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 calm or not quiet is kind or not funny and vice versa.
If someone is generous then someone is either creative or not rich.
If someone is either happy or not humble then lucy is not brave or not generous and vice versa.
Everyone who is both brave and not calm is either patient or not brave.
Everyone who is not rich or kind is strong.
If someone is not brave then paul is creative or humble and vice versa.
If someone is either funny or tall then lucy is either happy or rich.
Everyone who is either brave or not rich is either funny or strong.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is curious.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Someone is both not calm and not curious.
Fred is not strong or not creative.
Someone is generous or not kind. | Susan is not happy. | neutral | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|~funny(X))))&
((?[X]:(generous(X)))=>(?[X]:((creative(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~humble(X))))<=>((~brave(lucy)|~generous(lucy))))&
(![X]:((brave(X)&~calm(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)|kind(X))=>strong(X)))&
((?[X]:(~brave(X)))<=>((creative(paul)|humble(paul))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(lucy)<~>rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(funny(X)<~>strong(X))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~calm(X)&~curious(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is happy or not generous is wise or calm.
Everyone who is quiet or not kind is brave or not kind and vice versa.
If lucy is old or quiet then someone is either quiet or funny and vice versa.
Everyone who is generous or tall is not happy and vice versa.
If fred is not quiet then someone is humble or not strong and vice versa.
If someone is both quiet and rich then mary is calm.
If alice is happy then someone is either strong or patient and vice versa.
Everyone who is either not happy or not strong is either wise or not brave.
Everyone who is either not creative or creative is rich or not strong and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Everyone who is not quiet or not tall is either quiet or not strong and vice versa.
If john is either not tall or patient then paul is either not humble or curious and vice versa.
Everyone who is either not happy or not quiet is strong or kind and vice versa.
Someone is both not humble and not wise.
Lucy is either quiet or strong.
Someone is kind or not rich.
Someone is either not happy or not strong.
Alice is both generous and strong.
Paul is not brave.
Susan is not brave or not rich. | Mary is not calm. | contradiction | (![X]:((happy(X)|~generous(X))=>(wise(X)|calm(X))))&
(![X]:((quiet(X)|~kind(X))<=>(brave(X)|~kind(X))))&
(((old(lucy)|quiet(lucy)))<=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((generous(X)|tall(X))<=>~happy(X)))&
((~quiet(fred))<=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:((quiet(X)&rich(X))))=>(calm(mary)))&
((happy(alice))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((~happy(X)<~>~strong(X))=>(wise(X)<~>~brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(rich(X)|~strong(X))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
(![X]:((~quiet(X)|~tall(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(john)<~>patient(john)))<=>((~humble(paul)<~>curious(paul))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(strong(X)|kind(X))))&
(?[X]:((~humble(X)&~wise(X))))&
((quiet(lucy)<~>strong(lucy)))&
(?[X]:((kind(X)|~rich(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((generous(alice)&strong(alice)))&
(~brave(paul))&
((~brave(susan)|~rich(susan))) | ~calm(mary) | [
"p5",
"p8",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9198999635173433715723055
% SZS output start Proof for 9198999635173433715723055
6. ? [X0] : (rich(X0) & quiet(X0)) => calm(mary) [input p5]
9. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~strong(X0) | rich(X0))) [input p8]
14. ! [X0] : ((~tall(X0) | ~quiet(X0)) <=> (quiet(X0) <~> ~strong(X0))) [input p13]
21. strong(alice) & generous(alice) [input p20]
24. ~calm(mary) [input hypothesis]
29. calm(mary) | ! [X0] : (~rich(X0) | ~quiet(X0)) [ennf transformation 6]
50. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 9]
51. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 50]
65. ! [X0] : (((~tall(X0) | ~quiet(X0)) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (tall(X0) & quiet(X0)))) [nnf transformation 14]
66. ! [X0] : ((~tall(X0) | ~quiet(X0) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (tall(X0) & quiet(X0)))) [flattening 65]
96. calm(mary) | ~rich(X0) | ~quiet(X0) [cnf transformation 29]
105. ~strong(X0) | rich(X0) | creative(X0) | creative(X0) [cnf transformation 51]
106. ~strong(X0) | rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 51]
121. ~strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 66]
149. strong(alice) [cnf transformation 21]
152. ~calm(mary) [cnf transformation 24]
153. ~strong(X0) | quiet(X0) [duplicate literal removal 121]
155. ~strong(X0) | rich(X0) | creative(X0) [duplicate literal removal 105]
156. ~strong(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 106]
207. 12 <=> ! [X0] : (~rich(X0) | ~quiet(X0)) [avatar definition]
208. ~rich(X0) | ~quiet(X0) <- (12) [avatar component clause 207]
210. 13 <=> calm(mary) [avatar definition]
213. 12 | 13 [avatar split clause 96,210,207]
236. ~strong(X0) | rich(X0) [subsumption resolution 155,156]
348. ~13 [avatar split clause 152,210]
356. quiet(alice) [resolution 153,149]
359. rich(alice) [resolution 236,149]
360. ~quiet(alice) <- (12) [resolution 359,208]
361. $false <- (12) [subsumption resolution 360,356]
362. ~12 [avatar contradiction clause 361]
363. $false [avatar sat refutation 213,348,362]
% SZS output end Proof for 9198999635173433715723055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not quiet then someone is either calm or strong. Everyone who is both not brave and brave is either tall or not generous. Everyone who is brave or not wise is not generous. If alice is not patient or not calm then someone is either creative or not strong. Everyone who is both not generous and not kind is both rich and quiet and vice versa. Everyone who is not brave is old. Everyone who is both strong and not funny is both old and not rich and vice versa. Everyone who is kind is curious and vice versa. If susan is either patient or strong then someone is happy and vice versa. If mary is either happy or old then paul is both rich and not curious and vice versa. If susan is rich or not curious then someone is either quiet or not brave and vice versa. If someone is either not creative or not strong then susan is either wise or not generous. Everyone who is either rich or not quiet is both curious and not calm and vice versa. Everyone who is either funny or not calm is both patient and not old. Everyone who is happy is not funny and vice versa. Everyone who is both not generous and quiet is calm or not wise and vice versa. Alice is both not humble and not generous. Susan is not kind or not calm. Someone is both strong and not wise. Lucy is not curious. Paul is wise. Someone is generous. Lucy is generous or humble. Alice is not wise. | Susan is kind. | contradiction | ((?[X]:((creative(X)<~>~quiet(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((~brave(X)&brave(X))=>(tall(X)<~>~generous(X))))&
(![X]:((brave(X)|~wise(X))=>~generous(X)))&
(((~patient(alice)|~calm(alice)))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((~generous(X)&~kind(X))<=>(rich(X)&quiet(X))))&
(![X]:(~brave(X)=>old(X)))&
(![X]:((strong(X)&~funny(X))<=>(old(X)&~rich(X))))&
(![X]:(kind(X)<=>curious(X)))&
(((patient(susan)<~>strong(susan)))<=>(?[X]:(happy(X))))&
(((happy(mary)<~>old(mary)))<=>((rich(paul)&~curious(paul))))&
(((rich(susan)|~curious(susan)))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
((?[X]:((~creative(X)<~>~strong(X))))=>((wise(susan)<~>~generous(susan))))&
(![X]:((rich(X)<~>~quiet(X))<=>(curious(X)&~calm(X))))&
(![X]:((funny(X)<~>~calm(X))=>(patient(X)&~old(X))))&
(![X]:(happy(X)<=>~funny(X)))&
(![X]:((~generous(X)&quiet(X))<=>(calm(X)|~wise(X))))&
((~humble(alice)&~generous(alice)))&
((~kind(susan)|~calm(susan)))&
(?[X]:((strong(X)&~wise(X))))&
(~curious(lucy))&
(wise(paul))&
(?[X]:(generous(X)))&
((generous(lucy)|humble(lucy)))&
(~wise(alice)) | kind(susan) | [
"p2",
"p4",
"p5",
"p6",
"p7",
"p10",
"p12",
"p13",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8945870744008952223932515
% SZS output start Proof for 8945870744008952223932515
3. ! [X0] : ((~wise(X0) | brave(X0)) => ~generous(X0)) [input p2]
5. ! [X0] : ((~kind(X0) & ~generous(X0)) <=> (quiet(X0) & rich(X0))) [input p4]
6. ! [X0] : (~brave(X0) => old(X0)) [input p5]
7. ! [X0] : ((~funny(X0) & strong(X0)) <=> (~rich(X0) & old(X0))) [input p6]
8. ! [X0] : (kind(X0) <=> curious(X0)) [input p7]
11. (~curious(susan) | rich(susan)) <=> ? [X0] : (quiet(X0) <~> ~brave(X0)) [input p10]
13. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (~calm(X0) & curious(X0))) [input p12]
14. ! [X0] : ((funny(X0) <~> ~calm(X0)) => (~old(X0) & patient(X0))) [input p13]
16. ! [X0] : ((quiet(X0) & ~generous(X0)) <=> (~wise(X0) | calm(X0))) [input p15]
18. ~calm(susan) | ~kind(susan) [input p17]
22. ? [X0] : generous(X0) [input p21]
25. kind(susan) [input hypothesis]
30. ! [X0] : (~generous(X0) | (wise(X0) & ~brave(X0))) [ennf transformation 3]
32. ! [X0] : (old(X0) | brave(X0)) [ennf transformation 6]
34. ! [X0] : ((~old(X0) & patient(X0)) | (funny(X0) <=> ~calm(X0))) [ennf transformation 14]
43. ! [X0] : (((~kind(X0) & ~generous(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (kind(X0) | generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((~kind(X0) & ~generous(X0)) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | kind(X0) | generous(X0))) [flattening 43]
45. ! [X0] : (((~funny(X0) & strong(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (funny(X0) | ~strong(X0)))) [nnf transformation 7]
46. ! [X0] : (((~funny(X0) & strong(X0)) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | funny(X0) | ~strong(X0))) [flattening 45]
47. ! [X0] : ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))) [nnf transformation 8]
54. ((~curious(susan) | rich(susan)) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (? [X0] : ((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (curious(susan) & ~rich(susan))) [nnf transformation 11]
55. (~curious(susan) | rich(susan) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (? [X0] : ((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (curious(susan) & ~rich(susan))) [flattening 54]
56. (~curious(susan) | rich(susan) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (? [X1] : ((brave(X1) | ~quiet(X1)) & (~brave(X1) | quiet(X1))) | (curious(susan) & ~rich(susan))) [rectify 55]
57. ? [X1] : ((brave(X1) | ~quiet(X1)) & (~brave(X1) | quiet(X1))) => ((brave(sK3) | ~quiet(sK3)) & (~brave(sK3) | quiet(sK3))) [choice axiom]
58. (~curious(susan) | rich(susan) | ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(sK3) | ~quiet(sK3)) & (~brave(sK3) | quiet(sK3))) | (curious(susan) & ~rich(susan))) [skolemisation 56,57]
60. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (calm(X0) | ~curious(X0))) & ((~calm(X0) & curious(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 13]
61. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | calm(X0) | ~curious(X0)) & ((~calm(X0) & curious(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [flattening 60]
62. ! [X0] : ((~old(X0) & patient(X0)) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0)))) [nnf transformation 34]
64. ! [X0] : (((quiet(X0) & ~generous(X0)) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | (~quiet(X0) | generous(X0)))) [nnf transformation 16]
65. ! [X0] : (((quiet(X0) & ~generous(X0)) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~quiet(X0) | generous(X0))) [flattening 64]
68. ? [X0] : generous(X0) => generous(sK5) [choice axiom]
69. generous(sK5) [skolemisation 22,68]
76. ~generous(X0) | ~brave(X0) [cnf transformation 30]
84. ~rich(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 44]
85. ~rich(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 44]
86. old(X0) | brave(X0) [cnf transformation 32]
90. ~funny(X0) | rich(X0) | ~old(X0) [cnf transformation 46]
91. ~kind(X0) | curious(X0) [cnf transformation 47]
108. ~curious(susan) | rich(susan) | quiet(X0) | brave(X0) [cnf transformation 58]
118. ~curious(X0) | ~rich(X0) | calm(X0) | quiet(X0) [cnf transformation 61]
122. ~old(X0) | funny(X0) | calm(X0) [cnf transformation 62]
126. ~generous(X0) | ~calm(X0) [cnf transformation 65]
132. ~calm(susan) | ~kind(susan) [cnf transformation 18]
137. generous(sK5) [cnf transformation 69]
140. kind(susan) [cnf transformation 25]
221. 17 <=> ! [X0] : (quiet(X0) | brave(X0)) [avatar definition]
222. brave(X0) | quiet(X0) <- (17) [avatar component clause 221]
224. 18 <=> rich(susan) [avatar definition]
226. rich(susan) <- (18) [avatar component clause 224]
228. 19 <=> curious(susan) [avatar definition]
229. curious(susan) <- (19) [avatar component clause 228]
231. 17 | 18 | ~19 [avatar split clause 108,228,224,221]
265. 27 <=> kind(susan) [avatar definition]
266. kind(susan) <- (27) [avatar component clause 265]
269. 28 <=> calm(susan) [avatar definition]
271. ~calm(susan) <- (~28) [avatar component clause 269]
272. ~27 | ~28 [avatar split clause 132,269,265]
282. 27 [avatar split clause 140,265]
283. ~brave(sK5) [resolution 76,137]
288. curious(susan) <- (27) [resolution 91,266]
291. 19 | ~27 [avatar split clause 288,265,228]
408. funny(X0) | calm(X0) | brave(X0) [resolution 122,86]
424. ~rich(susan) | calm(susan) | quiet(susan) <- (19) [resolution 118,229]
466. ~rich(susan) | quiet(susan) <- (19, ~28) [subsumption resolution 424,271]
479. quiet(sK5) <- (17) [resolution 222,283]
531. calm(X2) | brave(X2) | rich(X2) | ~old(X2) [resolution 408,90]
537. rich(X2) | brave(X2) | calm(X2) [subsumption resolution 531,86]
616. 52 <=> quiet(susan) [avatar definition]
617. quiet(susan) <- (52) [avatar component clause 616]
620. 52 | ~18 | ~19 | 28 [avatar split clause 466,269,228,224,616]
626. ~quiet(susan) | ~kind(susan) <- (18) [resolution 226,85]
628. ~kind(susan) <- (18, 52) [subsumption resolution 626,617]
629. $false <- (18, 27, 52) [subsumption resolution 628,266]
630. ~18 | ~27 | ~52 [avatar contradiction clause 629]
756. brave(X5) | calm(X5) | ~quiet(X5) | ~generous(X5) [resolution 537,84]
761. calm(X5) | ~quiet(X5) | ~generous(X5) [subsumption resolution 756,76]
762. ~generous(X5) | ~quiet(X5) [subsumption resolution 761,126]
834. ~quiet(sK5) [resolution 762,137]
837. $false <- (17) [subsumption resolution 834,479]
838. ~17 [avatar contradiction clause 837]
841. $false [avatar sat refutation 231,272,282,291,620,630,838]
% SZS output end Proof for 8945870744008952223932515
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and quiet is both not happy and curious and vice versa. Everyone who is not wise is not generous and vice versa. If paul is not quiet then someone is old and vice versa. If paul is both not humble and old then john is wise or not patient. If fred is not tall then paul is humble and vice versa. If mary is tall or not creative then lucy is both not quiet and not humble. Everyone who is not humble is both not tall and not generous. If someone is both not brave and not wise then someone is both not rich and not humble. If someone is happy then susan is not brave or not kind and vice versa. Everyone who is generous or creative is not wise and vice versa. Everyone who is brave or funny is rich or not tall and vice versa. Everyone who is either not creative or not quiet is either happy or not kind and vice versa. Everyone who is not funny is either not humble or not strong and vice versa. If paul is calm then mary is humble or kind. Everyone who is funny or not humble is either happy or not brave and vice versa. Everyone who is both quiet and wise is both old and not quiet and vice versa. Mary is not calm. Alice is not brave. John is not humble. Someone is curious. Someone is both not old and not strong. Someone is either generous or not kind. Fred is not happy or not creative. | Fred is funny. | neutral | (![X]:((calm(X)&quiet(X))<=>(~happy(X)&curious(X))))&
(![X]:(~wise(X)<=>~generous(X)))&
((~quiet(paul))<=>(?[X]:(old(X))))&
(((~humble(paul)&old(paul)))=>((wise(john)|~patient(john))))&
((~tall(fred))<=>(humble(paul)))&
(((tall(mary)|~creative(mary)))=>((~quiet(lucy)&~humble(lucy))))&
(![X]:(~humble(X)=>(~tall(X)&~generous(X))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((~rich(X)&~humble(X)))))&
((?[X]:(happy(X)))<=>((~brave(susan)|~kind(susan))))&
(![X]:((generous(X)|creative(X))<=>~wise(X)))&
(![X]:((brave(X)|funny(X))<=>(rich(X)|~tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~strong(X))))&
((calm(paul))=>((humble(mary)|kind(mary))))&
(![X]:((funny(X)|~humble(X))<=>(happy(X)<~>~brave(X))))&
(![X]:((quiet(X)&wise(X))<=>(old(X)&~quiet(X))))&
(~calm(mary))&
(~brave(alice))&
(~humble(john))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
((~happy(fred)|~creative(fred))) | funny(fred) | [] | null | 0 |
If someone is not wise then john is both not creative and patient.
If someone is not old then alice is both kind and not generous and vice versa.
If alice is humble or rich then someone is not rich.
If someone is not calm or tall then someone is both not curious and old and vice versa.
Everyone who is either tall or brave is both not creative and not curious and vice versa.
Everyone who is both not curious and patient is patient or not humble.
Everyone who is both not generous and old is generous or brave and vice versa.
Everyone who is not tall is funny and vice versa.
Everyone who is both not patient and tall is not creative and vice versa.
If paul is not brave or calm then susan is either wise or not humble.
If someone is old then someone is not humble.
If someone is not curious or wise then alice is humble or happy and vice versa.
Everyone who is not quiet or not humble is either tall or not rich and vice versa.
Everyone who is not generous is not patient or not old and vice versa.
Everyone who is curious or not tall is wise or not calm.
If someone is both wise and calm then lucy is either not patient or not happy and vice versa.
John is funny or curious.
Paul is either not rich or not brave.
Susan is wise.
John is either not brave or quiet.
Someone is either not patient or not calm. | Lucy is not funny. | contradiction | ((?[X]:(~wise(X)))=>((~creative(john)&patient(john))))&
((?[X]:(~old(X)))<=>((kind(alice)&~generous(alice))))&
(((humble(alice)|rich(alice)))=>(?[X]:(~rich(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~curious(X)&old(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~creative(X)&~curious(X))))&
(![X]:((~curious(X)&patient(X))=>(patient(X)|~humble(X))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~patient(X)&tall(X))<=>~creative(X)))&
(((~brave(paul)|calm(paul)))=>((wise(susan)<~>~humble(susan))))&
((?[X]:(old(X)))=>(?[X]:(~humble(X))))&
((?[X]:((~curious(X)|wise(X))))<=>((humble(alice)|happy(alice))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~patient(X)|~old(X))))&
(![X]:((curious(X)|~tall(X))=>(wise(X)|~calm(X))))&
((?[X]:((wise(X)&calm(X))))<=>((~patient(lucy)<~>~happy(lucy))))&
((funny(john)|curious(john)))&
((~rich(paul)<~>~brave(paul)))&
(wise(susan))&
((~brave(john)<~>quiet(john)))&
(?[X]:((~patient(X)<~>~calm(X)))) | ~funny(lucy) | [
"p3",
"p4",
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7015725288818222270804068
% SZS output start Proof for 7015725288818222270804068
4. ? [X0] : (tall(X0) | ~calm(X0)) <=> ? [X0] : (old(X0) & ~curious(X0)) [input p3]
5. ! [X0] : ((tall(X0) <~> brave(X0)) <=> (~curious(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((old(X0) & ~generous(X0)) <=> (brave(X0) | generous(X0))) [input p6]
8. ! [X0] : (~tall(X0) <=> funny(X0)) [input p7]
9. ! [X0] : ((tall(X0) & ~patient(X0)) <=> ~creative(X0)) [input p8]
14. ! [X0] : (~generous(X0) <=> (~old(X0) | ~patient(X0))) [input p13]
22. ~funny(lucy) [input hypothesis]
23. ? [X0] : (tall(X0) | ~calm(X0)) <=> ? [X1] : (old(X1) & ~curious(X1)) [rectify 4]
40. (? [X0] : (tall(X0) | ~calm(X0)) | ! [X1] : (~old(X1) | curious(X1))) & (? [X1] : (old(X1) & ~curious(X1)) | ! [X0] : (~tall(X0) & calm(X0))) [nnf transformation 23]
41. (? [X0] : (tall(X0) | ~calm(X0)) | ! [X1] : (~old(X1) | curious(X1))) & (? [X2] : (old(X2) & ~curious(X2)) | ! [X3] : (~tall(X3) & calm(X3))) [rectify 40]
42. ? [X0] : (tall(X0) | ~calm(X0)) => (tall(sK2) | ~calm(sK2)) [choice axiom]
43. ? [X2] : (old(X2) & ~curious(X2)) => (old(sK3) & ~curious(sK3)) [choice axiom]
44. ((tall(sK2) | ~calm(sK2)) | ! [X1] : (~old(X1) | curious(X1))) & ((old(sK3) & ~curious(sK3)) | ! [X3] : (~tall(X3) & calm(X3))) [skolemisation 41,43,42]
45. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | (curious(X0) | creative(X0))) & ((~curious(X0) & ~creative(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 5]
46. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | curious(X0) | creative(X0)) & ((~curious(X0) & ~creative(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [flattening 45]
47. ! [X0] : (((old(X0) & ~generous(X0)) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | (~old(X0) | generous(X0)))) [nnf transformation 7]
48. ! [X0] : (((old(X0) & ~generous(X0)) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ~old(X0) | generous(X0))) [flattening 47]
49. ! [X0] : ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))) [nnf transformation 8]
50. ! [X0] : (((tall(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | (~tall(X0) | patient(X0)))) [nnf transformation 9]
51. ! [X0] : (((tall(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | ~tall(X0) | patient(X0))) [flattening 50]
63. ! [X0] : ((~generous(X0) | (old(X0) & patient(X0))) & ((~old(X0) | ~patient(X0)) | generous(X0))) [nnf transformation 14]
64. ! [X0] : ((~generous(X0) | (old(X0) & patient(X0))) & (~old(X0) | ~patient(X0) | generous(X0))) [flattening 63]
82. ~curious(sK3) | ~tall(X3) [cnf transformation 44]
84. old(sK3) | ~tall(X3) [cnf transformation 44]
87. ~brave(X0) | tall(X0) | ~creative(X0) [cnf transformation 46]
91. ~brave(X0) | ~tall(X0) | curious(X0) | creative(X0) [cnf transformation 46]
93. brave(X0) | generous(X0) | ~old(X0) | generous(X0) [cnf transformation 48]
94. ~generous(X0) | ~generous(X0) [cnf transformation 48]
98. funny(X0) | tall(X0) [cnf transformation 49]
100. ~tall(X0) | ~creative(X0) | patient(X0) [cnf transformation 51]
102. tall(X0) | creative(X0) [cnf transformation 51]
118. ~old(X0) | ~patient(X0) | generous(X0) [cnf transformation 64]
137. ~funny(lucy) [cnf transformation 22]
138. brave(X0) | generous(X0) | ~old(X0) [duplicate literal removal 93]
139. ~generous(X0) [duplicate literal removal 94]
198. 14 <=> ! [X3] : ~tall(X3) [avatar definition]
199. ~tall(X3) <- (14) [avatar component clause 198]
201. 15 <=> old(sK3) [avatar definition]
203. old(sK3) <- (15) [avatar component clause 201]
204. 14 | 15 [avatar split clause 84,201,198]
210. 17 <=> curious(sK3) [avatar definition]
212. ~curious(sK3) <- (~17) [avatar component clause 210]
213. 14 | ~17 [avatar split clause 82,210,198]
215. ~old(X0) | brave(X0) [subsumption resolution 138,139]
266. ~old(X0) | ~patient(X0) [subsumption resolution 118,139]
330. tall(lucy) [resolution 98,137]
340. brave(sK3) <- (15) [resolution 215,203]
342. ~patient(sK3) <- (15) [resolution 266,203]
473. ~tall(sK3) | curious(sK3) | creative(sK3) <- (15) [resolution 340,91]
475. tall(sK3) | ~creative(sK3) <- (15) [resolution 340,87]
478. ~tall(sK3) | creative(sK3) <- (15, ~17) [subsumption resolution 473,212]
479. creative(sK3) <- (15, ~17) [subsumption resolution 478,102]
480. tall(sK3) <- (15, ~17) [subsumption resolution 475,479]
514. ~creative(sK3) | patient(sK3) <- (15, ~17) [resolution 480,100]
530. patient(sK3) <- (15, ~17) [subsumption resolution 514,479]
531. $false <- (15, ~17) [subsumption resolution 530,342]
532. ~15 | 17 [avatar contradiction clause 531]
543. $false <- (14) [resolution 199,330]
544. ~14 [avatar contradiction clause 543]
547. $false [avatar sat refutation 204,213,532,544]
% SZS output end Proof for 7015725288818222270804068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not creative or not generous then someone is not brave and vice versa. If paul is not old or old then someone is strong and vice versa. If someone is either not creative or creative then alice is either rich or kind and vice versa. Everyone who is both not rich and not happy is strong. If fred is kind or patient then susan is both wise and not generous. Everyone who is tall is both not rich and not humble. Everyone who is both not humble and strong is not wise or creative. If lucy is both kind and not tall then john is curious and vice versa. If fred is quiet then someone is either curious or wise. Everyone who is both not brave and not happy is creative or quiet. If someone is both not tall and not wise then someone is not humble or creative and vice versa. Everyone who is both kind and not curious is not old or rich and vice versa. Everyone who is both strong and not tall is not calm. Everyone who is both not humble and not quiet is not kind. If mary is either happy or not calm then someone is either brave or not rich. Everyone who is humble is curious or not strong and vice versa. Someone is not funny. Lucy is both curious and not calm. Someone is either generous or tall. Someone is both funny and not generous. Someone is not tall or patient. Someone is either funny or not wise. Paul is both old and calm. Someone is rich. | Paul is not generous. | neutral | (((~creative(susan)|~generous(susan)))<=>(?[X]:(~brave(X))))&
(((~old(paul)|old(paul)))<=>(?[X]:(strong(X))))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
(![X]:((~humble(X)&~quiet(X))=>~kind(X)))&
(((happy(mary)<~>~calm(mary)))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(humble(X)<=>(curious(X)|~strong(X))))&
(?[X]:(~funny(X)))&
((curious(lucy)&~calm(lucy)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
((old(paul)&calm(paul)))&
(?[X]:(rich(X))) | ~generous(paul) | [] | null | 0 |
If someone is creative then someone is either tall or quiet.
Everyone who is happy is either funny or patient and vice versa.
Everyone who is tall is rich.
If john is either not patient or kind then someone is not creative and vice versa.
Everyone who is patient is both not curious and strong and vice versa.
Everyone who is strong is happy and vice versa.
If paul is curious then someone is not happy.
If someone is both funny and not tall then mary is either not happy or wise and vice versa.
If john is both not funny and not calm then someone is either not rich or quiet and vice versa.
Everyone who is both old and humble is either wise or calm and vice versa.
If fred is either not strong or not humble then fred is tall or not calm and vice versa.
Everyone who is either not brave or rich is not rich or not old and vice versa.
Everyone who is humble is both rich and not creative.
Everyone who is patient is either not curious or not creative and vice versa.
If someone is either curious or not brave then someone is either not happy or not strong.
Someone is not rich.
Paul is generous or curious.
John is either tall or humble.
Fred is not brave.
Someone is tall or not tall.
Alice is not calm or funny. | John is generous. | neutral | ((?[X]:(creative(X)))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:(happy(X)<=>(funny(X)<~>patient(X))))&
(![X]:(tall(X)=>rich(X)))&
(((~patient(john)<~>kind(john)))<=>(?[X]:(~creative(X))))&
(![X]:(patient(X)<=>(~curious(X)&strong(X))))&
(![X]:(strong(X)<=>happy(X)))&
((curious(paul))=>(?[X]:(~happy(X))))&
((?[X]:((funny(X)&~tall(X))))<=>((~happy(mary)<~>wise(mary))))&
(((~funny(john)&~calm(john)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:((old(X)&humble(X))<=>(wise(X)<~>calm(X))))&
(((~strong(fred)<~>~humble(fred)))<=>((tall(fred)|~calm(fred))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|~old(X))))&
(![X]:(humble(X)=>(rich(X)&~creative(X))))&
(![X]:(patient(X)<=>(~curious(X)<~>~creative(X))))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(?[X]:(~rich(X)))&
((generous(paul)|curious(paul)))&
((tall(john)<~>humble(john)))&
(~brave(fred))&
(?[X]:((tall(X)|~tall(X))))&
((~calm(alice)|funny(alice))) | generous(john) | [] | null | 0 |
If someone is both old and brave then lucy is not patient or quiet. Everyone who is either not brave or not happy is both tall and old and vice versa. If paul is both not calm and strong then susan is wise and vice versa. Everyone who is both strong and quiet is not curious or calm and vice versa. If paul is not quiet or rich then fred is both not strong and humble and vice versa. Everyone who is not calm is both strong and not strong and vice versa. If someone is both kind and not generous then john is either not humble or wise and vice versa. Everyone who is not curious is strong or calm. Everyone who is not generous or curious is either humble or not calm. Everyone who is not curious or brave is either not tall or strong. If someone is creative then someone is both not quiet and not humble and vice versa. Everyone who is either brave or old is quiet or calm. If someone is both not calm and tall then someone is both creative and not strong and vice versa. Everyone who is both wise and not quiet is rich and vice versa. If fred is both rich and strong then alice is funny or not creative. Everyone who is both not old and not funny is either not funny or not tall. Susan is happy or not patient. Someone is both old and not generous. Paul is humble or not creative. Someone is not rich or not creative. Someone is not generous. Someone is generous or happy. Fred is generous or not quiet. | John is quiet. | entailment | ((?[X]:((old(X)&brave(X))))=>((~patient(lucy)|quiet(lucy))))&
(![X]:((~brave(X)<~>~happy(X))<=>(tall(X)&old(X))))&
(((~calm(paul)&strong(paul)))<=>(wise(susan)))&
(![X]:((strong(X)&quiet(X))<=>(~curious(X)|calm(X))))&
(((~quiet(paul)|rich(paul)))<=>((~strong(fred)&humble(fred))))&
(![X]:(~calm(X)<=>(strong(X)&~strong(X))))&
((?[X]:((kind(X)&~generous(X))))<=>((~humble(john)<~>wise(john))))&
(![X]:(~curious(X)=>(strong(X)|calm(X))))&
(![X]:((~generous(X)|curious(X))=>(humble(X)<~>~calm(X))))&
(![X]:((~curious(X)|brave(X))=>(~tall(X)<~>strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:((brave(X)<~>old(X))=>(quiet(X)|calm(X))))&
((?[X]:((~calm(X)&tall(X))))<=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((wise(X)&~quiet(X))<=>rich(X)))&
(((rich(fred)&strong(fred)))=>((funny(alice)|~creative(alice))))&
(![X]:((~old(X)&~funny(X))=>(~funny(X)<~>~tall(X))))&
((happy(susan)|~patient(susan)))&
(?[X]:((old(X)&~generous(X))))&
((humble(paul)|~creative(paul)))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)|happy(X))))&
((generous(fred)|~quiet(fred))) | quiet(john) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8745716916428108686785450
% SZS output start Proof for 8745716916428108686785450
4. ! [X0] : ((quiet(X0) & strong(X0)) <=> (calm(X0) | ~curious(X0))) [input p3]
6. ! [X0] : (~calm(X0) <=> (~strong(X0) & strong(X0))) [input p5]
24. ~quiet(john) [input hypothesis]
43. ! [X0] : (((quiet(X0) & strong(X0)) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | (~quiet(X0) | ~strong(X0)))) [nnf transformation 4]
44. ! [X0] : (((quiet(X0) & strong(X0)) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | ~quiet(X0) | ~strong(X0))) [flattening 43]
47. ! [X0] : ((~calm(X0) | (strong(X0) | ~strong(X0))) & ((~strong(X0) & strong(X0)) | calm(X0))) [nnf transformation 6]
48. ! [X0] : ((~calm(X0) | strong(X0) | ~strong(X0)) & ((~strong(X0) & strong(X0)) | calm(X0))) [flattening 47]
90. ~calm(X0) | quiet(X0) [cnf transformation 44]
96. strong(X0) | calm(X0) [cnf transformation 48]
97. ~strong(X0) | calm(X0) [cnf transformation 48]
136. ~quiet(john) [cnf transformation 24]
174. calm(X0) [subsumption resolution 96,97]
288. quiet(X0) [resolution 90,174]
290. $false [resolution 288,136]
% SZS output end Proof for 8745716916428108686785450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not happy or quiet then lucy 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. Everyone who is kind or not old is both not calm and quiet and vice versa. Everyone who is either calm or old is tall or not calm and vice versa. Everyone who is not tall or funny is both not humble and rich. Everyone who is either not generous or old is not generous or patient. Everyone who is not humble or old is creative or not happy and vice versa. Someone is both rich and not wise. Someone is both patient and not brave. John is either not funny or not generous. Someone is either creative or generous. Someone is both brave and not rich. Alice is either kind or tall. | Fred is not old. | contradiction | (((~happy(lucy)|quiet(lucy)))<=>((~tall(lucy)<~>~old(lucy))))&
(![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]:((kind(X)|~old(X))<=>(~calm(X)&quiet(X))))&
(![X]:((calm(X)<~>old(X))<=>(tall(X)|~calm(X))))&
(![X]:((~tall(X)|funny(X))=>(~humble(X)&rich(X))))&
(![X]:((~generous(X)<~>old(X))=>(~generous(X)|patient(X))))&
(![X]:((~humble(X)|old(X))<=>(creative(X)|~happy(X))))&
(?[X]:((rich(X)&~wise(X))))&
(?[X]:((patient(X)&~brave(X))))&
((~funny(john)<~>~generous(john)))&
(?[X]:((creative(X)<~>generous(X))))&
(?[X]:((brave(X)&~rich(X))))&
((kind(alice)<~>tall(alice))) | ~old(fred) | [
"p1",
"p4",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7245015554231046927189518
% SZS output start Proof for 7245015554231046927189518
2. ! [X0] : (~quiet(X0) => (strong(X0) & quiet(X0))) [input p1]
5. ! [X0] : (quiet(X0) => (kind(X0) & creative(X0))) [input p4]
12. ! [X0] : ((~old(X0) | kind(X0)) <=> (quiet(X0) & ~calm(X0))) [input p11]
13. ! [X0] : ((calm(X0) <~> old(X0)) <=> (~calm(X0) | tall(X0))) [input p12]
23. ~old(fred) [input hypothesis]
27. ! [X0] : ((strong(X0) & quiet(X0)) | quiet(X0)) [ennf transformation 2]
30. ! [X0] : ((kind(X0) & creative(X0)) | ~quiet(X0)) [ennf transformation 5]
59. ! [X0] : (((~old(X0) | kind(X0)) | (~quiet(X0) | calm(X0))) & ((quiet(X0) & ~calm(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 12]
60. ! [X0] : ((~old(X0) | kind(X0) | ~quiet(X0) | calm(X0)) & ((quiet(X0) & ~calm(X0)) | (old(X0) & ~kind(X0)))) [flattening 59]
61. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | (calm(X0) & ~tall(X0))) & ((~calm(X0) | tall(X0)) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [nnf transformation 13]
62. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | (calm(X0) & ~tall(X0))) & (~calm(X0) | tall(X0) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [flattening 61]
83. quiet(X0) | quiet(X0) [cnf transformation 27]
93. kind(X0) | ~quiet(X0) [cnf transformation 30]
114. ~calm(X0) | ~kind(X0) [cnf transformation 60]
122. old(X0) | calm(X0) | calm(X0) [cnf transformation 62]
146. ~old(fred) [cnf transformation 23]
149. old(X0) | calm(X0) [duplicate literal removal 122]
150. quiet(X0) [duplicate literal removal 83]
201. kind(X0) [subsumption resolution 93,150]
247. ~calm(X0) [subsumption resolution 114,201]
248. old(X0) [subsumption resolution 149,247]
262. $false [subsumption resolution 146,248]
% SZS output end Proof for 7245015554231046927189518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or happy is either not tall or strong and vice versa. Everyone who is funny is either not curious or tall and vice versa. If susan is curious then susan is both funny and not humble and vice versa. Everyone who is not funny is tall. Everyone who is either patient or old is both rich and wise. If someone is both rich and happy then someone is strong and vice versa. Everyone who is not kind or not tall is wise. If someone is either creative or not rich then mary is not brave or tall. If someone is both calm and patient then fred is both not humble and not calm and vice versa. Everyone who is not kind or old is both not humble and kind. Everyone who is not calm or not quiet is both not calm and not strong and vice versa. Everyone who is not generous or not patient is calm. Everyone who is either tall or not wise is brave and vice versa. If someone is not brave then someone is both not generous and generous and vice versa. If lucy is both humble and not happy then fred is not old and vice versa. Everyone who is not old or not rich is either rich or not humble and vice versa. Someone is both not rich and calm. Paul is not curious. Fred is not quiet. John is not old or rich. Alice is either curious or happy. John is either curious or not brave. Someone is creative or not funny. | John is quiet. | neutral | (![X]:((~tall(X)<~>happy(X))<=>(~tall(X)<~>strong(X))))&
(![X]:(funny(X)<=>(~curious(X)<~>tall(X))))&
((curious(susan))<=>((funny(susan)&~humble(susan))))&
(![X]:(~funny(X)=>tall(X)))&
(![X]:((patient(X)<~>old(X))=>(rich(X)&wise(X))))&
((?[X]:((rich(X)&happy(X))))<=>(?[X]:(strong(X))))&
(![X]:((~kind(X)|~tall(X))=>wise(X)))&
((?[X]:((creative(X)<~>~rich(X))))=>((~brave(mary)|tall(mary))))&
((?[X]:((calm(X)&patient(X))))<=>((~humble(fred)&~calm(fred))))&
(![X]:((~kind(X)|old(X))=>(~humble(X)&kind(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~generous(X)|~patient(X))=>calm(X)))&
(![X]:((tall(X)<~>~wise(X))<=>brave(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~generous(X)&generous(X)))))&
(((humble(lucy)&~happy(lucy)))<=>(~old(fred)))&
(![X]:((~old(X)|~rich(X))<=>(rich(X)<~>~humble(X))))&
(?[X]:((~rich(X)&calm(X))))&
(~curious(paul))&
(~quiet(fred))&
((~old(john)|rich(john)))&
((curious(alice)<~>happy(alice)))&
((curious(john)<~>~brave(john)))&
(?[X]:((creative(X)|~funny(X)))) | quiet(john) | [] | null | 0 |
If fred is both not brave and not patient then paul is not creative and vice versa.
Everyone who is creative or not kind is not kind or creative and vice versa.
Everyone who is not creative is humble and vice versa.
If someone is not brave then someone is not old or not quiet.
Everyone who is not patient is either not strong or not quiet.
Everyone who is not creative is both not creative and not tall and vice versa.
If alice is not curious then fred is not calm and vice versa.
Everyone who is either rich or not humble is funny and vice versa.
Everyone who is either creative or not kind is brave or happy.
If someone is not tall or not generous then someone is either quiet or happy.
Everyone who is patient is either quiet or not wise and vice versa.
If someone is not kind then someone is not humble.
If john is rich then someone is either not calm or old.
Everyone who is either funny or wise is kind or not calm.
Everyone who is not creative or not calm is both not kind and tall and vice versa.
If mary is both wise and not kind then someone is both humble and not happy.
John is generous.
Fred is kind.
Someone is patient or not curious.
Someone is happy.
Mary is both not humble and not kind.
Alice is either creative or not tall.
Someone is either not tall or not happy.
Mary is both creative and quiet. | Mary is not patient. | entailment | (((~brave(fred)&~patient(fred)))<=>(~creative(paul)))&
(![X]:((creative(X)|~kind(X))<=>(~kind(X)|creative(X))))&
(![X]:(~creative(X)<=>humble(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:(~patient(X)=>(~strong(X)<~>~quiet(X))))&
(![X]:(~creative(X)<=>(~creative(X)&~tall(X))))&
((~curious(alice))<=>(~calm(fred)))&
(![X]:((rich(X)<~>~humble(X))<=>funny(X)))&
(![X]:((creative(X)<~>~kind(X))=>(brave(X)|happy(X))))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((quiet(X)<~>happy(X)))))&
(![X]:(patient(X)<=>(quiet(X)<~>~wise(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~humble(X))))&
((rich(john))=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:((funny(X)<~>wise(X))=>(kind(X)|~calm(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~kind(X)&tall(X))))&
(((wise(mary)&~kind(mary)))=>(?[X]:((humble(X)&~happy(X)))))&
(generous(john))&
(kind(fred))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:(happy(X)))&
((~humble(mary)&~kind(mary)))&
((creative(alice)<~>~tall(alice)))&
(?[X]:((~tall(X)<~>~happy(X))))&
((creative(mary)&quiet(mary))) | ~patient(mary) | [
"p2",
"p5",
"p10",
"p14",
"p15",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7951351531740070532638878
% SZS output start Proof for 7951351531740070532638878
3. ! [X0] : (~creative(X0) <=> humble(X0)) [input p2]
6. ! [X0] : (~creative(X0) <=> (~tall(X0) & ~creative(X0))) [input p5]
11. ! [X0] : (patient(X0) <=> (quiet(X0) <~> ~wise(X0))) [input p10]
15. ! [X0] : ((~calm(X0) | ~creative(X0)) <=> (tall(X0) & ~kind(X0))) [input p14]
16. (~kind(mary) & wise(mary)) => ? [X0] : (~happy(X0) & humble(X0)) [input p15]
21. ~kind(mary) & ~humble(mary) [input p20]
24. quiet(mary) & creative(mary) [input p23]
25. patient(mary) [input hypothesis]
40. ? [X0] : (~happy(X0) & humble(X0)) | (kind(mary) | ~wise(mary)) [ennf transformation 16]
41. ? [X0] : (~happy(X0) & humble(X0)) | kind(mary) | ~wise(mary) [flattening 40]
46. ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))) [nnf transformation 3]
51. ! [X0] : ((~creative(X0) | (tall(X0) | creative(X0))) & ((~tall(X0) & ~creative(X0)) | creative(X0))) [nnf transformation 6]
52. ! [X0] : ((~creative(X0) | tall(X0) | creative(X0)) & ((~tall(X0) & ~creative(X0)) | creative(X0))) [flattening 51]
60. ! [X0] : ((patient(X0) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ~patient(X0))) [nnf transformation 11]
68. ! [X0] : (((~calm(X0) | ~creative(X0)) | (~tall(X0) | kind(X0))) & ((tall(X0) & ~kind(X0)) | (calm(X0) & creative(X0)))) [nnf transformation 15]
69. ! [X0] : ((~calm(X0) | ~creative(X0) | ~tall(X0) | kind(X0)) & ((tall(X0) & ~kind(X0)) | (calm(X0) & creative(X0)))) [flattening 68]
70. ? [X0] : (~happy(X0) & humble(X0)) => (~happy(sK4) & humble(sK4)) [choice axiom]
71. (~happy(sK4) & humble(sK4)) | kind(mary) | ~wise(mary) [skolemisation 41,70]
88. ~humble(X0) | ~creative(X0) [cnf transformation 46]
93. ~tall(X0) | creative(X0) [cnf transformation 52]
106. ~quiet(X0) | wise(X0) | ~patient(X0) [cnf transformation 60]
116. tall(X0) | creative(X0) [cnf transformation 69]
119. humble(sK4) | kind(mary) | ~wise(mary) [cnf transformation 71]
125. ~kind(mary) [cnf transformation 21]
131. quiet(mary) [cnf transformation 24]
132. patient(mary) [cnf transformation 25]
206. creative(X0) [subsumption resolution 116,93]
208. 17 <=> wise(mary) [avatar definition]
212. 18 <=> kind(mary) [avatar definition]
221. 20 <=> humble(sK4) [avatar definition]
223. humble(sK4) <- (20) [avatar component clause 221]
224. ~17 | 18 | 20 [avatar split clause 119,221,212,208]
234. ~18 [avatar split clause 125,212]
264. wise(mary) | ~patient(mary) [resolution 106,131]
268. wise(mary) [subsumption resolution 264,132]
269. 17 [avatar split clause 268,208]
271. ~creative(sK4) <- (20) [resolution 223,88]
272. $false <- (20) [subsumption resolution 271,206]
273. ~20 [avatar contradiction clause 272]
274. $false [avatar sat refutation 224,234,269,273]
% SZS output end Proof for 7951351531740070532638878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not generous is not patient or kind.
Everyone who is either kind or not humble is not creative.
Everyone who is not curious or old is not generous or wise.
Everyone who is either not calm or not creative is brave or funny and vice versa.
If someone is either happy or not curious then someone is both not brave and strong.
Everyone who is both not creative and quiet is not tall and vice versa.
If lucy is not patient then susan is both quiet and creative.
Everyone who is not humble or calm is not tall and vice versa.
Everyone who is not curious is quiet or generous and vice versa.
If fred is wise or not happy then lucy is humble or funny.
If lucy is both not creative and not happy then lucy is not brave and vice versa.
If someone is not strong then lucy is not tall.
Everyone who is either not patient or calm is both humble and not old and vice versa.
Everyone who is calm is strong.
Everyone who is not happy or not curious is both wise and kind and vice versa.
If fred is generous or quiet then someone is happy or patient.
Someone is not creative or not calm.
Someone is creative or curious.
Someone is not humble or not calm.
Someone is either strong or not creative.
Fred is generous or strong.
Someone is either not quiet or not old.
Fred is both not strong and not funny.
John is not wise or calm. | Susan is old. | neutral | (![X]:((~wise(X)|~generous(X))=>(~patient(X)|kind(X))))&
(![X]:((kind(X)<~>~humble(X))=>~creative(X)))&
(![X]:((~curious(X)|old(X))=>(~generous(X)|wise(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(brave(X)|funny(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((~creative(X)&quiet(X))<=>~tall(X)))&
((~patient(lucy))=>((quiet(susan)&creative(susan))))&
(![X]:((~humble(X)|calm(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(quiet(X)|generous(X))))&
(((wise(fred)|~happy(fred)))=>((humble(lucy)|funny(lucy))))&
(((~creative(lucy)&~happy(lucy)))<=>(~brave(lucy)))&
((?[X]:(~strong(X)))=>(~tall(lucy)))&
(![X]:((~patient(X)<~>calm(X))<=>(humble(X)&~old(X))))&
(![X]:(calm(X)=>strong(X)))&
(![X]:((~happy(X)|~curious(X))<=>(wise(X)&kind(X))))&
(((generous(fred)|quiet(fred)))=>(?[X]:((happy(X)|patient(X)))))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
((generous(fred)|strong(fred)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~strong(fred)&~funny(fred)))&
((~wise(john)|calm(john))) | old(susan) | [] | null | 0 |
Everyone who is strong or not kind is old.
If mary is either not brave or not quiet then someone is both not patient and not curious and vice versa.
Everyone who is not funny or not kind is creative.
Everyone who is both not rich and not tall is both curious and not wise and vice versa.
If someone is both quiet and kind then someone is either brave or creative and vice versa.
If someone is not curious or brave then someone is both calm and not happy and vice versa.
Everyone who is both not humble and not funny is either not tall or not kind.
If john is not wise then john is both not tall and not humble and vice versa.
If someone is either happy or not patient then someone is not patient or not strong and vice versa.
If alice is both not calm and happy then someone is not rich or not humble and vice versa.
Everyone who is humble is both not old and quiet and vice versa.
If mary is either strong or creative then john is both rich and not quiet and vice versa.
If mary is quiet or patient then someone is calm.
Everyone who is brave is not funny.
Everyone who is either wise or not rich is both strong and brave.
If someone is calm or not happy then someone is both humble and not kind and vice versa.
Someone is either generous or not tall.
Someone is both not old and not brave.
Someone is kind or not calm.
Someone is old.
Fred is either not patient or not kind.
Lucy is either old or not quiet.
Fred is tall. | John is not happy. | contradiction | (![X]:((strong(X)|~kind(X))=>old(X)))&
(((~brave(mary)<~>~quiet(mary)))<=>(?[X]:((~patient(X)&~curious(X)))))&
(![X]:((~funny(X)|~kind(X))=>creative(X)))&
(![X]:((~rich(X)&~tall(X))<=>(curious(X)&~wise(X))))&
((?[X]:((quiet(X)&kind(X))))<=>(?[X]:((brave(X)<~>creative(X)))))&
((?[X]:((~curious(X)|brave(X))))<=>(?[X]:((calm(X)&~happy(X)))))&
(![X]:((~humble(X)&~funny(X))=>(~tall(X)<~>~kind(X))))&
((~wise(john))<=>((~tall(john)&~humble(john))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(?[X]:((~patient(X)|~strong(X)))))&
(((~calm(alice)&happy(alice)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:(humble(X)<=>(~old(X)&quiet(X))))&
(((strong(mary)<~>creative(mary)))<=>((rich(john)&~quiet(john))))&
(((quiet(mary)|patient(mary)))=>(?[X]:(calm(X))))&
(![X]:(brave(X)=>~funny(X)))&
(![X]:((wise(X)<~>~rich(X))=>(strong(X)&brave(X))))&
((?[X]:((calm(X)|~happy(X))))<=>(?[X]:((humble(X)&~kind(X)))))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((kind(X)|~calm(X))))&
(?[X]:(old(X)))&
((~patient(fred)<~>~kind(fred)))&
((old(lucy)<~>~quiet(lucy)))&
(tall(fred)) | ~happy(john) | [
"p0",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 908740272322932137667744
% SZS output start Proof for 908740272322932137667744
1. ! [X0] : ((~kind(X0) | strong(X0)) => old(X0)) [input p0]
11. ! [X0] : (humble(X0) <=> (quiet(X0) & ~old(X0))) [input p10]
16. ? [X0] : (~happy(X0) | calm(X0)) <=> ? [X0] : (~kind(X0) & humble(X0)) [input p15]
24. ~happy(john) [input hypothesis]
28. ? [X0] : (~happy(X0) | calm(X0)) <=> ? [X1] : (~kind(X1) & humble(X1)) [rectify 16]
29. ! [X0] : (old(X0) | (kind(X0) & ~strong(X0))) [ennf transformation 1]
65. ! [X0] : ((humble(X0) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | ~humble(X0))) [nnf transformation 11]
66. ! [X0] : ((humble(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | ~humble(X0))) [flattening 65]
72. (? [X0] : (~happy(X0) | calm(X0)) | ! [X1] : (kind(X1) | ~humble(X1))) & (? [X1] : (~kind(X1) & humble(X1)) | ! [X0] : (happy(X0) & ~calm(X0))) [nnf transformation 28]
73. (? [X0] : (~happy(X0) | calm(X0)) | ! [X1] : (kind(X1) | ~humble(X1))) & (? [X2] : (~kind(X2) & humble(X2)) | ! [X3] : (happy(X3) & ~calm(X3))) [rectify 72]
74. ? [X0] : (~happy(X0) | calm(X0)) => (~happy(sK9) | calm(sK9)) [choice axiom]
75. ? [X2] : (~kind(X2) & humble(X2)) => (~kind(sK10) & humble(sK10)) [choice axiom]
76. ((~happy(sK9) | calm(sK9)) | ! [X1] : (kind(X1) | ~humble(X1))) & ((~kind(sK10) & humble(sK10)) | ! [X3] : (happy(X3) & ~calm(X3))) [skolemisation 73,75,74]
89. old(X0) | kind(X0) [cnf transformation 29]
129. ~humble(X0) | ~old(X0) [cnf transformation 66]
146. humble(sK10) | happy(X3) [cnf transformation 76]
148. ~kind(sK10) | happy(X3) [cnf transformation 76]
161. ~happy(john) [cnf transformation 24]
369. 46 <=> ! [X3] : happy(X3) [avatar definition]
370. happy(X3) <- (46) [avatar component clause 369]
372. 47 <=> kind(sK10) [avatar definition]
374. ~kind(sK10) <- (~47) [avatar component clause 372]
375. 46 | ~47 [avatar split clause 148,372,369]
381. 49 <=> humble(sK10) [avatar definition]
383. humble(sK10) <- (49) [avatar component clause 381]
384. 46 | 49 [avatar split clause 146,381,369]
444. ~old(sK10) <- (49) [resolution 129,383]
447. kind(sK10) <- (49) [resolution 444,89]
448. $false <- (~47, 49) [subsumption resolution 447,374]
449. 47 | ~49 [avatar contradiction clause 448]
450. $false <- (46) [resolution 370,161]
451. ~46 [avatar contradiction clause 450]
452. $false [avatar sat refutation 375,384,449,451]
% SZS output end Proof for 908740272322932137667744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either not old or rich and vice versa. Everyone who is either patient or not old is not curious or old and vice versa. If someone is not strong then john is not rich and vice versa. Everyone who is not kind is either not quiet or not kind and vice versa. Everyone who is either generous or funny is both not brave and not rich. If alice is not rich then someone is either not tall or not humble. Everyone who is either funny or not curious is both happy and funny. If lucy is both strong and happy then lucy is not rich or not creative and vice versa. If someone is either curious or kind then someone is either not kind or happy and vice versa. Everyone who is either curious or calm is both not old and kind. If alice is either not humble or not strong then someone is patient. Everyone who is both not rich and not curious is not wise and vice versa. If someone is either creative or not patient then someone is not rich or not wise. If john is brave or not humble then mary is either not curious or not creative. If someone is both not curious and creative then someone is creative or not curious. Everyone who is both happy and not wise is quiet or not old and vice versa. Someone is either not tall or old. Mary is not old. Paul is not strong or not creative. John is not humble or generous. Alice is not funny or not tall. | John is brave. | neutral | (![X]:(~rich(X)<=>(~old(X)<~>rich(X))))&
(![X]:((patient(X)<~>~old(X))<=>(~curious(X)|old(X))))&
((?[X]:(~strong(X)))<=>(~rich(john)))&
(![X]:(~kind(X)<=>(~quiet(X)<~>~kind(X))))&
(![X]:((generous(X)<~>funny(X))=>(~brave(X)&~rich(X))))&
((~rich(alice))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((funny(X)<~>~curious(X))=>(happy(X)&funny(X))))&
(((strong(lucy)&happy(lucy)))<=>((~rich(lucy)|~creative(lucy))))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:((curious(X)<~>calm(X))=>(~old(X)&kind(X))))&
(((~humble(alice)<~>~strong(alice)))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&~curious(X))<=>~wise(X)))&
((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((~rich(X)|~wise(X)))))&
(((brave(john)|~humble(john)))=>((~curious(mary)<~>~creative(mary))))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((happy(X)&~wise(X))<=>(quiet(X)|~old(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(~old(mary))&
((~strong(paul)|~creative(paul)))&
((~humble(john)|generous(john)))&
((~funny(alice)|~tall(alice))) | brave(john) | [] | null | 0 |
Everyone who is strong or not rich is both old and calm and vice versa. If mary is not curious then someone is either not tall or kind and vice versa. If john is either not strong or strong then alice is curious. Everyone who is both not patient and generous is not calm or not generous. If john is both creative and rich then someone is not generous or not tall and vice versa. If someone is either curious or not brave then someone is wise and vice versa. If alice is both kind and not happy then someone is either curious or quiet and vice versa. Everyone who is not rich or wise is rich. If someone is not creative or not curious then fred is not strong. Everyone who is not funny or not quiet is either brave or not generous. If lucy is not happy or wise then john is strong or generous and vice versa. If alice is both happy and not humble then someone is not kind. If someone is brave or not patient then someone is not happy or curious. Everyone who is both funny and not strong is not strong or happy and vice versa. If paul is either tall or not patient then susan is both not funny and creative. Everyone who is not rich or calm is both happy and humble. Someone is curious. John is either not quiet or humble. Mary is either not funny or not humble. Paul is not patient. Alice is either generous or rich. Susan is either curious or not old. Someone is either not generous or not curious. | Lucy is not funny. | contradiction | (![X]:((strong(X)|~rich(X))<=>(old(X)&calm(X))))&
((~curious(mary))<=>(?[X]:((~tall(X)<~>kind(X)))))&
(((~strong(john)<~>strong(john)))=>(curious(alice)))&
(![X]:((~patient(X)&generous(X))=>(~calm(X)|~generous(X))))&
(((creative(john)&rich(john)))<=>(?[X]:((~generous(X)|~tall(X)))))&
((?[X]:((curious(X)<~>~brave(X))))<=>(?[X]:(wise(X))))&
(((kind(alice)&~happy(alice)))<=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:((~rich(X)|wise(X))=>rich(X)))&
((?[X]:((~creative(X)|~curious(X))))=>(~strong(fred)))&
(![X]:((~funny(X)|~quiet(X))=>(brave(X)<~>~generous(X))))&
(((~happy(lucy)|wise(lucy)))<=>((strong(john)|generous(john))))&
(((happy(alice)&~humble(alice)))=>(?[X]:(~kind(X))))&
((?[X]:((brave(X)|~patient(X))))=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:((funny(X)&~strong(X))<=>(~strong(X)|happy(X))))&
(((tall(paul)<~>~patient(paul)))=>((~funny(susan)&creative(susan))))&
(![X]:((~rich(X)|calm(X))=>(happy(X)&humble(X))))&
(?[X]:(curious(X)))&
((~quiet(john)<~>humble(john)))&
((~funny(mary)<~>~humble(mary)))&
(~patient(paul))&
((generous(alice)<~>rich(alice)))&
((curious(susan)<~>~old(susan)))&
(?[X]:((~generous(X)<~>~curious(X)))) | ~funny(lucy) | [
"p0",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 153005367038559047182608
% SZS output start Proof for 153005367038559047182608
1. ! [X0] : ((~rich(X0) | strong(X0)) <=> (calm(X0) & old(X0))) [input p0]
14. ! [X0] : ((~strong(X0) & funny(X0)) <=> (happy(X0) | ~strong(X0))) [input p13]
16. ! [X0] : ((calm(X0) | ~rich(X0)) => (humble(X0) & happy(X0))) [input p15]
24. ~funny(lucy) [input hypothesis]
37. ! [X0] : ((humble(X0) & happy(X0)) | (~calm(X0) & rich(X0))) [ennf transformation 16]
38. ! [X0] : (((~rich(X0) | strong(X0)) | (~calm(X0) | ~old(X0))) & ((calm(X0) & old(X0)) | (rich(X0) & ~strong(X0)))) [nnf transformation 1]
39. ! [X0] : ((~rich(X0) | strong(X0) | ~calm(X0) | ~old(X0)) & ((calm(X0) & old(X0)) | (rich(X0) & ~strong(X0)))) [flattening 38]
68. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 14]
69. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | strong(X0) | ~funny(X0))) [flattening 68]
82. ~strong(X0) | calm(X0) [cnf transformation 39]
123. funny(X0) | strong(X0) [cnf transformation 69]
124. ~happy(X0) | funny(X0) [cnf transformation 69]
132. ~calm(X0) | happy(X0) [cnf transformation 37]
147. ~funny(lucy) [cnf transformation 24]
281. 30 <=> happy(lucy) [avatar definition]
282. happy(lucy) <- (30) [avatar component clause 281]
391. strong(lucy) [resolution 123,147]
392. calm(lucy) [resolution 391,82]
396. happy(lucy) [resolution 132,392]
399. 30 [avatar split clause 396,281]
401. funny(lucy) <- (30) [resolution 282,124]
404. $false <- (30) [subsumption resolution 401,147]
405. ~30 [avatar contradiction clause 404]
406. $false [avatar sat refutation 399,405]
% SZS output end Proof for 153005367038559047182608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then someone is either not funny or patient and vice versa. Everyone who is not rich is not funny or generous and vice versa. Everyone who is not funny is happy or not quiet and vice versa. If someone is not humble or not quiet then susan is both strong and rich. Everyone who is tall or creative is patient or not humble. Everyone who is curious or kind is either not calm or rich. If lucy is either patient or not wise then mary is either not humble or not wise. If john is strong or patient then lucy is quiet. If john is not patient then paul is both not generous and quiet and vice versa. If john is old or happy then fred is either humble or not creative. Everyone who is both not old and not patient is both creative and old. If someone is both kind and tall then someone is not patient and vice versa. If john is both not calm and humble then someone is not humble or tall and vice versa. If someone is creative then fred is both not calm and old and vice versa. If someone is both curious and not wise then alice is either not brave or not curious and vice versa. If someone is humble or rich then susan is not kind. Fred is generous. Lucy is not wise or wise. Paul is both not funny and patient. Someone is both generous and wise. Paul is generous. Someone is both not brave and not patient. Someone is either happy or tall. | Susan is kind. | contradiction | ((?[X]:(humble(X)))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(~rich(X)<=>(~funny(X)|generous(X))))&
(![X]:(~funny(X)<=>(happy(X)|~quiet(X))))&
((?[X]:((~humble(X)|~quiet(X))))=>((strong(susan)&rich(susan))))&
(![X]:((tall(X)|creative(X))=>(patient(X)|~humble(X))))&
(![X]:((curious(X)|kind(X))=>(~calm(X)<~>rich(X))))&
(((patient(lucy)<~>~wise(lucy)))=>((~humble(mary)<~>~wise(mary))))&
(((strong(john)|patient(john)))=>(quiet(lucy)))&
((~patient(john))<=>((~generous(paul)&quiet(paul))))&
(((old(john)|happy(john)))=>((humble(fred)<~>~creative(fred))))&
(![X]:((~old(X)&~patient(X))=>(creative(X)&old(X))))&
((?[X]:((kind(X)&tall(X))))<=>(?[X]:(~patient(X))))&
(((~calm(john)&humble(john)))<=>(?[X]:((~humble(X)|tall(X)))))&
((?[X]:(creative(X)))<=>((~calm(fred)&old(fred))))&
((?[X]:((curious(X)&~wise(X))))<=>((~brave(alice)<~>~curious(alice))))&
((?[X]:((humble(X)|rich(X))))=>(~kind(susan)))&
(generous(fred))&
((~wise(lucy)|wise(lucy)))&
((~funny(paul)&patient(paul)))&
(?[X]:((generous(X)&wise(X))))&
(generous(paul))&
(?[X]:((~brave(X)&~patient(X))))&
(?[X]:((happy(X)<~>tall(X)))) | kind(susan) | [
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 329450806262544251654875
% SZS output start Proof for 329450806262544251654875
13. (humble(john) & ~calm(john)) <=> ? [X0] : (tall(X0) | ~humble(X0)) [input p12]
16. ? [X0] : (rich(X0) | humble(X0)) => ~kind(susan) [input p15]
24. kind(susan) [input hypothesis]
36. ~kind(susan) | ! [X0] : (~rich(X0) & ~humble(X0)) [ennf transformation 16]
56. ((humble(john) & ~calm(john)) | ! [X0] : (~tall(X0) & humble(X0))) & (? [X0] : (tall(X0) | ~humble(X0)) | (~humble(john) | calm(john))) [nnf transformation 13]
57. ((humble(john) & ~calm(john)) | ! [X0] : (~tall(X0) & humble(X0))) & (? [X0] : (tall(X0) | ~humble(X0)) | ~humble(john) | calm(john)) [flattening 56]
58. ((humble(john) & ~calm(john)) | ! [X0] : (~tall(X0) & humble(X0))) & (? [X1] : (tall(X1) | ~humble(X1)) | ~humble(john) | calm(john)) [rectify 57]
59. ? [X1] : (tall(X1) | ~humble(X1)) => (tall(sK4) | ~humble(sK4)) [choice axiom]
60. ((humble(john) & ~calm(john)) | ! [X0] : (~tall(X0) & humble(X0))) & ((tall(sK4) | ~humble(sK4)) | ~humble(john) | calm(john)) [skolemisation 58,59]
118. humble(john) | humble(X0) [cnf transformation 60]
129. ~kind(susan) | ~humble(X0) [cnf transformation 36]
142. kind(susan) [cnf transformation 24]
157. 4 <=> ! [X3] : ~humble(X3) [avatar definition]
158. ~humble(X3) <- (4) [avatar component clause 157]
178. 9 <=> ! [X0] : humble(X0) [avatar definition]
179. humble(X0) <- (9) [avatar component clause 178]
277. 30 <=> humble(john) [avatar definition]
279. humble(john) <- (30) [avatar component clause 277]
281. 9 | 30 [avatar split clause 118,277,178]
344. 44 <=> kind(susan) [avatar definition]
348. 4 | ~44 [avatar split clause 129,344,157]
360. 44 [avatar split clause 142,344]
363. $false <- (4, 9) [subsumption resolution 158,179]
364. ~4 | ~9 [avatar contradiction clause 363]
365. $false <- (4, 30) [subsumption resolution 279,158]
366. ~4 | ~30 [avatar contradiction clause 365]
369. $false [avatar sat refutation 281,348,360,364,366]
% SZS output end Proof for 329450806262544251654875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is calm then someone is wise or tall and vice versa.
If susan is not funny or not calm then lucy is wise or not funny and vice versa.
Everyone who is not calm is both not tall and not patient.
If lucy is either funny or not funny then someone is either not brave or not creative and vice versa.
If someone is either not brave or kind then john is not generous.
Everyone who is either curious or not brave is both quiet and tall.
If fred is either not wise or not creative then mary is rich or creative and vice versa.
If susan is either not old or old then someone is both not kind and not wise and vice versa.
Everyone who is happy is not brave or happy and vice versa.
Everyone who is rich is curious and vice versa.
If susan is humble or not rich then lucy is both not creative and patient.
Everyone who is not strong or kind is not rich and vice versa.
If susan is not calm or humble then someone is both not tall and not creative.
Everyone who is not strong or rich is tall or happy.
If someone is not wise then someone is brave or creative.
Everyone who is strong is either calm or wise and vice versa.
Fred is old or not funny.
Someone is not strong or not humble.
Susan is generous.
Mary is either not brave or not patient.
Mary is either not tall or strong.
Susan is both generous and not brave.
Fred is either old or generous.
Lucy is not wise or patient. | Susan is humble. | neutral | ((calm(lucy))<=>(?[X]:((wise(X)|tall(X)))))&
(((~funny(susan)|~calm(susan)))<=>((wise(lucy)|~funny(lucy))))&
(![X]:(~calm(X)=>(~tall(X)&~patient(X))))&
(((funny(lucy)<~>~funny(lucy)))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
((?[X]:((~brave(X)<~>kind(X))))=>(~generous(john)))&
(![X]:((curious(X)<~>~brave(X))=>(quiet(X)&tall(X))))&
(((~wise(fred)<~>~creative(fred)))<=>((rich(mary)|creative(mary))))&
(((~old(susan)<~>old(susan)))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:(happy(X)<=>(~brave(X)|happy(X))))&
(![X]:(rich(X)<=>curious(X)))&
(((humble(susan)|~rich(susan)))=>((~creative(lucy)&patient(lucy))))&
(![X]:((~strong(X)|kind(X))<=>~rich(X)))&
(((~calm(susan)|humble(susan)))=>(?[X]:((~tall(X)&~creative(X)))))&
(![X]:((~strong(X)|rich(X))=>(tall(X)|happy(X))))&
((?[X]:(~wise(X)))=>(?[X]:((brave(X)|creative(X)))))&
(![X]:(strong(X)<=>(calm(X)<~>wise(X))))&
((old(fred)|~funny(fred)))&
(?[X]:((~strong(X)|~humble(X))))&
(generous(susan))&
((~brave(mary)<~>~patient(mary)))&
((~tall(mary)<~>strong(mary)))&
((generous(susan)&~brave(susan)))&
((old(fred)<~>generous(fred)))&
((~wise(lucy)|patient(lucy))) | humble(susan) | [] | null | 0 |
Everyone who is either not generous or not kind is both creative and not kind and vice versa.
Everyone who is either humble or not generous is either not tall or funny and vice versa.
If lucy is either humble or generous then someone is not creative.
Everyone who is rich or not rich is not brave and vice versa.
If someone is both kind and not old then someone is strong or not tall and vice versa.
Everyone who is old or humble is both not generous and not brave.
Everyone who is both not old and creative is both not patient and not strong and vice versa.
If someone is both humble and strong then fred is happy or not kind and vice versa.
If someone is both not brave and generous then someone is either not funny or quiet.
If someone is calm or brave then someone is both not humble and not strong and vice versa.
If someone is not funny or not humble then someone is either calm or not wise and vice versa.
Everyone who is not calm or not creative is either not brave or not old.
Everyone who is not wise or not curious is not curious and vice versa.
If lucy is both not patient and quiet then someone is humble.
Everyone who is not quiet is either humble or kind.
Someone is both tall and calm.
Lucy is calm.
Alice is either not curious or happy.
Someone is either not brave or old.
Lucy is either not curious or creative.
Someone is either not creative or strong.
Someone is both not patient and happy.
Someone is not calm. | Lucy is quiet. | neutral | (![X]:((~generous(X)<~>~kind(X))<=>(creative(X)&~kind(X))))&
(![X]:((humble(X)<~>~generous(X))<=>(~tall(X)<~>funny(X))))&
(((humble(lucy)<~>generous(lucy)))=>(?[X]:(~creative(X))))&
(![X]:((rich(X)|~rich(X))<=>~brave(X)))&
((?[X]:((kind(X)&~old(X))))<=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((old(X)|humble(X))=>(~generous(X)&~brave(X))))&
(![X]:((~old(X)&creative(X))<=>(~patient(X)&~strong(X))))&
((?[X]:((humble(X)&strong(X))))<=>((happy(fred)|~kind(fred))))&
((?[X]:((~brave(X)&generous(X))))=>(?[X]:((~funny(X)<~>quiet(X)))))&
((?[X]:((calm(X)|brave(X))))<=>(?[X]:((~humble(X)&~strong(X)))))&
((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:((~calm(X)|~creative(X))=>(~brave(X)<~>~old(X))))&
(![X]:((~wise(X)|~curious(X))<=>~curious(X)))&
(((~patient(lucy)&quiet(lucy)))=>(?[X]:(humble(X))))&
(![X]:(~quiet(X)=>(humble(X)<~>kind(X))))&
(?[X]:((tall(X)&calm(X))))&
(calm(lucy))&
((~curious(alice)<~>happy(alice)))&
(?[X]:((~brave(X)<~>old(X))))&
((~curious(lucy)<~>creative(lucy)))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:((~patient(X)&happy(X))))&
(?[X]:(~calm(X))) | quiet(lucy) | [] | null | 0 |
Everyone who is not strong or generous is quiet and vice versa.
Everyone who is both not happy and tall is not wise and vice versa.
Everyone who is funny or humble is either generous or not calm.
Everyone who is not curious is either not happy or not rich and vice versa.
If someone is old or not old then someone is not rich or tall.
If mary is not wise then someone is not rich or not creative.
If mary is both not wise and tall then someone is both funny and not rich and vice versa.
If someone is not humble or not wise then mary is either not brave or quiet and vice versa.
Everyone who is wise is old and vice versa.
If susan is wise then lucy is either not funny or wise and vice versa.
Everyone who is happy is both not tall and quiet and vice versa.
Everyone who is both wise and not quiet is rich or kind.
Everyone who is not kind is not quiet or not tall and vice versa.
Everyone who is both patient and not quiet is either quiet or kind and vice versa.
Everyone who is not tall is not calm and vice versa.
If fred is not funny or not creative then someone is not brave.
Someone is not rich.
John is both creative and calm.
Someone is rich.
Lucy is strong.
Alice is not quiet or quiet. | Susan is quiet. | neutral | (![X]:((~strong(X)|generous(X))<=>quiet(X)))&
(![X]:((~happy(X)&tall(X))<=>~wise(X)))&
(![X]:((funny(X)|humble(X))=>(generous(X)<~>~calm(X))))&
(![X]:(~curious(X)<=>(~happy(X)<~>~rich(X))))&
((?[X]:((old(X)|~old(X))))=>(?[X]:((~rich(X)|tall(X)))))&
((~wise(mary))=>(?[X]:((~rich(X)|~creative(X)))))&
(((~wise(mary)&tall(mary)))<=>(?[X]:((funny(X)&~rich(X)))))&
((?[X]:((~humble(X)|~wise(X))))<=>((~brave(mary)<~>quiet(mary))))&
(![X]:(wise(X)<=>old(X)))&
((wise(susan))<=>((~funny(lucy)<~>wise(lucy))))&
(![X]:(happy(X)<=>(~tall(X)&quiet(X))))&
(![X]:((wise(X)&~quiet(X))=>(rich(X)|kind(X))))&
(![X]:(~kind(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((patient(X)&~quiet(X))<=>(quiet(X)<~>kind(X))))&
(![X]:(~tall(X)<=>~calm(X)))&
(((~funny(fred)|~creative(fred)))=>(?[X]:(~brave(X))))&
(?[X]:(~rich(X)))&
((creative(john)&calm(john)))&
(?[X]:(rich(X)))&
(strong(lucy))&
((~quiet(alice)|quiet(alice))) | quiet(susan) | [] | null | 0 |
Everyone who is both not creative and not old is not quiet or humble and vice versa.
Everyone who is not strong or wise is not brave.
If lucy is not humble or not old then mary is both brave and kind and vice versa.
Everyone who is either not calm or calm is both not creative and not old and vice versa.
If someone is both not quiet and strong then someone is either not quiet or not creative.
Everyone who is both not quiet and not humble is either not rich or generous.
If susan is not rich or not calm then john is creative.
Everyone who is both patient and curious is not tall.
Everyone who is either not strong or not old is not tall.
If someone is calm or kind then someone is either not tall or kind.
Everyone who is not humble is either funny or not calm and vice versa.
If someone is either not wise or not calm then someone is either tall or not brave and vice versa.
Everyone who is patient or curious is both creative and not old and vice versa.
Everyone who is not calm or not quiet is either not patient or not creative.
If someone is either not generous or curious then lucy is not brave or funny.
Susan is happy.
Alice is both wise and humble.
Susan is both strong and not generous.
Alice is either happy or not strong.
Alice is either calm or rich.
Someone is not brave.
Mary is either patient or not patient. | Mary is not calm. | contradiction | (![X]:((~creative(X)&~old(X))<=>(~quiet(X)|humble(X))))&
(![X]:((~strong(X)|wise(X))=>~brave(X)))&
(((~humble(lucy)|~old(lucy)))<=>((brave(mary)&kind(mary))))&
(![X]:((~calm(X)<~>calm(X))<=>(~creative(X)&~old(X))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(![X]:((~quiet(X)&~humble(X))=>(~rich(X)<~>generous(X))))&
(((~rich(susan)|~calm(susan)))=>(creative(john)))&
(![X]:((patient(X)&curious(X))=>~tall(X)))&
(![X]:((~strong(X)<~>~old(X))=>~tall(X)))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:(~humble(X)<=>(funny(X)<~>~calm(X))))&
((?[X]:((~wise(X)<~>~calm(X))))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(![X]:((patient(X)|curious(X))<=>(creative(X)&~old(X))))&
(![X]:((~calm(X)|~quiet(X))=>(~patient(X)<~>~creative(X))))&
((?[X]:((~generous(X)<~>curious(X))))=>((~brave(lucy)|funny(lucy))))&
(happy(susan))&
((wise(alice)&humble(alice)))&
((strong(susan)&~generous(susan)))&
((happy(alice)<~>~strong(alice)))&
((calm(alice)<~>rich(alice)))&
(?[X]:(~brave(X)))&
((patient(mary)<~>~patient(mary))) | ~calm(mary) | [
"p3",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6057368994689009358281750
% SZS output start Proof for 6057368994689009358281750
4. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (~old(X0) & ~creative(X0))) [input p3]
13. ! [X0] : ((curious(X0) | patient(X0)) <=> (~old(X0) & creative(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (~patient(X0) <~> ~creative(X0))) [input p13]
23. ~calm(mary) [input hypothesis]
36. ! [X0] : ((~patient(X0) <~> ~creative(X0)) | (quiet(X0) & calm(X0))) [ennf transformation 14]
43. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [flattening 43]
61. ! [X0] : (((curious(X0) | patient(X0)) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | (~curious(X0) & ~patient(X0)))) [nnf transformation 13]
62. ! [X0] : ((curious(X0) | patient(X0) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | (~curious(X0) & ~patient(X0)))) [flattening 61]
63. ! [X0] : (((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | (quiet(X0) & calm(X0))) [nnf transformation 36]
82. ~creative(X0) | calm(X0) | calm(X0) [cnf transformation 44]
83. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 44]
113. creative(X0) | ~patient(X0) [cnf transformation 62]
120. creative(X0) | patient(X0) | calm(X0) [cnf transformation 63]
136. ~calm(mary) [cnf transformation 23]
137. ~creative(X0) | calm(X0) [duplicate literal removal 82]
138. ~creative(X0) | ~calm(X0) [duplicate literal removal 83]
162. ~creative(X0) [subsumption resolution 137,138]
230. ~patient(X0) [subsumption resolution 113,162]
233. patient(X0) | calm(X0) [subsumption resolution 120,162]
234. calm(X0) [subsumption resolution 233,230]
259. $false [subsumption resolution 136,234]
% SZS output end Proof for 6057368994689009358281750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not calm is not patient. Everyone who is humble or quiet is both tall and calm. Everyone who is both not old and happy is both funny and humble. If lucy is not strong or not curious then fred is either not wise or not generous. If susan is either generous or not tall then someone is not humble or rich. Everyone who is old is either not generous or funny and vice versa. If someone is rich or not calm then someone is both calm and not funny and vice versa. If someone is not strong then someone is both funny and not humble. Everyone who is both rich and wise is either generous or funny and vice versa. Everyone who is either not kind or old is humble and vice versa. Everyone who is either kind or tall is both not kind and not generous. If alice is not curious then fred is both not brave and not creative and vice versa. If john is either not happy or not strong then paul is not funny or not calm. If lucy is not quiet then lucy is funny or patient and vice versa. Everyone who is either strong or generous is not strong and vice versa. Everyone who is curious is not kind and vice versa. Fred is both curious and not calm. John is patient or not funny. John is not strong. Someone is funny or creative. Mary is either happy or quiet. Someone is not wise or not creative. | Susan is strong. | neutral | (![X]:((~creative(X)|~calm(X))=>~patient(X)))&
(![X]:((humble(X)|quiet(X))=>(tall(X)&calm(X))))&
(![X]:((~old(X)&happy(X))=>(funny(X)&humble(X))))&
(((~strong(lucy)|~curious(lucy)))=>((~wise(fred)<~>~generous(fred))))&
(((generous(susan)<~>~tall(susan)))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:(old(X)<=>(~generous(X)<~>funny(X))))&
((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:((rich(X)&wise(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~kind(X)<~>old(X))<=>humble(X)))&
(![X]:((kind(X)<~>tall(X))=>(~kind(X)&~generous(X))))&
((~curious(alice))<=>((~brave(fred)&~creative(fred))))&
(((~happy(john)<~>~strong(john)))=>((~funny(paul)|~calm(paul))))&
((~quiet(lucy))<=>((funny(lucy)|patient(lucy))))&
(![X]:((strong(X)<~>generous(X))<=>~strong(X)))&
(![X]:(curious(X)<=>~kind(X)))&
((curious(fred)&~calm(fred)))&
((patient(john)|~funny(john)))&
(~strong(john))&
(?[X]:((funny(X)|creative(X))))&
((happy(mary)<~>quiet(mary)))&
(?[X]:((~wise(X)|~creative(X)))) | strong(susan) | [] | null | 0 |
Everyone who is brave is either not wise or not kind and vice versa.
Everyone who is either not wise or not curious is both kind and strong and vice versa.
If someone is not brave or funny then someone is not brave.
If mary is not strong or strong then john is calm or generous.
Everyone who is both not happy and tall is either not humble or not old.
If mary is not rich then someone is both not happy and old.
Everyone who is generous is both strong and not patient.
Everyone who is quiet or kind is happy or funny and vice versa.
Everyone who is both generous and wise is not humble and vice versa.
If someone is both not tall and not old then someone is brave or not generous and vice versa.
If susan is kind then someone is both funny and patient and vice versa.
Everyone who is not quiet is both creative and funny and vice versa.
Everyone who is not kind or not humble is not generous or not curious.
If john is not curious then someone is wise or not rich.
If someone is kind then someone is both curious and not kind.
Everyone who is kind or quiet is both strong and patient and vice versa.
Alice is either not curious or not wise.
Paul is not creative.
Someone is not tall.
Fred is not kind.
Paul is both not generous and not creative.
Alice is not creative.
Someone is not calm. | John is humble. | entailment | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(kind(X)&strong(X))))&
((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~brave(X))))&
(((~strong(mary)|strong(mary)))=>((calm(john)|generous(john))))&
(![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))&
((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
((~curious(alice)<~>~wise(alice)))&
(~creative(paul))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~generous(paul)&~creative(paul)))&
(~creative(alice))&
(?[X]:(~calm(X))) | humble(john) | [
"p1",
"p6",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5791679587534723393536245
% SZS output start Proof for 5791679587534723393536245
2. ! [X0] : ((~wise(X0) <~> ~curious(X0)) <=> (strong(X0) & kind(X0))) [input p1]
7. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p6]
9. ! [X0] : ((wise(X0) & generous(X0)) <=> ~humble(X0)) [input p8]
13. ! [X0] : ((~humble(X0) | ~kind(X0)) => (~curious(X0) | ~generous(X0))) [input p12]
16. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p15]
24. ~humble(john) [input hypothesis]
34. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 7]
35. ! [X0] : ((~curious(X0) | ~generous(X0)) | (humble(X0) & kind(X0))) [ennf transformation 13]
36. ! [X0] : (~curious(X0) | ~generous(X0) | (humble(X0) & kind(X0))) [flattening 35]
40. ! [X0] : ((((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0))))) [nnf transformation 2]
41. ! [X0] : ((((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0))))) [flattening 40]
50. ! [X0] : (((wise(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | (~wise(X0) | ~generous(X0)))) [nnf transformation 9]
51. ! [X0] : (((wise(X0) & generous(X0)) | humble(X0)) & (~humble(X0) | ~wise(X0) | ~generous(X0))) [flattening 50]
68. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 68]
80. ~wise(X0) | kind(X0) | curious(X0) [cnf transformation 41]
94. ~patient(X0) | ~generous(X0) [cnf transformation 34]
100. humble(X0) | generous(X0) [cnf transformation 51]
101. humble(X0) | wise(X0) [cnf transformation 51]
114. ~curious(X0) | ~generous(X0) | humble(X0) [cnf transformation 36]
120. ~kind(X0) | patient(X0) [cnf transformation 69]
132. ~humble(john) [cnf transformation 24]
154. 6 <=> generous(john) [avatar definition]
156. generous(john) <- (6) [avatar component clause 154]
221. ~curious(X0) | humble(X0) [subsumption resolution 114,100]
223. 21 <=> curious(john) [avatar definition]
225. curious(john) <- (21) [avatar component clause 223]
258. generous(john) [resolution 100,132]
259. 6 [avatar split clause 258,154]
261. wise(john) [resolution 101,132]
284. 29 <=> kind(john) [avatar definition]
286. kind(john) <- (29) [avatar component clause 284]
295. kind(john) | curious(john) [resolution 80,261]
296. 21 | 29 [avatar split clause 295,284,223]
298. humble(john) <- (21) [resolution 225,221]
299. $false <- (21) [subsumption resolution 298,132]
300. ~21 [avatar contradiction clause 299]
319. patient(john) <- (29) [resolution 286,120]
336. ~generous(john) <- (29) [resolution 319,94]
337. $false <- (6, 29) [subsumption resolution 336,156]
338. ~6 | ~29 [avatar contradiction clause 337]
339. $false [avatar sat refutation 259,296,300,338]
% SZS output end Proof for 5791679587534723393536245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is not strong.
Everyone who is not funny is either calm or not kind.
If someone is both not calm and rich then john is funny or calm and vice versa.
Everyone who is not brave is both quiet and not funny.
If someone is either not brave or not rich then alice is creative or not generous and vice versa.
Everyone who is not old is calm or quiet.
If someone is not kind or quiet then paul is both not patient and brave.
Everyone who is old or creative is happy.
Everyone who is both not tall and not brave is both old and not old.
Everyone who is both kind and not strong is both humble and not patient.
If susan is both not happy and not generous then someone is creative or not wise.
Everyone who is both generous and not quiet is either old or quiet.
Everyone who is quiet is not wise.
Everyone who is both not humble and kind is both not wise and strong and vice versa.
Everyone who is both not tall and calm is not happy or patient and vice versa.
If someone is not strong or humble then someone is either not happy or not humble.
Mary is both not strong and not curious.
Fred is not strong or not curious.
Someone is either funny or rich.
Alice is not old or curious.
Susan is not kind or funny.
Susan is either strong or patient.
Someone is both generous and tall.
Someone is either curious or strong. | Fred is not rich. | neutral | ((?[X]:(~generous(X)))=>(?[X]:(~strong(X))))&
(![X]:(~funny(X)=>(calm(X)<~>~kind(X))))&
((?[X]:((~calm(X)&rich(X))))<=>((funny(john)|calm(john))))&
(![X]:(~brave(X)=>(quiet(X)&~funny(X))))&
((?[X]:((~brave(X)<~>~rich(X))))<=>((creative(alice)|~generous(alice))))&
(![X]:(~old(X)=>(calm(X)|quiet(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((~patient(paul)&brave(paul))))&
(![X]:((old(X)|creative(X))=>happy(X)))&
(![X]:((~tall(X)&~brave(X))=>(old(X)&~old(X))))&
(![X]:((kind(X)&~strong(X))=>(humble(X)&~patient(X))))&
(((~happy(susan)&~generous(susan)))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:((generous(X)&~quiet(X))=>(old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>~wise(X)))&
(![X]:((~humble(X)&kind(X))<=>(~wise(X)&strong(X))))&
(![X]:((~tall(X)&calm(X))<=>(~happy(X)|patient(X))))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((~happy(X)<~>~humble(X)))))&
((~strong(mary)&~curious(mary)))&
((~strong(fred)|~curious(fred)))&
(?[X]:((funny(X)<~>rich(X))))&
((~old(alice)|curious(alice)))&
((~kind(susan)|funny(susan)))&
((strong(susan)<~>patient(susan)))&
(?[X]:((generous(X)&tall(X))))&
(?[X]:((curious(X)<~>strong(X)))) | ~rich(fred) | [] | null | 0 |
Everyone who is both rich and funny is rich or happy. If john is both generous and strong then someone is not old and vice versa. Everyone who is either not happy or not strong is brave and vice versa. Everyone who is old or creative is either not wise or generous and vice versa. Everyone who is wise is happy or not old. Everyone who is either not patient or quiet is calm. Everyone who is kind or old is both not tall and not funny and vice versa. Everyone who is patient or tall is either wise or not patient and vice versa. Everyone who is not generous is humble or kind and vice versa. Everyone who is both not curious and not patient is either not generous or not strong and vice versa. If fred is either generous or not funny then someone is both calm and not funny and vice versa. If susan is both not rich and not brave then someone is both brave and rich and vice versa. Everyone who is quiet is not curious. If someone is either not strong or rich then fred is both old and wise. If lucy is both not quiet and not happy then someone is either not brave or rich and vice versa. Everyone who is both wise and not brave is both not humble and quiet. Someone is either not curious or calm. Mary is both generous and old. Mary is not creative. Someone is rich or not tall. Alice is either brave or not strong. Someone is either calm or not calm. Alice is both not humble and not curious. | John is not humble. | entailment | (![X]:((rich(X)&funny(X))=>(rich(X)|happy(X))))&
(((generous(john)&strong(john)))<=>(?[X]:(~old(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>brave(X)))&
(![X]:((old(X)|creative(X))<=>(~wise(X)<~>generous(X))))&
(![X]:(wise(X)=>(happy(X)|~old(X))))&
(![X]:((~patient(X)<~>quiet(X))=>calm(X)))&
(![X]:((kind(X)|old(X))<=>(~tall(X)&~funny(X))))&
(![X]:((patient(X)|tall(X))<=>(wise(X)<~>~patient(X))))&
(![X]:(~generous(X)<=>(humble(X)|kind(X))))&
(![X]:((~curious(X)&~patient(X))<=>(~generous(X)<~>~strong(X))))&
(((generous(fred)<~>~funny(fred)))<=>(?[X]:((calm(X)&~funny(X)))))&
(((~rich(susan)&~brave(susan)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:(quiet(X)=>~curious(X)))&
((?[X]:((~strong(X)<~>rich(X))))=>((old(fred)&wise(fred))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(![X]:((wise(X)&~brave(X))=>(~humble(X)&quiet(X))))&
(?[X]:((~curious(X)<~>calm(X))))&
((generous(mary)&old(mary)))&
(~creative(mary))&
(?[X]:((rich(X)|~tall(X))))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~humble(alice)&~curious(alice))) | ~humble(john) | [
"p1",
"p3",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 221011950324342776698528
% SZS output start Proof for 221011950324342776698528
2. (strong(john) & generous(john)) <=> ? [X0] : ~old(X0) [input p1]
4. ! [X0] : ((creative(X0) | old(X0)) <=> (~wise(X0) <~> generous(X0))) [input p3]
7. ! [X0] : ((old(X0) | kind(X0)) <=> (~funny(X0) & ~tall(X0))) [input p6]
8. ! [X0] : ((tall(X0) | patient(X0)) <=> (wise(X0) <~> ~patient(X0))) [input p7]
9. ! [X0] : (~generous(X0) <=> (kind(X0) | humble(X0))) [input p8]
24. humble(john) [input hypothesis]
34. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (~strong(john) | ~generous(john))) [nnf transformation 2]
35. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~strong(john) | ~generous(john)) [flattening 34]
36. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~strong(john) | ~generous(john)) [rectify 35]
37. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
38. ((strong(john) & generous(john)) | ! [X0] : old(X0)) & (~old(sK0) | ~strong(john) | ~generous(john)) [skolemisation 36,37]
40. ! [X0] : (((creative(X0) | old(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & ~old(X0)))) [nnf transformation 4]
41. ! [X0] : ((creative(X0) | old(X0) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~creative(X0) & ~old(X0)))) [flattening 40]
43. ! [X0] : (((old(X0) | kind(X0)) | (funny(X0) | tall(X0))) & ((~funny(X0) & ~tall(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 7]
44. ! [X0] : ((old(X0) | kind(X0) | funny(X0) | tall(X0)) & ((~funny(X0) & ~tall(X0)) | (~old(X0) & ~kind(X0)))) [flattening 43]
45. ! [X0] : (((tall(X0) | patient(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~tall(X0) & ~patient(X0)))) [nnf transformation 8]
46. ! [X0] : ((tall(X0) | patient(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (~tall(X0) & ~patient(X0)))) [flattening 45]
47. ! [X0] : ((~generous(X0) | (~kind(X0) & ~humble(X0))) & ((kind(X0) | humble(X0)) | generous(X0))) [nnf transformation 9]
48. ! [X0] : ((~generous(X0) | (~kind(X0) & ~humble(X0))) & (kind(X0) | humble(X0) | generous(X0))) [flattening 47]
77. generous(john) | old(X0) [cnf transformation 38]
83. ~wise(X0) | generous(X0) | ~old(X0) [cnf transformation 41]
93. ~tall(X0) | ~old(X0) [cnf transformation 44]
97. ~patient(X0) | wise(X0) | ~patient(X0) [cnf transformation 46]
102. tall(X0) | patient(X0) | wise(X0) | patient(X0) [cnf transformation 46]
104. ~humble(X0) | ~generous(X0) [cnf transformation 48]
147. humble(john) [cnf transformation 24]
148. ~patient(X0) | wise(X0) [duplicate literal removal 97]
149. tall(X0) | patient(X0) | wise(X0) [duplicate literal removal 102]
151. 1 <=> ! [X0] : old(X0) [avatar definition]
152. old(X0) <- (1) [avatar component clause 151]
159. 3 <=> generous(john) [avatar definition]
160. ~generous(john) <- (~3) [avatar component clause 159]
162. 1 | 3 [avatar split clause 77,159,151]
289. ~generous(john) [resolution 104,147]
292. ~3 [avatar split clause 289,159]
431. patient(X2) | wise(X2) | ~old(X2) [resolution 149,93]
436. patient(X2) | wise(X2) <- (1) [subsumption resolution 431,152]
437. wise(X2) <- (1) [subsumption resolution 436,148]
474. generous(X3) | ~old(X3) <- (1) [resolution 437,83]
480. generous(X3) <- (1) [subsumption resolution 474,152]
555. $false <- (1, ~3) [resolution 480,160]
558. ~1 | 3 [avatar contradiction clause 555]
559. $false [avatar sat refutation 162,292,558]
% SZS output end Proof for 221011950324342776698528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both quiet and funny is either not rich or funny and vice versa.
If someone is strong or happy then someone is not curious or creative and vice versa.
If mary is generous or happy then someone is rich or not old and vice versa.
If someone is not tall or funny then mary is not creative.
If alice is kind or not patient then mary is either curious or not tall and vice versa.
If susan is not quiet or humble then susan is either generous or not kind and vice versa.
If paul is not old or not tall then someone is not brave or wise.
If someone is humble or not brave then someone is both not quiet and rich.
Everyone who is either not rich or not funny is funny.
If alice is either not humble or not creative then paul is either not funny or not quiet.
If alice is funny then someone is not happy.
Everyone who is either not patient or not quiet is not old or humble.
If paul is both not kind and not strong then someone is kind and vice versa.
Everyone who is either patient or not strong is either calm or strong.
Everyone who is not strong is either not humble or not brave and vice versa.
If fred is not curious or curious then someone is either not humble or patient and vice versa.
Alice is both old and creative.
Susan is both not humble and wise.
Someone is both happy and kind.
Lucy is brave.
Someone is not quiet or patient.
Someone is not creative or not tall.
Susan is not generous. | Paul is humble. | contradiction | (![X]:((quiet(X)&funny(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((strong(X)|happy(X))))<=>(?[X]:((~curious(X)|creative(X)))))&
(((generous(mary)|happy(mary)))<=>(?[X]:((rich(X)|~old(X)))))&
((?[X]:((~tall(X)|funny(X))))=>(~creative(mary)))&
(((kind(alice)|~patient(alice)))<=>((curious(mary)<~>~tall(mary))))&
(((~quiet(susan)|humble(susan)))<=>((generous(susan)<~>~kind(susan))))&
(((~old(paul)|~tall(paul)))=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((humble(X)|~brave(X))))=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:((~rich(X)<~>~funny(X))=>funny(X)))&
(((~humble(alice)<~>~creative(alice)))=>((~funny(paul)<~>~quiet(paul))))&
((funny(alice))=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)<~>~quiet(X))=>(~old(X)|humble(X))))&
(((~kind(paul)&~strong(paul)))<=>(?[X]:(kind(X))))&
(![X]:((patient(X)<~>~strong(X))=>(calm(X)<~>strong(X))))&
(![X]:(~strong(X)<=>(~humble(X)<~>~brave(X))))&
(((~curious(fred)|curious(fred)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
((old(alice)&creative(alice)))&
((~humble(susan)&wise(susan)))&
(?[X]:((happy(X)&kind(X))))&
(brave(lucy))&
(?[X]:((~quiet(X)|patient(X))))&
(?[X]:((~creative(X)|~tall(X))))&
(~generous(susan)) | humble(paul) | [
"p0",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1766129711928400602640004
% SZS output start Proof for 1766129711928400602640004
1. ! [X0] : ((funny(X0) & quiet(X0)) <=> (~rich(X0) <~> funny(X0))) [input p0]
8. ? [X0] : (~brave(X0) | humble(X0)) => ? [X0] : (rich(X0) & ~quiet(X0)) [input p7]
9. ! [X0] : ((~rich(X0) <~> ~funny(X0)) => funny(X0)) [input p8]
24. humble(paul) [input hypothesis]
26. ? [X0] : (~brave(X0) | humble(X0)) => ? [X1] : (rich(X1) & ~quiet(X1)) [rectify 8]
30. ? [X1] : (rich(X1) & ~quiet(X1)) | ! [X0] : (brave(X0) & ~humble(X0)) [ennf transformation 26]
31. ! [X0] : (funny(X0) | (~rich(X0) <=> ~funny(X0))) [ennf transformation 9]
37. ! [X0] : (((funny(X0) & quiet(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((funny(X0) & quiet(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | ~funny(X0) | ~quiet(X0))) [flattening 37]
53. ? [X0] : (rich(X0) & ~quiet(X0)) | ! [X1] : (brave(X1) & ~humble(X1)) [rectify 30]
54. ? [X0] : (rich(X0) & ~quiet(X0)) => (rich(sK3) & ~quiet(sK3)) [choice axiom]
55. (rich(sK3) & ~quiet(sK3)) | ! [X1] : (brave(X1) & ~humble(X1)) [skolemisation 53,54]
56. ! [X0] : (funny(X0) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) [nnf transformation 31]
82. ~rich(X0) | quiet(X0) | ~funny(X0) [cnf transformation 38]
83. funny(X0) | funny(X0) | rich(X0) [cnf transformation 38]
107. ~quiet(sK3) | ~humble(X1) [cnf transformation 55]
109. rich(sK3) | ~humble(X1) [cnf transformation 55]
112. funny(X0) | ~rich(X0) | funny(X0) [cnf transformation 56]
146. humble(paul) [cnf transformation 24]
149. funny(X0) | ~rich(X0) [duplicate literal removal 112]
151. rich(X0) | funny(X0) [duplicate literal removal 83]
271. 27 <=> rich(sK3) [avatar definition]
273. rich(sK3) <- (27) [avatar component clause 271]
276. 28 <=> ! [X1] : ~humble(X1) [avatar definition]
277. ~humble(X1) <- (28) [avatar component clause 276]
278. 28 | 27 [avatar split clause 109,271,276]
280. 29 <=> quiet(sK3) [avatar definition]
282. ~quiet(sK3) <- (~29) [avatar component clause 280]
284. 28 | ~29 [avatar split clause 107,280,276]
285. funny(X0) [subsumption resolution 149,151]
360. quiet(sK3) | ~funny(sK3) <- (27) [resolution 82,273]
362. ~funny(sK3) <- (27, ~29) [subsumption resolution 360,282]
363. $false <- (27, ~29) [subsumption resolution 362,285]
364. ~27 | 29 [avatar contradiction clause 363]
366. $false <- (28) [resolution 277,146]
367. ~28 [avatar contradiction clause 366]
368. $false [avatar sat refutation 278,284,364,367]
% SZS output end Proof for 1766129711928400602640004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and not generous is either quiet or not tall and vice versa.
If someone is both not funny and curious then someone is both quiet and not humble and vice versa.
If fred is either strong or not creative then someone is patient or creative.
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
If fred is not quiet or not kind then someone is both happy and creative and vice versa.
If susan is both strong and not patient then someone is either curious or quiet.
Everyone who is creative is funny.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
If someone is strong or not quiet then someone is curious or not tall.
If paul is either brave or not calm then mary is not kind or not humble and vice versa.
Everyone who is both not rich and brave is both brave and not calm and vice versa.
Susan is both not curious and old.
Someone is curious.
Fred is either not calm or not rich.
Someone is generous.
Someone is both quiet and not happy.
Someone is either curious or humble. | Paul is not brave. | neutral | (![X]:((~rich(X)&~generous(X))<=>(quiet(X)<~>~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(((brave(paul)<~>~calm(paul)))<=>((~kind(mary)|~humble(mary))))&
(![X]:((~rich(X)&brave(X))<=>(brave(X)&~calm(X))))&
((~curious(susan)&old(susan)))&
(?[X]:(curious(X)))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((curious(X)<~>humble(X)))) | ~brave(paul) | [] | null | 0 |
If lucy is either funny or not rich then susan is both calm and brave. If someone is wise then someone is rich or not strong. Everyone who is not strong is both not tall and generous and vice versa. Everyone who is both not funny and rich is not curious or not patient and vice versa. Everyone who is not tall or not humble is both not generous and not rich. If someone is quiet or old then someone is humble. If lucy is both not wise and patient then alice is not generous or kind. Everyone who is generous is both old and rich and vice versa. Everyone who is either not kind or not generous is not creative or strong and vice versa. Everyone who is either quiet or not tall is brave and vice versa. Everyone who is brave or quiet is not quiet or not brave and vice versa. If mary is tall or creative then someone is not strong or not happy. Everyone who is tall or patient is either quiet or rich and vice versa. Everyone who is not strong or not rich is either strong or not funny. If someone is either not patient or not rich then mary is rich or not creative and vice versa. Someone is either rich or kind. Someone is not humble or not happy. Mary is not old or patient. Someone is not curious or kind. Fred is either curious or rich. | Alice is not generous. | entailment | (((funny(lucy)<~>~rich(lucy)))=>((calm(susan)&brave(susan))))&
((?[X]:(wise(X)))=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&generous(X))))&
(![X]:((~funny(X)&rich(X))<=>(~curious(X)|~patient(X))))&
(![X]:((~tall(X)|~humble(X))=>(~generous(X)&~rich(X))))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:(humble(X))))&
(((~wise(lucy)&patient(lucy)))=>((~generous(alice)|kind(alice))))&
(![X]:(generous(X)<=>(old(X)&rich(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~creative(X)|strong(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>brave(X)))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|~brave(X))))&
(((tall(mary)|creative(mary)))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((tall(X)|patient(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~strong(X)|~rich(X))=>(strong(X)<~>~funny(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>((rich(mary)|~creative(mary))))&
(?[X]:((rich(X)<~>kind(X))))&
(?[X]:((~humble(X)|~happy(X))))&
((~old(mary)|patient(mary)))&
(?[X]:((~curious(X)|kind(X))))&
((curious(fred)<~>rich(fred))) | ~generous(alice) | [
"p4",
"p7",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6187679764539277750705203
% SZS output start Proof for 6187679764539277750705203
5. ! [X0] : ((~humble(X0) | ~tall(X0)) => (~rich(X0) & ~generous(X0))) [input p4]
8. ! [X0] : (generous(X0) <=> (rich(X0) & old(X0))) [input p7]
10. ! [X0] : ((quiet(X0) <~> ~tall(X0)) <=> brave(X0)) [input p9]
11. ! [X0] : ((quiet(X0) | brave(X0)) <=> (~brave(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : ((patient(X0) | tall(X0)) <=> (quiet(X0) <~> rich(X0))) [input p12]
21. generous(alice) [input hypothesis]
26. ! [X0] : (~tall(X0) => (~rich(X0) & ~generous(X0))) [pure predicate removal 5]
31. ! [X0] : ((~rich(X0) & ~generous(X0)) | tall(X0)) [ennf transformation 26]
43. ! [X0] : ((generous(X0) | (~rich(X0) | ~old(X0))) & ((rich(X0) & old(X0)) | ~generous(X0))) [nnf transformation 8]
44. ! [X0] : ((generous(X0) | ~rich(X0) | ~old(X0)) & ((rich(X0) & old(X0)) | ~generous(X0))) [flattening 43]
47. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | ~brave(X0)) & (brave(X0) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [nnf transformation 10]
48. ! [X0] : (((quiet(X0) | brave(X0)) | (brave(X0) & quiet(X0))) & ((~brave(X0) | ~quiet(X0)) | (~quiet(X0) & ~brave(X0)))) [nnf transformation 11]
49. ! [X0] : ((quiet(X0) | brave(X0) | (brave(X0) & quiet(X0))) & (~brave(X0) | ~quiet(X0) | (~quiet(X0) & ~brave(X0)))) [flattening 48]
50. ! [X0] : (((patient(X0) | tall(X0)) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | (~patient(X0) & ~tall(X0)))) [nnf transformation 13]
51. ! [X0] : ((patient(X0) | tall(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | (~patient(X0) & ~tall(X0)))) [flattening 50]
75. ~generous(X0) | tall(X0) [cnf transformation 31]
76. ~rich(X0) | tall(X0) [cnf transformation 31]
79. ~generous(X0) | rich(X0) [cnf transformation 44]
89. ~tall(X0) | quiet(X0) | ~brave(X0) [cnf transformation 47]
92. ~brave(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 49]
94. quiet(X0) | brave(X0) | brave(X0) [cnf transformation 49]
97. ~rich(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 51]
117. generous(alice) [cnf transformation 21]
120. ~quiet(X0) | ~brave(X0) [duplicate literal removal 92]
122. quiet(X0) | brave(X0) [duplicate literal removal 94]
158. 9 <=> generous(alice) [avatar definition]
159. generous(alice) <- (9) [avatar component clause 158]
168. ~quiet(X0) | ~rich(X0) [subsumption resolution 97,76]
235. 9 [avatar split clause 117,158]
244. tall(alice) <- (9) [resolution 75,159]
257. rich(alice) <- (9) [resolution 79,159]
268. ~rich(X0) | brave(X0) [resolution 168,122]
275. brave(alice) <- (9) [resolution 268,257]
295. quiet(alice) | ~brave(alice) <- (9) [resolution 89,244]
299. quiet(alice) <- (9) [subsumption resolution 295,275]
305. ~brave(alice) <- (9) [resolution 299,120]
308. $false <- (9) [subsumption resolution 305,275]
309. ~9 [avatar contradiction clause 308]
310. $false [avatar sat refutation 235,309]
% SZS output end Proof for 6187679764539277750705203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or tall is both not strong and wise.
Everyone who is kind or strong is either not tall or not quiet.
Everyone who is rich or not patient is either not generous or quiet and vice versa.
Everyone who is either tall or not creative is strong or patient and vice versa.
Everyone who is either not wise or not funny is kind and vice versa.
If someone is either happy or wise then someone is both wise and not rich and vice versa.
Everyone who is either not funny or old is both old and patient and vice versa.
If susan is rich or not patient then alice is both not calm and curious.
Everyone who is not funny or not patient is both creative and patient and vice versa.
Everyone who is both not rich and kind is humble.
Everyone who is not kind or not wise is not rich or not tall.
If paul is patient or funny then someone is rich and vice versa.
Everyone who is either not brave or brave is kind or not old and vice versa.
Everyone who is not calm is both not brave and not rich.
If alice is both not patient and quiet then someone is either generous or calm and vice versa.
Alice is not humble or patient.
Fred is both funny and wise.
Someone is either not humble or not strong.
Someone is either not quiet or not happy.
John is either not wise or not strong.
Fred is either quiet or not humble.
Someone is not kind. | Paul is funny. | entailment | (![X]:((quiet(X)<~>tall(X))=>(~strong(X)&wise(X))))&
(![X]:((kind(X)|strong(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((rich(X)|~patient(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((tall(X)<~>~creative(X))<=>(strong(X)|patient(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((happy(X)<~>wise(X))))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~funny(X)<~>old(X))<=>(old(X)&patient(X))))&
(((rich(susan)|~patient(susan)))=>((~calm(alice)&curious(alice))))&
(![X]:((~funny(X)|~patient(X))<=>(creative(X)&patient(X))))&
(![X]:((~rich(X)&kind(X))=>humble(X)))&
(![X]:((~kind(X)|~wise(X))=>(~rich(X)|~tall(X))))&
(((patient(paul)|funny(paul)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(kind(X)|~old(X))))&
(![X]:(~calm(X)=>(~brave(X)&~rich(X))))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:((generous(X)<~>calm(X)))))&
((~humble(alice)|patient(alice)))&
((funny(fred)&wise(fred)))&
(?[X]:((~humble(X)<~>~strong(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((~wise(john)<~>~strong(john)))&
((quiet(fred)<~>~humble(fred)))&
(?[X]:(~kind(X))) | funny(paul) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8290171064715544053356918
% SZS output start Proof for 8290171064715544053356918
7. ! [X0] : ((~funny(X0) <~> old(X0)) <=> (patient(X0) & old(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (patient(X0) & creative(X0))) [input p8]
23. ~funny(paul) [input hypothesis]
46. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [nnf transformation 7]
47. ! [X0] : ((((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0))))) [flattening 46]
48. ! [X0] : (((~patient(X0) | ~funny(X0)) | (~patient(X0) | ~creative(X0))) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 9]
49. ! [X0] : ((~patient(X0) | ~funny(X0) | ~patient(X0) | ~creative(X0)) & ((patient(X0) & creative(X0)) | (patient(X0) & funny(X0)))) [flattening 48]
102. old(X0) | old(X0) | funny(X0) [cnf transformation 47]
107. ~old(X0) | funny(X0) | ~patient(X0) | ~old(X0) [cnf transformation 47]
113. patient(X0) | patient(X0) [cnf transformation 49]
147. ~funny(paul) [cnf transformation 23]
150. patient(X0) [duplicate literal removal 113]
152. old(X0) | funny(X0) [duplicate literal removal 102]
153. ~old(X0) | funny(X0) | ~patient(X0) [duplicate literal removal 107]
204. 11 <=> funny(paul) [avatar definition]
206. ~funny(paul) <- (~11) [avatar component clause 204]
271. ~11 [avatar split clause 147,204]
409. funny(X1) | ~patient(X1) | funny(X1) [resolution 153,152]
410. funny(X1) | ~patient(X1) [duplicate literal removal 409]
412. funny(X1) [subsumption resolution 410,150]
413. $false <- (~11) [resolution 412,206]
417. 11 [avatar contradiction clause 413]
420. $false [avatar sat refutation 271,417]
% SZS output end Proof for 8290171064715544053356918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or strong is either humble or happy.
Everyone who is both funny and generous is not patient.
Everyone who is not strong or brave is not strong or quiet.
Everyone who is either not old or not rich is both strong and patient and vice versa.
Everyone who is not creative or not calm is both rich and tall.
If someone is either not curious or kind then someone is wise or strong.
Everyone who is rich is tall or not quiet.
Everyone who is tall or not calm is either calm or generous and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
Someone is not patient.
Fred is both rich and not wise.
Someone is not wise.
Someone is both not wise and brave.
Someone is humble.
Alice is either not humble or patient.
Lucy is not generous. | Fred is tall. | entailment | (![X]:((quiet(X)|strong(X))=>(humble(X)<~>happy(X))))&
(![X]:((funny(X)&generous(X))=>~patient(X)))&
(![X]:((~strong(X)|brave(X))=>(~strong(X)|quiet(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(strong(X)&patient(X))))&
(![X]:((~creative(X)|~calm(X))=>(rich(X)&tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(rich(X)=>(tall(X)|~quiet(X))))&
(![X]:((tall(X)|~calm(X))<=>(calm(X)<~>generous(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(?[X]:(~patient(X)))&
((rich(fred)&~wise(fred)))&
(?[X]:(~wise(X)))&
(?[X]:((~wise(X)&brave(X))))&
(?[X]:(humble(X)))&
((~humble(alice)<~>patient(alice)))&
(~generous(lucy)) | tall(fred) | [
"p2",
"p6",
"p9",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2492268794196059207868977
% SZS output start Proof for 2492268794196059207868977
3. ! [X0] : ((brave(X0) | ~strong(X0)) => (quiet(X0) | ~strong(X0))) [input p2]
7. ! [X0] : (rich(X0) => (~quiet(X0) | tall(X0))) [input p6]
10. ! [X0] : ((happy(X0) & ~curious(X0)) => (wise(X0) | tall(X0))) [input p9]
13. ! [X0] : ((~funny(X0) & brave(X0)) <=> (~happy(X0) & rich(X0))) [input p12]
14. ! [X0] : ((~calm(X0) | ~strong(X0)) => (creative(X0) & curious(X0))) [input p13]
16. ? [X0] : (~brave(X0) | ~strong(X0)) <=> (~wise(fred) & ~curious(fred)) [input p15]
18. ~wise(fred) & rich(fred) [input p17]
24. ~tall(fred) [input hypothesis]
29. ! [X0] : ((quiet(X0) | ~strong(X0)) | (~brave(X0) & strong(X0))) [ennf transformation 3]
30. ! [X0] : (quiet(X0) | ~strong(X0) | (~brave(X0) & strong(X0))) [flattening 29]
33. ! [X0] : ((~quiet(X0) | tall(X0)) | ~rich(X0)) [ennf transformation 7]
34. ! [X0] : (~quiet(X0) | tall(X0) | ~rich(X0)) [flattening 33]
37. ! [X0] : ((wise(X0) | tall(X0)) | (~happy(X0) | curious(X0))) [ennf transformation 10]
38. ! [X0] : (wise(X0) | tall(X0) | ~happy(X0) | curious(X0)) [flattening 37]
40. ! [X0] : ((creative(X0) & curious(X0)) | (calm(X0) & strong(X0))) [ennf transformation 14]
53. ! [X0] : (((~funny(X0) & brave(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (funny(X0) | ~brave(X0)))) [nnf transformation 13]
54. ! [X0] : (((~funny(X0) & brave(X0)) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | funny(X0) | ~brave(X0))) [flattening 53]
57. (? [X0] : (~brave(X0) | ~strong(X0)) | (wise(fred) | curious(fred))) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [nnf transformation 16]
58. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [flattening 57]
59. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [rectify 58]
60. ? [X0] : (~brave(X0) | ~strong(X0)) => (~brave(sK1) | ~strong(sK1)) [choice axiom]
61. ((~brave(sK1) | ~strong(sK1)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [skolemisation 59,60]
77. ~brave(X0) | ~strong(X0) | quiet(X0) [cnf transformation 30]
90. ~rich(X0) | tall(X0) | ~quiet(X0) [cnf transformation 34]
98. ~happy(X0) | tall(X0) | wise(X0) | curious(X0) [cnf transformation 38]
111. ~rich(X0) | happy(X0) | brave(X0) [cnf transformation 54]
113. curious(X0) | strong(X0) [cnf transformation 40]
120. ~curious(fred) | strong(X1) [cnf transformation 61]
121. ~curious(fred) | brave(X1) [cnf transformation 61]
126. rich(fred) [cnf transformation 18]
127. ~wise(fred) [cnf transformation 18]
135. ~tall(fred) [cnf transformation 24]
166. 7 <=> quiet(fred) [avatar definition]
168. ~quiet(fred) <- (~7) [avatar component clause 166]
173. 8 <=> curious(fred) [avatar definition]
174. ~curious(fred) <- (~8) [avatar component clause 173]
177. 9 <=> wise(fred) [avatar definition]
178. ~wise(fred) <- (~9) [avatar component clause 177]
190. 12 <=> ! [X1] : brave(X1) [avatar definition]
191. brave(X1) <- (12) [avatar component clause 190]
194. 13 <=> ! [X1] : strong(X1) [avatar definition]
195. strong(X1) <- (13) [avatar component clause 194]
197. 12 | ~8 [avatar split clause 121,173,190]
198. 13 | ~8 [avatar split clause 120,173,194]
199. ~9 [avatar split clause 127,177]
218. 16 <=> happy(fred) [avatar definition]
220. happy(fred) <- (16) [avatar component clause 218]
232. ~strong(X0) | quiet(X0) <- (12) [resolution 77,191]
234. quiet(X0) <- (12, 13) [subsumption resolution 232,195]
237. $false <- (~7, 12, 13) [resolution 234,168]
239. 7 | ~12 | ~13 [avatar contradiction clause 237]
268. strong(fred) <- (~8) [resolution 174,113]
271. tall(fred) | ~quiet(fred) [resolution 90,126]
322. happy(fred) | brave(fred) [resolution 111,126]
332. tall(fred) | wise(fred) | curious(fred) <- (16) [resolution 98,220]
333. wise(fred) | curious(fred) <- (16) [subsumption resolution 332,135]
334. curious(fred) <- (~9, 16) [subsumption resolution 333,178]
335. $false <- (~8, ~9, 16) [subsumption resolution 334,174]
336. 8 | 9 | ~16 [avatar contradiction clause 335]
343. 27 <=> brave(fred) [avatar definition]
345. brave(fred) <- (27) [avatar component clause 343]
346. 27 | 16 [avatar split clause 322,218,343]
361. ~strong(fred) | quiet(fred) <- (27) [resolution 345,77]
366. ~quiet(fred) [subsumption resolution 271,135]
367. ~7 [avatar split clause 366,166]
369. 29 <=> strong(fred) [avatar definition]
372. 7 | ~29 | ~27 [avatar split clause 361,343,369,166]
378. 29 | 8 [avatar split clause 268,173,369]
388. $false [avatar sat refutation 197,198,199,239,336,346,367,372,378]
% SZS output end Proof for 2492268794196059207868977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is strong or not rich.
If someone is either happy or not brave then someone is both not curious and rich.
Everyone who is happy is not happy or not funny.
Everyone who is either not patient or not happy is rich.
If someone is both not rich and calm then lucy is not calm or happy and vice versa.
Everyone who is both not wise and not curious is either old or wise and vice versa.
Everyone who is both not brave and curious is either brave or not quiet.
Everyone who is both curious and not brave is either rich or not patient and vice versa.
Everyone who is quiet or strong is funny.
Everyone who is both not calm and strong is either not rich or not humble.
Everyone who is both happy and rich is not generous.
If someone is generous then someone is strong or not strong and vice versa.
Everyone who is either funny or curious is funny or tall and vice versa.
If lucy is either strong or not rich then john is tall.
Everyone who is tall or kind is either kind or not creative.
If mary is funny then alice is humble or strong.
Lucy is both strong and not quiet.
Someone is both kind and generous.
Mary is not quiet or patient.
Mary is both not tall and strong.
Someone is not strong or kind.
Fred is not funny or calm.
Mary is both kind and not calm. | Alice is humble. | neutral | (![X]:(~quiet(X)=>(strong(X)|~rich(X))))&
((?[X]:((happy(X)<~>~brave(X))))=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:(happy(X)=>(~happy(X)|~funny(X))))&
(![X]:((~patient(X)<~>~happy(X))=>rich(X)))&
((?[X]:((~rich(X)&calm(X))))<=>((~calm(lucy)|happy(lucy))))&
(![X]:((~wise(X)&~curious(X))<=>(old(X)<~>wise(X))))&
(![X]:((~brave(X)&curious(X))=>(brave(X)<~>~quiet(X))))&
(![X]:((curious(X)&~brave(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((quiet(X)|strong(X))=>funny(X)))&
(![X]:((~calm(X)&strong(X))=>(~rich(X)<~>~humble(X))))&
(![X]:((happy(X)&rich(X))=>~generous(X)))&
((?[X]:(generous(X)))<=>(?[X]:((strong(X)|~strong(X)))))&
(![X]:((funny(X)<~>curious(X))<=>(funny(X)|tall(X))))&
(((strong(lucy)<~>~rich(lucy)))=>(tall(john)))&
(![X]:((tall(X)|kind(X))=>(kind(X)<~>~creative(X))))&
((funny(mary))=>((humble(alice)|strong(alice))))&
((strong(lucy)&~quiet(lucy)))&
(?[X]:((kind(X)&generous(X))))&
((~quiet(mary)|patient(mary)))&
((~tall(mary)&strong(mary)))&
(?[X]:((~strong(X)|kind(X))))&
((~funny(fred)|calm(fred)))&
((kind(mary)&~calm(mary))) | humble(alice) | [] | null | 0 |
Everyone who is both tall and not tall is not curious or not old.
Everyone who is either funny or not happy is patient.
If someone is humble then john is either old or curious.
Everyone who is kind is not rich.
Everyone who is not old or not kind is rich or not humble and vice versa.
Everyone who is patient is both creative and patient and vice versa.
If fred is not generous then someone is not kind.
Everyone who is not brave or curious is not humble or not generous.
If someone is not funny or wise then someone is either curious or rich and vice versa.
Everyone who is either happy or old is either humble or not creative and vice versa.
Everyone who is rich or not wise is either not old or not rich and vice versa.
Everyone who is patient or funny is not brave and vice versa.
If someone is either not wise or calm then someone is strong and vice versa.
If someone is either strong or not curious then alice is either not tall or wise.
If fred is quiet then john is either not old or wise and vice versa.
Everyone who is kind is happy.
Alice is both not quiet and not funny.
Lucy is not rich or not patient.
Someone is rich or not old.
Someone is both quiet and not kind.
Someone is not funny or humble.
Someone is either not kind or happy.
Someone is either not calm or not rich.
Someone is either not happy or rich. | Fred is not strong. | neutral | (![X]:((tall(X)&~tall(X))=>(~curious(X)|~old(X))))&
(![X]:((funny(X)<~>~happy(X))=>patient(X)))&
((?[X]:(humble(X)))=>((old(john)<~>curious(john))))&
(![X]:(kind(X)=>~rich(X)))&
(![X]:((~old(X)|~kind(X))<=>(rich(X)|~humble(X))))&
(![X]:(patient(X)<=>(creative(X)&patient(X))))&
((~generous(fred))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|curious(X))=>(~humble(X)|~generous(X))))&
((?[X]:((~funny(X)|wise(X))))<=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((happy(X)<~>old(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((rich(X)|~wise(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((patient(X)|funny(X))<=>~brave(X)))&
((?[X]:((~wise(X)<~>calm(X))))<=>(?[X]:(strong(X))))&
((?[X]:((strong(X)<~>~curious(X))))=>((~tall(alice)<~>wise(alice))))&
((quiet(fred))<=>((~old(john)<~>wise(john))))&
(![X]:(kind(X)=>happy(X)))&
((~quiet(alice)&~funny(alice)))&
((~rich(lucy)|~patient(lucy)))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~happy(X)<~>rich(X)))) | ~strong(fred) | [] | null | 0 |
Everyone who is either not generous or not rich is not wise and vice versa.
Everyone who is not kind is either not happy or curious and vice versa.
If someone is wise then someone is not funny or not quiet and vice versa.
Everyone who is not calm is not wise and vice versa.
Everyone who is quiet is both not tall and happy.
If someone is either brave or not kind then someone is either not funny or curious and vice versa.
Everyone who is either calm or creative is not kind.
If someone is both not funny and not humble then someone is both not quiet and not happy and vice versa.
Everyone who is both not old and not curious is patient or curious.
If john is both old and not strong then someone is not calm.
If paul is both not funny and curious then someone is not strong and vice versa.
Everyone who is not brave is not happy.
Everyone who is patient is both not quiet and not tall.
Everyone who is funny is rich and vice versa.
Everyone who is both not tall and not wise is strong or brave and vice versa.
Everyone who is either strong or calm is both humble and not generous and vice versa.
Lucy is either tall or not brave.
Someone is either creative or not creative.
Paul is rich or not patient.
Someone is funny or not tall.
Paul is either funny or not funny.
John is both rich and tall.
Susan is kind or generous. | John is not calm. | entailment | (![X]:((~generous(X)<~>~rich(X))<=>~wise(X)))&
(![X]:(~kind(X)<=>(~happy(X)<~>curious(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~funny(X)|~quiet(X)))))&
(![X]:(~calm(X)<=>~wise(X)))&
(![X]:(quiet(X)=>(~tall(X)&happy(X))))&
((?[X]:((brave(X)<~>~kind(X))))<=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((calm(X)<~>creative(X))=>~kind(X)))&
((?[X]:((~funny(X)&~humble(X))))<=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:((~old(X)&~curious(X))=>(patient(X)|curious(X))))&
(((old(john)&~strong(john)))=>(?[X]:(~calm(X))))&
(((~funny(paul)&curious(paul)))<=>(?[X]:(~strong(X))))&
(![X]:(~brave(X)=>~happy(X)))&
(![X]:(patient(X)=>(~quiet(X)&~tall(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:((~tall(X)&~wise(X))<=>(strong(X)|brave(X))))&
(![X]:((strong(X)<~>calm(X))<=>(humble(X)&~generous(X))))&
((tall(lucy)<~>~brave(lucy)))&
(?[X]:((creative(X)<~>~creative(X))))&
((rich(paul)|~patient(paul)))&
(?[X]:((funny(X)|~tall(X))))&
((funny(paul)<~>~funny(paul)))&
((rich(john)&tall(john)))&
((kind(susan)|generous(susan))) | ~calm(john) | [
"p0",
"p3",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4266668138258167765872092
% SZS output start Proof for 4266668138258167765872092
1. ! [X0] : ((~generous(X0) <~> ~rich(X0)) <=> ~wise(X0)) [input p0]
4. ! [X0] : (~calm(X0) <=> ~wise(X0)) [input p3]
15. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (brave(X0) | strong(X0))) [input p14]
16. ! [X0] : ((strong(X0) <~> calm(X0)) <=> (~generous(X0) & humble(X0))) [input p15]
22. tall(john) & rich(john) [input p21]
24. calm(john) [input hypothesis]
36. ! [X0] : ((((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | wise(X0)) & (~wise(X0) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))))) [nnf transformation 1]
43. ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))) [nnf transformation 4]
63. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 15]
64. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | wise(X0) | tall(X0))) [flattening 63]
65. ! [X0] : ((((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (generous(X0) | ~humble(X0))) & ((~generous(X0) & humble(X0)) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0))))) [nnf transformation 16]
66. ! [X0] : ((((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | generous(X0) | ~humble(X0)) & ((~generous(X0) & humble(X0)) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0))))) [flattening 65]
74. ~wise(X0) | ~rich(X0) | generous(X0) [cnf transformation 36]
86. ~calm(X0) | wise(X0) [cnf transformation 43]
114. ~strong(X0) | ~tall(X0) [cnf transformation 64]
121. ~calm(X0) | strong(X0) | ~generous(X0) [cnf transformation 66]
132. rich(john) [cnf transformation 22]
133. tall(john) [cnf transformation 22]
135. calm(john) [cnf transformation 24]
230. 22 <=> strong(john) [avatar definition]
231. ~strong(john) <- (~22) [avatar component clause 230]
232. strong(john) <- (22) [avatar component clause 230]
286. wise(john) [resolution 86,135]
296. ~rich(john) | generous(john) [resolution 74,286]
306. generous(john) [subsumption resolution 296,132]
397. ~tall(john) <- (22) [resolution 232,114]
400. $false <- (22) [subsumption resolution 397,133]
401. ~22 [avatar contradiction clause 400]
405. strong(john) | ~generous(john) [resolution 121,135]
407. ~generous(john) <- (~22) [subsumption resolution 405,231]
408. $false <- (~22) [subsumption resolution 407,306]
409. 22 [avatar contradiction clause 408]
410. $false [avatar sat refutation 401,409]
% SZS output end Proof for 4266668138258167765872092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not quiet or happy then someone is brave or old. Everyone who is not creative is both not happy and happy and vice versa. If someone is either not humble or not curious then paul is either brave or not humble. Everyone who is not generous or not patient is not calm. Everyone who is generous or not curious is both happy and not creative and vice versa. If john is not happy or not brave then someone is tall or calm. If alice is brave or curious then lucy is either not tall or calm. Everyone who is either not calm or humble is not creative or creative and vice versa. Everyone who is both tall and not strong is both tall and not generous. Everyone who is both calm and rich is not old or generous and vice versa. Everyone who is either kind or not wise is wise and vice versa. If paul is not kind or not patient then someone is both strong and not tall. Everyone who is either not calm or not brave is both tall and not patient. If someone is old or brave then someone is both strong and quiet. Everyone who is strong or not happy is calm or not tall and vice versa. Susan is tall or not funny. Someone is not old or not humble. Susan is tall or creative. Alice is not brave or happy. | Susan is not tall. | neutral | (((~quiet(john)|happy(john)))=>(?[X]:((brave(X)|old(X)))))&
(![X]:(~creative(X)<=>(~happy(X)&happy(X))))&
((?[X]:((~humble(X)<~>~curious(X))))=>((brave(paul)<~>~humble(paul))))&
(![X]:((~generous(X)|~patient(X))=>~calm(X)))&
(![X]:((generous(X)|~curious(X))<=>(happy(X)&~creative(X))))&
(((~happy(john)|~brave(john)))=>(?[X]:((tall(X)|calm(X)))))&
(((brave(alice)|curious(alice)))=>((~tall(lucy)<~>calm(lucy))))&
(![X]:((~calm(X)<~>humble(X))<=>(~creative(X)|creative(X))))&
(![X]:((tall(X)&~strong(X))=>(tall(X)&~generous(X))))&
(![X]:((calm(X)&rich(X))<=>(~old(X)|generous(X))))&
(![X]:((kind(X)<~>~wise(X))<=>wise(X)))&
(((~kind(paul)|~patient(paul)))=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((~calm(X)<~>~brave(X))=>(tall(X)&~patient(X))))&
((?[X]:((old(X)|brave(X))))=>(?[X]:((strong(X)&quiet(X)))))&
(![X]:((strong(X)|~happy(X))<=>(calm(X)|~tall(X))))&
((tall(susan)|~funny(susan)))&
(?[X]:((~old(X)|~humble(X))))&
((tall(susan)|creative(susan)))&
((~brave(alice)|happy(alice))) | ~tall(susan) | [] | null | 0 |
If someone is not calm then mary is either old or rich and vice versa.
Everyone who is both patient and wise is generous and vice versa.
If paul is either brave or quiet then someone is not creative or tall and vice versa.
If fred is strong then paul is not funny.
Everyone who is both not kind and rich is humble or not humble and vice versa.
Everyone who is both not strong and humble is rich.
If fred is either not quiet or not funny then someone is either not calm or not funny and vice versa.
Everyone who is generous or not happy is not tall.
If someone is both strong and kind then susan is kind or not tall and vice versa.
If someone is both brave and not creative then someone is not strong or not wise and vice versa.
Everyone who is both not old and patient is funny and vice versa.
Everyone who is either patient or humble is both strong and humble.
If alice is not kind then someone is rich.
If someone is either not old or not tall then someone is old.
Everyone who is both not old and rich is either not wise or patient and vice versa.
Everyone who is wise or not rich is calm or not tall and vice versa.
Fred is both patient and creative.
Someone is both tall and not funny.
Fred is both not strong and not wise.
Someone is not curious.
Someone is not quiet or not humble.
Lucy is either happy or rich.
Paul is not curious.
John is patient. | John is not rich. | contradiction | ((?[X]:(~calm(X)))<=>((old(mary)<~>rich(mary))))&
(![X]:((patient(X)&wise(X))<=>generous(X)))&
(((brave(paul)<~>quiet(paul)))<=>(?[X]:((~creative(X)|tall(X)))))&
((strong(fred))=>(~funny(paul)))&
(![X]:((~kind(X)&rich(X))<=>(humble(X)|~humble(X))))&
(![X]:((~strong(X)&humble(X))=>rich(X)))&
(((~quiet(fred)<~>~funny(fred)))<=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((generous(X)|~happy(X))=>~tall(X)))&
((?[X]:((strong(X)&kind(X))))<=>((kind(susan)|~tall(susan))))&
((?[X]:((brave(X)&~creative(X))))<=>(?[X]:((~strong(X)|~wise(X)))))&
(![X]:((~old(X)&patient(X))<=>funny(X)))&
(![X]:((patient(X)<~>humble(X))=>(strong(X)&humble(X))))&
((~kind(alice))=>(?[X]:(rich(X))))&
((?[X]:((~old(X)<~>~tall(X))))=>(?[X]:(old(X))))&
(![X]:((~old(X)&rich(X))<=>(~wise(X)<~>patient(X))))&
(![X]:((wise(X)|~rich(X))<=>(calm(X)|~tall(X))))&
((patient(fred)&creative(fred)))&
(?[X]:((tall(X)&~funny(X))))&
((~strong(fred)&~wise(fred)))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)|~humble(X))))&
((happy(lucy)<~>rich(lucy)))&
(~curious(paul))&
(patient(john)) | ~rich(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3706004904797461004954648
% SZS output start Proof for 3706004904797461004954648
5. ! [X0] : ((rich(X0) & ~kind(X0)) <=> (~humble(X0) | humble(X0))) [input p4]
25. ~rich(john) [input hypothesis]
48. ! [X0] : (((rich(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (~rich(X0) | kind(X0)))) [nnf transformation 5]
49. ! [X0] : (((rich(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | ~rich(X0) | kind(X0))) [flattening 48]
97. rich(X0) | ~humble(X0) [cnf transformation 49]
98. rich(X0) | humble(X0) [cnf transformation 49]
150. ~rich(john) [cnf transformation 25]
208. rich(X0) [subsumption resolution 97,98]
298. $false [subsumption resolution 150,208]
% SZS output end Proof for 3706004904797461004954648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or strong then someone is not wise. If someone is generous then someone is either not funny or not patient and vice versa. If alice is both strong and old then someone is both humble and not rich. If someone is rich or not quiet then someone is not rich or not old and vice versa. If someone is both tall and generous then someone is not calm or generous. Everyone who is humble is either quiet or not quiet and vice versa. Everyone who is both not wise and not creative is either brave or not patient and vice versa. Everyone who is both not tall and not strong is not humble or not patient and vice versa. If fred is not kind then lucy is either not happy or not old. Everyone who is not old is not humble and vice versa. If fred is either not quiet or strong then lucy is either happy or not generous. Everyone who is both kind and not funny is calm and vice versa. If someone is both creative and tall then paul is both creative and not curious. Everyone who is funny or rich is not kind or generous and vice versa. If susan is either not brave or happy then fred is not happy. Everyone who is both happy and not strong is both not strong and funny and vice versa. Alice is not strong. John is either not old or wise. Someone is either not quiet or tall. Paul is not old or not brave. Someone is rich or not rich. Mary is either not tall or wise. | Lucy is not tall. | neutral | ((?[X]:((patient(X)|strong(X))))=>(?[X]:(~wise(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
(((strong(alice)&old(alice)))=>(?[X]:((humble(X)&~rich(X)))))&
((?[X]:((rich(X)|~quiet(X))))<=>(?[X]:((~rich(X)|~old(X)))))&
((?[X]:((tall(X)&generous(X))))=>(?[X]:((~calm(X)|generous(X)))))&
(![X]:(humble(X)<=>(quiet(X)<~>~quiet(X))))&
(![X]:((~wise(X)&~creative(X))<=>(brave(X)<~>~patient(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~humble(X)|~patient(X))))&
((~kind(fred))=>((~happy(lucy)<~>~old(lucy))))&
(![X]:(~old(X)<=>~humble(X)))&
(((~quiet(fred)<~>strong(fred)))=>((happy(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)&~funny(X))<=>calm(X)))&
((?[X]:((creative(X)&tall(X))))=>((creative(paul)&~curious(paul))))&
(![X]:((funny(X)|rich(X))<=>(~kind(X)|generous(X))))&
(((~brave(susan)<~>happy(susan)))=>(~happy(fred)))&
(![X]:((happy(X)&~strong(X))<=>(~strong(X)&funny(X))))&
(~strong(alice))&
((~old(john)<~>wise(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((~old(paul)|~brave(paul)))&
(?[X]:((rich(X)|~rich(X))))&
((~tall(mary)<~>wise(mary))) | ~tall(lucy) | [] | null | 0 |
If mary is not strong or not old then someone is not quiet and vice versa.
Everyone who is wise or kind is curious and vice versa.
If someone is both calm and tall then someone is both patient and not strong and vice versa.
If someone is funny or not brave then fred is not rich or strong and vice versa.
Everyone who is either not curious or funny is happy or generous and vice versa.
Everyone who is generous is strong or creative and vice versa.
Everyone who is not calm is both generous and calm and vice versa.
Everyone who is both brave and not humble is either not quiet or wise.
Everyone who is not curious is not rich or not quiet.
If someone is either not tall or not wise then paul is not tall or kind and vice versa.
If someone is both not old and not kind then fred is not quiet and vice versa.
If someone is rich or old then someone is either old or not rich.
If someone is both not strong and not brave then mary is both creative and not curious and vice versa.
If someone is old then lucy is either calm or humble and vice versa.
Everyone who is either not curious or quiet is old and vice versa.
Everyone who is not curious or kind is not wise or not creative and vice versa.
Someone is either wise or not brave.
Someone is humble.
Someone is brave or not generous.
Someone is either strong or rich.
Someone is either not humble or funny.
Someone is both rich and not quiet. | Lucy is quiet. | neutral | (((~strong(mary)|~old(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:((wise(X)|kind(X))<=>curious(X)))&
((?[X]:((calm(X)&tall(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
((?[X]:((funny(X)|~brave(X))))<=>((~rich(fred)|strong(fred))))&
(![X]:((~curious(X)<~>funny(X))<=>(happy(X)|generous(X))))&
(![X]:(generous(X)<=>(strong(X)|creative(X))))&
(![X]:(~calm(X)<=>(generous(X)&calm(X))))&
(![X]:((brave(X)&~humble(X))=>(~quiet(X)<~>wise(X))))&
(![X]:(~curious(X)=>(~rich(X)|~quiet(X))))&
((?[X]:((~tall(X)<~>~wise(X))))<=>((~tall(paul)|kind(paul))))&
((?[X]:((~old(X)&~kind(X))))<=>(~quiet(fred)))&
((?[X]:((rich(X)|old(X))))=>(?[X]:((old(X)<~>~rich(X)))))&
((?[X]:((~strong(X)&~brave(X))))<=>((creative(mary)&~curious(mary))))&
((?[X]:(old(X)))<=>((calm(lucy)<~>humble(lucy))))&
(![X]:((~curious(X)<~>quiet(X))<=>old(X)))&
(![X]:((~curious(X)|kind(X))<=>(~wise(X)|~creative(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((rich(X)&~quiet(X)))) | quiet(lucy) | [] | null | 0 |
If someone is both happy and not brave then someone is either generous or tall and vice versa.
Everyone who is calm or not happy is both quiet and not quiet.
If alice is both tall and not wise then john is not creative.
If someone is both not humble and not generous then lucy is either not generous or not happy.
If someone is quiet then someone is strong.
If someone is either curious or quiet then someone is either wise or not humble and vice versa.
If alice is either humble or funny then someone is either not old or not strong and vice versa.
Everyone who is not generous or patient is wise or not patient and vice versa.
If someone is either not quiet or humble then someone is not quiet and vice versa.
If someone is tall or calm then someone is both old and curious and vice versa.
Everyone who is not tall or quiet is either not strong or tall and vice versa.
If alice is either quiet or old then someone is not generous or not calm and vice versa.
Everyone who is either not generous or rich is both not kind and kind.
Everyone who is both old and kind is either not brave or brave.
Everyone who is either tall or not wise is quiet or old.
Everyone who is not humble or not kind is not patient and vice versa.
Someone is generous.
Someone is either strong or happy.
Someone is happy or kind.
Someone is creative or not brave.
Someone is rich.
Someone is not tall.
Someone is both not brave and not strong.
Someone is not strong. | Lucy is not calm. | entailment | ((?[X]:((happy(X)&~brave(X))))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((calm(X)|~happy(X))=>(quiet(X)&~quiet(X))))&
(((tall(alice)&~wise(alice)))=>(~creative(john)))&
((?[X]:((~humble(X)&~generous(X))))=>((~generous(lucy)<~>~happy(lucy))))&
((?[X]:(quiet(X)))=>(?[X]:(strong(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>(?[X]:((wise(X)<~>~humble(X)))))&
(((humble(alice)<~>funny(alice)))<=>(?[X]:((~old(X)<~>~strong(X)))))&
(![X]:((~generous(X)|patient(X))<=>(wise(X)|~patient(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((tall(X)|calm(X))))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~tall(X)|quiet(X))<=>(~strong(X)<~>tall(X))))&
(((quiet(alice)<~>old(alice)))<=>(?[X]:((~generous(X)|~calm(X)))))&
(![X]:((~generous(X)<~>rich(X))=>(~kind(X)&kind(X))))&
(![X]:((old(X)&kind(X))=>(~brave(X)<~>brave(X))))&
(![X]:((tall(X)<~>~wise(X))=>(quiet(X)|old(X))))&
(![X]:((~humble(X)|~kind(X))<=>~patient(X)))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)<~>happy(X))))&
(?[X]:((happy(X)|kind(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:(rich(X)))&
(?[X]:(~tall(X)))&
(?[X]:((~brave(X)&~strong(X))))&
(?[X]:(~strong(X))) | ~calm(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 9134630055938220777461333
% SZS output start Proof for 9134630055938220777461333
2. ! [X0] : ((~happy(X0) | calm(X0)) => (~quiet(X0) & quiet(X0))) [input p1]
25. calm(lucy) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & quiet(X0)) | (happy(X0) & ~calm(X0))) [ennf transformation 2]
105. quiet(X0) | ~calm(X0) [cnf transformation 31]
107. ~quiet(X0) | ~calm(X0) [cnf transformation 31]
175. calm(lucy) [cnf transformation 25]
212. ~calm(X0) [subsumption resolution 105,107]
385. $false [subsumption resolution 175,212]
% SZS output end Proof for 9134630055938220777461333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not kind and not rich then mary is either creative or happy and vice versa.
Everyone who is not happy is calm or not calm.
If paul is both patient and not calm then someone is tall or generous and vice versa.
Everyone who is either wise or not funny is both not happy and funny and vice versa.
If someone is both not funny and brave then someone is both not patient and happy.
Everyone who is not strong is funny or tall and vice versa.
If paul is happy or not brave then lucy is tall and vice versa.
Everyone who is both curious and humble is either curious or not generous and vice versa.
Everyone who is quiet or rich is not wise or patient and vice versa.
If paul is strong or not old then someone is either not creative or not brave.
Everyone who is both old and happy is both not wise and curious and vice versa.
Everyone who is both not curious and humble is either tall or humble.
Everyone who is humble or not brave is both patient and quiet.
If fred is both not funny and kind then mary is not creative and vice versa.
Everyone who is either curious or tall is not patient.
Everyone who is either not old or not generous is either not old or not humble.
Mary is not generous or not kind.
John is creative.
Susan is both generous and curious.
Paul is either not old or kind.
Someone is both not wise and not brave.
Fred is both generous and patient.
Susan is old or not generous.
Alice is both funny and old. | Fred is strong. | neutral | (((~kind(john)&~rich(john)))<=>((creative(mary)<~>happy(mary))))&
(![X]:(~happy(X)=>(calm(X)|~calm(X))))&
(((patient(paul)&~calm(paul)))<=>(?[X]:((tall(X)|generous(X)))))&
(![X]:((wise(X)<~>~funny(X))<=>(~happy(X)&funny(X))))&
((?[X]:((~funny(X)&brave(X))))=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:(~strong(X)<=>(funny(X)|tall(X))))&
(((happy(paul)|~brave(paul)))<=>(tall(lucy)))&
(![X]:((curious(X)&humble(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((quiet(X)|rich(X))<=>(~wise(X)|patient(X))))&
(((strong(paul)|~old(paul)))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((old(X)&happy(X))<=>(~wise(X)&curious(X))))&
(![X]:((~curious(X)&humble(X))=>(tall(X)<~>humble(X))))&
(![X]:((humble(X)|~brave(X))=>(patient(X)&quiet(X))))&
(((~funny(fred)&kind(fred)))<=>(~creative(mary)))&
(![X]:((curious(X)<~>tall(X))=>~patient(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~old(X)<~>~humble(X))))&
((~generous(mary)|~kind(mary)))&
(creative(john))&
((generous(susan)&curious(susan)))&
((~old(paul)<~>kind(paul)))&
(?[X]:((~wise(X)&~brave(X))))&
((generous(fred)&patient(fred)))&
((old(susan)|~generous(susan)))&
((funny(alice)&old(alice))) | strong(fred) | [] | null | 0 |
Everyone who is not happy or not curious is either calm or wise.
If someone is either creative or not brave then someone is calm or not generous.
Everyone who is either creative or kind is not old.
Everyone who is generous is either not calm or wise and vice versa.
Everyone who is wise or not humble is not brave or funny and vice versa.
Everyone who is not quiet or wise is both calm and not curious and vice versa.
Everyone who is not funny or generous is either wise or not funny.
Everyone who is both wise and not curious is not tall or calm and vice versa.
If mary is either not kind or not generous then fred is either creative or not brave and vice versa.
If john is calm or old then alice is brave or tall.
If susan is generous then paul is old or not quiet.
If john is both not brave and humble then fred is both patient and not wise.
If paul is both quiet and happy then lucy is patient or not quiet.
Everyone who is humble is both happy and not patient.
Someone is patient.
Someone is either not brave or not creative.
Someone is either kind or patient.
Paul is not old or not rich.
Someone is either curious or funny. | Fred is not humble. | neutral | (![X]:((~happy(X)|~curious(X))=>(calm(X)<~>wise(X))))&
((?[X]:((creative(X)<~>~brave(X))))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((creative(X)<~>kind(X))=>~old(X)))&
(![X]:(generous(X)<=>(~calm(X)<~>wise(X))))&
(![X]:((wise(X)|~humble(X))<=>(~brave(X)|funny(X))))&
(![X]:((~quiet(X)|wise(X))<=>(calm(X)&~curious(X))))&
(![X]:((~funny(X)|generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((wise(X)&~curious(X))<=>(~tall(X)|calm(X))))&
(((~kind(mary)<~>~generous(mary)))<=>((creative(fred)<~>~brave(fred))))&
(((calm(john)|old(john)))=>((brave(alice)|tall(alice))))&
((generous(susan))=>((old(paul)|~quiet(paul))))&
(((~brave(john)&humble(john)))=>((patient(fred)&~wise(fred))))&
(((quiet(paul)&happy(paul)))=>((patient(lucy)|~quiet(lucy))))&
(![X]:(humble(X)=>(happy(X)&~patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:((kind(X)<~>patient(X))))&
((~old(paul)|~rich(paul)))&
(?[X]:((curious(X)<~>funny(X)))) | ~humble(fred) | [] | null | 0 |
Everyone who is either brave or tall is either kind or creative.
If someone is not tall then paul is either not funny or not quiet.
Everyone who is not tall or happy is either not quiet or patient.
Everyone who is both tall and brave is old or rich and vice versa.
If mary is both not funny and not brave then lucy is creative or not humble and vice versa.
Everyone who is either not strong or strong is not funny or patient and vice versa.
If alice is not kind or not calm then someone is either not wise or generous and vice versa.
If someone is both generous and not old then someone is not brave or wise.
If someone is either funny or not generous then someone is both not generous and not calm and vice versa.
If mary is both not kind and old then someone is either wise or calm and vice versa.
Everyone who is not tall or strong is not patient and vice versa.
If lucy is not strong then someone is both patient and generous and vice versa.
If fred is humble then someone is either strong or curious and vice versa.
If fred is calm then someone is both not patient and not generous.
Everyone who is either kind or old is either not happy or curious and vice versa.
Everyone who is either strong or not generous is not tall or not funny and vice versa.
Lucy is either generous or not strong.
Someone is either calm or not wise.
Paul is either happy or strong.
Paul is either not old or strong.
Alice is quiet or not strong.
Someone is both not calm and not rich.
Someone is both not funny and not rich.
Someone is either not humble or not brave. | Lucy is not funny. | entailment | (![X]:((brave(X)<~>tall(X))=>(kind(X)<~>creative(X))))&
((?[X]:(~tall(X)))=>((~funny(paul)<~>~quiet(paul))))&
(![X]:((~tall(X)|happy(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((tall(X)&brave(X))<=>(old(X)|rich(X))))&
(((~funny(mary)&~brave(mary)))<=>((creative(lucy)|~humble(lucy))))&
(![X]:((~strong(X)<~>strong(X))<=>(~funny(X)|patient(X))))&
(((~kind(alice)|~calm(alice)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
((?[X]:((generous(X)&~old(X))))=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~generous(X)&~calm(X)))))&
(((~kind(mary)&old(mary)))<=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((~tall(X)|strong(X))<=>~patient(X)))&
((~strong(lucy))<=>(?[X]:((patient(X)&generous(X)))))&
((humble(fred))<=>(?[X]:((strong(X)<~>curious(X)))))&
((calm(fred))=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((kind(X)<~>old(X))<=>(~happy(X)<~>curious(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~tall(X)|~funny(X))))&
((generous(lucy)<~>~strong(lucy)))&
(?[X]:((calm(X)<~>~wise(X))))&
((happy(paul)<~>strong(paul)))&
((~old(paul)<~>strong(paul)))&
((quiet(alice)|~strong(alice)))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((~funny(X)&~rich(X))))&
(?[X]:((~humble(X)<~>~brave(X)))) | ~funny(lucy) | [
"p5",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8625214256736726575258092
% SZS output start Proof for 8625214256736726575258092
6. ! [X0] : ((~strong(X0) <~> strong(X0)) <=> (patient(X0) | ~funny(X0))) [input p5]
11. ! [X0] : ((strong(X0) | ~tall(X0)) <=> ~patient(X0)) [input p10]
16. ! [X0] : ((strong(X0) <~> ~generous(X0)) <=> (~funny(X0) | ~tall(X0))) [input p15]
17. generous(lucy) <~> ~strong(lucy) [input p16]
25. funny(lucy) [input hypothesis]
40. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~patient(X0) & funny(X0))) & ((patient(X0) | ~funny(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [nnf transformation 6]
41. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~patient(X0) & funny(X0))) & (patient(X0) | ~funny(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [flattening 40]
60. ! [X0] : (((strong(X0) | ~tall(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) & tall(X0)))) [nnf transformation 11]
61. ! [X0] : ((strong(X0) | ~tall(X0) | patient(X0)) & (~patient(X0) | (~strong(X0) & tall(X0)))) [flattening 60]
73. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [nnf transformation 16]
74. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [flattening 73]
75. (strong(lucy) | ~generous(lucy)) & (~strong(lucy) | generous(lucy)) [nnf transformation 17]
108. patient(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 41]
109. patient(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 41]
133. ~patient(X0) | tall(X0) [cnf transformation 61]
134. ~strong(X0) | ~patient(X0) [cnf transformation 61]
154. ~funny(X0) | ~tall(X0) | strong(X0) | generous(X0) [cnf transformation 74]
160. strong(lucy) | ~generous(lucy) [cnf transformation 75]
174. funny(lucy) [cnf transformation 25]
175. patient(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 108]
176. ~strong(X0) | ~funny(X0) | patient(X0) [duplicate literal removal 109]
211. ~funny(X0) | patient(X0) [subsumption resolution 175,176]
315. 31 <=> strong(lucy) [avatar definition]
316. strong(lucy) <- (31) [avatar component clause 315]
317. ~strong(lucy) <- (~31) [avatar component clause 315]
366. 42 <=> generous(lucy) [avatar definition]
368. ~generous(lucy) <- (~42) [avatar component clause 366]
369. ~42 | 31 [avatar split clause 160,315,366]
417. patient(lucy) [resolution 211,174]
419. tall(lucy) [resolution 417,133]
478. ~patient(lucy) <- (31) [resolution 316,134]
479. $false <- (31) [subsumption resolution 478,417]
480. ~31 [avatar contradiction clause 479]
584. ~tall(lucy) | strong(lucy) | generous(lucy) [resolution 154,174]
587. strong(lucy) | generous(lucy) [subsumption resolution 584,419]
588. generous(lucy) <- (~31) [subsumption resolution 587,317]
589. $false <- (~31, ~42) [subsumption resolution 588,368]
590. 31 | 42 [avatar contradiction clause 589]
593. $false [avatar sat refutation 369,480,590]
% SZS output end Proof for 8625214256736726575258092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not wise and not calm then someone is both not funny and not patient. Everyone who is rich is either strong or creative and vice versa. Everyone who is either humble or patient is either quiet or not curious and vice versa. If someone is either not humble or tall then john is quiet and vice versa. Everyone who is not funny is not humble or not rich and vice versa. Everyone who is kind or not generous is both creative and not funny and vice versa. Everyone who is not happy or calm is both humble and not quiet. Everyone who is either happy or old is not generous or not funny and vice versa. Everyone who is not patient or not creative is either generous or not humble. Everyone who is wise is tall and vice versa. Everyone who is not funny is old and vice versa. Everyone who is not patient or patient is not old and vice versa. If someone is not patient then someone is both not brave and strong. If someone is brave then susan is funny and vice versa. Paul is not wise. Someone is both strong and not happy. Lucy is either creative or not tall. Someone is strong or not quiet. | Susan is strong. | neutral | (((~wise(lucy)&~calm(lucy)))=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:(rich(X)<=>(strong(X)<~>creative(X))))&
(![X]:((humble(X)<~>patient(X))<=>(quiet(X)<~>~curious(X))))&
((?[X]:((~humble(X)<~>tall(X))))<=>(quiet(john)))&
(![X]:(~funny(X)<=>(~humble(X)|~rich(X))))&
(![X]:((kind(X)|~generous(X))<=>(creative(X)&~funny(X))))&
(![X]:((~happy(X)|calm(X))=>(humble(X)&~quiet(X))))&
(![X]:((happy(X)<~>old(X))<=>(~generous(X)|~funny(X))))&
(![X]:((~patient(X)|~creative(X))=>(generous(X)<~>~humble(X))))&
(![X]:(wise(X)<=>tall(X)))&
(![X]:(~funny(X)<=>old(X)))&
(![X]:((~patient(X)|patient(X))<=>~old(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~brave(X)&strong(X)))))&
((?[X]:(brave(X)))<=>(funny(susan)))&
(~wise(paul))&
(?[X]:((strong(X)&~happy(X))))&
((creative(lucy)<~>~tall(lucy)))&
(?[X]:((strong(X)|~quiet(X)))) | strong(susan) | [] | null | 0 |
If someone is either not kind or strong then someone is not generous or not strong and vice versa. Everyone who is both humble and not creative is both not quiet and not generous and vice versa. Everyone who is either happy or strong is either not kind or not humble and vice versa. Everyone who is kind or not tall is either not wise or rich. If mary is not rich or wise then someone is either wise or not quiet and vice versa. Everyone who is quiet or creative is generous or wise and vice versa. If someone is quiet then someone is both not kind and creative. Everyone who is either not quiet or not brave is both humble and kind. Everyone who is not generous or brave is both tall and not quiet and vice versa. Everyone who is either old or quiet is either old or not curious. If lucy is not curious then someone is either kind or strong. If someone is both quiet and not strong then someone is quiet and vice versa. Everyone who is generous is brave and vice versa. If someone is either not humble or brave then someone is both old and patient. Everyone who is both creative and kind is humble or generous and vice versa. If paul is wise then mary is not creative. Susan is either strong or not brave. Lucy is either brave or not kind. Someone is calm. Alice is either not kind or funny. | Susan is strong. | entailment | ((?[X]:((~kind(X)<~>strong(X))))<=>(?[X]:((~generous(X)|~strong(X)))))&
(![X]:((humble(X)&~creative(X))<=>(~quiet(X)&~generous(X))))&
(![X]:((happy(X)<~>strong(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((kind(X)|~tall(X))=>(~wise(X)<~>rich(X))))&
(((~rich(mary)|wise(mary)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((quiet(X)|creative(X))<=>(generous(X)|wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~quiet(X)<~>~brave(X))=>(humble(X)&kind(X))))&
(![X]:((~generous(X)|brave(X))<=>(tall(X)&~quiet(X))))&
(![X]:((old(X)<~>quiet(X))=>(old(X)<~>~curious(X))))&
((~curious(lucy))=>(?[X]:((kind(X)<~>strong(X)))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
(![X]:(generous(X)<=>brave(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((creative(X)&kind(X))<=>(humble(X)|generous(X))))&
((wise(paul))=>(~creative(mary)))&
((strong(susan)<~>~brave(susan)))&
((brave(lucy)<~>~kind(lucy)))&
(?[X]:(calm(X)))&
((~kind(alice)<~>funny(alice))) | strong(susan) | [
"p1",
"p8",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1891547131981302055774954
% SZS output start Proof for 1891547131981302055774954
2. ! [X0] : ((~creative(X0) & humble(X0)) <=> (~generous(X0) & ~quiet(X0))) [input p1]
9. ! [X0] : ((brave(X0) | ~generous(X0)) <=> (~quiet(X0) & tall(X0))) [input p8]
13. ! [X0] : (generous(X0) <=> brave(X0)) [input p12]
15. ! [X0] : ((kind(X0) & creative(X0)) <=> (generous(X0) | humble(X0))) [input p14]
17. strong(susan) <~> ~brave(susan) [input p16]
21. ~strong(susan) [input hypothesis]
40. ! [X0] : (((~creative(X0) & humble(X0)) | (generous(X0) | quiet(X0))) & ((~generous(X0) & ~quiet(X0)) | (creative(X0) | ~humble(X0)))) [nnf transformation 2]
41. ! [X0] : (((~creative(X0) & humble(X0)) | generous(X0) | quiet(X0)) & ((~generous(X0) & ~quiet(X0)) | creative(X0) | ~humble(X0))) [flattening 40]
55. ! [X0] : (((brave(X0) | ~generous(X0)) | (quiet(X0) | ~tall(X0))) & ((~quiet(X0) & tall(X0)) | (~brave(X0) & generous(X0)))) [nnf transformation 9]
56. ! [X0] : ((brave(X0) | ~generous(X0) | quiet(X0) | ~tall(X0)) & ((~quiet(X0) & tall(X0)) | (~brave(X0) & generous(X0)))) [flattening 55]
66. ! [X0] : ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0))) [nnf transformation 13]
71. ! [X0] : (((kind(X0) & creative(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (~kind(X0) | ~creative(X0)))) [nnf transformation 15]
72. ! [X0] : (((kind(X0) & creative(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | ~kind(X0) | ~creative(X0))) [flattening 71]
73. (brave(susan) | ~strong(susan)) & (~brave(susan) | strong(susan)) [nnf transformation 17]
84. quiet(X0) | generous(X0) | humble(X0) [cnf transformation 41]
85. ~creative(X0) | generous(X0) | quiet(X0) [cnf transformation 41]
116. ~quiet(X0) | generous(X0) [cnf transformation 56]
128. ~generous(X0) | brave(X0) [cnf transformation 66]
133. ~humble(X0) | creative(X0) [cnf transformation 72]
134. ~generous(X0) | creative(X0) [cnf transformation 72]
138. ~brave(susan) | strong(susan) [cnf transformation 73]
144. ~strong(susan) [cnf transformation 21]
160. 4 <=> ! [X1] : generous(X1) [avatar definition]
161. generous(X1) <- (4) [avatar component clause 160]
276. 30 <=> strong(susan) [avatar definition]
280. 31 <=> brave(susan) [avatar definition]
281. ~brave(susan) <- (~31) [avatar component clause 280]
284. 30 | ~31 [avatar split clause 138,280,276]
305. ~30 [avatar split clause 144,276]
308. generous(X2) | humble(X2) | generous(X2) [resolution 84,116]
310. humble(X2) | generous(X2) [duplicate literal removal 308]
313. generous(X2) | creative(X2) [resolution 310,133]
315. creative(X2) [subsumption resolution 313,134]
329. generous(X0) | quiet(X0) [resolution 315,85]
335. brave(X2) <- (4) [resolution 161,128]
336. $false <- (4, ~31) [resolution 335,281]
340. ~4 | 31 [avatar contradiction clause 336]
341. generous(X0) [subsumption resolution 329,116]
342. 4 [avatar split clause 341,160]
345. $false [avatar sat refutation 284,305,340,342]
% SZS output end Proof for 1891547131981302055774954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not curious is both not humble and wise and vice versa.
Everyone who is generous is quiet or not patient.
Everyone who is both humble and funny is rich.
If alice is both funny and tall then someone is curious and vice versa.
If susan is not happy or creative then someone is humble.
If someone is both not creative and curious then mary is not creative or happy.
If someone is either tall or not generous then someone is either tall or not tall and vice versa.
Everyone who is not rich or not curious is not calm or not brave.
Everyone who is quiet is not happy.
Everyone who is kind is tall or not tall and vice versa.
Everyone who is curious is both humble and not kind and vice versa.
If someone is quiet or tall then someone is not creative and vice versa.
Everyone who is either patient or not patient is not brave and vice versa.
Everyone who is brave or strong is not calm.
If someone is not wise or patient then someone is not rich.
Everyone who is either old or brave is not funny.
Someone is both wise and kind.
Someone is calm or wise.
Someone is either not old or rich.
Someone is both strong and not creative.
Lucy is quiet.
Susan is either not patient or not quiet.
Alice is either brave or calm. | Alice is brave. | contradiction | (![X]:((calm(X)|~curious(X))<=>(~humble(X)&wise(X))))&
(![X]:(generous(X)=>(quiet(X)|~patient(X))))&
(![X]:((humble(X)&funny(X))=>rich(X)))&
(((funny(alice)&tall(alice)))<=>(?[X]:(curious(X))))&
(((~happy(susan)|creative(susan)))=>(?[X]:(humble(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~creative(mary)|happy(mary))))&
((?[X]:((tall(X)<~>~generous(X))))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~calm(X)|~brave(X))))&
(![X]:(quiet(X)=>~happy(X)))&
(![X]:(kind(X)<=>(tall(X)|~tall(X))))&
(![X]:(curious(X)<=>(humble(X)&~kind(X))))&
((?[X]:((quiet(X)|tall(X))))<=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((brave(X)|strong(X))=>~calm(X)))&
((?[X]:((~wise(X)|patient(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)<~>brave(X))=>~funny(X)))&
(?[X]:((wise(X)&kind(X))))&
(?[X]:((calm(X)|wise(X))))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:((strong(X)&~creative(X))))&
(quiet(lucy))&
((~patient(susan)<~>~quiet(susan)))&
((brave(alice)<~>calm(alice))) | brave(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7163272192208896821978337
% SZS output start Proof for 7163272192208896821978337
13. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> ~brave(X0)) [input p12]
24. brave(alice) [input hypothesis]
64. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | brave(X0)) & (~brave(X0) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 13]
113. ~brave(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 64]
114. ~brave(X0) | patient(X0) | patient(X0) [cnf transformation 64]
135. brave(alice) [cnf transformation 24]
136. ~brave(X0) | ~patient(X0) [duplicate literal removal 113]
137. ~brave(X0) | patient(X0) [duplicate literal removal 114]
228. ~brave(X0) [subsumption resolution 136,137]
264. $false [subsumption resolution 135,228]
% SZS output end Proof for 7163272192208896821978337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both creative and wise then someone is either wise or not humble and vice versa.
Everyone who is both patient and not old is rich or not patient.
Everyone who is quiet or not generous is either not humble or tall.
If someone is either curious or funny then fred is quiet.
If lucy is both not tall and not humble then someone is calm or not curious and vice versa.
If someone is both funny and kind then someone is either humble or not wise.
Everyone who is not tall is not generous or brave and vice versa.
Everyone who is not generous or not brave is not tall.
If lucy is not quiet or not tall then someone is not generous.
Everyone who is wise is not strong.
If someone is not calm or not old then someone is humble.
Everyone who is creative is both brave and not old and vice versa.
Everyone who is either not rich or not tall is creative.
Everyone who is old or not rich is old or not patient and vice versa.
If mary is both tall and not rich then alice is not funny or not rich and vice versa.
Someone is either funny or wise.
Fred is both not generous and not curious.
Someone is patient.
Someone is old.
Someone is not happy. | Fred is not rich. | neutral | (((creative(paul)&wise(paul)))<=>(?[X]:((wise(X)<~>~humble(X)))))&
(![X]:((patient(X)&~old(X))=>(rich(X)|~patient(X))))&
(![X]:((quiet(X)|~generous(X))=>(~humble(X)<~>tall(X))))&
((?[X]:((curious(X)<~>funny(X))))=>(quiet(fred)))&
(((~tall(lucy)&~humble(lucy)))<=>(?[X]:((calm(X)|~curious(X)))))&
((?[X]:((funny(X)&kind(X))))=>(?[X]:((humble(X)<~>~wise(X)))))&
(![X]:(~tall(X)<=>(~generous(X)|brave(X))))&
(![X]:((~generous(X)|~brave(X))=>~tall(X)))&
(((~quiet(lucy)|~tall(lucy)))=>(?[X]:(~generous(X))))&
(![X]:(wise(X)=>~strong(X)))&
((?[X]:((~calm(X)|~old(X))))=>(?[X]:(humble(X))))&
(![X]:(creative(X)<=>(brave(X)&~old(X))))&
(![X]:((~rich(X)<~>~tall(X))=>creative(X)))&
(![X]:((old(X)|~rich(X))<=>(old(X)|~patient(X))))&
(((tall(mary)&~rich(mary)))<=>((~funny(alice)|~rich(alice))))&
(?[X]:((funny(X)<~>wise(X))))&
((~generous(fred)&~curious(fred)))&
(?[X]:(patient(X)))&
(?[X]:(old(X)))&
(?[X]:(~happy(X))) | ~rich(fred) | [] | null | 0 |
Everyone who is not happy or not creative is not curious or not strong and vice versa. If lucy is either happy or not brave then lucy is either not kind or generous and vice versa. Everyone who is old is both strong and kind and vice versa. Everyone who is both not strong and tall is patient or not strong and vice versa. If someone is strong then mary is both not quiet and curious. If paul is both funny and not brave then alice is not creative or not happy. Everyone who is quiet is either old or not strong and vice versa. Everyone who is both old and not funny is old and vice versa. Everyone who is both not funny and not kind is not calm or funny. Everyone who is both brave and not funny is either not rich or funny and vice versa. Everyone who is both wise and rich is not curious or not quiet and vice versa. If mary is not humble then susan is both not calm and not brave. If someone is kind or not funny then fred is not happy. If someone is either not brave or wise then someone is not curious or not humble. Everyone who is either quiet or tall is not funny or not brave and vice versa. Everyone who is both wise and quiet is both creative and not funny and vice versa. Someone is either not quiet or happy. Someone is either happy or not happy. Someone is not curious or calm. Someone is either not funny or creative. Someone is quiet. | Lucy is not wise. | entailment | (![X]:((~happy(X)|~creative(X))<=>(~curious(X)|~strong(X))))&
(((happy(lucy)<~>~brave(lucy)))<=>((~kind(lucy)<~>generous(lucy))))&
(![X]:(old(X)<=>(strong(X)&kind(X))))&
(![X]:((~strong(X)&tall(X))<=>(patient(X)|~strong(X))))&
((?[X]:(strong(X)))=>((~quiet(mary)&curious(mary))))&
(((funny(paul)&~brave(paul)))=>((~creative(alice)|~happy(alice))))&
(![X]:(quiet(X)<=>(old(X)<~>~strong(X))))&
(![X]:((old(X)&~funny(X))<=>old(X)))&
(![X]:((~funny(X)&~kind(X))=>(~calm(X)|funny(X))))&
(![X]:((brave(X)&~funny(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((wise(X)&rich(X))<=>(~curious(X)|~quiet(X))))&
((~humble(mary))=>((~calm(susan)&~brave(susan))))&
((?[X]:((kind(X)|~funny(X))))=>(~happy(fred)))&
((?[X]:((~brave(X)<~>wise(X))))=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~funny(X)|~brave(X))))&
(![X]:((wise(X)&quiet(X))<=>(creative(X)&~funny(X))))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((~curious(X)|calm(X))))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:(quiet(X))) | ~wise(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5352247694277409035961435
% SZS output start Proof for 5352247694277409035961435
1. ! [X0] : ((~creative(X0) | ~happy(X0)) <=> (~strong(X0) | ~curious(X0))) [input p0]
3. ! [X0] : (old(X0) <=> (kind(X0) & strong(X0))) [input p2]
4. ! [X0] : ((tall(X0) & ~strong(X0)) <=> (~strong(X0) | patient(X0))) [input p3]
5. ? [X0] : strong(X0) => (curious(mary) & ~quiet(mary)) [input p4]
7. ! [X0] : (quiet(X0) <=> (old(X0) <~> ~strong(X0))) [input p6]
10. ! [X0] : ((~funny(X0) & brave(X0)) <=> (~rich(X0) <~> funny(X0))) [input p9]
11. ! [X0] : ((rich(X0) & wise(X0)) <=> (~quiet(X0) | ~curious(X0))) [input p10]
15. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (~brave(X0) | ~funny(X0))) [input p14]
16. ! [X0] : ((quiet(X0) & wise(X0)) <=> (~funny(X0) & creative(X0))) [input p15]
22. wise(lucy) [input hypothesis]
24. (curious(mary) & ~quiet(mary)) | ! [X0] : ~strong(X0) [ennf transformation 5]
32. ! [X0] : (((~creative(X0) | ~happy(X0)) | (strong(X0) & curious(X0))) & ((~strong(X0) | ~curious(X0)) | (creative(X0) & happy(X0)))) [nnf transformation 1]
33. ! [X0] : ((~creative(X0) | ~happy(X0) | (strong(X0) & curious(X0))) & (~strong(X0) | ~curious(X0) | (creative(X0) & happy(X0)))) [flattening 32]
35. ! [X0] : ((old(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | ~old(X0))) [nnf transformation 3]
36. ! [X0] : ((old(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | ~old(X0))) [flattening 35]
37. ! [X0] : (((tall(X0) & ~strong(X0)) | (strong(X0) & ~patient(X0))) & ((~strong(X0) | patient(X0)) | (~tall(X0) | strong(X0)))) [nnf transformation 4]
38. ! [X0] : (((tall(X0) & ~strong(X0)) | (strong(X0) & ~patient(X0))) & (~strong(X0) | patient(X0) | ~tall(X0) | strong(X0))) [flattening 37]
39. ! [X0] : ((quiet(X0) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0)))) & (((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | ~quiet(X0))) [nnf transformation 7]
42. ! [X0] : (((~funny(X0) & brave(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (funny(X0) | ~brave(X0)))) [nnf transformation 10]
43. ! [X0] : (((~funny(X0) & brave(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | funny(X0) | ~brave(X0))) [flattening 42]
44. ! [X0] : (((rich(X0) & wise(X0)) | (quiet(X0) & curious(X0))) & ((~quiet(X0) | ~curious(X0)) | (~rich(X0) | ~wise(X0)))) [nnf transformation 11]
45. ! [X0] : (((rich(X0) & wise(X0)) | (quiet(X0) & curious(X0))) & (~quiet(X0) | ~curious(X0) | ~rich(X0) | ~wise(X0))) [flattening 44]
50. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [flattening 50]
52. ! [X0] : (((quiet(X0) & wise(X0)) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | (~quiet(X0) | ~wise(X0)))) [nnf transformation 16]
53. ! [X0] : (((quiet(X0) & wise(X0)) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~quiet(X0) | ~wise(X0))) [flattening 52]
68. ~strong(X0) | ~curious(X0) | creative(X0) [cnf transformation 33]
79. ~old(X0) | strong(X0) [cnf transformation 36]
86. tall(X0) | strong(X0) [cnf transformation 38]
87. ~quiet(mary) | ~strong(X0) [cnf transformation 24]
88. curious(mary) | ~strong(X0) [cnf transformation 24]
93. quiet(X0) | old(X0) | strong(X0) [cnf transformation 39]
103. ~funny(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 43]
108. rich(X0) | quiet(X0) [cnf transformation 45]
119. ~quiet(X0) | ~tall(X0) | funny(X0) [cnf transformation 51]
122. ~wise(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 53]
124. ~creative(X0) | funny(X0) | quiet(X0) [cnf transformation 53]
133. wise(lucy) [cnf transformation 22]
135. ~rich(X0) | ~funny(X0) [duplicate literal removal 103]
162. 5 <=> ! [X0] : ~strong(X0) [avatar definition]
163. ~strong(X0) <- (5) [avatar component clause 162]
165. 6 <=> curious(mary) [avatar definition]
167. curious(mary) <- (6) [avatar component clause 165]
168. 5 | 6 [avatar split clause 88,165,162]
170. 7 <=> quiet(mary) [avatar definition]
172. ~quiet(mary) <- (~7) [avatar component clause 170]
173. 5 | ~7 [avatar split clause 87,170,162]
191. quiet(X0) | strong(X0) [subsumption resolution 93,79]
265. ~funny(X0) | quiet(X0) [resolution 135,108]
349. ~tall(X1) | funny(X1) | strong(X1) [resolution 119,191]
399. funny(X1) | strong(X1) [subsumption resolution 349,86]
410. strong(mary) <- (~7) [resolution 172,191]
423. ~quiet(lucy) | ~funny(lucy) [resolution 122,133]
467. ~curious(mary) | creative(mary) <- (~7) [resolution 410,68]
469. creative(mary) <- (6, ~7) [subsumption resolution 467,167]
530. funny(mary) | quiet(mary) <- (6, ~7) [resolution 469,124]
534. funny(mary) <- (6, ~7) [subsumption resolution 530,172]
584. quiet(mary) <- (6, ~7) [resolution 534,265]
586. $false <- (6, ~7) [subsumption resolution 584,172]
587. ~6 | 7 [avatar contradiction clause 586]
588. ~funny(lucy) [subsumption resolution 423,265]
653. strong(lucy) [resolution 588,399]
664. $false <- (5) [subsumption resolution 653,163]
665. ~5 [avatar contradiction clause 664]
667. $false [avatar sat refutation 168,173,587,665]
% SZS output end Proof for 5352247694277409035961435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both calm and creative and vice versa.
If someone is both not funny and curious then alice is both not calm and not generous and vice versa.
Everyone who is not curious or not quiet is either wise or not strong.
Everyone who is not strong or tall is not humble or generous.
Everyone who is not kind or not calm is both not happy and not funny and vice versa.
Everyone who is either not calm or brave is either brave or not rich and vice versa.
Everyone who is funny is not happy or rich.
Everyone who is strong or humble is not humble or not rich.
If john is both rich and not quiet then someone is creative or not curious.
Everyone who is either not patient or calm is not generous.
Everyone who is both wise and funny is both not wise and not humble and vice versa.
If fred is both kind and not humble then susan is funny and vice versa.
If mary is both calm and rich then someone is not calm.
Everyone who is not old is both creative and not generous.
Everyone who is not quiet is either not tall or wise and vice versa.
Everyone who is either funny or rich is either creative or not happy and vice versa.
Someone is both rich and not happy.
Alice is either not happy or curious.
Paul is old.
Someone is not creative or curious.
Susan is rich or strong.
Someone is strong or not brave.
Someone is both not curious and not creative.
Someone is curious or generous. | Mary is not wise. | contradiction | (![X]:(~wise(X)<=>(calm(X)&creative(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~calm(alice)&~generous(alice))))&
(![X]:((~curious(X)|~quiet(X))=>(wise(X)<~>~strong(X))))&
(![X]:((~strong(X)|tall(X))=>(~humble(X)|generous(X))))&
(![X]:((~kind(X)|~calm(X))<=>(~happy(X)&~funny(X))))&
(![X]:((~calm(X)<~>brave(X))<=>(brave(X)<~>~rich(X))))&
(![X]:(funny(X)=>(~happy(X)|rich(X))))&
(![X]:((strong(X)|humble(X))=>(~humble(X)|~rich(X))))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(((kind(fred)&~humble(fred)))<=>(funny(susan)))&
(((calm(mary)&rich(mary)))=>(?[X]:(~calm(X))))&
(![X]:(~old(X)=>(creative(X)&~generous(X))))&
(![X]:(~quiet(X)<=>(~tall(X)<~>wise(X))))&
(![X]:((funny(X)<~>rich(X))<=>(creative(X)<~>~happy(X))))&
(?[X]:((rich(X)&~happy(X))))&
((~happy(alice)<~>curious(alice)))&
(old(paul))&
(?[X]:((~creative(X)|curious(X))))&
((rich(susan)|strong(susan)))&
(?[X]:((strong(X)|~brave(X))))&
(?[X]:((~curious(X)&~creative(X))))&
(?[X]:((curious(X)|generous(X)))) | ~wise(mary) | [
"p0",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6120586038601516485401993
% SZS output start Proof for 6120586038601516485401993
1. ! [X0] : (~wise(X0) <=> (creative(X0) & calm(X0))) [input p0]
6. ! [X0] : ((~calm(X0) <~> brave(X0)) <=> (brave(X0) <~> ~rich(X0))) [input p5]
8. ! [X0] : ((humble(X0) | strong(X0)) => (~rich(X0) | ~humble(X0))) [input p7]
11. ! [X0] : ((funny(X0) & wise(X0)) <=> (~humble(X0) & ~wise(X0))) [input p10]
25. ~wise(mary) [input hypothesis]
34. ! [X0] : ((~rich(X0) | ~humble(X0)) | (~humble(X0) & ~strong(X0))) [ennf transformation 8]
35. ! [X0] : (~rich(X0) | ~humble(X0) | (~humble(X0) & ~strong(X0))) [flattening 34]
42. ! [X0] : ((~wise(X0) | (~creative(X0) | ~calm(X0))) & ((creative(X0) & calm(X0)) | wise(X0))) [nnf transformation 1]
43. ! [X0] : ((~wise(X0) | ~creative(X0) | ~calm(X0)) & ((creative(X0) & calm(X0)) | wise(X0))) [flattening 42]
52. ! [X0] : ((((~brave(X0) | calm(X0)) & (brave(X0) | ~calm(X0))) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))))) [nnf transformation 6]
56. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 11]
57. ! [X0] : (((funny(X0) & wise(X0)) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | ~funny(X0) | ~wise(X0))) [flattening 56]
75. calm(X0) | wise(X0) [cnf transformation 43]
96. rich(X0) | ~brave(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 52]
98. brave(X0) | ~calm(X0) | brave(X0) | rich(X0) [cnf transformation 52]
103. ~rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 35]
109. wise(X0) | humble(X0) | wise(X0) [cnf transformation 57]
135. ~wise(mary) [cnf transformation 25]
137. humble(X0) | wise(X0) [duplicate literal removal 109]
138. ~rich(X0) | ~humble(X0) [duplicate literal removal 103]
140. rich(X0) | ~brave(X0) | ~calm(X0) [duplicate literal removal 96]
141. ~calm(X0) | brave(X0) | rich(X0) [duplicate literal removal 98]
166. ~calm(X0) | rich(X0) [subsumption resolution 140,141]
266. rich(X0) | wise(X0) [resolution 166,75]
356. wise(X1) | ~humble(X1) [resolution 266,138]
358. wise(X1) [subsumption resolution 356,137]
363. $false [resolution 358,135]
% SZS output end Proof for 6120586038601516485401993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or tall is either brave or calm.
If someone is not generous or not humble then someone is calm and vice versa.
Everyone who is brave or patient is old or not calm and vice versa.
Everyone who is both patient and rich is tall.
If someone is either not wise or not old then someone is strong or humble.
If someone is funny or rich then someone is both humble and not patient and vice versa.
If someone is humble then paul is both not humble and funny.
Everyone who is not rich is not brave and vice versa.
Everyone who is either calm or quiet is rich and vice versa.
Everyone who is either wise or quiet is either not funny or not generous and vice versa.
Everyone who is happy or not kind is not patient or tall and vice versa.
Everyone who is both curious and not kind is either not quiet or strong and vice versa.
Everyone who is old or not patient is either tall or humble.
If fred is both not strong and not kind then john is not creative.
Everyone who is both not tall and not old is patient.
Everyone who is both funny and tall is strong or not rich and vice versa.
Someone is both curious and not funny.
John is funny.
Someone is both tall and funny.
Alice is not creative.
Fred is not patient.
Someone is patient.
Alice is not wise or not strong.
Susan is either old or brave. | Alice is strong. | neutral | (![X]:((~quiet(X)<~>tall(X))=>(brave(X)<~>calm(X))))&
((?[X]:((~generous(X)|~humble(X))))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)|patient(X))<=>(old(X)|~calm(X))))&
(![X]:((patient(X)&rich(X))=>tall(X)))&
((?[X]:((~wise(X)<~>~old(X))))=>(?[X]:((strong(X)|humble(X)))))&
((?[X]:((funny(X)|rich(X))))<=>(?[X]:((humble(X)&~patient(X)))))&
((?[X]:(humble(X)))=>((~humble(paul)&funny(paul))))&
(![X]:(~rich(X)<=>~brave(X)))&
(![X]:((calm(X)<~>quiet(X))<=>rich(X)))&
(![X]:((wise(X)<~>quiet(X))<=>(~funny(X)<~>~generous(X))))&
(![X]:((happy(X)|~kind(X))<=>(~patient(X)|tall(X))))&
(![X]:((curious(X)&~kind(X))<=>(~quiet(X)<~>strong(X))))&
(![X]:((old(X)|~patient(X))=>(tall(X)<~>humble(X))))&
(((~strong(fred)&~kind(fred)))=>(~creative(john)))&
(![X]:((~tall(X)&~old(X))=>patient(X)))&
(![X]:((funny(X)&tall(X))<=>(strong(X)|~rich(X))))&
(?[X]:((curious(X)&~funny(X))))&
(funny(john))&
(?[X]:((tall(X)&funny(X))))&
(~creative(alice))&
(~patient(fred))&
(?[X]:(patient(X)))&
((~wise(alice)|~strong(alice)))&
((old(susan)<~>brave(susan))) | strong(alice) | [] | null | 0 |
If susan is not generous then someone is either happy or wise.
Everyone who is rich is tall.
Everyone who is not generous or not quiet is both kind and not tall and vice versa.
If someone is both tall and rich then susan is both creative and not kind and vice versa.
Everyone who is not happy or generous is happy and vice versa.
If someone is either not kind or curious then someone is not generous and vice versa.
If john is not brave then mary is either not old or not quiet.
Everyone who is either wise or happy is not patient and vice versa.
Everyone who is kind or old is calm.
Everyone who is wise or brave is not calm and vice versa.
Everyone who is rich or not funny is old and vice versa.
If mary is either calm or not happy then someone is both kind and not patient and vice versa.
Everyone who is not humble is both curious and not patient.
Everyone who is creative is either curious or not tall and vice versa.
Everyone who is both old and not old is quiet and vice versa.
Paul is creative or not strong.
Someone is either not generous or not wise.
Fred is kind or strong.
Paul is not rich or curious. | Mary is not patient. | entailment | ((~generous(susan))=>(?[X]:((happy(X)<~>wise(X)))))&
(![X]:(rich(X)=>tall(X)))&
(![X]:((~generous(X)|~quiet(X))<=>(kind(X)&~tall(X))))&
((?[X]:((tall(X)&rich(X))))<=>((creative(susan)&~kind(susan))))&
(![X]:((~happy(X)|generous(X))<=>happy(X)))&
((?[X]:((~kind(X)<~>curious(X))))<=>(?[X]:(~generous(X))))&
((~brave(john))=>((~old(mary)<~>~quiet(mary))))&
(![X]:((wise(X)<~>happy(X))<=>~patient(X)))&
(![X]:((kind(X)|old(X))=>calm(X)))&
(![X]:((wise(X)|brave(X))<=>~calm(X)))&
(![X]:((rich(X)|~funny(X))<=>old(X)))&
(((calm(mary)<~>~happy(mary)))<=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:(~humble(X)=>(curious(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)<~>~tall(X))))&
(![X]:((old(X)&~old(X))<=>quiet(X)))&
((creative(paul)|~strong(paul)))&
(?[X]:((~generous(X)<~>~wise(X))))&
((kind(fred)|strong(fred)))&
((~rich(paul)|curious(paul))) | ~patient(mary) | [
"p2",
"p4",
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 63695257100428734429723
% SZS output start Proof for 63695257100428734429723
3. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (~tall(X0) & kind(X0))) [input p2]
5. ! [X0] : ((generous(X0) | ~happy(X0)) <=> happy(X0)) [input p4]
8. ! [X0] : ((wise(X0) <~> happy(X0)) <=> ~patient(X0)) [input p7]
9. ! [X0] : ((old(X0) | kind(X0)) => calm(X0)) [input p8]
10. ! [X0] : ((brave(X0) | wise(X0)) <=> ~calm(X0)) [input p9]
15. ! [X0] : ((~old(X0) & old(X0)) <=> quiet(X0)) [input p14]
20. patient(mary) [input hypothesis]
26. ! [X0] : (calm(X0) | (~old(X0) & ~kind(X0))) [ennf transformation 9]
30. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 3]
31. ! [X0] : ((~quiet(X0) | ~generous(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | (quiet(X0) & generous(X0)))) [flattening 30]
37. ! [X0] : (((generous(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (~generous(X0) & happy(X0)))) [nnf transformation 5]
38. ! [X0] : ((generous(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (~generous(X0) & happy(X0)))) [flattening 37]
45. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | patient(X0)) & (~patient(X0) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 8]
46. ! [X0] : (((brave(X0) | wise(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) & ~wise(X0)))) [nnf transformation 10]
47. ! [X0] : ((brave(X0) | wise(X0) | calm(X0)) & (~calm(X0) | (~brave(X0) & ~wise(X0)))) [flattening 46]
55. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) | ~old(X0)))) [nnf transformation 15]
56. ! [X0] : (((~old(X0) & old(X0)) | ~quiet(X0)) & (quiet(X0) | old(X0) | ~old(X0))) [flattening 55]
64. kind(X0) | quiet(X0) [cnf transformation 31]
72. happy(X0) | happy(X0) [cnf transformation 38]
82. ~patient(X0) | wise(X0) | ~happy(X0) [cnf transformation 45]
85. ~kind(X0) | calm(X0) [cnf transformation 26]
87. ~calm(X0) | ~wise(X0) [cnf transformation 47]
104. old(X0) | ~quiet(X0) [cnf transformation 56]
105. ~old(X0) | ~quiet(X0) [cnf transformation 56]
111. patient(mary) [cnf transformation 20]
112. happy(X0) [duplicate literal removal 72]
193. ~patient(X0) | wise(X0) [subsumption resolution 82,112]
215. ~quiet(X0) [subsumption resolution 104,105]
269. calm(X0) | quiet(X0) [resolution 85,64]
274. calm(X0) [subsumption resolution 269,215]
278. ~wise(X0) [resolution 87,274]
293. wise(mary) [resolution 193,111]
294. $false [subsumption resolution 293,278]
% SZS output end Proof for 63695257100428734429723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not rich or creative and vice versa.
If paul is not brave then someone is curious.
Everyone who is either tall or not quiet is not strong or not old.
Everyone who is either not humble or happy is tall or old.
Everyone who is generous is strong or not tall and vice versa.
If mary is either not happy or not kind then someone is not wise or not happy and vice versa.
Everyone who is patient is tall or happy and vice versa.
Everyone who is brave is kind or tall and vice versa.
Everyone who is old is either curious or funny.
Everyone who is either not patient or strong is not curious and vice versa.
If mary is both not generous and not happy then mary is old or rich.
Everyone who is both creative and calm is both patient and strong.
If someone is either calm or not wise then mary is brave and vice versa.
Everyone who is either not creative or generous is tall.
Everyone who is not wise or not kind is wise or not strong.
Everyone who is both patient and not old is not generous or funny and vice versa.
Someone is either calm or old.
Susan is not curious or generous.
Mary is either not brave or happy.
Someone is both kind and not generous.
Someone is not happy.
Someone is either not happy or quiet.
Susan is either not funny or calm.
Fred is both not patient and calm. | Fred is not happy. | entailment | (![X]:(~creative(X)<=>(~rich(X)|creative(X))))&
((~brave(paul))=>(?[X]:(curious(X))))&
(![X]:((tall(X)<~>~quiet(X))=>(~strong(X)|~old(X))))&
(![X]:((~humble(X)<~>happy(X))=>(tall(X)|old(X))))&
(![X]:(generous(X)<=>(strong(X)|~tall(X))))&
(((~happy(mary)<~>~kind(mary)))<=>(?[X]:((~wise(X)|~happy(X)))))&
(![X]:(patient(X)<=>(tall(X)|happy(X))))&
(![X]:(brave(X)<=>(kind(X)|tall(X))))&
(![X]:(old(X)=>(curious(X)<~>funny(X))))&
(![X]:((~patient(X)<~>strong(X))<=>~curious(X)))&
(((~generous(mary)&~happy(mary)))=>((old(mary)|rich(mary))))&
(![X]:((creative(X)&calm(X))=>(patient(X)&strong(X))))&
((?[X]:((calm(X)<~>~wise(X))))<=>(brave(mary)))&
(![X]:((~creative(X)<~>generous(X))=>tall(X)))&
(![X]:((~wise(X)|~kind(X))=>(wise(X)|~strong(X))))&
(![X]:((patient(X)&~old(X))<=>(~generous(X)|funny(X))))&
(?[X]:((calm(X)<~>old(X))))&
((~curious(susan)|generous(susan)))&
((~brave(mary)<~>happy(mary)))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>quiet(X))))&
((~funny(susan)<~>calm(susan)))&
((~patient(fred)&calm(fred))) | ~happy(fred) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3392211288008823722760715
% SZS output start Proof for 3392211288008823722760715
7. ! [X0] : (patient(X0) <=> (happy(X0) | tall(X0))) [input p6]
24. calm(fred) & ~patient(fred) [input p23]
25. happy(fred) [input hypothesis]
51. ! [X0] : ((patient(X0) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 7]
52. ! [X0] : ((patient(X0) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | ~patient(X0))) [flattening 51]
95. ~happy(X0) | patient(X0) [cnf transformation 52]
133. ~patient(fred) [cnf transformation 24]
135. happy(fred) [cnf transformation 25]
252. patient(fred) [resolution 95,135]
254. $false [subsumption resolution 252,133]
% SZS output end Proof for 3392211288008823722760715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and curious is curious.
If john is both not strong and not funny then someone is both not curious and not happy and vice versa.
If someone is not patient then someone is either not creative or creative.
If john is rich then someone is strong or not happy.
Everyone who is generous is not humble or happy and vice versa.
Everyone who is not generous or not patient is either not curious or not wise.
Everyone who is not funny is kind.
If someone is both humble and not funny then someone is not quiet and vice versa.
Everyone who is strong is not old and vice versa.
Everyone who is old is not quiet and vice versa.
If john is creative then mary is not humble or not kind and vice versa.
Everyone who is either quiet or not brave is not strong or humble and vice versa.
If someone is either rich or brave then mary is brave and vice versa.
Everyone who is either not patient or rich is not happy or not patient and vice versa.
If someone is not creative or creative then john is not patient or not happy.
Everyone who is not brave or not creative is either not tall or happy.
Someone is either curious or not kind.
Someone is either kind or calm.
Someone is either not curious or strong.
Someone is both strong and kind.
Someone is either old or not funny.
Mary is both not calm and not patient.
Someone is either not kind or not old.
Someone is brave or not happy. | John is not generous. | neutral | (![X]:((~creative(X)&curious(X))=>curious(X)))&
(((~strong(john)&~funny(john)))<=>(?[X]:((~curious(X)&~happy(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~creative(X)<~>creative(X)))))&
((rich(john))=>(?[X]:((strong(X)|~happy(X)))))&
(![X]:(generous(X)<=>(~humble(X)|happy(X))))&
(![X]:((~generous(X)|~patient(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(~funny(X)=>kind(X)))&
((?[X]:((humble(X)&~funny(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(strong(X)<=>~old(X)))&
(![X]:(old(X)<=>~quiet(X)))&
((creative(john))<=>((~humble(mary)|~kind(mary))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)|humble(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>(brave(mary)))&
(![X]:((~patient(X)<~>rich(X))<=>(~happy(X)|~patient(X))))&
((?[X]:((~creative(X)|creative(X))))=>((~patient(john)|~happy(john))))&
(![X]:((~brave(X)|~creative(X))=>(~tall(X)<~>happy(X))))&
(?[X]:((curious(X)<~>~kind(X))))&
(?[X]:((kind(X)<~>calm(X))))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:((old(X)<~>~funny(X))))&
((~calm(mary)&~patient(mary)))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:((brave(X)|~happy(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is both not funny and strong is both not wise and not quiet. Everyone who is both tall and wise is either not brave or tall. If someone is either not generous or tall then someone is brave or funny and vice versa. Everyone who is not patient is not creative. Everyone who is creative is both not happy and not old. If someone is either not brave or strong then paul is strong or patient and vice versa. Everyone who is patient or not funny is quiet and vice versa. Everyone who is humble is both patient and humble. If susan is either kind or not wise then paul is either generous or quiet. If someone is happy then someone is either rich or not patient and vice versa. Everyone who is quiet or not wise is not quiet and vice versa. Everyone who is rich is funny. If someone is rich or curious then someone is funny or tall and vice versa. Everyone who is both funny and not rich is both funny and kind. If someone is rich then susan is both not brave and creative. If fred is not strong or happy then someone is kind or curious. Someone is either creative or not tall. Susan is patient or not quiet. Someone is either not strong or humble. Someone is either not humble or not generous. Someone is kind. | Fred is funny. | entailment | (![X]:((~funny(X)&strong(X))=>(~wise(X)&~quiet(X))))&
(![X]:((tall(X)&wise(X))=>(~brave(X)<~>tall(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:((brave(X)|funny(X)))))&
(![X]:(~patient(X)=>~creative(X)))&
(![X]:(creative(X)=>(~happy(X)&~old(X))))&
((?[X]:((~brave(X)<~>strong(X))))<=>((strong(paul)|patient(paul))))&
(![X]:((patient(X)|~funny(X))<=>quiet(X)))&
(![X]:(humble(X)=>(patient(X)&humble(X))))&
(((kind(susan)<~>~wise(susan)))=>((generous(paul)<~>quiet(paul))))&
((?[X]:(happy(X)))<=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((quiet(X)|~wise(X))<=>~quiet(X)))&
(![X]:(rich(X)=>funny(X)))&
((?[X]:((rich(X)|curious(X))))<=>(?[X]:((funny(X)|tall(X)))))&
(![X]:((funny(X)&~rich(X))=>(funny(X)&kind(X))))&
((?[X]:(rich(X)))=>((~brave(susan)&creative(susan))))&
(((~strong(fred)|happy(fred)))=>(?[X]:((kind(X)|curious(X)))))&
(?[X]:((creative(X)<~>~tall(X))))&
((patient(susan)|~quiet(susan)))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:(kind(X))) | funny(fred) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3265013503971704995520730
% SZS output start Proof for 3265013503971704995520730
7. ! [X0] : ((~funny(X0) | patient(X0)) <=> quiet(X0)) [input p6]
11. ! [X0] : ((~wise(X0) | quiet(X0)) <=> ~quiet(X0)) [input p10]
22. ~funny(fred) [input hypothesis]
51. ! [X0] : (((~funny(X0) | patient(X0)) | ~quiet(X0)) & (quiet(X0) | (funny(X0) & ~patient(X0)))) [nnf transformation 7]
52. ! [X0] : ((~funny(X0) | patient(X0) | ~quiet(X0)) & (quiet(X0) | (funny(X0) & ~patient(X0)))) [flattening 51]
59. ! [X0] : (((~wise(X0) | quiet(X0)) | quiet(X0)) & (~quiet(X0) | (wise(X0) & ~quiet(X0)))) [nnf transformation 11]
60. ! [X0] : ((~wise(X0) | quiet(X0) | quiet(X0)) & (~quiet(X0) | (wise(X0) & ~quiet(X0)))) [flattening 59]
98. quiet(X0) | funny(X0) [cnf transformation 52]
110. ~quiet(X0) | ~quiet(X0) [cnf transformation 60]
132. ~funny(fred) [cnf transformation 22]
133. ~quiet(X0) [duplicate literal removal 110]
338. funny(X0) [resolution 98,133]
339. $false [resolution 338,132]
% SZS output end Proof for 3265013503971704995520730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or not patient is not happy and vice versa. Everyone who is not curious or not calm is not brave. Everyone who is either humble or not patient is both not rich and old. If someone is both not quiet and rich then someone is humble and vice versa. Everyone who is both not kind and not brave is rich. If someone is either brave or patient then someone is not curious. Everyone who is both funny and not kind is both tall and creative and vice versa. Everyone who is patient is brave or wise. Everyone who is kind is either kind or calm. Everyone who is not happy or funny is both not creative and not tall. If mary is both tall and calm then paul is either old or not wise. If john is generous then someone is both not creative and old and vice versa. If someone is both tall and not quiet then someone is brave or calm. Everyone who is both not tall and happy is both brave and rich and vice versa. Everyone who is both not brave and patient is not tall and vice versa. Everyone who is either brave or not humble is quiet or calm. Fred is both not quiet and kind. Someone is either not strong or not generous. Susan is brave or quiet. Alice is not old. Someone is both not calm and not funny. Someone is humble. John is kind or not old. Mary is not happy or happy. | Mary is happy. | neutral | (![X]:((~quiet(X)|~patient(X))<=>~happy(X)))&
(![X]:((~curious(X)|~calm(X))=>~brave(X)))&
(![X]:((humble(X)<~>~patient(X))=>(~rich(X)&old(X))))&
((?[X]:((~quiet(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((~kind(X)&~brave(X))=>rich(X)))&
((?[X]:((brave(X)<~>patient(X))))=>(?[X]:(~curious(X))))&
(![X]:((funny(X)&~kind(X))<=>(tall(X)&creative(X))))&
(![X]:(patient(X)=>(brave(X)|wise(X))))&
(![X]:(kind(X)=>(kind(X)<~>calm(X))))&
(![X]:((~happy(X)|funny(X))=>(~creative(X)&~tall(X))))&
(((tall(mary)&calm(mary)))=>((old(paul)<~>~wise(paul))))&
((generous(john))<=>(?[X]:((~creative(X)&old(X)))))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~tall(X)&happy(X))<=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((~quiet(fred)&kind(fred)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((brave(susan)|quiet(susan)))&
(~old(alice))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:(humble(X)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary))) | happy(mary) | [] | null | 0 |
If someone is either not rich or patient then fred is happy or curious and vice versa.
Everyone who is brave is happy or strong.
If someone is curious or not tall then mary is kind or not patient.
If mary is creative or not quiet then lucy is humble or generous.
Everyone who is either strong or wise is wise or not calm.
Everyone who is not funny or brave is both brave and not calm.
If fred is both not old and tall then someone is creative or funny and vice versa.
Everyone who is either rich or not wise is either not tall or wise and vice versa.
Everyone who is not curious or not funny is kind or not curious.
Everyone who is both happy and not tall is humble or not wise and vice versa.
Everyone who is both curious and quiet is brave.
Everyone who is either calm or curious is generous or not rich and vice versa.
If someone is both not creative and curious then mary is not strong or creative.
If fred is wise or not calm then fred is both not rich and strong and vice versa.
If someone is generous or not old then alice is not rich or funny.
Everyone who is not brave is either not tall or strong and vice versa.
Someone is both generous and rich.
Someone is kind or creative.
Someone is curious.
Lucy is old or patient.
Someone is not calm or tall. | Lucy is brave. | entailment | ((?[X]:((~rich(X)<~>patient(X))))<=>((happy(fred)|curious(fred))))&
(![X]:(brave(X)=>(happy(X)|strong(X))))&
((?[X]:((curious(X)|~tall(X))))=>((kind(mary)|~patient(mary))))&
(((creative(mary)|~quiet(mary)))=>((humble(lucy)|generous(lucy))))&
(![X]:((strong(X)<~>wise(X))=>(wise(X)|~calm(X))))&
(![X]:((~funny(X)|brave(X))=>(brave(X)&~calm(X))))&
(((~old(fred)&tall(fred)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~curious(X)|~funny(X))=>(kind(X)|~curious(X))))&
(![X]:((happy(X)&~tall(X))<=>(humble(X)|~wise(X))))&
(![X]:((curious(X)&quiet(X))=>brave(X)))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~strong(mary)|creative(mary))))&
(((wise(fred)|~calm(fred)))<=>((~rich(fred)&strong(fred))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:(curious(X)))&
((old(lucy)|patient(lucy)))&
(?[X]:((~calm(X)|tall(X)))) | brave(lucy) | [
"p5",
"p6",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 54624113244990466034671
% SZS output start Proof for 54624113244990466034671
6. ! [X0] : ((brave(X0) | ~funny(X0)) => (~calm(X0) & brave(X0))) [input p5]
7. (tall(fred) & ~old(fred)) <=> ? [X0] : (funny(X0) | creative(X0)) [input p6]
8. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p7]
10. ! [X0] : ((~tall(X0) & happy(X0)) <=> (~wise(X0) | humble(X0))) [input p9]
14. (~calm(fred) | wise(fred)) <=> (strong(fred) & ~rich(fred)) [input p13]
22. ~brave(lucy) [input hypothesis]
32. ! [X0] : ((~calm(X0) & brave(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 6]
45. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | (~tall(fred) | old(fred))) [nnf transformation 7]
46. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | ~tall(fred) | old(fred)) [flattening 45]
47. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X1] : (funny(X1) | creative(X1)) | ~tall(fred) | old(fred)) [rectify 46]
48. ? [X1] : (funny(X1) | creative(X1)) => (funny(sK1) | creative(sK1)) [choice axiom]
49. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & ((funny(sK1) | creative(sK1)) | ~tall(fred) | old(fred)) [skolemisation 47,48]
50. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 8]
51. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 10]
52. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | tall(X0) | ~happy(X0))) [flattening 51]
55. ((~calm(fred) | wise(fred)) | (~strong(fred) | rich(fred))) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [nnf transformation 14]
56. (~calm(fred) | wise(fred) | ~strong(fred) | rich(fred)) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [flattening 55]
75. funny(X0) | brave(X0) [cnf transformation 32]
83. tall(fred) | ~funny(X0) [cnf transformation 49]
85. wise(X0) | ~tall(X0) | rich(X0) | wise(X0) [cnf transformation 50]
89. ~wise(X0) | rich(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 50]
96. ~tall(X0) | wise(X0) [cnf transformation 52]
105. ~rich(fred) | ~wise(fred) [cnf transformation 56]
121. ~brave(lucy) [cnf transformation 22]
122. wise(X0) | ~tall(X0) | rich(X0) [duplicate literal removal 85]
124. ~wise(X0) | rich(X0) | ~tall(X0) [duplicate literal removal 89]
174. 11 <=> ! [X0] : ~funny(X0) [avatar definition]
175. ~funny(X0) <- (11) [avatar component clause 174]
177. 12 <=> tall(fred) [avatar definition]
179. tall(fred) <- (12) [avatar component clause 177]
180. 11 | 12 [avatar split clause 83,177,174]
201. ~tall(X0) | rich(X0) [subsumption resolution 122,124]
220. 21 <=> wise(fred) [avatar definition]
225. 22 <=> rich(fred) [avatar definition]
227. ~rich(fred) <- (~22) [avatar component clause 225]
229. ~21 | ~22 [avatar split clause 105,225,220]
264. brave(X0) <- (11) [resolution 75,175]
265. $false <- (11) [resolution 264,121]
266. ~11 [avatar contradiction clause 265]
272. wise(fred) <- (12) [resolution 96,179]
275. 21 | ~12 [avatar split clause 272,177,220]
278. rich(fred) <- (12) [resolution 201,179]
280. $false <- (12, ~22) [subsumption resolution 278,227]
281. ~12 | 22 [avatar contradiction clause 280]
282. $false [avatar sat refutation 180,229,266,275,281]
% SZS output end Proof for 54624113244990466034671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and wise then alice is kind or curious.
Everyone who is either not creative or happy is both not curious and not generous.
If someone is either generous or rich then alice is humble.
If someone is wise then alice is curious or brave and vice versa.
Everyone who is both not rich and old is not happy.
Everyone who is either funny or brave is either not kind or rich and vice versa.
Everyone who is either old or happy is not strong or not old and vice versa.
If paul is kind or not brave then someone is both not funny and not tall.
If alice is either strong or not funny then someone is either curious or not brave.
If fred is not strong then susan is strong and vice versa.
Everyone who is both not happy and not calm is both not kind and not old.
Everyone who is not calm or not curious is curious or not brave.
Everyone who is both not old and not strong is not tall and vice versa.
Everyone who is humble or brave is not funny or old and vice versa.
Everyone who is rich or generous is funny and vice versa.
Everyone who is not creative is calm or not tall.
Someone is both funny and tall.
Someone is kind or not quiet.
Someone is both kind and happy.
Susan is not rich or not quiet.
Susan is both not patient and kind.
John is both strong and not patient.
Paul is both old and kind.
Alice is tall. | Paul is kind. | entailment | ((?[X]:((kind(X)&wise(X))))=>((kind(alice)|curious(alice))))&
(![X]:((~creative(X)<~>happy(X))=>(~curious(X)&~generous(X))))&
((?[X]:((generous(X)<~>rich(X))))=>(humble(alice)))&
((?[X]:(wise(X)))<=>((curious(alice)|brave(alice))))&
(![X]:((~rich(X)&old(X))=>~happy(X)))&
(![X]:((funny(X)<~>brave(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((old(X)<~>happy(X))<=>(~strong(X)|~old(X))))&
(((kind(paul)|~brave(paul)))=>(?[X]:((~funny(X)&~tall(X)))))&
(((strong(alice)<~>~funny(alice)))=>(?[X]:((curious(X)<~>~brave(X)))))&
((~strong(fred))<=>(strong(susan)))&
(![X]:((~happy(X)&~calm(X))=>(~kind(X)&~old(X))))&
(![X]:((~calm(X)|~curious(X))=>(curious(X)|~brave(X))))&
(![X]:((~old(X)&~strong(X))<=>~tall(X)))&
(![X]:((humble(X)|brave(X))<=>(~funny(X)|old(X))))&
(![X]:((rich(X)|generous(X))<=>funny(X)))&
(![X]:(~creative(X)=>(calm(X)|~tall(X))))&
(?[X]:((funny(X)&tall(X))))&
(?[X]:((kind(X)|~quiet(X))))&
(?[X]:((kind(X)&happy(X))))&
((~rich(susan)|~quiet(susan)))&
((~patient(susan)&kind(susan)))&
((strong(john)&~patient(john)))&
((old(paul)&kind(paul)))&
(tall(alice)) | kind(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6601499347042338974302726
% SZS output start Proof for 6601499347042338974302726
23. kind(paul) & old(paul) [input p22]
25. ~kind(paul) [input hypothesis]
122. kind(paul) [cnf transformation 23]
124. ~kind(paul) [cnf transformation 25]
177. 12 <=> kind(paul) [avatar definition]
217. 12 [avatar split clause 122,177]
218. ~12 [avatar split clause 124,177]
219. $false [avatar sat refutation 217,218]
% SZS output end Proof for 6601499347042338974302726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not humble and humble then someone is not calm and vice versa. Everyone who is both not brave and strong is either generous or not old. Everyone who is either strong or not brave is either not calm or happy and vice versa. Everyone who is both quiet and not creative is creative. Everyone who is both not humble and wise is both brave and patient. If alice is not happy then lucy is either rich or not brave and vice versa. If susan is both strong and not quiet then someone is brave or not kind and vice versa. If someone is either generous or tall then john is both not kind and not wise and vice versa. Everyone who is either calm or creative is either wise or old and vice versa. If mary is both not wise and not old then someone is not tall. Everyone who is either calm or generous is either not wise or not happy and vice versa. Everyone who is not wise or not patient is either funny or kind. If someone is either not calm or not tall then susan is both old and brave. If someone is not curious then someone is calm or funny and vice versa. Everyone who is old or strong is not strong and vice versa. Everyone who is both funny and happy is either kind or not rich and vice versa. Alice is calm or not brave. Someone is either not wise or not strong. Paul is both tall and not patient. Someone is either old or not funny. Mary is not rich or curious. Someone is not creative or not brave. | Susan is not creative. | contradiction | (((~humble(john)&humble(john)))<=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)&strong(X))=>(generous(X)<~>~old(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((quiet(X)&~creative(X))=>creative(X)))&
(![X]:((~humble(X)&wise(X))=>(brave(X)&patient(X))))&
((~happy(alice))<=>((rich(lucy)<~>~brave(lucy))))&
(((strong(susan)&~quiet(susan)))<=>(?[X]:((brave(X)|~kind(X)))))&
((?[X]:((generous(X)<~>tall(X))))<=>((~kind(john)&~wise(john))))&
(![X]:((calm(X)<~>creative(X))<=>(wise(X)<~>old(X))))&
(((~wise(mary)&~old(mary)))=>(?[X]:(~tall(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((~wise(X)|~patient(X))=>(funny(X)<~>kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>((old(susan)&brave(susan))))&
((?[X]:(~curious(X)))<=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((old(X)|strong(X))<=>~strong(X)))&
(![X]:((funny(X)&happy(X))<=>(kind(X)<~>~rich(X))))&
((calm(alice)|~brave(alice)))&
(?[X]:((~wise(X)<~>~strong(X))))&
((tall(paul)&~patient(paul)))&
(?[X]:((old(X)<~>~funny(X))))&
((~rich(mary)|curious(mary)))&
(?[X]:((~creative(X)|~brave(X)))) | ~creative(susan) | [
"p0",
"p2",
"p6",
"p7",
"p8",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8162304771301038935467255
% SZS output start Proof for 8162304771301038935467255
1. (humble(john) & ~humble(john)) <=> ? [X0] : ~calm(X0) [input p0]
3. ! [X0] : ((strong(X0) <~> ~brave(X0)) <=> (~calm(X0) <~> happy(X0))) [input p2]
7. (~quiet(susan) & strong(susan)) <=> ? [X0] : (~kind(X0) | brave(X0)) [input p6]
8. ? [X0] : (generous(X0) <~> tall(X0)) <=> (~wise(john) & ~kind(john)) [input p7]
9. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (wise(X0) <~> old(X0))) [input p8]
11. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (~wise(X0) <~> ~happy(X0))) [input p10]
13. ? [X0] : (~calm(X0) <~> ~tall(X0)) => (brave(susan) & old(susan)) [input p12]
15. ! [X0] : ((strong(X0) | old(X0)) <=> ~strong(X0)) [input p14]
23. ~creative(susan) [input hypothesis]
34. (brave(susan) & old(susan)) | ! [X0] : (~calm(X0) <=> ~tall(X0)) [ennf transformation 13]
35. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | (~humble(john) | humble(john))) [nnf transformation 1]
36. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | ~humble(john) | humble(john)) [flattening 35]
37. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | ~humble(john) | humble(john)) [rectify 36]
38. ? [X1] : ~calm(X1) => ~calm(sK0) [choice axiom]
39. ((humble(john) & ~humble(john)) | ! [X0] : calm(X0)) & (~calm(sK0) | ~humble(john) | humble(john)) [skolemisation 37,38]
41. ! [X0] : ((((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0))))) [nnf transformation 3]
43. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & (? [X0] : (~kind(X0) | brave(X0)) | (quiet(susan) | ~strong(susan))) [nnf transformation 7]
44. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & (? [X0] : (~kind(X0) | brave(X0)) | quiet(susan) | ~strong(susan)) [flattening 43]
45. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & (? [X1] : (~kind(X1) | brave(X1)) | quiet(susan) | ~strong(susan)) [rectify 44]
46. ? [X1] : (~kind(X1) | brave(X1)) => (~kind(sK1) | brave(sK1)) [choice axiom]
47. ((~quiet(susan) & strong(susan)) | ! [X0] : (kind(X0) & ~brave(X0))) & ((~kind(sK1) | brave(sK1)) | quiet(susan) | ~strong(susan)) [skolemisation 45,46]
48. (? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (wise(john) | kind(john))) & ((~wise(john) & ~kind(john)) | ! [X0] : ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) [nnf transformation 8]
49. (? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | wise(john) | kind(john)) & ((~wise(john) & ~kind(john)) | ! [X0] : ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) [flattening 48]
50. (? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | wise(john) | kind(john)) & ((~wise(john) & ~kind(john)) | ! [X1] : ((generous(X1) | ~tall(X1)) & (tall(X1) | ~generous(X1)))) [rectify 49]
51. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) => ((~tall(sK2) | ~generous(sK2)) & (tall(sK2) | generous(sK2))) [choice axiom]
52. (((~tall(sK2) | ~generous(sK2)) & (tall(sK2) | generous(sK2))) | wise(john) | kind(john)) & ((~wise(john) & ~kind(john)) | ! [X1] : ((generous(X1) | ~tall(X1)) & (tall(X1) | ~generous(X1)))) [skolemisation 50,51]
53. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 11]
58. (brave(susan) & old(susan)) | ! [X0] : ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0))) [nnf transformation 34]
64. ! [X0] : (((strong(X0) | old(X0)) | strong(X0)) & (~strong(X0) | (~strong(X0) & ~old(X0)))) [nnf transformation 15]
65. ! [X0] : ((strong(X0) | old(X0) | strong(X0)) & (~strong(X0) | (~strong(X0) & ~old(X0)))) [flattening 64]
77. ~humble(john) | calm(X0) [cnf transformation 39]
78. humble(john) | calm(X0) [cnf transformation 39]
82. ~calm(X0) | happy(X0) | strong(X0) | brave(X0) [cnf transformation 41]
97. strong(susan) | ~brave(X0) [cnf transformation 47]
98. strong(susan) | kind(X0) [cnf transformation 47]
102. ~kind(john) | generous(X1) | ~tall(X1) [cnf transformation 52]
109. ~wise(X0) | ~old(X0) | creative(X0) | ~calm(X0) [cnf transformation 53]
122. ~happy(X0) | ~calm(X0) | ~generous(X0) | wise(X0) [cnf transformation 56]
131. brave(susan) | ~calm(X0) | tall(X0) [cnf transformation 58]
136. ~strong(X0) | ~strong(X0) [cnf transformation 65]
137. strong(X0) | old(X0) | strong(X0) [cnf transformation 65]
153. ~creative(susan) [cnf transformation 23]
154. ~strong(X0) [duplicate literal removal 136]
155. old(X0) | strong(X0) [duplicate literal removal 137]
158. 1 <=> ! [X0] : calm(X0) [avatar definition]
159. calm(X0) <- (1) [avatar component clause 158]
161. 2 <=> humble(john) [avatar definition]
164. 1 | 2 [avatar split clause 78,161,158]
165. 1 | ~2 [avatar split clause 77,161,158]
183. 6 <=> ! [X0] : kind(X0) [avatar definition]
184. kind(X0) <- (6) [avatar component clause 183]
191. 8 <=> ! [X0] : ~brave(X0) [avatar definition]
192. ~brave(X0) <- (8) [avatar component clause 191]
195. 9 <=> strong(susan) [avatar definition]
197. strong(susan) <- (9) [avatar component clause 195]
198. 6 | 9 [avatar split clause 98,195,183]
199. 8 | 9 [avatar split clause 97,195,191]
210. 12 <=> kind(john) [avatar definition]
211. ~kind(john) <- (~12) [avatar component clause 210]
228. 16 <=> ! [X1] : (generous(X1) | ~tall(X1)) [avatar definition]
229. ~tall(X1) | generous(X1) <- (16) [avatar component clause 228]
235. 16 | ~12 [avatar split clause 102,210,228]
251. 21 <=> ! [X0] : (~calm(X0) | tall(X0)) [avatar definition]
252. ~calm(X0) | tall(X0) <- (21) [avatar component clause 251]
254. 22 <=> brave(susan) [avatar definition]
256. brave(susan) <- (22) [avatar component clause 254]
257. 21 | 22 [avatar split clause 131,254,251]
336. $false <- (9) [subsumption resolution 197,154]
337. ~9 [avatar contradiction clause 336]
338. $false <- (6, ~12) [resolution 211,184]
339. ~6 | 12 [avatar contradiction clause 338]
404. happy(X0) | strong(X0) | brave(X0) <- (1) [resolution 82,159]
405. happy(X0) | brave(X0) <- (1) [subsumption resolution 404,154]
406. happy(X0) <- (1, 8) [subsumption resolution 405,192]
584. ~calm(X0) | ~generous(X0) | wise(X0) <- (1, 8) [resolution 122,406]
585. ~generous(X0) | wise(X0) <- (1, 8) [subsumption resolution 584,159]
611. $false <- (8, 22) [subsumption resolution 256,192]
612. ~8 | ~22 [avatar contradiction clause 611]
613. tall(X0) <- (1, 21) [subsumption resolution 252,159]
645. generous(X1) <- (1, 16, 21) [resolution 613,229]
698. wise(X0) <- (1, 8, 16, 21) [resolution 585,645]
708. ~old(X2) | creative(X2) | ~calm(X2) <- (1, 8, 16, 21) [resolution 698,109]
717. ~old(X2) | creative(X2) <- (1, 8, 16, 21) [subsumption resolution 708,159]
729. creative(X0) | strong(X0) <- (1, 8, 16, 21) [resolution 717,155]
737. creative(X0) <- (1, 8, 16, 21) [subsumption resolution 729,154]
740. $false <- (1, 8, 16, 21) [resolution 737,153]
743. ~1 | ~8 | ~16 | ~21 [avatar contradiction clause 740]
744. $false [avatar sat refutation 164,165,198,199,235,257,337,339,612,743]
% SZS output end Proof for 8162304771301038935467255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both patient and creative then someone is old or curious.
Everyone who is not funny is both creative and not creative.
If someone is kind then someone is not kind or curious.
Everyone who is both not wise and quiet is both not quiet and not rich.
Everyone who is not rich or not happy is not happy or tall.
Everyone who is generous or kind is both not kind and creative.
If someone is both not calm and not funny then someone is humble or not funny.
If someone is wise or not tall then lucy is humble.
If someone is both not rich and not patient then lucy is both rich and funny.
Everyone who is either not quiet or not old is either not wise or generous.
Everyone who is both not creative and not quiet is both generous and tall.
If mary is both not tall and not generous then someone is humble or creative and vice versa.
Everyone who is either kind or not generous is not wise or not calm.
Everyone who is either not rich or wise is creative.
Fred is either not curious or curious.
Someone is either not humble or calm.
Someone is not generous or not tall.
Someone is either not curious or calm. | Mary is not patient. | neutral | (((patient(mary)&creative(mary)))=>(?[X]:((old(X)|curious(X)))))&
(![X]:(~funny(X)=>(creative(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~rich(X)|~happy(X))=>(~happy(X)|tall(X))))&
(![X]:((generous(X)|kind(X))=>(~kind(X)&creative(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((humble(X)|~funny(X)))))&
((?[X]:((wise(X)|~tall(X))))=>(humble(lucy)))&
((?[X]:((~rich(X)&~patient(X))))=>((rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)<~>~old(X))=>(~wise(X)<~>generous(X))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)&tall(X))))&
(((~tall(mary)&~generous(mary)))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))=>creative(X)))&
((~curious(fred)<~>curious(fred)))&
(?[X]:((~humble(X)<~>calm(X))))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:((~curious(X)<~>calm(X)))) | ~patient(mary) | [] | null | 0 |
Everyone who is old is curious.
Everyone who is not happy is either humble or quiet and vice versa.
Everyone who is either rich or not wise is either not kind or kind.
If susan is not quiet then someone is both not generous and old and vice versa.
Everyone who is both not curious and creative is not patient.
Everyone who is either not funny or rich is not generous or creative and vice versa.
If someone is tall or happy then someone is not wise and vice versa.
If mary is tall then someone is either not humble or not quiet.
If alice is wise then john is either creative or happy.
Everyone who is brave or wise is either generous or not creative and vice versa.
If susan is brave or not funny then someone is not humble or generous.
Everyone who is not generous is tall or funny and vice versa.
Everyone who is not kind or wise is either not generous or wise and vice versa.
If someone is calm then paul is wise or not generous and vice versa.
If someone is both quiet and rich then paul is not kind and vice versa.
If john is both not brave and wise then someone is both not old and kind.
Alice is not creative.
Someone is both not creative and not humble.
Someone is not happy or not patient.
Someone is not calm.
Paul is both not tall and quiet.
Someone is not quiet or quiet.
Paul is not generous.
Someone is not wise or not patient. | Paul is not quiet. | contradiction | (![X]:(old(X)=>curious(X)))&
(![X]:(~happy(X)<=>(humble(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~wise(X))=>(~kind(X)<~>kind(X))))&
((~quiet(susan))<=>(?[X]:((~generous(X)&old(X)))))&
(![X]:((~curious(X)&creative(X))=>~patient(X)))&
(![X]:((~funny(X)<~>rich(X))<=>(~generous(X)|creative(X))))&
((?[X]:((tall(X)|happy(X))))<=>(?[X]:(~wise(X))))&
((tall(mary))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
((wise(alice))=>((creative(john)<~>happy(john))))&
(![X]:((brave(X)|wise(X))<=>(generous(X)<~>~creative(X))))&
(((brave(susan)|~funny(susan)))=>(?[X]:((~humble(X)|generous(X)))))&
(![X]:(~generous(X)<=>(tall(X)|funny(X))))&
(![X]:((~kind(X)|wise(X))<=>(~generous(X)<~>wise(X))))&
((?[X]:(calm(X)))<=>((wise(paul)|~generous(paul))))&
((?[X]:((quiet(X)&rich(X))))<=>(~kind(paul)))&
(((~brave(john)&wise(john)))=>(?[X]:((~old(X)&kind(X)))))&
(~creative(alice))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:((~happy(X)|~patient(X))))&
(?[X]:(~calm(X)))&
((~tall(paul)&quiet(paul)))&
(?[X]:((~quiet(X)|quiet(X))))&
(~generous(paul))&
(?[X]:((~wise(X)|~patient(X)))) | ~quiet(paul) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7109409261213683154641598
% SZS output start Proof for 7109409261213683154641598
21. quiet(paul) & ~tall(paul) [input p20]
25. ~quiet(paul) [input hypothesis]
133. quiet(paul) [cnf transformation 21]
136. ~quiet(paul) [cnf transformation 25]
282. $false [subsumption resolution 136,133]
% SZS output end Proof for 7109409261213683154641598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not generous or kind then alice is patient or curious and vice versa. Everyone who is either not rich or not patient is generous. If someone is creative or not happy then someone is either not wise or curious and vice versa. If someone is not calm or not curious then someone is not tall or wise and vice versa. If susan is old then alice is tall or not humble and vice versa. If someone is either strong or not happy then someone is both not strong and not old. Everyone who is tall is not humble and vice versa. If john is either patient or not tall then someone is both kind and strong. Everyone who is either not brave or generous is not funny and vice versa. If someone is both not rich and humble then someone is both not wise and not humble. Everyone who is not wise or curious is quiet. If john is both happy and calm then someone is kind or not rich and vice versa. Everyone who is patient is either strong or humble. If someone is either creative or not old then someone is happy. Everyone who is quiet or not curious is both not calm and not brave. Everyone who is both not brave and not calm is not kind or wise and vice versa. Someone is not generous. Alice is tall or wise. Someone is not generous or old. Someone is not happy. Someone is either humble or not curious. Lucy is strong or not calm. | Susan is kind. | contradiction | (((~generous(susan)|kind(susan)))<=>((patient(alice)|curious(alice))))&
(![X]:((~rich(X)<~>~patient(X))=>generous(X)))&
((?[X]:((creative(X)|~happy(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:((~tall(X)|wise(X)))))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:(tall(X)<=>~humble(X)))&
(((patient(john)<~>~tall(john)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>~funny(X)))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~wise(X)|curious(X))=>quiet(X)))&
(((happy(john)&calm(john)))<=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:(patient(X)=>(strong(X)<~>humble(X))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((quiet(X)|~curious(X))=>(~calm(X)&~brave(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~kind(X)|wise(X))))&
(?[X]:(~generous(X)))&
((tall(alice)|wise(alice)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)<~>~curious(X))))&
((strong(lucy)|~calm(lucy))) | kind(susan) | [
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2368934423876558681631780
% SZS output start Proof for 2368934423876558681631780
11. ! [X0] : ((curious(X0) | ~wise(X0)) => quiet(X0)) [input p10]
12. (calm(john) & happy(john)) <=> ? [X0] : (~rich(X0) | kind(X0)) [input p11]
15. ! [X0] : ((~curious(X0) | quiet(X0)) => (~brave(X0) & ~calm(X0))) [input p14]
16. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (wise(X0) | ~kind(X0))) [input p15]
23. kind(susan) [input hypothesis]
33. ! [X0] : (quiet(X0) | (~curious(X0) & wise(X0))) [ennf transformation 11]
36. ! [X0] : ((~brave(X0) & ~calm(X0)) | (curious(X0) & ~quiet(X0))) [ennf transformation 15]
63. ((calm(john) & happy(john)) | ! [X0] : (rich(X0) & ~kind(X0))) & (? [X0] : (~rich(X0) | kind(X0)) | (~calm(john) | ~happy(john))) [nnf transformation 12]
64. ((calm(john) & happy(john)) | ! [X0] : (rich(X0) & ~kind(X0))) & (? [X0] : (~rich(X0) | kind(X0)) | ~calm(john) | ~happy(john)) [flattening 63]
65. ((calm(john) & happy(john)) | ! [X0] : (rich(X0) & ~kind(X0))) & (? [X1] : (~rich(X1) | kind(X1)) | ~calm(john) | ~happy(john)) [rectify 64]
66. ? [X1] : (~rich(X1) | kind(X1)) => (~rich(sK7) | kind(sK7)) [choice axiom]
67. ((calm(john) & happy(john)) | ! [X0] : (rich(X0) & ~kind(X0))) & ((~rich(sK7) | kind(sK7)) | ~calm(john) | ~happy(john)) [skolemisation 65,66]
73. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & ((wise(X0) | ~kind(X0)) | (calm(X0) | brave(X0)))) [nnf transformation 16]
74. ! [X0] : (((~calm(X0) & ~brave(X0)) | (~wise(X0) & kind(X0))) & (wise(X0) | ~kind(X0) | calm(X0) | brave(X0))) [flattening 73]
115. quiet(X0) | wise(X0) [cnf transformation 33]
120. calm(john) | ~kind(X0) [cnf transformation 67]
126. ~quiet(X0) | ~calm(X0) [cnf transformation 36]
134. ~calm(X0) | ~wise(X0) [cnf transformation 74]
142. kind(susan) [cnf transformation 23]
152. 3 <=> kind(susan) [avatar definition]
154. kind(susan) <- (3) [avatar component clause 152]
299. 36 <=> calm(john) [avatar definition]
301. calm(john) <- (36) [avatar component clause 299]
304. 37 <=> ! [X0] : ~kind(X0) [avatar definition]
305. ~kind(X0) <- (37) [avatar component clause 304]
306. 37 | 36 [avatar split clause 120,299,304]
367. 3 [avatar split clause 142,152]
368. $false <- (3, 37) [subsumption resolution 154,305]
369. ~3 | ~37 [avatar contradiction clause 368]
375. ~calm(X0) | wise(X0) [resolution 126,115]
376. ~calm(X0) [subsumption resolution 375,134]
377. $false <- (36) [resolution 376,301]
378. ~36 [avatar contradiction clause 377]
379. $false [avatar sat refutation 306,367,369,378]
% SZS output end Proof for 2368934423876558681631780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or not quiet and vice versa.
If someone is either not quiet or humble then john is patient and vice versa.
If paul is either not funny or wise then someone is not curious and vice versa.
Everyone who is both not calm and generous is not strong and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Someone is funny.
Someone is either strong or tall.
John is both funny and not wise.
Someone is calm or not quiet. | Fred is not generous. | contradiction | (![X]:(~calm(X)<=>(humble(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(patient(john)))&
(((~funny(paul)<~>wise(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)&generous(X))<=>~strong(X)))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(?[X]:(funny(X)))&
(?[X]:((strong(X)<~>tall(X))))&
((funny(john)&~wise(john)))&
(?[X]:((calm(X)|~quiet(X)))) | ~generous(fred) | [
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 238078328659019319768583
% SZS output start Proof for 238078328659019319768583
8. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p7]
10. ! [X0] : ((~quiet(X0) | old(X0)) => (~brave(X0) & curious(X0))) [input p9]
13. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p12]
21. ~generous(fred) [input hypothesis]
25. ! [X0] : ((~brave(X0) & curious(X0)) | (quiet(X0) & ~old(X0))) [ennf transformation 10]
54. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 8]
55. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 54]
59. ! [X0] : (((quiet(X0) & ~quiet(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (~quiet(X0) | quiet(X0)))) [nnf transformation 13]
60. ! [X0] : (((quiet(X0) & ~quiet(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ~quiet(X0) | quiet(X0))) [flattening 59]
99. ~patient(X0) | ~patient(X0) [cnf transformation 55]
101. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 55]
104. curious(X0) | quiet(X0) [cnf transformation 25]
115. quiet(X0) | ~curious(X0) | generous(X0) [cnf transformation 60]
131. ~generous(fred) [cnf transformation 21]
132. ~patient(X0) [duplicate literal removal 99]
133. ~quiet(X0) | patient(X0) [duplicate literal removal 101]
179. 11 <=> generous(fred) [avatar definition]
181. ~generous(fred) <- (~11) [avatar component clause 179]
238. generous(X0) | quiet(X0) [subsumption resolution 115,104]
291. ~11 [avatar split clause 131,179]
326. quiet(fred) <- (~11) [resolution 238,181]
331. patient(fred) <- (~11) [resolution 326,133]
334. $false <- (~11) [subsumption resolution 331,132]
335. 11 [avatar contradiction clause 334]
336. $false [avatar sat refutation 291,335]
% SZS output end Proof for 238078328659019319768583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or calm then alice is both tall and not kind.
Everyone who is both not old and not wise is either humble or tall and vice versa.
Everyone who is both generous and funny is not tall or not funny and vice versa.
Everyone who is not wise or generous is not funny or not quiet and vice versa.
Everyone who is generous is both kind and happy.
Everyone who is both funny and not calm is either curious or wise and vice versa.
If fred is either rich or quiet then someone is both not tall and not quiet and vice versa.
If someone is not wise then someone is not calm or quiet and vice versa.
Everyone who is either humble or rich is either wise or not calm and vice versa.
If someone is not humble then mary is either not creative or not quiet and vice versa.
If someone is not funny then someone is both not strong and humble.
Everyone who is either creative or calm is both humble and not tall and vice versa.
If someone is both not humble and not curious then someone is both curious and happy.
If someone is both strong and generous then someone is either brave or happy and vice versa.
Susan is either curious or not wise.
Someone is either not old or not creative.
Someone is not calm or calm.
Susan is generous.
Lucy is either funny or not rich. | Mary is wise. | neutral | ((?[X]:((~rich(X)|calm(X))))=>((tall(alice)&~kind(alice))))&
(![X]:((~old(X)&~wise(X))<=>(humble(X)<~>tall(X))))&
(![X]:((generous(X)&funny(X))<=>(~tall(X)|~funny(X))))&
(![X]:((~wise(X)|generous(X))<=>(~funny(X)|~quiet(X))))&
(![X]:(generous(X)=>(kind(X)&happy(X))))&
(![X]:((funny(X)&~calm(X))<=>(curious(X)<~>wise(X))))&
(((rich(fred)<~>quiet(fred)))<=>(?[X]:((~tall(X)&~quiet(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((humble(X)<~>rich(X))<=>(wise(X)<~>~calm(X))))&
((?[X]:(~humble(X)))<=>((~creative(mary)<~>~quiet(mary))))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)&humble(X)))))&
(![X]:((creative(X)<~>calm(X))<=>(humble(X)&~tall(X))))&
((?[X]:((~humble(X)&~curious(X))))=>(?[X]:((curious(X)&happy(X)))))&
((?[X]:((strong(X)&generous(X))))<=>(?[X]:((brave(X)<~>happy(X)))))&
((curious(susan)<~>~wise(susan)))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:((~calm(X)|calm(X))))&
(generous(susan))&
((funny(lucy)<~>~rich(lucy))) | wise(mary) | [] | null | 0 |
Everyone who is both humble and brave is either not tall or wise and vice versa. Everyone who is either brave or not happy is happy or old and vice versa. Everyone who is not tall or not kind is funny. If someone is both not calm and kind then someone is both not creative and strong. Everyone who is not rich or not kind is both not strong and not old. Everyone who is not brave is either not old or not humble. Everyone who is generous or not strong is both not strong and not curious. Everyone who is not strong or not calm is both quiet and patient. Everyone who is either calm or humble is strong or wise and vice versa. If someone is both calm and not calm then susan is funny and vice versa. Everyone who is either not rich or not humble is either not happy or generous. If fred is tall or not patient then someone is not humble. Everyone who is quiet or kind is old. Everyone who is wise or kind is either brave or not curious. Fred is calm. Mary is not wise or creative. Someone is not humble. Susan is not happy or brave. John is not kind or curious. Someone is either happy or not rich. | Fred is kind. | entailment | (![X]:((humble(X)&brave(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(happy(X)|old(X))))&
(![X]:((~tall(X)|~kind(X))=>funny(X)))&
((?[X]:((~calm(X)&kind(X))))=>(?[X]:((~creative(X)&strong(X)))))&
(![X]:((~rich(X)|~kind(X))=>(~strong(X)&~old(X))))&
(![X]:(~brave(X)=>(~old(X)<~>~humble(X))))&
(![X]:((generous(X)|~strong(X))=>(~strong(X)&~curious(X))))&
(![X]:((~strong(X)|~calm(X))=>(quiet(X)&patient(X))))&
(![X]:((calm(X)<~>humble(X))<=>(strong(X)|wise(X))))&
((?[X]:((calm(X)&~calm(X))))<=>(funny(susan)))&
(![X]:((~rich(X)<~>~humble(X))=>(~happy(X)<~>generous(X))))&
(((tall(fred)|~patient(fred)))=>(?[X]:(~humble(X))))&
(![X]:((quiet(X)|kind(X))=>old(X)))&
(![X]:((wise(X)|kind(X))=>(brave(X)<~>~curious(X))))&
(calm(fred))&
((~wise(mary)|creative(mary)))&
(?[X]:(~humble(X)))&
((~happy(susan)|brave(susan)))&
((~kind(john)|curious(john)))&
(?[X]:((happy(X)<~>~rich(X)))) | kind(fred) | [
"p4",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6024182270056930579803272
% SZS output start Proof for 6024182270056930579803272
5. ! [X0] : ((~kind(X0) | ~rich(X0)) => (~old(X0) & ~strong(X0))) [input p4]
8. ! [X0] : ((~calm(X0) | ~strong(X0)) => (patient(X0) & quiet(X0))) [input p7]
13. ! [X0] : ((kind(X0) | quiet(X0)) => old(X0)) [input p12]
21. ~kind(fred) [input hypothesis]
23. ! [X0] : ((~calm(X0) | ~strong(X0)) => quiet(X0)) [pure predicate removal 8]
27. ! [X0] : ((~old(X0) & ~strong(X0)) | (kind(X0) & rich(X0))) [ennf transformation 5]
30. ! [X0] : (quiet(X0) | (calm(X0) & strong(X0))) [ennf transformation 23]
33. ! [X0] : (old(X0) | (~kind(X0) & ~quiet(X0))) [ennf transformation 13]
75. ~strong(X0) | kind(X0) [cnf transformation 27]
77. ~old(X0) | kind(X0) [cnf transformation 27]
84. quiet(X0) | strong(X0) [cnf transformation 30]
100. ~quiet(X0) | old(X0) [cnf transformation 33]
113. ~kind(fred) [cnf transformation 21]
183. strong(X1) | old(X1) [resolution 100,84]
202. old(X0) | kind(X0) [resolution 183,75]
204. kind(X0) [subsumption resolution 202,77]
211. $false [resolution 204,113]
% SZS output end Proof for 6024182270056930579803272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not curious is humble and vice versa.
If paul is both not calm and not strong then someone is either not patient or old and vice versa.
Everyone who is not calm is not old and vice versa.
Everyone who is not humble is either calm or old.
Everyone who is not generous or not quiet is both not humble and not funny and vice versa.
Everyone who is creative or not creative is both wise and old.
If someone is curious or tall then someone is both not happy and humble and vice versa.
If someone is both calm and patient then someone is rich or not old.
If someone is both kind and not happy then someone is either strong or not calm and vice versa.
Everyone who is either wise or not funny is not humble.
If lucy is not generous or wise then susan is wise or not quiet.
Everyone who is not funny is rich or strong.
Everyone who is not strong is both not brave and not wise.
John is not generous or brave.
Someone is either not rich or not happy.
Someone is not curious.
Someone is either not rich or generous. | John is not patient. | entailment | (![X]:((~creative(X)&~curious(X))<=>humble(X)))&
(((~calm(paul)&~strong(paul)))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:(~humble(X)=>(calm(X)<~>old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~humble(X)&~funny(X))))&
(![X]:((creative(X)|~creative(X))=>(wise(X)&old(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~happy(X)&humble(X)))))&
((?[X]:((calm(X)&patient(X))))=>(?[X]:((rich(X)|~old(X)))))&
((?[X]:((kind(X)&~happy(X))))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((wise(X)<~>~funny(X))=>~humble(X)))&
(((~generous(lucy)|wise(lucy)))=>((wise(susan)|~quiet(susan))))&
(![X]:(~funny(X)=>(rich(X)|strong(X))))&
(![X]:(~strong(X)=>(~brave(X)&~wise(X))))&
((~generous(john)|brave(john)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)<~>generous(X)))) | ~patient(john) | [
"p1",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5337965930906860809648960
% SZS output start Proof for 5337965930906860809648960
2. (~strong(paul) & ~calm(paul)) <=> ? [X0] : (~patient(X0) <~> old(X0)) [input p1]
6. ! [X0] : ((~creative(X0) | creative(X0)) => (old(X0) & wise(X0))) [input p5]
13. ! [X0] : (~strong(X0) => (~wise(X0) & ~brave(X0))) [input p12]
18. patient(john) [input hypothesis]
23. ! [X0] : ((old(X0) & wise(X0)) | (creative(X0) & ~creative(X0))) [ennf transformation 6]
30. ! [X0] : ((~wise(X0) & ~brave(X0)) | strong(X0)) [ennf transformation 13]
33. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (strong(paul) | calm(paul))) [nnf transformation 2]
34. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | strong(paul) | calm(paul)) [flattening 33]
35. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (? [X1] : ((~old(X1) | patient(X1)) & (old(X1) | ~patient(X1))) | strong(paul) | calm(paul)) [rectify 34]
36. ? [X1] : ((~old(X1) | patient(X1)) & (old(X1) | ~patient(X1))) => ((~old(sK0) | patient(sK0)) & (old(sK0) | ~patient(sK0))) [choice axiom]
37. ((~strong(paul) & ~calm(paul)) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(sK0) | patient(sK0)) & (old(sK0) | ~patient(sK0))) | strong(paul) | calm(paul)) [skolemisation 35,36]
72. ~strong(paul) | ~patient(X0) | ~old(X0) [cnf transformation 37]
82. wise(X0) | ~creative(X0) [cnf transformation 23]
83. wise(X0) | creative(X0) [cnf transformation 23]
84. old(X0) | ~creative(X0) [cnf transformation 23]
85. old(X0) | creative(X0) [cnf transformation 23]
104. ~wise(X0) | strong(X0) [cnf transformation 30]
111. patient(john) [cnf transformation 18]
113. 1 <=> ! [X0] : (~patient(X0) | ~old(X0)) [avatar definition]
114. ~patient(X0) | ~old(X0) <- (1) [avatar component clause 113]
116. 2 <=> strong(paul) [avatar definition]
118. ~strong(paul) <- (~2) [avatar component clause 116]
119. 1 | ~2 [avatar split clause 72,116,113]
145. old(X0) [subsumption resolution 84,85]
146. wise(X0) [subsumption resolution 82,83]
215. strong(X0) [subsumption resolution 104,146]
233. $false <- (~2) [subsumption resolution 118,215]
234. 2 [avatar contradiction clause 233]
235. ~patient(X0) <- (1) [subsumption resolution 114,145]
238. $false <- (1) [resolution 235,111]
239. ~1 [avatar contradiction clause 238]
240. $false [avatar sat refutation 119,234,239]
% SZS output end Proof for 5337965930906860809648960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or old then someone is both humble and not kind.
If someone is both not strong and not kind then someone is either not happy or patient and vice versa.
Everyone who is both quiet and generous is either not curious or rich and vice versa.
If lucy is both not generous and old then someone is either tall or patient and vice versa.
Everyone who is either not generous or not kind is strong or not kind and vice versa.
Everyone who is either calm or not creative is strong or not quiet and vice versa.
Everyone who is not brave is wise.
If someone is rich then john is not curious or not patient.
If mary is tall or not patient then mary is not rich.
Everyone who is either not old or not brave is calm or not generous.
Everyone who is old is happy.
Everyone who is either not wise or not brave is brave or not happy and vice versa.
Everyone who is strong or old is not generous or wise and vice versa.
Everyone who is humble or not happy is not rich or old and vice versa.
Everyone who is not strong or not humble is not calm or curious and vice versa.
If someone is both not old and happy then lucy is wise.
Alice is either humble or calm.
Mary is both not curious and kind.
Fred is patient.
Someone is not brave.
Someone is not old.
Someone is both wise and patient.
Someone is either not calm or not funny.
Fred is both not quiet and patient. | Mary is creative. | entailment | (((calm(john)|old(john)))=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((quiet(X)&generous(X))<=>(~curious(X)<~>rich(X))))&
(((~generous(lucy)&old(lucy)))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:((~generous(X)<~>~kind(X))<=>(strong(X)|~kind(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)|~quiet(X))))&
(![X]:(~brave(X)=>wise(X)))&
((?[X]:(rich(X)))=>((~curious(john)|~patient(john))))&
(((tall(mary)|~patient(mary)))=>(~rich(mary)))&
(![X]:((~old(X)<~>~brave(X))=>(calm(X)|~generous(X))))&
(![X]:(old(X)=>happy(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(brave(X)|~happy(X))))&
(![X]:((strong(X)|old(X))<=>(~generous(X)|wise(X))))&
(![X]:((humble(X)|~happy(X))<=>(~rich(X)|old(X))))&
(![X]:((~strong(X)|~humble(X))<=>(~calm(X)|curious(X))))&
((?[X]:((~old(X)&happy(X))))=>(wise(lucy)))&
((humble(alice)<~>calm(alice)))&
((~curious(mary)&kind(mary)))&
(patient(fred))&
(?[X]:(~brave(X)))&
(?[X]:(~old(X)))&
(?[X]:((wise(X)&patient(X))))&
(?[X]:((~calm(X)<~>~funny(X))))&
((~quiet(fred)&patient(fred))) | creative(mary) | [
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6303678406859539467543240
% SZS output start Proof for 6303678406859539467543240
3. ! [X0] : ((generous(X0) & quiet(X0)) <=> (~curious(X0) <~> rich(X0))) [input p2]
4. (old(lucy) & ~generous(lucy)) <=> ? [X0] : (tall(X0) <~> patient(X0)) [input p3]
5. ! [X0] : ((~generous(X0) <~> ~kind(X0)) <=> (~kind(X0) | strong(X0))) [input p4]
6. ! [X0] : ((calm(X0) <~> ~creative(X0)) <=> (~quiet(X0) | strong(X0))) [input p5]
7. ! [X0] : (~brave(X0) => wise(X0)) [input p6]
9. (~patient(mary) | tall(mary)) => ~rich(mary) [input p8]
11. ! [X0] : (old(X0) => happy(X0)) [input p10]
12. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (~happy(X0) | brave(X0))) [input p11]
13. ! [X0] : ((old(X0) | strong(X0)) <=> (wise(X0) | ~generous(X0))) [input p12]
14. ! [X0] : ((~happy(X0) | humble(X0)) <=> (old(X0) | ~rich(X0))) [input p13]
15. ! [X0] : ((~humble(X0) | ~strong(X0)) <=> (curious(X0) | ~calm(X0))) [input p14]
16. ? [X0] : (happy(X0) & ~old(X0)) => wise(lucy) [input p15]
18. kind(mary) & ~curious(mary) [input p17]
25. ~creative(mary) [input hypothesis]
28. ! [X0] : (wise(X0) | brave(X0)) [ennf transformation 7]
31. ~rich(mary) | (patient(mary) & ~tall(mary)) [ennf transformation 9]
34. ! [X0] : (happy(X0) | ~old(X0)) [ennf transformation 11]
35. wise(lucy) | ! [X0] : (~happy(X0) | old(X0)) [ennf transformation 16]
43. ! [X0] : (((generous(X0) & quiet(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) & (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (~generous(X0) | ~quiet(X0)))) [nnf transformation 3]
44. ! [X0] : (((generous(X0) & quiet(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) & (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | ~generous(X0) | ~quiet(X0))) [flattening 43]
45. ((old(lucy) & ~generous(lucy)) | ! [X0] : ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (? [X0] : ((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (~old(lucy) | generous(lucy))) [nnf transformation 4]
46. ((old(lucy) & ~generous(lucy)) | ! [X0] : ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (? [X0] : ((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | ~old(lucy) | generous(lucy)) [flattening 45]
47. ((old(lucy) & ~generous(lucy)) | ! [X0] : ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (? [X1] : ((~patient(X1) | ~tall(X1)) & (patient(X1) | tall(X1))) | ~old(lucy) | generous(lucy)) [rectify 46]
48. ? [X1] : ((~patient(X1) | ~tall(X1)) & (patient(X1) | tall(X1))) => ((~patient(sK3) | ~tall(sK3)) & (patient(sK3) | tall(sK3))) [choice axiom]
49. ((old(lucy) & ~generous(lucy)) | ! [X0] : ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(sK3) | ~tall(sK3)) & (patient(sK3) | tall(sK3))) | ~old(lucy) | generous(lucy)) [skolemisation 47,48]
50. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (kind(X0) & ~strong(X0))) & ((~kind(X0) | strong(X0)) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [nnf transformation 5]
51. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (kind(X0) & ~strong(X0))) & (~kind(X0) | strong(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [flattening 50]
52. ! [X0] : ((((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0))))) [nnf transformation 6]
53. ! [X0] : ((((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0))))) [flattening 52]
55. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 12]
56. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [flattening 55]
57. ! [X0] : (((old(X0) | strong(X0)) | (~wise(X0) & generous(X0))) & ((wise(X0) | ~generous(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 13]
58. ! [X0] : ((old(X0) | strong(X0) | (~wise(X0) & generous(X0))) & (wise(X0) | ~generous(X0) | (~old(X0) & ~strong(X0)))) [flattening 57]
59. ! [X0] : (((~happy(X0) | humble(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (happy(X0) & ~humble(X0)))) [nnf transformation 14]
60. ! [X0] : ((~happy(X0) | humble(X0) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | (happy(X0) & ~humble(X0)))) [flattening 59]
61. ! [X0] : (((~humble(X0) | ~strong(X0)) | (~curious(X0) & calm(X0))) & ((curious(X0) | ~calm(X0)) | (humble(X0) & strong(X0)))) [nnf transformation 15]
62. ! [X0] : ((~humble(X0) | ~strong(X0) | (~curious(X0) & calm(X0))) & (curious(X0) | ~calm(X0) | (humble(X0) & strong(X0)))) [flattening 61]
84. ~rich(X0) | curious(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 44]
85. rich(X0) | quiet(X0) | curious(X0) [cnf transformation 44]
87. rich(X0) | generous(X0) | curious(X0) [cnf transformation 44]
94. old(lucy) | tall(X0) | ~patient(X0) [cnf transformation 49]
95. ~kind(X0) | strong(X0) | ~kind(X0) | generous(X0) [cnf transformation 51]
97. ~generous(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 51]
100. kind(X0) | generous(X0) | kind(X0) [cnf transformation 51]
102. ~quiet(X0) | strong(X0) | calm(X0) | creative(X0) [cnf transformation 53]
105. ~strong(X0) | ~calm(X0) | creative(X0) [cnf transformation 53]
107. wise(X0) | brave(X0) [cnf transformation 28]
109. ~rich(mary) | ~tall(mary) [cnf transformation 31]
110. ~rich(mary) | patient(mary) [cnf transformation 31]
113. ~old(X0) | happy(X0) [cnf transformation 34]
115. ~happy(X0) | brave(X0) | ~wise(X0) | brave(X0) [cnf transformation 56]
116. ~brave(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 56]
121. ~generous(X0) | wise(X0) | ~old(X0) [cnf transformation 58]
125. old(X0) | ~rich(X0) | happy(X0) [cnf transformation 60]
127. ~happy(X0) | humble(X0) | ~old(X0) [cnf transformation 60]
128. ~calm(X0) | curious(X0) | strong(X0) [cnf transformation 62]
130. ~strong(X0) | ~humble(X0) | calm(X0) [cnf transformation 62]
132. wise(lucy) | ~happy(X0) | old(X0) [cnf transformation 35]
135. ~curious(mary) [cnf transformation 18]
136. kind(mary) [cnf transformation 18]
146. ~creative(mary) [cnf transformation 25]
147. ~happy(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 115]
148. ~wise(X0) | ~brave(X0) [duplicate literal removal 116]
149. ~kind(X0) | strong(X0) | generous(X0) [duplicate literal removal 95]
150. generous(X0) | kind(X0) [duplicate literal removal 100]
203. 12 <=> ! [X0] : (tall(X0) | ~patient(X0)) [avatar definition]
204. ~patient(X0) | tall(X0) <- (12) [avatar component clause 203]
206. 13 <=> old(lucy) [avatar definition]
208. old(lucy) <- (13) [avatar component clause 206]
209. 12 | 13 [avatar split clause 94,206,203]
230. generous(X0) | strong(X0) [subsumption resolution 149,150]
244. 21 <=> patient(mary) [avatar definition]
246. patient(mary) <- (21) [avatar component clause 244]
248. 22 <=> rich(mary) [avatar definition]
249. rich(mary) <- (22) [avatar component clause 248]
250. ~rich(mary) <- (~22) [avatar component clause 248]
251. 21 | ~22 [avatar split clause 110,248,244]
253. 23 <=> tall(mary) [avatar definition]
255. ~tall(mary) <- (~23) [avatar component clause 253]
256. ~23 | ~22 [avatar split clause 109,248,253]
257. ~wise(X0) | ~happy(X0) [subsumption resolution 147,148]
258. ~old(X0) | humble(X0) [subsumption resolution 127,113]
259. ~rich(X0) | happy(X0) [subsumption resolution 125,113]
261. 24 <=> ! [X0] : (~happy(X0) | old(X0)) [avatar definition]
262. ~happy(X0) | old(X0) <- (24) [avatar component clause 261]
264. 25 <=> wise(lucy) [avatar definition]
266. wise(lucy) <- (25) [avatar component clause 264]
267. 24 | 25 [avatar split clause 132,264,261]
295. ~happy(X0) | brave(X0) [resolution 257,107]
296. quiet(mary) | curious(mary) <- (~22) [resolution 85,250]
297. curious(X0) | quiet(X0) | happy(X0) [resolution 85,259]
298. quiet(mary) <- (~22) [subsumption resolution 296,135]
301. generous(mary) | curious(mary) <- (~22) [resolution 87,250]
303. curious(X1) | generous(X1) | happy(X1) [resolution 87,259]
304. generous(mary) <- (~22) [subsumption resolution 301,135]
310. ~kind(mary) | ~strong(mary) <- (~22) [resolution 97,304]
311. ~strong(mary) <- (~22) [subsumption resolution 310,136]
327. ~old(X0) | wise(X0) | strong(X0) [resolution 121,230]
331. 32 <=> old(mary) [avatar definition]
332. old(mary) <- (32) [avatar component clause 331]
335. 33 <=> wise(mary) [avatar definition]
337. wise(mary) <- (33) [avatar component clause 335]
368. quiet(mary) | happy(mary) [resolution 297,135]
371. generous(mary) | happy(mary) [resolution 303,135]
380. strong(mary) | calm(mary) | creative(mary) <- (~22) [resolution 102,298]
381. calm(mary) | creative(mary) <- (~22) [subsumption resolution 380,311]
382. calm(mary) <- (~22) [subsumption resolution 381,146]
384. curious(mary) | strong(mary) <- (~22) [resolution 382,128]
387. strong(mary) <- (~22) [subsumption resolution 384,135]
388. $false <- (~22) [subsumption resolution 387,311]
389. 22 [avatar contradiction clause 388]
391. 38 <=> happy(mary) [avatar definition]
393. happy(mary) <- (38) [avatar component clause 391]
395. 39 <=> generous(mary) [avatar definition]
398. 38 | 39 [avatar split clause 371,395,391]
400. 40 <=> quiet(mary) [avatar definition]
403. 38 | 40 [avatar split clause 368,400,391]
404. tall(mary) <- (12, 21) [resolution 246,204]
405. $false <- (12, 21, ~23) [subsumption resolution 404,255]
406. ~12 | ~21 | 23 [avatar contradiction clause 405]
409. happy(lucy) <- (13) [resolution 208,113]
421. curious(mary) | ~generous(mary) | ~quiet(mary) <- (22) [resolution 249,84]
426. ~generous(mary) | ~quiet(mary) <- (22) [subsumption resolution 421,135]
427. ~40 | ~39 | ~22 [avatar split clause 426,248,395,400]
431. ~happy(lucy) <- (25) [resolution 266,257]
433. $false <- (13, 25) [subsumption resolution 431,409]
434. ~13 | ~25 [avatar contradiction clause 433]
445. brave(mary) <- (38) [resolution 393,295]
446. old(mary) <- (24, 38) [resolution 393,262]
449. 32 | ~24 | ~38 [avatar split clause 446,391,261,331]
451. 42 <=> humble(mary) [avatar definition]
452. humble(mary) <- (42) [avatar component clause 451]
470. wise(mary) | strong(mary) <- (32) [resolution 332,327]
471. humble(mary) <- (32) [resolution 332,258]
474. 45 <=> strong(mary) [avatar definition]
476. strong(mary) <- (45) [avatar component clause 474]
477. 45 | 33 | ~32 [avatar split clause 470,331,335,474]
478. 42 | ~32 [avatar split clause 471,331,451]
612. ~humble(mary) | calm(mary) <- (45) [resolution 476,130]
613. ~calm(mary) | creative(mary) <- (45) [resolution 476,105]
614. calm(mary) <- (42, 45) [subsumption resolution 612,452]
615. creative(mary) <- (42, 45) [subsumption resolution 613,614]
616. $false <- (42, 45) [subsumption resolution 615,146]
617. ~42 | ~45 [avatar contradiction clause 616]
621. ~brave(mary) <- (33) [resolution 337,148]
624. $false <- (33, 38) [subsumption resolution 621,445]
625. ~33 | ~38 [avatar contradiction clause 624]
626. $false [avatar sat refutation 209,251,256,267,389,398,403,406,427,434,449,477,478,617,625]
% SZS output end Proof for 6303678406859539467543240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and wise is both wise and not old. If someone is either happy or not quiet then someone is either happy or not strong. If susan is both not quiet and creative then fred is either kind or not curious. If fred is not old then fred is either wise or calm. If john is both quiet and curious then susan is rich and vice versa. Everyone who is tall is both not happy and humble. Everyone who is not curious is both old and not curious and vice versa. If someone is old then someone is both not kind and not funny. Everyone who is generous or not tall is not generous or not curious. Everyone who is not calm is either quiet or not generous. Everyone who is both not calm and humble is both not tall and not calm. If someone is humble then someone is either funny or calm. If fred is funny then someone is either not humble or not old and vice versa. If someone is either not creative or humble then paul is both not old and not quiet and vice versa. Everyone who is either not creative or not old is both calm and creative and vice versa. If someone is either rich or happy then mary is either brave or curious and vice versa. Paul is brave or curious. Someone is both not quiet and not generous. Alice is either humble or strong. Someone is not rich. John is both not wise and not tall. Someone is quiet. Alice is both patient and not quiet. Someone is either patient or not strong. | Alice is not curious. | neutral | (![X]:((~patient(X)&wise(X))=>(wise(X)&~old(X))))&
((?[X]:((happy(X)<~>~quiet(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(((~quiet(susan)&creative(susan)))=>((kind(fred)<~>~curious(fred))))&
((~old(fred))=>((wise(fred)<~>calm(fred))))&
(((quiet(john)&curious(john)))<=>(rich(susan)))&
(![X]:(tall(X)=>(~happy(X)&humble(X))))&
(![X]:(~curious(X)<=>(old(X)&~curious(X))))&
((?[X]:(old(X)))=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((generous(X)|~tall(X))=>(~generous(X)|~curious(X))))&
(![X]:(~calm(X)=>(quiet(X)<~>~generous(X))))&
(![X]:((~calm(X)&humble(X))=>(~tall(X)&~calm(X))))&
((?[X]:(humble(X)))=>(?[X]:((funny(X)<~>calm(X)))))&
((funny(fred))<=>(?[X]:((~humble(X)<~>~old(X)))))&
((?[X]:((~creative(X)<~>humble(X))))<=>((~old(paul)&~quiet(paul))))&
(![X]:((~creative(X)<~>~old(X))<=>(calm(X)&creative(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>((brave(mary)<~>curious(mary))))&
((brave(paul)|curious(paul)))&
(?[X]:((~quiet(X)&~generous(X))))&
((humble(alice)<~>strong(alice)))&
(?[X]:(~rich(X)))&
((~wise(john)&~tall(john)))&
(?[X]:(quiet(X)))&
((patient(alice)&~quiet(alice)))&
(?[X]:((patient(X)<~>~strong(X)))) | ~curious(alice) | [] | null | 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa. If paul is not old or generous then someone is brave. Everyone who is either kind or not kind is both old and not wise. If someone is either quiet or not patient then someone is both generous and not brave and vice versa. If someone is calm or curious then paul is kind or rich. If someone is not quiet or wise then someone is both strong and brave. If mary is both happy and curious then susan is not curious. Everyone who is not patient or not old is either generous or rich and vice versa. If mary is either creative or humble then someone is patient or not funny. Everyone who is wise or not humble is either old or not brave and vice versa. Everyone who is old or not old is both not generous and not curious. Everyone who is humble or generous is either not generous or not strong. If someone is either not patient or rich then mary is both not quiet and not strong. Everyone who is both not curious and not old is not quiet and vice versa. Everyone who is old is kind. If mary is not patient or old then paul is not happy or strong. Someone is not strong or not tall. Mary is both rich and not humble. Fred is not strong or creative. Someone is either quiet or generous. Mary is not wise or calm. Someone is either humble or strong. Lucy is kind or not rich. | Mary is rich. | entailment | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
(((~old(paul)|generous(paul)))=>(?[X]:(brave(X))))&
(![X]:((kind(X)<~>~kind(X))=>(old(X)&~wise(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((calm(X)|curious(X))))=>((kind(paul)|rich(paul))))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((happy(mary)&curious(mary)))=>(~curious(susan)))&
(![X]:((~patient(X)|~old(X))<=>(generous(X)<~>rich(X))))&
(((creative(mary)<~>humble(mary)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((wise(X)|~humble(X))<=>(old(X)<~>~brave(X))))&
(![X]:((old(X)|~old(X))=>(~generous(X)&~curious(X))))&
(![X]:((humble(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(?[X]:((~strong(X)|~tall(X))))&
((rich(mary)&~humble(mary)))&
((~strong(fred)|creative(fred)))&
(?[X]:((quiet(X)<~>generous(X))))&
((~wise(mary)|calm(mary)))&
(?[X]:((humble(X)<~>strong(X))))&
((kind(lucy)|~rich(lucy))) | rich(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2005195753181101687734117
% SZS output start Proof for 2005195753181101687734117
18. ~humble(mary) & rich(mary) [input p17]
24. ~rich(mary) [input hypothesis]
125. rich(mary) [cnf transformation 18]
133. ~rich(mary) [cnf transformation 24]
275. $false [subsumption resolution 133,125]
% SZS output end Proof for 2005195753181101687734117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or curious is not old or not funny and vice versa.
Everyone who is not kind or not wise is generous and vice versa.
Everyone who is kind is creative or not curious and vice versa.
If john is both humble and patient then someone is both generous and not rich and vice versa.
If alice is old then fred is either not calm or not happy.
Everyone who is not patient or not quiet is not funny and vice versa.
Everyone who is not curious or calm is happy and vice versa.
If someone is both creative and tall then someone is either not patient or not tall.
Everyone who is both curious and tall is not quiet and vice versa.
If susan is not creative then mary is calm and vice versa.
Everyone who is both not rich and not curious is either calm or not kind and vice versa.
If fred is either funny or not kind then someone is curious.
Everyone who is creative or wise is either wise or kind.
If susan is either not old or not curious then susan is both not patient and calm and vice versa.
Everyone who is not patient is either kind or calm and vice versa.
Everyone who is not strong is both calm and not tall and vice versa.
Someone is either strong or rich.
Someone is both not rich and quiet.
Someone is not brave or not patient.
Someone is not funny.
Mary is calm.
John is not strong or old. | John is not tall. | entailment | (![X]:((patient(X)<~>curious(X))<=>(~old(X)|~funny(X))))&
(![X]:((~kind(X)|~wise(X))<=>generous(X)))&
(![X]:(kind(X)<=>(creative(X)|~curious(X))))&
(((humble(john)&patient(john)))<=>(?[X]:((generous(X)&~rich(X)))))&
((old(alice))=>((~calm(fred)<~>~happy(fred))))&
(![X]:((~patient(X)|~quiet(X))<=>~funny(X)))&
(![X]:((~curious(X)|calm(X))<=>happy(X)))&
((?[X]:((creative(X)&tall(X))))=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((curious(X)&tall(X))<=>~quiet(X)))&
((~creative(susan))<=>(calm(mary)))&
(![X]:((~rich(X)&~curious(X))<=>(calm(X)<~>~kind(X))))&
(((funny(fred)<~>~kind(fred)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)|wise(X))=>(wise(X)<~>kind(X))))&
(((~old(susan)<~>~curious(susan)))<=>((~patient(susan)&calm(susan))))&
(![X]:(~patient(X)<=>(kind(X)<~>calm(X))))&
(![X]:(~strong(X)<=>(calm(X)&~tall(X))))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((~rich(X)&quiet(X))))&
(?[X]:((~brave(X)|~patient(X))))&
(?[X]:(~funny(X)))&
(calm(mary))&
((~strong(john)|old(john))) | ~tall(john) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p8",
"p10",
"p12",
"p14",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6699232609356960489248762
% SZS output start Proof for 6699232609356960489248762
1. ! [X0] : ((patient(X0) <~> curious(X0)) <=> (~funny(X0) | ~old(X0))) [input p0]
2. ! [X0] : ((~wise(X0) | ~kind(X0)) <=> generous(X0)) [input p1]
3. ! [X0] : (kind(X0) <=> (~curious(X0) | creative(X0))) [input p2]
4. (patient(john) & humble(john)) <=> ? [X0] : (~rich(X0) & generous(X0)) [input p3]
6. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> ~funny(X0)) [input p5]
9. ! [X0] : ((tall(X0) & curious(X0)) <=> ~quiet(X0)) [input p8]
11. ! [X0] : ((~curious(X0) & ~rich(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p10]
13. ! [X0] : ((wise(X0) | creative(X0)) => (wise(X0) <~> kind(X0))) [input p12]
15. ! [X0] : (~patient(X0) <=> (kind(X0) <~> calm(X0))) [input p14]
16. ! [X0] : (~strong(X0) <=> (~tall(X0) & calm(X0))) [input p15]
18. ? [X0] : (quiet(X0) & ~rich(X0)) [input p17]
22. old(john) | ~strong(john) [input p21]
23. tall(john) [input hypothesis]
29. ! [X0] : ((wise(X0) <~> kind(X0)) | (~wise(X0) & ~creative(X0))) [ennf transformation 13]
30. ! [X0] : ((((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))))) [nnf transformation 1]
31. ! [X0] : ((((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0))))) [flattening 30]
32. ! [X0] : (((~wise(X0) | ~kind(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & kind(X0)))) [nnf transformation 2]
33. ! [X0] : ((~wise(X0) | ~kind(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & kind(X0)))) [flattening 32]
34. ! [X0] : ((kind(X0) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ~kind(X0))) [nnf transformation 3]
35. ! [X0] : ((kind(X0) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ~kind(X0))) [flattening 34]
36. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & (? [X0] : (~rich(X0) & generous(X0)) | (~patient(john) | ~humble(john))) [nnf transformation 4]
37. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & (? [X0] : (~rich(X0) & generous(X0)) | ~patient(john) | ~humble(john)) [flattening 36]
38. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & (? [X1] : (~rich(X1) & generous(X1)) | ~patient(john) | ~humble(john)) [rectify 37]
39. ? [X1] : (~rich(X1) & generous(X1)) => (~rich(sK0) & generous(sK0)) [choice axiom]
40. ((patient(john) & humble(john)) | ! [X0] : (rich(X0) | ~generous(X0))) & ((~rich(sK0) & generous(sK0)) | ~patient(john) | ~humble(john)) [skolemisation 38,39]
42. ! [X0] : (((~quiet(X0) | ~patient(X0)) | funny(X0)) & (~funny(X0) | (quiet(X0) & patient(X0)))) [nnf transformation 6]
43. ! [X0] : ((~quiet(X0) | ~patient(X0) | funny(X0)) & (~funny(X0) | (quiet(X0) & patient(X0)))) [flattening 42]
50. ! [X0] : (((tall(X0) & curious(X0)) | quiet(X0)) & (~quiet(X0) | (~tall(X0) | ~curious(X0)))) [nnf transformation 9]
51. ! [X0] : (((tall(X0) & curious(X0)) | quiet(X0)) & (~quiet(X0) | ~tall(X0) | ~curious(X0))) [flattening 50]
53. ! [X0] : (((~curious(X0) & ~rich(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (curious(X0) | rich(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & ~rich(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | curious(X0) | rich(X0))) [flattening 53]
58. ! [X0] : (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~wise(X0) & ~creative(X0))) [nnf transformation 29]
61. ! [X0] : ((~patient(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0)))) & (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | patient(X0))) [nnf transformation 15]
62. ! [X0] : ((~strong(X0) | (tall(X0) | ~calm(X0))) & ((~tall(X0) & calm(X0)) | strong(X0))) [nnf transformation 16]
63. ! [X0] : ((~strong(X0) | tall(X0) | ~calm(X0)) & ((~tall(X0) & calm(X0)) | strong(X0))) [flattening 62]
67. ? [X0] : (quiet(X0) & ~rich(X0)) => (quiet(sK4) & ~rich(sK4)) [choice axiom]
68. quiet(sK4) & ~rich(sK4) [skolemisation 18,67]
71. ~funny(X0) | ~old(X0) | curious(X0) | ~patient(X0) [cnf transformation 31]
74. funny(X0) | patient(X0) | curious(X0) [cnf transformation 31]
77. generous(X0) | kind(X0) [cnf transformation 33]
78. generous(X0) | wise(X0) [cnf transformation 33]
82. kind(X0) | curious(X0) [cnf transformation 35]
86. patient(john) | rich(X0) | ~generous(X0) [cnf transformation 40]
89. ~funny(X0) | patient(X0) [cnf transformation 43]
91. ~quiet(X0) | ~patient(X0) | funny(X0) [cnf transformation 43]
98. quiet(X0) | curious(X0) [cnf transformation 51]
106. ~calm(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 54]
107. ~curious(X0) | calm(X0) | kind(X0) [cnf transformation 54]
113. ~kind(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 58]
122. ~patient(X0) | calm(X0) | ~kind(X0) [cnf transformation 61]
123. ~patient(X0) | kind(X0) | ~calm(X0) [cnf transformation 61]
125. ~tall(X0) | strong(X0) [cnf transformation 63]
129. ~rich(sK4) [cnf transformation 68]
133. old(john) | ~strong(john) [cnf transformation 22]
134. tall(john) [cnf transformation 23]
135. ~wise(X0) | ~kind(X0) [duplicate literal removal 113]
137. 1 <=> ! [X0] : (rich(X0) | ~generous(X0)) [avatar definition]
138. ~generous(X0) | rich(X0) <- (1) [avatar component clause 137]
140. 2 <=> patient(john) [avatar definition]
142. patient(john) <- (2) [avatar component clause 140]
143. 1 | 2 [avatar split clause 86,140,137]
196. calm(X0) | kind(X0) [subsumption resolution 107,82]
232. ~patient(X0) | kind(X0) [subsumption resolution 123,196]
233. ~patient(X0) | calm(X0) [subsumption resolution 122,196]
246. 23 <=> strong(john) [avatar definition]
250. 24 <=> old(john) [avatar definition]
252. old(john) <- (24) [avatar component clause 250]
253. ~23 | 24 [avatar split clause 133,250,246]
257. strong(john) [resolution 125,134]
261. 23 [avatar split clause 257,246]
265. kind(john) <- (2) [resolution 232,142]
266. calm(john) <- (2) [resolution 233,142]
293. patient(X1) | curious(X1) | patient(X1) [resolution 74,89]
294. curious(X1) | patient(X1) [duplicate literal removal 293]
339. ~patient(X0) | funny(X0) | curious(X0) [resolution 91,98]
349. funny(X0) | curious(X0) [subsumption resolution 339,294]
390. ~kind(john) | ~curious(john) <- (2) [resolution 106,266]
476. curious(X1) | ~old(X1) | curious(X1) | ~patient(X1) [resolution 349,71]
480. curious(X1) | ~old(X1) | ~patient(X1) [duplicate literal removal 476]
481. ~old(X1) | curious(X1) [subsumption resolution 480,294]
483. curious(john) <- (24) [resolution 481,252]
488. ~curious(john) <- (2) [subsumption resolution 390,265]
489. $false <- (2, 24) [subsumption resolution 488,483]
490. ~2 | ~24 [avatar contradiction clause 489]
497. rich(X0) | wise(X0) <- (1) [resolution 138,78]
498. rich(X1) | kind(X1) <- (1) [resolution 138,77]
515. wise(sK4) <- (1) [resolution 497,129]
520. kind(sK4) <- (1) [resolution 498,129]
598. ~kind(sK4) <- (1) [resolution 515,135]
599. $false <- (1) [subsumption resolution 598,520]
600. ~1 [avatar contradiction clause 599]
601. $false [avatar sat refutation 143,253,261,490,600]
% SZS output end Proof for 6699232609356960489248762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or brave then someone is not happy and vice versa.
Everyone who is not tall or wise is calm or not patient.
If someone is not funny or not generous then someone is not calm or not brave.
If paul is patient then someone is either calm or not rich and vice versa.
If fred is not humble or not quiet then john is curious or quiet and vice versa.
Everyone who is not calm is not generous and vice versa.
Everyone who is either strong or funny is not kind or not quiet and vice versa.
If paul is both not creative and patient then susan is old and vice versa.
Everyone who is not curious or not quiet is both not patient and funny.
If someone is both kind and funny then paul is both calm and patient and vice versa.
Everyone who is not generous is either not strong or patient.
If susan is not humble then someone is either not calm or not happy and vice versa.
If someone is both not wise and wise then someone is both not humble and not quiet.
Everyone who is humble or not old is either rich or not strong and vice versa.
If susan is creative or not brave then someone is not generous and vice versa.
If paul is not old then someone is not generous or tall.
Alice is not calm or not patient.
Someone is either not curious or happy.
Paul is rich or not quiet.
Lucy is both not rich and not quiet.
Lucy is tall or quiet.
Lucy is both not humble and funny.
Mary is either not old or brave.
Lucy is happy or not generous. | Lucy is not tall. | contradiction | ((?[X]:((~curious(X)<~>brave(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|wise(X))=>(calm(X)|~patient(X))))&
((?[X]:((~funny(X)|~generous(X))))=>(?[X]:((~calm(X)|~brave(X)))))&
((patient(paul))<=>(?[X]:((calm(X)<~>~rich(X)))))&
(((~humble(fred)|~quiet(fred)))<=>((curious(john)|quiet(john))))&
(![X]:(~calm(X)<=>~generous(X)))&
(![X]:((strong(X)<~>funny(X))<=>(~kind(X)|~quiet(X))))&
(((~creative(paul)&patient(paul)))<=>(old(susan)))&
(![X]:((~curious(X)|~quiet(X))=>(~patient(X)&funny(X))))&
((?[X]:((kind(X)&funny(X))))<=>((calm(paul)&patient(paul))))&
(![X]:(~generous(X)=>(~strong(X)<~>patient(X))))&
((~humble(susan))<=>(?[X]:((~calm(X)<~>~happy(X)))))&
((?[X]:((~wise(X)&wise(X))))=>(?[X]:((~humble(X)&~quiet(X)))))&
(![X]:((humble(X)|~old(X))<=>(rich(X)<~>~strong(X))))&
(((creative(susan)|~brave(susan)))<=>(?[X]:(~generous(X))))&
((~old(paul))=>(?[X]:((~generous(X)|tall(X)))))&
((~calm(alice)|~patient(alice)))&
(?[X]:((~curious(X)<~>happy(X))))&
((rich(paul)|~quiet(paul)))&
((~rich(lucy)&~quiet(lucy)))&
((tall(lucy)|quiet(lucy)))&
((~humble(lucy)&funny(lucy)))&
((~old(mary)<~>brave(mary)))&
((happy(lucy)|~generous(lucy))) | ~tall(lucy) | [
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1112740192785194566627933
% SZS output start Proof for 1112740192785194566627933
20. ~quiet(lucy) & ~rich(lucy) [input p19]
21. quiet(lucy) | tall(lucy) [input p20]
25. ~tall(lucy) [input hypothesis]
139. ~quiet(lucy) [cnf transformation 20]
140. quiet(lucy) | tall(lucy) [cnf transformation 21]
146. ~tall(lucy) [cnf transformation 25]
338. tall(lucy) [subsumption resolution 140,139]
358. $false [subsumption resolution 146,338]
% SZS output end Proof for 1112740192785194566627933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either not funny or creative and vice versa. Everyone who is curious or tall is not brave. Everyone who is old is creative or not humble and vice versa. If someone is brave then lucy is not wise and vice versa. If someone is both happy and wise then susan is both kind and not brave. Everyone who is both wise and not funny is calm or not patient. Everyone who is both not creative and old is not kind. Everyone who is not quiet is quiet. Everyone who is both not wise and old is wise or rich. If someone is not curious or not generous then alice is brave and vice versa. If susan is not old or not kind then someone is both creative and not wise. If someone is both not brave and not happy then someone is not patient. Everyone who is not kind is both not tall and curious. Everyone who is either not old or strong is both not happy and creative and vice versa. Everyone who is both not tall and funny is both kind and not tall and vice versa. Everyone who is humble or kind is both curious and calm. Mary is both not brave and calm. Someone is quiet or curious. Someone is either not brave or not generous. Lucy is funny. Fred is either not old or curious. Alice is either not creative or old. Someone is either not rich or curious. | Fred is curious. | entailment | (![X]:(~humble(X)<=>(~funny(X)<~>creative(X))))&
(![X]:((curious(X)|tall(X))=>~brave(X)))&
(![X]:(old(X)<=>(creative(X)|~humble(X))))&
((?[X]:(brave(X)))<=>(~wise(lucy)))&
((?[X]:((happy(X)&wise(X))))=>((kind(susan)&~brave(susan))))&
(![X]:((wise(X)&~funny(X))=>(calm(X)|~patient(X))))&
(![X]:((~creative(X)&old(X))=>~kind(X)))&
(![X]:(~quiet(X)=>quiet(X)))&
(![X]:((~wise(X)&old(X))=>(wise(X)|rich(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>(brave(alice)))&
(((~old(susan)|~kind(susan)))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~brave(X)&~happy(X))))=>(?[X]:(~patient(X))))&
(![X]:(~kind(X)=>(~tall(X)&curious(X))))&
(![X]:((~old(X)<~>strong(X))<=>(~happy(X)&creative(X))))&
(![X]:((~tall(X)&funny(X))<=>(kind(X)&~tall(X))))&
(![X]:((humble(X)|kind(X))=>(curious(X)&calm(X))))&
((~brave(mary)&calm(mary)))&
(?[X]:((quiet(X)|curious(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(funny(lucy))&
((~old(fred)<~>curious(fred)))&
((~creative(alice)<~>old(alice)))&
(?[X]:((~rich(X)<~>curious(X)))) | curious(fred) | [
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7324292432891438690186736
% SZS output start Proof for 7324292432891438690186736
13. ! [X0] : (~kind(X0) => (curious(X0) & ~tall(X0))) [input p12]
16. ! [X0] : ((kind(X0) | humble(X0)) => (calm(X0) & curious(X0))) [input p15]
24. ~curious(fred) [input hypothesis]
30. ! [X0] : ((kind(X0) | humble(X0)) => curious(X0)) [pure predicate removal 16]
39. ! [X0] : ((curious(X0) & ~tall(X0)) | kind(X0)) [ennf transformation 13]
40. ! [X0] : (curious(X0) | (~kind(X0) & ~humble(X0))) [ennf transformation 30]
89. curious(X0) | kind(X0) [cnf transformation 39]
101. curious(X0) | ~kind(X0) [cnf transformation 40]
112. ~curious(fred) [cnf transformation 24]
158. 11 <=> ! [X1] : curious(X1) [avatar definition]
159. curious(X1) <- (11) [avatar component clause 158]
180. curious(X0) [subsumption resolution 101,89]
181. 11 [avatar split clause 180,158]
197. 18 <=> curious(fred) [avatar definition]
199. ~curious(fred) <- (~18) [avatar component clause 197]
221. ~18 [avatar split clause 112,197]
222. $false <- (11, ~18) [resolution 199,159]
223. ~11 | 18 [avatar contradiction clause 222]
224. $false [avatar sat refutation 181,221,223]
% SZS output end Proof for 7324292432891438690186736
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both generous and kind then someone is either funny or not funny and vice versa.
If paul is not creative then someone is both kind and strong and vice versa.
Everyone who is both strong and wise is not wise and vice versa.
Everyone who is not old or not funny is either not tall or not funny and vice versa.
If lucy is either not tall or not humble then someone is both tall and funny.
Everyone who is either not quiet or not tall is both kind and not wise and vice versa.
Everyone who is both not old and patient is old and vice versa.
If alice is not curious then someone is not brave or wise and vice versa.
Everyone who is both humble and not tall is either not kind or not happy and vice versa.
Everyone who is old is both not strong and curious.
If someone is either not happy or curious then someone is funny.
If someone is rich or not generous then susan is not tall.
If alice is both strong and not happy then someone is strong or not quiet.
If fred is curious then someone is kind or patient and vice versa.
If susan is old or not quiet then paul is either not tall or not old.
If lucy is creative then mary is either not quiet or generous and vice versa.
John is calm or strong.
John is not creative or curious.
Paul is either generous or not humble.
Lucy is both not quiet and curious. | Mary is generous. | neutral | (((generous(susan)&kind(susan)))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((~creative(paul))<=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((strong(X)&wise(X))<=>~wise(X)))&
(![X]:((~old(X)|~funny(X))<=>(~tall(X)<~>~funny(X))))&
(((~tall(lucy)<~>~humble(lucy)))=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((~quiet(X)<~>~tall(X))<=>(kind(X)&~wise(X))))&
(![X]:((~old(X)&patient(X))<=>old(X)))&
((~curious(alice))<=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((humble(X)&~tall(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:(old(X)=>(~strong(X)&curious(X))))&
((?[X]:((~happy(X)<~>curious(X))))=>(?[X]:(funny(X))))&
((?[X]:((rich(X)|~generous(X))))=>(~tall(susan)))&
(((strong(alice)&~happy(alice)))=>(?[X]:((strong(X)|~quiet(X)))))&
((curious(fred))<=>(?[X]:((kind(X)|patient(X)))))&
(((old(susan)|~quiet(susan)))=>((~tall(paul)<~>~old(paul))))&
((creative(lucy))<=>((~quiet(mary)<~>generous(mary))))&
((calm(john)|strong(john)))&
((~creative(john)|curious(john)))&
((generous(paul)<~>~humble(paul)))&
((~quiet(lucy)&curious(lucy))) | generous(mary) | [] | null | 0 |
Everyone who is either not generous or not curious is not funny or tall and vice versa. Everyone who is not humble or creative is quiet and vice versa. If someone is not humble then lucy is wise. Everyone who is funny is both kind and not funny and vice versa. If someone is not rich then alice is either happy or wise and vice versa. Everyone who is not humble is patient and vice versa. Everyone who is both funny and not wise is not generous and vice versa. If paul is either not funny or humble then mary is not tall. Everyone who is tall or not quiet is either tall or not happy. If someone is either not old or patient then john is creative or not quiet and vice versa. Everyone who is calm or tall is not tall. If paul is not strong or creative then someone is either quiet or not curious and vice versa. Everyone who is not brave or quiet is both not generous and funny. Everyone who is either quiet or creative is both strong and not wise and vice versa. If lucy is either not calm or not kind then someone is either not kind or strong and vice versa. Someone is not wise or not old. Mary is not quiet or not tall. Alice is both calm and not happy. Paul is both not curious and not kind. Lucy is curious or not tall. | Mary is brave. | entailment | (![X]:((~generous(X)<~>~curious(X))<=>(~funny(X)|tall(X))))&
(![X]:((~humble(X)|creative(X))<=>quiet(X)))&
((?[X]:(~humble(X)))=>(wise(lucy)))&
(![X]:(funny(X)<=>(kind(X)&~funny(X))))&
((?[X]:(~rich(X)))<=>((happy(alice)<~>wise(alice))))&
(![X]:(~humble(X)<=>patient(X)))&
(![X]:((funny(X)&~wise(X))<=>~generous(X)))&
(((~funny(paul)<~>humble(paul)))=>(~tall(mary)))&
(![X]:((tall(X)|~quiet(X))=>(tall(X)<~>~happy(X))))&
((?[X]:((~old(X)<~>patient(X))))<=>((creative(john)|~quiet(john))))&
(![X]:((calm(X)|tall(X))=>~tall(X)))&
(((~strong(paul)|creative(paul)))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
(![X]:((~brave(X)|quiet(X))=>(~generous(X)&funny(X))))&
(![X]:((quiet(X)<~>creative(X))<=>(strong(X)&~wise(X))))&
(((~calm(lucy)<~>~kind(lucy)))<=>(?[X]:((~kind(X)<~>strong(X)))))&
(?[X]:((~wise(X)|~old(X))))&
((~quiet(mary)|~tall(mary)))&
((calm(alice)&~happy(alice)))&
((~curious(paul)&~kind(paul)))&
((curious(lucy)|~tall(lucy))) | brave(mary) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4081464438068471555991350
% SZS output start Proof for 4081464438068471555991350
4. ! [X0] : (funny(X0) <=> (~funny(X0) & kind(X0))) [input p3]
13. ! [X0] : ((quiet(X0) | ~brave(X0)) => (funny(X0) & ~generous(X0))) [input p12]
21. ~brave(mary) [input hypothesis]
26. ! [X0] : ((funny(X0) & ~generous(X0)) | (~quiet(X0) & brave(X0))) [ennf transformation 13]
31. ! [X0] : ((funny(X0) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | ~funny(X0))) [nnf transformation 4]
32. ! [X0] : ((funny(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | ~funny(X0))) [flattening 31]
71. ~funny(X0) | ~funny(X0) [cnf transformation 32]
104. funny(X0) | brave(X0) [cnf transformation 26]
127. ~brave(mary) [cnf transformation 21]
130. ~funny(X0) [duplicate literal removal 71]
227. brave(X0) [subsumption resolution 104,130]
269. $false [subsumption resolution 127,227]
% SZS output end Proof for 4081464438068471555991350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not wise is kind or not tall and vice versa.
Everyone who is either generous or tall is either curious or wise.
If someone is both not generous and kind then someone is creative or not calm and vice versa.
Everyone who is either not old or patient is not rich and vice versa.
Everyone who is either not strong or not calm is either not wise or happy.
If mary is both not patient and not quiet then someone is both happy and rich.
If someone is both tall and humble then someone is not rich or curious.
Everyone who is both wise and not brave is either not happy or wise and vice versa.
If paul is not funny or not calm then alice is either not patient or not brave and vice versa.
Everyone who is both not quiet and rich is both not brave and not funny.
Everyone who is either not wise or not strong is not happy or not wise and vice versa.
Everyone who is not brave is either not strong or not happy and vice versa.
If someone is not happy or not curious then someone is not tall or not calm and vice versa.
If alice is either happy or wise then susan is either happy or funny.
If someone is either not kind or generous then lucy is not rich or brave.
Everyone who is not kind or not humble is both not happy and strong and vice versa.
Lucy is not old or wise.
Mary is quiet or happy.
John is either creative or happy.
Someone is not patient or not happy.
Fred is not generous. | Fred is not quiet. | contradiction | (![X]:((rich(X)&~wise(X))<=>(kind(X)|~tall(X))))&
(![X]:((generous(X)<~>tall(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~generous(X)&kind(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~old(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~strong(X)<~>~calm(X))=>(~wise(X)<~>happy(X))))&
(((~patient(mary)&~quiet(mary)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((tall(X)&humble(X))))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((wise(X)&~brave(X))<=>(~happy(X)<~>wise(X))))&
(((~funny(paul)|~calm(paul)))<=>((~patient(alice)<~>~brave(alice))))&
(![X]:((~quiet(X)&rich(X))=>(~brave(X)&~funny(X))))&
(![X]:((~wise(X)<~>~strong(X))<=>(~happy(X)|~wise(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~happy(X))))&
((?[X]:((~happy(X)|~curious(X))))<=>(?[X]:((~tall(X)|~calm(X)))))&
(((happy(alice)<~>wise(alice)))=>((happy(susan)<~>funny(susan))))&
((?[X]:((~kind(X)<~>generous(X))))=>((~rich(lucy)|brave(lucy))))&
(![X]:((~kind(X)|~humble(X))<=>(~happy(X)&strong(X))))&
((~old(lucy)|wise(lucy)))&
((quiet(mary)|happy(mary)))&
((creative(john)<~>happy(john)))&
(?[X]:((~patient(X)|~happy(X))))&
(~generous(fred)) | ~quiet(fred) | [
"p0",
"p7",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 637948701093932216427976
% SZS output start Proof for 637948701093932216427976
1. ! [X0] : ((~wise(X0) & rich(X0)) <=> (~tall(X0) | kind(X0))) [input p0]
8. ! [X0] : ((~brave(X0) & wise(X0)) <=> (~happy(X0) <~> wise(X0))) [input p7]
10. ! [X0] : ((rich(X0) & ~quiet(X0)) => (~funny(X0) & ~brave(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~wise(X0) | ~happy(X0))) [input p10]
12. ! [X0] : (~brave(X0) <=> (~strong(X0) <~> ~happy(X0))) [input p11]
16. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (strong(X0) & ~happy(X0))) [input p15]
22. ~quiet(fred) [input hypothesis]
31. ! [X0] : ((~funny(X0) & ~brave(X0)) | (~rich(X0) | quiet(X0))) [ennf transformation 10]
32. ! [X0] : ((~funny(X0) & ~brave(X0)) | ~rich(X0) | quiet(X0)) [flattening 31]
36. ! [X0] : (((~wise(X0) & rich(X0)) | (tall(X0) & ~kind(X0))) & ((~tall(X0) | kind(X0)) | (wise(X0) | ~rich(X0)))) [nnf transformation 1]
37. ! [X0] : (((~wise(X0) & rich(X0)) | (tall(X0) & ~kind(X0))) & (~tall(X0) | kind(X0) | wise(X0) | ~rich(X0))) [flattening 36]
51. ! [X0] : (((~brave(X0) & wise(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0)))) & (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (brave(X0) | ~wise(X0)))) [nnf transformation 8]
52. ! [X0] : (((~brave(X0) & wise(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0)))) & (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | brave(X0) | ~wise(X0))) [flattening 51]
55. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (wise(X0) & happy(X0))) & ((~wise(X0) | ~happy(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 11]
56. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (wise(X0) & happy(X0))) & (~wise(X0) | ~happy(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [flattening 55]
57. ! [X0] : ((~brave(X0) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | brave(X0))) [nnf transformation 12]
65. ! [X0] : (((~humble(X0) | ~kind(X0)) | (~strong(X0) | happy(X0))) & ((strong(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 16]
66. ! [X0] : ((~humble(X0) | ~kind(X0) | ~strong(X0) | happy(X0)) & ((strong(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [flattening 65]
71. ~kind(X0) | rich(X0) [cnf transformation 37]
73. ~kind(X0) | ~wise(X0) [cnf transformation 37]
96. ~wise(X0) | happy(X0) | brave(X0) | ~wise(X0) [cnf transformation 52]
97. wise(X0) | wise(X0) | happy(X0) [cnf transformation 52]
107. ~brave(X0) | ~rich(X0) | quiet(X0) [cnf transformation 32]
111. ~strong(X0) | ~wise(X0) | happy(X0) [cnf transformation 56]
114. strong(X0) | wise(X0) | wise(X0) [cnf transformation 56]
115. ~happy(X0) | ~strong(X0) | brave(X0) [cnf transformation 57]
129. ~happy(X0) | kind(X0) [cnf transformation 66]
131. strong(X0) | kind(X0) [cnf transformation 66]
140. ~quiet(fred) [cnf transformation 22]
142. strong(X0) | wise(X0) [duplicate literal removal 114]
143. ~wise(X0) | happy(X0) | brave(X0) [duplicate literal removal 96]
144. happy(X0) | wise(X0) [duplicate literal removal 97]
207. brave(X0) | happy(X0) [subsumption resolution 143,144]
230. ~strong(X0) | happy(X0) [subsumption resolution 111,144]
232. ~strong(X0) | brave(X0) [subsumption resolution 115,207]
349. happy(X1) | kind(X1) [resolution 230,131]
350. kind(X1) [subsumption resolution 349,129]
351. ~wise(X0) [resolution 350,73]
352. rich(X1) [resolution 350,71]
356. brave(X0) | wise(X0) [resolution 232,142]
359. brave(X0) [subsumption resolution 356,351]
416. ~rich(X0) | quiet(X0) [resolution 107,359]
419. quiet(X0) [subsumption resolution 416,352]
460. $false [resolution 419,140]
% SZS output end Proof for 637948701093932216427976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not tall or not wise then fred is not strong or strong. If someone is both patient and generous then mary is either not happy or not humble and vice versa. Everyone who is both not tall and not creative is kind or not calm and vice versa. If susan is not patient then mary is tall. If someone is either not funny or happy then susan is not quiet or creative. Everyone who is either strong or old is both rich and not creative and vice versa. Everyone who is not old or not calm is not happy or creative and vice versa. If someone is either tall or humble then john is either calm or not creative and vice versa. Everyone who is both creative and calm is not rich or not happy. If someone is funny then someone is both not rich and not curious and vice versa. If someone is either not creative or humble then someone is both rich and kind and vice versa. Everyone who is not old is old. Everyone who is not creative is funny and vice versa. If someone is humble or tall then mary is both quiet and not kind and vice versa. Everyone who is either rich or funny is either kind or not funny. Everyone who is not tall is both old and humble and vice versa. Alice is either not tall or quiet. Mary is rich. Paul is quiet. Someone is not brave or not old. Lucy is strong. Someone is either kind or not happy. Paul is either not tall or not funny. | Susan is creative. | contradiction | (((~tall(lucy)<~>~wise(lucy)))=>((~strong(fred)|strong(fred))))&
((?[X]:((patient(X)&generous(X))))<=>((~happy(mary)<~>~humble(mary))))&
(![X]:((~tall(X)&~creative(X))<=>(kind(X)|~calm(X))))&
((~patient(susan))=>(tall(mary)))&
((?[X]:((~funny(X)<~>happy(X))))=>((~quiet(susan)|creative(susan))))&
(![X]:((strong(X)<~>old(X))<=>(rich(X)&~creative(X))))&
(![X]:((~old(X)|~calm(X))<=>(~happy(X)|creative(X))))&
((?[X]:((tall(X)<~>humble(X))))<=>((calm(john)<~>~creative(john))))&
(![X]:((creative(X)&calm(X))=>(~rich(X)|~happy(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~rich(X)&~curious(X)))))&
((?[X]:((~creative(X)<~>humble(X))))<=>(?[X]:((rich(X)&kind(X)))))&
(![X]:(~old(X)=>old(X)))&
(![X]:(~creative(X)<=>funny(X)))&
((?[X]:((humble(X)|tall(X))))<=>((quiet(mary)&~kind(mary))))&
(![X]:((rich(X)<~>funny(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~tall(X)<=>(old(X)&humble(X))))&
((~tall(alice)<~>quiet(alice)))&
(rich(mary))&
(quiet(paul))&
(?[X]:((~brave(X)|~old(X))))&
(strong(lucy))&
(?[X]:((kind(X)<~>~happy(X))))&
((~tall(paul)<~>~funny(paul))) | creative(susan) | [
"p2",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 364091535018929810714424
% SZS output start Proof for 364091535018929810714424
3. ! [X0] : ((~creative(X0) & ~tall(X0)) <=> (~calm(X0) | kind(X0))) [input p2]
7. ! [X0] : ((~calm(X0) | ~old(X0)) <=> (creative(X0) | ~happy(X0))) [input p6]
12. ! [X0] : (~old(X0) => old(X0)) [input p11]
24. creative(susan) [input hypothesis]
35. ! [X0] : (old(X0) | old(X0)) [ennf transformation 12]
42. ! [X0] : (((~creative(X0) & ~tall(X0)) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | (creative(X0) | tall(X0)))) [nnf transformation 3]
43. ! [X0] : (((~creative(X0) & ~tall(X0)) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | creative(X0) | tall(X0))) [flattening 42]
47. ! [X0] : (((~calm(X0) | ~old(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (calm(X0) & old(X0)))) [nnf transformation 7]
48. ! [X0] : ((~calm(X0) | ~old(X0) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | (calm(X0) & old(X0)))) [flattening 47]
89. ~creative(X0) | calm(X0) [cnf transformation 43]
102. ~calm(X0) | ~old(X0) | ~creative(X0) [cnf transformation 48]
121. old(X0) | old(X0) [cnf transformation 35]
145. creative(susan) [cnf transformation 24]
148. old(X0) [duplicate literal removal 121]
191. 10 <=> creative(susan) [avatar definition]
193. creative(susan) <- (10) [avatar component clause 191]
199. ~old(X0) | ~creative(X0) [subsumption resolution 102,89]
344. 10 [avatar split clause 145,191]
357. ~creative(X0) [resolution 199,148]
359. $false <- (10) [resolution 357,193]
362. ~10 [avatar contradiction clause 359]
363. $false [avatar sat refutation 344,362]
% SZS output end Proof for 364091535018929810714424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then mary is not generous and vice versa.
Everyone who is not rich or not patient is generous.
If someone is creative or not happy then someone is either not wise or curious and vice versa.
If someone is not calm or not curious then someone is not tall or wise and vice versa.
If susan is old then alice is tall or not humble and vice versa.
If someone is either strong or not happy then someone is both not strong and not old.
Everyone who is tall is not humble and vice versa.
If john is either patient or not tall then someone is both kind and strong.
Everyone who is either not brave or generous is not funny and vice versa.
If someone is both not rich and humble then someone is both not wise and not humble.
Everyone who is not wise or curious is quiet.
If john is both happy and calm then someone is kind or not rich and vice versa.
Everyone who is patient is either strong or humble.
If someone is either creative or not old then someone is happy.
Everyone who is quiet or not curious is both not calm and not brave.
Everyone who is both not brave and not calm is not kind or wise and vice versa.
Someone is not generous.
Alice is tall or wise.
Someone is not generous or old.
Someone is not happy.
Someone is either humble or not curious.
Lucy is strong or not calm. | Susan is not generous. | neutral | ((?[X]:(~curious(X)))<=>(~generous(mary)))&
(![X]:((~rich(X)|~patient(X))=>generous(X)))&
((?[X]:((creative(X)|~happy(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:((~tall(X)|wise(X)))))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:(tall(X)<=>~humble(X)))&
(((patient(john)<~>~tall(john)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>~funny(X)))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~wise(X)|curious(X))=>quiet(X)))&
(((happy(john)&calm(john)))<=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:(patient(X)=>(strong(X)<~>humble(X))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((quiet(X)|~curious(X))=>(~calm(X)&~brave(X))))&
(![X]:((~brave(X)&~calm(X))<=>(~kind(X)|wise(X))))&
(?[X]:(~generous(X)))&
((tall(alice)|wise(alice)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)<~>~curious(X))))&
((strong(lucy)|~calm(lucy))) | ~generous(susan) | [] | null | 0 |
If someone is tall then someone is either not funny or creative and vice versa.
Everyone who is both not humble and wise is either not curious or not old.
If someone is not happy then someone is not patient or not generous and vice versa.
Everyone who is both not calm and strong is not patient and vice versa.
If mary is patient or not humble then mary is both not generous and calm.
Everyone who is generous is both calm and not wise.
If john is either not quiet or wise then paul is not happy and vice versa.
If someone is not creative then lucy is not patient.
If someone is not calm or not wise then fred is generous.
Everyone who is both happy and quiet is calm or rich.
If paul is happy or not funny then someone is not humble or not tall.
If someone is not curious then someone is not creative.
Everyone who is humble or brave is not rich.
If john is both rich and not quiet then someone is creative or not curious.
Everyone who is either not patient or calm is not generous.
Everyone who is both wise and funny is both not wise and not humble and vice versa.
Someone is either old or not humble.
Someone is both calm and rich.
Someone is either not old or strong.
Someone is not tall.
Someone is either not wise or not rich.
Alice is not happy. | Paul is not funny. | entailment | ((?[X]:(tall(X)))<=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~humble(X)&wise(X))=>(~curious(X)<~>~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(((patient(mary)|~humble(mary)))=>((~generous(mary)&calm(mary))))&
(![X]:(generous(X)=>(calm(X)&~wise(X))))&
(((~quiet(john)<~>wise(john)))<=>(~happy(paul)))&
((?[X]:(~creative(X)))=>(~patient(lucy)))&
((?[X]:((~calm(X)|~wise(X))))=>(generous(fred)))&
(![X]:((happy(X)&quiet(X))=>(calm(X)|rich(X))))&
(((happy(paul)|~funny(paul)))=>(?[X]:((~humble(X)|~tall(X)))))&
((?[X]:(~curious(X)))=>(?[X]:(~creative(X))))&
(![X]:((humble(X)|brave(X))=>~rich(X)))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(?[X]:((old(X)<~>~humble(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(~happy(alice)) | ~funny(paul) | [
"p3",
"p5",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6421346343753479826257650
% SZS output start Proof for 6421346343753479826257650
4. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p3]
6. ! [X0] : (generous(X0) => (~wise(X0) & calm(X0))) [input p5]
9. ? [X0] : (~wise(X0) | ~calm(X0)) => generous(fred) [input p8]
15. ! [X0] : ((~patient(X0) <~> calm(X0)) => ~generous(X0)) [input p14]
16. ! [X0] : ((funny(X0) & wise(X0)) <=> (~humble(X0) & ~wise(X0))) [input p15]
23. funny(paul) [input hypothesis]
31. ! [X0] : ((~wise(X0) & calm(X0)) | ~generous(X0)) [ennf transformation 6]
33. generous(fred) | ! [X0] : (wise(X0) & calm(X0)) [ennf transformation 9]
41. ! [X0] : (~generous(X0) | (~patient(X0) <=> calm(X0))) [ennf transformation 15]
53. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 4]
54. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 53]
63. ! [X0] : (~generous(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) [nnf transformation 41]
64. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 16]
65. ! [X0] : (((funny(X0) & wise(X0)) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | ~funny(X0) | ~wise(X0))) [flattening 64]
89. ~calm(X0) | patient(X0) [cnf transformation 54]
95. ~generous(X0) | calm(X0) [cnf transformation 31]
103. generous(fred) | wise(X0) [cnf transformation 33]
111. ~generous(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 63]
112. ~wise(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 65]
126. funny(paul) [cnf transformation 23]
127. ~wise(X0) | ~funny(X0) [duplicate literal removal 112]
223. 22 <=> ! [X0] : wise(X0) [avatar definition]
224. wise(X0) <- (22) [avatar component clause 223]
226. 23 <=> generous(fred) [avatar definition]
228. generous(fred) <- (23) [avatar component clause 226]
229. 22 | 23 [avatar split clause 103,226,223]
235. 25 <=> funny(paul) [avatar definition]
237. funny(paul) <- (25) [avatar component clause 235]
269. ~generous(X0) | ~calm(X0) [subsumption resolution 111,89]
270. ~generous(X0) [subsumption resolution 269,95]
301. 25 [avatar split clause 126,235]
302. $false <- (23) [subsumption resolution 228,270]
303. ~23 [avatar contradiction clause 302]
323. ~funny(X0) <- (22) [resolution 127,224]
325. $false <- (22, 25) [resolution 323,237]
328. ~22 | ~25 [avatar contradiction clause 325]
329. $false [avatar sat refutation 229,301,303,328]
% SZS output end Proof for 6421346343753479826257650
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not quiet is either generous or not creative and vice versa.
If someone is not wise then alice is not patient and vice versa.
Everyone who is both wise and not old is both not generous and generous.
Everyone who is not kind is both not humble and curious and vice versa.
If susan is not brave or calm then someone is not brave and vice versa.
Everyone who is funny or not creative is brave or not brave.
If someone is not funny or tall then someone is not humble.
Everyone who is not humble or not strong is creative or not strong.
Everyone who is old is both not old and tall.
If someone is not happy then someone is not wise.
If someone is either calm or not generous then someone is not wise and vice versa.
Everyone who is funny or not patient is either tall or wise.
Everyone who is both old and not creative is curious or calm and vice versa.
If susan is either calm or old then mary is either not funny or not patient.
If someone is both not tall and not strong then alice is either kind or not generous and vice versa.
Mary is both not tall and not calm.
Someone is kind.
Someone is either not rich or not brave.
Someone is either humble or wise.
Lucy is not humble or not curious.
Someone is not funny. | Mary is not funny. | entailment | (![X]:((creative(X)|~quiet(X))<=>(generous(X)<~>~creative(X))))&
((?[X]:(~wise(X)))<=>(~patient(alice)))&
(![X]:((wise(X)&~old(X))=>(~generous(X)&generous(X))))&
(![X]:(~kind(X)<=>(~humble(X)&curious(X))))&
(((~brave(susan)|calm(susan)))<=>(?[X]:(~brave(X))))&
(![X]:((funny(X)|~creative(X))=>(brave(X)|~brave(X))))&
((?[X]:((~funny(X)|tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|~strong(X))=>(creative(X)|~strong(X))))&
(![X]:(old(X)=>(~old(X)&tall(X))))&
((?[X]:(~happy(X)))=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)|~patient(X))=>(tall(X)<~>wise(X))))&
(![X]:((old(X)&~creative(X))<=>(curious(X)|calm(X))))&
(((calm(susan)<~>old(susan)))=>((~funny(mary)<~>~patient(mary))))&
((?[X]:((~tall(X)&~strong(X))))<=>((kind(alice)<~>~generous(alice))))&
((~tall(mary)&~calm(mary)))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((humble(X)<~>wise(X))))&
((~humble(lucy)|~curious(lucy)))&
(?[X]:(~funny(X))) | ~funny(mary) | [
"p2",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1630981292570449838533726
% SZS output start Proof for 1630981292570449838533726
3. ! [X0] : ((~old(X0) & wise(X0)) => (generous(X0) & ~generous(X0))) [input p2]
9. ! [X0] : (old(X0) => (tall(X0) & ~old(X0))) [input p8]
12. ! [X0] : ((~patient(X0) | funny(X0)) => (tall(X0) <~> wise(X0))) [input p11]
16. ~calm(mary) & ~tall(mary) [input p15]
22. funny(mary) [input hypothesis]
27. ! [X0] : ((generous(X0) & ~generous(X0)) | (old(X0) | ~wise(X0))) [ennf transformation 3]
28. ! [X0] : ((generous(X0) & ~generous(X0)) | old(X0) | ~wise(X0)) [flattening 27]
34. ! [X0] : ((tall(X0) & ~old(X0)) | ~old(X0)) [ennf transformation 9]
35. ! [X0] : ((tall(X0) <~> wise(X0)) | (patient(X0) & ~funny(X0))) [ennf transformation 12]
58. ! [X0] : (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (patient(X0) & ~funny(X0))) [nnf transformation 35]
84. ~generous(X0) | old(X0) | ~wise(X0) [cnf transformation 28]
85. ~wise(X0) | old(X0) | generous(X0) [cnf transformation 28]
98. ~old(X0) | ~old(X0) [cnf transformation 34]
104. ~funny(X0) | tall(X0) | wise(X0) [cnf transformation 58]
123. ~tall(mary) [cnf transformation 16]
132. funny(mary) [cnf transformation 22]
133. ~old(X0) [duplicate literal removal 98]
149. ~wise(X0) | old(X0) [subsumption resolution 84,85]
280. tall(mary) | wise(mary) [resolution 104,132]
281. wise(mary) [subsumption resolution 280,123]
284. old(mary) [resolution 281,149]
286. $false [subsumption resolution 284,133]
% SZS output end Proof for 1630981292570449838533726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or wise is either wise or curious. If someone is both not humble and brave then fred is either wise or not wise. Everyone who is wise is either old or not curious. Everyone who is not curious is generous or not patient. Everyone who is not kind is both not curious and not generous. If someone is either not kind or not tall then someone is either curious or not wise and vice versa. Everyone who is funny or not wise is tall. If someone is both old and creative then someone is not strong or not patient and vice versa. If mary is tall or humble then someone is both strong and not curious and vice versa. Everyone who is not kind is happy and vice versa. If someone is both not rich and patient then susan is not old. If fred is both not happy and tall then someone is either not rich or not brave. Everyone who is either not brave or not wise is curious or calm. Everyone who is both not funny and not happy is not curious and vice versa. Everyone who is either funny or not humble is not tall. Lucy is not brave or wise. Someone is either kind or brave. Someone is either strong or curious. Someone is both not strong and funny. Someone is brave. Susan is rich or not humble. | Mary is not patient. | neutral | (![X]:((patient(X)<~>wise(X))=>(wise(X)<~>curious(X))))&
((?[X]:((~humble(X)&brave(X))))=>((wise(fred)<~>~wise(fred))))&
(![X]:(wise(X)=>(old(X)<~>~curious(X))))&
(![X]:(~curious(X)=>(generous(X)|~patient(X))))&
(![X]:(~kind(X)=>(~curious(X)&~generous(X))))&
((?[X]:((~kind(X)<~>~tall(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(![X]:((funny(X)|~wise(X))=>tall(X)))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~strong(X)|~patient(X)))))&
(((tall(mary)|humble(mary)))<=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:(~kind(X)<=>happy(X)))&
((?[X]:((~rich(X)&patient(X))))=>(~old(susan)))&
(((~happy(fred)&tall(fred)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((~brave(X)<~>~wise(X))=>(curious(X)|calm(X))))&
(![X]:((~funny(X)&~happy(X))<=>~curious(X)))&
(![X]:((funny(X)<~>~humble(X))=>~tall(X)))&
((~brave(lucy)|wise(lucy)))&
(?[X]:((kind(X)<~>brave(X))))&
(?[X]:((strong(X)<~>curious(X))))&
(?[X]:((~strong(X)&funny(X))))&
(?[X]:(brave(X)))&
((rich(susan)|~humble(susan))) | ~patient(mary) | [] | null | 0 |
Everyone who is patient or calm is not curious or humble.
If susan is rich or patient then alice is both not strong and not calm and vice versa.
If mary is both not kind and not tall then someone is either tall or not happy.
If alice is either not tall or not funny then someone is wise or happy.
Everyone who is both creative and patient is funny or tall.
If fred is either not humble or creative then lucy is either not rich or humble and vice versa.
Everyone who is both not quiet and not patient is tall or not patient.
Everyone who is not generous or kind is not rich or not old.
If paul is either humble or not curious then paul is creative and vice versa.
Everyone who is both not generous and not happy is kind and vice versa.
Everyone who is both not curious and not creative is either not creative or generous.
Everyone who is strong is both not brave and tall.
Everyone who is both kind and brave is calm and vice versa.
Everyone who is either not brave or not curious is not wise and vice versa.
Everyone who is not calm or strong is not happy and vice versa.
Everyone who is both not calm and not generous is not strong and vice versa.
Someone is both not generous and not old.
Someone is either not funny or calm.
Someone is either old or quiet.
Someone is both old and not quiet.
Alice is not tall.
Alice is not kind or not funny. | Lucy is not generous. | neutral | (![X]:((patient(X)|calm(X))=>(~curious(X)|humble(X))))&
(((rich(susan)|patient(susan)))<=>((~strong(alice)&~calm(alice))))&
(((~kind(mary)&~tall(mary)))=>(?[X]:((tall(X)<~>~happy(X)))))&
(((~tall(alice)<~>~funny(alice)))=>(?[X]:((wise(X)|happy(X)))))&
(![X]:((creative(X)&patient(X))=>(funny(X)|tall(X))))&
(((~humble(fred)<~>creative(fred)))<=>((~rich(lucy)<~>humble(lucy))))&
(![X]:((~quiet(X)&~patient(X))=>(tall(X)|~patient(X))))&
(![X]:((~generous(X)|kind(X))=>(~rich(X)|~old(X))))&
(((humble(paul)<~>~curious(paul)))<=>(creative(paul)))&
(![X]:((~generous(X)&~happy(X))<=>kind(X)))&
(![X]:((~curious(X)&~creative(X))=>(~creative(X)<~>generous(X))))&
(![X]:(strong(X)=>(~brave(X)&tall(X))))&
(![X]:((kind(X)&brave(X))<=>calm(X)))&
(![X]:((~brave(X)<~>~curious(X))<=>~wise(X)))&
(![X]:((~calm(X)|strong(X))<=>~happy(X)))&
(![X]:((~calm(X)&~generous(X))<=>~strong(X)))&
(?[X]:((~generous(X)&~old(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((old(X)&~quiet(X))))&
(~tall(alice))&
((~kind(alice)|~funny(alice))) | ~generous(lucy) | [] | null | 0 |
If lucy is both wise and patient then someone is either old or strong.
Everyone who is either not wise or quiet is both not old and patient and vice versa.
If someone is happy then paul is not wise or strong.
If susan is brave or humble then someone is humble or rich and vice versa.
If someone is old then lucy is both patient and wise and vice versa.
Everyone who is curious is either rich or not generous.
Everyone who is either not happy or not humble is both quiet and happy.
Everyone who is both creative and tall is patient or not calm.
Everyone who is both kind and funny is humble and vice versa.
If fred is both not curious and not brave then someone is creative or not rich and vice versa.
If someone is old or strong then someone is not rich.
If mary is either brave or not strong then mary is either not happy or curious and vice versa.
If fred is both not generous and not curious then susan is not brave or creative.
Everyone who is both not curious and not tall is happy or patient and vice versa.
If someone is brave or creative then paul is both not quiet and creative.
Everyone who is both not happy and creative is not tall or calm and vice versa.
Someone is either not calm or not tall.
Someone is either not old or calm.
Fred is curious or not creative.
Someone is not funny or old. | Paul is not creative. | neutral | (((wise(lucy)&patient(lucy)))=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>(~old(X)&patient(X))))&
((?[X]:(happy(X)))=>((~wise(paul)|strong(paul))))&
(((brave(susan)|humble(susan)))<=>(?[X]:((humble(X)|rich(X)))))&
((?[X]:(old(X)))<=>((patient(lucy)&wise(lucy))))&
(![X]:(curious(X)=>(rich(X)<~>~generous(X))))&
(![X]:((~happy(X)<~>~humble(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)&tall(X))=>(patient(X)|~calm(X))))&
(![X]:((kind(X)&funny(X))<=>humble(X)))&
(((~curious(fred)&~brave(fred)))<=>(?[X]:((creative(X)|~rich(X)))))&
((?[X]:((old(X)|strong(X))))=>(?[X]:(~rich(X))))&
(((brave(mary)<~>~strong(mary)))<=>((~happy(mary)<~>curious(mary))))&
(((~generous(fred)&~curious(fred)))=>((~brave(susan)|creative(susan))))&
(![X]:((~curious(X)&~tall(X))<=>(happy(X)|patient(X))))&
((?[X]:((brave(X)|creative(X))))=>((~quiet(paul)&creative(paul))))&
(![X]:((~happy(X)&creative(X))<=>(~tall(X)|calm(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((curious(fred)|~creative(fred)))&
(?[X]:((~funny(X)|old(X)))) | ~creative(paul) | [] | null | 0 |
If someone is calm or not strong then someone is either not happy or old. Everyone who is either funny or not old is either not kind or not creative and vice versa. Everyone who is both not curious and not brave is either not kind or not creative. If lucy is creative or calm then someone is either quiet or not funny and vice versa. Everyone who is either quiet or rich is both kind and not quiet. Everyone who is either not old or not kind is either not curious or not patient and vice versa. Everyone who is creative is either not wise or not brave. Everyone who is not rich or not kind is not strong or not rich. If mary is curious or kind then fred is not curious or not humble and vice versa. If someone is both not calm and not funny then paul is not curious or not funny and vice versa. Everyone who is both not generous and quiet is not wise or not happy and vice versa. If someone is brave or not kind then someone is both not humble and patient and vice versa. If lucy is not generous or not rich then paul is both not creative and humble. Everyone who is not wise is either quiet or not happy and vice versa. If paul is either creative or tall then alice is either not patient or not kind and vice versa. If someone is both brave and not generous then mary is either strong or not funny. Mary is both not patient and strong. Someone is either not creative or not humble. Someone is old. Mary is tall. Lucy is either patient or not wise. Someone is either happy or not quiet. Lucy is old. Lucy is strong. | Alice is not patient. | neutral | ((?[X]:((calm(X)|~strong(X))))=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((funny(X)<~>~old(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((~curious(X)&~brave(X))=>(~kind(X)<~>~creative(X))))&
(((creative(lucy)|calm(lucy)))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:((quiet(X)<~>rich(X))=>(kind(X)&~quiet(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(~curious(X)<~>~patient(X))))&
(![X]:(creative(X)=>(~wise(X)<~>~brave(X))))&
(![X]:((~rich(X)|~kind(X))=>(~strong(X)|~rich(X))))&
(((curious(mary)|kind(mary)))<=>((~curious(fred)|~humble(fred))))&
((?[X]:((~calm(X)&~funny(X))))<=>((~curious(paul)|~funny(paul))))&
(![X]:((~generous(X)&quiet(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~generous(lucy)|~rich(lucy)))=>((~creative(paul)&humble(paul))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~happy(X))))&
(((creative(paul)<~>tall(paul)))<=>((~patient(alice)<~>~kind(alice))))&
((?[X]:((brave(X)&~generous(X))))=>((strong(mary)<~>~funny(mary))))&
((~patient(mary)&strong(mary)))&
(?[X]:((~creative(X)<~>~humble(X))))&
(?[X]:(old(X)))&
(tall(mary))&
((patient(lucy)<~>~wise(lucy)))&
(?[X]:((happy(X)<~>~quiet(X))))&
(old(lucy))&
(strong(lucy)) | ~patient(alice) | [] | null | 0 |
Everyone who is strong is creative or not brave.
Everyone who is both rich and not curious is strong.
Everyone who is either quiet or patient is both not generous and not curious and vice versa.
Everyone who is not curious or not strong is funny.
Everyone who is wise or brave is both not wise and not humble and vice versa.
Everyone who is not generous is not strong or quiet and vice versa.
Everyone who is not tall or humble is both kind and not rich and vice versa.
If alice is both not brave and not humble then someone is either curious or brave.
Everyone who is either tall or not old is not calm.
If someone is brave then someone is not calm.
If someone is either not happy or humble then lucy is wise or quiet and vice versa.
Everyone who is not happy is both curious and humble.
Everyone who is patient or funny is both not patient and rich and vice versa.
If someone is generous or not generous then susan is not patient and vice versa.
Everyone who is both not kind and not funny is generous or not curious and vice versa.
Everyone who is brave or not funny is both not old and curious.
Alice is brave.
Someone is both brave and not generous.
Fred is not creative or calm.
Someone is not kind.
Fred is either calm or quiet.
Alice is either kind or rich.
Someone is either not humble or quiet. | Fred is happy. | entailment | (![X]:(strong(X)=>(creative(X)|~brave(X))))&
(![X]:((rich(X)&~curious(X))=>strong(X)))&
(![X]:((quiet(X)<~>patient(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~curious(X)|~strong(X))=>funny(X)))&
(![X]:((wise(X)|brave(X))<=>(~wise(X)&~humble(X))))&
(![X]:(~generous(X)<=>(~strong(X)|quiet(X))))&
(![X]:((~tall(X)|humble(X))<=>(kind(X)&~rich(X))))&
(((~brave(alice)&~humble(alice)))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((tall(X)<~>~old(X))=>~calm(X)))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~happy(X)<~>humble(X))))<=>((wise(lucy)|quiet(lucy))))&
(![X]:(~happy(X)=>(curious(X)&humble(X))))&
(![X]:((patient(X)|funny(X))<=>(~patient(X)&rich(X))))&
((?[X]:((generous(X)|~generous(X))))<=>(~patient(susan)))&
(![X]:((~kind(X)&~funny(X))<=>(generous(X)|~curious(X))))&
(![X]:((brave(X)|~funny(X))=>(~old(X)&curious(X))))&
(brave(alice))&
(?[X]:((brave(X)&~generous(X))))&
((~creative(fred)|calm(fred)))&
(?[X]:(~kind(X)))&
((calm(fred)<~>quiet(fred)))&
((kind(alice)<~>rich(alice)))&
(?[X]:((~humble(X)<~>quiet(X)))) | happy(fred) | [
"p2",
"p3",
"p5",
"p6",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1247062222599792270146557
% SZS output start Proof for 1247062222599792270146557
3. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (~curious(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | ~curious(X0)) => funny(X0)) [input p3]
6. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~strong(X0))) [input p5]
7. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (~rich(X0) & kind(X0))) [input p6]
12. ! [X0] : (~happy(X0) => (humble(X0) & curious(X0))) [input p11]
13. ! [X0] : ((funny(X0) | patient(X0)) <=> (rich(X0) & ~patient(X0))) [input p12]
15. ! [X0] : ((~funny(X0) & ~kind(X0)) <=> (~curious(X0) | generous(X0))) [input p14]
24. ~happy(fred) [input hypothesis]
30. ! [X0] : (funny(X0) | (strong(X0) & curious(X0))) [ennf transformation 4]
35. ! [X0] : ((humble(X0) & curious(X0)) | happy(X0)) [ennf transformation 12]
37. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [flattening 37]
41. ! [X0] : ((~generous(X0) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | generous(X0))) [nnf transformation 6]
42. ! [X0] : ((~generous(X0) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | generous(X0))) [flattening 41]
43. ! [X0] : (((humble(X0) | ~tall(X0)) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | (~humble(X0) & tall(X0)))) [nnf transformation 7]
44. ! [X0] : ((humble(X0) | ~tall(X0) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | (~humble(X0) & tall(X0)))) [flattening 43]
57. ! [X0] : (((funny(X0) | patient(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (~funny(X0) & ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((funny(X0) | patient(X0) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | (~funny(X0) & ~patient(X0)))) [flattening 57]
63. ! [X0] : (((~funny(X0) & ~kind(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (funny(X0) | kind(X0)))) [nnf transformation 15]
64. ! [X0] : (((~funny(X0) & ~kind(X0)) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | funny(X0) | kind(X0))) [flattening 63]
78. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 38]
82. funny(X0) | curious(X0) [cnf transformation 30]
83. funny(X0) | strong(X0) [cnf transformation 30]
89. ~strong(X0) | quiet(X0) | generous(X0) [cnf transformation 42]
93. ~humble(X0) | kind(X0) [cnf transformation 44]
95. ~humble(X0) | ~rich(X0) [cnf transformation 44]
109. humble(X0) | happy(X0) [cnf transformation 35]
110. ~patient(X0) | ~patient(X0) [cnf transformation 58]
113. ~funny(X0) | rich(X0) [cnf transformation 58]
119. ~kind(X0) | ~generous(X0) [cnf transformation 64]
122. ~funny(X0) | curious(X0) [cnf transformation 64]
138. ~happy(fred) [cnf transformation 24]
139. ~patient(X0) [duplicate literal removal 110]
190. 11 <=> ! [X1] : (humble(X1) | happy(X1)) [avatar definition]
191. happy(X1) | humble(X1) <- (11) [avatar component clause 190]
193. 11 [avatar split clause 109,190]
194. curious(X0) [subsumption resolution 122,82]
207. 14 <=> quiet(fred) [avatar definition]
208. quiet(fred) <- (14) [avatar component clause 207]
209. ~quiet(fred) <- (~14) [avatar component clause 207]
237. rich(X0) | strong(X0) [resolution 113,83]
243. humble(fred) <- (11) [resolution 191,138]
251. ~rich(fred) <- (11) [resolution 243,95]
252. kind(fred) <- (11) [resolution 243,93]
302. ~generous(fred) <- (11) [resolution 252,119]
361. strong(fred) <- (11) [resolution 237,251]
397. patient(fred) | ~curious(fred) <- (14) [resolution 208,78]
398. ~curious(fred) <- (14) [subsumption resolution 397,139]
399. $false <- (14) [subsumption resolution 398,194]
400. ~14 [avatar contradiction clause 399]
429. quiet(fred) | generous(fred) <- (11) [resolution 361,89]
430. generous(fred) <- (11, ~14) [subsumption resolution 429,209]
431. $false <- (11, ~14) [subsumption resolution 430,302]
432. ~11 | 14 [avatar contradiction clause 431]
433. $false [avatar sat refutation 193,400,432]
% SZS output end Proof for 1247062222599792270146557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not tall or not patient then alice is not old and vice versa. Everyone who is either not quiet or not tall is either not humble or calm and vice versa. Everyone who is quiet or rich is both creative and funny and vice versa. Everyone who is curious is either not curious or strong. If someone is not funny then someone is both rich and not brave and vice versa. Everyone who is both calm and humble is creative or not strong and vice versa. If someone is either rich or not kind then someone is either not generous or not humble. Everyone who is wise is both not brave and creative. If alice is not strong then alice is either generous or curious. Everyone who is either not kind or brave is kind or rich. If paul is either calm or not funny then someone is both rich and strong and vice versa. Everyone who is strong or rich is patient or not kind and vice versa. Everyone who is not curious or creative is both not happy and not rich. If mary is both not curious and not brave then someone is curious or not strong. If susan is wise or creative then susan is creative or not strong. If lucy is old then lucy is either humble or strong. Someone is not happy. Mary is not creative. Susan is either strong or not rich. John is not calm. Fred is either creative or not quiet. Lucy is not creative or funny. Susan is not wise or not generous. Someone is both not quiet and not kind. | Susan is happy. | contradiction | (((~tall(paul)|~patient(paul)))<=>(~old(alice)))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((quiet(X)|rich(X))<=>(creative(X)&funny(X))))&
(![X]:(curious(X)=>(~curious(X)<~>strong(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((rich(X)&~brave(X)))))&
(![X]:((calm(X)&humble(X))<=>(creative(X)|~strong(X))))&
((?[X]:((rich(X)<~>~kind(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:(wise(X)=>(~brave(X)&creative(X))))&
((~strong(alice))=>((generous(alice)<~>curious(alice))))&
(![X]:((~kind(X)<~>brave(X))=>(kind(X)|rich(X))))&
(((calm(paul)<~>~funny(paul)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((strong(X)|rich(X))<=>(patient(X)|~kind(X))))&
(![X]:((~curious(X)|creative(X))=>(~happy(X)&~rich(X))))&
(((~curious(mary)&~brave(mary)))=>(?[X]:((curious(X)|~strong(X)))))&
(((wise(susan)|creative(susan)))=>((creative(susan)|~strong(susan))))&
((old(lucy))=>((humble(lucy)<~>strong(lucy))))&
(?[X]:(~happy(X)))&
(~creative(mary))&
((strong(susan)<~>~rich(susan)))&
(~calm(john))&
((creative(fred)<~>~quiet(fred)))&
((~creative(lucy)|funny(lucy)))&
((~wise(susan)|~generous(susan)))&
(?[X]:((~quiet(X)&~kind(X)))) | happy(susan) | [
"p2",
"p3",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5292843729410486841454953
% SZS output start Proof for 5292843729410486841454953
3. ! [X0] : ((rich(X0) | quiet(X0)) <=> (funny(X0) & creative(X0))) [input p2]
4. ! [X0] : (curious(X0) => (~curious(X0) <~> strong(X0))) [input p3]
13. ! [X0] : ((creative(X0) | ~curious(X0)) => (~rich(X0) & ~happy(X0))) [input p12]
19. strong(susan) <~> ~rich(susan) [input p18]
25. happy(susan) [input hypothesis]
31. ! [X0] : ((~curious(X0) <~> strong(X0)) | ~curious(X0)) [ennf transformation 4]
36. ! [X0] : ((~rich(X0) & ~happy(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 13]
45. ! [X0] : (((rich(X0) | quiet(X0)) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | (~rich(X0) & ~quiet(X0)))) [nnf transformation 3]
46. ! [X0] : ((rich(X0) | quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | (~rich(X0) & ~quiet(X0)))) [flattening 45]
47. ! [X0] : (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ~curious(X0)) [nnf transformation 31]
72. (rich(susan) | ~strong(susan)) & (~rich(susan) | strong(susan)) [nnf transformation 19]
88. ~rich(X0) | creative(X0) [cnf transformation 46]
92. strong(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 47]
120. ~happy(X0) | curious(X0) [cnf transformation 36]
123. ~rich(X0) | ~creative(X0) [cnf transformation 36]
131. rich(susan) | ~strong(susan) [cnf transformation 72]
138. happy(susan) [cnf transformation 25]
140. ~curious(X0) | strong(X0) [duplicate literal removal 92]
230. ~rich(X0) [subsumption resolution 123,88]
261. ~strong(susan) [subsumption resolution 131,230]
290. curious(susan) [resolution 120,138]
292. strong(susan) [resolution 290,140]
293. $false [subsumption resolution 292,261]
% SZS output end Proof for 5292843729410486841454953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not creative is either tall or generous. If paul is either brave or not generous then john is not creative and vice versa. Everyone who is either not brave or not funny is not humble and vice versa. Everyone who is either curious or creative is both not quiet and curious and vice versa. Everyone who is not curious is not old or brave and vice versa. If someone is either quiet or creative then lucy is both not quiet and not generous. Everyone who is both not strong and tall is both not curious and funny. Everyone who is either generous or calm is both not calm and happy and vice versa. Everyone who is both tall and quiet is not patient or rich and vice versa. Everyone who is not kind is quiet or wise and vice versa. Everyone who is both not brave and not wise is either old or not generous and vice versa. Everyone who is not curious is old or not kind. Everyone who is both not old and not happy is both not old and not rich and vice versa. Everyone who is either curious or not humble is not generous and vice versa. If mary is both not creative and curious then mary is not happy. Everyone who is both curious and not kind is not funny. Someone is both not generous and brave. Paul is not kind. Someone is not strong. Fred is not curious or wise. Someone is either brave or not happy. Fred is patient or happy. Someone is humble. Someone is curious. | Paul is generous. | neutral | (![X]:((funny(X)&~creative(X))=>(tall(X)<~>generous(X))))&
(((brave(paul)<~>~generous(paul)))<=>(~creative(john)))&
(![X]:((~brave(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~curious(X)<=>(~old(X)|brave(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>((~quiet(lucy)&~generous(lucy))))&
(![X]:((~strong(X)&tall(X))=>(~curious(X)&funny(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~calm(X)&happy(X))))&
(![X]:((tall(X)&quiet(X))<=>(~patient(X)|rich(X))))&
(![X]:(~kind(X)<=>(quiet(X)|wise(X))))&
(![X]:((~brave(X)&~wise(X))<=>(old(X)<~>~generous(X))))&
(![X]:(~curious(X)=>(old(X)|~kind(X))))&
(![X]:((~old(X)&~happy(X))<=>(~old(X)&~rich(X))))&
(![X]:((curious(X)<~>~humble(X))<=>~generous(X)))&
(((~creative(mary)&curious(mary)))=>(~happy(mary)))&
(![X]:((curious(X)&~kind(X))=>~funny(X)))&
(?[X]:((~generous(X)&brave(X))))&
(~kind(paul))&
(?[X]:(~strong(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(fred)|happy(fred)))&
(?[X]:(humble(X)))&
(?[X]:(curious(X))) | generous(paul) | [] | null | 0 |
Everyone who is both not brave and patient is either not funny or generous and vice versa. Everyone who is both humble and brave is humble or not creative and vice versa. Everyone who is not tall is either not old or not wise. Everyone who is both not happy and funny is not creative or not quiet. Everyone who is both not rich and tall is not happy and vice versa. If mary is both calm and patient then lucy is not humble or funny and vice versa. If someone is not generous then someone is not quiet or not kind and vice versa. If susan is not wise or brave then susan is both tall and not generous. If someone is strong then someone is tall or not old and vice versa. If someone is both humble and creative then fred is both tall and quiet. Everyone who is humble is either calm or curious and vice versa. Everyone who is not tall is not quiet or not calm and vice versa. Everyone who is happy is calm and vice versa. If lucy is funny or calm then fred is not wise or not funny and vice versa. Everyone who is both happy and humble is not brave. Everyone who is both not curious and patient is not rich or not old. Mary is either not humble or brave. John is not curious or funny. Someone is tall. Alice is both not old and not tall. Someone is either not rich or not brave. Someone is happy or not wise. Someone is either not kind or humble. | Alice is curious. | entailment | (![X]:((~brave(X)&patient(X))<=>(~funny(X)<~>generous(X))))&
(![X]:((humble(X)&brave(X))<=>(humble(X)|~creative(X))))&
(![X]:(~tall(X)=>(~old(X)<~>~wise(X))))&
(![X]:((~happy(X)&funny(X))=>(~creative(X)|~quiet(X))))&
(![X]:((~rich(X)&tall(X))<=>~happy(X)))&
(((calm(mary)&patient(mary)))<=>((~humble(lucy)|funny(lucy))))&
((?[X]:(~generous(X)))<=>(?[X]:((~quiet(X)|~kind(X)))))&
(((~wise(susan)|brave(susan)))=>((tall(susan)&~generous(susan))))&
((?[X]:(strong(X)))<=>(?[X]:((tall(X)|~old(X)))))&
((?[X]:((humble(X)&creative(X))))=>((tall(fred)&quiet(fred))))&
(![X]:(humble(X)<=>(calm(X)<~>curious(X))))&
(![X]:(~tall(X)<=>(~quiet(X)|~calm(X))))&
(![X]:(happy(X)<=>calm(X)))&
(((funny(lucy)|calm(lucy)))<=>((~wise(fred)|~funny(fred))))&
(![X]:((happy(X)&humble(X))=>~brave(X)))&
(![X]:((~curious(X)&patient(X))=>(~rich(X)|~old(X))))&
((~humble(mary)<~>brave(mary)))&
((~curious(john)|funny(john)))&
(?[X]:(tall(X)))&
((~old(alice)&~tall(alice)))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((happy(X)|~wise(X))))&
(?[X]:((~kind(X)<~>humble(X)))) | curious(alice) | [
"p1",
"p4",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4877246823306278177804259
% SZS output start Proof for 4877246823306278177804259
2. ! [X0] : ((brave(X0) & humble(X0)) <=> (~creative(X0) | humble(X0))) [input p1]
5. ! [X0] : ((tall(X0) & ~rich(X0)) <=> ~happy(X0)) [input p4]
11. ! [X0] : (humble(X0) <=> (calm(X0) <~> curious(X0))) [input p10]
12. ! [X0] : (~tall(X0) <=> (~calm(X0) | ~quiet(X0))) [input p11]
13. ! [X0] : (happy(X0) <=> calm(X0)) [input p12]
15. ! [X0] : ((humble(X0) & happy(X0)) => ~brave(X0)) [input p14]
24. ~curious(alice) [input hypothesis]
32. ! [X0] : (~brave(X0) | (~humble(X0) | ~happy(X0))) [ennf transformation 15]
33. ! [X0] : (~brave(X0) | ~humble(X0) | ~happy(X0)) [flattening 32]
38. ! [X0] : (((brave(X0) & humble(X0)) | (creative(X0) & ~humble(X0))) & ((~creative(X0) | humble(X0)) | (~brave(X0) | ~humble(X0)))) [nnf transformation 2]
39. ! [X0] : (((brave(X0) & humble(X0)) | (creative(X0) & ~humble(X0))) & (~creative(X0) | humble(X0) | ~brave(X0) | ~humble(X0))) [flattening 38]
41. ! [X0] : (((tall(X0) & ~rich(X0)) | happy(X0)) & (~happy(X0) | (~tall(X0) | rich(X0)))) [nnf transformation 5]
42. ! [X0] : (((tall(X0) & ~rich(X0)) | happy(X0)) & (~happy(X0) | ~tall(X0) | rich(X0))) [flattening 41]
55. ! [X0] : ((humble(X0) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ~humble(X0))) [nnf transformation 11]
56. ! [X0] : ((~tall(X0) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | tall(X0))) [nnf transformation 12]
57. ! [X0] : ((~tall(X0) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | tall(X0))) [flattening 56]
58. ! [X0] : ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))) [nnf transformation 13]
81. ~humble(X0) | brave(X0) [cnf transformation 39]
88. happy(X0) | tall(X0) [cnf transformation 42]
108. ~calm(X0) | curious(X0) | humble(X0) [cnf transformation 55]
112. ~tall(X0) | calm(X0) [cnf transformation 57]
113. ~happy(X0) | calm(X0) [cnf transformation 58]
114. ~calm(X0) | happy(X0) [cnf transformation 58]
119. ~brave(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 33]
132. ~curious(alice) [cnf transformation 24]
251. ~happy(X0) | ~humble(X0) [subsumption resolution 119,81]
303. calm(X0) | tall(X0) [resolution 113,88]
305. calm(X0) [subsumption resolution 303,112]
310. happy(X0) [resolution 114,305]
322. ~humble(X0) [resolution 310,251]
364. curious(X0) | humble(X0) [resolution 108,305]
367. curious(X0) [subsumption resolution 364,322]
393. $false [resolution 367,132]
% SZS output end Proof for 4877246823306278177804259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not curious or not quiet then someone is not generous or not patient.
If fred is either not tall or not kind then someone is both strong and brave.
Everyone who is wise is not happy and vice versa.
Everyone who is both not creative and old is not calm or old and vice versa.
If someone is both calm and happy then john is both not happy and not kind and vice versa.
If mary is either curious or not patient then someone is not rich or strong and vice versa.
Everyone who is not brave is either wise or creative and vice versa.
If someone is not generous or strong then paul is patient and vice versa.
If someone is either not strong or not rich then someone is both brave and curious and vice versa.
If someone is both not generous and happy then someone is both quiet and old.
Everyone who is both not old and not calm is old or not kind.
If someone is either not old or not curious then john is both humble and not wise and vice versa.
Everyone who is calm or curious is either happy or not brave.
If someone is tall or not wise then someone is both tall and creative.
If someone is not tall then someone is either not wise or not quiet.
Everyone who is brave is either not rich or not funny and vice versa.
Someone is both not patient and not kind.
Mary is either strong or humble.
Someone is both not brave and kind.
Fred is not curious.
Paul is not funny or not generous.
Someone is both quiet and funny.
Fred is not quiet or not generous.
Someone is not humble or not calm. | Fred is brave. | contradiction | ((?[X]:((~curious(X)<~>~quiet(X))))=>(?[X]:((~generous(X)|~patient(X)))))&
(((~tall(fred)<~>~kind(fred)))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:(wise(X)<=>~happy(X)))&
(![X]:((~creative(X)&old(X))<=>(~calm(X)|old(X))))&
((?[X]:((calm(X)&happy(X))))<=>((~happy(john)&~kind(john))))&
(((curious(mary)<~>~patient(mary)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(~brave(X)<=>(wise(X)<~>creative(X))))&
((?[X]:((~generous(X)|strong(X))))<=>(patient(paul)))&
((?[X]:((~strong(X)<~>~rich(X))))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((~old(X)&~calm(X))=>(old(X)|~kind(X))))&
((?[X]:((~old(X)<~>~curious(X))))<=>((humble(john)&~wise(john))))&
(![X]:((calm(X)|curious(X))=>(happy(X)<~>~brave(X))))&
((?[X]:((tall(X)|~wise(X))))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:(brave(X)<=>(~rich(X)<~>~funny(X))))&
(?[X]:((~patient(X)&~kind(X))))&
((strong(mary)<~>humble(mary)))&
(?[X]:((~brave(X)&kind(X))))&
(~curious(fred))&
((~funny(paul)|~generous(paul)))&
(?[X]:((quiet(X)&funny(X))))&
((~quiet(fred)|~generous(fred)))&
(?[X]:((~humble(X)|~calm(X)))) | brave(fred) | [
"p2",
"p3",
"p4",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1232899848849077991655703
% SZS output start Proof for 1232899848849077991655703
3. ! [X0] : (wise(X0) <=> ~happy(X0)) [input p2]
4. ! [X0] : ((old(X0) & ~creative(X0)) <=> (old(X0) | ~calm(X0))) [input p3]
5. ? [X0] : (happy(X0) & calm(X0)) <=> (~kind(john) & ~happy(john)) [input p4]
7. ! [X0] : (~brave(X0) <=> (wise(X0) <~> creative(X0))) [input p6]
13. ! [X0] : ((curious(X0) | calm(X0)) => (happy(X0) <~> ~brave(X0))) [input p12]
14. ? [X0] : (~wise(X0) | tall(X0)) => ? [X0] : (creative(X0) & tall(X0)) [input p13]
25. brave(fred) [input hypothesis]
29. ? [X0] : (~wise(X0) | tall(X0)) => ? [X1] : (creative(X1) & tall(X1)) [rectify 14]
36. ! [X0] : ((happy(X0) <~> ~brave(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 13]
37. ? [X1] : (creative(X1) & tall(X1)) | ! [X0] : (wise(X0) & ~tall(X0)) [ennf transformation 29]
46. ! [X0] : ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))) [nnf transformation 3]
47. ! [X0] : (((old(X0) & ~creative(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (~old(X0) | creative(X0)))) [nnf transformation 4]
48. ! [X0] : (((old(X0) & ~creative(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ~old(X0) | creative(X0))) [flattening 47]
49. (? [X0] : (happy(X0) & calm(X0)) | (kind(john) | happy(john))) & ((~kind(john) & ~happy(john)) | ! [X0] : (~happy(X0) | ~calm(X0))) [nnf transformation 5]
50. (? [X0] : (happy(X0) & calm(X0)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X0] : (~happy(X0) | ~calm(X0))) [flattening 49]
51. (? [X0] : (happy(X0) & calm(X0)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X1] : (~happy(X1) | ~calm(X1))) [rectify 50]
52. ? [X0] : (happy(X0) & calm(X0)) => (happy(sK2) & calm(sK2)) [choice axiom]
53. ((happy(sK2) & calm(sK2)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X1] : (~happy(X1) | ~calm(X1))) [skolemisation 51,52]
58. ! [X0] : ((~brave(X0) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0)))) & (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | brave(X0))) [nnf transformation 7]
76. ! [X0] : (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~curious(X0) & ~calm(X0))) [nnf transformation 36]
77. ? [X0] : (creative(X0) & tall(X0)) | ! [X1] : (wise(X1) & ~tall(X1)) [rectify 37]
78. ? [X0] : (creative(X0) & tall(X0)) => (creative(sK9) & tall(sK9)) [choice axiom]
79. (creative(sK9) & tall(sK9)) | ! [X1] : (wise(X1) & ~tall(X1)) [skolemisation 77,78]
100. ~happy(X0) | ~wise(X0) [cnf transformation 46]
101. happy(X0) | wise(X0) [cnf transformation 46]
103. ~creative(X0) | calm(X0) [cnf transformation 48]
104. ~old(X0) | ~creative(X0) [cnf transformation 48]
105. calm(X0) | old(X0) [cnf transformation 48]
107. ~happy(john) | ~happy(X1) | ~calm(X1) [cnf transformation 53]
108. ~kind(john) | ~happy(X1) | ~calm(X1) [cnf transformation 53]
110. happy(sK2) | kind(john) | happy(john) [cnf transformation 53]
117. creative(X0) | wise(X0) | brave(X0) [cnf transformation 58]
118. ~creative(X0) | ~wise(X0) | brave(X0) [cnf transformation 58]
119. ~wise(X0) | creative(X0) | ~brave(X0) [cnf transformation 58]
120. ~creative(X0) | wise(X0) | ~brave(X0) [cnf transformation 58]
139. ~calm(X0) | happy(X0) | ~brave(X0) [cnf transformation 76]
141. ~calm(X0) | ~happy(X0) | brave(X0) [cnf transformation 76]
144. tall(sK9) | wise(X1) [cnf transformation 79]
145. creative(sK9) | ~tall(X1) [cnf transformation 79]
165. brave(fred) [cnf transformation 25]
204. 9 <=> happy(john) [avatar definition]
208. 10 <=> kind(john) [avatar definition]
212. 11 <=> happy(sK2) [avatar definition]
214. happy(sK2) <- (11) [avatar component clause 212]
215. 9 | 10 | 11 [avatar split clause 110,212,208,204]
222. 13 <=> ! [X1] : (~happy(X1) | ~calm(X1)) [avatar definition]
223. ~calm(X1) | ~happy(X1) <- (13) [avatar component clause 222]
224. 13 | ~10 [avatar split clause 108,208,222]
225. 13 | ~9 [avatar split clause 107,204,222]
345. 40 <=> ! [X1] : wise(X1) [avatar definition]
346. wise(X1) <- (40) [avatar component clause 345]
348. 41 <=> creative(sK9) [avatar definition]
350. creative(sK9) <- (41) [avatar component clause 348]
353. 42 <=> ! [X1] : ~tall(X1) [avatar definition]
354. ~tall(X1) <- (42) [avatar component clause 353]
355. 42 | 41 [avatar split clause 145,348,353]
357. 43 <=> tall(sK9) [avatar definition]
359. tall(sK9) <- (43) [avatar component clause 357]
360. 40 | 43 [avatar split clause 144,357,345]
418. ~wise(sK2) <- (11) [resolution 100,214]
419. $false <- (11, 40) [subsumption resolution 418,346]
420. ~11 | ~40 [avatar contradiction clause 419]
428. ~happy(X0) | old(X0) <- (13) [resolution 223,105]
437. calm(X0) | brave(X0) | wise(X0) [resolution 117,103]
452. ~brave(X0) | happy(X0) | old(X0) [resolution 139,105]
457. ~brave(X0) | old(X0) <- (13) [subsumption resolution 452,428]
472. ~brave(X0) | creative(X0) <- (40) [resolution 346,119]
476. $false <- (42, 43) [resolution 359,354]
477. ~42 | ~43 [avatar contradiction clause 476]
525. old(fred) <- (13) [resolution 457,165]
530. creative(fred) <- (40) [resolution 472,165]
531. brave(X0) | wise(X0) | ~happy(X0) | brave(X0) [resolution 437,141]
534. brave(X0) | wise(X0) | ~happy(X0) [duplicate literal removal 531]
536. ~creative(fred) <- (13) [resolution 525,104]
539. $false <- (13, 40) [subsumption resolution 536,530]
540. ~13 | ~40 [avatar contradiction clause 539]
547. ~happy(X0) | brave(X0) [subsumption resolution 534,100]
561. wise(sK9) | ~brave(sK9) <- (41) [resolution 350,120]
562. ~wise(sK9) | brave(sK9) <- (41) [resolution 350,118]
563. calm(sK9) <- (41) [resolution 350,103]
565. 66 <=> brave(sK9) [avatar definition]
567. ~brave(sK9) <- (~66) [avatar component clause 565]
569. 67 <=> wise(sK9) [avatar definition]
570. ~wise(sK9) <- (~67) [avatar component clause 569]
571. wise(sK9) <- (67) [avatar component clause 569]
572. ~66 | 67 | ~41 [avatar split clause 561,348,569,565]
573. 66 | ~67 | ~41 [avatar split clause 562,348,569,565]
588. happy(sK9) | ~brave(sK9) <- (41) [resolution 563,139]
624. wise(X0) | brave(X0) [resolution 547,101]
634. brave(sK9) <- (~67) [resolution 624,570]
635. $false <- (~66, ~67) [subsumption resolution 634,567]
636. 66 | 67 [avatar contradiction clause 635]
638. 72 <=> happy(sK9) [avatar definition]
640. happy(sK9) <- (72) [avatar component clause 638]
641. ~66 | 72 | ~41 [avatar split clause 588,348,638,565]
659. ~wise(sK9) <- (72) [resolution 640,100]
660. $false <- (67, 72) [subsumption resolution 659,571]
661. ~67 | ~72 [avatar contradiction clause 660]
662. $false [avatar sat refutation 215,224,225,355,360,420,477,540,572,573,636,641,661]
% SZS output end Proof for 1232899848849077991655703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or quiet then susan is funny.
Everyone who is kind or happy is old and vice versa.
Everyone who is not curious is humble and vice versa.
Everyone who is patient or not strong is calm and vice versa.
Everyone who is both not creative and rich is not calm or quiet.
If paul is both not happy and not strong then john is both not old and kind.
If someone is either happy or not funny then lucy is quiet or not curious and vice versa.
Everyone who is both generous and not happy is happy.
Everyone who is not quiet or not strong is either not calm or quiet.
If paul is either calm or not tall then someone is both not brave and kind.
If someone is happy or not funny then mary is both not brave and not happy and vice versa.
Everyone who is not happy is not humble or rich.
Everyone who is happy or not brave is not tall.
Everyone who is both wise and not happy is not happy or patient and vice versa.
Everyone who is both not wise and not curious is not wise or curious and vice versa.
Everyone who is both not funny and not wise is quiet or happy.
Paul is not creative or not generous.
Someone is either strong or tall.
Susan is either not wise or quiet.
Someone is not quiet.
Fred is kind or not humble.
Someone is either humble or not generous.
Mary is either not old or not patient. | John is humble. | entailment | ((?[X]:((rich(X)<~>quiet(X))))=>(funny(susan)))&
(![X]:((kind(X)|happy(X))<=>old(X)))&
(![X]:(~curious(X)<=>humble(X)))&
(![X]:((patient(X)|~strong(X))<=>calm(X)))&
(![X]:((~creative(X)&rich(X))=>(~calm(X)|quiet(X))))&
(((~happy(paul)&~strong(paul)))=>((~old(john)&kind(john))))&
((?[X]:((happy(X)<~>~funny(X))))<=>((quiet(lucy)|~curious(lucy))))&
(![X]:((generous(X)&~happy(X))=>happy(X)))&
(![X]:((~quiet(X)|~strong(X))=>(~calm(X)<~>quiet(X))))&
(((calm(paul)<~>~tall(paul)))=>(?[X]:((~brave(X)&kind(X)))))&
((?[X]:((happy(X)|~funny(X))))<=>((~brave(mary)&~happy(mary))))&
(![X]:(~happy(X)=>(~humble(X)|rich(X))))&
(![X]:((happy(X)|~brave(X))=>~tall(X)))&
(![X]:((wise(X)&~happy(X))<=>(~happy(X)|patient(X))))&
(![X]:((~wise(X)&~curious(X))<=>(~wise(X)|curious(X))))&
(![X]:((~funny(X)&~wise(X))=>(quiet(X)|happy(X))))&
((~creative(paul)|~generous(paul)))&
(?[X]:((strong(X)<~>tall(X))))&
((~wise(susan)<~>quiet(susan)))&
(?[X]:(~quiet(X)))&
((kind(fred)|~humble(fred)))&
(?[X]:((humble(X)<~>~generous(X))))&
((~old(mary)<~>~patient(mary))) | humble(john) | [
"p2",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6121571092038235777507794
% SZS output start Proof for 6121571092038235777507794
3. ! [X0] : (~curious(X0) <=> humble(X0)) [input p2]
15. ! [X0] : ((~curious(X0) & ~wise(X0)) <=> (curious(X0) | ~wise(X0))) [input p14]
24. ~humble(john) [input hypothesis]
42. ! [X0] : ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0))) [nnf transformation 3]
61. ! [X0] : (((~curious(X0) & ~wise(X0)) | (~curious(X0) & wise(X0))) & ((curious(X0) | ~wise(X0)) | (curious(X0) | wise(X0)))) [nnf transformation 15]
62. ! [X0] : (((~curious(X0) & ~wise(X0)) | (~curious(X0) & wise(X0))) & (curious(X0) | ~wise(X0) | curious(X0) | wise(X0))) [flattening 61]
78. humble(X0) | curious(X0) [cnf transformation 42]
118. ~curious(X0) | ~curious(X0) [cnf transformation 62]
131. ~humble(john) [cnf transformation 24]
133. ~curious(X0) [duplicate literal removal 118]
301. curious(john) [resolution 78,131]
304. $false [subsumption resolution 301,133]
% SZS output end Proof for 6121571092038235777507794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or rich is either not kind or quiet and vice versa. Everyone who is strong or not rich is not strong or old and vice versa. If someone is not creative or not happy then someone is either tall or not funny. Everyone who is either not quiet or not wise is either tall or not strong and vice versa. Everyone who is not happy or not quiet is not humble. Everyone who is patient or not wise is not funny and vice versa. Everyone who is either not brave or old is both not patient and not funny. If alice is not quiet or not strong then paul is both not creative and not brave. If susan is not curious then someone is rich or not tall. Everyone who is either not happy or calm is either not patient or not funny. If someone is both not quiet and not funny then alice is not patient. If paul is either not calm or not creative then fred is either creative or calm and vice versa. Everyone who is rich or kind is wise and vice versa. Everyone who is either not funny or not tall is not rich or not generous. Everyone who is either creative or not patient is not curious and vice versa. If john is either not strong or not curious then someone is both humble and not strong. Someone is either kind or happy. Alice is either old or curious. Paul is both brave and wise. Someone is both humble and patient. John is both strong and tall. Lucy is not happy. Mary is either patient or funny. Someone is not funny. | John is quiet. | contradiction | (![X]:((~wise(X)<~>rich(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((strong(X)|~rich(X))<=>(~strong(X)|old(X))))&
((?[X]:((~creative(X)|~happy(X))))=>(?[X]:((tall(X)<~>~funny(X)))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((~happy(X)|~quiet(X))=>~humble(X)))&
(![X]:((patient(X)|~wise(X))<=>~funny(X)))&
(![X]:((~brave(X)<~>old(X))=>(~patient(X)&~funny(X))))&
(((~quiet(alice)|~strong(alice)))=>((~creative(paul)&~brave(paul))))&
((~curious(susan))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:((~happy(X)<~>calm(X))=>(~patient(X)<~>~funny(X))))&
((?[X]:((~quiet(X)&~funny(X))))=>(~patient(alice)))&
(((~calm(paul)<~>~creative(paul)))<=>((creative(fred)<~>calm(fred))))&
(![X]:((rich(X)|kind(X))<=>wise(X)))&
(![X]:((~funny(X)<~>~tall(X))=>(~rich(X)|~generous(X))))&
(![X]:((creative(X)<~>~patient(X))<=>~curious(X)))&
(((~strong(john)<~>~curious(john)))=>(?[X]:((humble(X)&~strong(X)))))&
(?[X]:((kind(X)<~>happy(X))))&
((old(alice)<~>curious(alice)))&
((brave(paul)&wise(paul)))&
(?[X]:((humble(X)&patient(X))))&
((strong(john)&tall(john)))&
(~happy(lucy))&
((patient(mary)<~>funny(mary)))&
(?[X]:(~funny(X))) | quiet(john) | [
"p0",
"p3",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2768705668410124392455656
% SZS output start Proof for 2768705668410124392455656
1. ! [X0] : ((~wise(X0) <~> rich(X0)) <=> (~kind(X0) <~> quiet(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) <~> ~wise(X0)) <=> (tall(X0) <~> ~strong(X0))) [input p3]
13. ! [X0] : ((kind(X0) | rich(X0)) <=> wise(X0)) [input p12]
21. tall(john) & strong(john) [input p20]
25. quiet(john) [input hypothesis]
36. ! [X0] : ((((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))))) [nnf transformation 1]
43. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0)))) & (((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [nnf transformation 4]
51. ! [X0] : (((kind(X0) | rich(X0)) | ~wise(X0)) & (wise(X0) | (~kind(X0) & ~rich(X0)))) [nnf transformation 13]
52. ! [X0] : ((kind(X0) | rich(X0) | ~wise(X0)) & (wise(X0) | (~kind(X0) & ~rich(X0)))) [flattening 51]
68. ~quiet(X0) | kind(X0) | rich(X0) | wise(X0) [cnf transformation 36]
86. ~tall(X0) | ~quiet(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 43]
117. ~rich(X0) | wise(X0) [cnf transformation 52]
118. ~kind(X0) | wise(X0) [cnf transformation 52]
119. ~wise(X0) | rich(X0) | kind(X0) [cnf transformation 52]
136. strong(john) [cnf transformation 21]
137. tall(john) [cnf transformation 21]
142. quiet(john) [cnf transformation 25]
229. 18 <=> strong(john) [avatar definition]
230. strong(john) <- (18) [avatar component clause 229]
265. 18 [avatar split clause 136,229]
407. kind(john) | rich(john) | wise(john) [resolution 68,142]
410. kind(john) | rich(john) [subsumption resolution 407,119]
412. 45 <=> rich(john) [avatar definition]
414. rich(john) <- (45) [avatar component clause 412]
416. 46 <=> kind(john) [avatar definition]
418. kind(john) <- (46) [avatar component clause 416]
419. 45 | 46 [avatar split clause 410,416,412]
449. 51 <=> wise(john) [avatar definition]
455. wise(john) <- (45) [resolution 414,117]
458. 51 | ~45 [avatar split clause 455,412,449]
476. wise(john) <- (46) [resolution 418,118]
510. ~quiet(john) | ~strong(john) | ~wise(john) [resolution 86,137]
511. ~strong(john) | ~wise(john) [subsumption resolution 510,142]
512. ~wise(john) <- (18) [subsumption resolution 511,230]
517. ~51 | ~18 [avatar split clause 512,229,449]
518. 51 | ~46 [avatar split clause 476,416,449]
519. $false [avatar sat refutation 265,419,458,517,518]
% SZS output end Proof for 2768705668410124392455656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not tall then john is not happy and vice versa.
If susan is both not strong and funny then someone is not quiet or wise and vice versa.
If someone is either old or creative then someone is either happy or not generous and vice versa.
If fred is tall or strong then john is curious.
Everyone who is both not quiet and not kind is not kind or rich and vice versa.
Everyone who is either not brave or not old is both funny and rich.
If someone is not creative or quiet then paul is both not wise and not calm.
If john is both generous and humble then mary is not wise.
Everyone who is not kind or humble is calm or funny.
Everyone who is not humble is not creative.
Everyone who is not rich or not wise is not rich or wise and vice versa.
Everyone who is not creative is calm.
Everyone who is both rich and not generous is not strong and vice versa.
If someone is not rich then someone is not curious and vice versa.
Everyone who is either generous or not wise is both not wise and not patient.
If someone is both funny and not strong then someone is both quiet and patient and vice versa.
Someone is both brave and tall.
Someone is both generous and humble.
Mary is either not curious or not funny.
Mary is not strong or not wise.
Someone is either not curious or brave.
Someone is either curious or not wise.
Someone is not old.
Someone is both creative and not rich. | John is not rich. | entailment | ((~tall(fred))<=>(~happy(john)))&
(((~strong(susan)&funny(susan)))<=>(?[X]:((~quiet(X)|wise(X)))))&
((?[X]:((old(X)<~>creative(X))))<=>(?[X]:((happy(X)<~>~generous(X)))))&
(((tall(fred)|strong(fred)))=>(curious(john)))&
(![X]:((~quiet(X)&~kind(X))<=>(~kind(X)|rich(X))))&
(![X]:((~brave(X)<~>~old(X))=>(funny(X)&rich(X))))&
((?[X]:((~creative(X)|quiet(X))))=>((~wise(paul)&~calm(paul))))&
(((generous(john)&humble(john)))=>(~wise(mary)))&
(![X]:((~kind(X)|humble(X))=>(calm(X)|funny(X))))&
(![X]:(~humble(X)=>~creative(X)))&
(![X]:((~rich(X)|~wise(X))<=>(~rich(X)|wise(X))))&
(![X]:(~creative(X)=>calm(X)))&
(![X]:((rich(X)&~generous(X))<=>~strong(X)))&
((?[X]:(~rich(X)))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)<~>~wise(X))=>(~wise(X)&~patient(X))))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:((quiet(X)&patient(X)))))&
(?[X]:((brave(X)&tall(X))))&
(?[X]:((generous(X)&humble(X))))&
((~curious(mary)<~>~funny(mary)))&
((~strong(mary)|~wise(mary)))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:(~old(X)))&
(?[X]:((creative(X)&~rich(X)))) | ~rich(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1428721534699049887468573
% SZS output start Proof for 1428721534699049887468573
11. ! [X0] : ((~wise(X0) | ~rich(X0)) <=> (wise(X0) | ~rich(X0))) [input p10]
25. rich(john) [input hypothesis]
53. ! [X0] : (((~wise(X0) | ~rich(X0)) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | (wise(X0) & rich(X0)))) [nnf transformation 11]
54. ! [X0] : ((~wise(X0) | ~rich(X0) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | (wise(X0) & rich(X0)))) [flattening 53]
118. wise(X0) | ~rich(X0) | wise(X0) [cnf transformation 54]
120. ~wise(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 54]
149. rich(john) [cnf transformation 25]
151. wise(X0) | ~rich(X0) [duplicate literal removal 118]
152. ~wise(X0) | ~rich(X0) [duplicate literal removal 120]
267. ~rich(X0) [subsumption resolution 151,152]
303. $false [subsumption resolution 149,267]
% SZS output end Proof for 1428721534699049887468573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and creative then mary is strong and vice versa.
Everyone who is either humble or not patient is either not rich or strong.
If someone is either not happy or kind then someone is kind and vice versa.
Everyone who is calm is not quiet or generous.
Everyone who is not old is kind and vice versa.
Everyone who is both not kind and generous is both not strong and wise.
Everyone who is curious is both not kind and not creative and vice versa.
If someone is either quiet or old then lucy is both not creative and tall and vice versa.
If someone is kind or not quiet then someone is either old or quiet.
If someone is creative or brave then paul is not old.
If someone is either not kind or wise then fred is old or not happy.
If someone is generous then someone is either not happy or not rich and vice versa.
If someone is either not happy or not kind then john is either not rich or not wise.
If alice is either not funny or not brave then someone is not tall.
If alice is both humble and not calm then someone is both not wise and brave.
Everyone who is either tall or not creative is happy.
Someone is not kind or not calm.
Someone is quiet.
Someone is both not curious and not strong.
Mary is either not generous or not brave.
Someone is both not humble and strong.
Someone is both not kind and not calm.
Someone is both not old and not curious.
John is rich. | Lucy is not tall. | contradiction | ((?[X]:((quiet(X)&creative(X))))<=>(strong(mary)))&
(![X]:((humble(X)<~>~patient(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((~happy(X)<~>kind(X))))<=>(?[X]:(kind(X))))&
(![X]:(calm(X)=>(~quiet(X)|generous(X))))&
(![X]:(~old(X)<=>kind(X)))&
(![X]:((~kind(X)&generous(X))=>(~strong(X)&wise(X))))&
(![X]:(curious(X)<=>(~kind(X)&~creative(X))))&
((?[X]:((quiet(X)<~>old(X))))<=>((~creative(lucy)&tall(lucy))))&
((?[X]:((kind(X)|~quiet(X))))=>(?[X]:((old(X)<~>quiet(X)))))&
((?[X]:((creative(X)|brave(X))))=>(~old(paul)))&
((?[X]:((~kind(X)<~>wise(X))))=>((old(fred)|~happy(fred))))&
((?[X]:(generous(X)))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
((?[X]:((~happy(X)<~>~kind(X))))=>((~rich(john)<~>~wise(john))))&
(((~funny(alice)<~>~brave(alice)))=>(?[X]:(~tall(X))))&
(((humble(alice)&~calm(alice)))=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((tall(X)<~>~creative(X))=>happy(X)))&
(?[X]:((~kind(X)|~calm(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~curious(X)&~strong(X))))&
((~generous(mary)<~>~brave(mary)))&
(?[X]:((~humble(X)&strong(X))))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((~old(X)&~curious(X))))&
(rich(john)) | ~tall(lucy) | [
"p4",
"p7",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1166974626687506504339000
% SZS output start Proof for 1166974626687506504339000
5. ! [X0] : (~old(X0) <=> kind(X0)) [input p4]
8. ? [X0] : (quiet(X0) <~> old(X0)) <=> (tall(lucy) & ~creative(lucy)) [input p7]
9. ? [X0] : (~quiet(X0) | kind(X0)) => ? [X0] : (old(X0) <~> quiet(X0)) [input p8]
23. ? [X0] : (~curious(X0) & ~old(X0)) [input p22]
25. ~tall(lucy) [input hypothesis]
27. ? [X0] : (~quiet(X0) | kind(X0)) => ? [X1] : (old(X1) <~> quiet(X1)) [rectify 9]
37. ? [X1] : (old(X1) <~> quiet(X1)) | ! [X0] : (quiet(X0) & ~kind(X0)) [ennf transformation 27]
56. ! [X0] : ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))) [nnf transformation 5]
57. (? [X0] : ((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | (~tall(lucy) | creative(lucy))) & ((tall(lucy) & ~creative(lucy)) | ! [X0] : ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0)))) [nnf transformation 8]
58. (? [X0] : ((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | ~tall(lucy) | creative(lucy)) & ((tall(lucy) & ~creative(lucy)) | ! [X0] : ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0)))) [flattening 57]
59. (? [X0] : ((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | ~tall(lucy) | creative(lucy)) & ((tall(lucy) & ~creative(lucy)) | ! [X1] : ((quiet(X1) | ~old(X1)) & (old(X1) | ~quiet(X1)))) [rectify 58]
60. ? [X0] : ((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) => ((~old(sK3) | ~quiet(sK3)) & (old(sK3) | quiet(sK3))) [choice axiom]
61. (((~old(sK3) | ~quiet(sK3)) & (old(sK3) | quiet(sK3))) | ~tall(lucy) | creative(lucy)) & ((tall(lucy) & ~creative(lucy)) | ! [X1] : ((quiet(X1) | ~old(X1)) & (old(X1) | ~quiet(X1)))) [skolemisation 59,60]
62. ? [X1] : ((~quiet(X1) | ~old(X1)) & (quiet(X1) | old(X1))) | ! [X0] : (quiet(X0) & ~kind(X0)) [nnf transformation 37]
63. ? [X0] : ((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) | ! [X1] : (quiet(X1) & ~kind(X1)) [rectify 62]
64. ? [X0] : ((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) => ((~quiet(sK4) | ~old(sK4)) & (quiet(sK4) | old(sK4))) [choice axiom]
65. ((~quiet(sK4) | ~old(sK4)) & (quiet(sK4) | old(sK4))) | ! [X1] : (quiet(X1) & ~kind(X1)) [skolemisation 63,64]
90. ? [X0] : (~curious(X0) & ~old(X0)) => (~curious(sK14) & ~old(sK14)) [choice axiom]
91. ~curious(sK14) & ~old(sK14) [skolemisation 23,90]
104. old(X0) | kind(X0) [cnf transformation 56]
111. tall(lucy) | old(X1) | ~quiet(X1) [cnf transformation 61]
112. tall(lucy) | quiet(X1) | ~old(X1) [cnf transformation 61]
115. quiet(sK4) | old(sK4) | ~kind(X1) [cnf transformation 65]
117. ~quiet(sK4) | ~old(sK4) | ~kind(X1) [cnf transformation 65]
147. ~old(sK14) [cnf transformation 91]
150. ~tall(lucy) [cnf transformation 25]
170. 5 <=> ! [X1] : ~kind(X1) [avatar definition]
171. ~kind(X1) <- (5) [avatar component clause 170]
199. 12 <=> tall(lucy) [avatar definition]
213. 15 <=> ! [X1] : (quiet(X1) | ~old(X1)) [avatar definition]
214. ~old(X1) | quiet(X1) <- (15) [avatar component clause 213]
215. 15 | 12 [avatar split clause 112,199,213]
217. 16 <=> ! [X1] : (old(X1) | ~quiet(X1)) [avatar definition]
218. ~quiet(X1) | old(X1) <- (16) [avatar component clause 217]
219. 16 | 12 [avatar split clause 111,199,217]
226. 18 <=> old(sK4) [avatar definition]
227. old(sK4) <- (18) [avatar component clause 226]
228. ~old(sK4) <- (~18) [avatar component clause 226]
230. 19 <=> quiet(sK4) [avatar definition]
231. quiet(sK4) <- (19) [avatar component clause 230]
232. ~quiet(sK4) <- (~19) [avatar component clause 230]
234. 5 | ~18 | ~19 [avatar split clause 117,230,226,170]
236. 5 | 18 | 19 [avatar split clause 115,230,226,170]
360. ~12 [avatar split clause 150,199]
373. kind(sK14) [resolution 104,147]
380. quiet(sK4) <- (15, 18) [resolution 214,227]
382. $false <- (15, 18, ~19) [subsumption resolution 380,232]
383. ~15 | ~18 | 19 [avatar contradiction clause 382]
386. old(sK4) <- (16, 19) [resolution 218,231]
387. $false <- (16, ~18, 19) [subsumption resolution 386,228]
388. ~16 | 18 | ~19 [avatar contradiction clause 387]
390. $false <- (5) [resolution 171,373]
391. ~5 [avatar contradiction clause 390]
393. $false [avatar sat refutation 215,219,234,236,360,383,388,391]
% SZS output end Proof for 1166974626687506504339000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and funny then susan is tall or not creative. Everyone who is both not wise and quiet is not wise. Everyone who is both creative and not patient is not kind or not wise and vice versa. Everyone who is either strong or not tall is not tall or not calm. Everyone who is either not creative or kind is not strong or strong and vice versa. Everyone who is generous or not rich is both not humble and not kind. Everyone who is both not wise and not quiet is either not old or kind. If susan is both not quiet and not brave then fred is both calm and tall and vice versa. Everyone who is either calm or not happy is not patient or not rich. Everyone who is both strong and not tall is not tall or not patient. Everyone who is both not funny and not curious is old. If lucy is rich then someone is both not funny and happy. If paul is humble or not happy then john is both kind and funny. Everyone who is quiet is rich. If alice is generous then someone is brave. Everyone who is wise is either humble or not creative. John is tall or wise. Someone is happy or not patient. John is either quiet or tall. Fred is tall or not creative. John is either not funny or not curious. Paul is wise or not kind. Mary is either rich or not tall. Someone is not quiet. | Alice is not generous. | entailment | ((?[X]:((~generous(X)&funny(X))))=>((tall(susan)|~creative(susan))))&
(![X]:((~wise(X)&quiet(X))=>~wise(X)))&
(![X]:((creative(X)&~patient(X))<=>(~kind(X)|~wise(X))))&
(![X]:((strong(X)<~>~tall(X))=>(~tall(X)|~calm(X))))&
(![X]:((~creative(X)<~>kind(X))<=>(~strong(X)|strong(X))))&
(![X]:((generous(X)|~rich(X))=>(~humble(X)&~kind(X))))&
(![X]:((~wise(X)&~quiet(X))=>(~old(X)<~>kind(X))))&
(((~quiet(susan)&~brave(susan)))<=>((calm(fred)&tall(fred))))&
(![X]:((calm(X)<~>~happy(X))=>(~patient(X)|~rich(X))))&
(![X]:((strong(X)&~tall(X))=>(~tall(X)|~patient(X))))&
(![X]:((~funny(X)&~curious(X))=>old(X)))&
((rich(lucy))=>(?[X]:((~funny(X)&happy(X)))))&
(((humble(paul)|~happy(paul)))=>((kind(john)&funny(john))))&
(![X]:(quiet(X)=>rich(X)))&
((generous(alice))=>(?[X]:(brave(X))))&
(![X]:(wise(X)=>(humble(X)<~>~creative(X))))&
((tall(john)|wise(john)))&
(?[X]:((happy(X)|~patient(X))))&
((quiet(john)<~>tall(john)))&
((tall(fred)|~creative(fred)))&
((~funny(john)<~>~curious(john)))&
((wise(paul)|~kind(paul)))&
((rich(mary)<~>~tall(mary)))&
(?[X]:(~quiet(X))) | ~generous(alice) | [
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3801942892655741153256856
% SZS output start Proof for 3801942892655741153256856
3. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~wise(X0) | ~kind(X0))) [input p2]
5. ! [X0] : ((~creative(X0) <~> kind(X0)) <=> (strong(X0) | ~strong(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | generous(X0)) => (~kind(X0) & ~humble(X0))) [input p5]
25. generous(alice) [input hypothesis]
32. ! [X0] : ((~kind(X0) & ~humble(X0)) | (rich(X0) & ~generous(X0))) [ennf transformation 6]
46. ! [X0] : (((~patient(X0) & creative(X0)) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 3]
47. ! [X0] : (((~patient(X0) & creative(X0)) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | patient(X0) | ~creative(X0))) [flattening 46]
49. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [nnf transformation 5]
50. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [flattening 49]
70. creative(X0) | kind(X0) [cnf transformation 47]
78. kind(X0) | ~creative(X0) | strong(X0) [cnf transformation 50]
79. kind(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 50]
80. ~kind(X0) | creative(X0) | strong(X0) [cnf transformation 50]
81. ~kind(X0) | creative(X0) | ~strong(X0) [cnf transformation 50]
84. ~kind(X0) | ~generous(X0) [cnf transformation 32]
117. generous(alice) [cnf transformation 25]
131. creative(X0) | ~strong(X0) [subsumption resolution 81,70]
132. creative(X0) | strong(X0) [subsumption resolution 80,70]
133. creative(X0) [subsumption resolution 132,131]
134. kind(X0) | ~strong(X0) [subsumption resolution 79,133]
135. kind(X0) | strong(X0) [subsumption resolution 78,133]
136. kind(X0) [subsumption resolution 135,134]
138. ~generous(X0) [subsumption resolution 84,136]
213. $false [subsumption resolution 117,138]
% SZS output end Proof for 3801942892655741153256856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not humble then someone is kind and vice versa.
If someone is not patient or funny then paul is not brave.
If paul is not rich or not happy then mary is either quiet or strong.
Everyone who is not old or old is both not brave and calm.
If lucy is not wise then someone is not wise or curious.
Everyone who is either creative or not calm is rich and vice versa.
Everyone who is creative is either not rich or generous.
If lucy is either not quiet or not rich then susan is not happy or not wise.
Everyone who is both wise and not wise is either not generous or rich and vice versa.
If paul is either not curious or not strong then someone is either not strong or not wise and vice versa.
Everyone who is not tall is both strong and not calm.
Everyone who is either not brave or not humble is either patient or not tall.
If someone is curious or strong then someone is not brave and vice versa.
If mary is curious or funny then susan is either patient or rich and vice versa.
Everyone who is not strong is both not strong and not tall.
If someone is not humble then someone is either old or not calm and vice versa.
Mary is either not humble or wise.
Susan is not brave.
Lucy is either not kind or not quiet.
Mary is either not wise or curious.
Someone is not happy or not creative.
Fred is not generous or not quiet. | Susan is not old. | neutral | ((~humble(john))<=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)|funny(X))))=>(~brave(paul)))&
(((~rich(paul)|~happy(paul)))=>((quiet(mary)<~>strong(mary))))&
(![X]:((~old(X)|old(X))=>(~brave(X)&calm(X))))&
((~wise(lucy))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((creative(X)<~>~calm(X))<=>rich(X)))&
(![X]:(creative(X)=>(~rich(X)<~>generous(X))))&
(((~quiet(lucy)<~>~rich(lucy)))=>((~happy(susan)|~wise(susan))))&
(![X]:((wise(X)&~wise(X))<=>(~generous(X)<~>rich(X))))&
(((~curious(paul)<~>~strong(paul)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:(~tall(X)=>(strong(X)&~calm(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(patient(X)<~>~tall(X))))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:(~brave(X))))&
(((curious(mary)|funny(mary)))<=>((patient(susan)<~>rich(susan))))&
(![X]:(~strong(X)=>(~strong(X)&~tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((old(X)<~>~calm(X)))))&
((~humble(mary)<~>wise(mary)))&
(~brave(susan))&
((~kind(lucy)<~>~quiet(lucy)))&
((~wise(mary)<~>curious(mary)))&
(?[X]:((~happy(X)|~creative(X))))&
((~generous(fred)|~quiet(fred))) | ~old(susan) | [] | null | 0 |
Everyone who is patient or kind is both generous and rich.
If john is rich then lucy is both not funny and not rich and vice versa.
Everyone who is calm or humble is both creative and tall and vice versa.
If alice is either creative or not calm then paul is not tall or generous.
Everyone who is strong is either not patient or not kind and vice versa.
Everyone who is not calm or old is brave.
Everyone who is either old or not rich is rich and vice versa.
Everyone who is both not quiet and not patient is both quiet and not kind.
Everyone who is both not kind and not generous is not brave.
If lucy is happy then someone is creative.
Everyone who is either curious or not humble is creative.
Everyone who is creative or brave is both not happy and generous.
If mary is brave or not rich then fred is calm or not generous and vice versa.
Everyone who is both strong and creative is either funny or not happy.
If mary is both patient and calm then susan is calm or strong and vice versa.
Someone is not tall.
Someone is either not creative or humble.
Someone is not humble.
Mary is not quiet or quiet.
Lucy is both wise and not quiet.
Paul is calm or old. | Lucy is not patient. | contradiction | (![X]:((patient(X)|kind(X))=>(generous(X)&rich(X))))&
((rich(john))<=>((~funny(lucy)&~rich(lucy))))&
(![X]:((calm(X)|humble(X))<=>(creative(X)&tall(X))))&
(((creative(alice)<~>~calm(alice)))=>((~tall(paul)|generous(paul))))&
(![X]:(strong(X)<=>(~patient(X)<~>~kind(X))))&
(![X]:((~calm(X)|old(X))=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>rich(X)))&
(![X]:((~quiet(X)&~patient(X))=>(quiet(X)&~kind(X))))&
(![X]:((~kind(X)&~generous(X))=>~brave(X)))&
((happy(lucy))=>(?[X]:(creative(X))))&
(![X]:((curious(X)<~>~humble(X))=>creative(X)))&
(![X]:((creative(X)|brave(X))=>(~happy(X)&generous(X))))&
(((brave(mary)|~rich(mary)))<=>((calm(fred)|~generous(fred))))&
(![X]:((strong(X)&creative(X))=>(funny(X)<~>~happy(X))))&
(((patient(mary)&calm(mary)))<=>((calm(susan)|strong(susan))))&
(?[X]:(~tall(X)))&
(?[X]:((~creative(X)<~>humble(X))))&
(?[X]:(~humble(X)))&
((~quiet(mary)|quiet(mary)))&
((wise(lucy)&~quiet(lucy)))&
((calm(paul)|old(paul))) | ~patient(lucy) | [
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5404277372085889001409913
% SZS output start Proof for 5404277372085889001409913
8. ! [X0] : ((~patient(X0) & ~quiet(X0)) => (~kind(X0) & quiet(X0))) [input p7]
20. ~quiet(lucy) & wise(lucy) [input p19]
22. ~patient(lucy) [input hypothesis]
23. ~quiet(lucy) [pure predicate removal 20]
28. ! [X0] : ((~kind(X0) & quiet(X0)) | (patient(X0) | quiet(X0))) [ennf transformation 8]
29. ! [X0] : ((~kind(X0) & quiet(X0)) | patient(X0) | quiet(X0)) [flattening 28]
83. quiet(X0) | patient(X0) | quiet(X0) [cnf transformation 29]
109. ~quiet(lucy) [cnf transformation 23]
111. ~patient(lucy) [cnf transformation 22]
112. quiet(X0) | patient(X0) [duplicate literal removal 83]
214. patient(lucy) [resolution 112,109]
215. $false [subsumption resolution 214,111]
% SZS output end Proof for 5404277372085889001409913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is creative or not funny then lucy is patient and vice versa.
Everyone who is not strong or old is both tall and patient and vice versa.
Everyone who is funny or curious is not rich.
Everyone who is not happy or not patient is either rich or funny and vice versa.
If someone is kind then someone is wise or rich and vice versa.
If someone is either not curious or rich then someone is both kind and creative.
Everyone who is not wise is both quiet and patient.
Everyone who is either brave or not humble is both not humble and strong and vice versa.
Everyone who is either generous or tall is patient or calm and vice versa.
If lucy is either rich or not creative then someone is not strong or not old and vice versa.
If paul is humble or calm then someone is both kind and not patient.
Everyone who is rich or not curious is not funny and vice versa.
Everyone who is not brave or not strong is either rich or not curious.
If someone is generous or not happy then someone is rich or not tall.
Everyone who is quiet is both calm and brave.
Everyone who is either not kind or not old is both rich and not wise and vice versa.
Lucy is happy.
Susan is humble or brave.
Susan is both humble and not old.
Fred is patient.
Someone is kind.
Paul is humble or not brave. | Susan is kind. | contradiction | (((creative(fred)|~funny(fred)))<=>(patient(lucy)))&
(![X]:((~strong(X)|old(X))<=>(tall(X)&patient(X))))&
(![X]:((funny(X)|curious(X))=>~rich(X)))&
(![X]:((~happy(X)|~patient(X))<=>(rich(X)<~>funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)|rich(X)))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(~wise(X)=>(quiet(X)&patient(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(~humble(X)&strong(X))))&
(![X]:((generous(X)<~>tall(X))<=>(patient(X)|calm(X))))&
(((rich(lucy)<~>~creative(lucy)))<=>(?[X]:((~strong(X)|~old(X)))))&
(((humble(paul)|calm(paul)))=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:((rich(X)|~curious(X))<=>~funny(X)))&
(![X]:((~brave(X)|~strong(X))=>(rich(X)<~>~curious(X))))&
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:(quiet(X)=>(calm(X)&brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(rich(X)&~wise(X))))&
(happy(lucy))&
((humble(susan)|brave(susan)))&
((humble(susan)&~old(susan)))&
(patient(fred))&
(?[X]:(kind(X)))&
((humble(paul)|~brave(paul))) | kind(susan) | [
"p2",
"p7",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 467484925352203256118005
% SZS output start Proof for 467484925352203256118005
3. ! [X0] : ((curious(X0) | funny(X0)) => ~rich(X0)) [input p2]
8. ! [X0] : ((brave(X0) <~> ~humble(X0)) <=> (strong(X0) & ~humble(X0))) [input p7]
13. ! [X0] : ((~strong(X0) | ~brave(X0)) => (rich(X0) <~> ~curious(X0))) [input p12]
16. ! [X0] : ((~kind(X0) <~> ~old(X0)) <=> (~wise(X0) & rich(X0))) [input p15]
19. ~old(susan) & humble(susan) [input p18]
23. kind(susan) [input hypothesis]
27. ! [X0] : (~rich(X0) | (~curious(X0) & ~funny(X0))) [ennf transformation 3]
31. ! [X0] : ((rich(X0) <~> ~curious(X0)) | (strong(X0) & brave(X0))) [ennf transformation 13]
49. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [nnf transformation 8]
50. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [flattening 49]
61. ! [X0] : (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (strong(X0) & brave(X0))) [nnf transformation 31]
65. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [nnf transformation 16]
66. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [flattening 65]
78. ~rich(X0) | ~curious(X0) [cnf transformation 27]
94. ~humble(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 50]
121. curious(X0) | ~rich(X0) | brave(X0) [cnf transformation 61]
128. ~kind(X0) | rich(X0) | old(X0) [cnf transformation 66]
135. humble(susan) [cnf transformation 19]
136. ~old(susan) [cnf transformation 19]
140. kind(susan) [cnf transformation 23]
141. ~humble(X0) | ~brave(X0) [duplicate literal removal 94]
247. ~rich(X0) | brave(X0) [subsumption resolution 121,78]
267. 27 <=> humble(susan) [avatar definition]
269. humble(susan) <- (27) [avatar component clause 267]
271. 28 <=> brave(susan) [avatar definition]
272. ~brave(susan) <- (~28) [avatar component clause 271]
275. 27 [avatar split clause 135,267]
283. ~brave(susan) <- (27) [resolution 141,269]
284. ~28 | ~27 [avatar split clause 283,267,271]
327. rich(susan) | old(susan) [resolution 128,140]
331. rich(susan) [subsumption resolution 327,136]
367. brave(susan) [resolution 331,247]
372. $false <- (~28) [subsumption resolution 367,272]
373. 28 [avatar contradiction clause 372]
374. $false [avatar sat refutation 275,284,373]
% SZS output end Proof for 467484925352203256118005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not quiet or brave then paul is patient or old and vice versa.
Everyone who is either not rich or not humble is not tall and vice versa.
If someone is curious or rich then someone is both not tall and happy.
If alice is old or not rich then fred is both not humble and kind and vice versa.
If someone is not rich then lucy is either calm or not tall and vice versa.
Everyone who is not funny is not humble or not quiet and vice versa.
If someone is not patient then paul is both not brave and old and vice versa.
If someone is either creative or not rich then someone is not tall or not funny.
Everyone who is not patient or curious is either old or not calm and vice versa.
Everyone who is brave or not curious is both not quiet and not rich and vice versa.
Everyone who is both not tall and not quiet is happy and vice versa.
If someone is not rich or curious then someone is not humble and vice versa.
Everyone who is not old or curious is both kind and generous.
If someone is both not humble and funny then someone is both not brave and not patient and vice versa.
If alice is calm then someone is not patient.
Everyone who is happy is patient and vice versa.
Fred is funny or generous.
John is not wise or not brave.
Someone is either not kind or not tall.
Someone is both not strong and not calm.
Paul is either not creative or tall.
Mary is both not generous and not quiet.
John is humble or creative.
Someone is either not old or generous. | Lucy is funny. | contradiction | (((~quiet(susan)<~>brave(susan)))<=>((patient(paul)|old(paul))))&
(![X]:((~rich(X)<~>~humble(X))<=>~tall(X)))&
((?[X]:((curious(X)|rich(X))))=>(?[X]:((~tall(X)&happy(X)))))&
(((old(alice)|~rich(alice)))<=>((~humble(fred)&kind(fred))))&
((?[X]:(~rich(X)))<=>((calm(lucy)<~>~tall(lucy))))&
(![X]:(~funny(X)<=>(~humble(X)|~quiet(X))))&
((?[X]:(~patient(X)))<=>((~brave(paul)&old(paul))))&
((?[X]:((creative(X)<~>~rich(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:((~patient(X)|curious(X))<=>(old(X)<~>~calm(X))))&
(![X]:((brave(X)|~curious(X))<=>(~quiet(X)&~rich(X))))&
(![X]:((~tall(X)&~quiet(X))<=>happy(X)))&
((?[X]:((~rich(X)|curious(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~old(X)|curious(X))=>(kind(X)&generous(X))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((~brave(X)&~patient(X)))))&
((calm(alice))=>(?[X]:(~patient(X))))&
(![X]:(happy(X)<=>patient(X)))&
((funny(fred)|generous(fred)))&
((~wise(john)|~brave(john)))&
(?[X]:((~kind(X)<~>~tall(X))))&
(?[X]:((~strong(X)&~calm(X))))&
((~creative(paul)<~>tall(paul)))&
((~generous(mary)&~quiet(mary)))&
((humble(john)|creative(john)))&
(?[X]:((~old(X)<~>generous(X)))) | funny(lucy) | [
"p5",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8591579989524237382249927
% SZS output start Proof for 8591579989524237382249927
6. ! [X0] : (~funny(X0) <=> (~quiet(X0) | ~humble(X0))) [input p5]
10. ! [X0] : ((~curious(X0) | brave(X0)) <=> (~rich(X0) & ~quiet(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) & ~tall(X0)) <=> happy(X0)) [input p10]
14. ? [X0] : (funny(X0) & ~humble(X0)) <=> ? [X0] : (~patient(X0) & ~brave(X0)) [input p13]
16. ! [X0] : (happy(X0) <=> patient(X0)) [input p15]
25. funny(lucy) [input hypothesis]
29. ? [X0] : (funny(X0) & ~humble(X0)) <=> ? [X1] : (~patient(X1) & ~brave(X1)) [rectify 14]
48. ! [X0] : ((~funny(X0) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | funny(X0))) [nnf transformation 6]
49. ! [X0] : ((~funny(X0) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | funny(X0))) [flattening 48]
61. ! [X0] : (((~curious(X0) | brave(X0)) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 10]
62. ! [X0] : ((~curious(X0) | brave(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | (curious(X0) & ~brave(X0)))) [flattening 61]
63. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ~happy(X0)) & (happy(X0) | (quiet(X0) | tall(X0)))) [nnf transformation 11]
64. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ~happy(X0)) & (happy(X0) | quiet(X0) | tall(X0))) [flattening 63]
70. (? [X0] : (funny(X0) & ~humble(X0)) | ! [X1] : (patient(X1) | brave(X1))) & (? [X1] : (~patient(X1) & ~brave(X1)) | ! [X0] : (~funny(X0) | humble(X0))) [nnf transformation 29]
71. (? [X0] : (funny(X0) & ~humble(X0)) | ! [X1] : (patient(X1) | brave(X1))) & (? [X2] : (~patient(X2) & ~brave(X2)) | ! [X3] : (~funny(X3) | humble(X3))) [rectify 70]
72. ? [X0] : (funny(X0) & ~humble(X0)) => (funny(sK6) & ~humble(sK6)) [choice axiom]
73. ? [X2] : (~patient(X2) & ~brave(X2)) => (~patient(sK7) & ~brave(sK7)) [choice axiom]
74. ((funny(sK6) & ~humble(sK6)) | ! [X1] : (patient(X1) | brave(X1))) & ((~patient(sK7) & ~brave(sK7)) | ! [X3] : (~funny(X3) | humble(X3))) [skolemisation 71,73,72]
77. ! [X0] : ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))) [nnf transformation 16]
111. ~funny(X0) | humble(X0) [cnf transformation 49]
112. ~funny(X0) | quiet(X0) [cnf transformation 49]
124. ~brave(X0) | ~quiet(X0) [cnf transformation 62]
131. ~happy(X0) | ~quiet(X0) [cnf transformation 64]
141. ~humble(sK6) | patient(X1) | brave(X1) [cnf transformation 74]
142. funny(sK6) | patient(X1) | brave(X1) [cnf transformation 74]
145. ~patient(X0) | happy(X0) [cnf transformation 77]
157. funny(lucy) [cnf transformation 25]
275. 25 <=> ! [X1] : (patient(X1) | brave(X1)) [avatar definition]
276. patient(X1) | brave(X1) <- (25) [avatar component clause 275]
278. 26 <=> funny(sK6) [avatar definition]
280. funny(sK6) <- (26) [avatar component clause 278]
281. 25 | 26 [avatar split clause 142,278,275]
283. 27 <=> humble(sK6) [avatar definition]
285. ~humble(sK6) <- (~27) [avatar component clause 283]
286. 25 | ~27 [avatar split clause 141,283,275]
343. quiet(lucy) [resolution 112,157]
367. happy(X0) | brave(X0) <- (25) [resolution 276,145]
547. brave(X1) | ~quiet(X1) <- (25) [resolution 367,131]
549. ~quiet(X1) <- (25) [subsumption resolution 547,124]
614. $false <- (25) [resolution 549,343]
617. ~25 [avatar contradiction clause 614]
628. humble(sK6) <- (26) [resolution 280,111]
629. $false <- (26, ~27) [subsumption resolution 628,285]
630. ~26 | 27 [avatar contradiction clause 629]
631. $false [avatar sat refutation 281,286,617,630]
% SZS output end Proof for 8591579989524237382249927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is not tall then someone is not patient. If someone is not creative then someone is either not curious or quiet. If someone is either happy or not brave then someone is both happy and creative and vice versa. Everyone who is not rich is either not rich or curious and vice versa. Everyone who is not curious is not happy and vice versa. If someone is both not rich and not brave then someone is not old and vice versa. Everyone who is both happy and patient is not strong. Everyone who is both not quiet and rich is not quiet or wise. Everyone who is creative or not rich is not strong or patient. Everyone who is either curious or old is both not curious and kind. If paul is both not strong and not kind then someone is wise or not calm and vice versa. Everyone who is not funny or not quiet is either not wise or creative. Everyone who is both curious and patient is both not strong and old. If alice is either not funny or rich then someone is either not patient or funny. Alice is not wise. Mary is both rich and not wise. Someone is either happy or calm. Susan is either not rich or patient. Mary is not creative or not patient. Alice is calm. Alice is both not curious and not creative. | Paul is kind. | entailment | ((~tall(paul))=>(?[X]:(~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~curious(X)<~>quiet(X)))))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:((happy(X)&creative(X)))))&
(![X]:(~rich(X)<=>(~rich(X)<~>curious(X))))&
(![X]:(~curious(X)<=>~happy(X)))&
((?[X]:((~rich(X)&~brave(X))))<=>(?[X]:(~old(X))))&
(![X]:((happy(X)&patient(X))=>~strong(X)))&
(![X]:((~quiet(X)&rich(X))=>(~quiet(X)|wise(X))))&
(![X]:((creative(X)|~rich(X))=>(~strong(X)|patient(X))))&
(![X]:((curious(X)<~>old(X))=>(~curious(X)&kind(X))))&
(((~strong(paul)&~kind(paul)))<=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:((~funny(X)|~quiet(X))=>(~wise(X)<~>creative(X))))&
(![X]:((curious(X)&patient(X))=>(~strong(X)&old(X))))&
(((~funny(alice)<~>rich(alice)))=>(?[X]:((~patient(X)<~>funny(X)))))&
(~wise(alice))&
((rich(mary)&~wise(mary)))&
(?[X]:((happy(X)<~>calm(X))))&
((~rich(susan)<~>patient(susan)))&
((~creative(mary)|~patient(mary)))&
(calm(alice))&
((~curious(alice)&~creative(alice))) | kind(paul) | [
"p2",
"p3",
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1572808118344641787237260
% SZS output start Proof for 1572808118344641787237260
3. ? [X0] : (happy(X0) <~> ~brave(X0)) <=> ? [X0] : (creative(X0) & happy(X0)) [input p2]
4. ! [X0] : (~rich(X0) <=> (~rich(X0) <~> curious(X0))) [input p3]
5. ! [X0] : (~curious(X0) <=> ~happy(X0)) [input p4]
6. ? [X0] : (~brave(X0) & ~rich(X0)) <=> ? [X0] : ~old(X0) [input p5]
10. ! [X0] : ((curious(X0) <~> old(X0)) => (kind(X0) & ~curious(X0))) [input p9]
22. ~kind(paul) [input hypothesis]
24. ? [X0] : (happy(X0) <~> ~brave(X0)) <=> ? [X1] : (creative(X1) & happy(X1)) [rectify 3]
25. ? [X0] : (~brave(X0) & ~rich(X0)) <=> ? [X1] : ~old(X1) [rectify 6]
34. ! [X0] : ((kind(X0) & ~curious(X0)) | (curious(X0) <=> old(X0))) [ennf transformation 10]
43. (? [X0] : ((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | ! [X1] : (~creative(X1) | ~happy(X1))) & (? [X1] : (creative(X1) & happy(X1)) | ! [X0] : ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) [nnf transformation 24]
44. (? [X0] : ((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | ! [X1] : (~creative(X1) | ~happy(X1))) & (? [X2] : (creative(X2) & happy(X2)) | ! [X3] : ((happy(X3) | brave(X3)) & (~brave(X3) | ~happy(X3)))) [rectify 43]
45. ? [X0] : ((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) => ((brave(sK1) | ~happy(sK1)) & (~brave(sK1) | happy(sK1))) [choice axiom]
46. ? [X2] : (creative(X2) & happy(X2)) => (creative(sK2) & happy(sK2)) [choice axiom]
47. (((brave(sK1) | ~happy(sK1)) & (~brave(sK1) | happy(sK1))) | ! [X1] : (~creative(X1) | ~happy(X1))) & ((creative(sK2) & happy(sK2)) | ! [X3] : ((happy(X3) | brave(X3)) & (~brave(X3) | ~happy(X3)))) [skolemisation 44,46,45]
48. ! [X0] : ((~rich(X0) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | rich(X0))) [nnf transformation 4]
49. ! [X0] : ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))) [nnf transformation 5]
50. (? [X0] : (~brave(X0) & ~rich(X0)) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : (brave(X0) | rich(X0))) [nnf transformation 25]
51. (? [X0] : (~brave(X0) & ~rich(X0)) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : (brave(X3) | rich(X3))) [rectify 50]
52. ? [X0] : (~brave(X0) & ~rich(X0)) => (~brave(sK3) & ~rich(sK3)) [choice axiom]
53. ? [X2] : ~old(X2) => ~old(sK4) [choice axiom]
54. ((~brave(sK3) & ~rich(sK3)) | ! [X1] : old(X1)) & (~old(sK4) | ! [X3] : (brave(X3) | rich(X3))) [skolemisation 51,53,52]
55. ! [X0] : ((kind(X0) & ~curious(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0)))) [nnf transformation 34]
72. happy(sK2) | happy(X3) | brave(X3) [cnf transformation 47]
78. ~curious(X0) | rich(X0) | rich(X0) [cnf transformation 48]
80. ~rich(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 48]
81. ~happy(X0) | curious(X0) [cnf transformation 49]
85. ~brave(sK3) | old(X1) [cnf transformation 54]
93. kind(X0) | curious(X0) | ~old(X0) [cnf transformation 55]
120. ~kind(paul) [cnf transformation 22]
122. ~curious(X0) | rich(X0) [duplicate literal removal 78]
123. ~rich(X0) | ~curious(X0) [duplicate literal removal 80]
151. 7 <=> ! [X3] : (happy(X3) | brave(X3)) [avatar definition]
152. happy(X3) | brave(X3) <- (7) [avatar component clause 151]
163. 10 <=> happy(sK2) [avatar definition]
165. happy(sK2) <- (10) [avatar component clause 163]
166. 7 | 10 [avatar split clause 72,163,151]
168. ~curious(X0) [subsumption resolution 122,123]
169. ~happy(X0) [subsumption resolution 81,168]
171. 11 <=> ! [X1] : old(X1) [avatar definition]
172. old(X1) <- (11) [avatar component clause 171]
174. 12 <=> brave(sK3) [avatar definition]
176. ~brave(sK3) <- (~12) [avatar component clause 174]
177. 11 | ~12 [avatar split clause 85,174,171]
191. ~old(X0) | kind(X0) [subsumption resolution 93,168]
196. 17 <=> kind(paul) [avatar definition]
198. ~kind(paul) <- (~17) [avatar component clause 196]
259. ~17 [avatar split clause 120,196]
260. brave(X3) <- (7) [subsumption resolution 152,169]
263. $false <- (7, ~12) [resolution 260,176]
264. ~7 | 12 [avatar contradiction clause 263]
265. $false <- (10) [subsumption resolution 165,169]
266. ~10 [avatar contradiction clause 265]
271. kind(X0) <- (11) [resolution 191,172]
272. $false <- (11, ~17) [resolution 271,198]
273. ~11 | 17 [avatar contradiction clause 272]
274. $false [avatar sat refutation 166,177,259,264,266,273]
% SZS output end Proof for 1572808118344641787237260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both tall and not humble then someone is curious and vice versa.
Everyone who is both not brave and old is quiet.
If someone is rich then fred is both curious and not kind and vice versa.
If someone is either generous or curious then someone is both generous and not curious.
Everyone who is either calm or not creative is funny and vice versa.
If mary is not kind then someone is brave or not generous.
Everyone who is strong or funny is both quiet and not tall.
Everyone who is calm or not curious is not happy or not humble.
If someone is not strong then someone is either not old or not generous and vice versa.
If alice is patient then susan is not brave or generous.
Everyone who is not strong or funny is both brave and curious and vice versa.
Everyone who is patient is either wise or happy and vice versa.
Everyone who is both curious and wise is not tall or not calm and vice versa.
Everyone who is both not rich and not calm is not generous and vice versa.
If john is either not generous or funny then fred is humble or creative.
If someone is not tall or not happy then alice is patient and vice versa.
Paul is not calm.
Susan is not curious or not happy.
Paul is both not old and wise.
Fred is old or tall.
Someone is either not creative or funny.
Alice is both rich and not wise. | Susan is not calm. | neutral | (((tall(lucy)&~humble(lucy)))<=>(?[X]:(curious(X))))&
(![X]:((~brave(X)&old(X))=>quiet(X)))&
((?[X]:(rich(X)))<=>((curious(fred)&~kind(fred))))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((calm(X)<~>~creative(X))<=>funny(X)))&
((~kind(mary))=>(?[X]:((brave(X)|~generous(X)))))&
(![X]:((strong(X)|funny(X))=>(quiet(X)&~tall(X))))&
(![X]:((calm(X)|~curious(X))=>(~happy(X)|~humble(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~old(X)<~>~generous(X)))))&
((patient(alice))=>((~brave(susan)|generous(susan))))&
(![X]:((~strong(X)|funny(X))<=>(brave(X)&curious(X))))&
(![X]:(patient(X)<=>(wise(X)<~>happy(X))))&
(![X]:((curious(X)&wise(X))<=>(~tall(X)|~calm(X))))&
(![X]:((~rich(X)&~calm(X))<=>~generous(X)))&
(((~generous(john)<~>funny(john)))=>((humble(fred)|creative(fred))))&
((?[X]:((~tall(X)|~happy(X))))<=>(patient(alice)))&
(~calm(paul))&
((~curious(susan)|~happy(susan)))&
((~old(paul)&wise(paul)))&
((old(fred)|tall(fred)))&
(?[X]:((~creative(X)<~>funny(X))))&
((rich(alice)&~wise(alice))) | ~calm(susan) | [] | null | 0 |
Everyone who is both not patient and curious is not curious or creative and vice versa.
If someone is both not brave and calm then john is happy and vice versa.
Everyone who is not creative or not tall is either not humble or happy and vice versa.
If someone is not quiet or tall then someone is old or strong.
If someone is either not curious or not generous then paul is either calm or not old.
Everyone who is either calm or old is humble.
Everyone who is both creative and not patient is both not happy and not brave.
If someone is funny or not old then someone is creative or wise and vice versa.
Everyone who is both not funny and old is both quiet and generous.
If paul is either not creative or brave then lucy is happy or not generous.
Everyone who is old or not brave is both brave and not kind.
Everyone who is both brave and not creative is either not funny or not humble and vice versa.
If john is not strong then someone is both not old and not patient and vice versa.
Everyone who is tall is either kind or not brave and vice versa.
If someone is calm or not rich then susan is both patient and strong.
Everyone who is both old and wise is not quiet or not wise.
Someone is not rich or patient.
Susan is calm or not strong.
Someone is funny or not humble.
Someone is not kind or not strong.
Someone is creative or not calm.
Someone is quiet.
Paul is either not quiet or tall. | Paul is calm. | neutral | (![X]:((~patient(X)&curious(X))<=>(~curious(X)|creative(X))))&
((?[X]:((~brave(X)&calm(X))))<=>(happy(john)))&
(![X]:((~creative(X)|~tall(X))<=>(~humble(X)<~>happy(X))))&
((?[X]:((~quiet(X)|tall(X))))=>(?[X]:((old(X)|strong(X)))))&
((?[X]:((~curious(X)<~>~generous(X))))=>((calm(paul)<~>~old(paul))))&
(![X]:((calm(X)<~>old(X))=>humble(X)))&
(![X]:((creative(X)&~patient(X))=>(~happy(X)&~brave(X))))&
((?[X]:((funny(X)|~old(X))))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~funny(X)&old(X))=>(quiet(X)&generous(X))))&
(((~creative(paul)<~>brave(paul)))=>((happy(lucy)|~generous(lucy))))&
(![X]:((old(X)|~brave(X))=>(brave(X)&~kind(X))))&
(![X]:((brave(X)&~creative(X))<=>(~funny(X)<~>~humble(X))))&
((~strong(john))<=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
((?[X]:((calm(X)|~rich(X))))=>((patient(susan)&strong(susan))))&
(![X]:((old(X)&wise(X))=>(~quiet(X)|~wise(X))))&
(?[X]:((~rich(X)|patient(X))))&
((calm(susan)|~strong(susan)))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:(quiet(X)))&
((~quiet(paul)<~>tall(paul))) | calm(paul) | [] | null | 0 |
Everyone who is either not old or rich is calm or strong.
If alice is not brave or creative then someone is either not curious or not humble.
If mary is funny then someone is wise.
If john is patient then someone is either not old or not quiet.
Everyone who is not funny is not happy.
If someone is both patient and brave then someone is not wise or strong and vice versa.
If someone is not brave then someone is not generous and vice versa.
Everyone who is both not strong and not calm is either funny or old and vice versa.
Everyone who is not brave is patient or not rich and vice versa.
If someone is either tall or calm then someone is either humble or generous and vice versa.
If lucy is either tall or not creative then susan is not strong and vice versa.
If someone is strong then susan is not brave or not curious and vice versa.
Everyone who is not quiet or brave is either old or not brave.
Everyone who is brave is not happy or kind.
Everyone who is either curious or not generous is both not kind and humble.
If susan is both humble and funny then fred is either humble or generous and vice versa.
Someone is both not brave and not strong.
Alice is either generous or old.
Mary is either funny or not strong.
Someone is not generous.
Someone is old or wise.
Mary is wise.
Paul is tall. | Fred is funny. | neutral | (![X]:((~old(X)<~>rich(X))=>(calm(X)|strong(X))))&
(((~brave(alice)|creative(alice)))=>(?[X]:((~curious(X)<~>~humble(X)))))&
((funny(mary))=>(?[X]:(wise(X))))&
((patient(john))=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:(~funny(X)=>~happy(X)))&
((?[X]:((patient(X)&brave(X))))<=>(?[X]:((~wise(X)|strong(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:(~generous(X))))&
(![X]:((~strong(X)&~calm(X))<=>(funny(X)<~>old(X))))&
(![X]:(~brave(X)<=>(patient(X)|~rich(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(?[X]:((humble(X)<~>generous(X)))))&
(((tall(lucy)<~>~creative(lucy)))<=>(~strong(susan)))&
((?[X]:(strong(X)))<=>((~brave(susan)|~curious(susan))))&
(![X]:((~quiet(X)|brave(X))=>(old(X)<~>~brave(X))))&
(![X]:(brave(X)=>(~happy(X)|kind(X))))&
(![X]:((curious(X)<~>~generous(X))=>(~kind(X)&humble(X))))&
(((humble(susan)&funny(susan)))<=>((humble(fred)<~>generous(fred))))&
(?[X]:((~brave(X)&~strong(X))))&
((generous(alice)<~>old(alice)))&
((funny(mary)<~>~strong(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)|wise(X))))&
(wise(mary))&
(tall(paul)) | funny(fred) | [] | null | 0 |
Everyone who is either not happy or not rich is either not brave or kind. Everyone who is both wise and not old is not wise. Everyone who is not generous or rich is either not strong or not old. If someone is either not creative or not quiet then someone is either kind or not wise. Everyone who is either wise or not funny is either creative or funny. Everyone who is quiet is not patient or not rich. If alice is both happy and creative then mary is either not patient or happy. Everyone who is both not patient and old is not old and vice versa. Everyone who is not curious or not old is both calm and not humble and vice versa. If someone is either not patient or not happy then lucy is either not humble or curious. Everyone who is not quiet is both kind and not kind and vice versa. Everyone who is rich or generous is both not happy and not old and vice versa. Everyone who is not rich or creative is both not happy and funny. If someone is patient then someone is brave or not curious and vice versa. Everyone who is generous or not curious is both calm and not brave and vice versa. Everyone who is not rich is not curious or not wise and vice versa. Fred is either wise or not curious. Susan is funny. Paul is either creative or kind. Someone is both not humble and quiet. Someone is either not quiet or not humble. Someone is both not curious and not strong. | Mary is strong. | contradiction | (![X]:((~happy(X)<~>~rich(X))=>(~brave(X)<~>kind(X))))&
(![X]:((wise(X)&~old(X))=>~wise(X)))&
(![X]:((~generous(X)|rich(X))=>(~strong(X)<~>~old(X))))&
((?[X]:((~creative(X)<~>~quiet(X))))=>(?[X]:((kind(X)<~>~wise(X)))))&
(![X]:((wise(X)<~>~funny(X))=>(creative(X)<~>funny(X))))&
(![X]:(quiet(X)=>(~patient(X)|~rich(X))))&
(((happy(alice)&creative(alice)))=>((~patient(mary)<~>happy(mary))))&
(![X]:((~patient(X)&old(X))<=>~old(X)))&
(![X]:((~curious(X)|~old(X))<=>(calm(X)&~humble(X))))&
((?[X]:((~patient(X)<~>~happy(X))))=>((~humble(lucy)<~>curious(lucy))))&
(![X]:(~quiet(X)<=>(kind(X)&~kind(X))))&
(![X]:((rich(X)|generous(X))<=>(~happy(X)&~old(X))))&
(![X]:((~rich(X)|creative(X))=>(~happy(X)&funny(X))))&
((?[X]:(patient(X)))<=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((generous(X)|~curious(X))<=>(calm(X)&~brave(X))))&
(![X]:(~rich(X)<=>(~curious(X)|~wise(X))))&
((wise(fred)<~>~curious(fred)))&
(funny(susan))&
((creative(paul)<~>kind(paul)))&
(?[X]:((~humble(X)&quiet(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:((~curious(X)&~strong(X)))) | strong(mary) | [
"p2",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9124296601435730798538197
% SZS output start Proof for 9124296601435730798538197
3. ! [X0] : ((rich(X0) | ~generous(X0)) => (~strong(X0) <~> ~old(X0))) [input p2]
8. ! [X0] : ((old(X0) & ~patient(X0)) <=> ~old(X0)) [input p7]
12. ! [X0] : ((generous(X0) | rich(X0)) <=> (~old(X0) & ~happy(X0))) [input p11]
23. strong(mary) [input hypothesis]
29. ! [X0] : ((~strong(X0) <~> ~old(X0)) | (~rich(X0) & generous(X0))) [ennf transformation 3]
39. ! [X0] : (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (~rich(X0) & generous(X0))) [nnf transformation 29]
46. ! [X0] : (((old(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | (~old(X0) | patient(X0)))) [nnf transformation 8]
47. ! [X0] : (((old(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | ~old(X0) | patient(X0))) [flattening 46]
53. ! [X0] : (((generous(X0) | rich(X0)) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | (~generous(X0) & ~rich(X0)))) [nnf transformation 12]
54. ! [X0] : ((generous(X0) | rich(X0) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | (~generous(X0) & ~rich(X0)))) [flattening 53]
78. ~strong(X0) | ~old(X0) | generous(X0) [cnf transformation 39]
95. old(X0) | old(X0) [cnf transformation 47]
111. ~old(X0) | ~generous(X0) [cnf transformation 54]
139. strong(mary) [cnf transformation 23]
141. old(X0) [duplicate literal removal 95]
197. ~generous(X0) [subsumption resolution 111,141]
228. ~old(mary) | generous(mary) [resolution 78,139]
229. generous(mary) [subsumption resolution 228,141]
230. $false [subsumption resolution 229,197]
% SZS output end Proof for 9124296601435730798538197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or patient is both not old and not strong and vice versa.
If someone is either old or not rich then mary is humble.
Everyone who is both patient and not calm is rich.
Everyone who is patient or not rich is happy or generous and vice versa.
If paul is either not strong or creative then someone is tall.
Everyone who is either strong or not kind is not patient.
If mary is both not creative and not generous then someone is not old.
If mary is not kind then someone is both happy and kind.
Everyone who is either kind or strong is creative.
If alice is not tall then someone is both not kind and not rich and vice versa.
Everyone who is not funny or not humble is not quiet or not brave and vice versa.
Everyone who is both not creative and humble is not generous and vice versa.
Everyone who is both not calm and generous is either not quiet or generous and vice versa.
If susan is both tall and patient then alice is both not creative and not patient and vice versa.
If someone is both patient and not creative then someone is curious and vice versa.
John is either not calm or humble.
Susan is strong or not rich.
Someone is brave.
Fred is happy or patient.
Someone is not brave. | John is tall. | neutral | (![X]:((~kind(X)|patient(X))<=>(~old(X)&~strong(X))))&
((?[X]:((old(X)<~>~rich(X))))=>(humble(mary)))&
(![X]:((patient(X)&~calm(X))=>rich(X)))&
(![X]:((patient(X)|~rich(X))<=>(happy(X)|generous(X))))&
(((~strong(paul)<~>creative(paul)))=>(?[X]:(tall(X))))&
(![X]:((strong(X)<~>~kind(X))=>~patient(X)))&
(((~creative(mary)&~generous(mary)))=>(?[X]:(~old(X))))&
((~kind(mary))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((kind(X)<~>strong(X))=>creative(X)))&
((~tall(alice))<=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:((~funny(X)|~humble(X))<=>(~quiet(X)|~brave(X))))&
(![X]:((~creative(X)&humble(X))<=>~generous(X)))&
(![X]:((~calm(X)&generous(X))<=>(~quiet(X)<~>generous(X))))&
(((tall(susan)&patient(susan)))<=>((~creative(alice)&~patient(alice))))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:(curious(X))))&
((~calm(john)<~>humble(john)))&
((strong(susan)|~rich(susan)))&
(?[X]:(brave(X)))&
((happy(fred)|patient(fred)))&
(?[X]:(~brave(X))) | tall(john) | [] | null | 0 |
If lucy is not patient then paul is both generous and not wise.
Everyone who is both wise and not rich is not tall or not curious and vice versa.
Everyone who is funny is both patient and not creative.
Everyone who is not quiet or not rich is both generous and curious and vice versa.
If paul is both not rich and old then mary is not brave.
Everyone who is not brave is patient or not old.
If susan is both not generous and rich then someone is either not generous or not rich.
If someone is curious or humble then alice is either quiet or curious and vice versa.
Everyone who is either not tall or not funny is not quiet or wise and vice versa.
If someone is both happy and kind then mary is not curious or quiet.
Everyone who is quiet or kind is both happy and rich and vice versa.
Everyone who is both strong and not brave is wise and vice versa.
Everyone who is both tall and rich is either humble or not patient and vice versa.
Everyone who is generous or rich is either rich or not tall.
If someone is either old or patient then john is not generous or not kind.
Everyone who is both not curious and curious is either not generous or calm and vice versa.
Paul is humble.
Lucy is kind.
Someone is rich.
Someone is both not humble and not calm.
Someone is not old or not generous.
Alice is both not calm and not patient.
Someone is creative or not kind.
Paul is not wise. | John is brave. | neutral | ((~patient(lucy))=>((generous(paul)&~wise(paul))))&
(![X]:((wise(X)&~rich(X))<=>(~tall(X)|~curious(X))))&
(![X]:(funny(X)=>(patient(X)&~creative(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(generous(X)&curious(X))))&
(((~rich(paul)&old(paul)))=>(~brave(mary)))&
(![X]:(~brave(X)=>(patient(X)|~old(X))))&
(((~generous(susan)&rich(susan)))=>(?[X]:((~generous(X)<~>~rich(X)))))&
((?[X]:((curious(X)|humble(X))))<=>((quiet(alice)<~>curious(alice))))&
(![X]:((~tall(X)<~>~funny(X))<=>(~quiet(X)|wise(X))))&
((?[X]:((happy(X)&kind(X))))=>((~curious(mary)|quiet(mary))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)&rich(X))))&
(![X]:((strong(X)&~brave(X))<=>wise(X)))&
(![X]:((tall(X)&rich(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((generous(X)|rich(X))=>(rich(X)<~>~tall(X))))&
((?[X]:((old(X)<~>patient(X))))=>((~generous(john)|~kind(john))))&
(![X]:((~curious(X)&curious(X))<=>(~generous(X)<~>calm(X))))&
(humble(paul))&
(kind(lucy))&
(?[X]:(rich(X)))&
(?[X]:((~humble(X)&~calm(X))))&
(?[X]:((~old(X)|~generous(X))))&
((~calm(alice)&~patient(alice)))&
(?[X]:((creative(X)|~kind(X))))&
(~wise(paul)) | brave(john) | [] | null | 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.