premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not old or patient is both not generous and old and vice versa.
Everyone who is not quiet or not wise is both not kind and quiet and vice versa.
Everyone who is either rich or happy is not strong and vice versa.
If mary is wise or creative then fred is both curious and not curious and vice versa.
Everyone who is not happy or kind is not creative or not happy and vice versa.
If someone is not rich or happy then john is both not old and patient and vice versa.
Everyone who is both humble and not happy is either not creative or brave and vice versa.
Everyone who is both brave and tall is either not strong or kind.
Everyone who is both curious and brave is not patient and vice versa.
If someone is both calm and not old then john is rich or not brave.
Everyone who is either curious or brave is not happy and vice versa.
Everyone who is both wise and not old is either generous or not quiet and vice versa.
Everyone who is strong is both patient and not generous.
Everyone who is happy is either not creative or not curious.
Everyone who is not calm is both old and brave.
Everyone who is either humble or calm is both happy and quiet.
John is rich or not happy.
Someone is both not calm and not funny.
Lucy is not brave.
Someone is either brave or not tall.
Someone is not wise. | Mary is old. | entailment | (![X]:((~old(X)|patient(X))<=>(~generous(X)&old(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~kind(X)&quiet(X))))&
(![X]:((rich(X)<~>happy(X))<=>~strong(X)))&
(((wise(mary)|creative(mary)))<=>((curious(fred)&~curious(fred))))&
(![X]:((~happy(X)|kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((~old(john)&patient(john))))&
(![X]:((humble(X)&~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((brave(X)&tall(X))=>(~strong(X)<~>kind(X))))&
(![X]:((curious(X)&brave(X))<=>~patient(X)))&
((?[X]:((calm(X)&~old(X))))=>((rich(john)|~brave(john))))&
(![X]:((curious(X)<~>brave(X))<=>~happy(X)))&
(![X]:((wise(X)&~old(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:(strong(X)=>(patient(X)&~generous(X))))&
(![X]:(happy(X)=>(~creative(X)<~>~curious(X))))&
(![X]:(~calm(X)=>(old(X)&brave(X))))&
(![X]:((humble(X)<~>calm(X))=>(happy(X)&quiet(X))))&
((rich(john)|~happy(john)))&
(?[X]:((~calm(X)&~funny(X))))&
(~brave(lucy))&
(?[X]:((brave(X)<~>~tall(X))))&
(?[X]:(~wise(X))) | old(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1051002522802339227434190
% SZS output start Proof for 1051002522802339227434190
1. ! [X0] : ((patient(X0) | ~old(X0)) <=> (old(X0) & ~generous(X0))) [input p0]
22. ~old(mary) [input hypothesis]
32. ! [X0] : (((patient(X0) | ~old(X0)) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 1]
33. ! [X0] : ((patient(X0) | ~old(X0) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | (~patient(X0) & old(X0)))) [flattening 32]
65. old(X0) | old(X0) [cnf transformation 33]
129. ~old(mary) [cnf transformation 22]
132. old(X0) [duplicate literal removal 65]
187. $false [subsumption resolution 129,132]
% SZS output end Proof for 1051002522802339227434190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either generous or not wise then someone is either not wise or creative. If paul is funny then someone is either patient or not humble and vice versa. Everyone who is both not kind and brave is either rich or humble and vice versa. If susan is wise or funny then alice is either not wise or quiet and vice versa. Everyone who is not generous is not kind or not brave. If someone is both not quiet and rich then someone is either not wise or calm and vice versa. If someone is humble then someone is either patient or not funny and vice versa. If someone is not happy then someone is both not patient and not funny and vice versa. Everyone who is rich or not wise is either patient or generous. Everyone who is either not funny or patient is kind or not brave and vice versa. Everyone who is either not patient or not happy is tall and vice versa. If someone is generous then someone is either calm or curious. If someone is wise then mary is generous or tall and vice versa. If fred is both not generous and happy then someone is strong and vice versa. Everyone who is kind or strong is either curious or tall. Everyone who is both not curious and not kind is kind and vice versa. Someone is both not wise and quiet. Mary is either patient or curious. Someone is both generous and not old. Susan is both tall and happy. Mary is not happy. | Susan is generous. | neutral | (((generous(lucy)<~>~wise(lucy)))=>(?[X]:((~wise(X)<~>creative(X)))))&
((funny(paul))<=>(?[X]:((patient(X)<~>~humble(X)))))&
(![X]:((~kind(X)&brave(X))<=>(rich(X)<~>humble(X))))&
(((wise(susan)|funny(susan)))<=>((~wise(alice)<~>quiet(alice))))&
(![X]:(~generous(X)=>(~kind(X)|~brave(X))))&
((?[X]:((~quiet(X)&rich(X))))<=>(?[X]:((~wise(X)<~>calm(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:((rich(X)|~wise(X))=>(patient(X)<~>generous(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(kind(X)|~brave(X))))&
(![X]:((~patient(X)<~>~happy(X))<=>tall(X)))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)<~>curious(X)))))&
((?[X]:(wise(X)))<=>((generous(mary)|tall(mary))))&
(((~generous(fred)&happy(fred)))<=>(?[X]:(strong(X))))&
(![X]:((kind(X)|strong(X))=>(curious(X)<~>tall(X))))&
(![X]:((~curious(X)&~kind(X))<=>kind(X)))&
(?[X]:((~wise(X)&quiet(X))))&
((patient(mary)<~>curious(mary)))&
(?[X]:((generous(X)&~old(X))))&
((tall(susan)&happy(susan)))&
(~happy(mary)) | generous(susan) | [] | null | 0 |
If someone is calm then someone is either not funny or not rich and vice versa.
Everyone who is kind or not wise is either funny or not brave and vice versa.
If susan is either not kind or kind then john is not brave or not wise.
Everyone who is both not rich and curious is both not kind and strong and vice versa.
Everyone who is rich is strong and vice versa.
Everyone who is patient or old is either not brave or rich and vice versa.
Everyone who is wise is not tall.
If mary is both not creative and old then paul is not humble or not quiet and vice versa.
If someone is not happy or humble then someone is either not happy or not quiet.
If lucy is happy or not happy then mary is not calm and vice versa.
Everyone who is not creative or not humble is not brave.
Everyone who is not humble is quiet or funny and vice versa.
Everyone who is either rich or humble is either creative or not rich and vice versa.
If john is funny then lucy is both calm and not generous and vice versa.
Everyone who is both old and not wise is both not rich and not tall and vice versa.
If someone is both patient and not brave then someone is funny.
John is humble.
Someone is not creative.
Someone is curious or not tall.
Someone is both not creative and not funny.
Fred is both quiet and curious.
Someone is rich or patient.
Someone is not funny or rich.
Someone is both not wise and rich. | Paul is not patient. | entailment | ((?[X]:(calm(X)))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
(![X]:((kind(X)|~wise(X))<=>(funny(X)<~>~brave(X))))&
(((~kind(susan)<~>kind(susan)))=>((~brave(john)|~wise(john))))&
(![X]:((~rich(X)&curious(X))<=>(~kind(X)&strong(X))))&
(![X]:(rich(X)<=>strong(X)))&
(![X]:((patient(X)|old(X))<=>(~brave(X)<~>rich(X))))&
(![X]:(wise(X)=>~tall(X)))&
(((~creative(mary)&old(mary)))<=>((~humble(paul)|~quiet(paul))))&
((?[X]:((~happy(X)|humble(X))))=>(?[X]:((~happy(X)<~>~quiet(X)))))&
(((happy(lucy)|~happy(lucy)))<=>(~calm(mary)))&
(![X]:((~creative(X)|~humble(X))=>~brave(X)))&
(![X]:(~humble(X)<=>(quiet(X)|funny(X))))&
(![X]:((rich(X)<~>humble(X))<=>(creative(X)<~>~rich(X))))&
((funny(john))<=>((calm(lucy)&~generous(lucy))))&
(![X]:((old(X)&~wise(X))<=>(~rich(X)&~tall(X))))&
((?[X]:((patient(X)&~brave(X))))=>(?[X]:(funny(X))))&
(humble(john))&
(?[X]:(~creative(X)))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~creative(X)&~funny(X))))&
((quiet(fred)&curious(fred)))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((~funny(X)|rich(X))))&
(?[X]:((~wise(X)&rich(X)))) | ~patient(paul) | [
"p1",
"p3",
"p4",
"p6",
"p10",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6531430467859974427112262
% SZS output start Proof for 6531430467859974427112262
2. ! [X0] : ((~wise(X0) | kind(X0)) <=> (funny(X0) <~> ~brave(X0))) [input p1]
4. ! [X0] : ((curious(X0) & ~rich(X0)) <=> (strong(X0) & ~kind(X0))) [input p3]
5. ! [X0] : (rich(X0) <=> strong(X0)) [input p4]
7. ! [X0] : (wise(X0) => ~tall(X0)) [input p6]
11. ! [X0] : ((~humble(X0) | ~creative(X0)) => ~brave(X0)) [input p10]
12. ! [X0] : (~humble(X0) <=> (funny(X0) | quiet(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> humble(X0)) <=> (creative(X0) <~> ~rich(X0))) [input p12]
15. ! [X0] : ((~wise(X0) & old(X0)) <=> (~tall(X0) & ~rich(X0))) [input p14]
16. ? [X0] : (~brave(X0) & patient(X0)) => ? [X0] : funny(X0) [input p15]
25. patient(paul) [input hypothesis]
28. ? [X0] : (~brave(X0) & patient(X0)) => ? [X1] : funny(X1) [rectify 16]
31. ! [X0] : (~tall(X0) | ~wise(X0)) [ennf transformation 7]
33. ! [X0] : (~brave(X0) | (humble(X0) & creative(X0))) [ennf transformation 11]
34. ? [X1] : funny(X1) | ! [X0] : (brave(X0) | ~patient(X0)) [ennf transformation 28]
40. ! [X0] : (((~wise(X0) | kind(X0)) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0)))) & (((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (wise(X0) & ~kind(X0)))) [nnf transformation 2]
41. ! [X0] : ((~wise(X0) | kind(X0) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0)))) & (((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (wise(X0) & ~kind(X0)))) [flattening 40]
43. ! [X0] : (((curious(X0) & ~rich(X0)) | (~strong(X0) | kind(X0))) & ((strong(X0) & ~kind(X0)) | (~curious(X0) | rich(X0)))) [nnf transformation 4]
44. ! [X0] : (((curious(X0) & ~rich(X0)) | ~strong(X0) | kind(X0)) & ((strong(X0) & ~kind(X0)) | ~curious(X0) | rich(X0))) [flattening 43]
45. ! [X0] : ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))) [nnf transformation 5]
56. ! [X0] : ((~humble(X0) | (~funny(X0) & ~quiet(X0))) & ((funny(X0) | quiet(X0)) | humble(X0))) [nnf transformation 12]
57. ! [X0] : ((~humble(X0) | (~funny(X0) & ~quiet(X0))) & (funny(X0) | quiet(X0) | humble(X0))) [flattening 56]
58. ! [X0] : ((((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))))) [nnf transformation 13]
61. ! [X0] : (((~wise(X0) & old(X0)) | (tall(X0) | rich(X0))) & ((~tall(X0) & ~rich(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 15]
62. ! [X0] : (((~wise(X0) & old(X0)) | tall(X0) | rich(X0)) & ((~tall(X0) & ~rich(X0)) | wise(X0) | ~old(X0))) [flattening 61]
63. ? [X0] : funny(X0) | ! [X1] : (brave(X1) | ~patient(X1)) [rectify 34]
64. ? [X0] : funny(X0) => funny(sK3) [choice axiom]
65. funny(sK3) | ! [X1] : (brave(X1) | ~patient(X1)) [skolemisation 63,64]
84. ~kind(X0) | ~funny(X0) | brave(X0) [cnf transformation 41]
85. ~funny(X0) | brave(X0) | wise(X0) [cnf transformation 41]
92. ~strong(X0) | ~rich(X0) | kind(X0) [cnf transformation 44]
94. ~rich(X0) | strong(X0) [cnf transformation 45]
102. ~tall(X0) | ~wise(X0) [cnf transformation 31]
115. ~brave(X0) | creative(X0) [cnf transformation 33]
116. ~brave(X0) | humble(X0) [cnf transformation 33]
119. ~humble(X0) | ~funny(X0) [cnf transformation 57]
123. rich(X0) | ~creative(X0) | rich(X0) | ~humble(X0) [cnf transformation 58]
126. ~humble(X0) | ~rich(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 58]
134. ~wise(X0) | tall(X0) | rich(X0) [cnf transformation 62]
135. funny(sK3) | brave(X1) | ~patient(X1) [cnf transformation 65]
147. patient(paul) [cnf transformation 25]
149. rich(X0) | ~creative(X0) | ~humble(X0) [duplicate literal removal 123]
151. ~humble(X0) | ~rich(X0) | ~creative(X0) [duplicate literal removal 126]
203. 12 <=> humble(paul) [avatar definition]
205. humble(paul) <- (12) [avatar component clause 203]
242. ~humble(X0) | ~creative(X0) [subsumption resolution 149,151]
259. ~wise(X0) | rich(X0) [subsumption resolution 134,102]
262. 23 <=> ! [X1] : (brave(X1) | ~patient(X1)) [avatar definition]
263. ~patient(X1) | brave(X1) <- (23) [avatar component clause 262]
265. 24 <=> funny(sK3) [avatar definition]
267. funny(sK3) <- (24) [avatar component clause 265]
268. 23 | 24 [avatar split clause 135,265,262]
308. brave(paul) <- (23) [resolution 263,147]
310. humble(paul) <- (23) [resolution 308,116]
311. creative(paul) <- (23) [resolution 308,115]
321. 12 | ~23 [avatar split clause 310,262,203]
322. ~creative(paul) <- (12) [resolution 205,242]
324. $false <- (12, 23) [subsumption resolution 322,311]
325. ~12 | ~23 [avatar contradiction clause 324]
328. brave(sK3) | wise(sK3) <- (24) [resolution 85,267]
339. 35 <=> wise(sK3) [avatar definition]
341. wise(sK3) <- (35) [avatar component clause 339]
343. 36 <=> brave(sK3) [avatar definition]
345. brave(sK3) <- (36) [avatar component clause 343]
346. 35 | 36 | ~24 [avatar split clause 328,265,343,339]
347. rich(sK3) <- (35) [resolution 341,259]
494. strong(sK3) <- (35) [resolution 347,94]
535. ~rich(sK3) | kind(sK3) <- (35) [resolution 494,92]
538. 57 <=> kind(sK3) [avatar definition]
540. kind(sK3) <- (57) [avatar component clause 538]
546. kind(sK3) <- (35) [subsumption resolution 535,347]
547. 57 | ~35 [avatar split clause 546,339,538]
548. ~funny(sK3) | brave(sK3) <- (57) [resolution 540,84]
549. brave(sK3) <- (24, 57) [subsumption resolution 548,267]
550. 36 | ~24 | ~57 [avatar split clause 549,538,265,343]
555. humble(sK3) <- (36) [resolution 345,116]
569. ~funny(sK3) <- (36) [resolution 555,119]
575. $false <- (24, 36) [subsumption resolution 569,267]
576. ~24 | ~36 [avatar contradiction clause 575]
577. $false [avatar sat refutation 268,321,325,346,547,550,576]
% SZS output end Proof for 6531430467859974427112262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not funny is either kind or calm and vice versa.
Everyone who is happy is not wise or not strong and vice versa.
Everyone who is either old or not patient is both funny and kind.
If someone is not brave then john is wise.
Everyone who is kind is both not rich and funny and vice versa.
If someone is kind or not wise then someone is calm and vice versa.
Everyone who is brave is not strong or humble.
Everyone who is either strong or not calm is either rich or funny.
Everyone who is not generous is not strong or creative.
Everyone who is both not kind and not wise is brave or not rich and vice versa.
If paul is either strong or old then paul is either not rich or humble and vice versa.
Everyone who is not brave or not funny is not humble.
If paul is not humble then susan is either kind or funny and vice versa.
If susan is not tall then mary is either quiet or not creative.
Everyone who is both not wise and strong is both patient and calm and vice versa.
Everyone who is not patient is either not tall or generous and vice versa.
Someone is not generous.
Someone is not strong.
Paul is either not brave or kind.
John is either funny or rich.
Someone is not kind or quiet.
Fred is either patient or curious.
Lucy is both old and calm. | Susan is happy. | contradiction | (![X]:(~funny(X)<=>(kind(X)<~>calm(X))))&
(![X]:(happy(X)<=>(~wise(X)|~strong(X))))&
(![X]:((old(X)<~>~patient(X))=>(funny(X)&kind(X))))&
((?[X]:(~brave(X)))=>(wise(john)))&
(![X]:(kind(X)<=>(~rich(X)&funny(X))))&
((?[X]:((kind(X)|~wise(X))))<=>(?[X]:(calm(X))))&
(![X]:(brave(X)=>(~strong(X)|humble(X))))&
(![X]:((strong(X)<~>~calm(X))=>(rich(X)<~>funny(X))))&
(![X]:(~generous(X)=>(~strong(X)|creative(X))))&
(![X]:((~kind(X)&~wise(X))<=>(brave(X)|~rich(X))))&
(((strong(paul)<~>old(paul)))<=>((~rich(paul)<~>humble(paul))))&
(![X]:((~brave(X)|~funny(X))=>~humble(X)))&
((~humble(paul))<=>((kind(susan)<~>funny(susan))))&
((~tall(susan))=>((quiet(mary)<~>~creative(mary))))&
(![X]:((~wise(X)&strong(X))<=>(patient(X)&calm(X))))&
(![X]:(~patient(X)<=>(~tall(X)<~>generous(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~strong(X)))&
((~brave(paul)<~>kind(paul)))&
((funny(john)<~>rich(john)))&
(?[X]:((~kind(X)|quiet(X))))&
((patient(fred)<~>curious(fred)))&
((old(lucy)&calm(lucy))) | happy(susan) | [
"p0",
"p1",
"p4",
"p7",
"p9",
"p11",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4019553059121966674171597
% SZS output start Proof for 4019553059121966674171597
1. ! [X0] : (~funny(X0) <=> (kind(X0) <~> calm(X0))) [input p0]
2. ! [X0] : (happy(X0) <=> (~strong(X0) | ~wise(X0))) [input p1]
5. ! [X0] : (kind(X0) <=> (funny(X0) & ~rich(X0))) [input p4]
8. ! [X0] : ((strong(X0) <~> ~calm(X0)) => (rich(X0) <~> funny(X0))) [input p7]
10. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~rich(X0) | brave(X0))) [input p9]
12. ! [X0] : ((~funny(X0) | ~brave(X0)) => ~humble(X0)) [input p11]
13. ~humble(paul) <=> (kind(susan) <~> funny(susan)) [input p12]
15. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (calm(X0) & patient(X0))) [input p14]
19. ~brave(paul) <~> kind(paul) [input p18]
24. happy(susan) [input hypothesis]
26. ! [X0] : (happy(X0) => (~strong(X0) | ~wise(X0))) [unused predicate definition removal 2]
27. ! [X0] : ((~strong(X0) | ~wise(X0)) | ~happy(X0)) [ennf transformation 26]
28. ! [X0] : (~strong(X0) | ~wise(X0) | ~happy(X0)) [flattening 27]
33. ! [X0] : ((rich(X0) <~> funny(X0)) | (strong(X0) <=> ~calm(X0))) [ennf transformation 8]
36. ! [X0] : (~humble(X0) | (funny(X0) & brave(X0))) [ennf transformation 12]
38. ! [X0] : ((~funny(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0)))) & (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | funny(X0))) [nnf transformation 1]
40. ! [X0] : ((kind(X0) | (~funny(X0) | rich(X0))) & ((funny(X0) & ~rich(X0)) | ~kind(X0))) [nnf transformation 5]
41. ! [X0] : ((kind(X0) | ~funny(X0) | rich(X0)) & ((funny(X0) & ~rich(X0)) | ~kind(X0))) [flattening 40]
47. ! [X0] : (((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) [nnf transformation 33]
48. ! [X0] : (((~wise(X0) & ~kind(X0)) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | (wise(X0) | kind(X0)))) [nnf transformation 10]
49. ! [X0] : (((~wise(X0) & ~kind(X0)) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | wise(X0) | kind(X0))) [flattening 48]
51. (~humble(paul) | ((kind(susan) | ~funny(susan)) & (funny(susan) | ~kind(susan)))) & (((~funny(susan) | ~kind(susan)) & (funny(susan) | kind(susan))) | humble(paul)) [nnf transformation 13]
53. ! [X0] : (((strong(X0) & ~wise(X0)) | (~calm(X0) | ~patient(X0))) & ((calm(X0) & patient(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 15]
54. ! [X0] : (((strong(X0) & ~wise(X0)) | ~calm(X0) | ~patient(X0)) & ((calm(X0) & patient(X0)) | ~strong(X0) | wise(X0))) [flattening 53]
60. (~kind(paul) | brave(paul)) & (kind(paul) | ~brave(paul)) [nnf transformation 19]
68. ~calm(X0) | kind(X0) | ~funny(X0) [cnf transformation 38]
69. ~strong(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 28]
75. ~rich(X0) | ~kind(X0) [cnf transformation 41]
76. ~kind(X0) | funny(X0) [cnf transformation 41]
77. ~funny(X0) | kind(X0) | rich(X0) [cnf transformation 41]
85. ~rich(X0) | ~funny(X0) | strong(X0) | calm(X0) [cnf transformation 47]
88. ~brave(X0) | ~kind(X0) [cnf transformation 49]
89. ~kind(X0) | rich(X0) [cnf transformation 49]
100. ~humble(X0) | brave(X0) [cnf transformation 36]
102. funny(susan) | kind(susan) | humble(paul) [cnf transformation 51]
109. ~strong(X0) | calm(X0) | wise(X0) [cnf transformation 54]
118. kind(paul) | ~brave(paul) [cnf transformation 60]
119. ~kind(paul) | brave(paul) [cnf transformation 60]
127. happy(susan) [cnf transformation 24]
157. 8 <=> ! [X3] : ~kind(X3) [avatar definition]
158. ~kind(X3) <- (8) [avatar component clause 157]
160. ~kind(X0) [subsumption resolution 89,75]
161. 8 [avatar split clause 160,157]
164. 9 <=> humble(paul) [avatar definition]
165. humble(paul) <- (9) [avatar component clause 164]
188. 13 <=> funny(susan) [avatar definition]
189. funny(susan) <- (13) [avatar component clause 188]
198. funny(susan) | humble(paul) [subsumption resolution 102,76]
199. 9 | 13 [avatar split clause 198,188,164]
214. ~kind(paul) [subsumption resolution 119,88]
215. ~brave(paul) [subsumption resolution 118,214]
254. brave(paul) <- (9) [resolution 100,165]
255. $false <- (9) [subsumption resolution 254,215]
256. ~9 [avatar contradiction clause 255]
294. kind(susan) | rich(susan) <- (13) [resolution 77,189]
295. rich(susan) <- (8, 13) [subsumption resolution 294,158]
363. 35 <=> wise(susan) [avatar definition]
419. 41 <=> strong(susan) [avatar definition]
420. strong(susan) <- (41) [avatar component clause 419]
423. 42 <=> calm(susan) [avatar definition]
424. calm(susan) <- (42) [avatar component clause 423]
425. ~calm(susan) <- (~42) [avatar component clause 423]
436. ~funny(susan) | strong(susan) | calm(susan) <- (8, 13) [resolution 85,295]
441. strong(susan) | calm(susan) <- (8, 13) [subsumption resolution 436,189]
450. 42 | 41 | ~8 | ~13 [avatar split clause 441,188,157,419,423]
535. calm(susan) | wise(susan) <- (41) [resolution 420,109]
538. ~wise(susan) | ~happy(susan) <- (41) [resolution 420,69]
551. ~wise(susan) <- (41) [subsumption resolution 538,127]
552. ~35 | ~41 [avatar split clause 551,419,363]
558. wise(susan) <- (41, ~42) [subsumption resolution 535,425]
559. 35 | ~41 | 42 [avatar split clause 558,423,419,363]
571. kind(susan) | ~funny(susan) <- (42) [resolution 424,68]
574. ~funny(susan) <- (8, 42) [subsumption resolution 571,158]
575. $false <- (8, 13, 42) [subsumption resolution 574,189]
576. ~8 | ~13 | ~42 [avatar contradiction clause 575]
577. $false [avatar sat refutation 161,199,256,450,552,559,576]
% SZS output end Proof for 4019553059121966674171597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and old is either generous or funny. If john is both not brave and not creative then someone is either rich or quiet and vice versa. Everyone who is both not rich and not calm is both not kind and patient and vice versa. Everyone who is both patient and curious is both not rich and not humble. If someone is not funny then someone is both creative and brave. Everyone who is not happy is not humble or creative. If someone is not patient or not calm then someone is either not old or wise and vice versa. Everyone who is both strong and not humble is kind. Everyone who is not creative is both not rich and quiet and vice versa. If someone is either patient or not old then john is both not strong and brave and vice versa. Everyone who is not wise or not kind is either brave or patient and vice versa. Everyone who is not patient or curious is not wise or happy. Everyone who is both not calm and generous is not humble or wise. Everyone who is both old and tall is either humble or not curious and vice versa. If someone is both not kind and not curious then john is both not funny and not creative. Everyone who is both kind and calm is both quiet and not rich. Someone is both not old and not brave. Lucy is quiet. Someone is both quiet and happy. Fred is patient. Someone is either quiet or not quiet. Someone is wise or brave. Fred is rich. | Fred is not calm. | entailment | (![X]:((strong(X)&old(X))=>(generous(X)<~>funny(X))))&
(((~brave(john)&~creative(john)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(![X]:((~rich(X)&~calm(X))<=>(~kind(X)&patient(X))))&
(![X]:((patient(X)&curious(X))=>(~rich(X)&~humble(X))))&
((?[X]:(~funny(X)))=>(?[X]:((creative(X)&brave(X)))))&
(![X]:(~happy(X)=>(~humble(X)|creative(X))))&
((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:((~old(X)<~>wise(X)))))&
(![X]:((strong(X)&~humble(X))=>kind(X)))&
(![X]:(~creative(X)<=>(~rich(X)&quiet(X))))&
((?[X]:((patient(X)<~>~old(X))))<=>((~strong(john)&brave(john))))&
(![X]:((~wise(X)|~kind(X))<=>(brave(X)<~>patient(X))))&
(![X]:((~patient(X)|curious(X))=>(~wise(X)|happy(X))))&
(![X]:((~calm(X)&generous(X))=>(~humble(X)|wise(X))))&
(![X]:((old(X)&tall(X))<=>(humble(X)<~>~curious(X))))&
((?[X]:((~kind(X)&~curious(X))))=>((~funny(john)&~creative(john))))&
(![X]:((kind(X)&calm(X))=>(quiet(X)&~rich(X))))&
(?[X]:((~old(X)&~brave(X))))&
(quiet(lucy))&
(?[X]:((quiet(X)&happy(X))))&
(patient(fred))&
(?[X]:((quiet(X)<~>~quiet(X))))&
(?[X]:((wise(X)|brave(X))))&
(rich(fred)) | ~calm(fred) | [
"p2",
"p15",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5932693736813126885761178
% SZS output start Proof for 5932693736813126885761178
3. ! [X0] : ((~calm(X0) & ~rich(X0)) <=> (patient(X0) & ~kind(X0))) [input p2]
16. ! [X0] : ((calm(X0) & kind(X0)) => (~rich(X0) & quiet(X0))) [input p15]
20. patient(fred) [input p19]
23. rich(fred) [input p22]
24. calm(fred) [input hypothesis]
40. ! [X0] : ((~rich(X0) & quiet(X0)) | (~calm(X0) | ~kind(X0))) [ennf transformation 16]
41. ! [X0] : ((~rich(X0) & quiet(X0)) | ~calm(X0) | ~kind(X0)) [flattening 40]
48. ! [X0] : (((~calm(X0) & ~rich(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (calm(X0) | rich(X0)))) [nnf transformation 3]
49. ! [X0] : (((~calm(X0) & ~rich(X0)) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | calm(X0) | rich(X0))) [flattening 48]
88. ~patient(X0) | ~rich(X0) | kind(X0) [cnf transformation 49]
126. ~kind(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 41]
131. patient(fred) [cnf transformation 20]
135. rich(fred) [cnf transformation 23]
136. calm(fred) [cnf transformation 24]
270. ~rich(fred) | kind(fred) [resolution 88,131]
274. kind(fred) [subsumption resolution 270,135]
357. ~calm(fred) | ~rich(fred) [resolution 126,274]
358. ~rich(fred) [subsumption resolution 357,136]
359. $false [subsumption resolution 358,135]
% SZS output end Proof for 5932693736813126885761178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not creative is not generous and vice versa.
If mary is both not generous and not rich then alice is not curious and vice versa.
If mary is not quiet then someone is not humble or funny.
If lucy is either calm or wise then someone is both kind and funny and vice versa.
Everyone who is either humble or wise is both generous and not quiet.
Everyone who is not rich is either strong or curious.
Everyone who is both happy and not brave is either creative or not kind and vice versa.
Everyone who is old or tall is either not creative or generous and vice versa.
If someone is happy or not calm then lucy is quiet or not rich.
Everyone who is either happy or not wise is strong and vice versa.
If mary is happy then lucy is both happy and generous.
Everyone who is both not creative and not tall is creative or curious.
If someone is either not brave or not happy then someone is either not tall or wise and vice versa.
If john is either creative or generous then someone is not tall or old and vice versa.
Everyone who is either not humble or not kind is brave or tall.
Everyone who is not patient or not quiet is both old and creative.
Alice is quiet.
Fred is not generous or not funny.
Someone is not old or wise.
Someone is both not calm and not generous.
Someone is funny.
Alice is both tall and curious. | John is strong. | neutral | (![X]:((brave(X)&~creative(X))<=>~generous(X)))&
(((~generous(mary)&~rich(mary)))<=>(~curious(alice)))&
((~quiet(mary))=>(?[X]:((~humble(X)|funny(X)))))&
(((calm(lucy)<~>wise(lucy)))<=>(?[X]:((kind(X)&funny(X)))))&
(![X]:((humble(X)<~>wise(X))=>(generous(X)&~quiet(X))))&
(![X]:(~rich(X)=>(strong(X)<~>curious(X))))&
(![X]:((happy(X)&~brave(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((old(X)|tall(X))<=>(~creative(X)<~>generous(X))))&
((?[X]:((happy(X)|~calm(X))))=>((quiet(lucy)|~rich(lucy))))&
(![X]:((happy(X)<~>~wise(X))<=>strong(X)))&
((happy(mary))=>((happy(lucy)&generous(lucy))))&
(![X]:((~creative(X)&~tall(X))=>(creative(X)|curious(X))))&
((?[X]:((~brave(X)<~>~happy(X))))<=>(?[X]:((~tall(X)<~>wise(X)))))&
(((creative(john)<~>generous(john)))<=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((~humble(X)<~>~kind(X))=>(brave(X)|tall(X))))&
(![X]:((~patient(X)|~quiet(X))=>(old(X)&creative(X))))&
(quiet(alice))&
((~generous(fred)|~funny(fred)))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((~calm(X)&~generous(X))))&
(?[X]:(funny(X)))&
((tall(alice)&curious(alice))) | strong(john) | [] | null | 0 |
Everyone who is quiet or funny is not brave or not strong and vice versa.
Everyone who is not patient is happy or not wise and vice versa.
If someone is either curious or quiet then someone is both wise and not happy and vice versa.
Everyone who is either not wise or funny is either creative or not funny and vice versa.
If paul is wise then someone is both not kind and not curious and vice versa.
Everyone who is either not humble or funny is either not creative or happy.
If someone is not brave then someone is both not old and quiet and vice versa.
Everyone who is either curious or not old is not rich.
If someone is either not tall or patient then someone is both old and not funny.
Everyone who is both not quiet and kind is both rich and creative.
Everyone who is not happy is generous and vice versa.
If mary is either not quiet or brave then someone is not rich or not generous and vice versa.
Everyone who is both quiet and not old is either old or not generous and vice versa.
Everyone who is both funny and old is both not curious and kind.
If someone is both tall and funny then someone is brave and vice versa.
Susan is both tall and not calm.
Someone is not kind or not happy.
Someone is rich.
Someone is old or not strong.
Mary is not calm.
Mary is kind or not rich. | Paul is curious. | neutral | (![X]:((quiet(X)|funny(X))<=>(~brave(X)|~strong(X))))&
(![X]:(~patient(X)<=>(happy(X)|~wise(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((~wise(X)<~>funny(X))<=>(creative(X)<~>~funny(X))))&
((wise(paul))<=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~humble(X)<~>funny(X))=>(~creative(X)<~>happy(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((~old(X)&quiet(X)))))&
(![X]:((curious(X)<~>~old(X))=>~rich(X)))&
((?[X]:((~tall(X)<~>patient(X))))=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((~quiet(X)&kind(X))=>(rich(X)&creative(X))))&
(![X]:(~happy(X)<=>generous(X)))&
(((~quiet(mary)<~>brave(mary)))<=>(?[X]:((~rich(X)|~generous(X)))))&
(![X]:((quiet(X)&~old(X))<=>(old(X)<~>~generous(X))))&
(![X]:((funny(X)&old(X))=>(~curious(X)&kind(X))))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:(brave(X))))&
((tall(susan)&~calm(susan)))&
(?[X]:((~kind(X)|~happy(X))))&
(?[X]:(rich(X)))&
(?[X]:((old(X)|~strong(X))))&
(~calm(mary))&
((kind(mary)|~rich(mary))) | curious(paul) | [] | null | 0 |
Everyone who is both not kind and quiet is either creative or not creative and vice versa. If someone is patient then someone is both not patient and not strong. If someone is both not rich and not calm then someone is not funny or curious and vice versa. Everyone who is calm or kind is rich or not rich. If someone is both strong and generous then someone is either not wise or funny and vice versa. Everyone who is both funny and not wise is wise or not patient. Everyone who is not generous is strong. If someone is not happy then someone is patient or not calm. Everyone who is either not wise or strong is not quiet and vice versa. Everyone who is not calm is humble or wise and vice versa. If someone is not happy then susan is either not patient or strong. If someone is wise or quiet then someone is both not curious and brave. If someone is either not quiet or not patient then someone is either not curious or funny. If someone is humble then paul is not quiet or not kind and vice versa. If susan is both not calm and not rich then mary is both not creative and not strong and vice versa. If mary is either not old or not generous then someone is quiet or wise and vice versa. Someone is quiet. Someone is both patient and not humble. Someone is both wise and generous. John is not funny or creative. John is not calm or not wise. Paul is wise. Someone is not tall. | Mary is not kind. | entailment | (![X]:((~kind(X)&quiet(X))<=>(creative(X)<~>~creative(X))))&
((?[X]:(patient(X)))=>(?[X]:((~patient(X)&~strong(X)))))&
((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:((calm(X)|kind(X))=>(rich(X)|~rich(X))))&
((?[X]:((strong(X)&generous(X))))<=>(?[X]:((~wise(X)<~>funny(X)))))&
(![X]:((funny(X)&~wise(X))=>(wise(X)|~patient(X))))&
(![X]:(~generous(X)=>strong(X)))&
((?[X]:(~happy(X)))=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((~wise(X)<~>strong(X))<=>~quiet(X)))&
(![X]:(~calm(X)<=>(humble(X)|wise(X))))&
((?[X]:(~happy(X)))=>((~patient(susan)<~>strong(susan))))&
((?[X]:((wise(X)|quiet(X))))=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:((~quiet(X)<~>~patient(X))))=>(?[X]:((~curious(X)<~>funny(X)))))&
((?[X]:(humble(X)))<=>((~quiet(paul)|~kind(paul))))&
(((~calm(susan)&~rich(susan)))<=>((~creative(mary)&~strong(mary))))&
(((~old(mary)<~>~generous(mary)))<=>(?[X]:((quiet(X)|wise(X)))))&
(?[X]:(quiet(X)))&
(?[X]:((patient(X)&~humble(X))))&
(?[X]:((wise(X)&generous(X))))&
((~funny(john)|creative(john)))&
((~calm(john)|~wise(john)))&
(wise(paul))&
(?[X]:(~tall(X))) | ~kind(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 79499241487768287701339
% SZS output start Proof for 79499241487768287701339
1. ! [X0] : ((quiet(X0) & ~kind(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p0]
24. kind(mary) [input hypothesis]
43. ! [X0] : (((quiet(X0) & ~kind(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~quiet(X0) | kind(X0)))) [nnf transformation 1]
44. ! [X0] : (((quiet(X0) & ~kind(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~quiet(X0) | kind(X0))) [flattening 43]
87. ~kind(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 44]
88. ~kind(X0) | creative(X0) | creative(X0) [cnf transformation 44]
142. kind(mary) [cnf transformation 24]
144. ~kind(X0) | ~creative(X0) [duplicate literal removal 87]
145. ~kind(X0) | creative(X0) [duplicate literal removal 88]
149. ~kind(X0) [subsumption resolution 144,145]
289. $false [subsumption resolution 142,149]
% SZS output end Proof for 79499241487768287701339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not happy is not strong.
Everyone who is not old or funny is strong.
Everyone who is not humble or happy is old.
Everyone who is either not patient or old is generous or funny and vice versa.
Everyone who is wise or not humble is both not strong and not funny.
If someone is happy or not tall then mary is curious and vice versa.
If susan is both patient and not kind then paul is either not old or not creative and vice versa.
Everyone who is not rich or generous is both not brave and calm and vice versa.
Everyone who is both not brave and strong is brave or not humble.
Everyone who is curious or not patient is either not happy or patient.
If someone is both not wise and not curious then lucy is not brave or not curious and vice versa.
If someone is either not generous or humble then someone is rich.
Everyone who is not tall or humble is both not calm and happy.
If someone is creative or not generous then john is not kind.
Everyone who is either not rich or not generous is strong.
If someone is both rich and patient then mary is strong or not curious.
Fred is either not funny or not quiet.
Someone is not rich.
Lucy is either not calm or generous.
Someone is both happy and not wise.
Lucy is either not calm or kind.
Someone is strong or not curious.
John is both wise and quiet. | Mary is not generous. | entailment | (![X]:((creative(X)&~happy(X))=>~strong(X)))&
(![X]:((~old(X)|funny(X))=>strong(X)))&
(![X]:((~humble(X)|happy(X))=>old(X)))&
(![X]:((~patient(X)<~>old(X))<=>(generous(X)|funny(X))))&
(![X]:((wise(X)|~humble(X))=>(~strong(X)&~funny(X))))&
((?[X]:((happy(X)|~tall(X))))<=>(curious(mary)))&
(((patient(susan)&~kind(susan)))<=>((~old(paul)<~>~creative(paul))))&
(![X]:((~rich(X)|generous(X))<=>(~brave(X)&calm(X))))&
(![X]:((~brave(X)&strong(X))=>(brave(X)|~humble(X))))&
(![X]:((curious(X)|~patient(X))=>(~happy(X)<~>patient(X))))&
((?[X]:((~wise(X)&~curious(X))))<=>((~brave(lucy)|~curious(lucy))))&
((?[X]:((~generous(X)<~>humble(X))))=>(?[X]:(rich(X))))&
(![X]:((~tall(X)|humble(X))=>(~calm(X)&happy(X))))&
((?[X]:((creative(X)|~generous(X))))=>(~kind(john)))&
(![X]:((~rich(X)<~>~generous(X))=>strong(X)))&
((?[X]:((rich(X)&patient(X))))=>((strong(mary)|~curious(mary))))&
((~funny(fred)<~>~quiet(fred)))&
(?[X]:(~rich(X)))&
((~calm(lucy)<~>generous(lucy)))&
(?[X]:((happy(X)&~wise(X))))&
((~calm(lucy)<~>kind(lucy)))&
(?[X]:((strong(X)|~curious(X))))&
((wise(john)&quiet(john))) | ~generous(mary) | [
"p2",
"p3",
"p4",
"p5",
"p7",
"p12",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8646294272597188823765536
% SZS output start Proof for 8646294272597188823765536
3. ! [X0] : ((happy(X0) | ~humble(X0)) => old(X0)) [input p2]
4. ! [X0] : ((~patient(X0) <~> old(X0)) <=> (funny(X0) | generous(X0))) [input p3]
5. ! [X0] : ((~humble(X0) | wise(X0)) => (~funny(X0) & ~strong(X0))) [input p4]
6. ? [X0] : (~tall(X0) | happy(X0)) <=> curious(mary) [input p5]
8. ! [X0] : ((generous(X0) | ~rich(X0)) <=> (calm(X0) & ~brave(X0))) [input p7]
13. ! [X0] : ((humble(X0) | ~tall(X0)) => (happy(X0) & ~calm(X0))) [input p12]
15. ! [X0] : ((~rich(X0) <~> ~generous(X0)) => strong(X0)) [input p14]
16. ? [X0] : (patient(X0) & rich(X0)) => (~curious(mary) | strong(mary)) [input p15]
20. ? [X0] : (~wise(X0) & happy(X0)) [input p19]
24. generous(mary) [input hypothesis]
29. ! [X0] : (old(X0) | (~happy(X0) & humble(X0))) [ennf transformation 3]
30. ! [X0] : ((~funny(X0) & ~strong(X0)) | (humble(X0) & ~wise(X0))) [ennf transformation 5]
35. ! [X0] : ((happy(X0) & ~calm(X0)) | (~humble(X0) & tall(X0))) [ennf transformation 13]
37. ! [X0] : (strong(X0) | (~rich(X0) <=> ~generous(X0))) [ennf transformation 15]
38. (~curious(mary) | strong(mary)) | ! [X0] : (~patient(X0) | ~rich(X0)) [ennf transformation 16]
39. ~curious(mary) | strong(mary) | ! [X0] : (~patient(X0) | ~rich(X0)) [flattening 38]
40. ! [X0] : ((((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (~funny(X0) & ~generous(X0))) & ((funny(X0) | generous(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (~funny(X0) & ~generous(X0))) & (funny(X0) | generous(X0) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))))) [flattening 40]
42. (? [X0] : (~tall(X0) | happy(X0)) | ~curious(mary)) & (curious(mary) | ! [X0] : (tall(X0) & ~happy(X0))) [nnf transformation 6]
43. (? [X0] : (~tall(X0) | happy(X0)) | ~curious(mary)) & (curious(mary) | ! [X1] : (tall(X1) & ~happy(X1))) [rectify 42]
44. ? [X0] : (~tall(X0) | happy(X0)) => (~tall(sK0) | happy(sK0)) [choice axiom]
45. ((~tall(sK0) | happy(sK0)) | ~curious(mary)) & (curious(mary) | ! [X1] : (tall(X1) & ~happy(X1))) [skolemisation 43,44]
48. ! [X0] : (((generous(X0) | ~rich(X0)) | (~calm(X0) | brave(X0))) & ((calm(X0) & ~brave(X0)) | (~generous(X0) & rich(X0)))) [nnf transformation 8]
49. ! [X0] : ((generous(X0) | ~rich(X0) | ~calm(X0) | brave(X0)) & ((calm(X0) & ~brave(X0)) | (~generous(X0) & rich(X0)))) [flattening 48]
60. ! [X0] : (strong(X0) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0)))) [nnf transformation 37]
65. ? [X0] : (~wise(X0) & happy(X0)) => (~wise(sK4) & happy(sK4)) [choice axiom]
66. ~wise(sK4) & happy(sK4) [skolemisation 20,65]
73. humble(X0) | old(X0) [cnf transformation 29]
79. ~generous(X0) | patient(X0) | ~old(X0) [cnf transformation 41]
82. ~strong(X0) | humble(X0) [cnf transformation 30]
85. curious(mary) | ~happy(X1) [cnf transformation 45]
97. ~generous(X0) | calm(X0) [cnf transformation 49]
112. ~calm(X0) | ~humble(X0) [cnf transformation 35]
117. ~generous(X0) | strong(X0) | rich(X0) [cnf transformation 60]
119. ~curious(mary) | strong(mary) | ~patient(X0) | ~rich(X0) [cnf transformation 39]
125. happy(sK4) [cnf transformation 66]
132. generous(mary) [cnf transformation 24]
136. 1 <=> curious(mary) [avatar definition]
153. 5 <=> ! [X1] : ~happy(X1) [avatar definition]
154. ~happy(X1) <- (5) [avatar component clause 153]
155. 5 | 1 [avatar split clause 85,136,153]
228. 21 <=> ! [X0] : (~patient(X0) | ~rich(X0)) [avatar definition]
229. ~rich(X0) | ~patient(X0) <- (21) [avatar component clause 228]
231. 22 <=> strong(mary) [avatar definition]
233. strong(mary) <- (22) [avatar component clause 231]
234. 21 | 22 | ~1 [avatar split clause 119,136,231,228]
269. $false <- (5) [resolution 154,125]
270. ~5 [avatar contradiction clause 269]
282. calm(mary) [resolution 97,132]
286. ~humble(mary) [resolution 112,282]
287. old(mary) [resolution 286,73]
308. patient(mary) | ~old(mary) [resolution 79,132]
309. patient(mary) [subsumption resolution 308,287]
318. strong(mary) | rich(mary) [resolution 117,132]
320. 30 <=> rich(mary) [avatar definition]
322. rich(mary) <- (30) [avatar component clause 320]
323. 30 | 22 [avatar split clause 318,231,320]
326. humble(mary) <- (22) [resolution 233,82]
327. $false <- (22) [subsumption resolution 326,286]
328. ~22 [avatar contradiction clause 327]
329. ~patient(mary) <- (21, 30) [resolution 322,229]
330. $false <- (21, 30) [subsumption resolution 329,309]
331. ~21 | ~30 [avatar contradiction clause 330]
332. $false [avatar sat refutation 155,234,270,323,328,331]
% SZS output end Proof for 8646294272597188823765536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or generous is both funny and not generous.
If mary is either creative or not funny then fred is not strong or not calm and vice versa.
Everyone who is not happy is both creative and not tall and vice versa.
Everyone who is not quiet is either not patient or kind.
If someone is both not creative and wise then someone is either generous or not happy and vice versa.
Everyone who is either not patient or calm is creative and vice versa.
If alice is tall then someone is rich and vice versa.
Everyone who is both rich and not kind is both tall and happy.
Everyone who is either not humble or quiet is not creative.
Everyone who is generous or patient is rich or calm and vice versa.
Everyone who is not humble is not tall and vice versa.
If someone is either strong or not tall then alice is not funny and vice versa.
Everyone who is curious is both not curious and not tall.
If someone is both not humble and not patient then someone is either not funny or curious.
If someone is both not wise and brave then lucy is either tall or humble and vice versa.
If alice is not funny or not happy then paul is both not creative and tall and vice versa.
Someone is not humble or not patient.
Paul is either not curious or strong.
Someone is not creative or strong.
Mary is either not funny or wise.
Lucy is both humble and not rich.
Paul is either happy or not happy. | Paul is quiet. | contradiction | (![X]:((~curious(X)|generous(X))=>(funny(X)&~generous(X))))&
(((creative(mary)<~>~funny(mary)))<=>((~strong(fred)|~calm(fred))))&
(![X]:(~happy(X)<=>(creative(X)&~tall(X))))&
(![X]:(~quiet(X)=>(~patient(X)<~>kind(X))))&
((?[X]:((~creative(X)&wise(X))))<=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:((~patient(X)<~>calm(X))<=>creative(X)))&
((tall(alice))<=>(?[X]:(rich(X))))&
(![X]:((rich(X)&~kind(X))=>(tall(X)&happy(X))))&
(![X]:((~humble(X)<~>quiet(X))=>~creative(X)))&
(![X]:((generous(X)|patient(X))<=>(rich(X)|calm(X))))&
(![X]:(~humble(X)<=>~tall(X)))&
((?[X]:((strong(X)<~>~tall(X))))<=>(~funny(alice)))&
(![X]:(curious(X)=>(~curious(X)&~tall(X))))&
((?[X]:((~humble(X)&~patient(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
((?[X]:((~wise(X)&brave(X))))<=>((tall(lucy)<~>humble(lucy))))&
(((~funny(alice)|~happy(alice)))<=>((~creative(paul)&tall(paul))))&
(?[X]:((~humble(X)|~patient(X))))&
((~curious(paul)<~>strong(paul)))&
(?[X]:((~creative(X)|strong(X))))&
((~funny(mary)<~>wise(mary)))&
((humble(lucy)&~rich(lucy)))&
((happy(paul)<~>~happy(paul))) | quiet(paul) | [
"p0",
"p2",
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 252452138840194877156307
% SZS output start Proof for 252452138840194877156307
1. ! [X0] : ((generous(X0) | ~curious(X0)) => (~generous(X0) & funny(X0))) [input p0]
3. ! [X0] : (~happy(X0) <=> (~tall(X0) & creative(X0))) [input p2]
6. ! [X0] : ((~patient(X0) <~> calm(X0)) <=> creative(X0)) [input p5]
7. tall(alice) <=> ? [X0] : rich(X0) [input p6]
9. ! [X0] : ((~humble(X0) <~> quiet(X0)) => ~creative(X0)) [input p8]
10. ! [X0] : ((patient(X0) | generous(X0)) <=> (calm(X0) | rich(X0))) [input p9]
11. ! [X0] : (~humble(X0) <=> ~tall(X0)) [input p10]
12. ? [X0] : (strong(X0) <~> ~tall(X0)) <=> ~funny(alice) [input p11]
13. ! [X0] : (curious(X0) => (~tall(X0) & ~curious(X0))) [input p12]
16. (~happy(alice) | ~funny(alice)) <=> (tall(paul) & ~creative(paul)) [input p15]
18. ~curious(paul) <~> strong(paul) [input p17]
23. quiet(paul) [input hypothesis]
26. ! [X0] : ((~generous(X0) & funny(X0)) | (~generous(X0) & curious(X0))) [ennf transformation 1]
30. ! [X0] : (~creative(X0) | (~humble(X0) <=> quiet(X0))) [ennf transformation 9]
31. ! [X0] : ((~tall(X0) & ~curious(X0)) | ~curious(X0)) [ennf transformation 13]
35. ! [X0] : ((~happy(X0) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | happy(X0))) [nnf transformation 3]
36. ! [X0] : ((~happy(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | happy(X0))) [flattening 35]
43. ! [X0] : ((((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ~creative(X0)) & (creative(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0))))) [nnf transformation 6]
44. (tall(alice) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ~tall(alice)) [nnf transformation 7]
45. (tall(alice) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ~tall(alice)) [rectify 44]
46. ? [X1] : rich(X1) => rich(sK2) [choice axiom]
47. (tall(alice) | ! [X0] : ~rich(X0)) & (rich(sK2) | ~tall(alice)) [skolemisation 45,46]
48. ! [X0] : (~creative(X0) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0)))) [nnf transformation 30]
49. ! [X0] : (((patient(X0) | generous(X0)) | (~calm(X0) & ~rich(X0))) & ((calm(X0) | rich(X0)) | (~patient(X0) & ~generous(X0)))) [nnf transformation 10]
50. ! [X0] : ((patient(X0) | generous(X0) | (~calm(X0) & ~rich(X0))) & (calm(X0) | rich(X0) | (~patient(X0) & ~generous(X0)))) [flattening 49]
51. ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0))) [nnf transformation 11]
52. (? [X0] : ((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | funny(alice)) & (~funny(alice) | ! [X0] : ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0)))) [nnf transformation 12]
53. (? [X0] : ((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | funny(alice)) & (~funny(alice) | ! [X1] : ((strong(X1) | tall(X1)) & (~tall(X1) | ~strong(X1)))) [rectify 52]
54. ? [X0] : ((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) => ((tall(sK3) | ~strong(sK3)) & (~tall(sK3) | strong(sK3))) [choice axiom]
55. (((tall(sK3) | ~strong(sK3)) & (~tall(sK3) | strong(sK3))) | funny(alice)) & (~funny(alice) | ! [X1] : ((strong(X1) | tall(X1)) & (~tall(X1) | ~strong(X1)))) [skolemisation 53,54]
64. ((~happy(alice) | ~funny(alice)) | (~tall(paul) | creative(paul))) & ((tall(paul) & ~creative(paul)) | (happy(alice) & funny(alice))) [nnf transformation 16]
65. (~happy(alice) | ~funny(alice) | ~tall(paul) | creative(paul)) & ((tall(paul) & ~creative(paul)) | (happy(alice) & funny(alice))) [flattening 64]
68. (~strong(paul) | curious(paul)) & (strong(paul) | ~curious(paul)) [nnf transformation 18]
73. funny(X0) | curious(X0) [cnf transformation 26]
76. ~generous(X0) | ~generous(X0) [cnf transformation 26]
84. ~tall(X0) | happy(X0) [cnf transformation 36]
94. patient(X0) | calm(X0) | creative(X0) [cnf transformation 43]
95. ~patient(X0) | creative(X0) | ~calm(X0) [cnf transformation 43]
99. tall(alice) | ~rich(X0) [cnf transformation 47]
103. ~humble(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 48]
105. ~patient(X0) | rich(X0) | calm(X0) [cnf transformation 50]
107. patient(X0) | generous(X0) | ~calm(X0) [cnf transformation 50]
108. ~tall(X0) | humble(X0) [cnf transformation 51]
111. ~funny(alice) | strong(X1) | tall(X1) [cnf transformation 55]
114. ~curious(X0) | ~curious(X0) [cnf transformation 31]
128. ~happy(alice) | ~funny(alice) | ~tall(paul) | creative(paul) [cnf transformation 65]
131. ~strong(paul) | curious(paul) [cnf transformation 68]
139. quiet(paul) [cnf transformation 23]
140. ~curious(X0) [duplicate literal removal 114]
141. ~generous(X0) [duplicate literal removal 76]
189. 10 <=> ! [X0] : ~rich(X0) [avatar definition]
190. ~rich(X0) <- (10) [avatar component clause 189]
192. 11 <=> tall(alice) [avatar definition]
194. tall(alice) <- (11) [avatar component clause 192]
195. 10 | 11 [avatar split clause 99,192,189]
201. ~calm(X0) | patient(X0) [subsumption resolution 107,141]
204. 13 <=> funny(alice) [avatar definition]
205. ~funny(alice) <- (~13) [avatar component clause 204]
218. 16 <=> ! [X1] : (strong(X1) | tall(X1)) [avatar definition]
219. tall(X1) | strong(X1) <- (16) [avatar component clause 218]
220. 16 | ~13 [avatar split clause 111,204,218]
246. 22 <=> creative(paul) [avatar definition]
247. ~creative(paul) <- (~22) [avatar component clause 246]
248. creative(paul) <- (22) [avatar component clause 246]
250. 23 <=> tall(paul) [avatar definition]
251. tall(paul) <- (23) [avatar component clause 250]
252. ~tall(paul) <- (~23) [avatar component clause 250]
254. 24 <=> happy(alice) [avatar definition]
256. ~happy(alice) <- (~24) [avatar component clause 254]
257. 22 | ~23 | ~13 | ~24 [avatar split clause 128,254,204,250,246]
271. ~strong(paul) [subsumption resolution 131,140]
291. curious(alice) <- (~13) [resolution 73,205]
295. $false <- (~13) [subsumption resolution 291,140]
296. 13 [avatar contradiction clause 295]
302. humble(paul) <- (23) [resolution 108,251]
434. ~creative(paul) | ~quiet(paul) <- (23) [resolution 103,302]
447. ~quiet(paul) <- (22, 23) [subsumption resolution 434,248]
448. $false <- (22, 23) [subsumption resolution 447,139]
449. ~22 | ~23 [avatar contradiction clause 448]
452. strong(paul) <- (16, ~23) [resolution 252,219]
453. $false <- (16, ~23) [subsumption resolution 452,271]
454. ~16 | 23 [avatar contradiction clause 453]
469. rich(X1) | calm(X1) | calm(X1) | creative(X1) [resolution 105,94]
470. rich(X1) | calm(X1) | creative(X1) [duplicate literal removal 469]
523. happy(alice) <- (11) [resolution 194,84]
528. $false <- (11, ~24) [subsumption resolution 523,256]
529. ~11 | 24 [avatar contradiction clause 528]
537. calm(X0) | creative(X0) <- (10) [resolution 470,190]
595. patient(X1) | creative(X1) <- (10) [resolution 537,201]
645. creative(X2) | creative(X2) | ~calm(X2) <- (10) [resolution 595,95]
648. creative(X2) | ~calm(X2) <- (10) [duplicate literal removal 645]
649. creative(X2) <- (10) [subsumption resolution 648,537]
653. $false <- (10, ~22) [resolution 649,247]
658. ~10 | 22 [avatar contradiction clause 653]
660. $false [avatar sat refutation 195,220,257,296,449,454,529,658]
% SZS output end Proof for 252452138840194877156307
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not brave and not generous is either not strong or generous.
If fred is not quiet or old then mary is quiet or humble.
Everyone who is tall is happy.
If fred is wise then susan is both not funny and not happy and vice versa.
Everyone who is either not old or funny is either curious or patient and vice versa.
If lucy is creative or not quiet then susan is generous.
Everyone who is not kind or kind is humble or strong.
If someone is not quiet or not old then someone is both not humble and not funny and vice versa.
Everyone who is not patient is creative or tall and vice versa.
Everyone who is both generous and creative is not curious or not quiet and vice versa.
If someone is both not curious and not creative then alice is generous or brave and vice versa.
Everyone who is kind or not humble is not calm or humble and vice versa.
If someone is not funny then alice is not humble or not curious.
If mary is either wise or creative then someone is wise and vice versa.
Everyone who is either kind or brave is not patient.
Susan is funny or not funny.
Someone is not humble.
Susan is not curious or happy.
Lucy is kind or quiet.
Alice is quiet or patient.
Fred is either happy or quiet. | Alice is kind. | entailment | (![X]:((~brave(X)&~generous(X))=>(~strong(X)<~>generous(X))))&
(((~quiet(fred)|old(fred)))=>((quiet(mary)|humble(mary))))&
(![X]:(tall(X)=>happy(X)))&
((wise(fred))<=>((~funny(susan)&~happy(susan))))&
(![X]:((~old(X)<~>funny(X))<=>(curious(X)<~>patient(X))))&
(((creative(lucy)|~quiet(lucy)))=>(generous(susan)))&
(![X]:((~kind(X)|kind(X))=>(humble(X)|strong(X))))&
((?[X]:((~quiet(X)|~old(X))))<=>(?[X]:((~humble(X)&~funny(X)))))&
(![X]:(~patient(X)<=>(creative(X)|tall(X))))&
(![X]:((generous(X)&creative(X))<=>(~curious(X)|~quiet(X))))&
((?[X]:((~curious(X)&~creative(X))))<=>((generous(alice)|brave(alice))))&
(![X]:((kind(X)|~humble(X))<=>(~calm(X)|humble(X))))&
((?[X]:(~funny(X)))=>((~humble(alice)|~curious(alice))))&
(((wise(mary)<~>creative(mary)))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)<~>brave(X))=>~patient(X)))&
((funny(susan)|~funny(susan)))&
(?[X]:(~humble(X)))&
((~curious(susan)|happy(susan)))&
((kind(lucy)|quiet(lucy)))&
((quiet(alice)|patient(alice)))&
((happy(fred)<~>quiet(fred))) | kind(alice) | [
"p0",
"p6",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1348357536172700343347231
% SZS output start Proof for 1348357536172700343347231
1. ! [X0] : ((~generous(X0) & ~brave(X0)) => (~strong(X0) <~> generous(X0))) [input p0]
7. ! [X0] : ((kind(X0) | ~kind(X0)) => (strong(X0) | humble(X0))) [input p6]
10. ! [X0] : ((creative(X0) & generous(X0)) <=> (~quiet(X0) | ~curious(X0))) [input p9]
11. ? [X0] : (~creative(X0) & ~curious(X0)) <=> (brave(alice) | generous(alice)) [input p10]
12. ! [X0] : ((~humble(X0) | kind(X0)) <=> (humble(X0) | ~calm(X0))) [input p11]
22. ~kind(alice) [input hypothesis]
24. ! [X0] : ((~strong(X0) <~> generous(X0)) | (generous(X0) | brave(X0))) [ennf transformation 1]
25. ! [X0] : ((~strong(X0) <~> generous(X0)) | generous(X0) | brave(X0)) [flattening 24]
30. ! [X0] : ((strong(X0) | humble(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 7]
31. ! [X0] : (strong(X0) | humble(X0) | (~kind(X0) & kind(X0))) [flattening 30]
35. ! [X0] : (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | generous(X0) | brave(X0)) [nnf transformation 25]
46. ! [X0] : (((creative(X0) & generous(X0)) | (quiet(X0) & curious(X0))) & ((~quiet(X0) | ~curious(X0)) | (~creative(X0) | ~generous(X0)))) [nnf transformation 10]
47. ! [X0] : (((creative(X0) & generous(X0)) | (quiet(X0) & curious(X0))) & (~quiet(X0) | ~curious(X0) | ~creative(X0) | ~generous(X0))) [flattening 46]
48. (? [X0] : (~creative(X0) & ~curious(X0)) | (~brave(alice) & ~generous(alice))) & ((brave(alice) | generous(alice)) | ! [X0] : (creative(X0) | curious(X0))) [nnf transformation 11]
49. (? [X0] : (~creative(X0) & ~curious(X0)) | (~brave(alice) & ~generous(alice))) & (brave(alice) | generous(alice) | ! [X0] : (creative(X0) | curious(X0))) [flattening 48]
50. (? [X0] : (~creative(X0) & ~curious(X0)) | (~brave(alice) & ~generous(alice))) & (brave(alice) | generous(alice) | ! [X1] : (creative(X1) | curious(X1))) [rectify 49]
51. ? [X0] : (~creative(X0) & ~curious(X0)) => (~creative(sK2) & ~curious(sK2)) [choice axiom]
52. ((~creative(sK2) & ~curious(sK2)) | (~brave(alice) & ~generous(alice))) & (brave(alice) | generous(alice) | ! [X1] : (creative(X1) | curious(X1))) [skolemisation 50,51]
53. ! [X0] : (((~humble(X0) | kind(X0)) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | (humble(X0) & ~kind(X0)))) [nnf transformation 12]
54. ! [X0] : ((~humble(X0) | kind(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | (humble(X0) & ~kind(X0)))) [flattening 53]
63. generous(X0) | ~strong(X0) | generous(X0) | brave(X0) [cnf transformation 35]
81. strong(X0) | humble(X0) | kind(X0) [cnf transformation 31]
82. ~kind(X0) | humble(X0) | strong(X0) [cnf transformation 31]
94. creative(X0) | curious(X0) [cnf transformation 47]
97. ~curious(sK2) | ~generous(alice) [cnf transformation 52]
98. ~curious(sK2) | ~brave(alice) [cnf transformation 52]
99. ~creative(sK2) | ~generous(alice) [cnf transformation 52]
100. ~creative(sK2) | ~brave(alice) [cnf transformation 52]
104. ~humble(X0) | kind(X0) | ~humble(X0) [cnf transformation 54]
119. ~kind(alice) [cnf transformation 22]
121. ~humble(X0) | kind(X0) [duplicate literal removal 104]
122. ~strong(X0) | generous(X0) | brave(X0) [duplicate literal removal 63]
170. humble(X0) | strong(X0) [subsumption resolution 81,82]
202. 18 <=> brave(alice) [avatar definition]
206. 19 <=> creative(sK2) [avatar definition]
208. ~creative(sK2) <- (~19) [avatar component clause 206]
209. ~18 | ~19 [avatar split clause 100,206,202]
211. 20 <=> generous(alice) [avatar definition]
213. ~generous(alice) <- (~20) [avatar component clause 211]
214. ~20 | ~19 [avatar split clause 99,206,211]
216. 21 <=> curious(sK2) [avatar definition]
219. ~18 | ~21 [avatar split clause 98,216,202]
220. ~20 | ~21 [avatar split clause 97,216,211]
225. 23 <=> humble(alice) [avatar definition]
226. humble(alice) <- (23) [avatar component clause 225]
227. ~humble(alice) <- (~23) [avatar component clause 225]
294. strong(alice) <- (~23) [resolution 170,227]
320. generous(alice) | brave(alice) <- (~23) [resolution 122,294]
323. brave(alice) <- (~20, ~23) [subsumption resolution 320,213]
344. 18 | 20 | 23 [avatar split clause 323,225,211,202]
354. curious(sK2) <- (~19) [resolution 208,94]
366. 21 | 19 [avatar split clause 354,206,216]
367. kind(alice) <- (23) [resolution 226,121]
368. $false <- (23) [subsumption resolution 367,119]
369. ~23 [avatar contradiction clause 368]
370. $false [avatar sat refutation 209,214,219,220,344,366,369]
% SZS output end Proof for 1348357536172700343347231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both creative and generous and vice versa.
Everyone who is both not old and rich is generous.
Everyone who is either not strong or not creative is either not funny or not strong.
Everyone who is both not brave and not rich is not brave or not rich.
Everyone who is strong is quiet.
If alice is either rich or happy then alice is creative or calm.
If john is not old or rich then mary is wise or not kind and vice versa.
Everyone who is not rich or tall is not generous and vice versa.
If someone is either not quiet or not tall then someone is either kind or happy and vice versa.
Everyone who is both creative and not patient is both funny and not tall and vice versa.
Everyone who is not tall is not kind.
Everyone who is both not calm and not patient is patient and vice versa.
Everyone who is not tall or not creative is not quiet and vice versa.
If someone is not old or not kind then someone is either not generous or not curious and vice versa.
If someone is either not humble or strong then susan is either not curious or brave.
John is both not tall and not brave.
Someone is rich.
Susan is both calm and old.
Susan is curious or not old.
Someone is either not brave or not creative. | John is not generous. | contradiction | (![X]:((strong(X)<~>~generous(X))<=>(creative(X)&generous(X))))&
(![X]:((~old(X)&rich(X))=>generous(X)))&
(![X]:((~strong(X)<~>~creative(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~brave(X)&~rich(X))=>(~brave(X)|~rich(X))))&
(![X]:(strong(X)=>quiet(X)))&
(((rich(alice)<~>happy(alice)))=>((creative(alice)|calm(alice))))&
(((~old(john)|rich(john)))<=>((wise(mary)|~kind(mary))))&
(![X]:((~rich(X)|tall(X))<=>~generous(X)))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((creative(X)&~patient(X))<=>(funny(X)&~tall(X))))&
(![X]:(~tall(X)=>~kind(X)))&
(![X]:((~calm(X)&~patient(X))<=>patient(X)))&
(![X]:((~tall(X)|~creative(X))<=>~quiet(X)))&
((?[X]:((~old(X)|~kind(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((~humble(X)<~>strong(X))))=>((~curious(susan)<~>brave(susan))))&
((~tall(john)&~brave(john)))&
(?[X]:(rich(X)))&
((calm(susan)&old(susan)))&
((curious(susan)|~old(susan)))&
(?[X]:((~brave(X)<~>~creative(X)))) | ~generous(john) | [
"p0",
"p4",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1653737647317095712360662
% SZS output start Proof for 1653737647317095712360662
1. ! [X0] : ((strong(X0) <~> ~generous(X0)) <=> (generous(X0) & creative(X0))) [input p0]
5. ! [X0] : (strong(X0) => quiet(X0)) [input p4]
13. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> ~quiet(X0)) [input p12]
16. ~brave(john) & ~tall(john) [input p15]
21. ~generous(john) [input hypothesis]
29. ! [X0] : (quiet(X0) | ~strong(X0)) [ennf transformation 5]
34. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [nnf transformation 1]
35. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [flattening 34]
51. ! [X0] : (((~creative(X0) | ~tall(X0)) | quiet(X0)) & (~quiet(X0) | (creative(X0) & tall(X0)))) [nnf transformation 13]
52. ! [X0] : ((~creative(X0) | ~tall(X0) | quiet(X0)) & (~quiet(X0) | (creative(X0) & tall(X0)))) [flattening 51]
67. generous(X0) | strong(X0) | generous(X0) [cnf transformation 35]
76. ~strong(X0) | quiet(X0) [cnf transformation 29]
102. ~quiet(X0) | tall(X0) [cnf transformation 52]
115. ~tall(john) [cnf transformation 16]
123. ~generous(john) [cnf transformation 21]
128. generous(X0) | strong(X0) [duplicate literal removal 67]
187. 13 <=> ! [X3] : (~quiet(X3) | tall(X3)) [avatar definition]
188. ~quiet(X3) | tall(X3) <- (13) [avatar component clause 187]
205. 13 [avatar split clause 102,187]
274. strong(john) [resolution 128,123]
280. quiet(john) [resolution 274,76]
324. tall(john) <- (13) [resolution 280,188]
326. $false <- (13) [subsumption resolution 324,115]
327. ~13 [avatar contradiction clause 326]
328. $false [avatar sat refutation 205,327]
% SZS output end Proof for 1653737647317095712360662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or generous then someone is rich or old. Everyone who is both not happy and generous is either not brave or brave. If paul is both not kind and not rich then someone is both calm and curious. If paul is either not creative or not humble then mary is both not kind and brave and vice versa. Everyone who is wise is both not happy and tall. If alice is either old or rich then susan is not patient or strong. Everyone who is rich or quiet is not rich or not humble. Everyone who is not humble or not rich is either wise or not brave. If lucy is either curious or calm then someone is either not brave or not humble. If susan is either not patient or rich then someone is both not calm and not happy and vice versa. Everyone who is either not happy or rich is not generous or not quiet and vice versa. Everyone who is either wise or not brave is either rich or strong and vice versa. If someone is not curious then mary is calm and vice versa. Everyone who is either not quiet or wise is both wise and not kind and vice versa. If someone is both not old and humble then lucy is not strong or rich. If susan is humble or strong then susan is tall or not generous. Lucy is either not humble or not wise. Someone is not curious or not old. Someone is not strong or not humble. Someone is not old. Someone is brave or happy. Someone is either curious or not happy. Alice is not old or not kind. Someone is not rich or kind. | Alice is not curious. | neutral | ((?[X]:((humble(X)|generous(X))))=>(?[X]:((rich(X)|old(X)))))&
(![X]:((~happy(X)&generous(X))=>(~brave(X)<~>brave(X))))&
(((~kind(paul)&~rich(paul)))=>(?[X]:((calm(X)&curious(X)))))&
(((~creative(paul)<~>~humble(paul)))<=>((~kind(mary)&brave(mary))))&
(![X]:(wise(X)=>(~happy(X)&tall(X))))&
(((old(alice)<~>rich(alice)))=>((~patient(susan)|strong(susan))))&
(![X]:((rich(X)|quiet(X))=>(~rich(X)|~humble(X))))&
(![X]:((~humble(X)|~rich(X))=>(wise(X)<~>~brave(X))))&
(((curious(lucy)<~>calm(lucy)))=>(?[X]:((~brave(X)<~>~humble(X)))))&
(((~patient(susan)<~>rich(susan)))<=>(?[X]:((~calm(X)&~happy(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(rich(X)<~>strong(X))))&
((?[X]:(~curious(X)))<=>(calm(mary)))&
(![X]:((~quiet(X)<~>wise(X))<=>(wise(X)&~kind(X))))&
((?[X]:((~old(X)&humble(X))))=>((~strong(lucy)|rich(lucy))))&
(((humble(susan)|strong(susan)))=>((tall(susan)|~generous(susan))))&
((~humble(lucy)<~>~wise(lucy)))&
(?[X]:((~curious(X)|~old(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)|happy(X))))&
(?[X]:((curious(X)<~>~happy(X))))&
((~old(alice)|~kind(alice)))&
(?[X]:((~rich(X)|kind(X)))) | ~curious(alice) | [] | null | 0 |
If john is tall or humble then someone is not happy or not kind and vice versa. Everyone who is both not funny and not old is either not funny or not patient and vice versa. Everyone who is either not wise or wise is either kind or not patient. Everyone who is both not humble and not curious is wise or happy and vice versa. If alice is either quiet or not creative then someone is not strong. Everyone who is generous or not rich is either not curious or creative. If someone is not humble or curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Everyone who is humble or not humble is both not rich and brave and vice versa. If someone is either not quiet or not wise then someone is not quiet and vice versa. If mary is not humble then someone is generous and vice versa. If someone is not quiet then paul is not wise. If lucy is not curious or not funny then lucy is either not funny or kind and vice versa. If someone is either strong or curious then someone is not curious or not brave. If fred is not patient then john is not old or wise. Someone is both creative and brave. Someone is both not happy and strong. Fred is wise. John is happy. Paul is both tall and humble. Someone is either brave or curious. | Mary is not curious. | neutral | (((tall(john)|humble(john)))<=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>wise(X))=>(kind(X)<~>~patient(X))))&
(![X]:((~humble(X)&~curious(X))<=>(wise(X)|happy(X))))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
(![X]:((generous(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
(![X]:((humble(X)|~humble(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>(?[X]:(~quiet(X))))&
((~humble(mary))<=>(?[X]:(generous(X))))&
((?[X]:(~quiet(X)))=>(~wise(paul)))&
(((~curious(lucy)|~funny(lucy)))<=>((~funny(lucy)<~>kind(lucy))))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~curious(X)|~brave(X)))))&
((~patient(fred))=>((~old(john)|wise(john))))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:((~happy(X)&strong(X))))&
(wise(fred))&
(happy(john))&
((tall(paul)&humble(paul)))&
(?[X]:((brave(X)<~>curious(X)))) | ~curious(mary) | [] | null | 0 |
Everyone who is wise or not old is not strong or generous and vice versa.
If fred is both kind and not wise then fred is either not brave or generous.
Everyone who is both not strong and tall is either brave or not quiet.
Everyone who is both creative and not wise is quiet.
Everyone who is both not quiet and calm is either not humble or generous and vice versa.
If someone is either wise or not wise then someone is both happy and not rich and vice versa.
If mary is brave then someone is either not brave or not kind and vice versa.
If susan is not brave then someone is tall or not old and vice versa.
Everyone who is either not quiet or wise is either strong or not funny.
Everyone who is not rich or old is kind and vice versa.
Everyone who is both not humble and quiet is brave and vice versa.
If john is happy or not funny then john is not patient and vice versa.
Everyone who is either not rich or funny is either not kind or humble.
Everyone who is old or not generous is happy and vice versa.
If someone is both not strong and not curious then alice is curious or calm and vice versa.
If someone is either old or not wise then paul is both old and rich.
Someone is not generous or generous.
Alice is both generous and not patient.
Someone is both not curious and not creative.
Susan is both funny and humble.
Someone is both not kind and funny.
Susan is humble.
Susan is either not strong or happy.
Fred is not humble. | John is happy. | neutral | (![X]:((wise(X)|~old(X))<=>(~strong(X)|generous(X))))&
(((kind(fred)&~wise(fred)))=>((~brave(fred)<~>generous(fred))))&
(![X]:((~strong(X)&tall(X))=>(brave(X)<~>~quiet(X))))&
(![X]:((creative(X)&~wise(X))=>quiet(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~humble(X)<~>generous(X))))&
((?[X]:((wise(X)<~>~wise(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
((brave(mary))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
((~brave(susan))<=>(?[X]:((tall(X)|~old(X)))))&
(![X]:((~quiet(X)<~>wise(X))=>(strong(X)<~>~funny(X))))&
(![X]:((~rich(X)|old(X))<=>kind(X)))&
(![X]:((~humble(X)&quiet(X))<=>brave(X)))&
(((happy(john)|~funny(john)))<=>(~patient(john)))&
(![X]:((~rich(X)<~>funny(X))=>(~kind(X)<~>humble(X))))&
(![X]:((old(X)|~generous(X))<=>happy(X)))&
((?[X]:((~strong(X)&~curious(X))))<=>((curious(alice)|calm(alice))))&
((?[X]:((old(X)<~>~wise(X))))=>((old(paul)&rich(paul))))&
(?[X]:((~generous(X)|generous(X))))&
((generous(alice)&~patient(alice)))&
(?[X]:((~curious(X)&~creative(X))))&
((funny(susan)&humble(susan)))&
(?[X]:((~kind(X)&funny(X))))&
(humble(susan))&
((~strong(susan)<~>happy(susan)))&
(~humble(fred)) | happy(john) | [] | null | 0 |
If paul is both quiet and not curious then fred is patient or not curious.
Everyone who is brave or not rich is both kind and happy and vice versa.
Everyone who is either calm or rich is both brave and not patient.
If someone is old then lucy is not patient or not tall.
Everyone who is not brave or not tall is either old or not calm and vice versa.
If someone is calm or not calm then john is not tall or creative.
Everyone who is either creative or funny is not old and vice versa.
Everyone who is not generous or humble is both not curious and old and vice versa.
Everyone who is either happy or calm is not humble and vice versa.
Everyone who is not rich or not patient is either not creative or not funny.
Everyone who is happy or generous is either not wise or not patient.
Everyone who is brave is either not old or happy and vice versa.
If john is either not happy or not tall then susan is both not brave and strong and vice versa.
Everyone who is tall is quiet or not patient and vice versa.
Everyone who is both not rich and quiet is both not quiet and not happy.
Everyone who is both happy and not humble is humble or not tall.
Alice is not calm.
Lucy is either old or strong.
Someone is either brave or patient.
Paul is either calm or kind.
Lucy is both not creative and not generous.
Fred is happy.
Someone is either not patient or not funny.
Someone is both not kind and rich. | Lucy is strong. | contradiction | (((quiet(paul)&~curious(paul)))=>((patient(fred)|~curious(fred))))&
(![X]:((brave(X)|~rich(X))<=>(kind(X)&happy(X))))&
(![X]:((calm(X)<~>rich(X))=>(brave(X)&~patient(X))))&
((?[X]:(old(X)))=>((~patient(lucy)|~tall(lucy))))&
(![X]:((~brave(X)|~tall(X))<=>(old(X)<~>~calm(X))))&
((?[X]:((calm(X)|~calm(X))))=>((~tall(john)|creative(john))))&
(![X]:((creative(X)<~>funny(X))<=>~old(X)))&
(![X]:((~generous(X)|humble(X))<=>(~curious(X)&old(X))))&
(![X]:((happy(X)<~>calm(X))<=>~humble(X)))&
(![X]:((~rich(X)|~patient(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((happy(X)|generous(X))=>(~wise(X)<~>~patient(X))))&
(![X]:(brave(X)<=>(~old(X)<~>happy(X))))&
(((~happy(john)<~>~tall(john)))<=>((~brave(susan)&strong(susan))))&
(![X]:(tall(X)<=>(quiet(X)|~patient(X))))&
(![X]:((~rich(X)&quiet(X))=>(~quiet(X)&~happy(X))))&
(![X]:((happy(X)&~humble(X))=>(humble(X)|~tall(X))))&
(~calm(alice))&
((old(lucy)<~>strong(lucy)))&
(?[X]:((brave(X)<~>patient(X))))&
((calm(paul)<~>kind(paul)))&
((~creative(lucy)&~generous(lucy)))&
(happy(fred))&
(?[X]:((~patient(X)<~>~funny(X))))&
(?[X]:((~kind(X)&rich(X)))) | strong(lucy) | [
"p7",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 399529034013737269377418
% SZS output start Proof for 399529034013737269377418
8. ! [X0] : ((humble(X0) | ~generous(X0)) <=> (old(X0) & ~curious(X0))) [input p7]
18. old(lucy) <~> strong(lucy) [input p17]
21. ~generous(lucy) & ~creative(lucy) [input p20]
25. strong(lucy) [input hypothesis]
45. ! [X0] : (((humble(X0) | ~generous(X0)) | (~old(X0) | curious(X0))) & ((old(X0) & ~curious(X0)) | (~humble(X0) & generous(X0)))) [nnf transformation 8]
46. ! [X0] : ((humble(X0) | ~generous(X0) | ~old(X0) | curious(X0)) & ((old(X0) & ~curious(X0)) | (~humble(X0) & generous(X0)))) [flattening 45]
55. (~strong(lucy) | ~old(lucy)) & (strong(lucy) | old(lucy)) [nnf transformation 18]
90. generous(X0) | old(X0) [cnf transformation 46]
123. ~strong(lucy) | ~old(lucy) [cnf transformation 55]
129. ~generous(lucy) [cnf transformation 21]
135. strong(lucy) [cnf transformation 25]
205. 15 <=> old(lucy) [avatar definition]
207. ~old(lucy) <- (~15) [avatar component clause 205]
209. 16 <=> strong(lucy) [avatar definition]
212. ~15 | ~16 [avatar split clause 123,209,205]
244. 16 [avatar split clause 135,209]
250. old(lucy) [resolution 90,129]
251. $false <- (~15) [subsumption resolution 250,207]
252. 15 [avatar contradiction clause 251]
253. $false [avatar sat refutation 212,244,252]
% SZS output end Proof for 399529034013737269377418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not happy or not brave.
If someone is not kind or funny then someone is both brave and not old.
If someone is not generous or not strong then paul is both not wise and funny and vice versa.
Everyone who is not strong or not quiet is either not tall or not old and vice versa.
Everyone who is not quiet is both quiet and strong.
If someone is either calm or happy then paul is both not patient and not strong and vice versa.
Everyone who is rich is generous or not funny.
Everyone who is quiet is both creative and kind.
Everyone who is not patient is both not funny and not tall and vice versa.
If someone is not brave then alice is either old or funny.
If someone is either calm or happy then fred is either not creative or not happy and vice versa.
If someone is both not patient and calm then someone is not humble.
If someone is both not old and not funny then someone is both tall and not creative.
Everyone who is either not quiet or not old is both not patient and brave.
Someone is both not humble and rich.
Fred is rich.
Alice is both creative and curious.
Alice is not humble or rich.
Paul is brave or not curious. | Paul is not kind. | contradiction | (![X]:(~generous(X)=>(~happy(X)|~brave(X))))&
((?[X]:((~kind(X)|funny(X))))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((~generous(X)|~strong(X))))<=>((~wise(paul)&funny(paul))))&
(![X]:((~strong(X)|~quiet(X))<=>(~tall(X)<~>~old(X))))&
(![X]:(~quiet(X)=>(quiet(X)&strong(X))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~patient(paul)&~strong(paul))))&
(![X]:(rich(X)=>(generous(X)|~funny(X))))&
(![X]:(quiet(X)=>(creative(X)&kind(X))))&
(![X]:(~patient(X)<=>(~funny(X)&~tall(X))))&
((?[X]:(~brave(X)))=>((old(alice)<~>funny(alice))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~creative(fred)<~>~happy(fred))))&
((?[X]:((~patient(X)&calm(X))))=>(?[X]:(~humble(X))))&
((?[X]:((~old(X)&~funny(X))))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~quiet(X)<~>~old(X))=>(~patient(X)&brave(X))))&
(?[X]:((~humble(X)&rich(X))))&
(rich(fred))&
((creative(alice)&curious(alice)))&
((~humble(alice)|rich(alice)))&
((brave(paul)|~curious(paul))) | ~kind(paul) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1173318693788605436154921
% SZS output start Proof for 1173318693788605436154921
5. ! [X0] : (~quiet(X0) => (strong(X0) & quiet(X0))) [input p4]
8. ! [X0] : (quiet(X0) => (kind(X0) & creative(X0))) [input p7]
20. ~kind(paul) [input hypothesis]
30. ! [X0] : ((strong(X0) & quiet(X0)) | quiet(X0)) [ennf transformation 5]
33. ! [X0] : ((kind(X0) & creative(X0)) | ~quiet(X0)) [ennf transformation 8]
81. quiet(X0) | quiet(X0) [cnf transformation 30]
91. kind(X0) | ~quiet(X0) [cnf transformation 33]
116. ~kind(paul) [cnf transformation 20]
117. quiet(X0) [duplicate literal removal 81]
127. 3 <=> ! [X1] : kind(X1) [avatar definition]
128. kind(X1) <- (3) [avatar component clause 127]
191. kind(X0) [subsumption resolution 91,117]
192. 3 [avatar split clause 191,127]
239. $false <- (3) [resolution 128,116]
240. ~3 [avatar contradiction clause 239]
241. $false [avatar sat refutation 192,240]
% SZS output end Proof for 1173318693788605436154921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then john is either 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. | John is generous. | contradiction | ((?[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))) | generous(john) | [
"p1",
"p5",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2439633517881123339234942
% SZS output start Proof for 2439633517881123339234942
2. ! [X0] : (~generous(X0) <=> (old(X0) | ~generous(X0))) [input p1]
6. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X0] : curious(X0) [input p5]
10. ! [X0] : (~generous(X0) <=> (~curious(X0) & ~old(X0))) [input p9]
16. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p15]
23. generous(john) [input hypothesis]
24. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X1] : curious(X1) [rectify 6]
37. ! [X0] : ((~generous(X0) | (~old(X0) & generous(X0))) & ((old(X0) | ~generous(X0)) | generous(X0))) [nnf transformation 2]
38. ! [X0] : ((~generous(X0) | (~old(X0) & generous(X0))) & (old(X0) | ~generous(X0) | generous(X0))) [flattening 37]
45. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (~brave(X0) | ~strong(X0))) [nnf transformation 24]
46. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (~brave(X3) | ~strong(X3))) [rectify 45]
47. ? [X0] : (brave(X0) & strong(X0)) => (brave(sK2) & strong(sK2)) [choice axiom]
48. ? [X2] : curious(X2) => curious(sK3) [choice axiom]
49. ((brave(sK2) & strong(sK2)) | ! [X1] : ~curious(X1)) & (curious(sK3) | ! [X3] : (~brave(X3) | ~strong(X3))) [skolemisation 46,48,47]
53. ! [X0] : ((~generous(X0) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | generous(X0))) [nnf transformation 10]
54. ! [X0] : ((~generous(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | generous(X0))) [flattening 53]
59. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 16]
60. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 59]
74. ~old(X0) | ~generous(X0) [cnf transformation 38]
88. brave(sK2) | ~curious(X1) [cnf transformation 49]
99. ~generous(X0) | curious(X0) | old(X0) [cnf transformation 54]
112. ~brave(X0) | ~brave(X0) [cnf transformation 60]
124. generous(john) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 112]
192. 14 <=> ! [X1] : ~curious(X1) [avatar definition]
193. ~curious(X1) <- (14) [avatar component clause 192]
195. 15 <=> brave(sK2) [avatar definition]
197. brave(sK2) <- (15) [avatar component clause 195]
198. 14 | 15 [avatar split clause 88,195,192]
228. ~generous(X0) | curious(X0) [subsumption resolution 99,74]
258. $false <- (15) [subsumption resolution 197,126]
259. ~15 [avatar contradiction clause 258]
276. curious(john) [resolution 228,124]
277. $false <- (14) [subsumption resolution 276,193]
278. ~14 [avatar contradiction clause 277]
279. $false [avatar sat refutation 198,259,278]
% SZS output end Proof for 2439633517881123339234942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not brave then someone is both not calm and not curious and vice versa.
Everyone who is either tall or brave is both curious and humble.
If someone is either not funny or wise then someone is not old or not generous.
Everyone who is not humble is both not strong and not calm.
If someone is either not happy or strong then someone is generous or not quiet and vice versa.
Everyone who is either not patient or not calm is not curious or calm and vice versa.
If alice is happy then alice is both strong and not quiet and vice versa.
Everyone who is both humble and not rich is either not old or not humble.
If someone is both generous and brave then someone is brave or creative and vice versa.
If lucy is not kind then someone is kind or not old.
Everyone who is either generous or not calm is not patient.
Everyone who is patient or funny is not generous and vice versa.
If fred is both not humble and not strong then someone is either quiet or kind.
If john is both generous and not tall then mary is either not rich or humble and vice versa.
Everyone who is old is not humble.
Everyone who is not curious or not creative is not humble.
Someone is wise.
Mary is tall or brave.
Someone is patient or not generous.
Someone is both not tall and wise.
Alice is tall.
John is patient or tall.
Someone is rich or wise.
Someone is patient or kind. | Fred is not curious. | contradiction | ((~brave(mary))<=>(?[X]:((~calm(X)&~curious(X)))))&
(![X]:((tall(X)<~>brave(X))=>(curious(X)&humble(X))))&
((?[X]:((~funny(X)<~>wise(X))))=>(?[X]:((~old(X)|~generous(X)))))&
(![X]:(~humble(X)=>(~strong(X)&~calm(X))))&
((?[X]:((~happy(X)<~>strong(X))))<=>(?[X]:((generous(X)|~quiet(X)))))&
(![X]:((~patient(X)<~>~calm(X))<=>(~curious(X)|calm(X))))&
((happy(alice))<=>((strong(alice)&~quiet(alice))))&
(![X]:((humble(X)&~rich(X))=>(~old(X)<~>~humble(X))))&
((?[X]:((generous(X)&brave(X))))<=>(?[X]:((brave(X)|creative(X)))))&
((~kind(lucy))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:((generous(X)<~>~calm(X))=>~patient(X)))&
(![X]:((patient(X)|funny(X))<=>~generous(X)))&
(((~humble(fred)&~strong(fred)))=>(?[X]:((quiet(X)<~>kind(X)))))&
(((generous(john)&~tall(john)))<=>((~rich(mary)<~>humble(mary))))&
(![X]:(old(X)=>~humble(X)))&
(![X]:((~curious(X)|~creative(X))=>~humble(X)))&
(?[X]:(wise(X)))&
((tall(mary)|brave(mary)))&
(?[X]:((patient(X)|~generous(X))))&
(?[X]:((~tall(X)&wise(X))))&
(tall(alice))&
((patient(john)|tall(john)))&
(?[X]:((rich(X)|wise(X))))&
(?[X]:((patient(X)|kind(X)))) | ~curious(fred) | [
"p3",
"p5",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3806666049843408510353523
% SZS output start Proof for 3806666049843408510353523
4. ! [X0] : (~humble(X0) => (~calm(X0) & ~strong(X0))) [input p3]
6. ! [X0] : ((~patient(X0) <~> ~calm(X0)) <=> (calm(X0) | ~curious(X0))) [input p5]
11. ! [X0] : ((generous(X0) <~> ~calm(X0)) => ~patient(X0)) [input p10]
12. ! [X0] : ((funny(X0) | patient(X0)) <=> ~generous(X0)) [input p11]
16. ! [X0] : ((~creative(X0) | ~curious(X0)) => ~humble(X0)) [input p15]
25. ~curious(fred) [input hypothesis]
31. ! [X0] : ((~calm(X0) & ~strong(X0)) | humble(X0)) [ennf transformation 4]
35. ! [X0] : (~patient(X0) | (generous(X0) <=> ~calm(X0))) [ennf transformation 11]
39. ! [X0] : (~humble(X0) | (creative(X0) & curious(X0))) [ennf transformation 16]
54. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [nnf transformation 6]
55. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [flattening 54]
66. ! [X0] : (~patient(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) [nnf transformation 35]
67. ! [X0] : (((funny(X0) | patient(X0)) | generous(X0)) & (~generous(X0) | (~funny(X0) & ~patient(X0)))) [nnf transformation 12]
68. ! [X0] : ((funny(X0) | patient(X0) | generous(X0)) & (~generous(X0) | (~funny(X0) & ~patient(X0)))) [flattening 67]
94. ~calm(X0) | humble(X0) [cnf transformation 31]
104. ~calm(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 55]
105. patient(X0) | calm(X0) | curious(X0) [cnf transformation 55]
119. ~patient(X0) | generous(X0) | calm(X0) [cnf transformation 66]
120. ~generous(X0) | ~patient(X0) [cnf transformation 68]
132. ~humble(X0) | curious(X0) [cnf transformation 39]
143. ~curious(fred) [cnf transformation 25]
146. ~patient(X0) | ~calm(X0) [duplicate literal removal 104]
148. 1 <=> ! [X0] : (curious(X0) | calm(X0)) [avatar definition]
149. curious(X0) | calm(X0) <- (1) [avatar component clause 148]
274. ~patient(X0) | generous(X0) [subsumption resolution 119,146]
276. ~patient(X0) [subsumption resolution 120,274]
279. 30 <=> humble(fred) [avatar definition]
280. ~humble(fred) <- (~30) [avatar component clause 279]
281. humble(fred) <- (30) [avatar component clause 279]
333. curious(fred) <- (30) [resolution 132,281]
335. $false <- (30) [subsumption resolution 333,143]
336. ~30 [avatar contradiction clause 335]
418. calm(fred) <- (1) [resolution 149,143]
434. calm(X3) | curious(X3) [resolution 105,276]
441. humble(fred) <- (1) [resolution 418,94]
442. $false <- (1, ~30) [subsumption resolution 441,280]
443. ~1 | 30 [avatar contradiction clause 442]
444. 1 [avatar split clause 434,148]
451. $false [avatar sat refutation 336,443,444]
% SZS output end Proof for 3806666049843408510353523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or tall is both not brave and old.
If mary is generous then alice is curious.
Everyone who is both not wise and curious is wise or patient and vice versa.
Everyone who is not funny is not curious and vice versa.
If lucy is quiet then someone is curious.
Everyone who is both generous and not kind is wise and vice versa.
Everyone who is not humble or not tall is kind.
If paul is not quiet then mary is calm and vice versa.
If susan is wise or not brave then lucy is quiet and vice versa.
If susan is both not humble and not strong then someone is both patient and tall.
If alice is not brave or wise then someone is both funny and not tall.
If fred is not rich then fred is both happy and not wise.
If mary is humble or not calm then someone is generous and vice versa.
If fred is both not curious and not creative then susan is both not humble and not patient and vice versa.
If paul is both kind and humble then someone is not funny or quiet and vice versa.
Everyone who is humble is either strong or not rich and vice versa.
Susan is either quiet or calm.
Someone is both patient and not creative.
Someone is curious.
Someone is either old or generous.
Someone is not creative or not patient.
Fred is funny.
Lucy is not curious or calm.
Lucy is patient. | Susan is curious. | neutral | (![X]:((~wise(X)<~>tall(X))=>(~brave(X)&old(X))))&
((generous(mary))=>(curious(alice)))&
(![X]:((~wise(X)&curious(X))<=>(wise(X)|patient(X))))&
(![X]:(~funny(X)<=>~curious(X)))&
((quiet(lucy))=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~kind(X))<=>wise(X)))&
(![X]:((~humble(X)|~tall(X))=>kind(X)))&
((~quiet(paul))<=>(calm(mary)))&
(((wise(susan)|~brave(susan)))<=>(quiet(lucy)))&
(((~humble(susan)&~strong(susan)))=>(?[X]:((patient(X)&tall(X)))))&
(((~brave(alice)|wise(alice)))=>(?[X]:((funny(X)&~tall(X)))))&
((~rich(fred))=>((happy(fred)&~wise(fred))))&
(((humble(mary)|~calm(mary)))<=>(?[X]:(generous(X))))&
(((~curious(fred)&~creative(fred)))<=>((~humble(susan)&~patient(susan))))&
(((kind(paul)&humble(paul)))<=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:(humble(X)<=>(strong(X)<~>~rich(X))))&
((quiet(susan)<~>calm(susan)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:(curious(X)))&
(?[X]:((old(X)<~>generous(X))))&
(?[X]:((~creative(X)|~patient(X))))&
(funny(fred))&
((~curious(lucy)|calm(lucy)))&
(patient(lucy)) | curious(susan) | [] | null | 0 |
Everyone who is tall or rich is rich or quiet and vice versa. If alice is either not creative or humble then someone is either humble or old and vice versa. Everyone who is generous or not quiet is either happy or strong and vice versa. Everyone who is either not funny or not humble is strong or generous. Everyone who is not happy or not kind is either tall or not happy and vice versa. If someone is either not calm or not rich then lucy is both quiet and calm and vice versa. Everyone who is either not tall or funny is happy and vice versa. Everyone who is not strong or not kind is brave and vice versa. If someone is either funny or happy then fred is not funny or not generous and vice versa. If someone is not quiet or patient then mary is either tall or generous. Everyone who is either old or generous is not calm and vice versa. If alice is calm then someone is calm. Everyone who is both not quiet and calm is old or tall. Everyone who is both brave and not calm is both wise and calm and vice versa. Everyone who is both not kind and not brave is not old or not kind and vice versa. Everyone who is quiet or not strong is strong or funny. Someone is both kind and wise. John is not generous or not wise. Lucy is generous. Mary is both quiet and not funny. Fred is not happy or not funny. Someone is calm. Lucy is wise or curious. Mary is either not generous or generous. | Alice is quiet. | entailment | (![X]:((tall(X)|rich(X))<=>(rich(X)|quiet(X))))&
(((~creative(alice)<~>humble(alice)))<=>(?[X]:((humble(X)<~>old(X)))))&
(![X]:((generous(X)|~quiet(X))<=>(happy(X)<~>strong(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(strong(X)|generous(X))))&
(![X]:((~happy(X)|~kind(X))<=>(tall(X)<~>~happy(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((quiet(lucy)&calm(lucy))))&
(![X]:((~tall(X)<~>funny(X))<=>happy(X)))&
(![X]:((~strong(X)|~kind(X))<=>brave(X)))&
((?[X]:((funny(X)<~>happy(X))))<=>((~funny(fred)|~generous(fred))))&
((?[X]:((~quiet(X)|patient(X))))=>((tall(mary)<~>generous(mary))))&
(![X]:((old(X)<~>generous(X))<=>~calm(X)))&
((calm(alice))=>(?[X]:(calm(X))))&
(![X]:((~quiet(X)&calm(X))=>(old(X)|tall(X))))&
(![X]:((brave(X)&~calm(X))<=>(wise(X)&calm(X))))&
(![X]:((~kind(X)&~brave(X))<=>(~old(X)|~kind(X))))&
(![X]:((quiet(X)|~strong(X))=>(strong(X)|funny(X))))&
(?[X]:((kind(X)&wise(X))))&
((~generous(john)|~wise(john)))&
(generous(lucy))&
((quiet(mary)&~funny(mary)))&
((~happy(fred)|~funny(fred)))&
(?[X]:(calm(X)))&
((wise(lucy)|curious(lucy)))&
((~generous(mary)<~>generous(mary))) | quiet(alice) | [
"p2",
"p4",
"p6",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8729943364412900824639412
% SZS output start Proof for 8729943364412900824639412
3. ! [X0] : ((~quiet(X0) | generous(X0)) <=> (happy(X0) <~> strong(X0))) [input p2]
5. ! [X0] : ((~kind(X0) | ~happy(X0)) <=> (tall(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((~tall(X0) <~> funny(X0)) <=> happy(X0)) [input p6]
10. ? [X0] : (patient(X0) | ~quiet(X0)) => (tall(mary) <~> generous(mary)) [input p9]
16. ! [X0] : ((~strong(X0) | quiet(X0)) => (funny(X0) | strong(X0))) [input p15]
20. ~funny(mary) & quiet(mary) [input p19]
25. ~quiet(alice) [input hypothesis]
27. ? [X0] : ~quiet(X0) => (tall(mary) <~> generous(mary)) [pure predicate removal 10]
30. (tall(mary) <~> generous(mary)) | ! [X0] : quiet(X0) [ennf transformation 27]
34. ! [X0] : ((funny(X0) | strong(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 16]
35. ! [X0] : (funny(X0) | strong(X0) | (strong(X0) & ~quiet(X0))) [flattening 34]
42. ! [X0] : (((~quiet(X0) | generous(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (quiet(X0) & ~generous(X0)))) [nnf transformation 3]
43. ! [X0] : ((~quiet(X0) | generous(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (quiet(X0) & ~generous(X0)))) [flattening 42]
45. ! [X0] : (((~kind(X0) | ~happy(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (kind(X0) & happy(X0)))) [nnf transformation 5]
46. ! [X0] : ((~kind(X0) | ~happy(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0)))) & (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (kind(X0) & happy(X0)))) [flattening 45]
52. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~happy(X0)) & (happy(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [nnf transformation 7]
60. ((~generous(mary) | ~tall(mary)) & (generous(mary) | tall(mary))) | ! [X0] : quiet(X0) [nnf transformation 30]
87. ~strong(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 43]
95. happy(X0) | ~tall(X0) | happy(X0) [cnf transformation 46]
105. happy(X0) | funny(X0) | tall(X0) [cnf transformation 52]
107. funny(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 52]
118. generous(mary) | tall(mary) | quiet(X0) [cnf transformation 60]
136. funny(X0) | strong(X0) | strong(X0) [cnf transformation 35]
142. ~funny(mary) [cnf transformation 20]
147. ~quiet(alice) [cnf transformation 25]
148. funny(X0) | strong(X0) [duplicate literal removal 136]
151. ~tall(X0) | happy(X0) [duplicate literal removal 95]
211. ~tall(X0) | funny(X0) [subsumption resolution 107,151]
212. funny(X0) | happy(X0) [subsumption resolution 105,211]
242. 19 <=> ! [X0] : quiet(X0) [avatar definition]
243. quiet(X0) <- (19) [avatar component clause 242]
245. 20 <=> tall(mary) [avatar definition]
246. tall(mary) <- (20) [avatar component clause 245]
249. 21 <=> generous(mary) [avatar definition]
250. generous(mary) <- (21) [avatar component clause 249]
253. 19 | 20 | 21 [avatar split clause 118,249,245,242]
282. $false <- (19) [resolution 243,147]
283. ~19 [avatar contradiction clause 282]
286. strong(mary) [resolution 148,142]
293. funny(mary) <- (20) [resolution 211,246]
294. $false <- (20) [subsumption resolution 293,142]
295. ~20 [avatar contradiction clause 294]
296. happy(mary) [resolution 212,142]
327. ~happy(mary) | ~generous(mary) [resolution 87,286]
332. ~generous(mary) [subsumption resolution 327,296]
333. $false <- (21) [subsumption resolution 332,250]
334. ~21 [avatar contradiction clause 333]
335. $false [avatar sat refutation 253,283,295,334]
% SZS output end Proof for 8729943364412900824639412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not wise and not curious then someone is either not strong or not generous.
Everyone who is funny or not curious is wise and vice versa.
Everyone who is rich is not wise or not patient.
Everyone who is humble is either not rich or not old.
Everyone who is either not creative or old is humble or funny and vice versa.
Everyone who is both not humble and not curious is both tall and not strong and vice versa.
If lucy is not quiet then someone is wise and vice versa.
Everyone who is either strong or not funny is not calm and vice versa.
If someone is either not humble or brave then someone is not creative or quiet.
If fred is patient then lucy is calm or not creative and vice versa.
Everyone who is either not generous or not old is both kind and curious.
Everyone who is not rich or old is either not tall or creative.
If susan is both not tall and funny then someone is both not curious and kind and vice versa.
Everyone who is either rich or not brave is either happy or not curious and vice versa.
Everyone who is not tall or humble is tall or calm and vice versa.
Everyone who is rich or not rich is either tall or patient and vice versa.
Susan is not funny or brave.
Fred is funny or humble.
Fred is either not creative or not patient.
Someone is quiet or brave.
Mary is either not kind or not strong.
Susan is both kind and old.
Someone is strong.
Someone is both not curious and rich. | Susan is not curious. | contradiction | (((~wise(mary)&~curious(mary)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((funny(X)|~curious(X))<=>wise(X)))&
(![X]:(rich(X)=>(~wise(X)|~patient(X))))&
(![X]:(humble(X)=>(~rich(X)<~>~old(X))))&
(![X]:((~creative(X)<~>old(X))<=>(humble(X)|funny(X))))&
(![X]:((~humble(X)&~curious(X))<=>(tall(X)&~strong(X))))&
((~quiet(lucy))<=>(?[X]:(wise(X))))&
(![X]:((strong(X)<~>~funny(X))<=>~calm(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
((patient(fred))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~generous(X)<~>~old(X))=>(kind(X)&curious(X))))&
(![X]:((~rich(X)|old(X))=>(~tall(X)<~>creative(X))))&
(((~tall(susan)&funny(susan)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(happy(X)<~>~curious(X))))&
(![X]:((~tall(X)|humble(X))<=>(tall(X)|calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(tall(X)<~>patient(X))))&
((~funny(susan)|brave(susan)))&
((funny(fred)|humble(fred)))&
((~creative(fred)<~>~patient(fred)))&
(?[X]:((quiet(X)|brave(X))))&
((~kind(mary)<~>~strong(mary)))&
((kind(susan)&old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~curious(X)&rich(X)))) | ~curious(susan) | [
"p1",
"p2",
"p4",
"p5",
"p11",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6872398329630598303759667
% SZS output start Proof for 6872398329630598303759667
2. ! [X0] : ((~curious(X0) | funny(X0)) <=> wise(X0)) [input p1]
3. ! [X0] : (rich(X0) => (~patient(X0) | ~wise(X0))) [input p2]
5. ! [X0] : ((~creative(X0) <~> old(X0)) <=> (funny(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> (~strong(X0) & tall(X0))) [input p5]
12. ! [X0] : ((old(X0) | ~rich(X0)) => (~tall(X0) <~> creative(X0))) [input p11]
13. (funny(susan) & ~tall(susan)) <=> ? [X0] : (kind(X0) & ~curious(X0)) [input p12]
15. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (calm(X0) | tall(X0))) [input p14]
16. ! [X0] : ((~rich(X0) | rich(X0)) <=> (tall(X0) <~> patient(X0))) [input p15]
22. old(susan) & kind(susan) [input p21]
25. ~curious(susan) [input hypothesis]
29. ! [X0] : ((~patient(X0) | ~wise(X0)) | ~rich(X0)) [ennf transformation 3]
30. ! [X0] : (~patient(X0) | ~wise(X0) | ~rich(X0)) [flattening 29]
34. ! [X0] : ((~tall(X0) <~> creative(X0)) | (~old(X0) & rich(X0))) [ennf transformation 12]
38. ! [X0] : (((~curious(X0) | funny(X0)) | ~wise(X0)) & (wise(X0) | (curious(X0) & ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : ((~curious(X0) | funny(X0) | ~wise(X0)) & (wise(X0) | (curious(X0) & ~funny(X0)))) [flattening 38]
41. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (~funny(X0) & ~humble(X0))) & ((funny(X0) | humble(X0)) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [nnf transformation 5]
42. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (~funny(X0) & ~humble(X0))) & (funny(X0) | humble(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [flattening 41]
43. ! [X0] : (((~curious(X0) & ~humble(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (curious(X0) | humble(X0)))) [nnf transformation 6]
44. ! [X0] : (((~curious(X0) & ~humble(X0)) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | curious(X0) | humble(X0))) [flattening 43]
57. ! [X0] : (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~old(X0) & rich(X0))) [nnf transformation 34]
58. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X0] : (kind(X0) & ~curious(X0)) | (~funny(susan) | tall(susan))) [nnf transformation 13]
59. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X0] : (kind(X0) & ~curious(X0)) | ~funny(susan) | tall(susan)) [flattening 58]
60. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X1] : (kind(X1) & ~curious(X1)) | ~funny(susan) | tall(susan)) [rectify 59]
61. ? [X1] : (kind(X1) & ~curious(X1)) => (kind(sK3) & ~curious(sK3)) [choice axiom]
62. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & ((kind(sK3) & ~curious(sK3)) | ~funny(susan) | tall(susan)) [skolemisation 60,61]
64. ! [X0] : (((humble(X0) | ~tall(X0)) | (~calm(X0) & ~tall(X0))) & ((calm(X0) | tall(X0)) | (~humble(X0) & tall(X0)))) [nnf transformation 15]
65. ! [X0] : ((humble(X0) | ~tall(X0) | (~calm(X0) & ~tall(X0))) & (calm(X0) | tall(X0) | (~humble(X0) & tall(X0)))) [flattening 64]
66. ! [X0] : (((~rich(X0) | rich(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [nnf transformation 16]
67. ! [X0] : ((~rich(X0) | rich(X0) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [flattening 66]
79. curious(X0) | wise(X0) [cnf transformation 39]
81. ~patient(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 30]
88. ~old(X0) | creative(X0) | ~humble(X0) [cnf transformation 42]
90. tall(X0) | curious(X0) | humble(X0) [cnf transformation 44]
111. ~creative(X0) | tall(X0) | rich(X0) [cnf transformation 57]
115. ~tall(susan) | ~kind(X0) | curious(X0) [cnf transformation 62]
127. humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
129. patient(X0) | tall(X0) | ~rich(X0) [cnf transformation 67]
130. patient(X0) | tall(X0) | rich(X0) [cnf transformation 67]
131. ~patient(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 67]
132. ~patient(X0) | ~tall(X0) | rich(X0) [cnf transformation 67]
142. kind(susan) [cnf transformation 22]
143. old(susan) [cnf transformation 22]
147. ~curious(susan) [cnf transformation 25]
149. ~tall(X0) | humble(X0) [duplicate literal removal 127]
213. 15 <=> ! [X0] : (~kind(X0) | curious(X0)) [avatar definition]
214. ~kind(X0) | curious(X0) <- (15) [avatar component clause 213]
221. 17 <=> tall(susan) [avatar definition]
223. ~tall(susan) <- (~17) [avatar component clause 221]
224. 15 | ~17 [avatar split clause 115,221,213]
235. ~tall(X0) | ~patient(X0) [subsumption resolution 131,132]
236. tall(X0) | patient(X0) [subsumption resolution 129,130]
280. wise(susan) [resolution 79,147]
281. curious(susan) <- (15) [resolution 214,142]
283. $false <- (15) [subsumption resolution 281,147]
284. ~15 [avatar contradiction clause 283]
288. humble(X1) | patient(X1) [resolution 236,149]
289. patient(susan) <- (~17) [resolution 236,223]
298. ~wise(susan) | ~rich(susan) <- (~17) [resolution 81,289]
300. ~rich(susan) <- (~17) [subsumption resolution 298,280]
303. creative(susan) | ~humble(susan) [resolution 88,143]
305. 29 <=> humble(susan) [avatar definition]
307. ~humble(susan) <- (~29) [avatar component clause 305]
309. 30 <=> creative(susan) [avatar definition]
311. creative(susan) <- (30) [avatar component clause 309]
312. ~29 | 30 [avatar split clause 303,309,305]
319. curious(X0) | humble(X0) | ~patient(X0) [resolution 90,235]
323. humble(X0) | curious(X0) [subsumption resolution 319,288]
325. curious(susan) <- (~29) [resolution 323,307]
326. $false <- (~29) [subsumption resolution 325,147]
327. 29 [avatar contradiction clause 326]
421. tall(susan) | rich(susan) <- (30) [resolution 111,311]
422. rich(susan) <- (~17, 30) [subsumption resolution 421,223]
423. $false <- (~17, 30) [subsumption resolution 422,300]
424. 17 | ~30 [avatar contradiction clause 423]
425. $false [avatar sat refutation 224,284,312,327,424]
% SZS output end Proof for 6872398329630598303759667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either strong or not patient then someone is both happy and funny and vice versa. If someone is rich then john is not strong and vice versa. If someone is both not old and calm then fred is either strong or happy and vice versa. Everyone who is both not kind and generous is either not kind or patient. Everyone who is strong or curious is either strong or brave and vice versa. Everyone who is both not generous and calm is tall or rich and vice versa. If paul is calm then alice is both not creative and creative. Everyone who is tall is not strong or old. Everyone who is either not patient or not old is humble and vice versa. If someone is kind then someone is not generous and vice versa. Everyone who is not funny is either not patient or not tall. Everyone who is either not patient or funny is not happy and vice versa. If fred is tall or not tall then someone is kind. If someone is either not patient or not wise then someone is either not calm or not old and vice versa. If john is tall then someone is old or brave. Everyone who is not strong or not brave is not humble and vice versa. Lucy is both wise and happy. Someone is not old. Fred is both not brave and not old. Mary is both patient and curious. John is both not happy and not brave. Someone is either not brave or not humble. Lucy is not rich or not generous. | Mary is happy. | neutral | (((strong(paul)<~>~patient(paul)))<=>(?[X]:((happy(X)&funny(X)))))&
((?[X]:(rich(X)))<=>(~strong(john)))&
((?[X]:((~old(X)&calm(X))))<=>((strong(fred)<~>happy(fred))))&
(![X]:((~kind(X)&generous(X))=>(~kind(X)<~>patient(X))))&
(![X]:((strong(X)|curious(X))<=>(strong(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>(tall(X)|rich(X))))&
((calm(paul))=>((~creative(alice)&creative(alice))))&
(![X]:(tall(X)=>(~strong(X)|old(X))))&
(![X]:((~patient(X)<~>~old(X))<=>humble(X)))&
((?[X]:(kind(X)))<=>(?[X]:(~generous(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>funny(X))<=>~happy(X)))&
(((tall(fred)|~tall(fred)))=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)<~>~wise(X))))<=>(?[X]:((~calm(X)<~>~old(X)))))&
((tall(john))=>(?[X]:((old(X)|brave(X)))))&
(![X]:((~strong(X)|~brave(X))<=>~humble(X)))&
((wise(lucy)&happy(lucy)))&
(?[X]:(~old(X)))&
((~brave(fred)&~old(fred)))&
((patient(mary)&curious(mary)))&
((~happy(john)&~brave(john)))&
(?[X]:((~brave(X)<~>~humble(X))))&
((~rich(lucy)|~generous(lucy))) | happy(mary) | [] | null | 0 |
Everyone who is both not strong and strong is old and vice versa. Everyone who is curious or not humble is generous and vice versa. If someone is calm or not creative then mary is either calm or not happy and vice versa. Everyone who is brave or patient is either not wise or not happy and vice versa. Everyone who is not kind is quiet. Everyone who is not humble or not tall is not creative and vice versa. Everyone who is either wise or generous is creative or generous. If fred is not curious or not happy then someone is not old. Everyone who is humble is kind. If fred is either not funny or creative then alice is either funny or quiet and vice versa. If lucy is both not old and not wise then susan is either happy or creative and vice versa. If someone is either quiet or not humble then someone is not brave. If john is either funny or not kind then mary is strong. Everyone who is curious is both not humble and creative. Everyone who is either patient or not generous is both curious and not tall. Everyone who is either not tall or rich is kind or not tall. John is either not kind or not quiet. Someone is either happy or not old. John is not old or humble. Someone is either not humble or not curious. Someone is funny. Someone is both tall and kind. Someone is both not curious and not brave. | Susan is curious. | contradiction | (![X]:((~strong(X)&strong(X))<=>old(X)))&
(![X]:((curious(X)|~humble(X))<=>generous(X)))&
((?[X]:((calm(X)|~creative(X))))<=>((calm(mary)<~>~happy(mary))))&
(![X]:((brave(X)|patient(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:(~kind(X)=>quiet(X)))&
(![X]:((~humble(X)|~tall(X))<=>~creative(X)))&
(![X]:((wise(X)<~>generous(X))=>(creative(X)|generous(X))))&
(((~curious(fred)|~happy(fred)))=>(?[X]:(~old(X))))&
(![X]:(humble(X)=>kind(X)))&
(((~funny(fred)<~>creative(fred)))<=>((funny(alice)<~>quiet(alice))))&
(((~old(lucy)&~wise(lucy)))<=>((happy(susan)<~>creative(susan))))&
((?[X]:((quiet(X)<~>~humble(X))))=>(?[X]:(~brave(X))))&
(((funny(john)<~>~kind(john)))=>(strong(mary)))&
(![X]:(curious(X)=>(~humble(X)&creative(X))))&
(![X]:((patient(X)<~>~generous(X))=>(curious(X)&~tall(X))))&
(![X]:((~tall(X)<~>rich(X))=>(kind(X)|~tall(X))))&
((~kind(john)<~>~quiet(john)))&
(?[X]:((happy(X)<~>~old(X))))&
((~old(john)|humble(john)))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:(funny(X)))&
(?[X]:((tall(X)&kind(X))))&
(?[X]:((~curious(X)&~brave(X)))) | curious(susan) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6089222058821566211794711
% SZS output start Proof for 6089222058821566211794711
6. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> ~creative(X0)) [input p5]
14. ! [X0] : (curious(X0) => (creative(X0) & ~humble(X0))) [input p13]
24. curious(susan) [input hypothesis]
33. ! [X0] : ((creative(X0) & ~humble(X0)) | ~curious(X0)) [ennf transformation 14]
47. ! [X0] : (((~tall(X0) | ~humble(X0)) | creative(X0)) & (~creative(X0) | (tall(X0) & humble(X0)))) [nnf transformation 6]
48. ! [X0] : ((~tall(X0) | ~humble(X0) | creative(X0)) & (~creative(X0) | (tall(X0) & humble(X0)))) [flattening 47]
94. ~creative(X0) | humble(X0) [cnf transformation 48]
120. ~humble(X0) | ~curious(X0) [cnf transformation 33]
121. ~curious(X0) | creative(X0) [cnf transformation 33]
140. curious(susan) [cnf transformation 24]
197. 11 <=> creative(susan) [avatar definition]
198. creative(susan) <- (11) [avatar component clause 197]
199. ~creative(susan) <- (~11) [avatar component clause 197]
258. humble(susan) <- (11) [resolution 94,198]
263. ~curious(susan) <- (11) [resolution 120,258]
265. $false <- (11) [subsumption resolution 263,140]
266. ~11 [avatar contradiction clause 265]
267. creative(susan) [resolution 121,140]
268. $false <- (~11) [subsumption resolution 267,199]
269. 11 [avatar contradiction clause 268]
270. $false [avatar sat refutation 266,269]
% SZS output end Proof for 6089222058821566211794711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not old is both not creative and not old and vice versa.
Everyone who is either creative or tall is both calm and not old and vice versa.
Everyone who is either wise or strong is either not quiet or not curious and vice versa.
Everyone who is either not brave or not happy is not quiet or calm and vice versa.
Everyone who is brave is not tall and vice versa.
Everyone who is either not patient or not strong is wise.
Everyone who is either not wise or not old is not brave.
Everyone who is both kind and not happy is both not funny and not calm.
Everyone who is humble is quiet.
If someone is tall then paul is both patient and not patient and vice versa.
Everyone who is quiet is old and vice versa.
Everyone who is tall is not happy or kind and vice versa.
If alice is not funny or curious then someone is both strong and not rich.
If someone is not brave or humble then someone is calm.
Everyone who is both kind and wise is both funny and generous.
Everyone who is both strong and not funny is either not funny or not old and vice versa.
Someone is patient.
Alice is not creative.
Lucy is old or not patient.
Someone is either not kind or not wise.
Mary is either patient or not curious. | Lucy is old. | entailment | (![X]:((~humble(X)&~old(X))<=>(~creative(X)&~old(X))))&
(![X]:((creative(X)<~>tall(X))<=>(calm(X)&~old(X))))&
(![X]:((wise(X)<~>strong(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((~brave(X)<~>~happy(X))<=>(~quiet(X)|calm(X))))&
(![X]:(brave(X)<=>~tall(X)))&
(![X]:((~patient(X)<~>~strong(X))=>wise(X)))&
(![X]:((~wise(X)<~>~old(X))=>~brave(X)))&
(![X]:((kind(X)&~happy(X))=>(~funny(X)&~calm(X))))&
(![X]:(humble(X)=>quiet(X)))&
((?[X]:(tall(X)))<=>((patient(paul)&~patient(paul))))&
(![X]:(quiet(X)<=>old(X)))&
(![X]:(tall(X)<=>(~happy(X)|kind(X))))&
(((~funny(alice)|curious(alice)))=>(?[X]:((strong(X)&~rich(X)))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:(calm(X))))&
(![X]:((kind(X)&wise(X))=>(funny(X)&generous(X))))&
(![X]:((strong(X)&~funny(X))<=>(~funny(X)<~>~old(X))))&
(?[X]:(patient(X)))&
(~creative(alice))&
((old(lucy)|~patient(lucy)))&
(?[X]:((~kind(X)<~>~wise(X))))&
((patient(mary)<~>~curious(mary))) | old(lucy) | [
"p3",
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 162353911922388802714077
% SZS output start Proof for 162353911922388802714077
4. ! [X0] : ((~brave(X0) <~> ~happy(X0)) <=> (calm(X0) | ~quiet(X0))) [input p3]
5. ! [X0] : (brave(X0) <=> ~tall(X0)) [input p4]
10. ? [X0] : tall(X0) <=> (~patient(paul) & patient(paul)) [input p9]
11. ! [X0] : (quiet(X0) <=> old(X0)) [input p10]
12. ! [X0] : (tall(X0) <=> (kind(X0) | ~happy(X0))) [input p11]
22. ~old(lucy) [input hypothesis]
40. ! [X0] : ((((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | (~calm(X0) & quiet(X0))) & ((calm(X0) | ~quiet(X0)) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))))) [nnf transformation 4]
41. ! [X0] : ((((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | (~calm(X0) & quiet(X0))) & (calm(X0) | ~quiet(X0) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))))) [flattening 40]
42. ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))) [nnf transformation 5]
45. (? [X0] : tall(X0) | (patient(paul) | ~patient(paul))) & ((~patient(paul) & patient(paul)) | ! [X0] : ~tall(X0)) [nnf transformation 10]
46. (? [X0] : tall(X0) | patient(paul) | ~patient(paul)) & ((~patient(paul) & patient(paul)) | ! [X0] : ~tall(X0)) [flattening 45]
47. (? [X0] : tall(X0) | patient(paul) | ~patient(paul)) & ((~patient(paul) & patient(paul)) | ! [X1] : ~tall(X1)) [rectify 46]
48. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
49. (tall(sK0) | patient(paul) | ~patient(paul)) & ((~patient(paul) & patient(paul)) | ! [X1] : ~tall(X1)) [skolemisation 47,48]
50. ! [X0] : ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0))) [nnf transformation 11]
51. ! [X0] : ((tall(X0) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | ~tall(X0))) [nnf transformation 12]
52. ! [X0] : ((tall(X0) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | ~tall(X0))) [flattening 51]
86. ~happy(X0) | ~brave(X0) | quiet(X0) [cnf transformation 41]
91. brave(X0) | tall(X0) [cnf transformation 42]
99. patient(paul) | ~tall(X1) [cnf transformation 49]
100. ~patient(paul) | ~tall(X1) [cnf transformation 49]
102. ~quiet(X0) | old(X0) [cnf transformation 50]
105. happy(X0) | tall(X0) [cnf transformation 52]
125. ~old(lucy) [cnf transformation 22]
129. 1 <=> ! [X1] : ~tall(X1) [avatar definition]
130. ~tall(X1) <- (1) [avatar component clause 129]
132. 2 <=> patient(paul) [avatar definition]
135. 1 | ~2 [avatar split clause 100,132,129]
136. 1 | 2 [avatar split clause 99,132,129]
165. 9 <=> old(lucy) [avatar definition]
166. ~old(lucy) <- (~9) [avatar component clause 165]
193. ~9 [avatar split clause 125,165]
201. ~brave(X0) | quiet(X0) | tall(X0) [resolution 86,105]
202. ~brave(X0) | quiet(X0) <- (1) [subsumption resolution 201,130]
205. quiet(X0) | tall(X0) <- (1) [resolution 202,91]
206. quiet(X0) <- (1) [subsumption resolution 205,130]
210. old(X0) <- (1) [resolution 206,102]
251. $false <- (1, ~9) [resolution 210,166]
253. ~1 | 9 [avatar contradiction clause 251]
254. $false [avatar sat refutation 135,136,193,253]
% SZS output end Proof for 162353911922388802714077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or kind is not curious.
If mary is kind or rich then paul is both calm and not wise and vice versa.
If someone is generous then someone is both not brave and not quiet and vice versa.
If lucy is either strong or funny then lucy is not tall.
Everyone who is tall or wise is both not tall and not calm and vice versa.
Everyone who is either tall or old is either wise or not kind.
If john is either funny or wise then someone is not quiet or humble.
Everyone who is not generous or not strong is tall or not calm.
If paul is both not wise and brave then lucy is either not happy or happy.
Everyone who is not creative is either not calm or not tall.
Everyone who is rich is tall or old and vice versa.
If someone is tall or not rich then someone is either quiet or creative and vice versa.
Everyone who is kind or not generous is either strong or not quiet and vice versa.
If someone is either calm or not wise then someone is not tall.
Everyone who is both not calm and brave is kind and vice versa.
If lucy is either not patient or not rich then susan is patient or not happy.
Someone is either not generous or not old.
Someone is calm.
Someone is not generous.
Susan is either humble or calm.
Someone is not patient or funny.
Paul is either not kind or calm.
Susan is calm.
Someone is kind or not happy. | Susan is quiet. | contradiction | (![X]:((generous(X)<~>kind(X))=>~curious(X)))&
(((kind(mary)|rich(mary)))<=>((calm(paul)&~wise(paul))))&
((?[X]:(generous(X)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(((strong(lucy)<~>funny(lucy)))=>(~tall(lucy)))&
(![X]:((tall(X)|wise(X))<=>(~tall(X)&~calm(X))))&
(![X]:((tall(X)<~>old(X))=>(wise(X)<~>~kind(X))))&
(((funny(john)<~>wise(john)))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~generous(X)|~strong(X))=>(tall(X)|~calm(X))))&
(((~wise(paul)&brave(paul)))=>((~happy(lucy)<~>happy(lucy))))&
(![X]:(~creative(X)=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)&brave(X))<=>kind(X)))&
(((~patient(lucy)<~>~rich(lucy)))=>((patient(susan)|~happy(susan))))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:(calm(X)))&
(?[X]:(~generous(X)))&
((humble(susan)<~>calm(susan)))&
(?[X]:((~patient(X)|funny(X))))&
((~kind(paul)<~>calm(paul)))&
(calm(susan))&
(?[X]:((kind(X)|~happy(X)))) | quiet(susan) | [
"p4",
"p7",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7982928713328621028469333
% SZS output start Proof for 7982928713328621028469333
5. ! [X0] : ((wise(X0) | tall(X0)) <=> (~calm(X0) & ~tall(X0))) [input p4]
8. ! [X0] : ((~strong(X0) | ~generous(X0)) => (~calm(X0) | tall(X0))) [input p7]
13. ! [X0] : ((~generous(X0) | kind(X0)) <=> (strong(X0) <~> ~quiet(X0))) [input p12]
15. ! [X0] : ((brave(X0) & ~calm(X0)) <=> kind(X0)) [input p14]
23. calm(susan) [input p22]
25. quiet(susan) [input hypothesis]
33. ! [X0] : ((~calm(X0) | tall(X0)) | (strong(X0) & generous(X0))) [ennf transformation 8]
34. ! [X0] : (~calm(X0) | tall(X0) | (strong(X0) & generous(X0))) [flattening 33]
49. ! [X0] : (((wise(X0) | tall(X0)) | (calm(X0) | tall(X0))) & ((~calm(X0) & ~tall(X0)) | (~wise(X0) & ~tall(X0)))) [nnf transformation 5]
50. ! [X0] : ((wise(X0) | tall(X0) | calm(X0) | tall(X0)) & ((~calm(X0) & ~tall(X0)) | (~wise(X0) & ~tall(X0)))) [flattening 49]
64. ! [X0] : (((~generous(X0) | kind(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (generous(X0) & ~kind(X0)))) [nnf transformation 13]
65. ! [X0] : ((~generous(X0) | kind(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (generous(X0) & ~kind(X0)))) [flattening 64]
70. ! [X0] : (((brave(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | (~brave(X0) | calm(X0)))) [nnf transformation 15]
71. ! [X0] : (((brave(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | ~brave(X0) | calm(X0))) [flattening 70]
96. ~tall(X0) | ~tall(X0) [cnf transformation 50]
107. ~calm(X0) | tall(X0) | generous(X0) [cnf transformation 34]
108. ~calm(X0) | tall(X0) | strong(X0) [cnf transformation 34]
126. ~strong(X0) | kind(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 65]
131. ~calm(X0) | ~kind(X0) [cnf transformation 71]
144. calm(susan) [cnf transformation 23]
146. quiet(susan) [cnf transformation 25]
147. ~tall(X0) [duplicate literal removal 96]
225. ~calm(X0) | strong(X0) [subsumption resolution 108,147]
226. ~calm(X0) | generous(X0) [subsumption resolution 107,147]
289. 30 <=> calm(susan) [avatar definition]
290. calm(susan) <- (30) [avatar component clause 289]
306. 30 [avatar split clause 144,289]
321. ~kind(susan) <- (30) [resolution 131,290]
327. strong(susan) <- (30) [resolution 225,290]
329. generous(susan) <- (30) [resolution 226,290]
356. kind(susan) | ~quiet(susan) | ~generous(susan) <- (30) [resolution 126,327]
359. ~quiet(susan) | ~generous(susan) <- (30) [subsumption resolution 356,321]
360. ~generous(susan) <- (30) [subsumption resolution 359,146]
361. $false <- (30) [subsumption resolution 360,329]
362. ~30 [avatar contradiction clause 361]
363. $false [avatar sat refutation 306,362]
% SZS output end Proof for 7982928713328621028469333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is not curious or not happy.
Everyone who is not curious is calm.
If someone is either brave or kind then someone is patient or not kind and vice versa.
Everyone who is generous or not funny is both funny and kind and vice versa.
Everyone who is calm is either tall or not humble and vice versa.
If susan is both not quiet and not patient then someone is generous or humble and vice versa.
Everyone who is old or kind is either brave or not patient and vice versa.
Everyone who is both not calm and wise is wise or not patient and vice versa.
If someone is not brave then alice is not funny and vice versa.
Everyone who is both curious and not generous is not old and vice versa.
Everyone who is tall or not patient is both rich and not strong.
Everyone who is humble or kind is not funny or rich and vice versa.
Everyone who is not happy or quiet is both creative and not funny and vice versa.
Everyone who is not old is either brave or not generous.
Everyone who is either quiet or not curious is funny or kind.
Someone is happy.
Mary is not quiet.
Susan is either strong or not strong. | Mary is not generous. | entailment | ((calm(fred))=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:(~curious(X)=>calm(X)))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((patient(X)|~kind(X)))))&
(![X]:((generous(X)|~funny(X))<=>(funny(X)&kind(X))))&
(![X]:(calm(X)<=>(tall(X)<~>~humble(X))))&
(((~quiet(susan)&~patient(susan)))<=>(?[X]:((generous(X)|humble(X)))))&
(![X]:((old(X)|kind(X))<=>(brave(X)<~>~patient(X))))&
(![X]:((~calm(X)&wise(X))<=>(wise(X)|~patient(X))))&
((?[X]:(~brave(X)))<=>(~funny(alice)))&
(![X]:((curious(X)&~generous(X))<=>~old(X)))&
(![X]:((tall(X)|~patient(X))=>(rich(X)&~strong(X))))&
(![X]:((humble(X)|kind(X))<=>(~funny(X)|rich(X))))&
(![X]:((~happy(X)|quiet(X))<=>(creative(X)&~funny(X))))&
(![X]:(~old(X)=>(brave(X)<~>~generous(X))))&
(![X]:((quiet(X)<~>~curious(X))=>(funny(X)|kind(X))))&
(?[X]:(happy(X)))&
(~quiet(mary))&
((strong(susan)<~>~strong(susan))) | ~generous(mary) | [
"p3",
"p5",
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4245156411905473874186637
% SZS output start Proof for 4245156411905473874186637
4. ! [X0] : ((~funny(X0) | generous(X0)) <=> (kind(X0) & funny(X0))) [input p3]
6. (~patient(susan) & ~quiet(susan)) <=> ? [X0] : (humble(X0) | generous(X0)) [input p5]
7. ! [X0] : ((kind(X0) | old(X0)) <=> (brave(X0) <~> ~patient(X0))) [input p6]
9. ? [X0] : ~brave(X0) <=> ~funny(alice) [input p8]
10. ! [X0] : ((~generous(X0) & curious(X0)) <=> ~old(X0)) [input p9]
14. ! [X0] : (~old(X0) => (brave(X0) <~> ~generous(X0))) [input p13]
19. generous(mary) [input hypothesis]
24. ! [X0] : ((brave(X0) <~> ~generous(X0)) | old(X0)) [ennf transformation 14]
34. ! [X0] : (((~funny(X0) | generous(X0)) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | (funny(X0) & ~generous(X0)))) [nnf transformation 4]
35. ! [X0] : ((~funny(X0) | generous(X0) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | (funny(X0) & ~generous(X0)))) [flattening 34]
37. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & (? [X0] : (humble(X0) | generous(X0)) | (patient(susan) | quiet(susan))) [nnf transformation 6]
38. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & (? [X0] : (humble(X0) | generous(X0)) | patient(susan) | quiet(susan)) [flattening 37]
39. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & (? [X1] : (humble(X1) | generous(X1)) | patient(susan) | quiet(susan)) [rectify 38]
40. ? [X1] : (humble(X1) | generous(X1)) => (humble(sK3) | generous(sK3)) [choice axiom]
41. ((~patient(susan) & ~quiet(susan)) | ! [X0] : (~humble(X0) & ~generous(X0))) & ((humble(sK3) | generous(sK3)) | patient(susan) | quiet(susan)) [skolemisation 39,40]
42. ! [X0] : (((kind(X0) | old(X0)) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | (~kind(X0) & ~old(X0)))) [nnf transformation 7]
43. ! [X0] : ((kind(X0) | old(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | (~kind(X0) & ~old(X0)))) [flattening 42]
46. (? [X0] : ~brave(X0) | funny(alice)) & (~funny(alice) | ! [X0] : brave(X0)) [nnf transformation 9]
47. (? [X0] : ~brave(X0) | funny(alice)) & (~funny(alice) | ! [X1] : brave(X1)) [rectify 46]
48. ? [X0] : ~brave(X0) => ~brave(sK4) [choice axiom]
49. (~brave(sK4) | funny(alice)) & (~funny(alice) | ! [X1] : brave(X1)) [skolemisation 47,48]
50. ! [X0] : (((~generous(X0) & curious(X0)) | old(X0)) & (~old(X0) | (generous(X0) | ~curious(X0)))) [nnf transformation 10]
51. ! [X0] : (((~generous(X0) & curious(X0)) | old(X0)) & (~old(X0) | generous(X0) | ~curious(X0))) [flattening 50]
56. ! [X0] : (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | old(X0)) [nnf transformation 24]
70. funny(X0) | funny(X0) [cnf transformation 35]
81. ~patient(susan) | ~generous(X0) [cnf transformation 41]
85. ~old(X0) | ~brave(X0) | patient(X0) [cnf transformation 43]
94. ~funny(alice) | brave(X1) [cnf transformation 49]
98. ~generous(X0) | old(X0) [cnf transformation 51]
113. generous(X0) | ~brave(X0) | old(X0) [cnf transformation 56]
120. generous(mary) [cnf transformation 19]
121. funny(X0) [duplicate literal removal 70]
174. 13 <=> patient(susan) [avatar definition]
176. ~patient(susan) <- (~13) [avatar component clause 174]
179. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
180. ~generous(X0) <- (14) [avatar component clause 179]
181. 14 | ~13 [avatar split clause 81,174,179]
197. brave(X1) [subsumption resolution 94,121]
202. generous(X0) | old(X0) [subsumption resolution 113,197]
203. old(X0) [subsumption resolution 202,98]
206. $false <- (14) [resolution 180,120]
207. ~14 [avatar contradiction clause 206]
227. ~brave(X1) | patient(X1) [resolution 85,203]
229. patient(X1) [subsumption resolution 227,197]
232. $false <- (~13) [resolution 229,176]
234. 13 [avatar contradiction clause 232]
235. $false [avatar sat refutation 181,207,234]
% SZS output end Proof for 4245156411905473874186637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and generous is either generous or happy and vice versa.
Everyone who is both not creative and funny is tall and vice versa.
If someone is humble then john is kind.
Everyone who is either calm or happy is strong.
If alice is not calm or not quiet then someone is not creative or generous and vice versa.
If someone is not humble then someone is either kind or not tall.
If someone is both not brave and generous then mary is old and vice versa.
If someone is curious then alice is either not patient or humble.
If paul is not quiet or not curious then paul is tall and vice versa.
Everyone who is rich or patient is not creative and vice versa.
Everyone who is funny is either not rich or not happy.
Everyone who is quiet or not calm is both rich and creative.
Everyone who is both funny and not generous is kind and vice versa.
Everyone who is brave or quiet is either curious or rich and vice versa.
If fred is either old or curious then someone is tall and vice versa.
Everyone who is both not generous and not calm is not curious or old and vice versa.
Someone is either brave or funny.
Fred is both happy and curious.
Mary is either not kind or wise.
Fred is wise or humble.
Lucy is both not creative and kind.
Someone is both patient and brave.
Someone is not quiet.
Someone is brave or not kind. | Paul is quiet. | contradiction | (![X]:((patient(X)&generous(X))<=>(generous(X)<~>happy(X))))&
(![X]:((~creative(X)&funny(X))<=>tall(X)))&
((?[X]:(humble(X)))=>(kind(john)))&
(![X]:((calm(X)<~>happy(X))=>strong(X)))&
(((~calm(alice)|~quiet(alice)))<=>(?[X]:((~creative(X)|generous(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)<~>~tall(X)))))&
((?[X]:((~brave(X)&generous(X))))<=>(old(mary)))&
((?[X]:(curious(X)))=>((~patient(alice)<~>humble(alice))))&
(((~quiet(paul)|~curious(paul)))<=>(tall(paul)))&
(![X]:((rich(X)|patient(X))<=>~creative(X)))&
(![X]:(funny(X)=>(~rich(X)<~>~happy(X))))&
(![X]:((quiet(X)|~calm(X))=>(rich(X)&creative(X))))&
(![X]:((funny(X)&~generous(X))<=>kind(X)))&
(![X]:((brave(X)|quiet(X))<=>(curious(X)<~>rich(X))))&
(((old(fred)<~>curious(fred)))<=>(?[X]:(tall(X))))&
(![X]:((~generous(X)&~calm(X))<=>(~curious(X)|old(X))))&
(?[X]:((brave(X)<~>funny(X))))&
((happy(fred)&curious(fred)))&
((~kind(mary)<~>wise(mary)))&
((wise(fred)|humble(fred)))&
((~creative(lucy)&kind(lucy)))&
(?[X]:((patient(X)&brave(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((brave(X)|~kind(X)))) | quiet(paul) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1944757859818464960605105
% SZS output start Proof for 1944757859818464960605105
10. ! [X0] : ((patient(X0) | rich(X0)) <=> ~creative(X0)) [input p9]
12. ! [X0] : ((~calm(X0) | quiet(X0)) => (creative(X0) & rich(X0))) [input p11]
25. quiet(paul) [input hypothesis]
32. ! [X0] : ((creative(X0) & rich(X0)) | (calm(X0) & ~quiet(X0))) [ennf transformation 12]
53. ! [X0] : (((patient(X0) | rich(X0)) | creative(X0)) & (~creative(X0) | (~patient(X0) & ~rich(X0)))) [nnf transformation 10]
54. ! [X0] : ((patient(X0) | rich(X0) | creative(X0)) & (~creative(X0) | (~patient(X0) & ~rich(X0)))) [flattening 53]
100. ~rich(X0) | ~creative(X0) [cnf transformation 54]
105. ~quiet(X0) | rich(X0) [cnf transformation 32]
107. ~quiet(X0) | creative(X0) [cnf transformation 32]
140. quiet(paul) [cnf transformation 25]
227. 20 <=> quiet(paul) [avatar definition]
228. quiet(paul) <- (20) [avatar component clause 227]
297. 20 [avatar split clause 140,227]
300. rich(paul) <- (20) [resolution 105,228]
303. ~creative(paul) <- (20) [resolution 300,100]
304. creative(paul) <- (20) [resolution 107,228]
305. $false <- (20) [subsumption resolution 304,303]
306. ~20 [avatar contradiction clause 305]
307. $false [avatar sat refutation 297,306]
% SZS output end Proof for 1944757859818464960605105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both not curious and not calm.
Everyone who is either not generous or creative is funny or curious.
Everyone who is not happy or calm is both not creative and strong.
Everyone who is not rich is both quiet and not brave and vice versa.
If john is either not humble or wise then someone is patient or old and vice versa.
Everyone who is either not rich or not old is either kind or old and vice versa.
Everyone who is both humble and funny is either happy or creative.
If someone is tall then someone is not rich or not kind.
If fred is not curious or not tall then someone is creative and vice versa.
Everyone who is not brave is not patient and vice versa.
Everyone who is both not quiet and funny is creative.
If lucy is not happy or old then alice is either not tall or not generous and vice versa.
Everyone who is not creative is not old or generous.
If someone is brave or wise then someone is brave or not funny.
If susan is happy or not generous then someone is funny and vice versa.
Everyone who is not patient or wise is not funny or brave.
Lucy is either strong or funny.
Someone is not humble or not tall.
Mary is either not funny or not old.
Someone is not creative or not happy.
Someone is both not calm and funny.
Someone is not patient or calm. | Lucy is tall. | neutral | (![X]:((~curious(X)|~patient(X))=>(~curious(X)&~calm(X))))&
(![X]:((~generous(X)<~>creative(X))=>(funny(X)|curious(X))))&
(![X]:((~happy(X)|calm(X))=>(~creative(X)&strong(X))))&
(![X]:(~rich(X)<=>(quiet(X)&~brave(X))))&
(((~humble(john)<~>wise(john)))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((~rich(X)<~>~old(X))<=>(kind(X)<~>old(X))))&
(![X]:((humble(X)&funny(X))=>(happy(X)<~>creative(X))))&
((?[X]:(tall(X)))=>(?[X]:((~rich(X)|~kind(X)))))&
(((~curious(fred)|~tall(fred)))<=>(?[X]:(creative(X))))&
(![X]:(~brave(X)<=>~patient(X)))&
(![X]:((~quiet(X)&funny(X))=>creative(X)))&
(((~happy(lucy)|old(lucy)))<=>((~tall(alice)<~>~generous(alice))))&
(![X]:(~creative(X)=>(~old(X)|generous(X))))&
((?[X]:((brave(X)|wise(X))))=>(?[X]:((brave(X)|~funny(X)))))&
(((happy(susan)|~generous(susan)))<=>(?[X]:(funny(X))))&
(![X]:((~patient(X)|wise(X))=>(~funny(X)|brave(X))))&
((strong(lucy)<~>funny(lucy)))&
(?[X]:((~humble(X)|~tall(X))))&
((~funny(mary)<~>~old(mary)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~calm(X)&funny(X))))&
(?[X]:((~patient(X)|calm(X)))) | tall(lucy) | [] | null | 0 |
If mary is not humble or not strong then fred is not creative and vice versa.
If someone is both not wise and kind then someone is both not creative and old.
Everyone who is strong is both old and curious and vice versa.
If someone is curious then susan is not curious.
If lucy is old then someone is either curious or not quiet.
If paul is either tall or patient then someone is both funny and wise.
Everyone who is both happy and not calm is patient and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Everyone who is not generous is both humble and curious and vice versa.
Lucy is not wise or calm.
Susan is rich.
Susan is not calm.
Someone is both humble and rich. | Lucy is not happy. | neutral | (((~humble(mary)|~strong(mary)))<=>(~creative(fred)))&
((?[X]:((~wise(X)&kind(X))))=>(?[X]:((~creative(X)&old(X)))))&
(![X]:(strong(X)<=>(old(X)&curious(X))))&
((?[X]:(curious(X)))=>(~curious(susan)))&
((old(lucy))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(((tall(paul)<~>patient(paul)))=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((happy(X)&~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X)))) | ~happy(lucy) | [] | null | 0 |
If paul is either not rich or creative then someone is both happy and old and vice versa.
Everyone who is wise is not generous or not funny and vice versa.
If someone is either creative or not tall then susan is both brave and old.
If someone is either brave or patient then john is either not generous or not old and vice versa.
If someone is both not tall and not curious then paul is not kind or not strong.
If alice is either not brave or tall then john is either not humble or quiet.
Everyone who is both patient and kind is not wise or not funny and vice versa.
If fred is funny or not curious then lucy is either not old or not quiet and vice versa.
Everyone who is either not creative or funny is either curious or not humble and vice versa.
If someone is either rich or not funny then someone is generous and vice versa.
Everyone who is either calm or rich is either not patient or not calm.
Everyone who is not brave or not old is not kind or not quiet and vice versa.
Everyone who is kind is rich or not happy.
If john is not curious then someone is strong.
If someone is kind then someone is happy or not funny.
Everyone who is happy is both not kind and not wise.
Susan is calm or kind.
Someone is either not brave or not generous.
Susan is both not tall and generous.
Paul is either happy or not creative.
Susan is either not strong or humble. | John is generous. | neutral | (((~rich(paul)<~>creative(paul)))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:(wise(X)<=>(~generous(X)|~funny(X))))&
((?[X]:((creative(X)<~>~tall(X))))=>((brave(susan)&old(susan))))&
((?[X]:((brave(X)<~>patient(X))))<=>((~generous(john)<~>~old(john))))&
((?[X]:((~tall(X)&~curious(X))))=>((~kind(paul)|~strong(paul))))&
(((~brave(alice)<~>tall(alice)))=>((~humble(john)<~>quiet(john))))&
(![X]:((patient(X)&kind(X))<=>(~wise(X)|~funny(X))))&
(((funny(fred)|~curious(fred)))<=>((~old(lucy)<~>~quiet(lucy))))&
(![X]:((~creative(X)<~>funny(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((rich(X)<~>~funny(X))))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>rich(X))=>(~patient(X)<~>~calm(X))))&
(![X]:((~brave(X)|~old(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(kind(X)=>(rich(X)|~happy(X))))&
((~curious(john))=>(?[X]:(strong(X))))&
((?[X]:(kind(X)))=>(?[X]:((happy(X)|~funny(X)))))&
(![X]:(happy(X)=>(~kind(X)&~wise(X))))&
((calm(susan)|kind(susan)))&
(?[X]:((~brave(X)<~>~generous(X))))&
((~tall(susan)&generous(susan)))&
((happy(paul)<~>~creative(paul)))&
((~strong(susan)<~>humble(susan))) | generous(john) | [] | null | 0 |
Everyone who is funny is either not wise or calm and vice versa.
If someone is funny or not tall then susan is not wise.
Everyone who is not patient or calm is either wise or humble and vice versa.
If lucy is not wise then susan is brave or creative.
Everyone who is both not wise and not brave is quiet or not rich and vice versa.
If someone is tall then someone is both not wise and generous and vice versa.
If someone is either not wise or not humble then someone is wise.
If someone is not wise then someone is not rich or humble and vice versa.
Everyone who is patient is either brave or not patient and vice versa.
If paul is funny then fred is strong and vice versa.
Everyone who is either not humble or not rich is not strong or not humble and vice versa.
Everyone who is rich or not old is both tall and old.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
Someone is not kind.
Someone is both not wise and not creative.
John is either tall or generous.
Someone is quiet or not kind.
Paul is either wise or funny.
Lucy is both not creative and not generous.
Alice is not funny.
Someone is not humble. | Lucy is quiet. | contradiction | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((funny(X)|~tall(X))))=>(~wise(susan)))&
(![X]:((~patient(X)|calm(X))<=>(wise(X)<~>humble(X))))&
((~wise(lucy))=>((brave(susan)|creative(susan))))&
(![X]:((~wise(X)&~brave(X))<=>(quiet(X)|~rich(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul)))&
((~creative(lucy)&~generous(lucy)))&
(~funny(alice))&
(?[X]:(~humble(X))) | quiet(lucy) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6697669255421411129742409
% SZS output start Proof for 6697669255421411129742409
5. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> (~rich(X0) | quiet(X0))) [input p4]
9. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p8]
25. quiet(lucy) [input hypothesis]
44. ! [X0] : (((~brave(X0) & ~wise(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (brave(X0) | wise(X0)))) [nnf transformation 5]
45. ! [X0] : (((~brave(X0) & ~wise(X0)) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | brave(X0) | wise(X0))) [flattening 44]
60. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 9]
96. ~quiet(X0) | ~brave(X0) [cnf transformation 45]
106. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 60]
109. patient(X0) | brave(X0) | patient(X0) [cnf transformation 60]
138. quiet(lucy) [cnf transformation 25]
141. ~patient(X0) | brave(X0) [duplicate literal removal 106]
142. patient(X0) | brave(X0) [duplicate literal removal 109]
225. brave(X0) [subsumption resolution 141,142]
303. ~brave(lucy) [resolution 96,138]
304. $false [subsumption resolution 303,225]
% SZS output end Proof for 6697669255421411129742409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not rich then someone is either not rich or not humble and vice versa.
Everyone who is either not creative or kind is not patient.
Everyone who is not happy is both not wise and not old.
If fred is humble then someone is either not humble or not tall.
If someone is both not quiet and tall then someone is quiet and vice versa.
Everyone who is not creative is not tall or creative and vice versa.
Everyone who is not quiet or not old is both not quiet and calm.
Everyone who is both calm and not generous is both kind and not rich and vice versa.
Everyone who is either generous or patient is both old and not old.
Everyone who is curious or not funny is not brave or strong.
If lucy is rich or generous then someone is either not old or not humble and vice versa.
Everyone who is not humble or kind is either not curious or brave and vice versa.
Everyone who is not wise is both not humble and kind and vice versa.
If someone is both humble and not quiet then someone is not quiet.
If fred is either generous or not patient then susan is not patient or tall and vice versa.
Someone is strong or happy.
Someone is either curious or not quiet.
Susan is either funny or generous.
Someone is curious or not rich.
John is wise.
Alice is not rich or humble.
Fred is not creative or happy. | Lucy is not calm. | contradiction | ((?[X]:((~curious(X)&~rich(X))))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~creative(X)<~>kind(X))=>~patient(X)))&
(![X]:(~happy(X)=>(~wise(X)&~old(X))))&
((humble(fred))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~tall(X)|creative(X))))&
(![X]:((~quiet(X)|~old(X))=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((generous(X)<~>patient(X))=>(old(X)&~old(X))))&
(![X]:((curious(X)|~funny(X))=>(~brave(X)|strong(X))))&
(((rich(lucy)|generous(lucy)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|kind(X))<=>(~curious(X)<~>brave(X))))&
(![X]:(~wise(X)<=>(~humble(X)&kind(X))))&
((?[X]:((humble(X)&~quiet(X))))=>(?[X]:(~quiet(X))))&
(((generous(fred)<~>~patient(fred)))<=>((~patient(susan)|tall(susan))))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
((funny(susan)<~>generous(susan)))&
(?[X]:((curious(X)|~rich(X))))&
(wise(john))&
((~rich(alice)|humble(alice)))&
((~creative(fred)|happy(fred))) | ~calm(lucy) | [
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3881876970391820663827668
% SZS output start Proof for 3881876970391820663827668
5. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X0] : quiet(X0) [input p4]
6. ! [X0] : (~creative(X0) <=> (creative(X0) | ~tall(X0))) [input p5]
7. ! [X0] : ((~old(X0) | ~quiet(X0)) => (calm(X0) & ~quiet(X0))) [input p6]
23. ~calm(lucy) [input hypothesis]
25. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X1] : quiet(X1) [rectify 5]
34. ! [X0] : ((calm(X0) & ~quiet(X0)) | (old(X0) & quiet(X0))) [ennf transformation 7]
48. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : (~tall(X0) | quiet(X0))) [nnf transformation 25]
49. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : (~tall(X3) | quiet(X3))) [rectify 48]
50. ? [X0] : (tall(X0) & ~quiet(X0)) => (tall(sK3) & ~quiet(sK3)) [choice axiom]
51. ? [X2] : quiet(X2) => quiet(sK4) [choice axiom]
52. ((tall(sK3) & ~quiet(sK3)) | ! [X1] : ~quiet(X1)) & (quiet(sK4) | ! [X3] : (~tall(X3) | quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & ((creative(X0) | ~tall(X0)) | creative(X0))) [nnf transformation 6]
54. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & (creative(X0) | ~tall(X0) | creative(X0))) [flattening 53]
88. tall(sK3) | ~quiet(X1) [cnf transformation 52]
89. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 54]
91. ~creative(X0) | ~creative(X0) [cnf transformation 54]
94. calm(X0) | quiet(X0) [cnf transformation 34]
131. ~calm(lucy) [cnf transformation 23]
132. creative(X0) | ~tall(X0) [duplicate literal removal 89]
133. ~creative(X0) [duplicate literal removal 91]
180. 11 <=> ! [X1] : ~quiet(X1) [avatar definition]
181. ~quiet(X1) <- (11) [avatar component clause 180]
183. 12 <=> tall(sK3) [avatar definition]
185. tall(sK3) <- (12) [avatar component clause 183]
186. 11 | 12 [avatar split clause 88,183,180]
200. ~tall(X0) [subsumption resolution 132,133]
291. quiet(lucy) [resolution 94,131]
292. $false <- (11) [subsumption resolution 291,181]
293. ~11 [avatar contradiction clause 292]
294. $false <- (12) [subsumption resolution 185,200]
295. ~12 [avatar contradiction clause 294]
296. $false [avatar sat refutation 186,293,295]
% SZS output end Proof for 3881876970391820663827668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not patient is not rich and vice versa.
Everyone who is humble or not tall is humble or not patient.
Everyone who is patient is either not funny or not quiet.
Everyone who is either tall or not strong is not funny or creative and vice versa.
Everyone who is either rich or funny is either not tall or not patient and vice versa.
If someone is either wise or quiet then someone is either humble or tall and vice versa.
If someone is either not humble or not strong then paul is calm and vice versa.
If someone is both not happy and not calm then mary is not kind or humble and vice versa.
Everyone who is either funny or happy is not rich.
If someone is both not wise and not happy then alice is old or creative.
If paul is either generous or quiet then someone is not generous or rich.
Everyone who is happy is either quiet or kind and vice versa.
If someone is both not tall and patient then fred is patient or not old.
Everyone who is either not wise or not quiet is both not creative and not humble.
If paul is either not happy or not funny then someone is not old or happy and vice versa.
If alice is either strong or not humble then alice is both not rich and not old and vice versa.
Someone is not wise.
John is not calm or creative.
Fred is brave or not quiet.
Alice is both not happy and not tall.
Susan is either not wise or happy.
John is strong or curious.
Someone is both not brave and not generous. | Paul is not curious. | neutral | (![X]:((~rich(X)<~>~patient(X))<=>~rich(X)))&
(![X]:((humble(X)|~tall(X))=>(humble(X)|~patient(X))))&
(![X]:(patient(X)=>(~funny(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>~strong(X))<=>(~funny(X)|creative(X))))&
(![X]:((rich(X)<~>funny(X))<=>(~tall(X)<~>~patient(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))<=>(calm(paul)))&
((?[X]:((~happy(X)&~calm(X))))<=>((~kind(mary)|humble(mary))))&
(![X]:((funny(X)<~>happy(X))=>~rich(X)))&
((?[X]:((~wise(X)&~happy(X))))=>((old(alice)|creative(alice))))&
(((generous(paul)<~>quiet(paul)))=>(?[X]:((~generous(X)|rich(X)))))&
(![X]:(happy(X)<=>(quiet(X)<~>kind(X))))&
((?[X]:((~tall(X)&patient(X))))=>((patient(fred)|~old(fred))))&
(![X]:((~wise(X)<~>~quiet(X))=>(~creative(X)&~humble(X))))&
(((~happy(paul)<~>~funny(paul)))<=>(?[X]:((~old(X)|happy(X)))))&
(((strong(alice)<~>~humble(alice)))<=>((~rich(alice)&~old(alice))))&
(?[X]:(~wise(X)))&
((~calm(john)|creative(john)))&
((brave(fred)|~quiet(fred)))&
((~happy(alice)&~tall(alice)))&
((~wise(susan)<~>happy(susan)))&
((strong(john)|curious(john)))&
(?[X]:((~brave(X)&~generous(X)))) | ~curious(paul) | [] | null | 0 |
Everyone who is funny is either not wise or calm and vice versa.
If someone is kind or not strong then paul is either not quiet or not strong.
Everyone who is happy or brave is either not brave or not curious.
If susan is either not generous or not rich then alice is both not kind and humble and vice versa.
If someone is either creative or not patient then john is generous and vice versa.
If someone is not quiet then paul is both quiet and not rich and vice versa.
If someone is tall then someone is both not wise and generous and vice versa.
If someone is either not wise or not humble then someone is wise.
If someone is not wise then someone is not rich or humble and vice versa.
Everyone who is patient is either brave or not patient and vice versa.
If paul is funny then fred is strong and vice versa.
Everyone who is either not humble or not rich is not strong or not humble and vice versa.
Everyone who is rich or not old is both tall and old.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
Paul is not calm.
Someone is not generous.
Someone is both not generous and not tall.
Someone is patient.
Someone is both tall and generous.
Someone is quiet or not kind.
Paul is either wise or funny. | Paul is curious. | contradiction | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((kind(X)|~strong(X))))=>((~quiet(paul)<~>~strong(paul))))&
(![X]:((happy(X)|brave(X))=>(~brave(X)<~>~curious(X))))&
(((~generous(susan)<~>~rich(susan)))<=>((~kind(alice)&humble(alice))))&
((?[X]:((creative(X)<~>~patient(X))))<=>(generous(john)))&
((?[X]:(~quiet(X)))<=>((quiet(paul)&~rich(paul))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
(~calm(paul))&
(?[X]:(~generous(X)))&
(?[X]:((~generous(X)&~tall(X))))&
(?[X]:(patient(X)))&
(?[X]:((tall(X)&generous(X))))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul))) | curious(paul) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5020996074410154750426255
% SZS output start Proof for 5020996074410154750426255
3. ! [X0] : ((brave(X0) | happy(X0)) => (~brave(X0) <~> ~curious(X0))) [input p2]
10. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p9]
24. curious(paul) [input hypothesis]
30. ! [X0] : ((~brave(X0) <~> ~curious(X0)) | (~brave(X0) & ~happy(X0))) [ennf transformation 3]
40. ! [X0] : (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | (~brave(X0) & ~happy(X0))) [nnf transformation 30]
66. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 10]
91. ~curious(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 40]
115. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 66]
118. patient(X0) | brave(X0) | patient(X0) [cnf transformation 66]
142. curious(paul) [cnf transformation 24]
145. ~patient(X0) | brave(X0) [duplicate literal removal 115]
146. patient(X0) | brave(X0) [duplicate literal removal 118]
147. ~curious(X0) | ~brave(X0) [duplicate literal removal 91]
281. brave(X0) [subsumption resolution 145,146]
321. ~brave(paul) [resolution 147,142]
322. $false [subsumption resolution 321,281]
% SZS output end Proof for 5020996074410154750426255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is not quiet or not patient.
If mary is not calm or old then john is not kind or not curious.
If lucy is calm or not brave then someone is creative or strong.
If someone is not kind then someone is curious.
If fred is both not humble and brave then mary is both not old and not humble.
Everyone who is either patient or calm is not tall and vice versa.
Everyone who is both kind and not rich is not tall.
Everyone who is both rich and kind is either not funny or not brave and vice versa.
Everyone who is either not funny or not strong is not curious or humble.
Everyone who is not old or not creative is not strong and vice versa.
Everyone who is either humble or wise is not old.
If susan is not creative then susan is either not curious or humble.
Everyone who is not curious is either strong or not happy and vice versa.
Everyone who is either brave or not brave is both old and rich and vice versa.
If fred is not brave or tall then someone is not calm.
Everyone who is creative or not tall is not quiet or creative and vice versa.
Fred is not kind.
Someone is both wise and tall.
Someone is both kind and not curious.
Fred is not humble.
Mary is curious or tall.
Alice is either not wise or not patient.
Someone is not kind. | Mary is humble. | neutral | ((?[X]:(~happy(X)))=>(?[X]:((~quiet(X)|~patient(X)))))&
(((~calm(mary)|old(mary)))=>((~kind(john)|~curious(john))))&
(((calm(lucy)|~brave(lucy)))=>(?[X]:((creative(X)|strong(X)))))&
((?[X]:(~kind(X)))=>(?[X]:(curious(X))))&
(((~humble(fred)&brave(fred)))=>((~old(mary)&~humble(mary))))&
(![X]:((patient(X)<~>calm(X))<=>~tall(X)))&
(![X]:((kind(X)&~rich(X))=>~tall(X)))&
(![X]:((rich(X)&kind(X))<=>(~funny(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>~strong(X))=>(~curious(X)|humble(X))))&
(![X]:((~old(X)|~creative(X))<=>~strong(X)))&
(![X]:((humble(X)<~>wise(X))=>~old(X)))&
((~creative(susan))=>((~curious(susan)<~>humble(susan))))&
(![X]:(~curious(X)<=>(strong(X)<~>~happy(X))))&
(![X]:((brave(X)<~>~brave(X))<=>(old(X)&rich(X))))&
(((~brave(fred)|tall(fred)))=>(?[X]:(~calm(X))))&
(![X]:((creative(X)|~tall(X))<=>(~quiet(X)|creative(X))))&
(~kind(fred))&
(?[X]:((wise(X)&tall(X))))&
(?[X]:((kind(X)&~curious(X))))&
(~humble(fred))&
((curious(mary)|tall(mary)))&
((~wise(alice)<~>~patient(alice)))&
(?[X]:(~kind(X))) | humble(mary) | [] | null | 0 |
Everyone who is not curious or not kind is both not patient and calm.
Everyone who is not humble or not wise is both rich and not creative.
If someone is strong or rich then someone is both wise and not generous.
If susan is either curious or happy then someone is both not wise and not quiet.
Everyone who is either not old or not rich is either quiet or funny and vice versa.
If someone is calm or rich then someone is both not strong and humble.
If john is either not generous or quiet then fred is kind.
Everyone who is not curious or not rich is both calm and not quiet.
If mary is either generous or rich then alice is not generous or happy.
If someone is both not brave and tall then susan is not quiet or not old.
Everyone who is either not generous or wise is tall or curious.
If paul is not old then someone is both tall and not calm and vice versa.
If someone is not curious then someone is not curious or funny and vice versa.
Everyone who is both not calm and not humble is both happy and not tall.
If someone is either not kind or quiet then fred is rich or not patient and vice versa.
Everyone who is both strong and not kind is either not funny or not patient.
John is not quiet or calm.
Alice is happy.
Someone is either humble or not brave.
Susan is not brave.
John is either strong or funny.
Lucy is happy.
Lucy is not curious.
Someone is both quiet and rich. | Lucy is calm. | entailment | (![X]:((~curious(X)|~kind(X))=>(~patient(X)&calm(X))))&
(![X]:((~humble(X)|~wise(X))=>(rich(X)&~creative(X))))&
((?[X]:((strong(X)|rich(X))))=>(?[X]:((wise(X)&~generous(X)))))&
(((curious(susan)<~>happy(susan)))=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((~old(X)<~>~rich(X))<=>(quiet(X)<~>funny(X))))&
((?[X]:((calm(X)|rich(X))))=>(?[X]:((~strong(X)&humble(X)))))&
(((~generous(john)<~>quiet(john)))=>(kind(fred)))&
(![X]:((~curious(X)|~rich(X))=>(calm(X)&~quiet(X))))&
(((generous(mary)<~>rich(mary)))=>((~generous(alice)|happy(alice))))&
((?[X]:((~brave(X)&tall(X))))=>((~quiet(susan)|~old(susan))))&
(![X]:((~generous(X)<~>wise(X))=>(tall(X)|curious(X))))&
((~old(paul))<=>(?[X]:((tall(X)&~calm(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((~curious(X)|funny(X)))))&
(![X]:((~calm(X)&~humble(X))=>(happy(X)&~tall(X))))&
((?[X]:((~kind(X)<~>quiet(X))))<=>((rich(fred)|~patient(fred))))&
(![X]:((strong(X)&~kind(X))=>(~funny(X)<~>~patient(X))))&
((~quiet(john)|calm(john)))&
(happy(alice))&
(?[X]:((humble(X)<~>~brave(X))))&
(~brave(susan))&
((strong(john)<~>funny(john)))&
(happy(lucy))&
(~curious(lucy))&
(?[X]:((quiet(X)&rich(X)))) | calm(lucy) | [
"p0",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6984212839862279560534180
% SZS output start Proof for 6984212839862279560534180
1. ! [X0] : ((~kind(X0) | ~curious(X0)) => (calm(X0) & ~patient(X0))) [input p0]
23. ~curious(lucy) [input p22]
25. ~calm(lucy) [input hypothesis]
30. ! [X0] : ((calm(X0) & ~patient(X0)) | (kind(X0) & curious(X0))) [ennf transformation 1]
83. calm(X0) | curious(X0) [cnf transformation 30]
142. ~curious(lucy) [cnf transformation 23]
145. ~calm(lucy) [cnf transformation 25]
337. curious(lucy) [resolution 83,145]
338. $false [subsumption resolution 337,142]
% SZS output end Proof for 6984212839862279560534180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not kind is both calm and not brave and vice versa.
Everyone who is both not creative and not generous is not quiet.
If alice is not generous or strong then mary is calm and vice versa.
If someone is not creative then lucy is both not calm and not kind and vice versa.
Everyone who is both calm and creative is either tall or creative.
If someone is funny then mary is either not kind or old and vice versa.
Everyone who is both old and rich is either wise or not rich and vice versa.
Everyone who is either not curious or not calm is both not quiet and strong.
Everyone who is humble or not tall is either happy or strong and vice versa.
If susan is rich or not strong then someone is patient or not creative.
If fred is either not generous or not tall then someone is either happy or not kind and vice versa.
Everyone who is wise is happy and vice versa.
Everyone who is both not creative and not generous is either not generous or not strong.
If someone is either quiet or not patient then susan is brave and vice versa.
Everyone who is brave is both generous and not strong.
If someone is both happy and creative then someone is either not kind or not calm.
Someone is either not humble or happy.
Mary is creative.
John is either not generous or funny.
Paul is old or not humble.
Alice is patient or curious.
Lucy is both kind and brave.
Someone is not happy or happy. | Paul is not brave. | neutral | (![X]:((wise(X)&~kind(X))<=>(calm(X)&~brave(X))))&
(![X]:((~creative(X)&~generous(X))=>~quiet(X)))&
(((~generous(alice)|strong(alice)))<=>(calm(mary)))&
((?[X]:(~creative(X)))<=>((~calm(lucy)&~kind(lucy))))&
(![X]:((calm(X)&creative(X))=>(tall(X)<~>creative(X))))&
((?[X]:(funny(X)))<=>((~kind(mary)<~>old(mary))))&
(![X]:((old(X)&rich(X))<=>(wise(X)<~>~rich(X))))&
(![X]:((~curious(X)<~>~calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((humble(X)|~tall(X))<=>(happy(X)<~>strong(X))))&
(((rich(susan)|~strong(susan)))=>(?[X]:((patient(X)|~creative(X)))))&
(((~generous(fred)<~>~tall(fred)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:(wise(X)<=>happy(X)))&
(![X]:((~creative(X)&~generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(brave(susan)))&
(![X]:(brave(X)=>(generous(X)&~strong(X))))&
((?[X]:((happy(X)&creative(X))))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(?[X]:((~humble(X)<~>happy(X))))&
(creative(mary))&
((~generous(john)<~>funny(john)))&
((old(paul)|~humble(paul)))&
((patient(alice)|curious(alice)))&
((kind(lucy)&brave(lucy)))&
(?[X]:((~happy(X)|happy(X)))) | ~brave(paul) | [] | null | 0 |
Everyone who is not rich or humble is both funny and not wise.
If someone is both wise and funny then someone is either not tall or strong.
Everyone who is not rich or not creative is rich or not calm.
Everyone who is happy is not brave and vice versa.
Everyone who is both not humble and rich is either not quiet or not creative and vice versa.
Everyone who is either not calm or happy is either curious or happy.
If susan is both creative and happy then someone is either not brave or humble.
If alice is either curious or generous then someone is old or happy and vice versa.
If susan is quiet or old then paul is both not old and curious and vice versa.
Everyone who is not creative is either wise or creative.
Everyone who is tall or not kind is both happy and wise.
Everyone who is creative is calm or not funny.
Everyone who is wise is not strong or not rich and vice versa.
If someone is patient or not funny then fred is both not generous and patient.
Everyone who is both not patient and not tall is calm and vice versa.
If someone is both not patient and rich then someone is not curious.
Someone is happy.
Someone is either brave or not rich.
Someone is not quiet or rich.
Someone is both not humble and generous.
Alice is not wise.
Someone is not quiet.
Someone is patient.
Someone is not wise or wise. | Susan is rich. | entailment | (![X]:((~rich(X)|humble(X))=>(funny(X)&~wise(X))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((~rich(X)|~creative(X))=>(rich(X)|~calm(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((~humble(X)&rich(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>happy(X))=>(curious(X)<~>happy(X))))&
(((creative(susan)&happy(susan)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
(![X]:(creative(X)=>(calm(X)|~funny(X))))&
(![X]:(wise(X)<=>(~strong(X)|~rich(X))))&
((?[X]:((patient(X)|~funny(X))))=>((~generous(fred)&patient(fred))))&
(![X]:((~patient(X)&~tall(X))<=>calm(X)))&
((?[X]:((~patient(X)&rich(X))))=>(?[X]:(~curious(X))))&
(?[X]:(happy(X)))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((~humble(X)&generous(X))))&
(~wise(alice))&
(?[X]:(~quiet(X)))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)|wise(X)))) | rich(susan) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6242379043732870691681673
% SZS output start Proof for 6242379043732870691681673
1. ! [X0] : ((humble(X0) | ~rich(X0)) => (~wise(X0) & funny(X0))) [input p0]
13. ! [X0] : (wise(X0) <=> (~rich(X0) | ~strong(X0))) [input p12]
25. ~rich(susan) [input hypothesis]
29. ! [X0] : ((~wise(X0) & funny(X0)) | (~humble(X0) & rich(X0))) [ennf transformation 1]
60. ! [X0] : ((wise(X0) | (rich(X0) & strong(X0))) & ((~rich(X0) | ~strong(X0)) | ~wise(X0))) [nnf transformation 13]
61. ! [X0] : ((wise(X0) | (rich(X0) & strong(X0))) & (~rich(X0) | ~strong(X0) | ~wise(X0))) [flattening 60]
84. ~wise(X0) | rich(X0) [cnf transformation 29]
122. wise(X0) | rich(X0) [cnf transformation 61]
141. ~rich(susan) [cnf transformation 25]
226. rich(X0) [subsumption resolution 122,84]
256. $false [subsumption resolution 141,226]
% SZS output end Proof for 6242379043732870691681673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or rich then someone is not old.
Everyone who is both quiet and not generous is not tall or rich.
Everyone who is either not wise or quiet is either rich or humble.
Everyone who is either not happy or patient is not wise or not brave and vice versa.
If someone is either tall or not brave then someone is tall or not kind.
If susan is wise then someone is both not old and happy.
If alice is tall or calm then paul is humble and vice versa.
If someone is either not happy or not curious then someone is funny or rich.
If someone is both not rich and not brave then mary is either not wise or not creative.
If someone is either not wise or curious then someone is not funny.
If someone is not creative or not tall then fred is both not generous and not funny.
Everyone who is quiet is not wise and vice versa.
Everyone who is either not quiet or calm is quiet or not tall and vice versa.
Everyone who is curious or not generous is either not funny or old and vice versa.
If john is either generous or not kind then someone is both not happy and not creative and vice versa.
If someone is not humble then someone is creative.
Someone is not tall.
Someone is humble.
Susan is either not kind or not humble.
Someone is both brave and generous.
Someone is not generous.
John is not rich or tall.
Paul is either not generous or curious.
Paul is happy or generous. | Fred is not funny. | entailment | ((?[X]:((brave(X)|rich(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)&~generous(X))=>(~tall(X)|rich(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(rich(X)<~>humble(X))))&
(![X]:((~happy(X)<~>patient(X))<=>(~wise(X)|~brave(X))))&
((?[X]:((tall(X)<~>~brave(X))))=>(?[X]:((tall(X)|~kind(X)))))&
((wise(susan))=>(?[X]:((~old(X)&happy(X)))))&
(((tall(alice)|calm(alice)))<=>(humble(paul)))&
((?[X]:((~happy(X)<~>~curious(X))))=>(?[X]:((funny(X)|rich(X)))))&
((?[X]:((~rich(X)&~brave(X))))=>((~wise(mary)<~>~creative(mary))))&
((?[X]:((~wise(X)<~>curious(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~creative(X)|~tall(X))))=>((~generous(fred)&~funny(fred))))&
(![X]:(quiet(X)<=>~wise(X)))&
(![X]:((~quiet(X)<~>calm(X))<=>(quiet(X)|~tall(X))))&
(![X]:((curious(X)|~generous(X))<=>(~funny(X)<~>old(X))))&
(((generous(john)<~>~kind(john)))<=>(?[X]:((~happy(X)&~creative(X)))))&
((?[X]:(~humble(X)))=>(?[X]:(creative(X))))&
(?[X]:(~tall(X)))&
(?[X]:(humble(X)))&
((~kind(susan)<~>~humble(susan)))&
(?[X]:((brave(X)&generous(X))))&
(?[X]:(~generous(X)))&
((~rich(john)|tall(john)))&
((~generous(paul)<~>curious(paul)))&
((happy(paul)|generous(paul))) | ~funny(fred) | [
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1830905527907478954780136
% SZS output start Proof for 1830905527907478954780136
11. ? [X0] : (~tall(X0) | ~creative(X0)) => (~funny(fred) & ~generous(fred)) [input p10]
17. ? [X0] : ~tall(X0) [input p16]
25. funny(fred) [input hypothesis]
40. (~funny(fred) & ~generous(fred)) | ! [X0] : (tall(X0) & creative(X0)) [ennf transformation 11]
77. ? [X0] : ~tall(X0) => ~tall(sK7) [choice axiom]
78. ~tall(sK7) [skolemisation 17,77]
116. ~funny(fred) | tall(X0) [cnf transformation 40]
138. ~tall(sK7) [cnf transformation 78]
149. funny(fred) [cnf transformation 25]
251. 24 <=> ! [X0] : tall(X0) [avatar definition]
252. tall(X0) <- (24) [avatar component clause 251]
254. 25 <=> funny(fred) [avatar definition]
257. 24 | ~25 [avatar split clause 116,254,251]
336. 25 [avatar split clause 149,254]
341. $false <- (24) [resolution 252,138]
342. ~24 [avatar contradiction clause 341]
343. $false [avatar sat refutation 257,336,342]
% SZS output end Proof for 1830905527907478954780136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and calm then someone is generous and vice versa. If someone is quiet then john is patient or strong and vice versa. If paul is wise or not wise then someone is brave and vice versa. If someone is not kind or strong then someone is either not funny or not rich and vice versa. Everyone who is either not funny or not quiet is both wise and not tall. If someone is both brave and not rich then someone is both not curious and kind. If john is both curious and not humble then someone is either humble or not patient and vice versa. Everyone who is either not brave or not generous is not funny and vice versa. If someone is either humble or not generous then someone is both wise and not patient and vice versa. Everyone who is either creative or not patient is both calm and not kind and vice versa. Everyone who is either funny or patient is generous and vice versa. Everyone who is not strong or not rich is creative. If fred is humble or kind then someone is both rich and not tall and vice versa. Everyone who is either not humble or generous is not patient or not quiet. Everyone who is kind is humble. If someone is quiet or not brave then fred is both happy and not brave. John is patient. John is either creative or funny. Mary is either curious or patient. Alice is not creative. Someone is happy. Fred is not strong. Mary is not humble or not calm. Paul is not old or generous. | Fred is creative. | entailment | ((?[X]:((rich(X)&calm(X))))<=>(?[X]:(generous(X))))&
((?[X]:(quiet(X)))<=>((patient(john)|strong(john))))&
(((wise(paul)|~wise(paul)))<=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)|strong(X))))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
(![X]:((~funny(X)<~>~quiet(X))=>(wise(X)&~tall(X))))&
((?[X]:((brave(X)&~rich(X))))=>(?[X]:((~curious(X)&kind(X)))))&
(((curious(john)&~humble(john)))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(![X]:((~brave(X)<~>~generous(X))<=>~funny(X)))&
((?[X]:((humble(X)<~>~generous(X))))<=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((creative(X)<~>~patient(X))<=>(calm(X)&~kind(X))))&
(![X]:((funny(X)<~>patient(X))<=>generous(X)))&
(![X]:((~strong(X)|~rich(X))=>creative(X)))&
(((humble(fred)|kind(fred)))<=>(?[X]:((rich(X)&~tall(X)))))&
(![X]:((~humble(X)<~>generous(X))=>(~patient(X)|~quiet(X))))&
(![X]:(kind(X)=>humble(X)))&
((?[X]:((quiet(X)|~brave(X))))=>((happy(fred)&~brave(fred))))&
(patient(john))&
((creative(john)<~>funny(john)))&
((curious(mary)<~>patient(mary)))&
(~creative(alice))&
(?[X]:(happy(X)))&
(~strong(fred))&
((~humble(mary)|~calm(mary)))&
((~old(paul)|generous(paul))) | creative(fred) | [
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4866164297010006756264275
% SZS output start Proof for 4866164297010006756264275
12. ! [X0] : ((~rich(X0) | ~strong(X0)) => creative(X0)) [input p11]
22. ~strong(fred) [input p21]
25. ~creative(fred) [input hypothesis]
35. ! [X0] : (creative(X0) | (rich(X0) & strong(X0))) [ennf transformation 12]
133. creative(X0) | strong(X0) [cnf transformation 35]
151. ~strong(fred) [cnf transformation 22]
153. ~creative(fred) [cnf transformation 25]
373. strong(fred) [resolution 133,153]
374. $false [subsumption resolution 373,151]
% SZS output end Proof for 4866164297010006756264275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then paul is not strong.
Everyone who is either not rich or funny is not tall and vice versa.
Everyone who is both not patient and rich is not generous or not curious and vice versa.
If someone is not strong then someone is generous or not strong and vice versa.
Everyone who is not tall or not curious is quiet or humble and vice versa.
If paul is rich or not creative then lucy is either not kind or not patient and vice versa.
Everyone who is patient is funny or not kind.
Everyone who is not funny is both not generous and not rich and vice versa.
If someone is either not generous or generous then someone is not patient or rich.
Everyone who is both calm and not rich is either humble or rich.
If someone is generous then lucy is not old or funny and vice versa.
Everyone who is not brave or patient is either not generous or happy and vice versa.
Everyone who is either funny or not humble is tall.
Everyone who is not funny or not tall is not patient or wise and vice versa.
Everyone who is not wise is not tall and vice versa.
Everyone who is curious is both generous and not creative and vice versa.
Someone is not happy or funny.
Mary is both quiet and strong.
Susan is strong.
Alice is either tall or funny.
John is happy. | Alice is patient. | contradiction | ((?[X]:(happy(X)))=>(~strong(paul)))&
(![X]:((~rich(X)<~>funny(X))<=>~tall(X)))&
(![X]:((~patient(X)&rich(X))<=>(~generous(X)|~curious(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((generous(X)|~strong(X)))))&
(![X]:((~tall(X)|~curious(X))<=>(quiet(X)|humble(X))))&
(((rich(paul)|~creative(paul)))<=>((~kind(lucy)<~>~patient(lucy))))&
(![X]:(patient(X)=>(funny(X)|~kind(X))))&
(![X]:(~funny(X)<=>(~generous(X)&~rich(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>(?[X]:((~patient(X)|rich(X)))))&
(![X]:((calm(X)&~rich(X))=>(humble(X)<~>rich(X))))&
((?[X]:(generous(X)))<=>((~old(lucy)|funny(lucy))))&
(![X]:((~brave(X)|patient(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((funny(X)<~>~humble(X))=>tall(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~patient(X)|wise(X))))&
(![X]:(~wise(X)<=>~tall(X)))&
(![X]:(curious(X)<=>(generous(X)&~creative(X))))&
(?[X]:((~happy(X)|funny(X))))&
((quiet(mary)&strong(mary)))&
(strong(susan))&
((tall(alice)<~>funny(alice)))&
(happy(john)) | patient(alice) | [
"p2",
"p7",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7090439650474325893442205
% SZS output start Proof for 7090439650474325893442205
3. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (~curious(X0) | ~generous(X0))) [input p2]
8. ! [X0] : (~funny(X0) <=> (~rich(X0) & ~generous(X0))) [input p7]
14. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (wise(X0) | ~patient(X0))) [input p13]
15. ! [X0] : (~wise(X0) <=> ~tall(X0)) [input p14]
20. tall(alice) <~> funny(alice) [input p19]
22. patient(alice) [input hypothesis]
32. ! [X0] : (((rich(X0) & ~patient(X0)) | (curious(X0) & generous(X0))) & ((~curious(X0) | ~generous(X0)) | (~rich(X0) | patient(X0)))) [nnf transformation 3]
33. ! [X0] : (((rich(X0) & ~patient(X0)) | (curious(X0) & generous(X0))) & (~curious(X0) | ~generous(X0) | ~rich(X0) | patient(X0))) [flattening 32]
43. ! [X0] : ((~funny(X0) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | funny(X0))) [nnf transformation 8]
44. ! [X0] : ((~funny(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | funny(X0))) [flattening 43]
57. ! [X0] : (((~tall(X0) | ~funny(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (tall(X0) & funny(X0)))) [nnf transformation 14]
58. ! [X0] : ((~tall(X0) | ~funny(X0) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | (tall(X0) & funny(X0)))) [flattening 57]
59. ! [X0] : ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0))) [nnf transformation 15]
64. (~funny(alice) | ~tall(alice)) & (funny(alice) | tall(alice)) [nnf transformation 20]
73. generous(X0) | rich(X0) [cnf transformation 33]
89. ~generous(X0) | funny(X0) [cnf transformation 44]
90. ~rich(X0) | funny(X0) [cnf transformation 44]
106. ~patient(X0) | wise(X0) | tall(X0) [cnf transformation 58]
110. ~wise(X0) | tall(X0) [cnf transformation 59]
119. ~funny(alice) | ~tall(alice) [cnf transformation 64]
121. patient(alice) [cnf transformation 22]
215. 20 <=> tall(alice) [avatar definition]
217. ~tall(alice) <- (~20) [avatar component clause 215]
219. 21 <=> funny(alice) [avatar definition]
221. ~funny(alice) <- (~21) [avatar component clause 219]
222. ~20 | ~21 [avatar split clause 119,219,215]
228. funny(X0) | rich(X0) [resolution 89,73]
232. funny(X0) [subsumption resolution 228,90]
233. $false <- (~21) [resolution 232,221]
234. 21 [avatar contradiction clause 233]
306. wise(alice) | tall(alice) [resolution 106,121]
308. wise(alice) <- (~20) [subsumption resolution 306,217]
312. tall(alice) <- (~20) [resolution 308,110]
313. $false <- (~20) [subsumption resolution 312,217]
314. 20 [avatar contradiction clause 313]
315. $false [avatar sat refutation 222,234,314]
% SZS output end Proof for 7090439650474325893442205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative is not calm.
Everyone who is happy or not rich is either not generous or creative.
Everyone who is both not generous and wise is curious or not happy and vice versa.
Everyone who is not tall is either strong or not tall.
Everyone who is both not curious and brave is not kind or not curious and vice versa.
Everyone who is kind is old.
If john is quiet then someone is either not wise or brave and vice versa.
If someone is either calm or not creative then someone is either wise or tall.
If someone is humble or not rich then someone is either generous or quiet and vice versa.
Everyone who is either happy or calm is either not old or not happy and vice versa.
If someone is both funny and creative then fred is either not patient or not happy.
Everyone who is not curious or not brave is either wise or not rich.
If someone is curious then someone is happy or calm.
Everyone who is not calm or happy is both wise and not rich.
Alice is not generous.
Alice is both funny and not patient.
Someone is funny or creative.
Alice is tall or happy.
Susan is funny.
Someone is not happy or tall. | Fred is curious. | entailment | (![X]:((humble(X)|~creative(X))=>~calm(X)))&
(![X]:((happy(X)|~rich(X))=>(~generous(X)<~>creative(X))))&
(![X]:((~generous(X)&wise(X))<=>(curious(X)|~happy(X))))&
(![X]:(~tall(X)=>(strong(X)<~>~tall(X))))&
(![X]:((~curious(X)&brave(X))<=>(~kind(X)|~curious(X))))&
(![X]:(kind(X)=>old(X)))&
((quiet(john))<=>(?[X]:((~wise(X)<~>brave(X)))))&
((?[X]:((calm(X)<~>~creative(X))))=>(?[X]:((wise(X)<~>tall(X)))))&
((?[X]:((humble(X)|~rich(X))))<=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((happy(X)<~>calm(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((funny(X)&creative(X))))=>((~patient(fred)<~>~happy(fred))))&
(![X]:((~curious(X)|~brave(X))=>(wise(X)<~>~rich(X))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~calm(X)|happy(X))=>(wise(X)&~rich(X))))&
(~generous(alice))&
((funny(alice)&~patient(alice)))&
(?[X]:((funny(X)|creative(X))))&
((tall(alice)|happy(alice)))&
(funny(susan))&
(?[X]:((~happy(X)|tall(X)))) | curious(fred) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p8",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4615779818146232370681747
% SZS output start Proof for 4615779818146232370681747
1. ! [X0] : ((~creative(X0) | humble(X0)) => ~calm(X0)) [input p0]
2. ! [X0] : ((~rich(X0) | happy(X0)) => (~generous(X0) <~> creative(X0))) [input p1]
3. ! [X0] : ((wise(X0) & ~generous(X0)) <=> (~happy(X0) | curious(X0))) [input p2]
5. ! [X0] : ((brave(X0) & ~curious(X0)) <=> (~curious(X0) | ~kind(X0))) [input p4]
6. ! [X0] : (kind(X0) => old(X0)) [input p5]
7. quiet(john) <=> ? [X0] : (~wise(X0) <~> brave(X0)) [input p6]
9. ? [X0] : (~rich(X0) | humble(X0)) <=> ? [X0] : (generous(X0) <~> quiet(X0)) [input p8]
10. ! [X0] : ((happy(X0) <~> calm(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p9]
12. ! [X0] : ((~brave(X0) | ~curious(X0)) => (wise(X0) <~> ~rich(X0))) [input p11]
14. ! [X0] : ((happy(X0) | ~calm(X0)) => (~rich(X0) & wise(X0))) [input p13]
21. ~curious(fred) [input hypothesis]
23. ? [X0] : (~rich(X0) | humble(X0)) <=> ? [X1] : (generous(X1) <~> quiet(X1)) [rectify 9]
25. ! [X0] : (~calm(X0) | (creative(X0) & ~humble(X0))) [ennf transformation 1]
26. ! [X0] : ((~generous(X0) <~> creative(X0)) | (rich(X0) & ~happy(X0))) [ennf transformation 2]
28. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 6]
31. ! [X0] : ((wise(X0) <~> ~rich(X0)) | (brave(X0) & curious(X0))) [ennf transformation 12]
33. ! [X0] : ((~rich(X0) & wise(X0)) | (~happy(X0) & calm(X0))) [ennf transformation 14]
34. ! [X0] : (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (rich(X0) & ~happy(X0))) [nnf transformation 26]
35. ! [X0] : (((wise(X0) & ~generous(X0)) | (happy(X0) & ~curious(X0))) & ((~happy(X0) | curious(X0)) | (~wise(X0) | generous(X0)))) [nnf transformation 3]
36. ! [X0] : (((wise(X0) & ~generous(X0)) | (happy(X0) & ~curious(X0))) & (~happy(X0) | curious(X0) | ~wise(X0) | generous(X0))) [flattening 35]
38. ! [X0] : (((brave(X0) & ~curious(X0)) | (curious(X0) & kind(X0))) & ((~curious(X0) | ~kind(X0)) | (~brave(X0) | curious(X0)))) [nnf transformation 5]
39. ! [X0] : (((brave(X0) & ~curious(X0)) | (curious(X0) & kind(X0))) & (~curious(X0) | ~kind(X0) | ~brave(X0) | curious(X0))) [flattening 38]
40. (quiet(john) | ! [X0] : ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (? [X0] : ((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | ~quiet(john)) [nnf transformation 7]
41. (quiet(john) | ! [X0] : ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (? [X1] : ((~brave(X1) | wise(X1)) & (brave(X1) | ~wise(X1))) | ~quiet(john)) [rectify 40]
42. ? [X1] : ((~brave(X1) | wise(X1)) & (brave(X1) | ~wise(X1))) => ((~brave(sK0) | wise(sK0)) & (brave(sK0) | ~wise(sK0))) [choice axiom]
43. (quiet(john) | ! [X0] : ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (((~brave(sK0) | wise(sK0)) & (brave(sK0) | ~wise(sK0))) | ~quiet(john)) [skolemisation 41,42]
48. (? [X0] : (~rich(X0) | humble(X0)) | ! [X1] : ((generous(X1) | ~quiet(X1)) & (quiet(X1) | ~generous(X1)))) & (? [X1] : ((~quiet(X1) | ~generous(X1)) & (quiet(X1) | generous(X1))) | ! [X0] : (rich(X0) & ~humble(X0))) [nnf transformation 23]
49. (? [X0] : (~rich(X0) | humble(X0)) | ! [X1] : ((generous(X1) | ~quiet(X1)) & (quiet(X1) | ~generous(X1)))) & (? [X2] : ((~quiet(X2) | ~generous(X2)) & (quiet(X2) | generous(X2))) | ! [X3] : (rich(X3) & ~humble(X3))) [rectify 48]
50. ? [X0] : (~rich(X0) | humble(X0)) => (~rich(sK2) | humble(sK2)) [choice axiom]
51. ? [X2] : ((~quiet(X2) | ~generous(X2)) & (quiet(X2) | generous(X2))) => ((~quiet(sK3) | ~generous(sK3)) & (quiet(sK3) | generous(sK3))) [choice axiom]
52. ((~rich(sK2) | humble(sK2)) | ! [X1] : ((generous(X1) | ~quiet(X1)) & (quiet(X1) | ~generous(X1)))) & (((~quiet(sK3) | ~generous(sK3)) & (quiet(sK3) | generous(sK3))) | ! [X3] : (rich(X3) & ~humble(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [nnf transformation 10]
55. ! [X0] : (((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (brave(X0) & curious(X0))) [nnf transformation 31]
63. ~calm(X0) | ~humble(X0) [cnf transformation 25]
64. ~calm(X0) | creative(X0) [cnf transformation 25]
68. ~creative(X0) | generous(X0) | rich(X0) [cnf transformation 34]
70. ~curious(X0) | ~generous(X0) [cnf transformation 36]
71. ~generous(X0) | happy(X0) [cnf transformation 36]
73. wise(X0) | happy(X0) [cnf transformation 36]
77. ~curious(X0) | kind(X0) [cnf transformation 39]
80. brave(X0) | curious(X0) [cnf transformation 39]
81. ~kind(X0) | old(X0) [cnf transformation 28]
85. quiet(john) | ~wise(X0) | ~brave(X0) [cnf transformation 43]
95. ~rich(sK2) | humble(sK2) | generous(X1) | ~quiet(X1) [cnf transformation 52]
96. ~happy(X0) | ~old(X0) | calm(X0) | ~happy(X0) [cnf transformation 53]
101. calm(X0) | happy(X0) | ~old(X0) | happy(X0) [cnf transformation 53]
108. ~wise(X0) | rich(X0) | curious(X0) [cnf transformation 55]
112. wise(X0) | ~happy(X0) [cnf transformation 33]
113. ~rich(X0) | calm(X0) [cnf transformation 33]
114. ~rich(X0) | ~happy(X0) [cnf transformation 33]
122. ~curious(fred) [cnf transformation 21]
123. ~happy(X0) | ~old(X0) | calm(X0) [duplicate literal removal 96]
125. ~old(X0) | happy(X0) | calm(X0) [duplicate literal removal 101]
129. 1 <=> ! [X0] : (~wise(X0) | ~brave(X0)) [avatar definition]
130. ~wise(X0) | ~brave(X0) <- (1) [avatar component clause 129]
132. 2 <=> quiet(john) [avatar definition]
134. quiet(john) <- (2) [avatar component clause 132]
135. 1 | 2 [avatar split clause 85,132,129]
152. 6 <=> ! [X1] : creative(X1) [avatar definition]
153. creative(X1) <- (6) [avatar component clause 152]
173. 10 <=> ! [X1] : (generous(X1) | ~quiet(X1)) [avatar definition]
174. ~quiet(X1) | generous(X1) <- (10) [avatar component clause 173]
176. 11 <=> humble(sK2) [avatar definition]
178. humble(sK2) <- (11) [avatar component clause 176]
180. 12 <=> rich(sK2) [avatar definition]
181. rich(sK2) <- (12) [avatar component clause 180]
182. ~rich(sK2) <- (~12) [avatar component clause 180]
183. 10 | 11 | ~12 [avatar split clause 95,180,176,173]
189. 14 <=> ! [X3] : rich(X3) [avatar definition]
190. rich(X3) <- (14) [avatar component clause 189]
207. ~old(X0) | calm(X0) [subsumption resolution 123,125]
234. wise(X0) [subsumption resolution 112,73]
277. curious(X1) | rich(X1) [resolution 108,234]
281. $false <- (~12, 14) [resolution 190,182]
286. 12 | ~14 [avatar contradiction clause 281]
299. calm(sK2) <- (12) [resolution 181,113]
314. ~humble(sK2) <- (12) [resolution 299,63]
315. $false <- (11, 12) [subsumption resolution 314,178]
316. ~11 | ~12 [avatar contradiction clause 315]
320. kind(X0) | rich(X0) [resolution 277,77]
322. ~generous(X2) | rich(X2) [resolution 277,70]
347. old(X0) | rich(X0) [resolution 320,81]
352. rich(X1) | calm(X1) [resolution 347,207]
354. calm(X1) [subsumption resolution 352,113]
359. creative(X1) [resolution 354,64]
361. 6 [avatar split clause 359,152]
363. generous(X0) | rich(X0) <- (6) [resolution 153,68]
372. rich(X0) <- (6) [subsumption resolution 363,322]
373. 14 | ~6 [avatar split clause 372,152,189]
377. ~happy(X2) <- (14) [resolution 190,114]
383. generous(john) <- (2, 10) [resolution 174,134]
397. happy(john) <- (2, 10) [resolution 383,71]
398. $false <- (2, 10, 14) [subsumption resolution 397,377]
399. ~2 | ~10 | ~14 [avatar contradiction clause 398]
400. ~brave(X0) <- (1) [subsumption resolution 130,234]
404. curious(X2) <- (1) [resolution 400,80]
408. $false <- (1) [resolution 404,122]
412. ~1 [avatar contradiction clause 408]
413. $false [avatar sat refutation 135,183,286,316,361,373,399,412]
% SZS output end Proof for 4615779818146232370681747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not patient is both calm and not rich.
If someone is kind then fred is either not funny or not calm.
If john is not rich then paul is either not curious or quiet and vice versa.
If someone is either not strong or not wise then susan is either curious or funny and vice versa.
Everyone who is not funny is either rich or not strong and vice versa.
Everyone who is either kind or generous is either old or brave and vice versa.
Everyone who is both humble and quiet is brave or funny and vice versa.
Everyone who is kind or happy is creative or old and vice versa.
If fred is not old then fred is both wise and kind.
Everyone who is not calm or not quiet is rich or not tall.
Everyone who is both not kind and generous is happy or not humble.
Everyone who is not humble is either not strong or not kind.
If mary is brave or not curious then someone is both not old and not generous and vice versa.
Everyone who is both patient and curious is either old or not old and vice versa.
Everyone who is both not old and not kind is not funny or not creative and vice versa.
Everyone who is not humble or wise is both tall and not kind and vice versa.
Fred is calm.
Someone is not generous.
Someone is either tall or happy.
Susan is curious or not brave.
Paul is both not creative and not tall.
John is not curious or not funny.
Mary is patient. | Paul is not creative. | entailment | (![X]:((old(X)&~patient(X))=>(calm(X)&~rich(X))))&
((?[X]:(kind(X)))=>((~funny(fred)<~>~calm(fred))))&
((~rich(john))<=>((~curious(paul)<~>quiet(paul))))&
((?[X]:((~strong(X)<~>~wise(X))))<=>((curious(susan)<~>funny(susan))))&
(![X]:(~funny(X)<=>(rich(X)<~>~strong(X))))&
(![X]:((kind(X)<~>generous(X))<=>(old(X)<~>brave(X))))&
(![X]:((humble(X)&quiet(X))<=>(brave(X)|funny(X))))&
(![X]:((kind(X)|happy(X))<=>(creative(X)|old(X))))&
((~old(fred))=>((wise(fred)&kind(fred))))&
(![X]:((~calm(X)|~quiet(X))=>(rich(X)|~tall(X))))&
(![X]:((~kind(X)&generous(X))=>(happy(X)|~humble(X))))&
(![X]:(~humble(X)=>(~strong(X)<~>~kind(X))))&
(((brave(mary)|~curious(mary)))<=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:((patient(X)&curious(X))<=>(old(X)<~>~old(X))))&
(![X]:((~old(X)&~kind(X))<=>(~funny(X)|~creative(X))))&
(![X]:((~humble(X)|wise(X))<=>(tall(X)&~kind(X))))&
(calm(fred))&
(?[X]:(~generous(X)))&
(?[X]:((tall(X)<~>happy(X))))&
((curious(susan)|~brave(susan)))&
((~creative(paul)&~tall(paul)))&
((~curious(john)|~funny(john)))&
(patient(mary)) | ~creative(paul) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 778871725622309410945717
% SZS output start Proof for 778871725622309410945717
21. ~tall(paul) & ~creative(paul) [input p20]
24. creative(paul) [input hypothesis]
133. ~creative(paul) [cnf transformation 21]
137. creative(paul) [cnf transformation 24]
253. $false [subsumption resolution 137,133]
% SZS output end Proof for 778871725622309410945717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong 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. | Alice is not old. | neutral | (![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))) | ~old(alice) | [] | null | 0 |
If someone is either patient or not brave then alice is not patient. If someone is both not generous and not kind then someone is old or happy and vice versa. If someone is either not happy or calm then fred is both rich and not brave. Everyone who is generous is not tall or humble and vice versa. If mary is happy then someone is both not rich and brave and vice versa. Everyone who is both not humble and wise is both creative and quiet and vice versa. If someone is either brave or not rich then susan is both calm and not funny and vice versa. Everyone who is not funny is curious. If someone is either calm or patient then someone is not funny. Everyone who is not tall or old is not curious and vice versa. If someone is wise or not creative then someone is either not quiet or kind. If alice is both tall and generous then someone is either not happy or strong and vice versa. Everyone who is not happy is both not curious and not old. Everyone who is both not kind and rich is either not kind or patient and vice versa. If alice is either generous or not curious then someone is patient and vice versa. Everyone who is not old or not happy is wise. John is either not creative or curious. Someone is both humble and not brave. Someone is generous. Someone is brave or not calm. Someone is strong. Susan is generous or strong. Mary is generous. Mary is both not tall and calm. | Alice is curious. | neutral | ((?[X]:((patient(X)<~>~brave(X))))=>(~patient(alice)))&
((?[X]:((~generous(X)&~kind(X))))<=>(?[X]:((old(X)|happy(X)))))&
((?[X]:((~happy(X)<~>calm(X))))=>((rich(fred)&~brave(fred))))&
(![X]:(generous(X)<=>(~tall(X)|humble(X))))&
((happy(mary))<=>(?[X]:((~rich(X)&brave(X)))))&
(![X]:((~humble(X)&wise(X))<=>(creative(X)&quiet(X))))&
((?[X]:((brave(X)<~>~rich(X))))<=>((calm(susan)&~funny(susan))))&
(![X]:(~funny(X)=>curious(X)))&
((?[X]:((calm(X)<~>patient(X))))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|old(X))<=>~curious(X)))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(((tall(alice)&generous(alice)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(~happy(X)=>(~curious(X)&~old(X))))&
(![X]:((~kind(X)&rich(X))<=>(~kind(X)<~>patient(X))))&
(((generous(alice)<~>~curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~old(X)|~happy(X))=>wise(X)))&
((~creative(john)<~>curious(john)))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:(generous(X)))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:(strong(X)))&
((generous(susan)|strong(susan)))&
(generous(mary))&
((~tall(mary)&calm(mary))) | curious(alice) | [] | null | 0 |
Everyone who is both curious and not kind is both not generous and brave.
Everyone who is not generous or curious is not calm or generous and vice versa.
Everyone who is either old or humble is both not patient and rich.
If susan is either not happy or quiet then someone is either generous or not funny and vice versa.
If someone is tall or brave then someone is either old or kind.
If lucy is humble or not calm then someone is not humble and vice versa.
If someone is not funny then lucy is either not generous or wise.
If mary is both rich and not kind then someone is not kind and vice versa.
Everyone who is either generous or not generous is tall and vice versa.
Everyone who is not strong or not funny is either not happy or not quiet.
Everyone who is creative or not strong is not kind.
If lucy is funny or quiet then someone is both tall and humble and vice versa.
If lucy is wise then someone is both strong and not strong and vice versa.
If mary is both not creative and not funny then someone is kind or funny.
Everyone who is either curious or strong is both strong and creative and vice versa.
If someone is either not generous or not happy then someone is either curious or quiet and vice versa.
Someone is either calm or not generous.
Someone is either happy or generous.
Susan is both generous and not funny.
Fred is not wise.
Someone is creative or not kind.
Alice is either curious or tall.
Mary is creative or funny.
Susan is either strong or creative. | Alice is generous. | contradiction | (![X]:((curious(X)&~kind(X))=>(~generous(X)&brave(X))))&
(![X]:((~generous(X)|curious(X))<=>(~calm(X)|generous(X))))&
(![X]:((old(X)<~>humble(X))=>(~patient(X)&rich(X))))&
(((~happy(susan)<~>quiet(susan)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
((?[X]:((tall(X)|brave(X))))=>(?[X]:((old(X)<~>kind(X)))))&
(((humble(lucy)|~calm(lucy)))<=>(?[X]:(~humble(X))))&
((?[X]:(~funny(X)))=>((~generous(lucy)<~>wise(lucy))))&
(((rich(mary)&~kind(mary)))<=>(?[X]:(~kind(X))))&
(![X]:((generous(X)<~>~generous(X))<=>tall(X)))&
(![X]:((~strong(X)|~funny(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((creative(X)|~strong(X))=>~kind(X)))&
(((funny(lucy)|quiet(lucy)))<=>(?[X]:((tall(X)&humble(X)))))&
((wise(lucy))<=>(?[X]:((strong(X)&~strong(X)))))&
(((~creative(mary)&~funny(mary)))=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((curious(X)<~>strong(X))<=>(strong(X)&creative(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((curious(X)<~>quiet(X)))))&
(?[X]:((calm(X)<~>~generous(X))))&
(?[X]:((happy(X)<~>generous(X))))&
((generous(susan)&~funny(susan)))&
(~wise(fred))&
(?[X]:((creative(X)|~kind(X))))&
((curious(alice)<~>tall(alice)))&
((creative(mary)|funny(mary)))&
((strong(susan)<~>creative(susan))) | generous(alice) | [
"p1",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4037617117499149593835159
% SZS output start Proof for 4037617117499149593835159
2. ! [X0] : ((curious(X0) | ~generous(X0)) <=> (generous(X0) | ~calm(X0))) [input p1]
9. ! [X0] : ((generous(X0) <~> ~generous(X0)) <=> tall(X0)) [input p8]
22. curious(alice) <~> tall(alice) [input p21]
25. generous(alice) [input hypothesis]
38. ! [X0] : (((curious(X0) | ~generous(X0)) | (~generous(X0) & calm(X0))) & ((generous(X0) | ~calm(X0)) | (~curious(X0) & generous(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~generous(X0) | (~generous(X0) & calm(X0))) & (generous(X0) | ~calm(X0) | (~curious(X0) & generous(X0)))) [flattening 38]
60. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | ~tall(X0)) & (tall(X0) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [nnf transformation 9]
88. (~tall(alice) | ~curious(alice)) & (tall(alice) | curious(alice)) [nnf transformation 22]
95. curious(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 39]
118. tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 60]
119. tall(X0) | generous(X0) | generous(X0) [cnf transformation 60]
160. ~tall(alice) | ~curious(alice) [cnf transformation 88]
164. generous(alice) [cnf transformation 25]
167. tall(X0) | ~generous(X0) [duplicate literal removal 118]
168. tall(X0) | generous(X0) [duplicate literal removal 119]
170. ~generous(X0) | curious(X0) [duplicate literal removal 95]
268. tall(X0) [subsumption resolution 167,168]
367. ~curious(alice) [subsumption resolution 160,268]
387. curious(alice) [resolution 170,164]
389. $false [subsumption resolution 387,367]
% SZS output end Proof for 4037617117499149593835159
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or curious is both not creative and not happy and vice versa.
Everyone who is both not creative and not brave is calm or brave and vice versa.
Everyone who is either calm or not curious is either not old or tall.
If someone is patient then john is either not funny or wise.
Everyone who is either not generous or not funny is not curious or not tall.
Everyone who is strong or quiet is either not rich or creative.
Everyone who is humble is either creative or not funny and vice versa.
Everyone who is both not old and not strong is not strong and vice versa.
If someone is either not strong or not curious then fred is not generous or strong and vice versa.
If someone is both rich and kind then someone is either not strong or happy.
If someone is either humble or not kind then someone is either not brave or not strong and vice versa.
Everyone who is tall is tall or not curious.
If someone is not creative or quiet then john is curious.
If someone is generous or strong then someone is both creative and not wise and vice versa.
If someone is both wise and brave then paul is not happy or not strong.
If someone is strong or not kind then alice is not wise or not brave and vice versa.
Someone is either quiet or not curious.
Someone is either rich or not curious.
Someone is either not strong or rich.
Lucy is either not creative or tall.
Someone is either not humble or not calm.
Someone is either not generous or not happy.
Someone is both happy and old.
Someone is both wise and not creative. | John is calm. | entailment | (![X]:((humble(X)|curious(X))<=>(~creative(X)&~happy(X))))&
(![X]:((~creative(X)&~brave(X))<=>(calm(X)|brave(X))))&
(![X]:((calm(X)<~>~curious(X))=>(~old(X)<~>tall(X))))&
((?[X]:(patient(X)))=>((~funny(john)<~>wise(john))))&
(![X]:((~generous(X)<~>~funny(X))=>(~curious(X)|~tall(X))))&
(![X]:((strong(X)|quiet(X))=>(~rich(X)<~>creative(X))))&
(![X]:(humble(X)<=>(creative(X)<~>~funny(X))))&
(![X]:((~old(X)&~strong(X))<=>~strong(X)))&
((?[X]:((~strong(X)<~>~curious(X))))<=>((~generous(fred)|strong(fred))))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:(tall(X)=>(tall(X)|~curious(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(curious(john)))&
((?[X]:((generous(X)|strong(X))))<=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((wise(X)&brave(X))))=>((~happy(paul)|~strong(paul))))&
((?[X]:((strong(X)|~kind(X))))<=>((~wise(alice)|~brave(alice))))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((rich(X)<~>~curious(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
((~creative(lucy)<~>tall(lucy)))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((happy(X)&old(X))))&
(?[X]:((wise(X)&~creative(X)))) | calm(john) | [
"p0",
"p1",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7682890770503557601120040
% SZS output start Proof for 7682890770503557601120040
1. ! [X0] : ((curious(X0) | humble(X0)) <=> (~happy(X0) & ~creative(X0))) [input p0]
2. ! [X0] : ((~brave(X0) & ~creative(X0)) <=> (brave(X0) | calm(X0))) [input p1]
13. ? [X0] : (quiet(X0) | ~creative(X0)) => curious(john) [input p12]
24. ? [X0] : (~creative(X0) & wise(X0)) [input p23]
25. ~calm(john) [input hypothesis]
37. curious(john) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 13]
40. ! [X0] : (((curious(X0) | humble(X0)) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | (~curious(X0) & ~humble(X0)))) [nnf transformation 1]
41. ! [X0] : ((curious(X0) | humble(X0) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | (~curious(X0) & ~humble(X0)))) [flattening 40]
42. ! [X0] : (((~brave(X0) & ~creative(X0)) | (~brave(X0) & ~calm(X0))) & ((brave(X0) | calm(X0)) | (brave(X0) | creative(X0)))) [nnf transformation 2]
43. ! [X0] : (((~brave(X0) & ~creative(X0)) | (~brave(X0) & ~calm(X0))) & (brave(X0) | calm(X0) | brave(X0) | creative(X0))) [flattening 42]
92. ? [X0] : (~creative(X0) & wise(X0)) => (~creative(sK13) & wise(sK13)) [choice axiom]
93. ~creative(sK13) & wise(sK13) [skolemisation 24,92]
95. ~creative(X0) | ~curious(X0) [cnf transformation 41]
99. brave(X0) | calm(X0) | brave(X0) | creative(X0) [cnf transformation 43]
103. ~brave(X0) | ~brave(X0) [cnf transformation 43]
138. curious(john) | creative(X0) [cnf transformation 37]
165. ~creative(sK13) [cnf transformation 93]
166. ~calm(john) [cnf transformation 25]
167. brave(X0) | calm(X0) | creative(X0) [duplicate literal removal 99]
168. ~brave(X0) [duplicate literal removal 103]
169. calm(X0) | creative(X0) [subsumption resolution 167,168]
246. 17 <=> curious(john) [avatar definition]
251. 18 <=> ! [X0] : creative(X0) [avatar definition]
252. creative(X0) <- (18) [avatar component clause 251]
253. 18 | 17 [avatar split clause 138,246,251]
365. creative(john) [resolution 169,166]
368. ~curious(john) [resolution 365,95]
372. ~17 [avatar split clause 368,246]
373. $false <- (18) [resolution 252,165]
378. ~18 [avatar contradiction clause 373]
379. $false [avatar sat refutation 253,372,378]
% SZS output end Proof for 7682890770503557601120040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is rich or not quiet.
If fred is not curious or not strong then someone is either wise or not generous.
Everyone who is not happy or not brave is rich or creative and vice versa.
Everyone who is either not rich or not tall is not generous or creative.
If someone is not rich then someone is both kind and not generous.
Everyone who is either not creative or wise is old and vice versa.
If fred is creative then mary is not generous and vice versa.
Everyone who is either generous or not generous is either rich or old and vice versa.
If mary is either humble or not rich then someone is both not quiet and patient and vice versa.
Everyone who is either quiet or not old is not patient.
Everyone who is both not brave and old is not curious or generous.
Everyone who is patient is brave and vice versa.
If paul is either kind or generous then paul is both rich and creative.
If someone is not happy then lucy is brave and vice versa.
If mary is patient or not old then susan is old and vice versa.
If mary is curious or calm then someone is quiet and vice versa.
Mary is creative or not strong.
Someone is generous.
Someone is both quiet and not happy.
Someone is not old.
Fred is quiet or tall.
Someone is strong or not generous.
Someone is both strong and wise.
Lucy is tall or happy. | Susan is wise. | neutral | (![X]:(~quiet(X)=>(rich(X)|~quiet(X))))&
(((~curious(fred)|~strong(fred)))=>(?[X]:((wise(X)<~>~generous(X)))))&
(![X]:((~happy(X)|~brave(X))<=>(rich(X)|creative(X))))&
(![X]:((~rich(X)<~>~tall(X))=>(~generous(X)|creative(X))))&
((?[X]:(~rich(X)))=>(?[X]:((kind(X)&~generous(X)))))&
(![X]:((~creative(X)<~>wise(X))<=>old(X)))&
((creative(fred))<=>(~generous(mary)))&
(![X]:((generous(X)<~>~generous(X))<=>(rich(X)<~>old(X))))&
(((humble(mary)<~>~rich(mary)))<=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:((quiet(X)<~>~old(X))=>~patient(X)))&
(![X]:((~brave(X)&old(X))=>(~curious(X)|generous(X))))&
(![X]:(patient(X)<=>brave(X)))&
(((kind(paul)<~>generous(paul)))=>((rich(paul)&creative(paul))))&
((?[X]:(~happy(X)))<=>(brave(lucy)))&
(((patient(mary)|~old(mary)))<=>(old(susan)))&
(((curious(mary)|calm(mary)))<=>(?[X]:(quiet(X))))&
((creative(mary)|~strong(mary)))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:(~old(X)))&
((quiet(fred)|tall(fred)))&
(?[X]:((strong(X)|~generous(X))))&
(?[X]:((strong(X)&wise(X))))&
((tall(lucy)|happy(lucy))) | wise(susan) | [] | null | 0 |
If lucy is strong or not creative then someone is either not quiet or generous and vice versa.
Everyone who is not funny or not generous is not funny and vice versa.
If paul is not rich or not quiet then alice is not patient.
Everyone who is either calm or quiet is both not rich and kind.
Everyone who is either not calm or not strong is curious or not calm.
If someone is either kind or not creative then someone is either not quiet or not curious.
If someone is funny or not tall then paul is not patient or creative and vice versa.
If someone is both not rich and not old then john is not old.
Everyone who is not strong is quiet or tall.
Everyone who is calm or old is either not funny or brave.
Everyone who is both wise and not brave is not happy or generous.
Everyone who is either happy or patient is either old or quiet and vice versa.
Everyone who is not generous or rich is rich or not calm.
Everyone who is either happy or not old is not wise and vice versa.
Everyone who is either not wise or not generous is not patient and vice versa.
Everyone who is wise or patient is patient or tall and vice versa.
Lucy is either quiet or generous.
Someone is brave or generous.
Paul is both humble and wise.
Alice is patient.
Someone is tall or creative.
John is not creative or happy.
Susan is not funny. | Lucy is not strong. | entailment | (((strong(lucy)|~creative(lucy)))<=>(?[X]:((~quiet(X)<~>generous(X)))))&
(![X]:((~funny(X)|~generous(X))<=>~funny(X)))&
(((~rich(paul)|~quiet(paul)))=>(~patient(alice)))&
(![X]:((calm(X)<~>quiet(X))=>(~rich(X)&kind(X))))&
(![X]:((~calm(X)<~>~strong(X))=>(curious(X)|~calm(X))))&
((?[X]:((kind(X)<~>~creative(X))))=>(?[X]:((~quiet(X)<~>~curious(X)))))&
((?[X]:((funny(X)|~tall(X))))<=>((~patient(paul)|creative(paul))))&
((?[X]:((~rich(X)&~old(X))))=>(~old(john)))&
(![X]:(~strong(X)=>(quiet(X)|tall(X))))&
(![X]:((calm(X)|old(X))=>(~funny(X)<~>brave(X))))&
(![X]:((wise(X)&~brave(X))=>(~happy(X)|generous(X))))&
(![X]:((happy(X)<~>patient(X))<=>(old(X)<~>quiet(X))))&
(![X]:((~generous(X)|rich(X))=>(rich(X)|~calm(X))))&
(![X]:((happy(X)<~>~old(X))<=>~wise(X)))&
(![X]:((~wise(X)<~>~generous(X))<=>~patient(X)))&
(![X]:((wise(X)|patient(X))<=>(patient(X)|tall(X))))&
((quiet(lucy)<~>generous(lucy)))&
(?[X]:((brave(X)|generous(X))))&
((humble(paul)&wise(paul)))&
(patient(alice))&
(?[X]:((tall(X)|creative(X))))&
((~creative(john)|happy(john)))&
(~funny(susan)) | ~strong(lucy) | [
"p0",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2882709013375789062371095
% SZS output start Proof for 2882709013375789062371095
1. (~creative(lucy) | strong(lucy)) <=> ? [X0] : (~quiet(X0) <~> generous(X0)) [input p0]
12. ! [X0] : ((happy(X0) <~> patient(X0)) <=> (old(X0) <~> quiet(X0))) [input p11]
14. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> ~wise(X0)) [input p13]
15. ! [X0] : ((~wise(X0) <~> ~generous(X0)) <=> ~patient(X0)) [input p14]
24. strong(lucy) [input hypothesis]
40. ((~creative(lucy) | strong(lucy)) | ! [X0] : ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) & (? [X0] : ((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (creative(lucy) & ~strong(lucy))) [nnf transformation 1]
41. (~creative(lucy) | strong(lucy) | ! [X0] : ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) & (? [X0] : ((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (creative(lucy) & ~strong(lucy))) [flattening 40]
42. (~creative(lucy) | strong(lucy) | ! [X0] : ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) & (? [X1] : ((~generous(X1) | quiet(X1)) & (generous(X1) | ~quiet(X1))) | (creative(lucy) & ~strong(lucy))) [rectify 41]
43. ? [X1] : ((~generous(X1) | quiet(X1)) & (generous(X1) | ~quiet(X1))) => ((~generous(sK0) | quiet(sK0)) & (generous(sK0) | ~quiet(sK0))) [choice axiom]
44. (~creative(lucy) | strong(lucy) | ! [X0] : ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) & (((~generous(sK0) | quiet(sK0)) & (generous(sK0) | ~quiet(sK0))) | (creative(lucy) & ~strong(lucy))) [skolemisation 42,43]
59. ! [X0] : ((((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0)))) & (((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))))) [nnf transformation 12]
60. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | wise(X0)) & (~wise(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 14]
61. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | patient(X0)) & (~patient(X0) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [nnf transformation 15]
69. generous(sK0) | ~quiet(sK0) | ~strong(lucy) [cnf transformation 44]
71. ~generous(sK0) | quiet(sK0) | ~strong(lucy) [cnf transformation 44]
101. ~happy(X0) | old(X0) | patient(X0) | quiet(X0) [cnf transformation 59]
102. ~patient(X0) | old(X0) | happy(X0) | quiet(X0) [cnf transformation 59]
103. ~happy(X0) | ~old(X0) | patient(X0) | ~quiet(X0) [cnf transformation 59]
104. ~old(X0) | ~quiet(X0) | happy(X0) | ~patient(X0) [cnf transformation 59]
105. ~old(X0) | happy(X0) | quiet(X0) | patient(X0) [cnf transformation 59]
106. ~quiet(X0) | happy(X0) | old(X0) | patient(X0) [cnf transformation 59]
107. ~happy(X0) | ~patient(X0) | quiet(X0) | ~old(X0) [cnf transformation 59]
108. ~happy(X0) | ~patient(X0) | old(X0) | ~quiet(X0) [cnf transformation 59]
111. ~happy(X0) | ~old(X0) | ~wise(X0) [cnf transformation 60]
112. ~wise(X0) | happy(X0) | old(X0) [cnf transformation 60]
113. ~old(X0) | happy(X0) | wise(X0) [cnf transformation 60]
114. ~happy(X0) | old(X0) | wise(X0) [cnf transformation 60]
115. ~patient(X0) | ~generous(X0) | wise(X0) [cnf transformation 61]
116. ~wise(X0) | ~patient(X0) | generous(X0) [cnf transformation 61]
117. ~wise(X0) | ~generous(X0) | patient(X0) [cnf transformation 61]
118. wise(X0) | generous(X0) | patient(X0) [cnf transformation 61]
131. strong(lucy) [cnf transformation 24]
137. 2 <=> strong(lucy) [avatar definition]
146. 4 <=> ! [X0] : (generous(X0) | quiet(X0)) [avatar definition]
147. generous(X0) | quiet(X0) <- (4) [avatar component clause 146]
150. 5 <=> quiet(sK0) [avatar definition]
151. ~quiet(sK0) <- (~5) [avatar component clause 150]
152. quiet(sK0) <- (5) [avatar component clause 150]
154. 6 <=> generous(sK0) [avatar definition]
155. generous(sK0) <- (6) [avatar component clause 154]
156. ~generous(sK0) <- (~6) [avatar component clause 154]
158. ~2 | 5 | ~6 [avatar split clause 71,154,150,137]
160. ~2 | ~5 | 6 [avatar split clause 69,154,150,137]
265. 2 [avatar split clause 131,137]
356. happy(X2) | patient(X2) | generous(X2) | old(X2) [resolution 118,112]
505. patient(X1) | generous(X1) | old(X1) | old(X1) | patient(X1) | quiet(X1) [resolution 356,101]
514. old(X1) | generous(X1) | patient(X1) | quiet(X1) [duplicate literal removal 505]
525. generous(X0) | patient(X0) | quiet(X0) | happy(X0) | quiet(X0) | patient(X0) [resolution 514,105]
532. happy(X0) | patient(X0) | quiet(X0) | generous(X0) [duplicate literal removal 525]
714. patient(X5) | quiet(X5) | generous(X5) | ~old(X5) | ~wise(X5) [resolution 532,111]
721. ~wise(X5) | quiet(X5) | ~old(X5) | patient(X5) [subsumption resolution 714,117]
784. quiet(X2) | ~old(X2) | patient(X2) | generous(X2) | patient(X2) [resolution 721,118]
786. quiet(X2) | ~old(X2) | patient(X2) | generous(X2) [duplicate literal removal 784]
790. patient(X2) | quiet(X2) | generous(X2) [subsumption resolution 786,514]
807. quiet(X2) | generous(X2) | old(X2) | happy(X2) | quiet(X2) [resolution 790,102]
813. happy(X2) | generous(X2) | old(X2) | quiet(X2) [duplicate literal removal 807]
946. generous(X6) | old(X6) | quiet(X6) | old(X6) | wise(X6) [resolution 813,114]
947. wise(X6) | old(X6) | quiet(X6) | generous(X6) [duplicate literal removal 946]
972. old(X1) | quiet(X1) | generous(X1) | ~patient(X1) | generous(X1) [resolution 947,116]
988. old(X1) | quiet(X1) | generous(X1) | ~patient(X1) [duplicate literal removal 972]
990. old(X1) | quiet(X1) | generous(X1) [subsumption resolution 988,790]
1010. happy(X2) | generous(X2) | quiet(X2) | wise(X2) [resolution 990,113]
1041. generous(X3) | quiet(X3) | wise(X3) | ~patient(X3) | quiet(X3) | ~old(X3) [resolution 1010,107]
1046. generous(X3) | quiet(X3) | wise(X3) | ~patient(X3) | ~old(X3) [duplicate literal removal 1041]
1049. generous(X3) | quiet(X3) | ~patient(X3) | ~old(X3) [subsumption resolution 1046,116]
1050. generous(X3) | quiet(X3) | ~old(X3) [subsumption resolution 1049,790]
1051. generous(X3) | quiet(X3) [subsumption resolution 1050,990]
1052. 4 [avatar split clause 1051,146]
1058. quiet(sK0) <- (4, ~6) [resolution 147,156]
1061. $false <- (4, ~5, ~6) [subsumption resolution 1058,151]
1062. ~4 | 5 | 6 [avatar contradiction clause 1061]
1064. happy(sK0) | old(sK0) | patient(sK0) <- (5) [resolution 152,106]
1071. 77 <=> patient(sK0) [avatar definition]
1073. patient(sK0) <- (77) [avatar component clause 1071]
1075. 78 <=> wise(sK0) [avatar definition]
1076. ~wise(sK0) <- (~78) [avatar component clause 1075]
1077. wise(sK0) <- (78) [avatar component clause 1075]
1080. 79 <=> old(sK0) [avatar definition]
1081. ~old(sK0) <- (~79) [avatar component clause 1080]
1082. old(sK0) <- (79) [avatar component clause 1080]
1084. 80 <=> happy(sK0) [avatar definition]
1086. happy(sK0) <- (80) [avatar component clause 1084]
1087. 77 | 79 | 80 | ~5 [avatar split clause 1064,150,1084,1080,1071]
1132. happy(sK0) | old(sK0) <- (78) [resolution 1077,112]
1134. ~generous(sK0) | patient(sK0) <- (78) [resolution 1077,117]
1143. patient(sK0) <- (6, 78) [subsumption resolution 1134,155]
1152. 77 | ~6 | ~78 [avatar split clause 1143,1075,154,1071]
1154. 79 | 80 | ~78 [avatar split clause 1132,1075,1084,1080]
1182. ~old(sK0) | patient(sK0) | ~quiet(sK0) <- (80) [resolution 1086,103]
1184. ~patient(sK0) | old(sK0) | ~quiet(sK0) <- (80) [resolution 1086,108]
1185. ~old(sK0) | ~wise(sK0) <- (80) [resolution 1086,111]
1186. old(sK0) | wise(sK0) <- (80) [resolution 1086,114]
1191. ~patient(sK0) | ~quiet(sK0) <- (~79, 80) [subsumption resolution 1184,1081]
1192. ~patient(sK0) <- (5, ~79, 80) [subsumption resolution 1191,152]
1193. ~77 | ~5 | 79 | ~80 [avatar split clause 1192,1084,1080,150,1071]
1196. old(sK0) <- (~78, 80) [subsumption resolution 1186,1076]
1197. 79 | 78 | ~80 [avatar split clause 1196,1084,1075,1080]
1201. patient(sK0) | ~quiet(sK0) <- (79, 80) [subsumption resolution 1182,1082]
1202. patient(sK0) <- (5, 79, 80) [subsumption resolution 1201,152]
1203. 77 | ~5 | ~79 | ~80 [avatar split clause 1202,1084,1080,150,1071]
1205. ~quiet(sK0) | happy(sK0) | ~patient(sK0) <- (79) [resolution 1082,104]
1206. happy(sK0) | wise(sK0) <- (79) [resolution 1082,113]
1209. ~generous(sK0) | wise(sK0) <- (77) [resolution 1073,115]
1210. wise(sK0) <- (6, 77) [subsumption resolution 1209,155]
1213. 78 | ~6 | ~77 [avatar split clause 1210,1071,154,1075]
1214. ~wise(sK0) <- (79, 80) [subsumption resolution 1185,1082]
1215. ~78 | ~79 | ~80 [avatar split clause 1214,1084,1080,1075]
1216. 78 | 80 | ~79 [avatar split clause 1206,1080,1084,1075]
1217. happy(sK0) | ~patient(sK0) <- (5, 79) [subsumption resolution 1205,152]
1218. ~77 | 80 | ~5 | ~79 [avatar split clause 1217,1080,150,1084,1071]
1219. $false [avatar sat refutation 158,160,265,1052,1062,1087,1152,1154,1193,1197,1203,1213,1215,1216,1218]
% SZS output end Proof for 2882709013375789062371095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then someone is not calm and vice versa.
Everyone who is not strong or rich is either curious or wise.
Everyone who is either not creative or wise is not happy and vice versa.
Everyone who is both calm and tall is not old.
If someone is wise then john is both not generous and not curious and vice versa.
Everyone who is not tall is brave and vice versa.
Everyone who is both rich and wise is not strong or not happy and vice versa.
Everyone who is not patient or not strong is not patient and vice versa.
Everyone who is both creative and not kind is not happy.
Everyone who is both not brave and old is both quiet and wise and vice versa.
Everyone who is patient or tall is both curious and quiet.
Everyone who is not generous is either patient or not humble.
Everyone who is strong or rich is either not kind or strong.
Everyone who is wise or funny is not old or funny.
Everyone who is either tall or not rich is not tall or happy.
If someone is funny or patient then paul is patient and vice versa.
Fred is both quiet and patient.
Fred is brave.
Paul is either wise or not generous.
Someone is strong or tall.
Someone is not curious.
Someone is either calm or not brave.
John is either curious or old.
Alice is not rich or not kind. | Alice is old. | neutral | ((?[X]:(generous(X)))<=>(?[X]:(~calm(X))))&
(![X]:((~strong(X)|rich(X))=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)<~>wise(X))<=>~happy(X)))&
(![X]:((calm(X)&tall(X))=>~old(X)))&
((?[X]:(wise(X)))<=>((~generous(john)&~curious(john))))&
(![X]:(~tall(X)<=>brave(X)))&
(![X]:((rich(X)&wise(X))<=>(~strong(X)|~happy(X))))&
(![X]:((~patient(X)|~strong(X))<=>~patient(X)))&
(![X]:((creative(X)&~kind(X))=>~happy(X)))&
(![X]:((~brave(X)&old(X))<=>(quiet(X)&wise(X))))&
(![X]:((patient(X)|tall(X))=>(curious(X)&quiet(X))))&
(![X]:(~generous(X)=>(patient(X)<~>~humble(X))))&
(![X]:((strong(X)|rich(X))=>(~kind(X)<~>strong(X))))&
(![X]:((wise(X)|funny(X))=>(~old(X)|funny(X))))&
(![X]:((tall(X)<~>~rich(X))=>(~tall(X)|happy(X))))&
((?[X]:((funny(X)|patient(X))))<=>(patient(paul)))&
((quiet(fred)&patient(fred)))&
(brave(fred))&
((wise(paul)<~>~generous(paul)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:(~curious(X)))&
(?[X]:((calm(X)<~>~brave(X))))&
((curious(john)<~>old(john)))&
((~rich(alice)|~kind(alice))) | old(alice) | [] | null | 0 |
Everyone who is funny or not calm is humble or old and vice versa. If someone is wise or tall then someone is either not wise or not rich and vice versa. Everyone who is wise is not curious and vice versa. Everyone who is both not wise and not rich is not wise or not rich and vice versa. Everyone who is not wise or not generous is curious. Everyone who is either old or not kind is both quiet and not wise and vice versa. If someone is not happy then someone is either not creative or calm and vice versa. If someone is humble or not curious then susan is old and vice versa. Everyone who is either happy or not rich is brave. Everyone who is happy or not tall is either rich or brave and vice versa. Everyone who is either not quiet or not kind is both strong and brave. Everyone who is either quiet or old is either not happy or not calm and vice versa. If lucy is wise then someone is not old. If someone is both not humble and not calm then someone is both old and tall. If someone is quiet or generous then someone is either not calm or humble and vice versa. If someone is either calm or not old then someone is strong. Someone is either not tall or not generous. Someone is not quiet or not creative. Alice is not creative or quiet. Fred is both not humble and not wise. Someone is either brave or not kind. Someone is either generous or calm. John is tall or not rich. | Alice is not curious. | contradiction | (![X]:((funny(X)|~calm(X))<=>(humble(X)|old(X))))&
((?[X]:((wise(X)|tall(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((~wise(X)&~rich(X))<=>(~wise(X)|~rich(X))))&
(![X]:((~wise(X)|~generous(X))=>curious(X)))&
(![X]:((old(X)<~>~kind(X))<=>(quiet(X)&~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
((?[X]:((humble(X)|~curious(X))))<=>(old(susan)))&
(![X]:((happy(X)<~>~rich(X))=>brave(X)))&
(![X]:((happy(X)|~tall(X))<=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(strong(X)&brave(X))))&
(![X]:((quiet(X)<~>old(X))<=>(~happy(X)<~>~calm(X))))&
((wise(lucy))=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)&~calm(X))))=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((quiet(X)|generous(X))))<=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((calm(X)<~>~old(X))))=>(?[X]:(strong(X))))&
(?[X]:((~tall(X)<~>~generous(X))))&
(?[X]:((~quiet(X)|~creative(X))))&
((~creative(alice)|quiet(alice)))&
((~humble(fred)&~wise(fred)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((generous(X)<~>calm(X))))&
((tall(john)|~rich(john))) | ~curious(alice) | [
"p1",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6122966442612598845685689
% SZS output start Proof for 6122966442612598845685689
2. ? [X0] : (tall(X0) | wise(X0)) <=> ? [X0] : (~wise(X0) <~> ~rich(X0)) [input p1]
3. ! [X0] : (wise(X0) <=> ~curious(X0)) [input p2]
4. ! [X0] : ((~rich(X0) & ~wise(X0)) <=> (~rich(X0) | ~wise(X0))) [input p3]
24. ~curious(alice) [input hypothesis]
25. ? [X0] : (tall(X0) | wise(X0)) <=> ? [X1] : (~wise(X1) <~> ~rich(X1)) [rectify 2]
39. (? [X0] : (tall(X0) | wise(X0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (? [X1] : ((rich(X1) | wise(X1)) & (~rich(X1) | ~wise(X1))) | ! [X0] : (~tall(X0) & ~wise(X0))) [nnf transformation 25]
40. (? [X0] : (tall(X0) | wise(X0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (? [X2] : ((rich(X2) | wise(X2)) & (~rich(X2) | ~wise(X2))) | ! [X3] : (~tall(X3) & ~wise(X3))) [rectify 39]
41. ? [X0] : (tall(X0) | wise(X0)) => (tall(sK0) | wise(sK0)) [choice axiom]
42. ? [X2] : ((rich(X2) | wise(X2)) & (~rich(X2) | ~wise(X2))) => ((rich(sK1) | wise(sK1)) & (~rich(sK1) | ~wise(sK1))) [choice axiom]
43. ((tall(sK0) | wise(sK0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (((rich(sK1) | wise(sK1)) & (~rich(sK1) | ~wise(sK1))) | ! [X3] : (~tall(X3) & ~wise(X3))) [skolemisation 40,42,41]
44. ! [X0] : ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0))) [nnf transformation 3]
45. ! [X0] : (((~rich(X0) & ~wise(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (rich(X0) | wise(X0)))) [nnf transformation 4]
46. ! [X0] : (((~rich(X0) & ~wise(X0)) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | rich(X0) | wise(X0))) [flattening 45]
88. ~rich(sK1) | ~wise(sK1) | ~wise(X3) [cnf transformation 43]
90. rich(sK1) | wise(sK1) | ~wise(X3) [cnf transformation 43]
95. curious(X0) | wise(X0) [cnf transformation 44]
98. ~wise(X0) | rich(X0) [cnf transformation 46]
99. ~rich(X0) | wise(X0) [cnf transformation 46]
154. ~curious(alice) [cnf transformation 24]
156. 1 <=> ! [X1] : (~wise(X1) | rich(X1)) [avatar definition]
157. ~wise(X1) | rich(X1) <- (1) [avatar component clause 156]
168. 4 <=> ! [X1] : (~rich(X1) | wise(X1)) [avatar definition]
169. ~rich(X1) | wise(X1) <- (4) [avatar component clause 168]
175. 6 <=> wise(sK1) [avatar definition]
176. ~wise(sK1) <- (~6) [avatar component clause 175]
177. wise(sK1) <- (6) [avatar component clause 175]
179. 7 <=> rich(sK1) [avatar definition]
180. ~rich(sK1) <- (~7) [avatar component clause 179]
181. rich(sK1) <- (7) [avatar component clause 179]
184. 8 <=> ! [X3] : ~wise(X3) [avatar definition]
185. ~wise(X3) <- (8) [avatar component clause 184]
186. 8 | 6 | 7 [avatar split clause 90,179,175,184]
188. 8 | ~6 | ~7 [avatar split clause 88,179,175,184]
189. 4 [avatar split clause 99,168]
190. 1 [avatar split clause 98,156]
351. wise(alice) [resolution 95,154]
355. rich(sK1) <- (1, 6) [resolution 157,177]
358. $false <- (1, 6, ~7) [subsumption resolution 355,180]
359. ~1 | ~6 | 7 [avatar contradiction clause 358]
361. wise(sK1) <- (4, 7) [resolution 169,181]
362. $false <- (4, ~6, 7) [subsumption resolution 361,176]
363. ~4 | 6 | ~7 [avatar contradiction clause 362]
367. $false <- (8) [resolution 185,351]
368. ~8 [avatar contradiction clause 367]
370. $false [avatar sat refutation 186,188,189,190,359,363,368]
% SZS output end Proof for 6122966442612598845685689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not funny or quiet then someone is not generous or old. If fred is both not old and not happy then john is not brave or not curious and vice versa. If someone is not brave or wise then fred is not strong or happy. If lucy is not humble or not curious then someone is calm and vice versa. Everyone who is either strong or not wise is happy or not brave. Everyone who is not quiet or not funny is either not strong or creative. Everyone who is not calm or old is not old and vice versa. If fred is both happy and not happy then someone is not quiet or rich. Everyone who is both brave and not brave is either not patient or not happy and vice versa. Everyone who is either not brave or tall is funny. Everyone who is either not happy or strong is not curious or tall. Everyone who is both not quiet and tall is either old or not happy and vice versa. If someone is not kind or not brave then john is not funny and vice versa. Everyone who is not tall is funny or brave and vice versa. Everyone who is not rich or not brave is creative. Everyone who is both not patient and wise is quiet or brave. Lucy is either not creative or not tall. Alice is not humble. Someone is not kind or not creative. Lucy is both not strong and not kind. Someone is kind. Someone is both strong and not old. | Lucy is not quiet. | contradiction | (((~funny(mary)|quiet(mary)))=>(?[X]:((~generous(X)|old(X)))))&
(((~old(fred)&~happy(fred)))<=>((~brave(john)|~curious(john))))&
((?[X]:((~brave(X)|wise(X))))=>((~strong(fred)|happy(fred))))&
(((~humble(lucy)|~curious(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((strong(X)<~>~wise(X))=>(happy(X)|~brave(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~strong(X)<~>creative(X))))&
(![X]:((~calm(X)|old(X))<=>~old(X)))&
(((happy(fred)&~happy(fred)))=>(?[X]:((~quiet(X)|rich(X)))))&
(![X]:((brave(X)&~brave(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:((~brave(X)<~>tall(X))=>funny(X)))&
(![X]:((~happy(X)<~>strong(X))=>(~curious(X)|tall(X))))&
(![X]:((~quiet(X)&tall(X))<=>(old(X)<~>~happy(X))))&
((?[X]:((~kind(X)|~brave(X))))<=>(~funny(john)))&
(![X]:(~tall(X)<=>(funny(X)|brave(X))))&
(![X]:((~rich(X)|~brave(X))=>creative(X)))&
(![X]:((~patient(X)&wise(X))=>(quiet(X)|brave(X))))&
((~creative(lucy)<~>~tall(lucy)))&
(~humble(alice))&
(?[X]:((~kind(X)|~creative(X))))&
((~strong(lucy)&~kind(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((strong(X)&~old(X)))) | ~quiet(lucy) | [
"p5",
"p13",
"p14",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 486193297716140831554016
% SZS output start Proof for 486193297716140831554016
6. ! [X0] : ((~funny(X0) | ~quiet(X0)) => (~strong(X0) <~> creative(X0))) [input p5]
14. ! [X0] : (~tall(X0) <=> (brave(X0) | funny(X0))) [input p13]
15. ! [X0] : ((~brave(X0) | ~rich(X0)) => creative(X0)) [input p14]
17. ~creative(lucy) <~> ~tall(lucy) [input p16]
20. ~kind(lucy) & ~strong(lucy) [input p19]
23. ~quiet(lucy) [input hypothesis]
25. ! [X0] : (~brave(X0) => creative(X0)) [pure predicate removal 15]
31. ! [X0] : ((~strong(X0) <~> creative(X0)) | (funny(X0) & quiet(X0))) [ennf transformation 6]
35. ! [X0] : (creative(X0) | brave(X0)) [ennf transformation 25]
46. ! [X0] : (((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | (funny(X0) & quiet(X0))) [nnf transformation 31]
59. ! [X0] : ((~tall(X0) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | tall(X0))) [nnf transformation 14]
60. ! [X0] : ((~tall(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | tall(X0))) [flattening 59]
61. (tall(lucy) | creative(lucy)) & (~tall(lucy) | ~creative(lucy)) [nnf transformation 17]
82. ~creative(X0) | strong(X0) | quiet(X0) [cnf transformation 46]
108. ~tall(X0) | ~brave(X0) [cnf transformation 60]
109. creative(X0) | brave(X0) [cnf transformation 35]
112. tall(lucy) | creative(lucy) [cnf transformation 61]
115. ~strong(lucy) [cnf transformation 20]
120. ~quiet(lucy) [cnf transformation 23]
198. 16 <=> creative(lucy) [avatar definition]
199. ~creative(lucy) <- (~16) [avatar component clause 198]
200. creative(lucy) <- (16) [avatar component clause 198]
202. 17 <=> tall(lucy) [avatar definition]
204. tall(lucy) <- (17) [avatar component clause 202]
205. 16 | 17 [avatar split clause 112,202,198]
239. strong(lucy) | quiet(lucy) <- (16) [resolution 82,200]
242. quiet(lucy) <- (16) [subsumption resolution 239,115]
243. $false <- (16) [subsumption resolution 242,120]
244. ~16 [avatar contradiction clause 243]
245. brave(lucy) <- (~16) [resolution 199,109]
246. ~brave(lucy) <- (17) [resolution 204,108]
248. $false <- (~16, 17) [subsumption resolution 246,245]
249. 16 | ~17 [avatar contradiction clause 248]
250. $false [avatar sat refutation 205,244,249]
% SZS output end Proof for 486193297716140831554016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is patient and vice versa.
Everyone who is not wise is both not kind and not patient and vice versa.
Everyone who is not kind or old is funny or old.
If someone is both old and not calm then susan is both calm and wise.
If alice is both curious and happy then mary is both not strong and happy.
Everyone who is happy is generous or kind and vice versa.
Everyone who is either patient or not tall is not patient or wise and vice versa.
Everyone who is happy is quiet.
If someone is either quiet or not rich then susan is not old.
Everyone who is both brave and funny is curious or generous and vice versa.
Everyone who is both strong and funny is either humble or wise.
Everyone who is either not curious or happy is either kind or not old.
Everyone who is either not old or calm is quiet.
Everyone who is either not patient or old is both not wise and generous.
If paul is not calm or not patient then paul is both not brave and not kind and vice versa.
If someone is either not kind or generous then someone is not kind and vice versa.
Someone is not patient or not old.
Someone is curious.
Someone is both brave and not kind.
Alice is either wise or quiet.
Fred is not creative.
John is not generous.
Someone is humble.
Fred is quiet or not wise. | Alice is wise. | neutral | (![X]:(~curious(X)<=>patient(X)))&
(![X]:(~wise(X)<=>(~kind(X)&~patient(X))))&
(![X]:((~kind(X)|old(X))=>(funny(X)|old(X))))&
((?[X]:((old(X)&~calm(X))))=>((calm(susan)&wise(susan))))&
(((curious(alice)&happy(alice)))=>((~strong(mary)&happy(mary))))&
(![X]:(happy(X)<=>(generous(X)|kind(X))))&
(![X]:((patient(X)<~>~tall(X))<=>(~patient(X)|wise(X))))&
(![X]:(happy(X)=>quiet(X)))&
((?[X]:((quiet(X)<~>~rich(X))))=>(~old(susan)))&
(![X]:((brave(X)&funny(X))<=>(curious(X)|generous(X))))&
(![X]:((strong(X)&funny(X))=>(humble(X)<~>wise(X))))&
(![X]:((~curious(X)<~>happy(X))=>(kind(X)<~>~old(X))))&
(![X]:((~old(X)<~>calm(X))=>quiet(X)))&
(![X]:((~patient(X)<~>old(X))=>(~wise(X)&generous(X))))&
(((~calm(paul)|~patient(paul)))<=>((~brave(paul)&~kind(paul))))&
((?[X]:((~kind(X)<~>generous(X))))<=>(?[X]:(~kind(X))))&
(?[X]:((~patient(X)|~old(X))))&
(?[X]:(curious(X)))&
(?[X]:((brave(X)&~kind(X))))&
((wise(alice)<~>quiet(alice)))&
(~creative(fred))&
(~generous(john))&
(?[X]:(humble(X)))&
((quiet(fred)|~wise(fred))) | wise(alice) | [] | null | 0 |
If alice is either calm or not quiet then john is generous and vice versa. Everyone who is either not strong or happy is not quiet and vice versa. If susan is both wise and rich then mary is kind or not patient and vice versa. Everyone who is quiet or not calm is either brave or quiet and vice versa. Everyone who is either not quiet or funny is brave or tall and vice versa. Everyone who is kind or not patient is either not quiet or happy. Everyone who is both not curious and brave is not creative or not curious. If fred is both strong and not kind then mary is not quiet or not funny. Everyone who is either curious or not patient is curious or not wise and vice versa. If fred is quiet then susan is either not happy or not tall and vice versa. Everyone who is curious or not old is both rich and not funny. Everyone who is either not old or creative is old or not wise. If paul is both brave and not generous then someone is either not funny or not humble. If susan is rich or creative then someone is not strong or not kind. Everyone who is not strong or brave is strong and vice versa. If someone is either not patient or not generous then someone is not patient. Paul is either not quiet or not curious. Someone is both not creative and not humble. Lucy is not kind. Susan is either not patient or curious. | Paul is kind. | contradiction | (((calm(alice)<~>~quiet(alice)))<=>(generous(john)))&
(![X]:((~strong(X)<~>happy(X))<=>~quiet(X)))&
(((wise(susan)&rich(susan)))<=>((kind(mary)|~patient(mary))))&
(![X]:((quiet(X)|~calm(X))<=>(brave(X)<~>quiet(X))))&
(![X]:((~quiet(X)<~>funny(X))<=>(brave(X)|tall(X))))&
(![X]:((kind(X)|~patient(X))=>(~quiet(X)<~>happy(X))))&
(![X]:((~curious(X)&brave(X))=>(~creative(X)|~curious(X))))&
(((strong(fred)&~kind(fred)))=>((~quiet(mary)|~funny(mary))))&
(![X]:((curious(X)<~>~patient(X))<=>(curious(X)|~wise(X))))&
((quiet(fred))<=>((~happy(susan)<~>~tall(susan))))&
(![X]:((curious(X)|~old(X))=>(rich(X)&~funny(X))))&
(![X]:((~old(X)<~>creative(X))=>(old(X)|~wise(X))))&
(((brave(paul)&~generous(paul)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((rich(susan)|creative(susan)))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((~strong(X)|brave(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(~patient(X))))&
((~quiet(paul)<~>~curious(paul)))&
(?[X]:((~creative(X)&~humble(X))))&
(~kind(lucy))&
((~patient(susan)<~>curious(susan))) | kind(paul) | [
"p1",
"p3",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1533420268452174155959737
% SZS output start Proof for 1533420268452174155959737
2. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> ~quiet(X0)) [input p1]
4. ! [X0] : ((~calm(X0) | quiet(X0)) <=> (brave(X0) <~> quiet(X0))) [input p3]
6. ! [X0] : ((~patient(X0) | kind(X0)) => (~quiet(X0) <~> happy(X0))) [input p5]
15. ! [X0] : ((brave(X0) | ~strong(X0)) <=> strong(X0)) [input p14]
21. kind(paul) [input hypothesis]
23. ! [X0] : ((~quiet(X0) <~> happy(X0)) | (patient(X0) & ~kind(X0))) [ennf transformation 6]
36. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | quiet(X0)) & (~quiet(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 2]
39. ! [X0] : (((~calm(X0) | quiet(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (calm(X0) & ~quiet(X0)))) [nnf transformation 4]
40. ! [X0] : ((~calm(X0) | quiet(X0) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (calm(X0) & ~quiet(X0)))) [flattening 39]
43. ! [X0] : (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (patient(X0) & ~kind(X0))) [nnf transformation 23]
53. ! [X0] : (((brave(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (~brave(X0) & strong(X0)))) [nnf transformation 15]
54. ! [X0] : ((brave(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (~brave(X0) & strong(X0)))) [flattening 53]
69. ~strong(X0) | happy(X0) | quiet(X0) [cnf transformation 36]
78. ~quiet(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 40]
90. ~kind(X0) | quiet(X0) | ~happy(X0) [cnf transformation 43]
114. strong(X0) | strong(X0) [cnf transformation 54]
116. brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 54]
126. kind(paul) [cnf transformation 21]
127. strong(X0) [duplicate literal removal 114]
128. ~strong(X0) | brave(X0) [duplicate literal removal 116]
132. ~brave(X0) | ~quiet(X0) [duplicate literal removal 78]
272. brave(X0) [resolution 128,127]
276. ~quiet(X0) [resolution 132,272]
282. happy(X0) | quiet(X0) [resolution 69,127]
283. happy(X0) [subsumption resolution 282,276]
297. quiet(paul) | ~happy(paul) [resolution 90,126]
298. ~happy(paul) [subsumption resolution 297,276]
299. $false [subsumption resolution 298,283]
% SZS output end Proof for 1533420268452174155959737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not wise is creative.
If lucy is not generous or tall then paul is humble or not humble and vice versa.
Everyone who is either not brave or not tall is not brave or not tall.
Everyone who is either not kind or calm is both curious and not humble and vice versa.
If someone is both not humble and not tall then someone is both not brave and not creative and vice versa.
If someone is both tall and patient then alice is humble.
If fred is not happy or not kind then someone is either not rich or funny and vice versa.
Everyone who is either kind or funny is not wise and vice versa.
Everyone who is both not old and quiet is both not quiet and patient and vice versa.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Everyone who is quiet or old is patient and vice versa.
Alice is either wise or curious.
Someone is not creative or not strong.
Susan is both not tall and not generous.
Alice is either not funny or strong.
Someone is both not kind and not humble.
Someone is either tall or quiet.
Someone is not humble. | Lucy is creative. | contradiction | (![X]:((~brave(X)<~>~wise(X))=>creative(X)))&
(((~generous(lucy)|tall(lucy)))<=>((humble(paul)|~humble(paul))))&
(![X]:((~brave(X)<~>~tall(X))=>(~brave(X)|~tall(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(curious(X)&~humble(X))))&
((?[X]:((~humble(X)&~tall(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
((?[X]:((tall(X)&patient(X))))=>(humble(alice)))&
(((~happy(fred)|~kind(fred)))<=>(?[X]:((~rich(X)<~>funny(X)))))&
(![X]:((kind(X)<~>funny(X))<=>~wise(X)))&
(![X]:((~old(X)&quiet(X))<=>(~quiet(X)&patient(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((quiet(X)|old(X))<=>patient(X)))&
((wise(alice)<~>curious(alice)))&
(?[X]:((~creative(X)|~strong(X))))&
((~tall(susan)&~generous(susan)))&
((~funny(alice)<~>strong(alice)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
(?[X]:(~humble(X))) | creative(lucy) | [
"p8",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4718840549961883173550786
% SZS output start Proof for 4718840549961883173550786
9. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (patient(X0) & ~quiet(X0))) [input p8]
10. ! [X0] : (quiet(X0) <=> creative(X0)) [input p9]
12. ! [X0] : (~patient(X0) => ~quiet(X0)) [input p11]
15. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X0] : (~patient(X0) <~> ~old(X0)) [input p14]
16. ! [X0] : ((old(X0) | quiet(X0)) <=> patient(X0)) [input p15]
24. creative(lucy) [input hypothesis]
26. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X1] : (~patient(X1) <~> ~old(X1)) [rectify 15]
32. ! [X0] : (~quiet(X0) | patient(X0)) [ennf transformation 12]
51. ! [X0] : (((quiet(X0) & ~old(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 9]
52. ! [X0] : (((quiet(X0) & ~old(X0)) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | ~quiet(X0) | old(X0))) [flattening 51]
53. ! [X0] : ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))) [nnf transformation 10]
56. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X1] : ((old(X1) | patient(X1)) & (~old(X1) | ~patient(X1))) | ! [X0] : (~brave(X0) & ~patient(X0))) [nnf transformation 26]
57. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) | ! [X3] : (~brave(X3) & ~patient(X3))) [rectify 56]
58. ? [X0] : (brave(X0) | patient(X0)) => (brave(sK3) | patient(sK3)) [choice axiom]
59. ? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) => ((old(sK4) | patient(sK4)) & (~old(sK4) | ~patient(sK4))) [choice axiom]
60. ((brave(sK3) | patient(sK3)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (((old(sK4) | patient(sK4)) & (~old(sK4) | ~patient(sK4))) | ! [X3] : (~brave(X3) & ~patient(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((old(X0) | quiet(X0)) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [nnf transformation 16]
62. ! [X0] : ((old(X0) | quiet(X0) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [flattening 61]
103. ~quiet(X0) | ~quiet(X0) | old(X0) [cnf transformation 52]
106. quiet(X0) | ~patient(X0) | quiet(X0) [cnf transformation 52]
108. ~creative(X0) | quiet(X0) [cnf transformation 53]
111. ~quiet(X0) | patient(X0) [cnf transformation 32]
120. ~old(sK4) | ~patient(sK4) | ~patient(X3) [cnf transformation 60]
122. old(sK4) | patient(sK4) | ~patient(X3) [cnf transformation 60]
127. patient(X0) | ~old(X0) [cnf transformation 62]
141. creative(lucy) [cnf transformation 24]
142. ~quiet(X0) | old(X0) [duplicate literal removal 103]
143. ~patient(X0) | quiet(X0) [duplicate literal removal 106]
248. 24 <=> ! [X1] : (~old(X1) | patient(X1)) [avatar definition]
249. ~old(X1) | patient(X1) <- (24) [avatar component clause 248]
255. 26 <=> patient(sK4) [avatar definition]
256. ~patient(sK4) <- (~26) [avatar component clause 255]
257. patient(sK4) <- (26) [avatar component clause 255]
259. 27 <=> old(sK4) [avatar definition]
260. ~old(sK4) <- (~27) [avatar component clause 259]
261. old(sK4) <- (27) [avatar component clause 259]
264. 28 <=> ! [X3] : ~patient(X3) [avatar definition]
265. ~patient(X3) <- (28) [avatar component clause 264]
266. 28 | 26 | 27 [avatar split clause 122,259,255,264]
268. 28 | ~26 | ~27 [avatar split clause 120,259,255,264]
269. 24 [avatar split clause 127,248]
309. quiet(lucy) [resolution 108,141]
312. patient(lucy) [resolution 111,309]
317. quiet(sK4) <- (26) [resolution 143,257]
319. old(sK4) <- (26) [resolution 317,142]
322. $false <- (26, ~27) [subsumption resolution 319,260]
323. ~26 | 27 [avatar contradiction clause 322]
330. patient(sK4) <- (24, 27) [resolution 249,261]
331. $false <- (24, ~26, 27) [subsumption resolution 330,256]
332. ~24 | 26 | ~27 [avatar contradiction clause 331]
333. $false <- (28) [resolution 265,312]
336. ~28 [avatar contradiction clause 333]
337. $false [avatar sat refutation 266,268,269,323,332,336]
% SZS output end Proof for 4718840549961883173550786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not brave and not curious then someone is not quiet.
Everyone who is not brave or not strong is either tall or strong and vice versa.
If mary is both quiet and kind then alice is both not old and happy.
If someone is not rich or not generous then alice is not happy.
If someone is either not tall or humble then mary is calm and vice versa.
Everyone who is generous or not brave is either not old or not generous.
Everyone who is not old is either quiet or not happy and vice versa.
If someone is either funny or not humble then someone is either not tall or old.
If someone is both tall and humble then lucy is not happy or not calm and vice versa.
If susan is both not kind and humble then someone is both not old and not patient and vice versa.
If someone is either not calm or old then alice is both not rich and not patient and vice versa.
If fred is humble then someone is not strong or old and vice versa.
If mary is both creative and not curious then someone is either not rich or not brave.
Everyone who is not patient or not quiet is quiet or calm and vice versa.
If someone is rich or not kind then someone is old.
Everyone who is wise is not humble and vice versa.
Paul is both curious and not wise.
John is both creative and tall.
Someone is both not generous and not creative.
Someone is not creative.
Susan is both not curious and strong.
Someone is not curious.
Someone is both funny and not humble.
Paul is both calm and quiet. | Paul is not patient. | entailment | (((~brave(susan)&~curious(susan)))=>(?[X]:(~quiet(X))))&
(![X]:((~brave(X)|~strong(X))<=>(tall(X)<~>strong(X))))&
(((quiet(mary)&kind(mary)))=>((~old(alice)&happy(alice))))&
((?[X]:((~rich(X)|~generous(X))))=>(~happy(alice)))&
((?[X]:((~tall(X)<~>humble(X))))<=>(calm(mary)))&
(![X]:((generous(X)|~brave(X))=>(~old(X)<~>~generous(X))))&
(![X]:(~old(X)<=>(quiet(X)<~>~happy(X))))&
((?[X]:((funny(X)<~>~humble(X))))=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:((tall(X)&humble(X))))<=>((~happy(lucy)|~calm(lucy))))&
(((~kind(susan)&humble(susan)))<=>(?[X]:((~old(X)&~patient(X)))))&
((?[X]:((~calm(X)<~>old(X))))<=>((~rich(alice)&~patient(alice))))&
((humble(fred))<=>(?[X]:((~strong(X)|old(X)))))&
(((creative(mary)&~curious(mary)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(quiet(X)|calm(X))))&
((?[X]:((rich(X)|~kind(X))))=>(?[X]:(old(X))))&
(![X]:(wise(X)<=>~humble(X)))&
((curious(paul)&~wise(paul)))&
((creative(john)&tall(john)))&
(?[X]:((~generous(X)&~creative(X))))&
(?[X]:(~creative(X)))&
((~curious(susan)&strong(susan)))&
(?[X]:(~curious(X)))&
(?[X]:((funny(X)&~humble(X))))&
((calm(paul)&quiet(paul))) | ~patient(paul) | [
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7203850275027746035172081
% SZS output start Proof for 7203850275027746035172081
14. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> (calm(X0) | quiet(X0))) [input p13]
24. quiet(paul) & calm(paul) [input p23]
25. patient(paul) [input hypothesis]
76. ! [X0] : (((~quiet(X0) | ~patient(X0)) | (~calm(X0) & ~quiet(X0))) & ((calm(X0) | quiet(X0)) | (quiet(X0) & patient(X0)))) [nnf transformation 14]
77. ! [X0] : ((~quiet(X0) | ~patient(X0) | (~calm(X0) & ~quiet(X0))) & (calm(X0) | quiet(X0) | (quiet(X0) & patient(X0)))) [flattening 76]
138. ~quiet(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 77]
156. quiet(paul) [cnf transformation 24]
157. patient(paul) [cnf transformation 25]
159. ~patient(X0) | ~quiet(X0) [duplicate literal removal 138]
368. ~quiet(paul) [resolution 159,157]
369. $false [subsumption resolution 368,156]
% SZS output end Proof for 7203850275027746035172081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and generous is patient or not curious.
Everyone who is either not rich or not happy is quiet or not kind and vice versa.
Everyone who is not creative is either not old or not kind.
If someone is not funny then someone is curious or funny.
If someone is not curious or not patient then someone is either not creative or quiet.
If john is wise then paul is both not rich and funny.
If alice is not old then lucy is both not creative and kind and vice versa.
If someone is humble then susan is either rich or not wise.
Everyone who is both funny and strong is rich or not strong and vice versa.
Everyone who is either not strong or calm is either calm or not quiet.
If someone is not calm then someone is both not old and not rich.
Everyone who is not wise is brave or not humble.
Everyone who is rich or happy is both wise and not calm and vice versa.
If someone is either wise or humble then someone is either not old or not happy and vice versa.
Everyone who is either not strong or not happy is not tall and vice versa.
Someone is either old or not happy.
Someone is either funny or kind.
John is humble.
Alice is either rich or not happy.
Someone is either kind or not generous.
Lucy is rich or not patient. | John is wise. | contradiction | (![X]:((old(X)&generous(X))=>(patient(X)|~curious(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(quiet(X)|~kind(X))))&
(![X]:(~creative(X)=>(~old(X)<~>~kind(X))))&
((?[X]:(~funny(X)))=>(?[X]:((curious(X)|funny(X)))))&
((?[X]:((~curious(X)|~patient(X))))=>(?[X]:((~creative(X)<~>quiet(X)))))&
((wise(john))=>((~rich(paul)&funny(paul))))&
((~old(alice))<=>((~creative(lucy)&kind(lucy))))&
((?[X]:(humble(X)))=>((rich(susan)<~>~wise(susan))))&
(![X]:((funny(X)&strong(X))<=>(rich(X)|~strong(X))))&
(![X]:((~strong(X)<~>calm(X))=>(calm(X)<~>~quiet(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:(~wise(X)=>(brave(X)|~humble(X))))&
(![X]:((rich(X)|happy(X))<=>(wise(X)&~calm(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(?[X]:((~old(X)<~>~happy(X)))))&
(![X]:((~strong(X)<~>~happy(X))<=>~tall(X)))&
(?[X]:((old(X)<~>~happy(X))))&
(?[X]:((funny(X)<~>kind(X))))&
(humble(john))&
((rich(alice)<~>~happy(alice)))&
(?[X]:((kind(X)<~>~generous(X))))&
((rich(lucy)|~patient(lucy))) | wise(john) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5825444290585551838900239
% SZS output start Proof for 5825444290585551838900239
6. wise(john) => (funny(paul) & ~rich(paul)) [input p5]
9. ! [X0] : ((strong(X0) & funny(X0)) <=> (~strong(X0) | rich(X0))) [input p8]
22. wise(john) [input hypothesis]
33. (funny(paul) & ~rich(paul)) | ~wise(john) [ennf transformation 6]
50. ! [X0] : (((strong(X0) & funny(X0)) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | (~strong(X0) | ~funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((strong(X0) & funny(X0)) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | ~strong(X0) | ~funny(X0))) [flattening 50]
87. ~rich(paul) | ~wise(john) [cnf transformation 33]
88. funny(paul) | ~wise(john) [cnf transformation 33]
94. ~strong(X0) | rich(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 51]
98. strong(X0) | strong(X0) [cnf transformation 51]
128. wise(john) [cnf transformation 22]
131. ~strong(X0) | rich(X0) | ~funny(X0) [duplicate literal removal 94]
132. strong(X0) [duplicate literal removal 98]
164. 8 <=> wise(john) [avatar definition]
168. 9 <=> funny(paul) [avatar definition]
170. funny(paul) <- (9) [avatar component clause 168]
171. ~8 | 9 [avatar split clause 88,168,164]
173. 10 <=> rich(paul) [avatar definition]
175. ~rich(paul) <- (~10) [avatar component clause 173]
176. ~8 | ~10 [avatar split clause 87,173,164]
205. ~funny(X0) | rich(X0) [subsumption resolution 131,132]
305. 8 [avatar split clause 128,164]
306. rich(paul) <- (9) [resolution 205,170]
308. $false <- (9, ~10) [subsumption resolution 306,175]
309. ~9 | 10 [avatar contradiction clause 308]
310. $false [avatar sat refutation 171,176,305,309]
% SZS output end Proof for 5825444290585551838900239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is not strong or wise.
If someone is not tall or quiet then fred is both rich and not brave and vice versa.
Everyone who is either tall or generous is wise and vice versa.
Everyone who is strong is generous and vice versa.
If someone is calm then alice is not creative or rich.
If lucy is not wise then paul is both quiet and curious and vice versa.
Everyone who is creative is curious or tall.
Everyone who is both not calm and tall is patient or not old.
Everyone who is humble or not creative is brave or curious and vice versa.
If fred is not tall or not happy then someone is both not brave and not generous and vice versa.
Everyone who is generous is strong or not wise.
Everyone who is not curious is either not creative or rich.
If someone is not kind then fred is either not rich or not calm.
If fred is both not kind and curious then someone is not creative or quiet.
Everyone who is not creative is wise.
If lucy is both rich and patient then lucy is strong or tall and vice versa.
Alice is not curious.
Someone is both not tall and happy.
Susan is kind or tall.
John is not strong.
Mary is not wise.
Paul is not calm or not patient.
Someone is happy or not kind.
John is either not kind or not generous. | Paul is calm. | neutral | ((kind(alice))=>(?[X]:((~strong(X)|wise(X)))))&
((?[X]:((~tall(X)|quiet(X))))<=>((rich(fred)&~brave(fred))))&
(![X]:((tall(X)<~>generous(X))<=>wise(X)))&
(![X]:(strong(X)<=>generous(X)))&
((?[X]:(calm(X)))=>((~creative(alice)|rich(alice))))&
((~wise(lucy))<=>((quiet(paul)&curious(paul))))&
(![X]:(creative(X)=>(curious(X)|tall(X))))&
(![X]:((~calm(X)&tall(X))=>(patient(X)|~old(X))))&
(![X]:((humble(X)|~creative(X))<=>(brave(X)|curious(X))))&
(((~tall(fred)|~happy(fred)))<=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:(generous(X)=>(strong(X)|~wise(X))))&
(![X]:(~curious(X)=>(~creative(X)<~>rich(X))))&
((?[X]:(~kind(X)))=>((~rich(fred)<~>~calm(fred))))&
(((~kind(fred)&curious(fred)))=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:(~creative(X)=>wise(X)))&
(((rich(lucy)&patient(lucy)))<=>((strong(lucy)|tall(lucy))))&
(~curious(alice))&
(?[X]:((~tall(X)&happy(X))))&
((kind(susan)|tall(susan)))&
(~strong(john))&
(~wise(mary))&
((~calm(paul)|~patient(paul)))&
(?[X]:((happy(X)|~kind(X))))&
((~kind(john)<~>~generous(john))) | calm(paul) | [] | null | 0 |
Everyone who is both funny and not funny is not humble or not calm and vice versa. If someone is not strong then fred is either not tall or not happy and vice versa. Everyone who is either not funny or old is both not calm and not strong and vice versa. If paul is either not quiet or not calm then john is curious or generous and vice versa. Everyone who is not old is both wise and humble. Everyone who is not strong is either not old or not humble and vice versa. Everyone who is not patient or not humble is either funny or old and vice versa. If alice is either rich or brave then someone is both tall and rich. Everyone who is not curious is not wise and vice versa. If someone is either funny or not brave then someone is either not creative or creative. If lucy is either not creative or old then someone is either not generous or not humble. Everyone who is strong or not wise is either not rich or rich and vice versa. If fred is either happy or not generous then someone is both quiet and not wise. If susan is funny or generous then paul is not happy or not wise. If someone is both patient and not wise then john is either not patient or not brave and vice versa. Someone is not humble or quiet. Fred is both not generous and brave. Fred is happy or generous. Susan is quiet. Lucy is not generous. Someone is either not curious or wise. | Lucy is not funny. | entailment | (![X]:((funny(X)&~funny(X))<=>(~humble(X)|~calm(X))))&
((?[X]:(~strong(X)))<=>((~tall(fred)<~>~happy(fred))))&
(![X]:((~funny(X)<~>old(X))<=>(~calm(X)&~strong(X))))&
(((~quiet(paul)<~>~calm(paul)))<=>((curious(john)|generous(john))))&
(![X]:(~old(X)=>(wise(X)&humble(X))))&
(![X]:(~strong(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~patient(X)|~humble(X))<=>(funny(X)<~>old(X))))&
(((rich(alice)<~>brave(alice)))=>(?[X]:((tall(X)&rich(X)))))&
(![X]:(~curious(X)<=>~wise(X)))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((~creative(X)<~>creative(X)))))&
(((~creative(lucy)<~>old(lucy)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((strong(X)|~wise(X))<=>(~rich(X)<~>rich(X))))&
(((happy(fred)<~>~generous(fred)))=>(?[X]:((quiet(X)&~wise(X)))))&
(((funny(susan)|generous(susan)))=>((~happy(paul)|~wise(paul))))&
((?[X]:((patient(X)&~wise(X))))<=>((~patient(john)<~>~brave(john))))&
(?[X]:((~humble(X)|quiet(X))))&
((~generous(fred)&brave(fred)))&
((happy(fred)|generous(fred)))&
(quiet(susan))&
(~generous(lucy))&
(?[X]:((~curious(X)<~>wise(X)))) | ~funny(lucy) | [
"p0",
"p2",
"p4",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2919016139229183605854186
% SZS output start Proof for 2919016139229183605854186
1. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~calm(X0) | ~humble(X0))) [input p0]
3. ! [X0] : ((~funny(X0) <~> old(X0)) <=> (~strong(X0) & ~calm(X0))) [input p2]
5. ! [X0] : (~old(X0) => (humble(X0) & wise(X0))) [input p4]
6. ! [X0] : (~strong(X0) <=> (~old(X0) <~> ~humble(X0))) [input p5]
12. ! [X0] : ((~wise(X0) | strong(X0)) <=> (~rich(X0) <~> rich(X0))) [input p11]
22. funny(lucy) [input hypothesis]
24. ! [X0] : ((humble(X0) & wise(X0)) | old(X0)) [ennf transformation 5]
31. ! [X0] : (((~funny(X0) & funny(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (funny(X0) | ~funny(X0)))) [nnf transformation 1]
32. ! [X0] : (((~funny(X0) & funny(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | funny(X0) | ~funny(X0))) [flattening 31]
37. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (strong(X0) | calm(X0))) & ((~strong(X0) & ~calm(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | strong(X0) | calm(X0)) & ((~strong(X0) & ~calm(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [flattening 37]
41. ! [X0] : ((~strong(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0)))) & (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | strong(X0))) [nnf transformation 6]
55. ! [X0] : (((~wise(X0) | strong(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (wise(X0) & ~strong(X0)))) [nnf transformation 12]
56. ! [X0] : ((~wise(X0) | strong(X0) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) & (((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (wise(X0) & ~strong(X0)))) [flattening 55]
70. funny(X0) | humble(X0) [cnf transformation 32]
71. funny(X0) | calm(X0) [cnf transformation 32]
72. ~funny(X0) | humble(X0) [cnf transformation 32]
73. ~funny(X0) | calm(X0) [cnf transformation 32]
79. ~calm(X0) | ~funny(X0) | ~old(X0) [cnf transformation 38]
90. wise(X0) | old(X0) [cnf transformation 24]
94. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 41]
120. ~wise(X0) | strong(X0) | rich(X0) | rich(X0) [cnf transformation 56]
121. ~wise(X0) | strong(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 56]
142. funny(lucy) [cnf transformation 22]
143. ~wise(X0) | strong(X0) | rich(X0) [duplicate literal removal 120]
144. ~wise(X0) | strong(X0) | ~rich(X0) [duplicate literal removal 121]
145. calm(X0) [subsumption resolution 71,73]
146. humble(X0) [subsumption resolution 70,72]
166. ~old(X0) | ~funny(X0) [subsumption resolution 79,145]
186. ~strong(X0) | old(X0) [subsumption resolution 94,146]
229. ~wise(X0) | strong(X0) [subsumption resolution 143,144]
289. strong(X0) | old(X0) [resolution 229,90]
290. old(X0) [subsumption resolution 289,186]
293. ~funny(X1) [resolution 290,166]
302. $false [resolution 293,142]
% SZS output end Proof for 2919016139229183605854186
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not rich is both quiet and not humble. If someone is both not calm and humble then lucy is not calm or generous and vice versa. Everyone who is patient or tall is happy or not old and vice versa. Everyone who is either not quiet or old is either curious or not kind. If john is not humble or not wise then someone is either not brave or not kind. Everyone who is kind or not generous is either curious or not tall and vice versa. If paul is both brave and humble then someone is funny or strong. If someone is both curious and wise then someone is not kind and vice versa. Everyone who is patient is quiet or strong and vice versa. Everyone who is not patient is both not rich and creative. If someone is either generous or strong then someone is both not quiet and not generous and vice versa. If susan is funny then susan is calm. If someone is not tall or generous then someone is not humble or kind and vice versa. If someone is both not patient and not funny then someone is both rich and curious. Everyone who is either kind or not strong is not patient. Everyone who is strong is happy. John is calm or not tall. Someone is both not creative and quiet. John is both not tall and humble. Mary is happy. Paul is both generous and not happy. Lucy is both not quiet and rich. Fred is not old or not brave. Someone is either not generous or not funny. | Paul is humble. | neutral | (![X]:((humble(X)&~rich(X))=>(quiet(X)&~humble(X))))&
((?[X]:((~calm(X)&humble(X))))<=>((~calm(lucy)|generous(lucy))))&
(![X]:((patient(X)|tall(X))<=>(happy(X)|~old(X))))&
(![X]:((~quiet(X)<~>old(X))=>(curious(X)<~>~kind(X))))&
(((~humble(john)|~wise(john)))=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:((kind(X)|~generous(X))<=>(curious(X)<~>~tall(X))))&
(((brave(paul)&humble(paul)))=>(?[X]:((funny(X)|strong(X)))))&
((?[X]:((curious(X)&wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:(patient(X)<=>(quiet(X)|strong(X))))&
(![X]:(~patient(X)=>(~rich(X)&creative(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((funny(susan))=>(calm(susan)))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((~humble(X)|kind(X)))))&
((?[X]:((~patient(X)&~funny(X))))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((kind(X)<~>~strong(X))=>~patient(X)))&
(![X]:(strong(X)=>happy(X)))&
((calm(john)|~tall(john)))&
(?[X]:((~creative(X)&quiet(X))))&
((~tall(john)&humble(john)))&
(happy(mary))&
((generous(paul)&~happy(paul)))&
((~quiet(lucy)&rich(lucy)))&
((~old(fred)|~brave(fred)))&
(?[X]:((~generous(X)<~>~funny(X)))) | humble(paul) | [] | null | 0 |
Everyone who is not brave or not calm is not kind and vice versa.
Everyone who is either funny or not quiet is happy or not wise and vice versa.
Everyone who is old or brave is both tall and not humble and vice versa.
Everyone who is either not happy or happy is both not curious and quiet.
Everyone who is not calm is both curious and not strong and vice versa.
Everyone who is not kind or not brave is either creative or not wise and vice versa.
Everyone who is both calm and wise is not old or not generous and vice versa.
Everyone who is old is not humble.
Everyone who is not funny or not brave is either not rich or brave.
Everyone who is calm or not curious is not kind and vice versa.
Everyone who is not funny or not quiet is quiet or not funny.
Everyone who is not brave is either rich or not generous and vice versa.
Everyone who is both calm and not creative is wise.
Everyone who is not tall or rich is tall or creative and vice versa.
If mary is both not humble and not happy then paul is both happy and not generous.
Someone is either patient or calm.
Someone is not brave or not funny.
Lucy is humble or calm.
Fred is either humble or brave.
Paul is not happy or not curious. | Paul is tall. | contradiction | (![X]:((~brave(X)|~calm(X))<=>~kind(X)))&
(![X]:((funny(X)<~>~quiet(X))<=>(happy(X)|~wise(X))))&
(![X]:((old(X)|brave(X))<=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)<~>happy(X))=>(~curious(X)&quiet(X))))&
(![X]:(~calm(X)<=>(curious(X)&~strong(X))))&
(![X]:((~kind(X)|~brave(X))<=>(creative(X)<~>~wise(X))))&
(![X]:((calm(X)&wise(X))<=>(~old(X)|~generous(X))))&
(![X]:(old(X)=>~humble(X)))&
(![X]:((~funny(X)|~brave(X))=>(~rich(X)<~>brave(X))))&
(![X]:((calm(X)|~curious(X))<=>~kind(X)))&
(![X]:((~funny(X)|~quiet(X))=>(quiet(X)|~funny(X))))&
(![X]:(~brave(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((calm(X)&~creative(X))=>wise(X)))&
(![X]:((~tall(X)|rich(X))<=>(tall(X)|creative(X))))&
(((~humble(mary)&~happy(mary)))=>((happy(paul)&~generous(paul))))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:((~brave(X)|~funny(X))))&
((humble(lucy)|calm(lucy)))&
((humble(fred)<~>brave(fred)))&
((~happy(paul)|~curious(paul))) | tall(paul) | [
"p0",
"p3",
"p4",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2736913085009285091984667
% SZS output start Proof for 2736913085009285091984667
1. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> ~kind(X0)) [input p0]
4. ! [X0] : ((~happy(X0) <~> happy(X0)) => (quiet(X0) & ~curious(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (~strong(X0) & curious(X0))) [input p4]
9. ! [X0] : ((~brave(X0) | ~funny(X0)) => (~rich(X0) <~> brave(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | calm(X0)) <=> ~kind(X0)) [input p9]
14. ! [X0] : ((rich(X0) | ~tall(X0)) <=> (creative(X0) | tall(X0))) [input p13]
21. tall(paul) [input hypothesis]
22. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~happy(X0) <=> happy(X0))) [ennf transformation 4]
24. ! [X0] : ((~rich(X0) <~> brave(X0)) | (brave(X0) & funny(X0))) [ennf transformation 9]
31. ! [X0] : (((~calm(X0) | ~brave(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [nnf transformation 1]
32. ! [X0] : ((~calm(X0) | ~brave(X0) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [flattening 31]
37. ! [X0] : ((quiet(X0) & ~curious(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 22]
38. ! [X0] : ((~calm(X0) | (strong(X0) | ~curious(X0))) & ((~strong(X0) & curious(X0)) | calm(X0))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | strong(X0) | ~curious(X0)) & ((~strong(X0) & curious(X0)) | calm(X0))) [flattening 38]
44. ! [X0] : (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (brave(X0) & funny(X0))) [nnf transformation 24]
45. ! [X0] : (((~curious(X0) | calm(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [nnf transformation 10]
46. ! [X0] : ((~curious(X0) | calm(X0) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [flattening 45]
48. ! [X0] : (((rich(X0) | ~tall(X0)) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | (~rich(X0) & tall(X0)))) [nnf transformation 14]
49. ! [X0] : ((rich(X0) | ~tall(X0) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | (~rich(X0) & tall(X0)))) [flattening 48]
58. ~calm(X0) | ~brave(X0) | kind(X0) [cnf transformation 32]
70. ~curious(X0) | happy(X0) | happy(X0) [cnf transformation 37]
71. ~curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 37]
74. curious(X0) | calm(X0) [cnf transformation 39]
90. brave(X0) | ~rich(X0) | brave(X0) [cnf transformation 44]
94. ~kind(X0) | curious(X0) [cnf transformation 46]
105. rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 49]
116. tall(paul) [cnf transformation 21]
118. ~tall(X0) | rich(X0) [duplicate literal removal 105]
120. ~rich(X0) | brave(X0) [duplicate literal removal 90]
121. ~curious(X0) | happy(X0) [duplicate literal removal 70]
122. ~curious(X0) | ~happy(X0) [duplicate literal removal 71]
126. ~curious(X0) [subsumption resolution 121,122]
127. calm(X0) [subsumption resolution 74,126]
131. ~kind(X0) [subsumption resolution 94,126]
177. rich(paul) [resolution 118,116]
178. brave(paul) [resolution 177,120]
185. ~brave(X0) | kind(X0) [resolution 58,127]
186. ~brave(X0) [subsumption resolution 185,131]
187. $false [resolution 186,178]
% SZS output end Proof for 2736913085009285091984667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or quiet is both wise and not brave. Everyone who is not happy or patient is not curious or not generous and vice versa. Everyone who is not patient or curious is not creative and vice versa. Everyone who is patient or not calm is tall. If susan is not kind or not patient then someone is either not quiet or happy and vice versa. If paul is not quiet then someone is not brave or not generous. If someone is either not strong or not rich then someone is either tall or not curious. Everyone who is not happy is either not kind or funny and vice versa. If john is both patient and not quiet then someone is both not brave and quiet and vice versa. If lucy is happy then alice is not calm or rich. Everyone who is not happy or not curious is both tall and brave. If someone is not happy then someone is both not brave and wise and vice versa. Everyone who is not patient is both not strong and creative and vice versa. Everyone who is both quiet and not calm is not happy or happy and vice versa. Everyone who is either curious or strong is not quiet or not brave and vice versa. Someone is wise. Someone is both patient and happy. Someone is both not old and quiet. Fred is not calm or not humble. Paul is both strong and rich. Lucy is either not calm or not rich. | Fred is not quiet. | contradiction | (![X]:((curious(X)<~>quiet(X))=>(wise(X)&~brave(X))))&
(![X]:((~happy(X)|patient(X))<=>(~curious(X)|~generous(X))))&
(![X]:((~patient(X)|curious(X))<=>~creative(X)))&
(![X]:((patient(X)|~calm(X))=>tall(X)))&
(((~kind(susan)|~patient(susan)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
((~quiet(paul))=>(?[X]:((~brave(X)|~generous(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>funny(X))))&
(((patient(john)&~quiet(john)))<=>(?[X]:((~brave(X)&quiet(X)))))&
((happy(lucy))=>((~calm(alice)|rich(alice))))&
(![X]:((~happy(X)|~curious(X))=>(tall(X)&brave(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:(~patient(X)<=>(~strong(X)&creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(~happy(X)|happy(X))))&
(![X]:((curious(X)<~>strong(X))<=>(~quiet(X)|~brave(X))))&
(?[X]:(wise(X)))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:((~old(X)&quiet(X))))&
((~calm(fred)|~humble(fred)))&
((strong(paul)&rich(paul)))&
((~calm(lucy)<~>~rich(lucy))) | ~quiet(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7109753277974846747692496
% SZS output start Proof for 7109753277974846747692496
14. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (happy(X0) | ~happy(X0))) [input p13]
22. ~quiet(fred) [input hypothesis]
63. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 14]
64. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | calm(X0) | ~quiet(X0))) [flattening 63]
118. quiet(X0) | happy(X0) [cnf transformation 64]
119. quiet(X0) | ~happy(X0) [cnf transformation 64]
136. ~quiet(fred) [cnf transformation 22]
256. quiet(X0) [subsumption resolution 118,119]
260. $false [subsumption resolution 136,256]
% SZS output end Proof for 7109753277974846747692496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not humble is both not brave and generous and vice versa. If mary is both brave and generous then paul is not patient and vice versa. Everyone who is generous or not generous is kind or old. If john is curious or not creative then someone is both not generous and rich and vice versa. Everyone who is not rich or not curious is patient and vice versa. Everyone who is both not calm and not funny is not calm or patient and vice versa. If someone is both tall and funny then someone is either quiet or rich. If someone is either strong or calm then someone is not wise or tall. If someone is both strong and not generous then someone is both humble and not curious. Everyone who is both not tall and not humble is both not curious and strong and vice versa. Everyone who is quiet or patient is happy and vice versa. Everyone who is either not strong or not kind is not quiet and vice versa. If lucy is both wise and rich then someone is either not rich or not creative. If someone is both not rich and creative then someone is not kind or creative and vice versa. Everyone who is not calm or funny is either not curious or happy and vice versa. Everyone who is not quiet is both not patient and not curious. Susan is not curious or creative. Someone is not strong or not happy. Someone is not generous. Someone is brave or rich. Paul is happy. Someone is both not humble and rich. | Susan is happy. | entailment | (![X]:((kind(X)<~>~humble(X))<=>(~brave(X)&generous(X))))&
(((brave(mary)&generous(mary)))<=>(~patient(paul)))&
(![X]:((generous(X)|~generous(X))=>(kind(X)|old(X))))&
(((curious(john)|~creative(john)))<=>(?[X]:((~generous(X)&rich(X)))))&
(![X]:((~rich(X)|~curious(X))<=>patient(X)))&
(![X]:((~calm(X)&~funny(X))<=>(~calm(X)|patient(X))))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:((quiet(X)<~>rich(X)))))&
((?[X]:((strong(X)<~>calm(X))))=>(?[X]:((~wise(X)|tall(X)))))&
((?[X]:((strong(X)&~generous(X))))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~tall(X)&~humble(X))<=>(~curious(X)&strong(X))))&
(![X]:((quiet(X)|patient(X))<=>happy(X)))&
(![X]:((~strong(X)<~>~kind(X))<=>~quiet(X)))&
(((wise(lucy)&rich(lucy)))=>(?[X]:((~rich(X)<~>~creative(X)))))&
((?[X]:((~rich(X)&creative(X))))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~calm(X)|funny(X))<=>(~curious(X)<~>happy(X))))&
(![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
((~curious(susan)|creative(susan)))&
(?[X]:((~strong(X)|~happy(X))))&
(?[X]:(~generous(X)))&
(?[X]:((brave(X)|rich(X))))&
(happy(paul))&
(?[X]:((~humble(X)&rich(X)))) | happy(susan) | [
"p4",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1749523135648777787493052
% SZS output start Proof for 1749523135648777787493052
5. ! [X0] : ((~curious(X0) | ~rich(X0)) <=> patient(X0)) [input p4]
11. ! [X0] : ((patient(X0) | quiet(X0)) <=> happy(X0)) [input p10]
16. ! [X0] : (~quiet(X0) => (~curious(X0) & ~patient(X0))) [input p15]
23. ~happy(susan) [input hypothesis]
33. ! [X0] : ((~curious(X0) & ~patient(X0)) | quiet(X0)) [ennf transformation 16]
43. ! [X0] : (((~curious(X0) | ~rich(X0)) | ~patient(X0)) & (patient(X0) | (curious(X0) & rich(X0)))) [nnf transformation 5]
44. ! [X0] : ((~curious(X0) | ~rich(X0) | ~patient(X0)) & (patient(X0) | (curious(X0) & rich(X0)))) [flattening 43]
56. ! [X0] : (((patient(X0) | quiet(X0)) | ~happy(X0)) & (happy(X0) | (~patient(X0) & ~quiet(X0)))) [nnf transformation 11]
57. ! [X0] : ((patient(X0) | quiet(X0) | ~happy(X0)) & (happy(X0) | (~patient(X0) & ~quiet(X0)))) [flattening 56]
89. curious(X0) | patient(X0) [cnf transformation 44]
104. ~quiet(X0) | happy(X0) [cnf transformation 57]
122. ~patient(X0) | quiet(X0) [cnf transformation 33]
123. ~curious(X0) | quiet(X0) [cnf transformation 33]
131. ~happy(susan) [cnf transformation 23]
264. quiet(X0) | patient(X0) [resolution 123,89]
266. quiet(X0) [subsumption resolution 264,122]
267. happy(X0) [resolution 266,104]
361. $false [resolution 267,131]
% SZS output end Proof for 1749523135648777787493052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either generous or not rich then alice is both brave and not kind.
Everyone who is both calm and old is not generous or not patient and vice versa.
If someone is kind or strong then paul is curious.
Everyone who is not strong is not generous or not calm.
Everyone who is either not rich or wise is both not wise and not happy and vice versa.
Everyone who is generous or wise is not generous and vice versa.
If someone is either kind or not rich then someone is either not tall or not kind.
Everyone who is both patient and not generous is not old or not kind.
Everyone who is either not old or not generous is not brave or not tall and vice versa.
Everyone who is either not calm or patient is both calm and happy.
Everyone who is kind or not quiet is both brave and not calm.
Everyone who is not calm or not curious is not tall or tall and vice versa.
If someone is both rich and not creative then fred is patient or kind and vice versa.
If lucy is happy then susan is both not curious and not strong.
Everyone who is either not calm or not funny is either not rich or not wise and vice versa.
Everyone who is not kind or not quiet is both not generous and not curious and vice versa.
Someone is wise or generous.
Someone is not tall or not generous.
Someone is not curious or not brave.
Susan is not happy.
Someone is not strong or not quiet.
Someone is either curious or not rich.
Mary is not happy. | Fred is tall. | neutral | (((generous(susan)<~>~rich(susan)))=>((brave(alice)&~kind(alice))))&
(![X]:((calm(X)&old(X))<=>(~generous(X)|~patient(X))))&
((?[X]:((kind(X)|strong(X))))=>(curious(paul)))&
(![X]:(~strong(X)=>(~generous(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(~wise(X)&~happy(X))))&
(![X]:((generous(X)|wise(X))<=>~generous(X)))&
((?[X]:((kind(X)<~>~rich(X))))=>(?[X]:((~tall(X)<~>~kind(X)))))&
(![X]:((patient(X)&~generous(X))=>(~old(X)|~kind(X))))&
(![X]:((~old(X)<~>~generous(X))<=>(~brave(X)|~tall(X))))&
(![X]:((~calm(X)<~>patient(X))=>(calm(X)&happy(X))))&
(![X]:((kind(X)|~quiet(X))=>(brave(X)&~calm(X))))&
(![X]:((~calm(X)|~curious(X))<=>(~tall(X)|tall(X))))&
((?[X]:((rich(X)&~creative(X))))<=>((patient(fred)|kind(fred))))&
((happy(lucy))=>((~curious(susan)&~strong(susan))))&
(![X]:((~calm(X)<~>~funny(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(~generous(X)&~curious(X))))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:((~tall(X)|~generous(X))))&
(?[X]:((~curious(X)|~brave(X))))&
(~happy(susan))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((curious(X)<~>~rich(X))))&
(~happy(mary)) | tall(fred) | [] | null | 0 |
Everyone who is not calm is either kind or generous and vice versa. Everyone who is both not brave and kind is both old and not kind. Everyone who is either not creative or not happy is old. Everyone who is both not humble and not rich is either generous or creative and vice versa. Everyone who is either not happy or strong is either not kind or not wise. Everyone who is both funny and not generous is not happy or not tall and vice versa. Everyone who is brave or not patient is both not creative and not tall and vice versa. If susan is not curious or not kind then someone is kind and vice versa. Everyone who is not tall is either wise or not quiet and vice versa. Everyone who is both not old and generous is both not creative and quiet. Everyone who is both not old and creative is either not quiet or not tall and vice versa. Everyone who is both not humble and not creative is strong or not kind and vice versa. If mary is both creative and not quiet then someone is both not happy and funny. If john is both not calm and not quiet then fred is creative or calm and vice versa. Everyone who is both rich and not wise is both tall and not curious and vice versa. If fred is either not patient or not creative then someone is both wise and creative. Someone is not curious or not quiet. Susan is both not brave and not humble. Mary is either not brave or rich. Someone is rich. Susan is not calm or not strong. | Fred is tall. | contradiction | (![X]:(~calm(X)<=>(kind(X)<~>generous(X))))&
(![X]:((~brave(X)&kind(X))=>(old(X)&~kind(X))))&
(![X]:((~creative(X)<~>~happy(X))=>old(X)))&
(![X]:((~humble(X)&~rich(X))<=>(generous(X)<~>creative(X))))&
(![X]:((~happy(X)<~>strong(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((funny(X)&~generous(X))<=>(~happy(X)|~tall(X))))&
(![X]:((brave(X)|~patient(X))<=>(~creative(X)&~tall(X))))&
(((~curious(susan)|~kind(susan)))<=>(?[X]:(kind(X))))&
(![X]:(~tall(X)<=>(wise(X)<~>~quiet(X))))&
(![X]:((~old(X)&generous(X))=>(~creative(X)&quiet(X))))&
(![X]:((~old(X)&creative(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((~humble(X)&~creative(X))<=>(strong(X)|~kind(X))))&
(((creative(mary)&~quiet(mary)))=>(?[X]:((~happy(X)&funny(X)))))&
(((~calm(john)&~quiet(john)))<=>((creative(fred)|calm(fred))))&
(![X]:((rich(X)&~wise(X))<=>(tall(X)&~curious(X))))&
(((~patient(fred)<~>~creative(fred)))=>(?[X]:((wise(X)&creative(X)))))&
(?[X]:((~curious(X)|~quiet(X))))&
((~brave(susan)&~humble(susan)))&
((~brave(mary)<~>rich(mary)))&
(?[X]:(rich(X)))&
((~calm(susan)|~strong(susan))) | tall(fred) | [
"p1",
"p6",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8906662181650018353925333
% SZS output start Proof for 8906662181650018353925333
2. ! [X0] : ((kind(X0) & ~brave(X0)) => (~kind(X0) & old(X0))) [input p1]
7. ! [X0] : ((~patient(X0) | brave(X0)) <=> (~tall(X0) & ~creative(X0))) [input p6]
12. ! [X0] : ((~creative(X0) & ~humble(X0)) <=> (~kind(X0) | strong(X0))) [input p11]
16. (~patient(fred) <~> ~creative(fred)) => ? [X0] : (creative(X0) & wise(X0)) [input p15]
22. tall(fred) [input hypothesis]
23. ! [X0] : ((~kind(X0) & old(X0)) | (~kind(X0) | brave(X0))) [ennf transformation 2]
24. ! [X0] : ((~kind(X0) & old(X0)) | ~kind(X0) | brave(X0)) [flattening 23]
31. ? [X0] : (creative(X0) & wise(X0)) | (~patient(fred) <=> ~creative(fred)) [ennf transformation 16]
39. ! [X0] : (((~patient(X0) | brave(X0)) | (tall(X0) | creative(X0))) & ((~tall(X0) & ~creative(X0)) | (patient(X0) & ~brave(X0)))) [nnf transformation 7]
40. ! [X0] : ((~patient(X0) | brave(X0) | tall(X0) | creative(X0)) & ((~tall(X0) & ~creative(X0)) | (patient(X0) & ~brave(X0)))) [flattening 39]
49. ! [X0] : (((~creative(X0) & ~humble(X0)) | (kind(X0) & ~strong(X0))) & ((~kind(X0) | strong(X0)) | (creative(X0) | humble(X0)))) [nnf transformation 12]
50. ! [X0] : (((~creative(X0) & ~humble(X0)) | (kind(X0) & ~strong(X0))) & (~kind(X0) | strong(X0) | creative(X0) | humble(X0))) [flattening 49]
57. ? [X0] : (creative(X0) & wise(X0)) | ((~patient(fred) | creative(fred)) & (~creative(fred) | patient(fred))) [nnf transformation 31]
58. ? [X0] : (creative(X0) & wise(X0)) => (creative(sK2) & wise(sK2)) [choice axiom]
59. (creative(sK2) & wise(sK2)) | ((~patient(fred) | creative(fred)) & (~creative(fred) | patient(fred))) [skolemisation 57,58]
70. ~kind(X0) | ~kind(X0) | brave(X0) [cnf transformation 24]
88. ~creative(X0) | ~brave(X0) [cnf transformation 40]
90. ~tall(X0) | ~brave(X0) [cnf transformation 40]
91. ~tall(X0) | patient(X0) [cnf transformation 40]
112. ~creative(X0) | kind(X0) [cnf transformation 50]
127. creative(sK2) | ~patient(fred) | creative(fred) [cnf transformation 59]
135. tall(fred) [cnf transformation 22]
136. ~kind(X0) | brave(X0) [duplicate literal removal 70]
183. 11 <=> creative(fred) [avatar definition]
184. creative(fred) <- (11) [avatar component clause 183]
195. 13 <=> patient(fred) [avatar definition]
199. 14 <=> creative(sK2) [avatar definition]
201. creative(sK2) <- (14) [avatar component clause 199]
202. 11 | ~13 | 14 [avatar split clause 127,199,195,183]
236. ~brave(fred) [resolution 90,135]
238. patient(fred) [resolution 91,135]
242. 13 [avatar split clause 238,195]
245. kind(fred) <- (11) [resolution 112,184]
247. brave(fred) <- (11) [resolution 245,136]
248. $false <- (11) [subsumption resolution 247,236]
249. ~11 [avatar contradiction clause 248]
250. kind(sK2) <- (14) [resolution 201,112]
252. ~brave(sK2) <- (14) [resolution 201,88]
255. brave(sK2) <- (14) [resolution 250,136]
256. $false <- (14) [subsumption resolution 255,252]
257. ~14 [avatar contradiction clause 256]
258. $false [avatar sat refutation 202,242,249,257]
% SZS output end Proof for 8906662181650018353925333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not funny is either not creative or not old. If someone is not rich or happy then alice is both kind and not patient and vice versa. If someone is either not funny or wise then john is happy or not rich and vice versa. If someone is old then someone is both not rich and not old. Everyone who is generous or not humble is either not kind or patient. If someone is both rich and not happy then mary is not creative or not rich. Everyone who is not rich or generous is both not creative and not generous. Everyone who is curious is not tall or not strong. If someone is both not creative and generous then someone is both not calm and tall and vice versa. Everyone who is quiet or humble is patient. Everyone who is quiet is old. Everyone who is not generous is rich or patient. If someone is not patient then mary is not patient or creative and vice versa. Everyone who is strong is old or tall and vice versa. Everyone who is not generous is not kind or quiet and vice versa. If fred is not curious or not quiet then john is not patient. Someone is both not kind and creative. John is either creative or patient. Someone is both tall and funny. Alice is calm. Susan is either not humble or not wise. | John is not quiet. | entailment | (![X]:((wise(X)&~funny(X))=>(~creative(X)<~>~old(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((kind(alice)&~patient(alice))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((happy(john)|~rich(john))))&
((?[X]:(old(X)))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((generous(X)|~humble(X))=>(~kind(X)<~>patient(X))))&
((?[X]:((rich(X)&~happy(X))))=>((~creative(mary)|~rich(mary))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&~generous(X))))&
(![X]:(curious(X)=>(~tall(X)|~strong(X))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((quiet(X)|humble(X))=>patient(X)))&
(![X]:(quiet(X)=>old(X)))&
(![X]:(~generous(X)=>(rich(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((~patient(mary)|creative(mary))))&
(![X]:(strong(X)<=>(old(X)|tall(X))))&
(![X]:(~generous(X)<=>(~kind(X)|quiet(X))))&
(((~curious(fred)|~quiet(fred)))=>(~patient(john)))&
(?[X]:((~kind(X)&creative(X))))&
((creative(john)<~>patient(john)))&
(?[X]:((tall(X)&funny(X))))&
(calm(alice))&
((~humble(susan)<~>~wise(susan))) | ~quiet(john) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4824030322420214289711834
% SZS output start Proof for 4824030322420214289711834
2. ? [X0] : (happy(X0) | ~rich(X0)) <=> (~patient(alice) & kind(alice)) [input p1]
4. ? [X0] : old(X0) => ? [X0] : (~old(X0) & ~rich(X0)) [input p3]
7. ! [X0] : ((generous(X0) | ~rich(X0)) => (~generous(X0) & ~creative(X0))) [input p6]
10. ! [X0] : ((humble(X0) | quiet(X0)) => patient(X0)) [input p9]
11. ! [X0] : (quiet(X0) => old(X0)) [input p10]
15. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~kind(X0))) [input p14]
22. quiet(john) [input hypothesis]
23. ? [X0] : old(X0) => ? [X1] : (~old(X1) & ~rich(X1)) [rectify 4]
28. ? [X1] : (~old(X1) & ~rich(X1)) | ! [X0] : ~old(X0) [ennf transformation 23]
32. ! [X0] : ((~generous(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 7]
35. ! [X0] : (patient(X0) | (~humble(X0) & ~quiet(X0))) [ennf transformation 10]
36. ! [X0] : (old(X0) | ~quiet(X0)) [ennf transformation 11]
42. (? [X0] : (happy(X0) | ~rich(X0)) | (patient(alice) | ~kind(alice))) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 2]
43. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 42]
44. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 43]
45. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
46. ((happy(sK0) | ~rich(sK0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 44,45]
52. ? [X0] : (~old(X0) & ~rich(X0)) | ! [X1] : ~old(X1) [rectify 28]
53. ? [X0] : (~old(X0) & ~rich(X0)) => (~old(sK2) & ~rich(sK2)) [choice axiom]
54. (~old(sK2) & ~rich(sK2)) | ! [X1] : ~old(X1) [skolemisation 52,53]
66. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | generous(X0))) [nnf transformation 15]
67. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | generous(X0))) [flattening 66]
76. kind(alice) | rich(X1) [cnf transformation 46]
78. ~patient(alice) | rich(X1) [cnf transformation 46]
87. ~rich(sK2) | ~old(X1) [cnf transformation 54]
97. ~generous(X0) | ~generous(X0) [cnf transformation 32]
103. ~quiet(X0) | patient(X0) [cnf transformation 35]
105. ~quiet(X0) | old(X0) [cnf transformation 36]
112. quiet(X0) | ~kind(X0) | generous(X0) [cnf transformation 67]
126. quiet(john) [cnf transformation 22]
127. ~generous(X0) [duplicate literal removal 97]
129. 1 <=> kind(alice) [avatar definition]
130. kind(alice) <- (1) [avatar component clause 129]
133. 2 <=> patient(alice) [avatar definition]
134. ~patient(alice) <- (~2) [avatar component clause 133]
150. 6 <=> ! [X1] : rich(X1) [avatar definition]
151. rich(X1) <- (6) [avatar component clause 150]
152. 6 | ~2 [avatar split clause 78,133,150]
154. 6 | 1 [avatar split clause 76,129,150]
184. 13 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (13) [avatar component clause 184]
192. 15 <=> rich(sK2) [avatar definition]
194. ~rich(sK2) <- (~15) [avatar component clause 192]
195. 13 | ~15 [avatar split clause 87,192,184]
224. ~kind(X0) | quiet(X0) [subsumption resolution 112,127]
259. $false <- (6, ~15) [resolution 194,151]
260. ~6 | 15 [avatar contradiction clause 259]
265. old(john) [resolution 105,126]
267. $false <- (13) [subsumption resolution 265,185]
268. ~13 [avatar contradiction clause 267]
285. quiet(alice) <- (1) [resolution 224,130]
289. patient(alice) <- (1) [resolution 285,103]
290. $false <- (1, ~2) [subsumption resolution 289,134]
291. ~1 | 2 [avatar contradiction clause 290]
292. $false [avatar sat refutation 152,154,195,260,268,291]
% SZS output end Proof for 4824030322420214289711834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not strong and not tall then susan is either humble or not generous and vice versa. Everyone who is either not old or creative is both not humble and tall. If john is creative or not curious then someone is not calm and vice versa. Everyone who is both rich and brave is rich or not curious and vice versa. Everyone who is old is both happy and tall. If someone is either generous or not kind then someone is not tall. Everyone who is not calm or curious is not calm and vice versa. If someone is humble or not funny then someone is both not strong and not old and vice versa. If alice is either not kind or not calm then someone is tall or happy and vice versa. If susan is both not generous and not creative then someone is humble or not patient. If someone is both not creative and old then someone is either kind or not patient. If someone is either wise or not kind then john is not strong and vice versa. Everyone who is curious or funny is either patient or old. Everyone who is not humble is wise or brave and vice versa. Everyone who is funny or old is not brave or patient. Everyone who is brave or not calm is tall or patient. Susan is not strong. Someone is either old or kind. Paul is either not strong or strong. Mary is not calm. Alice is both curious and patient. Someone is either happy or not tall. Paul is not generous or rich. Someone is tall. | Susan is creative. | neutral | (((~strong(paul)&~tall(paul)))<=>((humble(susan)<~>~generous(susan))))&
(![X]:((~old(X)<~>creative(X))=>(~humble(X)&tall(X))))&
(((creative(john)|~curious(john)))<=>(?[X]:(~calm(X))))&
(![X]:((rich(X)&brave(X))<=>(rich(X)|~curious(X))))&
(![X]:(old(X)=>(happy(X)&tall(X))))&
((?[X]:((generous(X)<~>~kind(X))))=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)|curious(X))<=>~calm(X)))&
((?[X]:((humble(X)|~funny(X))))<=>(?[X]:((~strong(X)&~old(X)))))&
(((~kind(alice)<~>~calm(alice)))<=>(?[X]:((tall(X)|happy(X)))))&
(((~generous(susan)&~creative(susan)))=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:((~creative(X)&old(X))))=>(?[X]:((kind(X)<~>~patient(X)))))&
((?[X]:((wise(X)<~>~kind(X))))<=>(~strong(john)))&
(![X]:((curious(X)|funny(X))=>(patient(X)<~>old(X))))&
(![X]:(~humble(X)<=>(wise(X)|brave(X))))&
(![X]:((funny(X)|old(X))=>(~brave(X)|patient(X))))&
(![X]:((brave(X)|~calm(X))=>(tall(X)|patient(X))))&
(~strong(susan))&
(?[X]:((old(X)<~>kind(X))))&
((~strong(paul)<~>strong(paul)))&
(~calm(mary))&
((curious(alice)&patient(alice)))&
(?[X]:((happy(X)<~>~tall(X))))&
((~generous(paul)|rich(paul)))&
(?[X]:(tall(X))) | creative(susan) | [] | null | 0 |
If fred is happy then someone is not wise and vice versa.
Everyone who is either curious or not happy is not happy or patient and vice versa.
Everyone who is brave or not kind is not kind.
If alice is both wise and funny then someone is not happy.
If paul is either not calm or not brave then john is quiet or not generous and vice versa.
Everyone who is not generous or rich is either not happy or not curious and vice versa.
Everyone who is curious or wise is not happy or not patient.
Everyone who is not brave or not curious is not quiet or calm.
Everyone who is both calm and kind is curious.
If lucy is not funny then someone is both not wise and brave and vice versa.
Everyone who is patient is not calm or not strong and vice versa.
If fred is both not tall and not wise then someone is either curious or not tall and vice versa.
Everyone who is not humble or not happy is both not creative and not old and vice versa.
If someone is calm then susan is both creative and not humble.
If someone is not wise or calm then john is both not calm and not funny and vice versa.
Someone is not brave.
Paul is not humble or not curious.
Someone is either not humble or not wise. | Alice is wise. | entailment | ((happy(fred))<=>(?[X]:(~wise(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(~happy(X)|patient(X))))&
(![X]:((brave(X)|~kind(X))=>~kind(X)))&
(((wise(alice)&funny(alice)))=>(?[X]:(~happy(X))))&
(((~calm(paul)<~>~brave(paul)))<=>((quiet(john)|~generous(john))))&
(![X]:((~generous(X)|rich(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:((curious(X)|wise(X))=>(~happy(X)|~patient(X))))&
(![X]:((~brave(X)|~curious(X))=>(~quiet(X)|calm(X))))&
(![X]:((calm(X)&kind(X))=>curious(X)))&
((~funny(lucy))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
(((~tall(fred)&~wise(fred)))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~humble(X)|~happy(X))<=>(~creative(X)&~old(X))))&
((?[X]:(calm(X)))=>((creative(susan)&~humble(susan))))&
((?[X]:((~wise(X)|calm(X))))<=>((~calm(john)&~funny(john))))&
(?[X]:(~brave(X)))&
((~humble(paul)|~curious(paul)))&
(?[X]:((~humble(X)<~>~wise(X)))) | wise(alice) | [
"p0",
"p1",
"p6",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 496073605703113564383232
% SZS output start Proof for 496073605703113564383232
1. happy(fred) <=> ? [X0] : ~wise(X0) [input p0]
2. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> (patient(X0) | ~happy(X0))) [input p1]
7. ! [X0] : ((wise(X0) | curious(X0)) => (~patient(X0) | ~happy(X0))) [input p6]
11. ! [X0] : (patient(X0) <=> (~strong(X0) | ~calm(X0))) [input p10]
13. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~old(X0) & ~creative(X0))) [input p12]
14. ? [X0] : calm(X0) => (~humble(susan) & creative(susan)) [input p13]
19. ~wise(alice) [input hypothesis]
23. ! [X0] : ((~patient(X0) | ~happy(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 7]
24. ! [X0] : (~patient(X0) | ~happy(X0) | (~wise(X0) & ~curious(X0))) [flattening 23]
29. (~humble(susan) & creative(susan)) | ! [X0] : ~calm(X0) [ennf transformation 14]
30. (happy(fred) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ~happy(fred)) [nnf transformation 1]
31. (happy(fred) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ~happy(fred)) [rectify 30]
32. ? [X1] : ~wise(X1) => ~wise(sK0) [choice axiom]
33. (happy(fred) | ! [X0] : wise(X0)) & (~wise(sK0) | ~happy(fred)) [skolemisation 31,32]
34. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~patient(X0) & happy(X0))) & ((patient(X0) | ~happy(X0)) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 2]
35. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~patient(X0) & happy(X0))) & (patient(X0) | ~happy(X0) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [flattening 34]
46. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~patient(X0))) [nnf transformation 11]
47. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~patient(X0))) [flattening 46]
53. ! [X0] : (((~happy(X0) | ~humble(X0)) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 13]
54. ! [X0] : ((~happy(X0) | ~humble(X0) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | (happy(X0) & humble(X0)))) [flattening 53]
66. happy(fred) | wise(X0) [cnf transformation 33]
67. patient(X0) | ~happy(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 35]
70. ~patient(X0) | curious(X0) | ~happy(X0) [cnf transformation 35]
71. happy(X0) | ~curious(X0) | happy(X0) [cnf transformation 35]
88. ~patient(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 24]
97. calm(X0) | patient(X0) [cnf transformation 47]
105. ~creative(X0) | humble(X0) [cnf transformation 54]
110. creative(susan) | ~calm(X0) [cnf transformation 29]
111. ~humble(susan) | ~calm(X0) [cnf transformation 29]
121. ~wise(alice) [cnf transformation 19]
122. patient(X0) | ~happy(X0) | ~curious(X0) [duplicate literal removal 67]
123. ~curious(X0) | happy(X0) [duplicate literal removal 71]
125. 1 <=> ! [X0] : wise(X0) [avatar definition]
126. wise(X0) <- (1) [avatar component clause 125]
128. 2 <=> happy(fred) [avatar definition]
130. happy(fred) <- (2) [avatar component clause 128]
131. 1 | 2 [avatar split clause 66,128,125]
137. ~curious(X0) | patient(X0) [subsumption resolution 122,123]
139. 4 <=> wise(alice) [avatar definition]
141. ~wise(alice) <- (~4) [avatar component clause 139]
177. ~patient(X0) | ~curious(X0) [subsumption resolution 88,123]
178. ~curious(X0) [subsumption resolution 177,137]
221. 19 <=> ! [X0] : ~calm(X0) [avatar definition]
222. ~calm(X0) <- (19) [avatar component clause 221]
224. 20 <=> humble(susan) [avatar definition]
226. ~humble(susan) <- (~20) [avatar component clause 224]
227. 19 | ~20 [avatar split clause 111,224,221]
229. 21 <=> creative(susan) [avatar definition]
231. creative(susan) <- (21) [avatar component clause 229]
232. 19 | 21 [avatar split clause 110,229,221]
264. ~4 [avatar split clause 121,139]
265. patient(X0) <- (19) [resolution 97,222]
268. curious(X0) | ~happy(X0) <- (19) [resolution 70,265]
269. ~happy(X0) <- (19) [subsumption resolution 268,178]
270. $false <- (2, 19) [resolution 269,130]
271. ~2 | ~19 [avatar contradiction clause 270]
274. humble(susan) <- (21) [resolution 231,105]
275. $false <- (~20, 21) [subsumption resolution 274,226]
276. 20 | ~21 [avatar contradiction clause 275]
278. $false <- (1, ~4) [resolution 126,141]
285. ~1 | 4 [avatar contradiction clause 278]
287. $false [avatar sat refutation 131,227,232,264,271,276,285]
% SZS output end Proof for 496073605703113564383232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or patient is patient and vice versa.
Everyone who is both patient and not funny is both not funny and funny and vice versa.
If someone is brave or happy then lucy is both not old and not generous.
If someone is both humble and brave then alice is not calm.
Everyone who is not quiet or not calm is both creative and humble and vice versa.
If alice is both brave and not creative then john is not strong.
Everyone who is both curious and humble is old or wise and vice versa.
Everyone who is rich or not brave is both generous and not quiet and vice versa.
If someone is either tall or not creative then fred is either not generous or patient.
If someone is not strong then john is not tall and vice versa.
If alice is both not rich and not happy then someone is not wise.
Everyone who is humble or funny is either kind or humble and vice versa.
If fred is strong then mary is not funny.
Everyone who is either not curious or kind is either not curious or not calm.
If someone is creative then alice is either not brave or rich and vice versa.
If alice is either not rich or not creative then fred is both funny and not funny and vice versa.
Lucy is either quiet or not creative.
Someone is curious or generous.
John is strong.
John is not old.
Paul is both not tall and calm.
Mary is either kind or not rich.
Someone is brave.
Lucy is not generous. | Alice is not brave. | contradiction | (![X]:((~curious(X)<~>patient(X))<=>patient(X)))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)&funny(X))))&
((?[X]:((brave(X)|happy(X))))=>((~old(lucy)&~generous(lucy))))&
((?[X]:((humble(X)&brave(X))))=>(~calm(alice)))&
(![X]:((~quiet(X)|~calm(X))<=>(creative(X)&humble(X))))&
(((brave(alice)&~creative(alice)))=>(~strong(john)))&
(![X]:((curious(X)&humble(X))<=>(old(X)|wise(X))))&
(![X]:((rich(X)|~brave(X))<=>(generous(X)&~quiet(X))))&
((?[X]:((tall(X)<~>~creative(X))))=>((~generous(fred)<~>patient(fred))))&
((?[X]:(~strong(X)))<=>(~tall(john)))&
(((~rich(alice)&~happy(alice)))=>(?[X]:(~wise(X))))&
(![X]:((humble(X)|funny(X))<=>(kind(X)<~>humble(X))))&
((strong(fred))=>(~funny(mary)))&
(![X]:((~curious(X)<~>kind(X))=>(~curious(X)<~>~calm(X))))&
((?[X]:(creative(X)))<=>((~brave(alice)<~>rich(alice))))&
(((~rich(alice)<~>~creative(alice)))<=>((funny(fred)&~funny(fred))))&
((quiet(lucy)<~>~creative(lucy)))&
(?[X]:((curious(X)|generous(X))))&
(strong(john))&
(~old(john))&
((~tall(paul)&calm(paul)))&
((kind(mary)<~>~rich(mary)))&
(?[X]:(brave(X)))&
(~generous(lucy)) | ~brave(alice) | [
"p4",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1480476714290615907490102
% SZS output start Proof for 1480476714290615907490102
5. ! [X0] : ((~calm(X0) | ~quiet(X0)) <=> (humble(X0) & creative(X0))) [input p4]
8. ! [X0] : ((~brave(X0) | rich(X0)) <=> (~quiet(X0) & generous(X0))) [input p7]
15. ? [X0] : creative(X0) <=> (~brave(alice) <~> rich(alice)) [input p14]
16. (~rich(alice) <~> ~creative(alice)) <=> (~funny(fred) & funny(fred)) [input p15]
25. ~brave(alice) [input hypothesis]
38. ! [X0] : (((~calm(X0) | ~quiet(X0)) | (~humble(X0) | ~creative(X0))) & ((humble(X0) & creative(X0)) | (calm(X0) & quiet(X0)))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | ~quiet(X0) | ~humble(X0) | ~creative(X0)) & ((humble(X0) & creative(X0)) | (calm(X0) & quiet(X0)))) [flattening 38]
42. ! [X0] : (((~brave(X0) | rich(X0)) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | (brave(X0) & ~rich(X0)))) [nnf transformation 8]
43. ! [X0] : ((~brave(X0) | rich(X0) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | (brave(X0) & ~rich(X0)))) [flattening 42]
54. (? [X0] : creative(X0) | ((~brave(alice) | ~rich(alice)) & (rich(alice) | brave(alice)))) & (((~rich(alice) | brave(alice)) & (rich(alice) | ~brave(alice))) | ! [X0] : ~creative(X0)) [nnf transformation 15]
55. (? [X0] : creative(X0) | ((~brave(alice) | ~rich(alice)) & (rich(alice) | brave(alice)))) & (((~rich(alice) | brave(alice)) & (rich(alice) | ~brave(alice))) | ! [X1] : ~creative(X1)) [rectify 54]
56. ? [X0] : creative(X0) => creative(sK2) [choice axiom]
57. (creative(sK2) | ((~brave(alice) | ~rich(alice)) & (rich(alice) | brave(alice)))) & (((~rich(alice) | brave(alice)) & (rich(alice) | ~brave(alice))) | ! [X1] : ~creative(X1)) [skolemisation 55,56]
58. (((creative(alice) | rich(alice)) & (~creative(alice) | ~rich(alice))) | (funny(fred) | ~funny(fred))) & ((~funny(fred) & funny(fred)) | ((~rich(alice) | creative(alice)) & (~creative(alice) | rich(alice)))) [nnf transformation 16]
59. (((creative(alice) | rich(alice)) & (~creative(alice) | ~rich(alice))) | funny(fred) | ~funny(fred)) & ((~funny(fred) & funny(fred)) | ((~rich(alice) | creative(alice)) & (~creative(alice) | rich(alice)))) [flattening 58]
79. creative(X0) | quiet(X0) [cnf transformation 39]
93. ~quiet(X0) | brave(X0) [cnf transformation 43]
114. ~rich(alice) | brave(alice) | ~creative(X1) [cnf transformation 57]
117. funny(fred) | ~creative(alice) | rich(alice) [cnf transformation 59]
119. ~funny(fred) | ~creative(alice) | rich(alice) [cnf transformation 59]
134. ~brave(alice) [cnf transformation 25]
171. 7 <=> brave(alice) [avatar definition]
173. ~brave(alice) <- (~7) [avatar component clause 171]
175. 8 <=> creative(alice) [avatar definition]
176. ~creative(alice) <- (~8) [avatar component clause 175]
177. creative(alice) <- (8) [avatar component clause 175]
216. 17 <=> rich(alice) [avatar definition]
245. 23 <=> ! [X1] : ~creative(X1) [avatar definition]
246. ~creative(X1) <- (23) [avatar component clause 245]
247. 23 | 7 | ~17 [avatar split clause 114,216,171,245]
250. 24 <=> funny(fred) [avatar definition]
254. 17 | ~8 | ~24 [avatar split clause 119,250,175,216]
256. 17 | ~8 | 24 [avatar split clause 117,250,175,216]
271. ~7 [avatar split clause 134,171]
272. quiet(alice) <- (~8) [resolution 79,176]
280. brave(alice) <- (~8) [resolution 93,272]
282. $false <- (~7, ~8) [subsumption resolution 280,173]
283. 7 | 8 [avatar contradiction clause 282]
284. $false <- (8, 23) [subsumption resolution 177,246]
285. ~8 | ~23 [avatar contradiction clause 284]
286. $false [avatar sat refutation 247,254,256,271,283,285]
% SZS output end Proof for 1480476714290615907490102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not quiet is not funny and vice versa. Everyone who is creative is either not brave or not creative and vice versa. Everyone who is not calm is either curious or not quiet. Everyone who is both calm and funny is both not strong and creative and vice versa. If lucy is old then someone is funny and vice versa. Everyone who is both not old and old is not wise and vice versa. If susan is funny or not happy then john is both kind and not strong. Everyone who is not brave or not kind is patient and vice versa. If john is calm or old then someone is either not brave or not funny and vice versa. If someone is both not patient and not kind then someone is not rich and vice versa. Everyone who is both not old and strong is rich or creative. If lucy is either not curious or not humble then paul is rich. Everyone who is both not generous and happy is both rich and not kind and vice versa. Everyone who is either tall or funny is kind or tall and vice versa. Everyone who is both tall and happy is either not calm or not quiet. Everyone who is generous or funny is both strong and patient and vice versa. Someone is not calm. Lucy is kind. Fred is not tall. John is kind or not generous. Someone is both creative and not funny. Someone is creative or not tall. Fred is either wise or strong. | Susan is patient. | entailment | (![X]:((funny(X)|~quiet(X))<=>~funny(X)))&
(![X]:(creative(X)<=>(~brave(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(curious(X)<~>~quiet(X))))&
(![X]:((calm(X)&funny(X))<=>(~strong(X)&creative(X))))&
((old(lucy))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)&old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(![X]:((tall(X)&happy(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(?[X]:(~calm(X)))&
(kind(lucy))&
(~tall(fred))&
((kind(john)|~generous(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((creative(X)|~tall(X))))&
((wise(fred)<~>strong(fred))) | patient(susan) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8295890614288018918518933
% SZS output start Proof for 8295890614288018918518933
2. ! [X0] : (creative(X0) <=> (~brave(X0) <~> ~creative(X0))) [input p1]
8. ! [X0] : ((~kind(X0) | ~brave(X0)) <=> patient(X0)) [input p7]
24. ~patient(susan) [input hypothesis]
35. ! [X0] : ((creative(X0) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | ~creative(X0))) [nnf transformation 2]
45. ! [X0] : (((~kind(X0) | ~brave(X0)) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [nnf transformation 8]
46. ! [X0] : ((~kind(X0) | ~brave(X0) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [flattening 45]
75. ~creative(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 35]
78. creative(X0) | ~brave(X0) | creative(X0) [cnf transformation 35]
94. patient(X0) | brave(X0) [cnf transformation 46]
135. ~patient(susan) [cnf transformation 24]
138. ~creative(X0) | ~brave(X0) [duplicate literal removal 75]
139. creative(X0) | ~brave(X0) [duplicate literal removal 78]
142. ~brave(X0) [subsumption resolution 138,139]
160. patient(X0) [subsumption resolution 94,142]
207. $false [subsumption resolution 135,160]
% SZS output end Proof for 8295890614288018918518933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both brave and not brave then john is either not patient or not quiet.
Everyone who is not brave is either not creative or not kind.
If alice is humble then someone is either rich or not creative.
Everyone who is either not rich or generous is not calm or not wise and vice versa.
If someone is quiet or not quiet then someone is both wise and creative.
If lucy is both not funny and wise then paul is either tall or generous.
Everyone who is both kind and wise is calm or quiet and vice versa.
Everyone who is both not happy and not old is either not rich or calm.
Everyone who is not calm is quiet or funny and vice versa.
Everyone who is both not brave and funny is not calm or not brave.
Everyone who is not happy or wise is strong or wise and vice versa.
If someone is not strong or not patient then paul is either tall or old and vice versa.
Everyone who is not rich is both tall and generous.
Everyone who is either not quiet or kind is either wise or not strong.
Everyone who is happy is not strong or tall and vice versa.
If someone is either tall or old then susan is quiet.
Someone is strong.
Someone is happy or not strong.
Fred is happy or funny.
Paul is either happy or not happy.
Someone is either happy or not patient.
Alice is not wise or not strong.
Susan is both not brave and not creative.
Someone is not tall. | Susan is generous. | entailment | (((brave(susan)&~brave(susan)))=>((~patient(john)<~>~quiet(john))))&
(![X]:(~brave(X)=>(~creative(X)<~>~kind(X))))&
((humble(alice))=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((~rich(X)<~>generous(X))<=>(~calm(X)|~wise(X))))&
((?[X]:((quiet(X)|~quiet(X))))=>(?[X]:((wise(X)&creative(X)))))&
(((~funny(lucy)&wise(lucy)))=>((tall(paul)<~>generous(paul))))&
(![X]:((kind(X)&wise(X))<=>(calm(X)|quiet(X))))&
(![X]:((~happy(X)&~old(X))=>(~rich(X)<~>calm(X))))&
(![X]:(~calm(X)<=>(quiet(X)|funny(X))))&
(![X]:((~brave(X)&funny(X))=>(~calm(X)|~brave(X))))&
(![X]:((~happy(X)|wise(X))<=>(strong(X)|wise(X))))&
((?[X]:((~strong(X)|~patient(X))))<=>((tall(paul)<~>old(paul))))&
(![X]:(~rich(X)=>(tall(X)&generous(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(wise(X)<~>~strong(X))))&
(![X]:(happy(X)<=>(~strong(X)|tall(X))))&
((?[X]:((tall(X)<~>old(X))))=>(quiet(susan)))&
(?[X]:(strong(X)))&
(?[X]:((happy(X)|~strong(X))))&
((happy(fred)|funny(fred)))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((happy(X)<~>~patient(X))))&
((~wise(alice)|~strong(alice)))&
((~brave(susan)&~creative(susan)))&
(?[X]:(~tall(X))) | generous(susan) | [
"p3",
"p6",
"p7",
"p8",
"p10",
"p11",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1384980930013192938385645
% SZS output start Proof for 1384980930013192938385645
4. ! [X0] : ((~rich(X0) <~> generous(X0)) <=> (~wise(X0) | ~calm(X0))) [input p3]
7. ! [X0] : ((wise(X0) & kind(X0)) <=> (quiet(X0) | calm(X0))) [input p6]
8. ! [X0] : ((~old(X0) & ~happy(X0)) => (~rich(X0) <~> calm(X0))) [input p7]
9. ! [X0] : (~calm(X0) <=> (funny(X0) | quiet(X0))) [input p8]
11. ! [X0] : ((wise(X0) | ~happy(X0)) <=> (wise(X0) | strong(X0))) [input p10]
12. ? [X0] : (~patient(X0) | ~strong(X0)) <=> (tall(paul) <~> old(paul)) [input p11]
13. ! [X0] : (~rich(X0) => (generous(X0) & tall(X0))) [input p12]
15. ! [X0] : (happy(X0) <=> (tall(X0) | ~strong(X0))) [input p14]
16. ? [X0] : (tall(X0) <~> old(X0)) => quiet(susan) [input p15]
22. ~strong(alice) | ~wise(alice) [input p21]
25. ~generous(susan) [input hypothesis]
34. ! [X0] : ((~rich(X0) <~> calm(X0)) | (old(X0) | happy(X0))) [ennf transformation 8]
35. ! [X0] : ((~rich(X0) <~> calm(X0)) | old(X0) | happy(X0)) [flattening 34]
38. ! [X0] : ((generous(X0) & tall(X0)) | rich(X0)) [ennf transformation 13]
40. quiet(susan) | ! [X0] : (tall(X0) <=> old(X0)) [ennf transformation 16]
43. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | (wise(X0) & calm(X0))) & ((~wise(X0) | ~calm(X0)) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | (wise(X0) & calm(X0))) & (~wise(X0) | ~calm(X0) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [flattening 43]
49. ! [X0] : (((wise(X0) & kind(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (~wise(X0) | ~kind(X0)))) [nnf transformation 7]
50. ! [X0] : (((wise(X0) & kind(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | ~wise(X0) | ~kind(X0))) [flattening 49]
51. ! [X0] : (((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | old(X0) | happy(X0)) [nnf transformation 35]
52. ! [X0] : ((~calm(X0) | (~funny(X0) & ~quiet(X0))) & ((funny(X0) | quiet(X0)) | calm(X0))) [nnf transformation 9]
53. ! [X0] : ((~calm(X0) | (~funny(X0) & ~quiet(X0))) & (funny(X0) | quiet(X0) | calm(X0))) [flattening 52]
54. ! [X0] : (((wise(X0) | ~happy(X0)) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | (~wise(X0) & happy(X0)))) [nnf transformation 11]
55. ! [X0] : ((wise(X0) | ~happy(X0) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | (~wise(X0) & happy(X0)))) [flattening 54]
56. (? [X0] : (~patient(X0) | ~strong(X0)) | ((tall(paul) | ~old(paul)) & (old(paul) | ~tall(paul)))) & (((~old(paul) | ~tall(paul)) & (old(paul) | tall(paul))) | ! [X0] : (patient(X0) & strong(X0))) [nnf transformation 12]
57. (? [X0] : (~patient(X0) | ~strong(X0)) | ((tall(paul) | ~old(paul)) & (old(paul) | ~tall(paul)))) & (((~old(paul) | ~tall(paul)) & (old(paul) | tall(paul))) | ! [X1] : (patient(X1) & strong(X1))) [rectify 56]
58. ? [X0] : (~patient(X0) | ~strong(X0)) => (~patient(sK1) | ~strong(sK1)) [choice axiom]
59. ((~patient(sK1) | ~strong(sK1)) | ((tall(paul) | ~old(paul)) & (old(paul) | ~tall(paul)))) & (((~old(paul) | ~tall(paul)) & (old(paul) | tall(paul))) | ! [X1] : (patient(X1) & strong(X1))) [skolemisation 57,58]
61. ! [X0] : ((happy(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~happy(X0))) [nnf transformation 15]
62. ! [X0] : ((happy(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~happy(X0))) [flattening 61]
63. quiet(susan) | ! [X0] : ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0))) [nnf transformation 40]
80. ~rich(X0) | generous(X0) | calm(X0) [cnf transformation 44]
83. ~generous(X0) | rich(X0) | wise(X0) [cnf transformation 44]
93. ~calm(X0) | wise(X0) [cnf transformation 50]
95. ~rich(X0) | calm(X0) | old(X0) | happy(X0) [cnf transformation 51]
98. ~calm(X0) | ~quiet(X0) [cnf transformation 53]
103. ~strong(X0) | ~happy(X0) | wise(X0) [cnf transformation 55]
105. old(paul) | tall(paul) | strong(X1) [cnf transformation 59]
107. ~old(paul) | ~tall(paul) | strong(X1) [cnf transformation 59]
112. generous(X0) | rich(X0) [cnf transformation 38]
119. ~tall(X0) | happy(X0) [cnf transformation 62]
120. quiet(susan) | old(X0) | ~tall(X0) [cnf transformation 63]
121. quiet(susan) | tall(X0) | ~old(X0) [cnf transformation 63]
129. ~strong(alice) | ~wise(alice) [cnf transformation 22]
133. ~generous(susan) [cnf transformation 25]
161. 7 <=> tall(paul) [avatar definition]
162. tall(paul) <- (7) [avatar component clause 161]
163. ~tall(paul) <- (~7) [avatar component clause 161]
171. 9 <=> old(paul) [avatar definition]
172. old(paul) <- (9) [avatar component clause 171]
173. ~old(paul) <- (~9) [avatar component clause 171]
189. 13 <=> ! [X1] : strong(X1) [avatar definition]
190. strong(X1) <- (13) [avatar component clause 189]
191. 13 | ~7 | ~9 [avatar split clause 107,171,161,189]
193. 13 | 7 | 9 [avatar split clause 105,171,161,189]
199. 14 <=> ! [X0] : (tall(X0) | ~old(X0)) [avatar definition]
200. ~old(X0) | tall(X0) <- (14) [avatar component clause 199]
202. 15 <=> quiet(susan) [avatar definition]
205. 14 | 15 [avatar split clause 121,202,199]
207. 16 <=> ! [X0] : (old(X0) | ~tall(X0)) [avatar definition]
208. ~tall(X0) | old(X0) <- (16) [avatar component clause 207]
209. 16 | 15 [avatar split clause 120,202,207]
231. 21 <=> wise(alice) [avatar definition]
233. ~wise(alice) <- (~21) [avatar component clause 231]
235. 22 <=> strong(alice) [avatar definition]
237. ~strong(alice) <- (~22) [avatar component clause 235]
238. ~21 | ~22 [avatar split clause 129,235,231]
242. rich(susan) [resolution 112,133]
251. generous(susan) | calm(susan) [resolution 80,242]
261. calm(susan) [subsumption resolution 251,133]
285. rich(X0) | wise(X0) | rich(X0) [resolution 83,112]
286. wise(X0) | rich(X0) [duplicate literal removal 285]
290. ~quiet(susan) [resolution 261,98]
295. ~15 [avatar split clause 290,202]
297. old(paul) <- (7, 16) [resolution 208,162]
299. $false <- (7, ~9, 16) [subsumption resolution 297,173]
300. ~7 | 9 | ~16 [avatar contradiction clause 299]
302. tall(paul) <- (9, 14) [resolution 172,200]
303. $false <- (~7, 9, 14) [subsumption resolution 302,163]
304. 7 | ~9 | ~14 [avatar contradiction clause 303]
321. ~happy(X1) | wise(X1) <- (13) [resolution 103,190]
518. 51 <=> happy(alice) [avatar definition]
519. ~happy(alice) <- (~51) [avatar component clause 518]
520. happy(alice) <- (51) [avatar component clause 518]
522. 52 <=> old(alice) [avatar definition]
524. old(alice) <- (52) [avatar component clause 522]
526. 53 <=> calm(alice) [avatar definition]
527. ~calm(alice) <- (~53) [avatar component clause 526]
528. calm(alice) <- (53) [avatar component clause 526]
702. wise(alice) <- (53) [resolution 528,93]
706. 21 | ~53 [avatar split clause 702,526,231]
707. $false <- (13, ~22) [subsumption resolution 237,190]
708. ~13 | 22 [avatar contradiction clause 707]
710. rich(alice) <- (~21) [resolution 233,286]
712. calm(alice) | old(alice) | happy(alice) <- (~21) [resolution 710,95]
717. wise(alice) <- (13, 51) [resolution 520,321]
718. $false <- (13, ~21, 51) [subsumption resolution 717,233]
719. ~13 | 21 | ~51 [avatar contradiction clause 718]
720. old(alice) | happy(alice) <- (~21, ~53) [subsumption resolution 712,527]
721. 51 | 52 | 21 | 53 [avatar split clause 720,526,231,522,518]
723. tall(alice) <- (14, 52) [resolution 524,200]
838. happy(alice) <- (14, 52) [resolution 723,119]
839. $false <- (14, ~51, 52) [subsumption resolution 838,519]
840. ~14 | 51 | ~52 [avatar contradiction clause 839]
841. $false [avatar sat refutation 191,193,205,209,238,295,300,304,706,708,719,721,840]
% SZS output end Proof for 1384980930013192938385645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is either not quiet or generous and vice versa.
Everyone who is either old or not brave is not humble or patient.
Everyone who is either not strong or not humble is either wise or not happy.
Everyone who is both kind and patient is quiet and vice versa.
Everyone who is either not funny or not rich is not wise or not creative.
Everyone who is curious or brave is both generous and not happy and vice versa.
Everyone who is either not brave or generous is rich or calm.
Everyone who is wise is not creative or not rich and vice versa.
If alice is not quiet or not wise then fred is either not tall or not humble.
Everyone who is brave is not wise.
Everyone who is both not creative and not rich is either happy or not old.
Everyone who is either not humble or brave is creative.
If lucy is either happy or curious then someone is not funny or funny.
Everyone who is both rich and generous is either generous or quiet and vice versa.
If paul is either brave or not quiet then alice is either rich or strong and vice versa.
If alice is either tall or not wise then paul is not generous or not humble.
Someone is patient or creative.
Alice is funny.
Someone is both not brave and creative.
Someone is not old or not strong.
Someone is both not brave and rich.
Paul is humble or patient.
Someone is happy.
Someone is either not humble or not curious. | Alice is not patient. | neutral | (![X]:(happy(X)<=>(~quiet(X)<~>generous(X))))&
(![X]:((old(X)<~>~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~strong(X)<~>~humble(X))=>(wise(X)<~>~happy(X))))&
(![X]:((kind(X)&patient(X))<=>quiet(X)))&
(![X]:((~funny(X)<~>~rich(X))=>(~wise(X)|~creative(X))))&
(![X]:((curious(X)|brave(X))<=>(generous(X)&~happy(X))))&
(![X]:((~brave(X)<~>generous(X))=>(rich(X)|calm(X))))&
(![X]:(wise(X)<=>(~creative(X)|~rich(X))))&
(((~quiet(alice)|~wise(alice)))=>((~tall(fred)<~>~humble(fred))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:((~creative(X)&~rich(X))=>(happy(X)<~>~old(X))))&
(![X]:((~humble(X)<~>brave(X))=>creative(X)))&
(((happy(lucy)<~>curious(lucy)))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:((rich(X)&generous(X))<=>(generous(X)<~>quiet(X))))&
(((brave(paul)<~>~quiet(paul)))<=>((rich(alice)<~>strong(alice))))&
(((tall(alice)<~>~wise(alice)))=>((~generous(paul)|~humble(paul))))&
(?[X]:((patient(X)|creative(X))))&
(funny(alice))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~brave(X)&rich(X))))&
((humble(paul)|patient(paul)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>~curious(X)))) | ~patient(alice) | [] | null | 0 |
Everyone who is brave or not humble is either calm or brave and vice versa.
Everyone who is both funny and happy is not wise or tall and vice versa.
Everyone who is happy or not quiet is not rich.
Everyone who is either not brave or creative is either calm or curious and vice versa.
If someone is either not brave or calm then lucy is either generous or not calm.
If someone is not kind then paul is not tall or brave and vice versa.
If someone is not curious then someone is not calm.
If someone is either not curious or generous then susan is either not rich or not brave.
If lucy is not quiet then mary is either not strong or wise and vice versa.
If mary is either quiet or rich then someone is not calm or not humble and vice versa.
If lucy is either brave or not creative then lucy is both not wise and tall.
If someone is both old and not tall then fred is not strong and vice versa.
Everyone who is either not brave or not humble is both not strong and not calm and vice versa.
Everyone who is not quiet is either strong or old.
Everyone who is either old or not humble is not creative or not tall.
Everyone who is not brave is either creative or not strong and vice versa.
Someone is generous.
Susan is funny or not creative.
Fred is both happy and not calm.
Lucy is either strong or not humble.
Alice is generous or not happy.
Someone is kind.
Susan is not kind.
Someone is not brave. | Lucy is brave. | neutral | (![X]:((brave(X)|~humble(X))<=>(calm(X)<~>brave(X))))&
(![X]:((funny(X)&happy(X))<=>(~wise(X)|tall(X))))&
(![X]:((happy(X)|~quiet(X))=>~rich(X)))&
(![X]:((~brave(X)<~>creative(X))<=>(calm(X)<~>curious(X))))&
((?[X]:((~brave(X)<~>calm(X))))=>((generous(lucy)<~>~calm(lucy))))&
((?[X]:(~kind(X)))<=>((~tall(paul)|brave(paul))))&
((?[X]:(~curious(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~curious(X)<~>generous(X))))=>((~rich(susan)<~>~brave(susan))))&
((~quiet(lucy))<=>((~strong(mary)<~>wise(mary))))&
(((quiet(mary)<~>rich(mary)))<=>(?[X]:((~calm(X)|~humble(X)))))&
(((brave(lucy)<~>~creative(lucy)))=>((~wise(lucy)&tall(lucy))))&
((?[X]:((old(X)&~tall(X))))<=>(~strong(fred)))&
(![X]:((~brave(X)<~>~humble(X))<=>(~strong(X)&~calm(X))))&
(![X]:(~quiet(X)=>(strong(X)<~>old(X))))&
(![X]:((old(X)<~>~humble(X))=>(~creative(X)|~tall(X))))&
(![X]:(~brave(X)<=>(creative(X)<~>~strong(X))))&
(?[X]:(generous(X)))&
((funny(susan)|~creative(susan)))&
((happy(fred)&~calm(fred)))&
((strong(lucy)<~>~humble(lucy)))&
((generous(alice)|~happy(alice)))&
(?[X]:(kind(X)))&
(~kind(susan))&
(?[X]:(~brave(X))) | brave(lucy) | [] | null | 0 |
Everyone who is brave or calm is not patient or not old and vice versa. Everyone who is either not strong or not creative is not brave and vice versa. Everyone who is both not rich and not tall is either happy or brave. If someone is both not humble and calm then someone is either not strong or not brave and vice versa. If someone is both funny and not patient then someone is both not calm and brave. Everyone who is either not patient or not tall is either strong or not patient and vice versa. If lucy is not quiet or wise then someone is either not rich or not tall and vice versa. Everyone who is curious is either not wise or not curious and vice versa. If someone is tall or calm then someone is calm. Everyone who is not tall or not generous is either rich or not patient and vice versa. If john is either not quiet or rich then susan is funny and vice versa. If someone is not tall or rich then someone is wise. If someone is not generous or calm then alice is both not strong and patient. Everyone who is not wise is both not happy and not humble. If someone is either patient or calm then someone is either happy or brave and vice versa. Everyone who is either not curious or not rich is not humble or not brave. Someone is not happy. John is either not calm or not humble. Paul is either not creative or not wise. Paul is quiet. John is not generous or not brave. Paul is both not strong and not funny. Lucy is both calm and curious. | Alice is not brave. | neutral | (![X]:((brave(X)|calm(X))<=>(~patient(X)|~old(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((~rich(X)&~tall(X))=>(happy(X)<~>brave(X))))&
((?[X]:((~humble(X)&calm(X))))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(strong(X)<~>~patient(X))))&
(((~quiet(lucy)|wise(lucy)))<=>(?[X]:((~rich(X)<~>~tall(X)))))&
(![X]:(curious(X)<=>(~wise(X)<~>~curious(X))))&
((?[X]:((tall(X)|calm(X))))=>(?[X]:(calm(X))))&
(![X]:((~tall(X)|~generous(X))<=>(rich(X)<~>~patient(X))))&
(((~quiet(john)<~>rich(john)))<=>(funny(susan)))&
((?[X]:((~tall(X)|rich(X))))=>(?[X]:(wise(X))))&
((?[X]:((~generous(X)|calm(X))))=>((~strong(alice)&patient(alice))))&
(![X]:(~wise(X)=>(~happy(X)&~humble(X))))&
((?[X]:((patient(X)<~>calm(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~curious(X)<~>~rich(X))=>(~humble(X)|~brave(X))))&
(?[X]:(~happy(X)))&
((~calm(john)<~>~humble(john)))&
((~creative(paul)<~>~wise(paul)))&
(quiet(paul))&
((~generous(john)|~brave(john)))&
((~strong(paul)&~funny(paul)))&
((calm(lucy)&curious(lucy))) | ~brave(alice) | [] | null | 0 |
Everyone who is humble or not creative is either not calm or not rich.
Everyone who is either patient or not creative is both not tall and not kind.
If alice is either humble or not old then paul is both not quiet and funny.
Everyone who is either curious or old is both not kind and brave and vice versa.
If mary is either funny or strong then someone is both humble and not wise.
If someone is not rich then fred is either not creative or tall and vice versa.
If someone is either quiet or not quiet then someone is not wise or creative.
If mary is both patient and wise then lucy is either not kind or not humble and vice versa.
Everyone who is both wise and patient is both calm and brave.
Everyone who is both old and not tall is both tall and curious and vice versa.
Everyone who is both brave and not wise is both old and patient.
If someone is both not creative and not quiet then someone is not happy.
Everyone who is wise or not funny is either tall or calm and vice versa.
Everyone who is both not quiet and happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
Susan is rich or creative.
Fred is both not generous and kind.
Fred is not happy or not rich.
Someone is funny or not rich.
Someone is wise or not calm.
Someone is either not humble or tall.
Someone is not strong or not happy. | Fred is patient. | contradiction | (![X]:((humble(X)|~creative(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((patient(X)<~>~creative(X))=>(~tall(X)&~kind(X))))&
(((humble(alice)<~>~old(alice)))=>((~quiet(paul)&funny(paul))))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)&brave(X))))&
(((funny(mary)<~>strong(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((?[X]:(~rich(X)))<=>((~creative(fred)<~>tall(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((rich(susan)|creative(susan)))&
((~generous(fred)&kind(fred)))&
((~happy(fred)|~rich(fred)))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((~humble(X)<~>tall(X))))&
(?[X]:((~strong(X)|~happy(X)))) | patient(fred) | [
"p1",
"p5",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7034578302669220103783585
% SZS output start Proof for 7034578302669220103783585
2. ! [X0] : ((patient(X0) <~> ~creative(X0)) => (~kind(X0) & ~tall(X0))) [input p1]
6. ? [X0] : ~rich(X0) <=> (~creative(fred) <~> tall(fred)) [input p5]
12. ? [X0] : (~quiet(X0) & ~creative(X0)) => ? [X0] : ~happy(X0) [input p11]
14. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~old(X0) | old(X0))) [input p13]
19. ~rich(fred) | ~happy(fred) [input p18]
24. patient(fred) [input hypothesis]
26. ? [X0] : (~quiet(X0) & ~creative(X0)) => ? [X1] : ~happy(X1) [rectify 12]
29. ! [X0] : ((~kind(X0) & ~tall(X0)) | (patient(X0) <=> ~creative(X0))) [ennf transformation 2]
37. ? [X1] : ~happy(X1) | ! [X0] : (quiet(X0) | creative(X0)) [ennf transformation 26]
41. ! [X0] : ((~kind(X0) & ~tall(X0)) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) [nnf transformation 29]
48. (? [X0] : ~rich(X0) | ((~creative(fred) | ~tall(fred)) & (tall(fred) | creative(fred)))) & (((~tall(fred) | creative(fred)) & (tall(fred) | ~creative(fred))) | ! [X0] : rich(X0)) [nnf transformation 6]
49. (? [X0] : ~rich(X0) | ((~creative(fred) | ~tall(fred)) & (tall(fred) | creative(fred)))) & (((~tall(fred) | creative(fred)) & (tall(fred) | ~creative(fred))) | ! [X1] : rich(X1)) [rectify 48]
50. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
51. (~rich(sK1) | ((~creative(fred) | ~tall(fred)) & (tall(fred) | creative(fred)))) & (((~tall(fred) | creative(fred)) & (tall(fred) | ~creative(fred))) | ! [X1] : rich(X1)) [skolemisation 49,50]
60. ? [X0] : ~happy(X0) | ! [X1] : (quiet(X1) | creative(X1)) [rectify 37]
61. ? [X0] : ~happy(X0) => ~happy(sK3) [choice axiom]
62. ~happy(sK3) | ! [X1] : (quiet(X1) | creative(X1)) [skolemisation 60,61]
65. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~happy(X0) | quiet(X0)))) [nnf transformation 14]
66. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~happy(X0) | quiet(X0))) [flattening 65]
83. ~tall(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 41]
101. tall(fred) | ~creative(fred) | rich(X1) [cnf transformation 51]
121. ~happy(sK3) | quiet(X1) | creative(X1) [cnf transformation 62]
129. ~quiet(X0) | ~old(X0) [cnf transformation 66]
130. ~quiet(X0) | old(X0) [cnf transformation 66]
131. happy(X0) | ~old(X0) [cnf transformation 66]
132. happy(X0) | old(X0) [cnf transformation 66]
142. ~rich(fred) | ~happy(fred) [cnf transformation 19]
148. patient(fred) [cnf transformation 24]
196. 9 <=> tall(fred) [avatar definition]
197. tall(fred) <- (9) [avatar component clause 196]
200. 10 <=> creative(fred) [avatar definition]
202. ~creative(fred) <- (~10) [avatar component clause 200]
210. 12 <=> ! [X1] : rich(X1) [avatar definition]
211. rich(X1) <- (12) [avatar component clause 210]
213. 12 | ~10 | 9 [avatar split clause 101,196,200,210]
227. 16 <=> ! [X1] : ~quiet(X1) [avatar definition]
228. ~quiet(X1) <- (16) [avatar component clause 227]
253. 21 <=> ! [X1] : (quiet(X1) | creative(X1)) [avatar definition]
254. quiet(X1) | creative(X1) <- (21) [avatar component clause 253]
256. 22 <=> happy(sK3) [avatar definition]
258. ~happy(sK3) <- (~22) [avatar component clause 256]
259. 21 | ~22 [avatar split clause 121,256,253]
260. happy(X0) [subsumption resolution 131,132]
261. ~quiet(X0) [subsumption resolution 129,130]
262. 16 [avatar split clause 261,227]
273. ~rich(fred) [subsumption resolution 142,260]
303. $false <- (~22) [subsumption resolution 258,260]
304. 22 [avatar contradiction clause 303]
305. creative(X1) <- (16, 21) [subsumption resolution 254,228]
306. $false <- (~10, 16, 21) [resolution 305,202]
307. 10 | ~16 | ~21 [avatar contradiction clause 306]
342. ~creative(fred) | ~patient(fred) <- (9) [resolution 83,197]
343. ~patient(fred) <- (9, 16, 21) [subsumption resolution 342,305]
344. $false <- (9, 16, 21) [subsumption resolution 343,148]
345. ~9 | ~16 | ~21 [avatar contradiction clause 344]
348. $false <- (12) [resolution 211,273]
353. ~12 [avatar contradiction clause 348]
354. $false [avatar sat refutation 213,259,262,304,307,345,353]
% SZS output end Proof for 7034578302669220103783585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or patient is both patient and not brave and vice versa.
If mary is either not creative or not generous then someone is both kind and patient.
Everyone who is funny or not old is both not rich and patient.
Everyone who is funny or not curious is patient or quiet and vice versa.
Everyone who is either not patient or happy is old and vice versa.
If someone is both not kind and not brave then someone is both not strong and not old.
If lucy is either not kind or not calm then someone is old or rich and vice versa.
Everyone who is either happy or generous is both calm and not happy.
If someone is both funny and not calm then someone is not calm and vice versa.
Everyone who is creative or humble is both brave and not old and vice versa.
Everyone who is either not funny or tall is either not tall or not humble and vice versa.
If someone is not kind then mary is either not kind or not generous and vice versa.
If lucy is kind then alice is wise or patient and vice versa.
Everyone who is not old is both not strong and not creative.
If someone is humble then susan is not calm.
If paul is creative then someone is curious.
Someone is either creative or strong.
Someone is not humble.
Lucy is not curious.
Lucy is funny or not happy.
John is not kind or funny.
Someone is not quiet.
Someone is not generous or generous. | Mary is patient. | entailment | (![X]:((wise(X)|patient(X))<=>(patient(X)&~brave(X))))&
(((~creative(mary)<~>~generous(mary)))=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((funny(X)|~old(X))=>(~rich(X)&patient(X))))&
(![X]:((funny(X)|~curious(X))<=>(patient(X)|quiet(X))))&
(![X]:((~patient(X)<~>happy(X))<=>old(X)))&
((?[X]:((~kind(X)&~brave(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(((~kind(lucy)<~>~calm(lucy)))<=>(?[X]:((old(X)|rich(X)))))&
(![X]:((happy(X)<~>generous(X))=>(calm(X)&~happy(X))))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)|humble(X))<=>(brave(X)&~old(X))))&
(![X]:((~funny(X)<~>tall(X))<=>(~tall(X)<~>~humble(X))))&
((?[X]:(~kind(X)))<=>((~kind(mary)<~>~generous(mary))))&
((kind(lucy))<=>((wise(alice)|patient(alice))))&
(![X]:(~old(X)=>(~strong(X)&~creative(X))))&
((?[X]:(humble(X)))=>(~calm(susan)))&
((creative(paul))=>(?[X]:(curious(X))))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:(~humble(X)))&
(~curious(lucy))&
((funny(lucy)|~happy(lucy)))&
((~kind(john)|funny(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)|generous(X)))) | patient(mary) | [
"p2",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1536579666054632521332356
% SZS output start Proof for 1536579666054632521332356
3. ! [X0] : ((~old(X0) | funny(X0)) => (patient(X0) & ~rich(X0))) [input p2]
10. ! [X0] : ((humble(X0) | creative(X0)) <=> (~old(X0) & brave(X0))) [input p9]
11. ! [X0] : ((~funny(X0) <~> tall(X0)) <=> (~tall(X0) <~> ~humble(X0))) [input p10]
24. ~patient(mary) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~rich(X0)) | (old(X0) & ~funny(X0))) [ennf transformation 3]
55. ! [X0] : (((humble(X0) | creative(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (~humble(X0) & ~creative(X0)))) [nnf transformation 10]
56. ! [X0] : ((humble(X0) | creative(X0) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | (~humble(X0) & ~creative(X0)))) [flattening 55]
57. ! [X0] : ((((~tall(X0) | funny(X0)) & (tall(X0) | ~funny(X0))) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ((~funny(X0) | ~tall(X0)) & (tall(X0) | funny(X0))))) [nnf transformation 11]
86. ~funny(X0) | patient(X0) [cnf transformation 28]
87. old(X0) | patient(X0) [cnf transformation 28]
114. ~humble(X0) | ~old(X0) [cnf transformation 56]
118. humble(X0) | tall(X0) | tall(X0) | funny(X0) [cnf transformation 57]
123. ~tall(X0) | funny(X0) | ~tall(X0) | humble(X0) [cnf transformation 57]
143. ~patient(mary) [cnf transformation 24]
145. humble(X0) | tall(X0) | funny(X0) [duplicate literal removal 118]
147. ~tall(X0) | funny(X0) | humble(X0) [duplicate literal removal 123]
231. humble(X0) | funny(X0) [subsumption resolution 145,147]
301. ~old(X0) | funny(X0) [resolution 231,114]
345. funny(X0) | patient(X0) [resolution 301,87]
347. patient(X0) [subsumption resolution 345,86]
351. $false [resolution 347,143]
% SZS output end Proof for 1536579666054632521332356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not happy is both generous and not generous and vice versa.
If john is both quiet and calm then alice is both curious and humble.
Everyone who is either not quiet or not calm is either rich or strong and vice versa.
Everyone who is not strong or not generous is not quiet and vice versa.
Everyone who is not patient or brave is happy or funny.
Everyone who is not rich or brave is either not calm or humble.
If someone is funny or not generous then susan is both brave and not wise.
If lucy is calm or not patient then someone is humble.
If someone is both rich and old then john is either not quiet or curious.
Everyone who is both quiet and not brave is either not rich or not happy and vice versa.
Everyone who is both not rich and strong is not rich or not brave and vice versa.
If someone is happy then paul is either not creative or happy.
Everyone who is creative or happy is not generous.
If someone is not tall then fred is both not funny and quiet and vice versa.
Everyone who is not generous or patient is not strong or quiet and vice versa.
Everyone who is both humble and not curious is either not curious or not brave.
Fred is not quiet or wise.
Someone is both brave and not curious.
Someone is not funny or wise.
Someone is strong or not quiet.
Paul is not kind or humble.
John is either not kind or calm.
Alice is patient or not humble. | Lucy is not calm. | entailment | (![X]:((brave(X)<~>~happy(X))<=>(generous(X)&~generous(X))))&
(((quiet(john)&calm(john)))=>((curious(alice)&humble(alice))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))&
(((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))&
(![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((~rich(X)&strong(X))<=>(~rich(X)|~brave(X))))&
((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))&
(![X]:((creative(X)|happy(X))=>~generous(X)))&
((?[X]:(~tall(X)))<=>((~funny(fred)&quiet(fred))))&
(![X]:((~generous(X)|patient(X))<=>(~strong(X)|quiet(X))))&
(![X]:((humble(X)&~curious(X))=>(~curious(X)<~>~brave(X))))&
((~quiet(fred)|wise(fred)))&
(?[X]:((brave(X)&~curious(X))))&
(?[X]:((~funny(X)|wise(X))))&
(?[X]:((strong(X)|~quiet(X))))&
((~kind(paul)|humble(paul)))&
((~kind(john)<~>calm(john)))&
((patient(alice)|~humble(alice))) | ~calm(lucy) | [
"p0",
"p2",
"p3",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5790450502131078488587001
% SZS output start Proof for 5790450502131078488587001
1. ! [X0] : ((brave(X0) <~> ~happy(X0)) <=> (~generous(X0) & generous(X0))) [input p0]
3. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (rich(X0) <~> strong(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p3]
10. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (~rich(X0) <~> ~happy(X0))) [input p9]
11. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (~brave(X0) | ~rich(X0))) [input p10]
13. ! [X0] : ((happy(X0) | creative(X0)) => ~generous(X0)) [input p12]
15. ! [X0] : ((patient(X0) | ~generous(X0)) <=> (quiet(X0) | ~strong(X0))) [input p14]
24. calm(lucy) [input hypothesis]
34. ! [X0] : (~generous(X0) | (~happy(X0) & ~creative(X0))) [ennf transformation 13]
37. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [nnf transformation 1]
38. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [flattening 37]
39. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 3]
40. ! [X0] : (((~generous(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) & strong(X0)))) [nnf transformation 4]
41. ! [X0] : ((~generous(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (generous(X0) & strong(X0)))) [flattening 40]
45. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 10]
46. ! [X0] : (((~brave(X0) & quiet(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) & (((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | brave(X0) | ~quiet(X0))) [flattening 45]
47. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~strong(X0) | rich(X0)))) [nnf transformation 11]
48. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~strong(X0) | rich(X0))) [flattening 47]
55. ! [X0] : (((patient(X0) | ~generous(X0)) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | (~patient(X0) & generous(X0)))) [nnf transformation 15]
56. ! [X0] : ((patient(X0) | ~generous(X0) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | (~patient(X0) & generous(X0)))) [flattening 55]
65. generous(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 38]
66. generous(X0) | brave(X0) | happy(X0) [cnf transformation 38]
67. ~generous(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 38]
68. ~generous(X0) | brave(X0) | happy(X0) [cnf transformation 38]
78. ~strong(X0) | ~quiet(X0) | rich(X0) | ~calm(X0) [cnf transformation 39]
81. ~quiet(X0) | strong(X0) [cnf transformation 41]
82. ~quiet(X0) | generous(X0) [cnf transformation 41]
83. ~strong(X0) | ~generous(X0) | quiet(X0) [cnf transformation 41]
101. ~brave(X0) | ~rich(X0) | happy(X0) [cnf transformation 46]
105. strong(X0) | rich(X0) [cnf transformation 48]
106. strong(X0) | brave(X0) [cnf transformation 48]
110. ~generous(X0) | ~happy(X0) [cnf transformation 34]
114. quiet(X0) | ~strong(X0) | generous(X0) [cnf transformation 56]
129. calm(lucy) [cnf transformation 24]
131. happy(X0) | brave(X0) [subsumption resolution 66,68]
132. ~happy(X0) | ~brave(X0) [subsumption resolution 65,67]
153. 5 <=> ! [X0] : generous(X0) [avatar definition]
154. generous(X0) <- (5) [avatar component clause 153]
180. 11 <=> calm(lucy) [avatar definition]
181. calm(lucy) <- (11) [avatar component clause 180]
184. ~rich(X0) | happy(X0) [subsumption resolution 101,131]
187. 12 <=> ! [X0] : ~happy(X0) [avatar definition]
188. ~happy(X0) <- (12) [avatar component clause 187]
218. ~strong(X0) | quiet(X0) [subsumption resolution 114,83]
253. 11 [avatar split clause 129,180]
267. quiet(X0) | brave(X0) [resolution 218,106]
268. rich(X1) | quiet(X1) [resolution 218,105]
271. generous(X1) | brave(X1) [resolution 267,82]
275. quiet(X0) | happy(X0) [resolution 268,184]
281. brave(X2) | ~happy(X2) [resolution 271,110]
283. ~happy(X2) [subsumption resolution 281,132]
284. 12 [avatar split clause 283,187]
291. 26 <=> rich(lucy) [avatar definition]
292. ~rich(lucy) <- (~26) [avatar component clause 291]
293. rich(lucy) <- (26) [avatar component clause 291]
299. happy(lucy) <- (26) [resolution 293,184]
301. $false <- (12, 26) [subsumption resolution 299,188]
302. ~12 | ~26 [avatar contradiction clause 301]
373. happy(X2) | generous(X2) [resolution 275,82]
374. happy(X3) | strong(X3) [resolution 275,81]
378. generous(X2) <- (12) [subsumption resolution 373,188]
379. 5 | ~12 [avatar split clause 378,187,153]
380. strong(X3) <- (12) [subsumption resolution 374,188]
393. ~generous(X2) | quiet(X2) <- (12) [resolution 380,83]
396. quiet(X2) <- (5, 12) [subsumption resolution 393,154]
397. ~quiet(X0) | rich(X0) | ~calm(X0) <- (12) [resolution 78,380]
403. ~calm(X0) | rich(X0) <- (5, 12) [subsumption resolution 397,396]
418. rich(lucy) <- (5, 11, 12) [resolution 403,181]
420. $false <- (5, 11, 12, ~26) [subsumption resolution 418,292]
421. ~5 | ~11 | ~12 | 26 [avatar contradiction clause 420]
424. $false [avatar sat refutation 253,284,302,379,421]
% SZS output end Proof for 5790450502131078488587001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not happy is not tall or kind.
Everyone who is either kind or not quiet is not brave or happy.
Everyone who is either not curious or happy is either humble or not happy.
If someone is tall or curious then alice is either not quiet or calm.
Everyone who is both patient and not happy is either kind or humble and vice versa.
Everyone who is both not funny and not strong is not kind and vice versa.
Everyone who is both not old and not kind is generous or not wise and vice versa.
If someone is not calm or not kind then paul is both humble and generous.
If someone is either funny or not tall then paul is strong.
If someone is old then alice is either not funny or wise and vice versa.
Everyone who is both not curious and not brave is calm or not quiet.
If someone is calm then susan is happy or tall and vice versa.
Everyone who is curious is both not strong and tall.
Everyone who is rich is both wise and strong and vice versa.
Everyone who is creative is both not wise and strong and vice versa.
If someone is wise or quiet then fred is not humble or not generous and vice versa.
Someone is not generous.
Someone is not old.
Someone is either generous or tall.
Fred is not brave.
John is patient.
Susan is either not funny or not generous. | Fred is not creative. | entailment | (![X]:((~generous(X)|~happy(X))=>(~tall(X)|kind(X))))&
(![X]:((kind(X)<~>~quiet(X))=>(~brave(X)|happy(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((patient(X)&~happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(![X]:(creative(X)<=>(~wise(X)&strong(X))))&
((?[X]:((wise(X)|quiet(X))))<=>((~humble(fred)|~generous(fred))))&
(?[X]:(~generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>tall(X))))&
(~brave(fred))&
(patient(john))&
((~funny(susan)<~>~generous(susan))) | ~creative(fred) | [
"p5",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 852954294877901757058862
% SZS output start Proof for 852954294877901757058862
6. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> ~kind(X0)) [input p5]
7. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p6]
15. ! [X0] : (creative(X0) <=> (strong(X0) & ~wise(X0))) [input p14]
23. creative(fred) [input hypothesis]
24. ! [X0] : (creative(X0) => (strong(X0) & ~wise(X0))) [unused predicate definition removal 15]
36. ! [X0] : ((strong(X0) & ~wise(X0)) | ~creative(X0)) [ennf transformation 24]
42. ! [X0] : (((~strong(X0) & ~funny(X0)) | kind(X0)) & (~kind(X0) | (strong(X0) | funny(X0)))) [nnf transformation 6]
43. ! [X0] : (((~strong(X0) & ~funny(X0)) | kind(X0)) & (~kind(X0) | strong(X0) | funny(X0))) [flattening 42]
44. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 7]
45. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 44]
89. ~strong(X0) | kind(X0) [cnf transformation 43]
94. ~kind(X0) | wise(X0) [cnf transformation 45]
111. ~creative(X0) | ~wise(X0) [cnf transformation 36]
112. ~creative(X0) | strong(X0) [cnf transformation 36]
125. creative(fred) [cnf transformation 23]
280. ~wise(fred) [resolution 111,125]
281. strong(fred) [resolution 112,125]
283. kind(fred) [resolution 281,89]
291. wise(fred) [resolution 283,94]
293. $false [subsumption resolution 291,280]
% SZS output end Proof for 852954294877901757058862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not old or not quiet.
If someone is either not patient or not generous then someone is rich.
If someone is creative then someone is tall and vice versa.
Everyone who is both tall and wise is strong or not happy.
Everyone who is both patient and not curious is both not strong and not creative and vice versa.
Everyone who is humble is either funny or brave.
Everyone who is either not curious or calm is happy.
Everyone who is quiet or not calm is either not tall or not wise.
Everyone who is old or humble is not funny and vice versa.
Everyone who is not happy or curious is either not curious or not calm.
If someone is not tall then alice is either not brave or not strong and vice versa.
Everyone who is both strong and creative is wise or not humble.
Everyone who is either not quiet or not kind is both rich and not wise and vice versa.
If susan is both not funny and calm then susan is humble or not strong.
If someone is either old or not humble then someone is both not calm and happy and vice versa.
Everyone who is not rich or wise is not rich and vice versa.
Someone is kind or not curious.
Lucy is funny or tall.
Fred is not generous.
Fred is both calm and rich.
Lucy is not old or humble.
Susan is both kind and not wise.
Someone is kind or not brave.
Someone is curious. | Susan is not creative. | neutral | (![X]:((old(X)|curious(X))=>(~old(X)|~quiet(X))))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(rich(X))))&
((?[X]:(creative(X)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)&wise(X))=>(strong(X)|~happy(X))))&
(![X]:((patient(X)&~curious(X))<=>(~strong(X)&~creative(X))))&
(![X]:(humble(X)=>(funny(X)<~>brave(X))))&
(![X]:((~curious(X)<~>calm(X))=>happy(X)))&
(![X]:((quiet(X)|~calm(X))=>(~tall(X)<~>~wise(X))))&
(![X]:((old(X)|humble(X))<=>~funny(X)))&
(![X]:((~happy(X)|curious(X))=>(~curious(X)<~>~calm(X))))&
((?[X]:(~tall(X)))<=>((~brave(alice)<~>~strong(alice))))&
(![X]:((strong(X)&creative(X))=>(wise(X)|~humble(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(rich(X)&~wise(X))))&
(((~funny(susan)&calm(susan)))=>((humble(susan)|~strong(susan))))&
((?[X]:((old(X)<~>~humble(X))))<=>(?[X]:((~calm(X)&happy(X)))))&
(![X]:((~rich(X)|wise(X))<=>~rich(X)))&
(?[X]:((kind(X)|~curious(X))))&
((funny(lucy)|tall(lucy)))&
(~generous(fred))&
((calm(fred)&rich(fred)))&
((~old(lucy)|humble(lucy)))&
((kind(susan)&~wise(susan)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:(curious(X))) | ~creative(susan) | [] | null | 0 |
If someone is both wise and rich then susan is not calm.
Everyone who is either generous or not wise is both curious and not generous.
Everyone who is creative or not patient is humble or tall and vice versa.
If someone is either not quiet or quiet then someone is not creative and vice versa.
Everyone who is not strong is either not rich or kind and vice versa.
If someone is not curious then lucy is both not patient and not brave and vice versa.
Everyone who is both patient and not calm is not patient.
If someone is both quiet and calm then someone is brave or old.
Everyone who is calm is either generous or happy and vice versa.
If someone is either curious or not funny then lucy is not kind or not rich and vice versa.
If fred is either not patient or not wise then paul is either funny or old.
If someone is both humble and brave then paul is either not tall or quiet and vice versa.
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.
Someone is humble.
Someone is both brave and not old.
Someone is kind or not strong.
Someone is either tall or not rich.
Someone is brave or tall.
Fred is both not rich and happy.
Lucy is old or quiet.
Someone is patient. | Fred is not strong. | contradiction | ((?[X]:((wise(X)&rich(X))))=>(~calm(susan)))&
(![X]:((generous(X)<~>~wise(X))=>(curious(X)&~generous(X))))&
(![X]:((creative(X)|~patient(X))<=>(humble(X)|tall(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)<=>(~rich(X)<~>kind(X))))&
((?[X]:(~curious(X)))<=>((~patient(lucy)&~brave(lucy))))&
(![X]:((patient(X)&~calm(X))=>~patient(X)))&
((?[X]:((quiet(X)&calm(X))))=>(?[X]:((brave(X)|old(X)))))&
(![X]:(calm(X)<=>(generous(X)<~>happy(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~kind(lucy)|~rich(lucy))))&
(((~patient(fred)<~>~wise(fred)))=>((funny(paul)<~>old(paul))))&
((?[X]:((humble(X)&brave(X))))<=>((~tall(paul)<~>quiet(paul))))&
(![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]:(humble(X)))&
(?[X]:((brave(X)&~old(X))))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:((tall(X)<~>~rich(X))))&
(?[X]:((brave(X)|tall(X))))&
((~rich(fred)&happy(fred)))&
((old(lucy)|quiet(lucy)))&
(?[X]:(patient(X))) | ~strong(fred) | [
"p4",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 569742259945880011382018
% SZS output start Proof for 569742259945880011382018
5. ! [X0] : (~strong(X0) <=> (~rich(X0) <~> kind(X0))) [input p4]
13. ! [X0] : ((~happy(X0) & quiet(X0)) <=> (~kind(X0) | rich(X0))) [input p12]
22. happy(fred) & ~rich(fred) [input p21]
25. ~strong(fred) [input hypothesis]
28. ! [X0] : (~strong(X0) => (~rich(X0) <~> kind(X0))) [unused predicate definition removal 5]
31. ! [X0] : ((~rich(X0) <~> kind(X0)) | strong(X0)) [ennf transformation 28]
46. ! [X0] : (((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | strong(X0)) [nnf transformation 31]
66. ! [X0] : (((~happy(X0) & quiet(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (happy(X0) | ~quiet(X0)))) [nnf transformation 13]
67. ! [X0] : (((~happy(X0) & quiet(X0)) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | happy(X0) | ~quiet(X0))) [flattening 66]
101. ~kind(X0) | rich(X0) | strong(X0) [cnf transformation 46]
131. ~happy(X0) | kind(X0) [cnf transformation 67]
150. ~rich(fred) [cnf transformation 22]
151. happy(fred) [cnf transformation 22]
154. ~strong(fred) [cnf transformation 25]
290. 30 <=> rich(fred) [avatar definition]
292. ~rich(fred) <- (~30) [avatar component clause 290]
335. ~30 [avatar split clause 150,290]
348. kind(fred) [resolution 131,151]
421. rich(fred) | strong(fred) [resolution 101,348]
423. strong(fred) <- (~30) [subsumption resolution 421,292]
424. $false <- (~30) [subsumption resolution 423,154]
425. 30 [avatar contradiction clause 424]
426. $false [avatar sat refutation 335,425]
% SZS output end Proof for 569742259945880011382018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not calm is not curious.
Everyone who is both not strong and not generous is both humble and patient.
Everyone who is both not strong and not old is either not strong or not old.
Everyone who is quiet or curious is either not kind or old.
Everyone who is not brave is funny or brave.
Everyone who is not patient or patient is not rich.
Everyone who is humble is either kind or not humble and vice versa.
Everyone who is not humble or not tall is both not tall and not creative.
If fred is not patient or tall then someone is both not curious and generous and vice versa.
Everyone who is not old or not calm is curious.
Everyone who is either quiet or humble is rich.
Everyone who is not tall or kind is creative or curious and vice versa.
Everyone who is funny or not generous is not kind or wise and vice versa.
Everyone who is not patient or not curious is either creative or strong and vice versa.
Everyone who is happy or old is either not calm or tall and vice versa.
Everyone who is both not patient and quiet is not kind or rich.
Someone is either not brave or kind.
Lucy is either wise or not brave.
Someone is both tall and wise.
Someone is either tall or not funny.
Someone is curious.
Lucy is both humble and patient. | Fred is not rich. | entailment | (![X]:((generous(X)|~calm(X))=>~curious(X)))&
(![X]:((~strong(X)&~generous(X))=>(humble(X)&patient(X))))&
(![X]:((~strong(X)&~old(X))=>(~strong(X)<~>~old(X))))&
(![X]:((quiet(X)|curious(X))=>(~kind(X)<~>old(X))))&
(![X]:(~brave(X)=>(funny(X)|brave(X))))&
(![X]:((~patient(X)|patient(X))=>~rich(X)))&
(![X]:(humble(X)<=>(kind(X)<~>~humble(X))))&
(![X]:((~humble(X)|~tall(X))=>(~tall(X)&~creative(X))))&
(((~patient(fred)|tall(fred)))<=>(?[X]:((~curious(X)&generous(X)))))&
(![X]:((~old(X)|~calm(X))=>curious(X)))&
(![X]:((quiet(X)<~>humble(X))=>rich(X)))&
(![X]:((~tall(X)|kind(X))<=>(creative(X)|curious(X))))&
(![X]:((funny(X)|~generous(X))<=>(~kind(X)|wise(X))))&
(![X]:((~patient(X)|~curious(X))<=>(creative(X)<~>strong(X))))&
(![X]:((happy(X)|old(X))<=>(~calm(X)<~>tall(X))))&
(![X]:((~patient(X)&quiet(X))=>(~kind(X)|rich(X))))&
(?[X]:((~brave(X)<~>kind(X))))&
((wise(lucy)<~>~brave(lucy)))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:(curious(X)))&
((humble(lucy)&patient(lucy))) | ~rich(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8209227216576642007523521
% SZS output start Proof for 8209227216576642007523521
6. ! [X0] : ((patient(X0) | ~patient(X0)) => ~rich(X0)) [input p5]
23. rich(fred) [input hypothesis]
32. ! [X0] : (~rich(X0) | (~patient(X0) & patient(X0))) [ennf transformation 6]
77. ~rich(X0) | patient(X0) [cnf transformation 32]
78. ~rich(X0) | ~patient(X0) [cnf transformation 32]
128. rich(fred) [cnf transformation 23]
133. ~rich(X0) [subsumption resolution 77,78]
194. $false [subsumption resolution 128,133]
% SZS output end Proof for 8209227216576642007523521
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and not wise then paul is kind and vice versa.
If someone is both generous and tall then susan is old or not humble and vice versa.
If paul is not patient then mary is quiet or calm and vice versa.
If someone is patient or curious then lucy is both not calm and wise.
Everyone who is both generous and funny is patient or not brave and vice versa.
Everyone who is both calm and kind is not funny.
If mary is both rich and happy then mary is either not kind or not strong and vice versa.
If someone is both creative and not rich then someone is not happy.
Everyone who is strong or happy is not humble or rich.
Everyone who is generous or not humble is either not curious or not creative.
Everyone who is not creative or brave is not kind and vice versa.
Everyone who is either old or curious is either not quiet or happy and vice versa.
If someone is both tall and not generous then someone is brave or not old and vice versa.
If someone is curious then lucy is either not happy or patient and vice versa.
If susan is both patient and not rich then susan is kind and vice versa.
Everyone who is not quiet or not wise is rich or funny and vice versa.
Fred is kind or brave.
Susan is both not rich and quiet.
Alice is not wise.
Fred is either not generous or rich.
John is kind.
Someone is either not funny or not rich.
Lucy is not happy. | Lucy is not creative. | neutral | ((?[X]:((wise(X)&~wise(X))))<=>(kind(paul)))&
((?[X]:((generous(X)&tall(X))))<=>((old(susan)|~humble(susan))))&
((~patient(paul))<=>((quiet(mary)|calm(mary))))&
((?[X]:((patient(X)|curious(X))))=>((~calm(lucy)&wise(lucy))))&
(![X]:((generous(X)&funny(X))<=>(patient(X)|~brave(X))))&
(![X]:((calm(X)&kind(X))=>~funny(X)))&
(((rich(mary)&happy(mary)))<=>((~kind(mary)<~>~strong(mary))))&
((?[X]:((creative(X)&~rich(X))))=>(?[X]:(~happy(X))))&
(![X]:((strong(X)|happy(X))=>(~humble(X)|rich(X))))&
(![X]:((generous(X)|~humble(X))=>(~curious(X)<~>~creative(X))))&
(![X]:((~creative(X)|brave(X))<=>~kind(X)))&
(![X]:((old(X)<~>curious(X))<=>(~quiet(X)<~>happy(X))))&
((?[X]:((tall(X)&~generous(X))))<=>(?[X]:((brave(X)|~old(X)))))&
((?[X]:(curious(X)))<=>((~happy(lucy)<~>patient(lucy))))&
(((patient(susan)&~rich(susan)))<=>(kind(susan)))&
(![X]:((~quiet(X)|~wise(X))<=>(rich(X)|funny(X))))&
((kind(fred)|brave(fred)))&
((~rich(susan)&quiet(susan)))&
(~wise(alice))&
((~generous(fred)<~>rich(fred)))&
(kind(john))&
(?[X]:((~funny(X)<~>~rich(X))))&
(~happy(lucy)) | ~creative(lucy) | [] | null | 0 |
Everyone who is not brave or not quiet is both not calm and rich and vice versa.
If john is not funny or not old then john is creative or not old.
If alice is quiet or not tall then lucy is not quiet or patient.
Everyone who is either wise or not humble is not brave or not rich.
Everyone who is either creative or curious is both not rich and kind and vice versa.
Everyone who is both not quiet and funny is either not old or rich and vice versa.
If paul is either strong or not creative then lucy is not kind or not tall and vice versa.
If someone is not patient then someone is not tall.
If alice is not patient then someone is either generous or creative.
If someone is old or not curious then susan is tall or kind.
Everyone who is patient or humble is not calm or wise.
Everyone who is both not old and happy is either not patient or not quiet and vice versa.
If someone is either creative or strong then susan is not curious or not humble.
If someone is not rich then paul is not quiet.
If someone is not happy then someone is both not tall and happy and vice versa.
Everyone who is quiet is both creative and wise.
Someone is strong.
Someone is not old.
Paul is either calm or wise.
John is happy or brave.
John is both not humble and calm.
John is either not patient or humble.
Someone is brave or quiet.
Mary is not old. | John is not rich. | contradiction | (![X]:((~brave(X)|~quiet(X))<=>(~calm(X)&rich(X))))&
(((~funny(john)|~old(john)))=>((creative(john)|~old(john))))&
(((quiet(alice)|~tall(alice)))=>((~quiet(lucy)|patient(lucy))))&
(![X]:((wise(X)<~>~humble(X))=>(~brave(X)|~rich(X))))&
(![X]:((creative(X)<~>curious(X))<=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)&funny(X))<=>(~old(X)<~>rich(X))))&
(((strong(paul)<~>~creative(paul)))<=>((~kind(lucy)|~tall(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:(~tall(X))))&
((~patient(alice))=>(?[X]:((generous(X)<~>creative(X)))))&
((?[X]:((old(X)|~curious(X))))=>((tall(susan)|kind(susan))))&
(![X]:((patient(X)|humble(X))=>(~calm(X)|wise(X))))&
(![X]:((~old(X)&happy(X))<=>(~patient(X)<~>~quiet(X))))&
((?[X]:((creative(X)<~>strong(X))))=>((~curious(susan)|~humble(susan))))&
((?[X]:(~rich(X)))=>(~quiet(paul)))&
((?[X]:(~happy(X)))<=>(?[X]:((~tall(X)&happy(X)))))&
(![X]:(quiet(X)=>(creative(X)&wise(X))))&
(?[X]:(strong(X)))&
(?[X]:(~old(X)))&
((calm(paul)<~>wise(paul)))&
((happy(john)|brave(john)))&
((~humble(john)&calm(john)))&
((~patient(john)<~>humble(john)))&
(?[X]:((brave(X)|quiet(X))))&
(~old(mary)) | ~rich(john) | [
"p0",
"p5",
"p11",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8548143807974874297271824
% SZS output start Proof for 8548143807974874297271824
1. ! [X0] : ((~quiet(X0) | ~brave(X0)) <=> (rich(X0) & ~calm(X0))) [input p0]
6. ! [X0] : ((funny(X0) & ~quiet(X0)) <=> (~old(X0) <~> rich(X0))) [input p5]
12. ! [X0] : ((happy(X0) & ~old(X0)) <=> (~patient(X0) <~> ~quiet(X0))) [input p11]
21. calm(john) & ~humble(john) [input p20]
22. ~patient(john) <~> humble(john) [input p21]
25. ~rich(john) [input hypothesis]
44. ! [X0] : (((~quiet(X0) | ~brave(X0)) | (~rich(X0) | calm(X0))) & ((rich(X0) & ~calm(X0)) | (quiet(X0) & brave(X0)))) [nnf transformation 1]
45. ! [X0] : ((~quiet(X0) | ~brave(X0) | ~rich(X0) | calm(X0)) & ((rich(X0) & ~calm(X0)) | (quiet(X0) & brave(X0)))) [flattening 44]
49. ! [X0] : (((funny(X0) & ~quiet(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) & (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (~funny(X0) | quiet(X0)))) [nnf transformation 6]
50. ! [X0] : (((funny(X0) & ~quiet(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) & (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | ~funny(X0) | quiet(X0))) [flattening 49]
59. ! [X0] : (((happy(X0) & ~old(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | (~happy(X0) | old(X0)))) [nnf transformation 12]
60. ! [X0] : (((happy(X0) & ~old(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ~happy(X0) | old(X0))) [flattening 59]
72. (~humble(john) | patient(john)) & (humble(john) | ~patient(john)) [nnf transformation 22]
76. ~calm(X0) | quiet(X0) [cnf transformation 45]
78. rich(X0) | quiet(X0) [cnf transformation 45]
94. ~quiet(X0) | rich(X0) | old(X0) [cnf transformation 50]
113. ~old(X0) | ~quiet(X0) | patient(X0) [cnf transformation 60]
130. ~humble(john) [cnf transformation 21]
131. calm(john) [cnf transformation 21]
132. humble(john) | ~patient(john) [cnf transformation 72]
136. ~rich(john) [cnf transformation 25]
146. 3 <=> old(john) [avatar definition]
147. old(john) <- (3) [avatar component clause 146]
148. ~old(john) <- (~3) [avatar component clause 146]
168. old(X0) | rich(X0) [subsumption resolution 94,78]
294. ~patient(john) [subsumption resolution 132,130]
314. quiet(john) [resolution 76,131]
328. rich(john) <- (~3) [resolution 168,148]
329. $false <- (~3) [subsumption resolution 328,136]
330. 3 [avatar contradiction clause 329]
365. ~quiet(john) | patient(john) <- (3) [resolution 113,147]
368. patient(john) <- (3) [subsumption resolution 365,314]
369. $false <- (3) [subsumption resolution 368,294]
370. ~3 [avatar contradiction clause 369]
371. $false [avatar sat refutation 330,370]
% SZS output end Proof for 8548143807974874297271824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is quiet or not generous then someone is brave and vice versa.
If fred is both funny and wise then someone is both not wise and creative.
Everyone who is not humble or not patient is quiet or not strong.
Everyone who is not curious is either not tall or happy.
If someone is not tall then john is not funny or not generous.
If someone is either quiet or funny then someone is both not strong and brave.
Everyone who is either curious or kind is either not calm or funny.
If someone is either not old or old then paul is not kind or tall and vice versa.
Everyone who is curious or not quiet is both not humble and curious and vice versa.
If fred is both strong and brave then someone is tall.
If lucy is either not kind or tall then alice is calm.
If someone is not kind or quiet then mary is not curious or not calm.
Everyone who is either not old or not strong is both curious and not kind.
If john is both not curious and calm then fred is either curious or strong and vice versa.
If someone is not generous then alice is kind or funny.
If someone is funny then someone is rich.
Mary is not calm.
Someone is either curious or not strong.
Alice is both strong and not curious.
Someone is quiet or strong.
Someone is either generous or kind.
Mary is humble.
Fred is both not funny and patient.
Someone is not brave or funny. | Alice is strong. | entailment | (((quiet(paul)|~generous(paul)))<=>(?[X]:(brave(X))))&
(((funny(fred)&wise(fred)))=>(?[X]:((~wise(X)&creative(X)))))&
(![X]:((~humble(X)|~patient(X))=>(quiet(X)|~strong(X))))&
(![X]:(~curious(X)=>(~tall(X)<~>happy(X))))&
((?[X]:(~tall(X)))=>((~funny(john)|~generous(john))))&
((?[X]:((quiet(X)<~>funny(X))))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((curious(X)<~>kind(X))=>(~calm(X)<~>funny(X))))&
((?[X]:((~old(X)<~>old(X))))<=>((~kind(paul)|tall(paul))))&
(![X]:((curious(X)|~quiet(X))<=>(~humble(X)&curious(X))))&
(((strong(fred)&brave(fred)))=>(?[X]:(tall(X))))&
(((~kind(lucy)<~>tall(lucy)))=>(calm(alice)))&
((?[X]:((~kind(X)|quiet(X))))=>((~curious(mary)|~calm(mary))))&
(![X]:((~old(X)<~>~strong(X))=>(curious(X)&~kind(X))))&
(((~curious(john)&calm(john)))<=>((curious(fred)<~>strong(fred))))&
((?[X]:(~generous(X)))=>((kind(alice)|funny(alice))))&
((?[X]:(funny(X)))=>(?[X]:(rich(X))))&
(~calm(mary))&
(?[X]:((curious(X)<~>~strong(X))))&
((strong(alice)&~curious(alice)))&
(?[X]:((quiet(X)|strong(X))))&
(?[X]:((generous(X)<~>kind(X))))&
(humble(mary))&
((~funny(fred)&patient(fred)))&
(?[X]:((~brave(X)|funny(X)))) | strong(alice) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6579654943335189982476536
% SZS output start Proof for 6579654943335189982476536
19. ~curious(alice) & strong(alice) [input p18]
25. ~strong(alice) [input hypothesis]
127. strong(alice) [cnf transformation 19]
135. ~strong(alice) [cnf transformation 25]
314. $false [subsumption resolution 135,127]
% SZS output end Proof for 6579654943335189982476536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both old and not wise then lucy is both not happy and not creative and vice versa.
Everyone who is either happy or quiet is quiet and vice versa.
Everyone who is both patient and not creative is not happy.
If mary is not wise or not patient then someone is both not tall and old.
Everyone who is happy or not strong is both old and strong.
Everyone who is old or creative is not generous.
Everyone who is generous is both creative and not curious.
If someone is either not creative or curious then someone is not creative or not rich.
Everyone who is rich is both not humble and not old and vice versa.
If someone is both kind and not wise then paul is generous or not rich.
If fred is patient or not kind then paul is both happy and tall and vice versa.
If fred is patient or wise then someone is both tall and not calm and vice versa.
If susan is not rich or curious then paul is both creative and generous.
If fred is both not generous and not tall then someone is both kind and not curious and vice versa.
Everyone who is not patient or not funny is either not funny or not happy.
If someone is both wise and not kind then fred is not calm.
Someone is either not quiet or happy.
Someone is curious or not rich.
Someone is both not kind and not rich.
Someone is either not humble or not curious.
Someone is humble.
Alice is both not tall and not humble. | Susan is rich. | entailment | (((old(fred)&~wise(fred)))<=>((~happy(lucy)&~creative(lucy))))&
(![X]:((happy(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((patient(X)&~creative(X))=>~happy(X)))&
(((~wise(mary)|~patient(mary)))=>(?[X]:((~tall(X)&old(X)))))&
(![X]:((happy(X)|~strong(X))=>(old(X)&strong(X))))&
(![X]:((old(X)|creative(X))=>~generous(X)))&
(![X]:(generous(X)=>(creative(X)&~curious(X))))&
((?[X]:((~creative(X)<~>curious(X))))=>(?[X]:((~creative(X)|~rich(X)))))&
(![X]:(rich(X)<=>(~humble(X)&~old(X))))&
((?[X]:((kind(X)&~wise(X))))=>((generous(paul)|~rich(paul))))&
(((patient(fred)|~kind(fred)))<=>((happy(paul)&tall(paul))))&
(((patient(fred)|wise(fred)))<=>(?[X]:((tall(X)&~calm(X)))))&
(((~rich(susan)|curious(susan)))=>((creative(paul)&generous(paul))))&
(((~generous(fred)&~tall(fred)))<=>(?[X]:((kind(X)&~curious(X)))))&
(![X]:((~patient(X)|~funny(X))=>(~funny(X)<~>~happy(X))))&
((?[X]:((wise(X)&~kind(X))))=>(~calm(fred)))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:(humble(X)))&
((~tall(alice)&~humble(alice))) | rich(susan) | [
"p5",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1504001215778145852193380
% SZS output start Proof for 1504001215778145852193380
6. ! [X0] : ((creative(X0) | old(X0)) => ~generous(X0)) [input p5]
7. ! [X0] : (generous(X0) => (~curious(X0) & creative(X0))) [input p6]
13. (curious(susan) | ~rich(susan)) => (generous(paul) & creative(paul)) [input p12]
23. ~rich(susan) [input hypothesis]
30. ! [X0] : (~generous(X0) | (~creative(X0) & ~old(X0))) [ennf transformation 6]
31. ! [X0] : ((~curious(X0) & creative(X0)) | ~generous(X0)) [ennf transformation 7]
35. (generous(paul) & creative(paul)) | (~curious(susan) & rich(susan)) [ennf transformation 13]
89. ~generous(X0) | ~creative(X0) [cnf transformation 30]
90. creative(X0) | ~generous(X0) [cnf transformation 31]
110. generous(paul) | rich(susan) [cnf transformation 35]
131. ~rich(susan) [cnf transformation 23]
176. ~generous(X0) [subsumption resolution 90,89]
237. rich(susan) [subsumption resolution 110,176]
287. $false [subsumption resolution 131,237]
% SZS output end Proof for 1504001215778145852193380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both creative and tall then someone is funny and vice versa. If someone is both not curious and not tall then someone is either curious or not old and vice versa. Everyone who is not tall or not brave is both kind and curious. Everyone who is tall or happy is not brave or humble. If alice is not patient then mary is either not creative or brave and vice versa. Everyone who is not strong or not wise is both calm and not humble and vice versa. Everyone who is both not funny and patient is either wise or not wise and vice versa. Everyone who is both generous and brave is either wise or not calm. Everyone who is rich or not patient is old. Everyone who is either funny or patient is humble. If susan is both brave and tall then someone is wise. If fred is humble then mary is either funny or rich. If alice is both not curious and not wise then someone is not generous or not quiet. Everyone who is creative is not happy and vice versa. Everyone who is not wise or not happy is happy. Everyone who is not brave is both not brave and not generous and vice versa. Someone is quiet. John is creative or brave. Paul is not old. Fred is not funny or wise. Someone is either brave or not quiet. Lucy is quiet or humble. | Alice is curious. | neutral | (((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(~brave(X)|humble(X))))&
((~patient(alice))<=>((~creative(mary)<~>brave(mary))))&
(![X]:((~strong(X)|~wise(X))<=>(calm(X)&~humble(X))))&
(![X]:((~funny(X)&patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((generous(X)&brave(X))=>(wise(X)<~>~calm(X))))&
(![X]:((rich(X)|~patient(X))=>old(X)))&
(![X]:((funny(X)<~>patient(X))=>humble(X)))&
(((brave(susan)&tall(susan)))=>(?[X]:(wise(X))))&
((humble(fred))=>((funny(mary)<~>rich(mary))))&
(((~curious(alice)&~wise(alice)))=>(?[X]:((~generous(X)|~quiet(X)))))&
(![X]:(creative(X)<=>~happy(X)))&
(![X]:((~wise(X)|~happy(X))=>happy(X)))&
(![X]:(~brave(X)<=>(~brave(X)&~generous(X))))&
(?[X]:(quiet(X)))&
((creative(john)|brave(john)))&
(~old(paul))&
((~funny(fred)|wise(fred)))&
(?[X]:((brave(X)<~>~quiet(X))))&
((quiet(lucy)|humble(lucy))) | curious(alice) | [] | null | 0 |
If john is either not rich or not curious then mary is both happy and not patient and vice versa. Everyone who is not curious is calm. If alice is creative then john is either tall or not humble. If someone is both not old and curious then fred is both not wise and not tall and vice versa. Everyone who is either not happy or not curious is generous or patient and vice versa. Everyone who is either not kind or not humble is humble or not happy. Everyone who is both strong and happy is both wise and not brave. Everyone who is not calm is either not happy or kind and vice versa. Everyone who is both tall and creative is kind or not humble. Everyone who is either happy or not calm is quiet or not humble and vice versa. If alice is not happy then john is either not wise or strong and vice versa. If john is both quiet and not strong then alice is patient. Everyone who is both quiet and not old is either not calm or not happy. If someone is tall or not old then someone is either not patient or humble and vice versa. Everyone who is quiet or not curious is not kind. If someone is not tall or not quiet then susan is not kind or generous. Susan is not humble. Alice is either not wise or old. Someone is both not quiet and brave. Someone is happy or not quiet. Someone is both not happy and wise. Susan is wise or not kind. Susan is either not tall or not strong. Someone is both not wise and not calm. | Susan is kind. | contradiction | (((~rich(john)<~>~curious(john)))<=>((happy(mary)&~patient(mary))))&
(![X]:(~curious(X)=>calm(X)))&
((creative(alice))=>((tall(john)<~>~humble(john))))&
((?[X]:((~old(X)&curious(X))))<=>((~wise(fred)&~tall(fred))))&
(![X]:((~happy(X)<~>~curious(X))<=>(generous(X)|patient(X))))&
(![X]:((~kind(X)<~>~humble(X))=>(humble(X)|~happy(X))))&
(![X]:((strong(X)&happy(X))=>(wise(X)&~brave(X))))&
(![X]:(~calm(X)<=>(~happy(X)<~>kind(X))))&
(![X]:((tall(X)&creative(X))=>(kind(X)|~humble(X))))&
(![X]:((happy(X)<~>~calm(X))<=>(quiet(X)|~humble(X))))&
((~happy(alice))<=>((~wise(john)<~>strong(john))))&
(((quiet(john)&~strong(john)))=>(patient(alice)))&
(![X]:((quiet(X)&~old(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:((tall(X)|~old(X))))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(![X]:((quiet(X)|~curious(X))=>~kind(X)))&
((?[X]:((~tall(X)|~quiet(X))))=>((~kind(susan)|generous(susan))))&
(~humble(susan))&
((~wise(alice)<~>old(alice)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((happy(X)|~quiet(X))))&
(?[X]:((~happy(X)&wise(X))))&
((wise(susan)|~kind(susan)))&
((~tall(susan)<~>~strong(susan)))&
(?[X]:((~wise(X)&~calm(X)))) | kind(susan) | [
"p4",
"p7",
"p9",
"p14",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8752084601910693122678516
% SZS output start Proof for 8752084601910693122678516
5. ! [X0] : ((~happy(X0) <~> ~curious(X0)) <=> (patient(X0) | generous(X0))) [input p4]
8. ! [X0] : (~calm(X0) <=> (~happy(X0) <~> kind(X0))) [input p7]
10. ! [X0] : ((happy(X0) <~> ~calm(X0)) <=> (~humble(X0) | quiet(X0))) [input p9]
15. ! [X0] : ((~curious(X0) | quiet(X0)) => ~kind(X0)) [input p14]
16. ? [X0] : (~quiet(X0) | ~tall(X0)) => (generous(susan) | ~kind(susan)) [input p15]
17. ~humble(susan) [input p16]
19. ? [X0] : (brave(X0) & ~quiet(X0)) [input p18]
25. kind(susan) [input hypothesis]
38. ! [X0] : (~kind(X0) | (curious(X0) & ~quiet(X0))) [ennf transformation 15]
39. (generous(susan) | ~kind(susan)) | ! [X0] : (quiet(X0) & tall(X0)) [ennf transformation 16]
40. generous(susan) | ~kind(susan) | ! [X0] : (quiet(X0) & tall(X0)) [flattening 39]
48. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (~patient(X0) & ~generous(X0))) & ((patient(X0) | generous(X0)) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [nnf transformation 5]
49. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (~patient(X0) & ~generous(X0))) & (patient(X0) | generous(X0) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [flattening 48]
51. ! [X0] : ((~calm(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0)))) & (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | calm(X0))) [nnf transformation 8]
52. ! [X0] : ((((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0))))) [nnf transformation 10]
53. ! [X0] : ((((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0))))) [flattening 52]
62. ? [X0] : (brave(X0) & ~quiet(X0)) => (brave(sK3) & ~quiet(sK3)) [choice axiom]
63. brave(sK3) & ~quiet(sK3) [skolemisation 19,62]
84. ~generous(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 49]
93. ~kind(X0) | happy(X0) | calm(X0) [cnf transformation 51]
99. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 53]
116. ~kind(X0) | curious(X0) [cnf transformation 38]
118. generous(susan) | ~kind(susan) | quiet(X0) [cnf transformation 40]
119. ~humble(susan) [cnf transformation 17]
122. ~quiet(sK3) [cnf transformation 63]
132. kind(susan) [cnf transformation 25]
241. 23 <=> ! [X0] : quiet(X0) [avatar definition]
242. quiet(X0) <- (23) [avatar component clause 241]
244. 24 <=> kind(susan) [avatar definition]
245. kind(susan) <- (24) [avatar component clause 244]
248. 25 <=> generous(susan) [avatar definition]
250. generous(susan) <- (25) [avatar component clause 248]
251. 23 | ~24 | 25 [avatar split clause 118,248,244,241]
290. 24 [avatar split clause 132,244]
292. curious(susan) <- (24) [resolution 116,245]
293. ~happy(susan) | ~curious(susan) <- (25) [resolution 84,250]
294. ~happy(susan) <- (24, 25) [subsumption resolution 293,292]
306. happy(susan) | calm(susan) <- (24) [resolution 93,245]
307. calm(susan) <- (24, 25) [subsumption resolution 306,294]
318. happy(susan) | humble(susan) <- (24, 25) [resolution 99,307]
319. humble(susan) <- (24, 25) [subsumption resolution 318,294]
320. $false <- (24, 25) [subsumption resolution 319,119]
321. ~24 | ~25 [avatar contradiction clause 320]
335. $false <- (23) [resolution 242,122]
338. ~23 [avatar contradiction clause 335]
340. $false [avatar sat refutation 251,290,321,338]
% SZS output end Proof for 8752084601910693122678516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not wise or wise then someone is kind and vice versa. Everyone who is not humble or strong is both not calm and kind. If someone is both not calm and quiet then john is either not strong or not funny. If paul is rich or not quiet then someone is not humble and vice versa. If someone is both humble and curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Everyone who is humble or not humble is both not rich and brave and vice versa. If someone is either not quiet or not wise then someone is not quiet and vice versa. If mary is not humble then someone is generous and vice versa. If someone is not quiet then paul is not wise. If lucy is not curious or not funny then lucy is either not funny or kind and vice versa. If someone is either strong or curious then someone is not curious or not brave. If fred is not patient then john is not old or wise. If john is funny or brave then mary is not happy or old and vice versa. If someone is both not wise and not calm then alice is both not humble and not old. Someone is kind. Fred is both not funny and calm. Someone is not old. Someone is both tall and creative. Fred is both quiet and generous. Someone is either not curious or brave. Someone is either quiet or not happy. Someone is not curious. | Paul is quiet. | contradiction | (((~wise(john)<~>wise(john)))<=>(?[X]:(kind(X))))&
(![X]:((~humble(X)|strong(X))=>(~calm(X)&kind(X))))&
((?[X]:((~calm(X)&quiet(X))))=>((~strong(john)<~>~funny(john))))&
(((rich(paul)|~quiet(paul)))<=>(?[X]:(~humble(X))))&
((?[X]:((humble(X)&curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
(![X]:((humble(X)|~humble(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>(?[X]:(~quiet(X))))&
((~humble(mary))<=>(?[X]:(generous(X))))&
((?[X]:(~quiet(X)))=>(~wise(paul)))&
(((~curious(lucy)|~funny(lucy)))<=>((~funny(lucy)<~>kind(lucy))))&
((?[X]:((strong(X)<~>curious(X))))=>(?[X]:((~curious(X)|~brave(X)))))&
((~patient(fred))=>((~old(john)|wise(john))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
(?[X]:(kind(X)))&
((~funny(fred)&calm(fred)))&
(?[X]:(~old(X)))&
(?[X]:((tall(X)&creative(X))))&
((quiet(fred)&generous(fred)))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:(~curious(X))) | quiet(paul) | [
"p3",
"p7",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1096993467648017988345771
% SZS output start Proof for 1096993467648017988345771
4. (~quiet(paul) | rich(paul)) <=> ? [X0] : ~humble(X0) [input p3]
8. ! [X0] : ((~humble(X0) | humble(X0)) <=> (brave(X0) & ~rich(X0))) [input p7]
10. ~humble(mary) <=> ? [X0] : generous(X0) [input p9]
21. generous(fred) & quiet(fred) [input p20]
25. quiet(paul) [input hypothesis]
42. ((~quiet(paul) | rich(paul)) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (quiet(paul) & ~rich(paul))) [nnf transformation 4]
43. (~quiet(paul) | rich(paul) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | (quiet(paul) & ~rich(paul))) [flattening 42]
44. (~quiet(paul) | rich(paul) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | (quiet(paul) & ~rich(paul))) [rectify 43]
45. ? [X1] : ~humble(X1) => ~humble(sK1) [choice axiom]
46. (~quiet(paul) | rich(paul) | ! [X0] : humble(X0)) & (~humble(sK1) | (quiet(paul) & ~rich(paul))) [skolemisation 44,45]
50. ! [X0] : (((~humble(X0) | humble(X0)) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | (humble(X0) & ~humble(X0)))) [nnf transformation 8]
51. ! [X0] : ((~humble(X0) | humble(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | (humble(X0) & ~humble(X0)))) [flattening 50]
57. (~humble(mary) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | humble(mary)) [nnf transformation 10]
58. (~humble(mary) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | humble(mary)) [rectify 57]
59. ? [X1] : generous(X1) => generous(sK4) [choice axiom]
60. (~humble(mary) | ! [X0] : ~generous(X0)) & (generous(sK4) | humble(mary)) [skolemisation 58,59]
95. ~quiet(paul) | rich(paul) | humble(X0) [cnf transformation 46]
108. ~rich(X0) | ~humble(X0) [cnf transformation 51]
109. ~rich(X0) | humble(X0) [cnf transformation 51]
118. ~humble(mary) | ~generous(X0) [cnf transformation 60]
140. generous(fred) [cnf transformation 21]
146. quiet(paul) [cnf transformation 25]
175. 6 <=> ! [X0] : humble(X0) [avatar definition]
176. humble(X0) <- (6) [avatar component clause 175]
178. 7 <=> rich(paul) [avatar definition]
180. rich(paul) <- (7) [avatar component clause 178]
182. 8 <=> quiet(paul) [avatar definition]
185. 6 | 7 | ~8 [avatar split clause 95,182,178,175]
206. ~rich(X0) [subsumption resolution 108,109]
233. 19 <=> ! [X0] : ~generous(X0) [avatar definition]
234. ~generous(X0) <- (19) [avatar component clause 233]
236. 20 <=> humble(mary) [avatar definition]
238. ~humble(mary) <- (~20) [avatar component clause 236]
239. 19 | ~20 [avatar split clause 118,236,233]
315. 8 [avatar split clause 146,182]
319. $false <- (7) [subsumption resolution 180,206]
320. ~7 [avatar contradiction clause 319]
323. $false <- (19) [resolution 234,140]
324. ~19 [avatar contradiction clause 323]
325. $false <- (6, ~20) [subsumption resolution 238,176]
326. ~6 | 20 [avatar contradiction clause 325]
327. $false [avatar sat refutation 185,239,315,320,324,326]
% SZS output end Proof for 1096993467648017988345771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and not funny then someone is humble or calm. If someone is both happy and rich then someone is curious or not old and vice versa. Everyone who is calm or not old is rich. Everyone who is old or not rich is either not kind or kind and vice versa. Everyone who is happy is both not wise and not tall and vice versa. If alice is either not quiet or happy then someone is either generous or tall. If john is both creative and not happy then susan is calm and vice versa. Everyone who is either not kind or not happy is either not calm or not funny. Everyone who is not old is both not old and tall. Everyone who is both quiet and not strong is patient. Everyone who is calm or humble is both not rich and not curious. If someone is either wise or not curious then someone is either humble or not patient. If lucy is either humble or strong then someone is both not generous and not tall. Everyone who is both not humble and quiet is either patient or not quiet and vice versa. If someone is both tall and not rich then someone is both not brave and not old. Everyone who is either quiet or not quiet is both strong and patient. Someone is not generous. Lucy is funny or patient. Lucy is either old or not creative. Fred is not humble or tall. Lucy is not happy or strong. Susan is both humble and old. Someone is funny. | Susan is rich. | contradiction | ((?[X]:((rich(X)&~funny(X))))=>(?[X]:((humble(X)|calm(X)))))&
((?[X]:((happy(X)&rich(X))))<=>(?[X]:((curious(X)|~old(X)))))&
(![X]:((calm(X)|~old(X))=>rich(X)))&
(![X]:((old(X)|~rich(X))<=>(~kind(X)<~>kind(X))))&
(![X]:(happy(X)<=>(~wise(X)&~tall(X))))&
(((~quiet(alice)<~>happy(alice)))=>(?[X]:((generous(X)<~>tall(X)))))&
(((creative(john)&~happy(john)))<=>(calm(susan)))&
(![X]:((~kind(X)<~>~happy(X))=>(~calm(X)<~>~funny(X))))&
(![X]:(~old(X)=>(~old(X)&tall(X))))&
(![X]:((quiet(X)&~strong(X))=>patient(X)))&
(![X]:((calm(X)|humble(X))=>(~rich(X)&~curious(X))))&
((?[X]:((wise(X)<~>~curious(X))))=>(?[X]:((humble(X)<~>~patient(X)))))&
(((humble(lucy)<~>strong(lucy)))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((~humble(X)&quiet(X))<=>(patient(X)<~>~quiet(X))))&
((?[X]:((tall(X)&~rich(X))))=>(?[X]:((~brave(X)&~old(X)))))&
(![X]:((quiet(X)<~>~quiet(X))=>(strong(X)&patient(X))))&
(?[X]:(~generous(X)))&
((funny(lucy)|patient(lucy)))&
((old(lucy)<~>~creative(lucy)))&
((~humble(fred)|tall(fred)))&
((~happy(lucy)|strong(lucy)))&
((humble(susan)&old(susan)))&
(?[X]:(funny(X))) | rich(susan) | [
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5680634094802743166262125
% SZS output start Proof for 5680634094802743166262125
11. ! [X0] : ((humble(X0) | calm(X0)) => (~curious(X0) & ~rich(X0))) [input p10]
22. old(susan) & humble(susan) [input p21]
24. rich(susan) [input hypothesis]
37. ! [X0] : ((~curious(X0) & ~rich(X0)) | (~humble(X0) & ~calm(X0))) [ennf transformation 11]
110. ~humble(X0) | ~rich(X0) [cnf transformation 37]
138. humble(susan) [cnf transformation 22]
141. rich(susan) [cnf transformation 24]
310. ~rich(susan) [resolution 110,138]
313. $false [subsumption resolution 310,141]
% SZS output end Proof for 5680634094802743166262125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is humble and vice versa.
Everyone who is not rich or rich is not tall.
Everyone who is kind is either humble or not rich and vice versa.
If someone is tall then paul is both not curious and not strong.
Everyone who is brave is either not brave or patient.
Everyone who is both not brave and kind is patient and vice versa.
Everyone who is both funny and humble is both not patient and not humble.
Everyone who is not curious is both brave and old and vice versa.
Everyone who is both old and not generous is both not creative and curious.
Everyone who is humble or strong is both not creative and not funny.
Everyone who is wise or not generous is both not rich and not patient.
If john is brave or not funny then someone is either rich or not quiet and vice versa.
Everyone who is either wise or not wise is either not rich or funny and vice versa.
Everyone who is either not calm or quiet is both not calm and not old.
If mary is not kind or happy then lucy is either not creative or quiet.
John is funny or not tall.
Someone is patient.
Lucy is curious or not happy.
John is kind or not rich.
Susan is patient or brave. | Mary is not patient. | neutral | (![X]:(~quiet(X)<=>humble(X)))&
(![X]:((~rich(X)|rich(X))=>~tall(X)))&
(![X]:(kind(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:(tall(X)))=>((~curious(paul)&~strong(paul))))&
(![X]:(brave(X)=>(~brave(X)<~>patient(X))))&
(![X]:((~brave(X)&kind(X))<=>patient(X)))&
(![X]:((funny(X)&humble(X))=>(~patient(X)&~humble(X))))&
(![X]:(~curious(X)<=>(brave(X)&old(X))))&
(![X]:((old(X)&~generous(X))=>(~creative(X)&curious(X))))&
(![X]:((humble(X)|strong(X))=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)|~generous(X))=>(~rich(X)&~patient(X))))&
(((brave(john)|~funny(john)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((wise(X)<~>~wise(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(~calm(X)&~old(X))))&
(((~kind(mary)|happy(mary)))=>((~creative(lucy)<~>quiet(lucy))))&
((funny(john)|~tall(john)))&
(?[X]:(patient(X)))&
((curious(lucy)|~happy(lucy)))&
((kind(john)|~rich(john)))&
((patient(susan)|brave(susan))) | ~patient(mary) | [] | null | 0 |
Everyone who is tall is not tall or not happy and vice versa.
Everyone who is not old or not tall is not tall or not kind.
If someone is both not patient and not humble then someone is quiet or not brave and vice versa.
Everyone who is not wise or strong is both not kind and rich and vice versa.
Everyone who is patient is either strong or wise.
If john is both quiet and not calm then someone is kind and vice versa.
If lucy is not calm or not creative then someone is not generous or patient and vice versa.
If someone is quiet or not quiet then someone is either patient or not tall.
Everyone who is tall or not kind is both not quiet and not creative.
If someone is not humble then fred is both patient and old.
Everyone who is either curious or generous is either not strong or not rich.
If lucy is either not curious or calm then john is brave or calm and vice versa.
If someone is tall or quiet then lucy is not humble or happy and vice versa.
Everyone who is funny or humble is not humble.
John is either calm or not rich.
John is rich or not generous.
Mary is not strong or not patient.
Someone is wise.
Someone is not creative.
Lucy is both old and wise.
Paul is tall.
Mary is either wise or not rich. | Lucy is kind. | contradiction | (![X]:(tall(X)<=>(~tall(X)|~happy(X))))&
(![X]:((~old(X)|~tall(X))=>(~tall(X)|~kind(X))))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:((quiet(X)|~brave(X)))))&
(![X]:((~wise(X)|strong(X))<=>(~kind(X)&rich(X))))&
(![X]:(patient(X)=>(strong(X)<~>wise(X))))&
(((quiet(john)&~calm(john)))<=>(?[X]:(kind(X))))&
(((~calm(lucy)|~creative(lucy)))<=>(?[X]:((~generous(X)|patient(X)))))&
((?[X]:((quiet(X)|~quiet(X))))=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((tall(X)|~kind(X))=>(~quiet(X)&~creative(X))))&
((?[X]:(~humble(X)))=>((patient(fred)&old(fred))))&
(![X]:((curious(X)<~>generous(X))=>(~strong(X)<~>~rich(X))))&
(((~curious(lucy)<~>calm(lucy)))<=>((brave(john)|calm(john))))&
((?[X]:((tall(X)|quiet(X))))<=>((~humble(lucy)|happy(lucy))))&
(![X]:((funny(X)|humble(X))=>~humble(X)))&
((calm(john)<~>~rich(john)))&
((rich(john)|~generous(john)))&
((~strong(mary)|~patient(mary)))&
(?[X]:(wise(X)))&
(?[X]:(~creative(X)))&
((old(lucy)&wise(lucy)))&
(tall(paul))&
((wise(mary)<~>~rich(mary))) | kind(lucy) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8843101609543713704394357
% SZS output start Proof for 8843101609543713704394357
1. ! [X0] : (tall(X0) <=> (~happy(X0) | ~tall(X0))) [input p0]
6. (~calm(john) & quiet(john)) <=> ? [X0] : kind(X0) [input p5]
9. ! [X0] : ((~kind(X0) | tall(X0)) => (~creative(X0) & ~quiet(X0))) [input p8]
23. kind(lucy) [input hypothesis]
34. ! [X0] : ((~creative(X0) & ~quiet(X0)) | (kind(X0) & ~tall(X0))) [ennf transformation 9]
38. ! [X0] : ((tall(X0) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | ~tall(X0))) [nnf transformation 1]
39. ! [X0] : ((tall(X0) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ~tall(X0))) [flattening 38]
48. ((~calm(john) & quiet(john)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | (calm(john) | ~quiet(john))) [nnf transformation 6]
49. ((~calm(john) & quiet(john)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | calm(john) | ~quiet(john)) [flattening 48]
50. ((~calm(john) & quiet(john)) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | calm(john) | ~quiet(john)) [rectify 49]
51. ? [X1] : kind(X1) => kind(sK2) [choice axiom]
52. ((~calm(john) & quiet(john)) | ! [X0] : ~kind(X0)) & (kind(sK2) | calm(john) | ~quiet(john)) [skolemisation 50,51]
77. tall(X0) | tall(X0) [cnf transformation 39]
93. quiet(john) | ~kind(X0) [cnf transformation 52]
103. ~quiet(X0) | ~tall(X0) [cnf transformation 34]
133. kind(lucy) [cnf transformation 23]
136. tall(X0) [duplicate literal removal 77]
147. 3 <=> ! [X1] : ~quiet(X1) [avatar definition]
148. ~quiet(X1) <- (3) [avatar component clause 147]
169. 8 <=> ! [X0] : ~kind(X0) [avatar definition]
170. ~kind(X0) <- (8) [avatar component clause 169]
177. 10 <=> quiet(john) [avatar definition]
179. quiet(john) <- (10) [avatar component clause 177]
180. 8 | 10 [avatar split clause 93,177,169]
224. ~quiet(X0) [subsumption resolution 103,136]
225. 3 [avatar split clause 224,147]
289. $false <- (8) [resolution 170,133]
290. ~8 [avatar contradiction clause 289]
291. $false <- (3, 10) [subsumption resolution 179,148]
292. ~3 | ~10 [avatar contradiction clause 291]
293. $false [avatar sat refutation 180,225,290,292]
% SZS output end Proof for 8843101609543713704394357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or quiet then fred is both generous and funny and vice versa.
Everyone who is not generous or not happy is quiet.
If someone is both curious and brave then john is not wise and vice versa.
If someone is either old or curious then mary is either quiet or not rich and vice versa.
If someone is both funny and not wise then someone is both tall and not happy and vice versa.
Everyone who is either patient or creative is not creative.
If someone is funny or rich then fred is either not calm or humble and vice versa.
Everyone who is humble is not funny and vice versa.
Everyone who is both not brave and rich is both tall and not humble and vice versa.
If someone is not funny or rich then mary is tall.
If someone is both old and creative then fred is both not brave and strong.
If someone is both strong and funny then someone is happy and vice versa.
Everyone who is happy is both not curious and not kind and vice versa.
Everyone who is tall or not calm is either not happy or not strong and vice versa.
If someone is not humble then someone is both not brave and not generous and vice versa.
Everyone who is both not generous and quiet is not old or not brave and vice versa.
Someone is tall or strong.
Paul is both kind and generous.
John is quiet or not curious.
Alice is both funny and tall.
Someone is either not patient or strong.
Fred is both wise and patient.
Alice is both tall and not creative. | Paul is not creative. | entailment | ((?[X]:((old(X)|quiet(X))))<=>((generous(fred)&funny(fred))))&
(![X]:((~generous(X)|~happy(X))=>quiet(X)))&
((?[X]:((curious(X)&brave(X))))<=>(~wise(john)))&
((?[X]:((old(X)<~>curious(X))))<=>((quiet(mary)<~>~rich(mary))))&
((?[X]:((funny(X)&~wise(X))))<=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((patient(X)<~>creative(X))=>~creative(X)))&
((?[X]:((funny(X)|rich(X))))<=>((~calm(fred)<~>humble(fred))))&
(![X]:(humble(X)<=>~funny(X)))&
(![X]:((~brave(X)&rich(X))<=>(tall(X)&~humble(X))))&
((?[X]:((~funny(X)|rich(X))))=>(tall(mary)))&
((?[X]:((old(X)&creative(X))))=>((~brave(fred)&strong(fred))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:(happy(X))))&
(![X]:(happy(X)<=>(~curious(X)&~kind(X))))&
(![X]:((tall(X)|~calm(X))<=>(~happy(X)<~>~strong(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((~generous(X)&quiet(X))<=>(~old(X)|~brave(X))))&
(?[X]:((tall(X)|strong(X))))&
((kind(paul)&generous(paul)))&
((quiet(john)|~curious(john)))&
((funny(alice)&tall(alice)))&
(?[X]:((~patient(X)<~>strong(X))))&
((wise(fred)&patient(fred)))&
((tall(alice)&~creative(alice))) | ~creative(paul) | [
"p0",
"p1",
"p10",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6144823451869281450648409
% SZS output start Proof for 6144823451869281450648409
1. ? [X0] : (quiet(X0) | old(X0)) <=> (funny(fred) & generous(fred)) [input p0]
2. ! [X0] : ((~happy(X0) | ~generous(X0)) => quiet(X0)) [input p1]
11. ? [X0] : (creative(X0) & old(X0)) => (strong(fred) & ~brave(fred)) [input p10]
16. ! [X0] : ((quiet(X0) & ~generous(X0)) <=> (~brave(X0) | ~old(X0))) [input p15]
18. generous(paul) & kind(paul) [input p17]
24. creative(paul) [input hypothesis]
28. ! [X0] : (quiet(X0) | (happy(X0) & generous(X0))) [ennf transformation 2]
31. (strong(fred) & ~brave(fred)) | ! [X0] : (~creative(X0) | ~old(X0)) [ennf transformation 11]
32. (? [X0] : (quiet(X0) | old(X0)) | (~funny(fred) | ~generous(fred))) & ((funny(fred) & generous(fred)) | ! [X0] : (~quiet(X0) & ~old(X0))) [nnf transformation 1]
33. (? [X0] : (quiet(X0) | old(X0)) | ~funny(fred) | ~generous(fred)) & ((funny(fred) & generous(fred)) | ! [X0] : (~quiet(X0) & ~old(X0))) [flattening 32]
34. (? [X0] : (quiet(X0) | old(X0)) | ~funny(fred) | ~generous(fred)) & ((funny(fred) & generous(fred)) | ! [X1] : (~quiet(X1) & ~old(X1))) [rectify 33]
35. ? [X0] : (quiet(X0) | old(X0)) => (quiet(sK0) | old(sK0)) [choice axiom]
36. ((quiet(sK0) | old(sK0)) | ~funny(fred) | ~generous(fred)) & ((funny(fred) & generous(fred)) | ! [X1] : (~quiet(X1) & ~old(X1))) [skolemisation 34,35]
72. ! [X0] : (((quiet(X0) & ~generous(X0)) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | (~quiet(X0) | generous(X0)))) [nnf transformation 16]
73. ! [X0] : (((quiet(X0) & ~generous(X0)) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | ~quiet(X0) | generous(X0))) [flattening 72]
80. generous(fred) | ~quiet(X1) [cnf transformation 36]
84. generous(X0) | quiet(X0) [cnf transformation 28]
117. ~brave(fred) | ~creative(X0) | ~old(X0) [cnf transformation 31]
135. ~generous(X0) | old(X0) [cnf transformation 73]
136. ~generous(X0) | brave(X0) [cnf transformation 73]
141. generous(paul) [cnf transformation 18]
151. creative(paul) [cnf transformation 24]
154. 1 <=> generous(fred) [avatar definition]
155. generous(fred) <- (1) [avatar component clause 154]
156. ~generous(fred) <- (~1) [avatar component clause 154]
171. 5 <=> ! [X1] : ~quiet(X1) [avatar definition]
172. ~quiet(X1) <- (5) [avatar component clause 171]
178. 5 | 1 [avatar split clause 80,154,171]
292. 31 <=> ! [X0] : (~creative(X0) | ~old(X0)) [avatar definition]
293. ~creative(X0) | ~old(X0) <- (31) [avatar component clause 292]
300. 33 <=> brave(fred) [avatar definition]
303. 31 | ~33 [avatar split clause 117,300,292]
397. old(paul) [resolution 135,141]
401. brave(fred) <- (1) [resolution 136,155]
403. 33 | ~1 [avatar split clause 401,154,300]
416. ~old(paul) <- (31) [resolution 293,151]
417. $false <- (31) [subsumption resolution 416,397]
418. ~31 [avatar contradiction clause 417]
419. quiet(fred) <- (~1) [resolution 156,84]
420. $false <- (~1, 5) [subsumption resolution 419,172]
421. 1 | ~5 [avatar contradiction clause 420]
422. $false [avatar sat refutation 178,303,403,418,421]
% SZS output end Proof for 6144823451869281450648409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not strong or strong then lucy is both not brave and not tall and vice versa.
Everyone who is not patient or brave is quiet and vice versa.
Everyone who is both humble and rich is both not generous and not calm and vice versa.
Everyone who is either brave or not calm is brave.
Everyone who is either not humble or not calm is both wise and humble.
Everyone who is either not humble or not old is kind or calm and vice versa.
Everyone who is not rich or not happy is quiet and vice versa.
If someone is either not old or not brave then someone is both rich and not curious.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
Alice is tall or not creative.
Alice is not creative or not strong.
Someone is both not strong and tall.
Mary is either not patient or tall.
Paul is not creative or not wise.
John is not wise.
Someone is kind or not generous.
Someone is curious or not wise. | Alice is not brave. | entailment | (((~strong(mary)|strong(mary)))<=>((~brave(lucy)&~tall(lucy))))&
(![X]:((~patient(X)|brave(X))<=>quiet(X)))&
(![X]:((humble(X)&rich(X))<=>(~generous(X)&~calm(X))))&
(![X]:((brave(X)<~>~calm(X))=>brave(X)))&
(![X]:((~humble(X)<~>~calm(X))=>(wise(X)&humble(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(kind(X)|calm(X))))&
(![X]:((~rich(X)|~happy(X))<=>quiet(X)))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:((rich(X)&~curious(X)))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
((tall(alice)|~creative(alice)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((~strong(X)&tall(X))))&
((~patient(mary)<~>tall(mary)))&
((~creative(paul)|~wise(paul)))&
(~wise(john))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((curious(X)|~wise(X)))) | ~brave(alice) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8210842114950882771906592
% SZS output start Proof for 8210842114950882771906592
2. ! [X0] : ((brave(X0) | ~patient(X0)) <=> quiet(X0)) [input p1]
3. ! [X0] : ((rich(X0) & humble(X0)) <=> (~calm(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((brave(X0) <~> ~calm(X0)) => brave(X0)) [input p3]
5. ! [X0] : ((~humble(X0) <~> ~calm(X0)) => (humble(X0) & wise(X0))) [input p4]
7. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> quiet(X0)) [input p6]
8. ? [X0] : (~old(X0) <~> ~brave(X0)) => ? [X0] : (~curious(X0) & rich(X0)) [input p7]
13. ? [X0] : old(X0) => ? [X0] : (~quiet(X0) & ~calm(X0)) [input p12]
15. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> happy(X0)) [input p14]
25. brave(alice) [input hypothesis]
26. ? [X0] : (~old(X0) <~> ~brave(X0)) => ? [X1] : (~curious(X1) & rich(X1)) [rectify 8]
28. ? [X0] : old(X0) => ? [X1] : (~quiet(X1) & ~calm(X1)) [rectify 13]
29. ! [X0] : (brave(X0) | (brave(X0) <=> ~calm(X0))) [ennf transformation 4]
30. ! [X0] : ((humble(X0) & wise(X0)) | (~humble(X0) <=> ~calm(X0))) [ennf transformation 5]
31. ? [X1] : (~curious(X1) & rich(X1)) | ! [X0] : (~old(X0) <=> ~brave(X0)) [ennf transformation 26]
33. ? [X1] : (~quiet(X1) & ~calm(X1)) | ! [X0] : ~old(X0) [ennf transformation 28]
38. ! [X0] : (((brave(X0) | ~patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((brave(X0) | ~patient(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & patient(X0)))) [flattening 38]
40. ! [X0] : (((rich(X0) & humble(X0)) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((rich(X0) & humble(X0)) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~rich(X0) | ~humble(X0))) [flattening 40]
42. ! [X0] : (brave(X0) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) [nnf transformation 29]
43. ! [X0] : ((humble(X0) & wise(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 30]
46. ! [X0] : (((~happy(X0) | ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (happy(X0) & rich(X0)))) [nnf transformation 7]
47. ! [X0] : ((~happy(X0) | ~rich(X0) | ~quiet(X0)) & (quiet(X0) | (happy(X0) & rich(X0)))) [flattening 46]
48. ? [X1] : (~curious(X1) & rich(X1)) | ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0))) [nnf transformation 31]
49. ? [X0] : (~curious(X0) & rich(X0)) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1))) [rectify 48]
50. ? [X0] : (~curious(X0) & rich(X0)) => (~curious(sK0) & rich(sK0)) [choice axiom]
51. (~curious(sK0) & rich(sK0)) | ! [X1] : ((~old(X1) | brave(X1)) & (~brave(X1) | old(X1))) [skolemisation 49,50]
67. ? [X0] : (~quiet(X0) & ~calm(X0)) | ! [X1] : ~old(X1) [rectify 33]
68. ? [X0] : (~quiet(X0) & ~calm(X0)) => (~quiet(sK5) & ~calm(sK5)) [choice axiom]
69. (~quiet(sK5) & ~calm(sK5)) | ! [X1] : ~old(X1) [skolemisation 67,68]
70. ! [X0] : (((~rich(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [nnf transformation 15]
71. ! [X0] : ((~rich(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [flattening 70]
85. ~brave(X0) | quiet(X0) [cnf transformation 39]
88. ~calm(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 41]
92. brave(X0) | brave(X0) | calm(X0) [cnf transformation 42]
95. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 43]
103. rich(X0) | quiet(X0) [cnf transformation 47]
105. ~happy(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 47]
106. rich(sK0) | ~brave(X1) | old(X1) [cnf transformation 51]
126. ~calm(sK5) | ~old(X1) [cnf transformation 69]
127. ~quiet(sK5) | ~old(X1) [cnf transformation 69]
129. happy(X0) | calm(X0) [cnf transformation 71]
143. brave(alice) [cnf transformation 25]
144. ~calm(X0) | humble(X0) [duplicate literal removal 95]
145. calm(X0) | brave(X0) [duplicate literal removal 92]
173. 6 <=> ! [X1] : (~brave(X1) | old(X1)) [avatar definition]
174. ~brave(X1) | old(X1) <- (6) [avatar component clause 173]
177. 7 <=> rich(sK0) [avatar definition]
179. rich(sK0) <- (7) [avatar component clause 177]
181. 6 | 7 [avatar split clause 106,177,173]
241. 21 <=> ! [X1] : ~old(X1) [avatar definition]
242. ~old(X1) <- (21) [avatar component clause 241]
244. 22 <=> quiet(sK5) [avatar definition]
247. 21 | ~22 [avatar split clause 127,244,241]
249. 23 <=> calm(sK5) [avatar definition]
251. ~calm(sK5) <- (~23) [avatar component clause 249]
252. 21 | ~23 [avatar split clause 126,249,241]
313. brave(sK5) <- (~23) [resolution 145,251]
314. humble(X0) | brave(X0) [resolution 145,144]
315. quiet(sK5) <- (~23) [resolution 313,85]
318. 22 | 23 [avatar split clause 315,249,244]
319. old(alice) <- (6) [resolution 174,143]
321. $false <- (6, 21) [subsumption resolution 319,242]
322. ~6 | ~21 [avatar contradiction clause 321]
328. ~rich(X0) | ~humble(X0) | brave(X0) [resolution 88,145]
330. ~rich(X0) | brave(X0) [subsumption resolution 328,314]
349. brave(X0) | quiet(X0) [resolution 330,103]
351. quiet(X0) [subsumption resolution 349,85]
360. ~rich(X1) | ~quiet(X1) | calm(X1) [resolution 105,129]
363. ~rich(X1) | calm(X1) [subsumption resolution 360,351]
389. calm(sK0) <- (7) [resolution 363,179]
394. ~rich(sK0) | ~humble(sK0) <- (7) [resolution 389,88]
395. humble(sK0) <- (7) [resolution 389,144]
396. ~humble(sK0) <- (7) [subsumption resolution 394,179]
397. $false <- (7) [subsumption resolution 395,396]
398. ~7 [avatar contradiction clause 397]
399. $false [avatar sat refutation 181,247,252,318,322,398]
% SZS output end Proof for 8210842114950882771906592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is humble and vice versa.
Everyone who is either not happy or not quiet is not happy or not humble.
If someone is not wise then paul is both tall and not patient and vice versa.
Everyone who is either wise or not humble is either calm or generous and vice versa.
If fred is not calm or not quiet then john is both not rich and quiet and vice versa.
Everyone who is not funny or rich is either funny or happy and vice versa.
If paul is not quiet or humble then alice is both generous and not funny.
If someone is either funny or patient then alice is not quiet or rich.
Everyone who is not curious is either wise or not old and vice versa.
If someone is either not patient or not tall then someone is either tall or not kind.
Everyone who is not patient or not generous is either old or not generous.
Everyone who is generous or curious is either not wise or not rich and vice versa.
If someone is old or not wise then susan is not old or humble.
If fred is rich or not rich then alice is old.
If paul is strong or generous then someone is not humble or quiet.
If someone is not calm then john is not calm and vice versa.
Fred is humble or funny.
Someone is funny or not happy.
Someone is both not wise and not brave.
Someone is both not humble and tall.
Susan is not patient or calm.
Someone is both generous and not rich.
Someone is both brave and curious.
Someone is not strong or not humble. | Paul is patient. | contradiction | (![X]:(~calm(X)<=>humble(X)))&
(![X]:((~happy(X)<~>~quiet(X))=>(~happy(X)|~humble(X))))&
((?[X]:(~wise(X)))<=>((tall(paul)&~patient(paul))))&
(![X]:((wise(X)<~>~humble(X))<=>(calm(X)<~>generous(X))))&
(((~calm(fred)|~quiet(fred)))<=>((~rich(john)&quiet(john))))&
(![X]:((~funny(X)|rich(X))<=>(funny(X)<~>happy(X))))&
(((~quiet(paul)|humble(paul)))=>((generous(alice)&~funny(alice))))&
((?[X]:((funny(X)<~>patient(X))))=>((~quiet(alice)|rich(alice))))&
(![X]:(~curious(X)<=>(wise(X)<~>~old(X))))&
((?[X]:((~patient(X)<~>~tall(X))))=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~generous(X))=>(old(X)<~>~generous(X))))&
(![X]:((generous(X)|curious(X))<=>(~wise(X)<~>~rich(X))))&
((?[X]:((old(X)|~wise(X))))=>((~old(susan)|humble(susan))))&
(((rich(fred)|~rich(fred)))=>(old(alice)))&
(((strong(paul)|generous(paul)))=>(?[X]:((~humble(X)|quiet(X)))))&
((?[X]:(~calm(X)))<=>(~calm(john)))&
((humble(fred)|funny(fred)))&
(?[X]:((funny(X)|~happy(X))))&
(?[X]:((~wise(X)&~brave(X))))&
(?[X]:((~humble(X)&tall(X))))&
((~patient(susan)|calm(susan)))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~strong(X)|~humble(X)))) | patient(paul) | [
"p2",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7152859454813833476848051
% SZS output start Proof for 7152859454813833476848051
3. ? [X0] : ~wise(X0) <=> (~patient(paul) & tall(paul)) [input p2]
19. ? [X0] : (~brave(X0) & ~wise(X0)) [input p18]
25. patient(paul) [input hypothesis]
42. (? [X0] : ~wise(X0) | (patient(paul) | ~tall(paul))) & ((~patient(paul) & tall(paul)) | ! [X0] : wise(X0)) [nnf transformation 3]
43. (? [X0] : ~wise(X0) | patient(paul) | ~tall(paul)) & ((~patient(paul) & tall(paul)) | ! [X0] : wise(X0)) [flattening 42]
44. (? [X0] : ~wise(X0) | patient(paul) | ~tall(paul)) & ((~patient(paul) & tall(paul)) | ! [X1] : wise(X1)) [rectify 43]
45. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
46. (~wise(sK0) | patient(paul) | ~tall(paul)) & ((~patient(paul) & tall(paul)) | ! [X1] : wise(X1)) [skolemisation 44,45]
69. ? [X0] : (~brave(X0) & ~wise(X0)) => (~brave(sK5) & ~wise(sK5)) [choice axiom]
70. ~brave(sK5) & ~wise(sK5) [skolemisation 19,69]
82. ~patient(paul) | wise(X1) [cnf transformation 46]
136. ~wise(sK5) [cnf transformation 70]
145. patient(paul) [cnf transformation 25]
155. 2 <=> patient(paul) [avatar definition]
164. 4 <=> ! [X1] : wise(X1) [avatar definition]
165. wise(X1) <- (4) [avatar component clause 164]
166. 4 | ~2 [avatar split clause 82,155,164]
319. 2 [avatar split clause 145,155]
320. $false <- (4) [resolution 165,136]
321. ~4 [avatar contradiction clause 320]
322. $false [avatar sat refutation 166,319,321]
% SZS output end Proof for 7152859454813833476848051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both humble and not brave then someone is not calm or curious and vice versa. If someone is happy then fred is not calm. If someone is patient then susan is either humble or rich. Everyone who is both not calm and quiet is quiet. If someone is either old or not rich then someone is not creative or curious and vice versa. Everyone who is not old is not tall or curious. Everyone who is either humble or kind is not happy or patient and vice versa. If someone is either not quiet or creative then someone is not funny or not kind. Everyone who is not humble is both not wise and not old. Everyone who is wise or old is both wise and calm. Everyone who is both patient and humble is either not quiet or generous. Everyone who is kind or funny is not wise. Everyone who is happy is either not patient or not wise and vice versa. Everyone who is curious is either patient or wise and vice versa. Everyone who is either not quiet or creative is both old and not funny. Everyone who is not brave is wise and vice versa. Someone is either not brave or not quiet. John is both strong and not tall. Someone is both kind and quiet. Paul is wise. Someone is not strong or curious. Paul is tall or not wise. John is patient. Paul is happy or not rich. | Paul is not wise. | contradiction | (((humble(susan)&~brave(susan)))<=>(?[X]:((~calm(X)|curious(X)))))&
((?[X]:(happy(X)))=>(~calm(fred)))&
((?[X]:(patient(X)))=>((humble(susan)<~>rich(susan))))&
(![X]:((~calm(X)&quiet(X))=>quiet(X)))&
((?[X]:((old(X)<~>~rich(X))))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:(~old(X)=>(~tall(X)|curious(X))))&
(![X]:((humble(X)<~>kind(X))<=>(~happy(X)|patient(X))))&
((?[X]:((~quiet(X)<~>creative(X))))=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:(~humble(X)=>(~wise(X)&~old(X))))&
(![X]:((wise(X)|old(X))=>(wise(X)&calm(X))))&
(![X]:((patient(X)&humble(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((kind(X)|funny(X))=>~wise(X)))&
(![X]:(happy(X)<=>(~patient(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(patient(X)<~>wise(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(old(X)&~funny(X))))&
(![X]:(~brave(X)<=>wise(X)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((strong(john)&~tall(john)))&
(?[X]:((kind(X)&quiet(X))))&
(wise(paul))&
(?[X]:((~strong(X)|curious(X))))&
((tall(paul)|~wise(paul)))&
(patient(john))&
((happy(paul)|~rich(paul))) | ~wise(paul) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6540760064491078651592184
% SZS output start Proof for 6540760064491078651592184
20. wise(paul) [input p19]
25. ~wise(paul) [input hypothesis]
117. wise(paul) [cnf transformation 20]
122. ~wise(paul) [cnf transformation 25]
227. $false [subsumption resolution 122,117]
% SZS output end Proof for 6540760064491078651592184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both generous and happy and vice versa. Everyone who is either not calm or not creative is both calm and curious. Everyone who is not generous is both old and happy. Everyone who is not wise or happy is not strong or not old. Everyone who is quiet or not humble is humble and vice versa. If someone is not curious or not rich then someone is not calm or not wise and vice versa. If someone is both patient and creative then someone is not creative. If someone is both not generous and wise then someone is both not brave and curious. Everyone who is not generous or calm is brave or not kind and vice versa. If someone is happy or generous then someone is not kind and vice versa. If someone is rich then fred is not wise. Everyone who is either not generous or not creative is not brave. If alice is not generous then fred is both brave and not humble and vice versa. Everyone who is both humble and not strong is either not creative or old. If alice is either not patient or not kind then lucy is not generous and vice versa. If mary is generous then john is quiet or not brave and vice versa. Someone is humble or not happy. Someone is not brave or not calm. Paul is both not wise and not tall. Someone is not kind or not old. Someone is either not kind or not creative. Fred is both not calm and kind. Someone is strong or not strong. Someone is either not brave or not creative. | Fred is not brave. | entailment | (![X]:(~quiet(X)<=>(generous(X)&happy(X))))&
(![X]:((~calm(X)<~>~creative(X))=>(calm(X)&curious(X))))&
(![X]:(~generous(X)=>(old(X)&happy(X))))&
(![X]:((~wise(X)|happy(X))=>(~strong(X)|~old(X))))&
(![X]:((quiet(X)|~humble(X))<=>humble(X)))&
((?[X]:((~curious(X)|~rich(X))))<=>(?[X]:((~calm(X)|~wise(X)))))&
((?[X]:((patient(X)&creative(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~generous(X)&wise(X))))=>(?[X]:((~brave(X)&curious(X)))))&
(![X]:((~generous(X)|calm(X))<=>(brave(X)|~kind(X))))&
((?[X]:((happy(X)|generous(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(rich(X)))=>(~wise(fred)))&
(![X]:((~generous(X)<~>~creative(X))=>~brave(X)))&
((~generous(alice))<=>((brave(fred)&~humble(fred))))&
(![X]:((humble(X)&~strong(X))=>(~creative(X)<~>old(X))))&
(((~patient(alice)<~>~kind(alice)))<=>(~generous(lucy)))&
((generous(mary))<=>((quiet(john)|~brave(john))))&
(?[X]:((humble(X)|~happy(X))))&
(?[X]:((~brave(X)|~calm(X))))&
((~wise(paul)&~tall(paul)))&
(?[X]:((~kind(X)|~old(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~calm(fred)&kind(fred)))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:((~brave(X)<~>~creative(X)))) | ~brave(fred) | [
"p2",
"p3",
"p4",
"p8",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 833693757288321921186592
% SZS output start Proof for 833693757288321921186592
3. ! [X0] : (~generous(X0) => (happy(X0) & old(X0))) [input p2]
4. ! [X0] : ((happy(X0) | ~wise(X0)) => (~old(X0) | ~strong(X0))) [input p3]
5. ! [X0] : ((~humble(X0) | quiet(X0)) <=> humble(X0)) [input p4]
9. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~kind(X0) | brave(X0))) [input p8]
12. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => ~brave(X0)) [input p11]
14. ! [X0] : ((~strong(X0) & humble(X0)) => (~creative(X0) <~> old(X0))) [input p13]
22. kind(fred) & ~calm(fred) [input p21]
25. brave(fred) [input hypothesis]
32. ! [X0] : ((happy(X0) & old(X0)) | generous(X0)) [ennf transformation 3]
33. ! [X0] : ((~old(X0) | ~strong(X0)) | (~happy(X0) & wise(X0))) [ennf transformation 4]
34. ! [X0] : (~old(X0) | ~strong(X0) | (~happy(X0) & wise(X0))) [flattening 33]
38. ! [X0] : (~brave(X0) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 12]
39. ! [X0] : ((~creative(X0) <~> old(X0)) | (strong(X0) | ~humble(X0))) [ennf transformation 14]
40. ! [X0] : ((~creative(X0) <~> old(X0)) | strong(X0) | ~humble(X0)) [flattening 39]
44. ! [X0] : (((~humble(X0) | quiet(X0)) | ~humble(X0)) & (humble(X0) | (humble(X0) & ~quiet(X0)))) [nnf transformation 5]
45. ! [X0] : ((~humble(X0) | quiet(X0) | ~humble(X0)) & (humble(X0) | (humble(X0) & ~quiet(X0)))) [flattening 44]
57. ! [X0] : (((calm(X0) | ~generous(X0)) | (kind(X0) & ~brave(X0))) & ((~kind(X0) | brave(X0)) | (~calm(X0) & generous(X0)))) [nnf transformation 9]
58. ! [X0] : ((calm(X0) | ~generous(X0) | (kind(X0) & ~brave(X0))) & (~kind(X0) | brave(X0) | (~calm(X0) & generous(X0)))) [flattening 57]
64. ! [X0] : (~brave(X0) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 38]
67. ! [X0] : (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | strong(X0) | ~humble(X0)) [nnf transformation 40]
92. old(X0) | generous(X0) [cnf transformation 32]
93. happy(X0) | generous(X0) [cnf transformation 32]
95. ~strong(X0) | ~old(X0) | ~happy(X0) [cnf transformation 34]
97. humble(X0) | humble(X0) [cnf transformation 45]
108. ~brave(X0) | ~generous(X0) | calm(X0) [cnf transformation 58]
114. ~brave(X0) | ~creative(X0) | generous(X0) [cnf transformation 64]
120. ~old(X0) | creative(X0) | strong(X0) | ~humble(X0) [cnf transformation 67]
134. ~calm(fred) [cnf transformation 22]
139. brave(fred) [cnf transformation 25]
140. humble(X0) [duplicate literal removal 97]
217. ~old(X0) | creative(X0) | strong(X0) [subsumption resolution 120,140]
322. ~generous(fred) | calm(fred) [resolution 108,139]
325. ~generous(fred) [subsumption resolution 322,134]
383. ~creative(fred) | generous(fred) [resolution 114,139]
386. ~creative(fred) [subsumption resolution 383,325]
393. strong(X0) | creative(X0) | generous(X0) [resolution 217,92]
423. creative(X0) | generous(X0) | ~old(X0) | ~happy(X0) [resolution 393,95]
425. creative(X0) | generous(X0) | ~happy(X0) [subsumption resolution 423,92]
426. creative(X0) | generous(X0) [subsumption resolution 425,93]
430. generous(fred) [resolution 426,386]
435. $false [subsumption resolution 430,325]
% SZS output end Proof for 833693757288321921186592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is curious or brave and vice versa.
Everyone who is not curious is either rich or not brave and vice versa.
If someone is not rich or quiet then lucy is both not patient and not happy.
Everyone who is happy is both old and curious.
Everyone who is either not strong or not quiet is funny or quiet.
If susan is either not brave or not calm then susan is either not old or not happy.
Everyone who is not quiet is curious and vice versa.
Everyone who is either curious or not wise is either not calm or not curious.
Everyone who is both strong and not rich is calm or tall and vice versa.
Everyone who is not happy is not funny or wise.
Everyone who is both curious and patient is not happy or not strong.
Everyone who is not tall is either brave or quiet.
Everyone who is kind or not generous is not creative or kind and vice versa.
If john is either not kind or tall then lucy is not calm and vice versa.
Everyone who is not generous is either happy or wise.
If someone is rich or humble then someone is happy.
Someone is not calm or not curious.
Lucy is tall.
John is strong.
Someone is either not strong or not humble.
John is old or not old.
Someone is either wise or not calm.
Someone is both not rich and curious. | Susan is not rich. | entailment | (![X]:(~quiet(X)<=>(curious(X)|brave(X))))&
(![X]:(~curious(X)<=>(rich(X)<~>~brave(X))))&
((?[X]:((~rich(X)|quiet(X))))=>((~patient(lucy)&~happy(lucy))))&
(![X]:(happy(X)=>(old(X)&curious(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>(funny(X)|quiet(X))))&
(((~brave(susan)<~>~calm(susan)))=>((~old(susan)<~>~happy(susan))))&
(![X]:(~quiet(X)<=>curious(X)))&
(![X]:((curious(X)<~>~wise(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((strong(X)&~rich(X))<=>(calm(X)|tall(X))))&
(![X]:(~happy(X)=>(~funny(X)|wise(X))))&
(![X]:((curious(X)&patient(X))=>(~happy(X)|~strong(X))))&
(![X]:(~tall(X)=>(brave(X)<~>quiet(X))))&
(![X]:((kind(X)|~generous(X))<=>(~creative(X)|kind(X))))&
(((~kind(john)<~>tall(john)))<=>(~calm(lucy)))&
(![X]:(~generous(X)=>(happy(X)<~>wise(X))))&
((?[X]:((rich(X)|humble(X))))=>(?[X]:(happy(X))))&
(?[X]:((~calm(X)|~curious(X))))&
(tall(lucy))&
(strong(john))&
(?[X]:((~strong(X)<~>~humble(X))))&
((old(john)|~old(john)))&
(?[X]:((wise(X)<~>~calm(X))))&
(?[X]:((~rich(X)&curious(X)))) | ~rich(susan) | [
"p0",
"p1",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4730215753722646898418458
% SZS output start Proof for 4730215753722646898418458
1. ! [X0] : (~quiet(X0) <=> (brave(X0) | curious(X0))) [input p0]
2. ! [X0] : (~curious(X0) <=> (rich(X0) <~> ~brave(X0))) [input p1]
7. ! [X0] : (~quiet(X0) <=> curious(X0)) [input p6]
9. ! [X0] : ((~rich(X0) & strong(X0)) <=> (tall(X0) | calm(X0))) [input p8]
12. ! [X0] : (~tall(X0) => (brave(X0) <~> quiet(X0))) [input p11]
24. rich(susan) [input hypothesis]
36. ! [X0] : ((brave(X0) <~> quiet(X0)) | tall(X0)) [ennf transformation 12]
39. ! [X0] : ((~quiet(X0) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | quiet(X0))) [nnf transformation 1]
40. ! [X0] : ((~quiet(X0) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | quiet(X0))) [flattening 39]
41. ! [X0] : ((~curious(X0) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | curious(X0))) [nnf transformation 2]
44. ! [X0] : ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))) [nnf transformation 7]
46. ! [X0] : (((~rich(X0) & strong(X0)) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | (rich(X0) | ~strong(X0)))) [nnf transformation 9]
47. ! [X0] : (((~rich(X0) & strong(X0)) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | rich(X0) | ~strong(X0))) [flattening 46]
48. ! [X0] : (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | tall(X0)) [nnf transformation 36]
67. ~curious(X0) | ~quiet(X0) [cnf transformation 40]
68. ~brave(X0) | ~quiet(X0) [cnf transformation 40]
70. ~rich(X0) | brave(X0) | curious(X0) [cnf transformation 41]
71. ~rich(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 41]
72. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 41]
83. curious(X0) | quiet(X0) [cnf transformation 44]
93. ~tall(X0) | ~rich(X0) [cnf transformation 47]
95. tall(X0) | brave(X0) | quiet(X0) [cnf transformation 48]
119. rich(susan) [cnf transformation 24]
141. 5 <=> brave(susan) [avatar definition]
142. brave(susan) <- (5) [avatar component clause 141]
143. ~brave(susan) <- (~5) [avatar component clause 141]
228. brave(susan) | curious(susan) [resolution 70,119]
229. curious(susan) <- (~5) [subsumption resolution 228,143]
230. ~quiet(susan) <- (~5) [resolution 229,67]
231. ~brave(susan) | ~curious(susan) [resolution 71,119]
232. rich(X0) | brave(X0) | quiet(X0) [resolution 72,83]
255. brave(X0) | quiet(X0) | ~rich(X0) [resolution 95,93]
266. brave(X0) | quiet(X0) [subsumption resolution 255,232]
274. quiet(susan) <- (~5) [resolution 266,143]
277. $false <- (~5) [subsumption resolution 274,230]
278. 5 [avatar contradiction clause 277]
280. 24 <=> curious(susan) [avatar definition]
282. ~curious(susan) <- (~24) [avatar component clause 280]
283. ~24 | ~5 [avatar split clause 231,141,280]
290. ~quiet(susan) <- (5) [resolution 142,68]
291. quiet(susan) <- (~24) [resolution 282,83]
292. $false <- (5, ~24) [subsumption resolution 291,290]
293. ~5 | 24 [avatar contradiction clause 292]
294. $false [avatar sat refutation 278,283,293]
% SZS output end Proof for 4730215753722646898418458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not creative is either not strong or brave. Everyone who is either not generous or old is either creative or old and vice versa. If alice is both creative and calm then john is either not rich or not brave. Everyone who is not patient or quiet is strong or not curious and vice versa. Everyone who is not patient is not kind or not brave and vice versa. Everyone who is either not humble or not funny is both not patient and not tall and vice versa. If someone is both not quiet and brave then susan is both kind and quiet and vice versa. Everyone who is not humble or not creative is both not wise and kind and vice versa. If someone is quiet then lucy is either creative or not old. If alice is either not kind or generous then someone is both not quiet and brave. Everyone who is both not curious and not old is strong. If someone is not brave or wise then fred is wise. Everyone who is happy is not kind or curious and vice versa. Everyone who is not humble is patient and vice versa. If someone is not patient then someone is either not old or not funny. Everyone who is both not tall and wise is either not quiet or not tall and vice versa. Someone is not creative or calm. John is both not brave and generous. Susan is wise. Someone is both not brave and curious. Someone is brave. Someone is generous or not happy. Someone is either rich or not wise. Someone is not patient. | John is not old. | contradiction | (![X]:((brave(X)|~creative(X))=>(~strong(X)<~>brave(X))))&
(![X]:((~generous(X)<~>old(X))<=>(creative(X)<~>old(X))))&
(((creative(alice)&calm(alice)))=>((~rich(john)<~>~brave(john))))&
(![X]:((~patient(X)|quiet(X))<=>(strong(X)|~curious(X))))&
(![X]:(~patient(X)<=>(~kind(X)|~brave(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(~patient(X)&~tall(X))))&
((?[X]:((~quiet(X)&brave(X))))<=>((kind(susan)&quiet(susan))))&
(![X]:((~humble(X)|~creative(X))<=>(~wise(X)&kind(X))))&
((?[X]:(quiet(X)))=>((creative(lucy)<~>~old(lucy))))&
(((~kind(alice)<~>generous(alice)))=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:((~curious(X)&~old(X))=>strong(X)))&
((?[X]:((~brave(X)|wise(X))))=>(wise(fred)))&
(![X]:(happy(X)<=>(~kind(X)|curious(X))))&
(![X]:(~humble(X)<=>patient(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~old(X)<~>~funny(X)))))&
(![X]:((~tall(X)&wise(X))<=>(~quiet(X)<~>~tall(X))))&
(?[X]:((~creative(X)|calm(X))))&
((~brave(john)&generous(john)))&
(wise(susan))&
(?[X]:((~brave(X)&curious(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:(~patient(X))) | ~old(john) | [
"p0",
"p1",
"p3",
"p4",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5481432454336657241659073
% SZS output start Proof for 5481432454336657241659073
1. ! [X0] : ((~creative(X0) | brave(X0)) => (~strong(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((~generous(X0) <~> old(X0)) <=> (creative(X0) <~> old(X0))) [input p1]
4. ! [X0] : ((quiet(X0) | ~patient(X0)) <=> (~curious(X0) | strong(X0))) [input p3]
5. ! [X0] : (~patient(X0) <=> (~brave(X0) | ~kind(X0))) [input p4]
11. ! [X0] : ((~old(X0) & ~curious(X0)) => strong(X0)) [input p10]
18. generous(john) & ~brave(john) [input p17]
25. ~old(john) [input hypothesis]
28. ! [X0] : ((~strong(X0) <~> brave(X0)) | (creative(X0) & ~brave(X0))) [ennf transformation 1]
33. ! [X0] : (strong(X0) | (old(X0) | curious(X0))) [ennf transformation 11]
34. ! [X0] : (strong(X0) | old(X0) | curious(X0)) [flattening 33]
38. ! [X0] : (((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (creative(X0) & ~brave(X0))) [nnf transformation 28]
39. ! [X0] : ((((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0)))) & (((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0))))) [nnf transformation 2]
41. ! [X0] : (((quiet(X0) | ~patient(X0)) | (curious(X0) & ~strong(X0))) & ((~curious(X0) | strong(X0)) | (~quiet(X0) & patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((quiet(X0) | ~patient(X0) | (curious(X0) & ~strong(X0))) & (~curious(X0) | strong(X0) | (~quiet(X0) & patient(X0)))) [flattening 41]
43. ! [X0] : ((~patient(X0) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | patient(X0))) [nnf transformation 5]
44. ! [X0] : ((~patient(X0) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | patient(X0))) [flattening 43]
79. ~strong(X0) | brave(X0) | creative(X0) [cnf transformation 38]
80. ~brave(X0) | strong(X0) | ~brave(X0) [cnf transformation 38]
85. ~old(X0) | ~creative(X0) | ~generous(X0) | ~old(X0) [cnf transformation 39]
86. old(X0) | ~generous(X0) | old(X0) | ~creative(X0) [cnf transformation 39]
92. ~curious(X0) | strong(X0) | patient(X0) [cnf transformation 42]
98. ~patient(X0) | brave(X0) [cnf transformation 44]
120. curious(X0) | old(X0) | strong(X0) [cnf transformation 34]
136. ~brave(john) [cnf transformation 18]
137. generous(john) [cnf transformation 18]
146. ~old(john) [cnf transformation 25]
150. ~old(X0) | ~creative(X0) | ~generous(X0) [duplicate literal removal 85]
151. ~generous(X0) | old(X0) | ~creative(X0) [duplicate literal removal 86]
153. ~brave(X0) | strong(X0) [duplicate literal removal 80]
154. ~generous(X0) | ~creative(X0) [subsumption resolution 150,151]
169. 4 <=> brave(john) [avatar definition]
170. ~brave(john) <- (~4) [avatar component clause 169]
265. ~4 [avatar split clause 136,169]
301. ~creative(john) [resolution 154,137]
361. old(X1) | strong(X1) | strong(X1) | patient(X1) [resolution 120,92]
363. patient(X1) | strong(X1) | old(X1) [duplicate literal removal 361]
425. strong(X2) | old(X2) | brave(X2) [resolution 363,98]
431. old(X2) | strong(X2) [subsumption resolution 425,153]
432. strong(john) [resolution 431,146]
437. brave(john) | creative(john) [resolution 432,79]
438. creative(john) <- (~4) [subsumption resolution 437,170]
439. $false <- (~4) [subsumption resolution 438,301]
440. 4 [avatar contradiction clause 439]
441. $false [avatar sat refutation 265,440]
% SZS output end Proof for 5481432454336657241659073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not old and calm and vice versa.
If paul is not curious then john is patient and vice versa.
Everyone who is brave or not old is either not quiet or strong.
If john is not funny or not calm then someone is both not humble and not curious.
Everyone who is strong is both not strong and strong and vice versa.
Everyone who is both strong and funny is not quiet and vice versa.
If someone is both old and kind then lucy is either creative or not kind.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
Everyone who is both not tall and tall is not quiet or not happy and vice versa.
If alice is either calm or not wise then susan is not wise and vice versa.
Everyone who is either humble or not tall is not kind or not calm and vice versa.
If someone is happy or not kind then someone is either generous or not curious.
If alice is generous or not creative then mary is both not funny and patient and vice versa.
If lucy is both not creative and rich then alice is not old or not brave.
Someone is either wise or not curious.
Someone is either curious or not tall.
Paul is quiet.
Someone is not calm or not humble.
Someone is not old or not patient.
Someone is calm or curious.
Susan is not kind. | Alice is old. | entailment | (![X]:(calm(X)<=>(~old(X)&calm(X))))&
((~curious(paul))<=>(patient(john)))&
(![X]:((brave(X)|~old(X))=>(~quiet(X)<~>strong(X))))&
(((~funny(john)|~calm(john)))=>(?[X]:((~humble(X)&~curious(X)))))&
(![X]:(strong(X)<=>(~strong(X)&strong(X))))&
(![X]:((strong(X)&funny(X))<=>~quiet(X)))&
((?[X]:((old(X)&kind(X))))=>((creative(lucy)<~>~kind(lucy))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((~tall(X)&tall(X))<=>(~quiet(X)|~happy(X))))&
(((calm(alice)<~>~wise(alice)))<=>(~wise(susan)))&
(![X]:((humble(X)<~>~tall(X))<=>(~kind(X)|~calm(X))))&
((?[X]:((happy(X)|~kind(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
(((generous(alice)|~creative(alice)))<=>((~funny(mary)&patient(mary))))&
(((~creative(lucy)&rich(lucy)))=>((~old(alice)|~brave(alice))))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((curious(X)<~>~tall(X))))&
(quiet(paul))&
(?[X]:((~calm(X)|~humble(X))))&
(?[X]:((~old(X)|~patient(X))))&
(?[X]:((calm(X)|curious(X))))&
(~kind(susan)) | old(alice) | [
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6760928569391659187812183
% SZS output start Proof for 6760928569391659187812183
3. ! [X0] : ((~old(X0) | brave(X0)) => (~quiet(X0) <~> strong(X0))) [input p2]
5. ! [X0] : (strong(X0) <=> (strong(X0) & ~strong(X0))) [input p4]
6. ! [X0] : ((funny(X0) & strong(X0)) <=> ~quiet(X0)) [input p5]
24. ~old(alice) [input hypothesis]
28. ! [X0] : ((~quiet(X0) <~> strong(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 3]
40. ! [X0] : (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | (old(X0) & ~brave(X0))) [nnf transformation 28]
43. ! [X0] : ((strong(X0) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [nnf transformation 5]
44. ! [X0] : ((strong(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((funny(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | (~funny(X0) | ~strong(X0)))) [nnf transformation 6]
46. ! [X0] : (((funny(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | ~funny(X0) | ~strong(X0))) [flattening 45]
81. ~quiet(X0) | strong(X0) | old(X0) [cnf transformation 40]
88. ~strong(X0) | ~strong(X0) [cnf transformation 44]
92. strong(X0) | quiet(X0) [cnf transformation 46]
136. ~old(alice) [cnf transformation 24]
137. ~strong(X0) [duplicate literal removal 88]
169. quiet(X0) [subsumption resolution 92,137]
302. strong(X0) | old(X0) [resolution 81,169]
303. old(X0) [subsumption resolution 302,137]
304. $false [resolution 303,136]
% SZS output end Proof for 6760928569391659187812183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.