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 not humble or not quiet is old and vice versa.
Everyone who is not creative or not humble is either not kind or not brave and vice versa.
Everyone who is both not wise and not calm is creative or not tall and vice versa.
If alice is either not patient or not calm then someone is either not tall or not humble and vice versa.
If someone is both not curious and not tall then someone is not strong and vice versa.
Everyone who is either strong or creative is wise and vice versa.
Everyone who is creative is not quiet or generous and vice versa.
Everyone who is not brave or curious is both not rich and not quiet and vice versa.
Everyone who is not quiet is both not creative and kind and vice versa.
If someone is rich then someone is both brave and tall and vice versa.
Everyone who is calm or wise is not creative.
Everyone who is not patient is both generous and not humble.
Everyone who is rich is either creative or not quiet.
Everyone who is not curious or patient is not kind or curious.
If lucy is either quiet or humble then paul is not rich and vice versa.
Someone is brave or not humble.
Susan is creative or not wise.
Mary is not calm. | Susan is not generous. | neutral | (![X]:((~humble(X)|~quiet(X))<=>old(X)))&
(![X]:((~creative(X)|~humble(X))<=>(~kind(X)<~>~brave(X))))&
(![X]:((~wise(X)&~calm(X))<=>(creative(X)|~tall(X))))&
(((~patient(alice)<~>~calm(alice)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
(![X]:((strong(X)<~>creative(X))<=>wise(X)))&
(![X]:(creative(X)<=>(~quiet(X)|generous(X))))&
(![X]:((~brave(X)|curious(X))<=>(~rich(X)&~quiet(X))))&
(![X]:(~quiet(X)<=>(~creative(X)&kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((calm(X)|wise(X))=>~creative(X)))&
(![X]:(~patient(X)=>(generous(X)&~humble(X))))&
(![X]:(rich(X)=>(creative(X)<~>~quiet(X))))&
(![X]:((~curious(X)|patient(X))=>(~kind(X)|curious(X))))&
(((quiet(lucy)<~>humble(lucy)))<=>(~rich(paul)))&
(?[X]:((brave(X)|~humble(X))))&
((creative(susan)|~wise(susan)))&
(~calm(mary)) | ~generous(susan) | [] | null | 0 |
If paul is wise then alice is either creative or not generous and vice versa.
Everyone who is either not old or not creative is either not calm or calm and vice versa.
Everyone who is rich is either not quiet or creative.
If someone is not curious or tall then fred is not old or not curious.
If lucy is not curious then someone is either not quiet or not strong and vice versa.
If someone is creative or not happy then fred is both brave and tall and vice versa.
Everyone who is rich or not patient is both curious and quiet.
Everyone who is both not wise and not generous is not brave or wise and vice versa.
If someone is both not creative and not funny then paul is not curious or not happy.
Everyone who is old or generous is not patient.
If someone is both not humble and happy then lucy is either not strong or creative and vice versa.
Everyone who is not old or happy is not tall.
If lucy is not curious then someone is strong.
If someone is not rich or old then alice is happy and vice versa.
If susan is not rich or quiet then someone is strong or not generous.
If someone is both creative and not funny then john is both funny and brave.
Mary is either not old or not tall.
Someone is calm or happy.
Lucy is not creative.
Mary is old or strong. | Mary is old. | entailment | ((wise(paul))<=>((creative(alice)<~>~generous(alice))))&
(![X]:((~old(X)<~>~creative(X))<=>(~calm(X)<~>calm(X))))&
(![X]:(rich(X)=>(~quiet(X)<~>creative(X))))&
((?[X]:((~curious(X)|tall(X))))=>((~old(fred)|~curious(fred))))&
((~curious(lucy))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
((?[X]:((creative(X)|~happy(X))))<=>((brave(fred)&tall(fred))))&
(![X]:((rich(X)|~patient(X))=>(curious(X)&quiet(X))))&
(![X]:((~wise(X)&~generous(X))<=>(~brave(X)|wise(X))))&
((?[X]:((~creative(X)&~funny(X))))=>((~curious(paul)|~happy(paul))))&
(![X]:((old(X)|generous(X))=>~patient(X)))&
((?[X]:((~humble(X)&happy(X))))<=>((~strong(lucy)<~>creative(lucy))))&
(![X]:((~old(X)|happy(X))=>~tall(X)))&
((~curious(lucy))=>(?[X]:(strong(X))))&
((?[X]:((~rich(X)|old(X))))<=>(happy(alice)))&
(((~rich(susan)|quiet(susan)))=>(?[X]:((strong(X)|~generous(X)))))&
((?[X]:((creative(X)&~funny(X))))=>((funny(john)&brave(john))))&
((~old(mary)<~>~tall(mary)))&
(?[X]:((calm(X)|happy(X))))&
(~creative(lucy))&
((old(mary)|strong(mary))) | old(mary) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 682650296711716227543733
% SZS output start Proof for 682650296711716227543733
12. ! [X0] : ((happy(X0) | ~old(X0)) => ~tall(X0)) [input p11]
17. ~old(mary) <~> ~tall(mary) [input p16]
21. ~old(mary) [input hypothesis]
29. ! [X0] : (~tall(X0) | (~happy(X0) & old(X0))) [ennf transformation 12]
58. (tall(mary) | old(mary)) & (~tall(mary) | ~old(mary)) [nnf transformation 17]
103. ~tall(X0) | old(X0) [cnf transformation 29]
112. tall(mary) | old(mary) [cnf transformation 58]
116. ~old(mary) [cnf transformation 21]
276. old(mary) [subsumption resolution 112,103]
288. $false [subsumption resolution 116,276]
% SZS output end Proof for 682650296711716227543733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not creative is not quiet and vice versa.
Everyone who is both not tall and humble is generous or calm.
Everyone who is not kind or old is either not rich or curious.
Everyone who is happy is either not strong or curious and vice versa.
Everyone who is not curious or kind is either not patient or not rich.
Everyone who is strong is both not funny and wise and vice versa.
If someone is either creative or funny then mary is either not quiet or not old.
Everyone who is both wise and not generous is not rich or kind.
Everyone who is either calm or humble is both happy and not kind and vice versa.
If susan is not tall or not generous then someone is either curious or not curious.
Everyone who is not wise is not patient or rich.
Everyone who is happy is either not strong or patient and vice versa.
Everyone who is both creative and tall is funny or not creative and vice versa.
Everyone who is either not calm or tall is patient or happy and vice versa.
If paul is both not generous and funny then someone is both quiet and happy.
Everyone who is calm or not calm is either not brave or strong.
Someone is tall or old.
Paul is either not tall or not quiet.
Paul is either not patient or not calm.
Mary is not wise.
Susan is both not calm and brave.
Someone is not curious.
Lucy is not rich. | Lucy is not wise. | contradiction | (![X]:((~generous(X)<~>~creative(X))<=>~quiet(X)))&
(![X]:((~tall(X)&humble(X))=>(generous(X)|calm(X))))&
(![X]:((~kind(X)|old(X))=>(~rich(X)<~>curious(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>curious(X))))&
(![X]:((~curious(X)|kind(X))=>(~patient(X)<~>~rich(X))))&
(![X]:(strong(X)<=>(~funny(X)&wise(X))))&
((?[X]:((creative(X)<~>funny(X))))=>((~quiet(mary)<~>~old(mary))))&
(![X]:((wise(X)&~generous(X))=>(~rich(X)|kind(X))))&
(![X]:((calm(X)<~>humble(X))<=>(happy(X)&~kind(X))))&
(((~tall(susan)|~generous(susan)))=>(?[X]:((curious(X)<~>~curious(X)))))&
(![X]:(~wise(X)=>(~patient(X)|rich(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>patient(X))))&
(![X]:((creative(X)&tall(X))<=>(funny(X)|~creative(X))))&
(![X]:((~calm(X)<~>tall(X))<=>(patient(X)|happy(X))))&
(((~generous(paul)&funny(paul)))=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((calm(X)|~calm(X))=>(~brave(X)<~>strong(X))))&
(?[X]:((tall(X)|old(X))))&
((~tall(paul)<~>~quiet(paul)))&
((~patient(paul)<~>~calm(paul)))&
(~wise(mary))&
((~calm(susan)&brave(susan)))&
(?[X]:(~curious(X)))&
(~rich(lucy)) | ~wise(lucy) | [
"p3",
"p4",
"p5",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3132065756652867187203776
% SZS output start Proof for 3132065756652867187203776
4. ! [X0] : (happy(X0) <=> (~strong(X0) <~> curious(X0))) [input p3]
5. ! [X0] : ((kind(X0) | ~curious(X0)) => (~patient(X0) <~> ~rich(X0))) [input p4]
6. ! [X0] : (strong(X0) <=> (wise(X0) & ~funny(X0))) [input p5]
11. ! [X0] : (~wise(X0) => (rich(X0) | ~patient(X0))) [input p10]
12. ! [X0] : (happy(X0) <=> (~strong(X0) <~> patient(X0))) [input p11]
23. ~rich(lucy) [input p22]
24. ~wise(lucy) [input hypothesis]
28. ! [X0] : ((~patient(X0) <~> ~rich(X0)) | (~kind(X0) & curious(X0))) [ennf transformation 5]
33. ! [X0] : ((rich(X0) | ~patient(X0)) | wise(X0)) [ennf transformation 11]
34. ! [X0] : (rich(X0) | ~patient(X0) | wise(X0)) [flattening 33]
40. ! [X0] : ((happy(X0) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) & (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 4]
41. ! [X0] : (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (~kind(X0) & curious(X0))) [nnf transformation 28]
42. ! [X0] : ((strong(X0) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | ~strong(X0))) [nnf transformation 6]
43. ! [X0] : ((strong(X0) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~strong(X0))) [flattening 42]
50. ! [X0] : ((happy(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 12]
74. ~happy(X0) | strong(X0) | ~curious(X0) [cnf transformation 40]
79. patient(X0) | rich(X0) | curious(X0) [cnf transformation 41]
82. ~strong(X0) | wise(X0) [cnf transformation 43]
99. ~patient(X0) | rich(X0) | wise(X0) [cnf transformation 34]
101. ~patient(X0) | strong(X0) | ~happy(X0) [cnf transformation 50]
102. patient(X0) | happy(X0) | strong(X0) [cnf transformation 50]
130. ~rich(lucy) [cnf transformation 23]
131. ~wise(lucy) [cnf transformation 24]
300. strong(X0) | ~happy(X0) | rich(X0) | curious(X0) [resolution 101,79]
301. ~happy(X0) | strong(X0) | rich(X0) [subsumption resolution 300,74]
314. happy(X1) | strong(X1) | rich(X1) | wise(X1) [resolution 102,99]
318. wise(X1) | rich(X1) | happy(X1) [subsumption resolution 314,82]
388. 32 <=> happy(lucy) [avatar definition]
390. happy(lucy) <- (32) [avatar component clause 388]
450. rich(lucy) | happy(lucy) [resolution 318,131]
453. happy(lucy) [subsumption resolution 450,130]
454. 32 [avatar split clause 453,388]
456. strong(lucy) | rich(lucy) <- (32) [resolution 390,301]
462. strong(lucy) <- (32) [subsumption resolution 456,130]
570. wise(lucy) <- (32) [resolution 462,82]
575. $false <- (32) [subsumption resolution 570,131]
576. ~32 [avatar contradiction clause 575]
578. $false [avatar sat refutation 454,576]
% SZS output end Proof for 3132065756652867187203776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or tall is quiet and vice versa. If someone is either calm or not curious then someone is not happy or strong and vice versa. If mary is not calm then someone is happy or patient. Everyone who is calm is either not wise or not calm and vice versa. Everyone who is strong or calm is either not funny or old. Everyone who is either not rich or tall is tall. Everyone who is not generous is either funny or not old and vice versa. If susan is either not quiet or not old then someone is kind or quiet. If fred is both humble and rich then fred is either not old or humble and vice versa. If someone is not funny then susan is both kind and not creative. Everyone who is both strong and kind is either tall or happy and vice versa. If lucy is strong then someone is wise and vice versa. Everyone who is either not generous or not tall is both generous and brave and vice versa. If someone is either generous or not happy then someone is either generous or strong and vice versa. If someone is not calm or not patient then susan is quiet and vice versa. Everyone who is generous is both tall and creative. Someone is not generous. Someone is strong. Someone is either quiet or not patient. Mary is not generous or not calm. Alice is wise or rich. Mary is not generous or not humble. | Mary is not calm. | neutral | (![X]:((~old(X)|tall(X))<=>quiet(X)))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~happy(X)|strong(X)))))&
((~calm(mary))=>(?[X]:((happy(X)|patient(X)))))&
(![X]:(calm(X)<=>(~wise(X)<~>~calm(X))))&
(![X]:((strong(X)|calm(X))=>(~funny(X)<~>old(X))))&
(![X]:((~rich(X)<~>tall(X))=>tall(X)))&
(![X]:(~generous(X)<=>(funny(X)<~>~old(X))))&
(((~quiet(susan)<~>~old(susan)))=>(?[X]:((kind(X)|quiet(X)))))&
(((humble(fred)&rich(fred)))<=>((~old(fred)<~>humble(fred))))&
((?[X]:(~funny(X)))=>((kind(susan)&~creative(susan))))&
(![X]:((strong(X)&kind(X))<=>(tall(X)<~>happy(X))))&
((strong(lucy))<=>(?[X]:(wise(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>(generous(X)&brave(X))))&
((?[X]:((generous(X)<~>~happy(X))))<=>(?[X]:((generous(X)<~>strong(X)))))&
((?[X]:((~calm(X)|~patient(X))))<=>(quiet(susan)))&
(![X]:(generous(X)=>(tall(X)&creative(X))))&
(?[X]:(~generous(X)))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)<~>~patient(X))))&
((~generous(mary)|~calm(mary)))&
((wise(alice)|rich(alice)))&
((~generous(mary)|~humble(mary))) | ~calm(mary) | [] | null | 0 |
If alice is either not brave or not patient then alice is not quiet or not generous and vice versa.
Everyone who is either not curious or strong is not old.
If someone is either not funny or not generous then someone is not curious or old and vice versa.
Everyone who is not creative is humble and vice versa.
Everyone who is both not quiet and not rich is strong or rich.
Everyone who is both not wise and brave is not kind and vice versa.
If someone is either patient or creative then someone is both funny and not funny.
Everyone who is not tall or humble is patient and vice versa.
If someone is not kind then someone is both creative and not calm.
If someone is kind or creative then susan is patient and vice versa.
If someone is strong or not happy then alice is both tall and not patient and vice versa.
If mary is rich or not patient then alice is not happy.
Everyone who is both not humble and not curious is both not kind and not tall and vice versa.
Everyone who is not curious is either happy or brave.
Fred is either funny or quiet.
Someone is not happy or curious.
Someone is rich.
Someone is not generous or funny.
Alice is either humble or wise. | Susan is tall. | contradiction | (((~brave(alice)<~>~patient(alice)))<=>((~quiet(alice)|~generous(alice))))&
(![X]:((~curious(X)<~>strong(X))=>~old(X)))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:((~quiet(X)&~rich(X))=>(strong(X)|rich(X))))&
(![X]:((~wise(X)&brave(X))<=>~kind(X)))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~tall(X)|humble(X))<=>patient(X)))&
((?[X]:(~kind(X)))=>(?[X]:((creative(X)&~calm(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(patient(susan)))&
((?[X]:((strong(X)|~happy(X))))<=>((tall(alice)&~patient(alice))))&
(((rich(mary)|~patient(mary)))=>(~happy(alice)))&
(![X]:((~humble(X)&~curious(X))<=>(~kind(X)&~tall(X))))&
(![X]:(~curious(X)=>(happy(X)<~>brave(X))))&
((funny(fred)<~>quiet(fred)))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((~generous(X)|funny(X))))&
((humble(alice)<~>wise(alice))) | tall(susan) | [
"p3",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7384785290526668164101281
% SZS output start Proof for 7384785290526668164101281
4. ! [X0] : (~creative(X0) <=> humble(X0)) [input p3]
7. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X0] : (~funny(X0) & funny(X0)) [input p6]
8. ! [X0] : ((humble(X0) | ~tall(X0)) <=> patient(X0)) [input p7]
10. ? [X0] : (creative(X0) | kind(X0)) <=> patient(susan) [input p9]
20. tall(susan) [input hypothesis]
22. ? [X0] : (patient(X0) <~> creative(X0)) => ? [X1] : (~funny(X1) & funny(X1)) [rectify 7]
28. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (patient(X0) <=> creative(X0)) [ennf transformation 22]
40. ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))) [nnf transformation 4]
43. ? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 28]
44. ? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [rectify 43]
45. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK2) & funny(sK2)) [choice axiom]
46. (~funny(sK2) & funny(sK2)) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1))) [skolemisation 44,45]
47. ! [X0] : (((humble(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [nnf transformation 8]
48. ! [X0] : ((humble(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [flattening 47]
52. (? [X0] : (creative(X0) | kind(X0)) | ~patient(susan)) & (patient(susan) | ! [X0] : (~creative(X0) & ~kind(X0))) [nnf transformation 10]
53. (? [X0] : (creative(X0) | kind(X0)) | ~patient(susan)) & (patient(susan) | ! [X1] : (~creative(X1) & ~kind(X1))) [rectify 52]
54. ? [X0] : (creative(X0) | kind(X0)) => (creative(sK4) | kind(sK4)) [choice axiom]
55. ((creative(sK4) | kind(sK4)) | ~patient(susan)) & (patient(susan) | ! [X1] : (~creative(X1) & ~kind(X1))) [skolemisation 53,54]
86. humble(X0) | creative(X0) [cnf transformation 40]
87. ~humble(X0) | ~creative(X0) [cnf transformation 40]
92. funny(sK2) | creative(X1) | ~patient(X1) [cnf transformation 46]
94. ~funny(sK2) | creative(X1) | ~patient(X1) [cnf transformation 46]
97. ~humble(X0) | patient(X0) [cnf transformation 48]
98. ~tall(X0) | humble(X0) | ~patient(X0) [cnf transformation 48]
101. patient(susan) | ~creative(X1) [cnf transformation 55]
123. tall(susan) [cnf transformation 20]
185. 14 <=> funny(sK2) [avatar definition]
190. 15 <=> ! [X1] : (creative(X1) | ~patient(X1)) [avatar definition]
191. ~patient(X1) | creative(X1) <- (15) [avatar component clause 190]
192. 15 | ~14 [avatar split clause 94,185,190]
194. 15 | 14 [avatar split clause 92,185,190]
204. 18 <=> patient(susan) [avatar definition]
205. patient(susan) <- (18) [avatar component clause 204]
217. 21 <=> ! [X1] : ~creative(X1) [avatar definition]
218. ~creative(X1) <- (21) [avatar component clause 217]
219. 21 | 18 [avatar split clause 101,204,217]
309. patient(X0) | creative(X0) [resolution 97,86]
312. creative(X0) <- (15) [subsumption resolution 309,191]
328. humble(susan) | ~patient(susan) [resolution 98,123]
331. humble(susan) <- (18) [subsumption resolution 328,205]
346. ~creative(susan) <- (18) [resolution 331,87]
347. $false <- (15, 18) [subsumption resolution 346,312]
348. ~15 | ~18 [avatar contradiction clause 347]
352. $false <- (15, 21) [subsumption resolution 218,312]
353. ~15 | ~21 [avatar contradiction clause 352]
356. $false [avatar sat refutation 192,194,219,348,353]
% SZS output end Proof for 7384785290526668164101281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and strong is either patient or kind. Everyone who is both funny and happy is strong or happy and vice versa. If someone is both funny and patient then paul is old. Everyone who is not tall is both not calm and not happy. If someone is either strong or not patient then someone is either not tall or humble. Everyone who is not creative or old is curious or not wise and vice versa. If mary is not kind then john is either not funny or strong. If john is either not brave or not humble then someone is both not strong and old and vice versa. Everyone who is not wise or old is either not strong or patient and vice versa. Everyone who is either curious or not happy is calm and vice versa. Everyone who is not humble is either patient or not kind and vice versa. Everyone who is not calm is curious and vice versa. If someone is both not kind and not strong then someone is both not calm and not generous and vice versa. Everyone who is either wise or not old is both curious and not quiet. If someone is either quiet or happy then someone is either not patient or not quiet. Everyone who is not tall or curious is not funny or not kind and vice versa. Someone is both not generous and not old. Alice is either not creative or tall. Paul is both not creative and not tall. Someone is both not curious and calm. Susan is wise or patient. Someone is quiet. Mary is not rich. Paul is old or not humble. | Alice is happy. | contradiction | (![X]:((~funny(X)&strong(X))=>(patient(X)<~>kind(X))))&
(![X]:((funny(X)&happy(X))<=>(strong(X)|happy(X))))&
((?[X]:((funny(X)&patient(X))))=>(old(paul)))&
(![X]:(~tall(X)=>(~calm(X)&~happy(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((~creative(X)|old(X))<=>(curious(X)|~wise(X))))&
((~kind(mary))=>((~funny(john)<~>strong(john))))&
(((~brave(john)<~>~humble(john)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~wise(X)|old(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(patient(X)<~>~kind(X))))&
(![X]:(~calm(X)<=>curious(X)))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((wise(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
((?[X]:((quiet(X)<~>happy(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((~tall(X)|curious(X))<=>(~funny(X)|~kind(X))))&
(?[X]:((~generous(X)&~old(X))))&
((~creative(alice)<~>tall(alice)))&
((~creative(paul)&~tall(paul)))&
(?[X]:((~curious(X)&calm(X))))&
((wise(susan)|patient(susan)))&
(?[X]:(quiet(X)))&
(~rich(mary))&
((old(paul)|~humble(paul))) | happy(alice) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 792458553246079229172940
% SZS output start Proof for 792458553246079229172940
10. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> calm(X0)) [input p9]
12. ! [X0] : (~calm(X0) <=> curious(X0)) [input p11]
25. happy(alice) [input hypothesis]
54. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~calm(X0)) & (calm(X0) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 10]
56. ! [X0] : ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0))) [nnf transformation 12]
108. ~curious(X0) | ~happy(X0) | calm(X0) [cnf transformation 54]
110. ~calm(X0) | curious(X0) | ~happy(X0) [cnf transformation 54]
116. curious(X0) | calm(X0) [cnf transformation 56]
117. ~curious(X0) | ~calm(X0) [cnf transformation 56]
145. happy(alice) [cnf transformation 25]
317. 34 <=> curious(alice) [avatar definition]
319. curious(alice) <- (34) [avatar component clause 317]
365. ~happy(X0) | calm(X0) | calm(X0) [resolution 108,116]
366. ~happy(X0) | calm(X0) [duplicate literal removal 365]
522. calm(alice) [resolution 366,145]
585. curious(alice) | ~happy(alice) [resolution 522,110]
587. curious(alice) [subsumption resolution 585,145]
588. 34 [avatar split clause 587,317]
593. ~calm(alice) <- (34) [resolution 319,117]
600. $false <- (34) [subsumption resolution 593,522]
601. ~34 [avatar contradiction clause 600]
602. $false [avatar sat refutation 588,601]
% SZS output end Proof for 792458553246079229172940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not humble is either rich or not kind and vice versa.
Everyone who is generous is not calm or wise and vice versa.
If paul is patient then someone is both not kind and not quiet.
Everyone who is brave is both rich and creative.
If mary is either not happy or not generous then someone is not patient.
Everyone who is not funny is strong.
Everyone who is both not humble and not strong is not calm and vice versa.
If paul is quiet or not patient then someone is not calm and vice versa.
Everyone who is both curious and not wise is both not rich and tall and vice versa.
If someone is happy or not brave then alice is both not brave and funny and vice versa.
If someone is brave then someone is both not quiet and not generous and vice versa.
Everyone who is both quiet and not tall is both calm and not generous.
If fred is either not happy or kind then paul is either brave or not kind.
If someone is quiet or not patient then someone is both quiet and not funny.
Everyone who is funny is either rich or not wise.
Everyone who is calm or not humble is not rich or tall.
John is either calm or not old.
Mary is not wise.
Mary is either not brave or not strong.
Alice is both not rich and not generous.
Susan is not patient.
Someone is both brave and wise.
Someone is happy or generous.
Someone is tall or humble. | Fred is not happy. | neutral | (![X]:((calm(X)&~humble(X))<=>(rich(X)<~>~kind(X))))&
(![X]:(generous(X)<=>(~calm(X)|wise(X))))&
((patient(paul))=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:(brave(X)=>(rich(X)&creative(X))))&
(((~happy(mary)<~>~generous(mary)))=>(?[X]:(~patient(X))))&
(![X]:(~funny(X)=>strong(X)))&
(![X]:((~humble(X)&~strong(X))<=>~calm(X)))&
(((quiet(paul)|~patient(paul)))<=>(?[X]:(~calm(X))))&
(![X]:((curious(X)&~wise(X))<=>(~rich(X)&tall(X))))&
((?[X]:((happy(X)|~brave(X))))<=>((~brave(alice)&funny(alice))))&
((?[X]:(brave(X)))<=>(?[X]:((~quiet(X)&~generous(X)))))&
(![X]:((quiet(X)&~tall(X))=>(calm(X)&~generous(X))))&
(((~happy(fred)<~>kind(fred)))=>((brave(paul)<~>~kind(paul))))&
((?[X]:((quiet(X)|~patient(X))))=>(?[X]:((quiet(X)&~funny(X)))))&
(![X]:(funny(X)=>(rich(X)<~>~wise(X))))&
(![X]:((calm(X)|~humble(X))=>(~rich(X)|tall(X))))&
((calm(john)<~>~old(john)))&
(~wise(mary))&
((~brave(mary)<~>~strong(mary)))&
((~rich(alice)&~generous(alice)))&
(~patient(susan))&
(?[X]:((brave(X)&wise(X))))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((tall(X)|humble(X)))) | ~happy(fred) | [] | null | 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. | Fred is tall. | contradiction | (![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))) | tall(fred) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8565343850359257945700742
% SZS output start Proof for 8565343850359257945700742
3. ! [X0] : ((brave(X0) & creative(X0)) <=> (~old(X0) | tall(X0))) [input p2]
6. ! [X0] : ((~creative(X0) <~> ~strong(X0)) <=> strong(X0)) [input p5]
20. tall(fred) [input hypothesis]
32. ! [X0] : (((brave(X0) & creative(X0)) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | (~brave(X0) | ~creative(X0)))) [nnf transformation 3]
33. ! [X0] : (((brave(X0) & creative(X0)) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~brave(X0) | ~creative(X0))) [flattening 32]
36. ! [X0] : ((((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | ~strong(X0)) & (strong(X0) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))))) [nnf transformation 6]
66. ~tall(X0) | creative(X0) [cnf transformation 33]
75. strong(X0) | ~creative(X0) | strong(X0) [cnf transformation 36]
76. ~strong(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 36]
113. tall(fred) [cnf transformation 20]
114. strong(X0) | ~creative(X0) [duplicate literal removal 75]
115. ~strong(X0) | ~creative(X0) [duplicate literal removal 76]
116. ~creative(X0) [subsumption resolution 114,115]
187. creative(fred) [resolution 66,113]
188. $false [subsumption resolution 187,116]
% SZS output end Proof for 8565343850359257945700742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not brave is not calm.
Everyone who is both not happy and generous is patient.
If someone is wise or creative then alice is both patient and not calm.
Everyone who is not strong is both not generous and not kind and vice versa.
Everyone who is not strong or not happy is both rich and not curious.
Everyone who is not kind or not patient is calm or wise and vice versa.
Everyone who is brave or generous is tall or not tall and vice versa.
If john is either not happy or kind then someone is not rich or not quiet and vice versa.
If someone is both curious and not kind then john is not creative.
Everyone who is rich is brave and vice versa.
If someone is calm then someone is not funny.
If lucy is either not brave or rich then someone is both generous and calm and vice versa.
If someone is either generous or calm then susan is either not quiet or humble.
If someone is rich or not strong then someone is both not old and funny and vice versa.
Everyone who is both not rich and generous is either rich or calm and vice versa.
If susan is not patient or not creative then someone is either not tall or quiet.
Someone is both not kind and not humble.
Someone is patient.
Susan is not happy.
Someone is not rich.
Someone is both not old and generous.
Someone is both not creative and brave.
Someone is not patient or calm.
Someone is tall or humble. | Susan is quiet. | neutral | (![X]:((creative(X)&~brave(X))=>~calm(X)))&
(![X]:((~happy(X)&generous(X))=>patient(X)))&
((?[X]:((wise(X)|creative(X))))=>((patient(alice)&~calm(alice))))&
(![X]:(~strong(X)<=>(~generous(X)&~kind(X))))&
(![X]:((~strong(X)|~happy(X))=>(rich(X)&~curious(X))))&
(![X]:((~kind(X)|~patient(X))<=>(calm(X)|wise(X))))&
(![X]:((brave(X)|generous(X))<=>(tall(X)|~tall(X))))&
(((~happy(john)<~>kind(john)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
((?[X]:((curious(X)&~kind(X))))=>(~creative(john)))&
(![X]:(rich(X)<=>brave(X)))&
((?[X]:(calm(X)))=>(?[X]:(~funny(X))))&
(((~brave(lucy)<~>rich(lucy)))<=>(?[X]:((generous(X)&calm(X)))))&
((?[X]:((generous(X)<~>calm(X))))=>((~quiet(susan)<~>humble(susan))))&
((?[X]:((rich(X)|~strong(X))))<=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((~rich(X)&generous(X))<=>(rich(X)<~>calm(X))))&
(((~patient(susan)|~creative(susan)))=>(?[X]:((~tall(X)<~>quiet(X)))))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:(patient(X)))&
(~happy(susan))&
(?[X]:(~rich(X)))&
(?[X]:((~old(X)&generous(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:((tall(X)|humble(X)))) | quiet(susan) | [] | null | 0 |
If someone is either calm or kind then susan is not kind or brave and vice versa.
If paul is curious or old then paul is tall or not generous.
If alice is both not wise and calm then alice is either not tall or not quiet and vice versa.
Everyone who is both not rich and generous is both not old and not brave and vice versa.
If lucy is not rich or tall then fred is both creative and not tall.
If alice is both not humble and strong then someone is either not funny or not tall.
Everyone who is both not humble and not patient is brave or rich and vice versa.
Everyone who is either funny or tall is rich or brave and vice versa.
Everyone who is either wise or not calm is not quiet and vice versa.
Everyone who is either not quiet or not creative is generous.
Everyone who is creative is either funny or old and vice versa.
If someone is not old or creative then someone is either tall or not kind and vice versa.
Everyone who is both creative and calm is old.
If someone is both not quiet and not calm then fred is not old or calm and vice versa.
Everyone who is both not creative and kind is not calm or rich and vice versa.
If alice is both old and not calm then someone is quiet or happy and vice versa.
Someone is happy.
Someone is not kind.
Someone is both humble and wise.
Someone is not tall or not calm.
Mary is both not generous and quiet.
Paul is not tall. | Alice is not wise. | entailment | ((?[X]:((calm(X)<~>kind(X))))<=>((~kind(susan)|brave(susan))))&
(((curious(paul)|old(paul)))=>((tall(paul)|~generous(paul))))&
(((~wise(alice)&calm(alice)))<=>((~tall(alice)<~>~quiet(alice))))&
(![X]:((~rich(X)&generous(X))<=>(~old(X)&~brave(X))))&
(((~rich(lucy)|tall(lucy)))=>((creative(fred)&~tall(fred))))&
(((~humble(alice)&strong(alice)))=>(?[X]:((~funny(X)<~>~tall(X)))))&
(![X]:((~humble(X)&~patient(X))<=>(brave(X)|rich(X))))&
(![X]:((funny(X)<~>tall(X))<=>(rich(X)|brave(X))))&
(![X]:((wise(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~quiet(X)<~>~creative(X))=>generous(X)))&
(![X]:(creative(X)<=>(funny(X)<~>old(X))))&
((?[X]:((~old(X)|creative(X))))<=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(?[X]:(happy(X)))&
(?[X]:(~kind(X)))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((~tall(X)|~calm(X))))&
((~generous(mary)&quiet(mary)))&
(~tall(paul)) | ~wise(alice) | [
"p2",
"p3",
"p7",
"p8",
"p9",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5347447732844224493536026
% SZS output start Proof for 5347447732844224493536026
3. (calm(alice) & ~wise(alice)) <=> (~tall(alice) <~> ~quiet(alice)) [input p2]
4. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (~brave(X0) & ~old(X0))) [input p3]
8. ! [X0] : ((funny(X0) <~> tall(X0)) <=> (brave(X0) | rich(X0))) [input p7]
9. ! [X0] : ((wise(X0) <~> ~calm(X0)) <=> ~quiet(X0)) [input p8]
10. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) => generous(X0)) [input p9]
11. ! [X0] : (creative(X0) <=> (funny(X0) <~> old(X0))) [input p10]
15. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
16. (~calm(alice) & old(alice)) <=> ? [X0] : (happy(X0) | quiet(X0)) [input p15]
17. ? [X0] : happy(X0) [input p16]
23. wise(alice) [input hypothesis]
30. ! [X0] : (generous(X0) | (~quiet(X0) <=> ~creative(X0))) [ennf transformation 10]
38. ((calm(alice) & ~wise(alice)) | ((~tall(alice) | quiet(alice)) & (~quiet(alice) | tall(alice)))) & (((quiet(alice) | tall(alice)) & (~quiet(alice) | ~tall(alice))) | (~calm(alice) | wise(alice))) [nnf transformation 3]
39. ((calm(alice) & ~wise(alice)) | ((~tall(alice) | quiet(alice)) & (~quiet(alice) | tall(alice)))) & (((quiet(alice) | tall(alice)) & (~quiet(alice) | ~tall(alice))) | ~calm(alice) | wise(alice)) [flattening 38]
40. ! [X0] : (((generous(X0) & ~rich(X0)) | (brave(X0) | old(X0))) & ((~brave(X0) & ~old(X0)) | (~generous(X0) | rich(X0)))) [nnf transformation 4]
41. ! [X0] : (((generous(X0) & ~rich(X0)) | brave(X0) | old(X0)) & ((~brave(X0) & ~old(X0)) | ~generous(X0) | rich(X0))) [flattening 40]
44. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [nnf transformation 8]
45. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [flattening 44]
46. ! [X0] : ((((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | quiet(X0)) & (~quiet(X0) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0))))) [nnf transformation 9]
47. ! [X0] : (generous(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) [nnf transformation 30]
48. ! [X0] : ((creative(X0) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | ~creative(X0))) [nnf transformation 11]
59. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 15]
60. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 59]
61. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | (calm(alice) | ~old(alice))) [nnf transformation 16]
62. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | calm(alice) | ~old(alice)) [flattening 61]
63. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X1] : (happy(X1) | quiet(X1)) | calm(alice) | ~old(alice)) [rectify 62]
64. ? [X1] : (happy(X1) | quiet(X1)) => (happy(sK4) | quiet(sK4)) [choice axiom]
65. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & ((happy(sK4) | quiet(sK4)) | calm(alice) | ~old(alice)) [skolemisation 63,64]
66. ? [X0] : happy(X0) => happy(sK5) [choice axiom]
67. happy(sK5) [skolemisation 17,66]
83. ~wise(alice) | ~quiet(alice) | tall(alice) [cnf transformation 39]
87. ~generous(X0) | ~old(X0) | rich(X0) [cnf transformation 41]
104. ~funny(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 45]
109. ~wise(X0) | calm(X0) | quiet(X0) [cnf transformation 46]
111. ~quiet(X0) | generous(X0) | creative(X0) [cnf transformation 47]
115. ~old(X0) | funny(X0) | creative(X0) [cnf transformation 48]
129. ~creative(X0) | calm(X0) [cnf transformation 60]
135. old(alice) | ~happy(X0) [cnf transformation 65]
137. ~calm(alice) | ~happy(X0) [cnf transformation 65]
138. happy(sK5) [cnf transformation 67]
146. wise(alice) [cnf transformation 23]
189. 10 <=> quiet(alice) [avatar definition]
191. quiet(alice) <- (10) [avatar component clause 189]
193. 11 <=> tall(alice) [avatar definition]
194. tall(alice) <- (11) [avatar component clause 193]
197. 12 <=> calm(alice) [avatar definition]
198. ~calm(alice) <- (~12) [avatar component clause 197]
203. 13 <=> wise(alice) [avatar definition]
204. wise(alice) <- (13) [avatar component clause 203]
207. 11 | ~10 | ~13 [avatar split clause 83,203,189,193]
289. 31 <=> ! [X0] : ~happy(X0) [avatar definition]
290. ~happy(X0) <- (31) [avatar component clause 289]
291. 31 | ~12 [avatar split clause 137,197,289]
297. 33 <=> old(alice) [avatar definition]
299. old(alice) <- (33) [avatar component clause 297]
300. 31 | 33 [avatar split clause 135,297,289]
321. 13 [avatar split clause 146,203]
322. $false <- (31) [resolution 290,138]
323. ~31 [avatar contradiction clause 322]
467. calm(alice) | quiet(alice) <- (13) [resolution 109,204]
478. quiet(alice) <- (~12, 13) [subsumption resolution 467,198]
481. 10 | 12 | ~13 [avatar split clause 478,203,197,189]
485. generous(alice) | creative(alice) <- (10) [resolution 111,191]
488. 60 <=> creative(alice) [avatar definition]
490. creative(alice) <- (60) [avatar component clause 488]
492. 61 <=> generous(alice) [avatar definition]
494. generous(alice) <- (61) [avatar component clause 492]
495. 60 | 61 | ~10 [avatar split clause 485,189,492,488]
502. funny(alice) | creative(alice) <- (33) [resolution 115,299]
551. 68 <=> funny(alice) [avatar definition]
553. funny(alice) <- (68) [avatar component clause 551]
555. 69 <=> rich(alice) [avatar definition]
557. rich(alice) <- (69) [avatar component clause 555]
577. calm(alice) <- (60) [resolution 490,129]
579. $false <- (~12, 60) [subsumption resolution 577,198]
580. 12 | ~60 [avatar contradiction clause 579]
581. 60 | 68 | ~33 [avatar split clause 502,297,551,488]
583. ~old(alice) | rich(alice) <- (61) [resolution 494,87]
586. rich(alice) <- (33, 61) [subsumption resolution 583,299]
587. 69 | ~33 | ~61 [avatar split clause 586,492,297,555]
593. ~tall(alice) | ~rich(alice) <- (68) [resolution 553,104]
597. ~rich(alice) <- (11, 68) [subsumption resolution 593,194]
598. $false <- (11, 68, 69) [subsumption resolution 597,557]
599. ~11 | ~68 | ~69 [avatar contradiction clause 598]
600. $false [avatar sat refutation 207,291,300,321,323,481,495,580,581,587,599]
% SZS output end Proof for 5347447732844224493536026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both wise and not generous and vice versa.
If someone is not kind or not strong then paul is not creative.
Everyone who is not creative or not old is both not humble and not creative and vice versa.
If someone is patient or kind then lucy is both curious and not quiet and vice versa.
If fred is either funny or calm then lucy is either not rich or curious and vice versa.
If someone is both not happy and creative then mary is not funny or not creative and vice versa.
Everyone who is not strong or not curious is either curious or humble.
If someone is both not generous and happy then someone is patient.
If someone is either not calm or generous then someone is both not humble and patient and vice versa.
If susan is both not kind and not tall then paul is rich and vice versa.
Everyone who is quiet is both not generous and tall.
If someone is either not old or happy then someone is calm or patient and vice versa.
If someone is either not old or wise then lucy is creative and vice versa.
Everyone who is either not curious or humble is both generous and kind.
If someone is both quiet and not humble then someone is either calm or not brave and vice versa.
Everyone who is creative or not quiet is both not patient and not tall and vice versa.
Susan is rich or not funny.
Fred is either old or rich.
Someone is both brave and not funny.
Someone is funny.
Fred is old.
Paul is creative.
Susan is both old and not patient.
Someone is wise. | Lucy is patient. | contradiction | (![X]:(~curious(X)<=>(wise(X)&~generous(X))))&
((?[X]:((~kind(X)|~strong(X))))=>(~creative(paul)))&
(![X]:((~creative(X)|~old(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((patient(X)|kind(X))))<=>((curious(lucy)&~quiet(lucy))))&
(((funny(fred)<~>calm(fred)))<=>((~rich(lucy)<~>curious(lucy))))&
((?[X]:((~happy(X)&creative(X))))<=>((~funny(mary)|~creative(mary))))&
(![X]:((~strong(X)|~curious(X))=>(curious(X)<~>humble(X))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:(patient(X))))&
((?[X]:((~calm(X)<~>generous(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~kind(susan)&~tall(susan)))<=>(rich(paul)))&
(![X]:(quiet(X)=>(~generous(X)&tall(X))))&
((?[X]:((~old(X)<~>happy(X))))<=>(?[X]:((calm(X)|patient(X)))))&
((?[X]:((~old(X)<~>wise(X))))<=>(creative(lucy)))&
(![X]:((~curious(X)<~>humble(X))=>(generous(X)&kind(X))))&
((?[X]:((quiet(X)&~humble(X))))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((creative(X)|~quiet(X))<=>(~patient(X)&~tall(X))))&
((rich(susan)|~funny(susan)))&
((old(fred)<~>rich(fred)))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:(funny(X)))&
(old(fred))&
(creative(paul))&
((old(susan)&~patient(susan)))&
(?[X]:(wise(X))) | patient(lucy) | [
"p1",
"p3",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7789379960508523431119217
% SZS output start Proof for 7789379960508523431119217
2. ? [X0] : (~strong(X0) | ~kind(X0)) => ~creative(paul) [input p1]
4. ? [X0] : (kind(X0) | patient(X0)) <=> (~quiet(lucy) & curious(lucy)) [input p3]
16. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (~tall(X0) & ~patient(X0))) [input p15]
22. creative(paul) [input p21]
25. patient(lucy) [input hypothesis]
30. ? [X0] : ~kind(X0) => ~creative(paul) [pure predicate removal 2]
32. ~creative(paul) | ! [X0] : kind(X0) [ennf transformation 30]
41. (? [X0] : (kind(X0) | patient(X0)) | (quiet(lucy) | ~curious(lucy))) & ((~quiet(lucy) & curious(lucy)) | ! [X0] : (~kind(X0) & ~patient(X0))) [nnf transformation 4]
42. (? [X0] : (kind(X0) | patient(X0)) | quiet(lucy) | ~curious(lucy)) & ((~quiet(lucy) & curious(lucy)) | ! [X0] : (~kind(X0) & ~patient(X0))) [flattening 41]
43. (? [X0] : (kind(X0) | patient(X0)) | quiet(lucy) | ~curious(lucy)) & ((~quiet(lucy) & curious(lucy)) | ! [X1] : (~kind(X1) & ~patient(X1))) [rectify 42]
44. ? [X0] : (kind(X0) | patient(X0)) => (kind(sK0) | patient(sK0)) [choice axiom]
45. ((kind(sK0) | patient(sK0)) | quiet(lucy) | ~curious(lucy)) & ((~quiet(lucy) & curious(lucy)) | ! [X1] : (~kind(X1) & ~patient(X1))) [skolemisation 43,44]
78. ! [X0] : (((~quiet(X0) | creative(X0)) | (tall(X0) | patient(X0))) & ((~tall(X0) & ~patient(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 16]
79. ! [X0] : ((~quiet(X0) | creative(X0) | tall(X0) | patient(X0)) & ((~tall(X0) & ~patient(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 78]
90. ~creative(paul) | kind(X0) [cnf transformation 32]
99. ~quiet(lucy) | ~kind(X1) [cnf transformation 45]
149. ~patient(X0) | quiet(X0) [cnf transformation 79]
160. creative(paul) [cnf transformation 22]
164. patient(lucy) [cnf transformation 25]
167. 1 <=> ! [X0] : kind(X0) [avatar definition]
168. kind(X0) <- (1) [avatar component clause 167]
170. 2 <=> creative(paul) [avatar definition]
173. 1 | ~2 [avatar split clause 90,170,167]
179. 4 <=> quiet(lucy) [avatar definition]
180. ~quiet(lucy) <- (~4) [avatar component clause 179]
192. 7 <=> ! [X1] : ~kind(X1) [avatar definition]
193. ~kind(X1) <- (7) [avatar component clause 192]
194. 7 | ~4 [avatar split clause 99,179,192]
403. 2 [avatar split clause 160,170]
404. $false <- (1, 7) [subsumption resolution 168,193]
405. ~1 | ~7 [avatar contradiction clause 404]
420. quiet(lucy) [resolution 149,164]
423. $false <- (~4) [subsumption resolution 420,180]
424. 4 [avatar contradiction clause 423]
425. $false [avatar sat refutation 173,194,403,405,424]
% SZS output end Proof for 7789379960508523431119217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not patient and creative then susan is quiet and vice versa. Everyone who is both generous and not generous is kind or not generous and vice versa. Everyone who is not generous or calm is strong or old. If someone is not quiet or not brave then john is not brave or quiet and vice versa. If paul is quiet or wise then someone is not brave or happy and vice versa. Everyone who is creative is both calm and creative. Everyone who is wise is either not kind or not generous and vice versa. Everyone who is either not patient or not old is not strong or not kind and vice versa. If someone is patient then someone is curious or creative and vice versa. Everyone who is brave is both rich and not creative. Everyone who is both rich and not generous is both not old and not generous. Everyone who is both humble and curious is not happy or funny. Everyone who is not curious is humble and vice versa. If john is brave or curious then fred is curious or happy. If someone is either brave or not calm then someone is not humble and vice versa. If someone is not happy then lucy is humble. Someone is either not old or brave. Someone is tall or not curious. Paul is not creative. Susan is both not brave and not happy. Lucy is not wise or humble. Someone is not rich. | John is humble. | neutral | ((?[X]:((~patient(X)&creative(X))))<=>(quiet(susan)))&
(![X]:((generous(X)&~generous(X))<=>(kind(X)|~generous(X))))&
(![X]:((~generous(X)|calm(X))=>(strong(X)|old(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>((~brave(john)|quiet(john))))&
(((quiet(paul)|wise(paul)))<=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:(creative(X)=>(calm(X)&creative(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~generous(X))))&
(![X]:((~patient(X)<~>~old(X))<=>(~strong(X)|~kind(X))))&
((?[X]:(patient(X)))<=>(?[X]:((curious(X)|creative(X)))))&
(![X]:(brave(X)=>(rich(X)&~creative(X))))&
(![X]:((rich(X)&~generous(X))=>(~old(X)&~generous(X))))&
(![X]:((humble(X)&curious(X))=>(~happy(X)|funny(X))))&
(![X]:(~curious(X)<=>humble(X)))&
(((brave(john)|curious(john)))=>((curious(fred)|happy(fred))))&
((?[X]:((brave(X)<~>~calm(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(~happy(X)))=>(humble(lucy)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((tall(X)|~curious(X))))&
(~creative(paul))&
((~brave(susan)&~happy(susan)))&
((~wise(lucy)|humble(lucy)))&
(?[X]:(~rich(X))) | humble(john) | [] | null | 0 |
Everyone who is not old is either funny or kind. Everyone who is both wise and curious is not curious. Everyone who is not brave or not old is either kind or strong and vice versa. Everyone who is both not calm and not kind is either not patient or not happy and vice versa. If paul is either not creative or not old then someone is both rich and not calm. Everyone who is not strong is both not generous and tall and vice versa. If lucy is not old or brave then someone is both not quiet and not old. If fred is not happy or wise then someone is funny. Everyone who is calm is either not humble or not strong and vice versa. If someone is either calm or curious then someone is rich or not creative and vice versa. Everyone who is both curious and rich is not funny or not strong and vice versa. If lucy is both kind and not strong then someone is quiet or calm and vice versa. Everyone who is brave or rich is kind and vice versa. Everyone who is not humble is quiet or generous and vice versa. If someone is either not strong or not curious then lucy is either not quiet or creative and vice versa. Susan is both not curious and not patient. Mary is both happy and not tall. Fred is creative. Lucy is curious. John is either funny or wise. Someone is either quiet or not old. Paul is not quiet or curious. Someone is not rich. | Fred is kind. | neutral | (![X]:(~old(X)=>(funny(X)<~>kind(X))))&
(![X]:((wise(X)&curious(X))=>~curious(X)))&
(![X]:((~brave(X)|~old(X))<=>(kind(X)<~>strong(X))))&
(![X]:((~calm(X)&~kind(X))<=>(~patient(X)<~>~happy(X))))&
(((~creative(paul)<~>~old(paul)))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:(~strong(X)<=>(~generous(X)&tall(X))))&
(((~old(lucy)|brave(lucy)))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~happy(fred)|wise(fred)))=>(?[X]:(funny(X))))&
(![X]:(calm(X)<=>(~humble(X)<~>~strong(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((curious(X)&rich(X))<=>(~funny(X)|~strong(X))))&
(((kind(lucy)&~strong(lucy)))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((brave(X)|rich(X))<=>kind(X)))&
(![X]:(~humble(X)<=>(quiet(X)|generous(X))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>((~quiet(lucy)<~>creative(lucy))))&
((~curious(susan)&~patient(susan)))&
((happy(mary)&~tall(mary)))&
(creative(fred))&
(curious(lucy))&
((funny(john)<~>wise(john)))&
(?[X]:((quiet(X)<~>~old(X))))&
((~quiet(paul)|curious(paul)))&
(?[X]:(~rich(X))) | kind(fred) | [] | null | 0 |
If john is both calm and not strong then someone is either not curious or tall and vice versa.
Everyone who is either creative or not quiet is quiet or not quiet.
If someone is tall then john is wise.
If someone is happy then someone is not generous.
If alice is not humble then someone is either not rich or strong.
If someone is not wise then alice is either not creative or creative and vice versa.
Everyone who is both not creative and calm is both rich and not generous.
Everyone who is either humble or generous is both not creative and quiet.
Everyone who is either funny or not calm is wise and vice versa.
If fred is both not funny and not old then lucy is either quiet or calm and vice versa.
If susan is either rich or not brave then lucy is either wise or generous and vice versa.
If lucy is either creative or not humble then someone is not wise.
Everyone who is not humble is both humble and not old and vice versa.
Everyone who is humble is both not funny and not happy and vice versa.
Everyone who is either not humble or not curious is either not humble or brave.
Everyone who is not generous is both not humble and humble.
Susan is not rich or patient.
Fred is creative.
Paul is either kind or not calm.
Someone is tall.
Alice is creative or not rich.
Lucy is not brave.
Someone is wise. | Paul is wise. | neutral | (((calm(john)&~strong(john)))<=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((creative(X)<~>~quiet(X))=>(quiet(X)|~quiet(X))))&
((?[X]:(tall(X)))=>(wise(john)))&
((?[X]:(happy(X)))=>(?[X]:(~generous(X))))&
((~humble(alice))=>(?[X]:((~rich(X)<~>strong(X)))))&
((?[X]:(~wise(X)))<=>((~creative(alice)<~>creative(alice))))&
(![X]:((~creative(X)&calm(X))=>(rich(X)&~generous(X))))&
(![X]:((humble(X)<~>generous(X))=>(~creative(X)&quiet(X))))&
(![X]:((funny(X)<~>~calm(X))<=>wise(X)))&
(((~funny(fred)&~old(fred)))<=>((quiet(lucy)<~>calm(lucy))))&
(((rich(susan)<~>~brave(susan)))<=>((wise(lucy)<~>generous(lucy))))&
(((creative(lucy)<~>~humble(lucy)))=>(?[X]:(~wise(X))))&
(![X]:(~humble(X)<=>(humble(X)&~old(X))))&
(![X]:(humble(X)<=>(~funny(X)&~happy(X))))&
(![X]:((~humble(X)<~>~curious(X))=>(~humble(X)<~>brave(X))))&
(![X]:(~generous(X)=>(~humble(X)&humble(X))))&
((~rich(susan)|patient(susan)))&
(creative(fred))&
((kind(paul)<~>~calm(paul)))&
(?[X]:(tall(X)))&
((creative(alice)|~rich(alice)))&
(~brave(lucy))&
(?[X]:(wise(X))) | wise(paul) | [] | null | 0 |
Everyone who is both tall and not kind is not funny and vice versa. Everyone who is either not curious or not brave is funny or calm and vice versa. Everyone who is either not calm or not wise is not creative or brave and vice versa. Everyone who is humble or funny is both not strong and not funny. Everyone who is either funny or not happy is not rich or not patient. Everyone who is not curious or strong is wise and vice versa. Everyone who is both not brave and not patient is brave or humble and vice versa. If someone is strong or not funny then someone is not happy or not brave and vice versa. Everyone who is either curious or not funny is either kind or not brave and vice versa. Everyone who is both patient and not old is both not patient and funny and vice versa. Everyone who is both not happy and not generous is either not creative or not funny. If john is not brave or old then fred is rich and vice versa. Everyone who is strong is either not patient or not strong and vice versa. Everyone who is not rich is either not calm or not brave. Everyone who is humble or rich is curious or not quiet. Someone is not old. Someone is quiet or not strong. John is either humble or not wise. Fred is both old and not patient. Paul is not wise or not kind. Someone is either quiet or not old. | Paul is not kind. | entailment | (![X]:((tall(X)&~kind(X))<=>~funny(X)))&
(![X]:((~curious(X)<~>~brave(X))<=>(funny(X)|calm(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(~creative(X)|brave(X))))&
(![X]:((humble(X)|funny(X))=>(~strong(X)&~funny(X))))&
(![X]:((funny(X)<~>~happy(X))=>(~rich(X)|~patient(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((patient(X)&~old(X))<=>(~patient(X)&funny(X))))&
(![X]:((~happy(X)&~generous(X))=>(~creative(X)<~>~funny(X))))&
(((~brave(john)|old(john)))<=>(rich(fred)))&
(![X]:(strong(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:(~rich(X)=>(~calm(X)<~>~brave(X))))&
(![X]:((humble(X)|rich(X))=>(curious(X)|~quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)|~strong(X))))&
((humble(john)<~>~wise(john)))&
((old(fred)&~patient(fred)))&
((~wise(paul)|~kind(paul)))&
(?[X]:((quiet(X)<~>~old(X)))) | ~kind(paul) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 595466072887343634951734
% SZS output start Proof for 595466072887343634951734
1. ! [X0] : ((~kind(X0) & tall(X0)) <=> ~funny(X0)) [input p0]
4. ! [X0] : ((funny(X0) | humble(X0)) => (~funny(X0) & ~strong(X0))) [input p3]
22. kind(paul) [input hypothesis]
25. ! [X0] : ((~funny(X0) & ~strong(X0)) | (~funny(X0) & ~humble(X0))) [ennf transformation 4]
31. ! [X0] : (((~kind(X0) & tall(X0)) | funny(X0)) & (~funny(X0) | (kind(X0) | ~tall(X0)))) [nnf transformation 1]
32. ! [X0] : (((~kind(X0) & tall(X0)) | funny(X0)) & (~funny(X0) | kind(X0) | ~tall(X0))) [flattening 31]
64. ~kind(X0) | funny(X0) [cnf transformation 32]
80. ~funny(X0) | ~funny(X0) [cnf transformation 25]
127. kind(paul) [cnf transformation 22]
134. ~funny(X0) [duplicate literal removal 80]
177. 8 <=> kind(paul) [avatar definition]
178. kind(paul) <- (8) [avatar component clause 177]
191. 8 [avatar split clause 127,177]
193. funny(paul) <- (8) [resolution 64,178]
194. $false <- (8) [subsumption resolution 193,134]
195. ~8 [avatar contradiction clause 194]
196. $false [avatar sat refutation 191,195]
% SZS output end Proof for 595466072887343634951734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not wise is both happy and not patient and vice versa. Everyone who is not happy or not tall is both rich and not strong and vice versa. If someone is both kind and not brave then someone is not funny or old and vice versa. Everyone who is not generous or not happy is both happy and not rich. Everyone who is both not strong and old is brave or patient. If alice is either rich or old then john is either patient or not wise and vice versa. If someone is quiet then alice is either funny or not quiet. Everyone who is either not patient or humble is not wise or funny and vice versa. Everyone who is strong is not funny. If mary is both funny and not creative then lucy is both not wise and curious. If alice is not tall then someone is both funny and not humble and vice versa. If susan is either not generous or brave then someone is patient. Everyone who is both patient and not humble is not brave or calm and vice versa. If someone is generous or quiet then someone is not creative or humble and vice versa. Everyone who is brave or not curious is humble or rich. Someone is either curious or funny. Paul is kind or humble. Paul is both quiet and not generous. | Paul is not old. | entailment | (![X]:((~brave(X)<~>~wise(X))<=>(happy(X)&~patient(X))))&
(![X]:((~happy(X)|~tall(X))<=>(rich(X)&~strong(X))))&
((?[X]:((kind(X)&~brave(X))))<=>(?[X]:((~funny(X)|old(X)))))&
(![X]:((~generous(X)|~happy(X))=>(happy(X)&~rich(X))))&
(![X]:((~strong(X)&old(X))=>(brave(X)|patient(X))))&
(((rich(alice)<~>old(alice)))<=>((patient(john)<~>~wise(john))))&
((?[X]:(quiet(X)))=>((funny(alice)<~>~quiet(alice))))&
(![X]:((~patient(X)<~>humble(X))<=>(~wise(X)|funny(X))))&
(![X]:(strong(X)=>~funny(X)))&
(((funny(mary)&~creative(mary)))=>((~wise(lucy)&curious(lucy))))&
((~tall(alice))<=>(?[X]:((funny(X)&~humble(X)))))&
(((~generous(susan)<~>brave(susan)))=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~humble(X))<=>(~brave(X)|calm(X))))&
((?[X]:((generous(X)|quiet(X))))<=>(?[X]:((~creative(X)|humble(X)))))&
(![X]:((brave(X)|~curious(X))=>(humble(X)|rich(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((kind(paul)|humble(paul)))&
((quiet(paul)&~generous(paul))) | ~old(paul) | [
"p0",
"p2",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2933947676467158563980694
% SZS output start Proof for 2933947676467158563980694
1. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (~patient(X0) & happy(X0))) [input p0]
3. ? [X0] : (~brave(X0) & kind(X0)) <=> ? [X0] : (old(X0) | ~funny(X0)) [input p2]
8. ! [X0] : ((~patient(X0) <~> humble(X0)) <=> (funny(X0) | ~wise(X0))) [input p7]
13. ! [X0] : ((~humble(X0) & patient(X0)) <=> (calm(X0) | ~brave(X0))) [input p12]
19. old(paul) [input hypothesis]
20. ? [X0] : (~brave(X0) & kind(X0)) <=> ? [X1] : (old(X1) | ~funny(X1)) [rectify 3]
32. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 1]
33. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [flattening 32]
36. (? [X0] : (~brave(X0) & kind(X0)) | ! [X1] : (~old(X1) & funny(X1))) & (? [X1] : (old(X1) | ~funny(X1)) | ! [X0] : (brave(X0) | ~kind(X0))) [nnf transformation 20]
37. (? [X0] : (~brave(X0) & kind(X0)) | ! [X1] : (~old(X1) & funny(X1))) & (? [X2] : (old(X2) | ~funny(X2)) | ! [X3] : (brave(X3) | ~kind(X3))) [rectify 36]
38. ? [X0] : (~brave(X0) & kind(X0)) => (~brave(sK0) & kind(sK0)) [choice axiom]
39. ? [X2] : (old(X2) | ~funny(X2)) => (old(sK1) | ~funny(sK1)) [choice axiom]
40. ((~brave(sK0) & kind(sK0)) | ! [X1] : (~old(X1) & funny(X1))) & ((old(sK1) | ~funny(sK1)) | ! [X3] : (brave(X3) | ~kind(X3))) [skolemisation 37,39,38]
43. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [nnf transformation 8]
44. ! [X0] : ((((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | ((~patient(X0) | ~humble(X0)) & (humble(X0) | patient(X0))))) [flattening 43]
52. ! [X0] : (((~humble(X0) & patient(X0)) | (~calm(X0) & brave(X0))) & ((calm(X0) | ~brave(X0)) | (humble(X0) | ~patient(X0)))) [nnf transformation 13]
53. ! [X0] : (((~humble(X0) & patient(X0)) | (~calm(X0) & brave(X0))) & (calm(X0) | ~brave(X0) | humble(X0) | ~patient(X0))) [flattening 52]
64. ~patient(X0) | ~wise(X0) | brave(X0) [cnf transformation 33]
77. ~brave(sK0) | ~old(X1) [cnf transformation 40]
95. ~patient(X0) | humble(X0) | wise(X0) [cnf transformation 44]
108. patient(X0) | brave(X0) [cnf transformation 53]
110. ~humble(X0) | brave(X0) [cnf transformation 53]
123. old(paul) [cnf transformation 19]
126. 1 <=> ! [X1] : ~old(X1) [avatar definition]
127. ~old(X1) <- (1) [avatar component clause 126]
129. 2 <=> brave(sK0) [avatar definition]
131. ~brave(sK0) <- (~2) [avatar component clause 129]
132. 1 | ~2 [avatar split clause 77,129,126]
301. ~wise(X0) | brave(X0) | brave(X0) [resolution 64,108]
302. ~wise(X0) | brave(X0) [duplicate literal removal 301]
305. humble(X0) | wise(X0) | brave(X0) [resolution 95,108]
306. wise(X0) | brave(X0) [subsumption resolution 305,110]
307. brave(X0) [subsumption resolution 306,302]
308. $false <- (~2) [resolution 307,131]
310. 2 [avatar contradiction clause 308]
311. $false <- (1) [resolution 127,123]
312. ~1 [avatar contradiction clause 311]
313. $false [avatar sat refutation 132,310,312]
% SZS output end Proof for 2933947676467158563980694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or curious is not funny.
If paul is not tall or not rich then someone is either tall or kind and vice versa.
Everyone who is either not curious or humble is both funny and curious.
Everyone who is not generous or funny is both not creative and not quiet.
Everyone who is brave or curious is not humble or not tall and vice versa.
Everyone who is not patient is old or happy.
If john is strong or not brave then someone is either not happy or not strong.
Everyone who is not quiet is patient.
If someone is curious then alice is both creative and generous.
Everyone who is not funny is both not wise and patient and vice versa.
If someone is either calm or quiet then mary is curious or not creative.
Everyone who is both not patient and not rich is both tall and creative.
If john is not happy then someone is happy and vice versa.
Everyone who is both creative and wise is not funny or strong and vice versa.
Everyone who is either creative or brave is either rich or not happy and vice versa.
Susan is wise.
Someone is both kind and not old.
John is not calm.
Lucy is wise. | Susan is generous. | neutral | (![X]:((rich(X)|curious(X))=>~funny(X)))&
(((~tall(paul)|~rich(paul)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
(wise(susan))&
(?[X]:((kind(X)&~old(X))))&
(~calm(john))&
(wise(lucy)) | generous(susan) | [] | null | 0 |
Everyone who is either tall or not creative is either not funny or strong.
If paul is not humble or tall then someone is quiet.
Everyone who is not brave or not calm is both not tall and calm and vice versa.
Everyone who is both not tall and not brave is both not curious and not creative and vice versa.
If susan is either rich or not patient then someone is either not funny or quiet.
If someone is both not creative and calm then susan is both patient and not quiet and vice versa.
Everyone who is creative is either kind or calm.
If fred is quiet then mary is either not strong or not curious and vice versa.
If john is both not funny and not kind then john is both happy and not patient and vice versa.
If susan is not curious or not tall then someone is not strong or old.
Everyone who is not happy or humble is quiet and vice versa.
If someone is either brave or quiet then someone is brave.
Everyone who is not kind is calm.
If paul is both strong and not quiet then susan is both old and tall.
Everyone who is both not calm and happy is not quiet and vice versa.
Everyone who is not strong is either not patient or not quiet and vice versa.
Susan is not old or not happy.
Alice is both generous and not kind.
Someone is both tall and calm.
Someone is either curious or old.
Mary is both not funny and generous.
Susan is either not brave or not rich.
Alice is patient or calm. | Susan is not quiet. | contradiction | (![X]:((tall(X)<~>~creative(X))=>(~funny(X)<~>strong(X))))&
(((~humble(paul)|tall(paul)))=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~tall(X)&calm(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~curious(X)&~creative(X))))&
(((rich(susan)<~>~patient(susan)))=>(?[X]:((~funny(X)<~>quiet(X)))))&
((?[X]:((~creative(X)&calm(X))))<=>((patient(susan)&~quiet(susan))))&
(![X]:(creative(X)=>(kind(X)<~>calm(X))))&
((quiet(fred))<=>((~strong(mary)<~>~curious(mary))))&
(((~funny(john)&~kind(john)))<=>((happy(john)&~patient(john))))&
(((~curious(susan)|~tall(susan)))=>(?[X]:((~strong(X)|old(X)))))&
(![X]:((~happy(X)|humble(X))<=>quiet(X)))&
((?[X]:((brave(X)<~>quiet(X))))=>(?[X]:(brave(X))))&
(![X]:(~kind(X)=>calm(X)))&
(((strong(paul)&~quiet(paul)))=>((old(susan)&tall(susan))))&
(![X]:((~calm(X)&happy(X))<=>~quiet(X)))&
(![X]:(~strong(X)<=>(~patient(X)<~>~quiet(X))))&
((~old(susan)|~happy(susan)))&
((generous(alice)&~kind(alice)))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((curious(X)<~>old(X))))&
((~funny(mary)&generous(mary)))&
((~brave(susan)<~>~rich(susan)))&
((patient(alice)|calm(alice))) | ~quiet(susan) | [
"p2",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6033115059107189306428135
% SZS output start Proof for 6033115059107189306428135
3. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (calm(X0) & ~tall(X0))) [input p2]
15. ! [X0] : ((happy(X0) & ~calm(X0)) <=> ~quiet(X0)) [input p14]
24. ~quiet(susan) [input hypothesis]
40. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~calm(X0) | tall(X0))) & ((calm(X0) & ~tall(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 3]
41. ! [X0] : ((~calm(X0) | ~brave(X0) | ~calm(X0) | tall(X0)) & ((calm(X0) & ~tall(X0)) | (calm(X0) & brave(X0)))) [flattening 40]
64. ! [X0] : (((happy(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (~happy(X0) | calm(X0)))) [nnf transformation 15]
65. ! [X0] : (((happy(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | ~happy(X0) | calm(X0))) [flattening 64]
82. calm(X0) | calm(X0) [cnf transformation 41]
117. ~calm(X0) | quiet(X0) [cnf transformation 65]
133. ~quiet(susan) [cnf transformation 24]
134. calm(X0) [duplicate literal removal 82]
269. quiet(X0) [subsumption resolution 117,134]
293. $false [subsumption resolution 133,269]
% SZS output end Proof for 6033115059107189306428135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or old is not creative.
Everyone who is both humble and not patient is either not strong or old and vice versa.
Everyone who is either not brave or not wise is either happy or not calm and vice versa.
Everyone who is quiet or not creative is either curious or brave.
Everyone who is either not old or happy is not old.
Everyone who is both happy and not quiet is not curious or funny.
Everyone who is both not strong and not kind is not wise and vice versa.
Everyone who is patient is both happy and rich.
If someone is both not rich and happy then someone is not tall or generous and vice versa.
If someone is both happy and not kind then someone is both not calm and not brave.
If someone is either not old or not kind then alice is both strong and humble.
Everyone who is not humble or not tall is brave.
If someone is either quiet or humble then alice is funny.
Everyone who is rich or old is both not old and old.
If someone is quiet or generous then someone is not rich or not wise and vice versa.
If someone is either patient or not creative then someone is humble and vice versa.
John is either not happy or not calm.
Someone is happy or not tall.
Someone is not quiet.
Someone is tall or not patient.
Someone is not rich.
Someone is kind or not creative.
Susan is both wise and quiet. | Alice is not kind. | entailment | (![X]:((~humble(X)<~>old(X))=>~creative(X)))&
(![X]:((humble(X)&~patient(X))<=>(~strong(X)<~>old(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((quiet(X)|~creative(X))=>(curious(X)<~>brave(X))))&
(![X]:((~old(X)<~>happy(X))=>~old(X)))&
(![X]:((happy(X)&~quiet(X))=>(~curious(X)|funny(X))))&
(![X]:((~strong(X)&~kind(X))<=>~wise(X)))&
(![X]:(patient(X)=>(happy(X)&rich(X))))&
((?[X]:((~rich(X)&happy(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
((?[X]:((happy(X)&~kind(X))))=>(?[X]:((~calm(X)&~brave(X)))))&
((?[X]:((~old(X)<~>~kind(X))))=>((strong(alice)&humble(alice))))&
(![X]:((~humble(X)|~tall(X))=>brave(X)))&
((?[X]:((quiet(X)<~>humble(X))))=>(funny(alice)))&
(![X]:((rich(X)|old(X))=>(~old(X)&old(X))))&
((?[X]:((quiet(X)|generous(X))))<=>(?[X]:((~rich(X)|~wise(X)))))&
((?[X]:((patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
((~happy(john)<~>~calm(john)))&
(?[X]:((happy(X)|~tall(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((tall(X)|~patient(X))))&
(?[X]:(~rich(X)))&
(?[X]:((kind(X)|~creative(X))))&
((wise(susan)&quiet(susan))) | ~kind(alice) | [
"p1",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8824803116642721940984803
% SZS output start Proof for 8824803116642721940984803
2. ! [X0] : ((~patient(X0) & humble(X0)) <=> (~strong(X0) <~> old(X0))) [input p1]
8. ! [X0] : (patient(X0) => (rich(X0) & happy(X0))) [input p7]
11. ? [X0] : (~old(X0) <~> ~kind(X0)) => (humble(alice) & strong(alice)) [input p10]
14. ! [X0] : ((old(X0) | rich(X0)) => (old(X0) & ~old(X0))) [input p13]
24. kind(alice) [input hypothesis]
34. ! [X0] : ((rich(X0) & happy(X0)) | ~patient(X0)) [ennf transformation 8]
36. (humble(alice) & strong(alice)) | ! [X0] : (~old(X0) <=> ~kind(X0)) [ennf transformation 11]
38. ! [X0] : ((old(X0) & ~old(X0)) | (~old(X0) & ~rich(X0))) [ennf transformation 14]
40. ! [X0] : (((~patient(X0) & humble(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (patient(X0) | ~humble(X0)))) [nnf transformation 2]
41. ! [X0] : (((~patient(X0) & humble(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | patient(X0) | ~humble(X0))) [flattening 40]
55. (humble(alice) & strong(alice)) | ! [X0] : ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0))) [nnf transformation 36]
79. ~strong(X0) | old(X0) | patient(X0) | ~humble(X0) [cnf transformation 41]
103. ~patient(X0) | rich(X0) [cnf transformation 34]
111. strong(alice) | ~kind(X0) | old(X0) [cnf transformation 55]
113. humble(alice) | ~kind(X0) | old(X0) [cnf transformation 55]
118. ~old(X0) | ~old(X0) [cnf transformation 38]
119. ~rich(X0) | old(X0) [cnf transformation 38]
138. kind(alice) [cnf transformation 24]
139. ~old(X0) [duplicate literal removal 118]
188. 12 <=> humble(alice) [avatar definition]
190. humble(alice) <- (12) [avatar component clause 188]
193. 13 <=> ! [X0] : (~kind(X0) | old(X0)) [avatar definition]
194. ~kind(X0) | old(X0) <- (13) [avatar component clause 193]
195. 13 | 12 [avatar split clause 113,188,193]
197. 14 <=> strong(alice) [avatar definition]
199. strong(alice) <- (14) [avatar component clause 197]
201. 13 | 14 [avatar split clause 111,197,193]
293. ~kind(X0) <- (13) [subsumption resolution 194,139]
294. $false <- (13) [resolution 293,138]
295. ~13 [avatar contradiction clause 294]
345. old(alice) | patient(alice) | ~humble(alice) <- (14) [resolution 79,199]
348. patient(alice) | ~humble(alice) <- (14) [subsumption resolution 345,139]
349. patient(alice) <- (12, 14) [subsumption resolution 348,190]
365. rich(alice) <- (12, 14) [resolution 349,103]
367. old(alice) <- (12, 14) [resolution 365,119]
368. $false <- (12, 14) [subsumption resolution 367,139]
369. ~12 | ~14 [avatar contradiction clause 368]
370. $false [avatar sat refutation 195,201,295,369]
% SZS output end Proof for 8824803116642721940984803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not funny and strong. Everyone who is either not curious or not creative is either not curious or wise. Everyone who is not strong is either not tall or not wise and vice versa. If someone is not wise or not old then paul is quiet or brave. If someone is old or curious then mary is either not calm or old and vice versa. If susan is either not kind or calm then someone is tall or brave and vice versa. If susan is either curious or not patient then mary is both strong and not curious. Everyone who is both not patient and not strong is either generous or not brave and vice versa. Everyone who is either not humble or not curious is wise. Everyone who is old or happy is not old. Everyone who is not humble is old or not old. If someone is humble then mary is both rich and kind and vice versa. If someone is either not happy or not brave then someone is both not quiet and happy and vice versa. If someone is either kind or tall then alice is not funny. Everyone who is not strong is generous. If susan is both not calm and calm then someone is strong and vice versa. Alice is both calm and not patient. Someone is patient or tall. Mary is both funny and not calm. Someone is not brave. Someone is creative or generous. Fred is not brave. Someone is either not kind or creative. | Mary is generous. | entailment | (![X]:(kind(X)=>(~funny(X)&strong(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(~curious(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(~tall(X)<~>~wise(X))))&
((?[X]:((~wise(X)|~old(X))))=>((quiet(paul)|brave(paul))))&
((?[X]:((old(X)|curious(X))))<=>((~calm(mary)<~>old(mary))))&
(((~kind(susan)<~>calm(susan)))<=>(?[X]:((tall(X)|brave(X)))))&
(((curious(susan)<~>~patient(susan)))=>((strong(mary)&~curious(mary))))&
(![X]:((~patient(X)&~strong(X))<=>(generous(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(![X]:((old(X)|happy(X))=>~old(X)))&
(![X]:(~humble(X)=>(old(X)|~old(X))))&
((?[X]:(humble(X)))<=>((rich(mary)&kind(mary))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:((kind(X)<~>tall(X))))=>(~funny(alice)))&
(![X]:(~strong(X)=>generous(X)))&
(((~calm(susan)&calm(susan)))<=>(?[X]:(strong(X))))&
((calm(alice)&~patient(alice)))&
(?[X]:((patient(X)|tall(X))))&
((funny(mary)&~calm(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)|generous(X))))&
(~brave(fred))&
(?[X]:((~kind(X)<~>creative(X)))) | generous(mary) | [
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3056976117370048090263637
% SZS output start Proof for 3056976117370048090263637
15. ! [X0] : (~strong(X0) => generous(X0)) [input p14]
16. (calm(susan) & ~calm(susan)) <=> ? [X0] : strong(X0) [input p15]
24. ~generous(mary) [input hypothesis]
36. ! [X0] : (generous(X0) | strong(X0)) [ennf transformation 15]
62. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (~calm(susan) | calm(susan))) [nnf transformation 16]
63. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | ~calm(susan) | calm(susan)) [flattening 62]
64. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | ~calm(susan) | calm(susan)) [rectify 63]
65. ? [X1] : strong(X1) => strong(sK5) [choice axiom]
66. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (strong(sK5) | ~calm(susan) | calm(susan)) [skolemisation 64,65]
126. generous(X0) | strong(X0) [cnf transformation 36]
128. ~calm(susan) | ~strong(X0) [cnf transformation 66]
129. calm(susan) | ~strong(X0) [cnf transformation 66]
140. ~generous(mary) [cnf transformation 24]
196. 13 <=> calm(susan) [avatar definition]
299. 35 <=> ! [X0] : ~strong(X0) [avatar definition]
300. ~strong(X0) <- (35) [avatar component clause 299]
301. 35 | 13 [avatar split clause 129,196,299]
302. 35 | ~13 [avatar split clause 128,196,299]
345. strong(mary) [resolution 126,140]
346. $false <- (35) [subsumption resolution 345,300]
347. ~35 [avatar contradiction clause 346]
348. $false [avatar sat refutation 301,302,347]
% SZS output end Proof for 3056976117370048090263637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or quiet is quiet. If someone is either happy or humble then someone is both tall and not wise. If alice is both curious and not humble then someone is either brave or not strong. If fred is both not brave and wise then john is calm. Everyone who is either curious or not old is not happy or calm. Everyone who is creative or not humble is both not generous and not happy and vice versa. If someone is not strong or not funny then lucy is both not wise and not old and vice versa. Everyone who is both creative and kind is not funny or not brave. Everyone who is both not wise and patient is either strong or patient and vice versa. If paul is either not patient or not wise then fred is brave and vice versa. Everyone who is not patient is either not strong or rich. Everyone who is both creative and rich is calm or not kind. If someone is both kind and not rich then mary is calm. If lucy is both not generous and brave then lucy is both tall and not rich. Everyone who is creative is either not funny or not brave. If someone is not brave or not generous then fred is either kind or not patient. Paul is either not patient or funny. Mary is both patient and humble. Susan is not tall. Someone is wise. Alice is both happy and funny. Someone is funny. Someone is not kind. Someone is either funny or quiet. | John is calm. | neutral | (![X]:((~rich(X)|quiet(X))=>quiet(X)))&
((?[X]:((happy(X)<~>humble(X))))=>(?[X]:((tall(X)&~wise(X)))))&
(((curious(alice)&~humble(alice)))=>(?[X]:((brave(X)<~>~strong(X)))))&
(((~brave(fred)&wise(fred)))=>(calm(john)))&
(![X]:((curious(X)<~>~old(X))=>(~happy(X)|calm(X))))&
(![X]:((creative(X)|~humble(X))<=>(~generous(X)&~happy(X))))&
((?[X]:((~strong(X)|~funny(X))))<=>((~wise(lucy)&~old(lucy))))&
(![X]:((creative(X)&kind(X))=>(~funny(X)|~brave(X))))&
(![X]:((~wise(X)&patient(X))<=>(strong(X)<~>patient(X))))&
(((~patient(paul)<~>~wise(paul)))<=>(brave(fred)))&
(![X]:(~patient(X)=>(~strong(X)<~>rich(X))))&
(![X]:((creative(X)&rich(X))=>(calm(X)|~kind(X))))&
((?[X]:((kind(X)&~rich(X))))=>(calm(mary)))&
(((~generous(lucy)&brave(lucy)))=>((tall(lucy)&~rich(lucy))))&
(![X]:(creative(X)=>(~funny(X)<~>~brave(X))))&
((?[X]:((~brave(X)|~generous(X))))=>((kind(fred)<~>~patient(fred))))&
((~patient(paul)<~>funny(paul)))&
((patient(mary)&humble(mary)))&
(~tall(susan))&
(?[X]:(wise(X)))&
((happy(alice)&funny(alice)))&
(?[X]:(funny(X)))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)<~>quiet(X)))) | calm(john) | [] | null | 0 |
Everyone who is curious is not generous and vice versa.
Everyone who is both old and not kind is not humble or generous and vice versa.
If paul is both humble and quiet then paul is either not funny or patient.
Everyone who is quiet is either not patient or rich.
If lucy is both calm and creative then someone is calm.
Everyone who is strong or not happy is both not brave and not wise.
If someone is not brave then someone is either creative or rich and vice versa.
Everyone who is both not wise and humble is both not humble and creative and vice versa.
If paul is both not quiet and not wise then someone is kind and vice versa.
If susan is quiet or not happy then someone is kind and vice versa.
Everyone who is both old and not quiet is either not rich or generous and vice versa.
Everyone who is either not generous or calm is either not kind or wise.
If someone is both rich and not generous then someone is not strong or strong.
Everyone who is rich or curious is either strong or brave and vice versa.
Everyone who is either not calm or not rich is humble or not happy and vice versa.
Someone is curious or not creative.
Fred is either curious or tall.
Someone is both quiet and not humble.
Susan is both not quiet and not patient.
Someone is wise.
Someone is funny.
Someone is either old or not tall. | Susan is not strong. | neutral | (![X]:(curious(X)<=>~generous(X)))&
(![X]:((old(X)&~kind(X))<=>(~humble(X)|generous(X))))&
(((humble(paul)&quiet(paul)))=>((~funny(paul)<~>patient(paul))))&
(![X]:(quiet(X)=>(~patient(X)<~>rich(X))))&
(((calm(lucy)&creative(lucy)))=>(?[X]:(calm(X))))&
(![X]:((strong(X)|~happy(X))=>(~brave(X)&~wise(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((creative(X)<~>rich(X)))))&
(![X]:((~wise(X)&humble(X))<=>(~humble(X)&creative(X))))&
(((~quiet(paul)&~wise(paul)))<=>(?[X]:(kind(X))))&
(((quiet(susan)|~happy(susan)))<=>(?[X]:(kind(X))))&
(![X]:((old(X)&~quiet(X))<=>(~rich(X)<~>generous(X))))&
(![X]:((~generous(X)<~>calm(X))=>(~kind(X)<~>wise(X))))&
((?[X]:((rich(X)&~generous(X))))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:((rich(X)|curious(X))<=>(strong(X)<~>brave(X))))&
(![X]:((~calm(X)<~>~rich(X))<=>(humble(X)|~happy(X))))&
(?[X]:((curious(X)|~creative(X))))&
((curious(fred)<~>tall(fred)))&
(?[X]:((quiet(X)&~humble(X))))&
((~quiet(susan)&~patient(susan)))&
(?[X]:(wise(X)))&
(?[X]:(funny(X)))&
(?[X]:((old(X)<~>~tall(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is patient is happy or patient.
Everyone who is not funny or calm is wise and vice versa.
Everyone who is not rich or not generous is not brave and vice versa.
If paul is not humble then someone is either not humble or not rich.
If someone is not kind or rich then someone is either rich or kind and vice versa.
Everyone who is both not brave and strong is either not wise or not curious and vice versa.
Everyone who is both calm and rich is not brave or old and vice versa.
If mary is either old or not tall then john is happy and vice versa.
Everyone who is generous or not old is not brave and vice versa.
If someone is creative or not old then lucy is not creative or strong.
Everyone who is either old or not patient is not generous.
If someone is not creative then someone is either humble or not creative and vice versa.
If paul is rich or calm then paul is not strong.
Everyone who is strong or kind is either not creative or not rich.
Everyone who is both wise and not brave is not creative and vice versa.
Paul is both not tall and kind.
Susan is calm or patient.
Paul is happy or not curious.
Fred is either not rich or not curious.
Mary is either not old or curious.
Alice is kind or strong. | John is curious. | neutral | (![X]:(patient(X)=>(happy(X)|patient(X))))&
(![X]:((~funny(X)|calm(X))<=>wise(X)))&
(![X]:((~rich(X)|~generous(X))<=>~brave(X)))&
((~humble(paul))=>(?[X]:((~humble(X)<~>~rich(X)))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((~brave(X)&strong(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:((calm(X)&rich(X))<=>(~brave(X)|old(X))))&
(((old(mary)<~>~tall(mary)))<=>(happy(john)))&
(![X]:((generous(X)|~old(X))<=>~brave(X)))&
((?[X]:((creative(X)|~old(X))))=>((~creative(lucy)|strong(lucy))))&
(![X]:((old(X)<~>~patient(X))=>~generous(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(((rich(paul)|calm(paul)))=>(~strong(paul)))&
(![X]:((strong(X)|kind(X))=>(~creative(X)<~>~rich(X))))&
(![X]:((wise(X)&~brave(X))<=>~creative(X)))&
((~tall(paul)&kind(paul)))&
((calm(susan)|patient(susan)))&
((happy(paul)|~curious(paul)))&
((~rich(fred)<~>~curious(fred)))&
((~old(mary)<~>curious(mary)))&
((kind(alice)|strong(alice))) | curious(john) | [] | null | 0 |
Everyone who is quiet or not quiet is not happy.
If someone is old then someone is funny or not rich and vice versa.
If mary is not strong then someone is not old or creative.
If someone is both not kind and funny then someone is either tall or not brave.
If mary is rich or not creative then someone is both old and curious and vice versa.
Everyone who is not tall or kind is both kind and brave and vice versa.
If someone is both creative and not generous then paul is either not wise or not funny.
Everyone who is either kind or not old is both not calm and generous.
If someone is not rich then lucy is not old.
Everyone who is either not tall or patient is not generous and vice versa.
If someone is rich or not patient then someone is both happy and creative.
If mary is either humble or brave then mary is not calm.
Everyone who is both not curious and not strong is both not funny and not brave.
Everyone who is either tall or not creative is both not curious and happy.
If john is both not quiet and happy then someone is not humble and vice versa.
Lucy is creative.
Alice is rich or humble.
Someone is both humble and not happy.
Someone is both generous and not curious.
John is tall.
Lucy is either not patient or not quiet.
Someone is not brave. | John is not patient. | contradiction | (![X]:((quiet(X)|~quiet(X))=>~happy(X)))&
((?[X]:(old(X)))<=>(?[X]:((funny(X)|~rich(X)))))&
((~strong(mary))=>(?[X]:((~old(X)|creative(X)))))&
((?[X]:((~kind(X)&funny(X))))=>(?[X]:((tall(X)<~>~brave(X)))))&
(((rich(mary)|~creative(mary)))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~tall(X)|kind(X))<=>(kind(X)&brave(X))))&
((?[X]:((creative(X)&~generous(X))))=>((~wise(paul)<~>~funny(paul))))&
(![X]:((kind(X)<~>~old(X))=>(~calm(X)&generous(X))))&
((?[X]:(~rich(X)))=>(~old(lucy)))&
(![X]:((~tall(X)<~>patient(X))<=>~generous(X)))&
((?[X]:((rich(X)|~patient(X))))=>(?[X]:((happy(X)&creative(X)))))&
(((humble(mary)<~>brave(mary)))=>(~calm(mary)))&
(![X]:((~curious(X)&~strong(X))=>(~funny(X)&~brave(X))))&
(![X]:((tall(X)<~>~creative(X))=>(~curious(X)&happy(X))))&
(((~quiet(john)&happy(john)))<=>(?[X]:(~humble(X))))&
(creative(lucy))&
((rich(alice)|humble(alice)))&
(?[X]:((humble(X)&~happy(X))))&
(?[X]:((generous(X)&~curious(X))))&
(tall(john))&
((~patient(lucy)<~>~quiet(lucy)))&
(?[X]:(~brave(X))) | ~patient(john) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7543236026980827039730304
% SZS output start Proof for 7543236026980827039730304
1. ! [X0] : ((~quiet(X0) | quiet(X0)) => ~happy(X0)) [input p0]
11. ? [X0] : (~patient(X0) | rich(X0)) => ? [X0] : (creative(X0) & happy(X0)) [input p10]
23. ~patient(john) [input hypothesis]
26. ? [X0] : (~patient(X0) | rich(X0)) => ? [X1] : (creative(X1) & happy(X1)) [rectify 11]
32. ! [X0] : (~happy(X0) | (quiet(X0) & ~quiet(X0))) [ennf transformation 1]
38. ? [X1] : (creative(X1) & happy(X1)) | ! [X0] : (patient(X0) & ~rich(X0)) [ennf transformation 26]
59. ? [X0] : (creative(X0) & happy(X0)) | ! [X1] : (patient(X1) & ~rich(X1)) [rectify 38]
60. ? [X0] : (creative(X0) & happy(X0)) => (creative(sK4) & happy(sK4)) [choice axiom]
61. (creative(sK4) & happy(sK4)) | ! [X1] : (patient(X1) & ~rich(X1)) [skolemisation 59,60]
75. ~happy(X0) | ~quiet(X0) [cnf transformation 32]
76. ~happy(X0) | quiet(X0) [cnf transformation 32]
100. happy(sK4) | patient(X1) [cnf transformation 61]
120. ~patient(john) [cnf transformation 23]
121. ~happy(X0) [subsumption resolution 75,76]
202. 19 <=> ! [X1] : patient(X1) [avatar definition]
203. patient(X1) <- (19) [avatar component clause 202]
213. patient(X1) [subsumption resolution 100,121]
214. 19 [avatar split clause 213,202]
230. $false <- (19) [resolution 203,120]
231. ~19 [avatar contradiction clause 230]
232. $false [avatar sat refutation 214,231]
% SZS output end Proof for 7543236026980827039730304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is kind. If susan is curious then paul is calm. Everyone who is both not old and not patient is funny or generous. Everyone who is both not tall and funny is either not wise or old. Everyone who is either not curious or humble is not calm and vice versa. Everyone who is tall is funny. Everyone who is not quiet or tall is both not happy and not patient. If paul is either strong or wise then john is both not strong and not kind and vice versa. Everyone who is both quiet and not tall is curious or old. If someone is both not humble and not funny then paul is either patient or not curious and vice versa. Everyone who is not curious is not generous or not kind. Everyone who is not rich or old is not kind or funny and vice versa. If someone is quiet then john is not generous. Everyone who is either not tall or not curious is both humble and not brave. Everyone who is quiet is tall and vice versa. Everyone who is strong is not old and vice versa. Fred is not kind or not creative. Someone is both humble and not tall. Someone is either tall or not tall. Susan is both humble and tall. John is not happy or not calm. Someone is not happy. Susan is either humble or calm. | Fred is not wise. | neutral | (![X]:(strong(X)=>kind(X)))&
((curious(susan))=>(calm(paul)))&
(![X]:((~old(X)&~patient(X))=>(funny(X)|generous(X))))&
(![X]:((~tall(X)&funny(X))=>(~wise(X)<~>old(X))))&
(![X]:((~curious(X)<~>humble(X))<=>~calm(X)))&
(![X]:(tall(X)=>funny(X)))&
(![X]:((~quiet(X)|tall(X))=>(~happy(X)&~patient(X))))&
(((strong(paul)<~>wise(paul)))<=>((~strong(john)&~kind(john))))&
(![X]:((quiet(X)&~tall(X))=>(curious(X)|old(X))))&
((?[X]:((~humble(X)&~funny(X))))<=>((patient(paul)<~>~curious(paul))))&
(![X]:(~curious(X)=>(~generous(X)|~kind(X))))&
(![X]:((~rich(X)|old(X))<=>(~kind(X)|funny(X))))&
((?[X]:(quiet(X)))=>(~generous(john)))&
(![X]:((~tall(X)<~>~curious(X))=>(humble(X)&~brave(X))))&
(![X]:(quiet(X)<=>tall(X)))&
(![X]:(strong(X)<=>~old(X)))&
((~kind(fred)|~creative(fred)))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
((humble(susan)&tall(susan)))&
((~happy(john)|~calm(john)))&
(?[X]:(~happy(X)))&
((humble(susan)<~>calm(susan))) | ~wise(fred) | [] | null | 0 |
Everyone who is not patient or not brave is generous.
If alice is kind then john is not humble or not patient and vice versa.
Everyone who is either calm or happy is brave.
If someone is not old then someone is both not kind and not strong and vice versa.
Everyone who is not funny is funny or not humble and vice versa.
If john is kind or not humble then paul is either funny or not rich and vice versa.
Everyone who is either wise or not calm is brave and vice versa.
Everyone who is happy or funny is strong or tall.
Everyone who is either not creative or generous is either not funny or not calm.
Everyone who is either strong or generous is either kind or not brave and vice versa.
Everyone who is not rich or creative is both not quiet and not generous.
Everyone who is either not creative or not humble is either funny or not rich and vice versa.
If lucy is rich then someone is both not creative and not kind.
Everyone who is happy is either kind or not kind and vice versa.
Everyone who is both not calm and not patient is generous or strong and vice versa.
If mary is generous then susan is not kind or happy and vice versa.
Someone is rich.
John is not patient.
Paul is curious.
Someone is happy.
Someone is not humble or not tall.
Someone is both not kind and not strong. | Paul is not strong. | entailment | (![X]:((~patient(X)|~brave(X))=>generous(X)))&
((kind(alice))<=>((~humble(john)|~patient(john))))&
(![X]:((calm(X)<~>happy(X))=>brave(X)))&
((?[X]:(~old(X)))<=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:(~funny(X)<=>(funny(X)|~humble(X))))&
(((kind(john)|~humble(john)))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)|funny(X))=>(strong(X)|tall(X))))&
(![X]:((~creative(X)<~>generous(X))=>(~funny(X)<~>~calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~rich(X)|creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~creative(X)<~>~humble(X))<=>(funny(X)<~>~rich(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:(happy(X)<=>(kind(X)<~>~kind(X))))&
(![X]:((~calm(X)&~patient(X))<=>(generous(X)|strong(X))))&
((generous(mary))<=>((~kind(susan)|happy(susan))))&
(?[X]:(rich(X)))&
(~patient(john))&
(curious(paul))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:((~kind(X)&~strong(X)))) | ~strong(paul) | [
"p0",
"p4",
"p5",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3334316392381239997460314
% SZS output start Proof for 3334316392381239997460314
1. ! [X0] : ((~brave(X0) | ~patient(X0)) => generous(X0)) [input p0]
5. ! [X0] : (~funny(X0) <=> (~humble(X0) | funny(X0))) [input p4]
6. (~humble(john) | kind(john)) <=> (funny(paul) <~> ~rich(paul)) [input p5]
11. ! [X0] : ((creative(X0) | ~rich(X0)) => (~generous(X0) & ~quiet(X0))) [input p10]
15. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> (strong(X0) | generous(X0))) [input p14]
23. strong(paul) [input hypothesis]
26. ! [X0] : ((creative(X0) | ~rich(X0)) => ~generous(X0)) [pure predicate removal 11]
27. ! [X0] : (generous(X0) | (brave(X0) & patient(X0))) [ennf transformation 1]
32. ! [X0] : (~generous(X0) | (~creative(X0) & rich(X0))) [ennf transformation 26]
42. ! [X0] : ((~funny(X0) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | funny(X0))) [nnf transformation 5]
43. ! [X0] : ((~funny(X0) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | funny(X0))) [flattening 42]
44. ((~humble(john) | kind(john)) | ((funny(paul) | rich(paul)) & (~rich(paul) | ~funny(paul)))) & (((rich(paul) | ~funny(paul)) & (~rich(paul) | funny(paul))) | (humble(john) & ~kind(john))) [nnf transformation 6]
45. (~humble(john) | kind(john) | ((funny(paul) | rich(paul)) & (~rich(paul) | ~funny(paul)))) & (((rich(paul) | ~funny(paul)) & (~rich(paul) | funny(paul))) | (humble(john) & ~kind(john))) [flattening 44]
53. ! [X0] : (((~patient(X0) & ~calm(X0)) | (~strong(X0) & ~generous(X0))) & ((strong(X0) | generous(X0)) | (patient(X0) | calm(X0)))) [nnf transformation 15]
54. ! [X0] : (((~patient(X0) & ~calm(X0)) | (~strong(X0) & ~generous(X0))) & (strong(X0) | generous(X0) | patient(X0) | calm(X0))) [flattening 53]
65. generous(X0) | patient(X0) [cnf transformation 27]
75. ~humble(X0) | funny(X0) | funny(X0) [cnf transformation 43]
76. ~funny(X0) | ~funny(X0) [cnf transformation 43]
79. ~rich(paul) | funny(paul) | humble(john) [cnf transformation 45]
102. ~generous(X0) | rich(X0) [cnf transformation 32]
122. ~strong(X0) | ~patient(X0) [cnf transformation 54]
132. strong(paul) [cnf transformation 23]
135. ~humble(X0) | funny(X0) [duplicate literal removal 75]
136. ~funny(X0) [duplicate literal removal 76]
173. ~humble(X0) [subsumption resolution 135,136]
174. ~rich(paul) | humble(john) [subsumption resolution 79,136]
175. ~rich(paul) [subsumption resolution 174,173]
205. rich(X1) | patient(X1) [resolution 102,65]
210. ~patient(paul) [resolution 122,132]
219. patient(paul) [resolution 205,175]
221. $false [subsumption resolution 219,210]
% SZS output end Proof for 3334316392381239997460314
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not patient is both rich and not creative and vice versa. Everyone who is both humble and not kind is not wise or not rich. Everyone who is not tall is not happy. If john is both not quiet and not wise then someone is both not strong and not brave and vice versa. Everyone who is either patient or creative is either humble or tall and vice versa. Everyone who is tall or not generous is generous. If someone is old then lucy is curious. If someone is quiet then susan is both not rich and not creative and vice versa. Everyone who is either happy or not generous is either not kind or wise and vice versa. Everyone who is curious is creative or not rich. If someone is either curious or old then someone is both calm and not old and vice versa. Everyone who is not creative or not generous is either not happy or wise. If someone is generous or not generous then someone is not wise and vice versa. Everyone who is not brave is either not wise or generous and vice versa. If someone is tall then paul is both not kind and not quiet and vice versa. Everyone who is patient is not happy or not humble and vice versa. Alice is either wise or patient. Someone is brave. Someone is either tall or not funny. Someone is humble. Mary is not calm. Paul is either not quiet or not funny. Susan is not quiet or curious. | John is not tall. | neutral | (![X]:((old(X)|~patient(X))<=>(rich(X)&~creative(X))))&
(![X]:((humble(X)&~kind(X))=>(~wise(X)|~rich(X))))&
(![X]:(~tall(X)=>~happy(X)))&
(((~quiet(john)&~wise(john)))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((patient(X)<~>creative(X))<=>(humble(X)<~>tall(X))))&
(![X]:((tall(X)|~generous(X))=>generous(X)))&
((?[X]:(old(X)))=>(curious(lucy)))&
((?[X]:(quiet(X)))<=>((~rich(susan)&~creative(susan))))&
(![X]:((happy(X)<~>~generous(X))<=>(~kind(X)<~>wise(X))))&
(![X]:(curious(X)=>(creative(X)|~rich(X))))&
((?[X]:((curious(X)<~>old(X))))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((~creative(X)|~generous(X))=>(~happy(X)<~>wise(X))))&
((?[X]:((generous(X)|~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)<~>generous(X))))&
((?[X]:(tall(X)))<=>((~kind(paul)&~quiet(paul))))&
(![X]:(patient(X)<=>(~happy(X)|~humble(X))))&
((wise(alice)<~>patient(alice)))&
(?[X]:(brave(X)))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:(humble(X)))&
(~calm(mary))&
((~quiet(paul)<~>~funny(paul)))&
((~quiet(susan)|curious(susan))) | ~tall(john) | [] | null | 0 |
Everyone who is not strong or not humble is both not happy and not rich. Everyone who is either not old or happy is not tall. Everyone who is not brave or not happy is old or not tall and vice versa. Everyone who is kind or generous is either creative or not strong and vice versa. Everyone who is both humble and not generous is both not patient and not humble. Everyone who is patient or not quiet is not patient and vice versa. Everyone who is either not brave or quiet is both generous and not curious. Everyone who is both not curious and old is not wise or not brave and vice versa. If mary is either not happy or curious then john is rich or not brave. Everyone who is old is both strong and not humble. Everyone who is not happy or not creative is funny or calm and vice versa. Everyone who is both not quiet and creative is both creative and quiet and vice versa. If someone is either not funny or not rich then mary is both generous and quiet and vice versa. If someone is both not funny and not brave then someone is either brave or not kind and vice versa. Everyone who is not quiet is curious or rich and vice versa. Everyone who is quiet is generous and vice versa. John is either not tall or not creative. Lucy is brave or not generous. Susan is not rich. Someone is not old or not creative. | Lucy is not curious. | contradiction | (![X]:((~strong(X)|~humble(X))=>(~happy(X)&~rich(X))))&
(![X]:((~old(X)<~>happy(X))=>~tall(X)))&
(![X]:((~brave(X)|~happy(X))<=>(old(X)|~tall(X))))&
(![X]:((kind(X)|generous(X))<=>(creative(X)<~>~strong(X))))&
(![X]:((humble(X)&~generous(X))=>(~patient(X)&~humble(X))))&
(![X]:((patient(X)|~quiet(X))<=>~patient(X)))&
(![X]:((~brave(X)<~>quiet(X))=>(generous(X)&~curious(X))))&
(![X]:((~curious(X)&old(X))<=>(~wise(X)|~brave(X))))&
(((~happy(mary)<~>curious(mary)))=>((rich(john)|~brave(john))))&
(![X]:(old(X)=>(strong(X)&~humble(X))))&
(![X]:((~happy(X)|~creative(X))<=>(funny(X)|calm(X))))&
(![X]:((~quiet(X)&creative(X))<=>(creative(X)&quiet(X))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>((generous(mary)&quiet(mary))))&
((?[X]:((~funny(X)&~brave(X))))<=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:(~quiet(X)<=>(curious(X)|rich(X))))&
(![X]:(quiet(X)<=>generous(X)))&
((~tall(john)<~>~creative(john)))&
((brave(lucy)|~generous(lucy)))&
(~rich(susan))&
(?[X]:((~old(X)|~creative(X)))) | ~curious(lucy) | [
"p0",
"p4",
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4920831255504198096488042
% SZS output start Proof for 4920831255504198096488042
1. ! [X0] : ((~humble(X0) | ~strong(X0)) => (~rich(X0) & ~happy(X0))) [input p0]
5. ! [X0] : ((~generous(X0) & humble(X0)) => (~humble(X0) & ~patient(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) | patient(X0)) <=> ~patient(X0)) [input p5]
15. ! [X0] : (~quiet(X0) <=> (rich(X0) | curious(X0))) [input p14]
16. ! [X0] : (quiet(X0) <=> generous(X0)) [input p15]
21. ~curious(lucy) [input hypothesis]
23. ! [X0] : ((~rich(X0) & ~happy(X0)) | (humble(X0) & strong(X0))) [ennf transformation 1]
25. ! [X0] : ((~humble(X0) & ~patient(X0)) | (generous(X0) | ~humble(X0))) [ennf transformation 5]
26. ! [X0] : ((~humble(X0) & ~patient(X0)) | generous(X0) | ~humble(X0)) [flattening 25]
36. ! [X0] : (((~quiet(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~patient(X0)))) [nnf transformation 6]
37. ! [X0] : ((~quiet(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~patient(X0)))) [flattening 36]
56. ! [X0] : ((~quiet(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | quiet(X0))) [nnf transformation 15]
57. ! [X0] : ((~quiet(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | quiet(X0))) [flattening 56]
58. ! [X0] : ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))) [nnf transformation 16]
65. ~rich(X0) | humble(X0) [cnf transformation 23]
79. ~humble(X0) | generous(X0) | ~humble(X0) [cnf transformation 26]
80. ~patient(X0) | ~patient(X0) [cnf transformation 37]
82. ~quiet(X0) | patient(X0) | patient(X0) [cnf transformation 37]
116. curious(X0) | rich(X0) | quiet(X0) [cnf transformation 57]
120. ~generous(X0) | quiet(X0) [cnf transformation 58]
126. ~curious(lucy) [cnf transformation 21]
129. ~patient(X0) [duplicate literal removal 80]
130. ~quiet(X0) | patient(X0) [duplicate literal removal 82]
131. ~humble(X0) | generous(X0) [duplicate literal removal 79]
216. 19 <=> generous(lucy) [avatar definition]
217. generous(lucy) <- (19) [avatar component clause 216]
335. rich(lucy) | quiet(lucy) [resolution 116,126]
344. 27 <=> quiet(lucy) [avatar definition]
345. ~quiet(lucy) <- (~27) [avatar component clause 344]
346. quiet(lucy) <- (27) [avatar component clause 344]
348. 28 <=> rich(lucy) [avatar definition]
350. rich(lucy) <- (28) [avatar component clause 348]
351. 27 | 28 [avatar split clause 335,348,344]
363. patient(lucy) <- (27) [resolution 346,130]
370. $false <- (27) [subsumption resolution 363,129]
371. ~27 [avatar contradiction clause 370]
379. humble(lucy) <- (28) [resolution 350,65]
404. generous(lucy) <- (28) [resolution 379,131]
407. 19 | ~28 [avatar split clause 404,348,216]
409. quiet(lucy) <- (19) [resolution 217,120]
413. $false <- (19, ~27) [subsumption resolution 409,345]
414. ~19 | 27 [avatar contradiction clause 413]
415. $false [avatar sat refutation 351,371,407,414]
% SZS output end Proof for 4920831255504198096488042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is quiet then john is quiet or brave and vice versa.
Everyone who is old is both funny and rich.
Everyone who is curious or not curious is either funny or calm.
Everyone who is generous or not old is either not patient or rich.
Everyone who is both not strong and not wise is both strong and not humble.
If someone is either not wise or calm then someone is not old or patient and vice versa.
If someone is both strong and brave then fred is not creative and vice versa.
Everyone who is patient or creative is either old or not brave.
If fred is not old then mary is calm or not quiet.
If someone is tall or not creative then john is both quiet and old.
Everyone who is kind or curious is either kind or not patient.
Everyone who is old is not patient or wise.
If someone is either not kind or old then someone is either quiet or not creative.
Everyone who is either quiet or funny is either funny or not patient and vice versa.
If someone is both not happy and not patient then someone is either not calm or wise and vice versa.
If susan is curious then lucy is both not calm and not funny.
John is not humble.
Someone is either not generous or kind.
Someone is either not curious or tall.
Someone is tall or rich.
Someone is either not creative or strong.
Someone is both not creative and happy.
Lucy is both not tall and generous.
Someone is not generous or quiet. | John is generous. | contradiction | ((quiet(lucy))<=>((quiet(john)|brave(john))))&
(![X]:(old(X)=>(funny(X)&rich(X))))&
(![X]:((curious(X)|~curious(X))=>(funny(X)<~>calm(X))))&
(![X]:((generous(X)|~old(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~strong(X)&~wise(X))=>(strong(X)&~humble(X))))&
((?[X]:((~wise(X)<~>calm(X))))<=>(?[X]:((~old(X)|patient(X)))))&
((?[X]:((strong(X)&brave(X))))<=>(~creative(fred)))&
(![X]:((patient(X)|creative(X))=>(old(X)<~>~brave(X))))&
((~old(fred))=>((calm(mary)|~quiet(mary))))&
((?[X]:((tall(X)|~creative(X))))=>((quiet(john)&old(john))))&
(![X]:((kind(X)|curious(X))=>(kind(X)<~>~patient(X))))&
(![X]:(old(X)=>(~patient(X)|wise(X))))&
((?[X]:((~kind(X)<~>old(X))))=>(?[X]:((quiet(X)<~>~creative(X)))))&
(![X]:((quiet(X)<~>funny(X))<=>(funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~patient(X))))<=>(?[X]:((~calm(X)<~>wise(X)))))&
((curious(susan))=>((~calm(lucy)&~funny(lucy))))&
(~humble(john))&
(?[X]:((~generous(X)<~>kind(X))))&
(?[X]:((~curious(X)<~>tall(X))))&
(?[X]:((tall(X)|rich(X))))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:((~creative(X)&happy(X))))&
((~tall(lucy)&generous(lucy)))&
(?[X]:((~generous(X)|quiet(X)))) | generous(john) | [
"p1",
"p3",
"p9",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2655341658484610892643424
% SZS output start Proof for 2655341658484610892643424
2. ! [X0] : (old(X0) => (rich(X0) & funny(X0))) [input p1]
4. ! [X0] : ((~old(X0) | generous(X0)) => (~patient(X0) <~> rich(X0))) [input p3]
10. ? [X0] : (~creative(X0) | tall(X0)) => (old(john) & quiet(john)) [input p9]
14. ! [X0] : ((quiet(X0) <~> funny(X0)) <=> (funny(X0) <~> ~patient(X0))) [input p13]
22. ? [X0] : (happy(X0) & ~creative(X0)) [input p21]
25. generous(john) [input hypothesis]
31. ! [X0] : ((rich(X0) & funny(X0)) | ~old(X0)) [ennf transformation 2]
33. ! [X0] : ((~patient(X0) <~> rich(X0)) | (old(X0) & ~generous(X0))) [ennf transformation 4]
39. (old(john) & quiet(john)) | ! [X0] : (creative(X0) & ~tall(X0)) [ennf transformation 10]
48. ! [X0] : (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (old(X0) & ~generous(X0))) [nnf transformation 33]
64. ! [X0] : ((((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0))))) [nnf transformation 14]
81. ? [X0] : (happy(X0) & ~creative(X0)) => (happy(sK10) & ~creative(sK10)) [choice axiom]
82. happy(sK10) & ~creative(sK10) [skolemisation 22,81]
89. ~old(X0) | rich(X0) [cnf transformation 31]
96. ~generous(X0) | patient(X0) | ~rich(X0) [cnf transformation 48]
114. quiet(john) | creative(X0) [cnf transformation 39]
116. old(john) | creative(X0) [cnf transformation 39]
126. ~patient(X0) | funny(X0) | funny(X0) | ~quiet(X0) [cnf transformation 64]
132. ~funny(X0) | ~quiet(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 64]
149. ~creative(sK10) [cnf transformation 82]
154. generous(john) [cnf transformation 25]
155. ~patient(X0) | funny(X0) | ~quiet(X0) [duplicate literal removal 126]
158. ~funny(X0) | ~quiet(X0) | ~patient(X0) [duplicate literal removal 132]
171. 3 <=> quiet(john) [avatar definition]
245. 19 <=> ! [X0] : creative(X0) [avatar definition]
246. creative(X0) <- (19) [avatar component clause 245]
248. 20 <=> old(john) [avatar definition]
250. old(john) <- (20) [avatar component clause 248]
251. 19 | 20 [avatar split clause 116,248,245]
256. 19 | 3 [avatar split clause 114,171,245]
277. ~patient(X0) | ~quiet(X0) [subsumption resolution 155,158]
366. rich(john) <- (20) [resolution 89,250]
382. patient(john) | ~rich(john) [resolution 96,154]
392. patient(john) <- (20) [subsumption resolution 382,366]
396. ~quiet(john) <- (20) [resolution 392,277]
400. ~3 | ~20 [avatar split clause 396,248,171]
404. $false <- (19) [resolution 246,149]
405. ~19 [avatar contradiction clause 404]
409. $false [avatar sat refutation 251,256,400,405]
% SZS output end Proof for 2655341658484610892643424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not quiet is either brave or humble.
If someone is either brave or happy then alice is either not calm or funny and vice versa.
If alice is not happy or curious then susan is brave or tall and vice versa.
If someone is both kind and not humble then susan is not patient or not tall.
Everyone who is either generous or old is both not funny and humble and vice versa.
Everyone who is both strong and not old is either not creative or funny and vice versa.
Everyone who is either not kind or creative is both not wise and quiet.
If paul is both not quiet and not old then someone is not old.
If fred is humble then mary is both not quiet and not tall.
Everyone who is brave is old.
If paul is calm then lucy is wise.
Everyone who is not quiet or happy is happy or humble and vice versa.
Everyone who is kind is both not generous and not kind and vice versa.
Everyone who is curious is both tall and quiet.
Everyone who is both curious and not humble is not calm or not creative and vice versa.
Everyone who is creative or not old is not calm.
Someone is not patient or wise.
Someone is either wise or old.
Someone is both not wise and not kind.
Lucy is generous or strong.
Paul is either not happy or humble.
Someone is generous. | Lucy is not brave. | contradiction | (![X]:((old(X)<~>~quiet(X))=>(brave(X)<~>humble(X))))&
((?[X]:((brave(X)<~>happy(X))))<=>((~calm(alice)<~>funny(alice))))&
(((~happy(alice)|curious(alice)))<=>((brave(susan)|tall(susan))))&
((?[X]:((kind(X)&~humble(X))))=>((~patient(susan)|~tall(susan))))&
(![X]:((generous(X)<~>old(X))<=>(~funny(X)&humble(X))))&
(![X]:((strong(X)&~old(X))<=>(~creative(X)<~>funny(X))))&
(![X]:((~kind(X)<~>creative(X))=>(~wise(X)&quiet(X))))&
(((~quiet(paul)&~old(paul)))=>(?[X]:(~old(X))))&
((humble(fred))=>((~quiet(mary)&~tall(mary))))&
(![X]:(brave(X)=>old(X)))&
((calm(paul))=>(wise(lucy)))&
(![X]:((~quiet(X)|happy(X))<=>(happy(X)|humble(X))))&
(![X]:(kind(X)<=>(~generous(X)&~kind(X))))&
(![X]:(curious(X)=>(tall(X)&quiet(X))))&
(![X]:((curious(X)&~humble(X))<=>(~calm(X)|~creative(X))))&
(![X]:((creative(X)|~old(X))=>~calm(X)))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:((~wise(X)&~kind(X))))&
((generous(lucy)|strong(lucy)))&
((~happy(paul)<~>humble(paul)))&
(?[X]:(generous(X))) | ~brave(lucy) | [
"p0",
"p4",
"p5",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 775715891137366367789483
% SZS output start Proof for 775715891137366367789483
1. ! [X0] : ((old(X0) <~> ~quiet(X0)) => (brave(X0) <~> humble(X0))) [input p0]
5. ! [X0] : ((generous(X0) <~> old(X0)) <=> (humble(X0) & ~funny(X0))) [input p4]
6. ! [X0] : ((~old(X0) & strong(X0)) <=> (~creative(X0) <~> funny(X0))) [input p5]
13. ! [X0] : (kind(X0) <=> (~kind(X0) & ~generous(X0))) [input p12]
14. ! [X0] : (curious(X0) => (quiet(X0) & tall(X0))) [input p13]
15. ! [X0] : ((~humble(X0) & curious(X0)) <=> (~creative(X0) | ~calm(X0))) [input p14]
16. ! [X0] : ((~old(X0) | creative(X0)) => ~calm(X0)) [input p15]
23. ~brave(lucy) [input hypothesis]
26. ! [X0] : ((brave(X0) <~> humble(X0)) | (old(X0) <=> ~quiet(X0))) [ennf transformation 1]
33. ! [X0] : ((quiet(X0) & tall(X0)) | ~curious(X0)) [ennf transformation 14]
34. ! [X0] : (~calm(X0) | (old(X0) & ~creative(X0))) [ennf transformation 16]
35. ! [X0] : (((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) [nnf transformation 26]
42. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (~humble(X0) | funny(X0))) & ((humble(X0) & ~funny(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | ~humble(X0) | funny(X0)) & ((humble(X0) & ~funny(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [flattening 42]
44. ! [X0] : (((~old(X0) & strong(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (old(X0) | ~strong(X0)))) [nnf transformation 6]
45. ! [X0] : (((~old(X0) & strong(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | old(X0) | ~strong(X0))) [flattening 44]
51. ! [X0] : ((kind(X0) | (kind(X0) | generous(X0))) & ((~kind(X0) & ~generous(X0)) | ~kind(X0))) [nnf transformation 13]
52. ! [X0] : ((kind(X0) | kind(X0) | generous(X0)) & ((~kind(X0) & ~generous(X0)) | ~kind(X0))) [flattening 51]
53. ! [X0] : (((~humble(X0) & curious(X0)) | (creative(X0) & calm(X0))) & ((~creative(X0) | ~calm(X0)) | (humble(X0) | ~curious(X0)))) [nnf transformation 15]
54. ! [X0] : (((~humble(X0) & curious(X0)) | (creative(X0) & calm(X0))) & (~creative(X0) | ~calm(X0) | humble(X0) | ~curious(X0))) [flattening 53]
63. ~quiet(X0) | brave(X0) | humble(X0) | ~old(X0) [cnf transformation 35]
81. ~generous(X0) | old(X0) | humble(X0) [cnf transformation 43]
84. ~generous(X0) | ~old(X0) | ~humble(X0) | funny(X0) [cnf transformation 43]
90. ~creative(X0) | ~old(X0) | ~funny(X0) [cnf transformation 45]
105. ~kind(X0) | ~kind(X0) [cnf transformation 52]
106. kind(X0) | kind(X0) | generous(X0) [cnf transformation 52]
108. ~curious(X0) | quiet(X0) [cnf transformation 33]
110. curious(X0) | calm(X0) [cnf transformation 54]
111. creative(X0) | curious(X0) [cnf transformation 54]
112. ~humble(X0) | calm(X0) [cnf transformation 54]
113. ~humble(X0) | creative(X0) [cnf transformation 54]
114. ~creative(X0) | ~calm(X0) [cnf transformation 34]
115. ~calm(X0) | old(X0) [cnf transformation 34]
124. ~brave(lucy) [cnf transformation 23]
125. ~kind(X0) [duplicate literal removal 105]
126. generous(X0) | kind(X0) [duplicate literal removal 106]
245. ~calm(X0) | curious(X0) [resolution 114,111]
246. curious(X0) [subsumption resolution 245,110]
247. quiet(X0) [resolution 246,108]
273. old(X0) | humble(X0) | kind(X0) [resolution 81,126]
284. humble(X0) | old(X0) [subsumption resolution 273,125]
358. brave(X0) | humble(X0) | ~old(X0) [resolution 63,247]
359. humble(X0) | brave(X0) [subsumption resolution 358,284]
382. old(X5) | calm(X5) [resolution 284,112]
390. old(X5) [subsumption resolution 382,115]
392. ~old(X0) | ~humble(X0) | funny(X0) | kind(X0) [resolution 84,126]
397. ~humble(X0) | funny(X0) | kind(X0) [subsumption resolution 392,390]
398. ~humble(X0) | funny(X0) [subsumption resolution 397,125]
442. creative(X5) | brave(X5) [resolution 359,113]
443. funny(X6) | brave(X6) [resolution 359,398]
504. brave(X3) | ~old(X3) | ~funny(X3) [resolution 442,90]
507. brave(X3) | ~funny(X3) [subsumption resolution 504,390]
508. brave(X3) [subsumption resolution 507,443]
516. $false [resolution 508,124]
% SZS output end Proof for 775715891137366367789483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not happy is rich or not kind and vice versa. If fred is either not curious or rich then someone is both not old and not funny and vice versa. Everyone who is both happy and not tall is both brave and not wise. Everyone who is not old is creative or not funny and vice versa. If someone is not quiet then john is either not strong or not old. Everyone who is either not quiet or not funny is not strong. Everyone who is funny or strong is patient and vice versa. Everyone who is either not creative or curious is not strong. If someone is both humble and calm then someone is tall or not quiet and vice versa. If susan is either old or not old then someone is quiet or kind and vice versa. Everyone who is not old is happy and vice versa. If susan is both not quiet and not brave then someone is both not calm and not brave and vice versa. If someone is both strong and wise then someone is not curious and vice versa. If someone is either brave or old then mary is rich and vice versa. Everyone who is either not strong or not patient is happy and vice versa. Everyone who is not wise or old is either quiet or funny. Someone is patient or not curious. Lucy is funny. Someone is not happy or not old. Someone is either not strong or not patient. Someone is either generous or creative. | Fred is curious. | entailment | (![X]:((quiet(X)&~happy(X))<=>(rich(X)|~kind(X))))&
(((~curious(fred)<~>rich(fred)))<=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((happy(X)&~tall(X))=>(brave(X)&~wise(X))))&
(![X]:(~old(X)<=>(creative(X)|~funny(X))))&
((?[X]:(~quiet(X)))=>((~strong(john)<~>~old(john))))&
(![X]:((~quiet(X)<~>~funny(X))=>~strong(X)))&
(![X]:((funny(X)|strong(X))<=>patient(X)))&
(![X]:((~creative(X)<~>curious(X))=>~strong(X)))&
((?[X]:((humble(X)&calm(X))))<=>(?[X]:((tall(X)|~quiet(X)))))&
(((old(susan)<~>~old(susan)))<=>(?[X]:((quiet(X)|kind(X)))))&
(![X]:(~old(X)<=>happy(X)))&
(((~quiet(susan)&~brave(susan)))<=>(?[X]:((~calm(X)&~brave(X)))))&
((?[X]:((strong(X)&wise(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)<~>old(X))))<=>(rich(mary)))&
(![X]:((~strong(X)<~>~patient(X))<=>happy(X)))&
(![X]:((~wise(X)|old(X))=>(quiet(X)<~>funny(X))))&
(?[X]:((patient(X)|~curious(X))))&
(funny(lucy))&
(?[X]:((~happy(X)|~old(X))))&
(?[X]:((~strong(X)<~>~patient(X))))&
(?[X]:((generous(X)<~>creative(X)))) | curious(fred) | [
"p3",
"p5",
"p6",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8644714152295236004225161
% SZS output start Proof for 8644714152295236004225161
4. ! [X0] : (~old(X0) <=> (~funny(X0) | creative(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) <~> ~funny(X0)) => ~strong(X0)) [input p5]
7. ! [X0] : ((strong(X0) | funny(X0)) <=> patient(X0)) [input p6]
11. ! [X0] : (~old(X0) <=> happy(X0)) [input p10]
13. ? [X0] : (wise(X0) & strong(X0)) <=> ? [X0] : ~curious(X0) [input p12]
15. ! [X0] : ((~strong(X0) <~> ~patient(X0)) <=> happy(X0)) [input p14]
16. ! [X0] : ((old(X0) | ~wise(X0)) => (quiet(X0) <~> funny(X0))) [input p15]
22. ~curious(fred) [input hypothesis]
24. ? [X0] : (wise(X0) & strong(X0)) <=> ? [X1] : ~curious(X1) [rectify 13]
28. ! [X0] : (~strong(X0) | (~quiet(X0) <=> ~funny(X0))) [ennf transformation 6]
30. ! [X0] : ((quiet(X0) <~> funny(X0)) | (~old(X0) & wise(X0))) [ennf transformation 16]
37. ! [X0] : ((~old(X0) | (funny(X0) & ~creative(X0))) & ((~funny(X0) | creative(X0)) | old(X0))) [nnf transformation 4]
38. ! [X0] : ((~old(X0) | (funny(X0) & ~creative(X0))) & (~funny(X0) | creative(X0) | old(X0))) [flattening 37]
40. ! [X0] : (~strong(X0) | ((~quiet(X0) | funny(X0)) & (~funny(X0) | quiet(X0)))) [nnf transformation 28]
41. ! [X0] : (((strong(X0) | funny(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~funny(X0)))) [nnf transformation 7]
42. ! [X0] : ((strong(X0) | funny(X0) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~funny(X0)))) [flattening 41]
53. ! [X0] : ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))) [nnf transformation 11]
59. (? [X0] : (wise(X0) & strong(X0)) | ! [X1] : curious(X1)) & (? [X1] : ~curious(X1) | ! [X0] : (~wise(X0) | ~strong(X0))) [nnf transformation 24]
60. (? [X0] : (wise(X0) & strong(X0)) | ! [X1] : curious(X1)) & (? [X2] : ~curious(X2) | ! [X3] : (~wise(X3) | ~strong(X3))) [rectify 59]
61. ? [X0] : (wise(X0) & strong(X0)) => (wise(sK5) & strong(sK5)) [choice axiom]
62. ? [X2] : ~curious(X2) => ~curious(sK6) [choice axiom]
63. ((wise(sK5) & strong(sK5)) | ! [X1] : curious(X1)) & (~curious(sK6) | ! [X3] : (~wise(X3) | ~strong(X3))) [skolemisation 60,62,61]
68. ! [X0] : ((((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~happy(X0)) & (happy(X0) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))))) [nnf transformation 15]
69. ! [X0] : (((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | (~old(X0) & wise(X0))) [nnf transformation 30]
95. ~old(X0) | funny(X0) [cnf transformation 38]
98. ~strong(X0) | ~funny(X0) | quiet(X0) [cnf transformation 40]
101. ~strong(X0) | patient(X0) [cnf transformation 42]
116. old(X0) | happy(X0) [cnf transformation 53]
123. strong(sK5) | curious(X1) [cnf transformation 63]
131. ~patient(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 68]
132. patient(X0) | strong(X0) | ~happy(X0) [cnf transformation 68]
136. ~funny(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 69]
144. ~curious(fred) [cnf transformation 22]
151. 2 <=> curious(fred) [avatar definition]
152. ~curious(fred) <- (~2) [avatar component clause 151]
236. 20 <=> ! [X1] : curious(X1) [avatar definition]
237. curious(X1) <- (20) [avatar component clause 236]
244. 22 <=> strong(sK5) [avatar definition]
246. strong(sK5) <- (22) [avatar component clause 244]
247. 20 | 22 [avatar split clause 123,244,236]
278. ~happy(X0) | patient(X0) [subsumption resolution 132,101]
279. ~strong(X0) | ~happy(X0) [subsumption resolution 131,278]
280. ~old(X0) | ~quiet(X0) [subsumption resolution 136,95]
302. ~2 [avatar split clause 144,151]
303. $false <- (~2, 20) [subsumption resolution 152,237]
304. 2 | ~20 [avatar contradiction clause 303]
312. funny(X0) | happy(X0) [resolution 116,95]
322. ~happy(sK5) <- (22) [resolution 279,246]
338. ~quiet(X0) | happy(X0) [resolution 280,116]
382. ~funny(sK5) | quiet(sK5) <- (22) [resolution 98,246]
384. 38 <=> quiet(sK5) [avatar definition]
386. quiet(sK5) <- (38) [avatar component clause 384]
388. 39 <=> funny(sK5) [avatar definition]
390. ~funny(sK5) <- (~39) [avatar component clause 388]
391. 38 | ~39 | ~22 [avatar split clause 382,244,388,384]
465. happy(sK5) <- (~39) [resolution 312,390]
467. $false <- (22, ~39) [subsumption resolution 465,322]
468. ~22 | 39 [avatar contradiction clause 467]
479. happy(sK5) <- (38) [resolution 338,386]
482. $false <- (22, 38) [subsumption resolution 479,322]
483. ~22 | ~38 [avatar contradiction clause 482]
484. $false [avatar sat refutation 247,302,304,391,468,483]
% SZS output end Proof for 8644714152295236004225161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both tall and not kind.
If paul is both not funny and old then someone is both not kind and patient and vice versa.
If someone is wise then alice is not generous.
If someone is both not wise and not calm then mary is both not patient and curious.
If someone is both humble and not tall then alice is both not tall and not kind and vice versa.
If lucy is strong or not patient then john is calm and vice versa.
Everyone who is both strong and not curious is not generous or tall and vice versa.
Everyone who is not quiet or patient is either not curious or brave.
If someone is not tall then john is not wise and vice versa.
If someone is both funny and tall then john is either brave or not humble and vice versa.
Everyone who is not happy is both patient and not creative.
If lucy is tall or old then someone is both humble and not creative and vice versa.
If someone is either funny or not wise then someone is strong or not tall.
Everyone who is both rich and not strong is creative.
Everyone who is quiet is both not strong and not humble and vice versa.
If paul is both not creative and not quiet then someone is brave and vice versa.
Mary is not quiet or not strong.
Someone is not kind.
Someone is either not quiet or not funny.
Someone is both not creative and tall.
Susan is not quiet.
Someone is old. | Mary is brave. | contradiction | (![X]:(generous(X)=>(tall(X)&~kind(X))))&
(((~funny(paul)&old(paul)))<=>(?[X]:((~kind(X)&patient(X)))))&
((?[X]:(wise(X)))=>(~generous(alice)))&
((?[X]:((~wise(X)&~calm(X))))=>((~patient(mary)&curious(mary))))&
((?[X]:((humble(X)&~tall(X))))<=>((~tall(alice)&~kind(alice))))&
(((strong(lucy)|~patient(lucy)))<=>(calm(john)))&
(![X]:((strong(X)&~curious(X))<=>(~generous(X)|tall(X))))&
(![X]:((~quiet(X)|patient(X))=>(~curious(X)<~>brave(X))))&
((?[X]:(~tall(X)))<=>(~wise(john)))&
((?[X]:((funny(X)&tall(X))))<=>((brave(john)<~>~humble(john))))&
(![X]:(~happy(X)=>(patient(X)&~creative(X))))&
(((tall(lucy)|old(lucy)))<=>(?[X]:((humble(X)&~creative(X)))))&
((?[X]:((funny(X)<~>~wise(X))))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((rich(X)&~strong(X))=>creative(X)))&
(![X]:(quiet(X)<=>(~strong(X)&~humble(X))))&
(((~creative(paul)&~quiet(paul)))<=>(?[X]:(brave(X))))&
((~quiet(mary)|~strong(mary)))&
(?[X]:(~kind(X)))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((~creative(X)&tall(X))))&
(~quiet(susan))&
(?[X]:(old(X))) | brave(mary) | [
"p0",
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5905852975178749794896939
% SZS output start Proof for 5905852975178749794896939
1. ! [X0] : (generous(X0) => (~kind(X0) & tall(X0))) [input p0]
7. ! [X0] : ((~curious(X0) & strong(X0)) <=> (tall(X0) | ~generous(X0))) [input p6]
8. ! [X0] : ((patient(X0) | ~quiet(X0)) => (~curious(X0) <~> brave(X0))) [input p7]
15. ! [X0] : (quiet(X0) <=> (~humble(X0) & ~strong(X0))) [input p14]
23. brave(mary) [input hypothesis]
27. ! [X0] : ((~kind(X0) & tall(X0)) | ~generous(X0)) [ennf transformation 1]
30. ! [X0] : ((~curious(X0) <~> brave(X0)) | (~patient(X0) & quiet(X0))) [ennf transformation 8]
44. ! [X0] : (((~curious(X0) & strong(X0)) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | (curious(X0) | ~strong(X0)))) [nnf transformation 7]
45. ! [X0] : (((~curious(X0) & strong(X0)) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | curious(X0) | ~strong(X0))) [flattening 44]
46. ! [X0] : (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (~patient(X0) & quiet(X0))) [nnf transformation 30]
64. ! [X0] : ((quiet(X0) | (humble(X0) | strong(X0))) & ((~humble(X0) & ~strong(X0)) | ~quiet(X0))) [nnf transformation 15]
65. ! [X0] : ((quiet(X0) | humble(X0) | strong(X0)) & ((~humble(X0) & ~strong(X0)) | ~quiet(X0))) [flattening 64]
80. ~generous(X0) | tall(X0) [cnf transformation 27]
97. strong(X0) | generous(X0) [cnf transformation 45]
98. ~tall(X0) | strong(X0) [cnf transformation 45]
99. ~curious(X0) | generous(X0) [cnf transformation 45]
100. ~curious(X0) | ~tall(X0) [cnf transformation 45]
103. ~brave(X0) | curious(X0) | quiet(X0) [cnf transformation 46]
120. ~quiet(X0) | ~strong(X0) [cnf transformation 65]
134. brave(mary) [cnf transformation 23]
170. 9 <=> curious(mary) [avatar definition]
172. curious(mary) <- (9) [avatar component clause 170]
319. curious(mary) | quiet(mary) [resolution 103,134]
322. 38 <=> quiet(mary) [avatar definition]
324. quiet(mary) <- (38) [avatar component clause 322]
325. 38 | 9 [avatar split clause 319,170,322]
376. ~strong(mary) <- (38) [resolution 324,120]
380. generous(mary) <- (38) [resolution 376,97]
382. tall(mary) <- (38) [resolution 380,80]
384. strong(mary) <- (38) [resolution 382,98]
385. $false <- (38) [subsumption resolution 384,376]
386. ~38 [avatar contradiction clause 385]
389. ~tall(mary) <- (9) [resolution 172,100]
390. generous(mary) <- (9) [resolution 172,99]
401. tall(mary) <- (9) [resolution 390,80]
402. $false <- (9) [subsumption resolution 401,389]
403. ~9 [avatar contradiction clause 402]
404. $false [avatar sat refutation 325,386,403]
% SZS output end Proof for 5905852975178749794896939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not happy then paul is either calm or happy and vice versa.
Everyone who is either tall or patient is not wise and vice versa.
If mary is not calm or not rich then someone is generous.
Everyone who is either calm or not rich is either generous or patient.
Everyone who is either not creative or strong is not creative and vice versa.
Everyone who is not patient is not funny or not quiet.
Everyone who is either tall or not tall is both not old and not generous and vice versa.
Everyone who is either not funny or not curious is either wise or funny.
If someone is wise or not happy then john is both happy and curious and vice versa.
Everyone who is either creative or not funny is either not generous or not happy.
If fred is tall then fred is kind and vice versa.
If someone is both not brave and rich then john is quiet and vice versa.
Everyone who is either not tall or not creative is both not patient and not calm.
Everyone who is either brave or not creative is wise.
If alice is wise then fred is not curious or not funny and vice versa.
Someone is either not tall or wise.
Susan is both not curious and not rich.
Mary is rich or not generous.
Someone is either humble or wise.
Someone is wise or not kind.
Someone is not wise.
Someone is both creative and patient. | Mary is old. | contradiction | ((?[X]:((wise(X)|~happy(X))))<=>((calm(paul)<~>happy(paul))))&
(![X]:((tall(X)<~>patient(X))<=>~wise(X)))&
(((~calm(mary)|~rich(mary)))=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>~rich(X))=>(generous(X)<~>patient(X))))&
(![X]:((~creative(X)<~>strong(X))<=>~creative(X)))&
(![X]:(~patient(X)=>(~funny(X)|~quiet(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~old(X)&~generous(X))))&
(![X]:((~funny(X)<~>~curious(X))=>(wise(X)<~>funny(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((happy(john)&curious(john))))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)<~>~happy(X))))&
((tall(fred))<=>(kind(fred)))&
((?[X]:((~brave(X)&rich(X))))<=>(quiet(john)))&
(![X]:((~tall(X)<~>~creative(X))=>(~patient(X)&~calm(X))))&
(![X]:((brave(X)<~>~creative(X))=>wise(X)))&
((wise(alice))<=>((~curious(fred)|~funny(fred))))&
(?[X]:((~tall(X)<~>wise(X))))&
((~curious(susan)&~rich(susan)))&
((rich(mary)|~generous(mary)))&
(?[X]:((humble(X)<~>wise(X))))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:(~wise(X)))&
(?[X]:((creative(X)&patient(X)))) | old(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8842401819802797731372587
% SZS output start Proof for 8842401819802797731372587
7. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> (~generous(X0) & ~old(X0))) [input p6]
23. old(mary) [input hypothesis]
41. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 7]
42. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [flattening 41]
92. ~old(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 42]
93. ~old(X0) | tall(X0) | tall(X0) [cnf transformation 42]
136. old(mary) [cnf transformation 23]
139. ~old(X0) | ~tall(X0) [duplicate literal removal 92]
140. ~old(X0) | tall(X0) [duplicate literal removal 93]
189. ~old(X0) [subsumption resolution 139,140]
285. $false [subsumption resolution 136,189]
% SZS output end Proof for 8842401819802797731372587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then lucy is old or not tall and vice versa.
Everyone who is not patient is both generous and not creative and vice versa.
Everyone who is either not quiet or kind is generous or brave and vice versa.
If someone is not rich then someone is not generous or quiet.
Everyone who is both not strong and not quiet is not creative and vice versa.
If mary is either not generous or quiet then fred is both not brave and kind.
Everyone who is either quiet or humble is both not wise and creative and vice versa.
Everyone who is either not strong or generous is tall or humble and vice versa.
If mary is not humble then mary is not humble or kind.
Everyone who is not rich or not calm is not kind or not curious and vice versa.
Everyone who is either creative or not wise is funny.
If paul is both old and generous then fred is not brave or tall and vice versa.
If someone is either brave or not strong then john is funny and vice versa.
Everyone who is happy or creative is either not rich or creative and vice versa.
Everyone who is not calm is not strong.
If someone is not funny then someone is not funny or not creative and vice versa.
John is curious or not patient.
Susan is either calm or not quiet.
Someone is either strong or not strong.
Lucy is both not quiet and not patient.
Paul is both not humble and happy.
Someone is not patient.
Paul is either not rich or not quiet.
Someone is both old and not calm. | Paul is wise. | entailment | ((?[X]:(~rich(X)))<=>((old(lucy)|~tall(lucy))))&
(![X]:(~patient(X)<=>(generous(X)&~creative(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(generous(X)|brave(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~generous(X)|quiet(X)))))&
(![X]:((~strong(X)&~quiet(X))<=>~creative(X)))&
(((~generous(mary)<~>quiet(mary)))=>((~brave(fred)&kind(fred))))&
(![X]:((quiet(X)<~>humble(X))<=>(~wise(X)&creative(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(tall(X)|humble(X))))&
((~humble(mary))=>((~humble(mary)|kind(mary))))&
(![X]:((~rich(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((creative(X)<~>~wise(X))=>funny(X)))&
(((old(paul)&generous(paul)))<=>((~brave(fred)|tall(fred))))&
((?[X]:((brave(X)<~>~strong(X))))<=>(funny(john)))&
(![X]:((happy(X)|creative(X))<=>(~rich(X)<~>creative(X))))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((~funny(X)|~creative(X)))))&
((curious(john)|~patient(john)))&
((calm(susan)<~>~quiet(susan)))&
(?[X]:((strong(X)<~>~strong(X))))&
((~quiet(lucy)&~patient(lucy)))&
((~humble(paul)&happy(paul)))&
(?[X]:(~patient(X)))&
((~rich(paul)<~>~quiet(paul)))&
(?[X]:((old(X)&~calm(X)))) | wise(paul) | [
"p4",
"p6",
"p13",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6294478706824844431504442
% SZS output start Proof for 6294478706824844431504442
5. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> ~creative(X0)) [input p4]
7. ! [X0] : ((quiet(X0) <~> humble(X0)) <=> (creative(X0) & ~wise(X0))) [input p6]
14. ! [X0] : ((creative(X0) | happy(X0)) <=> (~rich(X0) <~> creative(X0))) [input p13]
21. happy(paul) & ~humble(paul) [input p20]
23. ~rich(paul) <~> ~quiet(paul) [input p22]
25. ~wise(paul) [input hypothesis]
46. ! [X0] : (((~quiet(X0) & ~strong(X0)) | creative(X0)) & (~creative(X0) | (quiet(X0) | strong(X0)))) [nnf transformation 5]
47. ! [X0] : (((~quiet(X0) & ~strong(X0)) | creative(X0)) & (~creative(X0) | quiet(X0) | strong(X0))) [flattening 46]
49. ! [X0] : ((((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | (~creative(X0) | wise(X0))) & ((creative(X0) & ~wise(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))))) [nnf transformation 7]
50. ! [X0] : ((((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | ~creative(X0) | wise(X0)) & ((creative(X0) & ~wise(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))))) [flattening 49]
62. ! [X0] : (((creative(X0) | happy(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) & (((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~creative(X0) & ~happy(X0)))) [nnf transformation 14]
63. ! [X0] : ((creative(X0) | happy(X0) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) & (((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~creative(X0) & ~happy(X0)))) [flattening 62]
75. (quiet(paul) | rich(paul)) & (~quiet(paul) | ~rich(paul)) [nnf transformation 23]
92. ~quiet(X0) | creative(X0) [cnf transformation 47]
101. ~creative(X0) | quiet(X0) | humble(X0) | wise(X0) [cnf transformation 50]
125. ~happy(X0) | ~rich(X0) | creative(X0) [cnf transformation 63]
128. ~creative(X0) | rich(X0) | ~creative(X0) [cnf transformation 63]
142. ~humble(paul) [cnf transformation 21]
143. happy(paul) [cnf transformation 21]
145. ~quiet(paul) | ~rich(paul) [cnf transformation 75]
146. quiet(paul) | rich(paul) [cnf transformation 75]
149. ~wise(paul) [cnf transformation 25]
150. ~creative(X0) | rich(X0) [duplicate literal removal 128]
281. 28 <=> rich(paul) [avatar definition]
282. ~rich(paul) <- (~28) [avatar component clause 281]
283. rich(paul) <- (28) [avatar component clause 281]
285. 29 <=> quiet(paul) [avatar definition]
286. ~quiet(paul) <- (~29) [avatar component clause 285]
287. quiet(paul) <- (29) [avatar component clause 285]
288. 28 | 29 [avatar split clause 146,285,281]
289. ~28 | ~29 [avatar split clause 145,285,281]
338. ~rich(paul) | creative(paul) [resolution 125,143]
339. creative(paul) <- (28) [subsumption resolution 338,283]
392. quiet(paul) | humble(paul) | wise(paul) <- (28) [resolution 101,339]
393. humble(paul) | wise(paul) <- (28, ~29) [subsumption resolution 392,286]
394. wise(paul) <- (28, ~29) [subsumption resolution 393,142]
395. $false <- (28, ~29) [subsumption resolution 394,149]
396. ~28 | 29 [avatar contradiction clause 395]
401. creative(paul) <- (29) [resolution 287,92]
484. rich(paul) <- (29) [resolution 401,150]
486. $false <- (~28, 29) [subsumption resolution 484,282]
487. 28 | ~29 [avatar contradiction clause 486]
488. $false [avatar sat refutation 288,289,396,487]
% SZS output end Proof for 6294478706824844431504442
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not wise is strong.
Everyone who is not calm or rich is both not tall and not rich and vice versa.
Everyone who is either old or funny is both brave and not quiet.
If mary is either creative or patient then someone is both rich and funny and vice versa.
Everyone who is rich is either rich or patient and vice versa.
If someone is tall or not humble then paul is either not rich or rich.
Everyone who is not calm is patient or not funny.
If mary is not patient then fred is curious and vice versa.
If someone is both patient and not tall then paul is not generous.
If someone is both not curious and not wise then lucy is curious or not rich and vice versa.
Everyone who is either not generous or curious is either wise or happy and vice versa.
Everyone who is both not old and not happy is either kind or not generous and vice versa.
Everyone who is both not kind and not quiet is both not generous and calm.
Everyone who is either funny or not humble is not tall or not generous.
Everyone who is not patient is both old and not tall and vice versa.
If someone is either not creative or wise then john is not creative and vice versa.
Someone is either creative or happy.
Fred is not old or not rich.
Someone is curious or wise.
Mary is not happy.
Mary is tall or not creative.
Paul is both old and not strong. | John is funny. | contradiction | (![X]:((~kind(X)&~wise(X))=>strong(X)))&
(![X]:((~calm(X)|rich(X))<=>(~tall(X)&~rich(X))))&
(![X]:((old(X)<~>funny(X))=>(brave(X)&~quiet(X))))&
(((creative(mary)<~>patient(mary)))<=>(?[X]:((rich(X)&funny(X)))))&
(![X]:(rich(X)<=>(rich(X)<~>patient(X))))&
((?[X]:((tall(X)|~humble(X))))=>((~rich(paul)<~>rich(paul))))&
(![X]:(~calm(X)=>(patient(X)|~funny(X))))&
((~patient(mary))<=>(curious(fred)))&
((?[X]:((patient(X)&~tall(X))))=>(~generous(paul)))&
((?[X]:((~curious(X)&~wise(X))))<=>((curious(lucy)|~rich(lucy))))&
(![X]:((~generous(X)<~>curious(X))<=>(wise(X)<~>happy(X))))&
(![X]:((~old(X)&~happy(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((~kind(X)&~quiet(X))=>(~generous(X)&calm(X))))&
(![X]:((funny(X)<~>~humble(X))=>(~tall(X)|~generous(X))))&
(![X]:(~patient(X)<=>(old(X)&~tall(X))))&
((?[X]:((~creative(X)<~>wise(X))))<=>(~creative(john)))&
(?[X]:((creative(X)<~>happy(X))))&
((~old(fred)|~rich(fred)))&
(?[X]:((curious(X)|wise(X))))&
(~happy(mary))&
((tall(mary)|~creative(mary)))&
((old(paul)&~strong(paul))) | funny(john) | [
"p1",
"p4",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8945793731668323663213178
% SZS output start Proof for 8945793731668323663213178
2. ! [X0] : ((rich(X0) | ~calm(X0)) <=> (~rich(X0) & ~tall(X0))) [input p1]
5. ! [X0] : (rich(X0) <=> (rich(X0) <~> patient(X0))) [input p4]
7. ! [X0] : (~calm(X0) => (~funny(X0) | patient(X0))) [input p6]
15. ! [X0] : (~patient(X0) <=> (~tall(X0) & old(X0))) [input p14]
23. funny(john) [input hypothesis]
29. ! [X0] : ((~funny(X0) | patient(X0)) | calm(X0)) [ennf transformation 7]
30. ! [X0] : (~funny(X0) | patient(X0) | calm(X0)) [flattening 29]
36. ! [X0] : (((rich(X0) | ~calm(X0)) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | (~rich(X0) & calm(X0)))) [nnf transformation 2]
37. ! [X0] : ((rich(X0) | ~calm(X0) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | (~rich(X0) & calm(X0)))) [flattening 36]
43. ! [X0] : ((rich(X0) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | ~rich(X0))) [nnf transformation 5]
55. ! [X0] : ((~patient(X0) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | patient(X0))) [nnf transformation 15]
56. ! [X0] : ((~patient(X0) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | patient(X0))) [flattening 55]
70. ~rich(X0) | ~rich(X0) [cnf transformation 37]
71. rich(X0) | ~calm(X0) | rich(X0) | tall(X0) [cnf transformation 37]
83. rich(X0) | rich(X0) | ~patient(X0) [cnf transformation 43]
88. ~funny(X0) | patient(X0) | calm(X0) [cnf transformation 30]
116. ~tall(X0) | patient(X0) [cnf transformation 56]
130. funny(john) [cnf transformation 23]
132. rich(X0) | ~patient(X0) [duplicate literal removal 83]
133. ~rich(X0) [duplicate literal removal 70]
134. ~calm(X0) | rich(X0) | tall(X0) [duplicate literal removal 71]
153. ~patient(X0) [subsumption resolution 132,133]
154. ~funny(X0) | calm(X0) [subsumption resolution 88,153]
158. ~tall(X0) [subsumption resolution 116,153]
203. calm(john) [resolution 154,130]
224. rich(john) | tall(john) [resolution 134,203]
225. tall(john) [subsumption resolution 224,133]
226. $false [subsumption resolution 225,158]
% SZS output end Proof for 8945793731668323663213178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or patient is quiet and vice versa.
Everyone who is either happy or not quiet is not wise or quiet and vice versa.
If someone is rich then lucy is either strong or not humble.
Everyone who is both quiet and not happy is either strong or not curious.
Everyone who is not quiet is both humble and not strong and vice versa.
Everyone who is either creative or not calm is either generous or not rich.
Everyone who is either brave or not brave is both happy and not creative.
If someone is both old and patient then lucy is not generous and vice versa.
If someone is not brave or not happy then susan is not wise or patient.
Everyone who is patient or strong is either not happy or not wise.
If someone is either brave or not rich then alice is both kind and funny.
Everyone who is strong is either patient or curious and vice versa.
Everyone who is both wise and not creative is not brave.
If someone is humble then someone is not tall or old.
Everyone who is either not generous or happy is both rich and not curious.
Someone is either quiet or kind.
Someone is funny or not patient.
Mary is not generous.
Someone is curious or generous.
Fred is either brave or kind.
Someone is not old or brave.
Mary is strong.
Someone is both calm and quiet. | Lucy is not strong. | entailment | (![X]:((~creative(X)<~>patient(X))<=>quiet(X)))&
(![X]:((happy(X)<~>~quiet(X))<=>(~wise(X)|quiet(X))))&
((?[X]:(rich(X)))=>((strong(lucy)<~>~humble(lucy))))&
(![X]:((quiet(X)&~happy(X))=>(strong(X)<~>~curious(X))))&
(![X]:(~quiet(X)<=>(humble(X)&~strong(X))))&
(![X]:((creative(X)<~>~calm(X))=>(generous(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~brave(X))=>(happy(X)&~creative(X))))&
((?[X]:((old(X)&patient(X))))<=>(~generous(lucy)))&
((?[X]:((~brave(X)|~happy(X))))=>((~wise(susan)|patient(susan))))&
(![X]:((patient(X)|strong(X))=>(~happy(X)<~>~wise(X))))&
((?[X]:((brave(X)<~>~rich(X))))=>((kind(alice)&funny(alice))))&
(![X]:(strong(X)<=>(patient(X)<~>curious(X))))&
(![X]:((wise(X)&~creative(X))=>~brave(X)))&
((?[X]:(humble(X)))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((~generous(X)<~>happy(X))=>(rich(X)&~curious(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
(?[X]:((funny(X)|~patient(X))))&
(~generous(mary))&
(?[X]:((curious(X)|generous(X))))&
((brave(fred)<~>kind(fred)))&
(?[X]:((~old(X)|brave(X))))&
(strong(mary))&
(?[X]:((calm(X)&quiet(X)))) | ~strong(lucy) | [
"p0",
"p1",
"p4",
"p6",
"p7",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8280194328615879351457115
% SZS output start Proof for 8280194328615879351457115
1. ! [X0] : ((~creative(X0) <~> patient(X0)) <=> quiet(X0)) [input p0]
2. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (quiet(X0) | ~wise(X0))) [input p1]
5. ! [X0] : (~quiet(X0) <=> (~strong(X0) & humble(X0))) [input p4]
7. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (~creative(X0) & happy(X0))) [input p6]
8. ? [X0] : (patient(X0) & old(X0)) <=> ~generous(lucy) [input p7]
10. ! [X0] : ((strong(X0) | patient(X0)) => (~happy(X0) <~> ~wise(X0))) [input p9]
12. ! [X0] : (strong(X0) <=> (patient(X0) <~> curious(X0))) [input p11]
15. ! [X0] : ((~generous(X0) <~> happy(X0)) => (~curious(X0) & rich(X0))) [input p14]
24. strong(lucy) [input hypothesis]
33. ! [X0] : ((~creative(X0) & happy(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 7]
36. ! [X0] : ((~happy(X0) <~> ~wise(X0)) | (~strong(X0) & ~patient(X0))) [ennf transformation 10]
40. ! [X0] : ((~curious(X0) & rich(X0)) | (~generous(X0) <=> happy(X0))) [ennf transformation 15]
41. ! [X0] : ((((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~quiet(X0)) & (quiet(X0) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0))))) [nnf transformation 1]
42. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 2]
43. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [flattening 42]
46. ! [X0] : ((~quiet(X0) | (strong(X0) | ~humble(X0))) & ((~strong(X0) & humble(X0)) | quiet(X0))) [nnf transformation 5]
47. ! [X0] : ((~quiet(X0) | strong(X0) | ~humble(X0)) & ((~strong(X0) & humble(X0)) | quiet(X0))) [flattening 46]
49. ! [X0] : ((~creative(X0) & happy(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 33]
50. (? [X0] : (patient(X0) & old(X0)) | generous(lucy)) & (~generous(lucy) | ! [X0] : (~patient(X0) | ~old(X0))) [nnf transformation 8]
51. (? [X0] : (patient(X0) & old(X0)) | generous(lucy)) & (~generous(lucy) | ! [X1] : (~patient(X1) | ~old(X1))) [rectify 50]
52. ? [X0] : (patient(X0) & old(X0)) => (patient(sK0) & old(sK0)) [choice axiom]
53. ((patient(sK0) & old(sK0)) | generous(lucy)) & (~generous(lucy) | ! [X1] : (~patient(X1) | ~old(X1))) [skolemisation 51,52]
54. ! [X0] : (((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | (~strong(X0) & ~patient(X0))) [nnf transformation 36]
56. ! [X0] : ((strong(X0) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0)))) & (((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | ~strong(X0))) [nnf transformation 12]
57. ! [X0] : ((~curious(X0) & rich(X0)) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) [nnf transformation 40]
71. ~quiet(X0) | creative(X0) | ~patient(X0) [cnf transformation 41]
76. ~happy(X0) | quiet(X0) | wise(X0) [cnf transformation 43]
83. ~strong(X0) | quiet(X0) [cnf transformation 47]
89. happy(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 49]
90. happy(X0) | brave(X0) | brave(X0) [cnf transformation 49]
91. ~creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 49]
92. ~creative(X0) | brave(X0) | brave(X0) [cnf transformation 49]
95. patient(sK0) | generous(lucy) [cnf transformation 53]
98. ~wise(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 54]
104. ~strong(X0) | patient(X0) | curious(X0) [cnf transformation 56]
112. ~curious(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 57]
123. strong(lucy) [cnf transformation 24]
124. happy(X0) | ~brave(X0) [duplicate literal removal 89]
125. brave(X0) | happy(X0) [duplicate literal removal 90]
126. ~creative(X0) | ~brave(X0) [duplicate literal removal 91]
127. ~creative(X0) | brave(X0) [duplicate literal removal 92]
135. 2 <=> strong(lucy) [avatar definition]
136. strong(lucy) <- (2) [avatar component clause 135]
144. ~creative(X0) [subsumption resolution 126,127]
145. happy(X0) [subsumption resolution 124,125]
147. 4 <=> generous(lucy) [avatar definition]
149. generous(lucy) <- (4) [avatar component clause 147]
151. 5 <=> patient(sK0) [avatar definition]
153. patient(sK0) <- (5) [avatar component clause 151]
154. 4 | 5 [avatar split clause 95,151,147]
177. ~wise(X0) | ~patient(X0) [subsumption resolution 98,145]
191. ~generous(X0) | ~curious(X0) [subsumption resolution 112,145]
231. 2 [avatar split clause 123,135]
233. quiet(lucy) <- (2) [resolution 83,136]
251. creative(lucy) | ~patient(lucy) <- (2) [resolution 71,233]
256. ~patient(lucy) <- (2) [subsumption resolution 251,144]
260. wise(X0) | quiet(X0) [resolution 76,145]
264. patient(lucy) | curious(lucy) <- (2) [resolution 104,136]
266. curious(lucy) <- (2) [subsumption resolution 264,256]
303. ~patient(X0) | quiet(X0) [resolution 260,177]
327. quiet(sK0) <- (5) [resolution 303,153]
328. creative(sK0) | ~patient(sK0) <- (5) [resolution 327,71]
331. ~patient(sK0) <- (5) [subsumption resolution 328,144]
332. $false <- (5) [subsumption resolution 331,153]
333. ~5 [avatar contradiction clause 332]
341. ~curious(lucy) <- (4) [resolution 149,191]
353. $false <- (2, 4) [subsumption resolution 341,266]
354. ~2 | ~4 [avatar contradiction clause 353]
355. $false [avatar sat refutation 154,231,333,354]
% SZS output end Proof for 8280194328615879351457115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then paul is either rich or not old.
If lucy is not happy or creative then someone is humble and vice versa.
Everyone who is both happy and not rich is both generous and not generous and vice versa.
Everyone who is not rich or not creative is both generous and patient and vice versa.
Everyone who is either not happy or not brave is both not curious and old.
Everyone who is funny is rich and vice versa.
Everyone who is not happy is not wise.
Everyone who is not happy or not quiet is both brave and not old and vice versa.
If someone is not tall then lucy is either not generous or not rich and vice versa.
Everyone who is both not strong and not curious is both not calm and not funny and vice versa.
If alice is both quiet and strong then someone is both not strong and not funny.
If someone is both not calm and generous then someone is both not wise and brave and vice versa.
Everyone who is funny or patient is both not strong and curious.
If someone is both funny and calm then paul is not humble or calm and vice versa.
If susan is old then susan is either strong or not creative.
Everyone who is wise is both not patient and not generous.
Fred is creative.
Mary is both not strong and not wise.
Someone is either not creative or not patient.
Alice is both not strong and not quiet.
Someone is curious. | Fred is not brave. | contradiction | ((?[X]:(curious(X)))=>((rich(paul)<~>~old(paul))))&
(((~happy(lucy)|creative(lucy)))<=>(?[X]:(humble(X))))&
(![X]:((happy(X)&~rich(X))<=>(generous(X)&~generous(X))))&
(![X]:((~rich(X)|~creative(X))<=>(generous(X)&patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~curious(X)&old(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:(~happy(X)=>~wise(X)))&
(![X]:((~happy(X)|~quiet(X))<=>(brave(X)&~old(X))))&
((?[X]:(~tall(X)))<=>((~generous(lucy)<~>~rich(lucy))))&
(![X]:((~strong(X)&~curious(X))<=>(~calm(X)&~funny(X))))&
(((quiet(alice)&strong(alice)))=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((~calm(X)&generous(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)&curious(X))))&
((?[X]:((funny(X)&calm(X))))<=>((~humble(paul)|calm(paul))))&
((old(susan))=>((strong(susan)<~>~creative(susan))))&
(![X]:(wise(X)=>(~patient(X)&~generous(X))))&
(creative(fred))&
((~strong(mary)&~wise(mary)))&
(?[X]:((~creative(X)<~>~patient(X))))&
((~strong(alice)&~quiet(alice)))&
(?[X]:(curious(X))) | ~brave(fred) | [
"p3",
"p4",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1318862779120339668126107
% SZS output start Proof for 1318862779120339668126107
4. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (patient(X0) & generous(X0))) [input p3]
5. ! [X0] : ((~happy(X0) <~> ~brave(X0)) => (old(X0) & ~curious(X0))) [input p4]
6. ! [X0] : (funny(X0) <=> rich(X0)) [input p5]
8. ! [X0] : ((~quiet(X0) | ~happy(X0)) <=> (~old(X0) & brave(X0))) [input p7]
13. ! [X0] : ((patient(X0) | funny(X0)) => (curious(X0) & ~strong(X0))) [input p12]
22. ~brave(fred) [input hypothesis]
25. ! [X0] : ((old(X0) & ~curious(X0)) | (~happy(X0) <=> ~brave(X0))) [ennf transformation 5]
29. ! [X0] : ((curious(X0) & ~strong(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 13]
40. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 4]
41. ! [X0] : ((~creative(X0) | ~rich(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [flattening 40]
42. ! [X0] : ((old(X0) & ~curious(X0)) | ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0)))) [nnf transformation 25]
43. ! [X0] : ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))) [nnf transformation 6]
44. ! [X0] : (((~quiet(X0) | ~happy(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [nnf transformation 8]
45. ! [X0] : ((~quiet(X0) | ~happy(X0) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [flattening 44]
81. patient(X0) | rich(X0) [cnf transformation 41]
85. ~happy(X0) | ~curious(X0) | brave(X0) [cnf transformation 42]
89. ~rich(X0) | funny(X0) [cnf transformation 43]
91. brave(X0) | happy(X0) [cnf transformation 45]
112. ~funny(X0) | curious(X0) [cnf transformation 29]
113. ~patient(X0) | curious(X0) [cnf transformation 29]
131. ~brave(fred) [cnf transformation 22]
289. happy(fred) [resolution 91,131]
294. rich(X1) | curious(X1) [resolution 113,81]
350. ~curious(fred) | brave(fred) [resolution 85,289]
352. ~curious(fred) [subsumption resolution 350,131]
409. curious(X0) | funny(X0) [resolution 294,89]
410. curious(X0) [subsumption resolution 409,112]
438. $false [resolution 410,352]
% SZS output end Proof for 1318862779120339668126107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not brave is not strong and vice versa. If susan is not old or quiet then lucy is both wise and not patient. Everyone who is both not creative and patient is generous or strong and vice versa. Everyone who is rich is either patient or not curious. Everyone who is either quiet or generous is both not patient and quiet. If someone is both not old and rich then fred is both not quiet and not patient and vice versa. Everyone who is not patient or not funny is brave. Everyone who is either not tall or quiet is either not tall or old and vice versa. If paul is either brave or not calm then someone is either not funny or happy. If someone is either not humble or rich then someone is either brave or not wise and vice versa. Everyone who is both not happy and funny is either not generous or humble and vice versa. Everyone who is both patient and not wise is both not quiet and calm and vice versa. If fred is both not happy and wise then john is either not calm or humble. If someone is either not funny or funny then alice is either not quiet or creative. 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. Mary is not old. Mary is not kind. Someone is not creative. Alice is humble or not wise. Someone is either not curious or not humble. Someone is creative or calm. Alice is both not quiet and humble. Mary is tall or quiet. | Lucy is calm. | contradiction | (![X]:((~calm(X)|~brave(X))<=>~strong(X)))&
(((~old(susan)|quiet(susan)))=>((wise(lucy)&~patient(lucy))))&
(![X]:((~creative(X)&patient(X))<=>(generous(X)|strong(X))))&
(![X]:(rich(X)=>(patient(X)<~>~curious(X))))&
(![X]:((quiet(X)<~>generous(X))=>(~patient(X)&quiet(X))))&
((?[X]:((~old(X)&rich(X))))<=>((~quiet(fred)&~patient(fred))))&
(![X]:((~patient(X)|~funny(X))=>brave(X)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)<~>old(X))))&
(((brave(paul)<~>~calm(paul)))=>(?[X]:((~funny(X)<~>happy(X)))))&
((?[X]:((~humble(X)<~>rich(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~happy(X)&funny(X))<=>(~generous(X)<~>humble(X))))&
(![X]:((patient(X)&~wise(X))<=>(~quiet(X)&calm(X))))&
(((~happy(fred)&wise(fred)))=>((~calm(john)<~>humble(john))))&
((?[X]:((~funny(X)<~>funny(X))))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:(~old(X)))<=>((~calm(fred)&~creative(fred))))&
((?[X]:(strong(X)))<=>(old(fred)))&
(~old(mary))&
(~kind(mary))&
(?[X]:(~creative(X)))&
((humble(alice)|~wise(alice)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:((creative(X)|calm(X))))&
((~quiet(alice)&humble(alice)))&
((tall(mary)|quiet(mary))) | calm(lucy) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8562514249522017113258275
% SZS output start Proof for 8562514249522017113258275
1. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> ~strong(X0)) [input p0]
2. (quiet(susan) | ~old(susan)) => (~patient(lucy) & wise(lucy)) [input p1]
3. ! [X0] : ((patient(X0) & ~creative(X0)) <=> (strong(X0) | generous(X0))) [input p2]
7. ! [X0] : ((~funny(X0) | ~patient(X0)) => brave(X0)) [input p6]
8. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (~tall(X0) <~> old(X0))) [input p7]
25. calm(lucy) [input hypothesis]
28. (~patient(lucy) & wise(lucy)) | (~quiet(susan) & old(susan)) [ennf transformation 2]
31. ! [X0] : (brave(X0) | (funny(X0) & patient(X0))) [ennf transformation 7]
36. ! [X0] : (((~brave(X0) | ~calm(X0)) | strong(X0)) & (~strong(X0) | (brave(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | ~calm(X0) | strong(X0)) & (~strong(X0) | (brave(X0) & calm(X0)))) [flattening 36]
38. ! [X0] : (((patient(X0) & ~creative(X0)) | (~strong(X0) & ~generous(X0))) & ((strong(X0) | generous(X0)) | (~patient(X0) | creative(X0)))) [nnf transformation 3]
39. ! [X0] : (((patient(X0) & ~creative(X0)) | (~strong(X0) & ~generous(X0))) & (strong(X0) | generous(X0) | ~patient(X0) | creative(X0))) [flattening 38]
47. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) & (((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 8]
80. ~brave(X0) | ~calm(X0) | strong(X0) [cnf transformation 37]
83. ~patient(lucy) | old(susan) [cnf transformation 28]
84. ~patient(lucy) | ~quiet(susan) [cnf transformation 28]
89. ~strong(X0) | patient(X0) [cnf transformation 39]
100. patient(X0) | brave(X0) [cnf transformation 31]
104. ~old(X0) | tall(X0) | quiet(X0) | tall(X0) [cnf transformation 47]
107. quiet(X0) | ~tall(X0) | ~tall(X0) | ~old(X0) [cnf transformation 47]
152. calm(lucy) [cnf transformation 25]
158. ~old(X0) | tall(X0) | quiet(X0) [duplicate literal removal 104]
159. quiet(X0) | ~tall(X0) | ~old(X0) [duplicate literal removal 107]
163. 1 <=> quiet(susan) [avatar definition]
165. ~quiet(susan) <- (~1) [avatar component clause 163]
167. 2 <=> patient(lucy) [avatar definition]
169. ~patient(lucy) <- (~2) [avatar component clause 167]
170. ~1 | ~2 [avatar split clause 84,167,163]
172. 3 <=> old(susan) [avatar definition]
174. old(susan) <- (3) [avatar component clause 172]
175. 3 | ~2 [avatar split clause 83,167,172]
205. ~old(X0) | quiet(X0) [subsumption resolution 158,159]
375. quiet(susan) <- (3) [resolution 205,174]
377. $false <- (~1, 3) [subsumption resolution 375,165]
378. 1 | ~3 [avatar contradiction clause 377]
382. brave(lucy) <- (~2) [resolution 169,100]
390. ~calm(lucy) | strong(lucy) <- (~2) [resolution 80,382]
392. strong(lucy) <- (~2) [subsumption resolution 390,152]
431. patient(lucy) <- (~2) [resolution 392,89]
434. $false <- (~2) [subsumption resolution 431,169]
435. 2 [avatar contradiction clause 434]
436. $false [avatar sat refutation 170,175,378,435]
% SZS output end Proof for 8562514249522017113258275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and brave is either brave or not calm.
Everyone who is both not strong and generous is both not generous and not patient.
Everyone who is tall or happy is either calm or not old and vice versa.
Everyone who is both quiet and strong is not tall or not creative and vice versa.
Everyone who is either not kind or not curious is both tall and not kind and vice versa.
If someone is not calm then someone is generous or not funny.
Everyone who is either kind or patient is both tall and not strong.
Everyone who is not tall or curious is rich.
If mary is either brave or not strong then susan is either brave or not wise.
If susan is both happy and not kind then someone is either not funny or strong.
Everyone who is calm is not strong and vice versa.
If fred is not generous or calm then someone is not rich or not generous.
If alice is generous or old then john is both generous and kind.
If someone is tall then someone is either not brave or generous and vice versa.
If alice is both not rich and not strong then mary is either strong or not brave and vice versa.
Paul is creative.
Someone is funny.
Someone is either creative or rich.
Someone is brave or not quiet.
John is both not tall and rich.
Paul is either not rich or calm.
Susan is either not curious or calm. | Paul is generous. | contradiction | (![X]:((happy(X)&brave(X))=>(brave(X)<~>~calm(X))))&
(![X]:((~strong(X)&generous(X))=>(~generous(X)&~patient(X))))&
(![X]:((tall(X)|happy(X))<=>(calm(X)<~>~old(X))))&
(![X]:((quiet(X)&strong(X))<=>(~tall(X)|~creative(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>(tall(X)&~kind(X))))&
((?[X]:(~calm(X)))=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:((kind(X)<~>patient(X))=>(tall(X)&~strong(X))))&
(![X]:((~tall(X)|curious(X))=>rich(X)))&
(((brave(mary)<~>~strong(mary)))=>((brave(susan)<~>~wise(susan))))&
(((happy(susan)&~kind(susan)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:(calm(X)<=>~strong(X)))&
(((~generous(fred)|calm(fred)))=>(?[X]:((~rich(X)|~generous(X)))))&
(((generous(alice)|old(alice)))=>((generous(john)&kind(john))))&
((?[X]:(tall(X)))<=>(?[X]:((~brave(X)<~>generous(X)))))&
(((~rich(alice)&~strong(alice)))<=>((strong(mary)<~>~brave(mary))))&
(creative(paul))&
(?[X]:(funny(X)))&
(?[X]:((creative(X)<~>rich(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((~tall(john)&rich(john)))&
((~rich(paul)<~>calm(paul)))&
((~curious(susan)<~>calm(susan))) | generous(paul) | [
"p1",
"p4",
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6878019910248664031637756
% SZS output start Proof for 6878019910248664031637756
2. ! [X0] : ((generous(X0) & ~strong(X0)) => (~patient(X0) & ~generous(X0))) [input p1]
5. ! [X0] : ((~kind(X0) <~> ~curious(X0)) <=> (~kind(X0) & tall(X0))) [input p4]
8. ! [X0] : ((curious(X0) | ~tall(X0)) => rich(X0)) [input p7]
11. ! [X0] : (calm(X0) <=> ~strong(X0)) [input p10]
21. ~rich(paul) <~> calm(paul) [input p20]
23. generous(paul) [input hypothesis]
28. ! [X0] : ((~patient(X0) & ~generous(X0)) | (~generous(X0) | strong(X0))) [ennf transformation 2]
29. ! [X0] : ((~patient(X0) & ~generous(X0)) | ~generous(X0) | strong(X0)) [flattening 28]
32. ! [X0] : (rich(X0) | (~curious(X0) & tall(X0))) [ennf transformation 8]
43. ! [X0] : ((((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))))) [nnf transformation 5]
44. ! [X0] : ((((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))))) [flattening 43]
53. ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))) [nnf transformation 11]
70. (~calm(paul) | rich(paul)) & (calm(paul) | ~rich(paul)) [nnf transformation 21]
74. ~generous(X0) | ~generous(X0) | strong(X0) [cnf transformation 29]
90. ~kind(X0) | ~kind(X0) | curious(X0) [cnf transformation 44]
92. curious(X0) | kind(X0) | kind(X0) | ~tall(X0) [cnf transformation 44]
98. rich(X0) | tall(X0) [cnf transformation 32]
99. ~curious(X0) | rich(X0) [cnf transformation 32]
106. ~strong(X0) | ~calm(X0) [cnf transformation 53]
131. calm(paul) | ~rich(paul) [cnf transformation 70]
135. generous(paul) [cnf transformation 23]
136. ~kind(X0) | curious(X0) [duplicate literal removal 90]
137. ~tall(X0) | kind(X0) | curious(X0) [duplicate literal removal 92]
138. ~generous(X0) | strong(X0) [duplicate literal removal 74]
287. 32 <=> rich(paul) [avatar definition]
288. ~rich(paul) <- (~32) [avatar component clause 287]
291. 33 <=> calm(paul) [avatar definition]
295. ~32 | 33 [avatar split clause 131,291,287]
309. tall(paul) <- (~32) [resolution 98,288]
316. strong(paul) [resolution 138,135]
317. ~calm(paul) [resolution 316,106]
391. kind(paul) | curious(paul) <- (~32) [resolution 137,309]
398. curious(paul) <- (~32) [subsumption resolution 391,136]
448. rich(paul) <- (~32) [resolution 398,99]
449. $false <- (~32) [subsumption resolution 448,288]
450. 32 [avatar contradiction clause 449]
461. ~33 [avatar split clause 317,291]
462. $false [avatar sat refutation 295,450,461]
% SZS output end Proof for 6878019910248664031637756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not calm is either quiet or not happy.
Everyone who is both funny and not strong is generous or happy and vice versa.
Everyone who is both not curious and calm is both creative and not quiet.
Everyone who is not tall or funny is wise or not rich and vice versa.
If fred is not generous or not patient then someone is wise or calm.
Everyone who is not rich is generous and vice versa.
Everyone who is brave or happy is both curious and creative.
Everyone who is wise or not humble is not creative.
If someone is calm then someone is happy or kind and vice versa.
If john is not wise then paul is funny.
Everyone who is both not quiet and creative is humble.
Everyone who is either not happy or curious is not funny and vice versa.
Everyone who is not calm is both not old and not quiet and vice versa.
If paul is either humble or brave then someone is either not tall or patient.
If lucy is not kind then susan is both humble and strong.
If alice is brave or rich then someone is not old or generous.
Alice is either not generous or not funny.
Mary is not generous or humble.
Someone is either wise or quiet.
Paul is both not brave and not strong.
John is not creative.
Someone is generous or not generous.
Someone is tall. | Fred is rich. | neutral | (![X]:((creative(X)|~calm(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((funny(X)&~strong(X))<=>(generous(X)|happy(X))))&
(![X]:((~curious(X)&calm(X))=>(creative(X)&~quiet(X))))&
(![X]:((~tall(X)|funny(X))<=>(wise(X)|~rich(X))))&
(((~generous(fred)|~patient(fred)))=>(?[X]:((wise(X)|calm(X)))))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((brave(X)|happy(X))=>(curious(X)&creative(X))))&
(![X]:((wise(X)|~humble(X))=>~creative(X)))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)|kind(X)))))&
((~wise(john))=>(funny(paul)))&
(![X]:((~quiet(X)&creative(X))=>humble(X)))&
(![X]:((~happy(X)<~>curious(X))<=>~funny(X)))&
(![X]:(~calm(X)<=>(~old(X)&~quiet(X))))&
(((humble(paul)<~>brave(paul)))=>(?[X]:((~tall(X)<~>patient(X)))))&
((~kind(lucy))=>((humble(susan)&strong(susan))))&
(((brave(alice)|rich(alice)))=>(?[X]:((~old(X)|generous(X)))))&
((~generous(alice)<~>~funny(alice)))&
((~generous(mary)|humble(mary)))&
(?[X]:((wise(X)<~>quiet(X))))&
((~brave(paul)&~strong(paul)))&
(~creative(john))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:(tall(X))) | rich(fred) | [] | null | 0 |
If mary is calm then alice is both not curious and not brave and vice versa.
Everyone who is not brave is either not curious or tall.
Everyone who is either quiet or funny is patient or tall.
Everyone who is both not patient and not happy is either funny or not tall.
Everyone who is not brave is rich and vice versa.
If susan is rich then someone is either wise or not creative and vice versa.
If susan is humble or patient then someone is both happy and not curious.
If someone is not calm then mary is either curious or not patient.
Everyone who is creative or not patient is either brave or creative.
Everyone who is generous or humble is tall.
Everyone who is not rich or not old is patient and vice versa.
If someone is not tall or brave then someone is either quiet or not calm.
Everyone who is not creative is either patient or not creative and vice versa.
If paul is both not curious and not creative then alice is both not funny and wise.
If someone is either curious or old then someone is both not kind and not generous.
Lucy is either wise or not happy.
John is generous or not wise.
Susan is either tall or not calm.
Someone is happy or not old. | John is not generous. | neutral | ((calm(mary))<=>((~curious(alice)&~brave(alice))))&
(![X]:(~brave(X)=>(~curious(X)<~>tall(X))))&
(![X]:((quiet(X)<~>funny(X))=>(patient(X)|tall(X))))&
(![X]:((~patient(X)&~happy(X))=>(funny(X)<~>~tall(X))))&
(![X]:(~brave(X)<=>rich(X)))&
((rich(susan))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(((humble(susan)|patient(susan)))=>(?[X]:((happy(X)&~curious(X)))))&
((?[X]:(~calm(X)))=>((curious(mary)<~>~patient(mary))))&
(![X]:((creative(X)|~patient(X))=>(brave(X)<~>creative(X))))&
(![X]:((generous(X)|humble(X))=>tall(X)))&
(![X]:((~rich(X)|~old(X))<=>patient(X)))&
((?[X]:((~tall(X)|brave(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:(~creative(X)<=>(patient(X)<~>~creative(X))))&
(((~curious(paul)&~creative(paul)))=>((~funny(alice)&wise(alice))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&~generous(X)))))&
((wise(lucy)<~>~happy(lucy)))&
((generous(john)|~wise(john)))&
((tall(susan)<~>~calm(susan)))&
(?[X]:((happy(X)|~old(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is either patient or not strong is both not calm and not patient.
If someone is curious then someone is not rich.
Everyone who is not old or not brave is both not calm and not happy.
If mary is curious or not calm then fred is either wise or brave and vice versa.
Everyone who is not tall or not old is not tall or patient and vice versa.
Everyone who is calm is quiet or not wise and vice versa.
Everyone who is generous or not wise is either creative or rich and vice versa.
If someone is generous then john is both kind and not rich and vice versa.
If fred is both not wise and calm then alice is both not strong and quiet and vice versa.
Everyone who is both strong and not patient is quiet and vice versa.
If someone is creative then someone is both not patient and old and vice versa.
Everyone who is not old is not generous.
If susan is either generous or not patient then susan is not creative and vice versa.
Everyone who is old or not curious is both not rich and strong and vice versa.
If someone is happy or not rich then john is either creative or brave.
Everyone who is not curious or rich is both not curious and not calm and vice versa.
Alice is not old.
Someone is either not brave or strong.
Mary is generous or old.
Someone is both not rich and humble.
Lucy is kind or not happy.
Mary is not patient.
Someone is kind or not brave.
Someone is not happy. | Mary is not calm. | contradiction | (![X]:((patient(X)<~>~strong(X))=>(~calm(X)&~patient(X))))&
((?[X]:(curious(X)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)|~brave(X))=>(~calm(X)&~happy(X))))&
(((curious(mary)|~calm(mary)))<=>((wise(fred)<~>brave(fred))))&
(![X]:((~tall(X)|~old(X))<=>(~tall(X)|patient(X))))&
(![X]:(calm(X)<=>(quiet(X)|~wise(X))))&
(![X]:((generous(X)|~wise(X))<=>(creative(X)<~>rich(X))))&
((?[X]:(generous(X)))<=>((kind(john)&~rich(john))))&
(((~wise(fred)&calm(fred)))<=>((~strong(alice)&quiet(alice))))&
(![X]:((strong(X)&~patient(X))<=>quiet(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~patient(X)&old(X)))))&
(![X]:(~old(X)=>~generous(X)))&
(((generous(susan)<~>~patient(susan)))<=>(~creative(susan)))&
(![X]:((old(X)|~curious(X))<=>(~rich(X)&strong(X))))&
((?[X]:((happy(X)|~rich(X))))=>((creative(john)<~>brave(john))))&
(![X]:((~curious(X)|rich(X))<=>(~curious(X)&~calm(X))))&
(~old(alice))&
(?[X]:((~brave(X)<~>strong(X))))&
((generous(mary)|old(mary)))&
(?[X]:((~rich(X)&humble(X))))&
((kind(lucy)|~happy(lucy)))&
(~patient(mary))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:(~happy(X))) | ~calm(mary) | [
"p0",
"p5",
"p9",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7907331405710223671939237
% SZS output start Proof for 7907331405710223671939237
1. ! [X0] : ((patient(X0) <~> ~strong(X0)) => (~patient(X0) & ~calm(X0))) [input p0]
6. ! [X0] : (calm(X0) <=> (~wise(X0) | quiet(X0))) [input p5]
10. ! [X0] : ((~patient(X0) & strong(X0)) <=> quiet(X0)) [input p9]
12. ! [X0] : (~old(X0) => ~generous(X0)) [input p11]
14. ! [X0] : ((~curious(X0) | old(X0)) <=> (strong(X0) & ~rich(X0))) [input p13]
19. old(mary) | generous(mary) [input p18]
25. ~calm(mary) [input hypothesis]
33. ! [X0] : ((~patient(X0) & ~calm(X0)) | (patient(X0) <=> ~strong(X0))) [ennf transformation 1]
36. ! [X0] : (~generous(X0) | old(X0)) [ennf transformation 12]
38. ! [X0] : ((~patient(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) [nnf transformation 33]
46. ! [X0] : ((calm(X0) | (wise(X0) & ~quiet(X0))) & ((~wise(X0) | quiet(X0)) | ~calm(X0))) [nnf transformation 6]
47. ! [X0] : ((calm(X0) | (wise(X0) & ~quiet(X0))) & (~wise(X0) | quiet(X0) | ~calm(X0))) [flattening 46]
57. ! [X0] : (((~patient(X0) & strong(X0)) | ~quiet(X0)) & (quiet(X0) | (patient(X0) | ~strong(X0)))) [nnf transformation 10]
58. ! [X0] : (((~patient(X0) & strong(X0)) | ~quiet(X0)) & (quiet(X0) | patient(X0) | ~strong(X0))) [flattening 57]
65. ! [X0] : (((~curious(X0) | old(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (curious(X0) & ~old(X0)))) [nnf transformation 14]
66. ! [X0] : ((~curious(X0) | old(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (curious(X0) & ~old(X0)))) [flattening 65]
79. ~patient(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 38]
95. ~quiet(X0) | calm(X0) [cnf transformation 47]
110. quiet(X0) | patient(X0) | ~strong(X0) [cnf transformation 58]
116. ~generous(X0) | old(X0) [cnf transformation 36]
123. ~old(X0) | strong(X0) [cnf transformation 66]
136. old(mary) | generous(mary) [cnf transformation 19]
140. ~calm(mary) [cnf transformation 25]
141. ~strong(X0) | ~patient(X0) [duplicate literal removal 79]
163. 6 <=> calm(mary) [avatar definition]
165. ~calm(mary) <- (~6) [avatar component clause 163]
208. ~strong(X0) | quiet(X0) [subsumption resolution 110,141]
270. old(mary) [subsumption resolution 136,116]
280. ~6 [avatar split clause 140,163]
290. strong(mary) [resolution 123,270]
296. quiet(mary) [resolution 208,290]
312. calm(mary) [resolution 296,95]
313. $false <- (~6) [subsumption resolution 312,165]
314. 6 [avatar contradiction clause 313]
315. $false [avatar sat refutation 280,314]
% SZS output end Proof for 7907331405710223671939237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not patient then alice is both not calm and tall. Everyone who is both not brave and humble is not wise and vice versa. Everyone who is either patient or not funny is either curious or quiet and vice versa. Everyone who is not humble is both happy and not funny and vice versa. Everyone who is both tall and strong is either not tall or not curious. Everyone who is both calm and old is not wise and vice versa. If someone is both strong and not humble then john is either creative or not calm. Everyone who is not funny is either rich or not curious. Everyone who is not rich or curious is not patient or not old and vice versa. Everyone who is either wise or not old is either happy or kind. If alice is humble then alice is either not humble or not old and vice versa. If paul is not old then someone is either calm or not quiet. If someone is tall or not rich then lucy is not strong or not generous. Everyone who is both not rich and wise is not kind and vice versa. Everyone who is both not tall and not wise is either not kind or not humble. Everyone who is both not funny and not calm is calm or brave and vice versa. John is both humble and not curious. Alice is either not humble or tall. Someone is either not kind or tall. Fred is patient or curious. Alice is either not brave or tall. Someone is not patient or old. Someone is curious or not brave. | John is not happy. | entailment | ((~patient(susan))=>((~calm(alice)&tall(alice))))&
(![X]:((~brave(X)&humble(X))<=>~wise(X)))&
(![X]:((patient(X)<~>~funny(X))<=>(curious(X)<~>quiet(X))))&
(![X]:(~humble(X)<=>(happy(X)&~funny(X))))&
(![X]:((tall(X)&strong(X))=>(~tall(X)<~>~curious(X))))&
(![X]:((calm(X)&old(X))<=>~wise(X)))&
((?[X]:((strong(X)&~humble(X))))=>((creative(john)<~>~calm(john))))&
(![X]:(~funny(X)=>(rich(X)<~>~curious(X))))&
(![X]:((~rich(X)|curious(X))<=>(~patient(X)|~old(X))))&
(![X]:((wise(X)<~>~old(X))=>(happy(X)<~>kind(X))))&
((humble(alice))<=>((~humble(alice)<~>~old(alice))))&
((~old(paul))=>(?[X]:((calm(X)<~>~quiet(X)))))&
((?[X]:((tall(X)|~rich(X))))=>((~strong(lucy)|~generous(lucy))))&
(![X]:((~rich(X)&wise(X))<=>~kind(X)))&
(![X]:((~tall(X)&~wise(X))=>(~kind(X)<~>~humble(X))))&
(![X]:((~funny(X)&~calm(X))<=>(calm(X)|brave(X))))&
((humble(john)&~curious(john)))&
((~humble(alice)<~>tall(alice)))&
(?[X]:((~kind(X)<~>tall(X))))&
((patient(fred)|curious(fred)))&
((~brave(alice)<~>tall(alice)))&
(?[X]:((~patient(X)|old(X))))&
(?[X]:((curious(X)|~brave(X)))) | ~happy(john) | [
"p1",
"p3",
"p5",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7354115821816680164670534
% SZS output start Proof for 7354115821816680164670534
2. ! [X0] : ((humble(X0) & ~brave(X0)) <=> ~wise(X0)) [input p1]
4. ! [X0] : (~humble(X0) <=> (~funny(X0) & happy(X0))) [input p3]
6. ! [X0] : ((old(X0) & calm(X0)) <=> ~wise(X0)) [input p5]
16. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (brave(X0) | calm(X0))) [input p15]
17. ~curious(john) & humble(john) [input p16]
24. happy(john) [input hypothesis]
34. ! [X0] : (((humble(X0) & ~brave(X0)) | wise(X0)) & (~wise(X0) | (~humble(X0) | brave(X0)))) [nnf transformation 2]
35. ! [X0] : (((humble(X0) & ~brave(X0)) | wise(X0)) & (~wise(X0) | ~humble(X0) | brave(X0))) [flattening 34]
37. ! [X0] : ((~humble(X0) | (funny(X0) | ~happy(X0))) & ((~funny(X0) & happy(X0)) | humble(X0))) [nnf transformation 4]
38. ! [X0] : ((~humble(X0) | funny(X0) | ~happy(X0)) & ((~funny(X0) & happy(X0)) | humble(X0))) [flattening 37]
39. ! [X0] : (((old(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | (~old(X0) | ~calm(X0)))) [nnf transformation 6]
40. ! [X0] : (((old(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | ~old(X0) | ~calm(X0))) [flattening 39]
52. ! [X0] : (((~calm(X0) & ~funny(X0)) | (~brave(X0) & ~calm(X0))) & ((brave(X0) | calm(X0)) | (calm(X0) | funny(X0)))) [nnf transformation 16]
53. ! [X0] : (((~calm(X0) & ~funny(X0)) | (~brave(X0) & ~calm(X0))) & (brave(X0) | calm(X0) | calm(X0) | funny(X0))) [flattening 52]
65. ~wise(X0) | ~humble(X0) | brave(X0) [cnf transformation 35]
77. ~funny(X0) | humble(X0) [cnf transformation 38]
78. ~happy(X0) | funny(X0) | ~humble(X0) [cnf transformation 38]
80. wise(X0) | calm(X0) [cnf transformation 40]
103. brave(X0) | calm(X0) | calm(X0) | funny(X0) [cnf transformation 53]
105. ~funny(X0) | ~brave(X0) [cnf transformation 53]
106. ~calm(X0) | ~calm(X0) [cnf transformation 53]
108. humble(john) [cnf transformation 17]
119. happy(john) [cnf transformation 24]
120. brave(X0) | calm(X0) | funny(X0) [duplicate literal removal 103]
121. ~calm(X0) [duplicate literal removal 106]
164. funny(X0) | brave(X0) [subsumption resolution 120,121]
215. humble(X1) | brave(X1) [resolution 164,77]
217. ~humble(X1) | brave(X1) | calm(X1) [resolution 65,80]
222. ~humble(X1) | brave(X1) [subsumption resolution 217,121]
223. brave(X1) [subsumption resolution 222,215]
229. funny(john) | ~humble(john) [resolution 78,119]
231. funny(john) [subsumption resolution 229,108]
232. ~brave(john) [resolution 231,105]
234. $false [subsumption resolution 232,223]
% SZS output end Proof for 7354115821816680164670534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not strong is not quiet or tall.
Everyone who is not generous or not quiet is both humble and curious and vice versa.
If mary is both rich and kind then someone is either not quiet or not generous and vice versa.
Everyone who is curious is not happy.
Everyone who is both not curious and wise is both not kind and happy.
If john is both not old and not calm then john is not tall or not generous and vice versa.
If someone is not kind then john is either not quiet or happy and vice versa.
Everyone who is both strong and patient is happy or wise.
Everyone who is both not curious and curious is generous or creative and vice versa.
Everyone who is both calm and not brave is rich.
Everyone who is not brave or not creative is not patient.
If lucy is not strong or tall then someone is either not creative or not patient and vice versa.
If paul is happy or not strong then someone is both not calm and curious and vice versa.
Everyone who is wise is not humble or generous.
Everyone who is both funny and tall is not strong.
Everyone who is calm is both curious and generous.
Lucy is either quiet or humble.
Fred is not kind.
Alice is not kind.
John is either funny or patient.
Mary is either quiet or funny. | John is old. | contradiction | (![X]:((~happy(X)&~strong(X))=>(~quiet(X)|tall(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(humble(X)&curious(X))))&
(((rich(mary)&kind(mary)))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:(curious(X)=>~happy(X)))&
(![X]:((~curious(X)&wise(X))=>(~kind(X)&happy(X))))&
(((~old(john)&~calm(john)))<=>((~tall(john)|~generous(john))))&
((?[X]:(~kind(X)))<=>((~quiet(john)<~>happy(john))))&
(![X]:((strong(X)&patient(X))=>(happy(X)|wise(X))))&
(![X]:((~curious(X)&curious(X))<=>(generous(X)|creative(X))))&
(![X]:((calm(X)&~brave(X))=>rich(X)))&
(![X]:((~brave(X)|~creative(X))=>~patient(X)))&
(((~strong(lucy)|tall(lucy)))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
(((happy(paul)|~strong(paul)))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:(wise(X)=>(~humble(X)|generous(X))))&
(![X]:((funny(X)&tall(X))=>~strong(X)))&
(![X]:(calm(X)=>(curious(X)&generous(X))))&
((quiet(lucy)<~>humble(lucy)))&
(~kind(fred))&
(~kind(alice))&
((funny(john)<~>patient(john)))&
((quiet(mary)<~>funny(mary))) | old(john) | [
"p1",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7789319395634136569937134
% SZS output start Proof for 7789319395634136569937134
2. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (curious(X0) & humble(X0))) [input p1]
6. (~calm(john) & ~old(john)) <=> (~generous(john) | ~tall(john)) [input p5]
9. ! [X0] : ((curious(X0) & ~curious(X0)) <=> (creative(X0) | generous(X0))) [input p8]
22. old(john) [input hypothesis]
38. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 2]
39. ! [X0] : ((~quiet(X0) | ~generous(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | (quiet(X0) & generous(X0)))) [flattening 38]
45. ((~calm(john) & ~old(john)) | (generous(john) & tall(john))) & ((~generous(john) | ~tall(john)) | (calm(john) | old(john))) [nnf transformation 6]
46. ((~calm(john) & ~old(john)) | (generous(john) & tall(john))) & (~generous(john) | ~tall(john) | calm(john) | old(john)) [flattening 45]
51. ! [X0] : (((curious(X0) & ~curious(X0)) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | (~curious(X0) | curious(X0)))) [nnf transformation 9]
52. ! [X0] : (((curious(X0) & ~curious(X0)) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | ~curious(X0) | curious(X0))) [flattening 51]
69. curious(X0) | generous(X0) [cnf transformation 39]
83. ~old(john) | generous(john) [cnf transformation 46]
92. ~curious(X0) | ~generous(X0) [cnf transformation 52]
94. curious(X0) | ~generous(X0) [cnf transformation 52]
120. old(john) [cnf transformation 22]
150. 7 <=> generous(john) [avatar definition]
152. generous(john) <- (7) [avatar component clause 150]
164. 10 <=> old(john) [avatar definition]
167. 7 | ~10 [avatar split clause 83,164,150]
189. curious(X0) [subsumption resolution 94,69]
191. ~generous(X0) [subsumption resolution 92,189]
238. 10 [avatar split clause 120,164]
239. $false <- (7) [subsumption resolution 152,191]
240. ~7 [avatar contradiction clause 239]
241. $false [avatar sat refutation 167,238,240]
% SZS output end Proof for 7789319395634136569937134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not patient is either not funny or creative and vice versa. Everyone who is not creative or not happy is wise and vice versa. Everyone who is generous or not creative is both calm and quiet and vice versa. Everyone who is either kind or creative is not brave or calm and vice versa. Everyone who is humble is either not humble or humble and vice versa. Everyone who is either old or strong is both not rich and not happy. Everyone who is not calm or not funny is either not happy or wise. If someone is either brave or calm then susan is both not quiet and not wise. If someone is either quiet or not generous then someone is not tall or quiet. If someone is not creative then someone is both not funny and brave and vice versa. Everyone who is not funny is both tall and not calm. If mary is not generous then susan is not curious. Everyone who is rich or generous is quiet. If mary is not old or quiet then someone is not tall and vice versa. If mary is either rich or not curious then someone is either not humble or funny. Everyone who is not calm or brave is either not funny or happy and vice versa. Paul is not old. Susan is brave or strong. Someone is old or generous. Someone is either rich or not generous. Someone is quiet. Alice is not happy. | Alice is funny. | entailment | (![X]:((happy(X)|~patient(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~creative(X)|~happy(X))<=>wise(X)))&
(![X]:((generous(X)|~creative(X))<=>(calm(X)&quiet(X))))&
(![X]:((kind(X)<~>creative(X))<=>(~brave(X)|calm(X))))&
(![X]:(humble(X)<=>(~humble(X)<~>humble(X))))&
(![X]:((old(X)<~>strong(X))=>(~rich(X)&~happy(X))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)<~>wise(X))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(((~old(mary)|quiet(mary)))<=>(?[X]:(~tall(X))))&
(((rich(mary)<~>~curious(mary)))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|brave(X))<=>(~funny(X)<~>happy(X))))&
(~old(paul))&
((brave(susan)|strong(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:(quiet(X)))&
(~happy(alice)) | funny(alice) | [
"p1",
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7050759423629698990232556
% SZS output start Proof for 7050759423629698990232556
2. ! [X0] : ((~happy(X0) | ~creative(X0)) <=> wise(X0)) [input p1]
7. ! [X0] : ((~funny(X0) | ~calm(X0)) => (~happy(X0) <~> wise(X0))) [input p6]
11. ! [X0] : (~funny(X0) => (~calm(X0) & tall(X0))) [input p10]
16. ! [X0] : ((brave(X0) | ~calm(X0)) <=> (~funny(X0) <~> happy(X0))) [input p15]
23. ~funny(alice) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> wise(X0)) | (funny(X0) & calm(X0))) [ennf transformation 7]
30. ! [X0] : ((~calm(X0) & tall(X0)) | funny(X0)) [ennf transformation 11]
36. ! [X0] : (((~happy(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [flattening 36]
44. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (funny(X0) & calm(X0))) [nnf transformation 27]
63. ! [X0] : (((brave(X0) | ~calm(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [nnf transformation 16]
64. ! [X0] : ((brave(X0) | ~calm(X0) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [flattening 63]
79. wise(X0) | happy(X0) [cnf transformation 37]
102. ~wise(X0) | happy(X0) | calm(X0) [cnf transformation 44]
114. ~calm(X0) | funny(X0) [cnf transformation 30]
127. ~happy(X0) | funny(X0) | calm(X0) [cnf transformation 64]
138. ~funny(alice) [cnf transformation 23]
146. happy(X0) | calm(X0) [subsumption resolution 102,79]
252. funny(X0) | calm(X0) [subsumption resolution 127,146]
253. funny(X0) [subsumption resolution 252,114]
283. $false [subsumption resolution 138,253]
% SZS output end Proof for 7050759423629698990232556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or kind is either strong or not rich and vice versa. Everyone who is either not strong or creative is both creative and humble. Everyone who is both not wise and rich is generous or rich. If alice is both old and not patient then someone is either brave or creative and vice versa. Everyone who is patient is not tall and vice versa. Everyone who is not old or not happy is not brave or not funny and vice versa. Everyone who is either old or humble is both not generous and not patient and vice versa. Everyone who is either brave or not humble is not happy. If someone is not kind then someone is both not patient and not wise. Everyone who is either not kind or happy is either not funny or not generous and vice versa. If someone is both not rich and patient then someone is calm. If paul is both not humble and not creative then paul is not curious and vice versa. Everyone who is not generous or generous is not kind and vice versa. If lucy is funny then someone is both not generous and not happy and vice versa. Everyone who is either patient or not old is both not funny and generous. Everyone who is not humble or not calm is either strong or happy. Someone is not strong or funny. Fred is either not old or not happy. Mary is not patient or generous. Fred is generous or kind. Alice is not tall or curious. Fred is brave. Lucy is happy or not wise. | Lucy is not funny. | contradiction | (![X]:((rich(X)|kind(X))<=>(strong(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>creative(X))=>(creative(X)&humble(X))))&
(![X]:((~wise(X)&rich(X))=>(generous(X)|rich(X))))&
(((old(alice)&~patient(alice)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(![X]:(patient(X)<=>~tall(X)))&
(![X]:((~old(X)|~happy(X))<=>(~brave(X)|~funny(X))))&
(![X]:((old(X)<~>humble(X))<=>(~generous(X)&~patient(X))))&
(![X]:((brave(X)<~>~humble(X))=>~happy(X)))&
((?[X]:(~kind(X)))=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:((~kind(X)<~>happy(X))<=>(~funny(X)<~>~generous(X))))&
((?[X]:((~rich(X)&patient(X))))=>(?[X]:(calm(X))))&
(((~humble(paul)&~creative(paul)))<=>(~curious(paul)))&
(![X]:((~generous(X)|generous(X))<=>~kind(X)))&
((funny(lucy))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((patient(X)<~>~old(X))=>(~funny(X)&generous(X))))&
(![X]:((~humble(X)|~calm(X))=>(strong(X)<~>happy(X))))&
(?[X]:((~strong(X)|funny(X))))&
((~old(fred)<~>~happy(fred)))&
((~patient(mary)|generous(mary)))&
((generous(fred)|kind(fred)))&
((~tall(alice)|curious(alice)))&
(brave(fred))&
((happy(lucy)|~wise(lucy))) | ~funny(lucy) | [
"p0",
"p5",
"p6",
"p7",
"p9",
"p12",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5388892049266240874936653
% SZS output start Proof for 5388892049266240874936653
1. ! [X0] : ((kind(X0) | rich(X0)) <=> (strong(X0) <~> ~rich(X0))) [input p0]
6. ! [X0] : ((~happy(X0) | ~old(X0)) <=> (~funny(X0) | ~brave(X0))) [input p5]
7. ! [X0] : ((old(X0) <~> humble(X0)) <=> (~patient(X0) & ~generous(X0))) [input p6]
8. ! [X0] : ((brave(X0) <~> ~humble(X0)) => ~happy(X0)) [input p7]
10. ! [X0] : ((~kind(X0) <~> happy(X0)) <=> (~funny(X0) <~> ~generous(X0))) [input p9]
13. ! [X0] : ((generous(X0) | ~generous(X0)) <=> ~kind(X0)) [input p12]
14. funny(lucy) <=> ? [X0] : (~happy(X0) & ~generous(X0)) [input p13]
15. ! [X0] : ((patient(X0) <~> ~old(X0)) => (generous(X0) & ~funny(X0))) [input p14]
16. ! [X0] : ((~calm(X0) | ~humble(X0)) => (strong(X0) <~> happy(X0))) [input p15]
17. ? [X0] : (funny(X0) | ~strong(X0)) [input p16]
24. ~funny(lucy) [input hypothesis]
28. ! [X0] : (~humble(X0) => (strong(X0) <~> happy(X0))) [pure predicate removal 16]
32. ! [X0] : (~happy(X0) | (brave(X0) <=> ~humble(X0))) [ennf transformation 8]
34. ! [X0] : ((generous(X0) & ~funny(X0)) | (patient(X0) <=> ~old(X0))) [ennf transformation 15]
35. ! [X0] : ((strong(X0) <~> happy(X0)) | humble(X0)) [ennf transformation 28]
36. ! [X0] : (((kind(X0) | rich(X0)) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0)))) & (((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | (~kind(X0) & ~rich(X0)))) [nnf transformation 1]
37. ! [X0] : ((kind(X0) | rich(X0) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0)))) & (((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | (~kind(X0) & ~rich(X0)))) [flattening 36]
45. ! [X0] : (((~happy(X0) | ~old(X0)) | (funny(X0) & brave(X0))) & ((~funny(X0) | ~brave(X0)) | (happy(X0) & old(X0)))) [nnf transformation 6]
46. ! [X0] : ((~happy(X0) | ~old(X0) | (funny(X0) & brave(X0))) & (~funny(X0) | ~brave(X0) | (happy(X0) & old(X0)))) [flattening 45]
47. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (patient(X0) | generous(X0))) & ((~patient(X0) & ~generous(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | patient(X0) | generous(X0)) & ((~patient(X0) & ~generous(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [flattening 47]
49. ! [X0] : (~happy(X0) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0)))) [nnf transformation 32]
53. ! [X0] : ((((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) & (((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0))))) [nnf transformation 10]
56. ! [X0] : (((generous(X0) | ~generous(X0)) | kind(X0)) & (~kind(X0) | (~generous(X0) & generous(X0)))) [nnf transformation 13]
57. ! [X0] : ((generous(X0) | ~generous(X0) | kind(X0)) & (~kind(X0) | (~generous(X0) & generous(X0)))) [flattening 56]
58. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & (? [X0] : (~happy(X0) & ~generous(X0)) | ~funny(lucy)) [nnf transformation 14]
59. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & (? [X1] : (~happy(X1) & ~generous(X1)) | ~funny(lucy)) [rectify 58]
60. ? [X1] : (~happy(X1) & ~generous(X1)) => (~happy(sK2) & ~generous(sK2)) [choice axiom]
61. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & ((~happy(sK2) & ~generous(sK2)) | ~funny(lucy)) [skolemisation 59,60]
62. ! [X0] : ((generous(X0) & ~funny(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) [nnf transformation 34]
63. ! [X0] : (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | humble(X0)) [nnf transformation 35]
64. ? [X0] : (funny(X0) | ~strong(X0)) => (funny(sK3) | ~strong(sK3)) [choice axiom]
65. funny(sK3) | ~strong(sK3) [skolemisation 17,64]
67. ~rich(X0) | strong(X0) | ~rich(X0) [cnf transformation 37]
72. kind(X0) | rich(X0) | strong(X0) | rich(X0) [cnf transformation 37]
88. ~happy(X0) | ~old(X0) | brave(X0) [cnf transformation 46]
91. ~generous(X0) | old(X0) | ~humble(X0) [cnf transformation 48]
93. ~patient(X0) | old(X0) | ~humble(X0) [cnf transformation 48]
96. ~happy(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 49]
100. ~funny(X0) | ~generous(X0) | happy(X0) | kind(X0) [cnf transformation 53]
111. ~kind(X0) | generous(X0) [cnf transformation 57]
112. ~generous(X0) | ~kind(X0) [cnf transformation 57]
116. funny(lucy) | happy(X0) | generous(X0) [cnf transformation 61]
120. patient(X0) | generous(X0) | old(X0) [cnf transformation 62]
122. ~happy(X0) | ~strong(X0) | humble(X0) [cnf transformation 63]
123. funny(sK3) | ~strong(sK3) [cnf transformation 65]
131. ~funny(lucy) [cnf transformation 24]
133. ~rich(X0) | strong(X0) [duplicate literal removal 67]
134. strong(X0) | rich(X0) | kind(X0) [duplicate literal removal 72]
191. ~kind(X0) [subsumption resolution 111,112]
193. 13 <=> ! [X0] : (happy(X0) | generous(X0)) [avatar definition]
194. happy(X0) | generous(X0) <- (13) [avatar component clause 193]
196. 14 <=> funny(lucy) [avatar definition]
199. 13 | 14 [avatar split clause 116,196,193]
211. 17 <=> strong(sK3) [avatar definition]
212. strong(sK3) <- (17) [avatar component clause 211]
213. ~strong(sK3) <- (~17) [avatar component clause 211]
215. 18 <=> funny(sK3) [avatar definition]
217. funny(sK3) <- (18) [avatar component clause 215]
218. ~17 | 18 [avatar split clause 123,215,211]
257. ~14 [avatar split clause 131,196]
289. generous(X1) | old(X1) | old(X1) | ~humble(X1) [resolution 120,93]
294. generous(X1) | old(X1) | ~humble(X1) [duplicate literal removal 289]
296. ~humble(X1) | old(X1) [subsumption resolution 294,91]
330. rich(sK3) | kind(sK3) <- (~17) [resolution 134,213]
333. rich(sK3) <- (~17) [subsumption resolution 330,191]
334. strong(sK3) <- (~17) [resolution 333,133]
335. $false <- (~17) [subsumption resolution 334,213]
336. 17 [avatar contradiction clause 335]
343. 33 <=> old(sK3) [avatar definition]
345. old(sK3) <- (33) [avatar component clause 343]
353. 35 <=> happy(sK3) [avatar definition]
354. ~happy(sK3) <- (~35) [avatar component clause 353]
355. happy(sK3) <- (35) [avatar component clause 353]
357. 36 <=> brave(sK3) [avatar definition]
373. 37 <=> generous(sK3) [avatar definition]
374. generous(sK3) <- (37) [avatar component clause 373]
377. 38 <=> humble(sK3) [avatar definition]
378. ~humble(sK3) <- (~38) [avatar component clause 377]
379. humble(sK3) <- (38) [avatar component clause 377]
395. ~generous(sK3) | happy(sK3) | kind(sK3) <- (18) [resolution 100,217]
438. ~strong(sK3) | humble(sK3) <- (35) [resolution 355,122]
439. humble(sK3) <- (17, 35) [subsumption resolution 438,212]
440. $false <- (17, 35, ~38) [subsumption resolution 439,378]
441. ~17 | ~35 | 38 [avatar contradiction clause 440]
449. generous(sK3) <- (13, ~35) [resolution 354,194]
452. 37 | ~13 | 35 [avatar split clause 449,353,193,373]
456. happy(sK3) | kind(sK3) <- (18, 37) [subsumption resolution 395,374]
457. happy(sK3) <- (18, 37) [subsumption resolution 456,191]
458. 35 | ~18 | ~37 [avatar split clause 457,373,215,353]
459. ~old(sK3) | brave(sK3) <- (35) [resolution 355,88]
461. ~humble(sK3) | ~brave(sK3) <- (35) [resolution 355,96]
485. old(sK3) <- (38) [resolution 379,296]
488. 33 | ~38 [avatar split clause 485,377,343]
491. brave(sK3) <- (33, 35) [subsumption resolution 459,345]
492. 36 | ~33 | ~35 [avatar split clause 491,353,343,357]
493. ~brave(sK3) <- (35, 38) [subsumption resolution 461,379]
494. ~36 | ~35 | ~38 [avatar split clause 493,377,353,357]
495. $false [avatar sat refutation 199,218,257,336,441,452,458,488,492,494]
% SZS output end Proof for 5388892049266240874936653
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not happy is both not funny and strong. If someone is both not funny and funny then someone is not wise or not humble. Everyone who is both creative and not rich is brave or kind. If someone is both patient and not old then someone is not calm or humble. Everyone who is not humble or not curious is both not patient and not tall. If fred is not quiet then john is strong and vice versa. Everyone who is both not calm and not rich is calm and vice versa. If lucy is either funny or not curious then susan is generous. Everyone who is not calm is either not quiet or not strong. Everyone who is both strong and not tall is both not humble and creative and vice versa. Everyone who is not creative is brave. If someone is brave then someone is either humble or not tall and vice versa. Everyone who is not calm or not quiet is either not humble or happy and vice versa. Everyone who is both not old and humble is either not happy or funny and vice versa. If someone is either not strong or old then someone is both not curious and quiet and vice versa. Mary is either not calm or not creative. Alice is not generous or not funny. Fred is rich. John is kind or generous. Someone is both patient and humble. Someone is either not rich or not calm. Someone is both not patient and not calm. Mary is both kind and not funny. | Lucy is not old. | neutral | (![X]:((rich(X)&~happy(X))=>(~funny(X)&strong(X))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((creative(X)&~rich(X))=>(brave(X)|kind(X))))&
((?[X]:((patient(X)&~old(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~humble(X)|~curious(X))=>(~patient(X)&~tall(X))))&
((~quiet(fred))<=>(strong(john)))&
(![X]:((~calm(X)&~rich(X))<=>calm(X)))&
(((funny(lucy)<~>~curious(lucy)))=>(generous(susan)))&
(![X]:(~calm(X)=>(~quiet(X)<~>~strong(X))))&
(![X]:((strong(X)&~tall(X))<=>(~humble(X)&creative(X))))&
(![X]:(~creative(X)=>brave(X)))&
((?[X]:(brave(X)))<=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:((~calm(X)|~quiet(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~old(X)&humble(X))<=>(~happy(X)<~>funny(X))))&
((?[X]:((~strong(X)<~>old(X))))<=>(?[X]:((~curious(X)&quiet(X)))))&
((~calm(mary)<~>~creative(mary)))&
((~generous(alice)|~funny(alice)))&
(rich(fred))&
((kind(john)|generous(john)))&
(?[X]:((patient(X)&humble(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~patient(X)&~calm(X))))&
((kind(mary)&~funny(mary))) | ~old(lucy) | [] | null | 0 |
If someone is both not patient and kind then lucy is either funny or humble. Everyone who is not tall is either strong or not calm and vice versa. Everyone who is funny is not tall or not calm and vice versa. Everyone who is not funny or funny is tall or generous. Everyone who is both not happy and strong is rich or kind and vice versa. Everyone who is not old or not rich is both not funny and not happy and vice versa. Everyone who is either wise or strong is not funny or rich. If someone is not quiet then someone is either old or not strong. Everyone who is either not happy or not tall is brave or generous. If someone is quiet or not wise then susan is not patient or funny and vice versa. Everyone who is either not quiet or happy is curious or not quiet and vice versa. Everyone who is both not strong and generous is old. If someone is wise or rich then someone is not humble or not calm. Everyone who is not quiet is both happy and patient. Everyone who is either not tall or not humble is not tall or strong. Everyone who is both generous and not curious is not kind and vice versa. Susan is not tall or generous. Someone is not patient or brave. Fred is either generous or rich. Paul is both not tall and creative. Lucy is happy or not wise. Someone is not strong. Someone is either strong or kind. Susan is either happy or not creative. | Fred is old. | entailment | ((?[X]:((~patient(X)&kind(X))))=>((funny(lucy)<~>humble(lucy))))&
(![X]:(~tall(X)<=>(strong(X)<~>~calm(X))))&
(![X]:(funny(X)<=>(~tall(X)|~calm(X))))&
(![X]:((~funny(X)|funny(X))=>(tall(X)|generous(X))))&
(![X]:((~happy(X)&strong(X))<=>(rich(X)|kind(X))))&
(![X]:((~old(X)|~rich(X))<=>(~funny(X)&~happy(X))))&
(![X]:((wise(X)<~>strong(X))=>(~funny(X)|rich(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((old(X)<~>~strong(X)))))&
(![X]:((~happy(X)<~>~tall(X))=>(brave(X)|generous(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>((~patient(susan)|funny(susan))))&
(![X]:((~quiet(X)<~>happy(X))<=>(curious(X)|~quiet(X))))&
(![X]:((~strong(X)&generous(X))=>old(X)))&
((?[X]:((wise(X)|rich(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:(~quiet(X)=>(happy(X)&patient(X))))&
(![X]:((~tall(X)<~>~humble(X))=>(~tall(X)|strong(X))))&
(![X]:((generous(X)&~curious(X))<=>~kind(X)))&
((~tall(susan)|generous(susan)))&
(?[X]:((~patient(X)|brave(X))))&
((generous(fred)<~>rich(fred)))&
((~tall(paul)&creative(paul)))&
((happy(lucy)|~wise(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:((strong(X)<~>kind(X))))&
((happy(susan)<~>~creative(susan))) | old(fred) | [
"p1",
"p2",
"p4",
"p5",
"p10",
"p11",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6410519544025016172471988
% SZS output start Proof for 6410519544025016172471988
2. ! [X0] : (~tall(X0) <=> (strong(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : (funny(X0) <=> (~calm(X0) | ~tall(X0))) [input p2]
5. ! [X0] : ((strong(X0) & ~happy(X0)) <=> (kind(X0) | rich(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | ~old(X0)) <=> (~happy(X0) & ~funny(X0))) [input p5]
11. ! [X0] : ((~quiet(X0) <~> happy(X0)) <=> (~quiet(X0) | curious(X0))) [input p10]
12. ! [X0] : ((generous(X0) & ~strong(X0)) => old(X0)) [input p11]
14. ! [X0] : (~quiet(X0) => (patient(X0) & happy(X0))) [input p13]
16. ! [X0] : ((~curious(X0) & generous(X0)) <=> ~kind(X0)) [input p15]
19. generous(fred) <~> rich(fred) [input p18]
25. ~old(fred) [input hypothesis]
36. ! [X0] : (old(X0) | (~generous(X0) | strong(X0))) [ennf transformation 12]
37. ! [X0] : (old(X0) | ~generous(X0) | strong(X0)) [flattening 36]
39. ! [X0] : ((patient(X0) & happy(X0)) | quiet(X0)) [ennf transformation 14]
43. ! [X0] : ((~tall(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | tall(X0))) [nnf transformation 2]
44. ! [X0] : ((funny(X0) | (calm(X0) & tall(X0))) & ((~calm(X0) | ~tall(X0)) | ~funny(X0))) [nnf transformation 3]
45. ! [X0] : ((funny(X0) | (calm(X0) & tall(X0))) & (~calm(X0) | ~tall(X0) | ~funny(X0))) [flattening 44]
46. ! [X0] : (((strong(X0) & ~happy(X0)) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | (~strong(X0) | happy(X0)))) [nnf transformation 5]
47. ! [X0] : (((strong(X0) & ~happy(X0)) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ~strong(X0) | happy(X0))) [flattening 46]
48. ! [X0] : (((~rich(X0) | ~old(X0)) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | (rich(X0) & old(X0)))) [nnf transformation 6]
49. ! [X0] : ((~rich(X0) | ~old(X0) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | (rich(X0) & old(X0)))) [flattening 48]
60. ! [X0] : ((((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))))) [nnf transformation 11]
61. ! [X0] : ((((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))))) [flattening 60]
66. ! [X0] : (((~curious(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) | ~generous(X0)))) [nnf transformation 16]
67. ! [X0] : (((~curious(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | curious(X0) | ~generous(X0))) [flattening 66]
68. (~rich(fred) | ~generous(fred)) & (rich(fred) | generous(fred)) [nnf transformation 19]
79. ~calm(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 43]
82. tall(X0) | funny(X0) [cnf transformation 45]
83. calm(X0) | funny(X0) [cnf transformation 45]
86. ~strong(X0) | rich(X0) | kind(X0) | happy(X0) [cnf transformation 47]
87. ~rich(X0) | ~happy(X0) [cnf transformation 47]
89. ~rich(X0) | strong(X0) [cnf transformation 47]
90. ~kind(X0) | strong(X0) [cnf transformation 47]
91. ~funny(X0) | old(X0) [cnf transformation 49]
94. ~happy(X0) | rich(X0) [cnf transformation 49]
106. happy(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 61]
110. ~generous(X0) | old(X0) | strong(X0) [cnf transformation 37]
113. happy(X0) | quiet(X0) [cnf transformation 39]
117. ~generous(X0) | curious(X0) | ~kind(X0) [cnf transformation 67]
118. generous(X0) | kind(X0) [cnf transformation 67]
121. rich(fred) | generous(fred) [cnf transformation 68]
131. ~old(fred) [cnf transformation 25]
150. ~happy(X0) [subsumption resolution 94,87]
152. 4 <=> ! [X1] : quiet(X1) [avatar definition]
153. quiet(X1) <- (4) [avatar component clause 152]
190. ~curious(X0) | ~quiet(X0) [subsumption resolution 106,150]
207. quiet(X0) [subsumption resolution 113,150]
208. 4 [avatar split clause 207,152]
211. 17 <=> generous(fred) [avatar definition]
212. generous(fred) <- (17) [avatar component clause 211]
215. 18 <=> rich(fred) [avatar definition]
216. rich(fred) <- (18) [avatar component clause 215]
217. ~rich(fred) <- (~18) [avatar component clause 215]
219. 17 | 18 [avatar split clause 121,215,211]
256. ~tall(X0) | ~strong(X0) | funny(X0) [resolution 79,83]
257. ~strong(X0) | funny(X0) [subsumption resolution 256,82]
271. old(X1) | strong(X1) | kind(X1) [resolution 110,118]
282. old(X1) | strong(X1) [subsumption resolution 271,90]
309. 29 <=> kind(fred) [avatar definition]
313. 30 <=> curious(fred) [avatar definition]
315. curious(fred) <- (30) [avatar component clause 313]
346. strong(fred) <- (18) [resolution 216,89]
355. funny(fred) <- (18) [resolution 346,257]
361. strong(fred) [resolution 282,131]
370. old(fred) <- (18) [resolution 355,91]
371. $false <- (18) [subsumption resolution 370,131]
372. ~18 [avatar contradiction clause 371]
374. 34 <=> strong(fred) [avatar definition]
376. strong(fred) <- (34) [avatar component clause 374]
383. 34 [avatar split clause 361,374]
384. curious(fred) | ~kind(fred) <- (17) [resolution 212,117]
389. rich(fred) | kind(fred) | happy(fred) <- (34) [resolution 376,86]
392. kind(fred) | happy(fred) <- (~18, 34) [subsumption resolution 389,217]
396. kind(fred) <- (~18, 34) [subsumption resolution 392,150]
397. 29 | 18 | ~34 [avatar split clause 396,374,215,309]
398. ~29 | 30 | ~17 [avatar split clause 384,211,313,309]
401. ~quiet(fred) <- (30) [resolution 315,190]
403. $false <- (4, 30) [subsumption resolution 401,153]
404. ~4 | ~30 [avatar contradiction clause 403]
405. $false [avatar sat refutation 208,219,372,383,397,398,404]
% SZS output end Proof for 6410519544025016172471988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not strong is both happy and patient and vice versa. Everyone who is both old and happy is tall. Everyone who is either not kind or quiet is either not kind or generous. Everyone who is either not wise or not quiet is kind and vice versa. Everyone who is kind or not generous is both not strong and wise. Everyone who is creative or quiet is either strong or not generous. Everyone who is not kind or not happy is both not curious and not happy and vice versa. If mary is happy or patient then someone is either brave or not brave and vice versa. Everyone who is both patient and quiet is both not calm and happy and vice versa. If someone is not old then someone is generous or kind and vice versa. If paul is strong or not patient then fred is both not creative and not strong. If alice is not brave or wise then someone is not tall and vice versa. Everyone who is not quiet or not rich is not brave. Lucy is either not wise or not patient. Mary is humble or not tall. Someone is either not brave or brave. Someone is humble. Lucy is not humble. Alice is either rich or quiet. John is not tall or not kind. Lucy is both not curious and not creative. | Mary is not wise. | contradiction | (![X]:((funny(X)|~strong(X))<=>(happy(X)&patient(X))))&
(![X]:((old(X)&happy(X))=>tall(X)))&
(![X]:((~kind(X)<~>quiet(X))=>(~kind(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((kind(X)|~generous(X))=>(~strong(X)&wise(X))))&
(![X]:((creative(X)|quiet(X))=>(strong(X)<~>~generous(X))))&
(![X]:((~kind(X)|~happy(X))<=>(~curious(X)&~happy(X))))&
(((happy(mary)|patient(mary)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:((patient(X)&quiet(X))<=>(~calm(X)&happy(X))))&
((?[X]:(~old(X)))<=>(?[X]:((generous(X)|kind(X)))))&
(((strong(paul)|~patient(paul)))=>((~creative(fred)&~strong(fred))))&
(((~brave(alice)|wise(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~quiet(X)|~rich(X))=>~brave(X)))&
((~wise(lucy)<~>~patient(lucy)))&
((humble(mary)|~tall(mary)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
((rich(alice)<~>quiet(alice)))&
((~tall(john)|~kind(john)))&
((~curious(lucy)&~creative(lucy))) | ~wise(mary) | [
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6156135661866382592730542
% SZS output start Proof for 6156135661866382592730542
3. ! [X0] : ((~kind(X0) <~> quiet(X0)) => (~kind(X0) <~> generous(X0))) [input p2]
4. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> kind(X0)) [input p3]
5. ! [X0] : ((~generous(X0) | kind(X0)) => (wise(X0) & ~strong(X0))) [input p4]
22. ~wise(mary) [input hypothesis]
29. ! [X0] : ((~kind(X0) <~> generous(X0)) | (~kind(X0) <=> quiet(X0))) [ennf transformation 3]
30. ! [X0] : ((wise(X0) & ~strong(X0)) | (generous(X0) & ~kind(X0))) [ennf transformation 5]
36. ! [X0] : (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) [nnf transformation 29]
37. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ~kind(X0)) & (kind(X0) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 4]
73. ~generous(X0) | kind(X0) | quiet(X0) | kind(X0) [cnf transformation 36]
75. ~quiet(X0) | kind(X0) | wise(X0) [cnf transformation 37]
76. ~wise(X0) | kind(X0) | quiet(X0) [cnf transformation 37]
81. ~kind(X0) | wise(X0) [cnf transformation 30]
82. wise(X0) | generous(X0) [cnf transformation 30]
121. ~wise(mary) [cnf transformation 22]
125. ~generous(X0) | kind(X0) | quiet(X0) [duplicate literal removal 73]
259. kind(X1) | quiet(X1) | generous(X1) [resolution 76,82]
269. quiet(X1) | kind(X1) [subsumption resolution 259,125]
278. kind(X0) | kind(X0) | wise(X0) [resolution 269,75]
279. kind(X0) | wise(X0) [duplicate literal removal 278]
280. wise(X0) [subsumption resolution 279,81]
304. $false [resolution 280,121]
% SZS output end Proof for 6156135661866382592730542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or generous then mary is brave or not brave and vice versa.
Everyone who is either not brave or not creative is either wise or rich and vice versa.
Everyone who is not wise is happy or not creative and vice versa.
Everyone who is brave is not calm or rich and vice versa.
Everyone who is not creative or not brave is wise or funny and vice versa.
If fred is not quiet then paul is rich and vice versa.
Everyone who is patient or not funny is curious.
Everyone who is both not tall and not creative is both brave and happy.
Everyone who is both humble and kind is not happy and vice versa.
Everyone who is brave is rich or not wise and vice versa.
Everyone who is creative is creative or not quiet.
Everyone who is not brave is both not calm and calm and vice versa.
Everyone who is not old is both brave and not funny and vice versa.
Everyone who is either not patient or kind is both not funny and quiet and vice versa.
Everyone who is either old or not rich is both generous and not kind.
Everyone who is either not funny or kind is both strong and old.
Someone is not calm or not rich.
Someone is calm or not quiet.
Mary is either quiet or not funny. | Fred is creative. | contradiction | ((?[X]:((~generous(X)<~>generous(X))))<=>((brave(mary)|~brave(mary))))&
(![X]:((~brave(X)<~>~creative(X))<=>(wise(X)<~>rich(X))))&
(![X]:(~wise(X)<=>(happy(X)|~creative(X))))&
(![X]:(brave(X)<=>(~calm(X)|rich(X))))&
(![X]:((~creative(X)|~brave(X))<=>(wise(X)|funny(X))))&
((~quiet(fred))<=>(rich(paul)))&
(![X]:((patient(X)|~funny(X))=>curious(X)))&
(![X]:((~tall(X)&~creative(X))=>(brave(X)&happy(X))))&
(![X]:((humble(X)&kind(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(rich(X)|~wise(X))))&
(![X]:(creative(X)=>(creative(X)|~quiet(X))))&
(![X]:(~brave(X)<=>(~calm(X)&calm(X))))&
(![X]:(~old(X)<=>(brave(X)&~funny(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~funny(X)&quiet(X))))&
(![X]:((old(X)<~>~rich(X))=>(generous(X)&~kind(X))))&
(![X]:((~funny(X)<~>kind(X))=>(strong(X)&old(X))))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:((calm(X)|~quiet(X))))&
((quiet(mary)<~>~funny(mary))) | creative(fred) | [
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6443778530126203140500076
% SZS output start Proof for 6443778530126203140500076
2. ! [X0] : ((~brave(X0) <~> ~creative(X0)) <=> (wise(X0) <~> rich(X0))) [input p1]
3. ! [X0] : (~wise(X0) <=> (~creative(X0) | happy(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> (rich(X0) | ~calm(X0))) [input p3]
5. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (funny(X0) | wise(X0))) [input p4]
12. ! [X0] : (~brave(X0) <=> (calm(X0) & ~calm(X0))) [input p11]
13. ! [X0] : (~old(X0) <=> (~funny(X0) & brave(X0))) [input p12]
15. ! [X0] : ((old(X0) <~> ~rich(X0)) => (~kind(X0) & generous(X0))) [input p14]
16. ! [X0] : ((~funny(X0) <~> kind(X0)) => (old(X0) & strong(X0))) [input p15]
20. creative(fred) [input hypothesis]
21. ! [X0] : ((~funny(X0) <~> kind(X0)) => old(X0)) [pure predicate removal 16]
26. ! [X0] : ((~kind(X0) & generous(X0)) | (old(X0) <=> ~rich(X0))) [ennf transformation 15]
27. ! [X0] : (old(X0) | (~funny(X0) <=> kind(X0))) [ennf transformation 21]
33. ! [X0] : ((((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0)))) & (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))))) [nnf transformation 2]
34. ! [X0] : ((~wise(X0) | (creative(X0) & ~happy(X0))) & ((~creative(X0) | happy(X0)) | wise(X0))) [nnf transformation 3]
35. ! [X0] : ((~wise(X0) | (creative(X0) & ~happy(X0))) & (~creative(X0) | happy(X0) | wise(X0))) [flattening 34]
36. ! [X0] : ((brave(X0) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ~brave(X0))) [nnf transformation 4]
37. ! [X0] : ((brave(X0) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~brave(X0))) [flattening 36]
38. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~funny(X0) & ~wise(X0))) & ((funny(X0) | wise(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 5]
39. ! [X0] : ((~brave(X0) | ~creative(X0) | (~funny(X0) & ~wise(X0))) & (funny(X0) | wise(X0) | (brave(X0) & creative(X0)))) [flattening 38]
45. ! [X0] : ((~brave(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | brave(X0))) [nnf transformation 12]
46. ! [X0] : ((~brave(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | brave(X0))) [flattening 45]
47. ! [X0] : ((~old(X0) | (funny(X0) | ~brave(X0))) & ((~funny(X0) & brave(X0)) | old(X0))) [nnf transformation 13]
48. ! [X0] : ((~old(X0) | funny(X0) | ~brave(X0)) & ((~funny(X0) & brave(X0)) | old(X0))) [flattening 47]
51. ! [X0] : ((~kind(X0) & generous(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0)))) [nnf transformation 26]
52. ! [X0] : (old(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 27]
65. ~brave(X0) | wise(X0) | rich(X0) | creative(X0) [cnf transformation 33]
69. ~rich(X0) | ~brave(X0) | wise(X0) | ~creative(X0) [cnf transformation 33]
74. ~wise(X0) | creative(X0) [cnf transformation 35]
76. calm(X0) | brave(X0) [cnf transformation 37]
80. ~brave(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 39]
81. ~funny(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 39]
91. ~calm(X0) | brave(X0) [cnf transformation 46]
95. ~funny(X0) | old(X0) [cnf transformation 48]
96. ~old(X0) | funny(X0) | ~brave(X0) [cnf transformation 48]
106. ~kind(X0) | old(X0) | rich(X0) [cnf transformation 51]
107. old(X0) | kind(X0) | funny(X0) [cnf transformation 52]
113. creative(fred) [cnf transformation 20]
116. ~wise(X0) | ~brave(X0) [subsumption resolution 80,74]
128. brave(X0) [subsumption resolution 91,76]
129. ~old(X0) | funny(X0) [subsumption resolution 96,128]
130. old(X0) | kind(X0) [subsumption resolution 107,95]
163. kind(X0) | funny(X0) [resolution 130,129]
167. 9 <=> wise(fred) [avatar definition]
168. ~wise(fred) <- (~9) [avatar component clause 167]
169. wise(fred) <- (9) [avatar component clause 167]
185. ~brave(fred) <- (9) [resolution 169,116]
187. $false <- (9) [subsumption resolution 185,128]
188. ~9 [avatar contradiction clause 187]
239. old(X0) | rich(X0) | funny(X0) [resolution 106,163]
242. old(X0) | rich(X0) [subsumption resolution 239,95]
247. funny(X2) | rich(X2) [resolution 242,129]
248. wise(X0) | rich(X0) | creative(X0) [resolution 65,128]
249. rich(X0) | creative(X0) [subsumption resolution 248,74]
287. rich(X1) | ~creative(X1) | ~brave(X1) [resolution 247,81]
290. rich(X1) | ~creative(X1) [subsumption resolution 287,128]
291. rich(X1) [subsumption resolution 290,249]
314. ~brave(X1) | wise(X1) | ~creative(X1) [resolution 291,69]
318. ~creative(X1) | wise(X1) [subsumption resolution 314,128]
319. wise(fred) [resolution 318,113]
321. $false <- (~9) [subsumption resolution 319,168]
322. 9 [avatar contradiction clause 321]
325. $false [avatar sat refutation 188,322]
% SZS output end Proof for 6443778530126203140500076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not kind and vice versa.
Everyone who is not calm is not happy or strong and vice versa.
Everyone who is either strong or not wise is happy and vice versa.
Everyone who is curious is calm.
Everyone who is either curious or not brave is strong and vice versa.
Everyone who is either not wise or not kind is both quiet and brave and vice versa.
Everyone who is both curious and not creative is not funny or calm and vice versa.
If fred is rich then someone is both not strong and kind.
Everyone who is not brave or quiet is quiet and vice versa.
If mary is not wise then someone is either not old or brave.
Everyone who is not calm or not old is either not generous or calm and vice versa.
If fred is calm or not kind then alice is old and vice versa.
If someone is either generous or curious then someone is brave.
Everyone who is not quiet or not funny is both strong and wise and vice versa.
Someone is not strong.
Someone is brave or not old.
Someone is tall.
Susan is either not old or not happy. | Mary is not strong. | neutral | (![X]:(~curious(X)<=>~kind(X)))&
(![X]:(~calm(X)<=>(~happy(X)|strong(X))))&
(![X]:((strong(X)<~>~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
((rich(fred))=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(strong(X)&wise(X))))&
(?[X]:(~strong(X)))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:(tall(X)))&
((~old(susan)<~>~happy(susan))) | ~strong(mary) | [] | null | 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa. If someone is both kind and not brave then alice is both old and not strong. If someone is patient then john is rich. If mary is funny then someone is not wise or not strong. Everyone who is curious or not old is brave or not wise. Everyone who is tall is not generous and vice versa. Everyone who is brave is patient and vice versa. Everyone who is either patient or not strong is both not calm and brave and vice versa. Everyone who is not strong is kind or not calm and vice versa. If susan is old or not tall then someone is quiet. If someone is both quiet and happy then fred is happy or generous and vice versa. Everyone who is not wise or not rich is both not happy and not brave. Everyone who is either not curious or not brave is curious or funny and vice versa. Everyone who is not curious or not calm is not calm and vice versa. Everyone who is either rich or curious is brave or not quiet and vice versa. Someone is humble or not brave. Someone is not kind. Alice is both calm and not tall. Susan is not funny or funny. Someone is both not tall and not wise. Susan is either not generous or rich. Someone is either not calm or not quiet. | Alice is rich. | neutral | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((kind(X)&~brave(X))))=>((old(alice)&~strong(alice))))&
((?[X]:(patient(X)))=>(rich(john)))&
((funny(mary))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((curious(X)|~old(X))=>(brave(X)|~wise(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:(~kind(X)))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X)))) | rich(alice) | [] | null | 0 |
Everyone who is tall or humble is not curious or humble and vice versa.
Everyone who is not happy or not humble is either not rich or brave and vice versa.
Everyone who is not strong or not brave is not old and vice versa.
If someone is either old or not generous then lucy is patient or calm.
Everyone who is not funny or quiet is either patient or generous.
Everyone who is brave is curious or not generous.
If mary is not funny or not tall then someone is both not generous and not humble.
Everyone who is happy is not rich or kind and vice versa.
Everyone who is old is humble.
Everyone who is quiet or not patient is strong and vice versa.
If someone is both not generous and funny then someone is not generous or not rich and vice versa.
Everyone who is not quiet is either not tall or rich and vice versa.
Everyone who is quiet is both not curious and not old.
If someone is not kind or not strong then alice is both kind and rich.
Everyone who is calm is both kind and funny and vice versa.
Everyone who is not generous or calm is tall or not brave and vice versa.
Someone is not funny or creative.
John is both creative and not tall.
Alice is either not brave or not funny.
Someone is both not kind and not generous.
Someone is both not calm and curious.
John is kind or not strong.
Susan is both funny and not curious.
Susan is either happy or curious. | John is happy. | entailment | (![X]:((tall(X)|humble(X))<=>(~curious(X)|humble(X))))&
(![X]:((~happy(X)|~humble(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~strong(X)|~brave(X))<=>~old(X)))&
((?[X]:((old(X)<~>~generous(X))))=>((patient(lucy)|calm(lucy))))&
(![X]:((~funny(X)|quiet(X))=>(patient(X)<~>generous(X))))&
(![X]:(brave(X)=>(curious(X)|~generous(X))))&
(((~funny(mary)|~tall(mary)))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(happy(X)<=>(~rich(X)|kind(X))))&
(![X]:(old(X)=>humble(X)))&
(![X]:((quiet(X)|~patient(X))<=>strong(X)))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:(~quiet(X)<=>(~tall(X)<~>rich(X))))&
(![X]:(quiet(X)=>(~curious(X)&~old(X))))&
((?[X]:((~kind(X)|~strong(X))))=>((kind(alice)&rich(alice))))&
(![X]:(calm(X)<=>(kind(X)&funny(X))))&
(![X]:((~generous(X)|calm(X))<=>(tall(X)|~brave(X))))&
(?[X]:((~funny(X)|creative(X))))&
((creative(john)&~tall(john)))&
((~brave(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~calm(X)&curious(X))))&
((kind(john)|~strong(john)))&
((funny(susan)&~curious(susan)))&
((happy(susan)<~>curious(susan))) | happy(john) | [
"p1",
"p5",
"p7",
"p11",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8025325667166400251377067
% SZS output start Proof for 8025325667166400251377067
2. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> (~rich(X0) <~> brave(X0))) [input p1]
6. ! [X0] : (brave(X0) => (~generous(X0) | curious(X0))) [input p5]
8. ! [X0] : (happy(X0) <=> (kind(X0) | ~rich(X0))) [input p7]
12. ! [X0] : (~quiet(X0) <=> (~tall(X0) <~> rich(X0))) [input p11]
13. ! [X0] : (quiet(X0) => (~old(X0) & ~curious(X0))) [input p12]
16. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~brave(X0) | tall(X0))) [input p15]
18. ~tall(john) & creative(john) [input p17]
25. ~happy(john) [input hypothesis]
27. ~tall(john) [pure predicate removal 18]
32. ! [X0] : ((~generous(X0) | curious(X0)) | ~brave(X0)) [ennf transformation 6]
33. ! [X0] : (~generous(X0) | curious(X0) | ~brave(X0)) [flattening 32]
36. ! [X0] : ((~old(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 13]
40. ! [X0] : (((~humble(X0) | ~happy(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (humble(X0) & happy(X0)))) [nnf transformation 2]
41. ! [X0] : ((~humble(X0) | ~happy(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (humble(X0) & happy(X0)))) [flattening 40]
48. ! [X0] : ((happy(X0) | (~kind(X0) & rich(X0))) & ((kind(X0) | ~rich(X0)) | ~happy(X0))) [nnf transformation 8]
49. ! [X0] : ((happy(X0) | (~kind(X0) & rich(X0))) & (kind(X0) | ~rich(X0) | ~happy(X0))) [flattening 48]
57. ! [X0] : ((~quiet(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | quiet(X0))) [nnf transformation 12]
60. ! [X0] : (((calm(X0) | ~generous(X0)) | (brave(X0) & ~tall(X0))) & ((~brave(X0) | tall(X0)) | (~calm(X0) & generous(X0)))) [nnf transformation 16]
61. ! [X0] : ((calm(X0) | ~generous(X0) | (brave(X0) & ~tall(X0))) & (~brave(X0) | tall(X0) | (~calm(X0) & generous(X0)))) [flattening 60]
72. ~rich(X0) | brave(X0) | happy(X0) [cnf transformation 41]
87. ~generous(X0) | curious(X0) | ~brave(X0) [cnf transformation 33]
93. rich(X0) | happy(X0) [cnf transformation 49]
105. ~rich(X0) | tall(X0) | quiet(X0) [cnf transformation 57]
108. ~quiet(X0) | ~curious(X0) [cnf transformation 36]
117. ~brave(X0) | tall(X0) | generous(X0) [cnf transformation 61]
121. ~tall(john) [cnf transformation 27]
133. ~happy(john) [cnf transformation 25]
266. brave(X0) | happy(X0) | happy(X0) [resolution 72,93]
267. brave(X0) | happy(X0) [duplicate literal removal 266]
326. quiet(X0) | tall(X0) | happy(X0) [resolution 105,93]
345. generous(X0) | tall(X0) | happy(X0) [resolution 117,267]
415. ~curious(X5) | happy(X5) | tall(X5) [resolution 326,108]
426. tall(X3) | happy(X3) | curious(X3) | ~brave(X3) [resolution 345,87]
433. tall(X3) | happy(X3) | ~brave(X3) [subsumption resolution 426,415]
434. happy(X3) | tall(X3) [subsumption resolution 433,267]
445. tall(john) [resolution 434,133]
447. $false [subsumption resolution 445,121]
% SZS output end Proof for 8025325667166400251377067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or happy is strong and vice versa. Everyone who is not strong or not tall is either calm or brave. Everyone who is either not quiet or curious is brave or not kind and vice versa. Everyone who is patient is not patient or not wise and vice versa. If someone is old then someone is humble and vice versa. Everyone who is rich or kind is both not kind and not rich. Everyone who is both old and not kind is humble. Everyone who is kind or not creative is either strong or not strong and vice versa. Everyone who is not old is happy and vice versa. Everyone who is both patient and kind is both brave and not strong and vice versa. If someone is humble then susan is both not generous and old. If lucy is not creative then someone is not generous and vice versa. If susan is not tall then lucy is not strong or not tall and vice versa. If mary is either not strong or tall then someone is both not generous and not rich and vice versa. Everyone who is both not funny and not calm is not creative and vice versa. If lucy is both not calm and calm then susan is not wise or rich. Someone is either not humble or not calm. Alice is either wise or not rich. Someone is both not calm and not brave. Fred is both not old and patient. Someone is strong or not funny. Fred is both generous and not creative. | Susan is old. | entailment | (![X]:((~happy(X)<~>happy(X))<=>strong(X)))&
(![X]:((~strong(X)|~tall(X))=>(calm(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(brave(X)|~kind(X))))&
(![X]:(patient(X)<=>(~patient(X)|~wise(X))))&
((?[X]:(old(X)))<=>(?[X]:(humble(X))))&
(![X]:((rich(X)|kind(X))=>(~kind(X)&~rich(X))))&
(![X]:((old(X)&~kind(X))=>humble(X)))&
(![X]:((kind(X)|~creative(X))<=>(strong(X)<~>~strong(X))))&
(![X]:(~old(X)<=>happy(X)))&
(![X]:((patient(X)&kind(X))<=>(brave(X)&~strong(X))))&
((?[X]:(humble(X)))=>((~generous(susan)&old(susan))))&
((~creative(lucy))<=>(?[X]:(~generous(X))))&
((~tall(susan))<=>((~strong(lucy)|~tall(lucy))))&
(((~strong(mary)<~>tall(mary)))<=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((~funny(X)&~calm(X))<=>~creative(X)))&
(((~calm(lucy)&calm(lucy)))=>((~wise(susan)|rich(susan))))&
(?[X]:((~humble(X)<~>~calm(X))))&
((wise(alice)<~>~rich(alice)))&
(?[X]:((~calm(X)&~brave(X))))&
((~old(fred)&patient(fred)))&
(?[X]:((strong(X)|~funny(X))))&
((generous(fred)&~creative(fred))) | old(susan) | [
"p0",
"p5",
"p7",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7612777532267631516249542
% SZS output start Proof for 7612777532267631516249542
1. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> strong(X0)) [input p0]
6. ! [X0] : ((kind(X0) | rich(X0)) => (~rich(X0) & ~kind(X0))) [input p5]
8. ! [X0] : ((~creative(X0) | kind(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p7]
11. ? [X0] : humble(X0) => (old(susan) & ~generous(susan)) [input p10]
15. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> ~creative(X0)) [input p14]
17. ? [X0] : (~humble(X0) <~> ~calm(X0)) [input p16]
23. ~old(susan) [input hypothesis]
26. ! [X0] : ((~rich(X0) & ~kind(X0)) | (~kind(X0) & ~rich(X0))) [ennf transformation 6]
29. (old(susan) & ~generous(susan)) | ! [X0] : ~humble(X0) [ennf transformation 11]
32. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~strong(X0)) & (strong(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 1]
43. ! [X0] : (((~creative(X0) | kind(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (creative(X0) & ~kind(X0)))) [nnf transformation 8]
44. ! [X0] : ((~creative(X0) | kind(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (creative(X0) & ~kind(X0)))) [flattening 43]
58. ! [X0] : (((~calm(X0) & ~funny(X0)) | creative(X0)) & (~creative(X0) | (calm(X0) | funny(X0)))) [nnf transformation 15]
59. ! [X0] : (((~calm(X0) & ~funny(X0)) | creative(X0)) & (~creative(X0) | calm(X0) | funny(X0))) [flattening 58]
60. ? [X0] : ((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) [nnf transformation 17]
61. ? [X0] : ((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) => ((calm(sK4) | humble(sK4)) & (~calm(sK4) | ~humble(sK4))) [choice axiom]
62. (calm(sK4) | humble(sK4)) & (~calm(sK4) | ~humble(sK4)) [skolemisation 60,61]
68. strong(X0) | happy(X0) | happy(X0) [cnf transformation 32]
69. strong(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 32]
88. ~kind(X0) | ~kind(X0) [cnf transformation 26]
96. ~creative(X0) | kind(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 44]
105. old(susan) | ~humble(X0) [cnf transformation 29]
119. ~calm(X0) | creative(X0) [cnf transformation 59]
122. calm(sK4) | humble(sK4) [cnf transformation 62]
132. ~old(susan) [cnf transformation 23]
133. ~creative(X0) | kind(X0) | ~strong(X0) [duplicate literal removal 96]
135. ~kind(X0) [duplicate literal removal 88]
139. strong(X0) | happy(X0) [duplicate literal removal 68]
140. strong(X0) | ~happy(X0) [duplicate literal removal 69]
141. strong(X0) [subsumption resolution 139,140]
144. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
145. ~humble(X1) <- (1) [avatar component clause 144]
160. ~creative(X0) | ~strong(X0) [subsumption resolution 133,135]
161. ~creative(X0) [subsumption resolution 160,141]
163. 5 <=> old(susan) [avatar definition]
166. 1 | 5 [avatar split clause 105,163,144]
200. ~calm(X0) [subsumption resolution 119,161]
202. humble(sK4) [subsumption resolution 122,200]
203. ~5 [avatar split clause 132,163]
206. $false <- (1) [resolution 202,145]
207. ~1 [avatar contradiction clause 206]
208. $false [avatar sat refutation 166,203,207]
% SZS output end Proof for 7612777532267631516249542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or generous is both not wise and not strong.
If someone is not generous or not old then mary is both not quiet and not curious and vice versa.
If alice is both brave and creative then lucy is not kind or not curious.
Everyone who is not wise is not old.
If fred is not rich or kind then someone is not tall or not creative.
Everyone who is not curious or generous is both not happy and old.
If someone is either calm or not strong then someone is not humble or not curious and vice versa.
If john is curious or funny then alice is both not quiet and not funny.
Everyone who is tall is humble.
Everyone who is not happy or kind is not brave and vice versa.
If john is not wise then someone is not rich or kind and vice versa.
Everyone who is not quiet is either not funny or funny.
Everyone who is either not quiet or rich is both tall and patient and vice versa.
If lucy is not generous then someone is both humble and not happy.
If someone is both old and curious then someone is both not quiet and humble and vice versa.
Everyone who is funny is either not happy or not tall.
Someone is not quiet or not brave.
Someone is either not brave or not humble.
Someone is kind or wise.
Paul is both not funny and tall.
Mary is not brave.
Fred is either brave or curious. | Alice is not strong. | neutral | (![X]:((~rich(X)|generous(X))=>(~wise(X)&~strong(X))))&
((?[X]:((~generous(X)|~old(X))))<=>((~quiet(mary)&~curious(mary))))&
(((brave(alice)&creative(alice)))=>((~kind(lucy)|~curious(lucy))))&
(![X]:(~wise(X)=>~old(X)))&
(((~rich(fred)|kind(fred)))=>(?[X]:((~tall(X)|~creative(X)))))&
(![X]:((~curious(X)|generous(X))=>(~happy(X)&old(X))))&
((?[X]:((calm(X)<~>~strong(X))))<=>(?[X]:((~humble(X)|~curious(X)))))&
(((curious(john)|funny(john)))=>((~quiet(alice)&~funny(alice))))&
(![X]:(tall(X)=>humble(X)))&
(![X]:((~happy(X)|kind(X))<=>~brave(X)))&
((~wise(john))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:(~quiet(X)=>(~funny(X)<~>funny(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(tall(X)&patient(X))))&
((~generous(lucy))=>(?[X]:((humble(X)&~happy(X)))))&
((?[X]:((old(X)&curious(X))))<=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:(funny(X)=>(~happy(X)<~>~tall(X))))&
(?[X]:((~quiet(X)|~brave(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((kind(X)|wise(X))))&
((~funny(paul)&tall(paul)))&
(~brave(mary))&
((brave(fred)<~>curious(fred))) | ~strong(alice) | [] | null | 0 |
If paul is rich then fred is not tall or patient.
Everyone who is strong or not patient is both strong and quiet.
Everyone who is not creative or not curious is patient and vice versa.
If someone is calm or tall then susan is both old and creative and vice versa.
Everyone who is not generous is either creative or not rich and vice versa.
Everyone who is not generous is not wise.
Everyone who is both not curious and not creative is not strong and vice versa.
If someone is not tall then mary is not humble or wise.
If alice is curious then someone is either not rich or generous and vice versa.
Everyone who is not tall is both not quiet and not curious.
If someone is either tall or happy then lucy is both humble and brave.
Everyone who is not patient or quiet is both not curious and generous and vice versa.
Everyone who is either rich or not tall is either generous or not happy and vice versa.
If paul is not old then someone is either wise or not generous.
If someone is brave then someone is either not calm or not happy.
If someone is both not kind and not curious then someone is not brave or not creative and vice versa.
Alice is creative or brave.
Susan is not old or humble.
Fred is either not kind or not calm. | Fred is happy. | contradiction | ((rich(paul))=>((~tall(fred)|patient(fred))))&
(![X]:((strong(X)|~patient(X))=>(strong(X)&quiet(X))))&
(![X]:((~creative(X)|~curious(X))<=>patient(X)))&
((?[X]:((calm(X)|tall(X))))<=>((old(susan)&creative(susan))))&
(![X]:(~generous(X)<=>(creative(X)<~>~rich(X))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~curious(X)&~creative(X))<=>~strong(X)))&
((?[X]:(~tall(X)))=>((~humble(mary)|wise(mary))))&
((curious(alice))<=>(?[X]:((~rich(X)<~>generous(X)))))&
(![X]:(~tall(X)=>(~quiet(X)&~curious(X))))&
((?[X]:((tall(X)<~>happy(X))))=>((humble(lucy)&brave(lucy))))&
(![X]:((~patient(X)|quiet(X))<=>(~curious(X)&generous(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(generous(X)<~>~happy(X))))&
((~old(paul))=>(?[X]:((wise(X)<~>~generous(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)<~>~happy(X)))))&
((?[X]:((~kind(X)&~curious(X))))<=>(?[X]:((~brave(X)|~creative(X)))))&
((creative(alice)|brave(alice)))&
((~old(susan)|humble(susan)))&
((~kind(fred)<~>~calm(fred))) | happy(fred) | [
"p1",
"p2",
"p4",
"p6",
"p8",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2621373633932542758288516
% SZS output start Proof for 2621373633932542758288516
2. ! [X0] : ((~patient(X0) | strong(X0)) => (quiet(X0) & strong(X0))) [input p1]
3. ! [X0] : ((~curious(X0) | ~creative(X0)) <=> patient(X0)) [input p2]
5. ! [X0] : (~generous(X0) <=> (creative(X0) <~> ~rich(X0))) [input p4]
7. ! [X0] : ((~creative(X0) & ~curious(X0)) <=> ~strong(X0)) [input p6]
9. curious(alice) <=> ? [X0] : (~rich(X0) <~> generous(X0)) [input p8]
10. ! [X0] : (~tall(X0) => (~curious(X0) & ~quiet(X0))) [input p9]
12. ! [X0] : ((quiet(X0) | ~patient(X0)) <=> (generous(X0) & ~curious(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> ~tall(X0)) <=> (generous(X0) <~> ~happy(X0))) [input p12]
20. happy(fred) [input hypothesis]
25. ! [X0] : ((quiet(X0) & strong(X0)) | (patient(X0) & ~strong(X0))) [ennf transformation 2]
29. ! [X0] : ((~curious(X0) & ~quiet(X0)) | tall(X0)) [ennf transformation 10]
33. ! [X0] : (((~curious(X0) | ~creative(X0)) | ~patient(X0)) & (patient(X0) | (curious(X0) & creative(X0)))) [nnf transformation 3]
34. ! [X0] : ((~curious(X0) | ~creative(X0) | ~patient(X0)) & (patient(X0) | (curious(X0) & creative(X0)))) [flattening 33]
40. ! [X0] : ((~generous(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | generous(X0))) [nnf transformation 5]
41. ! [X0] : (((~creative(X0) & ~curious(X0)) | strong(X0)) & (~strong(X0) | (creative(X0) | curious(X0)))) [nnf transformation 7]
42. ! [X0] : (((~creative(X0) & ~curious(X0)) | strong(X0)) & (~strong(X0) | creative(X0) | curious(X0))) [flattening 41]
43. (curious(alice) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X0] : ((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ~curious(alice)) [nnf transformation 9]
44. (curious(alice) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) | ~curious(alice)) [rectify 43]
45. ? [X1] : ((~generous(X1) | rich(X1)) & (generous(X1) | ~rich(X1))) => ((~generous(sK1) | rich(sK1)) & (generous(sK1) | ~rich(sK1))) [choice axiom]
46. (curious(alice) | ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0)))) & (((~generous(sK1) | rich(sK1)) & (generous(sK1) | ~rich(sK1))) | ~curious(alice)) [skolemisation 44,45]
48. ! [X0] : (((quiet(X0) | ~patient(X0)) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | (~quiet(X0) & patient(X0)))) [nnf transformation 12]
49. ! [X0] : ((quiet(X0) | ~patient(X0) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | (~quiet(X0) & patient(X0)))) [flattening 48]
50. ! [X0] : ((((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0)))) & (((happy(X0) | ~generous(X0)) & (~happy(X0) | generous(X0))) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0))))) [nnf transformation 13]
67. ~strong(X0) | quiet(X0) [cnf transformation 25]
70. curious(X0) | patient(X0) [cnf transformation 34]
71. ~curious(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 34]
77. ~rich(X0) | creative(X0) | generous(X0) [cnf transformation 40]
80. ~generous(X0) | creative(X0) | rich(X0) [cnf transformation 40]
83. ~curious(X0) | strong(X0) [cnf transformation 42]
84. ~creative(X0) | strong(X0) [cnf transformation 42]
88. curious(alice) | generous(X0) | rich(X0) [cnf transformation 46]
89. curious(alice) | ~rich(X0) | ~generous(X0) [cnf transformation 46]
90. ~quiet(X0) | tall(X0) [cnf transformation 29]
96. ~curious(X0) | patient(X0) [cnf transformation 49]
97. ~curious(X0) | ~quiet(X0) [cnf transformation 49]
99. ~quiet(X0) | generous(X0) [cnf transformation 49]
100. quiet(X0) | ~patient(X0) | ~generous(X0) | curious(X0) [cnf transformation 49]
101. ~happy(X0) | generous(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 50]
105. ~happy(X0) | rich(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 50]
122. happy(fred) [cnf transformation 20]
128. 2 <=> tall(fred) [avatar definition]
130. ~tall(fred) <- (~2) [avatar component clause 128]
176. 13 <=> ! [X0] : (~rich(X0) | ~generous(X0)) [avatar definition]
177. ~generous(X0) | ~rich(X0) <- (13) [avatar component clause 176]
179. 14 <=> curious(alice) [avatar definition]
181. curious(alice) <- (14) [avatar component clause 179]
182. 13 | 14 [avatar split clause 89,179,176]
184. 15 <=> ! [X0] : (generous(X0) | rich(X0)) [avatar definition]
185. generous(X0) | rich(X0) <- (15) [avatar component clause 184]
186. 15 | 14 [avatar split clause 88,179,184]
215. ~generous(X0) | quiet(X0) | curious(X0) [subsumption resolution 100,70]
216. patient(X0) [subsumption resolution 96,70]
350. creative(X0) | rich(X0) | rich(X0) <- (15) [resolution 80,185]
352. creative(X0) | rich(X0) <- (15) [duplicate literal removal 350]
380. ~quiet(alice) <- (14) [resolution 181,97]
382. strong(alice) <- (14) [resolution 181,83]
383. curious(X0) | quiet(X0) | rich(X0) <- (15) [resolution 215,185]
396. generous(fred) | ~tall(fred) | ~rich(fred) [resolution 101,122]
423. quiet(alice) <- (14) [resolution 382,67]
424. $false <- (14) [subsumption resolution 423,380]
425. ~14 [avatar contradiction clause 424]
435. rich(fred) | ~tall(fred) | ~generous(fred) [resolution 105,122]
475. quiet(X0) | rich(X0) | ~creative(X0) | ~patient(X0) <- (15) [resolution 383,71]
482. quiet(X0) | rich(X0) | ~creative(X0) <- (15) [subsumption resolution 475,216]
483. quiet(X0) | rich(X0) <- (15) [subsumption resolution 482,352]
560. tall(X1) | rich(X1) <- (15) [resolution 483,90]
597. rich(fred) <- (~2, 15) [resolution 560,130]
601. creative(fred) | generous(fred) <- (~2, 15) [resolution 597,77]
603. 53 <=> generous(fred) [avatar definition]
605. generous(fred) <- (53) [avatar component clause 603]
607. 54 <=> creative(fred) [avatar definition]
609. creative(fred) <- (54) [avatar component clause 607]
610. 53 | 54 | 2 | ~15 [avatar split clause 601,184,128,607,603]
619. strong(fred) <- (54) [resolution 609,84]
623. quiet(fred) <- (54) [resolution 619,67]
626. generous(fred) <- (54) [resolution 623,99]
628. 53 | ~54 [avatar split clause 626,607,603]
631. rich(fred) | ~tall(fred) <- (15) [subsumption resolution 435,185]
632. rich(fred) <- (15) [subsumption resolution 631,560]
633. generous(fred) | ~tall(fred) <- (15) [subsumption resolution 396,632]
634. ~2 | 53 | ~15 [avatar split clause 633,184,603,128]
637. ~rich(fred) <- (13, 53) [resolution 605,177]
643. $false <- (13, 15, 53) [subsumption resolution 637,632]
644. ~13 | ~15 | ~53 [avatar contradiction clause 643]
654. $false [avatar sat refutation 182,186,425,610,628,634,644]
% SZS output end Proof for 2621373633932542758288516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not creative then someone is either brave or not calm and vice versa.
Everyone who is not strong is either not creative or patient and vice versa.
Everyone who is creative or curious is both not old and not curious.
If mary is not rich or not generous then lucy is not generous.
If alice is both brave and not generous then someone is both wise and rich.
Everyone who is both tall and wise is either not rich or rich and vice versa.
Everyone who is either not old or humble is both brave and wise.
If someone is either not funny or not strong then lucy is humble and vice versa.
Everyone who is either not old or not creative is old and vice versa.
If someone is rich or humble then someone is both not creative and generous.
Everyone who is either not kind or old is both not strong and humble.
Everyone who is both not funny and not happy is not creative or creative and vice versa.
If someone is not kind or not creative then someone is strong and vice versa.
If someone is either kind or not rich then john is either not kind or patient.
Everyone who is either not wise or rich is tall and vice versa.
Everyone who is either brave or happy is either wise or not brave.
Alice is either patient or not strong.
Paul is calm or funny.
Someone is either quiet or strong.
Someone is not curious or not calm.
Alice is either calm or happy.
Fred is not funny.
Someone is either patient or calm.
Alice is not brave. | John is curious. | contradiction | ((?[X]:(~creative(X)))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:(~strong(X)<=>(~creative(X)<~>patient(X))))&
(![X]:((creative(X)|curious(X))=>(~old(X)&~curious(X))))&
(((~rich(mary)|~generous(mary)))=>(~generous(lucy)))&
(((brave(alice)&~generous(alice)))=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((tall(X)&wise(X))<=>(~rich(X)<~>rich(X))))&
(![X]:((~old(X)<~>humble(X))=>(brave(X)&wise(X))))&
((?[X]:((~funny(X)<~>~strong(X))))<=>(humble(lucy)))&
(![X]:((~old(X)<~>~creative(X))<=>old(X)))&
((?[X]:((rich(X)|humble(X))))=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((~kind(X)<~>old(X))=>(~strong(X)&humble(X))))&
(![X]:((~funny(X)&~happy(X))<=>(~creative(X)|creative(X))))&
((?[X]:((~kind(X)|~creative(X))))<=>(?[X]:(strong(X))))&
((?[X]:((kind(X)<~>~rich(X))))=>((~kind(john)<~>patient(john))))&
(![X]:((~wise(X)<~>rich(X))<=>tall(X)))&
(![X]:((brave(X)<~>happy(X))=>(wise(X)<~>~brave(X))))&
((patient(alice)<~>~strong(alice)))&
((calm(paul)|funny(paul)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~curious(X)|~calm(X))))&
((calm(alice)<~>happy(alice)))&
(~funny(fred))&
(?[X]:((patient(X)<~>calm(X))))&
(~brave(alice)) | curious(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8446397952816339772236
% SZS output start Proof for 8446397952816339772236
3. ! [X0] : ((curious(X0) | creative(X0)) => (~curious(X0) & ~old(X0))) [input p2]
25. curious(john) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~old(X0)) | (~curious(X0) & ~creative(X0))) [ennf transformation 3]
89. ~curious(X0) | ~curious(X0) [cnf transformation 29]
152. curious(john) [cnf transformation 25]
161. ~curious(X0) [duplicate literal removal 89]
312. $false [subsumption resolution 152,161]
% SZS output end Proof for 8446397952816339772236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not rich then mary is rich or patient. If someone is either not quiet or not wise then someone is tall or not brave and vice versa. If fred is wise or not tall then someone is either creative or patient and vice versa. Everyone who is kind or not tall is not brave. Everyone who is either tall or quiet is either not rich or brave. If someone is strong then someone is either tall or not old and vice versa. If someone is either not calm or tall then susan is kind. Everyone who is either not funny or quiet is both not kind and tall and vice versa. If someone is both not creative and tall then someone is not generous and vice versa. Everyone who is not kind or tall is wise and vice versa. Everyone who is both not patient and not quiet is not funny. If john is both rich and kind then someone is not rich or brave. Everyone who is both not patient and humble is either wise or brave. Everyone who is either not strong or funny is wise. Everyone who is wise or not happy is both generous and creative. If someone is calm or not old then someone is either curious or generous and vice versa. Mary is both not funny and not patient. Fred is calm or rich. Mary is both curious and not calm. Someone is generous. Lucy is generous or not old. Fred is not rich or not calm. John is not patient or rich. | John is rich. | neutral | ((?[X]:((~creative(X)<~>~rich(X))))=>((rich(mary)|patient(mary))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>(?[X]:((tall(X)|~brave(X)))))&
(((wise(fred)|~tall(fred)))<=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:((kind(X)|~tall(X))=>~brave(X)))&
(![X]:((tall(X)<~>quiet(X))=>(~rich(X)<~>brave(X))))&
((?[X]:(strong(X)))<=>(?[X]:((tall(X)<~>~old(X)))))&
((?[X]:((~calm(X)<~>tall(X))))=>(kind(susan)))&
(![X]:((~funny(X)<~>quiet(X))<=>(~kind(X)&tall(X))))&
((?[X]:((~creative(X)&tall(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~kind(X)|tall(X))<=>wise(X)))&
(![X]:((~patient(X)&~quiet(X))=>~funny(X)))&
(((rich(john)&kind(john)))=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~patient(X)&humble(X))=>(wise(X)<~>brave(X))))&
(![X]:((~strong(X)<~>funny(X))=>wise(X)))&
(![X]:((wise(X)|~happy(X))=>(generous(X)&creative(X))))&
((?[X]:((calm(X)|~old(X))))<=>(?[X]:((curious(X)<~>generous(X)))))&
((~funny(mary)&~patient(mary)))&
((calm(fred)|rich(fred)))&
((curious(mary)&~calm(mary)))&
(?[X]:(generous(X)))&
((generous(lucy)|~old(lucy)))&
((~rich(fred)|~calm(fred)))&
((~patient(john)|rich(john))) | rich(john) | [] | null | 0 |
Everyone who is rich is kind or not generous.
If someone is either generous or wise then someone is both not humble and not happy.
Everyone who is either not strong or quiet is old.
Everyone who is both not curious and patient is both brave and not kind.
Everyone who is either not tall or rich is calm or strong.
If fred is both funny and not curious then someone is not rich and vice versa.
If alice is both tall and not rich then mary is calm.
If someone is generous then susan is either strong or wise.
Everyone who is not generous or not funny is rich or creative and vice versa.
If paul is not wise or creative then someone is quiet.
Everyone who is not happy or patient is both not old and not rich.
If susan is both not funny and not creative then someone is not wise or not strong and vice versa.
If lucy is not calm then someone is creative or wise and vice versa.
Everyone who is rich is either not creative or not curious.
If someone is both not rich and rich then someone is either creative or calm.
If fred is either not tall or wise then john is either not rich or not wise.
Someone is both not tall and calm.
Someone is both quiet and not rich.
Someone is both patient and generous.
Susan is strong or funny.
Paul is either funny or brave.
Alice is both not calm and not patient.
Someone is either patient or rich.
John is either not generous or kind. | Susan is not strong. | contradiction | (![X]:(rich(X)=>(kind(X)|~generous(X))))&
((?[X]:((generous(X)<~>wise(X))))=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>old(X)))&
(![X]:((~curious(X)&patient(X))=>(brave(X)&~kind(X))))&
(![X]:((~tall(X)<~>rich(X))=>(calm(X)|strong(X))))&
(((funny(fred)&~curious(fred)))<=>(?[X]:(~rich(X))))&
(((tall(alice)&~rich(alice)))=>(calm(mary)))&
((?[X]:(generous(X)))=>((strong(susan)<~>wise(susan))))&
(![X]:((~generous(X)|~funny(X))<=>(rich(X)|creative(X))))&
(((~wise(paul)|creative(paul)))=>(?[X]:(quiet(X))))&
(![X]:((~happy(X)|patient(X))=>(~old(X)&~rich(X))))&
(((~funny(susan)&~creative(susan)))<=>(?[X]:((~wise(X)|~strong(X)))))&
((~calm(lucy))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:(rich(X)=>(~creative(X)<~>~curious(X))))&
((?[X]:((~rich(X)&rich(X))))=>(?[X]:((creative(X)<~>calm(X)))))&
(((~tall(fred)<~>wise(fred)))=>((~rich(john)<~>~wise(john))))&
(?[X]:((~tall(X)&calm(X))))&
(?[X]:((quiet(X)&~rich(X))))&
(?[X]:((patient(X)&generous(X))))&
((strong(susan)|funny(susan)))&
((funny(paul)<~>brave(paul)))&
((~calm(alice)&~patient(alice)))&
(?[X]:((patient(X)<~>rich(X))))&
((~generous(john)<~>kind(john))) | ~strong(susan) | [
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7175639947267633468384835
% SZS output start Proof for 7175639947267633468384835
12. (~creative(susan) & ~funny(susan)) <=> ? [X0] : (~strong(X0) | ~wise(X0)) [input p11]
20. funny(susan) | strong(susan) [input p19]
25. ~strong(susan) [input hypothesis]
61. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & (? [X0] : (~strong(X0) | ~wise(X0)) | (creative(susan) | funny(susan))) [nnf transformation 12]
62. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & (? [X0] : (~strong(X0) | ~wise(X0)) | creative(susan) | funny(susan)) [flattening 61]
63. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & (? [X1] : (~strong(X1) | ~wise(X1)) | creative(susan) | funny(susan)) [rectify 62]
64. ? [X1] : (~strong(X1) | ~wise(X1)) => (~strong(sK3) | ~wise(sK3)) [choice axiom]
65. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & ((~strong(sK3) | ~wise(sK3)) | creative(susan) | funny(susan)) [skolemisation 63,64]
114. ~funny(susan) | strong(X0) [cnf transformation 65]
134. funny(susan) | strong(susan) [cnf transformation 20]
143. ~strong(susan) [cnf transformation 25]
191. 12 <=> strong(susan) [avatar definition]
193. ~strong(susan) <- (~12) [avatar component clause 191]
215. 17 <=> ! [X0] : strong(X0) [avatar definition]
216. strong(X0) <- (17) [avatar component clause 215]
227. 20 <=> funny(susan) [avatar definition]
230. 17 | ~20 [avatar split clause 114,227,215]
282. 12 | 20 [avatar split clause 134,227,191]
312. ~12 [avatar split clause 143,191]
315. $false <- (~12, 17) [subsumption resolution 193,216]
316. 12 | ~17 [avatar contradiction clause 315]
317. $false [avatar sat refutation 230,282,312,316]
% SZS output end Proof for 7175639947267633468384835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not calm is not rich. Everyone who is either calm or not quiet is not creative or funny and vice versa. If alice is either not quiet or not wise then john is both wise and curious. If someone is not old or not wise then someone is not kind and vice versa. Everyone who is either not humble or wise is not brave and vice versa. Everyone who is both not old and not happy is both not strong and curious and vice versa. Everyone who is not generous is either not curious or humble. Everyone who is happy or calm is both humble and not happy and vice versa. If someone is either quiet or not rich then susan is either wise or brave. If paul is tall then john is both not tall and not rich and vice versa. Everyone who is either not calm or strong is wise. If someone is both tall and not funny then someone is not brave or rich. Everyone who is patient or strong is rich and vice versa. Everyone who is creative or not strong is both not calm and strong and vice versa. If fred is both not rich and not humble then susan is both not funny and quiet and vice versa. Everyone who is strong is tall or not funny. Susan is patient or creative. Alice is both not kind and strong. Someone is both calm and tall. Fred is either not kind or not creative. John is either brave or generous. Alice is curious or tall. Someone is not happy. | Susan is not curious. | neutral | (![X]:((~funny(X)&~calm(X))=>~rich(X)))&
(![X]:((calm(X)<~>~quiet(X))<=>(~creative(X)|funny(X))))&
(((~quiet(alice)<~>~wise(alice)))=>((wise(john)&curious(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~brave(X)))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&curious(X))))&
(![X]:(~generous(X)=>(~curious(X)<~>humble(X))))&
(![X]:((happy(X)|calm(X))<=>(humble(X)&~happy(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>((wise(susan)<~>brave(susan))))&
((tall(paul))<=>((~tall(john)&~rich(john))))&
(![X]:((~calm(X)<~>strong(X))=>wise(X)))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(![X]:((patient(X)|strong(X))<=>rich(X)))&
(![X]:((creative(X)|~strong(X))<=>(~calm(X)&strong(X))))&
(((~rich(fred)&~humble(fred)))<=>((~funny(susan)&quiet(susan))))&
(![X]:(strong(X)=>(tall(X)|~funny(X))))&
((patient(susan)|creative(susan)))&
((~kind(alice)&strong(alice)))&
(?[X]:((calm(X)&tall(X))))&
((~kind(fred)<~>~creative(fred)))&
((brave(john)<~>generous(john)))&
((curious(alice)|tall(alice)))&
(?[X]:(~happy(X))) | ~curious(susan) | [] | null | 0 |
Everyone who is both not rich and rich is not rich or tall and vice versa. Everyone who is either curious or humble is brave. If john is not funny or rich then john is both wise and not funny. If someone is creative or old then someone is not humble or not happy. If someone is either not brave or brave then someone is either not curious or not patient. Everyone who is either strong or not humble is funny. If mary is patient or generous then someone is either calm or not quiet. If mary is quiet or calm then someone is not tall or humble and vice versa. Everyone who is old is not happy. Everyone who is either not old or not wise is both old and not happy. Everyone who is not curious is kind or rich. If someone is brave then susan is either old or not brave and vice versa. Everyone who is both not rich and not happy is either not creative or brave. Everyone who is both strong and not strong is not patient. Everyone who is both not kind and funny is brave and vice versa. Susan is either tall or rich. Someone is either not curious or not humble. Someone is both wise and not curious. Fred is rich. Someone is both not kind and not generous. John is both calm and not strong. Someone is either not curious or tall. Lucy is either not kind or not quiet. | John is tall. | contradiction | (![X]:((~rich(X)&rich(X))<=>(~rich(X)|tall(X))))&
(![X]:((curious(X)<~>humble(X))=>brave(X)))&
(((~funny(john)|rich(john)))=>((wise(john)&~funny(john))))&
((?[X]:((creative(X)|old(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
((?[X]:((~brave(X)<~>brave(X))))=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:((strong(X)<~>~humble(X))=>funny(X)))&
(((patient(mary)|generous(mary)))=>(?[X]:((calm(X)<~>~quiet(X)))))&
(((quiet(mary)|calm(mary)))<=>(?[X]:((~tall(X)|humble(X)))))&
(![X]:(old(X)=>~happy(X)))&
(![X]:((~old(X)<~>~wise(X))=>(old(X)&~happy(X))))&
(![X]:(~curious(X)=>(kind(X)|rich(X))))&
((?[X]:(brave(X)))<=>((old(susan)<~>~brave(susan))))&
(![X]:((~rich(X)&~happy(X))=>(~creative(X)<~>brave(X))))&
(![X]:((strong(X)&~strong(X))=>~patient(X)))&
(![X]:((~kind(X)&funny(X))<=>brave(X)))&
((tall(susan)<~>rich(susan)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:((wise(X)&~curious(X))))&
(rich(fred))&
(?[X]:((~kind(X)&~generous(X))))&
((calm(john)&~strong(john)))&
(?[X]:((~curious(X)<~>tall(X))))&
((~kind(lucy)<~>~quiet(lucy))) | tall(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8496440642684916630188844
% SZS output start Proof for 8496440642684916630188844
1. ! [X0] : ((rich(X0) & ~rich(X0)) <=> (tall(X0) | ~rich(X0))) [input p0]
24. tall(john) [input hypothesis]
43. ! [X0] : (((rich(X0) & ~rich(X0)) | (~tall(X0) & rich(X0))) & ((tall(X0) | ~rich(X0)) | (~rich(X0) | rich(X0)))) [nnf transformation 1]
44. ! [X0] : (((rich(X0) & ~rich(X0)) | (~tall(X0) & rich(X0))) & (tall(X0) | ~rich(X0) | ~rich(X0) | rich(X0))) [flattening 43]
84. ~rich(X0) | ~tall(X0) [cnf transformation 44]
85. rich(X0) | rich(X0) [cnf transformation 44]
137. tall(john) [cnf transformation 24]
144. rich(X0) [duplicate literal removal 85]
145. ~tall(X0) [subsumption resolution 84,144]
248. $false [subsumption resolution 137,145]
% SZS output end Proof for 8496440642684916630188844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm is calm.
Everyone who is both strong and generous is both not strong and not happy.
Everyone who is not curious or not generous is either old or patient.
Everyone who is both not brave and not strong is both not strong and not tall and vice versa.
Everyone who is brave or generous is old and vice versa.
Everyone who is wise is creative or old and vice versa.
Everyone who is both not wise and not happy is creative or rich and vice versa.
Everyone who is both quiet and not quiet is brave.
If someone is kind then mary is both not patient and generous.
Everyone who is brave is funny.
If someone is not patient then someone is rich and vice versa.
If someone is either not old or not funny then someone is both curious and old.
If someone is strong or not wise then mary is either not patient or happy.
If john is both not creative and creative then someone is kind or not kind.
If alice is both old and not quiet then lucy is curious.
Someone is either kind or not generous.
Someone is tall or brave.
Someone is both calm and wise.
Mary is funny.
Someone is both tall and funny.
Lucy is either patient or not quiet.
Susan is not funny.
John is kind or not wise. | Mary is not rich. | entailment | (![X]:((rich(X)<~>calm(X))=>calm(X)))&
(![X]:((strong(X)&generous(X))=>(~strong(X)&~happy(X))))&
(![X]:((~curious(X)|~generous(X))=>(old(X)<~>patient(X))))&
(![X]:((~brave(X)&~strong(X))<=>(~strong(X)&~tall(X))))&
(![X]:((brave(X)|generous(X))<=>old(X)))&
(![X]:(wise(X)<=>(creative(X)|old(X))))&
(![X]:((~wise(X)&~happy(X))<=>(creative(X)|rich(X))))&
(![X]:((quiet(X)&~quiet(X))=>brave(X)))&
((?[X]:(kind(X)))=>((~patient(mary)&generous(mary))))&
(![X]:(brave(X)=>funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(rich(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>(?[X]:((curious(X)&old(X)))))&
((?[X]:((strong(X)|~wise(X))))=>((~patient(mary)<~>happy(mary))))&
(((~creative(john)&creative(john)))=>(?[X]:((kind(X)|~kind(X)))))&
(((old(alice)&~quiet(alice)))=>(curious(lucy)))&
(?[X]:((kind(X)<~>~generous(X))))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((calm(X)&wise(X))))&
(funny(mary))&
(?[X]:((tall(X)&funny(X))))&
((patient(lucy)<~>~quiet(lucy)))&
(~funny(susan))&
((kind(john)|~wise(john))) | ~rich(mary) | [
"p2",
"p4",
"p5",
"p6",
"p8",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 449763153663712124260352
% SZS output start Proof for 449763153663712124260352
3. ! [X0] : ((~generous(X0) | ~curious(X0)) => (old(X0) <~> patient(X0))) [input p2]
5. ! [X0] : ((generous(X0) | brave(X0)) <=> old(X0)) [input p4]
6. ! [X0] : (wise(X0) <=> (old(X0) | creative(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & ~wise(X0)) <=> (rich(X0) | creative(X0))) [input p6]
9. ? [X0] : kind(X0) => (generous(mary) & ~patient(mary)) [input p8]
13. ? [X0] : (~wise(X0) | strong(X0)) => (~patient(mary) <~> happy(mary)) [input p12]
23. ~wise(john) | kind(john) [input p22]
24. rich(mary) [input hypothesis]
27. ! [X0] : (~generous(X0) => (old(X0) <~> patient(X0))) [pure predicate removal 3]
33. ! [X0] : ((old(X0) <~> patient(X0)) | generous(X0)) [ennf transformation 27]
36. (generous(mary) & ~patient(mary)) | ! [X0] : ~kind(X0) [ennf transformation 9]
39. (~patient(mary) <~> happy(mary)) | ! [X0] : (wise(X0) & ~strong(X0)) [ennf transformation 13]
43. ! [X0] : (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | generous(X0)) [nnf transformation 33]
46. ! [X0] : (((generous(X0) | brave(X0)) | ~old(X0)) & (old(X0) | (~generous(X0) & ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : ((generous(X0) | brave(X0) | ~old(X0)) & (old(X0) | (~generous(X0) & ~brave(X0)))) [flattening 46]
48. ! [X0] : ((wise(X0) | (~old(X0) & ~creative(X0))) & ((old(X0) | creative(X0)) | ~wise(X0))) [nnf transformation 6]
49. ! [X0] : ((wise(X0) | (~old(X0) & ~creative(X0))) & (old(X0) | creative(X0) | ~wise(X0))) [flattening 48]
50. ! [X0] : (((~happy(X0) & ~wise(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (happy(X0) | wise(X0)))) [nnf transformation 7]
51. ! [X0] : (((~happy(X0) & ~wise(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | happy(X0) | wise(X0))) [flattening 50]
61. ((~happy(mary) | patient(mary)) & (happy(mary) | ~patient(mary))) | ! [X0] : (wise(X0) & ~strong(X0)) [nnf transformation 39]
78. patient(X0) | old(X0) | generous(X0) [cnf transformation 43]
85. ~generous(X0) | old(X0) [cnf transformation 47]
89. ~old(X0) | wise(X0) [cnf transformation 49]
92. ~wise(X0) | ~rich(X0) [cnf transformation 51]
94. ~happy(X0) | ~rich(X0) [cnf transformation 51]
96. ~patient(mary) | ~kind(X0) [cnf transformation 36]
104. happy(mary) | ~patient(mary) | wise(X0) [cnf transformation 61]
119. ~wise(john) | kind(john) [cnf transformation 23]
120. rich(mary) [cnf transformation 24]
126. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
127. ~kind(X0) <- (1) [avatar component clause 126]
129. 2 <=> generous(mary) [avatar definition]
130. ~generous(mary) <- (~2) [avatar component clause 129]
131. generous(mary) <- (2) [avatar component clause 129]
134. 3 <=> patient(mary) [avatar definition]
136. ~patient(mary) <- (~3) [avatar component clause 134]
137. 1 | ~3 [avatar split clause 96,134,126]
167. 11 <=> ! [X0] : wise(X0) [avatar definition]
168. wise(X0) <- (11) [avatar component clause 167]
170. 12 <=> happy(mary) [avatar definition]
171. happy(mary) <- (12) [avatar component clause 170]
178. 11 | ~3 | 12 [avatar split clause 104,170,134,167]
210. 20 <=> kind(john) [avatar definition]
212. kind(john) <- (20) [avatar component clause 210]
214. 21 <=> wise(john) [avatar definition]
216. ~wise(john) <- (~21) [avatar component clause 214]
217. 20 | ~21 [avatar split clause 119,214,210]
222. old(mary) <- (2) [resolution 85,131]
224. wise(mary) <- (2) [resolution 89,222]
227. ~rich(mary) <- (2) [resolution 224,92]
228. $false <- (2) [subsumption resolution 227,120]
229. ~2 [avatar contradiction clause 228]
232. old(mary) | generous(mary) <- (~3) [resolution 78,136]
235. old(mary) <- (~2, ~3) [subsumption resolution 232,130]
240. wise(mary) <- (~2, ~3) [resolution 235,89]
338. ~rich(mary) <- (~2, ~3) [resolution 240,92]
339. $false <- (~2, ~3) [subsumption resolution 338,120]
340. 2 | 3 [avatar contradiction clause 339]
350. ~rich(mary) <- (12) [resolution 171,94]
351. $false <- (12) [subsumption resolution 350,120]
352. ~12 [avatar contradiction clause 351]
353. $false <- (11, ~21) [resolution 168,216]
356. ~11 | 21 [avatar contradiction clause 353]
359. $false <- (1, 20) [subsumption resolution 212,127]
360. ~1 | ~20 [avatar contradiction clause 359]
361. $false [avatar sat refutation 137,178,217,229,340,352,356,360]
% SZS output end Proof for 449763153663712124260352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not humble then lucy is either strong or rich and vice versa.
If someone is funny then someone is patient or wise.
Everyone who is either not humble or not quiet is calm or not strong and vice versa.
Everyone who is humble or not calm is not happy or not wise.
Everyone who is not quiet or wise is curious or not tall.
If someone is not quiet or calm then someone is happy or funny.
Everyone who is not strong is not rich and vice versa.
Everyone who is not humble is brave.
Everyone who is wise or not kind is not patient and vice versa.
Everyone who is creative is patient.
If someone is not generous or rich then someone is not patient or not funny.
Everyone who is either quiet or not happy is generous or not generous and vice versa.
Everyone who is curious or not patient is both not happy and happy and vice versa.
Everyone who is quiet is not wise or not curious.
If someone is not creative or quiet then someone is both happy and calm and vice versa.
Everyone who is not calm or not quiet is happy.
Someone is not wise.
Someone is both happy and not funny.
Alice is patient.
Someone is not brave.
Paul is both old and not wise.
Mary is generous or not wise. | Paul is not rich. | neutral | ((~humble(susan))<=>((strong(lucy)<~>rich(lucy))))&
((?[X]:(funny(X)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(calm(X)|~strong(X))))&
(![X]:((humble(X)|~calm(X))=>(~happy(X)|~wise(X))))&
(![X]:((~quiet(X)|wise(X))=>(curious(X)|~tall(X))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((happy(X)|funny(X)))))&
(![X]:(~strong(X)<=>~rich(X)))&
(![X]:(~humble(X)=>brave(X)))&
(![X]:((wise(X)|~kind(X))<=>~patient(X)))&
(![X]:(creative(X)=>patient(X)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))<=>(generous(X)|~generous(X))))&
(![X]:((curious(X)|~patient(X))<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~wise(X)|~curious(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((~calm(X)|~quiet(X))=>happy(X)))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)&~funny(X))))&
(patient(alice))&
(?[X]:(~brave(X)))&
((old(paul)&~wise(paul)))&
((generous(mary)|~wise(mary))) | ~rich(paul) | [] | null | 0 |
Everyone who is either happy or patient is either not strong or not quiet. If someone is not creative then someone is either tall or funny. If someone is both funny and strong then alice is both quiet and not curious and vice versa. If someone is not old then someone is curious and vice versa. Everyone who is kind is not kind. If someone is either not curious or quiet then someone is tall or brave and vice versa. Everyone who is both not quiet and kind is humble or not curious and vice versa. If mary is either creative or tall then alice is not creative or rich and vice versa. If someone is not quiet or quiet then lucy is either not humble or creative. If someone is either not rich or tall then fred is curious or not happy. If someone is either not old or humble then someone is either kind or calm. Everyone who is humble is wise. If someone is not brave or not humble then alice is both tall and curious. If someone is not happy then someone is not tall or brave and vice versa. If someone is not humble then someone is either rich or quiet. Mary is either strong or not wise. Alice is either not happy or not patient. Someone is tall. Someone is both not funny and creative. Susan is either not quiet or strong. | Susan is kind. | contradiction | (![X]:((happy(X)<~>patient(X))=>(~strong(X)<~>~quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:((tall(X)<~>funny(X)))))&
((?[X]:((funny(X)&strong(X))))<=>((quiet(alice)&~curious(alice))))&
((?[X]:(~old(X)))<=>(?[X]:(curious(X))))&
(![X]:(kind(X)=>~kind(X)))&
((?[X]:((~curious(X)<~>quiet(X))))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(humble(X)|~curious(X))))&
(((creative(mary)<~>tall(mary)))<=>((~creative(alice)|rich(alice))))&
((?[X]:((~quiet(X)|quiet(X))))=>((~humble(lucy)<~>creative(lucy))))&
((?[X]:((~rich(X)<~>tall(X))))=>((curious(fred)|~happy(fred))))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:(humble(X)=>wise(X)))&
((?[X]:((~brave(X)|~humble(X))))=>((tall(alice)&curious(alice))))&
((?[X]:(~happy(X)))<=>(?[X]:((~tall(X)|brave(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)<~>quiet(X)))))&
((strong(mary)<~>~wise(mary)))&
((~happy(alice)<~>~patient(alice)))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)&creative(X))))&
((~quiet(susan)<~>strong(susan))) | kind(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3937066634148715934377107
% SZS output start Proof for 3937066634148715934377107
5. ! [X0] : (kind(X0) => ~kind(X0)) [input p4]
21. kind(susan) [input hypothesis]
30. ! [X0] : (~kind(X0) | ~kind(X0)) [ennf transformation 5]
96. ~kind(X0) | ~kind(X0) [cnf transformation 30]
143. kind(susan) [cnf transformation 21]
144. ~kind(X0) [duplicate literal removal 96]
340. $false [subsumption resolution 143,144]
% SZS output end Proof for 3937066634148715934377107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not patient is generous and vice versa.
Everyone who is both patient and happy is old.
If someone is not wise or not calm then someone is both brave and strong and vice versa.
Everyone who is not patient is both rich and not calm and vice versa.
Everyone who is humble or not creative is wise or not tall and vice versa.
If someone is either not creative or not strong then mary is either curious or not tall and vice versa.
If mary is funny then someone is not humble or old.
If lucy is curious or not humble then someone is both not creative and tall.
If paul is calm or not humble then someone is wise or not humble.
Everyone who is kind is old or patient.
Everyone who is strong is both not old and not brave.
If alice is both happy and not curious then lucy is not creative.
Everyone who is either not tall or rich is humble or patient.
If susan is either funny or strong then someone is both old and not creative and vice versa.
If fred is not funny then someone is not generous or generous and vice versa.
Everyone who is either not strong or not creative is either curious or creative and vice versa.
Someone is both not quiet and humble.
Mary is happy.
Lucy is old.
Someone is either not rich or not humble.
Alice is not creative or not quiet.
Someone is strong or brave. | Fred is not kind. | neutral | (![X]:((strong(X)|~patient(X))<=>generous(X)))&
(![X]:((patient(X)&happy(X))=>old(X)))&
((?[X]:((~wise(X)|~calm(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:(~patient(X)<=>(rich(X)&~calm(X))))&
(![X]:((humble(X)|~creative(X))<=>(wise(X)|~tall(X))))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((curious(mary)<~>~tall(mary))))&
((funny(mary))=>(?[X]:((~humble(X)|old(X)))))&
(((curious(lucy)|~humble(lucy)))=>(?[X]:((~creative(X)&tall(X)))))&
(((calm(paul)|~humble(paul)))=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:(kind(X)=>(old(X)|patient(X))))&
(![X]:(strong(X)=>(~old(X)&~brave(X))))&
(((happy(alice)&~curious(alice)))=>(~creative(lucy)))&
(![X]:((~tall(X)<~>rich(X))=>(humble(X)|patient(X))))&
(((funny(susan)<~>strong(susan)))<=>(?[X]:((old(X)&~creative(X)))))&
((~funny(fred))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((~strong(X)<~>~creative(X))<=>(curious(X)<~>creative(X))))&
(?[X]:((~quiet(X)&humble(X))))&
(happy(mary))&
(old(lucy))&
(?[X]:((~rich(X)<~>~humble(X))))&
((~creative(alice)|~quiet(alice)))&
(?[X]:((strong(X)|brave(X)))) | ~kind(fred) | [] | null | 0 |
If someone is either calm or patient then mary is calm.
Everyone who is both tall and strong is kind.
Everyone who is not calm is not wise or not curious and vice versa.
Everyone who is either creative or quiet is curious.
If paul is strong or not happy then someone is not quiet.
If susan is both not curious and not brave then someone is both happy and not wise.
Everyone who is either not wise or not calm is quiet or curious and vice versa.
Everyone who is either tall or not happy is not rich and vice versa.
Everyone who is not generous or brave is both generous and not kind.
Everyone who is either not creative or not brave is either not creative or strong and vice versa.
Everyone who is both patient and curious is strong or not wise and vice versa.
Everyone who is either humble or not old is either not generous or happy and vice versa.
Everyone who is either not humble or calm is happy.
If alice is both not old and not tall then someone is happy and vice versa.
If someone is either not brave or patient then mary is generous.
If john is not strong or not brave then someone is humble.
Someone is either not old or brave.
Susan is brave or quiet.
Someone is wise or generous. | Alice is not brave. | contradiction | ((?[X]:((calm(X)<~>patient(X))))=>(calm(mary)))&
(![X]:((tall(X)&strong(X))=>kind(X)))&
(![X]:(~calm(X)<=>(~wise(X)|~curious(X))))&
(![X]:((creative(X)<~>quiet(X))=>curious(X)))&
(((strong(paul)|~happy(paul)))=>(?[X]:(~quiet(X))))&
(((~curious(susan)&~brave(susan)))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>(quiet(X)|curious(X))))&
(![X]:((tall(X)<~>~happy(X))<=>~rich(X)))&
(![X]:((~generous(X)|brave(X))=>(generous(X)&~kind(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(~creative(X)<~>strong(X))))&
(![X]:((patient(X)&curious(X))<=>(strong(X)|~wise(X))))&
(![X]:((humble(X)<~>~old(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((~humble(X)<~>calm(X))=>happy(X)))&
(((~old(alice)&~tall(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((~brave(X)<~>patient(X))))=>(generous(mary)))&
(((~strong(john)|~brave(john)))=>(?[X]:(humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((brave(susan)|quiet(susan)))&
(?[X]:((wise(X)|generous(X)))) | ~brave(alice) | [
"p2",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3995390089774062518849943
% SZS output start Proof for 3995390089774062518849943
3. ! [X0] : (~calm(X0) <=> (~curious(X0) | ~wise(X0))) [input p2]
7. ! [X0] : ((~wise(X0) <~> ~calm(X0)) <=> (curious(X0) | quiet(X0))) [input p6]
10. ! [X0] : ((~creative(X0) <~> ~brave(X0)) <=> (~creative(X0) <~> strong(X0))) [input p9]
11. ! [X0] : ((curious(X0) & patient(X0)) <=> (~wise(X0) | strong(X0))) [input p10]
20. ~brave(alice) [input hypothesis]
33. ! [X0] : ((~calm(X0) | (curious(X0) & wise(X0))) & ((~curious(X0) | ~wise(X0)) | calm(X0))) [nnf transformation 3]
34. ! [X0] : ((~calm(X0) | (curious(X0) & wise(X0))) & (~curious(X0) | ~wise(X0) | calm(X0))) [flattening 33]
40. ! [X0] : ((((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0))))) [nnf transformation 7]
41. ! [X0] : ((((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0))))) [flattening 40]
42. ! [X0] : ((((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ((~creative(X0) | ~strong(X0)) & (strong(X0) | creative(X0)))) & (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0))))) [nnf transformation 10]
43. ! [X0] : (((curious(X0) & patient(X0)) | (wise(X0) & ~strong(X0))) & ((~wise(X0) | strong(X0)) | (~curious(X0) | ~patient(X0)))) [nnf transformation 11]
44. ! [X0] : (((curious(X0) & patient(X0)) | (wise(X0) & ~strong(X0))) & (~wise(X0) | strong(X0) | ~curious(X0) | ~patient(X0))) [flattening 43]
63. ~curious(X0) | ~wise(X0) | calm(X0) [cnf transformation 34]
64. ~calm(X0) | wise(X0) [cnf transformation 34]
65. ~calm(X0) | curious(X0) [cnf transformation 34]
73. curious(X0) | quiet(X0) | ~wise(X0) | calm(X0) [cnf transformation 41]
74. ~calm(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 41]
75. ~calm(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 41]
76. calm(X0) | wise(X0) | ~quiet(X0) [cnf transformation 41]
77. calm(X0) | wise(X0) | ~curious(X0) [cnf transformation 41]
83. strong(X0) | ~creative(X0) | ~creative(X0) | brave(X0) [cnf transformation 42]
88. brave(X0) | creative(X0) | strong(X0) | creative(X0) [cnf transformation 42]
93. ~strong(X0) | curious(X0) [cnf transformation 44]
94. curious(X0) | wise(X0) [cnf transformation 44]
116. ~brave(alice) [cnf transformation 20]
117. strong(X0) | ~creative(X0) | brave(X0) [duplicate literal removal 83]
120. brave(X0) | creative(X0) | strong(X0) [duplicate literal removal 88]
166. ~curious(X0) | calm(X0) [subsumption resolution 77,63]
167. ~quiet(X0) | wise(X0) [subsumption resolution 76,64]
168. ~curious(X0) | ~wise(X0) [subsumption resolution 75,63]
169. ~quiet(X0) | ~calm(X0) [subsumption resolution 74,167]
170. curious(X0) | quiet(X0) | ~wise(X0) [subsumption resolution 73,65]
171. ~wise(X0) | quiet(X0) [subsumption resolution 170,168]
173. brave(X0) | strong(X0) [subsumption resolution 117,120]
230. calm(X0) | wise(X0) [resolution 166,94]
231. wise(X0) [subsumption resolution 230,64]
236. quiet(X0) [resolution 171,231]
239. strong(alice) [resolution 173,116]
244. curious(alice) [resolution 239,93]
262. ~calm(X0) [resolution 236,169]
272. ~wise(alice) | calm(alice) [resolution 244,63]
275. calm(alice) [subsumption resolution 272,231]
276. $false [subsumption resolution 275,262]
% SZS output end Proof for 3995390089774062518849943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or quiet is not happy.
If someone is old or creative then mary is happy and vice versa.
Everyone who is old is either calm or humble.
If someone is not quiet or generous then someone is not tall.
If someone is either strong or not patient then someone is both not generous and creative.
Everyone who is tall is either not brave or not curious and vice versa.
If someone is either not humble or not calm then someone is either kind or not patient and vice versa.
If lucy is either not patient or not curious then someone is either strong or creative and vice versa.
If someone is both not brave and not patient then someone is either wise or not wise and vice versa.
Everyone who is creative is either tall or kind.
If someone is wise or brave then alice is either kind or generous and vice versa.
If someone is both not curious and funny then someone is both not wise and not kind.
If fred is both not brave and tall then someone is either not creative or curious.
If someone is not curious or not brave then someone is both not old and not humble and vice versa.
If paul is generous or not wise then someone is patient or creative.
Everyone who is both tall and creative is not brave and vice versa.
Lucy is not creative.
Alice is rich.
Someone is not patient.
Someone is generous or not funny.
Someone is either not wise or not calm.
Someone is either quiet or generous.
Alice is not old or quiet.
Someone is brave or strong. | Mary is not curious. | contradiction | (![X]:((~creative(X)|quiet(X))=>~happy(X)))&
((?[X]:((old(X)|creative(X))))<=>(happy(mary)))&
(![X]:(old(X)=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)|generous(X))))=>(?[X]:(~tall(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~generous(X)&creative(X)))))&
(![X]:(tall(X)<=>(~brave(X)<~>~curious(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>(?[X]:((kind(X)<~>~patient(X)))))&
(((~patient(lucy)<~>~curious(lucy)))<=>(?[X]:((strong(X)<~>creative(X)))))&
((?[X]:((~brave(X)&~patient(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:(creative(X)=>(tall(X)<~>kind(X))))&
((?[X]:((wise(X)|brave(X))))<=>((kind(alice)<~>generous(alice))))&
((?[X]:((~curious(X)&funny(X))))=>(?[X]:((~wise(X)&~kind(X)))))&
(((~brave(fred)&tall(fred)))=>(?[X]:((~creative(X)<~>curious(X)))))&
((?[X]:((~curious(X)|~brave(X))))<=>(?[X]:((~old(X)&~humble(X)))))&
(((generous(paul)|~wise(paul)))=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((tall(X)&creative(X))<=>~brave(X)))&
(~creative(lucy))&
(rich(alice))&
(?[X]:(~patient(X)))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:((~wise(X)<~>~calm(X))))&
(?[X]:((quiet(X)<~>generous(X))))&
((~old(alice)|quiet(alice)))&
(?[X]:((brave(X)|strong(X)))) | ~curious(mary) | [
"p0",
"p1",
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5000924376036856512296095
% SZS output start Proof for 5000924376036856512296095
1. ! [X0] : ((quiet(X0) | ~creative(X0)) => ~happy(X0)) [input p0]
2. ? [X0] : (creative(X0) | old(X0)) <=> happy(mary) [input p1]
6. ! [X0] : (tall(X0) <=> (~brave(X0) <~> ~curious(X0))) [input p5]
9. ? [X0] : (~patient(X0) & ~brave(X0)) <=> ? [X0] : (wise(X0) <~> ~wise(X0)) [input p8]
16. ! [X0] : ((creative(X0) & tall(X0)) <=> ~brave(X0)) [input p15]
25. ~curious(mary) [input hypothesis]
29. ? [X0] : (~patient(X0) & ~brave(X0)) <=> ? [X1] : (wise(X1) <~> ~wise(X1)) [rectify 9]
35. ! [X0] : (~happy(X0) | (~quiet(X0) & creative(X0))) [ennf transformation 1]
43. (? [X0] : (creative(X0) | old(X0)) | ~happy(mary)) & (happy(mary) | ! [X0] : (~creative(X0) & ~old(X0))) [nnf transformation 2]
44. (? [X0] : (creative(X0) | old(X0)) | ~happy(mary)) & (happy(mary) | ! [X1] : (~creative(X1) & ~old(X1))) [rectify 43]
45. ? [X0] : (creative(X0) | old(X0)) => (creative(sK0) | old(sK0)) [choice axiom]
46. ((creative(sK0) | old(sK0)) | ~happy(mary)) & (happy(mary) | ! [X1] : (~creative(X1) & ~old(X1))) [skolemisation 44,45]
55. ! [X0] : ((tall(X0) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) & (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | ~tall(X0))) [nnf transformation 6]
65. (? [X0] : (~patient(X0) & ~brave(X0)) | ! [X1] : ((wise(X1) | wise(X1)) & (~wise(X1) | ~wise(X1)))) & (? [X1] : ((wise(X1) | ~wise(X1)) & (~wise(X1) | wise(X1))) | ! [X0] : (patient(X0) | brave(X0))) [nnf transformation 29]
66. (? [X0] : (~patient(X0) & ~brave(X0)) | ! [X1] : ((wise(X1) | wise(X1)) & (~wise(X1) | ~wise(X1)))) & (? [X2] : ((wise(X2) | ~wise(X2)) & (~wise(X2) | wise(X2))) | ! [X3] : (patient(X3) | brave(X3))) [rectify 65]
67. ? [X0] : (~patient(X0) & ~brave(X0)) => (~patient(sK6) & ~brave(sK6)) [choice axiom]
68. ? [X2] : ((wise(X2) | ~wise(X2)) & (~wise(X2) | wise(X2))) => ((wise(sK7) | ~wise(sK7)) & (~wise(sK7) | wise(sK7))) [choice axiom]
69. ((~patient(sK6) & ~brave(sK6)) | ! [X1] : ((wise(X1) | wise(X1)) & (~wise(X1) | ~wise(X1)))) & (((wise(sK7) | ~wise(sK7)) & (~wise(sK7) | wise(sK7))) | ! [X3] : (patient(X3) | brave(X3))) [skolemisation 66,68,67]
85. ! [X0] : (((creative(X0) & tall(X0)) | brave(X0)) & (~brave(X0) | (~creative(X0) | ~tall(X0)))) [nnf transformation 16]
86. ! [X0] : (((creative(X0) & tall(X0)) | brave(X0)) & (~brave(X0) | ~creative(X0) | ~tall(X0))) [flattening 85]
97. ~happy(X0) | creative(X0) [cnf transformation 35]
100. happy(mary) | ~creative(X1) [cnf transformation 46]
111. ~tall(X0) | brave(X0) | curious(X0) [cnf transformation 55]
113. ~brave(X0) | tall(X0) | curious(X0) [cnf transformation 55]
132. ~brave(sK6) | ~wise(X1) | ~wise(X1) [cnf transformation 69]
133. ~brave(sK6) | wise(X1) | wise(X1) [cnf transformation 69]
153. ~brave(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 86]
154. brave(X0) | tall(X0) [cnf transformation 86]
155. brave(X0) | creative(X0) [cnf transformation 86]
164. ~curious(mary) [cnf transformation 25]
165. ~brave(sK6) | ~wise(X1) [duplicate literal removal 132]
166. ~brave(sK6) | wise(X1) [duplicate literal removal 133]
170. 1 <=> happy(mary) [avatar definition]
171. happy(mary) <- (1) [avatar component clause 170]
183. 4 <=> ! [X1] : ~creative(X1) [avatar definition]
184. ~creative(X1) <- (4) [avatar component clause 183]
185. 4 | 1 [avatar split clause 100,170,183]
287. 27 <=> ! [X1] : wise(X1) [avatar definition]
288. wise(X1) <- (27) [avatar component clause 287]
295. 29 <=> ! [X1] : ~wise(X1) [avatar definition]
296. ~wise(X1) <- (29) [avatar component clause 295]
299. 30 <=> brave(sK6) [avatar definition]
301. ~brave(sK6) <- (~30) [avatar component clause 299]
302. 27 | ~30 [avatar split clause 166,299,287]
303. 29 | ~30 [avatar split clause 165,299,295]
434. creative(sK6) <- (~30) [resolution 155,301]
435. $false <- (4, ~30) [subsumption resolution 434,184]
436. ~4 | 30 [avatar contradiction clause 435]
440. creative(mary) <- (1) [resolution 171,97]
472. tall(X1) | curious(X1) | tall(X1) [resolution 113,154]
473. curious(X1) | tall(X1) [duplicate literal removal 472]
492. 64 <=> tall(mary) [avatar definition]
494. tall(mary) <- (64) [avatar component clause 492]
514. tall(mary) [resolution 473,164]
526. brave(mary) | curious(mary) <- (64) [resolution 494,111]
527. brave(mary) <- (64) [subsumption resolution 526,164]
536. ~creative(mary) | ~tall(mary) <- (64) [resolution 527,153]
538. ~tall(mary) <- (1, 64) [subsumption resolution 536,440]
539. $false <- (1, 64) [subsumption resolution 538,494]
540. ~1 | ~64 [avatar contradiction clause 539]
541. 64 [avatar split clause 514,492]
547. $false <- (27, 29) [subsumption resolution 288,296]
548. ~27 | ~29 [avatar contradiction clause 547]
549. $false [avatar sat refutation 185,302,303,436,540,541,548]
% SZS output end Proof for 5000924376036856512296095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both wise and not brave then susan is both not tall and wise. If lucy is not tall then someone is either funny or not creative and vice versa. Everyone who is rich or not humble is both not kind and not curious and vice versa. Everyone who is happy or curious is both not happy and not rich. Everyone who is not humble is not wise. Everyone who is both not humble and calm is either rich or calm. Everyone who is not tall is both funny and not tall. Everyone who is both humble and happy is both not calm and not kind. Everyone who is not quiet is both calm and strong and vice versa. Everyone who is both not wise and quiet is not strong and vice versa. If fred is either not patient or creative then someone is either strong or tall and vice versa. Everyone who is both strong and not calm is not patient or creative and vice versa. If john is happy or not happy then john is either not happy or creative and vice versa. Everyone who is quiet is either not patient or not creative and vice versa. Everyone who is either not wise or not humble is not patient or patient. If someone is not kind then lucy is not strong or not quiet. Someone is not tall. Someone is not tall or not wise. Someone is both patient and rich. Someone is humble. Alice is both kind and not brave. Lucy is either strong or old. | John is not quiet. | contradiction | ((?[X]:((wise(X)&~brave(X))))=>((~tall(susan)&wise(susan))))&
((~tall(lucy))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((rich(X)|~humble(X))<=>(~kind(X)&~curious(X))))&
(![X]:((happy(X)|curious(X))=>(~happy(X)&~rich(X))))&
(![X]:(~humble(X)=>~wise(X)))&
(![X]:((~humble(X)&calm(X))=>(rich(X)<~>calm(X))))&
(![X]:(~tall(X)=>(funny(X)&~tall(X))))&
(![X]:((humble(X)&happy(X))=>(~calm(X)&~kind(X))))&
(![X]:(~quiet(X)<=>(calm(X)&strong(X))))&
(![X]:((~wise(X)&quiet(X))<=>~strong(X)))&
(((~patient(fred)<~>creative(fred)))<=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:((strong(X)&~calm(X))<=>(~patient(X)|creative(X))))&
(((happy(john)|~happy(john)))<=>((~happy(john)<~>creative(john))))&
(![X]:(quiet(X)<=>(~patient(X)<~>~creative(X))))&
(![X]:((~wise(X)<~>~humble(X))=>(~patient(X)|patient(X))))&
((?[X]:(~kind(X)))=>((~strong(lucy)|~quiet(lucy))))&
(?[X]:(~tall(X)))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:(humble(X)))&
((kind(alice)&~brave(alice)))&
((strong(lucy)<~>old(lucy))) | ~quiet(john) | [
"p3",
"p8",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7767303168161538857536024
% SZS output start Proof for 7767303168161538857536024
4. ! [X0] : ((curious(X0) | happy(X0)) => (~rich(X0) & ~happy(X0))) [input p3]
9. ! [X0] : (~quiet(X0) <=> (strong(X0) & calm(X0))) [input p8]
12. ! [X0] : ((~calm(X0) & strong(X0)) <=> (creative(X0) | ~patient(X0))) [input p11]
13. (~happy(john) | happy(john)) <=> (~happy(john) <~> creative(john)) [input p12]
14. ! [X0] : (quiet(X0) <=> (~patient(X0) <~> ~creative(X0))) [input p13]
23. ~quiet(john) [input hypothesis]
25. ! [X0] : ((~rich(X0) & ~happy(X0)) | (~curious(X0) & ~happy(X0))) [ennf transformation 4]
43. ! [X0] : ((~quiet(X0) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | quiet(X0))) [nnf transformation 9]
44. ! [X0] : ((~quiet(X0) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | quiet(X0))) [flattening 43]
51. ! [X0] : (((~calm(X0) & strong(X0)) | (~creative(X0) & patient(X0))) & ((creative(X0) | ~patient(X0)) | (calm(X0) | ~strong(X0)))) [nnf transformation 12]
52. ! [X0] : (((~calm(X0) & strong(X0)) | (~creative(X0) & patient(X0))) & (creative(X0) | ~patient(X0) | calm(X0) | ~strong(X0))) [flattening 51]
53. ((~happy(john) | happy(john)) | ((~happy(john) | ~creative(john)) & (creative(john) | happy(john)))) & (((~creative(john) | happy(john)) & (creative(john) | ~happy(john))) | (happy(john) & ~happy(john))) [nnf transformation 13]
54. (~happy(john) | happy(john) | ((~happy(john) | ~creative(john)) & (creative(john) | happy(john)))) & (((~creative(john) | happy(john)) & (creative(john) | ~happy(john))) | (happy(john) & ~happy(john))) [flattening 53]
55. ! [X0] : ((quiet(X0) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0)))) & (((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | ~quiet(X0))) [nnf transformation 14]
77. ~happy(X0) | ~happy(X0) [cnf transformation 25]
88. quiet(X0) | calm(X0) [cnf transformation 44]
105. ~calm(X0) | patient(X0) [cnf transformation 52]
110. ~creative(john) | happy(john) | happy(john) [cnf transformation 54]
116. ~patient(X0) | quiet(X0) | creative(X0) [cnf transformation 55]
129. ~quiet(john) [cnf transformation 23]
131. ~creative(john) | happy(john) [duplicate literal removal 110]
135. ~happy(X0) [duplicate literal removal 77]
201. ~creative(john) [subsumption resolution 131,135]
233. calm(john) [resolution 88,129]
236. patient(john) [resolution 105,233]
302. quiet(john) | creative(john) [resolution 116,236]
308. creative(john) [subsumption resolution 302,129]
309. $false [subsumption resolution 308,201]
% SZS output end Proof for 7767303168161538857536024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either happy or not humble then someone is either kind or not curious. Everyone who is either tall or not patient is strong or tall and vice versa. If mary is both not brave and humble then john is both funny and not old and vice versa. If lucy is both tall and wise then someone is both calm and creative and vice versa. If someone is either kind or wise then paul is either curious or not creative. If alice is either wise or strong then alice is both not generous and calm and vice versa. If someone is both wise and curious then fred is not generous. Everyone who is not happy is both not tall and not calm. Everyone who is either rich or humble is quiet or creative. Everyone who is both not quiet and not generous is either strong or not brave and vice versa. Everyone who is either not generous or not wise is both rich and calm. If john is not creative then someone is both not patient and not brave and vice versa. Everyone who is both not tall and not happy is funny or curious and vice versa. Everyone who is both not quiet and happy is either not old or old and vice versa. Everyone who is both not curious and generous is old and vice versa. Everyone who is not funny is either not quiet or not generous and vice versa. Someone is not humble. Someone is either not tall or not happy. Someone is not curious or not calm. Someone is either not happy or wise. Someone is creative or kind. | Lucy is happy. | entailment | (((happy(paul)<~>~humble(paul)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((tall(X)<~>~patient(X))<=>(strong(X)|tall(X))))&
(((~brave(mary)&humble(mary)))<=>((funny(john)&~old(john))))&
(((tall(lucy)&wise(lucy)))<=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:((kind(X)<~>wise(X))))=>((curious(paul)<~>~creative(paul))))&
(((wise(alice)<~>strong(alice)))<=>((~generous(alice)&calm(alice))))&
((?[X]:((wise(X)&curious(X))))=>(~generous(fred)))&
(![X]:(~happy(X)=>(~tall(X)&~calm(X))))&
(![X]:((rich(X)<~>humble(X))=>(quiet(X)|creative(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((~generous(X)<~>~wise(X))=>(rich(X)&calm(X))))&
((~creative(john))<=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(funny(X)|curious(X))))&
(![X]:((~quiet(X)&happy(X))<=>(~old(X)<~>old(X))))&
(![X]:((~curious(X)&generous(X))<=>old(X)))&
(![X]:(~funny(X)<=>(~quiet(X)<~>~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~curious(X)|~calm(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:((creative(X)|kind(X)))) | happy(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6424366590140446989340352
% SZS output start Proof for 6424366590140446989340352
14. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~old(X0) <~> old(X0))) [input p13]
22. ~happy(lucy) [input hypothesis]
55. ! [X0] : (((happy(X0) & ~quiet(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | (~happy(X0) | quiet(X0)))) [nnf transformation 14]
56. ! [X0] : (((happy(X0) & ~quiet(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~happy(X0) | quiet(X0))) [flattening 55]
127. happy(X0) | old(X0) | old(X0) [cnf transformation 56]
128. happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 56]
143. ~happy(lucy) [cnf transformation 22]
146. happy(X0) | old(X0) [duplicate literal removal 127]
147. happy(X0) | ~old(X0) [duplicate literal removal 128]
281. happy(X0) [subsumption resolution 146,147]
305. $false [subsumption resolution 143,281]
% SZS output end Proof for 6424366590140446989340352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not curious or not strong then someone is not old or not wise and vice versa.
If paul is either not curious or creative then someone is both not generous and not happy.
Everyone who is generous or not creative is not happy or not quiet.
Everyone who is not kind is either strong or not funny and vice versa.
Everyone who is both strong and not generous is not generous or kind.
If someone is both generous and brave then someone is both not kind and humble.
Everyone who is both happy and not rich is tall or quiet and vice versa.
Everyone who is kind is brave and vice versa.
Everyone who is either not creative or not curious is generous and vice versa.
Everyone who is both not patient and not happy is not brave or not rich and vice versa.
If someone is both strong and not old then susan is both rich and not patient and vice versa.
Everyone who is either not generous or not kind is not old.
Everyone who is not brave is both not tall and not old.
If someone is brave then someone is not patient or happy and vice versa.
Everyone who is both generous and not funny is either kind or not quiet and vice versa.
If someone is both wise and not brave then paul is either brave or not funny and vice versa.
Paul is both brave and not strong.
Alice is either calm or not old.
Lucy is either happy or not quiet.
Paul is not creative.
Lucy is not patient or funny.
Susan is old or generous.
Someone is either kind or patient.
Fred is not calm. | Susan is tall. | contradiction | (((~curious(alice)|~strong(alice)))<=>(?[X]:((~old(X)|~wise(X)))))&
(((~curious(paul)<~>creative(paul)))=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((generous(X)|~creative(X))=>(~happy(X)|~quiet(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>~funny(X))))&
(![X]:((strong(X)&~generous(X))=>(~generous(X)|kind(X))))&
((?[X]:((generous(X)&brave(X))))=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((happy(X)&~rich(X))<=>(tall(X)|quiet(X))))&
(![X]:(kind(X)<=>brave(X)))&
(![X]:((~creative(X)<~>~curious(X))<=>generous(X)))&
(![X]:((~patient(X)&~happy(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((strong(X)&~old(X))))<=>((rich(susan)&~patient(susan))))&
(![X]:((~generous(X)<~>~kind(X))=>~old(X)))&
(![X]:(~brave(X)=>(~tall(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~patient(X)|happy(X)))))&
(![X]:((generous(X)&~funny(X))<=>(kind(X)<~>~quiet(X))))&
((?[X]:((wise(X)&~brave(X))))<=>((brave(paul)<~>~funny(paul))))&
((brave(paul)&~strong(paul)))&
((calm(alice)<~>~old(alice)))&
((happy(lucy)<~>~quiet(lucy)))&
(~creative(paul))&
((~patient(lucy)|funny(lucy)))&
((old(susan)|generous(susan)))&
(?[X]:((kind(X)<~>patient(X))))&
(~calm(fred)) | tall(susan) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 762032639273947892627283
% SZS output start Proof for 762032639273947892627283
7. ! [X0] : ((~rich(X0) & happy(X0)) <=> (quiet(X0) | tall(X0))) [input p6]
10. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (~rich(X0) | ~brave(X0))) [input p9]
25. tall(susan) [input hypothesis]
49. ! [X0] : (((~rich(X0) & happy(X0)) | (~quiet(X0) & ~tall(X0))) & ((quiet(X0) | tall(X0)) | (rich(X0) | ~happy(X0)))) [nnf transformation 7]
50. ! [X0] : (((~rich(X0) & happy(X0)) | (~quiet(X0) & ~tall(X0))) & (quiet(X0) | tall(X0) | rich(X0) | ~happy(X0))) [flattening 49]
53. ! [X0] : (((~happy(X0) & ~patient(X0)) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 10]
54. ! [X0] : (((~happy(X0) & ~patient(X0)) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | happy(X0) | patient(X0))) [flattening 53]
94. ~tall(X0) | happy(X0) [cnf transformation 50]
96. ~tall(X0) | ~rich(X0) [cnf transformation 50]
108. ~happy(X0) | rich(X0) [cnf transformation 54]
144. tall(susan) [cnf transformation 25]
200. 13 <=> rich(susan) [avatar definition]
202. ~rich(susan) <- (~13) [avatar component clause 200]
320. happy(susan) [resolution 94,144]
321. ~rich(susan) [resolution 96,144]
324. ~13 [avatar split clause 321,200]
333. rich(susan) [resolution 108,320]
334. $false <- (~13) [subsumption resolution 333,202]
335. 13 [avatar contradiction clause 334]
336. $false [avatar sat refutation 324,335]
% SZS output end Proof for 762032639273947892627283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is both not quiet and not rich and vice versa.
Everyone who is both not tall and quiet is both not wise and not humble.
If someone is not brave then someone is either calm or humble.
Everyone who is not curious or not creative is calm or rich and vice versa.
If mary is brave or generous then someone is rich.
If someone is calm or creative then someone is both rich and not rich and vice versa.
If alice is both old and not kind then paul is not tall or wise.
Everyone who is either patient or creative is creative and vice versa.
Everyone who is both wise and not humble is not strong or humble.
Everyone who is either not calm or strong is generous.
If someone is both humble and not rich then someone is either curious or not rich and vice versa.
If someone is calm or funny then someone is old and vice versa.
Everyone who is not rich or happy is generous and vice versa.
If john is not curious then someone is either happy or not patient.
If fred is brave then paul is humble or quiet.
Alice is both strong and not generous.
Mary is not calm.
Paul is both not old and not kind.
Susan is both not generous and not quiet.
Someone is either not tall or humble.
Someone is rich.
Someone is either not creative or patient. | Alice is not calm. | entailment | (![X]:(~brave(X)<=>(~quiet(X)&~rich(X))))&
(![X]:((~tall(X)&quiet(X))=>(~wise(X)&~humble(X))))&
((?[X]:(~brave(X)))=>(?[X]:((calm(X)<~>humble(X)))))&
(![X]:((~curious(X)|~creative(X))<=>(calm(X)|rich(X))))&
(((brave(mary)|generous(mary)))=>(?[X]:(rich(X))))&
((?[X]:((calm(X)|creative(X))))<=>(?[X]:((rich(X)&~rich(X)))))&
(((old(alice)&~kind(alice)))=>((~tall(paul)|wise(paul))))&
(![X]:((patient(X)<~>creative(X))<=>creative(X)))&
(![X]:((wise(X)&~humble(X))=>(~strong(X)|humble(X))))&
(![X]:((~calm(X)<~>strong(X))=>generous(X)))&
((?[X]:((humble(X)&~rich(X))))<=>(?[X]:((curious(X)<~>~rich(X)))))&
((?[X]:((calm(X)|funny(X))))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)|happy(X))<=>generous(X)))&
((~curious(john))=>(?[X]:((happy(X)<~>~patient(X)))))&
((brave(fred))=>((humble(paul)|quiet(paul))))&
((strong(alice)&~generous(alice)))&
(~calm(mary))&
((~old(paul)&~kind(paul)))&
((~generous(susan)&~quiet(susan)))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)<~>patient(X)))) | ~calm(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2352409216791813884479055
% SZS output start Proof for 2352409216791813884479055
6. ? [X0] : (creative(X0) | calm(X0)) <=> ? [X0] : (~rich(X0) & rich(X0)) [input p5]
23. calm(alice) [input hypothesis]
25. ? [X0] : (creative(X0) | calm(X0)) <=> ? [X1] : (~rich(X1) & rich(X1)) [rectify 6]
50. (? [X0] : (creative(X0) | calm(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X1] : (~rich(X1) & rich(X1)) | ! [X0] : (~creative(X0) & ~calm(X0))) [nnf transformation 25]
51. (? [X0] : (creative(X0) | calm(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X2] : (~rich(X2) & rich(X2)) | ! [X3] : (~creative(X3) & ~calm(X3))) [rectify 50]
52. ? [X0] : (creative(X0) | calm(X0)) => (creative(sK2) | calm(sK2)) [choice axiom]
53. ? [X2] : (~rich(X2) & rich(X2)) => (~rich(sK3) & rich(sK3)) [choice axiom]
54. ((creative(sK2) | calm(sK2)) | ! [X1] : (rich(X1) | ~rich(X1))) & ((~rich(sK3) & rich(sK3)) | ! [X3] : (~creative(X3) & ~calm(X3))) [skolemisation 51,53,52]
93. rich(sK3) | ~calm(X3) [cnf transformation 54]
95. ~rich(sK3) | ~calm(X3) [cnf transformation 54]
133. calm(alice) [cnf transformation 23]
168. 8 <=> rich(sK3) [avatar definition]
173. 9 <=> ! [X3] : ~calm(X3) [avatar definition]
174. ~calm(X3) <- (9) [avatar component clause 173]
175. 9 | ~8 [avatar split clause 95,168,173]
177. 9 | 8 [avatar split clause 93,168,173]
286. $false <- (9) [resolution 174,133]
287. ~9 [avatar contradiction clause 286]
288. $false [avatar sat refutation 175,177,287]
% SZS output end Proof for 2352409216791813884479055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not brave is patient and vice versa.
If someone is both not humble and patient then lucy is patient or happy.
Everyone who is curious or rich is not happy or curious.
If someone is both not generous and strong then alice is both not old and humble.
Everyone who is both wise and not calm is not curious and vice versa.
Everyone who is not humble or tall is either not generous or not creative.
Everyone who is patient is both humble and curious.
Everyone who is both curious and not old is either rich or strong and vice versa.
If someone is either calm or not curious then fred is not calm.
Everyone who is rich is not happy and vice versa.
If lucy is either not funny or not wise then john is both not tall and tall.
If someone is either patient or happy then someone is either happy or wise.
If someone is not brave then fred is funny.
Everyone who is not wise is both not generous and brave and vice versa.
If someone is both not kind and not generous then someone is either not wise or generous and vice versa.
Everyone who is both not old and not strong is not patient or not tall.
Someone is either rich or not generous.
Lucy is not curious or old.
Someone is not old.
Paul is not funny or not strong.
Alice is both not creative and not calm.
Someone is both happy and not funny.
Mary is either wise or not funny.
Someone is both not strong and not old. | Alice is not generous. | entailment | (![X]:((~curious(X)|~brave(X))<=>patient(X)))&
((?[X]:((~humble(X)&patient(X))))=>((patient(lucy)|happy(lucy))))&
(![X]:((curious(X)|rich(X))=>(~happy(X)|curious(X))))&
((?[X]:((~generous(X)&strong(X))))=>((~old(alice)&humble(alice))))&
(![X]:((wise(X)&~calm(X))<=>~curious(X)))&
(![X]:((~humble(X)|tall(X))=>(~generous(X)<~>~creative(X))))&
(![X]:(patient(X)=>(humble(X)&curious(X))))&
(![X]:((curious(X)&~old(X))<=>(rich(X)<~>strong(X))))&
((?[X]:((calm(X)<~>~curious(X))))=>(~calm(fred)))&
(![X]:(rich(X)<=>~happy(X)))&
(((~funny(lucy)<~>~wise(lucy)))=>((~tall(john)&tall(john))))&
((?[X]:((patient(X)<~>happy(X))))=>(?[X]:((happy(X)<~>wise(X)))))&
((?[X]:(~brave(X)))=>(funny(fred)))&
(![X]:(~wise(X)<=>(~generous(X)&brave(X))))&
((?[X]:((~kind(X)&~generous(X))))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((~old(X)&~strong(X))=>(~patient(X)|~tall(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
((~curious(lucy)|old(lucy)))&
(?[X]:(~old(X)))&
((~funny(paul)|~strong(paul)))&
((~creative(alice)&~calm(alice)))&
(?[X]:((happy(X)&~funny(X))))&
((wise(mary)<~>~funny(mary)))&
(?[X]:((~strong(X)&~old(X)))) | ~generous(alice) | [
"p0",
"p4",
"p6",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 75537905988745388179332
% SZS output start Proof for 75537905988745388179332
1. ! [X0] : ((~brave(X0) | ~curious(X0)) <=> patient(X0)) [input p0]
5. ! [X0] : ((~calm(X0) & wise(X0)) <=> ~curious(X0)) [input p4]
7. ! [X0] : (patient(X0) => (curious(X0) & humble(X0))) [input p6]
14. ! [X0] : (~wise(X0) <=> (brave(X0) & ~generous(X0))) [input p13]
21. ~calm(alice) & ~creative(alice) [input p20]
25. generous(alice) [input hypothesis]
30. ! [X0] : (patient(X0) => curious(X0)) [pure predicate removal 7]
36. ! [X0] : (curious(X0) | ~patient(X0)) [ennf transformation 30]
43. ! [X0] : (((~brave(X0) | ~curious(X0)) | ~patient(X0)) & (patient(X0) | (brave(X0) & curious(X0)))) [nnf transformation 1]
44. ! [X0] : ((~brave(X0) | ~curious(X0) | ~patient(X0)) & (patient(X0) | (brave(X0) & curious(X0)))) [flattening 43]
45. ! [X0] : (((~calm(X0) & wise(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~wise(X0)))) [nnf transformation 5]
46. ! [X0] : (((~calm(X0) & wise(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~wise(X0))) [flattening 45]
57. ! [X0] : ((~wise(X0) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | wise(X0))) [nnf transformation 14]
58. ! [X0] : ((~wise(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | wise(X0))) [flattening 57]
74. patient(X0) | curious(X0) [cnf transformation 44]
80. ~wise(X0) | calm(X0) | ~curious(X0) [cnf transformation 46]
85. curious(X0) | ~patient(X0) [cnf transformation 36]
105. ~generous(X0) | wise(X0) [cnf transformation 58]
121. ~calm(alice) [cnf transformation 21]
128. generous(alice) [cnf transformation 25]
137. curious(X0) [subsumption resolution 85,74]
261. wise(alice) [resolution 105,128]
271. calm(alice) | ~curious(alice) [resolution 80,261]
272. ~curious(alice) [subsumption resolution 271,121]
273. $false [subsumption resolution 272,137]
% SZS output end Proof for 75537905988745388179332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not generous and not calm then alice is not kind. Everyone who is strong is patient and vice versa. If lucy is not patient or funny then fred is tall or not patient and vice versa. If someone is either not brave or not generous then susan is kind or not old. Everyone who is not tall or not calm is humble. Everyone who is not calm or not rich is not humble or not kind and vice versa. If someone is either not quiet or not creative then someone is not creative or wise and vice versa. If susan is either old or funny then alice is both generous and old. If someone is not strong then fred is calm and vice versa. If john is either brave or not calm then john is not humble. If lucy is both not humble and not funny then fred is not creative or not strong and vice versa. Everyone who is wise or brave is both not wise and calm and vice versa. If someone is not tall or not calm then someone is brave or not calm. Everyone who is either happy or not kind is either not wise or generous. Everyone who is both not generous and happy is not rich or brave. Everyone who is humble is kind or not patient. Lucy is not patient. Mary is both patient and funny. Someone is not patient or rich. Susan is curious or not creative. Someone is either generous or humble. Someone is not patient. Someone is not creative or not tall. Mary is not old or curious. | Mary is brave. | entailment | (((~generous(mary)&~calm(mary)))=>(~kind(alice)))&
(![X]:(strong(X)<=>patient(X)))&
(((~patient(lucy)|funny(lucy)))<=>((tall(fred)|~patient(fred))))&
((?[X]:((~brave(X)<~>~generous(X))))=>((kind(susan)|~old(susan))))&
(![X]:((~tall(X)|~calm(X))=>humble(X)))&
(![X]:((~calm(X)|~rich(X))<=>(~humble(X)|~kind(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))<=>(?[X]:((~creative(X)|wise(X)))))&
(((old(susan)<~>funny(susan)))=>((generous(alice)&old(alice))))&
((?[X]:(~strong(X)))<=>(calm(fred)))&
(((brave(john)<~>~calm(john)))=>(~humble(john)))&
(((~humble(lucy)&~funny(lucy)))<=>((~creative(fred)|~strong(fred))))&
(![X]:((wise(X)|brave(X))<=>(~wise(X)&calm(X))))&
((?[X]:((~tall(X)|~calm(X))))=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((happy(X)<~>~kind(X))=>(~wise(X)<~>generous(X))))&
(![X]:((~generous(X)&happy(X))=>(~rich(X)|brave(X))))&
(![X]:(humble(X)=>(kind(X)|~patient(X))))&
(~patient(lucy))&
((patient(mary)&funny(mary)))&
(?[X]:((~patient(X)|rich(X))))&
((curious(susan)|~creative(susan)))&
(?[X]:((generous(X)<~>humble(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~creative(X)|~tall(X))))&
((~old(mary)|curious(mary))) | brave(mary) | [
"p4",
"p5",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 751152732399353725291754
% SZS output start Proof for 751152732399353725291754
5. ! [X0] : ((~calm(X0) | ~tall(X0)) => humble(X0)) [input p4]
6. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (~kind(X0) | ~humble(X0))) [input p5]
12. ! [X0] : ((brave(X0) | wise(X0)) <=> (calm(X0) & ~wise(X0))) [input p11]
16. ! [X0] : (humble(X0) => (~patient(X0) | kind(X0))) [input p15]
18. funny(mary) & patient(mary) [input p17]
25. ~brave(mary) [input hypothesis]
34. ! [X0] : (humble(X0) | (calm(X0) & tall(X0))) [ennf transformation 5]
41. ! [X0] : ((~patient(X0) | kind(X0)) | ~humble(X0)) [ennf transformation 16]
42. ! [X0] : (~patient(X0) | kind(X0) | ~humble(X0)) [flattening 41]
47. ! [X0] : (((~rich(X0) | ~calm(X0)) | (kind(X0) & humble(X0))) & ((~kind(X0) | ~humble(X0)) | (rich(X0) & calm(X0)))) [nnf transformation 6]
48. ! [X0] : ((~rich(X0) | ~calm(X0) | (kind(X0) & humble(X0))) & (~kind(X0) | ~humble(X0) | (rich(X0) & calm(X0)))) [flattening 47]
62. ! [X0] : (((brave(X0) | wise(X0)) | (~calm(X0) | wise(X0))) & ((calm(X0) & ~wise(X0)) | (~brave(X0) & ~wise(X0)))) [nnf transformation 12]
63. ! [X0] : ((brave(X0) | wise(X0) | ~calm(X0) | wise(X0)) & ((calm(X0) & ~wise(X0)) | (~brave(X0) & ~wise(X0)))) [flattening 62]
87. humble(X0) | calm(X0) [cnf transformation 34]
88. ~kind(X0) | ~humble(X0) | calm(X0) [cnf transformation 48]
111. ~wise(X0) | ~wise(X0) [cnf transformation 63]
115. brave(X0) | wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 63]
123. ~humble(X0) | kind(X0) | ~patient(X0) [cnf transformation 42]
125. patient(mary) [cnf transformation 18]
132. ~brave(mary) [cnf transformation 25]
133. ~wise(X0) [duplicate literal removal 111]
134. ~calm(X0) | wise(X0) | brave(X0) [duplicate literal removal 115]
140. 2 <=> calm(mary) [avatar definition]
142. calm(mary) <- (2) [avatar component clause 140]
185. ~kind(X0) | calm(X0) [subsumption resolution 88,87]
187. 12 <=> ! [X1] : ~wise(X1) [avatar definition]
188. ~wise(X1) <- (12) [avatar component clause 187]
281. 12 [avatar split clause 133,187]
337. kind(X0) | ~patient(X0) | calm(X0) [resolution 123,87]
339. ~patient(X0) | calm(X0) [subsumption resolution 337,185]
376. calm(mary) [resolution 339,125]
377. 2 [avatar split clause 376,140]
378. wise(mary) | brave(mary) <- (2) [resolution 142,134]
379. brave(mary) <- (2, 12) [subsumption resolution 378,188]
380. $false <- (2, 12) [subsumption resolution 379,132]
381. ~2 | ~12 [avatar contradiction clause 380]
382. $false [avatar sat refutation 281,377,381]
% SZS output end Proof for 751152732399353725291754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or humble then someone is both happy and kind.
If mary is either happy or not humble then someone is both rich and happy.
Everyone who is wise or not wise is both wise and not funny and vice versa.
Everyone who is brave is either not calm or strong.
Everyone who is old or curious is brave or not happy and vice versa.
Everyone who is not wise or not rich is creative.
If susan is both strong and not wise then someone is either calm or funny.
Everyone who is both not rich and not kind is not patient or not calm and vice versa.
If someone is not strong then someone is not patient or funny and vice versa.
If someone is both generous and not strong then john is funny or strong and vice versa.
Everyone who is both calm and not old is not patient and vice versa.
If paul is not strong then john is not happy.
Everyone who is not funny is either not funny or strong.
Everyone who is not creative is both not old and funny.
If john is either not creative or not old then someone is either quiet or not patient.
Someone is not humble or not curious.
Someone is either not funny or not calm.
Someone is both not quiet and not tall.
Lucy is either brave or not quiet.
Lucy is either calm or patient.
Alice is both patient and creative.
John is rich.
Susan is either kind or not kind. | Susan is not kind. | neutral | ((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((happy(X)&kind(X)))))&
(((happy(mary)<~>~humble(mary)))=>(?[X]:((rich(X)&happy(X)))))&
(![X]:((wise(X)|~wise(X))<=>(wise(X)&~funny(X))))&
(![X]:(brave(X)=>(~calm(X)<~>strong(X))))&
(![X]:((old(X)|curious(X))<=>(brave(X)|~happy(X))))&
(![X]:((~wise(X)|~rich(X))=>creative(X)))&
(((strong(susan)&~wise(susan)))=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((~rich(X)&~kind(X))<=>(~patient(X)|~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~patient(X)|funny(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>((funny(john)|strong(john))))&
(![X]:((calm(X)&~old(X))<=>~patient(X)))&
((~strong(paul))=>(~happy(john)))&
(![X]:(~funny(X)=>(~funny(X)<~>strong(X))))&
(![X]:(~creative(X)=>(~old(X)&funny(X))))&
(((~creative(john)<~>~old(john)))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:((~funny(X)<~>~calm(X))))&
(?[X]:((~quiet(X)&~tall(X))))&
((brave(lucy)<~>~quiet(lucy)))&
((calm(lucy)<~>patient(lucy)))&
((patient(alice)&creative(alice)))&
(rich(john))&
((kind(susan)<~>~kind(susan))) | ~kind(susan) | [] | null | 0 |
Everyone who is not old or old is happy or rich. Everyone who is both not curious and calm is old or not old and vice versa. If john is strong then lucy is tall or not kind. If john is either tall or not rich then someone is not quiet and vice versa. If fred is both not patient and wise then susan is not generous and vice versa. If someone is not creative then someone is old. Everyone who is tall is both not kind and not generous. If someone is humble or patient then someone is not tall or not wise and vice versa. Everyone who is either patient or not calm is curious or generous and vice versa. Everyone who is not quiet or not funny is both not patient and creative and vice versa. If someone is either not kind or not strong then someone is both kind and old and vice versa. Everyone who is not tall or not quiet is not brave and vice versa. Everyone who is either not happy or curious is calm and vice versa. Everyone who is generous is not brave and vice versa. Everyone who is both calm and tall is both wise and not curious and vice versa. Everyone who is not strong or not funny is not quiet and vice versa. Susan is creative. Someone is funny. Someone is generous or creative. Someone is either calm or old. Someone is happy or not old. Alice is quiet or not humble. | Fred is patient. | entailment | (![X]:((~old(X)|old(X))=>(happy(X)|rich(X))))&
(![X]:((~curious(X)&calm(X))<=>(old(X)|~old(X))))&
((strong(john))=>((tall(lucy)|~kind(lucy))))&
(((tall(john)<~>~rich(john)))<=>(?[X]:(~quiet(X))))&
(((~patient(fred)&wise(fred)))<=>(~generous(susan)))&
((?[X]:(~creative(X)))=>(?[X]:(old(X))))&
(![X]:(tall(X)=>(~kind(X)&~generous(X))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:((patient(X)<~>~calm(X))<=>(curious(X)|generous(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(~patient(X)&creative(X))))&
((?[X]:((~kind(X)<~>~strong(X))))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:((~tall(X)|~quiet(X))<=>~brave(X)))&
(![X]:((~happy(X)<~>curious(X))<=>calm(X)))&
(![X]:(generous(X)<=>~brave(X)))&
(![X]:((calm(X)&tall(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)|~funny(X))<=>~quiet(X)))&
(creative(susan))&
(?[X]:(funny(X)))&
(?[X]:((generous(X)|creative(X))))&
(?[X]:((calm(X)<~>old(X))))&
(?[X]:((happy(X)|~old(X))))&
((quiet(alice)|~humble(alice))) | patient(fred) | [
"p1",
"p4",
"p8",
"p9",
"p11",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6713692878712353536911093
% SZS output start Proof for 6713692878712353536911093
2. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (~old(X0) | old(X0))) [input p1]
5. (wise(fred) & ~patient(fred)) <=> ~generous(susan) [input p4]
9. ! [X0] : ((patient(X0) <~> ~calm(X0)) <=> (generous(X0) | curious(X0))) [input p8]
10. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> (creative(X0) & ~patient(X0))) [input p9]
12. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> ~brave(X0)) [input p11]
14. ! [X0] : (generous(X0) <=> ~brave(X0)) [input p13]
15. ! [X0] : ((tall(X0) & calm(X0)) <=> (~curious(X0) & wise(X0))) [input p14]
16. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p15]
17. creative(susan) [input p16]
23. ~patient(fred) [input hypothesis]
33. ! [X0] : (((calm(X0) & ~curious(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 2]
34. ! [X0] : (((calm(X0) & ~curious(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~calm(X0) | curious(X0))) [flattening 33]
39. ((wise(fred) & ~patient(fred)) | generous(susan)) & (~generous(susan) | (~wise(fred) | patient(fred))) [nnf transformation 5]
40. ((wise(fred) & ~patient(fred)) | generous(susan)) & (~generous(susan) | ~wise(fred) | patient(fred)) [flattening 39]
49. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [nnf transformation 9]
50. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [flattening 49]
51. ! [X0] : (((~funny(X0) | ~quiet(X0)) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | (funny(X0) & quiet(X0)))) [nnf transformation 10]
52. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | (funny(X0) & quiet(X0)))) [flattening 51]
58. ! [X0] : (((~quiet(X0) | ~tall(X0)) | brave(X0)) & (~brave(X0) | (quiet(X0) & tall(X0)))) [nnf transformation 12]
59. ! [X0] : ((~quiet(X0) | ~tall(X0) | brave(X0)) & (~brave(X0) | (quiet(X0) & tall(X0)))) [flattening 58]
61. ! [X0] : ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))) [nnf transformation 14]
62. ! [X0] : (((tall(X0) & calm(X0)) | (curious(X0) | ~wise(X0))) & ((~curious(X0) & wise(X0)) | (~tall(X0) | ~calm(X0)))) [nnf transformation 15]
63. ! [X0] : (((tall(X0) & calm(X0)) | curious(X0) | ~wise(X0)) & ((~curious(X0) & wise(X0)) | ~tall(X0) | ~calm(X0))) [flattening 62]
64. ! [X0] : (((~funny(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (funny(X0) & strong(X0)))) [nnf transformation 16]
65. ! [X0] : ((~funny(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (funny(X0) & strong(X0)))) [flattening 64]
78. ~curious(X0) | ~old(X0) [cnf transformation 34]
79. ~curious(X0) | old(X0) [cnf transformation 34]
80. calm(X0) | ~old(X0) [cnf transformation 34]
81. calm(X0) | old(X0) [cnf transformation 34]
87. ~generous(susan) | ~wise(fred) | patient(fred) [cnf transformation 40]
97. generous(X0) | curious(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 50]
100. ~calm(X0) | patient(X0) | ~generous(X0) [cnf transformation 50]
103. ~patient(X0) | quiet(X0) [cnf transformation 52]
107. ~funny(X0) | ~quiet(X0) | ~creative(X0) | patient(X0) [cnf transformation 52]
114. ~brave(X0) | tall(X0) [cnf transformation 59]
115. ~brave(X0) | quiet(X0) [cnf transformation 59]
122. brave(X0) | generous(X0) [cnf transformation 61]
123. wise(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 63]
128. ~quiet(X0) | funny(X0) [cnf transformation 65]
130. creative(susan) [cnf transformation 17]
137. ~patient(fred) [cnf transformation 23]
139. calm(X0) [subsumption resolution 80,81]
140. ~curious(X0) [subsumption resolution 78,79]
155. 4 <=> ! [X0] : quiet(X0) [avatar definition]
156. quiet(X0) <- (4) [avatar component clause 155]
174. 8 <=> generous(susan) [avatar definition]
175. ~generous(susan) <- (~8) [avatar component clause 174]
178. 9 <=> wise(fred) [avatar definition]
183. 10 <=> patient(fred) [avatar definition]
185. ~patient(fred) <- (~10) [avatar component clause 183]
187. 10 | ~9 | ~8 [avatar split clause 87,174,178,183]
228. ~generous(X0) | patient(X0) [subsumption resolution 100,139]
229. generous(X0) | ~calm(X0) | ~patient(X0) [subsumption resolution 97,140]
230. ~patient(X0) | generous(X0) [subsumption resolution 229,139]
265. ~tall(X0) | wise(X0) [subsumption resolution 123,139]
286. ~10 [avatar split clause 137,183]
290. generous(X1) | quiet(X1) [resolution 122,115]
291. generous(X2) | tall(X2) [resolution 122,114]
340. quiet(X0) | patient(X0) [resolution 290,228]
342. quiet(X0) [subsumption resolution 340,103]
343. 4 [avatar split clause 342,155]
346. funny(X1) <- (4) [resolution 156,128]
359. ~quiet(X0) | ~creative(X0) | patient(X0) <- (4) [resolution 346,107]
361. ~creative(X0) | patient(X0) <- (4) [subsumption resolution 359,156]
366. patient(X0) | tall(X0) [resolution 291,228]
383. patient(susan) <- (4) [resolution 361,130]
385. tall(fred) <- (~10) [resolution 366,185]
391. wise(fred) <- (~10) [resolution 385,265]
394. 9 | 10 [avatar split clause 391,183,178]
401. generous(susan) <- (4) [resolution 383,230]
404. $false <- (4, ~8) [subsumption resolution 401,175]
405. ~4 | 8 [avatar contradiction clause 404]
406. $false [avatar sat refutation 187,286,343,394,405]
% SZS output end Proof for 6713692878712353536911093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not patient is not old and vice versa.
Everyone who is either not funny or quiet is both not wise and generous and vice versa.
If paul is both not creative and creative then someone is strong.
If lucy is not old then someone is not brave or quiet.
If someone is both wise and calm then someone is funny or brave and vice versa.
If someone is both not old and not wise then someone is not humble and vice versa.
Everyone who is either not wise or not patient is old.
Everyone who is patient is kind and vice versa.
Everyone who is both not old and kind is happy or quiet and vice versa.
If lucy is either humble or not tall then john is either not humble or not curious.
Everyone who is both creative and not calm is strong.
If someone is generous or tall then someone is patient or not generous.
Everyone who is either happy or brave is not calm or generous and vice versa.
Everyone who is both not kind and not generous is humble or not calm.
If mary is both not brave and quiet then john is not kind.
Everyone who is not rich is not brave or not wise and vice versa.
Someone is either not funny or creative.
Someone is both brave and generous.
John is either not rich or not humble.
Someone is both humble and not patient.
Mary is wise or happy.
John is kind.
John is not old or not generous.
Someone is humble. | Mary is brave. | neutral | (![X]:((strong(X)<~>~patient(X))<=>~old(X)))&
(![X]:((~funny(X)<~>quiet(X))<=>(~wise(X)&generous(X))))&
(((~creative(paul)&creative(paul)))=>(?[X]:(strong(X))))&
((~old(lucy))=>(?[X]:((~brave(X)|quiet(X)))))&
((?[X]:((wise(X)&calm(X))))<=>(?[X]:((funny(X)|brave(X)))))&
((?[X]:((~old(X)&~wise(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~wise(X)<~>~patient(X))=>old(X)))&
(![X]:(patient(X)<=>kind(X)))&
(![X]:((~old(X)&kind(X))<=>(happy(X)|quiet(X))))&
(((humble(lucy)<~>~tall(lucy)))=>((~humble(john)<~>~curious(john))))&
(![X]:((creative(X)&~calm(X))=>strong(X)))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~calm(X)|generous(X))))&
(![X]:((~kind(X)&~generous(X))=>(humble(X)|~calm(X))))&
(((~brave(mary)&quiet(mary)))=>(~kind(john)))&
(![X]:(~rich(X)<=>(~brave(X)|~wise(X))))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:((brave(X)&generous(X))))&
((~rich(john)<~>~humble(john)))&
(?[X]:((humble(X)&~patient(X))))&
((wise(mary)|happy(mary)))&
(kind(john))&
((~old(john)|~generous(john)))&
(?[X]:(humble(X))) | brave(mary) | [] | null | 0 |
If mary is curious then fred is tall or kind.
Everyone who is either wise or creative is brave or not brave.
Everyone who is brave or rich is both not funny and funny and vice versa.
Everyone who is brave or not calm is either generous or happy and vice versa.
If someone is old then alice is both creative and strong and vice versa.
Everyone who is not happy or not strong is not curious.
Everyone who is either not curious or not happy is not generous.
Everyone who is both not happy and not quiet is not creative.
If someone is not curious or not funny then mary is not rich or not generous.
If paul is either old or not humble then someone is either not brave or kind and vice versa.
Everyone who is either not funny or not patient is both humble and not generous and vice versa.
Everyone who is not quiet or funny is both not curious and calm and vice versa.
Everyone who is creative is not rich.
If someone is old then susan is both humble and brave.
Everyone who is not strong or creative is not kind and vice versa.
If someone is tall then someone is either funny or wise.
Alice is not tall.
Someone is tall.
John is curious.
Someone is not wise.
Susan is both happy and creative.
Someone is wise or happy.
Alice is either not wise or patient.
Lucy is not patient. | Mary is not old. | entailment | ((curious(mary))=>((tall(fred)|kind(fred))))&
(![X]:((wise(X)<~>creative(X))=>(brave(X)|~brave(X))))&
(![X]:((brave(X)|rich(X))<=>(~funny(X)&funny(X))))&
(![X]:((brave(X)|~calm(X))<=>(generous(X)<~>happy(X))))&
((?[X]:(old(X)))<=>((creative(alice)&strong(alice))))&
(![X]:((~happy(X)|~strong(X))=>~curious(X)))&
(![X]:((~curious(X)<~>~happy(X))=>~generous(X)))&
(![X]:((~happy(X)&~quiet(X))=>~creative(X)))&
((?[X]:((~curious(X)|~funny(X))))=>((~rich(mary)|~generous(mary))))&
(((old(paul)<~>~humble(paul)))<=>(?[X]:((~brave(X)<~>kind(X)))))&
(![X]:((~funny(X)<~>~patient(X))<=>(humble(X)&~generous(X))))&
(![X]:((~quiet(X)|funny(X))<=>(~curious(X)&calm(X))))&
(![X]:(creative(X)=>~rich(X)))&
((?[X]:(old(X)))=>((humble(susan)&brave(susan))))&
(![X]:((~strong(X)|creative(X))<=>~kind(X)))&
((?[X]:(tall(X)))=>(?[X]:((funny(X)<~>wise(X)))))&
(~tall(alice))&
(?[X]:(tall(X)))&
(curious(john))&
(?[X]:(~wise(X)))&
((happy(susan)&creative(susan)))&
(?[X]:((wise(X)|happy(X))))&
((~wise(alice)<~>patient(alice)))&
(~patient(lucy)) | ~old(mary) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6881538786052103935867125
% SZS output start Proof for 6881538786052103935867125
3. ! [X0] : ((rich(X0) | brave(X0)) <=> (funny(X0) & ~funny(X0))) [input p2]
14. ? [X0] : old(X0) => (brave(susan) & humble(susan)) [input p13]
25. old(mary) [input hypothesis]
38. (brave(susan) & humble(susan)) | ! [X0] : ~old(X0) [ennf transformation 14]
41. ! [X0] : (((rich(X0) | brave(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (~rich(X0) & ~brave(X0)))) [nnf transformation 3]
42. ! [X0] : ((rich(X0) | brave(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (~rich(X0) & ~brave(X0)))) [flattening 41]
75. ~funny(X0) | ~brave(X0) [cnf transformation 42]
77. funny(X0) | ~brave(X0) [cnf transformation 42]
117. brave(susan) | ~old(X0) [cnf transformation 38]
133. old(mary) [cnf transformation 25]
148. ~brave(X0) [subsumption resolution 75,77]
165. 7 <=> ! [X1] : ~old(X1) [avatar definition]
166. ~old(X1) <- (7) [avatar component clause 165]
192. ~old(X0) [subsumption resolution 117,148]
193. 7 [avatar split clause 192,165]
231. $false <- (7) [resolution 166,133]
232. ~7 [avatar contradiction clause 231]
233. $false [avatar sat refutation 193,232]
% SZS output end Proof for 6881538786052103935867125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not old then someone is rich or generous.
Everyone who is not kind is either not brave or rich.
Everyone who is curious or quiet is either calm or creative.
If someone is kind then someone is rich or creative and vice versa.
If john is both not happy and not rich then lucy is generous or tall and vice versa.
If fred is not creative or creative then john is not patient or not happy and vice versa.
Everyone who is not brave or not creative is either not tall or happy.
Everyone who is both not brave and not kind is either strong or quiet and vice versa.
If someone is both not calm and curious then susan is quiet or not old.
Everyone who is either old or kind is strong or not tall and vice versa.
If someone is both not happy and not calm then someone is either not patient or brave and vice versa.
If john is strong then lucy is either not quiet or not calm and vice versa.
If someone is creative then john is calm or not brave.
Everyone who is not tall is not rich and vice versa.
Everyone who is quiet is not rich or not kind.
Everyone who is both kind and creative is both not humble and brave and vice versa.
Someone is both creative and not quiet.
Someone is either not strong or not generous.
Lucy is not creative or rich.
Someone is not funny.
Someone is both strong and not creative.
Someone is brave or creative.
Someone is brave.
Fred is either wise or not quiet. | Susan is not humble. | neutral | ((?[X]:((strong(X)|~old(X))))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:(~kind(X)=>(~brave(X)<~>rich(X))))&
(![X]:((curious(X)|quiet(X))=>(calm(X)<~>creative(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|creative(X)))))&
(((~happy(john)&~rich(john)))<=>((generous(lucy)|tall(lucy))))&
(((~creative(fred)|creative(fred)))<=>((~patient(john)|~happy(john))))&
(![X]:((~brave(X)|~creative(X))=>(~tall(X)<~>happy(X))))&
(![X]:((~brave(X)&~kind(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:((~calm(X)&curious(X))))=>((quiet(susan)|~old(susan))))&
(![X]:((old(X)<~>kind(X))<=>(strong(X)|~tall(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>(?[X]:((~patient(X)<~>brave(X)))))&
((strong(john))<=>((~quiet(lucy)<~>~calm(lucy))))&
((?[X]:(creative(X)))=>((calm(john)|~brave(john))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:(quiet(X)=>(~rich(X)|~kind(X))))&
(![X]:((kind(X)&creative(X))<=>(~humble(X)&brave(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
((~creative(lucy)|rich(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:(brave(X)))&
((wise(fred)<~>~quiet(fred))) | ~humble(susan) | [] | null | 0 |
If someone is either old or rich then lucy is either happy or patient.
If someone is not kind then paul is both not strong and kind and vice versa.
Everyone who is both not tall and brave is not old and vice versa.
Everyone who is both not funny and wise is patient or rich.
Everyone who is either not kind or not old is both not curious and patient and vice versa.
Everyone who is not curious or not generous is both curious and not creative and vice versa.
If mary is humble or not creative then someone is strong and vice versa.
If someone is either not calm or patient then someone is happy.
Everyone who is happy is not funny or funny.
If someone is not creative or quiet then mary is not humble or not happy and vice versa.
Everyone who is both not curious and humble is either not funny or patient and vice versa.
If someone is not funny then someone is not humble or not creative and vice versa.
Everyone who is not creative is either not old or not generous.
Everyone who is either humble or not strong is not tall.
Everyone who is both not strong and creative is not generous and vice versa.
If lucy is not calm then someone is happy or not rich and vice versa.
Alice is not tall.
Someone is curious or not generous.
Someone is not generous or not brave.
John is either quiet or not happy. | Mary is rich. | neutral | ((?[X]:((old(X)<~>rich(X))))=>((happy(lucy)<~>patient(lucy))))&
((?[X]:(~kind(X)))<=>((~strong(paul)&kind(paul))))&
(![X]:((~tall(X)&brave(X))<=>~old(X)))&
(![X]:((~funny(X)&wise(X))=>(patient(X)|rich(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(~curious(X)&patient(X))))&
(![X]:((~curious(X)|~generous(X))<=>(curious(X)&~creative(X))))&
(((humble(mary)|~creative(mary)))<=>(?[X]:(strong(X))))&
((?[X]:((~calm(X)<~>patient(X))))=>(?[X]:(happy(X))))&
(![X]:(happy(X)=>(~funny(X)|funny(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>((~humble(mary)|~happy(mary))))&
(![X]:((~curious(X)&humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~humble(X)|~creative(X)))))&
(![X]:(~creative(X)=>(~old(X)<~>~generous(X))))&
(![X]:((humble(X)<~>~strong(X))=>~tall(X)))&
(![X]:((~strong(X)&creative(X))<=>~generous(X)))&
((~calm(lucy))<=>(?[X]:((happy(X)|~rich(X)))))&
(~tall(alice))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((~generous(X)|~brave(X))))&
((quiet(john)<~>~happy(john))) | rich(mary) | [] | null | 0 |
If paul is not quiet or tall then susan is not strong.
If someone is not brave or kind then fred is both not brave and not creative and vice versa.
Everyone who is not tall or not strong is both generous and patient and vice versa.
Everyone who is both not kind and quiet is not patient and vice versa.
Everyone who is not creative or not strong is tall and vice versa.
Everyone who is either old or curious is not quiet.
Everyone who is both quiet and not rich is either patient or rich.
If john is not funny or not happy then someone is both not creative and not humble and vice versa.
Everyone who is curious or not rich is either brave or kind and vice versa.
Everyone who is either rich or quiet is quiet.
Everyone who is both not brave and not humble is not generous or tall and vice versa.
If susan is both patient and happy then someone is either creative or not generous and vice versa.
If lucy is both generous and patient then susan is not kind or funny and vice versa.
If someone is either not old or not generous then someone is not strong.
If someone is either not wise or tall then fred is either not strong or wise and vice versa.
If alice is either not curious or not creative then susan is either old or not curious.
John is not quiet.
Lucy is either wise or not quiet.
Alice is not strong or quiet.
Someone is both strong and not quiet.
Someone is strong.
Someone is humble or calm.
Someone is funny. | John is not creative. | neutral | (((~quiet(paul)|tall(paul)))=>(~strong(susan)))&
((?[X]:((~brave(X)|kind(X))))<=>((~brave(fred)&~creative(fred))))&
(![X]:((~tall(X)|~strong(X))<=>(generous(X)&patient(X))))&
(![X]:((~kind(X)&quiet(X))<=>~patient(X)))&
(![X]:((~creative(X)|~strong(X))<=>tall(X)))&
(![X]:((old(X)<~>curious(X))=>~quiet(X)))&
(![X]:((quiet(X)&~rich(X))=>(patient(X)<~>rich(X))))&
(((~funny(john)|~happy(john)))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((curious(X)|~rich(X))<=>(brave(X)<~>kind(X))))&
(![X]:((rich(X)<~>quiet(X))=>quiet(X)))&
(![X]:((~brave(X)&~humble(X))<=>(~generous(X)|tall(X))))&
(((patient(susan)&happy(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(((generous(lucy)&patient(lucy)))<=>((~kind(susan)|funny(susan))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~strong(fred)<~>wise(fred))))&
(((~curious(alice)<~>~creative(alice)))=>((old(susan)<~>~curious(susan))))&
(~quiet(john))&
((wise(lucy)<~>~quiet(lucy)))&
((~strong(alice)|quiet(alice)))&
(?[X]:((strong(X)&~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(funny(X))) | ~creative(john) | [] | null | 0 |
Everyone who is humble is strong or quiet and vice versa. Everyone who is not funny or calm is brave or patient. If paul is both quiet and tall then fred is either not kind or not curious. Everyone who is not calm or not quiet is both not kind and not generous. If someone is both not funny and curious then someone is creative and vice versa. If lucy is either humble or strong then john is not curious or not generous and vice versa. If lucy is strong or patient then susan is calm and vice versa. If fred is not rich or quiet then someone is either not generous or wise. If someone is both not old and not patient then someone is both not generous and generous and vice versa. If mary is wise then someone is either quiet or rich and vice versa. Everyone who is not kind or not humble is either patient or brave. Everyone who is both humble and rich is not kind or not brave and vice versa. If someone is not quiet or quiet then someone is both quiet and happy. If someone is not funny then susan is funny or tall. Everyone who is patient is curious and vice versa. If someone is either not humble or calm then someone is calm or not humble. Someone is both strong and kind. Someone is not creative. Susan is either not brave or rich. Mary is either not patient or not funny. Someone is brave. Someone is both humble and not kind. Someone is not quiet or quiet. | Susan is curious. | contradiction | (![X]:(humble(X)<=>(strong(X)|quiet(X))))&
(![X]:((~funny(X)|calm(X))=>(brave(X)|patient(X))))&
(((quiet(paul)&tall(paul)))=>((~kind(fred)<~>~curious(fred))))&
(![X]:((~calm(X)|~quiet(X))=>(~kind(X)&~generous(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:(creative(X))))&
(((humble(lucy)<~>strong(lucy)))<=>((~curious(john)|~generous(john))))&
(((strong(lucy)|patient(lucy)))<=>(calm(susan)))&
(((~rich(fred)|quiet(fred)))=>(?[X]:((~generous(X)<~>wise(X)))))&
((?[X]:((~old(X)&~patient(X))))<=>(?[X]:((~generous(X)&generous(X)))))&
((wise(mary))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((~kind(X)|~humble(X))=>(patient(X)<~>brave(X))))&
(![X]:((humble(X)&rich(X))<=>(~kind(X)|~brave(X))))&
((?[X]:((~quiet(X)|quiet(X))))=>(?[X]:((quiet(X)&happy(X)))))&
((?[X]:(~funny(X)))=>((funny(susan)|tall(susan))))&
(![X]:(patient(X)<=>curious(X)))&
((?[X]:((~humble(X)<~>calm(X))))=>(?[X]:((calm(X)|~humble(X)))))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:(~creative(X)))&
((~brave(susan)<~>rich(susan)))&
((~patient(mary)<~>~funny(mary)))&
(?[X]:(brave(X)))&
(?[X]:((humble(X)&~kind(X))))&
(?[X]:((~quiet(X)|quiet(X)))) | curious(susan) | [
"p0",
"p3",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 858245968982312121623213
% SZS output start Proof for 858245968982312121623213
1. ! [X0] : (humble(X0) <=> (quiet(X0) | strong(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (~generous(X0) & ~kind(X0))) [input p3]
11. ! [X0] : ((~humble(X0) | ~kind(X0)) => (patient(X0) <~> brave(X0))) [input p10]
12. ! [X0] : ((rich(X0) & humble(X0)) <=> (~brave(X0) | ~kind(X0))) [input p11]
15. ! [X0] : (patient(X0) <=> curious(X0)) [input p14]
19. ~brave(susan) <~> rich(susan) [input p18]
24. curious(susan) [input hypothesis]
34. ! [X0] : ((~generous(X0) & ~kind(X0)) | (quiet(X0) & calm(X0))) [ennf transformation 4]
36. ! [X0] : ((patient(X0) <~> brave(X0)) | (humble(X0) & kind(X0))) [ennf transformation 11]
41. ! [X0] : ((humble(X0) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | ~humble(X0))) [nnf transformation 1]
42. ! [X0] : ((humble(X0) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | ~humble(X0))) [flattening 41]
65. ! [X0] : (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (humble(X0) & kind(X0))) [nnf transformation 36]
66. ! [X0] : (((rich(X0) & humble(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 12]
67. ! [X0] : (((rich(X0) & humble(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | ~rich(X0) | ~humble(X0))) [flattening 66]
71. ! [X0] : ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))) [nnf transformation 15]
80. (~rich(susan) | brave(susan)) & (rich(susan) | ~brave(susan)) [nnf transformation 19]
90. ~quiet(X0) | humble(X0) [cnf transformation 42]
96. ~kind(X0) | quiet(X0) [cnf transformation 34]
125. ~patient(X0) | ~brave(X0) | kind(X0) [cnf transformation 65]
127. ~rich(X0) | ~kind(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 67]
128. kind(X0) | humble(X0) [cnf transformation 67]
131. rich(X0) | brave(X0) [cnf transformation 67]
136. ~curious(X0) | patient(X0) [cnf transformation 71]
142. rich(susan) | ~brave(susan) [cnf transformation 80]
143. ~rich(susan) | brave(susan) [cnf transformation 80]
150. curious(susan) [cnf transformation 24]
317. brave(susan) [subsumption resolution 143,131]
318. rich(susan) [subsumption resolution 142,317]
339. humble(X0) | quiet(X0) [resolution 128,96]
341. humble(X0) [subsumption resolution 339,90]
348. patient(susan) [resolution 136,150]
440. ~brave(susan) | kind(susan) [resolution 125,348]
458. kind(susan) [subsumption resolution 440,317]
493. ~kind(susan) | ~brave(susan) | ~humble(susan) [resolution 127,318]
496. ~brave(susan) | ~humble(susan) [subsumption resolution 493,458]
497. ~humble(susan) [subsumption resolution 496,317]
498. $false [subsumption resolution 497,341]
% SZS output end Proof for 858245968982312121623213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or creative is either wise or tall. If alice is both not brave and old then paul is not patient. Everyone who is tall is either not wise or not tall. If someone is quiet then someone is both rich and creative and vice versa. If fred is either creative or patient then john is both not old and happy. Everyone who is both not calm and not rich is not curious or not patient and vice versa. Everyone who is both wise and humble is creative or not creative and vice versa. If lucy is either not curious or quiet then someone is both wise and not kind. If susan is both not brave and not generous then john is kind or not calm. If someone is kind or funny then lucy is either happy or not strong. Everyone who is old or quiet is not creative or not calm and vice versa. Everyone who is old is not creative. Everyone who is both wise and patient is not curious and vice versa. If alice is both wise and not old then lucy is not funny or not happy. Everyone who is both calm and not happy is either not kind or not humble. Everyone who is not strong is both tall and strong. Someone is not humble or happy. Someone is patient or brave. Alice is either not curious or funny. Someone is curious. Someone is old or not calm. | Alice is strong. | entailment | (![X]:((brave(X)|creative(X))=>(wise(X)<~>tall(X))))&
(((~brave(alice)&old(alice)))=>(~patient(paul)))&
(![X]:(tall(X)=>(~wise(X)<~>~tall(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((rich(X)&creative(X)))))&
(((creative(fred)<~>patient(fred)))=>((~old(john)&happy(john))))&
(![X]:((~calm(X)&~rich(X))<=>(~curious(X)|~patient(X))))&
(![X]:((wise(X)&humble(X))<=>(creative(X)|~creative(X))))&
(((~curious(lucy)<~>quiet(lucy)))=>(?[X]:((wise(X)&~kind(X)))))&
(((~brave(susan)&~generous(susan)))=>((kind(john)|~calm(john))))&
((?[X]:((kind(X)|funny(X))))=>((happy(lucy)<~>~strong(lucy))))&
(![X]:((old(X)|quiet(X))<=>(~creative(X)|~calm(X))))&
(![X]:(old(X)=>~creative(X)))&
(![X]:((wise(X)&patient(X))<=>~curious(X)))&
(((wise(alice)&~old(alice)))=>((~funny(lucy)|~happy(lucy))))&
(![X]:((calm(X)&~happy(X))=>(~kind(X)<~>~humble(X))))&
(![X]:(~strong(X)=>(tall(X)&strong(X))))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:((patient(X)|brave(X))))&
((~curious(alice)<~>funny(alice)))&
(?[X]:(curious(X)))&
(?[X]:((old(X)|~calm(X)))) | strong(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5807937700222594645410576
% SZS output start Proof for 5807937700222594645410576
16. ! [X0] : (~strong(X0) => (strong(X0) & tall(X0))) [input p15]
22. ~strong(alice) [input hypothesis]
37. ! [X0] : ((strong(X0) & tall(X0)) | strong(X0)) [ennf transformation 16]
112. strong(X0) | strong(X0) [cnf transformation 37]
119. ~strong(alice) [cnf transformation 22]
120. strong(X0) [duplicate literal removal 112]
247. $false [subsumption resolution 119,120]
% SZS output end Proof for 5807937700222594645410576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then susan is either curious or not rich and vice versa.
Everyone who is either calm or old is not happy and vice versa.
If someone is not funny or calm then someone is both not patient and creative.
If paul is either calm or humble then paul is not kind.
Everyone who is either not creative or patient is rich.
Everyone who is both not quiet and calm is either old or not humble and vice versa.
If someone is either funny or rich then someone is not happy or humble and vice versa.
Everyone who is either not happy or brave is not brave or wise and vice versa.
Everyone who is creative or curious is either not generous or not creative and vice versa.
If someone is both not funny and wise then someone is not strong or not calm and vice versa.
Everyone who is either brave or not curious is either not funny or not rich.
Everyone who is funny is both not funny and not curious and vice versa.
If alice is either kind or quiet then alice is rich or not tall.
If alice is not tall or old then fred is humble and vice versa.
If alice is both rich and not happy then john is not quiet and vice versa.
Everyone who is patient is not quiet.
Lucy is not strong or not old.
Someone is not kind.
Susan is quiet or kind.
Someone is not quiet.
Someone is calm.
John is both kind and not brave.
Someone is not funny or not humble.
Someone is not old or not kind. | Susan is quiet. | neutral | ((?[X]:(quiet(X)))<=>((curious(susan)<~>~rich(susan))))&
(![X]:((calm(X)<~>old(X))<=>~happy(X)))&
((?[X]:((~funny(X)|calm(X))))=>(?[X]:((~patient(X)&creative(X)))))&
(((calm(paul)<~>humble(paul)))=>(~kind(paul)))&
(![X]:((~creative(X)<~>patient(X))=>rich(X)))&
(![X]:((~quiet(X)&calm(X))<=>(old(X)<~>~humble(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(~brave(X)|wise(X))))&
(![X]:((creative(X)|curious(X))<=>(~generous(X)<~>~creative(X))))&
((?[X]:((~funny(X)&wise(X))))<=>(?[X]:((~strong(X)|~calm(X)))))&
(![X]:((brave(X)<~>~curious(X))=>(~funny(X)<~>~rich(X))))&
(![X]:(funny(X)<=>(~funny(X)&~curious(X))))&
(((kind(alice)<~>quiet(alice)))=>((rich(alice)|~tall(alice))))&
(((~tall(alice)|old(alice)))<=>(humble(fred)))&
(((rich(alice)&~happy(alice)))<=>(~quiet(john)))&
(![X]:(patient(X)=>~quiet(X)))&
((~strong(lucy)|~old(lucy)))&
(?[X]:(~kind(X)))&
((quiet(susan)|kind(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:(calm(X)))&
((kind(john)&~brave(john)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((~old(X)|~kind(X)))) | quiet(susan) | [] | null | 0 |
If someone is not wise or not calm then someone is either funny or happy.
Everyone who is both not patient and quiet is both generous and not quiet.
Everyone who is calm is either old or not creative.
If fred is both calm and not brave then someone is not strong or not happy and vice versa.
Everyone who is either brave or not strong is quiet or not old and vice versa.
If someone is tall then someone is both wise and old and vice versa.
Everyone who is not funny is calm or funny and vice versa.
Everyone who is either not strong or not happy is creative and vice versa.
If someone is not quiet or not funny then fred is either not old or not wise.
If someone is old or rich then someone is either not patient or creative and vice versa.
Everyone who is funny is both not generous and patient and vice versa.
Everyone who is not rich is either happy or not calm and vice versa.
If someone is either patient or not tall then someone is not happy or not old and vice versa.
Everyone who is wise is tall or not quiet and vice versa.
Everyone who is both not rich and calm is not strong or old and vice versa.
Everyone who is both brave and wise is not kind or funny and vice versa.
Mary is funny or calm.
Someone is both not tall and not wise.
Someone is not quiet.
Someone is curious.
Paul is rich or not quiet. | Fred is not rich. | entailment | ((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((funny(X)<~>happy(X)))))&
(![X]:((~patient(X)&quiet(X))=>(generous(X)&~quiet(X))))&
(![X]:(calm(X)=>(old(X)<~>~creative(X))))&
(((calm(fred)&~brave(fred)))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>(quiet(X)|~old(X))))&
((?[X]:(tall(X)))<=>(?[X]:((wise(X)&old(X)))))&
(![X]:(~funny(X)<=>(calm(X)|funny(X))))&
(![X]:((~strong(X)<~>~happy(X))<=>creative(X)))&
((?[X]:((~quiet(X)|~funny(X))))=>((~old(fred)<~>~wise(fred))))&
((?[X]:((old(X)|rich(X))))<=>(?[X]:((~patient(X)<~>creative(X)))))&
(![X]:(funny(X)<=>(~generous(X)&patient(X))))&
(![X]:(~rich(X)<=>(happy(X)<~>~calm(X))))&
((?[X]:((patient(X)<~>~tall(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:(wise(X)<=>(tall(X)|~quiet(X))))&
(![X]:((~rich(X)&calm(X))<=>(~strong(X)|old(X))))&
(![X]:((brave(X)&wise(X))<=>(~kind(X)|funny(X))))&
((funny(mary)|calm(mary)))&
(?[X]:((~tall(X)&~wise(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(curious(X)))&
((rich(paul)|~quiet(paul))) | ~rich(fred) | [
"p3",
"p4",
"p6",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7637981046675760990525227
% SZS output start Proof for 7637981046675760990525227
4. (~brave(fred) & calm(fred)) <=> ? [X0] : (~happy(X0) | ~strong(X0)) [input p3]
5. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (~old(X0) | quiet(X0))) [input p4]
7. ! [X0] : (~funny(X0) <=> (funny(X0) | calm(X0))) [input p6]
12. ! [X0] : (~rich(X0) <=> (happy(X0) <~> ~calm(X0))) [input p11]
15. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (old(X0) | ~strong(X0))) [input p14]
22. rich(fred) [input hypothesis]
38. ((~brave(fred) & calm(fred)) | ! [X0] : (happy(X0) & strong(X0))) & (? [X0] : (~happy(X0) | ~strong(X0)) | (brave(fred) | ~calm(fred))) [nnf transformation 4]
39. ((~brave(fred) & calm(fred)) | ! [X0] : (happy(X0) & strong(X0))) & (? [X0] : (~happy(X0) | ~strong(X0)) | brave(fred) | ~calm(fred)) [flattening 38]
40. ((~brave(fred) & calm(fred)) | ! [X0] : (happy(X0) & strong(X0))) & (? [X1] : (~happy(X1) | ~strong(X1)) | brave(fred) | ~calm(fred)) [rectify 39]
41. ? [X1] : (~happy(X1) | ~strong(X1)) => (~happy(sK1) | ~strong(sK1)) [choice axiom]
42. ((~brave(fred) & calm(fred)) | ! [X0] : (happy(X0) & strong(X0))) & ((~happy(sK1) | ~strong(sK1)) | brave(fred) | ~calm(fred)) [skolemisation 40,41]
43. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (old(X0) & ~quiet(X0))) & ((~old(X0) | quiet(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 5]
44. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (old(X0) & ~quiet(X0))) & (~old(X0) | quiet(X0) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 43]
50. ! [X0] : ((~funny(X0) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | funny(X0))) [nnf transformation 7]
51. ! [X0] : ((~funny(X0) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | funny(X0))) [flattening 50]
61. ! [X0] : ((~rich(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | rich(X0))) [nnf transformation 12]
69. ! [X0] : (((calm(X0) & ~rich(X0)) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 15]
70. ! [X0] : (((calm(X0) & ~rich(X0)) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | ~calm(X0) | rich(X0))) [flattening 69]
89. ~brave(fred) | happy(X0) [cnf transformation 42]
93. ~strong(X0) | brave(X0) | old(X0) [cnf transformation 44]
99. funny(X0) | calm(X0) | funny(X0) [cnf transformation 51]
101. ~funny(X0) | ~funny(X0) [cnf transformation 51]
121. ~rich(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 61]
133. ~rich(X0) | strong(X0) [cnf transformation 70]
134. ~rich(X0) | ~old(X0) [cnf transformation 70]
147. rich(fred) [cnf transformation 22]
148. funny(X0) | calm(X0) [duplicate literal removal 99]
149. ~funny(X0) [duplicate literal removal 101]
152. 1 <=> ! [X1] : calm(X1) [avatar definition]
153. calm(X1) <- (1) [avatar component clause 152]
170. 5 <=> ! [X0] : happy(X0) [avatar definition]
171. happy(X0) <- (5) [avatar component clause 170]
173. 6 <=> brave(fred) [avatar definition]
176. 5 | ~6 [avatar split clause 89,173,170]
217. calm(X0) [subsumption resolution 148,149]
218. 1 [avatar split clause 217,152]
221. 16 <=> old(fred) [avatar definition]
222. ~old(fred) <- (~16) [avatar component clause 221]
321. strong(fred) [resolution 133,147]
322. ~old(fred) [resolution 134,147]
325. ~16 [avatar split clause 322,221]
340. brave(fred) | old(fred) [resolution 93,321]
344. brave(fred) <- (~16) [subsumption resolution 340,222]
345. 6 | 16 [avatar split clause 344,221,173]
385. ~calm(fred) | ~happy(fred) [resolution 121,147]
387. ~happy(fred) <- (1) [subsumption resolution 385,153]
388. $false <- (1, 5) [subsumption resolution 387,171]
389. ~1 | ~5 [avatar contradiction clause 388]
393. $false [avatar sat refutation 176,218,325,345,389]
% SZS output end Proof for 7637981046675760990525227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not strong or not quiet then paul is either curious or brave and vice versa.
Everyone who is both not curious and curious is not calm or old.
Everyone who is both wise and calm is patient and vice versa.
If someone is both not brave and not kind then alice is funny or brave and vice versa.
Everyone who is not creative is not happy and vice versa.
Everyone who is not funny or calm is curious and vice versa.
Everyone who is either not happy or not kind is not old.
If someone is not kind then lucy is both not funny and tall.
Everyone who is not old or tall is either not strong or happy and vice versa.
If alice is both not old and generous then fred is both strong and wise.
Everyone who is tall is brave and vice versa.
Everyone who is either tall or quiet is both rich and not quiet and vice versa.
If someone is both not rich and strong then susan is either humble or calm.
Everyone who is either not wise or quiet is both not rich and not brave.
If paul is both not brave and not humble then someone is not old or wise and vice versa.
If someone is not kind then alice is either funny or not creative.
Someone is both not generous and creative.
Alice is generous or kind.
Someone is wise.
Alice is either not humble or old.
Paul is both happy and not generous.
Lucy is both humble and not patient.
Susan is strong.
Someone is either wise or not funny. | Fred is strong. | neutral | ((?[X]:((~strong(X)<~>~quiet(X))))<=>((curious(paul)<~>brave(paul))))&
(![X]:((~curious(X)&curious(X))=>(~calm(X)|old(X))))&
(![X]:((wise(X)&calm(X))<=>patient(X)))&
((?[X]:((~brave(X)&~kind(X))))<=>((funny(alice)|brave(alice))))&
(![X]:(~creative(X)<=>~happy(X)))&
(![X]:((~funny(X)|calm(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~kind(X))=>~old(X)))&
((?[X]:(~kind(X)))=>((~funny(lucy)&tall(lucy))))&
(![X]:((~old(X)|tall(X))<=>(~strong(X)<~>happy(X))))&
(((~old(alice)&generous(alice)))=>((strong(fred)&wise(fred))))&
(![X]:(tall(X)<=>brave(X)))&
(![X]:((tall(X)<~>quiet(X))<=>(rich(X)&~quiet(X))))&
((?[X]:((~rich(X)&strong(X))))=>((humble(susan)<~>calm(susan))))&
(![X]:((~wise(X)<~>quiet(X))=>(~rich(X)&~brave(X))))&
(((~brave(paul)&~humble(paul)))<=>(?[X]:((~old(X)|wise(X)))))&
((?[X]:(~kind(X)))=>((funny(alice)<~>~creative(alice))))&
(?[X]:((~generous(X)&creative(X))))&
((generous(alice)|kind(alice)))&
(?[X]:(wise(X)))&
((~humble(alice)<~>old(alice)))&
((happy(paul)&~generous(paul)))&
((humble(lucy)&~patient(lucy)))&
(strong(susan))&
(?[X]:((wise(X)<~>~funny(X)))) | strong(fred) | [] | null | 0 |
If lucy is either not quiet or not wise then lucy is humble or quiet. Everyone who is kind is old or humble. If paul is both kind and old then alice is quiet. Everyone who is both not happy and not curious is both not rich and not generous and vice versa. Everyone who is happy or not curious is both not rich and curious and vice versa. If alice is funny or humble then john is either not brave or not happy. If susan is either tall or humble then paul is both not strong and rich and vice versa. If john is not calm then john is not creative and vice versa. If lucy is not wise or curious then someone is both generous and old. If someone is both not rich and not brave then someone is either patient or quiet and vice versa. Everyone who is not kind or humble is either not old or not patient and vice versa. If lucy is not happy or not humble then someone is either not old or curious and vice versa. Everyone who is either creative or calm is not generous. If susan is not wise then someone is either not wise or not strong and vice versa. If someone is curious or calm then someone is either not tall or tall. Everyone who is either patient or not curious is funny. Paul is both funny and not strong. Mary is both rich and strong. Paul is wise. Someone is tall. Someone is both not rich and not wise. Paul is both patient and not old. Someone is calm. | Lucy is not wise. | neutral | (((~quiet(lucy)<~>~wise(lucy)))=>((humble(lucy)|quiet(lucy))))&
(![X]:(kind(X)=>(old(X)|humble(X))))&
(((kind(paul)&old(paul)))=>(quiet(alice)))&
(![X]:((~happy(X)&~curious(X))<=>(~rich(X)&~generous(X))))&
(![X]:((happy(X)|~curious(X))<=>(~rich(X)&curious(X))))&
(((funny(alice)|humble(alice)))=>((~brave(john)<~>~happy(john))))&
(((tall(susan)<~>humble(susan)))<=>((~strong(paul)&rich(paul))))&
((~calm(john))<=>(~creative(john)))&
(((~wise(lucy)|curious(lucy)))=>(?[X]:((generous(X)&old(X)))))&
((?[X]:((~rich(X)&~brave(X))))<=>(?[X]:((patient(X)<~>quiet(X)))))&
(![X]:((~kind(X)|humble(X))<=>(~old(X)<~>~patient(X))))&
(((~happy(lucy)|~humble(lucy)))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((creative(X)<~>calm(X))=>~generous(X)))&
((~wise(susan))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
((?[X]:((curious(X)|calm(X))))=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((patient(X)<~>~curious(X))=>funny(X)))&
((funny(paul)&~strong(paul)))&
((rich(mary)&strong(mary)))&
(wise(paul))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)&~wise(X))))&
((patient(paul)&~old(paul)))&
(?[X]:(calm(X))) | ~wise(lucy) | [] | null | 0 |
If john is brave or not creative then paul is not tall and vice versa.
Everyone who is not wise or strong is either not generous or patient and vice versa.
Everyone who is not old is curious or not humble and vice versa.
If mary is either quiet or old then someone is both brave and generous.
If alice is both not generous and not rich then someone is either strong or not brave and vice versa.
Everyone who is either not happy or brave is curious or creative and vice versa.
If someone is both not wise and rich then someone is humble and vice versa.
Everyone who is either patient or kind is calm and vice versa.
Everyone who is both not creative and wise is not brave or rich and vice versa.
Everyone who is not funny or wise is both quiet and not kind and vice versa.
Everyone who is either not curious or happy is either humble or not generous.
If someone is not wise or brave then lucy is not humble and vice versa.
If someone is both strong and quiet then susan is calm and vice versa.
Everyone who is either tall or not brave is both strong and not generous and vice versa.
If someone is humble then alice is wise and vice versa.
If someone is not calm or not creative then someone is patient.
Susan is either humble or not curious.
Fred is brave or not kind.
John is not funny.
Mary is quiet.
Paul is not creative or kind.
Alice is not quiet or not old.
Someone is either not humble or brave. | Lucy is generous. | neutral | (((brave(john)|~creative(john)))<=>(~tall(paul)))&
(![X]:((~wise(X)|strong(X))<=>(~generous(X)<~>patient(X))))&
(![X]:(~old(X)<=>(curious(X)|~humble(X))))&
(((quiet(mary)<~>old(mary)))=>(?[X]:((brave(X)&generous(X)))))&
(((~generous(alice)&~rich(alice)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(curious(X)|creative(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>calm(X)))&
(![X]:((~creative(X)&wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~funny(X)|wise(X))<=>(quiet(X)&~kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~generous(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~humble(lucy)))&
((?[X]:((strong(X)&quiet(X))))<=>(calm(susan)))&
(![X]:((tall(X)<~>~brave(X))<=>(strong(X)&~generous(X))))&
((?[X]:(humble(X)))<=>(wise(alice)))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:(patient(X))))&
((humble(susan)<~>~curious(susan)))&
((brave(fred)|~kind(fred)))&
(~funny(john))&
(quiet(mary))&
((~creative(paul)|kind(paul)))&
((~quiet(alice)|~old(alice)))&
(?[X]:((~humble(X)<~>brave(X)))) | generous(lucy) | [] | null | 0 |
If mary is either not patient or patient then someone is quiet or not humble.
If someone is both not curious and brave then someone is either not generous or not kind.
If someone is not rich or not quiet then lucy is kind and vice versa.
Everyone who is not brave or not patient is both old and not curious and vice versa.
If someone is not humble then someone is not curious.
If john is creative or not wise then alice is not strong.
If someone is not kind or not creative then someone is both not old and not humble and vice versa.
If someone is both not creative and not tall then mary is not rich.
Everyone who is both not tall and not wise is happy or curious and vice versa.
Everyone who is calm is either quiet or not kind.
If lucy is both not creative and not strong then someone is rich or humble.
Everyone who is either not funny or funny is not patient or not old.
Everyone who is tall is either happy or not creative.
Everyone who is both quiet and not calm is either funny or not happy and vice versa.
If john is not rich or not patient then john is both not quiet and not brave.
Everyone who is both not patient and happy is not old and vice versa.
Someone is both not humble and rich.
Mary is rich.
Someone is both not humble and not tall.
John is not curious.
Someone is both not tall and kind.
Fred is not funny or curious. | Mary is tall. | contradiction | (((~patient(mary)<~>patient(mary)))=>(?[X]:((quiet(X)|~humble(X)))))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
((?[X]:((~rich(X)|~quiet(X))))<=>(kind(lucy)))&
(![X]:((~brave(X)|~patient(X))<=>(old(X)&~curious(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~curious(X))))&
(((creative(john)|~wise(john)))=>(~strong(alice)))&
((?[X]:((~kind(X)|~creative(X))))<=>(?[X]:((~old(X)&~humble(X)))))&
((?[X]:((~creative(X)&~tall(X))))=>(~rich(mary)))&
(![X]:((~tall(X)&~wise(X))<=>(happy(X)|curious(X))))&
(![X]:(calm(X)=>(quiet(X)<~>~kind(X))))&
(((~creative(lucy)&~strong(lucy)))=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((~funny(X)<~>funny(X))=>(~patient(X)|~old(X))))&
(![X]:(tall(X)=>(happy(X)<~>~creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(funny(X)<~>~happy(X))))&
(((~rich(john)|~patient(john)))=>((~quiet(john)&~brave(john))))&
(![X]:((~patient(X)&happy(X))<=>~old(X)))&
(?[X]:((~humble(X)&rich(X))))&
(rich(mary))&
(?[X]:((~humble(X)&~tall(X))))&
(~curious(john))&
(?[X]:((~tall(X)&kind(X))))&
((~funny(fred)|curious(fred))) | tall(mary) | [
"p3",
"p6",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7721642793322796827600978
% SZS output start Proof for 7721642793322796827600978
4. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> (~curious(X0) & old(X0))) [input p3]
7. ? [X0] : (~creative(X0) | ~kind(X0)) <=> ? [X0] : (~humble(X0) & ~old(X0)) [input p6]
9. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (curious(X0) | happy(X0))) [input p8]
13. ! [X0] : (tall(X0) => (happy(X0) <~> ~creative(X0))) [input p12]
16. ! [X0] : ((happy(X0) & ~patient(X0)) <=> ~old(X0)) [input p15]
23. tall(mary) [input hypothesis]
26. ? [X0] : (~creative(X0) | ~kind(X0)) <=> ? [X1] : (~humble(X1) & ~old(X1)) [rectify 7]
37. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~tall(X0)) [ennf transformation 13]
50. ! [X0] : (((~patient(X0) | ~brave(X0)) | (curious(X0) | ~old(X0))) & ((~curious(X0) & old(X0)) | (patient(X0) & brave(X0)))) [nnf transformation 4]
51. ! [X0] : ((~patient(X0) | ~brave(X0) | curious(X0) | ~old(X0)) & ((~curious(X0) & old(X0)) | (patient(X0) & brave(X0)))) [flattening 50]
55. (? [X0] : (~creative(X0) | ~kind(X0)) | ! [X1] : (humble(X1) | old(X1))) & (? [X1] : (~humble(X1) & ~old(X1)) | ! [X0] : (creative(X0) & kind(X0))) [nnf transformation 26]
56. (? [X0] : (~creative(X0) | ~kind(X0)) | ! [X1] : (humble(X1) | old(X1))) & (? [X2] : (~humble(X2) & ~old(X2)) | ! [X3] : (creative(X3) & kind(X3))) [rectify 55]
57. ? [X0] : (~creative(X0) | ~kind(X0)) => (~creative(sK4) | ~kind(sK4)) [choice axiom]
58. ? [X2] : (~humble(X2) & ~old(X2)) => (~humble(sK5) & ~old(sK5)) [choice axiom]
59. ((~creative(sK4) | ~kind(sK4)) | ! [X1] : (humble(X1) | old(X1))) & ((~humble(sK5) & ~old(sK5)) | ! [X3] : (creative(X3) & kind(X3))) [skolemisation 56,58,57]
60. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 9]
61. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | wise(X0) | tall(X0))) [flattening 60]
66. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~tall(X0)) [nnf transformation 37]
69. ! [X0] : (((happy(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | (~happy(X0) | patient(X0)))) [nnf transformation 16]
70. ! [X0] : (((happy(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | ~happy(X0) | patient(X0))) [flattening 69]
85. old(X0) | patient(X0) [cnf transformation 51]
93. ~old(sK5) | creative(X3) [cnf transformation 59]
99. ~happy(X0) | ~tall(X0) [cnf transformation 61]
108. ~creative(X0) | happy(X0) | ~tall(X0) [cnf transformation 66]
121. ~patient(X0) | old(X0) [cnf transformation 70]
132. tall(mary) [cnf transformation 23]
220. 20 <=> ! [X3] : creative(X3) [avatar definition]
221. creative(X3) <- (20) [avatar component clause 220]
232. 23 <=> old(sK5) [avatar definition]
234. ~old(sK5) <- (~23) [avatar component clause 232]
235. 20 | ~23 [avatar split clause 93,232,220]
263. ~tall(X0) | ~creative(X0) [subsumption resolution 108,99]
284. old(X0) [subsumption resolution 121,85]
296. $false <- (~23) [subsumption resolution 234,284]
297. 23 [avatar contradiction clause 296]
311. ~creative(mary) [resolution 263,132]
313. $false <- (20) [subsumption resolution 311,221]
314. ~20 [avatar contradiction clause 313]
315. $false [avatar sat refutation 235,297,314]
% SZS output end Proof for 7721642793322796827600978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is happy or not wise and vice versa.
Everyone who is not old is both not quiet and creative and vice versa.
If someone is either kind or not happy then lucy is both not rich and old and vice versa.
Everyone who is rich or not kind is both not happy and not creative and vice versa.
If someone is curious or generous then susan is either patient or old.
Everyone who is humble or not old is not humble or happy.
If paul is not rich then paul is either not patient or not kind.
Everyone who is calm or not happy is humble or wise.
If someone is strong or wise then someone is either not calm or calm and vice versa.
Everyone who is not old or rich is patient.
Everyone who is either patient or not patient is both not brave and not wise and vice versa.
Everyone who is kind or not creative is both happy and not calm.
If lucy is both not quiet and wise then someone is not wise.
If lucy is either not calm or not humble then paul is both generous and not wise.
Alice is either calm or patient.
Paul is both not calm and old.
Someone is either funny or not generous.
Someone is not quiet.
Mary is not patient or rich. | Alice is not quiet. | neutral | (![X]:(generous(X)<=>(happy(X)|~wise(X))))&
(![X]:(~old(X)<=>(~quiet(X)&creative(X))))&
((?[X]:((kind(X)<~>~happy(X))))<=>((~rich(lucy)&old(lucy))))&
(![X]:((rich(X)|~kind(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((curious(X)|generous(X))))=>((patient(susan)<~>old(susan))))&
(![X]:((humble(X)|~old(X))=>(~humble(X)|happy(X))))&
((~rich(paul))=>((~patient(paul)<~>~kind(paul))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)|wise(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~old(X)|rich(X))=>patient(X)))&
(![X]:((patient(X)<~>~patient(X))<=>(~brave(X)&~wise(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&~calm(X))))&
(((~quiet(lucy)&wise(lucy)))=>(?[X]:(~wise(X))))&
(((~calm(lucy)<~>~humble(lucy)))=>((generous(paul)&~wise(paul))))&
((calm(alice)<~>patient(alice)))&
((~calm(paul)&old(paul)))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:(~quiet(X)))&
((~patient(mary)|rich(mary))) | ~quiet(alice) | [] | null | 0 |
Everyone who is both not tall and funny is either not curious or generous. Everyone who is not generous or not old is creative. Everyone who is funny is either not creative or tall and vice versa. If alice is either not happy or not generous then paul is calm and vice versa. Everyone who is not funny is not generous. Everyone who is not quiet is patient or quiet. If susan is either not kind or not generous then paul is not curious. Everyone who is either not calm or creative is either rich or not rich and vice versa. If someone is patient then someone is not strong or not rich. Everyone who is not rich is not tall. If someone is not kind or not strong then someone is either calm or rich and vice versa. Everyone who is both not rich and not patient is strong and vice versa. Everyone who is creative or patient is not rich and vice versa. If lucy is either not tall or not old then mary is both not wise and strong. Everyone who is not quiet or old is not creative. If someone is both curious and old then john is either not patient or not wise. Fred is funny. Someone is either old or not tall. Someone is tall or not tall. Fred is rich or generous. Susan is both not kind and funny. Someone is brave. Lucy is not kind. Alice is creative or not kind. | Paul is not generous. | entailment | (![X]:((~tall(X)&funny(X))=>(~curious(X)<~>generous(X))))&
(![X]:((~generous(X)|~old(X))=>creative(X)))&
(![X]:(funny(X)<=>(~creative(X)<~>tall(X))))&
(((~happy(alice)<~>~generous(alice)))<=>(calm(paul)))&
(![X]:(~funny(X)=>~generous(X)))&
(![X]:(~quiet(X)=>(patient(X)|quiet(X))))&
(((~kind(susan)<~>~generous(susan)))=>(~curious(paul)))&
(![X]:((~calm(X)<~>creative(X))<=>(rich(X)<~>~rich(X))))&
((?[X]:(patient(X)))=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:(~rich(X)=>~tall(X)))&
((?[X]:((~kind(X)|~strong(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~rich(X)&~patient(X))<=>strong(X)))&
(![X]:((creative(X)|patient(X))<=>~rich(X)))&
(((~tall(lucy)<~>~old(lucy)))=>((~wise(mary)&strong(mary))))&
(![X]:((~quiet(X)|old(X))=>~creative(X)))&
((?[X]:((curious(X)&old(X))))=>((~patient(john)<~>~wise(john))))&
(funny(fred))&
(?[X]:((old(X)<~>~tall(X))))&
(?[X]:((tall(X)|~tall(X))))&
((rich(fred)|generous(fred)))&
((~kind(susan)&funny(susan)))&
(?[X]:(brave(X)))&
(~kind(lucy))&
((creative(alice)|~kind(alice))) | ~generous(paul) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p9",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8892417142990746151640537
% SZS output start Proof for 8892417142990746151640537
1. ! [X0] : ((funny(X0) & ~tall(X0)) => (~curious(X0) <~> generous(X0))) [input p0]
2. ! [X0] : ((~old(X0) | ~generous(X0)) => creative(X0)) [input p1]
3. ! [X0] : (funny(X0) <=> (~creative(X0) <~> tall(X0))) [input p2]
5. ! [X0] : (~funny(X0) => ~generous(X0)) [input p4]
7. (~kind(susan) <~> ~generous(susan)) => ~curious(paul) [input p6]
10. ! [X0] : (~rich(X0) => ~tall(X0)) [input p9]
13. ! [X0] : ((patient(X0) | creative(X0)) <=> ~rich(X0)) [input p12]
21. funny(susan) & ~kind(susan) [input p20]
25. generous(paul) [input hypothesis]
31. ! [X0] : ((~curious(X0) <~> generous(X0)) | (~funny(X0) | tall(X0))) [ennf transformation 1]
32. ! [X0] : ((~curious(X0) <~> generous(X0)) | ~funny(X0) | tall(X0)) [flattening 31]
33. ! [X0] : (creative(X0) | (old(X0) & generous(X0))) [ennf transformation 2]
34. ! [X0] : (~generous(X0) | funny(X0)) [ennf transformation 5]
35. ~curious(paul) | (~kind(susan) <=> ~generous(susan)) [ennf transformation 7]
37. ! [X0] : (~tall(X0) | rich(X0)) [ennf transformation 10]
41. ! [X0] : (((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | ~funny(X0) | tall(X0)) [nnf transformation 32]
42. ! [X0] : ((funny(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) & (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ~funny(X0))) [nnf transformation 3]
44. ~curious(paul) | ((~kind(susan) | generous(susan)) & (~generous(susan) | kind(susan))) [nnf transformation 35]
56. ! [X0] : (((patient(X0) | creative(X0)) | rich(X0)) & (~rich(X0) | (~patient(X0) & ~creative(X0)))) [nnf transformation 13]
57. ! [X0] : ((patient(X0) | creative(X0) | rich(X0)) & (~rich(X0) | (~patient(X0) & ~creative(X0)))) [flattening 56]
66. ~generous(X0) | curious(X0) | ~funny(X0) | tall(X0) [cnf transformation 41]
67. creative(X0) | generous(X0) [cnf transformation 33]
69. ~creative(X0) | tall(X0) | ~funny(X0) [cnf transformation 42]
70. ~funny(X0) | creative(X0) | ~tall(X0) [cnf transformation 42]
77. ~generous(X0) | funny(X0) [cnf transformation 34]
78. ~curious(paul) | ~generous(susan) | kind(susan) [cnf transformation 44]
89. ~tall(X0) | rich(X0) [cnf transformation 37]
99. ~rich(X0) | ~creative(X0) [cnf transformation 57]
114. ~kind(susan) [cnf transformation 21]
115. funny(susan) [cnf transformation 21]
118. generous(paul) [cnf transformation 25]
140. 4 <=> generous(susan) [avatar definition]
144. 5 <=> kind(susan) [avatar definition]
148. 6 <=> curious(paul) [avatar definition]
152. 5 | ~4 | ~6 [avatar split clause 78,148,140,144]
253. ~5 [avatar split clause 114,144]
263. funny(paul) [resolution 77,118]
279. ~funny(X1) | tall(X1) | generous(X1) [resolution 69,67]
291. creative(susan) | ~tall(susan) [resolution 70,115]
292. creative(paul) | ~tall(paul) [resolution 70,263]
295. 33 <=> tall(susan) [avatar definition]
296. tall(susan) <- (33) [avatar component clause 295]
299. 34 <=> creative(susan) [avatar definition]
301. creative(susan) <- (34) [avatar component clause 299]
302. ~33 | 34 [avatar split clause 291,299,295]
304. 35 <=> tall(paul) [avatar definition]
305. tall(paul) <- (35) [avatar component clause 304]
308. 36 <=> creative(paul) [avatar definition]
310. creative(paul) <- (36) [avatar component clause 308]
311. ~35 | 36 [avatar split clause 292,308,304]
360. curious(paul) | ~funny(paul) | tall(paul) [resolution 66,118]
362. curious(paul) | tall(paul) [subsumption resolution 360,263]
386. tall(susan) | generous(susan) [resolution 279,115]
399. rich(susan) <- (33) [resolution 296,89]
410. ~creative(susan) <- (33) [resolution 399,99]
411. $false <- (33, 34) [subsumption resolution 410,301]
412. ~33 | ~34 [avatar contradiction clause 411]
413. 4 | 33 [avatar split clause 386,295,140]
414. 35 | 6 [avatar split clause 362,148,304]
424. rich(paul) <- (35) [resolution 305,89]
443. ~creative(paul) <- (35) [resolution 424,99]
444. $false <- (35, 36) [subsumption resolution 443,310]
445. ~35 | ~36 [avatar contradiction clause 444]
446. $false [avatar sat refutation 152,253,302,311,412,413,414,445]
% SZS output end Proof for 8892417142990746151640537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not brave or funny then lucy is both not generous and not quiet and vice versa.
If someone is humble then someone is happy or not wise and vice versa.
If someone is either wise or not humble then someone is creative and vice versa.
Everyone who is either not rich or rich is both strong and not old and vice versa.
Everyone who is both creative and calm is not rich and vice versa.
If someone is not wise then susan is both not wise and happy and vice versa.
If susan is not rich or curious then someone is not strong or curious.
Everyone who is either brave or rich is not curious or not kind.
If someone is either not curious or not generous then john is either not tall or not wise.
Everyone who is not patient is not quiet and vice versa.
Everyone who is not patient is quiet.
If alice is not brave then someone is either not humble or not curious and vice versa.
If someone is either kind or not quiet then fred is either not curious or old.
Everyone who is not calm or not rich is both creative and not rich.
If susan is both not wise and quiet then someone is happy or not kind.
Paul is either not brave or curious.
Alice is kind or not quiet.
Susan is kind.
Lucy is not generous or tall.
Mary is not tall.
Fred is either not kind or wise. | Susan is not brave. | contradiction | ((?[X]:((~brave(X)|funny(X))))<=>((~generous(lucy)&~quiet(lucy))))&
((?[X]:(humble(X)))<=>(?[X]:((happy(X)|~wise(X)))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:(creative(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(strong(X)&~old(X))))&
(![X]:((creative(X)&calm(X))<=>~rich(X)))&
((?[X]:(~wise(X)))<=>((~wise(susan)&happy(susan))))&
(((~rich(susan)|curious(susan)))=>(?[X]:((~strong(X)|curious(X)))))&
(![X]:((brave(X)<~>rich(X))=>(~curious(X)|~kind(X))))&
((?[X]:((~curious(X)<~>~generous(X))))=>((~tall(john)<~>~wise(john))))&
(![X]:(~patient(X)<=>~quiet(X)))&
(![X]:(~patient(X)=>quiet(X)))&
((~brave(alice))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
((?[X]:((kind(X)<~>~quiet(X))))=>((~curious(fred)<~>old(fred))))&
(![X]:((~calm(X)|~rich(X))=>(creative(X)&~rich(X))))&
(((~wise(susan)&quiet(susan)))=>(?[X]:((happy(X)|~kind(X)))))&
((~brave(paul)<~>curious(paul)))&
((kind(alice)|~quiet(alice)))&
(kind(susan))&
((~generous(lucy)|tall(lucy)))&
(~tall(mary))&
((~kind(fred)<~>wise(fred))) | ~brave(susan) | [
"p0",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1089415284134344893238042
% SZS output start Proof for 1089415284134344893238042
1. ? [X0] : (funny(X0) | ~brave(X0)) <=> (~quiet(lucy) & ~generous(lucy)) [input p0]
10. ! [X0] : (~patient(X0) <=> ~quiet(X0)) [input p9]
11. ! [X0] : (~patient(X0) => quiet(X0)) [input p10]
22. ~brave(susan) [input hypothesis]
25. ! [X0] : (~quiet(X0) => ~patient(X0)) [unused predicate definition removal 10]
30. ! [X0] : (~patient(X0) | quiet(X0)) [ennf transformation 25]
31. ! [X0] : (quiet(X0) | patient(X0)) [ennf transformation 11]
36. (? [X0] : (funny(X0) | ~brave(X0)) | (quiet(lucy) | generous(lucy))) & ((~quiet(lucy) & ~generous(lucy)) | ! [X0] : (~funny(X0) & brave(X0))) [nnf transformation 1]
37. (? [X0] : (funny(X0) | ~brave(X0)) | quiet(lucy) | generous(lucy)) & ((~quiet(lucy) & ~generous(lucy)) | ! [X0] : (~funny(X0) & brave(X0))) [flattening 36]
38. (? [X0] : (funny(X0) | ~brave(X0)) | quiet(lucy) | generous(lucy)) & ((~quiet(lucy) & ~generous(lucy)) | ! [X1] : (~funny(X1) & brave(X1))) [rectify 37]
39. ? [X0] : (funny(X0) | ~brave(X0)) => (funny(sK0) | ~brave(sK0)) [choice axiom]
40. ((funny(sK0) | ~brave(sK0)) | quiet(lucy) | generous(lucy)) & ((~quiet(lucy) & ~generous(lucy)) | ! [X1] : (~funny(X1) & brave(X1))) [skolemisation 38,39]
75. ~quiet(lucy) | brave(X1) [cnf transformation 40]
105. ~patient(X0) | quiet(X0) [cnf transformation 30]
106. quiet(X0) | patient(X0) [cnf transformation 31]
128. ~brave(susan) [cnf transformation 22]
138. 2 <=> quiet(lucy) [avatar definition]
139. ~quiet(lucy) <- (~2) [avatar component clause 138]
155. 6 <=> ! [X1] : brave(X1) [avatar definition]
156. brave(X1) <- (6) [avatar component clause 155]
157. 6 | ~2 [avatar split clause 75,138,155]
260. quiet(X0) [subsumption resolution 106,105]
330. $false <- (~2) [subsumption resolution 139,260]
331. 2 [avatar contradiction clause 330]
332. $false <- (6) [resolution 156,128]
335. ~6 [avatar contradiction clause 332]
336. $false [avatar sat refutation 157,331,335]
% SZS output end Proof for 1089415284134344893238042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or curious is wise.
If paul is either brave or not brave then someone is not wise or old.
If someone is not curious or quiet then alice is either humble or not kind and vice versa.
If someone is not happy then someone is humble.
If someone is not tall or not brave then someone is both not tall and wise and vice versa.
Everyone who is creative or wise is quiet.
If someone is both happy and quiet then alice is either not strong or not creative and vice versa.
Everyone who is not humble or not tall is both not patient and not brave and vice versa.
Everyone who is either curious or not generous is not funny or not curious and vice versa.
If someone is either not rich or rich then paul is either quiet or not rich.
Everyone who is not funny is not happy or quiet and vice versa.
Everyone who is either creative or not humble is generous.
Everyone who is wise is not kind.
Everyone who is either not brave or not quiet is kind and vice versa.
Everyone who is either curious or patient is not tall.
If someone is not old or generous then someone is not brave and vice versa.
Susan is old.
Paul is either quiet or not old.
Someone is wise or not kind.
Mary is either not funny or not creative.
Mary is both not strong and not rich.
Alice is tall. | Alice is not creative. | entailment | (![X]:((generous(X)<~>curious(X))=>wise(X)))&
(((brave(paul)<~>~brave(paul)))=>(?[X]:((~wise(X)|old(X)))))&
((?[X]:((~curious(X)|quiet(X))))<=>((humble(alice)<~>~kind(alice))))&
((?[X]:(~happy(X)))=>(?[X]:(humble(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((creative(X)|wise(X))=>quiet(X)))&
((?[X]:((happy(X)&quiet(X))))<=>((~strong(alice)<~>~creative(alice))))&
(![X]:((~humble(X)|~tall(X))<=>(~patient(X)&~brave(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~rich(X)<~>rich(X))))=>((quiet(paul)<~>~rich(paul))))&
(![X]:(~funny(X)<=>(~happy(X)|quiet(X))))&
(![X]:((creative(X)<~>~humble(X))=>generous(X)))&
(![X]:(wise(X)=>~kind(X)))&
(![X]:((~brave(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((curious(X)<~>patient(X))=>~tall(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:(~brave(X))))&
(old(susan))&
((quiet(paul)<~>~old(paul)))&
(?[X]:((wise(X)|~kind(X))))&
((~funny(mary)<~>~creative(mary)))&
((~strong(mary)&~rich(mary)))&
(tall(alice)) | ~creative(alice) | [
"p4",
"p5",
"p7",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2201438045068929426296524
% SZS output start Proof for 2201438045068929426296524
5. ? [X0] : (~brave(X0) | ~tall(X0)) <=> ? [X0] : (wise(X0) & ~tall(X0)) [input p4]
6. ! [X0] : ((wise(X0) | creative(X0)) => quiet(X0)) [input p5]
8. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~brave(X0) & ~patient(X0))) [input p7]
12. ! [X0] : ((creative(X0) <~> ~humble(X0)) => generous(X0)) [input p11]
13. ! [X0] : (wise(X0) => ~kind(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) <=> kind(X0)) [input p13]
16. ? [X0] : (generous(X0) | ~old(X0)) <=> ? [X0] : ~brave(X0) [input p15]
23. creative(alice) [input hypothesis]
25. ? [X0] : (~brave(X0) | ~tall(X0)) <=> ? [X1] : (wise(X1) & ~tall(X1)) [rectify 5]
26. ? [X0] : (generous(X0) | ~old(X0)) <=> ? [X1] : ~brave(X1) [rectify 16]
30. ! [X0] : (quiet(X0) | (~wise(X0) & ~creative(X0))) [ennf transformation 6]
32. ! [X0] : (generous(X0) | (creative(X0) <=> ~humble(X0))) [ennf transformation 12]
33. ! [X0] : (~kind(X0) | ~wise(X0)) [ennf transformation 13]
46. (? [X0] : (~brave(X0) | ~tall(X0)) | ! [X1] : (~wise(X1) | tall(X1))) & (? [X1] : (wise(X1) & ~tall(X1)) | ! [X0] : (brave(X0) & tall(X0))) [nnf transformation 25]
47. (? [X0] : (~brave(X0) | ~tall(X0)) | ! [X1] : (~wise(X1) | tall(X1))) & (? [X2] : (wise(X2) & ~tall(X2)) | ! [X3] : (brave(X3) & tall(X3))) [rectify 46]
48. ? [X0] : (~brave(X0) | ~tall(X0)) => (~brave(sK3) | ~tall(sK3)) [choice axiom]
49. ? [X2] : (wise(X2) & ~tall(X2)) => (wise(sK4) & ~tall(sK4)) [choice axiom]
50. ((~brave(sK3) | ~tall(sK3)) | ! [X1] : (~wise(X1) | tall(X1))) & ((wise(sK4) & ~tall(sK4)) | ! [X3] : (brave(X3) & tall(X3))) [skolemisation 47,49,48]
55. ! [X0] : (((~tall(X0) | ~humble(X0)) | (brave(X0) | patient(X0))) & ((~brave(X0) & ~patient(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 8]
56. ! [X0] : ((~tall(X0) | ~humble(X0) | brave(X0) | patient(X0)) & ((~brave(X0) & ~patient(X0)) | (tall(X0) & humble(X0)))) [flattening 55]
62. ! [X0] : (generous(X0) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) [nnf transformation 32]
63. ! [X0] : ((((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ~kind(X0)) & (kind(X0) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0))))) [nnf transformation 14]
65. (? [X0] : (generous(X0) | ~old(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (~generous(X0) & old(X0))) [nnf transformation 26]
66. (? [X0] : (generous(X0) | ~old(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (~generous(X3) & old(X3))) [rectify 65]
67. ? [X0] : (generous(X0) | ~old(X0)) => (generous(sK6) | ~old(sK6)) [choice axiom]
68. ? [X2] : ~brave(X2) => ~brave(sK7) [choice axiom]
69. ((generous(sK6) | ~old(sK6)) | ! [X1] : brave(X1)) & (~brave(sK7) | ! [X3] : (~generous(X3) & old(X3))) [skolemisation 66,68,67]
86. ~tall(sK4) | brave(X3) [cnf transformation 50]
87. wise(sK4) | tall(X3) [cnf transformation 50]
91. ~wise(X0) | quiet(X0) [cnf transformation 30]
100. ~brave(X0) | humble(X0) [cnf transformation 56]
101. ~brave(X0) | tall(X0) [cnf transformation 56]
116. ~creative(X0) | ~humble(X0) | generous(X0) [cnf transformation 62]
118. ~kind(X0) | ~wise(X0) [cnf transformation 33]
119. ~quiet(X0) | kind(X0) | brave(X0) [cnf transformation 63]
126. ~brave(sK7) | ~generous(X3) [cnf transformation 69]
137. creative(alice) [cnf transformation 23]
165. 5 <=> humble(alice) [avatar definition]
166. ~humble(alice) <- (~5) [avatar component clause 165]
209. 15 <=> ! [X3] : brave(X3) [avatar definition]
210. brave(X3) <- (15) [avatar component clause 209]
212. 16 <=> wise(sK4) [avatar definition]
214. wise(sK4) <- (16) [avatar component clause 212]
217. 17 <=> ! [X3] : tall(X3) [avatar definition]
218. tall(X3) <- (17) [avatar component clause 217]
219. 17 | 16 [avatar split clause 87,212,217]
221. 18 <=> tall(sK4) [avatar definition]
223. ~tall(sK4) <- (~18) [avatar component clause 221]
224. 15 | ~18 [avatar split clause 86,221,209]
227. 19 <=> creative(alice) [avatar definition]
229. creative(alice) <- (19) [avatar component clause 227]
281. 30 <=> ! [X3] : ~generous(X3) [avatar definition]
282. ~generous(X3) <- (30) [avatar component clause 281]
284. 31 <=> brave(sK7) [avatar definition]
286. ~brave(sK7) <- (~31) [avatar component clause 284]
287. 30 | ~31 [avatar split clause 126,284,281]
309. 19 [avatar split clause 137,227]
320. ~humble(alice) | generous(alice) <- (19) [resolution 116,229]
341. 38 <=> brave(sK4) [avatar definition]
343. brave(sK4) <- (38) [avatar component clause 341]
345. 39 <=> kind(sK4) [avatar definition]
347. kind(sK4) <- (39) [avatar component clause 345]
355. $false <- (15, ~31) [resolution 210,286]
357. humble(X1) <- (15) [resolution 210,100]
358. ~15 | 31 [avatar contradiction clause 355]
362. $false <- (17, ~18) [resolution 218,223]
363. ~17 | 18 [avatar contradiction clause 362]
376. $false <- (~5, 15) [resolution 357,166]
377. 5 | ~15 [avatar contradiction clause 376]
397. quiet(sK4) <- (16) [resolution 214,91]
401. kind(sK4) | brave(sK4) <- (16) [resolution 397,119]
412. ~humble(alice) <- (19, 30) [subsumption resolution 320,282]
413. ~5 | ~19 | ~30 [avatar split clause 412,281,227,165]
467. tall(sK4) <- (38) [resolution 343,101]
469. $false <- (~18, 38) [subsumption resolution 467,223]
470. 18 | ~38 [avatar contradiction clause 469]
471. 38 | 39 | ~16 [avatar split clause 401,212,345,341]
474. ~wise(sK4) <- (39) [resolution 347,118]
475. $false <- (16, 39) [subsumption resolution 474,214]
476. ~16 | ~39 [avatar contradiction clause 475]
477. $false [avatar sat refutation 219,224,287,309,358,363,377,413,470,471,476]
% SZS output end Proof for 2201438045068929426296524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not tall is either not curious or curious and vice versa.
Everyone who is rich or patient is both not curious and calm.
Everyone who is not patient or calm is both not creative and not calm and vice versa.
If mary is either not quiet or kind then paul is either humble or quiet and vice versa.
If mary is kind then alice is tall and vice versa.
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.
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.
Mary is not generous.
John is not wise or curious.
Someone is either quiet or strong.
Someone is generous or happy.
Paul is either not brave or funny. | Paul is not rich. | entailment | (![X]:((strong(X)|~tall(X))<=>(~curious(X)<~>curious(X))))&
(![X]:((rich(X)|patient(X))=>(~curious(X)&calm(X))))&
(![X]:((~patient(X)|calm(X))<=>(~creative(X)&~calm(X))))&
(((~quiet(mary)<~>kind(mary)))<=>((humble(paul)<~>quiet(paul))))&
((kind(mary))<=>(tall(alice)))&
((?[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]:((~funny(X)|curious(X))<=>(funny(X)&happy(X))))&
((?[X]:((old(X)<~>quiet(X))))<=>(?[X]:((~happy(X)&~humble(X)))))&
(~generous(mary))&
((~wise(john)|curious(john)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((generous(X)|happy(X))))&
((~brave(paul)<~>funny(paul))) | ~rich(paul) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1071132235233978121956487
% SZS output start Proof for 1071132235233978121956487
2. ! [X0] : ((patient(X0) | rich(X0)) => (calm(X0) & ~curious(X0))) [input p1]
3. ! [X0] : ((calm(X0) | ~patient(X0)) <=> (~calm(X0) & ~creative(X0))) [input p2]
20. rich(paul) [input hypothesis]
23. ! [X0] : ((calm(X0) & ~curious(X0)) | (~patient(X0) & ~rich(X0))) [ennf transformation 2]
33. ! [X0] : (((calm(X0) | ~patient(X0)) | (calm(X0) | creative(X0))) & ((~calm(X0) & ~creative(X0)) | (~calm(X0) & patient(X0)))) [nnf transformation 3]
34. ! [X0] : ((calm(X0) | ~patient(X0) | calm(X0) | creative(X0)) & ((~calm(X0) & ~creative(X0)) | (~calm(X0) & patient(X0)))) [flattening 33]
62. ~rich(X0) | calm(X0) [cnf transformation 23]
67. ~calm(X0) | ~calm(X0) [cnf transformation 34]
114. rich(paul) [cnf transformation 20]
117. ~calm(X0) [duplicate literal removal 67]
241. calm(paul) [resolution 62,114]
242. $false [subsumption resolution 241,117]
% SZS output end Proof for 1071132235233978121956487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then john is not quiet or humble and vice versa.
Everyone who is not generous is not generous or old and vice versa.
If susan is generous then alice is both not kind and not wise and vice versa.
Everyone who is either not quiet or funny is rich.
If someone is either old or curious then lucy is either not brave or strong and vice versa.
If someone is both strong and brave then someone is curious and vice versa.
Everyone who is either funny or not calm is not humble.
If fred is either not humble or quiet then fred is strong and vice versa.
Everyone who is humble is either not curious or not brave.
Everyone who is not generous is both not old and not curious and vice versa.
Everyone who is patient is not creative or wise.
If alice is funny or not tall then someone is generous or brave.
Everyone who is not wise or tall is patient.
Everyone who is not calm or not kind is both humble and strong.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
Someone is either not old or brave.
Alice is both not creative and strong.
Someone is generous or not old.
Someone is both not brave and quiet.
John is not strong or not quiet.
Paul is generous or not generous. | Paul is kind. | entailment | ((?[X]:(kind(X)))<=>((~quiet(john)|humble(john))))&
(![X]:(~generous(X)<=>(~generous(X)|old(X))))&
((generous(susan))<=>((~kind(alice)&~wise(alice))))&
(![X]:((~quiet(X)<~>funny(X))=>rich(X)))&
((?[X]:((old(X)<~>curious(X))))<=>((~brave(lucy)<~>strong(lucy))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>~calm(X))=>~humble(X)))&
(((~humble(fred)<~>quiet(fred)))<=>(strong(fred)))&
(![X]:(humble(X)=>(~curious(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~old(X)&~curious(X))))&
(![X]:(patient(X)=>(~creative(X)|wise(X))))&
(((funny(alice)|~tall(alice)))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~wise(X)|tall(X))=>patient(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((~creative(alice)&strong(alice)))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((~strong(john)|~quiet(john)))&
((generous(paul)|~generous(paul))) | kind(paul) | [
"p5",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 89140490649957942930943
% SZS output start Proof for 89140490649957942930943
6. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X0] : curious(X0) [input p5]
9. ! [X0] : (humble(X0) => (~curious(X0) <~> ~brave(X0))) [input p8]
14. ! [X0] : ((~kind(X0) | ~calm(X0)) => (strong(X0) & humble(X0))) [input p13]
16. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p15]
23. ~kind(paul) [input hypothesis]
24. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X1] : curious(X1) [rectify 6]
29. ! [X0] : ((~curious(X0) <~> ~brave(X0)) | ~humble(X0)) [ennf transformation 9]
32. ! [X0] : ((strong(X0) & humble(X0)) | (kind(X0) & calm(X0))) [ennf transformation 14]
46. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (~brave(X0) | ~strong(X0))) [nnf transformation 24]
47. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (~brave(X3) | ~strong(X3))) [rectify 46]
48. ? [X0] : (brave(X0) & strong(X0)) => (brave(sK2) & strong(sK2)) [choice axiom]
49. ? [X2] : curious(X2) => curious(sK3) [choice axiom]
50. ((brave(sK2) & strong(sK2)) | ! [X1] : ~curious(X1)) & (curious(sK3) | ! [X3] : (~brave(X3) | ~strong(X3))) [skolemisation 47,49,48]
53. ! [X0] : (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | ~humble(X0)) [nnf transformation 29]
60. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 16]
61. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 60]
88. brave(sK2) | ~curious(X1) [cnf transformation 50]
96. ~humble(X0) | curious(X0) | brave(X0) [cnf transformation 53]
105. humble(X0) | kind(X0) [cnf transformation 32]
112. ~brave(X0) | ~brave(X0) [cnf transformation 61]
124. ~kind(paul) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 112]
191. 14 <=> ! [X1] : ~curious(X1) [avatar definition]
192. ~curious(X1) <- (14) [avatar component clause 191]
194. 15 <=> brave(sK2) [avatar definition]
196. brave(sK2) <- (15) [avatar component clause 194]
197. 14 | 15 [avatar split clause 88,194,191]
257. $false <- (15) [subsumption resolution 196,126]
258. ~15 [avatar contradiction clause 257]
297. curious(X0) | brave(X0) | kind(X0) [resolution 96,105]
301. brave(X0) | kind(X0) <- (14) [subsumption resolution 297,192]
302. kind(X0) <- (14) [subsumption resolution 301,126]
304. $false <- (14) [resolution 302,124]
305. ~14 [avatar contradiction clause 304]
306. $false [avatar sat refutation 197,258,305]
% SZS output end Proof for 89140490649957942930943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not wise then someone is either not kind or not curious and vice versa.
Everyone who is both wise and kind is wise.
Everyone who is funny is both not tall and not brave.
Everyone who is not humble or creative is tall or not tall.
If someone is both brave and not creative then fred is quiet and vice versa.
Everyone who is not generous or humble is either strong or not strong and vice versa.
Everyone who is creative or rich is not quiet or old.
Everyone who is tall is curious or patient and vice versa.
Everyone who is both not kind and calm is both not quiet and not kind and vice versa.
If someone is not happy then someone is not funny and vice versa.
Everyone who is both happy and not quiet is either humble or not curious.
If someone is not patient then someone is not calm or not happy.
Everyone who is both not strong and kind is both not tall and happy and vice versa.
If fred is both creative and kind then paul is either kind or quiet.
Everyone who is both not happy and brave is not creative or not kind.
If paul is both not wise and not kind then someone is not brave or humble.
Someone is wise or happy.
Fred is not brave or generous.
Someone is either curious or quiet.
Someone is either not happy or kind.
Susan is both humble and brave.
Paul is not curious.
Someone is both not wise and not rich.
John is either not tall or humble. | Susan is rich. | neutral | ((?[X]:((quiet(X)&~wise(X))))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
(![X]:((wise(X)&kind(X))=>wise(X)))&
(![X]:(funny(X)=>(~tall(X)&~brave(X))))&
(![X]:((~humble(X)|creative(X))=>(tall(X)|~tall(X))))&
((?[X]:((brave(X)&~creative(X))))<=>(quiet(fred)))&
(![X]:((~generous(X)|humble(X))<=>(strong(X)<~>~strong(X))))&
(![X]:((creative(X)|rich(X))=>(~quiet(X)|old(X))))&
(![X]:(tall(X)<=>(curious(X)|patient(X))))&
(![X]:((~kind(X)&calm(X))<=>(~quiet(X)&~kind(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~funny(X))))&
(![X]:((happy(X)&~quiet(X))=>(humble(X)<~>~curious(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~strong(X)&kind(X))<=>(~tall(X)&happy(X))))&
(((creative(fred)&kind(fred)))=>((kind(paul)<~>quiet(paul))))&
(![X]:((~happy(X)&brave(X))=>(~creative(X)|~kind(X))))&
(((~wise(paul)&~kind(paul)))=>(?[X]:((~brave(X)|humble(X)))))&
(?[X]:((wise(X)|happy(X))))&
((~brave(fred)|generous(fred)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
((humble(susan)&brave(susan)))&
(~curious(paul))&
(?[X]:((~wise(X)&~rich(X))))&
((~tall(john)<~>humble(john))) | rich(susan) | [] | null | 0 |
If fred is both not creative and humble then someone is funny and vice versa. Everyone who is either not funny or patient is both not kind and not generous. Everyone who is both not funny and creative is humble. Everyone who is not kind is not strong or happy and vice versa. If someone is either not funny or not generous then someone is both rich and patient and vice versa. If fred is happy then someone is both creative and not rich. Everyone who is either not strong or not funny is both funny and kind. If someone is not humble then someone is either brave or curious. If someone is not rich or not calm then paul is not calm or not happy and vice versa. Everyone who is either not kind or strong is both kind and not humble. If someone is both brave and calm then lucy is both old and not kind and vice versa. Everyone who is calm is either not patient or patient and vice versa. Everyone who is kind or not brave is either curious or patient and vice versa. If someone is curious or not strong then someone is either not quiet or not patient. Everyone who is not strong is both not old and not creative and vice versa. Everyone who is either funny or calm is both rich and not quiet and vice versa. Susan is both quiet and humble. Susan is not wise. Someone is either patient or not strong. Someone is not kind. Lucy is both curious and not happy. Fred is either rich or not funny. Someone is both not curious and quiet. Someone is both tall and patient. | Susan is not funny. | contradiction | (((~creative(fred)&humble(fred)))<=>(?[X]:(funny(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~kind(X)&~generous(X))))&
(![X]:((~funny(X)&creative(X))=>humble(X)))&
(![X]:(~kind(X)<=>(~strong(X)|happy(X))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(?[X]:((rich(X)&patient(X)))))&
((happy(fred))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~strong(X)<~>~funny(X))=>(funny(X)&kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:((brave(X)<~>curious(X)))))&
((?[X]:((~rich(X)|~calm(X))))<=>((~calm(paul)|~happy(paul))))&
(![X]:((~kind(X)<~>strong(X))=>(kind(X)&~humble(X))))&
((?[X]:((brave(X)&calm(X))))<=>((old(lucy)&~kind(lucy))))&
(![X]:(calm(X)<=>(~patient(X)<~>patient(X))))&
(![X]:((kind(X)|~brave(X))<=>(curious(X)<~>patient(X))))&
((?[X]:((curious(X)|~strong(X))))=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(![X]:(~strong(X)<=>(~old(X)&~creative(X))))&
(![X]:((funny(X)<~>calm(X))<=>(rich(X)&~quiet(X))))&
((quiet(susan)&humble(susan)))&
(~wise(susan))&
(?[X]:((patient(X)<~>~strong(X))))&
(?[X]:(~kind(X)))&
((curious(lucy)&~happy(lucy)))&
((rich(fred)<~>~funny(fred)))&
(?[X]:((~curious(X)&quiet(X))))&
(?[X]:((tall(X)&patient(X)))) | ~funny(susan) | [
"p3",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2190255490118517010728508
% SZS output start Proof for 2190255490118517010728508
4. ! [X0] : (~kind(X0) <=> (happy(X0) | ~strong(X0))) [input p3]
7. ! [X0] : ((~strong(X0) <~> ~funny(X0)) => (kind(X0) & funny(X0))) [input p6]
10. ! [X0] : ((~kind(X0) <~> strong(X0)) => (~humble(X0) & kind(X0))) [input p9]
25. ~funny(susan) [input hypothesis]
35. ! [X0] : ((kind(X0) & funny(X0)) | (~strong(X0) <=> ~funny(X0))) [ennf transformation 7]
37. ! [X0] : ((~humble(X0) & kind(X0)) | (~kind(X0) <=> strong(X0))) [ennf transformation 10]
45. ! [X0] : ((~kind(X0) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | kind(X0))) [nnf transformation 4]
46. ! [X0] : ((~kind(X0) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | kind(X0))) [flattening 45]
54. ! [X0] : ((kind(X0) & funny(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) [nnf transformation 35]
64. ! [X0] : ((~humble(X0) & kind(X0)) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) [nnf transformation 37]
100. ~kind(X0) | strong(X0) [cnf transformation 46]
111. funny(X0) | ~strong(X0) | funny(X0) [cnf transformation 54]
120. kind(X0) | strong(X0) | kind(X0) [cnf transformation 64]
163. ~funny(susan) [cnf transformation 25]
166. kind(X0) | strong(X0) [duplicate literal removal 120]
167. ~strong(X0) | funny(X0) [duplicate literal removal 111]
273. strong(X0) [subsumption resolution 166,100]
332. funny(X0) [resolution 167,273]
333. $false [resolution 332,163]
% SZS output end Proof for 2190255490118517010728508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is patient then someone is not curious or curious and vice versa.
If fred is old or calm then paul is curious and vice versa.
Everyone who is both not happy and funny is either old or not creative.
If someone is tall or not quiet then paul is both not strong and not old and vice versa.
If susan is tall then someone is calm.
Everyone who is tall or rich is either not calm or rich.
If lucy is either quiet or not generous then susan is both strong and not old.
Everyone who is both humble and not old is both not old and rich and vice versa.
Everyone who is either patient or not humble is not old or curious and vice versa.
Everyone who is funny is both not brave and not wise and vice versa.
If someone is tall then someone is not strong and vice versa.
Everyone who is either not patient or creative is both not calm and rich.
If someone is either wise or not happy then paul is rich or tall.
Everyone who is either not kind or not humble is both curious and not creative and vice versa.
Everyone who is patient is both not generous and kind.
Everyone who is both not humble and tall is either not quiet or not happy and vice versa.
Someone is either not old or rich.
Paul is both not humble and rich.
Susan is both quiet and not brave.
Someone is either creative or tall.
Someone is either not creative or curious.
Someone is either not humble or kind. | Susan is generous. | neutral | ((patient(fred))<=>(?[X]:((~curious(X)|curious(X)))))&
(((old(fred)|calm(fred)))<=>(curious(paul)))&
(![X]:((~happy(X)&funny(X))=>(old(X)<~>~creative(X))))&
((?[X]:((tall(X)|~quiet(X))))<=>((~strong(paul)&~old(paul))))&
((tall(susan))=>(?[X]:(calm(X))))&
(![X]:((tall(X)|rich(X))=>(~calm(X)<~>rich(X))))&
(((quiet(lucy)<~>~generous(lucy)))=>((strong(susan)&~old(susan))))&
(![X]:((humble(X)&~old(X))<=>(~old(X)&rich(X))))&
(![X]:((patient(X)<~>~humble(X))<=>(~old(X)|curious(X))))&
(![X]:(funny(X)<=>(~brave(X)&~wise(X))))&
((?[X]:(tall(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~calm(X)&rich(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>((rich(paul)|tall(paul))))&
(![X]:((~kind(X)<~>~humble(X))<=>(curious(X)&~creative(X))))&
(![X]:(patient(X)=>(~generous(X)&kind(X))))&
(![X]:((~humble(X)&tall(X))<=>(~quiet(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((~humble(paul)&rich(paul)))&
((quiet(susan)&~brave(susan)))&
(?[X]:((creative(X)<~>tall(X))))&
(?[X]:((~creative(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>kind(X)))) | generous(susan) | [] | null | 0 |
Everyone who is not brave is tall and vice versa.
Everyone who is creative or tall is funny or not tall.
If someone is funny or happy then someone is not funny or not generous and vice versa.
If susan is not kind or generous then someone is either curious or generous and vice versa.
Everyone who is both calm and not curious is funny and vice versa.
Everyone who is not old is both not humble and not tall and vice versa.
If someone is not creative or wise then someone is both not humble and quiet and vice versa.
If someone is both patient and not funny then paul is either not old or happy and vice versa.
If someone is not funny then john is happy or funny and vice versa.
If someone is either funny or not brave then someone is both strong and not strong.
Everyone who is either not strong or quiet is not tall.
If someone is not humble then someone is either humble or not humble.
Everyone who is both not curious and not funny is both not quiet and not calm.
Everyone who is not happy or not calm is both wise and not wise and vice versa.
Everyone who is funny or curious is not patient and vice versa.
If someone is both not quiet and not kind then someone is rich.
Fred is either not brave or rich.
Someone is both rich and not old.
Someone is either not patient or not generous.
Someone is kind or not creative.
Someone is not happy or not funny.
Lucy is not funny or curious.
Someone is either humble or not curious. | Susan is generous. | neutral | (![X]:(~brave(X)<=>tall(X)))&
(![X]:((creative(X)|tall(X))=>(funny(X)|~tall(X))))&
((?[X]:((funny(X)|happy(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((curious(X)<~>generous(X)))))&
(![X]:((calm(X)&~curious(X))<=>funny(X)))&
(![X]:(~old(X)<=>(~humble(X)&~tall(X))))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((patient(X)&~funny(X))))<=>((~old(paul)<~>happy(paul))))&
((?[X]:(~funny(X)))<=>((happy(john)|funny(john))))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>~tall(X)))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~curious(X)&~funny(X))=>(~quiet(X)&~calm(X))))&
(![X]:((~happy(X)|~calm(X))<=>(wise(X)&~wise(X))))&
(![X]:((funny(X)|curious(X))<=>~patient(X)))&
((?[X]:((~quiet(X)&~kind(X))))=>(?[X]:(rich(X))))&
((~brave(fred)<~>rich(fred)))&
(?[X]:((rich(X)&~old(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((kind(X)|~creative(X))))&
(?[X]:((~happy(X)|~funny(X))))&
((~funny(lucy)|curious(lucy)))&
(?[X]:((humble(X)<~>~curious(X)))) | generous(susan) | [] | null | 0 |
If someone is happy then someone is either not happy or not brave.
If alice is both not humble and not quiet then lucy is both calm and happy and vice versa.
Everyone who is not strong or rich is not old.
Everyone who is either strong or calm is either not old or happy.
Everyone who is both calm and not rich is both patient and calm.
If paul is both not strong and generous then fred is both not calm and not strong.
Everyone who is not curious or humble is both not curious and calm and vice versa.
If someone is either wise or quiet then lucy is not patient and vice versa.
Everyone who is not rich is not creative.
If someone is not funny or not old then someone is kind or tall and vice versa.
Everyone who is either not strong or not old is either not quiet or not generous.
Everyone who is both happy and humble is humble.
If mary is both not calm and not tall then alice is quiet.
If john is both not tall and calm then someone is wise.
If someone is either not rich or not patient then someone is both not strong and brave.
Everyone who is generous or not calm is not calm and vice versa.
John is either not strong or patient.
Someone is not tall or not brave.
Paul is either rich or not patient.
Susan is not quiet.
Lucy is tall or not humble.
Someone is not calm.
Someone is calm.
Alice is creative. | Alice is not old. | entailment | ((?[X]:(happy(X)))=>(?[X]:((~happy(X)<~>~brave(X)))))&
(((~humble(alice)&~quiet(alice)))<=>((calm(lucy)&happy(lucy))))&
(![X]:((~strong(X)|rich(X))=>~old(X)))&
(![X]:((strong(X)<~>calm(X))=>(~old(X)<~>happy(X))))&
(![X]:((calm(X)&~rich(X))=>(patient(X)&calm(X))))&
(((~strong(paul)&generous(paul)))=>((~calm(fred)&~strong(fred))))&
(![X]:((~curious(X)|humble(X))<=>(~curious(X)&calm(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(~patient(lucy)))&
(![X]:(~rich(X)=>~creative(X)))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((~strong(X)<~>~old(X))=>(~quiet(X)<~>~generous(X))))&
(![X]:((happy(X)&humble(X))=>humble(X)))&
(((~calm(mary)&~tall(mary)))=>(quiet(alice)))&
(((~tall(john)&calm(john)))=>(?[X]:(wise(X))))&
((?[X]:((~rich(X)<~>~patient(X))))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((generous(X)|~calm(X))<=>~calm(X)))&
((~strong(john)<~>patient(john)))&
(?[X]:((~tall(X)|~brave(X))))&
((rich(paul)<~>~patient(paul)))&
(~quiet(susan))&
((tall(lucy)|~humble(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:(calm(X)))&
(creative(alice)) | ~old(alice) | [
"p2",
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3757452416785855300208896
% SZS output start Proof for 3757452416785855300208896
3. ! [X0] : ((rich(X0) | ~strong(X0)) => ~old(X0)) [input p2]
9. ! [X0] : (~rich(X0) => ~creative(X0)) [input p8]
24. creative(alice) [input p23]
25. old(alice) [input hypothesis]
30. ! [X0] : (~old(X0) | (~rich(X0) & strong(X0))) [ennf transformation 3]
36. ! [X0] : (~creative(X0) | rich(X0)) [ennf transformation 9]
87. ~old(X0) | ~rich(X0) [cnf transformation 30]
105. ~creative(X0) | rich(X0) [cnf transformation 36]
133. creative(alice) [cnf transformation 24]
134. old(alice) [cnf transformation 25]
321. ~rich(alice) [resolution 87,134]
323. rich(alice) [resolution 105,133]
324. $false [subsumption resolution 323,321]
% SZS output end Proof for 3757452416785855300208896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not funny is either not curious or kind.
Everyone who is not calm or kind is not quiet or not old.
Everyone who is not calm or quiet is either curious or quiet and vice versa.
If paul is both generous and not creative then someone is either not happy or not tall and vice versa.
Everyone who is old is not quiet or not creative and vice versa.
Everyone who is calm is either not happy or strong and vice versa.
Everyone who is either not quiet or humble is tall and vice versa.
If paul is not kind then someone is both not quiet and not calm and vice versa.
If paul is rich or calm then alice is not funny.
If susan is not humble then john is both generous and not brave and vice versa.
Everyone who is curious or not wise is both not generous and not happy and vice versa.
If someone is not kind or humble then paul is both not quiet and not funny.
If someone is both wise and not curious then someone is both not quiet and humble.
Everyone who is either patient or tall is strong or not humble and vice versa.
Everyone who is either humble or not kind is funny or happy and vice versa.
Everyone who is not humble or humble is either not rich or humble and vice versa.
Someone is either not wise or tall.
Someone is either brave or wise.
Someone is both not strong and not curious.
Someone is either wise or not rich.
Someone is not wise.
Someone is both rich and old.
Paul is rich.
Fred is not brave. | Paul is calm. | entailment | (![X]:((~strong(X)|~funny(X))=>(~curious(X)<~>kind(X))))&
(![X]:((~calm(X)|kind(X))=>(~quiet(X)|~old(X))))&
(![X]:((~calm(X)|quiet(X))<=>(curious(X)<~>quiet(X))))&
(((generous(paul)&~creative(paul)))<=>(?[X]:((~happy(X)<~>~tall(X)))))&
(![X]:(old(X)<=>(~quiet(X)|~creative(X))))&
(![X]:(calm(X)<=>(~happy(X)<~>strong(X))))&
(![X]:((~quiet(X)<~>humble(X))<=>tall(X)))&
((~kind(paul))<=>(?[X]:((~quiet(X)&~calm(X)))))&
(((rich(paul)|calm(paul)))=>(~funny(alice)))&
((~humble(susan))<=>((generous(john)&~brave(john))))&
(![X]:((curious(X)|~wise(X))<=>(~generous(X)&~happy(X))))&
((?[X]:((~kind(X)|humble(X))))=>((~quiet(paul)&~funny(paul))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~humble(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(funny(X)|happy(X))))&
(![X]:((~humble(X)|humble(X))<=>(~rich(X)<~>humble(X))))&
(?[X]:((~wise(X)<~>tall(X))))&
(?[X]:((brave(X)<~>wise(X))))&
(?[X]:((~strong(X)&~curious(X))))&
(?[X]:((wise(X)<~>~rich(X))))&
(?[X]:(~wise(X)))&
(?[X]:((rich(X)&old(X))))&
(rich(paul))&
(~brave(fred)) | calm(paul) | [
"p0",
"p2",
"p7",
"p11",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 579491112276160985730060
% SZS output start Proof for 579491112276160985730060
1. ! [X0] : ((~funny(X0) | ~strong(X0)) => (~curious(X0) <~> kind(X0))) [input p0]
3. ! [X0] : ((quiet(X0) | ~calm(X0)) <=> (curious(X0) <~> quiet(X0))) [input p2]
8. ~kind(paul) <=> ? [X0] : (~calm(X0) & ~quiet(X0)) [input p7]
12. ? [X0] : (humble(X0) | ~kind(X0)) => (~funny(paul) & ~quiet(paul)) [input p11]
16. ! [X0] : ((humble(X0) | ~humble(X0)) <=> (~rich(X0) <~> humble(X0))) [input p15]
22. ? [X0] : (old(X0) & rich(X0)) [input p21]
25. ~calm(paul) [input hypothesis]
27. ! [X0] : ((~curious(X0) <~> kind(X0)) | (funny(X0) & strong(X0))) [ennf transformation 1]
31. (~funny(paul) & ~quiet(paul)) | ! [X0] : (~humble(X0) & kind(X0)) [ennf transformation 12]
33. ! [X0] : (((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | (funny(X0) & strong(X0))) [nnf transformation 27]
34. ! [X0] : (((quiet(X0) | ~calm(X0)) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (~quiet(X0) & calm(X0)))) [nnf transformation 3]
35. ! [X0] : ((quiet(X0) | ~calm(X0) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (~quiet(X0) & calm(X0)))) [flattening 34]
45. (~kind(paul) | ! [X0] : (calm(X0) | quiet(X0))) & (? [X0] : (~calm(X0) & ~quiet(X0)) | kind(paul)) [nnf transformation 8]
46. (~kind(paul) | ! [X0] : (calm(X0) | quiet(X0))) & (? [X1] : (~calm(X1) & ~quiet(X1)) | kind(paul)) [rectify 45]
47. ? [X1] : (~calm(X1) & ~quiet(X1)) => (~calm(sK1) & ~quiet(sK1)) [choice axiom]
48. (~kind(paul) | ! [X0] : (calm(X0) | quiet(X0))) & ((~calm(sK1) & ~quiet(sK1)) | kind(paul)) [skolemisation 46,47]
60. ! [X0] : (((humble(X0) | ~humble(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (~humble(X0) & humble(X0)))) [nnf transformation 16]
61. ! [X0] : ((humble(X0) | ~humble(X0) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (~humble(X0) & humble(X0)))) [flattening 60]
75. ? [X0] : (old(X0) & rich(X0)) => (old(sK8) & rich(sK8)) [choice axiom]
76. old(sK8) & rich(sK8) [skolemisation 22,75]
78. ~curious(X0) | kind(X0) | funny(X0) [cnf transformation 33]
83. quiet(X0) | curious(X0) | calm(X0) [cnf transformation 35]
108. ~kind(paul) | calm(X0) | quiet(X0) [cnf transformation 48]
120. ~quiet(paul) | ~humble(X0) [cnf transformation 31]
122. ~funny(paul) | ~humble(X0) [cnf transformation 31]
137. humble(X0) | ~rich(X0) | humble(X0) [cnf transformation 61]
152. rich(sK8) [cnf transformation 76]
156. ~calm(paul) [cnf transformation 25]
157. ~rich(X0) | humble(X0) [duplicate literal removal 137]
192. 7 <=> ! [X0] : (calm(X0) | quiet(X0)) [avatar definition]
193. quiet(X0) | calm(X0) <- (7) [avatar component clause 192]
195. 8 <=> kind(paul) [avatar definition]
197. ~kind(paul) <- (~8) [avatar component clause 195]
198. 7 | ~8 [avatar split clause 108,195,192]
210. 11 <=> calm(paul) [avatar definition]
212. ~calm(paul) <- (~11) [avatar component clause 210]
239. 17 <=> ! [X0] : ~humble(X0) [avatar definition]
240. ~humble(X0) <- (17) [avatar component clause 239]
242. 18 <=> funny(paul) [avatar definition]
244. ~funny(paul) <- (~18) [avatar component clause 242]
245. 17 | ~18 [avatar split clause 122,242,239]
251. 20 <=> quiet(paul) [avatar definition]
253. ~quiet(paul) <- (~20) [avatar component clause 251]
254. 17 | ~20 [avatar split clause 120,251,239]
300. ~11 [avatar split clause 156,210]
308. humble(sK8) [resolution 157,152]
389. calm(paul) <- (7, ~20) [resolution 193,253]
392. $false <- (7, ~11, ~20) [subsumption resolution 389,212]
393. ~7 | 11 | 20 [avatar contradiction clause 392]
399. 40 <=> curious(paul) [avatar definition]
401. curious(paul) <- (40) [avatar component clause 399]
413. $false <- (17) [resolution 240,308]
414. ~17 [avatar contradiction clause 413]
420. curious(paul) | calm(paul) <- (~20) [resolution 253,83]
421. curious(paul) <- (~11, ~20) [subsumption resolution 420,212]
422. 40 | 11 | 20 [avatar split clause 421,251,210,399]
428. kind(paul) | funny(paul) <- (40) [resolution 401,78]
430. funny(paul) <- (~8, 40) [subsumption resolution 428,197]
431. $false <- (~8, ~18, 40) [subsumption resolution 430,244]
432. 8 | 18 | ~40 [avatar contradiction clause 431]
433. $false [avatar sat refutation 198,245,254,300,393,414,422,432]
% SZS output end Proof for 579491112276160985730060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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