premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is both not curious and kind is not strong or tall.
Everyone who is funny or creative is both not strong and tall.
Everyone who is not brave or not patient is not funny.
Everyone who is happy or not tall is either not generous or generous and vice versa.
Everyone who is happy or brave is rich and vice versa.
Everyone who is curious or kind is both not old and not curious.
If paul is either strong or humble then lucy is not rich or curious.
If paul is generous or not kind then susan is creative and vice versa.
If someone is calm or kind then someone is patient or old and vice versa.
Everyone who is quiet or not funny is either not calm or curious.
Everyone who is rich is not quiet or funny.
If someone is not rich then someone is either not old or calm and vice versa.
Everyone who is not strong or not calm is either curious or quiet and vice versa.
If lucy is either humble or not curious then someone is both old and generous.
Someone is generous or funny.
Someone is both not funny and not brave.
John is not funny or rich.
Someone is not funny. | Paul is quiet. | entailment | (![X]:((~curious(X)&kind(X))=>(~strong(X)|tall(X))))&
(![X]:((funny(X)|creative(X))=>(~strong(X)&tall(X))))&
(![X]:((~brave(X)|~patient(X))=>~funny(X)))&
(![X]:((happy(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((happy(X)|brave(X))<=>rich(X)))&
(![X]:((curious(X)|kind(X))=>(~old(X)&~curious(X))))&
(((strong(paul)<~>humble(paul)))=>((~rich(lucy)|curious(lucy))))&
(((generous(paul)|~kind(paul)))<=>(creative(susan)))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~calm(X)<~>curious(X))))&
(![X]:(rich(X)=>(~quiet(X)|funny(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)<~>quiet(X))))&
(((humble(lucy)<~>~curious(lucy)))=>(?[X]:((old(X)&generous(X)))))&
(?[X]:((generous(X)|funny(X))))&
(?[X]:((~funny(X)&~brave(X))))&
((~funny(john)|rich(john)))&
(?[X]:(~funny(X))) | quiet(paul) | [
"p1",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4018098788332103313485481
% SZS output start Proof for 4018098788332103313485481
2. ! [X0] : ((creative(X0) | funny(X0)) => (tall(X0) & ~strong(X0))) [input p1]
6. ! [X0] : ((kind(X0) | curious(X0)) => (~curious(X0) & ~old(X0))) [input p5]
10. ! [X0] : ((~funny(X0) | quiet(X0)) => (~calm(X0) <~> curious(X0))) [input p9]
13. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> (curious(X0) <~> quiet(X0))) [input p12]
19. ~quiet(paul) [input hypothesis]
24. ! [X0] : ((tall(X0) & ~strong(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 2]
26. ! [X0] : ((~curious(X0) & ~old(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 6]
29. ! [X0] : ((~calm(X0) <~> curious(X0)) | (funny(X0) & ~quiet(X0))) [ennf transformation 10]
45. ! [X0] : (((~curious(X0) | calm(X0)) & (curious(X0) | ~calm(X0))) | (funny(X0) & ~quiet(X0))) [nnf transformation 29]
51. ! [X0] : (((~calm(X0) | ~strong(X0)) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (calm(X0) & strong(X0)))) [nnf transformation 13]
52. ! [X0] : ((~calm(X0) | ~strong(X0) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (calm(X0) & strong(X0)))) [flattening 51]
63. ~funny(X0) | ~strong(X0) [cnf transformation 24]
80. ~curious(X0) | ~curious(X0) [cnf transformation 26]
92. curious(X0) | ~calm(X0) | funny(X0) [cnf transformation 45]
100. quiet(X0) | curious(X0) | strong(X0) [cnf transformation 52]
101. quiet(X0) | curious(X0) | calm(X0) [cnf transformation 52]
115. ~quiet(paul) [cnf transformation 19]
116. ~curious(X0) [duplicate literal removal 80]
126. 2 <=> strong(paul) [avatar definition]
128. strong(paul) <- (2) [avatar component clause 126]
183. ~calm(X0) | funny(X0) [subsumption resolution 92,116]
210. quiet(X0) | calm(X0) [subsumption resolution 101,116]
211. quiet(X0) | strong(X0) [subsumption resolution 100,116]
255. calm(paul) [resolution 210,115]
257. funny(paul) [resolution 255,183]
258. strong(paul) [resolution 211,115]
260. 2 [avatar split clause 258,126]
276. ~strong(paul) [resolution 257,63]
277. $false <- (2) [subsumption resolution 276,128]
278. ~2 [avatar contradiction clause 277]
279. $false [avatar sat refutation 260,278]
% SZS output end Proof for 4018098788332103313485481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is wise and vice versa.
Everyone who is either not wise or not strong is not creative or rich.
Everyone who is generous or not calm is either patient or not humble and vice versa.
If lucy is either not happy or calm then someone is either curious or not curious and vice versa.
If alice is happy then someone is wise or not happy and vice versa.
If susan is not creative then someone is not calm or not humble and vice versa.
Everyone who is either strong or not funny is old and vice versa.
If someone is not quiet or humble then john is both not kind and rich.
If someone is both not generous and curious then mary is curious or quiet and vice versa.
If mary is funny then lucy is both funny and not patient.
If someone is old or rich then fred is both generous and not calm.
If susan is tall then lucy is not brave.
Everyone who is curious or not rich is wise.
Everyone who is brave or not brave is not funny or not wise.
Everyone who is wise is not humble.
Everyone who is both strong and not generous is not humble or wise and vice versa.
Someone is not brave or patient.
Susan is not generous.
John is both not generous and patient.
Susan is not brave. | Lucy is not generous. | neutral | (![X]:((~curious(X)<~>generous(X))<=>wise(X)))&
(![X]:((~wise(X)<~>~strong(X))=>(~creative(X)|rich(X))))&
(![X]:((generous(X)|~calm(X))<=>(patient(X)<~>~humble(X))))&
(((~happy(lucy)<~>calm(lucy)))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((happy(alice))<=>(?[X]:((wise(X)|~happy(X)))))&
((~creative(susan))<=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((strong(X)<~>~funny(X))<=>old(X)))&
((?[X]:((~quiet(X)|humble(X))))=>((~kind(john)&rich(john))))&
((?[X]:((~generous(X)&curious(X))))<=>((curious(mary)|quiet(mary))))&
((funny(mary))=>((funny(lucy)&~patient(lucy))))&
((?[X]:((old(X)|rich(X))))=>((generous(fred)&~calm(fred))))&
((tall(susan))=>(~brave(lucy)))&
(![X]:((curious(X)|~rich(X))=>wise(X)))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((strong(X)&~generous(X))<=>(~humble(X)|wise(X))))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~generous(john)&patient(john)))&
(~brave(susan)) | ~generous(lucy) | [] | null | 0 |
If someone is kind or happy then someone is not happy or brave and vice versa. Everyone who is both brave and not strong is curious or not funny and vice versa. If someone is strong or not old then lucy is either not old or not tall and vice versa. If someone is quiet then john is wise. Everyone who is humble is not strong or not patient and vice versa. If paul is not funny or not quiet then someone is either not brave or not funny and vice versa. Everyone who is strong is either not strong or not creative. If lucy is either not rich or kind then someone is not curious and vice versa. If alice is both humble and not happy then mary is both old and creative and vice versa. If paul is both quiet and patient then someone is not quiet and vice versa. Everyone who is creative is both not quiet and not wise and vice versa. If someone is both not curious and not funny then someone is either not creative or not curious and vice versa. If susan is both not tall and calm then lucy is both rich and tall and vice versa. Everyone who is both not brave and happy is either creative or not kind and vice versa. If someone is both not patient and kind then john is patient and vice versa. Everyone who is not generous is both old and not quiet and vice versa. Fred is both funny and quiet. Someone is either not humble or not patient. Paul is strong. Someone is strong or not wise. Someone is either not humble or not funny. Someone is both not kind and old. Someone is either quiet or not creative. | Alice is not funny. | contradiction | ((?[X]:((kind(X)|happy(X))))<=>(?[X]:((~happy(X)|brave(X)))))&
(![X]:((brave(X)&~strong(X))<=>(curious(X)|~funny(X))))&
((?[X]:((strong(X)|~old(X))))<=>((~old(lucy)<~>~tall(lucy))))&
((?[X]:(quiet(X)))=>(wise(john)))&
(![X]:(humble(X)<=>(~strong(X)|~patient(X))))&
(((~funny(paul)|~quiet(paul)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:(strong(X)=>(~strong(X)<~>~creative(X))))&
(((~rich(lucy)<~>kind(lucy)))<=>(?[X]:(~curious(X))))&
(((humble(alice)&~happy(alice)))<=>((old(mary)&creative(mary))))&
(((quiet(paul)&patient(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(creative(X)<=>(~quiet(X)&~wise(X))))&
((?[X]:((~curious(X)&~funny(X))))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(((~tall(susan)&calm(susan)))<=>((rich(lucy)&tall(lucy))))&
(![X]:((~brave(X)&happy(X))<=>(creative(X)<~>~kind(X))))&
((?[X]:((~patient(X)&kind(X))))<=>(patient(john)))&
(![X]:(~generous(X)<=>(old(X)&~quiet(X))))&
((funny(fred)&quiet(fred)))&
(?[X]:((~humble(X)<~>~patient(X))))&
(strong(paul))&
(?[X]:((strong(X)|~wise(X))))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:((~kind(X)&old(X))))&
(?[X]:((quiet(X)<~>~creative(X)))) | ~funny(alice) | [
"p1",
"p5",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 848749957139014205956124
% SZS output start Proof for 848749957139014205956124
2. ! [X0] : ((~strong(X0) & brave(X0)) <=> (~funny(X0) | curious(X0))) [input p1]
6. (~quiet(paul) | ~funny(paul)) <=> ? [X0] : (~brave(X0) <~> ~funny(X0)) [input p5]
10. (patient(paul) & quiet(paul)) <=> ? [X0] : ~quiet(X0) [input p9]
19. strong(paul) [input p18]
24. ~funny(alice) [input hypothesis]
34. ! [X0] : (((~strong(X0) & brave(X0)) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | (strong(X0) | ~brave(X0)))) [nnf transformation 2]
35. ! [X0] : (((~strong(X0) & brave(X0)) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | strong(X0) | ~brave(X0))) [flattening 34]
42. ((~quiet(paul) | ~funny(paul)) | ! [X0] : ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (quiet(paul) & funny(paul))) [nnf transformation 6]
43. (~quiet(paul) | ~funny(paul) | ! [X0] : ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (quiet(paul) & funny(paul))) [flattening 42]
44. (~quiet(paul) | ~funny(paul) | ! [X0] : ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (? [X1] : ((funny(X1) | brave(X1)) & (~funny(X1) | ~brave(X1))) | (quiet(paul) & funny(paul))) [rectify 43]
45. ? [X1] : ((funny(X1) | brave(X1)) & (~funny(X1) | ~brave(X1))) => ((funny(sK3) | brave(sK3)) & (~funny(sK3) | ~brave(sK3))) [choice axiom]
46. (~quiet(paul) | ~funny(paul) | ! [X0] : ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(sK3) | brave(sK3)) & (~funny(sK3) | ~brave(sK3))) | (quiet(paul) & funny(paul))) [skolemisation 44,45]
54. ((patient(paul) & quiet(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~patient(paul) | ~quiet(paul))) [nnf transformation 10]
55. ((patient(paul) & quiet(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~patient(paul) | ~quiet(paul)) [flattening 54]
56. ((patient(paul) & quiet(paul)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~patient(paul) | ~quiet(paul)) [rectify 55]
57. ? [X1] : ~quiet(X1) => ~quiet(sK5) [choice axiom]
58. ((patient(paul) & quiet(paul)) | ! [X0] : quiet(X0)) & (~quiet(sK5) | ~patient(paul) | ~quiet(paul)) [skolemisation 56,57]
93. funny(X0) | brave(X0) [cnf transformation 35]
95. ~strong(X0) | funny(X0) [cnf transformation 35]
111. ~quiet(paul) | ~funny(paul) | ~brave(X0) | funny(X0) [cnf transformation 46]
123. quiet(paul) | quiet(X0) [cnf transformation 58]
151. strong(paul) [cnf transformation 19]
159. ~funny(alice) [cnf transformation 24]
229. ~quiet(paul) | ~funny(paul) | funny(X0) [subsumption resolution 111,93]
231. 17 <=> ! [X0] : funny(X0) [avatar definition]
232. funny(X0) <- (17) [avatar component clause 231]
234. 18 <=> funny(paul) [avatar definition]
238. 19 <=> quiet(paul) [avatar definition]
240. ~quiet(paul) <- (~19) [avatar component clause 238]
241. 17 | ~18 | ~19 [avatar split clause 229,238,234,231]
297. 31 <=> ! [X0] : quiet(X0) [avatar definition]
298. quiet(X0) <- (31) [avatar component clause 297]
304. 31 | 19 [avatar split clause 123,238,297]
401. $false <- (~19, 31) [subsumption resolution 240,298]
402. 19 | ~31 [avatar contradiction clause 401]
411. funny(paul) [resolution 95,151]
414. 18 [avatar split clause 411,234]
415. $false <- (17) [resolution 232,159]
420. ~17 [avatar contradiction clause 415]
421. $false [avatar sat refutation 241,304,402,414,420]
% SZS output end Proof for 848749957139014205956124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or funny is old or not quiet and vice versa.
Everyone who is humble is either kind or funny and vice versa.
Everyone who is not quiet or rich is not strong or quiet.
Everyone who is not funny is not strong.
Everyone who is kind is either not generous or funny and vice versa.
Everyone who is both patient and not old is both curious and happy.
Everyone who is curious is both kind and strong.
If someone is either not quiet or curious then lucy is either not rich or quiet.
If alice is either generous or not curious then someone is both wise and not strong.
Everyone who is kind or not kind is both not happy and not strong.
If someone is either not patient or not calm then lucy is both curious and happy and vice versa.
If someone is not calm then susan is wise.
Everyone who is not tall is both quiet and wise.
If lucy is either happy or brave then someone is either quiet or not rich and vice versa.
Everyone who is happy or not humble is either not funny or not patient.
Everyone who is both not happy and not humble is either calm or not strong and vice versa.
Fred is either old or not kind.
Mary is not brave or humble.
Someone is not humble or not kind.
Fred is both not quiet and not patient.
Someone is both funny and not tall.
Someone is both not strong and calm. | Mary is not humble. | neutral | (![X]:((creative(X)|funny(X))<=>(old(X)|~quiet(X))))&
(![X]:(humble(X)<=>(kind(X)<~>funny(X))))&
(![X]:((~quiet(X)|rich(X))=>(~strong(X)|quiet(X))))&
(![X]:(~funny(X)=>~strong(X)))&
(![X]:(kind(X)<=>(~generous(X)<~>funny(X))))&
(![X]:((patient(X)&~old(X))=>(curious(X)&happy(X))))&
(![X]:(curious(X)=>(kind(X)&strong(X))))&
((?[X]:((~quiet(X)<~>curious(X))))=>((~rich(lucy)<~>quiet(lucy))))&
(((generous(alice)<~>~curious(alice)))=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:((kind(X)|~kind(X))=>(~happy(X)&~strong(X))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>((curious(lucy)&happy(lucy))))&
((?[X]:(~calm(X)))=>(wise(susan)))&
(![X]:(~tall(X)=>(quiet(X)&wise(X))))&
(((happy(lucy)<~>brave(lucy)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:((happy(X)|~humble(X))=>(~funny(X)<~>~patient(X))))&
(![X]:((~happy(X)&~humble(X))<=>(calm(X)<~>~strong(X))))&
((old(fred)<~>~kind(fred)))&
((~brave(mary)|humble(mary)))&
(?[X]:((~humble(X)|~kind(X))))&
((~quiet(fred)&~patient(fred)))&
(?[X]:((funny(X)&~tall(X))))&
(?[X]:((~strong(X)&calm(X)))) | ~humble(mary) | [] | null | 0 |
If someone is not brave then susan is either curious or brave.
If someone is both creative and humble then someone is not happy.
Everyone who is both not old and not curious is both not strong and not quiet and vice versa.
Everyone who is funny or wise is tall.
Everyone who is either not happy or not creative is kind or not rich.
Everyone who is either wise or not strong is not happy.
Everyone who is rich or not happy is both not happy and curious.
Everyone who is not old or curious is not patient or brave.
If someone is either not quiet or patient then someone is not old.
Everyone who is both not calm and tall is not rich and vice versa.
If someone is either happy or not tall then lucy is either not happy or kind.
Everyone who is both calm and not funny is happy or not generous and vice versa.
Everyone who is both not old and creative is both kind and not funny.
Everyone who is not generous or creative is calm or not creative.
If someone is either not humble or not rich then someone is happy or funny and vice versa.
If someone is quiet then someone is both not quiet and kind.
Paul is wise or not funny.
Someone is not tall.
Someone is both rich and not old.
Paul is both not old and rich.
Mary is both not rich and generous.
Someone is either happy or rich.
Alice is kind or creative. | Paul is not curious. | contradiction | ((?[X]:(~brave(X)))=>((curious(susan)<~>brave(susan))))&
((?[X]:((creative(X)&humble(X))))=>(?[X]:(~happy(X))))&
(![X]:((~old(X)&~curious(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((funny(X)|wise(X))=>tall(X)))&
(![X]:((~happy(X)<~>~creative(X))=>(kind(X)|~rich(X))))&
(![X]:((wise(X)<~>~strong(X))=>~happy(X)))&
(![X]:((rich(X)|~happy(X))=>(~happy(X)&curious(X))))&
(![X]:((~old(X)|curious(X))=>(~patient(X)|brave(X))))&
((?[X]:((~quiet(X)<~>patient(X))))=>(?[X]:(~old(X))))&
(![X]:((~calm(X)&tall(X))<=>~rich(X)))&
((?[X]:((happy(X)<~>~tall(X))))=>((~happy(lucy)<~>kind(lucy))))&
(![X]:((calm(X)&~funny(X))<=>(happy(X)|~generous(X))))&
(![X]:((~old(X)&creative(X))=>(kind(X)&~funny(X))))&
(![X]:((~generous(X)|creative(X))=>(calm(X)|~creative(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((~quiet(X)&kind(X)))))&
((wise(paul)|~funny(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((rich(X)&~old(X))))&
((~old(paul)&rich(paul)))&
((~rich(mary)&generous(mary)))&
(?[X]:((happy(X)<~>rich(X))))&
((kind(alice)|creative(alice))) | ~curious(paul) | [
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2842453455638283487207326
% SZS output start Proof for 2842453455638283487207326
7. ! [X0] : ((~happy(X0) | rich(X0)) => (curious(X0) & ~happy(X0))) [input p6]
20. rich(paul) & ~old(paul) [input p19]
24. ~curious(paul) [input hypothesis]
35. ! [X0] : ((curious(X0) & ~happy(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 7]
92. ~rich(X0) | curious(X0) [cnf transformation 35]
127. rich(paul) [cnf transformation 20]
133. ~curious(paul) [cnf transformation 24]
263. curious(paul) [resolution 92,127]
264. $false [subsumption resolution 263,133]
% SZS output end Proof for 2842453455638283487207326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and calm is not calm and vice versa. If someone is rich then mary is either rich or creative. Everyone who is either wise or not strong is humble or strong and vice versa. If lucy is humble or curious then someone is either not rich or old. Everyone who is both wise and tall is not wise or generous and vice versa. If someone is not old or not patient then someone is either not quiet or not rich and vice versa. Everyone who is both old and not old is brave or rich and vice versa. Everyone who is funny is not generous or rich. Everyone who is either not curious or not generous is either happy or strong. If someone is either generous or not funny then someone is not tall and vice versa. If alice is both not kind and not funny then someone is either not quiet or not humble. If lucy is not generous then paul is either not funny or not rich and vice versa. Everyone who is both not old and not curious is not rich or generous and vice versa. Everyone who is both not old and not curious is not kind or not quiet. If fred is not brave or humble then alice is not wise or humble. Everyone who is not rich or not quiet is not patient. Someone is tall or quiet. Someone is either curious or tall. Someone is either not quiet or not humble. Mary is not brave. Fred is generous or not brave. | Paul is tall. | neutral | (![X]:((creative(X)&calm(X))<=>~calm(X)))&
((?[X]:(rich(X)))=>((rich(mary)<~>creative(mary))))&
(![X]:((wise(X)<~>~strong(X))<=>(humble(X)|strong(X))))&
(((humble(lucy)|curious(lucy)))=>(?[X]:((~rich(X)<~>old(X)))))&
(![X]:((wise(X)&tall(X))<=>(~wise(X)|generous(X))))&
((?[X]:((~old(X)|~patient(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:((old(X)&~old(X))<=>(brave(X)|rich(X))))&
(![X]:(funny(X)=>(~generous(X)|rich(X))))&
(![X]:((~curious(X)<~>~generous(X))=>(happy(X)<~>strong(X))))&
((?[X]:((generous(X)<~>~funny(X))))<=>(?[X]:(~tall(X))))&
(((~kind(alice)&~funny(alice)))=>(?[X]:((~quiet(X)<~>~humble(X)))))&
((~generous(lucy))<=>((~funny(paul)<~>~rich(paul))))&
(![X]:((~old(X)&~curious(X))<=>(~rich(X)|generous(X))))&
(![X]:((~old(X)&~curious(X))=>(~kind(X)|~quiet(X))))&
(((~brave(fred)|humble(fred)))=>((~wise(alice)|humble(alice))))&
(![X]:((~rich(X)|~quiet(X))=>~patient(X)))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:((curious(X)<~>tall(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(~brave(mary))&
((generous(fred)|~brave(fred))) | tall(paul) | [] | null | 0 |
Everyone who is either not funny or old is not old and vice versa. If mary is both not wise and creative then someone is not strong and vice versa. Everyone who is not generous or not wise is wise or not creative and vice versa. If lucy is quiet or not creative then paul is creative or not funny and vice versa. Everyone who is generous or not old is not tall or generous and vice versa. Everyone who is generous or calm is either happy or tall. If someone is either not curious or rich then paul is creative or not curious and vice versa. Everyone who is either creative or old is not patient or quiet. If susan is curious or not generous then fred is both not patient and tall and vice versa. Everyone who is either not generous or not happy is either not creative or brave and vice versa. Everyone who is calm or rich is both not creative and not strong and vice versa. Everyone who is not old or not generous is both happy and wise. Everyone who is either not patient or not funny is either creative or calm and vice versa. If alice is either not wise or patient then john is not generous or not calm and vice versa. Everyone who is either not patient or creative is both kind and strong and vice versa. Fred is generous. Someone is both not brave and not quiet. Lucy is wise or not calm. Someone is either quiet or curious. Susan is humble or not funny. Lucy is both quiet and not brave. Someone is both not humble and not wise. | Lucy is not kind. | contradiction | (![X]:((~funny(X)<~>old(X))<=>~old(X)))&
(((~wise(mary)&creative(mary)))<=>(?[X]:(~strong(X))))&
(![X]:((~generous(X)|~wise(X))<=>(wise(X)|~creative(X))))&
(((quiet(lucy)|~creative(lucy)))<=>((creative(paul)|~funny(paul))))&
(![X]:((generous(X)|~old(X))<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(generous(fred))&
(?[X]:((~brave(X)&~quiet(X))))&
((wise(lucy)|~calm(lucy)))&
(?[X]:((quiet(X)<~>curious(X))))&
((humble(susan)|~funny(susan)))&
((quiet(lucy)&~brave(lucy)))&
(?[X]:((~humble(X)&~wise(X)))) | ~kind(lucy) | [
"p0",
"p1",
"p2",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6882879581422058726427508
% SZS output start Proof for 6882879581422058726427508
1. ! [X0] : ((~funny(X0) <~> old(X0)) <=> ~old(X0)) [input p0]
2. (creative(mary) & ~wise(mary)) <=> ? [X0] : ~strong(X0) [input p1]
3. ! [X0] : ((~wise(X0) | ~generous(X0)) <=> (~creative(X0) | wise(X0))) [input p2]
11. ! [X0] : ((rich(X0) | calm(X0)) <=> (~strong(X0) & ~creative(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (creative(X0) <~> calm(X0))) [input p12]
15. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (strong(X0) & kind(X0))) [input p14]
23. ~kind(lucy) [input hypothesis]
28. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | old(X0)) & (~old(X0) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [nnf transformation 1]
29. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | (~creative(mary) | wise(mary))) [nnf transformation 2]
30. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ~creative(mary) | wise(mary)) [flattening 29]
31. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ~creative(mary) | wise(mary)) [rectify 30]
32. ? [X1] : ~strong(X1) => ~strong(sK0) [choice axiom]
33. ((creative(mary) & ~wise(mary)) | ! [X0] : strong(X0)) & (~strong(sK0) | ~creative(mary) | wise(mary)) [skolemisation 31,32]
34. ! [X0] : (((~wise(X0) | ~generous(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (wise(X0) & generous(X0)))) [nnf transformation 3]
35. ! [X0] : ((~wise(X0) | ~generous(X0) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | (wise(X0) & generous(X0)))) [flattening 34]
50. ! [X0] : (((rich(X0) | calm(X0)) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 11]
51. ! [X0] : ((rich(X0) | calm(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 50]
52. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 13]
55. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 15]
56. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [flattening 55]
65. ~old(X0) | ~funny(X0) | ~old(X0) [cnf transformation 28]
66. old(X0) | ~funny(X0) | old(X0) [cnf transformation 28]
69. ~wise(mary) | strong(X0) [cnf transformation 33]
70. creative(mary) | strong(X0) [cnf transformation 33]
72. ~creative(X0) | wise(X0) | wise(X0) [cnf transformation 35]
108. ~calm(X0) | ~creative(X0) [cnf transformation 51]
110. ~calm(X0) | ~strong(X0) [cnf transformation 51]
118. calm(X0) | creative(X0) | ~patient(X0) | funny(X0) [cnf transformation 52]
123. funny(X0) | patient(X0) | calm(X0) | ~creative(X0) [cnf transformation 52]
124. funny(X0) | patient(X0) | creative(X0) | ~calm(X0) [cnf transformation 52]
131. kind(X0) | creative(X0) | patient(X0) [cnf transformation 56]
132. kind(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 56]
148. ~kind(lucy) [cnf transformation 23]
149. ~creative(X0) | wise(X0) [duplicate literal removal 72]
151. ~old(X0) | ~funny(X0) [duplicate literal removal 65]
152. ~funny(X0) | old(X0) [duplicate literal removal 66]
153. ~funny(X0) [subsumption resolution 151,152]
155. 1 <=> ! [X0] : strong(X0) [avatar definition]
156. strong(X0) <- (1) [avatar component clause 155]
158. 2 <=> creative(mary) [avatar definition]
160. creative(mary) <- (2) [avatar component clause 158]
161. 1 | 2 [avatar split clause 70,158,155]
163. 3 <=> wise(mary) [avatar definition]
165. ~wise(mary) <- (~3) [avatar component clause 163]
166. 1 | ~3 [avatar split clause 69,163,155]
178. 6 <=> creative(lucy) [avatar definition]
179. creative(lucy) <- (6) [avatar component clause 178]
232. patient(X0) | creative(X0) | ~calm(X0) [subsumption resolution 124,153]
233. ~calm(X0) | patient(X0) [subsumption resolution 232,108]
234. patient(X0) | calm(X0) | ~creative(X0) [subsumption resolution 123,153]
235. ~creative(X0) | patient(X0) [subsumption resolution 234,233]
236. ~patient(X0) | creative(X0) | calm(X0) [subsumption resolution 118,153]
261. ~creative(X0) | kind(X0) [subsumption resolution 132,235]
262. kind(X0) | patient(X0) [subsumption resolution 131,235]
268. 22 <=> calm(lucy) [avatar definition]
269. calm(lucy) <- (22) [avatar component clause 268]
287. wise(mary) <- (2) [resolution 149,160]
288. $false <- (2, ~3) [subsumption resolution 287,165]
289. ~2 | 3 [avatar contradiction clause 288]
297. patient(lucy) [resolution 262,148]
355. creative(lucy) | calm(lucy) [resolution 236,297]
368. kind(lucy) <- (6) [resolution 179,261]
372. $false <- (6) [subsumption resolution 368,148]
373. ~6 [avatar contradiction clause 372]
375. 22 | 6 [avatar split clause 355,178,268]
378. ~strong(lucy) <- (22) [resolution 269,110]
389. $false <- (1, 22) [subsumption resolution 378,156]
390. ~1 | ~22 [avatar contradiction clause 389]
391. $false [avatar sat refutation 161,166,289,373,375,390]
% SZS output end Proof for 6882879581422058726427508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or not creative then fred is both calm and humble and vice versa. If someone is either calm or not kind then someone is either not happy or quiet and vice versa. If mary is either patient or rich then someone is funny and vice versa. If john is not funny then fred is not humble or not strong and vice versa. If someone is both not strong and quiet then someone is not brave or quiet. Everyone who is not curious or not strong is wise. Everyone who is not humble is not wise and vice versa. Everyone who is not quiet is not kind or tall and vice versa. Everyone who is both not strong and old is either not quiet or patient and vice versa. Everyone who is both brave and not generous is either not creative or kind and vice versa. Everyone who is both not wise and not kind is both funny and not happy. Everyone who is either not tall or happy is both brave and funny and vice versa. Everyone who is old or not calm is calm or not quiet and vice versa. Everyone who is not generous or not humble is either kind or not tall and vice versa. Everyone who is not curious is either not happy or happy and vice versa. Everyone who is both not curious and not happy is humble. Someone is patient or not strong. Susan is strong. Someone is quiet. Susan is not creative. John is both not patient and not rich. Paul is both not rich and not patient. Alice is rich or generous. | Susan is not wise. | contradiction | ((?[X]:((~funny(X)<~>~creative(X))))<=>((calm(fred)&humble(fred))))&
((?[X]:((calm(X)<~>~kind(X))))<=>(?[X]:((~happy(X)<~>quiet(X)))))&
(((patient(mary)<~>rich(mary)))<=>(?[X]:(funny(X))))&
((~funny(john))<=>((~humble(fred)|~strong(fred))))&
((?[X]:((~strong(X)&quiet(X))))=>(?[X]:((~brave(X)|quiet(X)))))&
(![X]:((~curious(X)|~strong(X))=>wise(X)))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:(~quiet(X)<=>(~kind(X)|tall(X))))&
(![X]:((~strong(X)&old(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((brave(X)&~generous(X))<=>(~creative(X)<~>kind(X))))&
(![X]:((~wise(X)&~kind(X))=>(funny(X)&~happy(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(brave(X)&funny(X))))&
(![X]:((old(X)|~calm(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~generous(X)|~humble(X))<=>(kind(X)<~>~tall(X))))&
(![X]:(~curious(X)<=>(~happy(X)<~>happy(X))))&
(![X]:((~curious(X)&~happy(X))=>humble(X)))&
(?[X]:((patient(X)|~strong(X))))&
(strong(susan))&
(?[X]:(quiet(X)))&
(~creative(susan))&
((~patient(john)&~rich(john)))&
((~rich(paul)&~patient(paul)))&
((rich(alice)|generous(alice))) | ~wise(susan) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3503603994243766840696541
% SZS output start Proof for 3503603994243766840696541
6. ! [X0] : ((~strong(X0) | ~curious(X0)) => wise(X0)) [input p5]
15. ! [X0] : (~curious(X0) <=> (~happy(X0) <~> happy(X0))) [input p14]
24. ~wise(susan) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> happy(X0)) => ~curious(X0)) [unused predicate definition removal 15]
29. ! [X0] : (wise(X0) | (strong(X0) & curious(X0))) [ennf transformation 6]
32. ! [X0] : (~curious(X0) | (~happy(X0) <=> happy(X0))) [ennf transformation 27]
67. ! [X0] : (~curious(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 32]
94. wise(X0) | curious(X0) [cnf transformation 29]
131. ~curious(X0) | happy(X0) | happy(X0) [cnf transformation 67]
132. ~curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 67]
143. ~wise(susan) [cnf transformation 24]
144. ~curious(X0) | happy(X0) [duplicate literal removal 131]
145. ~curious(X0) | ~happy(X0) [duplicate literal removal 132]
254. ~curious(X0) [subsumption resolution 144,145]
275. curious(susan) [resolution 94,143]
276. $false [subsumption resolution 275,254]
% SZS output end Proof for 3503603994243766840696541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not calm is calm.
Everyone who is both not curious and old is not funny or kind and vice versa.
Everyone who is humble or quiet is either tall or not strong.
If someone is not brave then fred is not calm or not wise.
Everyone who is patient or tall is rich.
If susan is old then alice is tall or not humble and vice versa.
If someone is either strong or not happy then someone is both not strong and not old.
Everyone who is tall is not humble and vice versa.
If john is either patient or not tall then someone is both kind and strong.
Everyone who is either not brave or generous is not funny and vice versa.
If someone is both not rich and humble then someone is both not wise and not humble.
Everyone who is not wise or curious is quiet.
If john is both happy and calm then someone is kind or not rich and vice versa.
Everyone who is patient is either strong or humble.
If someone is either creative or not old then someone is happy.
Someone is calm.
Someone is not generous.
Someone is both calm and rich.
Alice is tall or wise.
Someone is both not quiet and brave.
Someone is not generous or old. | Susan is not brave. | neutral | (![X]:((strong(X)|~calm(X))=>calm(X)))&
(![X]:((~curious(X)&old(X))<=>(~funny(X)|kind(X))))&
(![X]:((humble(X)|quiet(X))=>(tall(X)<~>~strong(X))))&
((?[X]:(~brave(X)))=>((~calm(fred)|~wise(fred))))&
(![X]:((patient(X)|tall(X))=>rich(X)))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:(tall(X)<=>~humble(X)))&
(((patient(john)<~>~tall(john)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>~funny(X)))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~wise(X)|curious(X))=>quiet(X)))&
(((happy(john)&calm(john)))<=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:(patient(X)=>(strong(X)<~>humble(X))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(?[X]:(calm(X)))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)&rich(X))))&
((tall(alice)|wise(alice)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((~generous(X)|old(X)))) | ~brave(susan) | [] | null | 0 |
If paul is not strong or not calm then someone is both not wise and not strong and vice versa.
Everyone who is tall or not quiet is not kind or kind.
If susan is either not kind or funny then lucy is happy and vice versa.
If lucy is either not brave or not curious then mary is either not calm or not happy.
If someone is both not patient and not generous then alice is not kind.
If mary is old or not wise then alice is not creative or strong.
Everyone who is both wise and calm is humble and vice versa.
Everyone who is either patient or not strong is both not strong and patient and vice versa.
If someone is not funny or humble then someone is either kind or old and vice versa.
If fred is humble or not brave then someone is both patient and generous.
If paul is brave or not kind then paul is both calm and not strong and vice versa.
Everyone who is quiet or humble is not brave.
If paul is both not curious and brave then someone is either humble or not happy.
If mary is either not funny or not happy then alice is not calm.
Everyone who is calm is not funny or tall.
Everyone who is either creative or not funny is not strong or tall.
Someone is not rich or not humble.
Someone is either happy or not rich.
Someone is wise or patient.
Someone is not old.
Mary is both not humble and not brave. | Susan is rich. | neutral | (((~strong(paul)|~calm(paul)))<=>(?[X]:((~wise(X)&~strong(X)))))&
(![X]:((tall(X)|~quiet(X))=>(~kind(X)|kind(X))))&
(((~kind(susan)<~>funny(susan)))<=>(happy(lucy)))&
(((~brave(lucy)<~>~curious(lucy)))=>((~calm(mary)<~>~happy(mary))))&
((?[X]:((~patient(X)&~generous(X))))=>(~kind(alice)))&
(((old(mary)|~wise(mary)))=>((~creative(alice)|strong(alice))))&
(![X]:((wise(X)&calm(X))<=>humble(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~strong(X)&patient(X))))&
((?[X]:((~funny(X)|humble(X))))<=>(?[X]:((kind(X)<~>old(X)))))&
(((humble(fred)|~brave(fred)))=>(?[X]:((patient(X)&generous(X)))))&
(((brave(paul)|~kind(paul)))<=>((calm(paul)&~strong(paul))))&
(![X]:((quiet(X)|humble(X))=>~brave(X)))&
(((~curious(paul)&brave(paul)))=>(?[X]:((humble(X)<~>~happy(X)))))&
(((~funny(mary)<~>~happy(mary)))=>(~calm(alice)))&
(![X]:(calm(X)=>(~funny(X)|tall(X))))&
(![X]:((creative(X)<~>~funny(X))=>(~strong(X)|tall(X))))&
(?[X]:((~rich(X)|~humble(X))))&
(?[X]:((happy(X)<~>~rich(X))))&
(?[X]:((wise(X)|patient(X))))&
(?[X]:(~old(X)))&
((~humble(mary)&~brave(mary))) | rich(susan) | [] | null | 0 |
Everyone who is not generous or not creative is both not patient and wise and vice versa.
If someone is not kind then someone is kind and vice versa.
If fred is both creative and not humble then someone is curious or patient and vice versa.
Everyone who is both not funny and not strong is patient or curious and vice versa.
If someone is both wise and calm then fred is both patient and not brave.
If john is not humble or not quiet then someone is either not kind or old.
Everyone who is both not humble and creative is either not funny or not patient and vice versa.
If someone is both not happy and not calm then mary is quiet or patient and vice versa.
If someone is not humble then fred is not kind or generous and vice versa.
Everyone who is both not creative and not rich is curious or rich.
Everyone who is not calm or not brave is either not rich or rich and vice versa.
Everyone who is not humble is either brave or calm and vice versa.
If fred is both not tall and calm then someone is both patient and not creative.
Everyone who is either funny or not humble is strong or not patient and vice versa.
Everyone who is either humble or not strong is humble and vice versa.
Everyone who is both curious and not generous is either not quiet or rich and vice versa.
Someone is either not happy or not generous.
Someone is both not creative and not calm.
Someone is not quiet.
Someone is rich or not brave. | Fred is not happy. | contradiction | (![X]:((~generous(X)|~creative(X))<=>(~patient(X)&wise(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(kind(X))))&
(((creative(fred)&~humble(fred)))<=>(?[X]:((curious(X)|patient(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(patient(X)|curious(X))))&
((?[X]:((wise(X)&calm(X))))=>((patient(fred)&~brave(fred))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~humble(X)&creative(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>((quiet(mary)|patient(mary))))&
((?[X]:(~humble(X)))<=>((~kind(fred)|generous(fred))))&
(![X]:((~creative(X)&~rich(X))=>(curious(X)|rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(~humble(X)<=>(brave(X)<~>calm(X))))&
(((~tall(fred)&calm(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(strong(X)|~patient(X))))&
(![X]:((humble(X)<~>~strong(X))<=>humble(X)))&
(![X]:((curious(X)&~generous(X))<=>(~quiet(X)<~>rich(X))))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|~brave(X)))) | ~happy(fred) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7623474919377400451282009
% SZS output start Proof for 7623474919377400451282009
1. ! [X0] : ((~creative(X0) | ~generous(X0)) <=> (wise(X0) & ~patient(X0))) [input p0]
4. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (curious(X0) | patient(X0))) [input p3]
5. ? [X0] : (calm(X0) & wise(X0)) => (~brave(fred) & patient(fred)) [input p4]
7. ! [X0] : ((creative(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p6]
8. ? [X0] : (~calm(X0) & ~happy(X0)) <=> (patient(mary) | quiet(mary)) [input p7]
10. ! [X0] : ((~rich(X0) & ~creative(X0)) => (rich(X0) | curious(X0))) [input p9]
11. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (~rich(X0) <~> rich(X0))) [input p10]
12. ! [X0] : (~humble(X0) <=> (brave(X0) <~> calm(X0))) [input p11]
14. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~patient(X0) | strong(X0))) [input p13]
15. ! [X0] : ((humble(X0) <~> ~strong(X0)) <=> humble(X0)) [input p14]
16. ! [X0] : ((~generous(X0) & curious(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p15]
21. ~happy(fred) [input hypothesis]
24. (~brave(fred) & patient(fred)) | ! [X0] : (~calm(X0) | ~wise(X0)) [ennf transformation 5]
26. ! [X0] : ((rich(X0) | curious(X0)) | (rich(X0) | creative(X0))) [ennf transformation 10]
27. ! [X0] : (rich(X0) | curious(X0) | rich(X0) | creative(X0)) [flattening 26]
28. ! [X0] : (((~creative(X0) | ~generous(X0)) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | (creative(X0) & generous(X0)))) [nnf transformation 1]
29. ! [X0] : ((~creative(X0) | ~generous(X0) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | (creative(X0) & generous(X0)))) [flattening 28]
40. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 4]
41. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | strong(X0) | funny(X0))) [flattening 40]
45. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | (~creative(X0) | humble(X0)))) [nnf transformation 7]
46. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ~creative(X0) | humble(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) & ~happy(X0)) | (~patient(mary) & ~quiet(mary))) & ((patient(mary) | quiet(mary)) | ! [X0] : (calm(X0) | happy(X0))) [nnf transformation 8]
48. (? [X0] : (~calm(X0) & ~happy(X0)) | (~patient(mary) & ~quiet(mary))) & (patient(mary) | quiet(mary) | ! [X0] : (calm(X0) | happy(X0))) [flattening 47]
49. (? [X0] : (~calm(X0) & ~happy(X0)) | (~patient(mary) & ~quiet(mary))) & (patient(mary) | quiet(mary) | ! [X1] : (calm(X1) | happy(X1))) [rectify 48]
50. ? [X0] : (~calm(X0) & ~happy(X0)) => (~calm(sK4) & ~happy(sK4)) [choice axiom]
51. ((~calm(sK4) & ~happy(sK4)) | (~patient(mary) & ~quiet(mary))) & (patient(mary) | quiet(mary) | ! [X1] : (calm(X1) | happy(X1))) [skolemisation 49,50]
57. ! [X0] : (((~brave(X0) | ~calm(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (brave(X0) & calm(X0)))) [nnf transformation 11]
58. ! [X0] : ((~brave(X0) | ~calm(X0) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (brave(X0) & calm(X0)))) [flattening 57]
59. ! [X0] : ((~humble(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | humble(X0))) [nnf transformation 12]
60. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 14]
61. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 60]
62. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ~humble(X0)) & (humble(X0) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [nnf transformation 15]
63. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (generous(X0) | ~curious(X0)))) [nnf transformation 16]
64. ! [X0] : (((~generous(X0) & curious(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | generous(X0) | ~curious(X0))) [flattening 63]
77. wise(X0) | creative(X0) [cnf transformation 29]
87. ~funny(X0) | ~patient(X0) [cnf transformation 41]
89. ~strong(X0) | ~patient(X0) [cnf transformation 41]
90. ~strong(X0) | ~curious(X0) [cnf transformation 41]
91. patient(fred) | ~calm(X0) | ~wise(X0) [cnf transformation 24]
98. ~creative(X0) | funny(X0) | patient(X0) | humble(X0) [cnf transformation 46]
99. ~humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 46]
100. ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 46]
103. patient(mary) | quiet(mary) | calm(X1) | happy(X1) [cnf transformation 51]
111. rich(X0) | curious(X0) | rich(X0) | creative(X0) [cnf transformation 27]
116. ~brave(X0) | ~calm(X0) | rich(X0) | rich(X0) [cnf transformation 58]
117. ~brave(X0) | ~calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
118. brave(X0) | calm(X0) | humble(X0) [cnf transformation 59]
123. ~patient(X0) | strong(X0) | funny(X0) | humble(X0) [cnf transformation 61]
125. ~humble(X0) | funny(X0) | patient(X0) [cnf transformation 61]
127. humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 61]
129. humble(X0) | humble(X0) | strong(X0) [cnf transformation 62]
135. ~rich(X0) | ~quiet(X0) | curious(X0) [cnf transformation 64]
144. ~happy(fred) [cnf transformation 21]
145. humble(X0) | strong(X0) [duplicate literal removal 129]
147. ~brave(X0) | ~calm(X0) | rich(X0) [duplicate literal removal 116]
148. ~rich(X0) | ~calm(X0) | ~brave(X0) [duplicate literal removal 117]
149. rich(X0) | curious(X0) | creative(X0) [duplicate literal removal 111]
167. 5 <=> ! [X0] : ~patient(X0) [avatar definition]
168. ~patient(X0) <- (5) [avatar component clause 167]
175. 7 <=> ! [X0] : ~curious(X0) [avatar definition]
176. ~curious(X0) <- (7) [avatar component clause 175]
179. 8 <=> creative(fred) [avatar definition]
180. ~creative(fred) <- (~8) [avatar component clause 179]
181. creative(fred) <- (8) [avatar component clause 179]
194. 11 <=> ! [X0] : (~calm(X0) | ~wise(X0)) [avatar definition]
195. ~calm(X0) | ~wise(X0) <- (11) [avatar component clause 194]
197. 12 <=> brave(fred) [avatar definition]
198. brave(fred) <- (12) [avatar component clause 197]
199. ~brave(fred) <- (~12) [avatar component clause 197]
202. 13 <=> patient(fred) [avatar definition]
204. patient(fred) <- (13) [avatar component clause 202]
205. 11 | 13 [avatar split clause 91,202,194]
227. ~funny(X0) | ~humble(X0) [subsumption resolution 100,87]
228. ~humble(X0) | ~patient(X0) [subsumption resolution 99,227]
230. 18 <=> patient(mary) [avatar definition]
231. patient(mary) <- (18) [avatar component clause 230]
239. 20 <=> quiet(mary) [avatar definition]
240. quiet(mary) <- (20) [avatar component clause 239]
250. 22 <=> ! [X1] : (calm(X1) | happy(X1)) [avatar definition]
251. happy(X1) | calm(X1) <- (22) [avatar component clause 250]
252. 22 | 20 | 18 [avatar split clause 103,230,239,250]
271. ~brave(X0) | ~calm(X0) [subsumption resolution 147,148]
274. humble(X0) | ~funny(X0) [subsumption resolution 127,87]
275. ~funny(X0) [subsumption resolution 274,227]
276. ~humble(X0) | patient(X0) [subsumption resolution 125,275]
277. ~humble(X0) [subsumption resolution 276,228]
278. ~patient(X0) | strong(X0) | humble(X0) [subsumption resolution 123,275]
279. ~patient(X0) | strong(X0) [subsumption resolution 278,277]
280. ~patient(X0) [subsumption resolution 279,89]
281. 5 [avatar split clause 280,167]
282. strong(X0) [subsumption resolution 145,277]
306. $false <- (5, 18) [resolution 231,168]
307. ~5 | ~18 [avatar contradiction clause 306]
309. ~curious(X0) [resolution 90,282]
330. curious(X2) | creative(X2) | ~quiet(X2) | curious(X2) [resolution 149,135]
331. curious(X2) | creative(X2) | ~quiet(X2) [duplicate literal removal 330]
333. ~quiet(X2) | creative(X2) <- (7) [subsumption resolution 331,176]
336. creative(mary) <- (7, 20) [resolution 333,240]
341. funny(mary) | patient(mary) | humble(mary) <- (7, 20) [resolution 98,336]
346. patient(mary) | humble(mary) <- (7, 20) [subsumption resolution 341,275]
347. humble(mary) <- (5, 7, 20) [subsumption resolution 346,168]
348. $false <- (5, 7, 20) [subsumption resolution 347,277]
349. ~5 | ~7 | ~20 [avatar contradiction clause 348]
350. 7 [avatar split clause 309,175]
351. $false <- (5, 13) [subsumption resolution 204,168]
352. ~5 | ~13 [avatar contradiction clause 351]
353. funny(fred) | patient(fred) | humble(fred) <- (8) [resolution 181,98]
354. patient(fred) | humble(fred) <- (8) [subsumption resolution 353,275]
355. humble(fred) <- (5, 8) [subsumption resolution 354,168]
356. $false <- (5, 8) [subsumption resolution 355,277]
357. ~5 | ~8 [avatar contradiction clause 356]
360. calm(fred) | humble(fred) <- (~12) [resolution 199,118]
361. calm(fred) <- (~12) [subsumption resolution 360,277]
379. ~wise(fred) <- (11, ~12) [resolution 195,361]
380. calm(fred) <- (22) [resolution 251,144]
393. creative(fred) <- (11, ~12) [resolution 379,77]
395. $false <- (~8, 11, ~12) [subsumption resolution 393,180]
396. 8 | ~11 | 12 [avatar contradiction clause 395]
399. ~calm(fred) <- (12) [resolution 198,271]
400. $false <- (12, 22) [subsumption resolution 399,380]
401. ~12 | ~22 [avatar contradiction clause 400]
402. $false [avatar sat refutation 205,252,281,307,349,350,352,357,396,401]
% SZS output end Proof for 7623474919377400451282009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not strong.
Everyone who is rich is both not patient and not creative and vice versa.
If john is not calm then mary is happy or not patient and vice versa.
Everyone who is quiet is either patient or not creative.
If lucy is tall or not happy then lucy is either not old or humble and vice versa.
Everyone who is both creative and not creative is not strong or patient.
If someone is not old or not quiet then someone is rich.
If fred is both not generous and rich then john is either not tall or humble and vice versa.
Everyone who is either not calm or brave is not tall and vice versa.
If someone is creative then someone is not quiet.
Everyone who is wise or creative is humble.
Everyone who is humble or happy is not humble and vice versa.
If john is happy then someone is calm or not brave and vice versa.
Everyone who is either not quiet or not funny is both generous and kind and vice versa.
If someone is both not happy and happy then john is funny.
Everyone who is either not humble or funny is both not old and not wise and vice versa.
John is either not funny or not strong.
Someone is old or not generous.
Susan is tall.
Someone is both funny and not creative.
Someone is not patient.
Someone is rich. | Fred is not old. | neutral | (![X]:(~brave(X)=>~strong(X)))&
(![X]:(rich(X)<=>(~patient(X)&~creative(X))))&
((~calm(john))<=>((happy(mary)|~patient(mary))))&
(![X]:(quiet(X)=>(patient(X)<~>~creative(X))))&
(((tall(lucy)|~happy(lucy)))<=>((~old(lucy)<~>humble(lucy))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)|patient(X))))&
((?[X]:((~old(X)|~quiet(X))))=>(?[X]:(rich(X))))&
(((~generous(fred)&rich(fred)))<=>((~tall(john)<~>humble(john))))&
(![X]:((~calm(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(creative(X)))=>(?[X]:(~quiet(X))))&
(![X]:((wise(X)|creative(X))=>humble(X)))&
(![X]:((humble(X)|happy(X))<=>~humble(X)))&
((happy(john))<=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~quiet(X)<~>~funny(X))<=>(generous(X)&kind(X))))&
((?[X]:((~happy(X)&happy(X))))=>(funny(john)))&
(![X]:((~humble(X)<~>funny(X))<=>(~old(X)&~wise(X))))&
((~funny(john)<~>~strong(john)))&
(?[X]:((old(X)|~generous(X))))&
(tall(susan))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:(~patient(X)))&
(?[X]:(rich(X))) | ~old(fred) | [] | null | 0 |
Everyone who is not creative is not rich or not curious.
If fred is either not happy or not curious then mary is not humble and vice versa.
If fred is happy or old then john is either creative or not kind and vice versa.
If susan is both strong and creative then someone is either quiet or not quiet.
Everyone who is either not patient or quiet is kind or wise.
Everyone who is either not patient or kind is quiet or not rich.
Everyone who is both not tall and kind is not quiet and vice versa.
If fred is not creative then someone is either funny or generous and vice versa.
If alice is both humble and kind then someone is creative and vice versa.
Everyone who is not happy or rich is both old and strong.
If lucy is both patient and not brave then mary is not happy and vice versa.
If alice is tall then lucy is calm or humble and vice versa.
If lucy is quiet then someone is both tall and not funny and vice versa.
If someone is both funny and happy then someone is not curious or funny.
Everyone who is not calm is either generous or happy and vice versa.
If someone is not calm or rich then someone is either not calm or strong and vice versa.
Mary is both strong and not old.
Someone is either tall or not curious.
Paul is either not patient or quiet.
Someone is quiet.
Mary is both not wise and brave.
John is both not kind and brave.
Lucy is not generous or not happy. | John is not kind. | entailment | (![X]:(~creative(X)=>(~rich(X)|~curious(X))))&
(((~happy(fred)<~>~curious(fred)))<=>(~humble(mary)))&
(((happy(fred)|old(fred)))<=>((creative(john)<~>~kind(john))))&
(((strong(susan)&creative(susan)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~patient(X)<~>quiet(X))=>(kind(X)|wise(X))))&
(![X]:((~patient(X)<~>kind(X))=>(quiet(X)|~rich(X))))&
(![X]:((~tall(X)&kind(X))<=>~quiet(X)))&
((~creative(fred))<=>(?[X]:((funny(X)<~>generous(X)))))&
(((humble(alice)&kind(alice)))<=>(?[X]:(creative(X))))&
(![X]:((~happy(X)|rich(X))=>(old(X)&strong(X))))&
(((patient(lucy)&~brave(lucy)))<=>(~happy(mary)))&
((tall(alice))<=>((calm(lucy)|humble(lucy))))&
((quiet(lucy))<=>(?[X]:((tall(X)&~funny(X)))))&
((?[X]:((funny(X)&happy(X))))=>(?[X]:((~curious(X)|funny(X)))))&
(![X]:(~calm(X)<=>(generous(X)<~>happy(X))))&
((?[X]:((~calm(X)|rich(X))))<=>(?[X]:((~calm(X)<~>strong(X)))))&
((strong(mary)&~old(mary)))&
(?[X]:((tall(X)<~>~curious(X))))&
((~patient(paul)<~>quiet(paul)))&
(?[X]:(quiet(X)))&
((~wise(mary)&brave(mary)))&
((~kind(john)&brave(john)))&
((~generous(lucy)|~happy(lucy))) | ~kind(john) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4432297308377561625291712
% SZS output start Proof for 4432297308377561625291712
22. brave(john) & ~kind(john) [input p21]
24. kind(john) [input hypothesis]
139. ~kind(john) [cnf transformation 22]
142. kind(john) [cnf transformation 24]
160. 4 <=> kind(john) [avatar definition]
331. ~4 [avatar split clause 139,160]
341. 4 [avatar split clause 142,160]
342. $false [avatar sat refutation 331,341]
% SZS output end Proof for 4432297308377561625291712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble or rich then someone is both old and not generous.
If fred is not wise then mary is tall or humble and vice versa.
If someone is both tall and generous then susan is not rich or not funny and vice versa.
Everyone who is either not happy or patient is both creative and humble and vice versa.
If someone is both not strong and not brave then someone is either tall or not quiet and vice versa.
If someone is not strong then someone is kind or wise.
If mary is both not generous and brave then someone is brave or not calm and vice versa.
Everyone who is either generous or not generous is both not happy and not quiet and vice versa.
Everyone who is either curious or not quiet is happy.
Everyone who is both not funny and not patient is not funny.
If paul is not quiet then someone is humble or quiet.
If fred is both happy and not generous then someone is both strong and calm.
Everyone who is not strong is happy and vice versa.
Everyone who is not funny is humble.
Everyone who is either not funny or tall is either rich or calm and vice versa.
Someone is both old and not kind.
Lucy is both not creative and not rich.
Someone is either curious or humble.
Someone is strong or quiet.
Lucy is not funny or not wise.
Someone is either not old or generous. | Susan is not curious. | contradiction | ((?[X]:((humble(X)|rich(X))))=>(?[X]:((old(X)&~generous(X)))))&
((~wise(fred))<=>((tall(mary)|humble(mary))))&
((?[X]:((tall(X)&generous(X))))<=>((~rich(susan)|~funny(susan))))&
(![X]:((~happy(X)<~>patient(X))<=>(creative(X)&humble(X))))&
((?[X]:((~strong(X)&~brave(X))))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((kind(X)|wise(X)))))&
(((~generous(mary)&brave(mary)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((generous(X)<~>~generous(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:((~funny(X)&~patient(X))=>~funny(X)))&
((~quiet(paul))=>(?[X]:((humble(X)|quiet(X)))))&
(((happy(fred)&~generous(fred)))=>(?[X]:((strong(X)&calm(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:(~funny(X)=>humble(X)))&
(![X]:((~funny(X)<~>tall(X))<=>(rich(X)<~>calm(X))))&
(?[X]:((old(X)&~kind(X))))&
((~creative(lucy)&~rich(lucy)))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((strong(X)|quiet(X))))&
((~funny(lucy)|~wise(lucy)))&
(?[X]:((~old(X)<~>generous(X)))) | ~curious(susan) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8980271365166988846756582
% SZS output start Proof for 8980271365166988846756582
8. ! [X0] : ((generous(X0) <~> ~generous(X0)) <=> (~quiet(X0) & ~happy(X0))) [input p7]
9. ! [X0] : ((curious(X0) <~> ~quiet(X0)) => happy(X0)) [input p8]
22. ~curious(susan) [input hypothesis]
28. ! [X0] : (happy(X0) | (curious(X0) <=> ~quiet(X0))) [ennf transformation 9]
60. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (quiet(X0) | happy(X0))) & ((~quiet(X0) & ~happy(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [nnf transformation 8]
61. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | quiet(X0) | happy(X0)) & ((~quiet(X0) & ~happy(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [flattening 60]
62. ! [X0] : (happy(X0) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) [nnf transformation 28]
109. ~happy(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 61]
110. ~happy(X0) | generous(X0) | generous(X0) [cnf transformation 61]
111. ~quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 61]
112. ~quiet(X0) | generous(X0) | generous(X0) [cnf transformation 61]
116. happy(X0) | curious(X0) | quiet(X0) [cnf transformation 62]
142. ~curious(susan) [cnf transformation 22]
143. ~happy(X0) | ~generous(X0) [duplicate literal removal 109]
144. ~happy(X0) | generous(X0) [duplicate literal removal 110]
145. ~quiet(X0) | ~generous(X0) [duplicate literal removal 111]
146. ~quiet(X0) | generous(X0) [duplicate literal removal 112]
274. ~quiet(X0) [subsumption resolution 145,146]
275. ~happy(X0) [subsumption resolution 143,144]
276. curious(X0) | quiet(X0) [subsumption resolution 116,275]
277. curious(X0) [subsumption resolution 276,274]
303. $false [subsumption resolution 142,277]
% SZS output end Proof for 8980271365166988846756582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both patient and kind and vice versa.
Everyone who is not funny or not tall is either not strong or not patient and vice versa.
Everyone who is curious is both not old and not tall.
Everyone who is not wise is either not brave or not rich and vice versa.
Everyone who is not rich or not quiet is wise or old and vice versa.
Everyone who is either brave or calm is either humble or creative and vice versa.
If mary is both funny and patient then paul is not kind.
If fred is happy then someone is either not calm or not creative and vice versa.
If mary is both brave and not funny then paul is not patient or strong and vice versa.
Everyone who is not kind is either not wise or wise and vice versa.
Everyone who is both not old and happy is either not funny or not old.
If someone is either humble or not curious then someone is not generous and vice versa.
If someone is both tall and not patient then someone is humble or calm and vice versa.
Everyone who is not kind or not humble is not humble or tall and vice versa.
If someone is either humble or not quiet then someone is wise or not happy.
Everyone who is happy is not creative.
Susan is humble or not kind.
Someone is either rich or kind.
Lucy is patient or not calm.
Someone is either not brave or not quiet.
Someone is strong.
Susan is either happy or strong.
Someone is either not old or not curious. | Paul is not funny. | entailment | (![X]:(funny(X)<=>(patient(X)&kind(X))))&
(![X]:((~funny(X)|~tall(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:(curious(X)=>(~old(X)&~tall(X))))&
(![X]:(~wise(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((~rich(X)|~quiet(X))<=>(wise(X)|old(X))))&
(![X]:((brave(X)<~>calm(X))<=>(humble(X)<~>creative(X))))&
(((funny(mary)&patient(mary)))=>(~kind(paul)))&
((happy(fred))<=>(?[X]:((~calm(X)<~>~creative(X)))))&
(((brave(mary)&~funny(mary)))<=>((~patient(paul)|strong(paul))))&
(![X]:(~kind(X)<=>(~wise(X)<~>wise(X))))&
(![X]:((~old(X)&happy(X))=>(~funny(X)<~>~old(X))))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((~kind(X)|~humble(X))<=>(~humble(X)|tall(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:(happy(X)=>~creative(X)))&
((humble(susan)|~kind(susan)))&
(?[X]:((rich(X)<~>kind(X))))&
((patient(lucy)|~calm(lucy)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
(?[X]:(strong(X)))&
((happy(susan)<~>strong(susan)))&
(?[X]:((~old(X)<~>~curious(X)))) | ~funny(paul) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 572321469395814338941996
% SZS output start Proof for 572321469395814338941996
1. ! [X0] : (funny(X0) <=> (kind(X0) & patient(X0))) [input p0]
10. ! [X0] : (~kind(X0) <=> (~wise(X0) <~> wise(X0))) [input p9]
24. funny(paul) [input hypothesis]
35. ! [X0] : ((funny(X0) | (~kind(X0) | ~patient(X0))) & ((kind(X0) & patient(X0)) | ~funny(X0))) [nnf transformation 1]
36. ! [X0] : ((funny(X0) | ~kind(X0) | ~patient(X0)) & ((kind(X0) & patient(X0)) | ~funny(X0))) [flattening 35]
49. ! [X0] : ((~kind(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | kind(X0))) [nnf transformation 10]
80. ~funny(X0) | kind(X0) [cnf transformation 36]
118. ~kind(X0) | wise(X0) | wise(X0) [cnf transformation 49]
119. ~kind(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 49]
149. funny(paul) [cnf transformation 24]
151. ~kind(X0) | wise(X0) [duplicate literal removal 118]
152. ~kind(X0) | ~wise(X0) [duplicate literal removal 119]
205. ~kind(X0) [subsumption resolution 151,152]
319. kind(paul) [resolution 80,149]
320. $false [subsumption resolution 319,205]
% SZS output end Proof for 572321469395814338941996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or patient is both brave and kind. If someone is either patient or not kind then fred is both tall and wise. Everyone who is not strong is both curious and not rich and vice versa. Everyone who is both not tall and not patient is either old or not tall. If someone is not kind then susan is not humble or quiet. If fred is both not calm and quiet then fred is both not kind and happy and vice versa. If someone is either tall or not tall then susan is either generous or not kind and vice versa. Everyone who is not humble or not old is both curious and not old. Everyone who is generous is both quiet and not creative and vice versa. Everyone who is not creative or not calm is both not rich and not creative and vice versa. If lucy is either strong or happy then someone is curious and vice versa. If someone is not old then someone is both not wise and tall and vice versa. If fred is either not wise or not happy then someone is either funny or not quiet. Everyone who is both strong and funny is not tall or happy and vice versa. Everyone who is either not funny or old is both not calm and brave. Everyone who is both not happy and not kind is either patient or tall and vice versa. Mary is either strong or calm. Fred is either tall or humble. Fred is wise or rich. Someone is both not quiet and brave. Susan is not quiet or strong. Mary is not old or not funny. Someone is not funny or kind. Someone is not calm or not old. | Lucy is not happy. | entailment | (![X]:((~creative(X)<~>patient(X))=>(brave(X)&kind(X))))&
((?[X]:((patient(X)<~>~kind(X))))=>((tall(fred)&wise(fred))))&
(![X]:(~strong(X)<=>(curious(X)&~rich(X))))&
(![X]:((~tall(X)&~patient(X))=>(old(X)<~>~tall(X))))&
((?[X]:(~kind(X)))=>((~humble(susan)|quiet(susan))))&
(((~calm(fred)&quiet(fred)))<=>((~kind(fred)&happy(fred))))&
((?[X]:((tall(X)<~>~tall(X))))<=>((generous(susan)<~>~kind(susan))))&
(![X]:((~humble(X)|~old(X))=>(curious(X)&~old(X))))&
(![X]:(generous(X)<=>(quiet(X)&~creative(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~rich(X)&~creative(X))))&
(((strong(lucy)<~>happy(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&tall(X)))))&
(((~wise(fred)<~>~happy(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((strong(X)&funny(X))<=>(~tall(X)|happy(X))))&
(![X]:((~funny(X)<~>old(X))=>(~calm(X)&brave(X))))&
(![X]:((~happy(X)&~kind(X))<=>(patient(X)<~>tall(X))))&
((strong(mary)<~>calm(mary)))&
((tall(fred)<~>humble(fred)))&
((wise(fred)|rich(fred)))&
(?[X]:((~quiet(X)&brave(X))))&
((~quiet(susan)|strong(susan)))&
((~old(mary)|~funny(mary)))&
(?[X]:((~funny(X)|kind(X))))&
(?[X]:((~calm(X)|~old(X)))) | ~happy(lucy) | [
"p1",
"p7",
"p10",
"p11",
"p13",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6239546465127075998486916
% SZS output start Proof for 6239546465127075998486916
2. ? [X0] : (patient(X0) <~> ~kind(X0)) => (wise(fred) & tall(fred)) [input p1]
8. ! [X0] : ((~old(X0) | ~humble(X0)) => (~old(X0) & curious(X0))) [input p7]
11. (strong(lucy) <~> happy(lucy)) <=> ? [X0] : curious(X0) [input p10]
12. ? [X0] : ~old(X0) <=> ? [X0] : (tall(X0) & ~wise(X0)) [input p11]
14. ! [X0] : ((funny(X0) & strong(X0)) <=> (happy(X0) | ~tall(X0))) [input p13]
16. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (patient(X0) <~> tall(X0))) [input p15]
18. tall(fred) <~> humble(fred) [input p17]
22. ~funny(mary) | ~old(mary) [input p21]
25. happy(lucy) [input hypothesis]
26. ? [X0] : ~old(X0) <=> ? [X1] : (tall(X1) & ~wise(X1)) [rectify 12]
31. (wise(fred) & tall(fred)) | ! [X0] : (patient(X0) <=> ~kind(X0)) [ennf transformation 2]
36. ! [X0] : ((~old(X0) & curious(X0)) | (old(X0) & humble(X0))) [ennf transformation 8]
40. (wise(fred) & tall(fred)) | ! [X0] : ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))) [nnf transformation 31]
54. (((~happy(lucy) | ~strong(lucy)) & (happy(lucy) | strong(lucy))) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ((strong(lucy) | ~happy(lucy)) & (happy(lucy) | ~strong(lucy)))) [nnf transformation 11]
55. (((~happy(lucy) | ~strong(lucy)) & (happy(lucy) | strong(lucy))) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ((strong(lucy) | ~happy(lucy)) & (happy(lucy) | ~strong(lucy)))) [rectify 54]
56. ? [X1] : curious(X1) => curious(sK1) [choice axiom]
57. (((~happy(lucy) | ~strong(lucy)) & (happy(lucy) | strong(lucy))) | ! [X0] : ~curious(X0)) & (curious(sK1) | ((strong(lucy) | ~happy(lucy)) & (happy(lucy) | ~strong(lucy)))) [skolemisation 55,56]
58. (? [X0] : ~old(X0) | ! [X1] : (~tall(X1) | wise(X1))) & (? [X1] : (tall(X1) & ~wise(X1)) | ! [X0] : old(X0)) [nnf transformation 26]
59. (? [X0] : ~old(X0) | ! [X1] : (~tall(X1) | wise(X1))) & (? [X2] : (tall(X2) & ~wise(X2)) | ! [X3] : old(X3)) [rectify 58]
60. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
61. ? [X2] : (tall(X2) & ~wise(X2)) => (tall(sK3) & ~wise(sK3)) [choice axiom]
62. (~old(sK2) | ! [X1] : (~tall(X1) | wise(X1))) & ((tall(sK3) & ~wise(sK3)) | ! [X3] : old(X3)) [skolemisation 59,61,60]
66. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | (~funny(X0) | ~strong(X0)))) [nnf transformation 14]
67. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | ~funny(X0) | ~strong(X0))) [flattening 66]
69. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (kind(X0) | happy(X0)))) [nnf transformation 16]
70. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | kind(X0) | happy(X0))) [flattening 69]
72. (~humble(fred) | ~tall(fred)) & (humble(fred) | tall(fred)) [nnf transformation 18]
81. tall(fred) | ~kind(X0) | ~patient(X0) [cnf transformation 40]
82. tall(fred) | patient(X0) | kind(X0) [cnf transformation 40]
103. humble(X0) | curious(X0) [cnf transformation 36]
104. old(X0) | curious(X0) [cnf transformation 36]
118. ~happy(lucy) | ~strong(lucy) | ~curious(X0) [cnf transformation 57]
119. ~wise(sK3) | old(X3) [cnf transformation 62]
120. tall(sK3) | old(X3) [cnf transformation 62]
121. ~old(sK2) | ~tall(X1) | wise(X1) [cnf transformation 62]
128. ~happy(X0) | strong(X0) [cnf transformation 67]
129. funny(X0) | tall(X0) [cnf transformation 67]
130. ~happy(X0) | funny(X0) [cnf transformation 67]
134. ~tall(X0) | ~patient(X0) | kind(X0) | happy(X0) [cnf transformation 70]
138. ~tall(X0) | patient(X0) | ~kind(X0) [cnf transformation 70]
142. ~humble(fred) | ~tall(fred) [cnf transformation 72]
146. ~funny(mary) | ~old(mary) [cnf transformation 22]
149. happy(lucy) [cnf transformation 25]
156. 1 <=> ! [X0] : (patient(X0) | kind(X0)) [avatar definition]
157. kind(X0) | patient(X0) <- (1) [avatar component clause 156]
164. 3 <=> ! [X0] : (~kind(X0) | ~patient(X0)) [avatar definition]
165. ~kind(X0) | ~patient(X0) <- (3) [avatar component clause 164]
168. 4 <=> tall(fred) [avatar definition]
171. 1 | 4 [avatar split clause 82,168,156]
172. 3 | 4 [avatar split clause 81,168,164]
224. 16 <=> ! [X0] : ~curious(X0) [avatar definition]
225. ~curious(X0) <- (16) [avatar component clause 224]
227. 17 <=> strong(lucy) [avatar definition]
231. 18 <=> happy(lucy) [avatar definition]
232. happy(lucy) <- (18) [avatar component clause 231]
234. 16 | ~17 | ~18 [avatar split clause 118,231,227,224]
243. 20 <=> ! [X1] : (~tall(X1) | wise(X1)) [avatar definition]
244. ~tall(X1) | wise(X1) <- (20) [avatar component clause 243]
246. 21 <=> old(sK2) [avatar definition]
248. ~old(sK2) <- (~21) [avatar component clause 246]
249. 20 | ~21 [avatar split clause 121,246,243]
251. 22 <=> ! [X3] : old(X3) [avatar definition]
252. old(X3) <- (22) [avatar component clause 251]
254. 23 <=> tall(sK3) [avatar definition]
256. tall(sK3) <- (23) [avatar component clause 254]
257. 22 | 23 [avatar split clause 120,254,251]
259. 24 <=> wise(sK3) [avatar definition]
261. ~wise(sK3) <- (~24) [avatar component clause 259]
262. 22 | ~24 [avatar split clause 119,259,251]
286. 29 <=> humble(fred) [avatar definition]
288. ~humble(fred) <- (~29) [avatar component clause 286]
289. ~4 | ~29 [avatar split clause 142,286,168]
302. 32 <=> old(mary) [avatar definition]
304. ~old(mary) <- (~32) [avatar component clause 302]
306. 33 <=> funny(mary) [avatar definition]
308. ~funny(mary) <- (~33) [avatar component clause 306]
309. ~32 | ~33 [avatar split clause 146,306,302]
328. 18 [avatar split clause 149,231]
333. curious(fred) <- (~29) [resolution 103,288]
336. $false <- (16, ~29) [subsumption resolution 333,225]
337. ~16 | 29 [avatar contradiction clause 336]
346. strong(lucy) <- (18) [resolution 128,232]
349. 17 | ~18 [avatar split clause 346,231,227]
370. wise(sK3) <- (20, 23) [resolution 244,256]
372. $false <- (20, 23, ~24) [subsumption resolution 370,261]
373. ~20 | ~23 | 24 [avatar contradiction clause 372]
374. curious(sK2) <- (~21) [resolution 248,104]
375. $false <- (16, ~21) [subsumption resolution 374,225]
376. ~16 | 21 [avatar contradiction clause 375]
409. $false <- (22, ~32) [subsumption resolution 304,252]
410. ~22 | 32 [avatar contradiction clause 409]
439. tall(mary) <- (~33) [resolution 308,129]
490. ~patient(mary) | kind(mary) | happy(mary) <- (~33) [resolution 439,134]
491. patient(mary) | ~kind(mary) <- (~33) [resolution 439,138]
493. kind(mary) | happy(mary) <- (1, ~33) [subsumption resolution 490,157]
495. 47 <=> happy(mary) [avatar definition]
497. happy(mary) <- (47) [avatar component clause 495]
499. 48 <=> kind(mary) [avatar definition]
502. 47 | 48 | ~1 | 33 [avatar split clause 493,306,156,499,495]
503. ~kind(mary) <- (3, ~33) [subsumption resolution 491,165]
504. ~48 | ~3 | 33 [avatar split clause 503,306,164,499]
553. funny(mary) <- (47) [resolution 497,130]
556. $false <- (~33, 47) [subsumption resolution 553,308]
557. 33 | ~47 [avatar contradiction clause 556]
558. $false [avatar sat refutation 171,172,234,249,257,262,289,309,328,337,349,373,376,410,502,504,557]
% SZS output end Proof for 6239546465127075998486916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not rich or not funny then lucy is not tall or creative.
If lucy is not calm then fred is quiet and vice versa.
If someone is calm or not funny then john is not rich or creative and vice versa.
Everyone who is either not wise or not quiet is both not quiet and humble and vice versa.
Everyone who is happy or old is not quiet or not old and vice versa.
If fred is not funny or rich then fred is funny or old.
Everyone who is not tall is both strong and humble.
Everyone who is either curious or not old is both not strong and patient.
If someone is either not humble or not funny then someone is either strong or not rich.
If someone is both tall and not curious then paul is strong and vice versa.
Everyone who is creative is old or generous and vice versa.
Everyone who is not happy is both not creative and not calm.
If someone is strong or tall then someone is either old or happy and vice versa.
If someone is both happy and not brave then alice is both not curious and strong and vice versa.
If alice is both not old and patient then someone is either not generous or happy.
Everyone who is not happy or not humble is happy and vice versa.
Paul is not curious.
Fred is both calm and tall.
Susan is not wise or not funny.
Alice is tall or strong.
Someone is both calm and rich.
Alice is quiet.
Someone is generous or not old.
Fred is both tall and kind. | Alice is not old. | entailment | ((?[X]:((~rich(X)|~funny(X))))=>((~tall(lucy)|creative(lucy))))&
((~calm(lucy))<=>(quiet(fred)))&
((?[X]:((calm(X)|~funny(X))))<=>((~rich(john)|creative(john))))&
(![X]:((~wise(X)<~>~quiet(X))<=>(~quiet(X)&humble(X))))&
(![X]:((happy(X)|old(X))<=>(~quiet(X)|~old(X))))&
(((~funny(fred)|rich(fred)))=>((funny(fred)|old(fred))))&
(![X]:(~tall(X)=>(strong(X)&humble(X))))&
(![X]:((curious(X)<~>~old(X))=>(~strong(X)&patient(X))))&
((?[X]:((~humble(X)<~>~funny(X))))=>(?[X]:((strong(X)<~>~rich(X)))))&
((?[X]:((tall(X)&~curious(X))))<=>(strong(paul)))&
(![X]:(creative(X)<=>(old(X)|generous(X))))&
(![X]:(~happy(X)=>(~creative(X)&~calm(X))))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((old(X)<~>happy(X)))))&
((?[X]:((happy(X)&~brave(X))))<=>((~curious(alice)&strong(alice))))&
(((~old(alice)&patient(alice)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(![X]:((~happy(X)|~humble(X))<=>happy(X)))&
(~curious(paul))&
((calm(fred)&tall(fred)))&
((~wise(susan)|~funny(susan)))&
((tall(alice)|strong(alice)))&
(?[X]:((calm(X)&rich(X))))&
(quiet(alice))&
(?[X]:((generous(X)|~old(X))))&
((tall(fred)&kind(fred))) | ~old(alice) | [
"p4",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1325236852376802511625471
% SZS output start Proof for 1325236852376802511625471
5. ! [X0] : ((old(X0) | happy(X0)) <=> (~old(X0) | ~quiet(X0))) [input p4]
22. quiet(alice) [input p21]
25. old(alice) [input hypothesis]
47. ! [X0] : (((old(X0) | happy(X0)) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | (~old(X0) & ~happy(X0)))) [nnf transformation 5]
48. ! [X0] : ((old(X0) | happy(X0) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | (~old(X0) & ~happy(X0)))) [flattening 47]
94. ~old(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 48]
139. quiet(alice) [cnf transformation 22]
142. old(alice) [cnf transformation 25]
146. ~old(X0) | ~quiet(X0) [duplicate literal removal 94]
289. 32 <=> old(alice) [avatar definition]
291. old(alice) <- (32) [avatar component clause 289]
324. 32 [avatar split clause 142,289]
332. ~quiet(alice) <- (32) [resolution 146,291]
333. $false <- (32) [subsumption resolution 332,139]
334. ~32 [avatar contradiction clause 333]
335. $false [avatar sat refutation 324,334]
% SZS output end Proof for 1325236852376802511625471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or calm is both not tall and old and vice versa.
Everyone who is both not humble and generous is either brave or not strong and vice versa.
If lucy is both not old and patient then fred is wise or not generous.
If susan is not curious or strong then someone is either not humble or old and vice versa.
If someone is both brave and tall then someone is either funny or happy.
Everyone who is either happy or not generous is either tall or not quiet.
If alice is both not patient and not strong then someone is either not old or not generous and vice versa.
If fred is either not curious or funny then lucy is not funny or not tall and vice versa.
Everyone who is both brave and not curious is humble and vice versa.
Everyone who is creative is humble.
Everyone who is both not kind and not happy is either tall or not old.
Everyone who is not wise or wise is not patient or funny and vice versa.
If someone is not funny then someone is both tall and not old and vice versa.
Everyone who is either not tall or generous is either not brave or not quiet and vice versa.
Everyone who is not creative is either calm or strong.
Everyone who is both not wise and not strong is not funny and vice versa.
Someone is not happy.
Alice is both brave and not strong.
Lucy is both not old and quiet.
Paul is not tall.
Someone is both not humble and calm.
Susan is both not strong and not generous.
Someone is quiet or not rich. | Fred is not generous. | neutral | (![X]:((brave(X)|calm(X))<=>(~tall(X)&old(X))))&
(![X]:((~humble(X)&generous(X))<=>(brave(X)<~>~strong(X))))&
(((~old(lucy)&patient(lucy)))=>((wise(fred)|~generous(fred))))&
(((~curious(susan)|strong(susan)))<=>(?[X]:((~humble(X)<~>old(X)))))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:((funny(X)<~>happy(X)))))&
(![X]:((happy(X)<~>~generous(X))=>(tall(X)<~>~quiet(X))))&
(((~patient(alice)&~strong(alice)))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(((~curious(fred)<~>funny(fred)))<=>((~funny(lucy)|~tall(lucy))))&
(![X]:((brave(X)&~curious(X))<=>humble(X)))&
(![X]:(creative(X)=>humble(X)))&
(![X]:((~kind(X)&~happy(X))=>(tall(X)<~>~old(X))))&
(![X]:((~wise(X)|wise(X))<=>(~patient(X)|funny(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((tall(X)&~old(X)))))&
(![X]:((~tall(X)<~>generous(X))<=>(~brave(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>(calm(X)<~>strong(X))))&
(![X]:((~wise(X)&~strong(X))<=>~funny(X)))&
(?[X]:(~happy(X)))&
((brave(alice)&~strong(alice)))&
((~old(lucy)&quiet(lucy)))&
(~tall(paul))&
(?[X]:((~humble(X)&calm(X))))&
((~strong(susan)&~generous(susan)))&
(?[X]:((quiet(X)|~rich(X)))) | ~generous(fred) | [] | null | 0 |
If fred is creative or not creative then someone is humble or quiet and vice versa.
Everyone who is either wise or old is both calm and not tall.
Everyone who is not curious or not wise is both not brave and curious and vice versa.
Everyone who is old or kind is both not tall and wise.
If someone is not happy then someone is not old.
Everyone who is not rich or not brave is old.
If susan is not patient or not rich then someone is both generous and old and vice versa.
If alice is calm then someone is kind or tall.
Everyone who is not quiet or not generous is not funny or not happy.
If someone is creative then john is creative or not brave.
Everyone who is either not quiet or not calm is both not happy and not patient and vice versa.
Everyone who is both brave and not brave is both not humble and not curious and vice versa.
If someone is not tall or not creative then someone is both not humble and not creative and vice versa.
Everyone who is either not wise or generous is both not funny and happy.
If paul is either not brave or calm then someone is both brave and quiet.
Someone is either generous or not old.
Someone is patient.
Someone is either old or quiet.
Fred is both not tall and generous.
Someone is not calm or not humble.
Alice is either not creative or not generous.
Alice is both rich and creative. | John is not wise. | contradiction | (((creative(fred)|~creative(fred)))<=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:((wise(X)<~>old(X))=>(calm(X)&~tall(X))))&
(![X]:((~curious(X)|~wise(X))<=>(~brave(X)&curious(X))))&
(![X]:((old(X)|kind(X))=>(~tall(X)&wise(X))))&
((?[X]:(~happy(X)))=>(?[X]:(~old(X))))&
(![X]:((~rich(X)|~brave(X))=>old(X)))&
(((~patient(susan)|~rich(susan)))<=>(?[X]:((generous(X)&old(X)))))&
((calm(alice))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((~quiet(X)|~generous(X))=>(~funny(X)|~happy(X))))&
((?[X]:(creative(X)))=>((creative(john)|~brave(john))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~brave(X))<=>(~humble(X)&~curious(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~humble(X)&~creative(X)))))&
(![X]:((~wise(X)<~>generous(X))=>(~funny(X)&happy(X))))&
(((~brave(paul)<~>calm(paul)))=>(?[X]:((brave(X)&quiet(X)))))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:(patient(X)))&
(?[X]:((old(X)<~>quiet(X))))&
((~tall(fred)&generous(fred)))&
(?[X]:((~calm(X)|~humble(X))))&
((~creative(alice)<~>~generous(alice)))&
((rich(alice)&creative(alice))) | ~wise(john) | [
"p2",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4822446857456528857342081
% SZS output start Proof for 4822446857456528857342081
3. ! [X0] : ((~wise(X0) | ~curious(X0)) <=> (curious(X0) & ~brave(X0))) [input p2]
4. ! [X0] : ((kind(X0) | old(X0)) => (wise(X0) & ~tall(X0))) [input p3]
6. ! [X0] : ((~brave(X0) | ~rich(X0)) => old(X0)) [input p5]
23. ~wise(john) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~tall(X0)) | (~kind(X0) & ~old(X0))) [ennf transformation 4]
31. ! [X0] : (old(X0) | (brave(X0) & rich(X0))) [ennf transformation 6]
43. ! [X0] : (((~wise(X0) | ~curious(X0)) | (~curious(X0) | brave(X0))) & ((curious(X0) & ~brave(X0)) | (wise(X0) & curious(X0)))) [nnf transformation 3]
44. ! [X0] : ((~wise(X0) | ~curious(X0) | ~curious(X0) | brave(X0)) & ((curious(X0) & ~brave(X0)) | (wise(X0) & curious(X0)))) [flattening 43]
88. ~brave(X0) | wise(X0) [cnf transformation 44]
94. ~old(X0) | wise(X0) [cnf transformation 29]
98. brave(X0) | old(X0) [cnf transformation 31]
139. ~wise(john) [cnf transformation 23]
306. old(X0) | wise(X0) [resolution 98,88]
307. wise(X0) [subsumption resolution 306,94]
315. $false [resolution 307,139]
% SZS output end Proof for 4822446857456528857342081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or humble is either tall or not happy. Everyone who is either calm or creative is both funny and not strong. Everyone who is both tall and creative is both generous and calm. If someone is not tall or not calm then someone is humble or old and vice versa. If susan is calm then alice is both patient and calm. If someone is generous or not humble then mary is both kind and not happy. If susan is either not tall or creative then someone is either not old or humble. Everyone who is not generous or happy is not brave and vice versa. If john is both generous and happy then someone is either quiet or not calm and vice versa. Everyone who is either not generous or not funny is funny and vice versa. Everyone who is curious or not old is rich and vice versa. Everyone who is both not tall and not quiet is not humble and vice versa. Everyone who is not tall or brave is either wise or not brave and vice versa. Everyone who is either creative or not humble is both not humble and not wise. Everyone who is both calm and not tall is patient and vice versa. If someone is not happy or rich then someone is brave and vice versa. Someone is funny or rich. Someone is calm or happy. Lucy is not happy or calm. Someone is not brave. Someone is old or not tall. | Alice is not humble. | contradiction | (![X]:((rich(X)|humble(X))=>(tall(X)<~>~happy(X))))&
(![X]:((calm(X)<~>creative(X))=>(funny(X)&~strong(X))))&
(![X]:((tall(X)&creative(X))=>(generous(X)&calm(X))))&
((?[X]:((~tall(X)|~calm(X))))<=>(?[X]:((humble(X)|old(X)))))&
((calm(susan))=>((patient(alice)&calm(alice))))&
((?[X]:((generous(X)|~humble(X))))=>((kind(mary)&~happy(mary))))&
(((~tall(susan)<~>creative(susan)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~generous(X)|happy(X))<=>~brave(X)))&
(((generous(john)&happy(john)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~generous(X)<~>~funny(X))<=>funny(X)))&
(![X]:((curious(X)|~old(X))<=>rich(X)))&
(![X]:((~tall(X)&~quiet(X))<=>~humble(X)))&
(![X]:((~tall(X)|brave(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((creative(X)<~>~humble(X))=>(~humble(X)&~wise(X))))&
(![X]:((calm(X)&~tall(X))<=>patient(X)))&
((?[X]:((~happy(X)|rich(X))))<=>(?[X]:(brave(X))))&
(?[X]:((funny(X)|rich(X))))&
(?[X]:((calm(X)|happy(X))))&
((~happy(lucy)|calm(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)|~tall(X)))) | ~humble(alice) | [
"p5",
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 930089636438707148242083
% SZS output start Proof for 930089636438707148242083
6. ? [X0] : (~humble(X0) | generous(X0)) => (~happy(mary) & kind(mary)) [input p5]
8. ! [X0] : ((happy(X0) | ~generous(X0)) <=> ~brave(X0)) [input p7]
10. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> funny(X0)) [input p9]
16. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X0] : brave(X0) [input p15]
22. ~humble(alice) [input hypothesis]
24. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X1] : brave(X1) [rectify 16]
26. ? [X0] : (~humble(X0) | generous(X0)) => ~happy(mary) [pure predicate removal 6]
33. ~happy(mary) | ! [X0] : (humble(X0) & ~generous(X0)) [ennf transformation 26]
47. ! [X0] : (((happy(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [flattening 47]
54. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~funny(X0)) & (funny(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 10]
62. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X1] : brave(X1) | ! [X0] : (~rich(X0) & happy(X0))) [nnf transformation 24]
63. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X2] : brave(X2) | ! [X3] : (~rich(X3) & happy(X3))) [rectify 62]
64. ? [X0] : (rich(X0) | ~happy(X0)) => (rich(sK4) | ~happy(sK4)) [choice axiom]
65. ? [X2] : brave(X2) => brave(sK5) [choice axiom]
66. ((rich(sK4) | ~happy(sK4)) | ! [X1] : ~brave(X1)) & (brave(sK5) | ! [X3] : (~rich(X3) & happy(X3))) [skolemisation 63,65,64]
90. ~happy(mary) | humble(X0) [cnf transformation 33]
95. ~brave(X0) | generous(X0) [cnf transformation 48]
105. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 54]
106. ~funny(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 54]
126. brave(sK5) | happy(X3) [cnf transformation 66]
134. ~humble(alice) [cnf transformation 22]
138. funny(X0) | ~generous(X0) [duplicate literal removal 105]
139. ~funny(X0) | ~generous(X0) [duplicate literal removal 106]
187. 12 <=> ! [X0] : humble(X0) [avatar definition]
188. humble(X0) <- (12) [avatar component clause 187]
190. 13 <=> happy(mary) [avatar definition]
192. ~happy(mary) <- (~13) [avatar component clause 190]
193. 12 | ~13 [avatar split clause 90,190,187]
195. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
196. ~generous(X0) <- (14) [avatar component clause 195]
246. ~generous(X0) [subsumption resolution 138,139]
247. 14 [avatar split clause 246,195]
264. 29 <=> brave(sK5) [avatar definition]
266. brave(sK5) <- (29) [avatar component clause 264]
269. 30 <=> ! [X3] : happy(X3) [avatar definition]
270. happy(X3) <- (30) [avatar component clause 269]
271. 30 | 29 [avatar split clause 126,264,269]
308. generous(sK5) <- (29) [resolution 95,266]
309. $false <- (14, 29) [subsumption resolution 308,196]
310. ~14 | ~29 [avatar contradiction clause 309]
311. $false <- (~13, 30) [resolution 270,192]
318. 13 | ~30 [avatar contradiction clause 311]
319. $false <- (12) [resolution 188,134]
322. ~12 [avatar contradiction clause 319]
323. $false [avatar sat refutation 193,247,271,310,318,322]
% SZS output end Proof for 930089636438707148242083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not funny or generous then fred is not humble or not creative.
Everyone who is not brave is not kind and vice versa.
If someone is both not creative and not old then someone is both humble and not old and vice versa.
Everyone who is either old or not brave is both not kind and not happy.
Everyone who is both not patient and wise is calm or kind.
Everyone who is both not kind and not happy is either not tall or not quiet and vice versa.
Everyone who is not quiet or not generous is old or not generous and vice versa.
Everyone who is tall or not calm is both not wise and curious.
If susan is both calm and kind then someone is humble or wise and vice versa.
If susan is both not calm and funny then someone is generous or strong and vice versa.
If alice is both generous and humble then someone is both patient and not strong.
If someone is not curious then someone is strong and vice versa.
Everyone who is not happy or humble is both humble and rich and vice versa.
If susan is both not funny and old then susan is both brave and not curious and vice versa.
Everyone who is patient is either curious or funny.
Everyone who is both kind and patient is both not generous and not tall.
Someone is either not generous or tall.
Someone is generous or wise.
Alice is both old and happy.
Someone is brave or not humble.
Paul is both kind and happy.
Someone is both rich and curious.
Fred is both not old and generous.
Someone is not kind or humble. | Fred is not calm. | neutral | (((~funny(susan)|generous(susan)))=>((~humble(fred)|~creative(fred))))&
(![X]:(~brave(X)<=>~kind(X)))&
((?[X]:((~creative(X)&~old(X))))<=>(?[X]:((humble(X)&~old(X)))))&
(![X]:((old(X)<~>~brave(X))=>(~kind(X)&~happy(X))))&
(![X]:((~patient(X)&wise(X))=>(calm(X)|kind(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(old(X)|~generous(X))))&
(![X]:((tall(X)|~calm(X))=>(~wise(X)&curious(X))))&
(((calm(susan)&kind(susan)))<=>(?[X]:((humble(X)|wise(X)))))&
(((~calm(susan)&funny(susan)))<=>(?[X]:((generous(X)|strong(X)))))&
(((generous(alice)&humble(alice)))=>(?[X]:((patient(X)&~strong(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:(strong(X))))&
(![X]:((~happy(X)|humble(X))<=>(humble(X)&rich(X))))&
(((~funny(susan)&old(susan)))<=>((brave(susan)&~curious(susan))))&
(![X]:(patient(X)=>(curious(X)<~>funny(X))))&
(![X]:((kind(X)&patient(X))=>(~generous(X)&~tall(X))))&
(?[X]:((~generous(X)<~>tall(X))))&
(?[X]:((generous(X)|wise(X))))&
((old(alice)&happy(alice)))&
(?[X]:((brave(X)|~humble(X))))&
((kind(paul)&happy(paul)))&
(?[X]:((rich(X)&curious(X))))&
((~old(fred)&generous(fred)))&
(?[X]:((~kind(X)|humble(X)))) | ~calm(fred) | [] | null | 0 |
Everyone who is wise is either not kind or old. Everyone who is both curious and not strong is both not generous and not tall. If someone is both generous and patient then someone is not calm. Everyone who is both creative and humble is either wise or not creative. Everyone who is both happy and brave is not tall or quiet and vice versa. Everyone who is brave is calm or humble. Everyone who is either funny or not calm is humble or curious. Everyone who is not calm or not tall is rich and vice versa. If someone is not wise or happy then alice is both brave and wise and vice versa. If someone is either wise or patient then someone is not patient or not kind. If someone is generous or not generous then john is quiet. Everyone who is both not wise and not rich is not kind or not creative and vice versa. If john is not strong then someone is either quiet or humble and vice versa. Everyone who is both kind and not curious is either not rich or not curious. If someone is quiet or not creative then someone is not calm. Someone is either not quiet or not rich. John is old or strong. Alice is both not strong and not patient. Someone is both not wise and not brave. Alice is rich or humble. | John is kind. | neutral | (![X]:(wise(X)=>(~kind(X)<~>old(X))))&
(![X]:((curious(X)&~strong(X))=>(~generous(X)&~tall(X))))&
((?[X]:((generous(X)&patient(X))))=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&humble(X))=>(wise(X)<~>~creative(X))))&
(![X]:((happy(X)&brave(X))<=>(~tall(X)|quiet(X))))&
(![X]:(brave(X)=>(calm(X)|humble(X))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((~calm(X)|~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)|happy(X))))<=>((brave(alice)&wise(alice))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(quiet(john)))&
(![X]:((~wise(X)&~rich(X))<=>(~kind(X)|~creative(X))))&
((~strong(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((kind(X)&~curious(X))=>(~rich(X)<~>~curious(X))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:(~calm(X))))&
(?[X]:((~quiet(X)<~>~rich(X))))&
((old(john)|strong(john)))&
((~strong(alice)&~patient(alice)))&
(?[X]:((~wise(X)&~brave(X))))&
((rich(alice)|humble(alice))) | kind(john) | [] | null | 0 |
If john is not rich or rich then fred is not curious or not quiet.
Everyone who is either old or wise is rich and vice versa.
Everyone who is either not kind or quiet is wise or funny.
If someone is both brave and quiet then paul is both patient and wise.
If lucy is both not tall and calm then mary is not humble or not strong.
If someone is either not generous or not curious then someone is either not creative or not calm.
Everyone who is either generous or not patient is both kind and calm.
If paul is either not tall or rich then john is not calm and vice versa.
Everyone who is either not wise or not calm is either rich or not tall.
If susan is creative then someone is creative or not wise and vice versa.
If paul is funny then susan is not tall or not kind and vice versa.
If john is both not quiet and not kind then mary is brave and vice versa.
If someone is not wise or not funny then fred is either not calm or not patient.
If someone is not happy then paul is humble or not humble.
Everyone who is calm is both not humble and not generous.
If paul is old or not brave then susan is either not wise or tall and vice versa.
Someone is not rich.
John is not patient.
Someone is not patient or not funny.
Someone is not funny or not quiet.
Lucy is tall.
Someone is either not humble or not wise.
Someone is both creative and brave.
Someone is either not old or rich. | Fred is generous. | contradiction | (((~rich(john)|rich(john)))=>((~curious(fred)|~quiet(fred))))&
(![X]:((old(X)<~>wise(X))<=>rich(X)))&
(![X]:((~kind(X)<~>quiet(X))=>(wise(X)|funny(X))))&
((?[X]:((brave(X)&quiet(X))))=>((patient(paul)&wise(paul))))&
(((~tall(lucy)&calm(lucy)))=>((~humble(mary)|~strong(mary))))&
((?[X]:((~generous(X)<~>~curious(X))))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((generous(X)<~>~patient(X))=>(kind(X)&calm(X))))&
(((~tall(paul)<~>rich(paul)))<=>(~calm(john)))&
(![X]:((~wise(X)<~>~calm(X))=>(rich(X)<~>~tall(X))))&
((creative(susan))<=>(?[X]:((creative(X)|~wise(X)))))&
((funny(paul))<=>((~tall(susan)|~kind(susan))))&
(((~quiet(john)&~kind(john)))<=>(brave(mary)))&
((?[X]:((~wise(X)|~funny(X))))=>((~calm(fred)<~>~patient(fred))))&
((?[X]:(~happy(X)))=>((humble(paul)|~humble(paul))))&
(![X]:(calm(X)=>(~humble(X)&~generous(X))))&
(((old(paul)|~brave(paul)))<=>((~wise(susan)<~>tall(susan))))&
(?[X]:(~rich(X)))&
(~patient(john))&
(?[X]:((~patient(X)|~funny(X))))&
(?[X]:((~funny(X)|~quiet(X))))&
(tall(lucy))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:((~old(X)<~>rich(X)))) | generous(fred) | [
"p1",
"p6",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1682993586512104096742243
% SZS output start Proof for 1682993586512104096742243
2. ! [X0] : ((old(X0) <~> wise(X0)) <=> rich(X0)) [input p1]
7. ! [X0] : ((generous(X0) <~> ~patient(X0)) => (calm(X0) & kind(X0))) [input p6]
13. ? [X0] : (~funny(X0) | ~wise(X0)) => (~calm(fred) <~> ~patient(fred)) [input p12]
15. ! [X0] : (calm(X0) => (~generous(X0) & ~humble(X0))) [input p14]
24. ? [X0] : (~old(X0) <~> rich(X0)) [input p23]
25. generous(fred) [input hypothesis]
35. ! [X0] : ((calm(X0) & kind(X0)) | (generous(X0) <=> ~patient(X0))) [ennf transformation 7]
37. (~calm(fred) <~> ~patient(fred)) | ! [X0] : (funny(X0) & wise(X0)) [ennf transformation 13]
38. ! [X0] : ((~generous(X0) & ~humble(X0)) | ~calm(X0)) [ennf transformation 15]
39. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | ~rich(X0)) & (rich(X0) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [nnf transformation 2]
45. ! [X0] : ((calm(X0) & kind(X0)) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0)))) [nnf transformation 35]
56. ((patient(fred) | calm(fred)) & (~patient(fred) | ~calm(fred))) | ! [X0] : (funny(X0) & wise(X0)) [nnf transformation 37]
70. ? [X0] : ((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) [nnf transformation 24]
71. ? [X0] : ((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) => ((~rich(sK7) | old(sK7)) & (rich(sK7) | ~old(sK7))) [choice axiom]
72. (~rich(sK7) | old(sK7)) & (rich(sK7) | ~old(sK7)) [skolemisation 70,71]
76. ~wise(X0) | old(X0) | rich(X0) [cnf transformation 39]
78. ~wise(X0) | ~old(X0) | ~rich(X0) [cnf transformation 39]
89. ~generous(X0) | ~patient(X0) | calm(X0) [cnf transformation 45]
110. patient(fred) | calm(fred) | wise(X0) [cnf transformation 56]
113. ~generous(X0) | ~calm(X0) [cnf transformation 38]
129. rich(sK7) | ~old(sK7) [cnf transformation 72]
130. ~rich(sK7) | old(sK7) [cnf transformation 72]
131. generous(fred) [cnf transformation 25]
194. 14 <=> ! [X0] : wise(X0) [avatar definition]
195. wise(X0) <- (14) [avatar component clause 194]
248. 26 <=> calm(fred) [avatar definition]
249. ~calm(fred) <- (~26) [avatar component clause 248]
252. 27 <=> patient(fred) [avatar definition]
256. 14 | 26 | 27 [avatar split clause 110,252,248,194]
306. 37 <=> old(sK7) [avatar definition]
307. ~old(sK7) <- (~37) [avatar component clause 306]
308. old(sK7) <- (37) [avatar component clause 306]
310. 38 <=> rich(sK7) [avatar definition]
311. rich(sK7) <- (38) [avatar component clause 310]
312. ~rich(sK7) <- (~38) [avatar component clause 310]
313. 37 | ~38 [avatar split clause 130,310,306]
314. ~37 | 38 [avatar split clause 129,310,306]
326. ~calm(fred) [resolution 113,131]
329. ~26 [avatar split clause 326,248]
347. ~patient(fred) | calm(fred) [resolution 89,131]
352. ~patient(fred) <- (~26) [subsumption resolution 347,249]
353. ~27 | 26 [avatar split clause 352,248,252]
359. ~old(X0) | ~rich(X0) <- (14) [resolution 195,78]
360. old(X1) | rich(X1) <- (14) [resolution 195,76]
372. rich(sK7) <- (14, ~37) [resolution 360,307]
376. $false <- (14, ~37, ~38) [subsumption resolution 372,312]
377. ~14 | 37 | 38 [avatar contradiction clause 376]
378. ~rich(sK7) <- (14, 37) [resolution 308,359]
380. $false <- (14, 37, 38) [subsumption resolution 378,311]
381. ~14 | ~37 | ~38 [avatar contradiction clause 380]
382. $false [avatar sat refutation 256,313,314,329,353,377,381]
% SZS output end Proof for 1682993586512104096742243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not old or humble then fred is both not tall and not funny and vice versa.
Everyone who is quiet is brave or kind and vice versa.
If lucy is both not creative and tall then paul is happy.
If someone is curious then someone is calm.
Everyone who is patient or not kind is happy or funny and vice versa.
Everyone who is both not tall and strong is old.
If someone is patient then someone is either calm or rich.
Everyone who is tall or not funny is both happy and wise.
Everyone who is not patient or patient is funny and vice versa.
Everyone who is either not rich or patient is both not funny and kind and vice versa.
If mary is curious then someone is not curious or generous and vice versa.
Everyone who is not kind is either strong or not quiet and vice versa.
Everyone who is not quiet or generous is both strong and generous and vice versa.
Everyone who is either not generous or kind is strong or brave.
Everyone who is creative or not old is either creative or tall.
Everyone who is both generous and not kind is not strong.
Paul is not strong or patient.
Someone is not curious.
Someone is not brave or curious.
Someone is both not tall and not creative.
Alice is either creative or happy. | Mary is generous. | contradiction | ((?[X]:((~old(X)<~>humble(X))))<=>((~tall(fred)&~funny(fred))))&
(![X]:(quiet(X)<=>(brave(X)|kind(X))))&
(((~creative(lucy)&tall(lucy)))=>(happy(paul)))&
((?[X]:(curious(X)))=>(?[X]:(calm(X))))&
(![X]:((patient(X)|~kind(X))<=>(happy(X)|funny(X))))&
(![X]:((~tall(X)&strong(X))=>old(X)))&
((?[X]:(patient(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))=>(happy(X)&wise(X))))&
(![X]:((~patient(X)|patient(X))<=>funny(X)))&
(![X]:((~rich(X)<~>patient(X))<=>(~funny(X)&kind(X))))&
((curious(mary))<=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:(~kind(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|generous(X))<=>(strong(X)&generous(X))))&
(![X]:((~generous(X)<~>kind(X))=>(strong(X)|brave(X))))&
(![X]:((creative(X)|~old(X))=>(creative(X)<~>tall(X))))&
(![X]:((generous(X)&~kind(X))=>~strong(X)))&
((~strong(paul)|patient(paul)))&
(?[X]:(~curious(X)))&
(?[X]:((~brave(X)|curious(X))))&
(?[X]:((~tall(X)&~creative(X))))&
((creative(alice)<~>happy(alice))) | generous(mary) | [
"p1",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7138824762211232590329952
% SZS output start Proof for 7138824762211232590329952
2. ! [X0] : (quiet(X0) <=> (kind(X0) | brave(X0))) [input p1]
12. ! [X0] : (~kind(X0) <=> (strong(X0) <~> ~quiet(X0))) [input p11]
13. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (generous(X0) & strong(X0))) [input p12]
16. ! [X0] : ((~kind(X0) & generous(X0)) => ~strong(X0)) [input p15]
22. generous(mary) [input hypothesis]
36. ! [X0] : (~strong(X0) | (kind(X0) | ~generous(X0))) [ennf transformation 16]
37. ! [X0] : (~strong(X0) | kind(X0) | ~generous(X0)) [flattening 36]
43. ! [X0] : ((quiet(X0) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | ~quiet(X0))) [nnf transformation 2]
44. ! [X0] : ((quiet(X0) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | ~quiet(X0))) [flattening 43]
62. ! [X0] : ((~kind(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | kind(X0))) [nnf transformation 12]
63. ! [X0] : (((generous(X0) | ~quiet(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (~generous(X0) & quiet(X0)))) [nnf transformation 13]
64. ! [X0] : ((generous(X0) | ~quiet(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (~generous(X0) & quiet(X0)))) [flattening 63]
82. ~kind(X0) | quiet(X0) [cnf transformation 44]
108. ~kind(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 62]
111. ~generous(X0) | strong(X0) [cnf transformation 64]
121. ~strong(X0) | kind(X0) | ~generous(X0) [cnf transformation 37]
129. generous(mary) [cnf transformation 22]
217. ~strong(X0) | ~kind(X0) [subsumption resolution 108,82]
221. ~generous(X0) | kind(X0) [subsumption resolution 121,111]
255. strong(mary) [resolution 111,129]
264. ~kind(mary) [resolution 217,255]
266. kind(mary) [resolution 221,129]
268. $false [subsumption resolution 266,264]
% SZS output end Proof for 7138824762211232590329952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or strong is old and vice versa.
Everyone who is calm or rich is quiet or happy and vice versa.
Everyone who is either patient or not humble is either patient or not tall.
Everyone who is funny is both not funny and wise.
Everyone who is quiet or old is not patient.
Everyone who is both not curious and creative is happy or not wise and vice versa.
Everyone who is both not quiet and not old is not generous or happy.
Everyone who is not calm is both brave and calm.
Everyone who is both happy and kind is both old and not brave and vice versa.
Everyone who is not generous or tall is not old.
Everyone who is either not old or wise is not kind.
Everyone who is generous or curious is quiet.
Everyone who is humble or brave is either not generous or humble and vice versa.
Everyone who is both not strong and creative is either not patient or not old and vice versa.
If mary is both funny and not wise then someone is both rich and not funny and vice versa.
Everyone who is both not humble and not generous is either generous or happy and vice versa.
John is not brave.
Someone is not humble.
John is calm or not tall. | Mary is not patient. | entailment | (![X]:((~humble(X)|strong(X))<=>old(X)))&
(![X]:((calm(X)|rich(X))<=>(quiet(X)|happy(X))))&
(![X]:((patient(X)<~>~humble(X))=>(patient(X)<~>~tall(X))))&
(![X]:(funny(X)=>(~funny(X)&wise(X))))&
(![X]:((quiet(X)|old(X))=>~patient(X)))&
(![X]:((~curious(X)&creative(X))<=>(happy(X)|~wise(X))))&
(![X]:((~quiet(X)&~old(X))=>(~generous(X)|happy(X))))&
(![X]:(~calm(X)=>(brave(X)&calm(X))))&
(![X]:((happy(X)&kind(X))<=>(old(X)&~brave(X))))&
(![X]:((~generous(X)|tall(X))=>~old(X)))&
(![X]:((~old(X)<~>wise(X))=>~kind(X)))&
(![X]:((generous(X)|curious(X))=>quiet(X)))&
(![X]:((humble(X)|brave(X))<=>(~generous(X)<~>humble(X))))&
(![X]:((~strong(X)&creative(X))<=>(~patient(X)<~>~old(X))))&
(((funny(mary)&~wise(mary)))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((~humble(X)&~generous(X))<=>(generous(X)<~>happy(X))))&
(~brave(john))&
(?[X]:(~humble(X)))&
((calm(john)|~tall(john))) | ~patient(mary) | [
"p0",
"p4",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 848486044125951780681023
% SZS output start Proof for 848486044125951780681023
1. ! [X0] : ((strong(X0) | ~humble(X0)) <=> old(X0)) [input p0]
5. ! [X0] : ((old(X0) | quiet(X0)) => ~patient(X0)) [input p4]
10. ! [X0] : ((tall(X0) | ~generous(X0)) => ~old(X0)) [input p9]
12. ! [X0] : ((curious(X0) | generous(X0)) => quiet(X0)) [input p11]
13. ! [X0] : ((brave(X0) | humble(X0)) <=> (~generous(X0) <~> humble(X0))) [input p12]
20. patient(mary) [input hypothesis]
23. ! [X0] : (~patient(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 5]
27. ! [X0] : (~old(X0) | (~tall(X0) & generous(X0))) [ennf transformation 10]
29. ! [X0] : (quiet(X0) | (~curious(X0) & ~generous(X0))) [ennf transformation 12]
30. ! [X0] : (((strong(X0) | ~humble(X0)) | ~old(X0)) & (old(X0) | (~strong(X0) & humble(X0)))) [nnf transformation 1]
31. ! [X0] : ((strong(X0) | ~humble(X0) | ~old(X0)) & (old(X0) | (~strong(X0) & humble(X0)))) [flattening 30]
40. ! [X0] : (((brave(X0) | humble(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~brave(X0) & ~humble(X0)))) [nnf transformation 13]
41. ! [X0] : ((brave(X0) | humble(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (~brave(X0) & ~humble(X0)))) [flattening 40]
53. old(X0) | humble(X0) [cnf transformation 31]
66. ~patient(X0) | ~quiet(X0) [cnf transformation 23]
80. ~old(X0) | generous(X0) [cnf transformation 27]
84. ~generous(X0) | quiet(X0) [cnf transformation 29]
88. ~humble(X0) | generous(X0) | ~humble(X0) [cnf transformation 41]
111. patient(mary) [cnf transformation 20]
114. ~humble(X0) | generous(X0) [duplicate literal removal 88]
139. ~quiet(mary) [resolution 66,111]
143. generous(X0) | humble(X0) [resolution 80,53]
144. generous(X0) [subsumption resolution 143,114]
145. quiet(X0) [resolution 84,144]
146. $false [resolution 145,139]
% SZS output end Proof for 848486044125951780681023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is strong or curious.
Everyone who is tall is either rich or not quiet and vice versa.
If someone is generous or humble then someone is creative or wise.
If someone is either strong or patient then someone is tall or not happy and vice versa.
Everyone who is not old or brave is old.
Everyone who is not rich or happy is tall.
If someone is humble then someone is both not curious and strong and vice versa.
If mary is both strong and not old then someone is either tall or not curious.
If someone is not tall or tall then paul is either not patient or quiet and vice versa.
If lucy is rich then someone is both not generous and not humble and vice versa.
Everyone who is either not brave or brave is either not brave or not generous.
Everyone who is either kind or not humble is either not quiet or not creative and vice versa.
If mary is humble or quiet then mary is curious or not generous and vice versa.
If mary is brave then alice is not strong and vice versa.
If susan is either not patient or not funny then someone is either happy or not generous.
Everyone who is either wise or creative is not quiet or not kind and vice versa.
Alice is not generous or not quiet.
John is not happy or tall.
Alice is not tall.
Someone is quiet or happy.
Someone is both happy and not generous.
Someone is not tall or patient. | Susan is wise. | neutral | (![X]:(patient(X)=>(strong(X)|curious(X))))&
(![X]:(tall(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((generous(X)|humble(X))))=>(?[X]:((creative(X)|wise(X)))))&
((?[X]:((strong(X)<~>patient(X))))<=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((~old(X)|brave(X))=>old(X)))&
(![X]:((~rich(X)|happy(X))=>tall(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~curious(X)&strong(X)))))&
(((strong(mary)&~old(mary)))=>(?[X]:((tall(X)<~>~curious(X)))))&
((?[X]:((~tall(X)|tall(X))))<=>((~patient(paul)<~>quiet(paul))))&
((rich(lucy))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((~brave(X)<~>brave(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(~quiet(X)<~>~creative(X))))&
(((humble(mary)|quiet(mary)))<=>((curious(mary)|~generous(mary))))&
((brave(mary))<=>(~strong(alice)))&
(((~patient(susan)<~>~funny(susan)))=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:((wise(X)<~>creative(X))<=>(~quiet(X)|~kind(X))))&
((~generous(alice)|~quiet(alice)))&
((~happy(john)|tall(john)))&
(~tall(alice))&
(?[X]:((quiet(X)|happy(X))))&
(?[X]:((happy(X)&~generous(X))))&
(?[X]:((~tall(X)|patient(X)))) | wise(susan) | [] | null | 0 |
If someone is not happy then john is either not strong or not curious and vice versa.
If john is either generous or not rich then someone is happy or not creative.
Everyone who is both tall and quiet is humble or not quiet.
If paul is happy then paul is old and vice versa.
If someone is not curious then lucy is patient or not old and vice versa.
Everyone who is both creative and not calm is humble and vice versa.
If lucy is either strong or generous then someone is both patient and not humble.
Everyone who is happy or not quiet is both curious and kind and vice versa.
Everyone who is not happy or not humble is not creative.
Everyone who is either wise or not wise is either generous or not happy and vice versa.
If paul is both not curious and not strong then susan is either generous or not brave and vice versa.
Everyone who is either not rich or funny is both strong and calm and vice versa.
Everyone who is old is not humble or not wise and vice versa.
If someone is either kind or not tall then fred is either not humble or humble and vice versa.
Everyone who is brave is both not strong and humble and vice versa.
Everyone who is both wise and rich is not old or not wise and vice versa.
Someone is quiet or old.
Someone is brave or not brave.
Someone is both kind and not brave.
Susan is either generous or funny.
Someone is not happy or not curious.
Alice is strong or not strong.
Someone is both happy and not creative. | Susan is kind. | entailment | ((?[X]:(~happy(X)))<=>((~strong(john)<~>~curious(john))))&
(((generous(john)<~>~rich(john)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((tall(X)&quiet(X))=>(humble(X)|~quiet(X))))&
((happy(paul))<=>(old(paul)))&
((?[X]:(~curious(X)))<=>((patient(lucy)|~old(lucy))))&
(![X]:((creative(X)&~calm(X))<=>humble(X)))&
(((strong(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:((happy(X)|~quiet(X))<=>(curious(X)&kind(X))))&
(![X]:((~happy(X)|~humble(X))=>~creative(X)))&
(![X]:((wise(X)<~>~wise(X))<=>(generous(X)<~>~happy(X))))&
(((~curious(paul)&~strong(paul)))<=>((generous(susan)<~>~brave(susan))))&
(![X]:((~rich(X)<~>funny(X))<=>(strong(X)&calm(X))))&
(![X]:(old(X)<=>(~humble(X)|~wise(X))))&
((?[X]:((kind(X)<~>~tall(X))))<=>((~humble(fred)<~>humble(fred))))&
(![X]:(brave(X)<=>(~strong(X)&humble(X))))&
(![X]:((wise(X)&rich(X))<=>(~old(X)|~wise(X))))&
(?[X]:((quiet(X)|old(X))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((kind(X)&~brave(X))))&
((generous(susan)<~>funny(susan)))&
(?[X]:((~happy(X)|~curious(X))))&
((strong(alice)|~strong(alice)))&
(?[X]:((happy(X)&~creative(X)))) | kind(susan) | [
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 978160860088302763367959
% SZS output start Proof for 978160860088302763367959
4. happy(paul) <=> old(paul) [input p3]
6. ! [X0] : ((~calm(X0) & creative(X0)) <=> humble(X0)) [input p5]
8. ! [X0] : ((~quiet(X0) | happy(X0)) <=> (kind(X0) & curious(X0))) [input p7]
9. ! [X0] : ((~humble(X0) | ~happy(X0)) => ~creative(X0)) [input p8]
10. ! [X0] : ((wise(X0) <~> ~wise(X0)) <=> (generous(X0) <~> ~happy(X0))) [input p9]
11. (~strong(paul) & ~curious(paul)) <=> (generous(susan) <~> ~brave(susan)) [input p10]
13. ! [X0] : (old(X0) <=> (~wise(X0) | ~humble(X0))) [input p12]
15. ! [X0] : (brave(X0) <=> (humble(X0) & ~strong(X0))) [input p14]
24. ~kind(susan) [input hypothesis]
29. ! [X0] : (~creative(X0) | (humble(X0) & happy(X0))) [ennf transformation 9]
37. (happy(paul) | ~old(paul)) & (old(paul) | ~happy(paul)) [nnf transformation 4]
43. ! [X0] : (((~calm(X0) & creative(X0)) | ~humble(X0)) & (humble(X0) | (calm(X0) | ~creative(X0)))) [nnf transformation 6]
44. ! [X0] : (((~calm(X0) & creative(X0)) | ~humble(X0)) & (humble(X0) | calm(X0) | ~creative(X0))) [flattening 43]
48. ! [X0] : (((~quiet(X0) | happy(X0)) | (~kind(X0) | ~curious(X0))) & ((kind(X0) & curious(X0)) | (quiet(X0) & ~happy(X0)))) [nnf transformation 8]
49. ! [X0] : ((~quiet(X0) | happy(X0) | ~kind(X0) | ~curious(X0)) & ((kind(X0) & curious(X0)) | (quiet(X0) & ~happy(X0)))) [flattening 48]
50. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [nnf transformation 10]
51. ((~strong(paul) & ~curious(paul)) | ((generous(susan) | brave(susan)) & (~brave(susan) | ~generous(susan)))) & (((brave(susan) | ~generous(susan)) & (~brave(susan) | generous(susan))) | (strong(paul) | curious(paul))) [nnf transformation 11]
52. ((~strong(paul) & ~curious(paul)) | ((generous(susan) | brave(susan)) & (~brave(susan) | ~generous(susan)))) & (((brave(susan) | ~generous(susan)) & (~brave(susan) | generous(susan))) | strong(paul) | curious(paul)) [flattening 51]
55. ! [X0] : ((old(X0) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | ~old(X0))) [nnf transformation 13]
56. ! [X0] : ((old(X0) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | ~old(X0))) [flattening 55]
61. ! [X0] : ((brave(X0) | (~humble(X0) | strong(X0))) & ((humble(X0) & ~strong(X0)) | ~brave(X0))) [nnf transformation 15]
62. ! [X0] : ((brave(X0) | ~humble(X0) | strong(X0)) & ((humble(X0) & ~strong(X0)) | ~brave(X0))) [flattening 61]
84. happy(paul) | ~old(paul) [cnf transformation 37]
89. ~humble(X0) | creative(X0) [cnf transformation 44]
95. ~happy(X0) | curious(X0) [cnf transformation 49]
97. ~happy(X0) | kind(X0) [cnf transformation 49]
100. ~creative(X0) | happy(X0) [cnf transformation 29]
104. happy(X0) | ~generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 50]
105. happy(X0) | ~generous(X0) | wise(X0) | wise(X0) [cnf transformation 50]
113. ~curious(paul) | generous(susan) | brave(susan) [cnf transformation 52]
123. old(X0) | humble(X0) [cnf transformation 56]
134. ~brave(X0) | humble(X0) [cnf transformation 62]
151. ~kind(susan) [cnf transformation 24]
160. happy(X0) | ~generous(X0) | ~wise(X0) [duplicate literal removal 104]
161. ~generous(X0) | happy(X0) | wise(X0) [duplicate literal removal 105]
201. 9 <=> old(paul) [avatar definition]
203. ~old(paul) <- (~9) [avatar component clause 201]
205. 10 <=> happy(paul) [avatar definition]
206. ~happy(paul) <- (~10) [avatar component clause 205]
207. happy(paul) <- (10) [avatar component clause 205]
208. ~9 | 10 [avatar split clause 84,205,201]
248. ~generous(X0) | happy(X0) [subsumption resolution 160,161]
251. 19 <=> brave(susan) [avatar definition]
253. brave(susan) <- (19) [avatar component clause 251]
255. 20 <=> generous(susan) [avatar definition]
257. generous(susan) <- (20) [avatar component clause 255]
265. 22 <=> curious(paul) [avatar definition]
268. 19 | 20 | ~22 [avatar split clause 113,265,255,251]
309. humble(paul) <- (~9) [resolution 123,203]
311. creative(paul) <- (~9) [resolution 309,89]
318. happy(susan) <- (20) [resolution 248,257]
321. kind(susan) <- (20) [resolution 318,97]
323. $false <- (20) [subsumption resolution 321,151]
324. ~20 [avatar contradiction clause 323]
329. happy(paul) <- (~9) [resolution 311,100]
330. $false <- (~9, ~10) [subsumption resolution 329,206]
331. 9 | 10 [avatar contradiction clause 330]
335. curious(paul) <- (10) [resolution 207,95]
338. 22 | ~10 [avatar split clause 335,205,265]
339. humble(susan) <- (19) [resolution 253,134]
347. creative(susan) <- (19) [resolution 339,89]
366. happy(susan) <- (19) [resolution 347,100]
415. kind(susan) <- (19) [resolution 366,97]
419. $false <- (19) [subsumption resolution 415,151]
420. ~19 [avatar contradiction clause 419]
421. $false [avatar sat refutation 208,268,324,331,338,420]
% SZS output end Proof for 978160860088302763367959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or brave is both not brave and not old and vice versa. If someone is humble or happy then mary is either tall or not creative. Everyone who is not brave or kind is not funny and vice versa. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Everyone who is either quiet or calm is both not wise and funny and vice versa. If someone is both humble and curious then someone is either humble or not creative and vice versa. Fred is either not generous or old. Alice is either patient or rich. Lucy is both tall and not curious. Someone is either not calm or generous. Susan is either not wise or rich. Someone is either not calm or funny. Someone is not tall. | Fred is patient. | neutral | (![X]:((~old(X)|brave(X))<=>(~brave(X)&~old(X))))&
((?[X]:((humble(X)|happy(X))))=>((tall(mary)<~>~creative(mary))))&
(![X]:((~brave(X)|kind(X))<=>~funny(X)))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~wise(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>funny(X))))&
(?[X]:(~tall(X))) | patient(fred) | [] | null | 0 |
If lucy is either not creative or not quiet then john is both tall and not strong. Everyone who is either old or quiet is not old or not kind. If someone is both not patient and strong then paul is quiet or funny and vice versa. Everyone who is either not tall or funny is not funny or not tall and vice versa. Everyone who is either old or not wise is either kind or not tall and vice versa. Everyone who is both not happy and old is both not brave and not wise. Everyone who is not brave is either humble or funny. Everyone who is either not wise or patient is both old and patient. Everyone who is both wise and not kind is brave or not funny and vice versa. If alice is either generous or strong then lucy is either not brave or not happy and vice versa. Everyone who is not calm is either not curious or not generous. Everyone who is either not patient or not tall is old and vice versa. Everyone who is either patient or not tall is humble or not humble. Everyone who is generous or strong is either not happy or not creative and vice versa. Everyone who is humble is strong. Someone is both patient and not generous. Alice is either not tall or tall. Someone is creative. Someone is either not patient or brave. Mary is rich. | Lucy is not happy. | contradiction | (((~creative(lucy)<~>~quiet(lucy)))=>((tall(john)&~strong(john))))&
(![X]:((old(X)<~>quiet(X))=>(~old(X)|~kind(X))))&
((?[X]:((~patient(X)&strong(X))))<=>((quiet(paul)|funny(paul))))&
(![X]:((~tall(X)<~>funny(X))<=>(~funny(X)|~tall(X))))&
(![X]:((old(X)<~>~wise(X))<=>(kind(X)<~>~tall(X))))&
(![X]:((~happy(X)&old(X))=>(~brave(X)&~wise(X))))&
(![X]:(~brave(X)=>(humble(X)<~>funny(X))))&
(![X]:((~wise(X)<~>patient(X))=>(old(X)&patient(X))))&
(![X]:((wise(X)&~kind(X))<=>(brave(X)|~funny(X))))&
(((generous(alice)<~>strong(alice)))<=>((~brave(lucy)<~>~happy(lucy))))&
(![X]:(~calm(X)=>(~curious(X)<~>~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>old(X)))&
(![X]:((patient(X)<~>~tall(X))=>(humble(X)|~humble(X))))&
(![X]:((generous(X)|strong(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(humble(X)=>strong(X)))&
(?[X]:((patient(X)&~generous(X))))&
((~tall(alice)<~>tall(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)<~>brave(X))))&
(rich(mary)) | ~happy(lucy) | [
"p3",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1634059887196921173157752
% SZS output start Proof for 1634059887196921173157752
4. ! [X0] : ((~tall(X0) <~> funny(X0)) <=> (~tall(X0) | ~funny(X0))) [input p3]
5. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (kind(X0) <~> ~tall(X0))) [input p4]
6. ! [X0] : ((old(X0) & ~happy(X0)) => (~wise(X0) & ~brave(X0))) [input p5]
9. ! [X0] : ((~kind(X0) & wise(X0)) <=> (~funny(X0) | brave(X0))) [input p8]
21. ~happy(lucy) [input hypothesis]
27. ! [X0] : ((~wise(X0) & ~brave(X0)) | (~old(X0) | happy(X0))) [ennf transformation 6]
28. ! [X0] : ((~wise(X0) & ~brave(X0)) | ~old(X0) | happy(X0)) [flattening 27]
41. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [flattening 41]
43. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0)))) & (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 5]
46. ! [X0] : (((~kind(X0) & wise(X0)) | (funny(X0) & ~brave(X0))) & ((~funny(X0) | brave(X0)) | (kind(X0) | ~wise(X0)))) [nnf transformation 9]
47. ! [X0] : (((~kind(X0) & wise(X0)) | (funny(X0) & ~brave(X0))) & (~funny(X0) | brave(X0) | kind(X0) | ~wise(X0))) [flattening 46]
73. ~tall(X0) | ~funny(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 42]
74. funny(X0) | ~tall(X0) | funny(X0) [cnf transformation 42]
77. ~funny(X0) | tall(X0) | tall(X0) [cnf transformation 42]
83. ~wise(X0) | old(X0) | kind(X0) | tall(X0) [cnf transformation 43]
87. ~wise(X0) | ~old(X0) | happy(X0) [cnf transformation 28]
96. wise(X0) | funny(X0) [cnf transformation 47]
98. ~kind(X0) | funny(X0) [cnf transformation 47]
127. ~happy(lucy) [cnf transformation 21]
129. ~tall(X0) | ~funny(X0) [duplicate literal removal 73]
130. ~tall(X0) | funny(X0) [duplicate literal removal 74]
131. ~funny(X0) | tall(X0) [duplicate literal removal 77]
177. ~funny(X0) [subsumption resolution 129,131]
179. ~kind(X0) [subsumption resolution 98,177]
180. wise(X0) [subsumption resolution 96,177]
182. 10 <=> happy(lucy) [avatar definition]
183. ~happy(lucy) <- (~10) [avatar component clause 182]
215. ~10 [avatar split clause 127,182]
223. ~old(X1) | happy(X1) [resolution 87,180]
322. old(X1) | kind(X1) | tall(X1) [resolution 83,180]
325. old(X1) | tall(X1) [subsumption resolution 322,179]
413. happy(X3) | tall(X3) [resolution 325,223]
424. tall(lucy) <- (~10) [resolution 413,183]
430. funny(lucy) <- (~10) [resolution 424,130]
432. $false <- (~10) [subsumption resolution 430,177]
433. 10 [avatar contradiction clause 432]
434. $false [avatar sat refutation 215,433]
% SZS output end Proof for 1634059887196921173157752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not old is both calm and brave.
Everyone who is happy or not kind is not rich and vice versa.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
If someone is brave then paul is not patient and vice versa.
If someone is funny or not quiet then someone is kind or brave.
Everyone who is not funny is both not funny and calm.
If mary is not brave or not patient then mary is either kind or not creative and vice versa.
John is not rich.
Susan is either funny or quiet.
Fred is either not strong or calm. | John is not kind. | entailment | (![X]:((tall(X)|~old(X))=>(calm(X)&brave(X))))&
(![X]:((happy(X)|~kind(X))<=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:(~funny(X)=>(~funny(X)&calm(X))))&
(((~brave(mary)|~patient(mary)))<=>((kind(mary)<~>~creative(mary))))&
(~rich(john))&
((funny(susan)<~>quiet(susan)))&
((~strong(fred)<~>calm(fred))) | ~kind(john) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3891102143708434278709465
% SZS output start Proof for 3891102143708434278709465
1. ! [X0] : ((~old(X0) | tall(X0)) => (brave(X0) & calm(X0))) [input p0]
2. ! [X0] : ((~kind(X0) | happy(X0)) <=> ~rich(X0)) [input p1]
3. ! [X0] : ((~old(X0) & happy(X0)) <=> ~calm(X0)) [input p2]
4. ! [X0] : (happy(X0) <=> (brave(X0) & ~creative(X0))) [input p3]
6. ! [X0] : ((~calm(X0) | creative(X0)) <=> (brave(X0) | funny(X0))) [input p5]
15. ~rich(john) [input p14]
18. kind(john) [input hypothesis]
21. ! [X0] : ((brave(X0) & calm(X0)) | (old(X0) & ~tall(X0))) [ennf transformation 1]
26. ! [X0] : (((~kind(X0) | happy(X0)) | rich(X0)) & (~rich(X0) | (kind(X0) & ~happy(X0)))) [nnf transformation 2]
27. ! [X0] : ((~kind(X0) | happy(X0) | rich(X0)) & (~rich(X0) | (kind(X0) & ~happy(X0)))) [flattening 26]
28. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 3]
29. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | old(X0) | ~happy(X0))) [flattening 28]
30. ! [X0] : ((happy(X0) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [nnf transformation 4]
31. ! [X0] : ((happy(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [flattening 30]
36. ! [X0] : (((~calm(X0) | creative(X0)) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 6]
37. ! [X0] : ((~calm(X0) | creative(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | (calm(X0) & ~creative(X0)))) [flattening 36]
54. calm(X0) | old(X0) [cnf transformation 21]
59. ~kind(X0) | happy(X0) | rich(X0) [cnf transformation 27]
62. ~old(X0) | calm(X0) [cnf transformation 29]
63. ~creative(X0) | ~happy(X0) [cnf transformation 31]
64. ~happy(X0) | brave(X0) [cnf transformation 31]
73. ~calm(X0) | creative(X0) | ~brave(X0) [cnf transformation 37]
96. ~rich(john) [cnf transformation 15]
101. kind(john) [cnf transformation 18]
104. calm(X0) [subsumption resolution 62,54]
111. 2 <=> kind(john) [avatar definition]
113. kind(john) <- (2) [avatar component clause 111]
121. ~brave(X0) | creative(X0) [subsumption resolution 73,104]
201. 2 [avatar split clause 101,111]
219. happy(john) | rich(john) <- (2) [resolution 59,113]
222. happy(john) <- (2) [subsumption resolution 219,96]
233. brave(john) <- (2) [resolution 222,64]
250. creative(john) <- (2) [resolution 233,121]
252. ~happy(john) <- (2) [resolution 250,63]
253. $false <- (2) [subsumption resolution 252,222]
254. ~2 [avatar contradiction clause 253]
255. $false [avatar sat refutation 201,254]
% SZS output end Proof for 3891102143708434278709465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not brave or old. Everyone who is either strong or not brave is both not patient and kind. If someone is both creative and wise then paul is either not humble or generous. Everyone who is either brave or humble is creative. If alice is both creative and calm then fred is old. If susan is either not funny or not generous then fred is kind and vice versa. If someone is either not curious or creative then someone is quiet and vice versa. Everyone who is not brave or not calm is both brave and not brave. If someone is not old then someone is either not wise or happy. If someone is both humble and not funny then alice is both not humble and tall and vice versa. If someone is either not brave or not patient then fred is either not brave or quiet and vice versa. Everyone who is either not curious or not kind is either not rich or creative. Everyone who is both not generous and kind is funny or creative and vice versa. If someone is either not funny or funny then someone is either quiet or not brave and vice versa. Everyone who is not generous or funny is not creative. Everyone who is both strong and not old is not happy or wise. Someone is either not kind or patient. Paul is not happy. Someone is either creative or not rich. Susan is either kind or old. Someone is humble. | Fred is brave. | entailment | (![X]:(~curious(X)=>(~brave(X)|old(X))))&
(![X]:((strong(X)<~>~brave(X))=>(~patient(X)&kind(X))))&
((?[X]:((creative(X)&wise(X))))=>((~humble(paul)<~>generous(paul))))&
(![X]:((brave(X)<~>humble(X))=>creative(X)))&
(((creative(alice)&calm(alice)))=>(old(fred)))&
(((~funny(susan)<~>~generous(susan)))<=>(kind(fred)))&
((?[X]:((~curious(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~calm(X))=>(brave(X)&~brave(X))))&
((?[X]:(~old(X)))=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((humble(X)&~funny(X))))<=>((~humble(alice)&tall(alice))))&
((?[X]:((~brave(X)<~>~patient(X))))<=>((~brave(fred)<~>quiet(fred))))&
(![X]:((~curious(X)<~>~kind(X))=>(~rich(X)<~>creative(X))))&
(![X]:((~generous(X)&kind(X))<=>(funny(X)|creative(X))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
(![X]:((~generous(X)|funny(X))=>~creative(X)))&
(![X]:((strong(X)&~old(X))=>(~happy(X)|wise(X))))&
(?[X]:((~kind(X)<~>patient(X))))&
(~happy(paul))&
(?[X]:((creative(X)<~>~rich(X))))&
((kind(susan)<~>old(susan)))&
(?[X]:(humble(X))) | brave(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8301895365825784039361033
% SZS output start Proof for 8301895365825784039361033
8. ! [X0] : ((~calm(X0) | ~brave(X0)) => (~brave(X0) & brave(X0))) [input p7]
22. ~brave(fred) [input hypothesis]
33. ! [X0] : ((~brave(X0) & brave(X0)) | (calm(X0) & brave(X0))) [ennf transformation 8]
96. brave(X0) | brave(X0) [cnf transformation 33]
142. ~brave(fred) [cnf transformation 22]
147. brave(X0) [duplicate literal removal 96]
305. $false [subsumption resolution 142,147]
% SZS output end Proof for 8301895365825784039361033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not patient is either not rich or calm and vice versa.
Everyone who is not calm is brave.
If someone is not brave or not creative then mary is quiet.
Everyone who is kind or not wise is either not funny or old.
Everyone who is not kind or quiet is not humble or wise and vice versa.
Everyone who is either not humble or not kind is either not tall or wise and vice versa.
Everyone who is not happy or curious is calm or not quiet and vice versa.
Everyone who is not calm or not generous is either not humble or not kind and vice versa.
If john is not rich then susan is both funny and not strong and vice versa.
If susan is calm or curious then someone is both strong and old.
Everyone who is not generous or not patient is not creative or rich and vice versa.
If fred is either curious or calm then lucy is either not brave or not strong.
Everyone who is strong or calm is generous or tall.
Everyone who is both happy and not calm is generous or strong and vice versa.
If someone is either kind or not strong then lucy is not strong and vice versa.
Everyone who is humble or generous is not tall.
John is creative or not creative.
Lucy is either not strong or tall.
Fred is either curious or not generous.
Mary is both not patient and not humble.
Someone is either not creative or not funny.
Lucy is not wise.
Mary is not strong or strong. | Lucy is not old. | neutral | (![X]:((~kind(X)<~>~patient(X))<=>(~rich(X)<~>calm(X))))&
(![X]:(~calm(X)=>brave(X)))&
((?[X]:((~brave(X)|~creative(X))))=>(quiet(mary)))&
(![X]:((kind(X)|~wise(X))=>(~funny(X)<~>old(X))))&
(![X]:((~kind(X)|quiet(X))<=>(~humble(X)|wise(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~happy(X)|curious(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~humble(X)<~>~kind(X))))&
((~rich(john))<=>((funny(susan)&~strong(susan))))&
(((calm(susan)|curious(susan)))=>(?[X]:((strong(X)&old(X)))))&
(![X]:((~generous(X)|~patient(X))<=>(~creative(X)|rich(X))))&
(((curious(fred)<~>calm(fred)))=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:((strong(X)|calm(X))=>(generous(X)|tall(X))))&
(![X]:((happy(X)&~calm(X))<=>(generous(X)|strong(X))))&
((?[X]:((kind(X)<~>~strong(X))))<=>(~strong(lucy)))&
(![X]:((humble(X)|generous(X))=>~tall(X)))&
((creative(john)|~creative(john)))&
((~strong(lucy)<~>tall(lucy)))&
((curious(fred)<~>~generous(fred)))&
((~patient(mary)&~humble(mary)))&
(?[X]:((~creative(X)<~>~funny(X))))&
(~wise(lucy))&
((~strong(mary)|strong(mary))) | ~old(lucy) | [] | null | 0 |
Everyone who is either not generous or not rich is funny.
Everyone who is either strong or not tall is old or strong and vice versa.
Everyone who is either not generous or not calm is not curious or not quiet.
If mary is not tall or creative then susan is both funny and not old.
Everyone who is not wise or kind is curious or rich.
Everyone who is tall is both not rich and not quiet and vice versa.
If someone is both not wise and not strong then someone is tall.
Everyone who is kind or wise is both generous and humble.
Everyone who is generous or not curious is quiet and vice versa.
If someone is either not creative or old then paul is wise or not humble and vice versa.
If susan is both not curious and not old then alice is both not quiet and not creative.
Everyone who is quiet or not rich is quiet or curious and vice versa.
Everyone who is patient or quiet is both not humble and calm and vice versa.
If john is either curious or not funny then john is not rich or old and vice versa.
If fred is both not patient and calm then lucy is either quiet or not humble.
Everyone who is happy or old is both not wise and not patient and vice versa.
Alice is not happy or tall.
Someone is either not humble or happy.
Mary is either not patient or strong.
Lucy is either not wise or not brave.
John is not curious.
Someone is either not tall or not patient. | Mary is funny. | neutral | (![X]:((~generous(X)<~>~rich(X))=>funny(X)))&
(![X]:((strong(X)<~>~tall(X))<=>(old(X)|strong(X))))&
(![X]:((~generous(X)<~>~calm(X))=>(~curious(X)|~quiet(X))))&
(((~tall(mary)|creative(mary)))=>((funny(susan)&~old(susan))))&
(![X]:((~wise(X)|kind(X))=>(curious(X)|rich(X))))&
(![X]:(tall(X)<=>(~rich(X)&~quiet(X))))&
((?[X]:((~wise(X)&~strong(X))))=>(?[X]:(tall(X))))&
(![X]:((kind(X)|wise(X))=>(generous(X)&humble(X))))&
(![X]:((generous(X)|~curious(X))<=>quiet(X)))&
((?[X]:((~creative(X)<~>old(X))))<=>((wise(paul)|~humble(paul))))&
(((~curious(susan)&~old(susan)))=>((~quiet(alice)&~creative(alice))))&
(![X]:((quiet(X)|~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:((patient(X)|quiet(X))<=>(~humble(X)&calm(X))))&
(((curious(john)<~>~funny(john)))<=>((~rich(john)|old(john))))&
(((~patient(fred)&calm(fred)))=>((quiet(lucy)<~>~humble(lucy))))&
(![X]:((happy(X)|old(X))<=>(~wise(X)&~patient(X))))&
((~happy(alice)|tall(alice)))&
(?[X]:((~humble(X)<~>happy(X))))&
((~patient(mary)<~>strong(mary)))&
((~wise(lucy)<~>~brave(lucy)))&
(~curious(john))&
(?[X]:((~tall(X)<~>~patient(X)))) | funny(mary) | [] | null | 0 |
Everyone who is both old and rich is not kind. If john is not curious then mary is not tall or wise and vice versa. If someone is not brave then paul is either not happy or not funny. Everyone who is both not calm and creative is either calm or not funny. If someone is both wise and tall then john is both kind and old. Everyone who is either calm or not wise is either quiet or funny and vice versa. Everyone who is happy or humble is not old or not calm. Everyone who is either not generous or not wise is calm and vice versa. Everyone who is not happy or not old is either rich or not rich and vice versa. If john is not generous then someone is both humble and generous and vice versa. If alice is creative or not rich then paul is either wise or happy. If someone is old then someone is patient. If someone is strong then susan is both quiet and not happy and vice versa. If someone is both not funny and not calm then someone is both not curious and kind and vice versa. If john is either not quiet or not humble then someone is either not kind or humble and vice versa. If someone is both not quiet and generous then someone is both not wise and not calm and vice versa. Susan is rich. Someone is both strong and not happy. Someone is either not generous or not quiet. Lucy is both not patient and quiet. Mary is humble or not brave. Someone is both not patient and creative. Someone is not curious. Susan is both not curious and humble. | Lucy is patient. | contradiction | (![X]:((old(X)&rich(X))=>~kind(X)))&
((~curious(john))<=>((~tall(mary)|wise(mary))))&
((?[X]:(~brave(X)))=>((~happy(paul)<~>~funny(paul))))&
(![X]:((~calm(X)&creative(X))=>(calm(X)<~>~funny(X))))&
((?[X]:((wise(X)&tall(X))))=>((kind(john)&old(john))))&
(![X]:((calm(X)<~>~wise(X))<=>(quiet(X)<~>funny(X))))&
(![X]:((happy(X)|humble(X))=>(~old(X)|~calm(X))))&
(![X]:((~generous(X)<~>~wise(X))<=>calm(X)))&
(![X]:((~happy(X)|~old(X))<=>(rich(X)<~>~rich(X))))&
((~generous(john))<=>(?[X]:((humble(X)&generous(X)))))&
(((creative(alice)|~rich(alice)))=>((wise(paul)<~>happy(paul))))&
((?[X]:(old(X)))=>(?[X]:(patient(X))))&
((?[X]:(strong(X)))<=>((quiet(susan)&~happy(susan))))&
((?[X]:((~funny(X)&~calm(X))))<=>(?[X]:((~curious(X)&kind(X)))))&
(((~quiet(john)<~>~humble(john)))<=>(?[X]:((~kind(X)<~>humble(X)))))&
((?[X]:((~quiet(X)&generous(X))))<=>(?[X]:((~wise(X)&~calm(X)))))&
(rich(susan))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((~generous(X)<~>~quiet(X))))&
((~patient(lucy)&quiet(lucy)))&
((humble(mary)|~brave(mary)))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:(~curious(X)))&
((~curious(susan)&humble(susan))) | patient(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4812912170142714363287453
% SZS output start Proof for 4812912170142714363287453
20. quiet(lucy) & ~patient(lucy) [input p19]
25. patient(lucy) [input hypothesis]
145. ~patient(lucy) [cnf transformation 20]
153. patient(lucy) [cnf transformation 25]
360. $false [subsumption resolution 153,145]
% SZS output end Proof for 4812912170142714363287453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not tall is old and vice versa.
If someone is quiet or not creative then alice is not generous or old.
If mary is either not patient or not calm then fred is both not creative and calm.
If alice is rich or wise then someone is both rich and creative and vice versa.
Everyone who is not calm is either tall or rich and vice versa.
If fred is both brave and not calm then mary is tall.
If mary is either curious or happy then someone is both not patient and not creative and vice versa.
Everyone who is tall or not quiet is both quiet and not funny and vice versa.
If lucy is happy then someone is not old and vice versa.
Everyone who is both not brave and not rich is both not generous and not tall.
Everyone who is either not brave or not generous is either not tall or not quiet.
If someone is not old then someone is not brave.
Everyone who is calm or old is either brave or humble.
Everyone who is both not funny and not rich is not curious or not patient.
If someone is strong then someone is either patient or not strong.
If mary is both not happy and not old then someone is humble.
John is creative.
Fred is either old or quiet.
Someone is not patient.
Someone is both not old and generous.
Susan is either not patient or not curious.
Paul is both not strong and not happy.
Paul is not humble. | Paul is old. | contradiction | (![X]:((~brave(X)&~tall(X))<=>old(X)))&
((?[X]:((quiet(X)|~creative(X))))=>((~generous(alice)|old(alice))))&
(((~patient(mary)<~>~calm(mary)))=>((~creative(fred)&calm(fred))))&
(((rich(alice)|wise(alice)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~calm(X)<=>(tall(X)<~>rich(X))))&
(((brave(fred)&~calm(fred)))=>(tall(mary)))&
(((curious(mary)<~>happy(mary)))<=>(?[X]:((~patient(X)&~creative(X)))))&
(![X]:((tall(X)|~quiet(X))<=>(quiet(X)&~funny(X))))&
((happy(lucy))<=>(?[X]:(~old(X))))&
(![X]:((~brave(X)&~rich(X))=>(~generous(X)&~tall(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:(~brave(X))))&
(![X]:((calm(X)|old(X))=>(brave(X)<~>humble(X))))&
(![X]:((~funny(X)&~rich(X))=>(~curious(X)|~patient(X))))&
((?[X]:(strong(X)))=>(?[X]:((patient(X)<~>~strong(X)))))&
(((~happy(mary)&~old(mary)))=>(?[X]:(humble(X))))&
(creative(john))&
((old(fred)<~>quiet(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((~old(X)&generous(X))))&
((~patient(susan)<~>~curious(susan)))&
((~strong(paul)&~happy(paul)))&
(~humble(paul)) | old(paul) | [
"p0",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7830803521853834734897559
% SZS output start Proof for 7830803521853834734897559
1. ! [X0] : ((~tall(X0) & ~brave(X0)) <=> old(X0)) [input p0]
13. ! [X0] : ((old(X0) | calm(X0)) => (brave(X0) <~> humble(X0))) [input p12]
23. ~humble(paul) [input p22]
24. old(paul) [input hypothesis]
36. ! [X0] : ((brave(X0) <~> humble(X0)) | (~old(X0) & ~calm(X0))) [ennf transformation 13]
42. ! [X0] : (((~tall(X0) & ~brave(X0)) | ~old(X0)) & (old(X0) | (tall(X0) | brave(X0)))) [nnf transformation 1]
43. ! [X0] : (((~tall(X0) & ~brave(X0)) | ~old(X0)) & (old(X0) | tall(X0) | brave(X0))) [flattening 42]
65. ! [X0] : (((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | (~old(X0) & ~calm(X0))) [nnf transformation 36]
79. ~old(X0) | ~brave(X0) [cnf transformation 43]
118. humble(X0) | brave(X0) | ~old(X0) [cnf transformation 65]
135. ~humble(paul) [cnf transformation 23]
136. old(paul) [cnf transformation 24]
253. ~old(X0) | humble(X0) [subsumption resolution 118,79]
291. humble(paul) [resolution 253,136]
292. $false [subsumption resolution 291,135]
% SZS output end Proof for 7830803521853834734897559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or creative is both not calm and happy.
Everyone who is either wise or not quiet is both tall and brave.
Everyone who is either funny or brave is both not generous and not kind and vice versa.
Everyone who is not old or curious is either not tall or generous and vice versa.
Everyone who is happy or kind is not brave or kind and vice versa.
Everyone who is both not creative and quiet is not brave and vice versa.
If someone is not rich then someone is not quiet or brave and vice versa.
If lucy is not quiet then john is not creative.
Everyone who is either not kind or humble is not tall or not rich.
Everyone who is either happy or quiet is not curious.
Everyone who is not kind or quiet is generous or not calm and vice versa.
Everyone who is either rich or not strong is calm or not quiet and vice versa.
Everyone who is happy or not creative is not tall.
If someone is either happy or tall then mary is not rich and vice versa.
Everyone who is not generous or not tall is either not calm or not rich.
If someone is not calm or not patient then susan is both not kind and patient.
Someone is not patient or generous.
Mary is both wise and patient.
John is either not happy or patient.
Someone is both old and not kind.
Alice is both not humble and old.
Someone is either funny or old.
John is either old or not humble.
Someone is either happy or not quiet. | Mary is brave. | entailment | (![X]:((brave(X)<~>creative(X))=>(~calm(X)&happy(X))))&
(![X]:((wise(X)<~>~quiet(X))=>(tall(X)&brave(X))))&
(![X]:((funny(X)<~>brave(X))<=>(~generous(X)&~kind(X))))&
(![X]:((~old(X)|curious(X))<=>(~tall(X)<~>generous(X))))&
(![X]:((happy(X)|kind(X))<=>(~brave(X)|kind(X))))&
(![X]:((~creative(X)&quiet(X))<=>~brave(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~quiet(X)|brave(X)))))&
((~quiet(lucy))=>(~creative(john)))&
(![X]:((~kind(X)<~>humble(X))=>(~tall(X)|~rich(X))))&
(![X]:((happy(X)<~>quiet(X))=>~curious(X)))&
(![X]:((~kind(X)|quiet(X))<=>(generous(X)|~calm(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(calm(X)|~quiet(X))))&
(![X]:((happy(X)|~creative(X))=>~tall(X)))&
((?[X]:((happy(X)<~>tall(X))))<=>(~rich(mary)))&
(![X]:((~generous(X)|~tall(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((~calm(X)|~patient(X))))=>((~kind(susan)&patient(susan))))&
(?[X]:((~patient(X)|generous(X))))&
((wise(mary)&patient(mary)))&
((~happy(john)<~>patient(john)))&
(?[X]:((old(X)&~kind(X))))&
((~humble(alice)&old(alice)))&
(?[X]:((funny(X)<~>old(X))))&
((old(john)<~>~humble(john)))&
(?[X]:((happy(X)<~>~quiet(X)))) | brave(mary) | [
"p1",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1393286328259679766932763
% SZS output start Proof for 1393286328259679766932763
2. ! [X0] : ((wise(X0) <~> ~quiet(X0)) => (brave(X0) & tall(X0))) [input p1]
6. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> ~brave(X0)) [input p5]
18. patient(mary) & wise(mary) [input p17]
25. ~brave(mary) [input hypothesis]
28. ! [X0] : ((brave(X0) & tall(X0)) | (wise(X0) <=> ~quiet(X0))) [ennf transformation 2]
37. ! [X0] : ((brave(X0) & tall(X0)) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 28]
44. ! [X0] : (((quiet(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | (~quiet(X0) | creative(X0)))) [nnf transformation 6]
45. ! [X0] : (((quiet(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | ~quiet(X0) | creative(X0))) [flattening 44]
80. ~quiet(X0) | brave(X0) | ~wise(X0) [cnf transformation 37]
100. quiet(X0) | brave(X0) [cnf transformation 45]
134. wise(mary) [cnf transformation 18]
148. ~brave(mary) [cnf transformation 25]
302. brave(X1) | ~wise(X1) | brave(X1) [resolution 80,100]
303. ~wise(X1) | brave(X1) [duplicate literal removal 302]
327. brave(mary) [resolution 303,134]
328. $false [subsumption resolution 327,148]
% SZS output end Proof for 1393286328259679766932763
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both 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.
If alice is both not rich and quiet then 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.
Alice is both not funny and not calm.
John is either not wise or patient.
Lucy is both not rich and not humble.
Alice is brave. | Fred is not quiet. | neutral | (![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))))&
((~funny(alice)&~calm(alice)))&
((~wise(john)<~>patient(john)))&
((~rich(lucy)&~humble(lucy)))&
(brave(alice)) | ~quiet(fred) | [] | null | 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. | Fred 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(fred) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6263947437756227906315121
% SZS output start Proof for 6263947437756227906315121
3. ! [X0] : ((generous(X0) & ~calm(X0)) <=> ~funny(X0)) [input p2]
5. ! [X0] : (~calm(X0) => (~generous(X0) & ~calm(X0))) [input p4]
25. ~funny(fred) [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(fred) [cnf transformation 25]
295. generous(fred) [resolution 88,140]
297. calm(fred) [resolution 94,295]
299. funny(fred) [resolution 297,87]
300. $false [subsumption resolution 299,140]
% SZS output end Proof for 6263947437756227906315121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or brave then someone is both not wise and humble.
Everyone who is both not funny and strong is wise or quiet and vice versa.
If paul is brave or not tall then someone is brave or happy.
Everyone who is not curious is patient and vice versa.
Everyone who is not generous is curious and vice versa.
Everyone who is not strong or old is both funny and not tall.
Everyone who is not creative or not brave is both tall and curious and vice versa.
Everyone who is both funny and not patient is either rich or not calm and vice versa.
If someone is not generous or funny then someone is funny and vice versa.
Everyone who is either not old or not calm is not strong or strong and vice versa.
Everyone who is both curious and tall is both not patient and creative.
Everyone who is either not quiet or generous is rich or creative and vice versa.
Everyone who is either not patient or not rich is both quiet and calm.
Everyone who is either not brave or not wise is either not funny or curious.
Everyone who is funny is either not brave or wise and vice versa.
Everyone who is both patient and strong is strong and vice versa.
Lucy is not patient or not tall.
Fred is either humble or strong.
Susan is wise or quiet.
Lucy is either curious or not rich.
Fred is both not happy and not rich. | Paul is not brave. | contradiction | ((?[X]:((~strong(X)<~>brave(X))))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:((~funny(X)&strong(X))<=>(wise(X)|quiet(X))))&
(((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((~patient(lucy)|~tall(lucy)))&
((humble(fred)<~>strong(fred)))&
((wise(susan)|quiet(susan)))&
((curious(lucy)<~>~rich(lucy)))&
((~happy(fred)&~rich(fred))) | ~brave(paul) | [
"p3",
"p5",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5836053563871471841491973
% SZS output start Proof for 5836053563871471841491973
4. ! [X0] : (~curious(X0) <=> patient(X0)) [input p3]
6. ! [X0] : ((old(X0) | ~strong(X0)) => (~tall(X0) & funny(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & tall(X0))) [input p6]
16. ! [X0] : ((strong(X0) & patient(X0)) <=> strong(X0)) [input p15]
22. ~brave(paul) [input hypothesis]
27. ! [X0] : ((~tall(X0) & funny(X0)) | (~old(X0) & strong(X0))) [ennf transformation 6]
40. ! [X0] : ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))) [nnf transformation 4]
42. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [flattening 42]
58. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | (~strong(X0) | ~patient(X0)))) [nnf transformation 16]
59. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | ~strong(X0) | ~patient(X0))) [flattening 58]
74. ~patient(X0) | ~curious(X0) [cnf transformation 40]
79. ~tall(X0) | strong(X0) [cnf transformation 27]
82. tall(X0) | brave(X0) [cnf transformation 43]
84. curious(X0) | brave(X0) [cnf transformation 43]
122. ~strong(X0) | patient(X0) [cnf transformation 59]
132. ~brave(paul) [cnf transformation 22]
152. 5 <=> tall(paul) [avatar definition]
153. ~tall(paul) <- (~5) [avatar component clause 152]
154. tall(paul) <- (5) [avatar component clause 152]
165. 8 <=> brave(paul) [avatar definition]
167. ~brave(paul) <- (~8) [avatar component clause 165]
234. ~8 [avatar split clause 132,165]
243. strong(paul) <- (5) [resolution 79,154]
249. patient(paul) <- (5) [resolution 122,243]
252. ~curious(paul) <- (5) [resolution 249,74]
256. brave(paul) <- (5) [resolution 252,84]
257. $false <- (5, ~8) [subsumption resolution 256,167]
258. ~5 | 8 [avatar contradiction clause 257]
259. brave(paul) <- (~5) [resolution 153,82]
260. $false <- (~5, ~8) [subsumption resolution 259,167]
261. 5 | 8 [avatar contradiction clause 260]
262. $false [avatar sat refutation 234,258,261]
% SZS output end Proof for 5836053563871471841491973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is creative or not kind and vice versa.
Everyone who is creative is either not patient or generous and vice versa.
If someone is patient then someone is rich or patient.
If someone is not strong or not old then lucy is both humble and not rich and vice versa.
If susan is either not creative or calm then someone is both not funny and funny.
Everyone who is either not calm or not funny is not calm and vice versa.
Everyone who is either brave or not curious is either calm or kind.
Everyone who is either not old or rich is curious or not tall.
If mary is not brave or not calm then mary is both curious and rich.
Everyone who is funny is tall or not tall.
Everyone who is both brave and not wise is not humble or tall and vice versa.
If someone is both strong and not generous then someone is wise.
Everyone who is not quiet or happy is both rich and not tall.
Everyone who is both not generous and not calm is not strong or wise.
Everyone who is both not quiet and old is humble or not wise.
Everyone who is either tall or not patient is tall or generous.
John is brave or wise.
Someone is not humble.
Paul is either not kind or not patient.
Someone is not humble or happy.
Alice is not old or not wise.
Someone is not old or not wise.
Lucy is either not rich or not calm. | Paul is not wise. | entailment | (![X]:(kind(X)<=>(creative(X)|~kind(X))))&
(![X]:(creative(X)<=>(~patient(X)<~>generous(X))))&
((?[X]:(patient(X)))=>(?[X]:((rich(X)|patient(X)))))&
((?[X]:((~strong(X)|~old(X))))<=>((humble(lucy)&~rich(lucy))))&
(((~creative(susan)<~>calm(susan)))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:((~calm(X)<~>~funny(X))<=>~calm(X)))&
(![X]:((brave(X)<~>~curious(X))=>(calm(X)<~>kind(X))))&
(![X]:((~old(X)<~>rich(X))=>(curious(X)|~tall(X))))&
(((~brave(mary)|~calm(mary)))=>((curious(mary)&rich(mary))))&
(![X]:(funny(X)=>(tall(X)|~tall(X))))&
(![X]:((brave(X)&~wise(X))<=>(~humble(X)|tall(X))))&
((?[X]:((strong(X)&~generous(X))))=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)|happy(X))=>(rich(X)&~tall(X))))&
(![X]:((~generous(X)&~calm(X))=>(~strong(X)|wise(X))))&
(![X]:((~quiet(X)&old(X))=>(humble(X)|~wise(X))))&
(![X]:((tall(X)<~>~patient(X))=>(tall(X)|generous(X))))&
((brave(john)|wise(john)))&
(?[X]:(~humble(X)))&
((~kind(paul)<~>~patient(paul)))&
(?[X]:((~humble(X)|happy(X))))&
((~old(alice)|~wise(alice)))&
(?[X]:((~old(X)|~wise(X))))&
((~rich(lucy)<~>~calm(lucy))) | ~wise(paul) | [
"p0",
"p1",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5889959240089308143135355
% SZS output start Proof for 5889959240089308143135355
1. ! [X0] : (kind(X0) <=> (~kind(X0) | creative(X0))) [input p0]
2. ! [X0] : (creative(X0) <=> (~patient(X0) <~> generous(X0))) [input p1]
11. ! [X0] : ((~wise(X0) & brave(X0)) <=> (tall(X0) | ~humble(X0))) [input p10]
16. ! [X0] : ((tall(X0) <~> ~patient(X0)) => (generous(X0) | tall(X0))) [input p15]
19. ~kind(paul) <~> ~patient(paul) [input p18]
24. wise(paul) [input hypothesis]
41. ! [X0] : ((generous(X0) | tall(X0)) | (tall(X0) <=> ~patient(X0))) [ennf transformation 16]
42. ! [X0] : (generous(X0) | tall(X0) | (tall(X0) <=> ~patient(X0))) [flattening 41]
43. ! [X0] : ((kind(X0) | (kind(X0) & ~creative(X0))) & ((~kind(X0) | creative(X0)) | ~kind(X0))) [nnf transformation 1]
44. ! [X0] : ((kind(X0) | (kind(X0) & ~creative(X0))) & (~kind(X0) | creative(X0) | ~kind(X0))) [flattening 43]
45. ! [X0] : ((creative(X0) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) & (((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ~creative(X0))) [nnf transformation 2]
60. ! [X0] : (((~wise(X0) & brave(X0)) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | (wise(X0) | ~brave(X0)))) [nnf transformation 11]
61. ! [X0] : (((~wise(X0) & brave(X0)) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | wise(X0) | ~brave(X0))) [flattening 60]
65. ! [X0] : (generous(X0) | tall(X0) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) [nnf transformation 42]
68. (patient(paul) | kind(paul)) & (~patient(paul) | ~kind(paul)) [nnf transformation 19]
74. ~kind(X0) | creative(X0) | ~kind(X0) [cnf transformation 44]
76. kind(X0) | kind(X0) [cnf transformation 44]
77. generous(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 45]
78. ~generous(X0) | patient(X0) | ~creative(X0) [cnf transformation 45]
110. ~wise(X0) | ~tall(X0) [cnf transformation 61]
116. generous(X0) | tall(X0) | tall(X0) | patient(X0) [cnf transformation 65]
119. ~patient(paul) | ~kind(paul) [cnf transformation 68]
126. wise(paul) [cnf transformation 24]
127. generous(X0) | tall(X0) | patient(X0) [duplicate literal removal 116]
130. ~kind(X0) | creative(X0) [duplicate literal removal 74]
131. kind(X0) [duplicate literal removal 76]
132. creative(X0) [subsumption resolution 130,131]
133. ~generous(X0) | patient(X0) [subsumption resolution 78,132]
134. ~patient(X0) | generous(X0) [subsumption resolution 77,132]
217. tall(X0) | generous(X0) [subsumption resolution 127,134]
227. ~patient(paul) [subsumption resolution 119,131]
262. ~tall(paul) [resolution 110,126]
266. generous(paul) [resolution 217,262]
274. patient(paul) [resolution 266,133]
275. $false [subsumption resolution 274,227]
% SZS output end Proof for 5889959240089308143135355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not funny or tall and vice versa. Everyone who is creative or kind is not kind or not rich. Everyone who is either curious or kind is either not happy or calm and vice versa. If someone is both not calm and curious then fred is both not tall and calm and vice versa. If fred is strong then someone is either humble or not happy. If lucy is either generous or not rich then someone is both not happy and brave. If someone is not humble then someone is humble and vice versa. If fred is not curious or strong then someone is both not happy and not funny and vice versa. Everyone who is both tall and not kind is not funny and vice versa. If lucy is both rich and happy then mary is both rich and quiet and vice versa. Everyone who is patient or kind is both rich and quiet and vice versa. If someone is either quiet or not patient then susan is both calm and patient. If paul is not creative then someone is not quiet or curious. Everyone who is either tall or not kind is rich and vice versa. If alice is old then someone is wise or old. If someone is not funny or rich then susan is rich. Alice is happy. Lucy is happy. John is strong. Someone is creative or not calm. Someone is either quiet or not old. | Susan is not calm. | contradiction | (![X]:(old(X)<=>(~funny(X)|tall(X))))&
(![X]:((creative(X)|kind(X))=>(~kind(X)|~rich(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((~calm(X)&curious(X))))<=>((~tall(fred)&calm(fred))))&
((strong(fred))=>(?[X]:((humble(X)<~>~happy(X)))))&
(((generous(lucy)<~>~rich(lucy)))=>(?[X]:((~happy(X)&brave(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(humble(X))))&
(((~curious(fred)|strong(fred)))<=>(?[X]:((~happy(X)&~funny(X)))))&
(![X]:((tall(X)&~kind(X))<=>~funny(X)))&
(((rich(lucy)&happy(lucy)))<=>((rich(mary)&quiet(mary))))&
(![X]:((patient(X)|kind(X))<=>(rich(X)&quiet(X))))&
((?[X]:((quiet(X)<~>~patient(X))))=>((calm(susan)&patient(susan))))&
((~creative(paul))=>(?[X]:((~quiet(X)|curious(X)))))&
(![X]:((tall(X)<~>~kind(X))<=>rich(X)))&
((old(alice))=>(?[X]:((wise(X)|old(X)))))&
((?[X]:((~funny(X)|rich(X))))=>(rich(susan)))&
(happy(alice))&
(happy(lucy))&
(strong(john))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((quiet(X)<~>~old(X)))) | ~calm(susan) | [
"p1",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 667342532626885389481766
% SZS output start Proof for 667342532626885389481766
2. ! [X0] : ((kind(X0) | creative(X0)) => (~rich(X0) | ~kind(X0))) [input p1]
9. ! [X0] : ((~kind(X0) & tall(X0)) <=> ~funny(X0)) [input p8]
11. ! [X0] : ((kind(X0) | patient(X0)) <=> (quiet(X0) & rich(X0))) [input p10]
12. ? [X0] : (quiet(X0) <~> ~patient(X0)) => (patient(susan) & calm(susan)) [input p11]
14. ! [X0] : ((tall(X0) <~> ~kind(X0)) <=> rich(X0)) [input p13]
16. ? [X0] : (rich(X0) | ~funny(X0)) => rich(susan) [input p15]
22. ~calm(susan) [input hypothesis]
26. ! [X0] : ((~rich(X0) | ~kind(X0)) | (~kind(X0) & ~creative(X0))) [ennf transformation 2]
27. ! [X0] : (~rich(X0) | ~kind(X0) | (~kind(X0) & ~creative(X0))) [flattening 26]
30. (patient(susan) & calm(susan)) | ! [X0] : (quiet(X0) <=> ~patient(X0)) [ennf transformation 12]
32. rich(susan) | ! [X0] : (~rich(X0) & funny(X0)) [ennf transformation 16]
57. ! [X0] : (((~kind(X0) & tall(X0)) | funny(X0)) & (~funny(X0) | (kind(X0) | ~tall(X0)))) [nnf transformation 9]
58. ! [X0] : (((~kind(X0) & tall(X0)) | funny(X0)) & (~funny(X0) | kind(X0) | ~tall(X0))) [flattening 57]
61. ! [X0] : (((kind(X0) | patient(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (~kind(X0) & ~patient(X0)))) [nnf transformation 11]
62. ! [X0] : ((kind(X0) | patient(X0) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | (~kind(X0) & ~patient(X0)))) [flattening 61]
63. (patient(susan) & calm(susan)) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))) [nnf transformation 30]
66. ! [X0] : ((((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | ~rich(X0)) & (rich(X0) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0))))) [nnf transformation 14]
76. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 27]
100. ~tall(X0) | kind(X0) | ~funny(X0) [cnf transformation 58]
108. rich(X0) | ~kind(X0) [cnf transformation 62]
109. ~patient(X0) | quiet(X0) [cnf transformation 62]
111. kind(X0) | patient(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 62]
112. calm(susan) | ~patient(X0) | ~quiet(X0) [cnf transformation 63]
113. calm(susan) | quiet(X0) | patient(X0) [cnf transformation 63]
118. rich(X0) | tall(X0) | kind(X0) [cnf transformation 66]
121. rich(susan) | funny(X0) [cnf transformation 32]
129. ~calm(susan) [cnf transformation 22]
130. ~rich(X0) | ~kind(X0) [duplicate literal removal 76]
234. ~quiet(X0) | patient(X0) | ~rich(X0) [subsumption resolution 111,130]
235. ~kind(X0) [subsumption resolution 108,130]
238. 23 <=> ! [X0] : quiet(X0) [avatar definition]
239. quiet(X0) <- (23) [avatar component clause 238]
247. 25 <=> ! [X0] : ~patient(X0) [avatar definition]
248. ~patient(X0) <- (25) [avatar component clause 247]
250. calm(susan) | quiet(X0) [subsumption resolution 113,109]
252. 26 <=> calm(susan) [avatar definition]
255. 23 | 26 [avatar split clause 250,252,238]
256. calm(susan) | ~patient(X0) [subsumption resolution 112,109]
257. 25 | 26 [avatar split clause 256,252,247]
272. rich(X0) | tall(X0) [subsumption resolution 118,235]
274. 30 <=> ! [X0] : ~rich(X0) [avatar definition]
275. ~rich(X0) <- (30) [avatar component clause 274]
277. 31 <=> rich(susan) [avatar definition]
279. rich(susan) <- (31) [avatar component clause 277]
282. 32 <=> ! [X0] : funny(X0) [avatar definition]
283. funny(X0) <- (32) [avatar component clause 282]
284. 32 | 31 [avatar split clause 121,277,282]
305. ~26 [avatar split clause 129,252]
336. patient(X0) | ~rich(X0) <- (23) [resolution 234,239]
337. ~rich(X0) <- (23, 25) [subsumption resolution 336,248]
338. 30 | ~23 | ~25 [avatar split clause 337,247,238,274]
339. $false <- (30, 31) [resolution 275,279]
340. tall(X0) <- (30) [resolution 275,272]
341. ~30 | ~31 [avatar contradiction clause 339]
368. kind(X0) | ~funny(X0) <- (30) [resolution 340,100]
371. ~funny(X0) <- (30) [subsumption resolution 368,235]
372. $false <- (30, 32) [subsumption resolution 371,283]
373. ~30 | ~32 [avatar contradiction clause 372]
374. $false [avatar sat refutation 255,257,284,305,338,341,373]
% SZS output end Proof for 667342532626885389481766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not generous is both generous and curious.
If someone is tall then someone is both humble and wise and vice versa.
Everyone who is not creative or brave is both not curious and not strong and vice versa.
If lucy is either happy or brave then mary is generous or not rich.
If someone is not humble or not quiet then mary is either not patient or strong.
Everyone who is curious or funny is either not happy or not creative.
Everyone who is either not wise or not quiet is both old and creative.
If mary is curious or not quiet then someone is either not curious or funny and vice versa.
Everyone who is humble is either calm or not humble and vice versa.
Everyone who is not humble or patient is curious.
Everyone who is either humble or happy is both brave and patient and vice versa.
Everyone who is not happy is either not happy or brave and vice versa.
If lucy is both not rich and not patient then fred is both not tall and not old and vice versa.
Everyone who is both creative and not rich is both not happy and rich and vice versa.
Everyone who is not generous is generous.
Fred is not curious or wise.
Someone is both not brave and kind.
Someone is not tall. | Lucy is not calm. | contradiction | (![X]:((~quiet(X)<~>~generous(X))=>(generous(X)&curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((~creative(X)|brave(X))<=>(~curious(X)&~strong(X))))&
(((happy(lucy)<~>brave(lucy)))=>((generous(mary)|~rich(mary))))&
((?[X]:((~humble(X)|~quiet(X))))=>((~patient(mary)<~>strong(mary))))&
(![X]:((curious(X)|funny(X))=>(~happy(X)<~>~creative(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(old(X)&creative(X))))&
(((curious(mary)|~quiet(mary)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(humble(X)<=>(calm(X)<~>~humble(X))))&
(![X]:((~humble(X)|patient(X))=>curious(X)))&
(![X]:((humble(X)<~>happy(X))<=>(brave(X)&patient(X))))&
(![X]:(~happy(X)<=>(~happy(X)<~>brave(X))))&
(((~rich(lucy)&~patient(lucy)))<=>((~tall(fred)&~old(fred))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&rich(X))))&
(![X]:(~generous(X)=>generous(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((~brave(X)&kind(X))))&
(?[X]:(~tall(X))) | ~calm(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7338781286574234092992273
% SZS output start Proof for 7338781286574234092992273
9. ! [X0] : (humble(X0) <=> (calm(X0) <~> ~humble(X0))) [input p8]
19. ~calm(lucy) [input hypothesis]
47. ! [X0] : ((humble(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0)))) & (((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | ~humble(X0))) [nnf transformation 9]
91. ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 47]
94. humble(X0) | calm(X0) | humble(X0) [cnf transformation 47]
119. ~calm(lucy) [cnf transformation 19]
125. ~humble(X0) | calm(X0) [duplicate literal removal 91]
126. humble(X0) | calm(X0) [duplicate literal removal 94]
214. calm(X0) [subsumption resolution 125,126]
245. $false [subsumption resolution 119,214]
% SZS output end Proof for 7338781286574234092992273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not calm and not humble then alice is not kind and vice versa.
Everyone who is either brave or not old is quiet and vice versa.
If john is both happy and rich then someone is not humble or funny and vice versa.
If paul is not funny or creative then alice is both not curious and not strong and vice versa.
Everyone who is both patient and not tall is rich or not patient and vice versa.
Everyone who is quiet or wise is not quiet or not funny.
If john is kind then susan is calm or not humble and vice versa.
Everyone who is either funny or strong is tall.
If someone is not wise then paul is both brave and creative and vice versa.
Everyone who is either not old or funny is either not quiet or creative and vice versa.
If john is both patient and tall then someone is brave and vice versa.
If someone is both strong and curious then someone is both curious and not patient and vice versa.
If john is old then someone is either brave or rich.
If alice is either not creative or not curious then someone is both calm and brave and vice versa.
If alice is both not curious and not funny then susan is either not calm or wise and vice versa.
Everyone who is both not old and not wise is curious and vice versa.
Susan is either not generous or not funny.
Mary is kind or not happy.
Paul is generous or not kind.
Mary is brave.
Someone is either not curious or rich.
Someone is not curious or quiet.
Mary is not happy or not kind. | Mary is not creative. | entailment | (((~calm(lucy)&~humble(lucy)))<=>(~kind(alice)))&
(![X]:((brave(X)<~>~old(X))<=>quiet(X)))&
(((happy(john)&rich(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
(((~funny(paul)|creative(paul)))<=>((~curious(alice)&~strong(alice))))&
(![X]:((patient(X)&~tall(X))<=>(rich(X)|~patient(X))))&
(![X]:((quiet(X)|wise(X))=>(~quiet(X)|~funny(X))))&
((kind(john))<=>((calm(susan)|~humble(susan))))&
(![X]:((funny(X)<~>strong(X))=>tall(X)))&
((?[X]:(~wise(X)))<=>((brave(paul)&creative(paul))))&
(![X]:((~old(X)<~>funny(X))<=>(~quiet(X)<~>creative(X))))&
(((patient(john)&tall(john)))<=>(?[X]:(brave(X))))&
((?[X]:((strong(X)&curious(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
((old(john))=>(?[X]:((brave(X)<~>rich(X)))))&
(((~creative(alice)<~>~curious(alice)))<=>(?[X]:((calm(X)&brave(X)))))&
(((~curious(alice)&~funny(alice)))<=>((~calm(susan)<~>wise(susan))))&
(![X]:((~old(X)&~wise(X))<=>curious(X)))&
((~generous(susan)<~>~funny(susan)))&
((kind(mary)|~happy(mary)))&
((generous(paul)|~kind(paul)))&
(brave(mary))&
(?[X]:((~curious(X)<~>rich(X))))&
(?[X]:((~curious(X)|quiet(X))))&
((~happy(mary)|~kind(mary))) | ~creative(mary) | [
"p1",
"p2",
"p4",
"p5",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8440133024652472771529663
% SZS output start Proof for 8440133024652472771529663
2. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> quiet(X0)) [input p1]
3. (rich(john) & happy(john)) <=> ? [X0] : (funny(X0) | ~humble(X0)) [input p2]
5. ! [X0] : ((~tall(X0) & patient(X0)) <=> (~patient(X0) | rich(X0))) [input p4]
6. ! [X0] : ((wise(X0) | quiet(X0)) => (~funny(X0) | ~quiet(X0))) [input p5]
10. ! [X0] : ((~old(X0) <~> funny(X0)) <=> (~quiet(X0) <~> creative(X0))) [input p9]
11. (tall(john) & patient(john)) <=> ? [X0] : brave(X0) [input p10]
20. brave(mary) [input p19]
24. creative(mary) [input hypothesis]
26. ! [X0] : ((~funny(X0) | ~quiet(X0)) | (~wise(X0) & ~quiet(X0))) [ennf transformation 6]
27. ! [X0] : (~funny(X0) | ~quiet(X0) | (~wise(X0) & ~quiet(X0))) [flattening 26]
32. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~quiet(X0)) & (quiet(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 2]
33. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | (~rich(john) | ~happy(john))) [nnf transformation 3]
34. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | ~rich(john) | ~happy(john)) [flattening 33]
35. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X1] : (funny(X1) | ~humble(X1)) | ~rich(john) | ~happy(john)) [rectify 34]
36. ? [X1] : (funny(X1) | ~humble(X1)) => (funny(sK0) | ~humble(sK0)) [choice axiom]
37. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & ((funny(sK0) | ~humble(sK0)) | ~rich(john) | ~happy(john)) [skolemisation 35,36]
40. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & ((~patient(X0) | rich(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 5]
41. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & (~patient(X0) | rich(X0) | tall(X0) | ~patient(X0))) [flattening 40]
50. ! [X0] : ((((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0)))) & (((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0))))) [nnf transformation 10]
51. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~tall(john) | ~patient(john))) [nnf transformation 11]
52. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~tall(john) | ~patient(john)) [flattening 51]
53. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~tall(john) | ~patient(john)) [rectify 52]
54. ? [X1] : brave(X1) => brave(sK2) [choice axiom]
55. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (brave(sK2) | ~tall(john) | ~patient(john)) [skolemisation 53,54]
81. ~old(X0) | quiet(X0) | ~brave(X0) [cnf transformation 32]
84. ~quiet(X0) | ~brave(X0) | old(X0) [cnf transformation 32]
89. rich(john) | ~funny(X0) [cnf transformation 37]
98. ~tall(X0) | ~rich(X0) [cnf transformation 41]
100. ~funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 27]
112. ~creative(X0) | quiet(X0) | funny(X0) | old(X0) [cnf transformation 50]
115. funny(X0) | ~old(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 50]
120. tall(john) | ~brave(X0) [cnf transformation 55]
146. brave(mary) [cnf transformation 20]
151. creative(mary) [cnf transformation 24]
152. ~funny(X0) | ~quiet(X0) [duplicate literal removal 100]
171. 4 <=> ! [X0] : ~funny(X0) [avatar definition]
172. ~funny(X0) <- (4) [avatar component clause 171]
174. 5 <=> rich(john) [avatar definition]
177. 4 | 5 [avatar split clause 89,174,171]
249. ~creative(X0) | ~quiet(X0) | ~old(X0) [subsumption resolution 115,152]
253. 20 <=> ! [X0] : ~brave(X0) [avatar definition]
254. ~brave(X0) <- (20) [avatar component clause 253]
256. 21 <=> tall(john) [avatar definition]
258. tall(john) <- (21) [avatar component clause 256]
259. 20 | 21 [avatar split clause 120,256,253]
372. $false <- (20) [resolution 254,146]
373. ~20 [avatar contradiction clause 372]
376. ~rich(john) <- (21) [resolution 98,258]
413. ~quiet(mary) | ~old(mary) [resolution 249,151]
415. 46 <=> old(mary) [avatar definition]
416. old(mary) <- (46) [avatar component clause 415]
417. ~old(mary) <- (~46) [avatar component clause 415]
419. 47 <=> quiet(mary) [avatar definition]
420. quiet(mary) <- (47) [avatar component clause 419]
421. ~quiet(mary) <- (~47) [avatar component clause 419]
422. ~46 | ~47 [avatar split clause 413,419,415]
439. quiet(mary) | funny(mary) | old(mary) [resolution 112,151]
442. quiet(mary) | old(mary) <- (4) [subsumption resolution 439,172]
445. 46 | 47 | ~4 [avatar split clause 442,171,419,415]
446. quiet(mary) | ~brave(mary) <- (46) [resolution 416,81]
447. ~brave(mary) <- (46, ~47) [subsumption resolution 446,421]
448. $false <- (46, ~47) [subsumption resolution 447,146]
449. ~46 | 47 [avatar contradiction clause 448]
451. ~brave(mary) | old(mary) <- (47) [resolution 420,84]
453. old(mary) <- (47) [subsumption resolution 451,146]
454. $false <- (~46, 47) [subsumption resolution 453,417]
455. 46 | ~47 [avatar contradiction clause 454]
462. ~5 | ~21 [avatar split clause 376,256,174]
463. $false [avatar sat refutation 177,259,373,422,445,449,455,462]
% SZS output end Proof for 8440133024652472771529663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or generous is not happy or strong.
Everyone who is brave is both not funny and not kind.
Everyone who is either not patient or patient is both old and not patient and vice versa.
If someone is either not curious or not humble then someone is either generous or humble and vice versa.
If someone is tall then alice is both brave and not humble and vice versa.
If someone is either not tall or not wise then someone is both calm and not curious.
If someone is patient then someone is both not kind and humble and vice versa.
If alice is tall then lucy is either strong or not happy and vice versa.
Everyone who is not funny is kind or generous and vice versa.
Everyone who is both quiet and not happy is either not patient or creative and vice versa.
Everyone who is either generous or happy is not old.
If someone is kind or not funny then someone is either kind or generous.
If alice is not wise then john is either not curious or tall and vice versa.
Everyone who is calm is both tall and curious.
Everyone who is either not happy or old is not strong or rich and vice versa.
Everyone who is not strong or not kind is both generous and patient.
Lucy is either not calm or not humble.
Fred is not rich or calm.
John is both not calm and not generous.
Lucy is not generous or tall.
John is not quiet.
Paul is not brave.
Someone is not patient or old. | John is wise. | contradiction | (![X]:((tall(X)<~>generous(X))=>(~happy(X)|strong(X))))&
(![X]:(brave(X)=>(~funny(X)&~kind(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(old(X)&~patient(X))))&
((?[X]:((~curious(X)<~>~humble(X))))<=>(?[X]:((generous(X)<~>humble(X)))))&
((?[X]:(tall(X)))<=>((brave(alice)&~humble(alice))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((calm(X)&~curious(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~kind(X)&humble(X)))))&
((tall(alice))<=>((strong(lucy)<~>~happy(lucy))))&
(![X]:(~funny(X)<=>(kind(X)|generous(X))))&
(![X]:((quiet(X)&~happy(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((generous(X)<~>happy(X))=>~old(X)))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
((~wise(alice))<=>((~curious(john)<~>tall(john))))&
(![X]:(calm(X)=>(tall(X)&curious(X))))&
(![X]:((~happy(X)<~>old(X))<=>(~strong(X)|rich(X))))&
(![X]:((~strong(X)|~kind(X))=>(generous(X)&patient(X))))&
((~calm(lucy)<~>~humble(lucy)))&
((~rich(fred)|calm(fred)))&
((~calm(john)&~generous(john)))&
((~generous(lucy)|tall(lucy)))&
(~quiet(john))&
(~brave(paul))&
(?[X]:((~patient(X)|old(X)))) | wise(john) | [
"p1",
"p2",
"p4",
"p5",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2001198907827495497174412
% SZS output start Proof for 2001198907827495497174412
2. ! [X0] : (brave(X0) => (~kind(X0) & ~funny(X0))) [input p1]
3. ! [X0] : ((~patient(X0) <~> patient(X0)) <=> (~patient(X0) & old(X0))) [input p2]
5. ? [X0] : tall(X0) <=> (~humble(alice) & brave(alice)) [input p4]
6. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X0] : (~curious(X0) & calm(X0)) [input p5]
14. ! [X0] : (calm(X0) => (curious(X0) & tall(X0))) [input p13]
16. ! [X0] : ((~kind(X0) | ~strong(X0)) => (patient(X0) & generous(X0))) [input p15]
24. wise(john) [input hypothesis]
26. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X1] : (~curious(X1) & calm(X1)) [rectify 6]
31. ! [X0] : ((~kind(X0) & ~funny(X0)) | ~brave(X0)) [ennf transformation 2]
32. ? [X1] : (~curious(X1) & calm(X1)) | ! [X0] : (~tall(X0) <=> ~wise(X0)) [ennf transformation 26]
35. ! [X0] : ((curious(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 14]
36. ! [X0] : ((patient(X0) & generous(X0)) | (kind(X0) & strong(X0))) [ennf transformation 16]
38. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [nnf transformation 3]
39. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [flattening 38]
45. (? [X0] : tall(X0) | (humble(alice) | ~brave(alice))) & ((~humble(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [nnf transformation 5]
46. (? [X0] : tall(X0) | humble(alice) | ~brave(alice)) & ((~humble(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [flattening 45]
47. (? [X0] : tall(X0) | humble(alice) | ~brave(alice)) & ((~humble(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [rectify 46]
48. ? [X0] : tall(X0) => tall(sK2) [choice axiom]
49. (tall(sK2) | humble(alice) | ~brave(alice)) & ((~humble(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [skolemisation 47,48]
50. ? [X1] : (~curious(X1) & calm(X1)) | ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 32]
51. ? [X0] : (~curious(X0) & calm(X0)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [rectify 50]
52. ? [X0] : (~curious(X0) & calm(X0)) => (~curious(sK3) & calm(sK3)) [choice axiom]
53. (~curious(sK3) & calm(sK3)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [skolemisation 51,52]
78. ~kind(X0) | ~brave(X0) [cnf transformation 31]
82. ~patient(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 39]
93. brave(alice) | ~tall(X1) [cnf transformation 49]
96. calm(sK3) | ~wise(X1) | tall(X1) [cnf transformation 53]
126. ~calm(X0) | tall(X0) [cnf transformation 35]
137. patient(X0) | kind(X0) [cnf transformation 36]
147. wise(john) [cnf transformation 24]
151. ~patient(X0) [duplicate literal removal 82]
192. 9 <=> brave(alice) [avatar definition]
193. brave(alice) <- (9) [avatar component clause 192]
205. 12 <=> ! [X1] : ~tall(X1) [avatar definition]
206. ~tall(X1) <- (12) [avatar component clause 205]
208. 12 | 9 [avatar split clause 93,192,205]
218. 15 <=> ! [X1] : (~wise(X1) | tall(X1)) [avatar definition]
219. ~wise(X1) | tall(X1) <- (15) [avatar component clause 218]
222. 16 <=> calm(sK3) [avatar definition]
224. calm(sK3) <- (16) [avatar component clause 222]
226. 15 | 16 [avatar split clause 96,222,218]
268. 24 <=> tall(john) [avatar definition]
269. tall(john) <- (24) [avatar component clause 268]
270. ~tall(john) <- (~24) [avatar component clause 268]
286. kind(X0) [subsumption resolution 137,151]
318. ~brave(X0) [resolution 78,286]
319. $false <- (9) [resolution 318,193]
320. ~9 [avatar contradiction clause 319]
327. tall(john) <- (15) [resolution 219,147]
328. $false <- (15, ~24) [subsumption resolution 327,270]
329. ~15 | 24 [avatar contradiction clause 328]
331. tall(sK3) <- (16) [resolution 224,126]
334. $false <- (12, 16) [subsumption resolution 331,206]
335. ~12 | ~16 [avatar contradiction clause 334]
336. $false <- (12, 24) [subsumption resolution 269,206]
337. ~12 | ~24 [avatar contradiction clause 336]
339. $false [avatar sat refutation 208,226,320,329,335,337]
% SZS output end Proof for 2001198907827495497174412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and wise is both not rich and curious.
If paul is generous or happy then fred is both not quiet and not happy.
Everyone who is both happy and not rich is either strong or funny.
Everyone who is both humble and rich is both happy and not wise and vice versa.
Everyone who is happy is generous.
Everyone who is both not wise and quiet is either not patient or not humble.
Everyone who is old is quiet or not patient and vice versa.
Everyone who is both not curious and creative is not tall and vice versa.
If someone is strong or not creative then lucy is not creative.
Everyone who is funny is generous or not strong.
Everyone who is either happy or not humble is both strong and curious and vice versa.
If someone is both happy and funny then john is both not tall and wise.
If someone is both not patient and creative then alice is either creative or happy and vice versa.
Everyone who is wise or not kind is both tall and funny and vice versa.
If someone is tall then someone is not wise or humble and vice versa.
If lucy is either not curious or not humble then alice is both wise and not calm.
Someone is brave.
Mary is both not humble and generous.
Someone is brave or not curious.
Paul is wise or strong.
Someone is not creative.
Alice is both not quiet and brave. | Alice is patient. | neutral | (![X]:((~rich(X)&wise(X))=>(~rich(X)&curious(X))))&
(((generous(paul)|happy(paul)))=>((~quiet(fred)&~happy(fred))))&
(![X]:((happy(X)&~rich(X))=>(strong(X)<~>funny(X))))&
(![X]:((humble(X)&rich(X))<=>(happy(X)&~wise(X))))&
(![X]:(happy(X)=>generous(X)))&
(![X]:((~wise(X)&quiet(X))=>(~patient(X)<~>~humble(X))))&
(![X]:(old(X)<=>(quiet(X)|~patient(X))))&
(![X]:((~curious(X)&creative(X))<=>~tall(X)))&
((?[X]:((strong(X)|~creative(X))))=>(~creative(lucy)))&
(![X]:(funny(X)=>(generous(X)|~strong(X))))&
(![X]:((happy(X)<~>~humble(X))<=>(strong(X)&curious(X))))&
((?[X]:((happy(X)&funny(X))))=>((~tall(john)&wise(john))))&
((?[X]:((~patient(X)&creative(X))))<=>((creative(alice)<~>happy(alice))))&
(![X]:((wise(X)|~kind(X))<=>(tall(X)&funny(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
(((~curious(lucy)<~>~humble(lucy)))=>((wise(alice)&~calm(alice))))&
(?[X]:(brave(X)))&
((~humble(mary)&generous(mary)))&
(?[X]:((brave(X)|~curious(X))))&
((wise(paul)|strong(paul)))&
(?[X]:(~creative(X)))&
((~quiet(alice)&brave(alice))) | patient(alice) | [] | null | 0 |
Everyone who is both not calm and rich is old or not generous and vice versa.
Everyone who is not rich is curious.
Everyone who is humble is not brave and vice versa.
Everyone who is not rich or not strong is either not kind or curious and vice versa.
If someone is kind or not funny then someone is not generous or not creative.
Everyone who is not humble is both generous and not generous and vice versa.
Everyone who is both brave and not funny is creative or not humble.
If alice is not kind then john is not patient.
If someone is both not tall and humble then john is both quiet and not quiet.
Everyone who is not calm is both calm and funny and vice versa.
If john is both not rich and happy then someone is not funny or not happy.
If someone is either not wise or not patient then lucy is generous and vice versa.
If mary is both calm and not brave then someone is kind or not funny and vice versa.
Everyone who is either tall or not old is both not happy and not quiet.
If someone is not generous then mary is quiet or not rich.
Lucy is both calm and not brave.
Someone is tall.
Paul is either brave or not rich.
Lucy is either not kind or wise.
Mary is calm or not kind.
Mary is not generous or not happy. | Paul is tall. | entailment | (![X]:((~calm(X)&rich(X))<=>(old(X)|~generous(X))))&
(![X]:(~rich(X)=>curious(X)))&
(![X]:(humble(X)<=>~brave(X)))&
(![X]:((~rich(X)|~strong(X))<=>(~kind(X)<~>curious(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:((~generous(X)|~creative(X)))))&
(![X]:(~humble(X)<=>(generous(X)&~generous(X))))&
(![X]:((brave(X)&~funny(X))=>(creative(X)|~humble(X))))&
((~kind(alice))=>(~patient(john)))&
((?[X]:((~tall(X)&humble(X))))=>((quiet(john)&~quiet(john))))&
(![X]:(~calm(X)<=>(calm(X)&funny(X))))&
(((~rich(john)&happy(john)))=>(?[X]:((~funny(X)|~happy(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(generous(lucy)))&
(((calm(mary)&~brave(mary)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((tall(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
((?[X]:(~generous(X)))=>((quiet(mary)|~rich(mary))))&
((calm(lucy)&~brave(lucy)))&
(?[X]:(tall(X)))&
((brave(paul)<~>~rich(paul)))&
((~kind(lucy)<~>wise(lucy)))&
((calm(mary)|~kind(mary)))&
((~generous(mary)|~happy(mary))) | tall(paul) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5464223723163066841946139
% SZS output start Proof for 5464223723163066841946139
6. ! [X0] : (~humble(X0) <=> (~generous(X0) & generous(X0))) [input p5]
9. ? [X0] : (humble(X0) & ~tall(X0)) => (~quiet(john) & quiet(john)) [input p8]
22. ~tall(paul) [input hypothesis]
32. (~quiet(john) & quiet(john)) | ! [X0] : (~humble(X0) | tall(X0)) [ennf transformation 9]
44. ! [X0] : ((~humble(X0) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | humble(X0))) [nnf transformation 6]
45. ! [X0] : ((~humble(X0) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | humble(X0))) [flattening 44]
78. generous(X0) | humble(X0) [cnf transformation 45]
79. ~generous(X0) | humble(X0) [cnf transformation 45]
83. quiet(john) | ~humble(X0) | tall(X0) [cnf transformation 32]
84. ~quiet(john) | ~humble(X0) | tall(X0) [cnf transformation 32]
108. ~tall(paul) [cnf transformation 22]
129. humble(X0) [subsumption resolution 78,79]
139. ~quiet(john) | tall(X0) [subsumption resolution 84,129]
141. 7 <=> ! [X0] : tall(X0) [avatar definition]
142. tall(X0) <- (7) [avatar component clause 141]
144. 8 <=> quiet(john) [avatar definition]
147. 7 | ~8 [avatar split clause 139,144,141]
148. quiet(john) | tall(X0) [subsumption resolution 83,129]
149. 7 | 8 [avatar split clause 148,144,141]
220. $false <- (7) [resolution 142,108]
221. ~7 [avatar contradiction clause 220]
222. $false [avatar sat refutation 147,149,221]
% SZS output end Proof for 5464223723163066841946139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not happy is not funny or funny and vice versa.
Everyone who is not old or not kind is generous or humble.
Everyone who is quiet is either not happy or strong and vice versa.
Everyone who is not happy or wise is both not happy and tall and vice versa.
If someone is not patient or strong then someone is both not old and not humble.
Everyone who is both strong and brave is wise or not humble.
If someone is both not generous and not brave then someone is patient or wise and vice versa.
If mary is both not quiet and quiet then someone is either not tall or not funny and vice versa.
Everyone who is not calm is not curious or not kind and vice versa.
Everyone who is either curious or not kind is not humble.
Everyone who is happy or kind is both not creative and patient.
If someone is either not brave or not quiet then someone is both rich and not curious.
Everyone who is both strong and old is either not old or patient.
Someone is not kind or funny.
Someone is both not curious and tall.
Someone is both not happy and not quiet.
Lucy is either creative or not funny.
Someone is creative.
Lucy is not tall or curious. | Mary is not happy. | entailment | (![X]:((~old(X)&~happy(X))<=>(~funny(X)|funny(X))))&
(![X]:((~old(X)|~kind(X))=>(generous(X)|humble(X))))&
(![X]:(quiet(X)<=>(~happy(X)<~>strong(X))))&
(![X]:((~happy(X)|wise(X))<=>(~happy(X)&tall(X))))&
((?[X]:((~patient(X)|strong(X))))=>(?[X]:((~old(X)&~humble(X)))))&
(![X]:((strong(X)&brave(X))=>(wise(X)|~humble(X))))&
((?[X]:((~generous(X)&~brave(X))))<=>(?[X]:((patient(X)|wise(X)))))&
(((~quiet(mary)&quiet(mary)))<=>(?[X]:((~tall(X)<~>~funny(X)))))&
(![X]:(~calm(X)<=>(~curious(X)|~kind(X))))&
(![X]:((curious(X)<~>~kind(X))=>~humble(X)))&
(![X]:((happy(X)|kind(X))=>(~creative(X)&patient(X))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>(?[X]:((rich(X)&~curious(X)))))&
(![X]:((strong(X)&old(X))=>(~old(X)<~>patient(X))))&
(?[X]:((~kind(X)|funny(X))))&
(?[X]:((~curious(X)&tall(X))))&
(?[X]:((~happy(X)&~quiet(X))))&
((creative(lucy)<~>~funny(lucy)))&
(?[X]:(creative(X)))&
((~tall(lucy)|curious(lucy))) | ~happy(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 3348800736055437056146499
% SZS output start Proof for 3348800736055437056146499
1. ! [X0] : ((~happy(X0) & ~old(X0)) <=> (funny(X0) | ~funny(X0))) [input p0]
20. happy(mary) [input hypothesis]
35. ! [X0] : (((~happy(X0) & ~old(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (happy(X0) | old(X0)))) [nnf transformation 1]
36. ! [X0] : (((~happy(X0) & ~old(X0)) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | happy(X0) | old(X0))) [flattening 35]
71. ~happy(X0) | funny(X0) [cnf transformation 36]
72. ~happy(X0) | ~funny(X0) [cnf transformation 36]
119. happy(mary) [cnf transformation 20]
121. ~happy(X0) [subsumption resolution 71,72]
212. $false [subsumption resolution 119,121]
% SZS output end Proof for 3348800736055437056146499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not strong and old then susan is not humble.
Everyone who is both rich and not old is both not calm and kind.
Everyone who is both funny and generous is either tall or humble and vice versa.
Everyone who is curious is not strong and vice versa.
If someone is rich or not curious then someone is not humble or not happy.
Everyone who is either not calm or kind is both not generous and not happy.
Everyone who is both creative and not patient is both kind and strong and vice versa.
Everyone who is not old is either not strong or old.
Everyone who is both not creative and not strong is generous or kind.
Everyone who is both not calm and not brave is strong or not strong.
Everyone who is either wise or old is not calm or generous.
Everyone who is either tall or calm is creative and vice versa.
If fred is both not happy and not calm then john is curious or wise and vice versa.
Everyone who is both creative and curious is both happy and tall and vice versa.
Everyone who is either not brave or rich is both not wise and not brave and vice versa.
Everyone who is not tall is not wise or rich.
Someone is either not brave or not kind.
Fred is both brave and tall.
Paul is either brave or humble.
Susan is calm or quiet.
Someone is either brave or generous.
Someone is not old or calm.
Fred is not rich or wise.
Someone is funny. | Paul is strong. | neutral | ((?[X]:((~strong(X)&old(X))))=>(~humble(susan)))&
(![X]:((rich(X)&~old(X))=>(~calm(X)&kind(X))))&
(![X]:((funny(X)&generous(X))<=>(tall(X)<~>humble(X))))&
(![X]:(curious(X)<=>~strong(X)))&
((?[X]:((rich(X)|~curious(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~calm(X)<~>kind(X))=>(~generous(X)&~happy(X))))&
(![X]:((creative(X)&~patient(X))<=>(kind(X)&strong(X))))&
(![X]:(~old(X)=>(~strong(X)<~>old(X))))&
(![X]:((~creative(X)&~strong(X))=>(generous(X)|kind(X))))&
(![X]:((~calm(X)&~brave(X))=>(strong(X)|~strong(X))))&
(![X]:((wise(X)<~>old(X))=>(~calm(X)|generous(X))))&
(![X]:((tall(X)<~>calm(X))<=>creative(X)))&
(((~happy(fred)&~calm(fred)))<=>((curious(john)|wise(john))))&
(![X]:((creative(X)&curious(X))<=>(happy(X)&tall(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~wise(X)&~brave(X))))&
(![X]:(~tall(X)=>(~wise(X)|rich(X))))&
(?[X]:((~brave(X)<~>~kind(X))))&
((brave(fred)&tall(fred)))&
((brave(paul)<~>humble(paul)))&
((calm(susan)|quiet(susan)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((~old(X)|calm(X))))&
((~rich(fred)|wise(fred)))&
(?[X]:(funny(X))) | strong(paul) | [] | null | 0 |
Everyone who is either brave or not calm is both happy and strong. If susan is generous then paul is generous and vice versa. Everyone who is both curious and quiet is either not wise or generous and vice versa. Everyone who is both not calm and wise is not happy or creative and vice versa. If someone is not happy then john is old or tall. Everyone who is brave or quiet is both not happy and not generous. Everyone who is either rich or not funny is either patient or not tall and vice versa. If someone is not humble then alice is either old or not happy. Everyone who is both tall and happy is strong. Everyone who is not humble or not funny is strong and vice versa. If someone is either wise or quiet then lucy is calm. Everyone who is either humble or kind is both not quiet and creative and vice versa. If someone is not old then fred is both not calm and not creative and vice versa. If someone is strong then fred is old and vice versa. If mary is not old then mary is not kind. If susan is both not curious and brave then someone is not old or not brave. Paul is either humble or calm. Paul is creative. Alice is not funny or curious. Someone is not tall or not rich. Alice is not quiet. Someone is both not calm and not strong. | Susan is wise. | entailment | (![X]:((brave(X)<~>~calm(X))=>(happy(X)&strong(X))))&
((generous(susan))<=>(generous(paul)))&
(![X]:((curious(X)&quiet(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((~calm(X)&wise(X))<=>(~happy(X)|creative(X))))&
((?[X]:(~happy(X)))=>((old(john)|tall(john))))&
(![X]:((brave(X)|quiet(X))=>(~happy(X)&~generous(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(patient(X)<~>~tall(X))))&
((?[X]:(~humble(X)))=>((old(alice)<~>~happy(alice))))&
(![X]:((tall(X)&happy(X))=>strong(X)))&
(![X]:((~humble(X)|~funny(X))<=>strong(X)))&
((?[X]:((wise(X)<~>quiet(X))))=>(calm(lucy)))&
(![X]:((humble(X)<~>kind(X))<=>(~quiet(X)&creative(X))))&
((?[X]:(~old(X)))<=>((~calm(fred)&~creative(fred))))&
((?[X]:(strong(X)))<=>(old(fred)))&
((~old(mary))=>(~kind(mary)))&
(((~curious(susan)&brave(susan)))=>(?[X]:((~old(X)|~brave(X)))))&
((humble(paul)<~>calm(paul)))&
(creative(paul))&
((~funny(alice)|curious(alice)))&
(?[X]:((~tall(X)|~rich(X))))&
(~quiet(alice))&
(?[X]:((~calm(X)&~strong(X)))) | wise(susan) | [
"p1",
"p2",
"p3",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5811013689889139256286714
% SZS output start Proof for 5811013689889139256286714
2. generous(susan) <=> generous(paul) [input p1]
3. ! [X0] : ((quiet(X0) & curious(X0)) <=> (~wise(X0) <~> generous(X0))) [input p2]
4. ! [X0] : ((wise(X0) & ~calm(X0)) <=> (creative(X0) | ~happy(X0))) [input p3]
6. ! [X0] : ((quiet(X0) | brave(X0)) => (~generous(X0) & ~happy(X0))) [input p5]
18. creative(paul) [input p17]
23. ~wise(susan) [input hypothesis]
27. ! [X0] : ((~generous(X0) & ~happy(X0)) | (~quiet(X0) & ~brave(X0))) [ennf transformation 6]
36. (generous(susan) | ~generous(paul)) & (generous(paul) | ~generous(susan)) [nnf transformation 2]
37. ! [X0] : (((quiet(X0) & curious(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~quiet(X0) | ~curious(X0)))) [nnf transformation 3]
38. ! [X0] : (((quiet(X0) & curious(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | ~quiet(X0) | ~curious(X0))) [flattening 37]
39. ! [X0] : (((wise(X0) & ~calm(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~wise(X0) | calm(X0)))) [nnf transformation 4]
40. ! [X0] : (((wise(X0) & ~calm(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~wise(X0) | calm(X0))) [flattening 39]
68. generous(paul) | ~generous(susan) [cnf transformation 36]
74. wise(X0) | generous(X0) | quiet(X0) [cnf transformation 38]
75. ~wise(X0) | quiet(X0) | ~generous(X0) [cnf transformation 38]
79. wise(X0) | happy(X0) [cnf transformation 40]
80. ~creative(X0) | wise(X0) [cnf transformation 40]
83. ~quiet(X0) | ~happy(X0) [cnf transformation 27]
85. ~quiet(X0) | ~generous(X0) [cnf transformation 27]
117. creative(paul) [cnf transformation 18]
123. ~wise(susan) [cnf transformation 23]
125. 1 <=> generous(paul) [avatar definition]
129. 2 <=> generous(susan) [avatar definition]
130. ~generous(susan) <- (~2) [avatar component clause 129]
133. ~2 | 1 [avatar split clause 68,125,129]
260. happy(susan) [resolution 79,123]
261. wise(paul) [resolution 80,117]
294. generous(susan) | quiet(susan) [resolution 74,123]
296. quiet(susan) <- (~2) [subsumption resolution 294,130]
300. quiet(paul) | ~generous(paul) [resolution 75,261]
304. ~happy(susan) <- (~2) [resolution 296,83]
305. $false <- (~2) [subsumption resolution 304,260]
306. 2 [avatar contradiction clause 305]
307. ~generous(paul) [subsumption resolution 300,85]
308. ~1 [avatar split clause 307,125]
319. $false [avatar sat refutation 133,306,308]
% SZS output end Proof for 5811013689889139256286714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not rich is both quiet and kind and vice versa. Everyone who is patient or tall is either brave or not patient and vice versa. If paul is both curious and not brave then someone is both not quiet and not rich and vice versa. If someone is not old then susan is happy or not creative and vice versa. Everyone who is both rich and not humble is both not humble and not brave and vice versa. Everyone who is not rich or kind is not strong. Everyone who is not strong or patient is not wise and vice versa. If someone is either not funny or curious then lucy is not creative or not humble. Everyone who is humble is both not brave and strong and vice versa. If someone is both not rich and generous then someone is tall or curious. Everyone who is not rich is both not patient and not old. If someone is not happy then someone is brave or not funny. Everyone who is not generous or brave is funny or generous. Everyone who is not rich is not kind or not generous. Everyone who is brave or not kind is not kind and vice versa. If fred is generous then someone is either not humble or rich. Alice is both not humble and not funny. Someone is wise. Someone is either calm or not creative. Someone is both not creative and funny. Susan is calm. Someone is either happy or not happy. Susan is not generous. Someone is funny. | Fred is generous. | neutral | (![X]:((~wise(X)<~>~rich(X))<=>(quiet(X)&kind(X))))&
(![X]:((patient(X)|tall(X))<=>(brave(X)<~>~patient(X))))&
(((curious(paul)&~brave(paul)))<=>(?[X]:((~quiet(X)&~rich(X)))))&
((?[X]:(~old(X)))<=>((happy(susan)|~creative(susan))))&
(![X]:((rich(X)&~humble(X))<=>(~humble(X)&~brave(X))))&
(![X]:((~rich(X)|kind(X))=>~strong(X)))&
(![X]:((~strong(X)|patient(X))<=>~wise(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>((~creative(lucy)|~humble(lucy))))&
(![X]:(humble(X)<=>(~brave(X)&strong(X))))&
((?[X]:((~rich(X)&generous(X))))=>(?[X]:((tall(X)|curious(X)))))&
(![X]:(~rich(X)=>(~patient(X)&~old(X))))&
((?[X]:(~happy(X)))=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~generous(X)|brave(X))=>(funny(X)|generous(X))))&
(![X]:(~rich(X)=>(~kind(X)|~generous(X))))&
(![X]:((brave(X)|~kind(X))<=>~kind(X)))&
((generous(fred))=>(?[X]:((~humble(X)<~>rich(X)))))&
((~humble(alice)&~funny(alice)))&
(?[X]:(wise(X)))&
(?[X]:((calm(X)<~>~creative(X))))&
(?[X]:((~creative(X)&funny(X))))&
(calm(susan))&
(?[X]:((happy(X)<~>~happy(X))))&
(~generous(susan))&
(?[X]:(funny(X))) | generous(fred) | [] | null | 0 |
Everyone who is both not humble and not calm is either rich or humble. If someone is either not calm or not wise then someone is strong or wise and vice versa. Everyone who is not calm or happy is not humble and vice versa. Everyone who is either not funny or calm is both funny and not rich. Everyone who is both brave and not quiet is both generous and not calm and vice versa. If susan is not tall then someone is either not happy or not old and vice versa. Everyone who is not calm or not old is not happy. If someone is humble or old then someone is both happy and not calm and vice versa. Everyone who is either old or not funny is either quiet or calm. Everyone who is both quiet and curious is wise or kind and vice versa. If susan is either calm or brave then alice is both old and not kind. If someone is either not wise or not humble then lucy is rich or not funny. Everyone who is not funny is either calm or not rich. Everyone who is generous or kind is calm. If susan is not brave or generous then alice is both creative and not old and vice versa. Everyone who is not calm or not curious is either tall or kind and vice versa. Someone is brave or quiet. Someone is both creative and not happy. Paul is either not curious or not quiet. Someone is either not quiet or not funny. Someone is not humble. Someone is either creative or old. Someone is strong. | Alice is not tall. | contradiction | (![X]:((~humble(X)&~calm(X))=>(rich(X)<~>humble(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~calm(X)|happy(X))<=>~humble(X)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(((calm(susan)<~>brave(susan)))=>((old(alice)&~kind(alice))))&
((?[X]:((~wise(X)<~>~humble(X))))=>((rich(lucy)|~funny(lucy))))&
(![X]:(~funny(X)=>(calm(X)<~>~rich(X))))&
(![X]:((generous(X)|kind(X))=>calm(X)))&
(((~brave(susan)|generous(susan)))<=>((creative(alice)&~old(alice))))&
(![X]:((~calm(X)|~curious(X))<=>(tall(X)<~>kind(X))))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:((creative(X)&~happy(X))))&
((~curious(paul)<~>~quiet(paul)))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:(~humble(X)))&
(?[X]:((creative(X)<~>old(X))))&
(?[X]:(strong(X))) | ~tall(alice) | [
"p2",
"p6",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6664508117421532443550505
% SZS output start Proof for 6664508117421532443550505
3. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~humble(X0)) [input p2]
7. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p6]
8. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p7]
10. ! [X0] : ((curious(X0) & quiet(X0)) <=> (kind(X0) | wise(X0))) [input p9]
14. ! [X0] : ((kind(X0) | generous(X0)) => calm(X0)) [input p13]
16. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (tall(X0) <~> kind(X0))) [input p15]
24. ~tall(alice) [input hypothesis]
26. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 8]
30. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 7]
36. ! [X0] : (calm(X0) | (~kind(X0) & ~generous(X0))) [ennf transformation 14]
43. ! [X0] : (((happy(X0) | ~calm(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 3]
44. ! [X0] : ((happy(X0) | ~calm(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [flattening 43]
52. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 26]
53. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 52]
54. ? [X0] : (old(X0) | humble(X0)) => (old(sK3) | humble(sK3)) [choice axiom]
55. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK4) & happy(sK4)) [choice axiom]
56. ((old(sK3) | humble(sK3)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK4) & happy(sK4)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 53,55,54]
58. ! [X0] : (((curious(X0) & quiet(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 10]
59. ! [X0] : (((curious(X0) & quiet(X0)) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ~curious(X0) | ~quiet(X0))) [flattening 58]
65. ! [X0] : (((~curious(X0) | ~calm(X0)) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0)))) & (((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | (curious(X0) & calm(X0)))) [nnf transformation 16]
66. ! [X0] : ((~curious(X0) | ~calm(X0) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0)))) & (((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | (curious(X0) & calm(X0)))) [flattening 65]
92. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 44]
105. ~happy(X0) | calm(X0) [cnf transformation 30]
106. ~happy(X0) | old(X0) [cnf transformation 30]
107. happy(sK4) | ~humble(X3) [cnf transformation 56]
108. happy(sK4) | ~old(X3) [cnf transformation 56]
109. ~calm(sK4) | ~humble(X3) [cnf transformation 56]
110. ~calm(sK4) | ~old(X3) [cnf transformation 56]
120. ~kind(X0) | curious(X0) [cnf transformation 59]
130. ~kind(X0) | calm(X0) [cnf transformation 36]
136. kind(X0) | tall(X0) | calm(X0) [cnf transformation 66]
141. ~curious(X0) | ~calm(X0) | tall(X0) | ~kind(X0) [cnf transformation 66]
153. ~tall(alice) [cnf transformation 24]
191. 9 <=> ! [X0] : (~happy(X0) | old(X0)) [avatar definition]
192. ~happy(X0) | old(X0) <- (9) [avatar component clause 191]
212. 9 [avatar split clause 106,191]
214. 14 <=> ! [X3] : ~old(X3) [avatar definition]
215. ~old(X3) <- (14) [avatar component clause 214]
217. 15 <=> calm(sK4) [avatar definition]
219. ~calm(sK4) <- (~15) [avatar component clause 217]
220. 14 | ~15 [avatar split clause 110,217,214]
222. 16 <=> ! [X3] : ~humble(X3) [avatar definition]
223. ~humble(X3) <- (16) [avatar component clause 222]
224. 16 | ~15 [avatar split clause 109,217,222]
226. 17 <=> happy(sK4) [avatar definition]
228. happy(sK4) <- (17) [avatar component clause 226]
229. 14 | 17 [avatar split clause 108,226,214]
230. 16 | 17 [avatar split clause 107,226,222]
283. ~calm(X0) | tall(X0) | ~kind(X0) [subsumption resolution 141,120]
284. ~kind(X0) | tall(X0) [subsumption resolution 283,130]
286. tall(X0) | calm(X0) [subsumption resolution 136,284]
326. ~happy(X0) <- (9, 14) [subsumption resolution 192,215]
332. calm(alice) [resolution 286,153]
334. happy(alice) | humble(alice) [resolution 92,332]
341. humble(alice) <- (9, 14) [subsumption resolution 334,326]
342. $false <- (9, 14, 16) [subsumption resolution 341,223]
343. ~9 | ~14 | ~16 [avatar contradiction clause 342]
358. calm(sK4) <- (17) [resolution 228,105]
360. $false <- (~15, 17) [subsumption resolution 358,219]
361. 15 | ~17 [avatar contradiction clause 360]
362. $false [avatar sat refutation 212,220,224,229,230,343,361]
% SZS output end Proof for 6664508117421532443550505
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not patient is kind or not brave and vice versa.
If mary is creative or not generous then mary is both not curious and rich.
Everyone who is both not generous and not quiet is strong or creative and vice versa.
If alice is not wise or happy then alice is patient and vice versa.
If someone is not kind or calm then someone is not happy and vice versa.
Everyone who is both generous and kind is old or not wise and vice versa.
Everyone who is both happy and not patient is funny or curious.
Everyone who is both curious and not kind is kind or quiet and vice versa.
Everyone who is either curious or not wise is both not patient and happy.
If someone is either strong or not funny then fred is brave and vice versa.
If susan is either creative or not kind then someone is not rich.
Everyone who is humble is both not kind and creative.
If someone is both tall and patient then someone is not kind.
If someone is not curious then someone is either kind or not happy.
Everyone who is both brave and funny is happy or not patient and vice versa.
Everyone who is either not creative or quiet is both not funny and patient.
Paul is not generous or patient.
Susan is either not tall or strong.
Fred is not curious or old.
Mary is either not old or tall.
Someone is either not happy or brave.
Susan is not funny.
Someone is either kind or generous. | Susan is not old. | entailment | (![X]:((~funny(X)|~patient(X))<=>(kind(X)|~brave(X))))&
(((creative(mary)|~generous(mary)))=>((~curious(mary)&rich(mary))))&
(![X]:((~generous(X)&~quiet(X))<=>(strong(X)|creative(X))))&
(((~wise(alice)|happy(alice)))<=>(patient(alice)))&
((?[X]:((~kind(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(![X]:((generous(X)&kind(X))<=>(old(X)|~wise(X))))&
(![X]:((happy(X)&~patient(X))=>(funny(X)|curious(X))))&
(![X]:((curious(X)&~kind(X))<=>(kind(X)|quiet(X))))&
(![X]:((curious(X)<~>~wise(X))=>(~patient(X)&happy(X))))&
((?[X]:((strong(X)<~>~funny(X))))<=>(brave(fred)))&
(((creative(susan)<~>~kind(susan)))=>(?[X]:(~rich(X))))&
(![X]:(humble(X)=>(~kind(X)&creative(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((brave(X)&funny(X))<=>(happy(X)|~patient(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(~funny(X)&patient(X))))&
((~generous(paul)|patient(paul)))&
((~tall(susan)<~>strong(susan)))&
((~curious(fred)|old(fred)))&
((~old(mary)<~>tall(mary)))&
(?[X]:((~happy(X)<~>brave(X))))&
(~funny(susan))&
(?[X]:((kind(X)<~>generous(X)))) | ~old(susan) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2042057650425557712365022
% SZS output start Proof for 2042057650425557712365022
6. ! [X0] : ((kind(X0) & generous(X0)) <=> (~wise(X0) | old(X0))) [input p5]
8. ! [X0] : ((~kind(X0) & curious(X0)) <=> (quiet(X0) | kind(X0))) [input p7]
24. old(susan) [input hypothesis]
48. ! [X0] : (((kind(X0) & generous(X0)) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | (~kind(X0) | ~generous(X0)))) [nnf transformation 6]
49. ! [X0] : (((kind(X0) & generous(X0)) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | ~kind(X0) | ~generous(X0))) [flattening 48]
50. ! [X0] : (((~kind(X0) & curious(X0)) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | (kind(X0) | ~curious(X0)))) [nnf transformation 8]
51. ! [X0] : (((~kind(X0) & curious(X0)) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | kind(X0) | ~curious(X0))) [flattening 50]
100. ~old(X0) | kind(X0) [cnf transformation 49]
106. ~kind(X0) | ~kind(X0) [cnf transformation 51]
141. old(susan) [cnf transformation 24]
143. ~kind(X0) [duplicate literal removal 106]
300. kind(susan) [resolution 100,141]
301. $false [subsumption resolution 300,143]
% SZS output end Proof for 2042057650425557712365022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or not curious then alice is either patient or brave.
If mary is not funny then lucy is not humble.
Everyone who is either not creative or wise is both wise and not patient.
Everyone who is wise or creative is rich and vice versa.
Everyone who is both humble and not generous is both old and not curious.
Everyone who is either not old or not creative is not funny or not brave and vice versa.
If paul is either not patient or not quiet then alice is happy or not happy.
If someone is creative or generous then someone is funny.
If someone is not patient or quiet then someone is either curious or not rich.
Everyone who is both not curious and not old is tall and vice versa.
If alice is kind or happy then mary is not creative and vice versa.
Everyone who is both not funny and humble is both not brave and creative.
If someone is either not rich or quiet then lucy is not tall and vice versa.
Everyone who is either tall or brave is both not calm and funny.
Everyone who is both not old and not calm is either not generous or not wise and vice versa.
Everyone who is wise or quiet is wise and vice versa.
Someone is not happy or patient.
John is brave or funny.
Someone is brave or not brave.
Paul is both not patient and not old.
John is rich or patient.
Someone is either curious or not curious.
Mary is either not old or not tall.
Someone is humble. | Alice is not rich. | contradiction | (((quiet(mary)<~>~curious(mary)))=>((patient(alice)<~>brave(alice))))&
((~funny(mary))=>(~humble(lucy)))&
(![X]:((~creative(X)<~>wise(X))=>(wise(X)&~patient(X))))&
(![X]:((wise(X)|creative(X))<=>rich(X)))&
(![X]:((humble(X)&~generous(X))=>(old(X)&~curious(X))))&
(![X]:((~old(X)<~>~creative(X))<=>(~funny(X)|~brave(X))))&
(((~patient(paul)<~>~quiet(paul)))=>((happy(alice)|~happy(alice))))&
((?[X]:((creative(X)|generous(X))))=>(?[X]:(funny(X))))&
((?[X]:((~patient(X)|quiet(X))))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((~curious(X)&~old(X))<=>tall(X)))&
(((kind(alice)|happy(alice)))<=>(~creative(mary)))&
(![X]:((~funny(X)&humble(X))=>(~brave(X)&creative(X))))&
((?[X]:((~rich(X)<~>quiet(X))))<=>(~tall(lucy)))&
(![X]:((tall(X)<~>brave(X))=>(~calm(X)&funny(X))))&
(![X]:((~old(X)&~calm(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((wise(X)|quiet(X))<=>wise(X)))&
(?[X]:((~happy(X)|patient(X))))&
((brave(john)|funny(john)))&
(?[X]:((brave(X)|~brave(X))))&
((~patient(paul)&~old(paul)))&
((rich(john)|patient(john)))&
(?[X]:((curious(X)<~>~curious(X))))&
((~old(mary)<~>~tall(mary)))&
(?[X]:(humble(X))) | ~rich(alice) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 608124998685114990944748
% SZS output start Proof for 608124998685114990944748
3. ! [X0] : ((~creative(X0) <~> wise(X0)) => (~patient(X0) & wise(X0))) [input p2]
4. ! [X0] : ((creative(X0) | wise(X0)) <=> rich(X0)) [input p3]
25. ~rich(alice) [input hypothesis]
30. ! [X0] : ((~patient(X0) & wise(X0)) | (~creative(X0) <=> wise(X0))) [ennf transformation 3]
41. ! [X0] : ((~patient(X0) & wise(X0)) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) [nnf transformation 30]
42. ! [X0] : (((creative(X0) | wise(X0)) | ~rich(X0)) & (rich(X0) | (~creative(X0) & ~wise(X0)))) [nnf transformation 4]
43. ! [X0] : ((creative(X0) | wise(X0) | ~rich(X0)) & (rich(X0) | (~creative(X0) & ~wise(X0)))) [flattening 42]
82. wise(X0) | wise(X0) | creative(X0) [cnf transformation 41]
86. ~wise(X0) | rich(X0) [cnf transformation 43]
87. ~creative(X0) | rich(X0) [cnf transformation 43]
141. ~rich(alice) [cnf transformation 25]
142. wise(X0) | creative(X0) [duplicate literal removal 82]
278. creative(X0) | rich(X0) [resolution 142,86]
279. rich(X0) [subsumption resolution 278,87]
280. $false [resolution 279,141]
% SZS output end Proof for 608124998685114990944748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not curious is not happy or not tall and vice versa. Everyone who is calm is not creative or strong and vice versa. Everyone who is both creative and brave is tall or not old and vice versa. Everyone who is both not generous and not funny is rich or not wise. Everyone who is kind or humble is not wise and vice versa. Everyone who is either not creative or not strong is strong and vice versa. If john is not calm then someone is tall or not patient. If someone is both not curious and not wise then someone is either not tall or not strong and vice versa. Everyone who is not funny or not curious is not strong or old and vice versa. If someone is happy then someone is either not patient or kind and vice versa. Everyone who is generous or brave is both happy and not strong. Everyone who is wise is patient and vice versa. Everyone who is rich or not old is both creative and curious and vice versa. Someone is both not humble and old. John is both generous and old. Lucy is not creative. Someone is not rich or brave. John is not wise or generous. Fred is both not creative and not strong. | Lucy is brave. | neutral | (![X]:((~brave(X)<~>~curious(X))<=>(~happy(X)|~tall(X))))&
(![X]:(calm(X)<=>(~creative(X)|strong(X))))&
(![X]:((creative(X)&brave(X))<=>(tall(X)|~old(X))))&
(![X]:((~generous(X)&~funny(X))=>(rich(X)|~wise(X))))&
(![X]:((kind(X)|humble(X))<=>~wise(X)))&
(![X]:((~creative(X)<~>~strong(X))<=>strong(X)))&
((~calm(john))=>(?[X]:((tall(X)|~patient(X)))))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((~funny(X)|~curious(X))<=>(~strong(X)|old(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((generous(X)|brave(X))=>(happy(X)&~strong(X))))&
(![X]:(wise(X)<=>patient(X)))&
(![X]:((rich(X)|~old(X))<=>(creative(X)&curious(X))))&
(?[X]:((~humble(X)&old(X))))&
((generous(john)&old(john)))&
(~creative(lucy))&
(?[X]:((~rich(X)|brave(X))))&
((~wise(john)|generous(john)))&
((~creative(fred)&~strong(fred))) | brave(lucy) | [] | null | 0 |
If someone is both not curious and happy then lucy is not humble or humble. Everyone who is not calm is either not humble or not happy and vice versa. If someone is curious or happy then susan is both not generous and generous and vice versa. If someone is funny or not happy then someone is not strong and vice versa. Everyone who is both not funny and not generous is both humble and generous and vice versa. If paul is not rich then mary is not kind. If susan is either patient or generous then paul is creative or strong. Everyone who is both not curious and kind is not rich or not quiet. Everyone who is brave or rich is both not old and not patient. Everyone who is both not calm and not rich is patient. If lucy is not calm then someone is either patient or not quiet and vice versa. If someone is not rich then paul is either not curious or happy and vice versa. If lucy is rich or not happy then someone is not patient and vice versa. Everyone who is either not curious or not patient is quiet or old. If someone is quiet then alice is either not funny or not brave. Everyone who is both funny and calm is not humble. Someone is not brave or not happy. Someone is humble. Mary is either not strong or quiet. Mary is both creative and rich. Lucy is both not quiet and rich. Someone is not brave. Someone is not old or quiet. Someone is both old and not rich. | Alice is brave. | neutral | ((?[X]:((~curious(X)&happy(X))))=>((~humble(lucy)|humble(lucy))))&
(![X]:(~calm(X)<=>(~humble(X)<~>~happy(X))))&
((?[X]:((curious(X)|happy(X))))<=>((~generous(susan)&generous(susan))))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~funny(X)&~generous(X))<=>(humble(X)&generous(X))))&
((~rich(paul))=>(~kind(mary)))&
(((patient(susan)<~>generous(susan)))=>((creative(paul)|strong(paul))))&
(![X]:((~curious(X)&kind(X))=>(~rich(X)|~quiet(X))))&
(![X]:((brave(X)|rich(X))=>(~old(X)&~patient(X))))&
(![X]:((~calm(X)&~rich(X))=>patient(X)))&
((~calm(lucy))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:(~rich(X)))<=>((~curious(paul)<~>happy(paul))))&
(((rich(lucy)|~happy(lucy)))<=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)<~>~patient(X))=>(quiet(X)|old(X))))&
((?[X]:(quiet(X)))=>((~funny(alice)<~>~brave(alice))))&
(![X]:((funny(X)&calm(X))=>~humble(X)))&
(?[X]:((~brave(X)|~happy(X))))&
(?[X]:(humble(X)))&
((~strong(mary)<~>quiet(mary)))&
((creative(mary)&rich(mary)))&
((~quiet(lucy)&rich(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~old(X)|quiet(X))))&
(?[X]:((old(X)&~rich(X)))) | brave(alice) | [] | null | 0 |
Everyone who is not generous or not old is quiet or not curious.
Everyone who is happy is quiet and vice versa.
Everyone who is calm or humble is either funny or not humble and vice versa.
Everyone who is not rich or humble is kind or generous and vice versa.
Everyone who is brave or not old is both not wise and curious.
If someone is not patient or not wise then lucy is wise and vice versa.
Everyone who is both not creative and patient is both not humble and happy.
If someone is either not generous or tall then someone is either not happy or generous and vice versa.
If someone is both generous and humble then lucy is both kind and generous and vice versa.
Everyone who is not quiet or creative is not happy or funny.
Everyone who is not creative is funny or not humble and vice versa.
If someone is happy or brave then someone is both not generous and funny.
If susan is either creative or not humble then paul is not patient and vice versa.
Everyone who is either wise or patient is either not generous or not humble.
If susan is generous then susan is happy and vice versa.
If someone is both kind and not humble then fred is either not funny or creative.
Susan is not strong.
Susan is not brave.
Paul is humble.
Someone is either not tall or not rich.
Someone is not creative or creative.
Someone is either wise or not humble.
Someone is not patient.
Someone is both not calm and not tall. | Lucy is not generous. | neutral | (![X]:((~generous(X)|~old(X))=>(quiet(X)|~curious(X))))&
(![X]:(happy(X)<=>quiet(X)))&
(![X]:((calm(X)|humble(X))<=>(funny(X)<~>~humble(X))))&
(![X]:((~rich(X)|humble(X))<=>(kind(X)|generous(X))))&
(![X]:((brave(X)|~old(X))=>(~wise(X)&curious(X))))&
((?[X]:((~patient(X)|~wise(X))))<=>(wise(lucy)))&
(![X]:((~creative(X)&patient(X))=>(~humble(X)&happy(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((generous(X)&humble(X))))<=>((kind(lucy)&generous(lucy))))&
(![X]:((~quiet(X)|creative(X))=>(~happy(X)|funny(X))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(~strong(susan))&
(~brave(susan))&
(humble(paul))&
(?[X]:((~tall(X)<~>~rich(X))))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:((wise(X)<~>~humble(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)&~tall(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is humble is both wise and not quiet and vice versa. Everyone who is both not patient and funny is not tall and vice versa. Everyone who is both not strong and not tall is not curious. If john is either humble or rich then john is either rich or not tall. If someone is not brave then paul is not wise and vice versa. If paul is quiet then someone is patient. If alice is not generous then paul is generous or not happy and vice versa. Everyone who is both quiet and not rich is both not kind and not tall and vice versa. If someone is either not curious or curious then mary is funny or brave and vice versa. If someone is curious or not rich then fred is not quiet or not strong. Everyone who is either funny or curious is either curious or not rich and vice versa. Everyone who is not curious or not strong is not brave or not strong and vice versa. Everyone who is creative or calm is both not kind and not quiet and vice versa. If john is funny or not creative then john is both happy and curious and vice versa. If someone is either strong or tall then alice is both not quiet and not old. If lucy is not creative or rich then john is not tall or not kind and vice versa. Someone is generous. Lucy is old. Mary is both patient and not wise. Paul is curious. Alice is either not rich or not creative. Someone is strong. Someone is not brave. Someone is not quiet. | Fred is old. | neutral | (![X]:(humble(X)<=>(wise(X)&~quiet(X))))&
(![X]:((~patient(X)&funny(X))<=>~tall(X)))&
(![X]:((~strong(X)&~tall(X))=>~curious(X)))&
(((humble(john)<~>rich(john)))=>((rich(john)<~>~tall(john))))&
((?[X]:(~brave(X)))<=>(~wise(paul)))&
((quiet(paul))=>(?[X]:(patient(X))))&
((~generous(alice))<=>((generous(paul)|~happy(paul))))&
(![X]:((quiet(X)&~rich(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((~curious(X)<~>curious(X))))<=>((funny(mary)|brave(mary))))&
((?[X]:((curious(X)|~rich(X))))=>((~quiet(fred)|~strong(fred))))&
(![X]:((funny(X)<~>curious(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~curious(X)|~strong(X))<=>(~brave(X)|~strong(X))))&
(![X]:((creative(X)|calm(X))<=>(~kind(X)&~quiet(X))))&
(((funny(john)|~creative(john)))<=>((happy(john)&curious(john))))&
((?[X]:((strong(X)<~>tall(X))))=>((~quiet(alice)&~old(alice))))&
(((~creative(lucy)|rich(lucy)))<=>((~tall(john)|~kind(john))))&
(?[X]:(generous(X)))&
(old(lucy))&
((patient(mary)&~wise(mary)))&
(curious(paul))&
((~rich(alice)<~>~creative(alice)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X)))&
(?[X]:(~quiet(X))) | old(fred) | [] | null | 0 |
If someone is both not humble and not happy then paul is either humble or quiet and vice versa.
Everyone who is not rich is not happy or not generous.
Everyone who is either not strong or not calm is not patient.
If paul is not calm or curious then someone is either not quiet or humble and vice versa.
Everyone who is either not calm or calm is either not happy or brave and vice versa.
Everyone who is not old or not brave is not strong and vice versa.
Everyone who is both brave and not patient is either rich or old and vice versa.
Everyone who is not funny is both happy and not kind and vice versa.
Everyone who is not strong or not creative is not patient and vice versa.
Everyone who is both not old and quiet is not wise or not quiet and vice versa.
If john is either not quiet or brave then someone is generous.
Everyone who is not wise is happy.
If someone is both quiet and not generous then someone is both creative and not brave.
If someone is either generous or humble then someone is strong and vice versa.
If alice is not creative then susan is not creative.
If someone is humble or brave then someone is not quiet.
Someone is not happy or not old.
Paul is old.
Someone is both rich and tall.
Someone is not kind or wise.
Alice is either old or tall.
Someone is curious or kind. | Alice is tall. | contradiction | ((?[X]:((~humble(X)&~happy(X))))<=>((humble(paul)<~>quiet(paul))))&
(![X]:(~rich(X)=>(~happy(X)|~generous(X))))&
(![X]:((~strong(X)<~>~calm(X))=>~patient(X)))&
(((~calm(paul)|curious(paul)))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~old(X)|~brave(X))<=>~strong(X)))&
(![X]:((brave(X)&~patient(X))<=>(rich(X)<~>old(X))))&
(![X]:(~funny(X)<=>(happy(X)&~kind(X))))&
(![X]:((~strong(X)|~creative(X))<=>~patient(X)))&
(![X]:((~old(X)&quiet(X))<=>(~wise(X)|~quiet(X))))&
(((~quiet(john)<~>brave(john)))=>(?[X]:(generous(X))))&
(![X]:(~wise(X)=>happy(X)))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:((generous(X)<~>humble(X))))<=>(?[X]:(strong(X))))&
((~creative(alice))=>(~creative(susan)))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~quiet(X))))&
(?[X]:((~happy(X)|~old(X))))&
(old(paul))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
((old(alice)<~>tall(alice)))&
(?[X]:((curious(X)|kind(X)))) | tall(alice) | [
"p4",
"p9",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7754327152034031055233705
% SZS output start Proof for 7754327152034031055233705
5. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (~happy(X0) <~> brave(X0))) [input p4]
10. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (~quiet(X0) | ~wise(X0))) [input p9]
12. ! [X0] : (~wise(X0) => happy(X0)) [input p11]
16. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~quiet(X0) [input p15]
21. old(alice) <~> tall(alice) [input p20]
23. tall(alice) [input hypothesis]
26. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~quiet(X1) [rectify 16]
31. ! [X0] : (happy(X0) | wise(X0)) [ennf transformation 12]
34. ? [X1] : ~quiet(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 26]
45. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 5]
52. ! [X0] : (((quiet(X0) & ~old(X0)) | (quiet(X0) & wise(X0))) & ((~quiet(X0) | ~wise(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 10]
53. ! [X0] : (((quiet(X0) & ~old(X0)) | (quiet(X0) & wise(X0))) & (~quiet(X0) | ~wise(X0) | ~quiet(X0) | old(X0))) [flattening 52]
65. ? [X0] : ~quiet(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 34]
66. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
67. ~quiet(sK6) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 65,66]
74. (~tall(alice) | ~old(alice)) & (tall(alice) | old(alice)) [nnf transformation 21]
92. brave(X0) | ~happy(X0) | calm(X0) | calm(X0) [cnf transformation 45]
93. brave(X0) | ~happy(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
112. ~quiet(X0) | ~wise(X0) | ~quiet(X0) | old(X0) [cnf transformation 53]
116. quiet(X0) | quiet(X0) [cnf transformation 53]
119. wise(X0) | happy(X0) [cnf transformation 31]
128. ~quiet(sK6) | ~brave(X1) [cnf transformation 67]
135. ~tall(alice) | ~old(alice) [cnf transformation 74]
137. tall(alice) [cnf transformation 23]
138. ~quiet(X0) | ~wise(X0) | old(X0) [duplicate literal removal 112]
139. quiet(X0) [duplicate literal removal 116]
140. brave(X0) | ~happy(X0) | calm(X0) [duplicate literal removal 92]
141. brave(X0) | ~happy(X0) | ~calm(X0) [duplicate literal removal 93]
198. ~happy(X0) | brave(X0) [subsumption resolution 140,141]
199. ~wise(X0) | old(X0) [subsumption resolution 138,139]
259. ~brave(X1) [subsumption resolution 128,139]
280. 29 <=> old(alice) [avatar definition]
282. ~old(alice) <- (~29) [avatar component clause 280]
284. 30 <=> tall(alice) [avatar definition]
287. ~29 | ~30 [avatar split clause 135,284,280]
298. 30 [avatar split clause 137,284]
317. old(X0) | happy(X0) [resolution 199,119]
320. happy(alice) <- (~29) [resolution 317,282]
328. brave(alice) <- (~29) [resolution 320,198]
329. $false <- (~29) [subsumption resolution 328,259]
330. 29 [avatar contradiction clause 329]
331. $false [avatar sat refutation 287,298,330]
% SZS output end Proof for 7754327152034031055233705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or old then someone is not happy or generous.
If susan is both humble and patient then someone is old or not quiet.
If lucy is generous or curious then someone is creative or not humble.
Everyone who is either not kind or strong is either curious or old.
If john is not kind or not old then someone is either curious or funny.
Everyone who is either not brave or not tall is both not happy and curious and vice versa.
Everyone who is wise or not curious is either rich or brave.
If lucy is generous or not happy then john is not patient or old and vice versa.
If someone is both wise and not funny then john is rich and vice versa.
If someone is both not humble and wise then paul is either not humble or patient.
If someone is funny or not tall then lucy is not wise.
Everyone who is not old or not curious is either not kind or brave and vice versa.
Everyone who is not kind or rich is quiet or wise.
Everyone who is either old or not old is happy and vice versa.
If alice is both brave and curious then someone is not happy and vice versa.
Everyone who is either strong or generous is humble or not patient.
Mary is both not kind and wise.
Someone is not tall or creative.
Someone is not strong or not generous.
Alice is both not brave and curious.
Someone is either humble or not kind.
Lucy is quiet or not creative.
Someone is not old. | Alice is not tall. | entailment | ((?[X]:((kind(X)<~>old(X))))=>(?[X]:((~happy(X)|generous(X)))))&
(((humble(susan)&patient(susan)))=>(?[X]:((old(X)|~quiet(X)))))&
(((generous(lucy)|curious(lucy)))=>(?[X]:((creative(X)|~humble(X)))))&
(![X]:((~kind(X)<~>strong(X))=>(curious(X)<~>old(X))))&
(((~kind(john)|~old(john)))=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((~brave(X)<~>~tall(X))<=>(~happy(X)&curious(X))))&
(![X]:((wise(X)|~curious(X))=>(rich(X)<~>brave(X))))&
(((generous(lucy)|~happy(lucy)))<=>((~patient(john)|old(john))))&
((?[X]:((wise(X)&~funny(X))))<=>(rich(john)))&
((?[X]:((~humble(X)&wise(X))))=>((~humble(paul)<~>patient(paul))))&
((?[X]:((funny(X)|~tall(X))))=>(~wise(lucy)))&
(![X]:((~old(X)|~curious(X))<=>(~kind(X)<~>brave(X))))&
(![X]:((~kind(X)|rich(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)<~>~old(X))<=>happy(X)))&
(((brave(alice)&curious(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((strong(X)<~>generous(X))=>(humble(X)|~patient(X))))&
((~kind(mary)&wise(mary)))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((~strong(X)|~generous(X))))&
((~brave(alice)&curious(alice)))&
(?[X]:((humble(X)<~>~kind(X))))&
((quiet(lucy)|~creative(lucy)))&
(?[X]:(~old(X))) | ~tall(alice) | [
"p5",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7037699718378280548349248
% SZS output start Proof for 7037699718378280548349248
6. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (curious(X0) & ~happy(X0))) [input p5]
14. ! [X0] : ((old(X0) <~> ~old(X0)) <=> happy(X0)) [input p13]
20. curious(alice) & ~brave(alice) [input p19]
24. tall(alice) [input hypothesis]
51. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (~curious(X0) | happy(X0))) & ((curious(X0) & ~happy(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 6]
52. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | ~curious(X0) | happy(X0)) & ((curious(X0) & ~happy(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [flattening 51]
63. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ~happy(X0)) & (happy(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 14]
92. ~tall(X0) | ~happy(X0) | brave(X0) [cnf transformation 52]
121. happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 63]
122. happy(X0) | old(X0) | old(X0) [cnf transformation 63]
134. ~brave(alice) [cnf transformation 20]
140. tall(alice) [cnf transformation 24]
141. happy(X0) | ~old(X0) [duplicate literal removal 121]
142. happy(X0) | old(X0) [duplicate literal removal 122]
269. happy(X0) [subsumption resolution 141,142]
272. 29 <=> brave(alice) [avatar definition]
274. ~brave(alice) <- (~29) [avatar component clause 272]
299. ~29 [avatar split clause 134,272]
323. ~happy(alice) | brave(alice) [resolution 92,140]
324. brave(alice) [subsumption resolution 323,269]
325. $false <- (~29) [subsumption resolution 324,274]
326. 29 [avatar contradiction clause 325]
327. $false [avatar sat refutation 299,326]
% SZS output end Proof for 7037699718378280548349248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not patient and kind is both not calm and kind. If someone is both not quiet and kind then someone is kind and vice versa. Everyone who is old or kind is not kind. Everyone who is either wise or not quiet is both not old and funny and vice versa. If mary is quiet or not humble then someone is either kind or old and vice versa. If lucy is not brave then someone is strong or old and vice versa. Everyone who is not kind is either kind or not generous and vice versa. If someone is rich then someone is both not rich and wise. If someone is kind then alice is happy or not tall and vice versa. If someone is either not humble or not wise then someone is happy. If someone is not creative or strong then mary is not calm or creative and vice versa. Everyone who is both tall and not kind is either not creative or quiet and vice versa. If someone is both not humble and not rich then fred is kind or creative. Everyone who is not strong or humble is not wise and vice versa. If alice is either patient or not generous then paul is not humble. Everyone who is either calm or kind is not rich or not creative. John is not creative or brave. Someone is curious. Someone is either not curious or funny. John is not creative or not happy. Paul is both not quiet and patient. Paul is brave. Mary is either kind or humble. | Alice is not tall. | contradiction | (![X]:((~patient(X)&kind(X))=>(~calm(X)&kind(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:(kind(X))))&
(![X]:((old(X)|kind(X))=>~kind(X)))&
(![X]:((wise(X)<~>~quiet(X))<=>(~old(X)&funny(X))))&
(((quiet(mary)|~humble(mary)))<=>(?[X]:((kind(X)<~>old(X)))))&
((~brave(lucy))<=>(?[X]:((strong(X)|old(X)))))&
(![X]:(~kind(X)<=>(kind(X)<~>~generous(X))))&
((?[X]:(rich(X)))=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:(kind(X)))<=>((happy(alice)|~tall(alice))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(?[X]:(happy(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~calm(mary)|creative(mary))))&
(![X]:((tall(X)&~kind(X))<=>(~creative(X)<~>quiet(X))))&
((?[X]:((~humble(X)&~rich(X))))=>((kind(fred)|creative(fred))))&
(![X]:((~strong(X)|humble(X))<=>~wise(X)))&
(((patient(alice)<~>~generous(alice)))=>(~humble(paul)))&
(![X]:((calm(X)<~>kind(X))=>(~rich(X)|~creative(X))))&
((~creative(john)|brave(john)))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)<~>funny(X))))&
((~creative(john)|~happy(john)))&
((~quiet(paul)&patient(paul)))&
(brave(paul))&
((kind(mary)<~>humble(mary))) | ~tall(alice) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 458172374307058709991085
% SZS output start Proof for 458172374307058709991085
3. ! [X0] : ((kind(X0) | old(X0)) => ~kind(X0)) [input p2]
9. ? [X0] : kind(X0) <=> (~tall(alice) | happy(alice)) [input p8]
24. ~tall(alice) [input hypothesis]
30. ! [X0] : (~kind(X0) | (~kind(X0) & ~old(X0))) [ennf transformation 3]
58. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & ((~tall(alice) | happy(alice)) | ! [X0] : ~kind(X0)) [nnf transformation 9]
59. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X0] : ~kind(X0)) [flattening 58]
60. (? [X0] : kind(X0) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X1] : ~kind(X1)) [rectify 59]
61. ? [X0] : kind(X0) => kind(sK5) [choice axiom]
62. (kind(sK5) | (tall(alice) & ~happy(alice))) & (~tall(alice) | happy(alice) | ! [X1] : ~kind(X1)) [skolemisation 60,61]
90. ~kind(X0) | ~kind(X0) [cnf transformation 30]
114. kind(sK5) | tall(alice) [cnf transformation 62]
145. ~tall(alice) [cnf transformation 24]
148. ~kind(X0) [duplicate literal removal 90]
150. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
151. ~kind(X1) <- (1) [avatar component clause 150]
170. 1 [avatar split clause 148,150]
229. 18 <=> tall(alice) [avatar definition]
233. 19 <=> kind(sK5) [avatar definition]
235. kind(sK5) <- (19) [avatar component clause 233]
236. 18 | 19 [avatar split clause 114,233,229]
330. ~18 [avatar split clause 145,229]
331. $false <- (1, 19) [resolution 235,151]
332. ~1 | ~19 [avatar contradiction clause 331]
333. $false [avatar sat refutation 170,236,330,332]
% SZS output end Proof for 458172374307058709991085
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and kind then someone is either not brave or kind.
If someone is not funny then john is not happy or happy.
Everyone who is creative or not calm is not kind or not curious and vice versa.
Everyone who is rich or not strong is not brave or not kind and vice versa.
Everyone who is not kind or patient is both not brave and not tall.
Everyone who is creative is rich and vice versa.
If alice is rich then mary is both patient and not happy and vice versa.
Everyone who is not kind is funny or creative.
If susan is not happy then someone is both not happy and not kind.
Everyone who is not generous or not calm is either funny or patient and vice versa.
Everyone who is both quiet and not tall is both generous and not wise and vice versa.
Everyone who is not curious or not generous is generous.
Everyone who is either creative or not happy is old or happy.
Everyone who is both not curious and not funny is not patient or happy and vice versa.
Everyone who is either not old or not funny is both kind and not strong and vice versa.
Everyone who is quiet is generous and vice versa.
Someone is not old.
Someone is either not tall or kind.
Mary is both not curious and not creative.
Someone is either kind or not funny.
Someone is wise. | Alice is kind. | entailment | ((?[X]:((tall(X)&kind(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
((?[X]:(~funny(X)))=>((~happy(john)|happy(john))))&
(![X]:((creative(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)<~>kind(X))))&
((~curious(mary)&~creative(mary)))&
(?[X]:((kind(X)<~>~funny(X))))&
(?[X]:(wise(X))) | kind(alice) | [
"p2",
"p5",
"p6",
"p7",
"p9",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1232413504804642193680116
% SZS output start Proof for 1232413504804642193680116
3. ! [X0] : ((~calm(X0) | creative(X0)) <=> (~curious(X0) | ~kind(X0))) [input p2]
6. ! [X0] : (creative(X0) <=> rich(X0)) [input p5]
7. rich(alice) <=> (~happy(mary) & patient(mary)) [input p6]
8. ! [X0] : (~kind(X0) => (creative(X0) | funny(X0))) [input p7]
10. ! [X0] : ((~calm(X0) | ~generous(X0)) <=> (funny(X0) <~> patient(X0))) [input p9]
14. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p13]
19. ~creative(mary) & ~curious(mary) [input p18]
22. ~kind(alice) [input hypothesis]
28. ! [X0] : ((creative(X0) | funny(X0)) | kind(X0)) [ennf transformation 8]
29. ! [X0] : (creative(X0) | funny(X0) | kind(X0)) [flattening 28]
38. ! [X0] : (((~calm(X0) | creative(X0)) | (curious(X0) & kind(X0))) & ((~curious(X0) | ~kind(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 3]
39. ! [X0] : ((~calm(X0) | creative(X0) | (curious(X0) & kind(X0))) & (~curious(X0) | ~kind(X0) | (calm(X0) & ~creative(X0)))) [flattening 38]
42. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 6]
43. (rich(alice) | (happy(mary) | ~patient(mary))) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [nnf transformation 7]
44. (rich(alice) | happy(mary) | ~patient(mary)) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [flattening 43]
47. ! [X0] : (((~calm(X0) | ~generous(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [nnf transformation 10]
48. ! [X0] : ((~calm(X0) | ~generous(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (calm(X0) & generous(X0)))) [flattening 47]
52. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 14]
53. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 52]
72. ~calm(X0) | creative(X0) | kind(X0) [cnf transformation 39]
73. ~calm(X0) | creative(X0) | curious(X0) [cnf transformation 39]
82. ~creative(X0) | rich(X0) [cnf transformation 42]
84. patient(mary) | ~rich(alice) [cnf transformation 44]
85. ~happy(mary) | ~rich(alice) [cnf transformation 44]
87. creative(X0) | funny(X0) | kind(X0) [cnf transformation 29]
93. ~patient(X0) | ~funny(X0) | calm(X0) [cnf transformation 48]
104. ~patient(X0) | happy(X0) | funny(X0) | curious(X0) [cnf transformation 53]
107. ~funny(X0) | patient(X0) [cnf transformation 53]
120. ~curious(mary) [cnf transformation 19]
121. ~creative(mary) [cnf transformation 19]
125. ~kind(alice) [cnf transformation 22]
142. 4 <=> patient(mary) [avatar definition]
143. patient(mary) <- (4) [avatar component clause 142]
146. 5 <=> happy(mary) [avatar definition]
150. 6 <=> rich(alice) [avatar definition]
151. ~rich(alice) <- (~6) [avatar component clause 150]
154. ~6 | ~5 [avatar split clause 85,146,150]
155. ~6 | 4 [avatar split clause 84,142,150]
191. rich(X0) | kind(X0) | funny(X0) [resolution 87,82]
197. 15 <=> funny(mary) [avatar definition]
205. 16 <=> calm(mary) [avatar definition]
206. ~calm(mary) <- (~16) [avatar component clause 205]
207. calm(mary) <- (16) [avatar component clause 205]
215. creative(mary) | curious(mary) <- (16) [resolution 207,73]
217. curious(mary) <- (16) [subsumption resolution 215,121]
218. $false <- (16) [subsumption resolution 217,120]
219. ~16 [avatar contradiction clause 218]
220. ~funny(mary) | calm(mary) <- (4) [resolution 143,93]
259. happy(mary) | funny(mary) | curious(mary) <- (4) [resolution 104,143]
297. ~funny(mary) <- (4, ~16) [subsumption resolution 220,206]
298. ~15 | ~4 | 16 [avatar split clause 297,205,142,197]
299. happy(mary) | funny(mary) <- (4) [subsumption resolution 259,120]
300. 15 | 5 | ~4 [avatar split clause 299,142,146,197]
302. kind(alice) | funny(alice) <- (~6) [resolution 151,191]
303. funny(alice) <- (~6) [subsumption resolution 302,125]
310. patient(alice) <- (~6) [resolution 303,107]
361. ~funny(alice) | calm(alice) <- (~6) [resolution 310,93]
365. calm(alice) <- (~6) [subsumption resolution 361,303]
408. creative(alice) | kind(alice) <- (~6) [resolution 365,72]
414. 31 <=> creative(alice) [avatar definition]
416. creative(alice) <- (31) [avatar component clause 414]
418. creative(alice) <- (~6) [subsumption resolution 408,125]
419. 31 | 6 [avatar split clause 418,150,414]
428. rich(alice) <- (31) [resolution 416,82]
429. $false <- (~6, 31) [subsumption resolution 428,151]
430. 6 | ~31 [avatar contradiction clause 429]
431. $false [avatar sat refutation 154,155,219,298,300,419,430]
% SZS output end Proof for 1232413504804642193680116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not funny is both not tall and happy and vice versa. Everyone who is tall is not patient or not kind and vice versa. Everyone who is both not brave and not tall is either rich or calm and vice versa. Everyone who is either creative or kind is both quiet and rich. If lucy is old or not patient then someone is both brave and generous and vice versa. Everyone who is both not curious and not funny is not rich. Everyone who is old or not kind is both not curious and kind. If susan is either humble or not brave then paul is either not strong or not generous and vice versa. Everyone who is calm or funny is not strong. Everyone who is both old and not rich is either not brave or not quiet and vice versa. If someone is calm or not patient then fred is either not tall or not wise and vice versa. Everyone who is not creative or calm is calm or not quiet and vice versa. If someone is happy then someone is brave or wise. Everyone who is kind is either patient or not creative. Everyone who is both not curious and not quiet is both not old and funny and vice versa. Everyone who is not brave is not generous or not old and vice versa. Someone is rich or curious. Mary is not rich. Someone is both not patient and calm. Someone is curious or not humble. Someone is both quiet and not patient. Mary is either not tall or wise. | Paul is not wise. | neutral | (![X]:((~tall(X)<~>~funny(X))<=>(~tall(X)&happy(X))))&
(![X]:(tall(X)<=>(~patient(X)|~kind(X))))&
(![X]:((~brave(X)&~tall(X))<=>(rich(X)<~>calm(X))))&
(![X]:((creative(X)<~>kind(X))=>(quiet(X)&rich(X))))&
(((old(lucy)|~patient(lucy)))<=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((~curious(X)&~funny(X))=>~rich(X)))&
(![X]:((old(X)|~kind(X))=>(~curious(X)&kind(X))))&
(((humble(susan)<~>~brave(susan)))<=>((~strong(paul)<~>~generous(paul))))&
(![X]:((calm(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)&~rich(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((calm(X)|~patient(X))))<=>((~tall(fred)<~>~wise(fred))))&
(![X]:((~creative(X)|calm(X))<=>(calm(X)|~quiet(X))))&
((?[X]:(happy(X)))=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(kind(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~old(X)&funny(X))))&
(![X]:(~brave(X)<=>(~generous(X)|~old(X))))&
(?[X]:((rich(X)|curious(X))))&
(~rich(mary))&
(?[X]:((~patient(X)&calm(X))))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((quiet(X)&~patient(X))))&
((~tall(mary)<~>wise(mary))) | ~wise(paul) | [] | null | 0 |
If mary is both brave and kind then fred is either not rich or patient. If lucy is both funny and not tall then someone is either not rich or not old. Everyone who is not wise is either patient or not happy. Everyone who is either brave or not generous is tall. If mary is happy then mary is both happy and not old. If mary is either rich or calm then john is either calm or not generous and vice versa. Everyone who is either curious or quiet is both not wise and creative and vice versa. Everyone who is either not quiet or creative is not old and vice versa. Everyone who is wise is humble and vice versa. If john is not rich or not happy then someone is both not strong and brave and vice versa. Everyone who is both not patient and old is curious or not funny and vice versa. If mary is either rich or not funny then someone is both calm and not brave and vice versa. Everyone who is not strong or brave is either old or not strong. If lucy is wise or not kind then someone is both not creative and tall and vice versa. Everyone who is strong is both happy and not funny. Everyone who is either brave or creative is either not patient or creative. Fred is both not curious and not humble. Someone is both wise and not kind. Lucy is old. Lucy is both rich and not tall. Someone is both kind and happy. Someone is both kind and old. Fred is either kind or not rich. | Mary is not patient. | neutral | (((brave(mary)&kind(mary)))=>((~rich(fred)<~>patient(fred))))&
(((funny(lucy)&~tall(lucy)))=>(?[X]:((~rich(X)<~>~old(X)))))&
(![X]:(~wise(X)=>(patient(X)<~>~happy(X))))&
(![X]:((brave(X)<~>~generous(X))=>tall(X)))&
((happy(mary))=>((happy(mary)&~old(mary))))&
(((rich(mary)<~>calm(mary)))<=>((calm(john)<~>~generous(john))))&
(![X]:((curious(X)<~>quiet(X))<=>(~wise(X)&creative(X))))&
(![X]:((~quiet(X)<~>creative(X))<=>~old(X)))&
(![X]:(wise(X)<=>humble(X)))&
(((~rich(john)|~happy(john)))<=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((~patient(X)&old(X))<=>(curious(X)|~funny(X))))&
(((rich(mary)<~>~funny(mary)))<=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:((~strong(X)|brave(X))=>(old(X)<~>~strong(X))))&
(((wise(lucy)|~kind(lucy)))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:(strong(X)=>(happy(X)&~funny(X))))&
(![X]:((brave(X)<~>creative(X))=>(~patient(X)<~>creative(X))))&
((~curious(fred)&~humble(fred)))&
(?[X]:((wise(X)&~kind(X))))&
(old(lucy))&
((rich(lucy)&~tall(lucy)))&
(?[X]:((kind(X)&happy(X))))&
(?[X]:((kind(X)&old(X))))&
((kind(fred)<~>~rich(fred))) | ~patient(mary) | [] | null | 0 |
If someone is either wise or generous then susan is both not kind and kind. If susan is either wise or not funny then paul is either brave or not funny and vice versa. Everyone who is either calm or not tall is brave. Everyone who is both strong and not generous is either not generous or not quiet. If someone is both creative and rich then someone is either not generous or patient. If someone is both not brave and not strong then someone is not tall or humble and vice versa. Everyone who is either kind or tall is kind or not old and vice versa. Everyone who is not quiet is either curious or generous. If someone is not creative then paul is either not quiet or not tall and vice versa. Everyone who is funny or not strong is both patient and brave. If mary is not old then someone is kind or quiet and vice versa. If paul is either creative or not rich then someone is old or not rich and vice versa. If someone is not old then paul is funny and vice versa. Everyone who is funny or tall is not funny or not quiet. If someone is both not creative and not happy then someone is both not quiet and not wise. Everyone who is both brave and not tall is both not old and creative. Someone is not wise or not kind. Someone is not strong. Mary is either wise or not wise. Susan is either wise or patient. Mary is either not quiet or not funny. Someone is creative or not happy. Lucy is not happy or not quiet. Someone is both patient and quiet. | Paul is not brave. | contradiction | ((?[X]:((wise(X)<~>generous(X))))=>((~kind(susan)&kind(susan))))&
(((wise(susan)<~>~funny(susan)))<=>((brave(paul)<~>~funny(paul))))&
(![X]:((calm(X)<~>~tall(X))=>brave(X)))&
(![X]:((strong(X)&~generous(X))=>(~generous(X)<~>~quiet(X))))&
((?[X]:((creative(X)&rich(X))))=>(?[X]:((~generous(X)<~>patient(X)))))&
((?[X]:((~brave(X)&~strong(X))))<=>(?[X]:((~tall(X)|humble(X)))))&
(![X]:((kind(X)<~>tall(X))<=>(kind(X)|~old(X))))&
(![X]:(~quiet(X)=>(curious(X)<~>generous(X))))&
((?[X]:(~creative(X)))<=>((~quiet(paul)<~>~tall(paul))))&
(![X]:((funny(X)|~strong(X))=>(patient(X)&brave(X))))&
((~old(mary))<=>(?[X]:((kind(X)|quiet(X)))))&
(((creative(paul)<~>~rich(paul)))<=>(?[X]:((old(X)|~rich(X)))))&
((?[X]:(~old(X)))<=>(funny(paul)))&
(![X]:((funny(X)|tall(X))=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)&~happy(X))))=>(?[X]:((~quiet(X)&~wise(X)))))&
(![X]:((brave(X)&~tall(X))=>(~old(X)&creative(X))))&
(?[X]:((~wise(X)|~kind(X))))&
(?[X]:(~strong(X)))&
((wise(mary)<~>~wise(mary)))&
((wise(susan)<~>patient(susan)))&
((~quiet(mary)<~>~funny(mary)))&
(?[X]:((creative(X)|~happy(X))))&
((~happy(lucy)|~quiet(lucy)))&
(?[X]:((patient(X)&quiet(X)))) | ~brave(paul) | [
"p9",
"p10",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2191160994472973636826828
% SZS output start Proof for 2191160994472973636826828
10. ! [X0] : ((~strong(X0) | funny(X0)) => (brave(X0) & patient(X0))) [input p9]
11. ~old(mary) <=> ? [X0] : (quiet(X0) | kind(X0)) [input p10]
13. ? [X0] : ~old(X0) <=> funny(paul) [input p12]
24. ? [X0] : (quiet(X0) & patient(X0)) [input p23]
25. ~brave(paul) [input hypothesis]
35. ! [X0] : ((brave(X0) & patient(X0)) | (strong(X0) & ~funny(X0))) [ennf transformation 10]
61. (~old(mary) | ! [X0] : (~quiet(X0) & ~kind(X0))) & (? [X0] : (quiet(X0) | kind(X0)) | old(mary)) [nnf transformation 11]
62. (~old(mary) | ! [X0] : (~quiet(X0) & ~kind(X0))) & (? [X1] : (quiet(X1) | kind(X1)) | old(mary)) [rectify 61]
63. ? [X1] : (quiet(X1) | kind(X1)) => (quiet(sK4) | kind(sK4)) [choice axiom]
64. (~old(mary) | ! [X0] : (~quiet(X0) & ~kind(X0))) & ((quiet(sK4) | kind(sK4)) | old(mary)) [skolemisation 62,63]
69. (? [X0] : ~old(X0) | ~funny(paul)) & (funny(paul) | ! [X0] : old(X0)) [nnf transformation 13]
70. (? [X0] : ~old(X0) | ~funny(paul)) & (funny(paul) | ! [X1] : old(X1)) [rectify 69]
71. ? [X0] : ~old(X0) => ~old(sK6) [choice axiom]
72. (~old(sK6) | ~funny(paul)) & (funny(paul) | ! [X1] : old(X1)) [skolemisation 70,71]
85. ? [X0] : (quiet(X0) & patient(X0)) => (quiet(sK11) & patient(sK11)) [choice axiom]
86. quiet(sK11) & patient(sK11) [skolemisation 24,85]
124. ~funny(X0) | brave(X0) [cnf transformation 35]
128. ~old(mary) | ~quiet(X0) [cnf transformation 64]
135. funny(paul) | old(X1) [cnf transformation 72]
154. quiet(sK11) [cnf transformation 86]
155. ~brave(paul) [cnf transformation 25]
175. 4 <=> funny(paul) [avatar definition]
177. funny(paul) <- (4) [avatar component clause 175]
179. 5 <=> brave(paul) [avatar definition]
180. ~brave(paul) <- (~5) [avatar component clause 179]
263. 22 <=> ! [X0] : ~quiet(X0) [avatar definition]
264. ~quiet(X0) <- (22) [avatar component clause 263]
266. 23 <=> old(mary) [avatar definition]
268. ~old(mary) <- (~23) [avatar component clause 266]
269. 22 | ~23 [avatar split clause 128,266,263]
317. 34 <=> ! [X1] : old(X1) [avatar definition]
318. old(X1) <- (34) [avatar component clause 317]
319. 34 | 4 [avatar split clause 135,175,317]
376. ~5 [avatar split clause 155,179]
377. $false <- (22) [resolution 264,154]
378. ~22 [avatar contradiction clause 377]
384. brave(paul) <- (4) [resolution 124,177]
385. $false <- (4, ~5) [subsumption resolution 384,180]
386. ~4 | 5 [avatar contradiction clause 385]
391. $false <- (~23, 34) [resolution 318,268]
394. 23 | ~34 [avatar contradiction clause 391]
395. $false [avatar sat refutation 269,319,376,378,386,394]
% SZS output end Proof for 2191160994472973636826828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and happy is strong. If someone is both not patient and rich then lucy is funny or not brave and vice versa. If john is quiet then susan is both not brave and not tall. Everyone who is quiet or not patient is both not rich and quiet and vice versa. Everyone who is both quiet and happy is not kind and vice versa. Everyone who is both happy and kind is kind or not tall and vice versa. Everyone who is patient or not old is rich and vice versa. Everyone who is not creative is not calm or brave. If someone is either happy or not funny then someone is both brave and not brave and vice versa. Everyone who is not kind is not patient. If john is either generous or old then someone is not funny. Everyone who is both not curious and curious is both wise and funny. Everyone who is both calm and happy is both not curious and not humble and vice versa. Everyone who is not humble is both not funny and quiet. Everyone who is both brave and not generous is either not tall or quiet and vice versa. Everyone who is old is either not quiet or not patient and vice versa. Lucy is both strong and generous. John is not quiet or old. Susan is both humble and rich. Paul is creative or not strong. Alice is strong or not quiet. Mary is either not calm or curious. | Lucy is not wise. | neutral | (![X]:((~happy(X)&happy(X))=>strong(X)))&
((?[X]:((~patient(X)&rich(X))))<=>((funny(lucy)|~brave(lucy))))&
((quiet(john))=>((~brave(susan)&~tall(susan))))&
(![X]:((quiet(X)|~patient(X))<=>(~rich(X)&quiet(X))))&
(![X]:((quiet(X)&happy(X))<=>~kind(X)))&
(![X]:((happy(X)&kind(X))<=>(kind(X)|~tall(X))))&
(![X]:((patient(X)|~old(X))<=>rich(X)))&
(![X]:(~creative(X)=>(~calm(X)|brave(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:(~kind(X)=>~patient(X)))&
(((generous(john)<~>old(john)))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&curious(X))=>(wise(X)&funny(X))))&
(![X]:((calm(X)&happy(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)&quiet(X))))&
(![X]:((brave(X)&~generous(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>~patient(X))))&
((strong(lucy)&generous(lucy)))&
((~quiet(john)|old(john)))&
((humble(susan)&rich(susan)))&
((creative(paul)|~strong(paul)))&
((strong(alice)|~quiet(alice)))&
((~calm(mary)<~>curious(mary))) | ~wise(lucy) | [] | null | 0 |
If john is quiet then someone is not rich.
Everyone who is both wise and generous is both funny and not humble and vice versa.
If someone is either strong or not patient then someone is not patient and vice versa.
Everyone who is either not kind or not generous is humble or tall.
If alice is both not humble and not funny then someone is not wise or not creative and vice versa.
If paul is either happy or not calm then someone is not kind or strong.
If someone is either not funny or curious then someone is patient or creative and vice versa.
Everyone who is both quiet and not tall is both tall and not funny.
Everyone who is tall is both rich and funny.
Everyone who is both not creative and not humble is either rich or not funny.
Everyone who is either brave or creative is both wise and not rich and vice versa.
If someone is strong then someone is not strong.
Everyone who is both not curious and rich is both calm and wise and vice versa.
If someone is brave or not humble then someone is quiet or not creative and vice versa.
Everyone who is creative is old or not curious and vice versa.
If lucy is not patient then alice is either tall or old and vice versa.
Alice is not calm or creative.
Someone is wise or not happy.
John is not brave or funny.
Someone is not happy.
Someone is not wise.
Mary is both humble and not patient.
Lucy is either not funny or not happy.
Someone is either rich or patient. | Lucy is not funny. | neutral | ((quiet(john))=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&generous(X))<=>(funny(X)&~humble(X))))&
((?[X]:((strong(X)<~>~patient(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(humble(X)|tall(X))))&
(((~humble(alice)&~funny(alice)))<=>(?[X]:((~wise(X)|~creative(X)))))&
(((happy(paul)<~>~calm(paul)))=>(?[X]:((~kind(X)|strong(X)))))&
((?[X]:((~funny(X)<~>curious(X))))<=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((quiet(X)&~tall(X))=>(tall(X)&~funny(X))))&
(![X]:(tall(X)=>(rich(X)&funny(X))))&
(![X]:((~creative(X)&~humble(X))=>(rich(X)<~>~funny(X))))&
(![X]:((brave(X)<~>creative(X))<=>(wise(X)&~rich(X))))&
((?[X]:(strong(X)))=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&rich(X))<=>(calm(X)&wise(X))))&
((?[X]:((brave(X)|~humble(X))))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:(creative(X)<=>(old(X)|~curious(X))))&
((~patient(lucy))<=>((tall(alice)<~>old(alice))))&
((~calm(alice)|creative(alice)))&
(?[X]:((wise(X)|~happy(X))))&
((~brave(john)|funny(john)))&
(?[X]:(~happy(X)))&
(?[X]:(~wise(X)))&
((humble(mary)&~patient(mary)))&
((~funny(lucy)<~>~happy(lucy)))&
(?[X]:((rich(X)<~>patient(X)))) | ~funny(lucy) | [] | null | 0 |
If lucy is not creative or not rich then someone is not creative or not funny and vice versa.
Everyone who is both humble and creative is generous and vice versa.
Everyone who is both quiet and funny is both not happy and tall.
Everyone who is both not tall and not strong is not creative.
Everyone who is not strong or rich is either generous or quiet.
Everyone who is not patient or not old is both calm and not happy.
If someone is not curious or not old then susan is old or not quiet.
If alice is both generous and not brave then susan is humble.
Everyone who is patient is brave or not patient and vice versa.
If someone is both not patient and not brave then someone is either old or not patient and vice versa.
If someone is both not kind and not quiet then someone is not creative.
If someone is both not creative and not funny then fred is not happy or not old.
If someone is either wise or tall then fred is not kind.
Everyone who is both not rich and creative is not wise or not kind.
Everyone who is either not calm or old is not wise and vice versa.
If someone is humble then someone is not wise or patient and vice versa.
Someone is not old.
Fred is rich.
Someone is not humble.
Someone is tall or not kind.
Someone is old or quiet. | Fred is creative. | neutral | (((~creative(lucy)|~rich(lucy)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((humble(X)&creative(X))<=>generous(X)))&
(![X]:((quiet(X)&funny(X))=>(~happy(X)&tall(X))))&
(![X]:((~tall(X)&~strong(X))=>~creative(X)))&
(![X]:((~strong(X)|rich(X))=>(generous(X)<~>quiet(X))))&
(![X]:((~patient(X)|~old(X))=>(calm(X)&~happy(X))))&
((?[X]:((~curious(X)|~old(X))))=>((old(susan)|~quiet(susan))))&
(((generous(alice)&~brave(alice)))=>(humble(susan)))&
(![X]:(patient(X)<=>(brave(X)|~patient(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((old(X)<~>~patient(X)))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~creative(X)&~funny(X))))=>((~happy(fred)|~old(fred))))&
((?[X]:((wise(X)<~>tall(X))))=>(~kind(fred)))&
(![X]:((~rich(X)&creative(X))=>(~wise(X)|~kind(X))))&
(![X]:((~calm(X)<~>old(X))<=>~wise(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~wise(X)|patient(X)))))&
(?[X]:(~old(X)))&
(rich(fred))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((old(X)|quiet(X)))) | creative(fred) | [] | null | 0 |
Everyone who is not brave or creative is calm or not generous.
If someone is wise or not tall then paul is generous.
Everyone who is patient is not funny and vice versa.
Everyone who is either not rich or rich is not quiet or not generous and vice versa.
If someone is either not generous or calm then susan is either generous or not tall and vice versa.
If someone is not creative then paul is both curious and humble and vice versa.
Everyone who is both not wise and not tall is either not rich or quiet.
Everyone who is both funny and rich is either humble or tall and vice versa.
Everyone who is old is both not generous and happy.
Everyone who is both tall and not kind is both old and not tall and vice versa.
Everyone who is either not humble or not calm is both brave and not rich and vice versa.
If someone is not funny then someone is either not quiet or happy.
Everyone who is not happy or not calm is strong.
If someone is not old or humble then someone is both rich and not generous and vice versa.
If mary is not old or not happy then fred is not brave or funny.
Everyone who is curious or not patient is both old and not calm and vice versa.
Someone is both tall and not old.
Alice is either funny or not quiet.
Someone is both old and rich.
Mary is either not quiet or tall.
Someone is old.
Someone is both not tall and generous.
Fred is patient or not tall.
Someone is rich. | Mary is not old. | neutral | (![X]:((~brave(X)|creative(X))=>(calm(X)|~generous(X))))&
((?[X]:((wise(X)|~tall(X))))=>(generous(paul)))&
(![X]:(patient(X)<=>~funny(X)))&
(![X]:((~rich(X)<~>rich(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((generous(susan)<~>~tall(susan))))&
((?[X]:(~creative(X)))<=>((curious(paul)&humble(paul))))&
(![X]:((~wise(X)&~tall(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((funny(X)&rich(X))<=>(humble(X)<~>tall(X))))&
(![X]:(old(X)=>(~generous(X)&happy(X))))&
(![X]:((tall(X)&~kind(X))<=>(old(X)&~tall(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(brave(X)&~rich(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~happy(X)|~calm(X))=>strong(X)))&
((?[X]:((~old(X)|humble(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
(((~old(mary)|~happy(mary)))=>((~brave(fred)|funny(fred))))&
(![X]:((curious(X)|~patient(X))<=>(old(X)&~calm(X))))&
(?[X]:((tall(X)&~old(X))))&
((funny(alice)<~>~quiet(alice)))&
(?[X]:((old(X)&rich(X))))&
((~quiet(mary)<~>tall(mary)))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)&generous(X))))&
((patient(fred)|~tall(fred)))&
(?[X]:(rich(X))) | ~old(mary) | [] | null | 0 |
If someone is tall then someone is strong and vice versa.
If lucy is not strong or tall then alice is either not creative or curious and vice versa.
If someone is not brave then someone is either patient or not brave.
Everyone who is both not funny and happy is both calm and not quiet and vice versa.
If fred is not generous then john is either not kind or not brave.
Everyone who is both not creative and not old is either not strong or calm and vice versa.
Everyone who is both creative and not kind is creative and vice versa.
Everyone who is both funny and calm is curious or not creative and vice versa.
If john is not humble or not brave then someone is either not curious or wise and vice versa.
If alice is either tall or humble then lucy is both not brave and not funny and vice versa.
If someone is rich or strong then john is not happy.
Everyone who is not quiet or patient is both happy and rich and vice versa.
Everyone who is funny or not curious is both humble and not kind.
Everyone who is not calm is either not generous or not creative.
Everyone who is not patient or rich is either generous or old.
Everyone who is happy is not funny or creative and vice versa.
Someone is generous or brave.
Alice is either not curious or not rich.
John is not creative or not strong.
Someone is kind or rich.
Susan is not tall.
Someone is both generous and funny.
Someone is either calm or not wise.
Lucy is either creative or patient. | Lucy is creative. | entailment | ((?[X]:(tall(X)))<=>(?[X]:(strong(X))))&
(((~strong(lucy)|tall(lucy)))<=>((~creative(alice)<~>curious(alice))))&
((?[X]:(~brave(X)))=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((~funny(X)&happy(X))<=>(calm(X)&~quiet(X))))&
((~generous(fred))=>((~kind(john)<~>~brave(john))))&
(![X]:((~creative(X)&~old(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((creative(X)&~kind(X))<=>creative(X)))&
(![X]:((funny(X)&calm(X))<=>(curious(X)|~creative(X))))&
(((~humble(john)|~brave(john)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(((tall(alice)<~>humble(alice)))<=>((~brave(lucy)&~funny(lucy))))&
((?[X]:((rich(X)|strong(X))))=>(~happy(john)))&
(![X]:((~quiet(X)|patient(X))<=>(happy(X)&rich(X))))&
(![X]:((funny(X)|~curious(X))=>(humble(X)&~kind(X))))&
(![X]:(~calm(X)=>(~generous(X)<~>~creative(X))))&
(![X]:((~patient(X)|rich(X))=>(generous(X)<~>old(X))))&
(![X]:(happy(X)<=>(~funny(X)|creative(X))))&
(?[X]:((generous(X)|brave(X))))&
((~curious(alice)<~>~rich(alice)))&
((~creative(john)|~strong(john)))&
(?[X]:((kind(X)|rich(X))))&
(~tall(susan))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
((creative(lucy)<~>patient(lucy))) | creative(lucy) | [
"p7",
"p11",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5708626193764497763775386
% SZS output start Proof for 5708626193764497763775386
8. ! [X0] : ((calm(X0) & funny(X0)) <=> (~creative(X0) | curious(X0))) [input p7]
12. ! [X0] : ((patient(X0) | ~quiet(X0)) <=> (rich(X0) & happy(X0))) [input p11]
16. ! [X0] : (happy(X0) <=> (creative(X0) | ~funny(X0))) [input p15]
24. creative(lucy) <~> patient(lucy) [input p23]
25. ~creative(lucy) [input hypothesis]
52. ! [X0] : (((calm(X0) & funny(X0)) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | (~calm(X0) | ~funny(X0)))) [nnf transformation 8]
53. ! [X0] : (((calm(X0) & funny(X0)) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ~calm(X0) | ~funny(X0))) [flattening 52]
61. ! [X0] : (((patient(X0) | ~quiet(X0)) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | (~patient(X0) & quiet(X0)))) [nnf transformation 12]
62. ! [X0] : ((patient(X0) | ~quiet(X0) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | (~patient(X0) & quiet(X0)))) [flattening 61]
65. ! [X0] : ((happy(X0) | (~creative(X0) & funny(X0))) & ((creative(X0) | ~funny(X0)) | ~happy(X0))) [nnf transformation 16]
66. ! [X0] : ((happy(X0) | (~creative(X0) & funny(X0))) & (creative(X0) | ~funny(X0) | ~happy(X0))) [flattening 65]
77. (~patient(lucy) | ~creative(lucy)) & (patient(lucy) | creative(lucy)) [nnf transformation 24]
105. funny(X0) | creative(X0) [cnf transformation 53]
123. ~patient(X0) | happy(X0) [cnf transformation 62]
137. creative(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 66]
150. patient(lucy) | creative(lucy) [cnf transformation 77]
152. ~creative(lucy) [cnf transformation 25]
274. ~happy(X0) | creative(X0) [subsumption resolution 137,105]
319. 35 <=> creative(lucy) [avatar definition]
321. ~creative(lucy) <- (~35) [avatar component clause 319]
323. 36 <=> patient(lucy) [avatar definition]
324. patient(lucy) <- (36) [avatar component clause 323]
327. 35 | 36 [avatar split clause 150,323,319]
328. ~35 [avatar split clause 152,319]
335. happy(lucy) <- (36) [resolution 123,324]
366. creative(lucy) <- (36) [resolution 274,335]
368. $false <- (~35, 36) [subsumption resolution 366,321]
369. 35 | ~36 [avatar contradiction clause 368]
370. $false [avatar sat refutation 327,328,369]
% SZS output end Proof for 5708626193764497763775386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is not rich.
Everyone who is not strong or not funny is both old and not rich and vice versa.
Everyone who is both not wise and not creative is either not creative or calm.
Everyone who is either not old or not funny is both brave and creative and vice versa.
Everyone who is both not calm and not creative is either funny or not creative.
Everyone who is either not rich or not brave is either not tall or brave.
If alice is happy or not brave then fred is either wise or creative.
Everyone who is both not creative and not patient is tall and vice versa.
Everyone who is either not happy or not patient is both not calm and not brave.
Everyone who is either not generous or humble is patient and vice versa.
If fred is both kind and curious then someone is not humble.
Everyone who is not tall is both not funny and not humble and vice versa.
Everyone who is both curious and not funny is not humble or humble.
If alice is either curious or generous then someone is not patient and vice versa.
If someone is either not generous or not calm then someone is not patient or not brave.
Everyone who is either kind or humble is either tall or not funny.
John is not creative.
Fred is not brave.
Mary is either not tall or humble.
Someone is either curious or not humble.
Someone is curious.
Susan is wise. | Alice is not creative. | entailment | ((?[X]:(~generous(X)))=>(?[X]:(~rich(X))))&
(![X]:((~strong(X)|~funny(X))<=>(old(X)&~rich(X))))&
(![X]:((~wise(X)&~creative(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(brave(X)&creative(X))))&
(![X]:((~calm(X)&~creative(X))=>(funny(X)<~>~creative(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(~tall(X)<~>brave(X))))&
(((happy(alice)|~brave(alice)))=>((wise(fred)<~>creative(fred))))&
(![X]:((~creative(X)&~patient(X))<=>tall(X)))&
(![X]:((~happy(X)<~>~patient(X))=>(~calm(X)&~brave(X))))&
(![X]:((~generous(X)<~>humble(X))<=>patient(X)))&
(((kind(fred)&curious(fred)))=>(?[X]:(~humble(X))))&
(![X]:(~tall(X)<=>(~funny(X)&~humble(X))))&
(![X]:((curious(X)&~funny(X))=>(~humble(X)|humble(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((kind(X)<~>humble(X))=>(tall(X)<~>~funny(X))))&
(~creative(john))&
(~brave(fred))&
((~tall(mary)<~>humble(mary)))&
(?[X]:((curious(X)<~>~humble(X))))&
(?[X]:(curious(X)))&
(wise(susan)) | ~creative(alice) | [
"p1",
"p3",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1036565657995377083431601
% SZS output start Proof for 1036565657995377083431601
2. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> (~rich(X0) & old(X0))) [input p1]
4. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> (creative(X0) & brave(X0))) [input p3]
6. ! [X0] : ((~rich(X0) <~> ~brave(X0)) => (~tall(X0) <~> brave(X0))) [input p5]
8. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> tall(X0)) [input p7]
12. ! [X0] : (~tall(X0) <=> (~humble(X0) & ~funny(X0))) [input p11]
23. creative(alice) [input hypothesis]
31. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~rich(X0) <=> ~brave(X0))) [ennf transformation 6]
43. ! [X0] : (((~funny(X0) | ~strong(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (funny(X0) & strong(X0)))) [nnf transformation 2]
44. ! [X0] : ((~funny(X0) | ~strong(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (funny(X0) & strong(X0)))) [flattening 43]
46. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 4]
47. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [flattening 46]
49. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0)))) [nnf transformation 31]
51. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (patient(X0) | creative(X0)))) [nnf transformation 8]
52. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | patient(X0) | creative(X0))) [flattening 51]
57. ! [X0] : ((~tall(X0) | (humble(X0) | funny(X0))) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [nnf transformation 12]
58. ! [X0] : ((~tall(X0) | humble(X0) | funny(X0)) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [flattening 57]
76. old(X0) | funny(X0) [cnf transformation 44]
78. ~rich(X0) | funny(X0) [cnf transformation 44]
83. brave(X0) | ~old(X0) | funny(X0) [cnf transformation 47]
92. ~brave(X0) | tall(X0) | ~brave(X0) | rich(X0) [cnf transformation 49]
99. ~tall(X0) | ~creative(X0) [cnf transformation 52]
110. ~funny(X0) | tall(X0) [cnf transformation 58]
132. creative(alice) [cnf transformation 23]
134. ~brave(X0) | tall(X0) | rich(X0) [duplicate literal removal 92]
147. brave(X0) | funny(X0) [subsumption resolution 83,76]
355. tall(X1) | rich(X1) | funny(X1) [resolution 134,147]
365. tall(X1) | funny(X1) [subsumption resolution 355,78]
366. tall(X1) [subsumption resolution 365,110]
455. ~creative(X2) [resolution 366,99]
503. $false [resolution 455,132]
% SZS output end Proof for 1036565657995377083431601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not patient is wise or not humble and vice versa. If susan is either not generous or kind then someone is either humble or not tall. Everyone who is either brave or not tall is either not quiet or not patient. Everyone who is not happy or happy is either not tall or creative. Everyone who is either tall or humble is curious and vice versa. If mary is both not rich and brave then mary is both happy and old. Everyone who is both tall and strong is both generous and old and vice versa. If mary is not happy or not old then someone is both not curious and not old. Everyone who is not old is both brave and kind. Everyone who is either not generous or old is either not humble or quiet. Everyone who is not tall or calm is wise. Everyone who is rich or not tall is both not rich and not happy and vice versa. Everyone who is both creative and kind is not tall or old and vice versa. Everyone who is both tall and not brave is not happy and vice versa. Everyone who is both not generous and brave is not strong or brave and vice versa. If john is not patient or not brave then john is happy and vice versa. Alice is rich or funny. Someone is not rich or curious. Fred is either brave or not calm. Fred is happy. John is either not humble or funny. | Fred is calm. | entailment | (![X]:((quiet(X)|~patient(X))<=>(wise(X)|~humble(X))))&
(((~generous(susan)<~>kind(susan)))=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:((brave(X)<~>~tall(X))=>(~quiet(X)<~>~patient(X))))&
(![X]:((~happy(X)|happy(X))=>(~tall(X)<~>creative(X))))&
(![X]:((tall(X)<~>humble(X))<=>curious(X)))&
(((~rich(mary)&brave(mary)))=>((happy(mary)&old(mary))))&
(![X]:((tall(X)&strong(X))<=>(generous(X)&old(X))))&
(((~happy(mary)|~old(mary)))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:(~old(X)=>(brave(X)&kind(X))))&
(![X]:((~generous(X)<~>old(X))=>(~humble(X)<~>quiet(X))))&
(![X]:((~tall(X)|calm(X))=>wise(X)))&
(![X]:((rich(X)|~tall(X))<=>(~rich(X)&~happy(X))))&
(![X]:((creative(X)&kind(X))<=>(~tall(X)|old(X))))&
(![X]:((tall(X)&~brave(X))<=>~happy(X)))&
(![X]:((~generous(X)&brave(X))<=>(~strong(X)|brave(X))))&
(((~patient(john)|~brave(john)))<=>(happy(john)))&
((rich(alice)|funny(alice)))&
(?[X]:((~rich(X)|curious(X))))&
((brave(fred)<~>~calm(fred)))&
(happy(fred))&
((~humble(john)<~>funny(john))) | calm(fred) | [
"p11",
"p13",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 619730241309964789910816
% SZS output start Proof for 619730241309964789910816
12. ! [X0] : ((~tall(X0) | rich(X0)) <=> (~happy(X0) & ~rich(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & tall(X0)) <=> ~happy(X0)) [input p13]
19. brave(fred) <~> ~calm(fred) [input p18]
20. happy(fred) [input p19]
22. ~calm(fred) [input hypothesis]
45. ! [X0] : (((~tall(X0) | rich(X0)) | (happy(X0) | rich(X0))) & ((~happy(X0) & ~rich(X0)) | (tall(X0) & ~rich(X0)))) [nnf transformation 12]
46. ! [X0] : ((~tall(X0) | rich(X0) | happy(X0) | rich(X0)) & ((~happy(X0) & ~rich(X0)) | (tall(X0) & ~rich(X0)))) [flattening 45]
49. ! [X0] : (((~brave(X0) & tall(X0)) | happy(X0)) & (~happy(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 14]
50. ! [X0] : (((~brave(X0) & tall(X0)) | happy(X0)) & (~happy(X0) | brave(X0) | ~tall(X0))) [flattening 49]
57. (calm(fred) | ~brave(fred)) & (~calm(fred) | brave(fred)) [nnf transformation 19]
100. ~happy(X0) | tall(X0) [cnf transformation 46]
107. ~happy(X0) | brave(X0) | ~tall(X0) [cnf transformation 50]
108. tall(X0) | happy(X0) [cnf transformation 50]
121. calm(fred) | ~brave(fred) [cnf transformation 57]
122. happy(fred) [cnf transformation 20]
125. ~calm(fred) [cnf transformation 22]
184. tall(X0) [subsumption resolution 108,100]
185. ~happy(X0) | brave(X0) [subsumption resolution 107,184]
200. 13 <=> brave(fred) [avatar definition]
202. ~brave(fred) <- (~13) [avatar component clause 200]
204. 14 <=> calm(fred) [avatar definition]
207. ~13 | 14 [avatar split clause 121,204,200]
219. ~14 [avatar split clause 125,204]
240. brave(fred) [resolution 185,122]
243. $false <- (~13) [subsumption resolution 240,202]
244. 13 [avatar contradiction clause 243]
245. $false [avatar sat refutation 207,219,244]
% SZS output end Proof for 619730241309964789910816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is both tall and not quiet.
Everyone who is wise or not old is funny or not brave and vice versa.
Everyone who is not calm is both not strong and wise and vice versa.
If fred is both not strong and kind then lucy is kind.
Everyone who is either patient or not old is not creative or not calm and vice versa.
Everyone who is funny or not brave is either not wise or not kind.
Everyone who is old is curious and vice versa.
Everyone who is generous is funny.
Everyone who is not creative or funny is not brave or tall.
If lucy is curious or humble then alice is kind or not calm and vice versa.
If someone is not humble or rich then susan is funny and vice versa.
Everyone who is either not humble or not calm is not rich and vice versa.
If paul is either not funny or not curious then someone is creative.
If someone is not old or kind then fred is not rich and vice versa.
If someone is quiet or rich then someone is either not patient or brave.
Everyone who is either happy or humble is funny and vice versa.
Someone is either not kind or rich.
Susan is not curious.
Someone is either not kind or funny.
Lucy is happy or rich.
Someone is not strong.
Someone is either not strong or tall.
Someone is old or not creative.
Paul is both rich and not old. | Susan is old. | contradiction | (![X]:(quiet(X)=>(tall(X)&~quiet(X))))&
(![X]:((wise(X)|~old(X))<=>(funny(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~strong(X)&wise(X))))&
(((~strong(fred)&kind(fred)))=>(kind(lucy)))&
(![X]:((patient(X)<~>~old(X))<=>(~creative(X)|~calm(X))))&
(![X]:((funny(X)|~brave(X))=>(~wise(X)<~>~kind(X))))&
(![X]:(old(X)<=>curious(X)))&
(![X]:(generous(X)=>funny(X)))&
(![X]:((~creative(X)|funny(X))=>(~brave(X)|tall(X))))&
(((curious(lucy)|humble(lucy)))<=>((kind(alice)|~calm(alice))))&
((?[X]:((~humble(X)|rich(X))))<=>(funny(susan)))&
(![X]:((~humble(X)<~>~calm(X))<=>~rich(X)))&
(((~funny(paul)<~>~curious(paul)))=>(?[X]:(creative(X))))&
((?[X]:((~old(X)|kind(X))))<=>(~rich(fred)))&
((?[X]:((quiet(X)|rich(X))))=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:((happy(X)<~>humble(X))<=>funny(X)))&
(?[X]:((~kind(X)<~>rich(X))))&
(~curious(susan))&
(?[X]:((~kind(X)<~>funny(X))))&
((happy(lucy)|rich(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:((~strong(X)<~>tall(X))))&
(?[X]:((old(X)|~creative(X))))&
((rich(paul)&~old(paul))) | old(susan) | [
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3418756260635709364643536
% SZS output start Proof for 3418756260635709364643536
7. ! [X0] : (old(X0) <=> curious(X0)) [input p6]
18. ~curious(susan) [input p17]
25. old(susan) [input hypothesis]
44. ! [X0] : ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))) [nnf transformation 7]
95. ~old(X0) | curious(X0) [cnf transformation 44]
123. ~curious(susan) [cnf transformation 18]
133. old(susan) [cnf transformation 25]
281. curious(susan) [resolution 95,133]
282. $false [subsumption resolution 281,123]
% SZS output end Proof for 3418756260635709364643536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either tall or not generous then someone is both not rich and not funny and vice versa.
Everyone who is not funny or brave is not patient and vice versa.
Everyone who is either not creative or happy is both not patient and not funny and vice versa.
Everyone who is both brave and not creative is both kind and strong.
If someone is curious then someone is both patient and tall.
Everyone who is curious or calm is both not happy and not wise and vice versa.
Everyone who is not rich or quiet is not rich or old.
Everyone who is both not old and patient is either not kind or generous.
If someone is tall or old then someone is either not funny or curious.
Everyone who is not strong or not calm is both calm and quiet.
If fred is both not curious and patient then lucy is either not brave or generous.
Everyone who is either rich or wise is curious.
If fred is patient or not humble then susan is both not curious and not funny and vice versa.
Everyone who is both generous and wise is not quiet or not generous and vice versa.
If someone is not calm or calm then mary is not strong and vice versa.
Everyone who is kind or not wise is either not wise or kind.
Fred is both funny and humble.
Someone is not funny.
Alice is not strong.
John is both not curious and generous.
Paul is kind or quiet.
Paul is either not wise or not quiet. | Alice is not happy. | entailment | (((tall(susan)<~>~generous(susan)))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((~funny(X)|brave(X))<=>~patient(X)))&
(![X]:((~creative(X)<~>happy(X))<=>(~patient(X)&~funny(X))))&
(![X]:((brave(X)&~creative(X))=>(kind(X)&strong(X))))&
((?[X]:(curious(X)))=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((curious(X)|calm(X))<=>(~happy(X)&~wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(~rich(X)|old(X))))&
(![X]:((~old(X)&patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
(![X]:((kind(X)|~wise(X))=>(~wise(X)<~>kind(X))))&
((funny(fred)&humble(fred)))&
(?[X]:(~funny(X)))&
(~strong(alice))&
((~curious(john)&generous(john)))&
((kind(paul)|quiet(paul)))&
((~wise(paul)<~>~quiet(paul))) | ~happy(alice) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4985901564971549328691246
% SZS output start Proof for 4985901564971549328691246
6. ! [X0] : ((calm(X0) | curious(X0)) <=> (~wise(X0) & ~happy(X0))) [input p5]
10. ! [X0] : ((~calm(X0) | ~strong(X0)) => (quiet(X0) & calm(X0))) [input p9]
23. happy(alice) [input hypothesis]
34. ! [X0] : ((quiet(X0) & calm(X0)) | (calm(X0) & strong(X0))) [ennf transformation 10]
50. ! [X0] : (((calm(X0) | curious(X0)) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | (~calm(X0) & ~curious(X0)))) [nnf transformation 6]
51. ! [X0] : ((calm(X0) | curious(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | (~calm(X0) & ~curious(X0)))) [flattening 50]
91. ~calm(X0) | ~happy(X0) [cnf transformation 51]
104. calm(X0) | calm(X0) [cnf transformation 34]
137. happy(alice) [cnf transformation 23]
142. calm(X0) [duplicate literal removal 104]
260. ~happy(X0) [resolution 91,142]
261. $false [resolution 260,137]
% SZS output end Proof for 4985901564971549328691246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and humble is either rich or not curious and vice versa.
Everyone who is either happy or calm is not creative and vice versa.
Everyone who is tall or not kind is either not patient or creative.
Everyone who is rich is both funny and not kind and vice versa.
Everyone who is not kind is either quiet or not rich and vice versa.
If susan is either not kind or not generous then susan is both not creative and quiet and vice versa.
If paul is either old or not funny then someone is kind.
If paul is both strong and happy then john is creative or curious.
Everyone who is either humble or not curious is not happy or not tall and vice versa.
Everyone who is happy or funny is either not funny or not rich.
Everyone who is both strong and quiet is both not calm and not humble.
If someone is not funny then paul is both not humble and humble and vice versa.
Everyone who is both not happy and wise is funny.
Everyone who is happy or not strong is both quiet and happy and vice versa.
Everyone who is old is both not patient and strong and vice versa.
If someone is not rich then someone is quiet or not old and vice versa.
Someone is either not strong or calm.
Fred is either funny or not generous.
Someone is creative.
Someone is tall or creative.
Someone is quiet or not wise.
Someone is not curious or not brave.
Fred is humble. | Fred is not strong. | entailment | (![X]:((rich(X)&humble(X))<=>(rich(X)<~>~curious(X))))&
(![X]:((happy(X)<~>calm(X))<=>~creative(X)))&
(![X]:((tall(X)|~kind(X))=>(~patient(X)<~>creative(X))))&
(![X]:(rich(X)<=>(funny(X)&~kind(X))))&
(![X]:(~kind(X)<=>(quiet(X)<~>~rich(X))))&
(((~kind(susan)<~>~generous(susan)))<=>((~creative(susan)&quiet(susan))))&
(((old(paul)<~>~funny(paul)))=>(?[X]:(kind(X))))&
(((strong(paul)&happy(paul)))=>((creative(john)|curious(john))))&
(![X]:((humble(X)<~>~curious(X))<=>(~happy(X)|~tall(X))))&
(![X]:((happy(X)|funny(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((strong(X)&quiet(X))=>(~calm(X)&~humble(X))))&
((?[X]:(~funny(X)))<=>((~humble(paul)&humble(paul))))&
(![X]:((~happy(X)&wise(X))=>funny(X)))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)&happy(X))))&
(![X]:(old(X)<=>(~patient(X)&strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((quiet(X)|~old(X)))))&
(?[X]:((~strong(X)<~>calm(X))))&
((funny(fred)<~>~generous(fred)))&
(?[X]:(creative(X)))&
(?[X]:((tall(X)|creative(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(humble(fred)) | ~strong(fred) | [
"p3",
"p4",
"p9",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1450003476093839574206652
% SZS output start Proof for 1450003476093839574206652
4. ! [X0] : (rich(X0) <=> (~kind(X0) & funny(X0))) [input p3]
5. ! [X0] : (~kind(X0) <=> (quiet(X0) <~> ~rich(X0))) [input p4]
10. ! [X0] : ((funny(X0) | happy(X0)) => (~funny(X0) <~> ~rich(X0))) [input p9]
11. ! [X0] : ((quiet(X0) & strong(X0)) => (~humble(X0) & ~calm(X0))) [input p10]
12. ? [X0] : ~funny(X0) <=> (humble(paul) & ~humble(paul)) [input p11]
23. humble(fred) [input p22]
24. strong(fred) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~rich(X0)) | (~funny(X0) & ~happy(X0))) [ennf transformation 10]
34. ! [X0] : ((~humble(X0) & ~calm(X0)) | (~quiet(X0) | ~strong(X0))) [ennf transformation 11]
35. ! [X0] : ((~humble(X0) & ~calm(X0)) | ~quiet(X0) | ~strong(X0)) [flattening 34]
40. ! [X0] : ((rich(X0) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | ~rich(X0))) [nnf transformation 4]
41. ! [X0] : ((rich(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | ~rich(X0))) [flattening 40]
42. ! [X0] : ((~kind(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0)))) & (((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | kind(X0))) [nnf transformation 5]
50. ! [X0] : (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | (~funny(X0) & ~happy(X0))) [nnf transformation 33]
51. (? [X0] : ~funny(X0) | (~humble(paul) | humble(paul))) & ((humble(paul) & ~humble(paul)) | ! [X0] : funny(X0)) [nnf transformation 12]
52. (? [X0] : ~funny(X0) | ~humble(paul) | humble(paul)) & ((humble(paul) & ~humble(paul)) | ! [X0] : funny(X0)) [flattening 51]
53. (? [X0] : ~funny(X0) | ~humble(paul) | humble(paul)) & ((humble(paul) & ~humble(paul)) | ! [X1] : funny(X1)) [rectify 52]
54. ? [X0] : ~funny(X0) => ~funny(sK1) [choice axiom]
55. (~funny(sK1) | ~humble(paul) | humble(paul)) & ((humble(paul) & ~humble(paul)) | ! [X1] : funny(X1)) [skolemisation 53,54]
87. ~rich(X0) | funny(X0) [cnf transformation 41]
88. ~kind(X0) | ~rich(X0) [cnf transformation 41]
89. ~funny(X0) | kind(X0) | rich(X0) [cnf transformation 41]
93. ~kind(X0) | quiet(X0) | rich(X0) [cnf transformation 42]
110. ~rich(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 50]
114. ~strong(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 35]
115. ~humble(paul) | funny(X1) [cnf transformation 55]
116. humble(paul) | funny(X1) [cnf transformation 55]
135. humble(fred) [cnf transformation 23]
136. strong(fred) [cnf transformation 24]
137. ~rich(X0) | ~funny(X0) [duplicate literal removal 110]
141. ~kind(X0) | quiet(X0) [subsumption resolution 93,88]
200. ~rich(X0) [subsumption resolution 137,87]
202. 12 <=> ! [X1] : funny(X1) [avatar definition]
203. funny(X1) <- (12) [avatar component clause 202]
205. 13 <=> humble(paul) [avatar definition]
208. 12 | 13 [avatar split clause 116,205,202]
209. 12 | ~13 [avatar split clause 115,205,202]
335. kind(X0) | rich(X0) <- (12) [resolution 89,203]
336. kind(X0) <- (12) [subsumption resolution 335,200]
352. quiet(X0) <- (12) [resolution 336,141]
364. ~quiet(fred) | ~humble(fred) [resolution 114,136]
368. ~humble(fred) <- (12) [subsumption resolution 364,352]
369. $false <- (12) [subsumption resolution 368,135]
370. ~12 [avatar contradiction clause 369]
375. $false [avatar sat refutation 208,209,370]
% SZS output end Proof for 1450003476093839574206652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise then someone is old or not tall and vice versa.
Everyone who is brave or not generous is curious.
Everyone who is either quiet or not humble is both generous and wise and vice versa.
Everyone who is not wise or not generous is wise or curious.
Everyone who is tall or quiet is not kind.
Everyone who is both funny and not humble is not curious or curious and vice versa.
If someone is tall then someone is both calm and curious and vice versa.
Everyone who is either generous or not calm is not brave.
If susan is either not curious or creative then mary is either funny or kind.
Everyone who is not funny is either brave or curious and vice versa.
If mary is not generous then someone is either patient or not patient and vice versa.
If fred is either tall or rich then someone is old.
Everyone who is either not brave or curious is both brave and not patient.
If someone is either not funny or calm then john is funny or humble and vice versa.
Everyone who is kind or not brave is old or wise and vice versa.
Mary is either humble or happy.
Someone is funny or not brave.
John is curious or humble.
Mary is not patient or not tall.
John is strong or not quiet.
Fred is either calm or kind.
Fred is tall. | Fred is not quiet. | contradiction | ((~wise(mary))<=>(?[X]:((old(X)|~tall(X)))))&
(![X]:((brave(X)|~generous(X))=>curious(X)))&
(![X]:((quiet(X)<~>~humble(X))<=>(generous(X)&wise(X))))&
(![X]:((~wise(X)|~generous(X))=>(wise(X)|curious(X))))&
(![X]:((tall(X)|quiet(X))=>~kind(X)))&
(![X]:((funny(X)&~humble(X))<=>(~curious(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((calm(X)&curious(X)))))&
(![X]:((generous(X)<~>~calm(X))=>~brave(X)))&
(((~curious(susan)<~>creative(susan)))=>((funny(mary)<~>kind(mary))))&
(![X]:(~funny(X)<=>(brave(X)<~>curious(X))))&
((~generous(mary))<=>(?[X]:((patient(X)<~>~patient(X)))))&
(((tall(fred)<~>rich(fred)))=>(?[X]:(old(X))))&
(![X]:((~brave(X)<~>curious(X))=>(brave(X)&~patient(X))))&
((?[X]:((~funny(X)<~>calm(X))))<=>((funny(john)|humble(john))))&
(![X]:((kind(X)|~brave(X))<=>(old(X)|wise(X))))&
((humble(mary)<~>happy(mary)))&
(?[X]:((funny(X)|~brave(X))))&
((curious(john)|humble(john)))&
((~patient(mary)|~tall(mary)))&
((strong(john)|~quiet(john)))&
((calm(fred)<~>kind(fred)))&
(tall(fred)) | ~quiet(fred) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p9",
"p12",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3189042692648974233864203
% SZS output start Proof for 3189042692648974233864203
2. ! [X0] : ((~generous(X0) | brave(X0)) => curious(X0)) [input p1]
3. ! [X0] : ((quiet(X0) <~> ~humble(X0)) <=> (wise(X0) & generous(X0))) [input p2]
5. ! [X0] : ((quiet(X0) | tall(X0)) => ~kind(X0)) [input p4]
6. ! [X0] : ((~humble(X0) & funny(X0)) <=> (curious(X0) | ~curious(X0))) [input p5]
8. ! [X0] : ((generous(X0) <~> ~calm(X0)) => ~brave(X0)) [input p7]
10. ! [X0] : (~funny(X0) <=> (brave(X0) <~> curious(X0))) [input p9]
13. ! [X0] : ((~brave(X0) <~> curious(X0)) => (~patient(X0) & brave(X0))) [input p12]
21. calm(fred) <~> kind(fred) [input p20]
22. tall(fred) [input p21]
23. ~quiet(fred) [input hypothesis]
26. ! [X0] : (curious(X0) | (generous(X0) & ~brave(X0))) [ennf transformation 2]
29. ! [X0] : (~kind(X0) | (~quiet(X0) & ~tall(X0))) [ennf transformation 5]
30. ! [X0] : (~brave(X0) | (generous(X0) <=> ~calm(X0))) [ennf transformation 8]
33. ! [X0] : ((~patient(X0) & brave(X0)) | (~brave(X0) <=> curious(X0))) [ennf transformation 13]
38. ! [X0] : ((((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | (~wise(X0) | ~generous(X0))) & ((wise(X0) & generous(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0))))) [nnf transformation 3]
39. ! [X0] : ((((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | ~wise(X0) | ~generous(X0)) & ((wise(X0) & generous(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0))))) [flattening 38]
40. ! [X0] : (((~humble(X0) & funny(X0)) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | (humble(X0) | ~funny(X0)))) [nnf transformation 6]
41. ! [X0] : (((~humble(X0) & funny(X0)) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | humble(X0) | ~funny(X0))) [flattening 40]
47. ! [X0] : (~brave(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) [nnf transformation 30]
49. ! [X0] : ((~funny(X0) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | funny(X0))) [nnf transformation 10]
57. ! [X0] : ((~patient(X0) & brave(X0)) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0)))) [nnf transformation 33]
68. (~kind(fred) | ~calm(fred)) & (kind(fred) | calm(fred)) [nnf transformation 21]
72. ~brave(X0) | curious(X0) [cnf transformation 26]
75. humble(X0) | quiet(X0) | generous(X0) [cnf transformation 39]
82. ~kind(X0) | ~tall(X0) [cnf transformation 29]
85. funny(X0) | curious(X0) [cnf transformation 41]
86. ~curious(X0) | funny(X0) [cnf transformation 41]
88. ~humble(X0) | ~curious(X0) [cnf transformation 41]
92. ~calm(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 47]
101. ~funny(X0) | brave(X0) | ~curious(X0) [cnf transformation 49]
108. brave(X0) | curious(X0) | brave(X0) [cnf transformation 57]
127. kind(fred) | calm(fred) [cnf transformation 68]
129. tall(fred) [cnf transformation 22]
130. ~quiet(fred) [cnf transformation 23]
131. brave(X0) | curious(X0) [duplicate literal removal 108]
157. funny(X0) [subsumption resolution 85,86]
195. ~curious(X0) | brave(X0) [subsumption resolution 101,157]
213. 18 <=> tall(fred) [avatar definition]
215. tall(fred) <- (18) [avatar component clause 213]
224. curious(X0) [subsumption resolution 131,72]
238. 22 <=> calm(fred) [avatar definition]
239. calm(fred) <- (22) [avatar component clause 238]
242. 23 <=> kind(fred) [avatar definition]
243. kind(fred) <- (23) [avatar component clause 242]
246. 22 | 23 [avatar split clause 127,242,238]
247. 18 [avatar split clause 129,213]
258. brave(X2) [resolution 195,224]
262. quiet(X1) | generous(X1) | ~curious(X1) [resolution 75,88]
265. quiet(X1) | generous(X1) [subsumption resolution 262,224]
268. generous(fred) [resolution 265,130]
277. ~brave(fred) | ~generous(fred) <- (22) [resolution 92,239]
280. ~generous(fred) <- (22) [subsumption resolution 277,258]
281. $false <- (22) [subsumption resolution 280,268]
282. ~22 [avatar contradiction clause 281]
284. ~tall(fred) <- (23) [resolution 243,82]
285. $false <- (18, 23) [subsumption resolution 284,215]
286. ~18 | ~23 [avatar contradiction clause 285]
287. $false [avatar sat refutation 246,247,282,286]
% SZS output end Proof for 3189042692648974233864203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not wise.
If someone is either not patient or not curious then alice is not calm and vice versa.
If john is not generous then someone is either wise or happy and vice versa.
Everyone who is not generous or not brave is either not humble or curious and vice versa.
If john is not kind or not generous then paul is both not creative and happy.
Everyone who is both not humble and not creative is not kind and vice versa.
Everyone who is both not happy and patient is both not patient and not old.
If john is both strong and patient then someone is not calm or not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Everyone who is not tall or not quiet is not old or generous.
John is not funny.
John is not old.
Someone is patient.
Susan is both curious and old.
Someone is either not tall or funny.
Someone is either strong or creative. | Fred is calm. | neutral | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(~calm(alice)))&
((~generous(john))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((~generous(X)|~brave(X))<=>(~humble(X)<~>curious(X))))&
(((~kind(john)|~generous(john)))=>((~creative(paul)&happy(paul))))&
(![X]:((~humble(X)&~creative(X))<=>~kind(X)))&
(![X]:((~happy(X)&patient(X))=>(~patient(X)&~old(X))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(~funny(john))&
(~old(john))&
(?[X]:(patient(X)))&
((curious(susan)&old(susan)))&
(?[X]:((~tall(X)<~>funny(X))))&
(?[X]:((strong(X)<~>creative(X)))) | calm(fred) | [] | null | 0 |
If someone is not humble or not patient then susan is either tall or not old.
If john is not old or kind then someone is both not humble and funny.
Everyone who is both old and not wise is either not patient or quiet and vice versa.
Everyone who is both brave and not rich is creative.
If mary is either happy or funny then someone is not creative or generous.
If alice is both not generous and not curious then someone is either brave or not funny and vice versa.
Everyone who is quiet is both not humble and not old and vice versa.
Everyone who is both patient and humble is either brave or not patient and vice versa.
If someone is either not wise or funny then someone is both brave and not generous.
If someone is both brave and tall then someone is either not wise or strong and vice versa.
If lucy is both strong and funny then someone is not patient and vice versa.
If mary is curious then someone is not curious.
Everyone who is generous or humble is not rich or old and vice versa.
If mary is either not funny or funny then someone is not brave and vice versa.
Everyone who is curious is either not patient or not rich.
Everyone who is old is tall or brave and vice versa.
Someone is either not happy or not brave.
Someone is not calm or brave.
Lucy is both not brave and not funny.
Susan is not rich or not brave.
Mary is either generous or not patient.
Fred is not creative.
John is not tall. | Fred is old. | entailment | ((?[X]:((~humble(X)|~patient(X))))=>((tall(susan)<~>~old(susan))))&
(((~old(john)|kind(john)))=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:((old(X)&~wise(X))<=>(~patient(X)<~>quiet(X))))&
(![X]:((brave(X)&~rich(X))=>creative(X)))&
(((happy(mary)<~>funny(mary)))=>(?[X]:((~creative(X)|generous(X)))))&
(((~generous(alice)&~curious(alice)))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:(quiet(X)<=>(~humble(X)&~old(X))))&
(![X]:((patient(X)&humble(X))<=>(brave(X)<~>~patient(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(((strong(lucy)&funny(lucy)))<=>(?[X]:(~patient(X))))&
((curious(mary))=>(?[X]:(~curious(X))))&
(![X]:((generous(X)|humble(X))<=>(~rich(X)|old(X))))&
(((~funny(mary)<~>funny(mary)))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>(~patient(X)<~>~rich(X))))&
(![X]:(old(X)<=>(tall(X)|brave(X))))&
(?[X]:((~happy(X)<~>~brave(X))))&
(?[X]:((~calm(X)|brave(X))))&
((~brave(lucy)&~funny(lucy)))&
((~rich(susan)|~brave(susan)))&
((generous(mary)<~>~patient(mary)))&
(~creative(fred))&
(~tall(john)) | old(fred) | [
"p2",
"p6",
"p7",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2115680436315752559735129
% SZS output start Proof for 2115680436315752559735129
3. ! [X0] : ((~wise(X0) & old(X0)) <=> (~patient(X0) <~> quiet(X0))) [input p2]
7. ! [X0] : (quiet(X0) <=> (~old(X0) & ~humble(X0))) [input p6]
8. ! [X0] : ((humble(X0) & patient(X0)) <=> (brave(X0) <~> ~patient(X0))) [input p7]
11. (funny(lucy) & strong(lucy)) <=> ? [X0] : ~patient(X0) [input p10]
16. ! [X0] : (old(X0) <=> (brave(X0) | tall(X0))) [input p15]
19. ~funny(lucy) & ~brave(lucy) [input p18]
24. ~old(fred) [input hypothesis]
40. ! [X0] : (((~wise(X0) & old(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (wise(X0) | ~old(X0)))) [nnf transformation 3]
41. ! [X0] : (((~wise(X0) & old(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) & (((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | wise(X0) | ~old(X0))) [flattening 40]
50. ! [X0] : ((quiet(X0) | (old(X0) | humble(X0))) & ((~old(X0) & ~humble(X0)) | ~quiet(X0))) [nnf transformation 7]
51. ! [X0] : ((quiet(X0) | old(X0) | humble(X0)) & ((~old(X0) & ~humble(X0)) | ~quiet(X0))) [flattening 50]
52. ! [X0] : (((humble(X0) & patient(X0)) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | (~humble(X0) | ~patient(X0)))) [nnf transformation 8]
53. ! [X0] : (((humble(X0) & patient(X0)) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~humble(X0) | ~patient(X0))) [flattening 52]
63. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (~funny(lucy) | ~strong(lucy))) [nnf transformation 11]
64. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ~funny(lucy) | ~strong(lucy)) [flattening 63]
65. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ~funny(lucy) | ~strong(lucy)) [rectify 64]
66. ? [X1] : ~patient(X1) => ~patient(sK6) [choice axiom]
67. ((funny(lucy) & strong(lucy)) | ! [X0] : patient(X0)) & (~patient(sK6) | ~funny(lucy) | ~strong(lucy)) [skolemisation 65,66]
77. ! [X0] : ((old(X0) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | ~old(X0))) [nnf transformation 16]
78. ! [X0] : ((old(X0) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | ~old(X0))) [flattening 77]
92. ~quiet(X0) | ~patient(X0) | old(X0) [cnf transformation 41]
106. quiet(X0) | old(X0) | humble(X0) [cnf transformation 51]
107. ~patient(X0) | brave(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 53]
110. patient(X0) | brave(X0) | patient(X0) [cnf transformation 53]
125. funny(lucy) | patient(X0) [cnf transformation 67]
139. ~brave(X0) | old(X0) [cnf transformation 78]
143. ~funny(lucy) [cnf transformation 19]
149. ~old(fred) [cnf transformation 24]
152. ~patient(X0) | brave(X0) | ~humble(X0) [duplicate literal removal 107]
153. brave(X0) | patient(X0) [duplicate literal removal 110]
155. 1 <=> ! [X0] : patient(X0) [avatar definition]
156. patient(X0) <- (1) [avatar component clause 155]
232. ~humble(X0) | brave(X0) [subsumption resolution 152,153]
283. 29 <=> funny(lucy) [avatar definition]
286. 1 | 29 [avatar split clause 125,283,155]
322. ~29 [avatar split clause 143,283]
381. old(X1) | humble(X1) | ~patient(X1) | old(X1) [resolution 106,92]
384. old(X1) | humble(X1) | ~patient(X1) [duplicate literal removal 381]
386. old(X1) | humble(X1) <- (1) [subsumption resolution 384,156]
387. humble(fred) <- (1) [resolution 386,149]
390. brave(fred) <- (1) [resolution 387,232]
567. old(fred) <- (1) [resolution 390,139]
569. $false <- (1) [subsumption resolution 567,149]
570. ~1 [avatar contradiction clause 569]
571. $false [avatar sat refutation 286,322,570]
% SZS output end Proof for 2115680436315752559735129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and calm is both brave and not strong and vice versa. Everyone who is not rich or not funny is either brave or old and vice versa. Everyone who is either rich or not creative is either generous or not brave and vice versa. Everyone who is curious is either not funny or rich. Everyone who is not curious or not strong is both not happy and quiet and vice versa. Everyone who is both generous and not patient is humble or strong and vice versa. Everyone who is not curious is not humble or not rich. Everyone who is both strong and rich is both brave and not generous. Everyone who is strong is both quiet and creative and vice versa. If mary is both creative and patient then someone is both not happy and tall and vice versa. Everyone who is not creative is tall. If someone is not curious then john is either quiet or not quiet and vice versa. Everyone who is both not humble and not funny is both brave and not strong. Everyone who is not funny is not kind and vice versa. Everyone who is either happy or not rich is not tall or happy and vice versa. If paul is calm then john is both funny and not patient. Someone is both not happy and generous. Mary is not wise or not old. Someone is generous or not calm. Someone is either not wise or funny. Susan is either not quiet or not rich. Someone is wise or not creative. | John is curious. | contradiction | (![X]:((~happy(X)&calm(X))<=>(brave(X)&~strong(X))))&
(![X]:((~rich(X)|~funny(X))<=>(brave(X)<~>old(X))))&
(![X]:((rich(X)<~>~creative(X))<=>(generous(X)<~>~brave(X))))&
(![X]:(curious(X)=>(~funny(X)<~>rich(X))))&
(![X]:((~curious(X)|~strong(X))<=>(~happy(X)&quiet(X))))&
(![X]:((generous(X)&~patient(X))<=>(humble(X)|strong(X))))&
(![X]:(~curious(X)=>(~humble(X)|~rich(X))))&
(![X]:((strong(X)&rich(X))=>(brave(X)&~generous(X))))&
(![X]:(strong(X)<=>(quiet(X)&creative(X))))&
(((creative(mary)&patient(mary)))<=>(?[X]:((~happy(X)&tall(X)))))&
(![X]:(~creative(X)=>tall(X)))&
((?[X]:(~curious(X)))<=>((quiet(john)<~>~quiet(john))))&
(![X]:((~humble(X)&~funny(X))=>(brave(X)&~strong(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(![X]:((happy(X)<~>~rich(X))<=>(~tall(X)|happy(X))))&
((calm(paul))=>((funny(john)&~patient(john))))&
(?[X]:((~happy(X)&generous(X))))&
((~wise(mary)|~old(mary)))&
(?[X]:((generous(X)|~calm(X))))&
(?[X]:((~wise(X)<~>funny(X))))&
((~quiet(susan)<~>~rich(susan)))&
(?[X]:((wise(X)|~creative(X)))) | curious(john) | [
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8078676486939279546538020
% SZS output start Proof for 8078676486939279546538020
5. ! [X0] : ((~strong(X0) | ~curious(X0)) <=> (quiet(X0) & ~happy(X0))) [input p4]
6. ! [X0] : ((~patient(X0) & generous(X0)) <=> (strong(X0) | humble(X0))) [input p5]
8. ! [X0] : ((rich(X0) & strong(X0)) => (~generous(X0) & brave(X0))) [input p7]
9. ! [X0] : (strong(X0) <=> (creative(X0) & quiet(X0))) [input p8]
10. (patient(mary) & creative(mary)) <=> ? [X0] : (tall(X0) & ~happy(X0)) [input p9]
11. ! [X0] : (~creative(X0) => tall(X0)) [input p10]
15. ! [X0] : ((happy(X0) <~> ~rich(X0)) <=> (happy(X0) | ~tall(X0))) [input p14]
23. curious(john) [input hypothesis]
27. ! [X0] : ((~generous(X0) & brave(X0)) | (~rich(X0) | ~strong(X0))) [ennf transformation 8]
28. ! [X0] : ((~generous(X0) & brave(X0)) | ~rich(X0) | ~strong(X0)) [flattening 27]
29. ! [X0] : (tall(X0) | creative(X0)) [ennf transformation 11]
39. ! [X0] : (((~strong(X0) | ~curious(X0)) | (~quiet(X0) | happy(X0))) & ((quiet(X0) & ~happy(X0)) | (strong(X0) & curious(X0)))) [nnf transformation 5]
40. ! [X0] : ((~strong(X0) | ~curious(X0) | ~quiet(X0) | happy(X0)) & ((quiet(X0) & ~happy(X0)) | (strong(X0) & curious(X0)))) [flattening 39]
41. ! [X0] : (((~patient(X0) & generous(X0)) | (~strong(X0) & ~humble(X0))) & ((strong(X0) | humble(X0)) | (patient(X0) | ~generous(X0)))) [nnf transformation 6]
42. ! [X0] : (((~patient(X0) & generous(X0)) | (~strong(X0) & ~humble(X0))) & (strong(X0) | humble(X0) | patient(X0) | ~generous(X0))) [flattening 41]
43. ! [X0] : ((strong(X0) | (~creative(X0) | ~quiet(X0))) & ((creative(X0) & quiet(X0)) | ~strong(X0))) [nnf transformation 9]
44. ! [X0] : ((strong(X0) | ~creative(X0) | ~quiet(X0)) & ((creative(X0) & quiet(X0)) | ~strong(X0))) [flattening 43]
45. ((patient(mary) & creative(mary)) | ! [X0] : (~tall(X0) | happy(X0))) & (? [X0] : (tall(X0) & ~happy(X0)) | (~patient(mary) | ~creative(mary))) [nnf transformation 10]
46. ((patient(mary) & creative(mary)) | ! [X0] : (~tall(X0) | happy(X0))) & (? [X0] : (tall(X0) & ~happy(X0)) | ~patient(mary) | ~creative(mary)) [flattening 45]
47. ((patient(mary) & creative(mary)) | ! [X0] : (~tall(X0) | happy(X0))) & (? [X1] : (tall(X1) & ~happy(X1)) | ~patient(mary) | ~creative(mary)) [rectify 46]
48. ? [X1] : (tall(X1) & ~happy(X1)) => (tall(sK0) & ~happy(sK0)) [choice axiom]
49. ((patient(mary) & creative(mary)) | ! [X0] : (~tall(X0) | happy(X0))) & ((tall(sK0) & ~happy(sK0)) | ~patient(mary) | ~creative(mary)) [skolemisation 47,48]
55. ! [X0] : ((((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0))))) [nnf transformation 15]
56. ! [X0] : ((((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0))))) [flattening 55]
88. ~happy(X0) | strong(X0) [cnf transformation 40]
90. quiet(X0) | strong(X0) [cnf transformation 40]
91. ~quiet(X0) | ~curious(X0) | ~strong(X0) | happy(X0) [cnf transformation 40]
94. ~strong(X0) | generous(X0) [cnf transformation 42]
96. ~patient(X0) | ~strong(X0) [cnf transformation 42]
99. ~generous(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 28]
100. quiet(X0) | ~strong(X0) [cnf transformation 44]
102. strong(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 44]
105. creative(mary) | ~tall(X0) | happy(X0) [cnf transformation 49]
106. patient(mary) | ~tall(X0) | happy(X0) [cnf transformation 49]
107. tall(X0) | creative(X0) [cnf transformation 29]
121. rich(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 56]
133. curious(john) [cnf transformation 23]
135. ~happy(X0) | rich(X0) [duplicate literal removal 121]
138. ~rich(X0) | ~strong(X0) [subsumption resolution 99,94]
139. ~creative(X0) | strong(X0) [subsumption resolution 102,90]
140. quiet(X0) [subsumption resolution 100,90]
142. 1 <=> ! [X0] : (~tall(X0) | happy(X0)) [avatar definition]
143. ~tall(X0) | happy(X0) <- (1) [avatar component clause 142]
145. 2 <=> patient(mary) [avatar definition]
147. patient(mary) <- (2) [avatar component clause 145]
148. 1 | 2 [avatar split clause 106,145,142]
150. 3 <=> creative(mary) [avatar definition]
152. creative(mary) <- (3) [avatar component clause 150]
153. 1 | 3 [avatar split clause 105,150,142]
218. ~strong(mary) <- (2) [resolution 96,147]
219. strong(mary) <- (3) [resolution 139,152]
220. $false <- (2, 3) [subsumption resolution 219,218]
221. ~2 | ~3 [avatar contradiction clause 220]
223. creative(X0) | happy(X0) <- (1) [resolution 143,107]
265. happy(X0) | strong(X0) <- (1) [resolution 223,139]
266. strong(X0) <- (1) [subsumption resolution 265,88]
269. 21 <=> rich(john) [avatar definition]
271. rich(john) <- (21) [avatar component clause 269]
381. ~curious(X2) | ~strong(X2) | happy(X2) [resolution 91,140]
382. ~curious(X2) | happy(X2) <- (1) [subsumption resolution 381,266]
402. happy(john) <- (1) [resolution 382,133]
417. rich(john) <- (1) [resolution 402,135]
422. 21 | ~1 [avatar split clause 417,142,269]
439. ~strong(john) <- (21) [resolution 271,138]
442. $false <- (1, 21) [subsumption resolution 439,266]
443. ~1 | ~21 [avatar contradiction clause 442]
444. $false [avatar sat refutation 148,153,221,422,443]
% SZS output end Proof for 8078676486939279546538020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not funny is patient and vice versa.
Everyone who is not old is not rich or not brave.
Everyone who is both not tall and rich is both rich and not tall and vice versa.
Everyone who is both strong and curious is both not brave and quiet.
Everyone who is both brave and creative is either brave or patient and vice versa.
Everyone who is kind or not kind is not funny and vice versa.
Everyone who is kind or not quiet is either not funny or not strong.
Everyone who is both not strong and kind is either not happy or not humble and vice versa.
If lucy is happy or tall then someone is both not wise and not humble.
If someone is either not tall or rich then john is generous or not calm.
Everyone who is both not brave and not quiet is wise or not kind.
Everyone who is both not quiet and wise is not kind or not quiet and vice versa.
Everyone who is strong is generous or wise and vice versa.
Everyone who is not kind is either humble or creative and vice versa.
If someone is both happy and not old then someone is humble or not wise.
Everyone who is kind is not old or not happy and vice versa.
Someone is both not patient and creative.
Paul is either not brave or patient.
Someone is curious or generous.
Someone is patient or not brave.
Someone is both patient and calm.
Mary is not kind.
Someone is either not creative or not rich.
Someone is either not brave or kind. | Paul is calm. | neutral | (![X]:((~old(X)<~>~funny(X))<=>patient(X)))&
(![X]:(~old(X)=>(~rich(X)|~brave(X))))&
(![X]:((~tall(X)&rich(X))<=>(rich(X)&~tall(X))))&
(![X]:((strong(X)&curious(X))=>(~brave(X)&quiet(X))))&
(![X]:((brave(X)&creative(X))<=>(brave(X)<~>patient(X))))&
(![X]:((kind(X)|~kind(X))<=>~funny(X)))&
(![X]:((kind(X)|~quiet(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~strong(X)&kind(X))<=>(~happy(X)<~>~humble(X))))&
(((happy(lucy)|tall(lucy)))=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((~tall(X)<~>rich(X))))=>((generous(john)|~calm(john))))&
(![X]:((~brave(X)&~quiet(X))=>(wise(X)|~kind(X))))&
(![X]:((~quiet(X)&wise(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(strong(X)<=>(generous(X)|wise(X))))&
(![X]:(~kind(X)<=>(humble(X)<~>creative(X))))&
((?[X]:((happy(X)&~old(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:(kind(X)<=>(~old(X)|~happy(X))))&
(?[X]:((~patient(X)&creative(X))))&
((~brave(paul)<~>patient(paul)))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((patient(X)&calm(X))))&
(~kind(mary))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((~brave(X)<~>kind(X)))) | calm(paul) | [] | null | 0 |
Everyone who is not rich is quiet or curious and vice versa.
If someone is not generous then fred is both not wise and funny and vice versa.
Everyone who is not curious or not calm is either not curious or not patient and vice versa.
Everyone who is not generous or wise is not tall or wise.
Everyone who is both curious and old is strong and vice versa.
Everyone who is not patient or funny is both quiet and not funny and vice versa.
If fred is either patient or not humble then someone is curious or not wise.
Everyone who is not brave or not kind is either happy or not funny and vice versa.
If alice is both tall and calm then someone is either not patient or curious.
If someone is wise or creative then alice is either not brave or humble and vice versa.
If someone is either curious or kind then fred is either not kind or not old.
Everyone who is both not brave and not humble is either generous or old.
If someone is not wise then someone is both not funny and not happy.
If susan is either old or not brave then susan is brave and vice versa.
If john is not old or creative then mary is either rich or not patient.
If someone is not humble or not old then fred is both not old and not calm and vice versa.
Someone is either tall or not generous.
Someone is both generous and curious.
Someone is not curious.
Someone is not happy or creative.
Someone is both not wise and happy.
Susan is brave. | Fred is not generous. | contradiction | (![X]:(~rich(X)<=>(quiet(X)|curious(X))))&
((?[X]:(~generous(X)))<=>((~wise(fred)&funny(fred))))&
(![X]:((~curious(X)|~calm(X))<=>(~curious(X)<~>~patient(X))))&
(![X]:((~generous(X)|wise(X))=>(~tall(X)|wise(X))))&
(![X]:((curious(X)&old(X))<=>strong(X)))&
(![X]:((~patient(X)|funny(X))<=>(quiet(X)&~funny(X))))&
(((patient(fred)<~>~humble(fred)))=>(?[X]:((curious(X)|~wise(X)))))&
(![X]:((~brave(X)|~kind(X))<=>(happy(X)<~>~funny(X))))&
(((tall(alice)&calm(alice)))=>(?[X]:((~patient(X)<~>curious(X)))))&
((?[X]:((wise(X)|creative(X))))<=>((~brave(alice)<~>humble(alice))))&
((?[X]:((curious(X)<~>kind(X))))=>((~kind(fred)<~>~old(fred))))&
(![X]:((~brave(X)&~humble(X))=>(generous(X)<~>old(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~funny(X)&~happy(X)))))&
(((old(susan)<~>~brave(susan)))<=>(brave(susan)))&
(((~old(john)|creative(john)))=>((rich(mary)<~>~patient(mary))))&
((?[X]:((~humble(X)|~old(X))))<=>((~old(fred)&~calm(fred))))&
(?[X]:((tall(X)<~>~generous(X))))&
(?[X]:((generous(X)&curious(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((~wise(X)&happy(X))))&
(brave(susan)) | ~generous(fred) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5535182911119168892648278
% SZS output start Proof for 5535182911119168892648278
2. ? [X0] : ~generous(X0) <=> (funny(fred) & ~wise(fred)) [input p1]
6. ! [X0] : ((funny(X0) | ~patient(X0)) <=> (~funny(X0) & quiet(X0))) [input p5]
23. ~generous(fred) [input hypothesis]
37. (? [X0] : ~generous(X0) | (~funny(fred) | wise(fred))) & ((funny(fred) & ~wise(fred)) | ! [X0] : generous(X0)) [nnf transformation 2]
38. (? [X0] : ~generous(X0) | ~funny(fred) | wise(fred)) & ((funny(fred) & ~wise(fred)) | ! [X0] : generous(X0)) [flattening 37]
39. (? [X0] : ~generous(X0) | ~funny(fred) | wise(fred)) & ((funny(fred) & ~wise(fred)) | ! [X1] : generous(X1)) [rectify 38]
40. ? [X0] : ~generous(X0) => ~generous(sK0) [choice axiom]
41. (~generous(sK0) | ~funny(fred) | wise(fred)) & ((funny(fred) & ~wise(fred)) | ! [X1] : generous(X1)) [skolemisation 39,40]
44. ! [X0] : (((funny(X0) | ~patient(X0)) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | (~funny(X0) & patient(X0)))) [nnf transformation 6]
45. ! [X0] : ((funny(X0) | ~patient(X0) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | (~funny(X0) & patient(X0)))) [flattening 44]
85. funny(fred) | generous(X1) [cnf transformation 41]
98. ~funny(X0) | ~funny(X0) [cnf transformation 45]
146. ~generous(fred) [cnf transformation 23]
149. ~funny(X0) [duplicate literal removal 98]
158. 2 <=> funny(fred) [avatar definition]
159. funny(fred) <- (2) [avatar component clause 158]
167. 4 <=> ! [X1] : generous(X1) [avatar definition]
168. generous(X1) <- (4) [avatar component clause 167]
169. 4 | 2 [avatar split clause 85,158,167]
339. $false <- (2) [subsumption resolution 159,149]
340. ~2 [avatar contradiction clause 339]
341. $false <- (4) [resolution 168,146]
344. ~4 [avatar contradiction clause 341]
345. $false [avatar sat refutation 169,340,344]
% SZS output end Proof for 5535182911119168892648278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and tall is both generous and patient.
If someone is not humble or calm then someone is either not funny or rich.
Everyone who is both brave and patient is both not wise and not humble.
Everyone who is wise is both old and happy.
Everyone who is either not wise or wise is either not generous or not patient.
If someone is either happy or not calm then paul is either not curious or not tall and vice versa.
If someone is either happy or not kind then someone is both not patient and rich.
If someone is either kind or not kind then someone is not brave or not happy and vice versa.
If lucy is either brave or not quiet then someone is both quiet and old and vice versa.
If alice is generous then john is both not quiet and not curious.
If someone is not brave or creative then someone is humble or not tall and vice versa.
Everyone who is both not old and calm is not curious.
Everyone who is not happy is curious and vice versa.
Everyone who is either quiet or curious is either not kind or strong and vice versa.
Everyone who is kind is calm or not quiet and vice versa.
If susan is not rich or funny then someone is both not strong and not calm.
Fred is quiet or generous.
Someone is not kind or quiet.
Susan is either old or tall.
Someone is not rich.
Someone is both creative and not wise.
Someone is either not tall or not calm.
Someone is both quiet and old.
Paul is strong. | Paul is wise. | contradiction | (![X]:((calm(X)&tall(X))=>(generous(X)&patient(X))))&
((?[X]:((~humble(X)|calm(X))))=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((brave(X)&patient(X))=>(~wise(X)&~humble(X))))&
(![X]:(wise(X)=>(old(X)&happy(X))))&
(![X]:((~wise(X)<~>wise(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>((~curious(paul)<~>~tall(paul))))&
((?[X]:((happy(X)<~>~kind(X))))=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:((kind(X)<~>~kind(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
(((brave(lucy)<~>~quiet(lucy)))<=>(?[X]:((quiet(X)&old(X)))))&
((generous(alice))=>((~quiet(john)&~curious(john))))&
((?[X]:((~brave(X)|creative(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~old(X)&calm(X))=>~curious(X)))&
(![X]:(~happy(X)<=>curious(X)))&
(![X]:((quiet(X)<~>curious(X))<=>(~kind(X)<~>strong(X))))&
(![X]:(kind(X)<=>(calm(X)|~quiet(X))))&
(((~rich(susan)|funny(susan)))=>(?[X]:((~strong(X)&~calm(X)))))&
((quiet(fred)|generous(fred)))&
(?[X]:((~kind(X)|quiet(X))))&
((old(susan)<~>tall(susan)))&
(?[X]:(~rich(X)))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((~tall(X)<~>~calm(X))))&
(?[X]:((quiet(X)&old(X))))&
(strong(paul)) | wise(paul) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 328052714641626620174153
% SZS output start Proof for 328052714641626620174153
1. ! [X0] : ((tall(X0) & calm(X0)) => (patient(X0) & generous(X0))) [input p0]
4. ! [X0] : (wise(X0) => (happy(X0) & old(X0))) [input p3]
5. ! [X0] : ((~wise(X0) <~> wise(X0)) => (~generous(X0) <~> ~patient(X0))) [input p4]
6. ? [X0] : (happy(X0) <~> ~calm(X0)) <=> (~curious(paul) <~> ~tall(paul)) [input p5]
13. ! [X0] : (~happy(X0) <=> curious(X0)) [input p12]
14. ! [X0] : ((quiet(X0) <~> curious(X0)) <=> (~kind(X0) <~> strong(X0))) [input p13]
15. ! [X0] : (kind(X0) <=> (~quiet(X0) | calm(X0))) [input p14]
24. strong(paul) [input p23]
25. wise(paul) [input hypothesis]
30. ! [X0] : ((patient(X0) & generous(X0)) | (~tall(X0) | ~calm(X0))) [ennf transformation 1]
31. ! [X0] : ((patient(X0) & generous(X0)) | ~tall(X0) | ~calm(X0)) [flattening 30]
35. ! [X0] : ((happy(X0) & old(X0)) | ~wise(X0)) [ennf transformation 4]
36. ! [X0] : ((~generous(X0) <~> ~patient(X0)) | (~wise(X0) <=> wise(X0))) [ennf transformation 5]
46. ! [X0] : (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 36]
47. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ((~curious(paul) | tall(paul)) & (~tall(paul) | curious(paul)))) & (((tall(paul) | curious(paul)) & (~tall(paul) | ~curious(paul))) | ! [X0] : ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 6]
48. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ((~curious(paul) | tall(paul)) & (~tall(paul) | curious(paul)))) & (((tall(paul) | curious(paul)) & (~tall(paul) | ~curious(paul))) | ! [X1] : ((happy(X1) | calm(X1)) & (~calm(X1) | ~happy(X1)))) [rectify 47]
49. ? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) => ((calm(sK1) | ~happy(sK1)) & (~calm(sK1) | happy(sK1))) [choice axiom]
50. (((calm(sK1) | ~happy(sK1)) & (~calm(sK1) | happy(sK1))) | ((~curious(paul) | tall(paul)) & (~tall(paul) | curious(paul)))) & (((tall(paul) | curious(paul)) & (~tall(paul) | ~curious(paul))) | ! [X1] : ((happy(X1) | calm(X1)) & (~calm(X1) | ~happy(X1)))) [skolemisation 48,49]
69. ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 13]
70. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [nnf transformation 14]
71. ! [X0] : ((kind(X0) | (quiet(X0) & ~calm(X0))) & ((~quiet(X0) | calm(X0)) | ~kind(X0))) [nnf transformation 15]
72. ! [X0] : ((kind(X0) | (quiet(X0) & ~calm(X0))) & (~quiet(X0) | calm(X0) | ~kind(X0))) [flattening 71]
87. ~tall(X0) | generous(X0) | ~calm(X0) [cnf transformation 31]
88. ~tall(X0) | patient(X0) | ~calm(X0) [cnf transformation 31]
96. ~wise(X0) | happy(X0) [cnf transformation 35]
97. ~patient(X0) | ~generous(X0) | wise(X0) | wise(X0) [cnf transformation 46]
98. ~patient(X0) | ~generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 46]
103. tall(paul) | curious(paul) | ~calm(X1) | ~happy(X1) [cnf transformation 50]
133. ~curious(X0) | ~happy(X0) [cnf transformation 69]
136. ~strong(X0) | kind(X0) | curious(X0) | ~quiet(X0) [cnf transformation 70]
139. ~strong(X0) | quiet(X0) | ~kind(X0) | curious(X0) [cnf transformation 70]
142. ~quiet(X0) | calm(X0) | ~kind(X0) [cnf transformation 72]
144. quiet(X0) | kind(X0) [cnf transformation 72]
160. strong(paul) [cnf transformation 24]
161. wise(paul) [cnf transformation 25]
164. ~patient(X0) | ~generous(X0) | wise(X0) [duplicate literal removal 97]
165. ~wise(X0) | ~generous(X0) | ~patient(X0) [duplicate literal removal 98]
187. ~patient(X0) | ~generous(X0) [subsumption resolution 164,165]
189. 5 <=> tall(paul) [avatar definition]
191. tall(paul) <- (5) [avatar component clause 189]
193. 6 <=> curious(paul) [avatar definition]
194. curious(paul) <- (6) [avatar component clause 193]
195. ~curious(paul) <- (~6) [avatar component clause 193]
213. 10 <=> ! [X1] : (~calm(X1) | ~happy(X1)) [avatar definition]
214. ~happy(X1) | ~calm(X1) <- (10) [avatar component clause 213]
215. 10 | 6 | 5 [avatar split clause 103,189,193,213]
374. happy(paul) [resolution 96,161]
386. generous(paul) | ~calm(paul) <- (5) [resolution 87,191]
389. 45 <=> calm(paul) [avatar definition]
390. calm(paul) <- (45) [avatar component clause 389]
391. ~calm(paul) <- (~45) [avatar component clause 389]
393. 46 <=> generous(paul) [avatar definition]
395. generous(paul) <- (46) [avatar component clause 393]
396. ~45 | 46 | ~5 [avatar split clause 386,189,393,389]
405. 48 <=> patient(paul) [avatar definition]
406. patient(paul) <- (48) [avatar component clause 405]
469. kind(paul) | curious(paul) | ~quiet(paul) [resolution 136,160]
470. kind(paul) | ~quiet(paul) <- (~6) [subsumption resolution 469,195]
471. kind(paul) <- (~6) [subsumption resolution 470,144]
480. quiet(paul) | ~kind(paul) | curious(paul) [resolution 139,160]
483. quiet(paul) | curious(paul) <- (~6) [subsumption resolution 480,471]
484. quiet(paul) <- (~6) [subsumption resolution 483,195]
486. calm(paul) | ~kind(paul) <- (~6) [resolution 484,142]
487. ~kind(paul) <- (~6, ~45) [subsumption resolution 486,391]
488. $false <- (~6, ~45) [subsumption resolution 487,471]
489. 6 | 45 [avatar contradiction clause 488]
503. ~happy(paul) <- (6) [resolution 194,133]
504. $false <- (6) [subsumption resolution 503,374]
505. ~6 [avatar contradiction clause 504]
513. ~calm(paul) <- (10) [resolution 214,374]
516. $false <- (10, 45) [subsumption resolution 513,390]
517. ~10 | ~45 [avatar contradiction clause 516]
518. patient(paul) | ~calm(paul) <- (5) [resolution 191,88]
520. patient(paul) <- (5, 45) [subsumption resolution 518,390]
521. 48 | ~5 | ~45 [avatar split clause 520,389,189,405]
528. ~generous(paul) <- (48) [resolution 406,187]
529. $false <- (46, 48) [subsumption resolution 528,395]
530. ~46 | ~48 [avatar contradiction clause 529]
531. $false [avatar sat refutation 215,396,489,505,517,521,530]
% SZS output end Proof for 328052714641626620174153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not quiet is kind or rich and vice versa.
Everyone who is generous or not funny is either creative or not rich.
If someone is either happy or not humble then lucy is not brave or not generous and vice versa.
Everyone who is both brave and not calm is either patient or not brave.
Everyone who is not rich or kind is strong.
If someone is not brave then paul is creative or humble and vice versa.
If someone is either funny or tall then lucy is either happy or rich.
Everyone who is either brave or not rich is either funny or strong.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is curious.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Someone is both not calm and not curious.
Fred is not strong or not creative.
Someone is generous or not kind. | Lucy is not quiet. | contradiction | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|rich(X))))&
(![X]:((generous(X)|~funny(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((happy(X)<~>~humble(X))))<=>((~brave(lucy)|~generous(lucy))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)|kind(X))=>strong(X)))&
((?[X]:(~brave(X)))<=>((creative(paul)|humble(paul))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(lucy)<~>rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(funny(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~calm(X)&~curious(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | ~quiet(lucy) | [
"p1",
"p4",
"p8",
"p9",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7227692848609525257322416
% SZS output start Proof for 7227692848609525257322416
2. ! [X0] : ((~funny(X0) | generous(X0)) => (creative(X0) <~> ~rich(X0))) [input p1]
5. ! [X0] : ((kind(X0) | ~rich(X0)) => strong(X0)) [input p4]
9. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p9]
12. ~happy(lucy) <=> (~creative(fred) <~> rich(fred)) [input p11]
16. ! [X0] : (~happy(X0) <=> rich(X0)) [input p15]
22. ~creative(fred) | ~strong(fred) [input p21]
24. ~quiet(lucy) [input hypothesis]
27. ! [X0] : ((creative(X0) <~> ~rich(X0)) | (funny(X0) & ~generous(X0))) [ennf transformation 2]
30. ! [X0] : (strong(X0) | (~kind(X0) & rich(X0))) [ennf transformation 5]
33. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 9]
37. ! [X0] : (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | (funny(X0) & ~generous(X0))) [nnf transformation 27]
51. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 10]
52. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 51]
55. (~happy(lucy) | ((~creative(fred) | ~rich(fred)) & (rich(fred) | creative(fred)))) & (((~rich(fred) | creative(fred)) & (rich(fred) | ~creative(fred))) | happy(lucy)) [nnf transformation 12]
58. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 16]
76. ~rich(X0) | creative(X0) | funny(X0) [cnf transformation 37]
87. strong(X0) | rich(X0) [cnf transformation 30]
100. ~rich(X0) | quiet(X0) [cnf transformation 33]
102. ~funny(X0) | ~rich(X0) [cnf transformation 52]
103. ~funny(X0) | rich(X0) [cnf transformation 52]
110. ~happy(lucy) | rich(fred) | creative(fred) [cnf transformation 55]
111. ~happy(lucy) | ~creative(fred) | ~rich(fred) [cnf transformation 55]
116. happy(X0) | rich(X0) [cnf transformation 58]
125. ~creative(fred) | ~strong(fred) [cnf transformation 22]
127. ~quiet(lucy) [cnf transformation 24]
179. 12 <=> happy(lucy) [avatar definition]
181. ~happy(lucy) <- (~12) [avatar component clause 179]
183. 13 <=> rich(lucy) [avatar definition]
184. rich(lucy) <- (13) [avatar component clause 183]
195. ~funny(X0) [subsumption resolution 102,103]
197. 15 <=> rich(fred) [avatar definition]
198. rich(fred) <- (15) [avatar component clause 197]
201. 16 <=> creative(fred) [avatar definition]
203. ~creative(fred) <- (~16) [avatar component clause 201]
204. ~15 | ~16 | ~12 [avatar split clause 111,179,201,197]
205. 16 | 15 | ~12 [avatar split clause 110,179,197,201]
227. 21 <=> strong(fred) [avatar definition]
229. ~strong(fred) <- (~21) [avatar component clause 227]
230. ~21 | ~16 [avatar split clause 125,201,227]
244. rich(lucy) <- (~12) [resolution 116,181]
249. 13 | 12 [avatar split clause 244,179,183]
282. creative(fred) | funny(fred) <- (15) [resolution 76,198]
284. funny(fred) <- (15, ~16) [subsumption resolution 282,203]
285. $false <- (15, ~16) [subsumption resolution 284,195]
286. ~15 | 16 [avatar contradiction clause 285]
288. rich(fred) <- (~21) [resolution 229,87]
291. 15 | 21 [avatar split clause 288,227,197]
295. quiet(lucy) <- (13) [resolution 184,100]
297. $false <- (13) [subsumption resolution 295,127]
298. ~13 [avatar contradiction clause 297]
299. $false [avatar sat refutation 204,205,230,249,286,291,298]
% SZS output end Proof for 7227692848609525257322416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and quiet is wise or brave and vice versa.
Everyone who is both generous and not brave is brave or not calm and vice versa.
Everyone who is either not humble or not generous is not strong or not generous.
Everyone who is not strong is both calm and not brave.
If susan is both funny and not humble then someone is 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 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 curious. | neutral | (![X]:((~old(X)&quiet(X))<=>(wise(X)|brave(X))))&
(![X]:((generous(X)&~brave(X))<=>(brave(X)|~calm(X))))&
(![X]:((~humble(X)<~>~generous(X))=>(~strong(X)|~generous(X))))&
(![X]:(~strong(X)=>(calm(X)&~brave(X))))&
(((funny(susan)&~humble(susan)))=>(?[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]:((~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)) | curious(mary) | [] | null | 0 |
If john is both humble and not humble then someone is either not quiet or happy and vice versa.
If john is curious or quiet then susan is humble.
Everyone who is both brave and curious is either patient or not quiet.
Everyone who is not patient is patient.
If lucy is both not calm and calm then someone is both not creative and not quiet.
Everyone who is not generous or not patient is both not happy and generous.
If susan is both wise and not kind then fred is either old or not creative.
If susan is both not happy and humble then someone is either old or strong.
Everyone who is kind or tall is both old and wise and vice versa.
If john is curious then mary is both not kind and not patient.
If paul is both not curious and not kind then alice is happy and vice versa.
If susan is creative then someone is either not happy or not rich and vice versa.
Everyone who is either kind or not old is either curious or not rich.
If someone is both not rich and not kind then mary is not old and vice versa.
If alice is either not creative or old then susan is both tall and not patient.
If someone is tall or not happy then fred is either not patient or creative and vice versa.
Fred is either humble or not rich.
Alice is brave or not funny.
Mary is either not old or not creative.
Someone is either happy or not rich.
Someone is either humble or creative.
Paul is either patient or not humble. | Alice is not generous. | contradiction | (((humble(john)&~humble(john)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
(((curious(john)|quiet(john)))=>(humble(susan)))&
(![X]:((brave(X)&curious(X))=>(patient(X)<~>~quiet(X))))&
(![X]:(~patient(X)=>patient(X)))&
(((~calm(lucy)&calm(lucy)))=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~generous(X)|~patient(X))=>(~happy(X)&generous(X))))&
(((wise(susan)&~kind(susan)))=>((old(fred)<~>~creative(fred))))&
(((~happy(susan)&humble(susan)))=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((kind(X)|tall(X))<=>(old(X)&wise(X))))&
((curious(john))=>((~kind(mary)&~patient(mary))))&
(((~curious(paul)&~kind(paul)))<=>(happy(alice)))&
((creative(susan))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:((kind(X)<~>~old(X))=>(curious(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~kind(X))))<=>(~old(mary)))&
(((~creative(alice)<~>old(alice)))=>((tall(susan)&~patient(susan))))&
((?[X]:((tall(X)|~happy(X))))<=>((~patient(fred)<~>creative(fred))))&
((humble(fred)<~>~rich(fred)))&
((brave(alice)|~funny(alice)))&
((~old(mary)<~>~creative(mary)))&
(?[X]:((happy(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>creative(X))))&
((patient(paul)<~>~humble(paul))) | ~generous(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8508347921969032205850904
% SZS output start Proof for 8508347921969032205850904
6. ! [X0] : ((~patient(X0) | ~generous(X0)) => (generous(X0) & ~happy(X0))) [input p5]
23. ~generous(alice) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~happy(X0)) | (patient(X0) & generous(X0))) [ennf transformation 6]
89. generous(X0) | generous(X0) [cnf transformation 30]
136. ~generous(alice) [cnf transformation 23]
137. generous(X0) [duplicate literal removal 89]
340. $false [subsumption resolution 136,137]
% SZS output end Proof for 8508347921969032205850904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or strong then someone is both humble and not calm.
If someone is brave then someone is not wise or tall.
Everyone who is either wise or rich is not generous or not funny.
Everyone who is either quiet or old is patient or not old and vice versa.
Everyone who is humble is not calm and vice versa.
If lucy is curious or not patient then john is not generous or not creative and vice versa.
Everyone who is both not calm and patient is not wise or funny and vice versa.
If alice is creative then someone is not patient or wise.
Everyone who is wise or not creative is both not rich and curious and vice versa.
Everyone who is both curious and funny is both not curious and curious and vice versa.
If john is either curious or patient then mary is both brave and generous and vice versa.
Everyone who is both not calm and not creative is happy or kind.
Everyone who is not kind or quiet is either kind or generous and vice versa.
Everyone who is both creative and not curious is either tall or not curious and vice versa.
Everyone who is kind or creative is either rich or not curious.
Everyone who is either rich or not quiet is not tall or not strong and vice versa.
Someone is funny or not rich.
Someone is either not kind or strong.
Someone is either not curious or creative.
Susan is not calm or not curious.
Mary is both not old and strong.
Someone is both humble and not calm.
Someone is both not creative and not rich.
Alice is either not generous or not rich. | Mary is not humble. | contradiction | ((?[X]:((kind(X)<~>strong(X))))=>(?[X]:((humble(X)&~calm(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:((wise(X)<~>rich(X))=>(~generous(X)|~funny(X))))&
(![X]:((quiet(X)<~>old(X))<=>(patient(X)|~old(X))))&
(![X]:(humble(X)<=>~calm(X)))&
(((curious(lucy)|~patient(lucy)))<=>((~generous(john)|~creative(john))))&
(![X]:((~calm(X)&patient(X))<=>(~wise(X)|funny(X))))&
((creative(alice))=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((wise(X)|~creative(X))<=>(~rich(X)&curious(X))))&
(![X]:((curious(X)&funny(X))<=>(~curious(X)&curious(X))))&
(((curious(john)<~>patient(john)))<=>((brave(mary)&generous(mary))))&
(![X]:((~calm(X)&~creative(X))=>(happy(X)|kind(X))))&
(![X]:((~kind(X)|quiet(X))<=>(kind(X)<~>generous(X))))&
(![X]:((creative(X)&~curious(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((kind(X)|creative(X))=>(rich(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~quiet(X))<=>(~tall(X)|~strong(X))))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((~kind(X)<~>strong(X))))&
(?[X]:((~curious(X)<~>creative(X))))&
((~calm(susan)|~curious(susan)))&
((~old(mary)&strong(mary)))&
(?[X]:((humble(X)&~calm(X))))&
(?[X]:((~creative(X)&~rich(X))))&
((~generous(alice)<~>~rich(alice))) | ~humble(mary) | [
"p3",
"p4",
"p6",
"p8",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4358520897110637820471278
% SZS output start Proof for 4358520897110637820471278
4. ! [X0] : ((quiet(X0) <~> old(X0)) <=> (~old(X0) | patient(X0))) [input p3]
5. ! [X0] : (humble(X0) <=> ~calm(X0)) [input p4]
7. ! [X0] : ((patient(X0) & ~calm(X0)) <=> (funny(X0) | ~wise(X0))) [input p6]
9. ! [X0] : ((~creative(X0) | wise(X0)) <=> (curious(X0) & ~rich(X0))) [input p8]
14. ! [X0] : ((~curious(X0) & creative(X0)) <=> (tall(X0) <~> ~curious(X0))) [input p13]
16. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (~strong(X0) | ~tall(X0))) [input p15]
21. strong(mary) & ~old(mary) [input p20]
25. ~humble(mary) [input hypothesis]
43. ! [X0] : ((((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | (old(X0) & ~patient(X0))) & ((~old(X0) | patient(X0)) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | (old(X0) & ~patient(X0))) & (~old(X0) | patient(X0) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0))))) [flattening 43]
45. ! [X0] : ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))) [nnf transformation 5]
48. ! [X0] : (((patient(X0) & ~calm(X0)) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | (~patient(X0) | calm(X0)))) [nnf transformation 7]
49. ! [X0] : (((patient(X0) & ~calm(X0)) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | ~patient(X0) | calm(X0))) [flattening 48]
52. ! [X0] : (((~creative(X0) | wise(X0)) | (~curious(X0) | rich(X0))) & ((curious(X0) & ~rich(X0)) | (creative(X0) & ~wise(X0)))) [nnf transformation 9]
53. ! [X0] : ((~creative(X0) | wise(X0) | ~curious(X0) | rich(X0)) & ((curious(X0) & ~rich(X0)) | (creative(X0) & ~wise(X0)))) [flattening 52]
60. ! [X0] : (((~curious(X0) & creative(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (curious(X0) | ~creative(X0)))) [nnf transformation 14]
61. ! [X0] : (((~curious(X0) & creative(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | curious(X0) | ~creative(X0))) [flattening 60]
63. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 16]
64. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [flattening 63]
88. old(X0) | quiet(X0) | old(X0) [cnf transformation 44]
92. calm(X0) | humble(X0) [cnf transformation 45]
98. ~calm(X0) | wise(X0) [cnf transformation 49]
103. ~rich(X0) | ~wise(X0) [cnf transformation 53]
106. creative(X0) | curious(X0) [cnf transformation 53]
125. curious(X0) | ~tall(X0) | curious(X0) | ~creative(X0) [cnf transformation 61]
128. ~curious(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 61]
136. ~quiet(X0) | rich(X0) | tall(X0) [cnf transformation 64]
146. ~old(mary) [cnf transformation 21]
154. ~humble(mary) [cnf transformation 25]
155. curious(X0) | ~tall(X0) | ~creative(X0) [duplicate literal removal 125]
156. ~curious(X0) | ~tall(X0) [duplicate literal removal 128]
162. old(X0) | quiet(X0) [duplicate literal removal 88]
246. ~creative(X0) | ~tall(X0) [subsumption resolution 155,156]
292. wise(X0) | humble(X0) [resolution 98,92]
314. quiet(mary) [resolution 162,146]
318. ~tall(X0) | curious(X0) [resolution 246,106]
319. ~tall(X0) [subsumption resolution 318,156]
372. rich(mary) | tall(mary) [resolution 136,314]
375. rich(mary) [subsumption resolution 372,319]
474. ~wise(mary) [resolution 375,103]
490. humble(mary) [resolution 474,292]
491. $false [subsumption resolution 490,154]
% SZS output end Proof for 4358520897110637820471278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not kind or not happy then susan is not curious and vice versa. Everyone who is both funny and not creative is either not patient or patient. If someone is not creative or not funny then susan is both not quiet and rich and vice versa. If john is not strong or not calm then someone is both not kind and not brave and vice versa. Everyone who is wise is both rich and old. Everyone who is not old is both not rich and kind and vice versa. Everyone who is curious or not strong is both not rich and calm. Everyone who is happy is either wise or not strong. Everyone who is generous is either kind or not generous. If someone is either brave or kind then someone is either rich or not strong and vice versa. If lucy is wise or not generous then someone is not old or not wise and vice versa. If someone is either old or calm then someone is strong. Everyone who is either not rich or not funny is both curious and not calm and vice versa. Everyone who is quiet is not funny. If paul is not happy or not curious then alice is both not funny and tall. If alice is rich then paul is calm or not generous and vice versa. Lucy is both not quiet and kind. Alice is either not patient or calm. Paul is not creative or not tall. Alice is both not creative and rich. Someone is either not wise or not humble. Someone is either tall or rich. John is both curious and old. | Paul is not happy. | contradiction | (((~kind(fred)<~>~happy(fred)))<=>(~curious(susan)))&
(![X]:((funny(X)&~creative(X))=>(~patient(X)<~>patient(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>((~quiet(susan)&rich(susan))))&
(((~strong(john)|~calm(john)))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:(wise(X)=>(rich(X)&old(X))))&
(![X]:(~old(X)<=>(~rich(X)&kind(X))))&
(![X]:((curious(X)|~strong(X))=>(~rich(X)&calm(X))))&
(![X]:(happy(X)=>(wise(X)<~>~strong(X))))&
(![X]:(generous(X)=>(kind(X)<~>~generous(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((rich(X)<~>~strong(X)))))&
(((wise(lucy)|~generous(lucy)))<=>(?[X]:((~old(X)|~wise(X)))))&
((?[X]:((old(X)<~>calm(X))))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(curious(X)&~calm(X))))&
(![X]:(quiet(X)=>~funny(X)))&
(((~happy(paul)|~curious(paul)))=>((~funny(alice)&tall(alice))))&
((rich(alice))<=>((calm(paul)|~generous(paul))))&
((~quiet(lucy)&kind(lucy)))&
((~patient(alice)<~>calm(alice)))&
((~creative(paul)|~tall(paul)))&
((~creative(alice)&rich(alice)))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:((tall(X)<~>rich(X))))&
((curious(john)&old(john))) | ~happy(paul) | [
"p6",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7862165900995810315695907
% SZS output start Proof for 7862165900995810315695907
7. ! [X0] : ((~strong(X0) | curious(X0)) => (calm(X0) & ~rich(X0))) [input p6]
13. ! [X0] : ((~rich(X0) <~> ~funny(X0)) <=> (~calm(X0) & curious(X0))) [input p12]
15. (~curious(paul) | ~happy(paul)) => (tall(alice) & ~funny(alice)) [input p14]
20. rich(alice) & ~creative(alice) [input p19]
24. ~happy(paul) [input hypothesis]
30. ! [X0] : ((calm(X0) & ~rich(X0)) | (strong(X0) & ~curious(X0))) [ennf transformation 7]
35. (tall(alice) & ~funny(alice)) | (curious(paul) & happy(paul)) [ennf transformation 15]
66. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (calm(X0) | ~curious(X0))) & ((~calm(X0) & curious(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [nnf transformation 13]
67. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | calm(X0) | ~curious(X0)) & ((~calm(X0) & curious(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [flattening 66]
98. ~rich(X0) | ~curious(X0) [cnf transformation 30]
121. curious(X0) | ~rich(X0) | funny(X0) [cnf transformation 67]
127. ~funny(alice) | happy(paul) [cnf transformation 35]
140. rich(alice) [cnf transformation 20]
147. ~happy(paul) [cnf transformation 24]
290. ~rich(X0) | funny(X0) [subsumption resolution 121,98]
301. 33 <=> happy(paul) [avatar definition]
306. 34 <=> funny(alice) [avatar definition]
308. ~funny(alice) <- (~34) [avatar component clause 306]
310. 33 | ~34 [avatar split clause 127,306,301]
316. 36 <=> rich(alice) [avatar definition]
318. rich(alice) <- (36) [avatar component clause 316]
345. 36 [avatar split clause 140,316]
366. ~33 [avatar split clause 147,301]
382. funny(alice) <- (36) [resolution 290,318]
384. $false <- (~34, 36) [subsumption resolution 382,308]
385. 34 | ~36 [avatar contradiction clause 384]
386. $false [avatar sat refutation 310,345,366,385]
% SZS output end Proof for 7862165900995810315695907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not strong then susan is curious.
Everyone who is not calm is rich or not quiet.
If someone is either not funny or not generous then mary is either not curious or not humble.
Everyone who is not kind is both creative and funny.
Everyone who is rich or not happy is wise and vice versa.
Everyone who is tall or not creative is either funny or rich.
Everyone who is both tall and not calm is kind and vice versa.
If someone is both not quiet and not creative then someone is both not calm and patient.
Everyone who is not funny or curious is both funny and happy and vice versa.
If someone is either old or quiet then someone is both not happy and not humble and vice versa.
If someone is either humble or not rich then someone is both rich and wise and vice versa.
Everyone who is quiet or creative is both wise and strong.
Everyone who is quiet or not creative is humble or not tall and vice versa.
If someone is not funny or generous then alice is generous or happy.
Everyone who is creative or happy is quiet or not brave and vice versa.
Everyone who is curious or wise is either not kind or not funny.
Susan is not generous.
Someone is either not brave or strong.
Someone is either not tall or tall.
Fred is either quiet or patient.
Someone is either generous or quiet.
Alice is wise. | Susan is not strong. | contradiction | ((?[X]:((quiet(X)&~strong(X))))=>(curious(susan)))&
(![X]:(~calm(X)=>(rich(X)|~quiet(X))))&
((?[X]:((~funny(X)<~>~generous(X))))=>((~curious(mary)<~>~humble(mary))))&
(![X]:(~kind(X)=>(creative(X)&funny(X))))&
(![X]:((rich(X)|~happy(X))<=>wise(X)))&
(![X]:((tall(X)|~creative(X))=>(funny(X)<~>rich(X))))&
(![X]:((tall(X)&~calm(X))<=>kind(X)))&
((?[X]:((~quiet(X)&~creative(X))))=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((~funny(X)|curious(X))<=>(funny(X)&happy(X))))&
((?[X]:((old(X)<~>quiet(X))))<=>(?[X]:((~happy(X)&~humble(X)))))&
((?[X]:((humble(X)<~>~rich(X))))<=>(?[X]:((rich(X)&wise(X)))))&
(![X]:((quiet(X)|creative(X))=>(wise(X)&strong(X))))&
(![X]:((quiet(X)|~creative(X))<=>(humble(X)|~tall(X))))&
((?[X]:((~funny(X)|generous(X))))=>((generous(alice)|happy(alice))))&
(![X]:((creative(X)|happy(X))<=>(quiet(X)|~brave(X))))&
(![X]:((curious(X)|wise(X))=>(~kind(X)<~>~funny(X))))&
(~generous(susan))&
(?[X]:((~brave(X)<~>strong(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
((quiet(fred)<~>patient(fred)))&
(?[X]:((generous(X)<~>quiet(X))))&
(wise(alice)) | ~strong(susan) | [
"p3",
"p4",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6222934742018846955922895
% SZS output start Proof for 6222934742018846955922895
4. ! [X0] : (~kind(X0) => (funny(X0) & creative(X0))) [input p3]
5. ! [X0] : ((~happy(X0) | rich(X0)) <=> wise(X0)) [input p4]
9. ! [X0] : ((curious(X0) | ~funny(X0)) <=> (happy(X0) & funny(X0))) [input p8]
12. ! [X0] : ((creative(X0) | quiet(X0)) => (strong(X0) & wise(X0))) [input p11]
16. ! [X0] : ((wise(X0) | curious(X0)) => (~kind(X0) <~> ~funny(X0))) [input p15]
23. ~strong(susan) [input hypothesis]
31. ! [X0] : ((funny(X0) & creative(X0)) | kind(X0)) [ennf transformation 4]
34. ! [X0] : ((strong(X0) & wise(X0)) | (~creative(X0) & ~quiet(X0))) [ennf transformation 12]
37. ! [X0] : ((~kind(X0) <~> ~funny(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 16]
39. ! [X0] : (((~happy(X0) | rich(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) & ~rich(X0)))) [nnf transformation 5]
40. ! [X0] : ((~happy(X0) | rich(X0) | ~wise(X0)) & (wise(X0) | (happy(X0) & ~rich(X0)))) [flattening 39]
47. ! [X0] : (((curious(X0) | ~funny(X0)) | (~happy(X0) | ~funny(X0))) & ((happy(X0) & funny(X0)) | (~curious(X0) & funny(X0)))) [nnf transformation 9]
48. ! [X0] : ((curious(X0) | ~funny(X0) | ~happy(X0) | ~funny(X0)) & ((happy(X0) & funny(X0)) | (~curious(X0) & funny(X0)))) [flattening 47]
63. ! [X0] : (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~wise(X0) & ~curious(X0))) [nnf transformation 37]
80. creative(X0) | kind(X0) [cnf transformation 31]
83. wise(X0) | happy(X0) [cnf transformation 40]
94. funny(X0) | funny(X0) [cnf transformation 48]
98. curious(X0) | ~funny(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 48]
114. ~creative(X0) | strong(X0) [cnf transformation 34]
125. ~funny(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 63]
126. ~funny(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 63]
139. ~strong(susan) [cnf transformation 23]
140. funny(X0) [duplicate literal removal 94]
141. ~happy(X0) | ~funny(X0) | curious(X0) [duplicate literal removal 98]
258. ~wise(X0) | ~kind(X0) [subsumption resolution 126,140]
259. ~kind(X0) | ~curious(X0) [subsumption resolution 125,140]
299. kind(X0) | strong(X0) [resolution 114,80]
327. ~kind(X0) | happy(X0) [resolution 258,83]
372. ~curious(X0) | strong(X0) [resolution 299,259]
414. happy(X0) | strong(X0) [resolution 327,299]
511. strong(X0) | ~funny(X0) | curious(X0) [resolution 414,141]
512. strong(X0) | curious(X0) [subsumption resolution 511,140]
513. strong(X0) [subsumption resolution 512,372]
538. $false [resolution 513,139]
% SZS output end Proof for 6222934742018846955922895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is not creative. Everyone who is both not strong and wise is creative. Everyone who is either not strong or not patient is kind. If someone is wise or not brave then someone is either rich or not quiet. Everyone who is either not wise or kind is both happy and tall. Everyone who is either funny or not creative is not quiet. Everyone who is either not strong or not rich is either happy or not funny and vice versa. If someone is both wise and happy then susan is both not curious and not brave. Everyone who is either happy or kind is not tall and vice versa. If fred is brave then alice is not generous or not brave. Everyone who is not strong is either strong or brave and vice versa. If someone is not happy or quiet then someone is old. If someone is humble or not happy then alice is curious or not funny. Everyone who is either not quiet or strong is either creative or humble. Everyone who is wise is both not brave and wise and vice versa. If someone is not quiet or funny then someone is strong or curious. Lucy is either calm or not happy. Someone is not wise. Someone is humble. Someone is not rich or happy. Someone is not happy or not tall. Fred is either not wise or not old. John is both happy and not patient. Someone is brave or funny. | Fred is old. | entailment | (![X]:(happy(X)=>~creative(X)))&
(![X]:((~strong(X)&wise(X))=>creative(X)))&
(![X]:((~strong(X)<~>~patient(X))=>kind(X)))&
((?[X]:((wise(X)|~brave(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>kind(X))=>(happy(X)&tall(X))))&
(![X]:((funny(X)<~>~creative(X))=>~quiet(X)))&
(![X]:((~strong(X)<~>~rich(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:((wise(X)&happy(X))))=>((~curious(susan)&~brave(susan))))&
(![X]:((happy(X)<~>kind(X))<=>~tall(X)))&
((brave(fred))=>((~generous(alice)|~brave(alice))))&
(![X]:(~strong(X)<=>(strong(X)<~>brave(X))))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)|~happy(X))))=>((curious(alice)|~funny(alice))))&
(![X]:((~quiet(X)<~>strong(X))=>(creative(X)<~>humble(X))))&
(![X]:(wise(X)<=>(~brave(X)&wise(X))))&
((?[X]:((~quiet(X)|funny(X))))=>(?[X]:((strong(X)|curious(X)))))&
((calm(lucy)<~>~happy(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:(humble(X)))&
(?[X]:((~rich(X)|happy(X))))&
(?[X]:((~happy(X)|~tall(X))))&
((~wise(fred)<~>~old(fred)))&
((happy(john)&~patient(john)))&
(?[X]:((brave(X)|funny(X)))) | old(fred) | [
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1451543617554794503957389
% SZS output start Proof for 1451543617554794503957389
11. ! [X0] : (~strong(X0) <=> (strong(X0) <~> brave(X0))) [input p10]
15. ! [X0] : (wise(X0) <=> (wise(X0) & ~brave(X0))) [input p14]
22. ~wise(fred) <~> ~old(fred) [input p21]
25. ~old(fred) [input hypothesis]
52. ! [X0] : ((~strong(X0) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | strong(X0))) [nnf transformation 11]
57. ! [X0] : ((wise(X0) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | ~wise(X0))) [nnf transformation 15]
58. ! [X0] : ((wise(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | ~wise(X0))) [flattening 57]
71. (old(fred) | wise(fred)) & (~old(fred) | ~wise(fred)) [nnf transformation 22]
102. brave(X0) | strong(X0) | strong(X0) [cnf transformation 52]
104. ~strong(X0) | brave(X0) | ~strong(X0) [cnf transformation 52]
114. ~brave(X0) | ~wise(X0) [cnf transformation 58]
126. old(fred) | wise(fred) [cnf transformation 71]
130. ~old(fred) [cnf transformation 25]
131. brave(X0) | strong(X0) [duplicate literal removal 102]
132. ~strong(X0) | brave(X0) [duplicate literal removal 104]
134. 1 <=> ! [X1] : brave(X1) [avatar definition]
135. brave(X1) <- (1) [avatar component clause 134]
146. 4 <=> ! [X1] : ~wise(X1) [avatar definition]
147. ~wise(X1) <- (4) [avatar component clause 146]
164. brave(X0) [subsumption resolution 131,132]
165. 1 [avatar split clause 164,134]
236. 24 <=> wise(fred) [avatar definition]
238. wise(fred) <- (24) [avatar component clause 236]
240. 25 <=> old(fred) [avatar definition]
243. 24 | 25 [avatar split clause 126,240,236]
254. ~25 [avatar split clause 130,240]
257. ~wise(X0) <- (1) [resolution 114,135]
259. 4 | ~1 [avatar split clause 257,134,146]
260. $false <- (4, 24) [resolution 147,238]
261. ~4 | ~24 [avatar contradiction clause 260]
262. $false [avatar sat refutation 165,243,254,259,261]
% SZS output end Proof for 1451543617554794503957389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and humble is both kind and not calm.
Everyone who is not tall is either funny or not curious.
Everyone who is either kind or not creative is patient and vice versa.
If susan is either not tall or not wise then someone is not patient and vice versa.
If someone is either humble or not old then lucy is both old and funny and vice versa.
Everyone who is not brave or not curious is both tall and humble and vice versa.
If someone is not wise or not brave then someone is curious or happy and vice versa.
Everyone who is not happy is both quiet and curious and vice versa.
Everyone who is both curious and strong is both creative and not strong.
If someone is patient or calm then someone is funny or not rich.
If alice is brave or not generous then fred is curious and vice versa.
Everyone who is not brave is both happy and kind.
Everyone who is both wise and not happy is not strong and vice versa.
Everyone who is kind is creative and vice versa.
Everyone who is not brave is generous or not creative and vice versa.
Mary is rich.
Someone is both brave and quiet.
Someone is either curious or old.
Fred is either not brave or not old.
John is kind or happy.
Alice is old or not quiet. | Mary is not kind. | contradiction | (![X]:((~rich(X)&humble(X))=>(kind(X)&~calm(X))))&
(![X]:(~tall(X)=>(funny(X)<~>~curious(X))))&
(![X]:((kind(X)<~>~creative(X))<=>patient(X)))&
(((~tall(susan)<~>~wise(susan)))<=>(?[X]:(~patient(X))))&
((?[X]:((humble(X)<~>~old(X))))<=>((old(lucy)&funny(lucy))))&
(![X]:((~brave(X)|~curious(X))<=>(tall(X)&humble(X))))&
((?[X]:((~wise(X)|~brave(X))))<=>(?[X]:((curious(X)|happy(X)))))&
(![X]:(~happy(X)<=>(quiet(X)&curious(X))))&
(![X]:((curious(X)&strong(X))=>(creative(X)&~strong(X))))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:((funny(X)|~rich(X)))))&
(((brave(alice)|~generous(alice)))<=>(curious(fred)))&
(![X]:(~brave(X)=>(happy(X)&kind(X))))&
(![X]:((wise(X)&~happy(X))<=>~strong(X)))&
(![X]:(kind(X)<=>creative(X)))&
(![X]:(~brave(X)<=>(generous(X)|~creative(X))))&
(rich(mary))&
(?[X]:((brave(X)&quiet(X))))&
(?[X]:((curious(X)<~>old(X))))&
((~brave(fred)<~>~old(fred)))&
((kind(john)|happy(john)))&
((old(alice)|~quiet(alice))) | ~kind(mary) | [
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7594614695659369174566664
% SZS output start Proof for 7594614695659369174566664
12. ! [X0] : (~brave(X0) => (kind(X0) & happy(X0))) [input p11]
14. ! [X0] : (kind(X0) <=> creative(X0)) [input p13]
15. ! [X0] : (~brave(X0) <=> (~creative(X0) | generous(X0))) [input p14]
22. ~kind(mary) [input hypothesis]
34. ! [X0] : ((kind(X0) & happy(X0)) | brave(X0)) [ennf transformation 12]
61. ! [X0] : ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0))) [nnf transformation 14]
62. ! [X0] : ((~brave(X0) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | brave(X0))) [nnf transformation 15]
63. ! [X0] : ((~brave(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | brave(X0))) [flattening 62]
106. brave(X0) | kind(X0) [cnf transformation 34]
110. ~creative(X0) | kind(X0) [cnf transformation 61]
113. ~brave(X0) | creative(X0) [cnf transformation 63]
123. ~kind(mary) [cnf transformation 22]
277. creative(X0) | kind(X0) [resolution 113,106]
280. kind(X0) [subsumption resolution 277,110]
291. $false [resolution 280,123]
% SZS output end Proof for 7594614695659369174566664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not creative or curious and vice versa. Everyone who is either not brave or brave is both creative and quiet. Everyone who is not strong or not curious is both funny and not rich and vice versa. If susan is either not curious or not brave then someone is both rich and strong and vice versa. Everyone who is either not creative or creative is not funny or not strong and vice versa. Everyone who is both not quiet and not brave is both not funny and old. If someone is brave then paul is strong and vice versa. Everyone who is both tall and quiet is generous and vice versa. If alice is either calm or curious then john is not quiet or not humble and vice versa. Everyone who is not generous or not brave is funny or not generous and vice versa. Everyone who is creative is not patient or not happy. Everyone who is both wise and not patient is either wise or not generous. Everyone who is creative or rich is not generous. Everyone who is either brave or humble is not curious or curious and vice versa. If someone is either creative or not happy then someone is calm or humble and vice versa. Susan is both not humble and kind. Someone is both not generous and not tall. Someone is either happy or not generous. Someone is either old or funny. Someone is both not humble and not strong. Lucy is patient. Someone is either not patient or not kind. Paul is both not rich and happy. | Paul is funny. | contradiction | (![X]:(~rich(X)<=>(~creative(X)|curious(X))))&
(![X]:((~brave(X)<~>brave(X))=>(creative(X)&quiet(X))))&
(![X]:((~strong(X)|~curious(X))<=>(funny(X)&~rich(X))))&
(((~curious(susan)<~>~brave(susan)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)|~strong(X))))&
(![X]:((~quiet(X)&~brave(X))=>(~funny(X)&old(X))))&
((?[X]:(brave(X)))<=>(strong(paul)))&
(![X]:((tall(X)&quiet(X))<=>generous(X)))&
(((calm(alice)<~>curious(alice)))<=>((~quiet(john)|~humble(john))))&
(![X]:((~generous(X)|~brave(X))<=>(funny(X)|~generous(X))))&
(![X]:(creative(X)=>(~patient(X)|~happy(X))))&
(![X]:((wise(X)&~patient(X))=>(wise(X)<~>~generous(X))))&
(![X]:((creative(X)|rich(X))=>~generous(X)))&
(![X]:((brave(X)<~>humble(X))<=>(~curious(X)|curious(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>(?[X]:((calm(X)|humble(X)))))&
((~humble(susan)&kind(susan)))&
(?[X]:((~generous(X)&~tall(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((~humble(X)&~strong(X))))&
(patient(lucy))&
(?[X]:((~patient(X)<~>~kind(X))))&
((~rich(paul)&happy(paul))) | funny(paul) | [
"p1",
"p4",
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3944080509027643386773919
% SZS output start Proof for 3944080509027643386773919
2. ! [X0] : ((~brave(X0) <~> brave(X0)) => (quiet(X0) & creative(X0))) [input p1]
5. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~strong(X0) | ~funny(X0))) [input p4]
7. ? [X0] : brave(X0) <=> strong(paul) [input p6]
14. ! [X0] : ((brave(X0) <~> humble(X0)) <=> (curious(X0) | ~curious(X0))) [input p13]
20. ? [X0] : (~strong(X0) & ~humble(X0)) [input p19]
24. funny(paul) [input hypothesis]
26. ! [X0] : ((quiet(X0) & creative(X0)) | (~brave(X0) <=> brave(X0))) [ennf transformation 2]
36. ! [X0] : ((quiet(X0) & creative(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 26]
43. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 43]
45. (? [X0] : brave(X0) | ~strong(paul)) & (strong(paul) | ! [X0] : ~brave(X0)) [nnf transformation 7]
46. (? [X0] : brave(X0) | ~strong(paul)) & (strong(paul) | ! [X1] : ~brave(X1)) [rectify 45]
47. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
48. (brave(sK1) | ~strong(paul)) & (strong(paul) | ! [X1] : ~brave(X1)) [skolemisation 46,47]
56. ! [X0] : ((((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0))))) [nnf transformation 14]
57. ! [X0] : ((((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0))))) [flattening 56]
71. ? [X0] : (~strong(X0) & ~humble(X0)) => (~strong(sK7) & ~humble(sK7)) [choice axiom]
72. ~strong(sK7) & ~humble(sK7) [skolemisation 20,71]
79. creative(X0) | brave(X0) | brave(X0) [cnf transformation 36]
80. creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 36]
95. ~strong(X0) | ~funny(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 44]
102. strong(paul) | ~brave(X1) [cnf transformation 48]
124. humble(X0) | brave(X0) | curious(X0) [cnf transformation 57]
125. humble(X0) | brave(X0) | ~curious(X0) [cnf transformation 57]
142. ~humble(sK7) [cnf transformation 72]
149. funny(paul) [cnf transformation 24]
152. ~strong(X0) | ~funny(X0) | ~creative(X0) [duplicate literal removal 95]
153. creative(X0) | brave(X0) [duplicate literal removal 79]
154. ~brave(X0) | creative(X0) [duplicate literal removal 80]
158. creative(X0) [subsumption resolution 153,154]
179. ~funny(X0) | ~strong(X0) [subsumption resolution 152,158]
181. 4 <=> strong(paul) [avatar definition]
190. 6 <=> ! [X1] : ~brave(X1) [avatar definition]
191. ~brave(X1) <- (6) [avatar component clause 190]
192. 6 | 4 [avatar split clause 102,181,190]
215. humble(X0) | brave(X0) [subsumption resolution 124,125]
280. ~strong(paul) [resolution 179,149]
285. ~4 [avatar split clause 280,181]
291. brave(sK7) [resolution 215,142]
296. $false <- (6) [subsumption resolution 291,191]
297. ~6 [avatar contradiction clause 296]
300. $false [avatar sat refutation 192,285,297]
% SZS output end Proof for 3944080509027643386773919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not creative or not tall then someone is both kind and quiet.
Everyone who is either not brave or not strong is both wise and not brave and vice versa.
Everyone who is not strong or patient is wise or not tall and vice versa.
If someone is strong or curious then someone is either not calm or not humble and vice versa.
Everyone who is both not funny and old is generous or not generous.
If paul is both not rich and funny then someone is not strong and vice versa.
Everyone who is not quiet or kind is calm.
Everyone who is either not old or not patient is either patient or not strong.
If susan is either happy or wise then someone is either old or not tall.
Everyone who is old is both not patient and funny.
If lucy is either not curious or humble then alice is both not kind and quiet.
Everyone who is either not tall or not kind is not generous or quiet and vice versa.
Everyone who is both old and not creative is wise.
Everyone who is wise or not wise is either patient or brave and vice versa.
If someone is either quiet or not wise then paul is not generous.
Everyone who is curious is both humble and not tall.
Mary is both not generous and curious.
Someone is either creative or humble.
John is either not calm or old.
John is not brave or not happy.
Susan is not kind or not funny.
Paul is both kind and not creative.
Someone is both rich and not quiet. | John is not strong. | contradiction | (((~creative(paul)<~>~tall(paul)))=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(wise(X)&~brave(X))))&
(![X]:((~strong(X)|patient(X))<=>(wise(X)|~tall(X))))&
((?[X]:((strong(X)|curious(X))))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(![X]:((~funny(X)&old(X))=>(generous(X)|~generous(X))))&
(((~rich(paul)&funny(paul)))<=>(?[X]:(~strong(X))))&
(![X]:((~quiet(X)|kind(X))=>calm(X)))&
(![X]:((~old(X)<~>~patient(X))=>(patient(X)<~>~strong(X))))&
(((happy(susan)<~>wise(susan)))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(old(X)=>(~patient(X)&funny(X))))&
(((~curious(lucy)<~>humble(lucy)))=>((~kind(alice)&quiet(alice))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~generous(X)|quiet(X))))&
(![X]:((old(X)&~creative(X))=>wise(X)))&
(![X]:((wise(X)|~wise(X))<=>(patient(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>~wise(X))))=>(~generous(paul)))&
(![X]:(curious(X)=>(humble(X)&~tall(X))))&
((~generous(mary)&curious(mary)))&
(?[X]:((creative(X)<~>humble(X))))&
((~calm(john)<~>old(john)))&
((~brave(john)|~happy(john)))&
((~kind(susan)|~funny(susan)))&
((kind(paul)&~creative(paul)))&
(?[X]:((rich(X)&~quiet(X)))) | ~strong(john) | [
"p1",
"p2",
"p6",
"p9",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4804651475625256255819725
% SZS output start Proof for 4804651475625256255819725
2. ! [X0] : ((~brave(X0) <~> ~strong(X0)) <=> (~brave(X0) & wise(X0))) [input p1]
3. ! [X0] : ((patient(X0) | ~strong(X0)) <=> (~tall(X0) | wise(X0))) [input p2]
7. ! [X0] : ((kind(X0) | ~quiet(X0)) => calm(X0)) [input p6]
10. ! [X0] : (old(X0) => (funny(X0) & ~patient(X0))) [input p9]
12. ! [X0] : ((~tall(X0) <~> ~kind(X0)) <=> (quiet(X0) | ~generous(X0))) [input p11]
14. ! [X0] : ((~wise(X0) | wise(X0)) <=> (patient(X0) <~> brave(X0))) [input p13]
19. ~calm(john) <~> old(john) [input p18]
24. ~strong(john) [input hypothesis]
29. ! [X0] : (calm(X0) | (~kind(X0) & quiet(X0))) [ennf transformation 7]
32. ! [X0] : ((funny(X0) & ~patient(X0)) | ~old(X0)) [ennf transformation 10]
41. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (brave(X0) | ~wise(X0))) & ((~brave(X0) & wise(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [nnf transformation 2]
42. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | brave(X0) | ~wise(X0)) & ((~brave(X0) & wise(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [flattening 41]
43. ! [X0] : (((patient(X0) | ~strong(X0)) | (tall(X0) & ~wise(X0))) & ((~tall(X0) | wise(X0)) | (~patient(X0) & strong(X0)))) [nnf transformation 3]
44. ! [X0] : ((patient(X0) | ~strong(X0) | (tall(X0) & ~wise(X0))) & (~tall(X0) | wise(X0) | (~patient(X0) & strong(X0)))) [flattening 43]
60. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [nnf transformation 12]
61. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [flattening 60]
62. ! [X0] : (((~wise(X0) | wise(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (wise(X0) & ~wise(X0)))) [nnf transformation 14]
63. ! [X0] : ((~wise(X0) | wise(X0) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (wise(X0) & ~wise(X0)))) [flattening 62]
68. (~old(john) | calm(john)) & (old(john) | ~calm(john)) [nnf transformation 19]
78. ~brave(X0) | ~brave(X0) | strong(X0) [cnf transformation 42]
80. strong(X0) | brave(X0) | brave(X0) | ~wise(X0) [cnf transformation 42]
81. ~tall(X0) | wise(X0) | strong(X0) [cnf transformation 44]
95. calm(X0) | quiet(X0) [cnf transformation 29]
96. ~kind(X0) | calm(X0) [cnf transformation 29]
105. ~old(X0) | ~patient(X0) [cnf transformation 32]
116. ~quiet(X0) | tall(X0) | kind(X0) [cnf transformation 61]
118. brave(X0) | patient(X0) | ~wise(X0) [cnf transformation 63]
119. patient(X0) | brave(X0) | wise(X0) [cnf transformation 63]
132. old(john) | ~calm(john) [cnf transformation 68]
140. ~strong(john) [cnf transformation 24]
143. ~brave(X0) | strong(X0) [duplicate literal removal 78]
144. ~wise(X0) | brave(X0) | strong(X0) [duplicate literal removal 80]
258. patient(X0) | brave(X0) [subsumption resolution 118,119]
282. 30 <=> calm(john) [avatar definition]
283. ~calm(john) <- (~30) [avatar component clause 282]
286. 31 <=> old(john) [avatar definition]
287. old(john) <- (31) [avatar component clause 286]
290. ~30 | 31 [avatar split clause 132,286,282]
292. 32 <=> brave(john) [avatar definition]
293. brave(john) <- (32) [avatar component clause 292]
294. ~brave(john) <- (~32) [avatar component clause 292]
333. 38 <=> kind(john) [avatar definition]
334. kind(john) <- (38) [avatar component clause 333]
337. 39 <=> tall(john) [avatar definition]
338. tall(john) <- (39) [avatar component clause 337]
353. 40 <=> wise(john) [avatar definition]
355. wise(john) <- (40) [avatar component clause 353]
361. quiet(john) <- (~30) [resolution 283,95]
362. tall(john) | kind(john) <- (~30) [resolution 361,116]
368. calm(john) <- (38) [resolution 334,96]
369. $false <- (~30, 38) [subsumption resolution 368,283]
370. 30 | ~38 [avatar contradiction clause 369]
371. 38 | 39 | 30 [avatar split clause 362,282,337,333]
376. wise(john) | strong(john) <- (39) [resolution 338,81]
377. wise(john) <- (39) [subsumption resolution 376,140]
378. 40 | ~39 [avatar split clause 377,337,353]
382. ~patient(john) <- (31) [resolution 287,105]
388. brave(john) | strong(john) <- (40) [resolution 144,355]
389. brave(john) <- (40) [subsumption resolution 388,140]
390. 32 | ~40 [avatar split clause 389,353,292]
391. strong(john) <- (32) [resolution 293,143]
392. $false <- (32) [subsumption resolution 391,140]
393. ~32 [avatar contradiction clause 392]
400. brave(john) <- (31) [resolution 382,258]
404. $false <- (31, ~32) [subsumption resolution 400,294]
405. ~31 | 32 [avatar contradiction clause 404]
406. $false [avatar sat refutation 290,370,371,378,390,393,405]
% SZS output end Proof for 4804651475625256255819725
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not brave or creative then fred is both not humble and old.
Everyone who is not creative or quiet is not wise and vice versa.
Everyone who is both patient and not old is not kind and vice versa.
Everyone who is not strong or happy is both funny and not wise and vice versa.
If someone is both not generous and not brave then alice is not brave and vice versa.
Everyone who is not curious is either tall or old and vice versa.
If someone is either not calm or happy then alice is not quiet or not humble and vice versa.
Everyone who is funny or not patient is rich or not generous and vice versa.
If someone is generous then someone is not humble or creative.
Everyone who is not generous or not happy is not wise.
Everyone who is quiet is old or patient.
If fred is happy then susan is either funny or creative and vice versa.
If lucy is wise or quiet then paul is not brave.
Everyone who is both happy and not curious is both not humble and not kind.
If someone is humble or not funny then alice is either patient or rich and vice versa.
Everyone who is tall or not kind is both old and wise.
John is either creative or wise.
Someone is not humble or not old.
John is either not kind or not calm.
Paul is either not quiet or not creative.
Fred is not generous or not strong.
Alice is not patient or not rich.
Alice is not wise.
Alice is happy or humble. | Lucy is not wise. | entailment | (((~brave(fred)|creative(fred)))=>((~humble(fred)&old(fred))))&
(![X]:((~creative(X)|quiet(X))<=>~wise(X)))&
(![X]:((patient(X)&~old(X))<=>~kind(X)))&
(![X]:((~strong(X)|happy(X))<=>(funny(X)&~wise(X))))&
((?[X]:((~generous(X)&~brave(X))))<=>(~brave(alice)))&
(![X]:(~curious(X)<=>(tall(X)<~>old(X))))&
((?[X]:((~calm(X)<~>happy(X))))<=>((~quiet(alice)|~humble(alice))))&
(![X]:((funny(X)|~patient(X))<=>(rich(X)|~generous(X))))&
((?[X]:(generous(X)))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((~generous(X)|~happy(X))=>~wise(X)))&
(![X]:(quiet(X)=>(old(X)|patient(X))))&
((happy(fred))<=>((funny(susan)<~>creative(susan))))&
(((wise(lucy)|quiet(lucy)))=>(~brave(paul)))&
(![X]:((happy(X)&~curious(X))=>(~humble(X)&~kind(X))))&
((?[X]:((humble(X)|~funny(X))))<=>((patient(alice)<~>rich(alice))))&
(![X]:((tall(X)|~kind(X))=>(old(X)&wise(X))))&
((creative(john)<~>wise(john)))&
(?[X]:((~humble(X)|~old(X))))&
((~kind(john)<~>~calm(john)))&
((~quiet(paul)<~>~creative(paul)))&
((~generous(fred)|~strong(fred)))&
((~patient(alice)|~rich(alice)))&
(~wise(alice))&
((happy(alice)|humble(alice))) | ~wise(lucy) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5487639385662430657153526
% SZS output start Proof for 5487639385662430657153526
4. ! [X0] : ((happy(X0) | ~strong(X0)) <=> (~wise(X0) & funny(X0))) [input p3]
10. ! [X0] : ((~happy(X0) | ~generous(X0)) => ~wise(X0)) [input p9]
25. wise(lucy) [input hypothesis]
31. ! [X0] : (~wise(X0) | (happy(X0) & generous(X0))) [ennf transformation 10]
42. ! [X0] : (((happy(X0) | ~strong(X0)) | (wise(X0) | ~funny(X0))) & ((~wise(X0) & funny(X0)) | (~happy(X0) & strong(X0)))) [nnf transformation 4]
43. ! [X0] : ((happy(X0) | ~strong(X0) | wise(X0) | ~funny(X0)) & ((~wise(X0) & funny(X0)) | (~happy(X0) & strong(X0)))) [flattening 42]
82. ~wise(X0) | ~happy(X0) [cnf transformation 43]
101. ~wise(X0) | happy(X0) [cnf transformation 31]
132. wise(lucy) [cnf transformation 25]
211. ~wise(X0) [subsumption resolution 101,82]
303. $false [subsumption resolution 132,211]
% SZS output end Proof for 5487639385662430657153526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and not curious then someone is either wise or not tall and vice versa.
Everyone who is both not generous and not wise is curious.
Everyone who is either wise or not funny is either not brave or not strong and vice versa.
Everyone who is either not strong or not quiet is rich or not creative and vice versa.
Everyone who is either wise or tall is both not brave and not calm and vice versa.
Everyone who is both generous and strong is both not brave and calm and vice versa.
Everyone who is not calm or tall is both old and not curious.
If fred is either not funny or old then someone is either patient or not tall.
If paul is both happy and not calm then someone is kind or rich.
If john is either funny or generous then alice is humble or not tall and vice versa.
Everyone who is not kind is both not humble and not old.
If someone is both not humble and tall then alice is humble or not creative and vice versa.
If paul is both not patient and kind then lucy is both not strong and calm and vice versa.
Everyone who is not kind or not curious is either not happy or not curious.
Everyone who is either not quiet or not patient is happy or not strong.
Everyone who is both humble and not kind is funny and vice versa.
John is both not calm and wise.
Someone is not generous or not tall.
Someone is funny or not humble.
Someone is old or wise.
Fred is generous or not creative.
Someone is both not patient and not curious.
Mary is both not calm and not wise. | Alice is not quiet. | neutral | ((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((~generous(X)&~wise(X))=>curious(X)))&
(![X]:((wise(X)<~>~funny(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(rich(X)|~creative(X))))&
(![X]:((wise(X)<~>tall(X))<=>(~brave(X)&~calm(X))))&
(![X]:((generous(X)&strong(X))<=>(~brave(X)&calm(X))))&
(![X]:((~calm(X)|tall(X))=>(old(X)&~curious(X))))&
(((~funny(fred)<~>old(fred)))=>(?[X]:((patient(X)<~>~tall(X)))))&
(((happy(paul)&~calm(paul)))=>(?[X]:((kind(X)|rich(X)))))&
(((funny(john)<~>generous(john)))<=>((humble(alice)|~tall(alice))))&
(![X]:(~kind(X)=>(~humble(X)&~old(X))))&
((?[X]:((~humble(X)&tall(X))))<=>((humble(alice)|~creative(alice))))&
(((~patient(paul)&kind(paul)))<=>((~strong(lucy)&calm(lucy))))&
(![X]:((~kind(X)|~curious(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(happy(X)|~strong(X))))&
(![X]:((humble(X)&~kind(X))<=>funny(X)))&
((~calm(john)&wise(john)))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((old(X)|wise(X))))&
((generous(fred)|~creative(fred)))&
(?[X]:((~patient(X)&~curious(X))))&
((~calm(mary)&~wise(mary))) | ~quiet(alice) | [] | null | 0 |
Everyone who is not old or not tall is funny or happy and vice versa.
Everyone who is both not strong and tall is rich and vice versa.
If someone is both not strong and not quiet then someone is brave or not humble.
Everyone who is both quiet and curious is either not generous or not quiet and vice versa.
Everyone who is happy or not brave is not kind.
Everyone who is not funny or kind is not happy and vice versa.
If fred is either curious or not calm then lucy is both not strong and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is either old or curious is either calm or curious and vice versa.
Everyone who is rich is either not brave or wise.
Paul is not rich or not patient.
Susan is either brave or not quiet.
Alice is not humble.
Someone is either not old or old.
Fred is old or not patient.
Paul is wise.
Someone is either not quiet or not strong. | Alice is not patient. | entailment | (![X]:((~old(X)|~tall(X))<=>(funny(X)|happy(X))))&
(![X]:((~strong(X)&tall(X))<=>rich(X)))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>~kind(X)))&
(![X]:((~funny(X)|kind(X))<=>~happy(X)))&
(((curious(fred)<~>~calm(fred)))=>((~strong(lucy)&~quiet(lucy))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:(rich(X)=>(~brave(X)<~>wise(X))))&
((~rich(paul)|~patient(paul)))&
((brave(susan)<~>~quiet(susan)))&
(~humble(alice))&
(?[X]:((~old(X)<~>old(X))))&
((old(fred)|~patient(fred)))&
(wise(paul))&
(?[X]:((~quiet(X)<~>~strong(X)))) | ~patient(alice) | [
"p3",
"p4",
"p7",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6747996989703059661169062
% SZS output start Proof for 6747996989703059661169062
4. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p3]
5. ! [X0] : ((~brave(X0) | happy(X0)) => ~kind(X0)) [input p4]
8. (happy(alice) <~> calm(alice)) => (quiet(susan) & ~quiet(susan)) [input p7]
10. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p10]
13. ! [X0] : (quiet(X0) <=> (~kind(X0) | ~generous(X0))) [input p12]
15. ! [X0] : ((old(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p14]
24. patient(alice) [input hypothesis]
30. ! [X0] : (~kind(X0) | (brave(X0) & ~happy(X0))) [ennf transformation 5]
32. (quiet(susan) & ~quiet(susan)) | (happy(alice) <=> calm(alice)) [ennf transformation 8]
33. ! [X0] : ((~patient(X0) & funny(X0)) | old(X0)) [ennf transformation 10]
40. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | ~curious(X0) | ~quiet(X0))) [flattening 40]
45. (quiet(susan) & ~quiet(susan)) | ((happy(alice) | ~calm(alice)) & (calm(alice) | ~happy(alice))) [nnf transformation 32]
50. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 11]
51. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 50]
57. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ~quiet(X0))) [nnf transformation 13]
58. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ~quiet(X0))) [flattening 57]
63. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 15]
81. quiet(X0) | ~generous(X0) | quiet(X0) [cnf transformation 41]
84. ~kind(X0) | ~happy(X0) [cnf transformation 30]
94. ~quiet(susan) | happy(alice) | ~calm(alice) [cnf transformation 45]
102. ~patient(X0) | old(X0) [cnf transformation 33]
105. kind(X0) | kind(X0) [cnf transformation 51]
115. quiet(X0) | generous(X0) [cnf transformation 58]
121. curious(X0) | calm(X0) | curious(X0) | ~old(X0) [cnf transformation 63]
128. ~curious(X0) | ~old(X0) | calm(X0) | ~curious(X0) [cnf transformation 63]
141. patient(alice) [cnf transformation 24]
142. curious(X0) | calm(X0) | ~old(X0) [duplicate literal removal 121]
145. ~curious(X0) | ~old(X0) | calm(X0) [duplicate literal removal 128]
146. kind(X0) [duplicate literal removal 105]
151. ~generous(X0) | quiet(X0) [duplicate literal removal 81]
186. 8 <=> calm(alice) [avatar definition]
190. 9 <=> happy(alice) [avatar definition]
192. happy(alice) <- (9) [avatar component clause 190]
194. 10 <=> quiet(susan) [avatar definition]
195. ~quiet(susan) <- (~10) [avatar component clause 194]
199. ~8 | 9 | ~10 [avatar split clause 94,194,190,186]
239. quiet(X0) [subsumption resolution 115,151]
261. ~old(X0) | calm(X0) [subsumption resolution 142,145]
273. $false <- (~10) [subsumption resolution 195,239]
274. 10 [avatar contradiction clause 273]
277. ~happy(X0) [resolution 84,146]
281. old(alice) [resolution 102,141]
288. calm(alice) [resolution 261,281]
291. 8 [avatar split clause 288,186]
292. $false <- (9) [subsumption resolution 192,277]
293. ~9 [avatar contradiction clause 292]
294. $false [avatar sat refutation 199,274,291,293]
% SZS output end Proof for 6747996989703059661169062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If john is generous then alice is both not old and not patient and vice versa. Everyone who is not creative or not calm is not rich. If alice is either not humble or happy then mary is not patient and vice versa. If someone is happy or brave then susan is not brave or not creative and vice versa. Everyone who is either not tall or not rich is either not brave or humble and vice versa. If someone is both strong and wise then john is strong or creative. Everyone who is old or not brave is quiet or strong. Everyone who is not strong or not brave is humble. Everyone who is both not curious and not strong is strong or not creative. Everyone who is not happy is humble or not brave. If someone is both calm and not rich then someone is calm or kind. Everyone who is wise or creative is either rich or not wise. Everyone who is both not calm and not patient is brave or not brave and vice versa. If susan is kind or not calm then someone is not creative or not quiet. If mary is not strong then susan is either strong or not generous. If someone is not old or not generous then someone is not brave or not kind and vice versa. Someone is either not kind or not generous. Someone is not strong or not rich. Someone is either not brave or not strong. Fred is calm or strong. Alice is kind or not brave. Lucy is old or not calm. | Mary is not rich. | entailment | ((generous(john))<=>((~old(alice)&~patient(alice))))&
(![X]:((~creative(X)|~calm(X))=>~rich(X)))&
(((~humble(alice)<~>happy(alice)))<=>(~patient(mary)))&
((?[X]:((happy(X)|brave(X))))<=>((~brave(susan)|~creative(susan))))&
(![X]:((~tall(X)<~>~rich(X))<=>(~brave(X)<~>humble(X))))&
((?[X]:((strong(X)&wise(X))))=>((strong(john)|creative(john))))&
(![X]:((old(X)|~brave(X))=>(quiet(X)|strong(X))))&
(![X]:((~strong(X)|~brave(X))=>humble(X)))&
(![X]:((~curious(X)&~strong(X))=>(strong(X)|~creative(X))))&
(![X]:(~happy(X)=>(humble(X)|~brave(X))))&
((?[X]:((calm(X)&~rich(X))))=>(?[X]:((calm(X)|kind(X)))))&
(![X]:((wise(X)|creative(X))=>(rich(X)<~>~wise(X))))&
(![X]:((~calm(X)&~patient(X))<=>(brave(X)|~brave(X))))&
(((kind(susan)|~calm(susan)))=>(?[X]:((~creative(X)|~quiet(X)))))&
((~strong(mary))=>((strong(susan)<~>~generous(susan))))&
((?[X]:((~old(X)|~generous(X))))<=>(?[X]:((~brave(X)|~kind(X)))))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((~brave(X)<~>~strong(X))))&
((calm(fred)|strong(fred)))&
((kind(alice)|~brave(alice)))&
((old(lucy)|~calm(lucy))) | ~rich(mary) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 888273529220373157612575
% SZS output start Proof for 888273529220373157612575
2. ! [X0] : ((~calm(X0) | ~creative(X0)) => ~rich(X0)) [input p1]
13. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> (~brave(X0) | brave(X0))) [input p12]
23. rich(mary) [input hypothesis]
27. ! [X0] : (~rich(X0) | (calm(X0) & creative(X0))) [ennf transformation 2]
52. ! [X0] : (((~patient(X0) & ~calm(X0)) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | (patient(X0) | calm(X0)))) [nnf transformation 13]
53. ! [X0] : (((~patient(X0) & ~calm(X0)) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | patient(X0) | calm(X0))) [flattening 52]
74. ~rich(X0) | calm(X0) [cnf transformation 27]
103. ~calm(X0) | ~brave(X0) [cnf transformation 53]
104. ~calm(X0) | brave(X0) [cnf transformation 53]
123. rich(mary) [cnf transformation 23]
209. ~calm(X0) [subsumption resolution 103,104]
313. calm(mary) [resolution 74,123]
314. $false [subsumption resolution 313,209]
% SZS output end Proof for 888273529220373157612575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and rich then someone is both creative and not kind. Everyone who is wise is both not happy and strong. Everyone who is brave is either not quiet or not kind. Everyone who is either not patient or patient is not happy and vice versa. If someone is old then someone is both not strong and wise and vice versa. Everyone who is wise is both creative and not brave. Everyone who is either not patient or not generous is both brave and not patient. Everyone who is generous or rich is not funny. If mary is both rich and not curious then lucy is both wise and not tall. Everyone who is both humble and not patient is not quiet or not strong. If alice is both not old and not rich then alice is either curious or not happy. Everyone who is happy or tall is rich. Everyone who is not rich or not tall is either not happy or strong and vice versa. If fred is not quiet then someone is not wise. If someone is not strong then someone is not wise and vice versa. Everyone who is not calm or not generous is not creative or creative and vice versa. Someone is not old or rich. John is either generous or patient. Fred is either happy or creative. Paul is either not old or kind. Lucy is not brave or kind. Someone is wise. Someone is either not strong or brave. | Mary is curious. | neutral | ((?[X]:((patient(X)&rich(X))))=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:(wise(X)=>(~happy(X)&strong(X))))&
(![X]:(brave(X)=>(~quiet(X)<~>~kind(X))))&
(![X]:((~patient(X)<~>patient(X))<=>~happy(X)))&
((?[X]:(old(X)))<=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:(wise(X)=>(creative(X)&~brave(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(brave(X)&~patient(X))))&
(![X]:((generous(X)|rich(X))=>~funny(X)))&
(((rich(mary)&~curious(mary)))=>((wise(lucy)&~tall(lucy))))&
(![X]:((humble(X)&~patient(X))=>(~quiet(X)|~strong(X))))&
(((~old(alice)&~rich(alice)))=>((curious(alice)<~>~happy(alice))))&
(![X]:((happy(X)|tall(X))=>rich(X)))&
(![X]:((~rich(X)|~tall(X))<=>(~happy(X)<~>strong(X))))&
((~quiet(fred))=>(?[X]:(~wise(X))))&
((?[X]:(~strong(X)))<=>(?[X]:(~wise(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~creative(X)|creative(X))))&
(?[X]:((~old(X)|rich(X))))&
((generous(john)<~>patient(john)))&
((happy(fred)<~>creative(fred)))&
((~old(paul)<~>kind(paul)))&
((~brave(lucy)|kind(lucy)))&
(?[X]:(wise(X)))&
(?[X]:((~strong(X)<~>brave(X)))) | curious(mary) | [] | null | 0 |
Everyone who is not patient or tall is not generous and vice versa.
Everyone who is not calm or not creative is both wise and tall.
Everyone who is quiet or not tall is kind.
Everyone who is both rich and not curious is both old and not old and vice versa.
Everyone who is kind or old is happy.
Everyone who is both not curious and not calm is either not happy or brave and vice versa.
Everyone who is strong or tall is both humble and brave.
If lucy is either generous or not strong then someone is old or not calm and vice versa.
Everyone who is generous is rich or not happy and vice versa.
Everyone who is either not calm or curious is not quiet or humble.
Everyone who is not kind or funny is not brave.
Everyone who is either not creative or tall is either calm or not generous and vice versa.
Everyone who is either not wise or quiet is either not generous or wise.
Everyone who is strong is tall or not wise and vice versa.
Lucy is either humble or old.
Susan is curious or strong.
Someone is not wise or not old. | Susan is quiet. | contradiction | (![X]:((~patient(X)|tall(X))<=>~generous(X)))&
(![X]:((~calm(X)|~creative(X))=>(wise(X)&tall(X))))&
(![X]:((quiet(X)|~tall(X))=>kind(X)))&
(![X]:((rich(X)&~curious(X))<=>(old(X)&~old(X))))&
(![X]:((kind(X)|old(X))=>happy(X)))&
(![X]:((~curious(X)&~calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((strong(X)|tall(X))=>(humble(X)&brave(X))))&
(((generous(lucy)<~>~strong(lucy)))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(generous(X)<=>(rich(X)|~happy(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~quiet(X)|humble(X))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~generous(X)<~>wise(X))))&
(![X]:(strong(X)<=>(tall(X)|~wise(X))))&
((humble(lucy)<~>old(lucy)))&
((curious(susan)|strong(susan)))&
(?[X]:((~wise(X)|~old(X)))) | quiet(susan) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9017813566495473240603203
% SZS output start Proof for 9017813566495473240603203
1. ! [X0] : ((tall(X0) | ~patient(X0)) <=> ~generous(X0)) [input p0]
2. ! [X0] : ((~creative(X0) | ~calm(X0)) => (tall(X0) & wise(X0))) [input p1]
5. ! [X0] : ((old(X0) | kind(X0)) => happy(X0)) [input p4]
6. ! [X0] : ((~calm(X0) & ~curious(X0)) <=> (~happy(X0) <~> brave(X0))) [input p5]
7. ! [X0] : ((tall(X0) | strong(X0)) => (brave(X0) & humble(X0))) [input p6]
11. ! [X0] : ((funny(X0) | ~kind(X0)) => ~brave(X0)) [input p10]
12. ! [X0] : ((~creative(X0) <~> tall(X0)) <=> (calm(X0) <~> ~generous(X0))) [input p11]
13. ! [X0] : ((~wise(X0) <~> quiet(X0)) => (~generous(X0) <~> wise(X0))) [input p12]
14. ! [X0] : (strong(X0) <=> (~wise(X0) | tall(X0))) [input p13]
18. quiet(susan) [input hypothesis]
19. ! [X0] : (~kind(X0) => ~brave(X0)) [pure predicate removal 11]
20. ! [X0] : ((tall(X0) & wise(X0)) | (creative(X0) & calm(X0))) [ennf transformation 2]
22. ! [X0] : (happy(X0) | (~old(X0) & ~kind(X0))) [ennf transformation 5]
23. ! [X0] : ((brave(X0) & humble(X0)) | (~tall(X0) & ~strong(X0))) [ennf transformation 7]
26. ! [X0] : (~brave(X0) | kind(X0)) [ennf transformation 19]
27. ! [X0] : ((~generous(X0) <~> wise(X0)) | (~wise(X0) <=> quiet(X0))) [ennf transformation 13]
28. ! [X0] : (((tall(X0) | ~patient(X0)) | generous(X0)) & (~generous(X0) | (~tall(X0) & patient(X0)))) [nnf transformation 1]
29. ! [X0] : ((tall(X0) | ~patient(X0) | generous(X0)) & (~generous(X0) | (~tall(X0) & patient(X0)))) [flattening 28]
32. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (calm(X0) | curious(X0)))) [nnf transformation 6]
33. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | calm(X0) | curious(X0))) [flattening 32]
41. ! [X0] : ((((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))))) [nnf transformation 12]
42. ! [X0] : (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) [nnf transformation 27]
43. ! [X0] : ((strong(X0) | (wise(X0) & ~tall(X0))) & ((~wise(X0) | tall(X0)) | ~strong(X0))) [nnf transformation 14]
44. ! [X0] : ((strong(X0) | (wise(X0) & ~tall(X0))) & (~wise(X0) | tall(X0) | ~strong(X0))) [flattening 43]
49. ~generous(X0) | ~tall(X0) [cnf transformation 29]
51. wise(X0) | calm(X0) [cnf transformation 20]
53. calm(X0) | tall(X0) [cnf transformation 20]
54. creative(X0) | tall(X0) [cnf transformation 20]
61. ~kind(X0) | happy(X0) [cnf transformation 22]
68. ~brave(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 33]
71. ~strong(X0) | brave(X0) [cnf transformation 23]
84. ~brave(X0) | kind(X0) [cnf transformation 26]
89. tall(X0) | ~creative(X0) | ~generous(X0) | ~calm(X0) [cnf transformation 41]
96. ~wise(X0) | generous(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 42]
99. strong(X0) | wise(X0) [cnf transformation 44]
104. quiet(susan) [cnf transformation 18]
106. ~quiet(X0) | generous(X0) | ~wise(X0) [duplicate literal removal 96]
137. ~creative(X0) | ~generous(X0) | ~calm(X0) [subsumption resolution 89,49]
181. brave(X0) | wise(X0) [resolution 99,71]
183. kind(X0) | wise(X0) [resolution 181,84]
199. happy(X0) | wise(X0) [resolution 183,61]
201. ~happy(X0) | ~calm(X0) | wise(X0) [resolution 68,181]
202. ~happy(X0) | wise(X0) [subsumption resolution 201,51]
203. wise(X0) [subsumption resolution 202,199]
209. 15 <=> generous(susan) [avatar definition]
210. generous(susan) <- (15) [avatar component clause 209]
221. generous(susan) | ~wise(susan) [resolution 106,104]
225. generous(susan) [subsumption resolution 221,203]
226. 15 [avatar split clause 225,209]
234. ~generous(X1) | ~calm(X1) | tall(X1) [resolution 137,54]
235. ~generous(X1) | tall(X1) [subsumption resolution 234,53]
236. ~generous(X1) [subsumption resolution 235,49]
237. $false <- (15) [resolution 236,210]
238. ~15 [avatar contradiction clause 237]
239. $false [avatar sat refutation 226,238]
% SZS output end Proof for 9017813566495473240603203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and creative is generous or not strong.
If someone is both not patient and funny then fred is either not happy or calm.
Everyone who is not generous is both kind and not curious and vice versa.
If someone is not humble or strong then paul is both not patient and not wise.
If someone is quiet or not wise then someone is both not rich and generous.
If john is happy then someone is both happy and curious.
Everyone who is both not tall and not humble is both not old and creative.
Everyone who is either not funny or not patient is both kind and wise.
Everyone who is both not humble and wise is not curious.
Everyone who is both not happy and not funny is generous or not rich and vice versa.
Everyone who is either not rich or generous is either not kind or kind and vice versa.
If mary is happy then someone is either not creative or old and vice versa.
If someone is funny or not calm then john is either not tall or not strong.
Everyone who is creative or not brave is either not happy or not generous and vice versa.
If fred is brave or funny then someone is not tall or not strong and vice versa.
If susan is kind then fred is both not brave and not strong.
Lucy is both brave and rich.
John is either not happy or not tall.
Paul is not rich or not generous.
Someone is not kind.
Someone is happy or patient.
Lucy is not funny.
Someone is wise. | Mary is humble. | entailment | (![X]:((quiet(X)&creative(X))=>(generous(X)|~strong(X))))&
((?[X]:((~patient(X)&funny(X))))=>((~happy(fred)<~>calm(fred))))&
(![X]:(~generous(X)<=>(kind(X)&~curious(X))))&
((?[X]:((~humble(X)|strong(X))))=>((~patient(paul)&~wise(paul))))&
((?[X]:((quiet(X)|~wise(X))))=>(?[X]:((~rich(X)&generous(X)))))&
((happy(john))=>(?[X]:((happy(X)&curious(X)))))&
(![X]:((~tall(X)&~humble(X))=>(~old(X)&creative(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(kind(X)&wise(X))))&
(![X]:((~humble(X)&wise(X))=>~curious(X)))&
(![X]:((~happy(X)&~funny(X))<=>(generous(X)|~rich(X))))&
(![X]:((~rich(X)<~>generous(X))<=>(~kind(X)<~>kind(X))))&
((happy(mary))<=>(?[X]:((~creative(X)<~>old(X)))))&
((?[X]:((funny(X)|~calm(X))))=>((~tall(john)<~>~strong(john))))&
(![X]:((creative(X)|~brave(X))<=>(~happy(X)<~>~generous(X))))&
(((brave(fred)|funny(fred)))<=>(?[X]:((~tall(X)|~strong(X)))))&
((kind(susan))=>((~brave(fred)&~strong(fred))))&
((brave(lucy)&rich(lucy)))&
((~happy(john)<~>~tall(john)))&
((~rich(paul)|~generous(paul)))&
(?[X]:(~kind(X)))&
(?[X]:((happy(X)|patient(X))))&
(~funny(lucy))&
(?[X]:(wise(X))) | humble(mary) | [
"p2",
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5972825934959399815323147
% SZS output start Proof for 5972825934959399815323147
3. ! [X0] : (~generous(X0) <=> (~curious(X0) & kind(X0))) [input p2]
4. ? [X0] : (strong(X0) | ~humble(X0)) => (~wise(paul) & ~patient(paul)) [input p3]
5. ? [X0] : (~wise(X0) | quiet(X0)) => ? [X0] : (generous(X0) & ~rich(X0)) [input p4]
11. ! [X0] : ((~rich(X0) <~> generous(X0)) <=> (~kind(X0) <~> kind(X0))) [input p10]
24. ~humble(mary) [input hypothesis]
25. ? [X0] : (~wise(X0) | quiet(X0)) => ? [X1] : (generous(X1) & ~rich(X1)) [rectify 5]
27. ? [X0] : ~wise(X0) => ? [X1] : (generous(X1) & ~rich(X1)) [pure predicate removal 25]
29. (~wise(paul) & ~patient(paul)) | ! [X0] : (~strong(X0) & humble(X0)) [ennf transformation 4]
30. ? [X1] : (generous(X1) & ~rich(X1)) | ! [X0] : wise(X0) [ennf transformation 27]
40. ! [X0] : ((~generous(X0) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | generous(X0))) [nnf transformation 3]
41. ! [X0] : ((~generous(X0) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | generous(X0))) [flattening 40]
42. ? [X0] : (generous(X0) & ~rich(X0)) | ! [X1] : wise(X1) [rectify 30]
43. ? [X0] : (generous(X0) & ~rich(X0)) => (generous(sK0) & ~rich(sK0)) [choice axiom]
44. (generous(sK0) & ~rich(sK0)) | ! [X1] : wise(X1) [skolemisation 42,43]
50. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [nnf transformation 11]
72. kind(X0) | generous(X0) [cnf transformation 41]
77. ~wise(paul) | humble(X0) [cnf transformation 29]
79. ~rich(sK0) | wise(X1) [cnf transformation 44]
80. generous(sK0) | wise(X1) [cnf transformation 44]
101. ~generous(X0) | rich(X0) | kind(X0) | kind(X0) [cnf transformation 50]
102. ~generous(X0) | rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 50]
132. ~humble(mary) [cnf transformation 24]
135. ~generous(X0) | rich(X0) | kind(X0) [duplicate literal removal 101]
136. ~kind(X0) | rich(X0) | ~generous(X0) [duplicate literal removal 102]
154. 5 <=> wise(paul) [avatar definition]
156. ~wise(paul) <- (~5) [avatar component clause 154]
159. 6 <=> ! [X0] : humble(X0) [avatar definition]
160. humble(X0) <- (6) [avatar component clause 159]
161. 6 | ~5 [avatar split clause 77,154,159]
169. 8 <=> ! [X1] : wise(X1) [avatar definition]
170. wise(X1) <- (8) [avatar component clause 169]
172. 9 <=> generous(sK0) [avatar definition]
174. generous(sK0) <- (9) [avatar component clause 172]
175. 8 | 9 [avatar split clause 80,172,169]
177. 10 <=> rich(sK0) [avatar definition]
179. ~rich(sK0) <- (~10) [avatar component clause 177]
180. 8 | ~10 [avatar split clause 79,177,169]
195. rich(X0) | kind(X0) [subsumption resolution 135,72]
287. $false <- (~5, 8) [subsumption resolution 156,170]
288. 5 | ~8 [avatar contradiction clause 287]
289. $false <- (6) [resolution 160,132]
290. ~6 [avatar contradiction clause 289]
297. kind(sK0) <- (~10) [resolution 195,179]
396. rich(sK0) | ~generous(sK0) <- (~10) [resolution 136,297]
398. ~generous(sK0) <- (~10) [subsumption resolution 396,179]
399. $false <- (9, ~10) [subsumption resolution 398,174]
400. ~9 | 10 [avatar contradiction clause 399]
401. $false [avatar sat refutation 161,175,180,288,290,400]
% SZS output end Proof for 5972825934959399815323147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is humble or funny then someone is patient and vice versa.
If fred is funny or not old then someone is old and vice versa.
Everyone who is not calm is happy or not humble.
Everyone who is either rich or not tall is not funny and vice versa.
Everyone who is either not rich or old is not calm or not happy and vice versa.
Everyone who is either not calm or not old is both not kind and curious.
Everyone who is both not generous and not kind is generous.
Everyone who is both not strong and not brave is either not tall or not brave.
Everyone who is both not creative and not calm is funny or not patient and vice versa.
If someone is both not generous and not funny then someone is either generous or not funny.
If john is not calm then someone is either generous or happy.
Everyone who is both patient and not humble is strong or not kind and vice versa.
If john is generous or not quiet then mary is both not kind and quiet.
Everyone who is both not brave and generous is funny or not generous and vice versa.
Everyone who is both not wise and not tall is tall or not wise and vice versa.
Everyone who is both strong and not calm is not quiet.
Someone is not tall or old.
Someone is wise or not strong.
Fred is humble or wise.
Mary is not kind or not curious.
John is both not humble and old. | Fred is creative. | neutral | (((humble(john)|funny(john)))<=>(?[X]:(patient(X))))&
(((funny(fred)|~old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~calm(X)=>(happy(X)|~humble(X))))&
(![X]:((rich(X)<~>~tall(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>old(X))<=>(~calm(X)|~happy(X))))&
(![X]:((~calm(X)<~>~old(X))=>(~kind(X)&curious(X))))&
(![X]:((~generous(X)&~kind(X))=>generous(X)))&
(![X]:((~strong(X)&~brave(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((~creative(X)&~calm(X))<=>(funny(X)|~patient(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:((generous(X)<~>~funny(X)))))&
((~calm(john))=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|~kind(X))))&
(((generous(john)|~quiet(john)))=>((~kind(mary)&quiet(mary))))&
(![X]:((~brave(X)&generous(X))<=>(funny(X)|~generous(X))))&
(![X]:((~wise(X)&~tall(X))<=>(tall(X)|~wise(X))))&
(![X]:((strong(X)&~calm(X))=>~quiet(X)))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((wise(X)|~strong(X))))&
((humble(fred)|wise(fred)))&
((~kind(mary)|~curious(mary)))&
((~humble(john)&old(john))) | creative(fred) | [] | null | 0 |
Everyone who is either brave or not patient is not old and vice versa.
If someone is humble then someone is both humble and not humble.
Everyone who is either patient or not old is either not rich or not kind and vice versa.
Everyone who is both patient and not strong is old and vice versa.
Everyone who is old or not tall is either not calm or quiet and vice versa.
Everyone who is rich is tall or curious and vice versa.
If fred is either not wise or not strong then someone is either not funny or strong.
If someone is happy then susan is not quiet and vice versa.
Everyone who is funny or humble is either not calm or not rich and vice versa.
If john is rich then someone is both not rich and not strong.
If someone is not rich or not patient then someone is both not kind and not old.
Everyone who is quiet or not happy is either strong or quiet and vice versa.
If john is happy or creative then someone is quiet and vice versa.
Everyone who is both not quiet and patient is either brave or not humble.
If someone is kind then someone is not happy.
John is both not happy and old.
Mary is either funny or not old.
John is either not kind or not generous.
John is not humble or not patient.
Fred is both wise and not happy.
Alice is both not wise and curious. | John is not brave. | entailment | (![X]:((brave(X)<~>~patient(X))<=>~old(X)))&
((?[X]:(humble(X)))=>(?[X]:((humble(X)&~humble(X)))))&
(![X]:((patient(X)<~>~old(X))<=>(~rich(X)<~>~kind(X))))&
(![X]:((patient(X)&~strong(X))<=>old(X)))&
(![X]:((old(X)|~tall(X))<=>(~calm(X)<~>quiet(X))))&
(![X]:(rich(X)<=>(tall(X)|curious(X))))&
(((~wise(fred)<~>~strong(fred)))=>(?[X]:((~funny(X)<~>strong(X)))))&
((?[X]:(happy(X)))<=>(~quiet(susan)))&
(![X]:((funny(X)|humble(X))<=>(~calm(X)<~>~rich(X))))&
((rich(john))=>(?[X]:((~rich(X)&~strong(X)))))&
((?[X]:((~rich(X)|~patient(X))))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((quiet(X)|~happy(X))<=>(strong(X)<~>quiet(X))))&
(((happy(john)|creative(john)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&patient(X))=>(brave(X)<~>~humble(X))))&
((?[X]:(kind(X)))=>(?[X]:(~happy(X))))&
((~happy(john)&old(john)))&
((funny(mary)<~>~old(mary)))&
((~kind(john)<~>~generous(john)))&
((~humble(john)|~patient(john)))&
((wise(fred)&~happy(fred)))&
((~wise(alice)&curious(alice))) | ~brave(john) | [
"p0",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7176463190227549495865027
% SZS output start Proof for 7176463190227549495865027
1. ! [X0] : ((brave(X0) <~> ~patient(X0)) <=> ~old(X0)) [input p0]
4. ! [X0] : ((~strong(X0) & patient(X0)) <=> old(X0)) [input p3]
16. old(john) & ~happy(john) [input p15]
22. brave(john) [input hypothesis]
33. ! [X0] : ((((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | old(X0)) & (~old(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0))))) [nnf transformation 1]
38. ! [X0] : (((~strong(X0) & patient(X0)) | ~old(X0)) & (old(X0) | (strong(X0) | ~patient(X0)))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) & patient(X0)) | ~old(X0)) & (old(X0) | strong(X0) | ~patient(X0))) [flattening 38]
71. ~old(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 33]
86. ~old(X0) | patient(X0) [cnf transformation 39]
128. old(john) [cnf transformation 16]
138. brave(john) [cnf transformation 22]
267. 28 <=> patient(john) [avatar definition]
268. patient(john) <- (28) [avatar component clause 267]
272. patient(john) [resolution 86,128]
273. 28 [avatar split clause 272,267]
275. ~patient(john) | ~brave(john) [resolution 71,128]
276. ~brave(john) <- (28) [subsumption resolution 275,268]
277. $false <- (28) [subsumption resolution 276,138]
278. ~28 [avatar contradiction clause 277]
279. $false [avatar sat refutation 273,278]
% SZS output end Proof for 7176463190227549495865027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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