]
129. ~patient(X0) [subsumption resolution 127,128]
244. $false [subsumption resolution 124,129]
% SZS output end Proof for 4366171538367179879422884
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not patient is either brave or calm and vice versa. If someone is patient or not kind then someone is both not funny and tall and vice versa. If someone is either calm or not curious then someone is both not tall and not brave. Everyone who is either curious or not tall is creative or not quiet and vice versa. Everyone who is either old or not strong is not strong and vice versa. If someone is either old or wise then someone is not humble or funny and vice versa. Everyone who is happy or funny is funny or not brave and vice versa. Everyone who is not tall or rich is creative or brave and vice versa. Everyone who is humble or not generous is either quiet or tall and vice versa. If someone is either not calm or not rich then paul is both not humble and rich. Everyone who is generous or not tall is both not happy and not brave. Everyone who is not quiet or rich is both quiet and not humble and vice versa. Everyone who is brave or patient is either not funny or not creative. If someone is old then lucy is happy or rich. Everyone who is both happy and curious is strong. John is not strong. Lucy is wise. Someone is quiet. Paul is not curious or not funny. | Lucy is generous. | neutral | (![X]:((~kind(X)|~patient(X))<=>(brave(X)<~>calm(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(?[X]:((~funny(X)&tall(X)))))&
((?[X]:((calm(X)<~>~curious(X))))=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>(creative(X)|~quiet(X))))&
(![X]:((old(X)<~>~strong(X))<=>~strong(X)))&
((?[X]:((old(X)<~>wise(X))))<=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((happy(X)|funny(X))<=>(funny(X)|~brave(X))))&
(![X]:((~tall(X)|rich(X))<=>(creative(X)|brave(X))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
(![X]:((brave(X)|patient(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:(old(X)))=>((happy(lucy)|rich(lucy))))&
(![X]:((happy(X)&curious(X))=>strong(X)))&
(~strong(john))&
(wise(lucy))&
(?[X]:(quiet(X)))&
((~curious(paul)|~funny(paul))) | generous(lucy) | [] | null | 0 |
Everyone who is not quiet is either old or not wise and vice versa. If someone is either rich or calm then mary is rich or strong. Everyone who is not calm is both not old and calm. If mary is not tall or not brave then someone is kind or strong. If someone is both not kind and not wise then someone is funny or wise. If someone is calm then someone is wise and vice versa. Everyone who is both curious and not tall is rich and vice versa. If someone is either not wise or kind then mary is tall and vice versa. Everyone who is not curious or brave is not tall or curious and vice versa. Everyone who is either quiet or not brave is both not strong and funny and vice versa. Everyone who is either not calm or not tall is both not funny and not happy and vice versa. If fred is either not brave or not wise then someone is either creative or brave and vice versa. If susan is either curious or kind then mary is not creative and vice versa. Everyone who is humble or creative is both not tall and not old and vice versa. Everyone who is not generous is funny. Everyone who is not patient or calm is not tall and vice versa. Someone is both not curious and not old. Someone is not creative or not tall. Someone is tall or not creative. Someone is creative or humble. Alice is either not happy or kind. Someone is tall or not tall. Paul is brave or not creative. | Alice is happy. | contradiction | (![X]:(~quiet(X)<=>(old(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>calm(X))))=>((rich(mary)|strong(mary))))&
(![X]:(~calm(X)=>(~old(X)&calm(X))))&
(((~tall(mary)|~brave(mary)))=>(?[X]:((kind(X)|strong(X)))))&
((?[X]:((~kind(X)&~wise(X))))=>(?[X]:((funny(X)|wise(X)))))&
((?[X]:(calm(X)))<=>(?[X]:(wise(X))))&
(![X]:((curious(X)&~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)<~>kind(X))))<=>(tall(mary)))&
(![X]:((~curious(X)|brave(X))<=>(~tall(X)|curious(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)&funny(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~funny(X)&~happy(X))))&
(((~brave(fred)<~>~wise(fred)))<=>(?[X]:((creative(X)<~>brave(X)))))&
(((curious(susan)<~>kind(susan)))<=>(~creative(mary)))&
(![X]:((humble(X)|creative(X))<=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)=>funny(X)))&
(![X]:((~patient(X)|calm(X))<=>~tall(X)))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:((~creative(X)|~tall(X))))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((creative(X)|humble(X))))&
((~happy(alice)<~>kind(alice)))&
(?[X]:((tall(X)|~tall(X))))&
((brave(paul)|~creative(paul))) | happy(alice) | [
"p2",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2799498477800097939734895
% SZS output start Proof for 2799498477800097939734895
3. ! [X0] : (~calm(X0) => (calm(X0) & ~old(X0))) [input p2]
11. ! [X0] : ((~calm(X0) <~> ~tall(X0)) <=> (~happy(X0) & ~funny(X0))) [input p10]
16. ! [X0] : ((calm(X0) | ~patient(X0)) <=> ~tall(X0)) [input p15]
24. happy(alice) [input hypothesis]
30. ! [X0] : ((calm(X0) & ~old(X0)) | calm(X0)) [ennf transformation 3]
55. ! [X0] : ((((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))))) [nnf transformation 11]
56. ! [X0] : ((((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))))) [flattening 55]
64. ! [X0] : (((calm(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [nnf transformation 16]
65. ! [X0] : ((calm(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [flattening 64]
84. calm(X0) | calm(X0) [cnf transformation 30]
110. ~happy(X0) | ~calm(X0) | tall(X0) [cnf transformation 56]
131. ~tall(X0) | ~calm(X0) [cnf transformation 65]
142. happy(alice) [cnf transformation 24]
145. calm(X0) [duplicate literal removal 84]
209. ~happy(X0) | tall(X0) [subsumption resolution 110,145]
257. ~tall(X0) [subsumption resolution 131,145]
269. 26 <=> happy(alice) [avatar definition]
271. happy(alice) <- (26) [avatar component clause 269]
287. 26 [avatar split clause 142,269]
302. tall(alice) <- (26) [resolution 209,271]
303. $false <- (26) [subsumption resolution 302,257]
304. ~26 [avatar contradiction clause 303]
305. $false [avatar sat refutation 287,304]
% SZS output end Proof for 2799498477800097939734895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not patient then someone is tall and vice versa. Everyone who is generous is quiet or not happy. If someone is either not brave or wise then someone is both curious and not calm and vice versa. Everyone who is not creative is either not patient or brave and vice versa. Everyone who is either not old or not creative is both old and wise and vice versa. Everyone who is either brave or not brave is generous or not strong and vice versa. If john is generous or not calm then fred is both not happy and not kind and vice versa. If john is not tall or not curious then mary is happy and vice versa. Everyone who is generous or strong is not curious or kind. If someone is both happy and calm then mary is not brave or not generous. If fred is either quiet or not quiet then someone is rich and vice versa. Everyone who is either not happy or humble is not calm and vice versa. Everyone who is both not quiet and not tall is not patient and vice versa. Everyone who is either strong or not humble is calm or brave. If lucy is either curious or not generous then susan is both brave and not brave. Everyone who is not brave is both not curious and happy. Someone is both not old and quiet. Lucy is happy or not humble. Paul is either not funny or quiet. Fred is both generous and not wise. Someone is both strong and not funny. Someone is either calm or funny. Someone is either not brave or creative. Someone is either not brave or not humble. | Lucy is generous. | neutral | ((~patient(susan))<=>(?[X]:(tall(X))))&
(![X]:(generous(X)=>(quiet(X)|~happy(X))))&
((?[X]:((~brave(X)<~>wise(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:(~creative(X)<=>(~patient(X)<~>brave(X))))&
(![X]:((~old(X)<~>~creative(X))<=>(old(X)&wise(X))))&
(![X]:((brave(X)<~>~brave(X))<=>(generous(X)|~strong(X))))&
(((generous(john)|~calm(john)))<=>((~happy(fred)&~kind(fred))))&
(((~tall(john)|~curious(john)))<=>(happy(mary)))&
(![X]:((generous(X)|strong(X))=>(~curious(X)|kind(X))))&
((?[X]:((happy(X)&calm(X))))=>((~brave(mary)|~generous(mary))))&
(((quiet(fred)<~>~quiet(fred)))<=>(?[X]:(rich(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~quiet(X)&~tall(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~humble(X))=>(calm(X)|brave(X))))&
(((curious(lucy)<~>~generous(lucy)))=>((brave(susan)&~brave(susan))))&
(![X]:(~brave(X)=>(~curious(X)&happy(X))))&
(?[X]:((~old(X)&quiet(X))))&
((happy(lucy)|~humble(lucy)))&
((~funny(paul)<~>quiet(paul)))&
((generous(fred)&~wise(fred)))&
(?[X]:((strong(X)&~funny(X))))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~brave(X)<~>creative(X))))&
(?[X]:((~brave(X)<~>~humble(X)))) | generous(lucy) | [] | null | 0 |
If someone is both not calm and funny then someone is either strong or tall. If alice is not funny or not quiet then mary is either tall or strong. If someone is brave then paul is either rich or strong and vice versa. If someone is either funny or not quiet then john is either not humble or not generous. Everyone who is not wise or strong is both calm and generous. Everyone who is either not calm or quiet is both old and not humble. Everyone who is either not kind or tall is either old or not wise. Everyone who is not strong or patient is either not old or kind. Everyone who is not funny or not tall is both tall and not brave and vice versa. If paul is brave or patient then someone is either strong or not happy and vice versa. Everyone who is both tall and kind is either wise or old and vice versa. If someone is old then someone is both not calm and not tall and vice versa. If someone is both creative and not funny then paul is both generous and funny. Everyone who is both calm and not kind is either not humble or not funny and vice versa. Everyone who is both not humble and happy is not old or generous and vice versa. If paul is both not quiet and happy then alice is not rich and vice versa. Paul is either not funny or happy. Someone is both curious and not quiet. Alice is not funny or not creative. Someone is not kind or patient. | John is not funny. | contradiction | ((?[X]:((~calm(X)&funny(X))))=>(?[X]:((strong(X)<~>tall(X)))))&
(((~funny(alice)|~quiet(alice)))=>((tall(mary)<~>strong(mary))))&
((?[X]:(brave(X)))<=>((rich(paul)<~>strong(paul))))&
((?[X]:((funny(X)<~>~quiet(X))))=>((~humble(john)<~>~generous(john))))&
(![X]:((~wise(X)|strong(X))=>(calm(X)&generous(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)&~humble(X))))&
(![X]:((~kind(X)<~>tall(X))=>(old(X)<~>~wise(X))))&
(![X]:((~strong(X)|patient(X))=>(~old(X)<~>kind(X))))&
(![X]:((~funny(X)|~tall(X))<=>(tall(X)&~brave(X))))&
(((brave(paul)|patient(paul)))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((tall(X)&kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(old(X)))<=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:((creative(X)&~funny(X))))=>((generous(paul)&funny(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~humble(X)&happy(X))<=>(~old(X)|generous(X))))&
(((~quiet(paul)&happy(paul)))<=>(~rich(alice)))&
((~funny(paul)<~>happy(paul)))&
(?[X]:((curious(X)&~quiet(X))))&
((~funny(alice)|~creative(alice)))&
(?[X]:((~kind(X)|patient(X)))) | ~funny(john) | [
"p4",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3963160672000743438507101
% SZS output start Proof for 3963160672000743438507101
5. ! [X0] : ((strong(X0) | ~wise(X0)) => (generous(X0) & calm(X0))) [input p4]
7. ! [X0] : ((~kind(X0) <~> tall(X0)) => (old(X0) <~> ~wise(X0))) [input p6]
8. ! [X0] : ((patient(X0) | ~strong(X0)) => (~old(X0) <~> kind(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (~brave(X0) & tall(X0))) [input p8]
11. ! [X0] : ((kind(X0) & tall(X0)) <=> (wise(X0) <~> old(X0))) [input p10]
12. ? [X0] : old(X0) <=> ? [X0] : (~tall(X0) & ~calm(X0)) [input p11]
14. ! [X0] : ((~kind(X0) & calm(X0)) <=> (~humble(X0) <~> ~funny(X0))) [input p13]
15. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (generous(X0) | ~old(X0))) [input p14]
21. ~funny(john) [input hypothesis]
23. ? [X0] : old(X0) <=> ? [X1] : (~tall(X1) & ~calm(X1)) [rectify 12]
30. ! [X0] : ((generous(X0) & calm(X0)) | (~strong(X0) & wise(X0))) [ennf transformation 5]
32. ! [X0] : ((old(X0) <~> ~wise(X0)) | (~kind(X0) <=> tall(X0))) [ennf transformation 7]
33. ! [X0] : ((~old(X0) <~> kind(X0)) | (~patient(X0) & strong(X0))) [ennf transformation 8]
45. ! [X0] : (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0)))) [nnf transformation 32]
46. ! [X0] : (((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (~patient(X0) & strong(X0))) [nnf transformation 33]
47. ! [X0] : (((~tall(X0) | ~funny(X0)) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [nnf transformation 9]
48. ! [X0] : ((~tall(X0) | ~funny(X0) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [flattening 47]
54. ! [X0] : (((kind(X0) & tall(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | (~kind(X0) | ~tall(X0)))) [nnf transformation 11]
55. ! [X0] : (((kind(X0) & tall(X0)) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ~kind(X0) | ~tall(X0))) [flattening 54]
56. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X1] : (~tall(X1) & ~calm(X1)) | ! [X0] : ~old(X0)) [nnf transformation 23]
57. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X2] : (~tall(X2) & ~calm(X2)) | ! [X3] : ~old(X3)) [rectify 56]
58. ? [X0] : old(X0) => old(sK3) [choice axiom]
59. ? [X2] : (~tall(X2) & ~calm(X2)) => (~tall(sK4) & ~calm(sK4)) [choice axiom]
60. (old(sK3) | ! [X1] : (tall(X1) | calm(X1))) & ((~tall(sK4) & ~calm(sK4)) | ! [X3] : ~old(X3)) [skolemisation 57,59,58]
61. ! [X0] : (((~kind(X0) & calm(X0)) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0)))) & (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | (kind(X0) | ~calm(X0)))) [nnf transformation 14]
62. ! [X0] : (((~kind(X0) & calm(X0)) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0)))) & (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | kind(X0) | ~calm(X0))) [flattening 61]
63. ! [X0] : (((happy(X0) & ~humble(X0)) | (~generous(X0) & old(X0))) & ((generous(X0) | ~old(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 15]
64. ! [X0] : (((happy(X0) & ~humble(X0)) | (~generous(X0) & old(X0))) & (generous(X0) | ~old(X0) | ~happy(X0) | humble(X0))) [flattening 63]
86. wise(X0) | calm(X0) [cnf transformation 30]
87. ~strong(X0) | calm(X0) [cnf transformation 30]
95. ~kind(X0) | old(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 45]
100. ~kind(X0) | old(X0) | strong(X0) [cnf transformation 46]
103. tall(X0) | tall(X0) [cnf transformation 48]
113. old(X0) | wise(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 55]
117. ~wise(X0) | old(X0) | kind(X0) [cnf transformation 55]
120. ~tall(sK4) | ~old(X3) [cnf transformation 60]
123. ~calm(X0) | humble(X0) | kind(X0) | funny(X0) [cnf transformation 62]
129. ~humble(X0) | old(X0) [cnf transformation 64]
140. ~funny(john) [cnf transformation 21]
141. tall(X0) [duplicate literal removal 103]
242. ~kind(X0) | wise(X0) | old(X0) [subsumption resolution 113,141]
243. ~old(X3) [subsumption resolution 120,141]
245. ~humble(X0) [subsumption resolution 129,243]
295. old(X1) | kind(X1) | calm(X1) [resolution 117,86]
297. kind(X1) | calm(X1) [subsumption resolution 295,243]
316. calm(X2) | old(X2) | strong(X2) [resolution 297,100]
318. calm(X2) | strong(X2) [subsumption resolution 316,243]
319. calm(X2) [subsumption resolution 318,87]
339. humble(X0) | kind(X0) | funny(X0) [resolution 123,319]
345. kind(X0) | funny(X0) [subsumption resolution 339,245]
347. funny(X0) | old(X0) | ~wise(X0) | ~tall(X0) [resolution 345,95]
353. funny(X6) | wise(X6) | old(X6) [resolution 345,242]
356. funny(X0) | ~wise(X0) | ~tall(X0) [subsumption resolution 347,243]
357. funny(X0) | ~wise(X0) [subsumption resolution 356,141]
359. funny(X6) | wise(X6) [subsumption resolution 353,243]
360. funny(X6) [subsumption resolution 359,357]
363. $false [resolution 360,140]
% SZS output end Proof for 3963160672000743438507101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or happy is rich or patient.
Everyone who is either not quiet or not strong is curious and vice versa.
If someone is both not kind and quiet then someone is generous or humble.
If alice is both humble and not funny then someone is rich and vice versa.
If someone is not humble then someone is brave or not quiet and vice versa.
If someone is not strong then someone is not funny and vice versa.
Everyone who is either not strong or not wise is both calm and not curious.
Everyone who is not generous or not happy is curious and vice versa.
If paul is both not strong and calm then paul is not funny or tall.
Everyone who is not calm or not strong is patient or not tall and vice versa.
If someone is both not quiet and funny then someone is strong or quiet and vice versa.
If someone is both not creative and not patient then alice is quiet.
Everyone who is humble or curious is either not quiet or calm and vice versa.
If someone is not strong then someone is either kind or not rich.
Everyone who is patient is creative or wise and vice versa.
Everyone who is either kind or not patient is not quiet or not generous.
Alice is not humble.
Someone is not old.
Alice is not curious or not tall.
Someone is either patient or rich.
Mary is both calm and old.
Lucy is rich or not strong.
Someone is both not tall and old.
Someone is either funny or old. | Alice is calm. | neutral | (![X]:((rich(X)<~>happy(X))=>(rich(X)|patient(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>curious(X)))&
((?[X]:((~kind(X)&quiet(X))))=>(?[X]:((generous(X)|humble(X)))))&
(((humble(alice)&~funny(alice)))<=>(?[X]:(rich(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((brave(X)|~quiet(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:(~funny(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(calm(X)&~curious(X))))&
(![X]:((~generous(X)|~happy(X))<=>curious(X)))&
(((~strong(paul)&calm(paul)))=>((~funny(paul)|tall(paul))))&
(![X]:((~calm(X)|~strong(X))<=>(patient(X)|~tall(X))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((strong(X)|quiet(X)))))&
((?[X]:((~creative(X)&~patient(X))))=>(quiet(alice)))&
(![X]:((humble(X)|curious(X))<=>(~quiet(X)<~>calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:(patient(X)<=>(creative(X)|wise(X))))&
(![X]:((kind(X)<~>~patient(X))=>(~quiet(X)|~generous(X))))&
(~humble(alice))&
(?[X]:(~old(X)))&
((~curious(alice)|~tall(alice)))&
(?[X]:((patient(X)<~>rich(X))))&
((calm(mary)&old(mary)))&
((rich(lucy)|~strong(lucy)))&
(?[X]:((~tall(X)&old(X))))&
(?[X]:((funny(X)<~>old(X)))) | calm(alice) | [] | null | 0 |
Everyone who is brave or not creative is not old or quiet.
Everyone who is not calm or funny is both generous and not brave and vice versa.
Everyone who is either not curious or quiet is not brave or wise and vice versa.
If someone is not quiet or creative then someone is not calm or humble.
Everyone who is either wise or funny is both brave and not old.
Everyone who is not quiet or curious is funny and vice versa.
Everyone who is either old or creative is either creative or patient.
Everyone who is patient or not quiet is not brave and vice versa.
Everyone who is either not kind or not curious is not tall or not generous.
If someone is both funny and not brave then someone is either generous or kind.
If mary is either patient or curious then mary is either patient or not happy.
If someone is both generous and not funny then susan is both not funny and curious and vice versa.
If someone is both not funny and patient then alice is creative or not creative.
If someone is both not patient and calm then someone is calm and vice versa.
If alice is not tall or not funny then alice is kind or generous and vice versa.
If someone is both not funny and patient then someone is either curious or not tall.
Someone is both old and brave.
Someone is either not strong or strong.
Someone is tall or not strong.
Someone is either not creative or not wise.
Alice is calm or not wise.
Paul is both not funny and not humble.
Someone is either curious or not curious.
Mary is not wise. | Mary is calm. | entailment | (![X]:((brave(X)|~creative(X))=>(~old(X)|quiet(X))))&
(![X]:((~calm(X)|funny(X))<=>(generous(X)&~brave(X))))&
(![X]:((~curious(X)<~>quiet(X))<=>(~brave(X)|wise(X))))&
((?[X]:((~quiet(X)|creative(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((wise(X)<~>funny(X))=>(brave(X)&~old(X))))&
(![X]:((~quiet(X)|curious(X))<=>funny(X)))&
(![X]:((old(X)<~>creative(X))=>(creative(X)<~>patient(X))))&
(![X]:((patient(X)|~quiet(X))<=>~brave(X)))&
(![X]:((~kind(X)<~>~curious(X))=>(~tall(X)|~generous(X))))&
((?[X]:((funny(X)&~brave(X))))=>(?[X]:((generous(X)<~>kind(X)))))&
(((patient(mary)<~>curious(mary)))=>((patient(mary)<~>~happy(mary))))&
((?[X]:((generous(X)&~funny(X))))<=>((~funny(susan)&curious(susan))))&
((?[X]:((~funny(X)&patient(X))))=>((creative(alice)|~creative(alice))))&
((?[X]:((~patient(X)&calm(X))))<=>(?[X]:(calm(X))))&
(((~tall(alice)|~funny(alice)))<=>((kind(alice)|generous(alice))))&
((?[X]:((~funny(X)&patient(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(?[X]:((old(X)&brave(X))))&
(?[X]:((~strong(X)<~>strong(X))))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:((~creative(X)<~>~wise(X))))&
((calm(alice)|~wise(alice)))&
((~funny(paul)&~humble(paul)))&
(?[X]:((curious(X)<~>~curious(X))))&
(~wise(mary)) | calm(mary) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 141022170645165712386786
% SZS output start Proof for 141022170645165712386786
2. ! [X0] : ((funny(X0) | ~calm(X0)) <=> (~brave(X0) & generous(X0))) [input p1]
3. ! [X0] : ((~curious(X0) <~> quiet(X0)) <=> (wise(X0) | ~brave(X0))) [input p2]
5. ! [X0] : ((wise(X0) <~> funny(X0)) => (~old(X0) & brave(X0))) [input p4]
6. ! [X0] : ((curious(X0) | ~quiet(X0)) <=> funny(X0)) [input p5]
8. ! [X0] : ((~quiet(X0) | patient(X0)) <=> ~brave(X0)) [input p7]
24. ~wise(mary) [input p23]
25. ~calm(mary) [input hypothesis]
33. ! [X0] : ((~old(X0) & brave(X0)) | (wise(X0) <=> funny(X0))) [ennf transformation 5]
42. ! [X0] : (((funny(X0) | ~calm(X0)) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | (~funny(X0) & calm(X0)))) [nnf transformation 2]
43. ! [X0] : ((funny(X0) | ~calm(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | (~funny(X0) & calm(X0)))) [flattening 42]
44. ! [X0] : ((((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))))) [nnf transformation 3]
45. ! [X0] : ((((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))))) [flattening 44]
49. ! [X0] : ((~old(X0) & brave(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) [nnf transformation 33]
50. ! [X0] : (((curious(X0) | ~quiet(X0)) | ~funny(X0)) & (funny(X0) | (~curious(X0) & quiet(X0)))) [nnf transformation 6]
51. ! [X0] : ((curious(X0) | ~quiet(X0) | ~funny(X0)) & (funny(X0) | (~curious(X0) & quiet(X0)))) [flattening 50]
53. ! [X0] : (((~quiet(X0) | patient(X0)) | brave(X0)) & (~brave(X0) | (quiet(X0) & ~patient(X0)))) [nnf transformation 8]
54. ! [X0] : ((~quiet(X0) | patient(X0) | brave(X0)) & (~brave(X0) | (quiet(X0) & ~patient(X0)))) [flattening 53]
94. ~brave(X0) | calm(X0) [cnf transformation 43]
95. ~funny(X0) | ~brave(X0) [cnf transformation 43]
101. ~quiet(X0) | curious(X0) | brave(X0) [cnf transformation 45]
106. brave(X0) | wise(X0) | ~funny(X0) [cnf transformation 49]
109. funny(X0) | quiet(X0) [cnf transformation 51]
110. ~curious(X0) | funny(X0) [cnf transformation 51]
116. ~patient(X0) | ~brave(X0) [cnf transformation 54]
118. ~quiet(X0) | patient(X0) | brave(X0) [cnf transformation 54]
153. ~wise(mary) [cnf transformation 24]
154. ~calm(mary) [cnf transformation 25]
175. ~funny(X0) | wise(X0) [subsumption resolution 106,95]
192. 8 <=> curious(mary) [avatar definition]
194. curious(mary) <- (8) [avatar component clause 192]
196. 9 <=> patient(mary) [avatar definition]
197. patient(mary) <- (9) [avatar component clause 196]
198. ~patient(mary) <- (~9) [avatar component clause 196]
311. wise(X0) | quiet(X0) [resolution 175,109]
433. quiet(mary) [resolution 311,153]
438. patient(mary) | brave(mary) [resolution 433,118]
439. curious(mary) | brave(mary) [resolution 433,101]
440. brave(mary) <- (~9) [subsumption resolution 438,198]
518. calm(mary) <- (~9) [resolution 440,94]
519. $false <- (~9) [subsumption resolution 518,154]
520. 9 [avatar contradiction clause 519]
522. 53 <=> brave(mary) [avatar definition]
525. 53 | 8 [avatar split clause 439,192,522]
529. funny(mary) <- (8) [resolution 194,110]
534. ~brave(mary) <- (9) [resolution 197,116]
546. wise(mary) <- (8) [resolution 529,175]
551. $false <- (8) [subsumption resolution 546,153]
552. ~8 [avatar contradiction clause 551]
553. ~53 | ~9 [avatar split clause 534,196,522]
554. $false [avatar sat refutation 520,525,552,553]
% SZS output end Proof for 141022170645165712386786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not calm is both funny and not patient and vice versa.
Everyone who is rich or not patient is both not patient and humble and vice versa.
If someone is either not wise or not happy then alice is both not calm and not kind.
Everyone who is either not happy or not patient is both rich and not wise.
Everyone who is either old or not tall is not generous or rich.
If fred is kind then susan is either tall or happy and vice versa.
Everyone who is either happy or not curious is old or patient.
If someone is not humble or tall then someone is either not old or not kind and vice versa.
If someone is not humble then someone is both kind and calm and vice versa.
Everyone who is both not humble and humble is either not calm or not brave and vice versa.
Everyone who is either creative or generous is either not wise or not funny.
If john is either kind or tall then susan is creative or not strong.
Everyone who is either curious or not old is happy and vice versa.
If someone is curious then someone is not generous or kind and vice versa.
Everyone who is either generous or not calm is brave and vice versa.
If someone is patient then lucy is both not creative and wise.
Fred is not rich or not curious.
Mary is both not wise and humble.
Susan is either not tall or not old.
Alice is patient or not quiet.
Susan is either old or humble. | John is not kind. | neutral | (![X]:((generous(X)<~>~calm(X))<=>(funny(X)&~patient(X))))&
(![X]:((rich(X)|~patient(X))<=>(~patient(X)&humble(X))))&
((?[X]:((~wise(X)<~>~happy(X))))=>((~calm(alice)&~kind(alice))))&
(![X]:((~happy(X)<~>~patient(X))=>(rich(X)&~wise(X))))&
(![X]:((old(X)<~>~tall(X))=>(~generous(X)|rich(X))))&
((kind(fred))<=>((tall(susan)<~>happy(susan))))&
(![X]:((happy(X)<~>~curious(X))=>(old(X)|patient(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~old(X)<~>~kind(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((~humble(X)&humble(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((creative(X)<~>generous(X))=>(~wise(X)<~>~funny(X))))&
(((kind(john)<~>tall(john)))=>((creative(susan)|~strong(susan))))&
(![X]:((curious(X)<~>~old(X))<=>happy(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:((generous(X)<~>~calm(X))<=>brave(X)))&
((?[X]:(patient(X)))=>((~creative(lucy)&wise(lucy))))&
((~rich(fred)|~curious(fred)))&
((~wise(mary)&humble(mary)))&
((~tall(susan)<~>~old(susan)))&
((patient(alice)|~quiet(alice)))&
((old(susan)<~>humble(susan))) | ~kind(john) | [] | null | 0 |
If someone is not generous or not quiet then someone is either happy or not calm and vice versa.
Everyone who is both quiet and not old is not strong or not funny and vice versa.
If someone is either not rich or old then someone is either not wise or quiet and vice versa.
Everyone who is both not strong and patient is not quiet and vice versa.
If john is either happy or not old then someone is both not curious and not tall and vice versa.
If paul is not strong then someone is calm and vice versa.
Everyone who is either kind or not calm is not happy or not old and vice versa.
If paul is both not wise and not old then alice is happy and vice versa.
If someone is wise then lucy is not brave and vice versa.
If paul is not strong then someone is not kind and vice versa.
Everyone who is both strong and humble is quiet.
Everyone who is either not quiet or kind is either not curious or not funny.
Everyone who is both wise and not funny is both calm and not tall.
Everyone who is either rich or not funny is either not creative or wise and vice versa.
Everyone who is either curious or quiet is either not generous or not happy.
Everyone who is both generous and not humble is not old or not creative and vice versa.
Someone is calm.
Paul is not wise or not creative.
Someone is not humble.
Someone is not strong or not humble.
Someone is humble or brave.
Someone is either not quiet or quiet.
Paul is both curious and creative.
Someone is either not creative or happy. | John is not tall. | neutral | ((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((happy(X)<~>~calm(X)))))&
(![X]:((quiet(X)&~old(X))<=>(~strong(X)|~funny(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((~strong(X)&patient(X))<=>~quiet(X)))&
(((happy(john)<~>~old(john)))<=>(?[X]:((~curious(X)&~tall(X)))))&
((~strong(paul))<=>(?[X]:(calm(X))))&
(![X]:((kind(X)<~>~calm(X))<=>(~happy(X)|~old(X))))&
(((~wise(paul)&~old(paul)))<=>(happy(alice)))&
((?[X]:(wise(X)))<=>(~brave(lucy)))&
((~strong(paul))<=>(?[X]:(~kind(X))))&
(![X]:((strong(X)&humble(X))=>quiet(X)))&
(![X]:((~quiet(X)<~>kind(X))=>(~curious(X)<~>~funny(X))))&
(![X]:((wise(X)&~funny(X))=>(calm(X)&~tall(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((curious(X)<~>quiet(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((generous(X)&~humble(X))<=>(~old(X)|~creative(X))))&
(?[X]:(calm(X)))&
((~wise(paul)|~creative(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((~quiet(X)<~>quiet(X))))&
((curious(paul)&creative(paul)))&
(?[X]:((~creative(X)<~>happy(X)))) | ~tall(john) | [] | null | 0 |
If john is both wise and rich then lucy is not happy. Everyone who is both not humble and kind is both rich and not kind and vice versa. If alice is tall then someone is not old. If someone is old or strong then fred is funny and vice versa. Everyone who is both curious and not patient is humble or not humble. Everyone who is either not rich or not humble is brave or funny. If susan is either not happy or calm then someone is either brave or not happy and vice versa. If susan is quiet then someone is brave and vice versa. Everyone who is old or not strong is either not wise or not generous. If paul is not old then lucy is either not rich or happy and vice versa. If someone is either patient or not kind then lucy is both strong and not strong. Everyone who is either patient or not rich is both kind and not humble. If lucy is brave then someone is not tall or strong. If someone is either not creative or not calm then someone is both not wise and old and vice versa. Everyone who is either not calm or not old is generous and vice versa. Everyone who is either not generous or not patient is rich. Fred is kind or not strong. Lucy is both not quiet and not brave. Someone is either creative or strong. Someone is either not calm or not humble. Alice is both kind and not creative. Someone is both not old and curious. Someone is not generous or not funny. | Alice is patient. | contradiction | (((wise(john)&rich(john)))=>(~happy(lucy)))&
(![X]:((~humble(X)&kind(X))<=>(rich(X)&~kind(X))))&
((tall(alice))=>(?[X]:(~old(X))))&
((?[X]:((old(X)|strong(X))))<=>(funny(fred)))&
(![X]:((curious(X)&~patient(X))=>(humble(X)|~humble(X))))&
(![X]:((~rich(X)<~>~humble(X))=>(brave(X)|funny(X))))&
(((~happy(susan)<~>calm(susan)))<=>(?[X]:((brave(X)<~>~happy(X)))))&
((quiet(susan))<=>(?[X]:(brave(X))))&
(![X]:((old(X)|~strong(X))=>(~wise(X)<~>~generous(X))))&
((~old(paul))<=>((~rich(lucy)<~>happy(lucy))))&
((?[X]:((patient(X)<~>~kind(X))))=>((strong(lucy)&~strong(lucy))))&
(![X]:((patient(X)<~>~rich(X))=>(kind(X)&~humble(X))))&
((brave(lucy))=>(?[X]:((~tall(X)|strong(X)))))&
((?[X]:((~creative(X)<~>~calm(X))))<=>(?[X]:((~wise(X)&old(X)))))&
(![X]:((~calm(X)<~>~old(X))<=>generous(X)))&
(![X]:((~generous(X)<~>~patient(X))=>rich(X)))&
((kind(fred)|~strong(fred)))&
((~quiet(lucy)&~brave(lucy)))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:((~calm(X)<~>~humble(X))))&
((kind(alice)&~creative(alice)))&
(?[X]:((~old(X)&curious(X))))&
(?[X]:((~generous(X)|~funny(X)))) | patient(alice) | [
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6654607580093871582434349
% SZS output start Proof for 6654607580093871582434349
11. ? [X0] : (patient(X0) <~> ~kind(X0)) => (~strong(lucy) & strong(lucy)) [input p10]
21. ~creative(alice) & kind(alice) [input p20]
24. patient(alice) [input hypothesis]
35. (~strong(lucy) & strong(lucy)) | ! [X0] : (patient(X0) <=> ~kind(X0)) [ennf transformation 11]
55. (~strong(lucy) & strong(lucy)) | ! [X0] : ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))) [nnf transformation 35]
103. strong(lucy) | ~kind(X0) | ~patient(X0) [cnf transformation 55]
105. ~strong(lucy) | ~kind(X0) | ~patient(X0) [cnf transformation 55]
130. kind(alice) [cnf transformation 21]
135. patient(alice) [cnf transformation 24]
231. 21 <=> strong(lucy) [avatar definition]
236. 22 <=> ! [X0] : (~kind(X0) | ~patient(X0)) [avatar definition]
237. ~patient(X0) | ~kind(X0) <- (22) [avatar component clause 236]
238. 22 | ~21 [avatar split clause 105,231,236]
240. 22 | 21 [avatar split clause 103,231,236]
313. ~kind(alice) <- (22) [resolution 237,135]
315. $false <- (22) [subsumption resolution 313,130]
316. ~22 [avatar contradiction clause 315]
317. $false [avatar sat refutation 238,240,316]
% SZS output end Proof for 6654607580093871582434349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is quiet.
If lucy is not patient then someone is tall or happy and vice versa.
Everyone who is both not wise and wise is either kind or not calm.
Everyone who is either calm or not wise is both not patient and humble and vice versa.
If lucy is funny or not patient then someone is not funny or rich and vice versa.
If someone is calm then someone is funny or old and vice versa.
Everyone who is not rich is not humble and vice versa.
Everyone who is either patient or not patient is either not tall or not creative.
Everyone who is not brave or not calm is either calm or quiet and vice versa.
If someone is both patient and not tall then susan is both not quiet and happy and vice versa.
Everyone who is both not happy and not curious is not curious or tall and vice versa.
Everyone who is either humble or brave is both not humble and curious.
If someone is calm then someone is curious and vice versa.
If someone is both not patient and wise then someone is either funny or not tall.
If someone is either tall or not rich then lucy is both not calm and not quiet and vice versa.
If someone is not quiet or not curious then john is either not patient or funny.
Susan is both humble and not calm.
Lucy is either not curious or quiet.
Fred is both calm and not patient.
Paul is both not curious and not tall.
Alice is either kind or not curious.
Lucy is curious or quiet.
Someone is either tall or kind.
Paul is not tall. | Lucy is not brave. | contradiction | (![X]:(funny(X)=>quiet(X)))&
((~patient(lucy))<=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((~wise(X)&wise(X))=>(kind(X)<~>~calm(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~patient(X)&humble(X))))&
(((funny(lucy)|~patient(lucy)))<=>(?[X]:((~funny(X)|rich(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((funny(X)|old(X)))))&
(![X]:(~rich(X)<=>~humble(X)))&
(![X]:((patient(X)<~>~patient(X))=>(~tall(X)<~>~creative(X))))&
(![X]:((~brave(X)|~calm(X))<=>(calm(X)<~>quiet(X))))&
((?[X]:((patient(X)&~tall(X))))<=>((~quiet(susan)&happy(susan))))&
(![X]:((~happy(X)&~curious(X))<=>(~curious(X)|tall(X))))&
(![X]:((humble(X)<~>brave(X))=>(~humble(X)&curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:(curious(X))))&
((?[X]:((~patient(X)&wise(X))))=>(?[X]:((funny(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>~rich(X))))<=>((~calm(lucy)&~quiet(lucy))))&
((?[X]:((~quiet(X)|~curious(X))))=>((~patient(john)<~>funny(john))))&
((humble(susan)&~calm(susan)))&
((~curious(lucy)<~>quiet(lucy)))&
((calm(fred)&~patient(fred)))&
((~curious(paul)&~tall(paul)))&
((kind(alice)<~>~curious(alice)))&
((curious(lucy)|quiet(lucy)))&
(?[X]:((tall(X)<~>kind(X))))&
(~tall(paul)) | ~brave(lucy) | [
"p6",
"p10",
"p11",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8825450789865742357644078
% SZS output start Proof for 8825450789865742357644078
7. ! [X0] : (~rich(X0) <=> ~humble(X0)) [input p6]
11. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> (tall(X0) | ~curious(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> brave(X0)) => (curious(X0) & ~humble(X0))) [input p11]
15. ? [X0] : (tall(X0) <~> ~rich(X0)) <=> (~quiet(lucy) & ~calm(lucy)) [input p14]
18. ~curious(lucy) <~> quiet(lucy) [input p17]
22. quiet(lucy) | curious(lucy) [input p21]
25. ~brave(lucy) [input hypothesis]
33. ! [X0] : ((curious(X0) & ~humble(X0)) | (humble(X0) <=> brave(X0))) [ennf transformation 12]
53. ! [X0] : ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))) [nnf transformation 7]
62. ! [X0] : (((~curious(X0) & ~happy(X0)) | (~tall(X0) & curious(X0))) & ((tall(X0) | ~curious(X0)) | (curious(X0) | happy(X0)))) [nnf transformation 11]
63. ! [X0] : (((~curious(X0) & ~happy(X0)) | (~tall(X0) & curious(X0))) & (tall(X0) | ~curious(X0) | curious(X0) | happy(X0))) [flattening 62]
64. ! [X0] : ((curious(X0) & ~humble(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) [nnf transformation 33]
74. (? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | (quiet(lucy) | calm(lucy))) & ((~quiet(lucy) & ~calm(lucy)) | ! [X0] : ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [nnf transformation 15]
75. (? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | quiet(lucy) | calm(lucy)) & ((~quiet(lucy) & ~calm(lucy)) | ! [X0] : ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [flattening 74]
76. (? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | quiet(lucy) | calm(lucy)) & ((~quiet(lucy) & ~calm(lucy)) | ! [X1] : ((tall(X1) | rich(X1)) & (~rich(X1) | ~tall(X1)))) [rectify 75]
77. ? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) => ((rich(sK8) | ~tall(sK8)) & (~rich(sK8) | tall(sK8))) [choice axiom]
78. (((rich(sK8) | ~tall(sK8)) & (~rich(sK8) | tall(sK8))) | quiet(lucy) | calm(lucy)) & ((~quiet(lucy) & ~calm(lucy)) | ! [X1] : ((tall(X1) | rich(X1)) & (~rich(X1) | ~tall(X1)))) [skolemisation 76,77]
80. (~quiet(lucy) | curious(lucy)) & (quiet(lucy) | ~curious(lucy)) [nnf transformation 18]
105. ~rich(X0) | humble(X0) [cnf transformation 53]
124. ~curious(X0) | ~tall(X0) [cnf transformation 63]
125. ~humble(X0) | brave(X0) | ~humble(X0) [cnf transformation 64]
136. ~quiet(lucy) | tall(X1) | rich(X1) [cnf transformation 78]
145. quiet(lucy) | ~curious(lucy) [cnf transformation 80]
146. ~quiet(lucy) | curious(lucy) [cnf transformation 80]
153. quiet(lucy) | curious(lucy) [cnf transformation 22]
157. ~brave(lucy) [cnf transformation 25]
158. ~humble(X0) | brave(X0) [duplicate literal removal 125]
284. 28 <=> ! [X1] : (tall(X1) | rich(X1)) [avatar definition]
285. rich(X1) | tall(X1) <- (28) [avatar component clause 284]
287. 29 <=> quiet(lucy) [avatar definition]
290. 28 | ~29 [avatar split clause 136,287,284]
320. 36 <=> curious(lucy) [avatar definition]
322. curious(lucy) <- (36) [avatar component clause 320]
323. 36 | ~29 [avatar split clause 146,287,320]
324. ~36 | 29 [avatar split clause 145,287,320]
335. 36 | 29 [avatar split clause 153,287,320]
357. ~tall(lucy) <- (36) [resolution 124,322]
370. humble(X0) | tall(X0) <- (28) [resolution 285,105]
462. brave(X1) | tall(X1) <- (28) [resolution 370,158]
467. tall(lucy) <- (28) [resolution 462,157]
470. $false <- (28, 36) [subsumption resolution 467,357]
471. ~28 | ~36 [avatar contradiction clause 470]
473. $false [avatar sat refutation 290,323,324,335,471]
% SZS output end Proof for 8825450789865742357644078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and rich is either not creative or old and vice versa.
If fred is funny or strong then someone is either not wise or not tall and vice versa.
If lucy is both not patient and tall then mary is brave or generous and vice versa.
Everyone who is both not humble and not rich is both curious and not happy and vice versa.
If john is either old or not strong then susan is both not wise and tall.
If someone is strong or not calm then someone is not kind or not wise.
Everyone who is not old is humble.
Everyone who is both not curious and not strong is both not quiet and not happy.
Everyone who is both not happy and happy is either not kind or not quiet and vice versa.
Everyone who is not strong or calm is not wise or funny and vice versa.
Everyone who is either funny or curious is not tall.
If paul is either tall or not happy then susan is calm and vice versa.
If someone is happy or patient then alice is brave or not creative and vice versa.
Everyone who is not curious or generous is kind or not patient and vice versa.
Everyone who is either not kind or rich is not generous or patient and vice versa.
If lucy is both humble and brave then someone is both kind and not happy and vice versa.
Mary is not generous or curious.
Someone is not curious.
Someone is both creative and old.
Someone is either not funny or not wise.
John is not funny.
Someone is both generous and not happy.
Someone is both not brave and tall. | Lucy is not wise. | neutral | (![X]:((curious(X)&rich(X))<=>(~creative(X)<~>old(X))))&
(((funny(fred)|strong(fred)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
(((~patient(lucy)&tall(lucy)))<=>((brave(mary)|generous(mary))))&
(![X]:((~humble(X)&~rich(X))<=>(curious(X)&~happy(X))))&
(((old(john)<~>~strong(john)))=>((~wise(susan)&tall(susan))))&
((?[X]:((strong(X)|~calm(X))))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:(~old(X)=>humble(X)))&
(![X]:((~curious(X)&~strong(X))=>(~quiet(X)&~happy(X))))&
(![X]:((~happy(X)&happy(X))<=>(~kind(X)<~>~quiet(X))))&
(![X]:((~strong(X)|calm(X))<=>(~wise(X)|funny(X))))&
(![X]:((funny(X)<~>curious(X))=>~tall(X)))&
(((tall(paul)<~>~happy(paul)))<=>(calm(susan)))&
((?[X]:((happy(X)|patient(X))))<=>((brave(alice)|~creative(alice))))&
(![X]:((~curious(X)|generous(X))<=>(kind(X)|~patient(X))))&
(![X]:((~kind(X)<~>rich(X))<=>(~generous(X)|patient(X))))&
(((humble(lucy)&brave(lucy)))<=>(?[X]:((kind(X)&~happy(X)))))&
((~generous(mary)|curious(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((creative(X)&old(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(~funny(john))&
(?[X]:((generous(X)&~happy(X))))&
(?[X]:((~brave(X)&tall(X)))) | ~wise(lucy) | [] | null | 0 |
Everyone who is both not calm and generous is both not old and not humble.
If john is both calm and not funny then alice is either calm or generous and vice versa.
If alice is both not strong and happy then someone is curious or not calm and vice versa.
Everyone who is not happy or not brave is creative or not quiet.
If susan is patient then fred is either not patient or happy and vice versa.
Everyone who is kind is both not curious and not brave and vice versa.
If someone is not old then fred is both not happy and quiet and vice versa.
Everyone who is either strong or not calm is both humble and not generous and vice versa.
Everyone who is both not creative and generous is either tall or old.
If someone is not strong or generous then someone is both calm and curious.
Everyone who is both not strong and not tall is either not happy or not kind.
If john is either curious or quiet then susan is not old and vice versa.
Everyone who is not kind is both curious and not generous.
If mary is kind or wise then lucy is either patient or creative.
If someone is not humble then fred is both funny and not funny and vice versa.
If fred is curious then someone is creative and vice versa.
Someone is kind.
Someone is either not tall or strong.
Someone is both strong and tall.
Someone is not happy.
Lucy is brave or not curious.
Alice is not creative or not funny.
Mary is curious. | Lucy is not funny. | neutral | (![X]:((~calm(X)&generous(X))=>(~old(X)&~humble(X))))&
(((calm(john)&~funny(john)))<=>((calm(alice)<~>generous(alice))))&
(((~strong(alice)&happy(alice)))<=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:((~happy(X)|~brave(X))=>(creative(X)|~quiet(X))))&
((patient(susan))<=>((~patient(fred)<~>happy(fred))))&
(![X]:(kind(X)<=>(~curious(X)&~brave(X))))&
((?[X]:(~old(X)))<=>((~happy(fred)&quiet(fred))))&
(![X]:((strong(X)<~>~calm(X))<=>(humble(X)&~generous(X))))&
(![X]:((~creative(X)&generous(X))=>(tall(X)<~>old(X))))&
((?[X]:((~strong(X)|generous(X))))=>(?[X]:((calm(X)&curious(X)))))&
(![X]:((~strong(X)&~tall(X))=>(~happy(X)<~>~kind(X))))&
(((curious(john)<~>quiet(john)))<=>(~old(susan)))&
(![X]:(~kind(X)=>(curious(X)&~generous(X))))&
(((kind(mary)|wise(mary)))=>((patient(lucy)<~>creative(lucy))))&
((?[X]:(~humble(X)))<=>((funny(fred)&~funny(fred))))&
((curious(fred))<=>(?[X]:(creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((~tall(X)<~>strong(X))))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:(~happy(X)))&
((brave(lucy)|~curious(lucy)))&
((~creative(alice)|~funny(alice)))&
(curious(mary)) | ~funny(lucy) | [] | null | 0 |
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