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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If john is funny or not old then alice is not funny and vice versa. Everyone who is both quiet and happy is both not calm and not brave and vice versa. Everyone who is generous is either not quiet or not kind. Everyone who is tall or not happy is either not patient or not brave. Everyone who is either not brave or not wise is not patient or not funny and vice versa. Everyone who is either patient or not happy is calm or not calm and vice versa. Everyone who is both rich and not happy is generous or not calm and vice versa. If someone is creative then paul is curious and vice versa. If someone is both quiet and not happy then paul is not creative. Everyone who is both tall and not kind is not quiet and vice versa. If susan is strong then someone is either quiet or generous and vice versa. If someone is either calm or not creative then someone is not old and vice versa. If alice is funny then paul is not rich and vice versa. Everyone who is not rich or not creative is either happy or strong and vice versa. If someone is not quiet or not patient then mary is both strong and not generous and vice versa. Everyone who is both calm and not strong is either not patient or not creative. Someone is either tall or patient. Fred is either not creative or not wise. Susan is both not quiet and patient. Someone is both tall and funny. Someone is not humble. Mary is either not funny or not generous. Someone is not quiet or not old. | Mary is wise. | contradiction | (((funny(john)|~old(john)))<=>(~funny(alice)))&
(![X]:((quiet(X)&happy(X))<=>(~calm(X)&~brave(X))))&
(![X]:(generous(X)=>(~quiet(X)<~>~kind(X))))&
(![X]:((tall(X)|~happy(X))=>(~patient(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(~patient(X)|~funny(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(calm(X)|~calm(X))))&
(![X]:((rich(X)&~happy(X))<=>(generous(X)|~calm(X))))&
((?[X]:(creative(X)))<=>(curious(paul)))&
((?[X]:((quiet(X)&~happy(X))))=>(~creative(paul)))&
(![X]:((tall(X)&~kind(X))<=>~quiet(X)))&
((strong(susan))<=>(?[X]:((quiet(X)<~>generous(X)))))&
((?[X]:((calm(X)<~>~creative(X))))<=>(?[X]:(~old(X))))&
((funny(alice))<=>(~rich(paul)))&
(![X]:((~rich(X)|~creative(X))<=>(happy(X)<~>strong(X))))&
((?[X]:((~quiet(X)|~patient(X))))<=>((strong(mary)&~generous(mary))))&
(![X]:((calm(X)&~strong(X))=>(~patient(X)<~>~creative(X))))&
(?[X]:((tall(X)<~>patient(X))))&
((~creative(fred)<~>~wise(fred)))&
((~quiet(susan)&patient(susan)))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:(~humble(X)))&
((~funny(mary)<~>~generous(mary)))&
(?[X]:((~quiet(X)|~old(X)))) | wise(mary) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4011227875023722069411046
% SZS output start Proof for 4011227875023722069411046
2. ! [X0] : ((happy(X0) & quiet(X0)) <=> (~brave(X0) & ~calm(X0))) [input p1]
4. ! [X0] : ((~happy(X0) | tall(X0)) => (~patient(X0) <~> ~brave(X0))) [input p3]
5. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (~funny(X0) | ~patient(X0))) [input p4]
6. ! [X0] : ((patient(X0) <~> ~happy(X0)) <=> (~calm(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & rich(X0)) <=> (~calm(X0) | generous(X0))) [input p6]
10. ! [X0] : ((~kind(X0) & tall(X0)) <=> ~quiet(X0)) [input p9]
15. ? [X0] : (~patient(X0) | ~quiet(X0)) <=> (~generous(mary) & strong(mary)) [input p14]
19. patient(susan) & ~quiet(susan) [input p18]
22. ~funny(mary) <~> ~generous(mary) [input p21]
24. wise(mary) [input hypothesis]
28. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | (happy(X0) & ~tall(X0))) [ennf transformation 4]
34. ! [X0] : (((happy(X0) & quiet(X0)) | (brave(X0) | calm(X0))) & ((~brave(X0) & ~calm(X0)) | (~happy(X0) | ~quiet(X0)))) [nnf transformation 2]
35. ! [X0] : (((happy(X0) & quiet(X0)) | brave(X0) | calm(X0)) & ((~brave(X0) & ~calm(X0)) | ~happy(X0) | ~quiet(X0))) [flattening 34]
37. ! [X0] : (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (happy(X0) & ~tall(X0))) [nnf transformation 28]
38. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 5]
39. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [flattening 38]
40. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (calm(X0) & ~calm(X0))) & ((~calm(X0) | calm(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [nnf transformation 6]
41. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (calm(X0) & ~calm(X0))) & (~calm(X0) | calm(X0) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [flattening 40]
42. ! [X0] : (((~happy(X0) & rich(X0)) | (calm(X0) & ~generous(X0))) & ((~calm(X0) | generous(X0)) | (happy(X0) | ~rich(X0)))) [nnf transformation 7]
43. ! [X0] : (((~happy(X0) & rich(X0)) | (calm(X0) & ~generous(X0))) & (~calm(X0) | generous(X0) | happy(X0) | ~rich(X0))) [flattening 42]
48. ! [X0] : (((~kind(X0) & tall(X0)) | quiet(X0)) & (~quiet(X0) | (kind(X0) | ~tall(X0)))) [nnf transformation 10]
49. ! [X0] : (((~kind(X0) & tall(X0)) | quiet(X0)) & (~quiet(X0) | kind(X0) | ~tall(X0))) [flattening 48]
62. (? [X0] : (~patient(X0) | ~quiet(X0)) | (generous(mary) | ~strong(mary))) & ((~generous(mary) & strong(mary)) | ! [X0] : (patient(X0) & quiet(X0))) [nnf transformation 15]
63. (? [X0] : (~patient(X0) | ~quiet(X0)) | generous(mary) | ~strong(mary)) & ((~generous(mary) & strong(mary)) | ! [X0] : (patient(X0) & quiet(X0))) [flattening 62]
64. (? [X0] : (~patient(X0) | ~quiet(X0)) | generous(mary) | ~strong(mary)) & ((~generous(mary) & strong(mary)) | ! [X1] : (patient(X1) & quiet(X1))) [rectify 63]
65. ? [X0] : (~patient(X0) | ~quiet(X0)) => (~patient(sK4) | ~quiet(sK4)) [choice axiom]
66. ((~patient(sK4) | ~quiet(sK4)) | generous(mary) | ~strong(mary)) & ((~generous(mary) & strong(mary)) | ! [X1] : (patient(X1) & quiet(X1))) [skolemisation 64,65]
74. (generous(mary) | funny(mary)) & (~generous(mary) | ~funny(mary)) [nnf transformation 22]
80. ~calm(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 35]
81. ~brave(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 35]
83. brave(X0) | happy(X0) | calm(X0) [cnf transformation 35]
86. ~patient(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 37]
88. ~tall(X0) | patient(X0) | brave(X0) [cnf transformation 37]
89. patient(X0) | brave(X0) | happy(X0) [cnf transformation 37]
90. ~wise(X0) | ~patient(X0) | ~funny(X0) | brave(X0) [cnf transformation 39]
92. ~wise(X0) | ~brave(X0) | patient(X0) [cnf transformation 39]
100. happy(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 41]
101. ~patient(X0) | happy(X0) | calm(X0) [cnf transformation 41]
106. ~happy(X0) | calm(X0) [cnf transformation 43]
111. tall(X0) | quiet(X0) [cnf transformation 49]
131. ~generous(mary) | quiet(X1) [cnf transformation 66]
140. ~quiet(susan) [cnf transformation 19]
145. generous(mary) | funny(mary) [cnf transformation 74]
147. wise(mary) [cnf transformation 24]
163. ~patient(X0) | happy(X0) [subsumption resolution 100,101]
244. 22 <=> generous(mary) [avatar definition]
261. 26 <=> ! [X1] : quiet(X1) [avatar definition]
262. quiet(X1) <- (26) [avatar component clause 261]
263. 26 | ~22 [avatar split clause 131,244,261]
287. 31 <=> funny(mary) [avatar definition]
289. funny(mary) <- (31) [avatar component clause 287]
290. 31 | 22 [avatar split clause 145,244,287]
302. $false <- (26) [resolution 262,140]
303. ~26 [avatar contradiction clause 302]
326. patient(X0) | brave(X0) | quiet(X0) [resolution 88,111]
345. brave(X2) | happy(X2) | happy(X2) [resolution 89,163]
346. brave(X2) | happy(X2) [duplicate literal removal 345]
358. ~brave(mary) | patient(mary) [resolution 92,147]
360. 40 <=> patient(mary) [avatar definition]
361. ~patient(mary) <- (~40) [avatar component clause 360]
362. patient(mary) <- (40) [avatar component clause 360]
364. 41 <=> brave(mary) [avatar definition]
365. brave(mary) <- (41) [avatar component clause 364]
366. ~brave(mary) <- (~41) [avatar component clause 364]
367. 40 | ~41 [avatar split clause 358,364,360]
379. happy(mary) | calm(mary) <- (~41) [resolution 366,83]
381. calm(mary) <- (~41) [subsumption resolution 379,106]
413. ~happy(mary) | ~quiet(mary) <- (~41) [resolution 381,80]
415. 47 <=> quiet(mary) [avatar definition]
417. ~quiet(mary) <- (~47) [avatar component clause 415]
419. 48 <=> happy(mary) [avatar definition]
420. happy(mary) <- (48) [avatar component clause 419]
421. ~happy(mary) <- (~48) [avatar component clause 419]
422. ~47 | ~48 | 41 [avatar split clause 413,364,419,415]
454. happy(mary) <- (~41) [resolution 346,366]
456. $false <- (~41, ~48) [subsumption resolution 454,421]
457. 41 | 48 [avatar contradiction clause 456]
461. ~patient(mary) | ~funny(mary) | brave(mary) [resolution 90,147]
469. happy(mary) <- (40) [resolution 362,163]
475. $false <- (40, ~48) [subsumption resolution 469,421]
476. ~40 | 48 [avatar contradiction clause 475]
477. ~patient(mary) | brave(mary) <- (31) [subsumption resolution 461,289]
478. 41 | ~40 | ~31 [avatar split clause 477,287,360,364]
564. brave(mary) | quiet(mary) <- (~40) [resolution 326,361]
567. quiet(mary) <- (~40, ~41) [subsumption resolution 564,366]
568. $false <- (~40, ~41, ~47) [subsumption resolution 567,417]
569. 40 | 41 | 47 [avatar contradiction clause 568]
573. ~brave(mary) | ~tall(mary) <- (40) [resolution 362,86]
575. ~tall(mary) <- (40, 41) [subsumption resolution 573,365]
576. ~happy(mary) | ~quiet(mary) <- (41) [resolution 365,81]
577. quiet(mary) <- (40, 41) [resolution 575,111]
580. 47 | ~40 | ~41 [avatar split clause 577,364,360,415]
581. ~quiet(mary) <- (41, 48) [subsumption resolution 576,420]
582. ~47 | ~41 | ~48 [avatar split clause 581,419,364,415]
583. $false [avatar sat refutation 263,290,303,367,422,457,476,478,569,580,582]
% SZS output end Proof for 4011227875023722069411046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not tall then john is both tall and calm.
If someone is not brave then someone is both not happy and calm and vice versa.
Everyone who is not humble or brave is either not funny or not brave.
Everyone who is old or kind is funny and vice versa.
Everyone who is both rich and not tall is not funny or kind and vice versa.
Everyone who is both not old and rich is both not rich and not curious.
If mary is both not calm and creative then susan is brave or curious and vice versa.
Everyone who is either not tall or generous is not generous or creative.
Everyone who is either not humble or funny is strong.
Everyone who is either brave or generous is both brave and quiet.
Everyone who is funny is either humble or tall.
If mary is either not kind or not creative then john is both not creative and not generous and vice versa.
If someone is both not funny and curious then lucy is both not creative and not happy and vice versa.
Everyone who is not curious or brave is not patient or not generous.
Mary is either patient or funny.
Someone is old or strong.
Alice is calm or not creative.
Someone is both creative and strong. | Susan is not quiet. | neutral | ((?[X]:((kind(X)<~>~tall(X))))=>((tall(john)&calm(john))))&
((?[X]:(~brave(X)))<=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:((~humble(X)|brave(X))=>(~funny(X)<~>~brave(X))))&
(![X]:((old(X)|kind(X))<=>funny(X)))&
(![X]:((rich(X)&~tall(X))<=>(~funny(X)|kind(X))))&
(![X]:((~old(X)&rich(X))=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(![X]:((~curious(X)|brave(X))=>(~patient(X)|~generous(X))))&
((patient(mary)<~>funny(mary)))&
(?[X]:((old(X)|strong(X))))&
((calm(alice)|~creative(alice)))&
(?[X]:((creative(X)&strong(X)))) | ~quiet(susan) | [] | null | 0 |
If paul is not calm then someone is patient and vice versa.
Everyone who is curious is kind and vice versa.
Everyone who is both quiet and wise is both brave and not creative and vice versa.
Everyone who is both not humble and quiet is both curious and kind.
If someone is rich then someone is funny or calm and vice versa.
Everyone who is both not strong and kind is both not wise and not humble.
Everyone who is both rich and strong is both old and not curious.
Everyone who is not brave is both not old and humble.
If mary is both brave and not funny then someone is kind and vice versa.
If john is both not rich and not generous then someone is both happy and not old and vice versa.
Everyone who is not kind is either rich or brave.
Everyone who is not brave or funny is either funny or brave and vice versa.
If someone is not patient then alice is not rich.
If someone is both not humble and creative then someone is both quiet and not tall and vice versa.
Everyone who is both not strong and not humble is not generous.
Everyone who is both generous and rich is not brave.
Someone is not old.
Someone is both not happy and quiet.
Someone is either not funny or generous.
John is creative or funny. | Mary is not curious. | entailment | ((~calm(paul))<=>(?[X]:(patient(X))))&
(![X]:(curious(X)<=>kind(X)))&
(![X]:((quiet(X)&wise(X))<=>(brave(X)&~creative(X))))&
(![X]:((~humble(X)&quiet(X))=>(curious(X)&kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:((funny(X)|calm(X)))))&
(![X]:((~strong(X)&kind(X))=>(~wise(X)&~humble(X))))&
(![X]:((rich(X)&strong(X))=>(old(X)&~curious(X))))&
(![X]:(~brave(X)=>(~old(X)&humble(X))))&
(((brave(mary)&~funny(mary)))<=>(?[X]:(kind(X))))&
(((~rich(john)&~generous(john)))<=>(?[X]:((happy(X)&~old(X)))))&
(![X]:(~kind(X)=>(rich(X)<~>brave(X))))&
(![X]:((~brave(X)|funny(X))<=>(funny(X)<~>brave(X))))&
((?[X]:(~patient(X)))=>(~rich(alice)))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~strong(X)&~humble(X))=>~generous(X)))&
(![X]:((generous(X)&rich(X))=>~brave(X)))&
(?[X]:(~old(X)))&
(?[X]:((~happy(X)&quiet(X))))&
(?[X]:((~funny(X)<~>generous(X))))&
((creative(john)|funny(john))) | ~curious(mary) | [
"p1",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3453025784024011662935366
% SZS output start Proof for 3453025784024011662935366
2. ! [X0] : (curious(X0) <=> kind(X0)) [input p1]
9. (~funny(mary) & brave(mary)) <=> ? [X0] : kind(X0) [input p8]
12. ! [X0] : ((funny(X0) | ~brave(X0)) <=> (funny(X0) <~> brave(X0))) [input p11]
21. curious(mary) [input hypothesis]
41. ! [X0] : ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))) [nnf transformation 2]
49. ((~funny(mary) & brave(mary)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | (funny(mary) | ~brave(mary))) [nnf transformation 9]
50. ((~funny(mary) & brave(mary)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | funny(mary) | ~brave(mary)) [flattening 49]
51. ((~funny(mary) & brave(mary)) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | funny(mary) | ~brave(mary)) [rectify 50]
52. ? [X1] : kind(X1) => kind(sK3) [choice axiom]
53. ((~funny(mary) & brave(mary)) | ! [X0] : ~kind(X0)) & (kind(sK3) | funny(mary) | ~brave(mary)) [skolemisation 51,52]
60. ! [X0] : (((funny(X0) | ~brave(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~funny(X0) & brave(X0)))) [nnf transformation 12]
61. ! [X0] : ((funny(X0) | ~brave(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~funny(X0) & brave(X0)))) [flattening 60]
76. ~curious(X0) | kind(X0) [cnf transformation 41]
94. brave(mary) | ~kind(X0) [cnf transformation 53]
105. ~brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 61]
107. funny(X0) | ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 61]
121. curious(mary) [cnf transformation 21]
123. ~brave(X0) | ~funny(X0) [duplicate literal removal 105]
124. funny(X0) | ~brave(X0) [duplicate literal removal 107]
163. 10 <=> ! [X0] : ~kind(X0) [avatar definition]
164. ~kind(X0) <- (10) [avatar component clause 163]
171. 12 <=> brave(mary) [avatar definition]
173. brave(mary) <- (12) [avatar component clause 171]
174. 10 | 12 [avatar split clause 94,171,163]
203. ~brave(X0) [subsumption resolution 123,124]
242. kind(mary) [resolution 76,121]
243. $false <- (10) [subsumption resolution 242,164]
244. ~10 [avatar contradiction clause 243]
245. $false <- (12) [subsumption resolution 173,203]
246. ~12 [avatar contradiction clause 245]
249. $false [avatar sat refutation 174,244,246]
% SZS output end Proof for 3453025784024011662935366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or humble is either tall or not happy. Everyone who is either calm or creative is both funny and not strong. Everyone who is both tall and creative is both generous and calm. If someone is not tall or not calm then someone is humble or old and vice versa. If susan is calm then alice is both patient and calm. If someone is generous or not humble then mary is both kind and not happy. If susan is either not tall or creative then someone is either not old or humble. Everyone who is not generous or happy is not brave and vice versa. If john is both generous and happy then someone is either quiet or not calm and vice versa. Everyone who is either not generous or not funny is funny and vice versa. Everyone who is curious or not old is rich and vice versa. Everyone who is both not tall and not quiet is not humble and vice versa. Everyone who is not tall or brave is either wise or not brave and vice versa. Everyone who is either creative or not humble is both not humble and not wise. Everyone who is both calm and not tall is patient and vice versa. If someone is not happy or rich then someone is brave and vice versa. Someone is funny or rich. Someone is calm or happy. Lucy is not happy or calm. Someone is not brave. Someone is old or not tall. | Lucy is rich. | contradiction | (![X]:((rich(X)|humble(X))=>(tall(X)<~>~happy(X))))&
(![X]:((calm(X)<~>creative(X))=>(funny(X)&~strong(X))))&
(![X]:((tall(X)&creative(X))=>(generous(X)&calm(X))))&
((?[X]:((~tall(X)|~calm(X))))<=>(?[X]:((humble(X)|old(X)))))&
((calm(susan))=>((patient(alice)&calm(alice))))&
((?[X]:((generous(X)|~humble(X))))=>((kind(mary)&~happy(mary))))&
(((~tall(susan)<~>creative(susan)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~generous(X)|happy(X))<=>~brave(X)))&
(((generous(john)&happy(john)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~generous(X)<~>~funny(X))<=>funny(X)))&
(![X]:((curious(X)|~old(X))<=>rich(X)))&
(![X]:((~tall(X)&~quiet(X))<=>~humble(X)))&
(![X]:((~tall(X)|brave(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((creative(X)<~>~humble(X))=>(~humble(X)&~wise(X))))&
(![X]:((calm(X)&~tall(X))<=>patient(X)))&
((?[X]:((~happy(X)|rich(X))))<=>(?[X]:(brave(X))))&
(?[X]:((funny(X)|rich(X))))&
(?[X]:((calm(X)|happy(X))))&
((~happy(lucy)|calm(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)|~tall(X)))) | rich(lucy) | [
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7419975148004730613586376
% SZS output start Proof for 7419975148004730613586376
8. ! [X0] : ((happy(X0) | ~generous(X0)) <=> ~brave(X0)) [input p7]
10. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> funny(X0)) [input p9]
16. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X0] : brave(X0) [input p15]
22. rich(lucy) [input hypothesis]
24. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X1] : brave(X1) [rectify 16]
47. ! [X0] : (((happy(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [flattening 47]
54. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~funny(X0)) & (funny(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 10]
62. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X1] : brave(X1) | ! [X0] : (~rich(X0) & happy(X0))) [nnf transformation 24]
63. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X2] : brave(X2) | ! [X3] : (~rich(X3) & happy(X3))) [rectify 62]
64. ? [X0] : (rich(X0) | ~happy(X0)) => (rich(sK4) | ~happy(sK4)) [choice axiom]
65. ? [X2] : brave(X2) => brave(sK5) [choice axiom]
66. ((rich(sK4) | ~happy(sK4)) | ! [X1] : ~brave(X1)) & (brave(sK5) | ! [X3] : (~rich(X3) & happy(X3))) [skolemisation 63,65,64]
95. ~brave(X0) | generous(X0) [cnf transformation 48]
105. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 54]
106. ~funny(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 54]
127. brave(sK5) | ~rich(X3) [cnf transformation 66]
134. rich(lucy) [cnf transformation 22]
138. funny(X0) | ~generous(X0) [duplicate literal removal 105]
139. ~funny(X0) | ~generous(X0) [duplicate literal removal 106]
195. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
196. ~generous(X0) <- (14) [avatar component clause 195]
246. ~generous(X0) [subsumption resolution 138,139]
247. 14 [avatar split clause 246,195]
261. 28 <=> ! [X3] : ~rich(X3) [avatar definition]
262. ~rich(X3) <- (28) [avatar component clause 261]
264. 29 <=> brave(sK5) [avatar definition]
266. brave(sK5) <- (29) [avatar component clause 264]
267. 28 | 29 [avatar split clause 127,264,261]
308. generous(sK5) <- (29) [resolution 95,266]
309. $false <- (14, 29) [subsumption resolution 308,196]
310. ~14 | ~29 [avatar contradiction clause 309]
311. $false <- (28) [resolution 262,134]
312. ~28 [avatar contradiction clause 311]
313. $false [avatar sat refutation 247,267,310,312]
% SZS output end Proof for 7419975148004730613586376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or wise is both funny and not creative and vice versa.
If someone is both strong and wise then someone is either not quiet or quiet.
Everyone who is strong is happy or not rich.
If someone is humble or not old then fred is old and vice versa.
Everyone who is calm or not creative is either not humble or calm.
If someone is both not kind and not calm then someone is either not creative or not patient and vice versa.
If susan is rich then someone is brave or not creative and vice versa.
Everyone who is both happy and old is not strong or calm and vice versa.
Everyone who is creative or funny is calm or not strong.
If fred is both patient and not quiet then someone is either not quiet or not strong and vice versa.
Everyone who is not wise is both not tall and quiet.
If alice is not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
Someone is not generous.
Paul is wise.
Someone is either not calm or not curious.
Fred is either not kind or patient.
Fred is not tall.
Someone is either not brave or calm.
Fred is both not kind and old. | Alice is not patient. | entailment | (![X]:((old(X)|wise(X))<=>(funny(X)&~creative(X))))&
((?[X]:((strong(X)&wise(X))))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:(strong(X)=>(happy(X)|~rich(X))))&
((?[X]:((humble(X)|~old(X))))<=>(old(fred)))&
(![X]:((calm(X)|~creative(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
((rich(susan))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((happy(X)&old(X))<=>(~strong(X)|calm(X))))&
(![X]:((creative(X)|funny(X))=>(calm(X)|~strong(X))))&
(((patient(fred)&~quiet(fred)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:(~wise(X)=>(~tall(X)&quiet(X))))&
(((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
(?[X]:(~generous(X)))&
(wise(paul))&
(?[X]:((~calm(X)<~>~curious(X))))&
((~kind(fred)<~>patient(fred)))&
(~tall(fred))&
(?[X]:((~brave(X)<~>calm(X))))&
((~kind(fred)&old(fred))) | ~patient(alice) | [
"p0",
"p5",
"p7",
"p8",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3218951414033954332247263
% SZS output start Proof for 3218951414033954332247263
1. ! [X0] : ((wise(X0) | old(X0)) <=> (~creative(X0) & funny(X0))) [input p0]
6. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X0] : (~creative(X0) <~> ~patient(X0)) [input p5]
8. ! [X0] : ((old(X0) & happy(X0)) <=> (calm(X0) | ~strong(X0))) [input p7]
9. ! [X0] : ((funny(X0) | creative(X0)) => (~strong(X0) | calm(X0))) [input p8]
16. ? [X0] : (~calm(X0) | quiet(X0)) => ~old(paul) [input p15]
18. wise(paul) [input p17]
24. patient(alice) [input hypothesis]
26. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X1] : (~creative(X1) <~> ~patient(X1)) [rectify 6]
33. ! [X0] : ((~strong(X0) | calm(X0)) | (~funny(X0) & ~creative(X0))) [ennf transformation 9]
34. ! [X0] : (~strong(X0) | calm(X0) | (~funny(X0) & ~creative(X0))) [flattening 33]
38. ~old(paul) | ! [X0] : (calm(X0) & ~quiet(X0)) [ennf transformation 16]
39. ! [X0] : (((wise(X0) | old(X0)) | (creative(X0) | ~funny(X0))) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 1]
40. ! [X0] : ((wise(X0) | old(X0) | creative(X0) | ~funny(X0)) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [flattening 39]
50. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : ((~creative(X1) | patient(X1)) & (~patient(X1) | creative(X1)))) & (? [X1] : ((patient(X1) | creative(X1)) & (~patient(X1) | ~creative(X1))) | ! [X0] : (calm(X0) | kind(X0))) [nnf transformation 26]
51. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : ((~creative(X1) | patient(X1)) & (~patient(X1) | creative(X1)))) & (? [X2] : ((patient(X2) | creative(X2)) & (~patient(X2) | ~creative(X2))) | ! [X3] : (calm(X3) | kind(X3))) [rectify 50]
52. ? [X0] : (~calm(X0) & ~kind(X0)) => (~calm(sK2) & ~kind(sK2)) [choice axiom]
53. ? [X2] : ((patient(X2) | creative(X2)) & (~patient(X2) | ~creative(X2))) => ((patient(sK3) | creative(sK3)) & (~patient(sK3) | ~creative(sK3))) [choice axiom]
54. ((~calm(sK2) & ~kind(sK2)) | ! [X1] : ((~creative(X1) | patient(X1)) & (~patient(X1) | creative(X1)))) & (((patient(sK3) | creative(sK3)) & (~patient(sK3) | ~creative(sK3))) | ! [X3] : (calm(X3) | kind(X3))) [skolemisation 51,53,52]
59. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (~old(X0) | ~happy(X0)))) [nnf transformation 8]
60. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ~old(X0) | ~happy(X0))) [flattening 59]
86. ~wise(X0) | funny(X0) [cnf transformation 40]
87. ~creative(X0) | ~old(X0) [cnf transformation 40]
104. ~calm(sK2) | ~patient(X1) | creative(X1) [cnf transformation 54]
112. strong(X0) | old(X0) [cnf transformation 60]
113. ~calm(X0) | old(X0) [cnf transformation 60]
114. ~strong(X0) | calm(X0) | ~creative(X0) [cnf transformation 34]
115. ~strong(X0) | calm(X0) | ~funny(X0) [cnf transformation 34]
136. ~old(paul) | calm(X0) [cnf transformation 38]
138. wise(paul) [cnf transformation 18]
147. patient(alice) [cnf transformation 24]
174. 7 <=> calm(sK2) [avatar definition]
176. ~calm(sK2) <- (~7) [avatar component clause 174]
179. 8 <=> ! [X1] : (~patient(X1) | creative(X1)) [avatar definition]
180. ~patient(X1) | creative(X1) <- (8) [avatar component clause 179]
181. 8 | ~7 [avatar split clause 104,174,179]
298. 34 <=> ! [X0] : calm(X0) [avatar definition]
299. calm(X0) <- (34) [avatar component clause 298]
301. 35 <=> old(paul) [avatar definition]
304. 34 | ~35 [avatar split clause 136,301,298]
341. funny(paul) [resolution 86,138]
357. creative(alice) <- (8) [resolution 180,147]
375. calm(X0) | ~creative(X0) | old(X0) [resolution 114,112]
376. ~creative(X0) | old(X0) [subsumption resolution 375,113]
377. ~creative(X0) [subsumption resolution 376,87]
378. $false <- (8) [resolution 377,357]
379. ~8 [avatar contradiction clause 378]
382. calm(X0) | ~funny(X0) | old(X0) [resolution 115,112]
383. ~funny(X0) | old(X0) [subsumption resolution 382,113]
486. old(paul) [resolution 383,341]
490. 35 [avatar split clause 486,301]
496. $false <- (~7, 34) [resolution 299,176]
501. 7 | ~34 [avatar contradiction clause 496]
504. $false [avatar sat refutation 181,304,379,490,501]
% SZS output end Proof for 3218951414033954332247263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or brave is rich.
If mary is patient or strong then paul is not generous or strong.
Everyone who is either happy or kind is both not brave and patient and vice versa.
Everyone who is either creative or calm is not happy or brave and vice versa.
Everyone who is patient or not happy is humble.
Everyone who is either not strong or happy is not happy or brave and vice versa.
If someone is tall or quiet then someone is either quiet or generous and vice versa.
If someone is either quiet or not curious then someone is both not humble and quiet.
Everyone who is kind is curious or not old and vice versa.
If someone is either not generous or wise then someone is either not happy or not brave and vice versa.
Everyone who is both not humble and not curious is not humble.
Everyone who is both not old and strong is not kind or rich and vice versa.
If john is both humble and kind then someone is either old or brave.
Everyone who is not calm or not quiet is either not brave or not calm and vice versa.
Everyone who is either quiet or rich is either not old or not curious.
If susan is not rich or humble then fred is either curious or not curious and vice versa.
John is either not generous or quiet.
Someone is not brave or rich.
John is wise or humble.
Lucy is either quiet or not strong.
John is both funny and creative.
Alice is both not curious and not generous.
Susan is either rich or not patient. | Mary is kind. | entailment | (![X]:((~brave(X)<~>brave(X))=>rich(X)))&
(((patient(mary)|strong(mary)))=>((~generous(paul)|strong(paul))))&
(![X]:((happy(X)<~>kind(X))<=>(~brave(X)&patient(X))))&
(![X]:((creative(X)<~>calm(X))<=>(~happy(X)|brave(X))))&
(![X]:((patient(X)|~happy(X))=>humble(X)))&
(![X]:((~strong(X)<~>happy(X))<=>(~happy(X)|brave(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((quiet(X)<~>generous(X)))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:(kind(X)<=>(curious(X)|~old(X))))&
((?[X]:((~generous(X)<~>wise(X))))<=>(?[X]:((~happy(X)<~>~brave(X)))))&
(![X]:((~humble(X)&~curious(X))=>~humble(X)))&
(![X]:((~old(X)&strong(X))<=>(~kind(X)|rich(X))))&
(((humble(john)&kind(john)))=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~quiet(X))<=>(~brave(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>rich(X))=>(~old(X)<~>~curious(X))))&
(((~rich(susan)|humble(susan)))<=>((curious(fred)<~>~curious(fred))))&
((~generous(john)<~>quiet(john)))&
(?[X]:((~brave(X)|rich(X))))&
((wise(john)|humble(john)))&
((quiet(lucy)<~>~strong(lucy)))&
((funny(john)&creative(john)))&
((~curious(alice)&~generous(alice)))&
((rich(susan)<~>~patient(susan))) | kind(mary) | [
"p0",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6584115236769000790668161
% SZS output start Proof for 6584115236769000790668161
1. ! [X0] : ((~brave(X0) <~> brave(X0)) => rich(X0)) [input p0]
9. ! [X0] : (kind(X0) <=> (~old(X0) | curious(X0))) [input p8]
12. ! [X0] : ((strong(X0) & ~old(X0)) <=> (rich(X0) | ~kind(X0))) [input p11]
24. ~kind(mary) [input hypothesis]
29. ! [X0] : (rich(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 1]
39. ! [X0] : (rich(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 29]
55. ! [X0] : ((kind(X0) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | ~kind(X0))) [nnf transformation 9]
56. ! [X0] : ((kind(X0) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | ~kind(X0))) [flattening 55]
62. ! [X0] : (((strong(X0) & ~old(X0)) | (~rich(X0) & kind(X0))) & ((rich(X0) | ~kind(X0)) | (~strong(X0) | old(X0)))) [nnf transformation 12]
63. ! [X0] : (((strong(X0) & ~old(X0)) | (~rich(X0) & kind(X0))) & (rich(X0) | ~kind(X0) | ~strong(X0) | old(X0))) [flattening 62]
77. rich(X0) | brave(X0) | brave(X0) [cnf transformation 39]
78. rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 39]
113. old(X0) | kind(X0) [cnf transformation 56]
125. ~old(X0) | ~rich(X0) [cnf transformation 63]
157. ~kind(mary) [cnf transformation 24]
164. rich(X0) | brave(X0) [duplicate literal removal 77]
165. rich(X0) | ~brave(X0) [duplicate literal removal 78]
166. rich(X0) [subsumption resolution 164,165]
275. ~old(X0) [subsumption resolution 125,166]
323. kind(X0) [resolution 113,275]
324. $false [resolution 323,157]
% SZS output end Proof for 6584115236769000790668161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not brave and kind then susan is rich or quiet.
Everyone who is either rich or not funny is either rich or creative.
Everyone who is strong is either not patient or calm and vice versa.
Everyone who is both kind and generous is both generous and not curious.
Everyone who is both quiet and funny is both not creative and not quiet.
Everyone who is either not curious or rich is curious and vice versa.
Everyone who is calm is both not strong and not curious and vice versa.
If lucy is brave then john is both not strong and not curious and vice versa.
Everyone who is creative or not tall is either not curious or not funny and vice versa.
Everyone who is both curious and not rich is wise.
If fred is old then someone is both strong and not humble and vice versa.
Everyone who is not generous is wise or humble and vice versa.
If someone is both calm and humble then someone is both not old and not brave.
If someone is old or quiet then someone is not rich.
Everyone who is both wise and not rich is both not brave and humble and vice versa.
Everyone who is both calm and not brave is either not patient or not strong and vice versa.
Lucy is both happy and not tall.
Someone is not curious.
Someone is either not brave or calm.
John is either wise or brave.
Someone is generous or not patient.
John is tall or patient.
Someone is not funny. | Mary is quiet. | contradiction | (((~brave(mary)&kind(mary)))=>((rich(susan)|quiet(susan))))&
(![X]:((rich(X)<~>~funny(X))=>(rich(X)<~>creative(X))))&
(![X]:(strong(X)<=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)&generous(X))=>(generous(X)&~curious(X))))&
(![X]:((quiet(X)&funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)<~>rich(X))<=>curious(X)))&
(![X]:(calm(X)<=>(~strong(X)&~curious(X))))&
((brave(lucy))<=>((~strong(john)&~curious(john))))&
(![X]:((creative(X)|~tall(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((curious(X)&~rich(X))=>wise(X)))&
((old(fred))<=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:(~generous(X)<=>(wise(X)|humble(X))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((~old(X)&~brave(X)))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&~rich(X))<=>(~brave(X)&humble(X))))&
(![X]:((calm(X)&~brave(X))<=>(~patient(X)<~>~strong(X))))&
((happy(lucy)&~tall(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:((~brave(X)<~>calm(X))))&
((wise(john)<~>brave(john)))&
(?[X]:((generous(X)|~patient(X))))&
((tall(john)|patient(john)))&
(?[X]:(~funny(X))) | quiet(mary) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8452583111933969127433975
% SZS output start Proof for 8452583111933969127433975
6. ! [X0] : ((~curious(X0) <~> rich(X0)) <=> curious(X0)) [input p5]
14. ? [X0] : (quiet(X0) | old(X0)) => ? [X0] : ~rich(X0) [input p13]
24. quiet(mary) [input hypothesis]
26. ? [X0] : (quiet(X0) | old(X0)) => ? [X1] : ~rich(X1) [rectify 14]
38. ? [X1] : ~rich(X1) | ! [X0] : (~quiet(X0) & ~old(X0)) [ennf transformation 26]
41. ! [X0] : ((((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0))))) [nnf transformation 6]
55. ? [X0] : ~rich(X0) | ! [X1] : (~quiet(X1) & ~old(X1)) [rectify 38]
56. ? [X0] : ~rich(X0) => ~rich(sK2) [choice axiom]
57. ~rich(sK2) | ! [X1] : (~quiet(X1) & ~old(X1)) [skolemisation 55,56]
82. curious(X0) | rich(X0) | curious(X0) [cnf transformation 41]
84. rich(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 41]
107. ~rich(sK2) | ~quiet(X1) [cnf transformation 57]
127. quiet(mary) [cnf transformation 24]
128. curious(X0) | rich(X0) [duplicate literal removal 82]
129. rich(X0) | ~curious(X0) [duplicate literal removal 84]
133. rich(X0) [subsumption resolution 128,129]
180. ~quiet(X1) [subsumption resolution 107,133]
216. $false [subsumption resolution 127,180]
% SZS output end Proof for 8452583111933969127433975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not creative and not calm then someone is both not rich and not funny.
Everyone who is not funny is not strong or not patient.
If someone is either not calm or not patient then someone is wise or curious.
Everyone who is wise is generous or not generous and vice versa.
Everyone who is tall is not tall or not creative and vice versa.
Everyone who is both patient and tall is either calm or strong.
If john is generous then someone is either not creative or patient and vice versa.
Everyone who is not wise is either not funny or old.
If someone is both not strong and kind then someone is not creative or rich.
Everyone who is not patient is quiet or happy and vice versa.
Everyone who is both patient and kind is not strong.
Everyone who is quiet is either happy or strong.
If someone is either not generous or patient then someone is either not brave or patient.
If someone is either wise or not generous then someone is both not humble and not strong.
If john is not curious or patient then lucy is strong or not patient.
Alice is either kind or generous.
Someone is either not patient or strong.
Paul is either not curious or not old.
John is either not old or calm.
John is rich or not rich.
Someone is both not kind and calm. | John is not creative. | entailment | (((~creative(fred)&~calm(fred)))=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:(~funny(X)=>(~strong(X)|~patient(X))))&
((?[X]:((~calm(X)<~>~patient(X))))=>(?[X]:((wise(X)|curious(X)))))&
(![X]:(wise(X)<=>(generous(X)|~generous(X))))&
(![X]:(tall(X)<=>(~tall(X)|~creative(X))))&
(![X]:((patient(X)&tall(X))=>(calm(X)<~>strong(X))))&
((generous(john))<=>(?[X]:((~creative(X)<~>patient(X)))))&
(![X]:(~wise(X)=>(~funny(X)<~>old(X))))&
((?[X]:((~strong(X)&kind(X))))=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:(~patient(X)<=>(quiet(X)|happy(X))))&
(![X]:((patient(X)&kind(X))=>~strong(X)))&
(![X]:(quiet(X)=>(happy(X)<~>strong(X))))&
((?[X]:((~generous(X)<~>patient(X))))=>(?[X]:((~brave(X)<~>patient(X)))))&
((?[X]:((wise(X)<~>~generous(X))))=>(?[X]:((~humble(X)&~strong(X)))))&
(((~curious(john)|patient(john)))=>((strong(lucy)|~patient(lucy))))&
((kind(alice)<~>generous(alice)))&
(?[X]:((~patient(X)<~>strong(X))))&
((~curious(paul)<~>~old(paul)))&
((~old(john)<~>calm(john)))&
((rich(john)|~rich(john)))&
(?[X]:((~kind(X)&calm(X)))) | ~creative(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5684475949022553852977982
% SZS output start Proof for 5684475949022553852977982
5. ! [X0] : (tall(X0) <=> (~creative(X0) | ~tall(X0))) [input p4]
22. creative(john) [input hypothesis]
52. ! [X0] : ((tall(X0) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | ~tall(X0))) [nnf transformation 5]
53. ! [X0] : ((tall(X0) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~tall(X0))) [flattening 52]
90. ~creative(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 53]
91. tall(X0) | tall(X0) [cnf transformation 53]
127. creative(john) [cnf transformation 22]
128. ~creative(X0) | ~tall(X0) [duplicate literal removal 90]
129. tall(X0) [duplicate literal removal 91]
165. ~creative(X0) [subsumption resolution 128,129]
268. $false [subsumption resolution 127,165]
% SZS output end Proof for 5684475949022553852977982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and rich then someone is rich or strong.
Everyone who is both not rich and not strong is quiet and vice versa.
If susan is not curious then paul is not generous or not wise.
Everyone who is not creative is not tall and vice versa.
Everyone who is either not humble or tall is not strong or not happy.
Everyone who is creative or quiet is either calm or brave.
If lucy is either not quiet or not funny then someone is both not quiet and not old and vice versa.
Everyone who is not wise is either not curious or old and vice versa.
Everyone who is patient is either quiet or not strong and vice versa.
Everyone who is either not patient or brave is creative or not generous and vice versa.
Everyone who is either not patient or not tall is creative and vice versa.
Everyone who is either tall or brave is not rich and vice versa.
If someone is rich then someone is either humble or not creative and vice versa.
Everyone who is either not kind or not calm is kind and vice versa.
If fred is patient then someone is either humble or tall.
Everyone who is either rich or not calm is calm or strong and vice versa.
Fred is either happy or not tall.
Someone is either happy or old.
Someone is either kind or not curious.
Paul is both curious and old. | Susan is strong. | entailment | ((?[X]:((strong(X)&rich(X))))=>(?[X]:((rich(X)|strong(X)))))&
(![X]:((~rich(X)&~strong(X))<=>quiet(X)))&
((~curious(susan))=>((~generous(paul)|~wise(paul))))&
(![X]:(~creative(X)<=>~tall(X)))&
(![X]:((~humble(X)<~>tall(X))=>(~strong(X)|~happy(X))))&
(![X]:((creative(X)|quiet(X))=>(calm(X)<~>brave(X))))&
(((~quiet(lucy)<~>~funny(lucy)))<=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:(~wise(X)<=>(~curious(X)<~>old(X))))&
(![X]:(patient(X)<=>(quiet(X)<~>~strong(X))))&
(![X]:((~patient(X)<~>brave(X))<=>(creative(X)|~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>creative(X)))&
(![X]:((tall(X)<~>brave(X))<=>~rich(X)))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>kind(X)))&
((patient(fred))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((rich(X)<~>~calm(X))<=>(calm(X)|strong(X))))&
((happy(fred)<~>~tall(fred)))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((kind(X)<~>~curious(X))))&
((curious(paul)&old(paul))) | strong(susan) | [
"p1",
"p3",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6287965014229113649302361
% SZS output start Proof for 6287965014229113649302361
2. ! [X0] : ((~strong(X0) & ~rich(X0)) <=> quiet(X0)) [input p1]
4. ! [X0] : (~creative(X0) <=> ~tall(X0)) [input p3]
9. ! [X0] : (patient(X0) <=> (quiet(X0) <~> ~strong(X0))) [input p8]
11. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> creative(X0)) [input p10]
14. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> kind(X0)) [input p13]
16. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> (strong(X0) | calm(X0))) [input p15]
21. ~strong(susan) [input hypothesis]
36. ! [X0] : (((~strong(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (strong(X0) | rich(X0)))) [nnf transformation 2]
37. ! [X0] : (((~strong(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | strong(X0) | rich(X0))) [flattening 36]
38. ! [X0] : ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0))) [nnf transformation 4]
46. ! [X0] : ((patient(X0) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | ~patient(X0))) [nnf transformation 9]
49. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ~creative(X0)) & (creative(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 11]
56. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | ~kind(X0)) & (kind(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 14]
60. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~strong(X0) & ~calm(X0))) & ((strong(X0) | calm(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [nnf transformation 16]
61. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (~strong(X0) & ~calm(X0))) & (strong(X0) | calm(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [flattening 60]
71. ~quiet(X0) | ~rich(X0) [cnf transformation 37]
74. ~tall(X0) | creative(X0) [cnf transformation 38]
75. ~creative(X0) | tall(X0) [cnf transformation 38]
93. patient(X0) | quiet(X0) | strong(X0) [cnf transformation 46]
101. creative(X0) | ~patient(X0) | tall(X0) [cnf transformation 49]
102. ~tall(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 49]
112. kind(X0) | ~calm(X0) | kind(X0) [cnf transformation 56]
114. ~calm(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 56]
119. strong(X0) | calm(X0) | rich(X0) | calm(X0) [cnf transformation 61]
123. calm(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 61]
132. ~strong(susan) [cnf transformation 21]
133. strong(X0) | calm(X0) | rich(X0) [duplicate literal removal 119]
135. kind(X0) | ~calm(X0) [duplicate literal removal 112]
136. ~kind(X0) | ~calm(X0) [duplicate literal removal 114]
138. 1 <=> ! [X1] : (~rich(X1) | ~strong(X1)) [avatar definition]
139. ~rich(X1) | ~strong(X1) <- (1) [avatar component clause 138]
189. ~patient(X0) | ~tall(X0) [subsumption resolution 102,74]
190. ~patient(X0) | tall(X0) [subsumption resolution 101,75]
191. ~patient(X0) [subsumption resolution 190,189]
205. 15 <=> ! [X3] : ~rich(X3) [avatar definition]
206. ~rich(X3) <- (15) [avatar component clause 205]
217. ~calm(X0) [subsumption resolution 135,136]
218. ~rich(X0) | ~strong(X0) [subsumption resolution 123,217]
219. 1 [avatar split clause 218,138]
220. rich(X0) | strong(X0) [subsumption resolution 133,217]
274. quiet(X3) | strong(X3) [resolution 93,191]
278. strong(X2) | ~rich(X2) [resolution 274,71]
282. ~rich(X2) <- (1) [subsumption resolution 278,139]
283. 15 | ~1 [avatar split clause 282,138,205]
285. strong(X0) <- (15) [resolution 206,220]
287. $false <- (15) [resolution 285,132]
288. ~15 [avatar contradiction clause 287]
289. $false [avatar sat refutation 219,283,288]
% SZS output end Proof for 6287965014229113649302361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not generous or tall then paul is either not wise or not funny and vice versa.
If mary is quiet then someone is both quiet and funny.
If someone is not wise or not strong then someone is both not curious and not wise.
Everyone who is either old or not humble is not calm or not wise.
Everyone who is creative is either not old or not tall.
Everyone who is not wise or not creative is quiet or not brave and vice versa.
If alice is not quiet or not creative then someone is both patient and funny.
Everyone who is either not creative or not funny is either kind or calm and vice versa.
If john is not creative then john is happy or not creative and vice versa.
Everyone who is not happy is both not creative and strong.
Everyone who is both not kind and not old is not rich and vice versa.
Everyone who is either generous or rich is not happy.
If mary is tall or not creative then paul is both old and not strong.
Everyone who is not wise or not patient is either not happy or not creative.
Paul is not humble.
Fred is either creative or not patient.
Susan is tall.
Susan is both creative and brave.
Fred is not brave.
Paul is rich.
Someone is curious or not funny.
Someone is patient. | Susan is not strong. | neutral | (((~generous(lucy)<~>tall(lucy)))<=>((~wise(paul)<~>~funny(paul))))&
((quiet(mary))=>(?[X]:((quiet(X)&funny(X)))))&
((?[X]:((~wise(X)|~strong(X))))=>(?[X]:((~curious(X)&~wise(X)))))&
(![X]:((old(X)<~>~humble(X))=>(~calm(X)|~wise(X))))&
(![X]:(creative(X)=>(~old(X)<~>~tall(X))))&
(![X]:((~wise(X)|~creative(X))<=>(quiet(X)|~brave(X))))&
(((~quiet(alice)|~creative(alice)))=>(?[X]:((patient(X)&funny(X)))))&
(![X]:((~creative(X)<~>~funny(X))<=>(kind(X)<~>calm(X))))&
((~creative(john))<=>((happy(john)|~creative(john))))&
(![X]:(~happy(X)=>(~creative(X)&strong(X))))&
(![X]:((~kind(X)&~old(X))<=>~rich(X)))&
(![X]:((generous(X)<~>rich(X))=>~happy(X)))&
(((tall(mary)|~creative(mary)))=>((old(paul)&~strong(paul))))&
(![X]:((~wise(X)|~patient(X))=>(~happy(X)<~>~creative(X))))&
(~humble(paul))&
((creative(fred)<~>~patient(fred)))&
(tall(susan))&
((creative(susan)&brave(susan)))&
(~brave(fred))&
(rich(paul))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:(patient(X))) | ~strong(susan) | [] | null | 0 |
Everyone who is not generous or not kind is both happy and not brave. Everyone who is both humble and not rich is not calm or not humble. If lucy is either generous or not patient then susan is not strong and vice versa. If lucy is both curious and humble then john is both not strong and old and vice versa. Everyone who is both not curious and funny is calm. Everyone who is humble is both creative and strong and vice versa. Everyone who is not humble is both not calm and not rich. If someone is either not happy or not humble then fred is either kind or funny and vice versa. If someone is both not happy and wise then someone is both not strong and not calm and vice versa. If someone is either curious or not quiet then someone is not creative. Everyone who is strong or creative is both not rich and not humble. If mary is not quiet or calm then someone is both funny and old and vice versa. If lucy is not humble then someone is quiet. If someone is either not wise or creative then susan is either brave or not brave and vice versa. Everyone who is both tall and not quiet is either not creative or brave. If someone is not strong or not tall then someone is not happy or not patient and vice versa. Someone is not wise. Someone is either wise or generous. Someone is either not brave or humble. Someone is quiet. Paul is funny or humble. Alice is both kind and not brave. Someone is not strong. Alice is either tall or not tall. | John is humble. | contradiction | (![X]:((~generous(X)|~kind(X))=>(happy(X)&~brave(X))))&
(![X]:((humble(X)&~rich(X))=>(~calm(X)|~humble(X))))&
(((generous(lucy)<~>~patient(lucy)))<=>(~strong(susan)))&
(((curious(lucy)&humble(lucy)))<=>((~strong(john)&old(john))))&
(![X]:((~curious(X)&funny(X))=>calm(X)))&
(![X]:(humble(X)<=>(creative(X)&strong(X))))&
(![X]:(~humble(X)=>(~calm(X)&~rich(X))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>((kind(fred)<~>funny(fred))))&
((?[X]:((~happy(X)&wise(X))))<=>(?[X]:((~strong(X)&~calm(X)))))&
((?[X]:((curious(X)<~>~quiet(X))))=>(?[X]:(~creative(X))))&
(![X]:((strong(X)|creative(X))=>(~rich(X)&~humble(X))))&
(((~quiet(mary)|calm(mary)))<=>(?[X]:((funny(X)&old(X)))))&
((~humble(lucy))=>(?[X]:(quiet(X))))&
((?[X]:((~wise(X)<~>creative(X))))<=>((brave(susan)<~>~brave(susan))))&
(![X]:((tall(X)&~quiet(X))=>(~creative(X)<~>brave(X))))&
((?[X]:((~strong(X)|~tall(X))))<=>(?[X]:((~happy(X)|~patient(X)))))&
(?[X]:(~wise(X)))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((~brave(X)<~>humble(X))))&
(?[X]:(quiet(X)))&
((funny(paul)|humble(paul)))&
((kind(alice)&~brave(alice)))&
(?[X]:(~strong(X)))&
((tall(alice)<~>~tall(alice))) | humble(john) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4205395087001268439664409
% SZS output start Proof for 4205395087001268439664409
6. ! [X0] : (humble(X0) <=> (strong(X0) & creative(X0))) [input p5]
11. ! [X0] : ((creative(X0) | strong(X0)) => (~humble(X0) & ~rich(X0))) [input p10]
25. humble(john) [input hypothesis]
36. ! [X0] : ((~humble(X0) & ~rich(X0)) | (~creative(X0) & ~strong(X0))) [ennf transformation 11]
43. ! [X0] : ((humble(X0) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | ~humble(X0))) [nnf transformation 6]
44. ! [X0] : ((humble(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | ~humble(X0))) [flattening 43]
102. creative(X0) | ~humble(X0) [cnf transformation 44]
124. ~humble(X0) | ~creative(X0) [cnf transformation 36]
157. humble(john) [cnf transformation 25]
267. ~humble(X0) [subsumption resolution 124,102]
353. $false [subsumption resolution 157,267]
% SZS output end Proof for 4205395087001268439664409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not humble is either old or rich and vice versa. If someone is either not humble or kind then alice is not happy or not humble. Everyone who is calm or not brave is not old. Everyone who is both not calm and patient is not strong or not tall and vice versa. If john is both not brave and rich then someone is patient or not strong and vice versa. If alice is either not quiet or generous then alice is either not old or calm and vice versa. Everyone who is not generous is either kind or rich and vice versa. If susan is not brave then alice is wise or rich. Everyone who is both tall and not brave is both not happy and not humble. Everyone who is not tall is not brave or old and vice versa. Everyone who is either calm or curious is strong. Everyone who is either not strong or not funny is either tall or not kind and vice versa. If john is tall then someone is both curious and not creative. If someone is patient or not curious then lucy is kind. If mary is both not patient and humble then mary is both not kind and generous and vice versa. Everyone who is either old or quiet is either not humble or patient and vice versa. Susan is not creative. Mary is either not patient or not curious. | Mary is quiet. | contradiction | (![X]:((~rich(X)&~humble(X))<=>(old(X)<~>rich(X))))&
((?[X]:((~humble(X)<~>kind(X))))=>((~happy(alice)|~humble(alice))))&
(![X]:((calm(X)|~brave(X))=>~old(X)))&
(![X]:((~calm(X)&patient(X))<=>(~strong(X)|~tall(X))))&
(((~brave(john)&rich(john)))<=>(?[X]:((patient(X)|~strong(X)))))&
(((~quiet(alice)<~>generous(alice)))<=>((~old(alice)<~>calm(alice))))&
(![X]:(~generous(X)<=>(kind(X)<~>rich(X))))&
((~brave(susan))=>((wise(alice)|rich(alice))))&
(![X]:((tall(X)&~brave(X))=>(~happy(X)&~humble(X))))&
(![X]:(~tall(X)<=>(~brave(X)|old(X))))&
(![X]:((calm(X)<~>curious(X))=>strong(X)))&
(![X]:((~strong(X)<~>~funny(X))<=>(tall(X)<~>~kind(X))))&
((tall(john))=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((patient(X)|~curious(X))))=>(kind(lucy)))&
(((~patient(mary)&humble(mary)))<=>((~kind(mary)&generous(mary))))&
(![X]:((old(X)<~>quiet(X))<=>(~humble(X)<~>patient(X))))&
(~creative(susan))&
((~patient(mary)<~>~curious(mary))) | quiet(mary) | [
"p0",
"p2",
"p3",
"p4",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8353219576172448669465190
% SZS output start Proof for 8353219576172448669465190
1. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (old(X0) <~> rich(X0))) [input p0]
3. ! [X0] : ((~brave(X0) | calm(X0)) => ~old(X0)) [input p2]
4. ! [X0] : ((patient(X0) & ~calm(X0)) <=> (~tall(X0) | ~strong(X0))) [input p3]
5. (rich(john) & ~brave(john)) <=> ? [X0] : (~strong(X0) | patient(X0)) [input p4]
10. ! [X0] : (~tall(X0) <=> (old(X0) | ~brave(X0))) [input p9]
16. ! [X0] : ((old(X0) <~> quiet(X0)) <=> (~humble(X0) <~> patient(X0))) [input p15]
19. quiet(mary) [input hypothesis]
25. ! [X0] : (~old(X0) | (brave(X0) & ~calm(X0))) [ennf transformation 3]
31. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0)))) & (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (humble(X0) | rich(X0)))) [nnf transformation 1]
32. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0)))) & (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | humble(X0) | rich(X0))) [flattening 31]
33. ! [X0] : (((patient(X0) & ~calm(X0)) | (tall(X0) & strong(X0))) & ((~tall(X0) | ~strong(X0)) | (~patient(X0) | calm(X0)))) [nnf transformation 4]
34. ! [X0] : (((patient(X0) & ~calm(X0)) | (tall(X0) & strong(X0))) & (~tall(X0) | ~strong(X0) | ~patient(X0) | calm(X0))) [flattening 33]
35. ((rich(john) & ~brave(john)) | ! [X0] : (strong(X0) & ~patient(X0))) & (? [X0] : (~strong(X0) | patient(X0)) | (~rich(john) | brave(john))) [nnf transformation 5]
36. ((rich(john) & ~brave(john)) | ! [X0] : (strong(X0) & ~patient(X0))) & (? [X0] : (~strong(X0) | patient(X0)) | ~rich(john) | brave(john)) [flattening 35]
37. ((rich(john) & ~brave(john)) | ! [X0] : (strong(X0) & ~patient(X0))) & (? [X1] : (~strong(X1) | patient(X1)) | ~rich(john) | brave(john)) [rectify 36]
38. ? [X1] : (~strong(X1) | patient(X1)) => (~strong(sK0) | patient(sK0)) [choice axiom]
39. ((rich(john) & ~brave(john)) | ! [X0] : (strong(X0) & ~patient(X0))) & ((~strong(sK0) | patient(sK0)) | ~rich(john) | brave(john)) [skolemisation 37,38]
42. ! [X0] : ((~tall(X0) | (~old(X0) & brave(X0))) & ((old(X0) | ~brave(X0)) | tall(X0))) [nnf transformation 10]
43. ! [X0] : ((~tall(X0) | (~old(X0) & brave(X0))) & (old(X0) | ~brave(X0) | tall(X0))) [flattening 42]
50. ! [X0] : ((((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) | ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) & (((~patient(X0) | humble(X0)) & (patient(X0) | ~humble(X0))) | ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0))))) [nnf transformation 16]
52. rich(X0) | old(X0) | humble(X0) | rich(X0) [cnf transformation 32]
55. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 32]
59. ~old(X0) | brave(X0) [cnf transformation 25]
64. tall(X0) | patient(X0) [cnf transformation 34]
66. ~brave(john) | ~patient(X0) [cnf transformation 39]
68. rich(john) | ~patient(X0) [cnf transformation 39]
85. ~tall(X0) | ~old(X0) [cnf transformation 43]
104. patient(X0) | ~humble(X0) | old(X0) | ~quiet(X0) [cnf transformation 50]
109. ~quiet(X0) | ~old(X0) | patient(X0) | humble(X0) [cnf transformation 50]
113. quiet(mary) [cnf transformation 19]
114. rich(X0) | old(X0) | humble(X0) [duplicate literal removal 52]
115. ~rich(X0) | old(X0) [duplicate literal removal 55]
116. old(X0) | humble(X0) [subsumption resolution 114,115]
121. 2 <=> rich(john) [avatar definition]
123. rich(john) <- (2) [avatar component clause 121]
126. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
127. ~patient(X0) <- (3) [avatar component clause 126]
128. 3 | 2 [avatar split clause 68,121,126]
130. 4 <=> brave(john) [avatar definition]
134. 3 | ~4 [avatar split clause 66,130,126]
206. ~quiet(X0) | patient(X0) | humble(X0) [subsumption resolution 109,116]
209. ~quiet(X0) | old(X0) | patient(X0) [subsumption resolution 104,206]
222. ~old(X0) | patient(X0) [resolution 85,64]
223. old(john) <- (2) [resolution 115,123]
226. brave(john) <- (2) [resolution 223,59]
229. 4 | ~2 [avatar split clause 226,121,130]
316. old(mary) | patient(mary) [resolution 209,113]
317. old(mary) <- (3) [subsumption resolution 316,127]
324. patient(mary) <- (3) [resolution 317,222]
327. $false <- (3) [subsumption resolution 324,127]
328. ~3 [avatar contradiction clause 327]
332. $false [avatar sat refutation 128,134,229,328]
% SZS output end Proof for 8353219576172448669465190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and not patient then paul is quiet.
If paul is brave then john is either quiet or not wise.
If someone is happy then alice is brave or not tall.
Everyone who is either kind or wise is either old or brave.
Everyone who is rich or creative is not funny and vice versa.
If susan is either not happy or not funny then someone is both not brave and calm.
If susan is both not calm and tall then someone is both happy and strong and vice versa.
Everyone who is not happy is both happy and quiet and vice versa.
Everyone who is not humble or not curious is not calm or not curious and vice versa.
Everyone who is either not generous or not humble is creative or patient.
Everyone who is both tall and not old is both not patient and not curious and vice versa.
Everyone who is either not wise or generous is creative or not humble and vice versa.
If someone is both not creative and happy then paul is old and vice versa.
Everyone who is both brave and wise is happy or brave.
Everyone who is not quiet or old is both not kind and not old and vice versa.
John is either wise or calm.
Alice is either not kind or patient.
Someone is both creative and not funny.
Someone is either not quiet or not curious.
Paul is either not old or not brave.
Someone is both not kind and tall.
Someone is not calm or calm.
Someone is curious or not rich. | Paul is not brave. | contradiction | ((?[X]:((~rich(X)&~patient(X))))=>(quiet(paul)))&
((brave(paul))=>((quiet(john)<~>~wise(john))))&
((?[X]:(happy(X)))=>((brave(alice)|~tall(alice))))&
(![X]:((kind(X)<~>wise(X))=>(old(X)<~>brave(X))))&
(![X]:((rich(X)|creative(X))<=>~funny(X)))&
(((~happy(susan)<~>~funny(susan)))=>(?[X]:((~brave(X)&calm(X)))))&
(((~calm(susan)&tall(susan)))<=>(?[X]:((happy(X)&strong(X)))))&
(![X]:(~happy(X)<=>(happy(X)&quiet(X))))&
(![X]:((~humble(X)|~curious(X))<=>(~calm(X)|~curious(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(creative(X)|patient(X))))&
(![X]:((tall(X)&~old(X))<=>(~patient(X)&~curious(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(creative(X)|~humble(X))))&
((?[X]:((~creative(X)&happy(X))))<=>(old(paul)))&
(![X]:((brave(X)&wise(X))=>(happy(X)|brave(X))))&
(![X]:((~quiet(X)|old(X))<=>(~kind(X)&~old(X))))&
((wise(john)<~>calm(john)))&
((~kind(alice)<~>patient(alice)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((~quiet(X)<~>~curious(X))))&
((~old(paul)<~>~brave(paul)))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((curious(X)|~rich(X)))) | ~brave(paul) | [
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3933302662818480113342390
% SZS output start Proof for 3933302662818480113342390
15. ! [X0] : ((old(X0) | ~quiet(X0)) <=> (~old(X0) & ~kind(X0))) [input p14]
20. ~old(paul) <~> ~brave(paul) [input p19]
24. ~brave(paul) [input hypothesis]
60. ! [X0] : (((old(X0) | ~quiet(X0)) | (old(X0) | kind(X0))) & ((~old(X0) & ~kind(X0)) | (~old(X0) & quiet(X0)))) [nnf transformation 15]
61. ! [X0] : ((old(X0) | ~quiet(X0) | old(X0) | kind(X0)) & ((~old(X0) & ~kind(X0)) | (~old(X0) & quiet(X0)))) [flattening 60]
69. (brave(paul) | old(paul)) & (~brave(paul) | ~old(paul)) [nnf transformation 20]
121. ~old(X0) | ~old(X0) [cnf transformation 61]
132. brave(paul) | old(paul) [cnf transformation 69]
137. ~brave(paul) [cnf transformation 24]
138. ~old(X0) [duplicate literal removal 121]
151. 3 <=> brave(paul) [avatar definition]
259. brave(paul) [subsumption resolution 132,138]
260. 3 [avatar split clause 259,151]
270. ~3 [avatar split clause 137,151]
271. $false [avatar sat refutation 260,270]
% SZS output end Proof for 3933302662818480113342390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not creative is not curious or wise. Everyone who is not strong is both calm and rich and vice versa. Everyone who is old or not old is either strong or creative and vice versa. Everyone who is either 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 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. Susan is humble. Someone is quiet. Lucy is either not old or not humble. Someone is funny or humble. | Lucy is not generous. | contradiction | (![X]:((~curious(X)<~>~creative(X))=>(~curious(X)|wise(X))))&
(![X]:(~strong(X)<=>(calm(X)&rich(X))))&
(![X]:((old(X)|~old(X))<=>(strong(X)<~>creative(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)|creative(X))=>(~happy(X)&funny(X))))&
((?[X]:(patient(X)))<=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((generous(X)|~curious(X))<=>(calm(X)&~brave(X))))&
(humble(susan))&
(?[X]:(quiet(X)))&
((~old(lucy)<~>~humble(lucy)))&
(?[X]:((funny(X)|humble(X)))) | ~generous(lucy) | [
"p1",
"p3",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9058011574404413998829662
% SZS output start Proof for 9058011574404413998829662
2. ! [X0] : (~strong(X0) <=> (rich(X0) & calm(X0))) [input p1]
4. ! [X0] : ((~generous(X0) <~> rich(X0)) => (~strong(X0) <~> ~old(X0))) [input p3]
7. ! [X0] : (quiet(X0) => (~rich(X0) | ~patient(X0))) [input p6]
9. ! [X0] : ((old(X0) & ~patient(X0)) <=> ~old(X0)) [input p8]
12. ! [X0] : (~quiet(X0) <=> (~kind(X0) & kind(X0))) [input p11]
20. ~generous(lucy) [input hypothesis]
25. ! [X0] : ((~strong(X0) <~> ~old(X0)) | (~generous(X0) <=> rich(X0))) [ennf transformation 4]
28. ! [X0] : ((~rich(X0) | ~patient(X0)) | ~quiet(X0)) [ennf transformation 7]
29. ! [X0] : (~rich(X0) | ~patient(X0) | ~quiet(X0)) [flattening 28]
35. ! [X0] : ((~strong(X0) | (~rich(X0) | ~calm(X0))) & ((rich(X0) & calm(X0)) | strong(X0))) [nnf transformation 2]
36. ! [X0] : ((~strong(X0) | ~rich(X0) | ~calm(X0)) & ((rich(X0) & calm(X0)) | strong(X0))) [flattening 35]
39. ! [X0] : (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) [nnf transformation 25]
46. ! [X0] : (((old(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | (~old(X0) | patient(X0)))) [nnf transformation 9]
47. ! [X0] : (((old(X0) & ~patient(X0)) | old(X0)) & (~old(X0) | ~old(X0) | patient(X0))) [flattening 46]
51. ! [X0] : ((~quiet(X0) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | quiet(X0))) [nnf transformation 12]
52. ! [X0] : ((~quiet(X0) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | quiet(X0))) [flattening 51]
68. rich(X0) | strong(X0) [cnf transformation 36]
76. ~old(X0) | ~strong(X0) | rich(X0) | generous(X0) [cnf transformation 39]
88. ~patient(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 29]
91. ~old(X0) | ~old(X0) | patient(X0) [cnf transformation 47]
93. old(X0) | old(X0) [cnf transformation 47]
103. kind(X0) | quiet(X0) [cnf transformation 52]
104. ~kind(X0) | quiet(X0) [cnf transformation 52]
123. ~generous(lucy) [cnf transformation 20]
124. ~old(X0) | patient(X0) [duplicate literal removal 91]
125. old(X0) [duplicate literal removal 93]
132. ~old(X0) | rich(X0) | generous(X0) [subsumption resolution 76,68]
169. patient(X0) [subsumption resolution 124,125]
184. quiet(X0) [subsumption resolution 103,104]
210. ~rich(X0) | ~quiet(X0) [resolution 88,169]
211. ~rich(X0) [subsumption resolution 210,184]
240. rich(X1) | generous(X1) [resolution 132,125]
241. generous(X1) [subsumption resolution 240,211]
242. $false [resolution 241,123]
% SZS output end Proof for 9058011574404413998829662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not quiet is both brave and not generous and vice versa.
Everyone who is not happy is not funny.
If john is kind or creative then someone is both patient and creative and vice versa.
Everyone who is either generous or quiet is either brave or old and vice versa.
If someone is both kind and not quiet then lucy is rich or not strong.
Everyone who is not old is either not kind or generous.
Everyone who is both kind and not strong is both creative and calm.
Everyone who is either not patient or rich is both not curious and not humble and vice versa.
Everyone who is both generous and calm is both wise and creative and vice versa.
If someone is not quiet then someone is not kind and vice versa.
If alice is both not kind and creative then someone is not funny.
If susan is tall then lucy is not curious or humble.
Everyone who is both not humble and old is strong or not brave and vice versa.
Everyone who is either rich or not creative is not humble.
Everyone who is either not rich or not generous is not creative and vice versa.
Everyone who is not generous or not tall is humble and vice versa.
Mary is kind or not brave.
Someone is both wise and not happy.
Someone is either not patient or happy.
Susan is not curious or tall.
Lucy is not quiet.
John is not kind or strong. | Susan is not quiet. | entailment | (![X]:((strong(X)|~quiet(X))<=>(brave(X)&~generous(X))))&
(![X]:(~happy(X)=>~funny(X)))&
(((kind(john)|creative(john)))<=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((generous(X)<~>quiet(X))<=>(brave(X)<~>old(X))))&
((?[X]:((kind(X)&~quiet(X))))=>((rich(lucy)|~strong(lucy))))&
(![X]:(~old(X)=>(~kind(X)<~>generous(X))))&
(![X]:((kind(X)&~strong(X))=>(creative(X)&calm(X))))&
(![X]:((~patient(X)<~>rich(X))<=>(~curious(X)&~humble(X))))&
(![X]:((generous(X)&calm(X))<=>(wise(X)&creative(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(~kind(X))))&
(((~kind(alice)&creative(alice)))=>(?[X]:(~funny(X))))&
((tall(susan))=>((~curious(lucy)|humble(lucy))))&
(![X]:((~humble(X)&old(X))<=>(strong(X)|~brave(X))))&
(![X]:((rich(X)<~>~creative(X))=>~humble(X)))&
(![X]:((~rich(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((~generous(X)|~tall(X))<=>humble(X)))&
((kind(mary)|~brave(mary)))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:((~patient(X)<~>happy(X))))&
((~curious(susan)|tall(susan)))&
(~quiet(lucy))&
((~kind(john)|strong(john))) | ~quiet(susan) | [
"p0",
"p3",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4733523802156654644113519
% SZS output start Proof for 4733523802156654644113519
1. ! [X0] : ((~quiet(X0) | strong(X0)) <=> (~generous(X0) & brave(X0))) [input p0]
4. ! [X0] : ((generous(X0) <~> quiet(X0)) <=> (brave(X0) <~> old(X0))) [input p3]
13. ! [X0] : ((old(X0) & ~humble(X0)) <=> (~brave(X0) | strong(X0))) [input p12]
14. ! [X0] : ((rich(X0) <~> ~creative(X0)) => ~humble(X0)) [input p13]
15. ! [X0] : ((~rich(X0) <~> ~generous(X0)) <=> ~creative(X0)) [input p14]
16. ! [X0] : ((~tall(X0) | ~generous(X0)) <=> humble(X0)) [input p15]
23. quiet(susan) [input hypothesis]
34. ! [X0] : (~humble(X0) | (rich(X0) <=> ~creative(X0))) [ennf transformation 14]
35. ! [X0] : (((~quiet(X0) | strong(X0)) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | (quiet(X0) & ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((~quiet(X0) | strong(X0) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | (quiet(X0) & ~strong(X0)))) [flattening 35]
42. ! [X0] : ((((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) & (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | ((generous(X0) | ~quiet(X0)) & (quiet(X0) | ~generous(X0))))) [nnf transformation 4]
53. ! [X0] : (((old(X0) & ~humble(X0)) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | (~old(X0) | humble(X0)))) [nnf transformation 13]
54. ! [X0] : (((old(X0) & ~humble(X0)) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ~old(X0) | humble(X0))) [flattening 53]
55. ! [X0] : (~humble(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) [nnf transformation 34]
56. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | creative(X0)) & (~creative(X0) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [nnf transformation 15]
57. ! [X0] : (((~tall(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (tall(X0) & generous(X0)))) [nnf transformation 16]
58. ! [X0] : ((~tall(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (tall(X0) & generous(X0)))) [flattening 57]
65. brave(X0) | quiet(X0) [cnf transformation 36]
66. ~generous(X0) | ~strong(X0) [cnf transformation 36]
67. ~generous(X0) | quiet(X0) [cnf transformation 36]
68. ~brave(X0) | strong(X0) | generous(X0) | ~quiet(X0) [cnf transformation 36]
80. ~quiet(X0) | ~generous(X0) | old(X0) | ~brave(X0) [cnf transformation 42]
81. ~quiet(X0) | ~generous(X0) | brave(X0) | ~old(X0) [cnf transformation 42]
100. ~old(X0) | strong(X0) | ~brave(X0) | humble(X0) [cnf transformation 54]
101. ~humble(X0) | ~strong(X0) [cnf transformation 54]
102. ~humble(X0) | brave(X0) [cnf transformation 54]
104. old(X0) | brave(X0) [cnf transformation 54]
105. ~humble(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 55]
106. ~humble(X0) | rich(X0) | creative(X0) [cnf transformation 55]
107. ~creative(X0) | ~generous(X0) | rich(X0) [cnf transformation 56]
109. ~rich(X0) | ~generous(X0) | creative(X0) [cnf transformation 56]
111. humble(X0) | generous(X0) [cnf transformation 58]
122. quiet(susan) [cnf transformation 23]
147. ~old(X0) | brave(X0) | ~generous(X0) [subsumption resolution 81,65]
148. ~generous(X0) | old(X0) | ~brave(X0) [subsumption resolution 80,67]
223. generous(X0) | brave(X0) [resolution 111,102]
224. generous(X1) | ~strong(X1) [resolution 111,101]
225. ~strong(X1) [subsumption resolution 224,66]
272. brave(X1) | ~generous(X1) | brave(X1) [resolution 147,104]
273. brave(X1) | ~generous(X1) [duplicate literal removal 272]
274. brave(X1) [subsumption resolution 273,223]
302. strong(X0) | generous(X0) | ~quiet(X0) [resolution 68,274]
306. ~quiet(X0) | generous(X0) [subsumption resolution 302,225]
394. generous(susan) [resolution 306,122]
395. old(susan) | ~brave(susan) [resolution 394,148]
399. old(susan) [subsumption resolution 395,274]
407. strong(susan) | ~brave(susan) | humble(susan) [resolution 399,100]
410. ~brave(susan) | humble(susan) [subsumption resolution 407,225]
411. humble(susan) [subsumption resolution 410,274]
416. rich(susan) | creative(susan) [resolution 411,106]
417. ~creative(susan) | ~rich(susan) [resolution 411,105]
423. 33 <=> creative(susan) [avatar definition]
424. ~creative(susan) <- (~33) [avatar component clause 423]
425. creative(susan) <- (33) [avatar component clause 423]
427. 34 <=> rich(susan) [avatar definition]
428. ~rich(susan) <- (~34) [avatar component clause 427]
429. rich(susan) <- (34) [avatar component clause 427]
430. 33 | 34 [avatar split clause 416,427,423]
431. ~34 | ~33 [avatar split clause 417,423,427]
457. ~generous(susan) | creative(susan) <- (34) [resolution 429,109]
459. creative(susan) <- (34) [subsumption resolution 457,394]
460. $false <- (~33, 34) [subsumption resolution 459,424]
461. 33 | ~34 [avatar contradiction clause 460]
488. ~generous(susan) | rich(susan) <- (33) [resolution 425,107]
489. rich(susan) <- (33) [subsumption resolution 488,394]
490. $false <- (33, ~34) [subsumption resolution 489,428]
491. ~33 | 34 [avatar contradiction clause 490]
492. $false [avatar sat refutation 430,431,461,491]
% SZS output end Proof for 4733523802156654644113519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or funny is tall and vice versa.
If alice is both not calm and not patient then someone is either not patient or quiet.
If alice is either not patient or kind then someone is either patient or generous.
Everyone who is either tall or happy is not rich or not tall and vice versa.
Everyone who is both old and not quiet is either creative or generous and vice versa.
Everyone who is both not tall and old is either strong or generous and vice versa.
Everyone who is happy or tall is humble and vice versa.
Everyone who is not kind is either not brave or not funny and vice versa.
If fred is both old and not generous then someone is both rich and brave and vice versa.
Everyone who is not humble or brave is both brave and tall.
If someone is either strong or curious then susan is quiet and vice versa.
If someone is either not strong or funny then someone is not funny and vice versa.
If susan is not tall or old then someone is both not calm and not funny.
Everyone who is not tall or not strong is either kind or not kind and vice versa.
Everyone who is both not quiet and strong is not patient and vice versa.
Everyone who is not brave or quiet is not old.
Someone is either creative or not old.
Susan is funny or brave.
Alice is both quiet and rich.
Paul is strong or rich.
Someone is either not patient or not strong.
John is funny.
Someone is tall or generous.
Alice is not kind or not generous. | Susan is not old. | neutral | (![X]:((~strong(X)|funny(X))<=>tall(X)))&
(((~calm(alice)&~patient(alice)))=>(?[X]:((~patient(X)<~>quiet(X)))))&
(((~patient(alice)<~>kind(alice)))=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((tall(X)<~>happy(X))<=>(~rich(X)|~tall(X))))&
(![X]:((old(X)&~quiet(X))<=>(creative(X)<~>generous(X))))&
(![X]:((~tall(X)&old(X))<=>(strong(X)<~>generous(X))))&
(![X]:((happy(X)|tall(X))<=>humble(X)))&
(![X]:(~kind(X)<=>(~brave(X)<~>~funny(X))))&
(((old(fred)&~generous(fred)))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((~humble(X)|brave(X))=>(brave(X)&tall(X))))&
((?[X]:((strong(X)<~>curious(X))))<=>(quiet(susan)))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:(~funny(X))))&
(((~tall(susan)|old(susan)))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((~quiet(X)&strong(X))<=>~patient(X)))&
(![X]:((~brave(X)|quiet(X))=>~old(X)))&
(?[X]:((creative(X)<~>~old(X))))&
((funny(susan)|brave(susan)))&
((quiet(alice)&rich(alice)))&
((strong(paul)|rich(paul)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(funny(john))&
(?[X]:((tall(X)|generous(X))))&
((~kind(alice)|~generous(alice))) | ~old(susan) | [] | null | 0 |
If paul is either kind or rich then alice is kind or not generous.
If someone is not brave or quiet then lucy is either not generous or creative and vice versa.
If someone is humble then alice is not brave.
If someone is curious then mary is not old and vice versa.
If john is not strong or not wise then john is either not wise or humble and vice versa.
Everyone who is either creative or not brave is either not brave or not humble.
Everyone who is both not quiet and strong is not kind and vice versa.
If susan is both tall and not creative then someone is creative or not calm and vice versa.
If mary is wise then john is not calm.
If someone is either strong or rich then john is not curious and vice versa.
Everyone who is kind or not quiet is both not kind and strong and vice versa.
If someone is both not humble and tall then someone is curious.
Everyone who is both brave and not creative is both not brave and wise and vice versa.
If someone is either not generous or generous then fred is both not old and not funny.
If someone is either not tall or not brave then mary is curious and vice versa.
Everyone who is both rich and not brave is both rich and not wise and vice versa.
Someone is either wise or not kind.
Someone is not old or not rich.
Someone is both humble and calm.
Someone is curious.
Alice is not curious or kind.
Alice is not brave.
Susan is either not calm or not old. | Fred is not kind. | entailment | (((kind(paul)<~>rich(paul)))=>((kind(alice)|~generous(alice))))&
((?[X]:((~brave(X)|quiet(X))))<=>((~generous(lucy)<~>creative(lucy))))&
((?[X]:(humble(X)))=>(~brave(alice)))&
((?[X]:(curious(X)))<=>(~old(mary)))&
(((~strong(john)|~wise(john)))<=>((~wise(john)<~>humble(john))))&
(![X]:((creative(X)<~>~brave(X))=>(~brave(X)<~>~humble(X))))&
(![X]:((~quiet(X)&strong(X))<=>~kind(X)))&
(((tall(susan)&~creative(susan)))<=>(?[X]:((creative(X)|~calm(X)))))&
((wise(mary))=>(~calm(john)))&
((?[X]:((strong(X)<~>rich(X))))<=>(~curious(john)))&
(![X]:((kind(X)|~quiet(X))<=>(~kind(X)&strong(X))))&
((?[X]:((~humble(X)&tall(X))))=>(?[X]:(curious(X))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)&wise(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>((~old(fred)&~funny(fred))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(curious(mary)))&
(![X]:((rich(X)&~brave(X))<=>(rich(X)&~wise(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:((humble(X)&calm(X))))&
(?[X]:(curious(X)))&
((~curious(alice)|kind(alice)))&
(~brave(alice))&
((~calm(susan)<~>~old(susan))) | ~kind(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3465627689180414895599939
% SZS output start Proof for 3465627689180414895599939
11. ! [X0] : ((~quiet(X0) | kind(X0)) <=> (strong(X0) & ~kind(X0))) [input p10]
24. kind(fred) [input hypothesis]
57. ! [X0] : (((~quiet(X0) | kind(X0)) | (~strong(X0) | kind(X0))) & ((strong(X0) & ~kind(X0)) | (quiet(X0) & ~kind(X0)))) [nnf transformation 11]
58. ! [X0] : ((~quiet(X0) | kind(X0) | ~strong(X0) | kind(X0)) & ((strong(X0) & ~kind(X0)) | (quiet(X0) & ~kind(X0)))) [flattening 57]
115. ~kind(X0) | ~kind(X0) [cnf transformation 58]
145. kind(fred) [cnf transformation 24]
150. ~kind(X0) [duplicate literal removal 115]
362. $false [subsumption resolution 145,150]
% SZS output end Proof for 3465627689180414895599939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or creative is not wise and vice versa. Everyone who is wise or not old is both not generous and rich and vice versa. Everyone who is either quiet or happy is both generous and not tall. If mary is either happy or not humble then mary is not curious. Everyone who is both patient and not generous is not creative and vice versa. Everyone who is either not generous or patient is both kind and humble. If alice is either funny or creative then john is curious or not wise. If mary is not kind then john is either not funny or strong. If john is either not brave or not humble then someone is both not strong and old and vice versa. Everyone who is not wise or old is either not strong or patient and vice versa. Everyone who is either curious or not happy is calm and vice versa. Everyone who is not humble is either patient or not kind and vice versa. Everyone who is not calm is curious and vice versa. If someone is both not kind and not strong then someone is both not calm and not generous and vice versa. Everyone who is either wise or not old is both curious and not quiet. If someone is either quiet or happy then someone is either not patient or not quiet. Susan is brave or not quiet. Someone is both wise and not quiet. Susan is not old or funny. Someone is both creative and not funny. John is not tall. Someone is both not curious and calm. Susan is wise or patient. | Susan is happy. | contradiction | (![X]:((~strong(X)|creative(X))<=>~wise(X)))&
(![X]:((wise(X)|~old(X))<=>(~generous(X)&rich(X))))&
(![X]:((quiet(X)<~>happy(X))=>(generous(X)&~tall(X))))&
(((happy(mary)<~>~humble(mary)))=>(~curious(mary)))&
(![X]:((patient(X)&~generous(X))<=>~creative(X)))&
(![X]:((~generous(X)<~>patient(X))=>(kind(X)&humble(X))))&
(((funny(alice)<~>creative(alice)))=>((curious(john)|~wise(john))))&
((~kind(mary))=>((~funny(john)<~>strong(john))))&
(((~brave(john)<~>~humble(john)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~wise(X)|old(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(patient(X)<~>~kind(X))))&
(![X]:(~calm(X)<=>curious(X)))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((wise(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
((?[X]:((quiet(X)<~>happy(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
((brave(susan)|~quiet(susan)))&
(?[X]:((wise(X)&~quiet(X))))&
((~old(susan)|funny(susan)))&
(?[X]:((creative(X)&~funny(X))))&
(~tall(john))&
(?[X]:((~curious(X)&calm(X))))&
((wise(susan)|patient(susan))) | happy(susan) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p9",
"p11",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6964597905400600240113758
% SZS output start Proof for 6964597905400600240113758
1. ! [X0] : ((creative(X0) | ~strong(X0)) <=> ~wise(X0)) [input p0]
2. ! [X0] : ((~old(X0) | wise(X0)) <=> (rich(X0) & ~generous(X0))) [input p1]
3. ! [X0] : ((quiet(X0) <~> happy(X0)) => (~tall(X0) & generous(X0))) [input p2]
5. ! [X0] : ((~generous(X0) & patient(X0)) <=> ~creative(X0)) [input p4]
6. ! [X0] : ((~generous(X0) <~> patient(X0)) => (humble(X0) & kind(X0))) [input p5]
10. ! [X0] : ((old(X0) | ~wise(X0)) <=> (~strong(X0) <~> patient(X0))) [input p9]
12. ! [X0] : (~humble(X0) <=> (patient(X0) <~> ~kind(X0))) [input p11]
15. ! [X0] : ((wise(X0) <~> ~old(X0)) => (~quiet(X0) & curious(X0))) [input p14]
23. patient(susan) | wise(susan) [input p22]
24. happy(susan) [input hypothesis]
28. ! [X0] : ((quiet(X0) <~> happy(X0)) => generous(X0)) [pure predicate removal 3]
29. ! [X0] : (generous(X0) | (quiet(X0) <=> happy(X0))) [ennf transformation 28]
31. ! [X0] : ((humble(X0) & kind(X0)) | (~generous(X0) <=> patient(X0))) [ennf transformation 6]
35. ! [X0] : ((~quiet(X0) & curious(X0)) | (wise(X0) <=> ~old(X0))) [ennf transformation 15]
37. ! [X0] : (((creative(X0) | ~strong(X0)) | wise(X0)) & (~wise(X0) | (~creative(X0) & strong(X0)))) [nnf transformation 1]
38. ! [X0] : ((creative(X0) | ~strong(X0) | wise(X0)) & (~wise(X0) | (~creative(X0) & strong(X0)))) [flattening 37]
39. ! [X0] : (((~old(X0) | wise(X0)) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | (old(X0) & ~wise(X0)))) [nnf transformation 2]
40. ! [X0] : ((~old(X0) | wise(X0) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | (old(X0) & ~wise(X0)))) [flattening 39]
41. ! [X0] : (generous(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) [nnf transformation 29]
43. ! [X0] : (((~generous(X0) & patient(X0)) | creative(X0)) & (~creative(X0) | (generous(X0) | ~patient(X0)))) [nnf transformation 5]
44. ! [X0] : (((~generous(X0) & patient(X0)) | creative(X0)) & (~creative(X0) | generous(X0) | ~patient(X0))) [flattening 43]
45. ! [X0] : ((humble(X0) & kind(X0)) | ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0)))) [nnf transformation 31]
52. ! [X0] : (((old(X0) | ~wise(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~old(X0) & wise(X0)))) [nnf transformation 10]
53. ! [X0] : ((old(X0) | ~wise(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~old(X0) & wise(X0)))) [flattening 52]
55. ! [X0] : ((~humble(X0) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | humble(X0))) [nnf transformation 12]
62. ! [X0] : ((~quiet(X0) & curious(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) [nnf transformation 35]
73. ~wise(X0) | strong(X0) [cnf transformation 38]
74. ~wise(X0) | ~creative(X0) [cnf transformation 38]
75. ~strong(X0) | creative(X0) | wise(X0) [cnf transformation 38]
76. ~generous(X0) | ~wise(X0) [cnf transformation 40]
82. ~happy(X0) | quiet(X0) | generous(X0) [cnf transformation 41]
85. ~patient(X0) | generous(X0) | ~creative(X0) [cnf transformation 44]
86. patient(X0) | creative(X0) [cnf transformation 44]
89. ~patient(X0) | ~generous(X0) | kind(X0) [cnf transformation 45]
91. ~patient(X0) | ~generous(X0) | humble(X0) [cnf transformation 45]
104. ~patient(X0) | strong(X0) | wise(X0) [cnf transformation 53]
107. old(X0) | ~wise(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 53]
114. ~kind(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 55]
124. ~quiet(X0) | ~old(X0) | ~wise(X0) [cnf transformation 62]
138. patient(susan) | wise(susan) [cnf transformation 23]
139. happy(susan) [cnf transformation 24]
211. ~patient(X0) | ~wise(X0) | old(X0) [subsumption resolution 107,73]
212. ~patient(X0) | strong(X0) [subsumption resolution 104,73]
262. 27 <=> quiet(susan) [avatar definition]
263. quiet(susan) <- (27) [avatar component clause 262]
264. ~quiet(susan) <- (~27) [avatar component clause 262]
267. 28 <=> old(susan) [avatar definition]
276. 30 <=> wise(susan) [avatar definition]
278. wise(susan) <- (30) [avatar component clause 276]
280. 31 <=> patient(susan) [avatar definition]
282. patient(susan) <- (31) [avatar component clause 280]
283. 30 | 31 [avatar split clause 138,280,276]
315. quiet(susan) | generous(susan) [resolution 82,139]
316. generous(susan) <- (~27) [subsumption resolution 315,264]
319. ~wise(susan) <- (~27) [resolution 316,76]
324. $false <- (~27, 30) [subsumption resolution 319,278]
325. 27 | ~30 [avatar contradiction clause 324]
327. 34 <=> generous(susan) [avatar definition]
328. ~generous(susan) <- (~34) [avatar component clause 327]
329. generous(susan) <- (34) [avatar component clause 327]
505. ~old(susan) | ~wise(susan) <- (27) [resolution 124,263]
519. ~wise(X1) | old(X1) | creative(X1) [resolution 211,86]
523. ~wise(X1) | old(X1) [subsumption resolution 519,74]
581. generous(susan) | ~creative(susan) <- (31) [resolution 282,85]
582. ~generous(susan) | kind(susan) <- (31) [resolution 282,89]
583. ~generous(susan) | humble(susan) <- (31) [resolution 282,91]
587. strong(susan) <- (31) [resolution 282,212]
588. kind(susan) <- (31, 34) [subsumption resolution 582,329]
589. humble(susan) <- (31, 34) [subsumption resolution 583,329]
591. creative(susan) | wise(susan) <- (31) [resolution 587,75]
592. ~humble(susan) | ~patient(susan) <- (31, 34) [resolution 588,114]
594. ~patient(susan) <- (31, 34) [subsumption resolution 592,589]
595. $false <- (31, 34) [subsumption resolution 594,282]
596. ~31 | ~34 [avatar contradiction clause 595]
617. ~creative(susan) <- (31, ~34) [subsumption resolution 581,328]
618. wise(susan) <- (31, ~34) [subsumption resolution 591,617]
619. 30 | ~31 | 34 [avatar split clause 618,327,280,276]
647. old(susan) <- (30) [resolution 523,278]
654. 28 | ~30 [avatar split clause 647,276,267]
655. ~old(susan) <- (27, 30) [subsumption resolution 505,278]
656. ~28 | ~27 | ~30 [avatar split clause 655,276,262,267]
657. $false [avatar sat refutation 283,325,596,619,654,656]
% SZS output end Proof for 6964597905400600240113758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and brave is not tall and vice versa.
Everyone who is funny is both not curious and not quiet.
Everyone who is creative or rich is happy and vice versa.
Everyone who is not old or humble is not kind and vice versa.
Everyone who is not calm or humble is not creative or strong and vice versa.
If fred is both happy and patient then someone is humble or not wise and vice versa.
If john is either humble or happy then susan is both not brave and not rich.
Everyone who is either funny or rich is either not creative or not funny.
Everyone who is both patient and rich is both strong and humble.
Everyone who is not funny is not creative or tall and vice versa.
Everyone who is humble is both brave and not old.
Everyone who is both not brave and not wise is both rich and not quiet.
Everyone who is happy or patient is both not humble and humble and vice versa.
Everyone who is either tall or curious is calm or creative and vice versa.
If paul is not tall then someone is happy or brave.
If someone is not humble then lucy is brave or not humble and vice versa.
Someone is not calm.
Someone is both not funny and not rich.
Fred is kind or wise.
Someone is strong or not humble.
Fred is not funny or not old. | Lucy is humble. | contradiction | (![X]:((rich(X)&brave(X))<=>~tall(X)))&
(![X]:(funny(X)=>(~curious(X)&~quiet(X))))&
(![X]:((creative(X)|rich(X))<=>happy(X)))&
(![X]:((~old(X)|humble(X))<=>~kind(X)))&
(![X]:((~calm(X)|humble(X))<=>(~creative(X)|strong(X))))&
(((happy(fred)&patient(fred)))<=>(?[X]:((humble(X)|~wise(X)))))&
(((humble(john)<~>happy(john)))=>((~brave(susan)&~rich(susan))))&
(![X]:((funny(X)<~>rich(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((patient(X)&rich(X))=>(strong(X)&humble(X))))&
(![X]:(~funny(X)<=>(~creative(X)|tall(X))))&
(![X]:(humble(X)=>(brave(X)&~old(X))))&
(![X]:((~brave(X)&~wise(X))=>(rich(X)&~quiet(X))))&
(![X]:((happy(X)|patient(X))<=>(~humble(X)&humble(X))))&
(![X]:((tall(X)<~>curious(X))<=>(calm(X)|creative(X))))&
((~tall(paul))=>(?[X]:((happy(X)|brave(X)))))&
((?[X]:(~humble(X)))<=>((brave(lucy)|~humble(lucy))))&
(?[X]:(~calm(X)))&
(?[X]:((~funny(X)&~rich(X))))&
((kind(fred)|wise(fred)))&
(?[X]:((strong(X)|~humble(X))))&
((~funny(fred)|~old(fred))) | humble(lucy) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4183987386504839792126375
% SZS output start Proof for 4183987386504839792126375
6. (patient(fred) & happy(fred)) <=> ? [X0] : (~wise(X0) | humble(X0)) [input p5]
13. ! [X0] : ((patient(X0) | happy(X0)) <=> (humble(X0) & ~humble(X0))) [input p12]
22. humble(lucy) [input hypothesis]
42. ((patient(fred) & happy(fred)) | ! [X0] : (wise(X0) & ~humble(X0))) & (? [X0] : (~wise(X0) | humble(X0)) | (~patient(fred) | ~happy(fred))) [nnf transformation 6]
43. ((patient(fred) & happy(fred)) | ! [X0] : (wise(X0) & ~humble(X0))) & (? [X0] : (~wise(X0) | humble(X0)) | ~patient(fred) | ~happy(fred)) [flattening 42]
44. ((patient(fred) & happy(fred)) | ! [X0] : (wise(X0) & ~humble(X0))) & (? [X1] : (~wise(X1) | humble(X1)) | ~patient(fred) | ~happy(fred)) [rectify 43]
45. ? [X1] : (~wise(X1) | humble(X1)) => (~wise(sK0) | humble(sK0)) [choice axiom]
46. ((patient(fred) & happy(fred)) | ! [X0] : (wise(X0) & ~humble(X0))) & ((~wise(sK0) | humble(sK0)) | ~patient(fred) | ~happy(fred)) [skolemisation 44,45]
51. ! [X0] : (((patient(X0) | happy(X0)) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | (~patient(X0) & ~happy(X0)))) [nnf transformation 13]
52. ! [X0] : ((patient(X0) | happy(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | (~patient(X0) & ~happy(X0)))) [flattening 51]
82. happy(fred) | ~humble(X0) [cnf transformation 46]
102. ~humble(X0) | ~happy(X0) [cnf transformation 52]
104. humble(X0) | ~happy(X0) [cnf transformation 52]
123. humble(lucy) [cnf transformation 22]
135. 3 <=> ! [X0] : ~humble(X0) [avatar definition]
136. ~humble(X0) <- (3) [avatar component clause 135]
139. 4 <=> happy(fred) [avatar definition]
141. happy(fred) <- (4) [avatar component clause 139]
143. 3 | 4 [avatar split clause 82,139,135]
174. ~happy(X0) [subsumption resolution 102,104]
186. 13 <=> humble(lucy) [avatar definition]
188. humble(lucy) <- (13) [avatar component clause 186]
226. 13 [avatar split clause 123,186]
227. $false <- (4) [subsumption resolution 141,174]
228. ~4 [avatar contradiction clause 227]
233. $false <- (3, 13) [resolution 188,136]
234. ~3 | ~13 [avatar contradiction clause 233]
235. $false [avatar sat refutation 143,226,228,234]
% SZS output end Proof for 4183987386504839792126375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm and tall is not rich. If susan is both not curious and tall then mary is not quiet or funny and vice versa. Everyone who is strong is both not quiet and not funny and vice versa. Everyone who is both humble and not curious is either wise or not tall. If mary is either not wise or patient then someone is not rich or not kind and vice versa. If someone is not patient then susan is both old and wise. Everyone who is old or creative is either calm or not tall. Everyone who is not old is both not kind and not tall. If john is both not brave and not old then john is humble. If lucy is either brave or rich then someone is humble and vice versa. Everyone who is brave or funny is both not happy and not tall. If lucy is either not generous or old then mary is not curious and vice versa. If someone is both happy and not humble then fred is not tall or generous. Everyone who is kind or humble is both tall and generous. Everyone who is either funny or kind is not rich or not quiet and vice versa. If alice is not curious or not rich then someone is both happy and generous and vice versa. Someone is creative or not kind. Someone is not old or patient. Someone is creative or not patient. Mary is either creative or brave. Someone is tall or not generous. Someone is calm. Someone is both not brave and not patient. | Susan is old. | entailment | (![X]:((~calm(X)&tall(X))=>~rich(X)))&
(((~curious(susan)&tall(susan)))<=>((~quiet(mary)|funny(mary))))&
(![X]:(strong(X)<=>(~quiet(X)&~funny(X))))&
(![X]:((humble(X)&~curious(X))=>(wise(X)<~>~tall(X))))&
(((~wise(mary)<~>patient(mary)))<=>(?[X]:((~rich(X)|~kind(X)))))&
((?[X]:(~patient(X)))=>((old(susan)&wise(susan))))&
(![X]:((old(X)|creative(X))=>(calm(X)<~>~tall(X))))&
(![X]:(~old(X)=>(~kind(X)&~tall(X))))&
(((~brave(john)&~old(john)))=>(humble(john)))&
(((brave(lucy)<~>rich(lucy)))<=>(?[X]:(humble(X))))&
(![X]:((brave(X)|funny(X))=>(~happy(X)&~tall(X))))&
(((~generous(lucy)<~>old(lucy)))<=>(~curious(mary)))&
((?[X]:((happy(X)&~humble(X))))=>((~tall(fred)|generous(fred))))&
(![X]:((kind(X)|humble(X))=>(tall(X)&generous(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~rich(X)|~quiet(X))))&
(((~curious(alice)|~rich(alice)))<=>(?[X]:((happy(X)&generous(X)))))&
(?[X]:((creative(X)|~kind(X))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((creative(X)|~patient(X))))&
((creative(mary)<~>brave(mary)))&
(?[X]:((tall(X)|~generous(X))))&
(?[X]:(calm(X)))&
(?[X]:((~brave(X)&~patient(X)))) | old(susan) | [
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3287058154609705223404501
% SZS output start Proof for 3287058154609705223404501
6. ? [X0] : ~patient(X0) => (wise(susan) & old(susan)) [input p5]
23. ? [X0] : (~patient(X0) & ~brave(X0)) [input p22]
24. ~old(susan) [input hypothesis]
29. (wise(susan) & old(susan)) | ! [X0] : patient(X0) [ennf transformation 6]
69. ? [X0] : (~patient(X0) & ~brave(X0)) => (~patient(sK8) & ~brave(sK8)) [choice axiom]
70. ~patient(sK8) & ~brave(sK8) [skolemisation 23,69]
85. old(susan) | patient(X0) [cnf transformation 29]
130. ~patient(sK8) [cnf transformation 70]
131. ~old(susan) [cnf transformation 24]
182. 11 <=> ! [X0] : patient(X0) [avatar definition]
183. patient(X0) <- (11) [avatar component clause 182]
190. 13 <=> old(susan) [avatar definition]
193. 11 | 13 [avatar split clause 85,190,182]
324. ~13 [avatar split clause 131,190]
327. $false <- (11) [resolution 183,130]
328. ~11 [avatar contradiction clause 327]
329. $false [avatar sat refutation 193,324,328]
% SZS output end Proof for 3287058154609705223404501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both not strong and creative and vice versa. Everyone who is both quiet and not calm is not happy or happy and vice versa. Everyone who is either curious or strong is not quiet or not brave and vice versa. If someone is not happy then john is rich or happy and vice versa. If someone is creative then paul is not patient and vice versa. If someone is not old then someone is both not brave and not tall. Everyone who is either humble or strong is strong or patient and vice versa. Everyone who is curious or not wise is either quiet or patient. If someone is not kind then someone is old and vice versa. If fred is old or not happy then someone is not curious. If lucy is either calm or not kind then lucy is not brave or patient and vice versa. If someone is not humble or patient then paul is both curious and not patient and vice versa. Everyone who is not funny is both brave and not curious. If someone is calm then someone is either not old or funny and vice versa. Everyone who is either creative or not happy is both humble and not old. Everyone who is both not funny and happy is not kind or happy. Someone is wise. Susan is not brave or not generous. Someone is either not tall or rich. Lucy is either calm or funny. Someone is either not old or creative. Someone is both brave and kind. Paul is wise or tall. Someone is calm or not calm. | Paul is happy. | contradiction | (![X]:(~patient(X)<=>(~strong(X)&creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(~happy(X)|happy(X))))&
(![X]:((curious(X)<~>strong(X))<=>(~quiet(X)|~brave(X))))&
((?[X]:(~happy(X)))<=>((rich(john)|happy(john))))&
((?[X]:(creative(X)))<=>(~patient(paul)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((humble(X)<~>strong(X))<=>(strong(X)|patient(X))))&
(![X]:((curious(X)|~wise(X))=>(quiet(X)<~>patient(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(old(X))))&
(((old(fred)|~happy(fred)))=>(?[X]:(~curious(X))))&
(((calm(lucy)<~>~kind(lucy)))<=>((~brave(lucy)|patient(lucy))))&
((?[X]:((~humble(X)|patient(X))))<=>((curious(paul)&~patient(paul))))&
(![X]:(~funny(X)=>(brave(X)&~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((creative(X)<~>~happy(X))=>(humble(X)&~old(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)|happy(X))))&
(?[X]:(wise(X)))&
((~brave(susan)|~generous(susan)))&
(?[X]:((~tall(X)<~>rich(X))))&
((calm(lucy)<~>funny(lucy)))&
(?[X]:((~old(X)<~>creative(X))))&
(?[X]:((brave(X)&kind(X))))&
((wise(paul)|tall(paul)))&
(?[X]:((calm(X)|~calm(X)))) | happy(paul) | [
"p0",
"p1",
"p6",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 465506229201914325046640
% SZS output start Proof for 465506229201914325046640
1. ! [X0] : (~patient(X0) <=> (creative(X0) & ~strong(X0))) [input p0]
2. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (happy(X0) | ~happy(X0))) [input p1]
7. ! [X0] : ((humble(X0) <~> strong(X0)) <=> (patient(X0) | strong(X0))) [input p6]
8. ! [X0] : ((~wise(X0) | curious(X0)) => (quiet(X0) <~> patient(X0))) [input p7]
12. ? [X0] : (patient(X0) | ~humble(X0)) <=> (~patient(paul) & curious(paul)) [input p11]
15. ! [X0] : ((creative(X0) <~> ~happy(X0)) => (~old(X0) & humble(X0))) [input p14]
25. happy(paul) [input hypothesis]
30. ! [X0] : (curious(X0) => (quiet(X0) <~> patient(X0))) [pure predicate removal 8]
34. ! [X0] : ((quiet(X0) <~> patient(X0)) | ~curious(X0)) [ennf transformation 30]
37. ! [X0] : ((~old(X0) & humble(X0)) | (creative(X0) <=> ~happy(X0))) [ennf transformation 15]
40. ! [X0] : ((~patient(X0) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | patient(X0))) [nnf transformation 1]
41. ! [X0] : ((~patient(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | patient(X0))) [flattening 40]
42. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 2]
43. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | calm(X0) | ~quiet(X0))) [flattening 42]
58. ! [X0] : ((((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0))))) [nnf transformation 7]
59. ! [X0] : ((((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0))))) [flattening 58]
60. ! [X0] : (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | ~curious(X0)) [nnf transformation 34]
70. (? [X0] : (patient(X0) | ~humble(X0)) | (patient(paul) | ~curious(paul))) & ((~patient(paul) & curious(paul)) | ! [X0] : (~patient(X0) & humble(X0))) [nnf transformation 12]
71. (? [X0] : (patient(X0) | ~humble(X0)) | patient(paul) | ~curious(paul)) & ((~patient(paul) & curious(paul)) | ! [X0] : (~patient(X0) & humble(X0))) [flattening 70]
72. (? [X0] : (patient(X0) | ~humble(X0)) | patient(paul) | ~curious(paul)) & ((~patient(paul) & curious(paul)) | ! [X1] : (~patient(X1) & humble(X1))) [rectify 71]
73. ? [X0] : (patient(X0) | ~humble(X0)) => (patient(sK6) | ~humble(sK6)) [choice axiom]
74. ((patient(sK6) | ~humble(sK6)) | patient(paul) | ~curious(paul)) & ((~patient(paul) & curious(paul)) | ! [X1] : (~patient(X1) & humble(X1))) [skolemisation 72,73]
80. ! [X0] : ((~old(X0) & humble(X0)) | ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) [nnf transformation 37]
92. ~strong(X0) | patient(X0) [cnf transformation 41]
93. creative(X0) | patient(X0) [cnf transformation 41]
96. quiet(X0) | happy(X0) [cnf transformation 43]
97. ~happy(X0) | quiet(X0) [cnf transformation 43]
113. patient(X0) | strong(X0) | strong(X0) | ~humble(X0) [cnf transformation 59]
118. ~strong(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 59]
120. ~patient(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 60]
132. curious(paul) | ~patient(X1) [cnf transformation 74]
142. ~happy(X0) | humble(X0) | ~creative(X0) [cnf transformation 80]
156. happy(paul) [cnf transformation 25]
157. patient(X0) | strong(X0) | ~humble(X0) [duplicate literal removal 113]
160. quiet(X0) [subsumption resolution 96,97]
182. 5 <=> patient(paul) [avatar definition]
183. ~patient(paul) <- (~5) [avatar component clause 182]
184. patient(paul) <- (5) [avatar component clause 182]
207. ~humble(X0) | ~strong(X0) [subsumption resolution 118,92]
208. ~humble(X0) | patient(X0) [subsumption resolution 157,207]
209. ~curious(X0) | ~patient(X0) [subsumption resolution 120,160]
259. 21 <=> ! [X1] : ~patient(X1) [avatar definition]
260. ~patient(X1) <- (21) [avatar component clause 259]
267. 23 <=> curious(paul) [avatar definition]
269. curious(paul) <- (23) [avatar component clause 267]
270. 21 | 23 [avatar split clause 132,267,259]
309. ~patient(paul) <- (23) [resolution 209,269]
387. humble(paul) | ~creative(paul) [resolution 142,156]
389. 40 <=> creative(paul) [avatar definition]
391. ~creative(paul) <- (~40) [avatar component clause 389]
393. 41 <=> humble(paul) [avatar definition]
395. humble(paul) <- (41) [avatar component clause 393]
396. ~40 | 41 [avatar split clause 387,393,389]
397. patient(paul) <- (~40) [resolution 391,93]
398. $false <- (~5, ~40) [subsumption resolution 397,183]
399. 5 | 40 [avatar contradiction clause 398]
415. patient(paul) <- (41) [resolution 395,208]
417. $false <- (~5, 41) [subsumption resolution 415,183]
418. 5 | ~41 [avatar contradiction clause 417]
419. ~5 | ~23 [avatar split clause 309,267,182]
420. $false <- (5, 21) [subsumption resolution 184,260]
421. ~5 | ~21 [avatar contradiction clause 420]
422. $false [avatar sat refutation 270,396,399,418,419,421]
% SZS output end Proof for 465506229201914325046640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not strong or strong then lucy is not rich or creative and vice versa.
Everyone who is either not creative or not generous is both not humble and not calm.
Everyone who is generous is not rich and vice versa.
Everyone who is either not humble or generous is kind or humble.
If john is not patient or not curious then someone is both not quiet and not patient and vice versa.
Everyone who is either humble or not humble is either tall or rich and vice versa.
If someone is not generous or not patient then fred is either humble or generous.
If mary is both not brave and creative then someone is generous.
Everyone who is not quiet is not rich or brave and vice versa.
If mary is brave or not strong then someone is both not creative and not humble.
Everyone who is either not patient or tall is old and vice versa.
If someone is either not curious or kind then someone is humble or not tall and vice versa.
Everyone who is both creative and patient is either not strong or not curious and vice versa.
Everyone who is either kind or calm is rich and vice versa.
Everyone who is kind is patient or not creative and vice versa.
Everyone who is brave is either not old or not tall.
Someone is either kind or not creative.
Fred is not creative or humble.
Someone is wise or not kind.
Someone is not generous.
Someone is not calm.
Alice is not old or wise.
John is both quiet and wise.
Alice is happy. | Alice is not old. | neutral | (((~strong(lucy)|strong(lucy)))<=>((~rich(lucy)|creative(lucy))))&
(![X]:((~creative(X)<~>~generous(X))=>(~humble(X)&~calm(X))))&
(![X]:(generous(X)<=>~rich(X)))&
(![X]:((~humble(X)<~>generous(X))=>(kind(X)|humble(X))))&
(((~patient(john)|~curious(john)))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((humble(X)<~>~humble(X))<=>(tall(X)<~>rich(X))))&
((?[X]:((~generous(X)|~patient(X))))=>((humble(fred)<~>generous(fred))))&
(((~brave(mary)&creative(mary)))=>(?[X]:(generous(X))))&
(![X]:(~quiet(X)<=>(~rich(X)|brave(X))))&
(((brave(mary)|~strong(mary)))=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((~patient(X)<~>tall(X))<=>old(X)))&
((?[X]:((~curious(X)<~>kind(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((creative(X)&patient(X))<=>(~strong(X)<~>~curious(X))))&
(![X]:((kind(X)<~>calm(X))<=>rich(X)))&
(![X]:(kind(X)<=>(patient(X)|~creative(X))))&
(![X]:(brave(X)=>(~old(X)<~>~tall(X))))&
(?[X]:((kind(X)<~>~creative(X))))&
((~creative(fred)|humble(fred)))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~calm(X)))&
((~old(alice)|wise(alice)))&
((quiet(john)&wise(john)))&
(happy(alice)) | ~old(alice) | [] | null | 0 |
Everyone who is both creative and rich is creative or strong and vice versa.
If someone is either rich or happy then someone is both not funny and not curious and vice versa.
If someone is either not humble or not generous then someone is either brave or strong.
Everyone who is not rich or brave is both not tall and strong.
If mary is both brave and not creative then someone is funny or not quiet and vice versa.
Everyone who is either creative or old is both not patient and not kind and vice versa.
Everyone who is either not curious or generous is not rich or humble.
Everyone who is either not strong or not patient is humble.
Everyone who is not brave is not rich.
If mary is both not wise and curious then someone is either calm or not tall and vice versa.
If someone is not old or not quiet then lucy is both not rich and creative and vice versa.
Everyone who is both not humble and wise is not generous.
Everyone who is both not funny and not kind is curious or patient and vice versa.
Everyone who is either not wise or calm is not curious or not brave.
Everyone who is either not old or not quiet is both humble and strong and vice versa.
Paul is both not funny and not kind.
Someone is either kind or not wise.
Someone is not calm. | Mary is not creative. | contradiction | (![X]:((creative(X)&rich(X))<=>(creative(X)|strong(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((~funny(X)&~curious(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(?[X]:((brave(X)<~>strong(X)))))&
(![X]:((~rich(X)|brave(X))=>(~tall(X)&strong(X))))&
(((brave(mary)&~creative(mary)))<=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:((creative(X)<~>old(X))<=>(~patient(X)&~kind(X))))&
(![X]:((~curious(X)<~>generous(X))=>(~rich(X)|humble(X))))&
(![X]:((~strong(X)<~>~patient(X))=>humble(X)))&
(![X]:(~brave(X)=>~rich(X)))&
(((~wise(mary)&curious(mary)))<=>(?[X]:((calm(X)<~>~tall(X)))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~rich(lucy)&creative(lucy))))&
(![X]:((~humble(X)&wise(X))=>~generous(X)))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)|patient(X))))&
(![X]:((~wise(X)<~>calm(X))=>(~curious(X)|~brave(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(humble(X)&strong(X))))&
((~funny(paul)&~kind(paul)))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:(~calm(X))) | ~creative(mary) | [
"p0",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1801848160858008101917299
% SZS output start Proof for 1801848160858008101917299
1. ! [X0] : ((rich(X0) & creative(X0)) <=> (strong(X0) | creative(X0))) [input p0]
4. ! [X0] : ((brave(X0) | ~rich(X0)) => (strong(X0) & ~tall(X0))) [input p3]
9. ! [X0] : (~brave(X0) => ~rich(X0)) [input p8]
19. ~creative(mary) [input hypothesis]
23. ! [X0] : ((strong(X0) & ~tall(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 4]
27. ! [X0] : (~rich(X0) | brave(X0)) [ennf transformation 9]
32. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | ~rich(X0) | ~creative(X0))) [flattening 32]
74. ~strong(X0) | creative(X0) [cnf transformation 33]
76. ~strong(X0) | rich(X0) [cnf transformation 33]
89. strong(X0) | rich(X0) [cnf transformation 23]
90. ~brave(X0) | strong(X0) [cnf transformation 23]
106. ~rich(X0) | brave(X0) [cnf transformation 27]
137. ~creative(mary) [cnf transformation 19]
187. rich(X0) [subsumption resolution 89,76]
192. 13 <=> creative(mary) [avatar definition]
194. ~creative(mary) <- (~13) [avatar component clause 192]
217. brave(X0) [subsumption resolution 106,187]
271. ~13 [avatar split clause 137,192]
278. strong(X0) [resolution 90,217]
281. creative(X1) [resolution 278,74]
286. $false <- (~13) [resolution 281,194]
288. 13 [avatar contradiction clause 286]
289. $false [avatar sat refutation 271,288]
% SZS output end Proof for 1801848160858008101917299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old and not strong is either humble or happy and vice versa.
Everyone who is both not wise and not generous is not brave and vice versa.
If paul is both tall and not humble then fred is creative.
If someone is both not happy and not humble then lucy is either not wise or strong and vice versa.
If someone is not old or brave then someone is not wise or not strong and vice versa.
If mary is both tall and humble then someone is not creative and vice versa.
If someone is either not strong or calm then mary is happy.
If someone is either humble or curious then susan is not calm or not generous and vice versa.
Everyone who is strong or tall is calm and vice versa.
Everyone who is either funny or not creative is both old and not rich.
Everyone who is not generous or not happy is funny.
If someone is both not tall and not humble then someone is either not creative or creative.
Everyone who is not happy is either not kind or creative and vice versa.
Everyone who is either happy or curious is both not wise and not humble and vice versa.
Everyone who is not strong or generous is either curious or not funny.
If someone is both patient and not quiet then alice is both not patient and humble and vice versa.
Lucy is not happy or not calm.
Paul is calm.
Susan is either not happy or not old.
Someone is old or kind.
John is either curious or creative.
Susan is curious.
Alice is either not generous or kind. | Susan is old. | neutral | (![X]:((~old(X)&~strong(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~wise(X)&~generous(X))<=>~brave(X)))&
(((tall(paul)&~humble(paul)))=>(creative(fred)))&
((?[X]:((~happy(X)&~humble(X))))<=>((~wise(lucy)<~>strong(lucy))))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:((~wise(X)|~strong(X)))))&
(((tall(mary)&humble(mary)))<=>(?[X]:(~creative(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(happy(mary)))&
((?[X]:((humble(X)<~>curious(X))))<=>((~calm(susan)|~generous(susan))))&
(![X]:((strong(X)|tall(X))<=>calm(X)))&
(![X]:((funny(X)<~>~creative(X))=>(old(X)&~rich(X))))&
(![X]:((~generous(X)|~happy(X))=>funny(X)))&
((?[X]:((~tall(X)&~humble(X))))=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((happy(X)<~>curious(X))<=>(~wise(X)&~humble(X))))&
(![X]:((~strong(X)|generous(X))=>(curious(X)<~>~funny(X))))&
((?[X]:((patient(X)&~quiet(X))))<=>((~patient(alice)&humble(alice))))&
((~happy(lucy)|~calm(lucy)))&
(calm(paul))&
((~happy(susan)<~>~old(susan)))&
(?[X]:((old(X)|kind(X))))&
((curious(john)<~>creative(john)))&
(curious(susan))&
((~generous(alice)<~>kind(alice))) | old(susan) | [] | null | 0 |
If susan is both not wise and quiet then someone is both not humble and creative.
Everyone who is either not humble or not wise is quiet or kind and vice versa.
If fred is not funny or curious then john is both not curious and quiet.
Everyone who is calm is brave or happy and vice versa.
Everyone who is not happy or creative is either funny or creative and vice versa.
Everyone who is not happy or not wise is either not quiet or not happy and vice versa.
Everyone who is generous or not happy is not curious or not brave and vice versa.
If lucy is rich then john is not curious or not quiet and vice versa.
If fred is both creative and not patient then john is both not brave and wise and vice versa.
If someone is either not happy or curious then someone is kind or brave and vice versa.
If someone is strong or brave then susan is either brave or not patient.
If someone is both humble and not creative then someone is either happy or strong and vice versa.
Everyone who is not generous is either not rich or not happy and vice versa.
Everyone who is humble is either humble or calm and vice versa.
Everyone who is either quiet or not curious is either creative or not curious and vice versa.
Everyone who is not patient or not strong is not strong or creative and vice versa.
Paul is either kind or not rich.
Someone is not creative or rich.
Someone is either brave or quiet.
John is either not curious or not humble.
Paul is either generous or old. | Susan is quiet. | entailment | (((~wise(susan)&quiet(susan)))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~humble(X)<~>~wise(X))<=>(quiet(X)|kind(X))))&
(((~funny(fred)|curious(fred)))=>((~curious(john)&quiet(john))))&
(![X]:(calm(X)<=>(brave(X)|happy(X))))&
(![X]:((~happy(X)|creative(X))<=>(funny(X)<~>creative(X))))&
(![X]:((~happy(X)|~wise(X))<=>(~quiet(X)<~>~happy(X))))&
(![X]:((generous(X)|~happy(X))<=>(~curious(X)|~brave(X))))&
((rich(lucy))<=>((~curious(john)|~quiet(john))))&
(((creative(fred)&~patient(fred)))<=>((~brave(john)&wise(john))))&
((?[X]:((~happy(X)<~>curious(X))))<=>(?[X]:((kind(X)|brave(X)))))&
((?[X]:((strong(X)|brave(X))))=>((brave(susan)<~>~patient(susan))))&
((?[X]:((humble(X)&~creative(X))))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:(~generous(X)<=>(~rich(X)<~>~happy(X))))&
(![X]:(humble(X)<=>(humble(X)<~>calm(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((~patient(X)|~strong(X))<=>(~strong(X)|creative(X))))&
((kind(paul)<~>~rich(paul)))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:((brave(X)<~>quiet(X))))&
((~curious(john)<~>~humble(john)))&
((generous(paul)<~>old(paul))) | quiet(susan) | [
"p3",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7886659197326884681916487
% SZS output start Proof for 7886659197326884681916487
4. ! [X0] : (calm(X0) <=> (happy(X0) | brave(X0))) [input p3]
6. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~quiet(X0) <~> ~happy(X0))) [input p5]
14. ! [X0] : (humble(X0) <=> (humble(X0) <~> calm(X0))) [input p13]
22. ~quiet(susan) [input hypothesis]
33. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ~calm(X0))) [nnf transformation 4]
34. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~calm(X0))) [flattening 33]
37. ! [X0] : (((~wise(X0) | ~happy(X0)) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0)))) & (((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (wise(X0) & happy(X0)))) [nnf transformation 6]
38. ! [X0] : ((~wise(X0) | ~happy(X0) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0)))) & (((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (wise(X0) & happy(X0)))) [flattening 37]
57. ! [X0] : ((humble(X0) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 14]
83. ~happy(X0) | calm(X0) [cnf transformation 34]
92. happy(X0) | quiet(X0) | happy(X0) [cnf transformation 38]
128. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 57]
130. humble(X0) | humble(X0) | ~calm(X0) [cnf transformation 57]
152. ~quiet(susan) [cnf transformation 22]
157. ~calm(X0) | ~humble(X0) [duplicate literal removal 128]
158. ~calm(X0) | humble(X0) [duplicate literal removal 130]
159. happy(X0) | quiet(X0) [duplicate literal removal 92]
168. 2 <=> quiet(susan) [avatar definition]
170. ~quiet(susan) <- (~2) [avatar component clause 168]
308. ~calm(X0) [subsumption resolution 157,158]
356. ~2 [avatar split clause 152,168]
361. quiet(X0) | calm(X0) [resolution 159,83]
362. quiet(X0) [subsumption resolution 361,308]
364. $false <- (~2) [resolution 362,170]
365. 2 [avatar contradiction clause 364]
366. $false [avatar sat refutation 356,365]
% SZS output end Proof for 7886659197326884681916487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or not kind is both not creative and not humble. If mary is quiet then someone is quiet or not tall. Everyone who is either not happy or not kind is calm or not patient. Everyone who is either not funny or creative is not creative and vice versa. Everyone who is either not rich or not happy is rich. Everyone who is not strong or rich is both calm and quiet and vice versa. If someone is either not old or creative then someone is both calm and not brave. Everyone who is either not wise or kind is both not old and not tall and vice versa. Everyone who is creative is not generous or not creative and vice versa. If paul is either not happy or not generous then someone is wise or not rich. If susan is old or not humble then someone is either generous or not humble and vice versa. Everyone who is not wise is either rich or strong and vice versa. Everyone who is happy or creative is either not calm or not quiet and vice versa. If mary is wise then fred is either not rich or not humble and vice versa. If alice is not curious then alice is both old and curious. Everyone who is either not curious or humble is both calm and not tall and vice versa. Someone is creative or calm. Someone is either brave or not wise. Someone is strong. Susan is either old or not funny. Someone is not wise. | Paul is not wise. | entailment | (![X]:((creative(X)<~>~kind(X))=>(~creative(X)&~humble(X))))&
((quiet(mary))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>(calm(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
(![X]:((~rich(X)<~>~happy(X))=>rich(X)))&
(![X]:((~strong(X)|rich(X))<=>(calm(X)&quiet(X))))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:((~wise(X)<~>kind(X))<=>(~old(X)&~tall(X))))&
(![X]:(creative(X)<=>(~generous(X)|~creative(X))))&
(((~happy(paul)<~>~generous(paul)))=>(?[X]:((wise(X)|~rich(X)))))&
(((old(susan)|~humble(susan)))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:(~wise(X)<=>(rich(X)<~>strong(X))))&
(![X]:((happy(X)|creative(X))<=>(~calm(X)<~>~quiet(X))))&
((wise(mary))<=>((~rich(fred)<~>~humble(fred))))&
((~curious(alice))=>((old(alice)&curious(alice))))&
(![X]:((~curious(X)<~>humble(X))<=>(calm(X)&~tall(X))))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((brave(X)<~>~wise(X))))&
(?[X]:(strong(X)))&
((old(susan)<~>~funny(susan)))&
(?[X]:(~wise(X))) | ~wise(paul) | [
"p5",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6703197650300754564811643
% SZS output start Proof for 6703197650300754564811643
6. ! [X0] : ((rich(X0) | ~strong(X0)) <=> (quiet(X0) & calm(X0))) [input p5]
9. ! [X0] : (creative(X0) <=> (~creative(X0) | ~generous(X0))) [input p8]
12. ! [X0] : (~wise(X0) <=> (rich(X0) <~> strong(X0))) [input p11]
13. ! [X0] : ((creative(X0) | happy(X0)) <=> (~calm(X0) <~> ~quiet(X0))) [input p12]
22. wise(paul) [input hypothesis]
36. ! [X0] : (((rich(X0) | ~strong(X0)) | (~quiet(X0) | ~calm(X0))) & ((quiet(X0) & calm(X0)) | (~rich(X0) & strong(X0)))) [nnf transformation 6]
37. ! [X0] : ((rich(X0) | ~strong(X0) | ~quiet(X0) | ~calm(X0)) & ((quiet(X0) & calm(X0)) | (~rich(X0) & strong(X0)))) [flattening 36]
44. ! [X0] : ((creative(X0) | (creative(X0) & generous(X0))) & ((~creative(X0) | ~generous(X0)) | ~creative(X0))) [nnf transformation 9]
45. ! [X0] : ((creative(X0) | (creative(X0) & generous(X0))) & (~creative(X0) | ~generous(X0) | ~creative(X0))) [flattening 44]
54. ! [X0] : ((~wise(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | wise(X0))) [nnf transformation 12]
55. ! [X0] : (((creative(X0) | happy(X0)) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0)))) & (((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (~creative(X0) & ~happy(X0)))) [nnf transformation 13]
56. ! [X0] : ((creative(X0) | happy(X0) | ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0)))) & (((quiet(X0) | calm(X0)) & (~quiet(X0) | ~calm(X0))) | (~creative(X0) & ~happy(X0)))) [flattening 55]
81. strong(X0) | calm(X0) [cnf transformation 37]
82. ~rich(X0) | calm(X0) [cnf transformation 37]
83. strong(X0) | quiet(X0) [cnf transformation 37]
84. ~rich(X0) | quiet(X0) [cnf transformation 37]
98. creative(X0) | creative(X0) [cnf transformation 45]
110. ~wise(X0) | rich(X0) | ~strong(X0) [cnf transformation 54]
112. ~quiet(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 56]
136. wise(paul) [cnf transformation 22]
139. creative(X0) [duplicate literal removal 98]
213. ~calm(X0) | ~quiet(X0) [subsumption resolution 112,139]
333. 34 <=> rich(paul) [avatar definition]
334. rich(paul) <- (34) [avatar component clause 333]
337. 35 <=> strong(paul) [avatar definition]
338. ~strong(paul) <- (~35) [avatar component clause 337]
344. rich(paul) | ~strong(paul) [resolution 110,136]
450. quiet(paul) <- (~35) [resolution 338,83]
451. calm(paul) <- (~35) [resolution 338,81]
470. ~quiet(paul) <- (~35) [resolution 451,213]
473. $false <- (~35) [subsumption resolution 470,450]
474. 35 [avatar contradiction clause 473]
475. ~35 | 34 [avatar split clause 344,333,337]
476. quiet(paul) <- (34) [resolution 334,84]
477. calm(paul) <- (34) [resolution 334,82]
503. ~quiet(paul) <- (34) [resolution 477,213]
506. $false <- (34) [subsumption resolution 503,476]
507. ~34 [avatar contradiction clause 506]
508. $false [avatar sat refutation 474,475,507]
% SZS output end Proof for 6703197650300754564811643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not patient and patient then john is not strong. Everyone who is kind or not old is both tall and wise. Everyone who is not funny is not kind and vice versa. If someone is not wise or creative then alice is curious or brave and vice versa. If fred is creative then someone is not curious or not kind and vice versa. Everyone who is both calm and not happy is either not humble or not wise and vice versa. If paul is tall or humble then someone is tall. Everyone who is either brave or not happy is both quiet and not patient and vice versa. Everyone who is both not creative and not rich is either not rich or generous. If paul is both not old and not curious then susan is not generous and vice versa. Everyone who is calm or not old is both not kind and not calm and vice versa. If susan is not generous or not creative then fred is kind or not quiet. If fred is both not brave and not calm then someone is both not kind and rich. If john is either not creative or not quiet then paul is not humble or funny and vice versa. Everyone who is patient or quiet is either patient or not brave and vice versa. If susan is funny or not generous then susan is not happy. John is either not quiet or not tall. Someone is either not generous or not quiet. Fred is either not creative or not generous. Susan is either strong or not curious. | John is happy. | contradiction | (((~patient(susan)&patient(susan)))=>(~strong(john)))&
(![X]:((kind(X)|~old(X))=>(tall(X)&wise(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
((?[X]:((~wise(X)|creative(X))))<=>((curious(alice)|brave(alice))))&
((creative(fred))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((calm(X)&~happy(X))<=>(~humble(X)<~>~wise(X))))&
(((tall(paul)|humble(paul)))=>(?[X]:(tall(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(quiet(X)&~patient(X))))&
(![X]:((~creative(X)&~rich(X))=>(~rich(X)<~>generous(X))))&
(((~old(paul)&~curious(paul)))<=>(~generous(susan)))&
(![X]:((calm(X)|~old(X))<=>(~kind(X)&~calm(X))))&
(((~generous(susan)|~creative(susan)))=>((kind(fred)|~quiet(fred))))&
(((~brave(fred)&~calm(fred)))=>(?[X]:((~kind(X)&rich(X)))))&
(((~creative(john)<~>~quiet(john)))<=>((~humble(paul)|funny(paul))))&
(![X]:((patient(X)|quiet(X))<=>(patient(X)<~>~brave(X))))&
(((funny(susan)|~generous(susan)))=>(~happy(susan)))&
((~quiet(john)<~>~tall(john)))&
(?[X]:((~generous(X)<~>~quiet(X))))&
((~creative(fred)<~>~generous(fred)))&
((strong(susan)<~>~curious(susan))) | happy(john) | [
"p1",
"p7",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1315420969824256984628
% SZS output start Proof for 1315420969824256984628
2. ! [X0] : ((~old(X0) | kind(X0)) => (wise(X0) & tall(X0))) [input p1]
8. ! [X0] : ((brave(X0) <~> ~happy(X0)) <=> (~patient(X0) & quiet(X0))) [input p7]
11. ! [X0] : ((~old(X0) | calm(X0)) <=> (~calm(X0) & ~kind(X0))) [input p10]
15. ! [X0] : ((quiet(X0) | patient(X0)) <=> (patient(X0) <~> ~brave(X0))) [input p14]
17. ~quiet(john) <~> ~tall(john) [input p16]
21. happy(john) [input hypothesis]
24. ! [X0] : ((wise(X0) & tall(X0)) | (old(X0) & ~kind(X0))) [ennf transformation 2]
47. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (patient(X0) | ~quiet(X0))) & ((~patient(X0) & quiet(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [nnf transformation 8]
48. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | patient(X0) | ~quiet(X0)) & ((~patient(X0) & quiet(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [flattening 47]
52. ! [X0] : (((~old(X0) | calm(X0)) | (calm(X0) | kind(X0))) & ((~calm(X0) & ~kind(X0)) | (old(X0) & ~calm(X0)))) [nnf transformation 11]
53. ! [X0] : ((~old(X0) | calm(X0) | calm(X0) | kind(X0)) & ((~calm(X0) & ~kind(X0)) | (old(X0) & ~calm(X0)))) [flattening 52]
58. ! [X0] : (((quiet(X0) | patient(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (~quiet(X0) & ~patient(X0)))) [nnf transformation 15]
59. ! [X0] : ((quiet(X0) | patient(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (~quiet(X0) & ~patient(X0)))) [flattening 58]
60. (tall(john) | quiet(john)) & (~tall(john) | ~quiet(john)) [nnf transformation 17]
67. ~kind(X0) | tall(X0) [cnf transformation 24]
68. tall(X0) | old(X0) [cnf transformation 24]
88. ~happy(X0) | quiet(X0) | ~brave(X0) [cnf transformation 48]
90. ~happy(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 48]
101. ~calm(X0) | ~calm(X0) [cnf transformation 53]
103. ~old(X0) | calm(X0) | calm(X0) | kind(X0) [cnf transformation 53]
116. brave(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 59]
119. quiet(X0) | patient(X0) | patient(X0) | brave(X0) [cnf transformation 59]
122. ~tall(john) | ~quiet(john) [cnf transformation 60]
130. happy(john) [cnf transformation 21]
131. ~patient(X0) | brave(X0) [duplicate literal removal 116]
132. quiet(X0) | patient(X0) | brave(X0) [duplicate literal removal 119]
133. ~calm(X0) [duplicate literal removal 101]
134. ~old(X0) | calm(X0) | kind(X0) [duplicate literal removal 103]
251. 26 <=> quiet(john) [avatar definition]
252. ~quiet(john) <- (~26) [avatar component clause 251]
271. 29 <=> tall(john) [avatar definition]
272. ~tall(john) <- (~29) [avatar component clause 271]
275. ~26 | ~29 [avatar split clause 122,271,251]
303. old(john) <- (~29) [resolution 68,272]
326. quiet(john) | ~brave(john) [resolution 88,130]
338. ~patient(john) | ~brave(john) [resolution 90,130]
339. ~patient(john) [subsumption resolution 338,131]
358. calm(john) | kind(john) <- (~29) [resolution 134,303]
361. kind(john) <- (~29) [subsumption resolution 358,133]
400. tall(john) <- (~29) [resolution 361,67]
403. $false <- (~29) [subsumption resolution 400,272]
404. 29 [avatar contradiction clause 403]
406. 43 <=> brave(john) [avatar definition]
408. ~brave(john) <- (~43) [avatar component clause 406]
409. ~43 | 26 [avatar split clause 326,251,406]
410. patient(john) | brave(john) <- (~26) [resolution 252,132]
412. brave(john) <- (~26) [subsumption resolution 410,339]
413. $false <- (~26, ~43) [subsumption resolution 412,408]
414. 26 | 43 [avatar contradiction clause 413]
415. $false [avatar sat refutation 275,404,409,414]
% SZS output end Proof for 1315420969824256984628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not generous is not kind.
If mary is either generous or not patient then someone is not strong or quiet.
Everyone who is not tall is either creative or not brave.
Everyone who is both kind and not creative is either calm or tall.
If lucy is not strong then someone is both curious and happy.
If mary is either happy or generous then fred is not patient.
Everyone who is both not old and funny is both generous and not brave and vice versa.
If someone is not wise then someone is calm or not creative.
Everyone who is patient is both funny and not kind.
Everyone who is either not creative or not brave is both not tall and not creative and vice versa.
Everyone who is either quiet or not quiet is not tall and vice versa.
Everyone who is either old or not curious is not happy or not curious.
Everyone who is not old is tall.
If susan is not wise or not rich then someone is calm or not strong.
If someone is happy or not brave then someone is both strong and humble.
If paul is both calm and quiet then susan is both not rich and not calm.
Susan is tall or kind.
Alice is not quiet.
Someone is generous.
Mary is not strong.
Mary is either calm or not generous.
Susan is not tall.
Someone is either not generous or kind. | Paul is not brave. | contradiction | (![X]:((wise(X)<~>~generous(X))=>~kind(X)))&
(((generous(mary)<~>~patient(mary)))=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:(~tall(X)=>(creative(X)<~>~brave(X))))&
(![X]:((kind(X)&~creative(X))=>(calm(X)<~>tall(X))))&
((~strong(lucy))=>(?[X]:((curious(X)&happy(X)))))&
(((happy(mary)<~>generous(mary)))=>(~patient(fred)))&
(![X]:((~old(X)&funny(X))<=>(generous(X)&~brave(X))))&
((?[X]:(~wise(X)))=>(?[X]:((calm(X)|~creative(X)))))&
(![X]:(patient(X)=>(funny(X)&~kind(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(~tall(X)&~creative(X))))&
(![X]:((quiet(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((old(X)<~>~curious(X))=>(~happy(X)|~curious(X))))&
(![X]:(~old(X)=>tall(X)))&
(((~wise(susan)|~rich(susan)))=>(?[X]:((calm(X)|~strong(X)))))&
((?[X]:((happy(X)|~brave(X))))=>(?[X]:((strong(X)&humble(X)))))&
(((calm(paul)&quiet(paul)))=>((~rich(susan)&~calm(susan))))&
((tall(susan)|kind(susan)))&
(~quiet(alice))&
(?[X]:(generous(X)))&
(~strong(mary))&
((calm(mary)<~>~generous(mary)))&
(~tall(susan))&
(?[X]:((~generous(X)<~>kind(X)))) | ~brave(paul) | [
"p2",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 93437896072058323813152
% SZS output start Proof for 93437896072058323813152
3. ! [X0] : (~tall(X0) => (creative(X0) <~> ~brave(X0))) [input p2]
10. ! [X0] : ((~creative(X0) <~> ~brave(X0)) <=> (~creative(X0) & ~tall(X0))) [input p9]
11. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) <=> ~tall(X0)) [input p10]
24. ~brave(paul) [input hypothesis]
30. ! [X0] : ((creative(X0) <~> ~brave(X0)) | tall(X0)) [ennf transformation 3]
48. ! [X0] : (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | tall(X0)) [nnf transformation 30]
58. ! [X0] : ((((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0))))) [nnf transformation 10]
59. ! [X0] : ((((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0))))) [flattening 58]
60. ! [X0] : ((((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | tall(X0)) & (~tall(X0) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))))) [nnf transformation 11]
77. ~brave(X0) | creative(X0) | tall(X0) [cnf transformation 48]
95. ~creative(X0) | ~creative(X0) | brave(X0) [cnf transformation 59]
97. brave(X0) | creative(X0) | creative(X0) | tall(X0) [cnf transformation 59]
98. ~tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 60]
99. ~tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 60]
120. ~brave(paul) [cnf transformation 24]
122. ~tall(X0) | ~quiet(X0) [duplicate literal removal 98]
123. ~tall(X0) | quiet(X0) [duplicate literal removal 99]
124. ~creative(X0) | brave(X0) [duplicate literal removal 95]
125. brave(X0) | creative(X0) | tall(X0) [duplicate literal removal 97]
180. creative(X0) | tall(X0) [subsumption resolution 125,77]
182. ~tall(X0) [subsumption resolution 122,123]
203. 17 <=> ! [X1] : brave(X1) [avatar definition]
204. brave(X1) <- (17) [avatar component clause 203]
246. tall(X0) | brave(X0) [resolution 180,124]
249. brave(X0) [subsumption resolution 246,182]
250. 17 [avatar split clause 249,203]
252. $false <- (17) [resolution 204,120]
253. ~17 [avatar contradiction clause 252]
254. $false [avatar sat refutation 250,253]
% SZS output end Proof for 93437896072058323813152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and strong is rich or old. Everyone who is both not brave and not funny is either quiet or curious. If someone is both humble and generous then someone is either strong or happy and vice versa. Everyone who is both not strong and not creative is wise and vice versa. If someone is not tall then someone is kind and vice versa. If someone is both not patient and not curious then someone is not wise. If mary is wise then alice is both not creative and not happy. Everyone who is both old and not old is wise and vice versa. Everyone who is happy is wise and vice versa. If someone is not happy or tall then fred is either not generous or funny and vice versa. Everyone who is creative or patient is either not old or curious and vice versa. If someone is old then lucy is not humble. Everyone who is not patient is not curious or not humble. If fred is not curious or creative then paul is both old and kind. If mary is either curious or not humble then john is happy or patient and vice versa. Everyone who is tall is both curious and not creative and vice versa. Someone is not rich. Someone is both not curious and not wise. John is either not strong or not quiet. John is either not humble or creative. John is either curious or not funny. Alice is not quiet or not brave. John is not quiet or wise. Someone is curious. | John is patient. | neutral | (![X]:((generous(X)&strong(X))=>(rich(X)|old(X))))&
(![X]:((~brave(X)&~funny(X))=>(quiet(X)<~>curious(X))))&
((?[X]:((humble(X)&generous(X))))<=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((~strong(X)&~creative(X))<=>wise(X)))&
((?[X]:(~tall(X)))<=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)&~curious(X))))=>(?[X]:(~wise(X))))&
((wise(mary))=>((~creative(alice)&~happy(alice))))&
(![X]:((old(X)&~old(X))<=>wise(X)))&
(![X]:(happy(X)<=>wise(X)))&
((?[X]:((~happy(X)|tall(X))))<=>((~generous(fred)<~>funny(fred))))&
(![X]:((creative(X)|patient(X))<=>(~old(X)<~>curious(X))))&
((?[X]:(old(X)))=>(~humble(lucy)))&
(![X]:(~patient(X)=>(~curious(X)|~humble(X))))&
(((~curious(fred)|creative(fred)))=>((old(paul)&kind(paul))))&
(((curious(mary)<~>~humble(mary)))<=>((happy(john)|patient(john))))&
(![X]:(tall(X)<=>(curious(X)&~creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~curious(X)&~wise(X))))&
((~strong(john)<~>~quiet(john)))&
((~humble(john)<~>creative(john)))&
((curious(john)<~>~funny(john)))&
((~quiet(alice)|~brave(alice)))&
((~quiet(john)|wise(john)))&
(?[X]:(curious(X))) | patient(john) | [] | null | 0 |
Everyone who is happy or not wise is either generous or quiet and vice versa.
Everyone who is either calm or patient is not strong.
If alice is funny then john is funny and vice versa.
If someone is either not rich or old then someone is either strong or old and vice versa.
Everyone who is both generous and not funny is both not strong and happy and vice versa.
If someone is strong or not curious then lucy is not curious or wise and vice versa.
If paul is either not kind or curious then susan is both not quiet and calm and vice versa.
Everyone who is both not curious and not tall is not calm.
If paul is not rich then alice is not humble or brave and vice versa.
Everyone who is both curious and funny is either not funny or not generous and vice versa.
Everyone who is tall or not calm is both rich and kind.
Everyone who is old is not humble.
Everyone who is not generous or not brave is both generous and not old and vice versa.
If susan is either funny or not curious then someone is both not funny and happy.
Everyone who is both not happy and happy is tall and vice versa.
Everyone who is either not brave or not humble is either not happy or not calm.
Alice is not old.
Paul is not tall or patient.
Susan is funny.
Lucy is both strong and humble.
Someone is either not generous or generous.
John is kind or not happy.
Someone is either humble or patient. | Alice is patient. | contradiction | (![X]:((happy(X)|~wise(X))<=>(generous(X)<~>quiet(X))))&
(![X]:((calm(X)<~>patient(X))=>~strong(X)))&
((funny(alice))<=>(funny(john)))&
((?[X]:((~rich(X)<~>old(X))))<=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:((generous(X)&~funny(X))<=>(~strong(X)&happy(X))))&
((?[X]:((strong(X)|~curious(X))))<=>((~curious(lucy)|wise(lucy))))&
(((~kind(paul)<~>curious(paul)))<=>((~quiet(susan)&calm(susan))))&
(![X]:((~curious(X)&~tall(X))=>~calm(X)))&
((~rich(paul))<=>((~humble(alice)|brave(alice))))&
(![X]:((curious(X)&funny(X))<=>(~funny(X)<~>~generous(X))))&
(![X]:((tall(X)|~calm(X))=>(rich(X)&kind(X))))&
(![X]:(old(X)=>~humble(X)))&
(![X]:((~generous(X)|~brave(X))<=>(generous(X)&~old(X))))&
(((funny(susan)<~>~curious(susan)))=>(?[X]:((~funny(X)&happy(X)))))&
(![X]:((~happy(X)&happy(X))<=>tall(X)))&
(![X]:((~brave(X)<~>~humble(X))=>(~happy(X)<~>~calm(X))))&
(~old(alice))&
((~tall(paul)|patient(paul)))&
(funny(susan))&
((strong(lucy)&humble(lucy)))&
(?[X]:((~generous(X)<~>generous(X))))&
((kind(john)|~happy(john)))&
(?[X]:((humble(X)<~>patient(X)))) | patient(alice) | [
"p1",
"p4",
"p7",
"p8",
"p9",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5944740545134060913916123
% SZS output start Proof for 5944740545134060913916123
2. ! [X0] : ((calm(X0) <~> patient(X0)) => ~strong(X0)) [input p1]
5. ! [X0] : ((~funny(X0) & generous(X0)) <=> (happy(X0) & ~strong(X0))) [input p4]
8. ! [X0] : ((~tall(X0) & ~curious(X0)) => ~calm(X0)) [input p7]
9. ~rich(paul) <=> (brave(alice) | ~humble(alice)) [input p8]
10. ! [X0] : ((funny(X0) & curious(X0)) <=> (~funny(X0) <~> ~generous(X0))) [input p9]
11. ! [X0] : ((~calm(X0) | tall(X0)) => (kind(X0) & rich(X0))) [input p10]
13. ! [X0] : ((~brave(X0) | ~generous(X0)) <=> (~old(X0) & generous(X0))) [input p12]
15. ! [X0] : ((happy(X0) & ~happy(X0)) <=> tall(X0)) [input p14]
16. ! [X0] : ((~brave(X0) <~> ~humble(X0)) => (~happy(X0) <~> ~calm(X0))) [input p15]
24. patient(alice) [input hypothesis]
26. ! [X0] : (~strong(X0) | (calm(X0) <=> patient(X0))) [ennf transformation 2]
27. ! [X0] : (~calm(X0) | (tall(X0) | curious(X0))) [ennf transformation 8]
28. ! [X0] : (~calm(X0) | tall(X0) | curious(X0)) [flattening 27]
29. ! [X0] : ((kind(X0) & rich(X0)) | (calm(X0) & ~tall(X0))) [ennf transformation 11]
32. ! [X0] : ((~happy(X0) <~> ~calm(X0)) | (~brave(X0) <=> ~humble(X0))) [ennf transformation 16]
35. ! [X0] : (~strong(X0) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0)))) [nnf transformation 26]
42. ! [X0] : (((~funny(X0) & generous(X0)) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | (funny(X0) | ~generous(X0)))) [nnf transformation 5]
43. ! [X0] : (((~funny(X0) & generous(X0)) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | funny(X0) | ~generous(X0))) [flattening 42]
51. (~rich(paul) | (~brave(alice) & humble(alice))) & ((brave(alice) | ~humble(alice)) | rich(paul)) [nnf transformation 9]
52. (~rich(paul) | (~brave(alice) & humble(alice))) & (brave(alice) | ~humble(alice) | rich(paul)) [flattening 51]
53. ! [X0] : (((funny(X0) & curious(X0)) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) & (((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | (~funny(X0) | ~curious(X0)))) [nnf transformation 10]
54. ! [X0] : (((funny(X0) & curious(X0)) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) & (((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | ~funny(X0) | ~curious(X0))) [flattening 53]
55. ! [X0] : (((~brave(X0) | ~generous(X0)) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | (brave(X0) & generous(X0)))) [nnf transformation 13]
56. ! [X0] : ((~brave(X0) | ~generous(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | (brave(X0) & generous(X0)))) [flattening 55]
60. ! [X0] : (((happy(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | (~happy(X0) | happy(X0)))) [nnf transformation 15]
61. ! [X0] : (((happy(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | ~happy(X0) | happy(X0))) [flattening 60]
62. ! [X0] : (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) [nnf transformation 32]
76. ~strong(X0) | calm(X0) | ~patient(X0) [cnf transformation 35]
90. ~funny(X0) | ~happy(X0) | strong(X0) [cnf transformation 43]
101. ~calm(X0) | tall(X0) | curious(X0) [cnf transformation 28]
103. ~rich(paul) | humble(alice) [cnf transformation 52]
104. ~rich(paul) | ~brave(alice) [cnf transformation 52]
105. ~generous(X0) | ~funny(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 54]
109. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 54]
112. rich(X0) | calm(X0) [cnf transformation 29]
116. generous(X0) | generous(X0) [cnf transformation 56]
126. ~happy(X0) | ~tall(X0) [cnf transformation 61]
127. ~tall(X0) | happy(X0) [cnf transformation 61]
130. ~humble(X0) | happy(X0) | calm(X0) | brave(X0) [cnf transformation 62]
142. patient(alice) [cnf transformation 24]
143. generous(X0) [duplicate literal removal 116]
145. ~generous(X0) | ~funny(X0) | ~curious(X0) [duplicate literal removal 105]
146. ~generous(X0) | funny(X0) [duplicate literal removal 109]
232. 20 <=> curious(paul) [avatar definition]
233. curious(paul) <- (20) [avatar component clause 232]
242. 21 <=> brave(alice) [avatar definition]
244. ~brave(alice) <- (~21) [avatar component clause 242]
246. 22 <=> rich(paul) [avatar definition]
248. ~rich(paul) <- (~22) [avatar component clause 246]
249. ~21 | ~22 [avatar split clause 104,246,242]
251. 23 <=> humble(alice) [avatar definition]
253. humble(alice) <- (23) [avatar component clause 251]
254. 23 | ~22 [avatar split clause 103,246,251]
256. ~curious(X0) | ~generous(X0) [subsumption resolution 145,146]
277. ~tall(X0) [subsumption resolution 126,127]
299. calm(paul) <- (~22) [resolution 112,248]
303. funny(X0) [resolution 146,143]
342. ~happy(X0) | strong(X0) [resolution 90,303]
354. tall(paul) | curious(paul) <- (~22) [resolution 101,299]
359. curious(paul) <- (~22) [subsumption resolution 354,277]
362. 20 | 22 [avatar split clause 359,246,232]
363. ~generous(paul) <- (20) [resolution 233,256]
364. $false <- (20) [subsumption resolution 363,143]
365. ~20 [avatar contradiction clause 364]
398. 41 <=> calm(alice) [avatar definition]
399. calm(alice) <- (41) [avatar component clause 398]
400. ~calm(alice) <- (~41) [avatar component clause 398]
402. 42 <=> happy(alice) [avatar definition]
403. happy(alice) <- (42) [avatar component clause 402]
423. happy(alice) | calm(alice) | brave(alice) <- (23) [resolution 130,253]
454. tall(alice) | curious(alice) <- (41) [resolution 399,101]
455. curious(alice) <- (41) [subsumption resolution 454,277]
475. ~generous(alice) <- (41) [resolution 455,256]
476. $false <- (41) [subsumption resolution 475,143]
477. ~41 [avatar contradiction clause 476]
478. happy(alice) | calm(alice) <- (~21, 23) [subsumption resolution 423,244]
479. 41 | 42 | 21 | ~23 [avatar split clause 478,251,242,402,398]
480. strong(alice) <- (42) [resolution 403,342]
490. calm(alice) | ~patient(alice) <- (42) [resolution 480,76]
492. ~patient(alice) <- (~41, 42) [subsumption resolution 490,400]
493. $false <- (~41, 42) [subsumption resolution 492,142]
494. 41 | ~42 [avatar contradiction clause 493]
495. $false [avatar sat refutation 249,254,362,365,477,479,494]
% SZS output end Proof for 5944740545134060913916123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
If someone is both happy and calm then alice is either not brave or curious and vice versa.
If someone is either not brave or generous then fred is quiet and vice versa.
If someone is both curious and not funny then someone is wise.
If someone is both not tall and not patient then someone is both quiet and not creative.
If someone is not brave or not curious then paul is old and vice versa.
Lucy is wise or not humble.
Alice is not brave.
Susan is both not humble and quiet.
Someone is not kind.
Susan is both tall and not kind.
John is both kind and wise.
Someone is either kind or not quiet.
John is both brave and not patient. | Paul is curious. | entailment | (![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
((?[X]:((happy(X)&calm(X))))<=>((~brave(alice)<~>curious(alice))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(quiet(fred)))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:(wise(X))))&
((?[X]:((~tall(X)&~patient(X))))=>(?[X]:((quiet(X)&~creative(X)))))&
((?[X]:((~brave(X)|~curious(X))))<=>(old(paul)))&
((wise(lucy)|~humble(lucy)))&
(~brave(alice))&
((~humble(susan)&quiet(susan)))&
(?[X]:(~kind(X)))&
((tall(susan)&~kind(susan)))&
((kind(john)&wise(john)))&
(?[X]:((kind(X)<~>~quiet(X))))&
((brave(john)&~patient(john))) | curious(paul) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4316604852557823734616547
% SZS output start Proof for 4316604852557823734616547
4. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~patient(X0) <~> calm(X0))) [input p3]
8. ? [X0] : ~curious(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p7]
25. ~curious(paul) [input hypothesis]
26. ? [X0] : ~curious(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 8]
39. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : curious(X0) [ennf transformation 26]
49. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 4]
53. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : curious(X1) [rectify 39]
54. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK0) & quiet(sK0)) [choice axiom]
55. (patient(sK0) & quiet(sK0)) | ! [X1] : curious(X1) [skolemisation 53,54]
89. calm(X0) | ~patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 49]
93. ~calm(X0) | ~quiet(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 49]
106. quiet(sK0) | curious(X1) [cnf transformation 55]
107. patient(sK0) | curious(X1) [cnf transformation 55]
140. ~curious(paul) [cnf transformation 25]
141. calm(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 89]
143. ~calm(X0) | ~quiet(X0) | ~patient(X0) [duplicate literal removal 93]
146. ~quiet(X0) | ~patient(X0) [subsumption resolution 141,143]
148. 1 <=> ! [X1] : curious(X1) [avatar definition]
149. curious(X1) <- (1) [avatar component clause 148]
151. 2 <=> patient(sK0) [avatar definition]
153. patient(sK0) <- (2) [avatar component clause 151]
154. 1 | 2 [avatar split clause 107,151,148]
156. 3 <=> quiet(sK0) [avatar definition]
158. quiet(sK0) <- (3) [avatar component clause 156]
159. 1 | 3 [avatar split clause 106,156,148]
279. ~patient(sK0) <- (3) [resolution 146,158]
280. $false <- (2, 3) [subsumption resolution 279,153]
281. ~2 | ~3 [avatar contradiction clause 280]
282. $false <- (1) [resolution 149,140]
285. ~1 [avatar contradiction clause 282]
286. $false [avatar sat refutation 154,159,281,285]
% SZS output end Proof for 4316604852557823734616547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or happy is brave and vice versa.
If susan is not humble or old then alice is not quiet or patient.
If fred is both humble and not wise then susan is not patient and vice versa.
If someone is not calm then someone is both humble and rich and vice versa.
Everyone who is either strong or not quiet is generous and vice versa.
Everyone who is creative or wise is creative or not strong and vice versa.
Everyone who is both tall and calm is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
John is either not tall or brave.
Someone is not calm or calm.
Someone is either not patient or not rich.
Someone is wise.
Susan is both happy and humble.
Alice is both tall and not old.
Someone is not old or not generous. | Fred is old. | neutral | (![X]:((~tall(X)|happy(X))<=>brave(X)))&
(((~humble(susan)|old(susan)))=>((~quiet(alice)|patient(alice))))&
(((humble(fred)&~wise(fred)))<=>(~patient(susan)))&
((?[X]:(~calm(X)))<=>(?[X]:((humble(X)&rich(X)))))&
(![X]:((strong(X)<~>~quiet(X))<=>generous(X)))&
(![X]:((creative(X)|wise(X))<=>(creative(X)|~strong(X))))&
(![X]:((tall(X)&calm(X))=>(~curious(X)&patient(X))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
((~tall(john)<~>brave(john)))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:(wise(X)))&
((happy(susan)&humble(susan)))&
((tall(alice)&~old(alice)))&
(?[X]:((~old(X)|~generous(X)))) | old(fred) | [] | null | 0 |
Everyone who is funny or not quiet is both not patient and kind.
Everyone who is not wise or not calm is either calm or humble and vice versa.
Everyone who is not tall or not calm is either quiet or not creative.
Everyone who is not calm or calm is not creative or curious.
Everyone who is not quiet or rich is both patient and kind.
Everyone who is strong or funny is generous and vice versa.
If paul is strong or not happy then john is not brave or not wise.
Everyone who is not happy is generous or not brave.
If someone is either not brave or patient then susan is either wise or not brave.
Everyone who is not funny or creative is both not strong and not calm and vice versa.
If susan is not strong then someone is rich and vice versa.
If john is both not kind and not rich then someone is either not curious or humble and vice versa.
Everyone who is either brave or old is both not quiet and not brave.
If someone is both quiet and tall then someone is not quiet or strong and vice versa.
Everyone who is both not happy and not quiet is both creative and kind and vice versa.
Everyone who is not kind or not generous is both not generous and strong.
Susan is not generous or not wise.
Someone is not curious. | Susan is quiet. | entailment | (![X]:((funny(X)|~quiet(X))=>(~patient(X)&kind(X))))&
(![X]:((~wise(X)|~calm(X))<=>(calm(X)<~>humble(X))))&
(![X]:((~tall(X)|~calm(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)|calm(X))=>(~creative(X)|curious(X))))&
(![X]:((~quiet(X)|rich(X))=>(patient(X)&kind(X))))&
(![X]:((strong(X)|funny(X))<=>generous(X)))&
(((strong(paul)|~happy(paul)))=>((~brave(john)|~wise(john))))&
(![X]:(~happy(X)=>(generous(X)|~brave(X))))&
((?[X]:((~brave(X)<~>patient(X))))=>((wise(susan)<~>~brave(susan))))&
(![X]:((~funny(X)|creative(X))<=>(~strong(X)&~calm(X))))&
((~strong(susan))<=>(?[X]:(rich(X))))&
(((~kind(john)&~rich(john)))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(![X]:((brave(X)<~>old(X))=>(~quiet(X)&~brave(X))))&
((?[X]:((quiet(X)&tall(X))))<=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(creative(X)&kind(X))))&
(![X]:((~kind(X)|~generous(X))=>(~generous(X)&strong(X))))&
((~generous(susan)|~wise(susan)))&
(?[X]:(~curious(X))) | quiet(susan) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5660534378842345321931390
% SZS output start Proof for 5660534378842345321931390
1. ! [X0] : ((~quiet(X0) | funny(X0)) => (kind(X0) & ~patient(X0))) [input p0]
5. ! [X0] : ((rich(X0) | ~quiet(X0)) => (kind(X0) & patient(X0))) [input p4]
19. ~quiet(susan) [input hypothesis]
21. ! [X0] : ((kind(X0) & ~patient(X0)) | (quiet(X0) & ~funny(X0))) [ennf transformation 1]
25. ! [X0] : ((kind(X0) & patient(X0)) | (~rich(X0) & quiet(X0))) [ennf transformation 5]
61. ~patient(X0) | quiet(X0) [cnf transformation 21]
76. patient(X0) | quiet(X0) [cnf transformation 25]
122. ~quiet(susan) [cnf transformation 19]
127. quiet(X0) [subsumption resolution 76,61]
231. $false [subsumption resolution 122,127]
% SZS output end Proof for 5660534378842345321931390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or not strong then fred is not old or generous. Everyone who is both calm and not tall is quiet or not funny and vice versa. If lucy is either not quiet or not tall then someone is strong. If susan is both not strong and humble then fred is both curious and not calm and vice versa. If susan is not curious or humble then john is both not humble and not funny. Everyone who is both quiet and brave is both kind and humble. Everyone who is both not creative and not funny is both not old and not kind. Everyone who is not funny is either not kind or happy. If someone is either not happy or not kind then someone is both not rich and kind and vice versa. If alice is either generous or not generous then alice is not old or happy and vice versa. If paul is both not wise and not brave then susan is not happy and vice versa. Everyone who is either brave or not generous is not quiet or not tall and vice versa. If susan is either not brave or generous then alice is both not old and generous. If lucy is strong then someone is happy and vice versa. Everyone who is happy or not brave is strong or brave and vice versa. If someone is either not creative or tall then alice is not generous or not strong and vice versa. Someone is not old or not creative. Paul is wise or not strong. Fred is either rich or not brave. Mary is both old and humble. Someone is rich or old. Fred is old or rich. John is brave or not patient. Susan is not wise. | Alice is old. | contradiction | (((~rich(lucy)|~strong(lucy)))=>((~old(fred)|generous(fred))))&
(![X]:((calm(X)&~tall(X))<=>(quiet(X)|~funny(X))))&
(((~quiet(lucy)<~>~tall(lucy)))=>(?[X]:(strong(X))))&
(((~strong(susan)&humble(susan)))<=>((curious(fred)&~calm(fred))))&
(((~curious(susan)|humble(susan)))=>((~humble(john)&~funny(john))))&
(![X]:((quiet(X)&brave(X))=>(kind(X)&humble(X))))&
(![X]:((~creative(X)&~funny(X))=>(~old(X)&~kind(X))))&
(![X]:(~funny(X)=>(~kind(X)<~>happy(X))))&
((?[X]:((~happy(X)<~>~kind(X))))<=>(?[X]:((~rich(X)&kind(X)))))&
(((generous(alice)<~>~generous(alice)))<=>((~old(alice)|happy(alice))))&
(((~wise(paul)&~brave(paul)))<=>(~happy(susan)))&
(![X]:((brave(X)<~>~generous(X))<=>(~quiet(X)|~tall(X))))&
(((~brave(susan)<~>generous(susan)))=>((~old(alice)&generous(alice))))&
((strong(lucy))<=>(?[X]:(happy(X))))&
(![X]:((happy(X)|~brave(X))<=>(strong(X)|brave(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>((~generous(alice)|~strong(alice))))&
(?[X]:((~old(X)|~creative(X))))&
((wise(paul)|~strong(paul)))&
((rich(fred)<~>~brave(fred)))&
((old(mary)&humble(mary)))&
(?[X]:((rich(X)|old(X))))&
((old(fred)|rich(fred)))&
((brave(john)|~patient(john)))&
(~wise(susan)) | old(alice) | [
"p1",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8060056283687720442150913
% SZS output start Proof for 8060056283687720442150913
2. ! [X0] : ((~tall(X0) & calm(X0)) <=> (~funny(X0) | quiet(X0))) [input p1]
12. ! [X0] : ((brave(X0) <~> ~generous(X0)) <=> (~tall(X0) | ~quiet(X0))) [input p11]
13. (~brave(susan) <~> generous(susan)) => (generous(alice) & ~old(alice)) [input p12]
25. old(alice) [input hypothesis]
37. (generous(alice) & ~old(alice)) | (~brave(susan) <=> generous(susan)) [ennf transformation 13]
38. ! [X0] : (((~tall(X0) & calm(X0)) | (funny(X0) & ~quiet(X0))) & ((~funny(X0) | quiet(X0)) | (tall(X0) | ~calm(X0)))) [nnf transformation 2]
39. ! [X0] : (((~tall(X0) & calm(X0)) | (funny(X0) & ~quiet(X0))) & (~funny(X0) | quiet(X0) | tall(X0) | ~calm(X0))) [flattening 38]
55. ! [X0] : ((((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))))) [nnf transformation 12]
56. ! [X0] : ((((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))))) [flattening 55]
57. (generous(alice) & ~old(alice)) | ((~brave(susan) | ~generous(susan)) & (generous(susan) | brave(susan))) [nnf transformation 37]
79. ~quiet(X0) | ~tall(X0) [cnf transformation 39]
114. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 56]
115. ~generous(X0) | brave(X0) | tall(X0) [cnf transformation 56]
116. ~brave(X0) | generous(X0) | quiet(X0) [cnf transformation 56]
117. ~brave(X0) | generous(X0) | tall(X0) [cnf transformation 56]
118. ~old(alice) | generous(susan) | brave(susan) [cnf transformation 57]
119. ~old(alice) | ~brave(susan) | ~generous(susan) [cnf transformation 57]
143. old(alice) [cnf transformation 25]
254. 23 <=> old(alice) [avatar definition]
279. 28 <=> generous(susan) [avatar definition]
280. generous(susan) <- (28) [avatar component clause 279]
281. ~generous(susan) <- (~28) [avatar component clause 279]
283. 29 <=> brave(susan) [avatar definition]
284. brave(susan) <- (29) [avatar component clause 283]
285. ~brave(susan) <- (~29) [avatar component clause 283]
288. ~28 | ~29 | ~23 [avatar split clause 119,254,283,279]
289. 29 | 28 | ~23 [avatar split clause 118,254,279,283]
357. 23 [avatar split clause 143,254]
537. brave(susan) | quiet(susan) <- (28) [resolution 114,280]
547. quiet(susan) <- (28, ~29) [subsumption resolution 537,285]
550. brave(susan) | tall(susan) <- (28) [resolution 115,280]
556. tall(susan) <- (28, ~29) [subsumption resolution 550,285]
609. ~tall(susan) <- (28, ~29) [resolution 547,79]
611. $false <- (28, ~29) [subsumption resolution 609,556]
612. ~28 | 29 [avatar contradiction clause 611]
618. 77 <=> tall(susan) [avatar definition]
620. tall(susan) <- (77) [avatar component clause 618]
622. 78 <=> quiet(susan) [avatar definition]
624. quiet(susan) <- (78) [avatar component clause 622]
626. generous(susan) | tall(susan) <- (29) [resolution 284,117]
627. generous(susan) | quiet(susan) <- (29) [resolution 284,116]
631. tall(susan) <- (~28, 29) [subsumption resolution 626,281]
632. 77 | 28 | ~29 [avatar split clause 631,283,279,618]
633. quiet(susan) <- (~28, 29) [subsumption resolution 627,281]
634. 78 | 28 | ~29 [avatar split clause 633,283,279,622]
660. ~tall(susan) <- (78) [resolution 624,79]
662. $false <- (77, 78) [subsumption resolution 660,620]
663. ~77 | ~78 [avatar contradiction clause 662]
666. $false [avatar sat refutation 288,289,357,612,632,634,663]
% SZS output end Proof for 8060056283687720442150913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If alice is kind then someone is not creative.
Everyone who is either not patient or funny is brave or creative and vice versa.
Everyone who is patient is both wise and patient.
Everyone who is either happy or brave is both not generous and rich and vice versa.
If lucy is not tall then lucy is humble and vice versa.
Everyone who is either not strong or not creative is not creative and vice versa.
If paul is not strong then someone is quiet.
Everyone who is not curious is not strong and vice versa.
Everyone who is strong is both creative and not quiet and vice versa.
Everyone who is both not curious and strong is either strong or rich.
Everyone who is both quiet and not calm is both curious and not strong.
If susan is either not quiet or tall then someone is either brave or not strong.
Everyone who is not patient is quiet.
If someone is either not strong or brave then someone is either not strong or calm and vice versa.
If someone is either wise or quiet then someone is not happy or not creative and vice versa.
Someone is both not old and not kind.
Someone is rich.
Lucy is generous or creative.
Alice is not tall.
Susan is strong or happy.
Someone is not tall or not rich.
John is rich. | Paul is happy. | neutral | ((kind(alice))=>(?[X]:(~creative(X))))&
(![X]:((~patient(X)<~>funny(X))<=>(brave(X)|creative(X))))&
(![X]:(patient(X)=>(wise(X)&patient(X))))&
(![X]:((happy(X)<~>brave(X))<=>(~generous(X)&rich(X))))&
((~tall(lucy))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>~creative(X))<=>~creative(X)))&
((~strong(paul))=>(?[X]:(quiet(X))))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:(strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~curious(X)&strong(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)&~calm(X))=>(curious(X)&~strong(X))))&
(((~quiet(susan)<~>tall(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(?[X]:((~old(X)&~kind(X))))&
(?[X]:(rich(X)))&
((generous(lucy)|creative(lucy)))&
(~tall(alice))&
((strong(susan)|happy(susan)))&
(?[X]:((~tall(X)|~rich(X))))&
(rich(john)) | happy(paul) | [] | null | 0 |
If someone is either old or quiet then lucy is not quiet or tall.
If someone is not kind then john is both kind and not quiet.
If someone is either quiet or wise then mary is both not kind and generous and vice versa.
If susan is either calm or kind then someone is both not kind and creative.
Everyone who is both not creative and tall is strong and vice versa.
Everyone who is humble or not tall is both tall and curious.
If paul is not old then someone is not quiet or not kind.
Everyone who is not curious is tall.
Everyone who is both not happy and not old is both wise and generous.
If paul is either not calm or creative then someone is funny and vice versa.
Everyone who is both not kind and wise is not happy or happy.
Everyone who is rich or tall is brave or kind.
If someone is not tall or curious then someone is not happy and vice versa.
Everyone who is both happy and patient is both not strong and rich and vice versa.
Everyone who is funny or not patient is generous.
If someone is not generous then susan is not rich or curious.
Lucy is either rich or not funny.
Someone is both not humble and old.
Someone is either not curious or not kind.
Mary is not happy or not kind.
Someone is strong.
John is both rich and creative.
Susan is not wise.
Susan is either not happy or not rich. | Lucy is tall. | entailment | ((?[X]:((old(X)<~>quiet(X))))=>((~quiet(lucy)|tall(lucy))))&
((?[X]:(~kind(X)))=>((kind(john)&~quiet(john))))&
((?[X]:((quiet(X)<~>wise(X))))<=>((~kind(mary)&generous(mary))))&
(((calm(susan)<~>kind(susan)))=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((~creative(X)&tall(X))<=>strong(X)))&
(![X]:((humble(X)|~tall(X))=>(tall(X)&curious(X))))&
((~old(paul))=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:(~curious(X)=>tall(X)))&
(![X]:((~happy(X)&~old(X))=>(wise(X)&generous(X))))&
(((~calm(paul)<~>creative(paul)))<=>(?[X]:(funny(X))))&
(![X]:((~kind(X)&wise(X))=>(~happy(X)|happy(X))))&
(![X]:((rich(X)|tall(X))=>(brave(X)|kind(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:(~happy(X))))&
(![X]:((happy(X)&patient(X))<=>(~strong(X)&rich(X))))&
(![X]:((funny(X)|~patient(X))=>generous(X)))&
((?[X]:(~generous(X)))=>((~rich(susan)|curious(susan))))&
((rich(lucy)<~>~funny(lucy)))&
(?[X]:((~humble(X)&old(X))))&
(?[X]:((~curious(X)<~>~kind(X))))&
((~happy(mary)|~kind(mary)))&
(?[X]:(strong(X)))&
((rich(john)&creative(john)))&
(~wise(susan))&
((~happy(susan)<~>~rich(susan))) | tall(lucy) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 294366556756560954695839
% SZS output start Proof for 294366556756560954695839
6. ! [X0] : ((~tall(X0) | humble(X0)) => (curious(X0) & tall(X0))) [input p5]
25. ~tall(lucy) [input hypothesis]
29. ! [X0] : (~tall(X0) => (curious(X0) & tall(X0))) [pure predicate removal 6]
34. ! [X0] : ((curious(X0) & tall(X0)) | tall(X0)) [ennf transformation 29]
94. tall(X0) | tall(X0) [cnf transformation 34]
127. ~tall(lucy) [cnf transformation 25]
128. tall(X0) [duplicate literal removal 94]
298. $false [subsumption resolution 127,128]
% SZS output end Proof for 294366556756560954695839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or brave is either not happy or calm.
Everyone who is brave is curious and vice versa.
If john is not wise or not creative then john is brave and vice versa.
Everyone who is both not tall and tall is both curious and strong and vice versa.
Everyone who is both humble and not calm is either funny or not humble.
Everyone who is tall is both not humble and not quiet and vice versa.
Everyone who is not brave or strong is old and vice versa.
If someone is both curious and funny then lucy is not happy or not creative and vice versa.
Everyone who is not calm is both patient and tall.
If someone is either curious or creative then someone is old and vice versa.
Everyone who is either not brave or curious is both creative and not tall.
Everyone who is not curious is not brave or strong.
If someone is either creative or generous then someone is either not humble or not happy.
If susan is rich then paul is happy or not humble.
If someone is not kind then lucy is tall or patient.
If paul is both brave and patient then someone is both funny and quiet and vice versa.
Lucy is brave or not humble.
Lucy is generous or not quiet.
John is strong.
Someone is not tall.
Someone is strong or not calm.
Someone is not creative or kind.
Someone is not strong. | Paul is kind. | neutral | (![X]:((~humble(X)<~>brave(X))=>(~happy(X)<~>calm(X))))&
(![X]:(brave(X)<=>curious(X)))&
(((~wise(john)|~creative(john)))<=>(brave(john)))&
(![X]:((~tall(X)&tall(X))<=>(curious(X)&strong(X))))&
(![X]:((humble(X)&~calm(X))=>(funny(X)<~>~humble(X))))&
(![X]:(tall(X)<=>(~humble(X)&~quiet(X))))&
(![X]:((~brave(X)|strong(X))<=>old(X)))&
((?[X]:((curious(X)&funny(X))))<=>((~happy(lucy)|~creative(lucy))))&
(![X]:(~calm(X)=>(patient(X)&tall(X))))&
((?[X]:((curious(X)<~>creative(X))))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)<~>curious(X))=>(creative(X)&~tall(X))))&
(![X]:(~curious(X)=>(~brave(X)|strong(X))))&
((?[X]:((creative(X)<~>generous(X))))=>(?[X]:((~humble(X)<~>~happy(X)))))&
((rich(susan))=>((happy(paul)|~humble(paul))))&
((?[X]:(~kind(X)))=>((tall(lucy)|patient(lucy))))&
(((brave(paul)&patient(paul)))<=>(?[X]:((funny(X)&quiet(X)))))&
((brave(lucy)|~humble(lucy)))&
((generous(lucy)|~quiet(lucy)))&
(strong(john))&
(?[X]:(~tall(X)))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((~creative(X)|kind(X))))&
(?[X]:(~strong(X))) | kind(paul) | [] | null | 0 |
Everyone who is not humble is generous or humble and vice versa.
Everyone who is tall is both generous and strong and vice versa.
Everyone who is either not humble or not happy is both not patient and not happy and vice versa.
If someone is both calm and patient then someone is not calm and vice versa.
Everyone who is either calm or funny is both not creative and not humble.
Everyone who is either old or brave is either not generous or rich.
If someone is either not strong or generous then someone is not strong and vice versa.
Everyone who is both patient and strong is either wise or not quiet.
If lucy is either calm or humble then someone is either rich or not kind and vice versa.
Everyone who is both not old and strong is brave or not creative.
Everyone who is both creative and brave is wise or brave and vice versa.
If fred is both not happy and humble then susan is creative and vice versa.
Everyone who is not brave is not calm or tall.
If paul is not rich or creative then someone is either brave or tall and vice versa.
Everyone who is both humble and brave is both tall and humble and vice versa.
Susan is either curious or not tall.
Susan is either not generous or patient.
Fred is not old.
Paul is either rich or quiet.
Paul is either not curious or not brave.
John is both kind and tall.
Someone is either not creative or not brave.
Mary is either not creative or calm. | Susan is not patient. | contradiction | (![X]:(~humble(X)<=>(generous(X)|humble(X))))&
(![X]:(tall(X)<=>(generous(X)&strong(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~patient(X)&~happy(X))))&
((?[X]:((calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
(![X]:((calm(X)<~>funny(X))=>(~creative(X)&~humble(X))))&
(![X]:((old(X)<~>brave(X))=>(~generous(X)<~>rich(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:((patient(X)&strong(X))=>(wise(X)<~>~quiet(X))))&
(((calm(lucy)<~>humble(lucy)))<=>(?[X]:((rich(X)<~>~kind(X)))))&
(![X]:((~old(X)&strong(X))=>(brave(X)|~creative(X))))&
(![X]:((creative(X)&brave(X))<=>(wise(X)|brave(X))))&
(((~happy(fred)&humble(fred)))<=>(creative(susan)))&
(![X]:(~brave(X)=>(~calm(X)|tall(X))))&
(((~rich(paul)|creative(paul)))<=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((humble(X)&brave(X))<=>(tall(X)&humble(X))))&
((curious(susan)<~>~tall(susan)))&
((~generous(susan)<~>patient(susan)))&
(~old(fred))&
((rich(paul)<~>quiet(paul)))&
((~curious(paul)<~>~brave(paul)))&
((kind(john)&tall(john)))&
(?[X]:((~creative(X)<~>~brave(X))))&
((~creative(mary)<~>calm(mary))) | ~patient(susan) | [
"p0",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7633025005089090737568074
% SZS output start Proof for 7633025005089090737568074
1. ! [X0] : (~humble(X0) <=> (humble(X0) | generous(X0))) [input p0]
17. ~generous(susan) <~> patient(susan) [input p16]
24. ~patient(susan) [input hypothesis]
35. ! [X0] : ((~humble(X0) | (~humble(X0) & ~generous(X0))) & ((humble(X0) | generous(X0)) | humble(X0))) [nnf transformation 1]
36. ! [X0] : ((~humble(X0) | (~humble(X0) & ~generous(X0))) & (humble(X0) | generous(X0) | humble(X0))) [flattening 35]
70. (~patient(susan) | generous(susan)) & (patient(susan) | ~generous(susan)) [nnf transformation 17]
77. humble(X0) | generous(X0) | humble(X0) [cnf transformation 36]
79. ~humble(X0) | ~humble(X0) [cnf transformation 36]
136. patient(susan) | ~generous(susan) [cnf transformation 70]
149. ~patient(susan) [cnf transformation 24]
152. humble(X0) | generous(X0) [duplicate literal removal 77]
153. ~humble(X0) [duplicate literal removal 79]
154. generous(X0) [subsumption resolution 152,153]
264. patient(susan) [subsumption resolution 136,154]
293. $false [subsumption resolution 149,264]
% SZS output end Proof for 7633025005089090737568074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not happy is either not curious or not patient and vice versa. If someone is funny or old then someone is both strong and not old and vice versa. Everyone who is funny is both not wise and funny and vice versa. If alice is both not patient and not happy then mary is happy or not quiet. If someone is not happy then someone is either strong or creative and vice versa. Everyone who is creative or not creative is both not old and curious and vice versa. Everyone who is either not funny or old is not generous and vice versa. If mary is either old or not old then john is both calm and not creative. Everyone who is both patient and not happy is either not calm or patient and vice versa. If someone is either not kind or old then paul is both curious and not patient. If someone is both happy and tall then susan is either brave or strong. If someone is humble or not creative then john is not quiet and vice versa. If paul is not strong then john is generous or not tall and vice versa. If fred is either not rich or not curious then mary is either funny or not old and vice versa. Everyone who is either tall or not brave is both wise and quiet and vice versa. Everyone who is not patient or funny is both not funny and not calm. Someone is kind or tall. Someone is kind or not patient. Someone is both not strong and not generous. Fred is patient or not kind. Someone is kind or strong. Lucy is not creative. | Paul is happy. | contradiction | (![X]:((~strong(X)<~>~happy(X))<=>(~curious(X)<~>~patient(X))))&
((?[X]:((funny(X)|old(X))))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:(funny(X)<=>(~wise(X)&funny(X))))&
(((~patient(alice)&~happy(alice)))=>((happy(mary)|~quiet(mary))))&
((?[X]:(~happy(X)))<=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((creative(X)|~creative(X))<=>(~old(X)&curious(X))))&
(![X]:((~funny(X)<~>old(X))<=>~generous(X)))&
(((old(mary)<~>~old(mary)))=>((calm(john)&~creative(john))))&
(![X]:((patient(X)&~happy(X))<=>(~calm(X)<~>patient(X))))&
((?[X]:((~kind(X)<~>old(X))))=>((curious(paul)&~patient(paul))))&
((?[X]:((happy(X)&tall(X))))=>((brave(susan)<~>strong(susan))))&
((?[X]:((humble(X)|~creative(X))))<=>(~quiet(john)))&
((~strong(paul))<=>((generous(john)|~tall(john))))&
(((~rich(fred)<~>~curious(fred)))<=>((funny(mary)<~>~old(mary))))&
(![X]:((tall(X)<~>~brave(X))<=>(wise(X)&quiet(X))))&
(![X]:((~patient(X)|funny(X))=>(~funny(X)&~calm(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((kind(X)|~patient(X))))&
(?[X]:((~strong(X)&~generous(X))))&
((patient(fred)|~kind(fred)))&
(?[X]:((kind(X)|strong(X))))&
(~creative(lucy)) | happy(paul) | [
"p0",
"p1",
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7749870950629974696535396
% SZS output start Proof for 7749870950629974696535396
1. ! [X0] : ((~strong(X0) <~> ~happy(X0)) <=> (~curious(X0) <~> ~patient(X0))) [input p0]
2. ? [X0] : (old(X0) | funny(X0)) <=> ? [X0] : (~old(X0) & strong(X0)) [input p1]
6. ! [X0] : ((~creative(X0) | creative(X0)) <=> (curious(X0) & ~old(X0))) [input p5]
9. ! [X0] : ((~happy(X0) & patient(X0)) <=> (~calm(X0) <~> patient(X0))) [input p8]
16. ! [X0] : ((funny(X0) | ~patient(X0)) => (~calm(X0) & ~funny(X0))) [input p15]
23. happy(paul) [input hypothesis]
24. ? [X0] : (old(X0) | funny(X0)) <=> ? [X1] : (~old(X1) & strong(X1)) [rectify 2]
31. ! [X0] : ((~calm(X0) & ~funny(X0)) | (~funny(X0) & patient(X0))) [ennf transformation 16]
32. ! [X0] : ((((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0))))) [nnf transformation 1]
33. (? [X0] : (old(X0) | funny(X0)) | ! [X1] : (old(X1) | ~strong(X1))) & (? [X1] : (~old(X1) & strong(X1)) | ! [X0] : (~old(X0) & ~funny(X0))) [nnf transformation 24]
34. (? [X0] : (old(X0) | funny(X0)) | ! [X1] : (old(X1) | ~strong(X1))) & (? [X2] : (~old(X2) & strong(X2)) | ! [X3] : (~old(X3) & ~funny(X3))) [rectify 33]
35. ? [X0] : (old(X0) | funny(X0)) => (old(sK0) | funny(sK0)) [choice axiom]
36. ? [X2] : (~old(X2) & strong(X2)) => (~old(sK1) & strong(sK1)) [choice axiom]
37. ((old(sK0) | funny(sK0)) | ! [X1] : (old(X1) | ~strong(X1))) & ((~old(sK1) & strong(sK1)) | ! [X3] : (~old(X3) & ~funny(X3))) [skolemisation 34,36,35]
45. ! [X0] : (((~creative(X0) | creative(X0)) | (~curious(X0) | old(X0))) & ((curious(X0) & ~old(X0)) | (creative(X0) & ~creative(X0)))) [nnf transformation 6]
46. ! [X0] : ((~creative(X0) | creative(X0) | ~curious(X0) | old(X0)) & ((curious(X0) & ~old(X0)) | (creative(X0) & ~creative(X0)))) [flattening 45]
49. ! [X0] : (((~happy(X0) & patient(X0)) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 9]
50. ! [X0] : (((~happy(X0) & patient(X0)) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | happy(X0) | ~patient(X0))) [flattening 49]
70. ~patient(X0) | ~curious(X0) | ~happy(X0) | strong(X0) [cnf transformation 32]
82. old(sK0) | funny(sK0) | old(X1) | ~strong(X1) [cnf transformation 37]
91. ~old(X0) | ~creative(X0) [cnf transformation 46]
92. ~old(X0) | creative(X0) [cnf transformation 46]
93. curious(X0) | ~creative(X0) [cnf transformation 46]
94. creative(X0) | curious(X0) [cnf transformation 46]
106. patient(X0) | patient(X0) | calm(X0) [cnf transformation 50]
137. ~funny(X0) | ~funny(X0) [cnf transformation 31]
138. ~calm(X0) | patient(X0) [cnf transformation 31]
147. happy(paul) [cnf transformation 23]
148. ~funny(X0) [duplicate literal removal 137]
150. calm(X0) | patient(X0) [duplicate literal removal 106]
156. 1 <=> ! [X1] : (old(X1) | ~strong(X1)) [avatar definition]
157. old(X1) | ~strong(X1) <- (1) [avatar component clause 156]
159. 2 <=> funny(sK0) [avatar definition]
161. funny(sK0) <- (2) [avatar component clause 159]
163. 3 <=> old(sK0) [avatar definition]
165. old(sK0) <- (3) [avatar component clause 163]
166. 1 | 2 | 3 [avatar split clause 82,163,159,156]
168. 4 <=> ! [X3] : ~old(X3) [avatar definition]
169. ~old(X3) <- (4) [avatar component clause 168]
176. 6 <=> ! [X3] : ~funny(X3) [avatar definition]
177. ~funny(X3) <- (6) [avatar component clause 176]
227. curious(X0) [subsumption resolution 93,94]
228. ~old(X0) [subsumption resolution 91,92]
229. 4 [avatar split clause 228,168]
324. patient(X0) [subsumption resolution 138,150]
325. 6 [avatar split clause 148,176]
349. $false <- (2, 6) [subsumption resolution 161,177]
350. ~2 | ~6 [avatar contradiction clause 349]
352. $false <- (3, 4) [subsumption resolution 165,169]
353. ~3 | ~4 [avatar contradiction clause 352]
354. ~strong(X1) <- (1, 4) [subsumption resolution 157,169]
383. ~curious(X0) | ~happy(X0) | strong(X0) [resolution 70,324]
384. ~happy(X0) | strong(X0) [subsumption resolution 383,227]
385. ~happy(X0) <- (1, 4) [subsumption resolution 384,354]
386. $false <- (1, 4) [resolution 385,147]
387. ~1 | ~4 [avatar contradiction clause 386]
388. $false [avatar sat refutation 166,229,325,350,353,387]
% SZS output end Proof for 7749870950629974696535396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not strong or funny then someone is quiet.
Everyone who is both not old and wise is not creative or brave.
If someone is either not creative or not wise then paul is either not rich or not funny.
If someone is either not patient or quiet then paul is either not strong or not curious.
Everyone who is both not humble and quiet is either not wise or not tall.
Everyone who is not funny is not curious or rich.
Everyone who is not creative or calm is both not calm and not patient and vice versa.
If someone is both not calm and not humble then someone is not humble or curious and vice versa.
Everyone who is not patient is creative or humble and vice versa.
If paul is tall or not generous then someone is funny or quiet.
Everyone who is not funny or not brave is creative and vice versa.
If john is both not generous and humble then susan is either calm or brave and vice versa.
If someone is either tall or brave then someone is not funny.
If someone is both kind and not patient then someone is both old and not tall.
Mary is brave.
Someone is either not brave or quiet.
Someone is not creative or quiet.
Alice is either not kind or wise.
Someone is not kind or not strong. | John is humble. | entailment | (((~strong(lucy)|funny(lucy)))=>(?[X]:(quiet(X))))&
(![X]:((~old(X)&wise(X))=>(~creative(X)|brave(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>((~rich(paul)<~>~funny(paul))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((~strong(paul)<~>~curious(paul))))&
(![X]:((~humble(X)&quiet(X))=>(~wise(X)<~>~tall(X))))&
(![X]:(~funny(X)=>(~curious(X)|rich(X))))&
(![X]:((~creative(X)|calm(X))<=>(~calm(X)&~patient(X))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:(~patient(X)<=>(creative(X)|humble(X))))&
(((tall(paul)|~generous(paul)))=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:((~funny(X)|~brave(X))<=>creative(X)))&
(((~generous(john)&humble(john)))<=>((calm(susan)<~>brave(susan))))&
((?[X]:((tall(X)<~>brave(X))))=>(?[X]:(~funny(X))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((old(X)&~tall(X)))))&
(brave(mary))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~creative(X)|quiet(X))))&
((~kind(alice)<~>wise(alice)))&
(?[X]:((~kind(X)|~strong(X)))) | humble(john) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7613929053921212189124
% SZS output start Proof for 7613929053921212189124
7. ! [X0] : ((calm(X0) | ~creative(X0)) <=> (~patient(X0) & ~calm(X0))) [input p6]
9. ! [X0] : (~patient(X0) <=> (humble(X0) | creative(X0))) [input p8]
20. ~humble(john) [input hypothesis]
41. ! [X0] : (((calm(X0) | ~creative(X0)) | (patient(X0) | calm(X0))) & ((~patient(X0) & ~calm(X0)) | (~calm(X0) & creative(X0)))) [nnf transformation 7]
42. ! [X0] : ((calm(X0) | ~creative(X0) | patient(X0) | calm(X0)) & ((~patient(X0) & ~calm(X0)) | (~calm(X0) & creative(X0)))) [flattening 41]
48. ! [X0] : ((~patient(X0) | (~humble(X0) & ~creative(X0))) & ((humble(X0) | creative(X0)) | patient(X0))) [nnf transformation 9]
49. ! [X0] : ((~patient(X0) | (~humble(X0) & ~creative(X0))) & (humble(X0) | creative(X0) | patient(X0))) [flattening 48]
85. ~calm(X0) | ~calm(X0) [cnf transformation 42]
86. ~patient(X0) | creative(X0) [cnf transformation 42]
88. calm(X0) | ~creative(X0) | patient(X0) | calm(X0) [cnf transformation 42]
94. humble(X0) | creative(X0) | patient(X0) [cnf transformation 49]
95. ~patient(X0) | ~creative(X0) [cnf transformation 49]
118. ~humble(john) [cnf transformation 20]
119. ~calm(X0) [duplicate literal removal 85]
120. ~creative(X0) | calm(X0) | patient(X0) [duplicate literal removal 88]
193. ~patient(X0) [subsumption resolution 95,86]
194. humble(X0) | creative(X0) [subsumption resolution 94,193]
219. 22 <=> humble(john) [avatar definition]
220. ~humble(john) <- (~22) [avatar component clause 219]
290. ~22 [avatar split clause 118,219]
295. creative(john) <- (~22) [resolution 194,220]
310. calm(john) | patient(john) <- (~22) [resolution 120,295]
316. patient(john) <- (~22) [subsumption resolution 310,119]
317. $false <- (~22) [subsumption resolution 316,193]
318. 22 [avatar contradiction clause 317]
328. $false [avatar sat refutation 290,318]
% SZS output end Proof for 7613929053921212189124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If john is not humble or generous then mary is humble. Everyone who is either not patient or calm is either kind or calm and vice versa. If john is not patient then lucy is either not quiet or humble and vice versa. Everyone who is both wise and not quiet is creative and vice versa. Everyone who is not patient or wise is both not patient and quiet. If someone is both not old and humble then mary is either humble or rich. Everyone who is funny is either not creative or not kind and vice versa. If someone is either not calm or not curious then someone is not strong or not rich. Everyone who is not wise is not funny. If someone is not happy then susan is not patient. Everyone who is brave is either brave or kind and vice versa. If alice is both not patient and not quiet then someone is either not brave or not wise and vice versa. If someone is both not generous and rich then paul is either curious or rich and vice versa. If fred is not brave or wise then fred is either creative or calm. If mary is both humble and kind then alice is strong. Everyone who is both not wise and not creative is calm. Someone is both not old and happy. Someone is old or brave. Someone is both not wise and calm. Fred is not humble. Someone is humble. Someone is not happy or happy. | Mary is not creative. | entailment | (((~humble(john)|generous(john)))=>(humble(mary)))&
(![X]:((~patient(X)<~>calm(X))<=>(kind(X)<~>calm(X))))&
((~patient(john))<=>((~quiet(lucy)<~>humble(lucy))))&
(![X]:((wise(X)&~quiet(X))<=>creative(X)))&
(![X]:((~patient(X)|wise(X))=>(~patient(X)&quiet(X))))&
((?[X]:((~old(X)&humble(X))))=>((humble(mary)<~>rich(mary))))&
(![X]:(funny(X)<=>(~creative(X)<~>~kind(X))))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:(~wise(X)=>~funny(X)))&
((?[X]:(~happy(X)))=>(~patient(susan)))&
(![X]:(brave(X)<=>(brave(X)<~>kind(X))))&
(((~patient(alice)&~quiet(alice)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((?[X]:((~generous(X)&rich(X))))<=>((curious(paul)<~>rich(paul))))&
(((~brave(fred)|wise(fred)))=>((creative(fred)<~>calm(fred))))&
(((humble(mary)&kind(mary)))=>(strong(alice)))&
(![X]:((~wise(X)&~creative(X))=>calm(X)))&
(?[X]:((~old(X)&happy(X))))&
(?[X]:((old(X)|brave(X))))&
(?[X]:((~wise(X)&calm(X))))&
(~humble(fred))&
(?[X]:(humble(X)))&
(?[X]:((~happy(X)|happy(X)))) | ~creative(mary) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 9126241781116426522155437
% SZS output start Proof for 9126241781116426522155437
4. ! [X0] : ((~quiet(X0) & wise(X0)) <=> creative(X0)) [input p3]
5. ! [X0] : ((wise(X0) | ~patient(X0)) => (quiet(X0) & ~patient(X0))) [input p4]
23. creative(mary) [input hypothesis]
27. ! [X0] : ((quiet(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 5]
40. ! [X0] : (((~quiet(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | (quiet(X0) | ~wise(X0)))) [nnf transformation 4]
41. ! [X0] : (((~quiet(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | quiet(X0) | ~wise(X0))) [flattening 40]
84. ~creative(X0) | wise(X0) [cnf transformation 41]
85. ~creative(X0) | ~quiet(X0) [cnf transformation 41]
87. ~wise(X0) | ~patient(X0) [cnf transformation 27]
88. quiet(X0) | patient(X0) [cnf transformation 27]
128. creative(mary) [cnf transformation 23]
275. wise(mary) [resolution 84,128]
278. ~quiet(mary) [resolution 85,128]
279. ~patient(mary) [resolution 87,275]
282. patient(mary) [resolution 88,278]
285. $false [subsumption resolution 282,279]
% SZS output end Proof for 9126241781116426522155437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either not quiet or tall then someone is not kind or not generous and vice versa. Everyone who is both tall and kind is not wise. If someone is both humble and creative then someone is both humble and not curious. Everyone who is either not calm or not strong is happy or kind. If lucy is both quiet and not rich then someone is rich. Everyone who is not quiet or strong is both rich and old and vice versa. Everyone who is not brave or old is generous. Everyone who is both kind and not old is quiet or curious and vice versa. If john is either not tall or not humble then someone is not generous and vice versa. If someone is either funny or happy then someone is both not wise and kind. If someone is not curious or wise then mary is not quiet and vice versa. If someone is quiet or not funny then fred is not patient or not strong and vice versa. Everyone who is not calm or not rich is either not old or not strong. Everyone who is not funny or funny is not quiet. If someone is either curious or not generous then paul is both happy and not old and vice versa. Everyone who is either not kind or brave is rich and vice versa. Alice is strong or calm. Lucy is either tall or old. Paul is both generous and brave. Mary is either not tall or not old. Fred is patient. Alice is creative or kind. Alice is old or not quiet. | Alice is calm. | entailment | (((~quiet(john)<~>tall(john)))<=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:((tall(X)&kind(X))=>~wise(X)))&
((?[X]:((humble(X)&creative(X))))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~calm(X)<~>~strong(X))=>(happy(X)|kind(X))))&
(((quiet(lucy)&~rich(lucy)))=>(?[X]:(rich(X))))&
(![X]:((~quiet(X)|strong(X))<=>(rich(X)&old(X))))&
(![X]:((~brave(X)|old(X))=>generous(X)))&
(![X]:((kind(X)&~old(X))<=>(quiet(X)|curious(X))))&
(((~tall(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((~curious(X)|wise(X))))<=>(~quiet(mary)))&
((?[X]:((quiet(X)|~funny(X))))<=>((~patient(fred)|~strong(fred))))&
(![X]:((~calm(X)|~rich(X))=>(~old(X)<~>~strong(X))))&
(![X]:((~funny(X)|funny(X))=>~quiet(X)))&
((?[X]:((curious(X)<~>~generous(X))))<=>((happy(paul)&~old(paul))))&
(![X]:((~kind(X)<~>brave(X))<=>rich(X)))&
((strong(alice)|calm(alice)))&
((tall(lucy)<~>old(lucy)))&
((generous(paul)&brave(paul)))&
((~tall(mary)<~>~old(mary)))&
(patient(fred))&
((creative(alice)|kind(alice)))&
((old(alice)|~quiet(alice))) | calm(alice) | [
"p5",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2213559705007827601100377
% SZS output start Proof for 2213559705007827601100377
6. ! [X0] : ((strong(X0) | ~quiet(X0)) <=> (old(X0) & rich(X0))) [input p5]
13. ! [X0] : ((~rich(X0) | ~calm(X0)) => (~old(X0) <~> ~strong(X0))) [input p12]
17. calm(alice) | strong(alice) [input p16]
24. ~calm(alice) [input hypothesis]
36. ! [X0] : ((~old(X0) <~> ~strong(X0)) | (rich(X0) & calm(X0))) [ennf transformation 13]
48. ! [X0] : (((strong(X0) | ~quiet(X0)) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | (~strong(X0) & quiet(X0)))) [nnf transformation 6]
49. ! [X0] : ((strong(X0) | ~quiet(X0) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | (~strong(X0) & quiet(X0)))) [flattening 48]
69. ! [X0] : (((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (rich(X0) & calm(X0))) [nnf transformation 36]
93. old(X0) | ~strong(X0) [cnf transformation 49]
117. ~strong(X0) | ~old(X0) | calm(X0) [cnf transformation 69]
119. strong(X0) | old(X0) | calm(X0) [cnf transformation 69]
133. calm(alice) | strong(alice) [cnf transformation 17]
143. ~calm(alice) [cnf transformation 24]
276. old(X0) | calm(X0) [subsumption resolution 119,93]
277. ~strong(X0) | calm(X0) [subsumption resolution 117,276]
308. calm(alice) [subsumption resolution 133,277]
340. $false [subsumption resolution 143,308]
% SZS output end Proof for 2213559705007827601100377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or creative is both wise and rich. If someone is both rich and not funny then alice is not happy or not rich and vice versa. Everyone who is curious or not happy is either not rich or curious and vice versa. Everyone who is not patient is not creative or not curious. If someone is either not calm or not tall then someone is funny or not creative. If someone is calm then lucy is both patient and rich and vice versa. Everyone who is both not patient and humble is happy and vice versa. Everyone who is both patient and not strong is either not humble or funny and vice versa. Everyone who is not brave or not tall is brave or not wise and vice versa. Everyone who is either humble or calm is both strong and not generous and vice versa. If someone is either not calm or not quiet then someone is either not quiet or curious and vice versa. If someone is tall then someone is not patient and vice versa. Everyone who is humble or rich is either patient or not creative. Everyone who is not calm or rich is not patient. If mary is either wise or not creative then paul is humble or not curious and vice versa. Someone is not humble or happy. Alice is not old or not wise. Someone is not old or not wise. Lucy is either not rich or not calm. Mary is brave. Someone is not calm or calm. Someone is happy. | Mary is not calm. | entailment | (![X]:((~curious(X)|creative(X))=>(wise(X)&rich(X))))&
((?[X]:((rich(X)&~funny(X))))<=>((~happy(alice)|~rich(alice))))&
(![X]:((curious(X)|~happy(X))<=>(~rich(X)<~>curious(X))))&
(![X]:(~patient(X)=>(~creative(X)|~curious(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:((funny(X)|~creative(X)))))&
((?[X]:(calm(X)))<=>((patient(lucy)&rich(lucy))))&
(![X]:((~patient(X)&humble(X))<=>happy(X)))&
(![X]:((patient(X)&~strong(X))<=>(~humble(X)<~>funny(X))))&
(![X]:((~brave(X)|~tall(X))<=>(brave(X)|~wise(X))))&
(![X]:((humble(X)<~>calm(X))<=>(strong(X)&~generous(X))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:(tall(X)))<=>(?[X]:(~patient(X))))&
(![X]:((humble(X)|rich(X))=>(patient(X)<~>~creative(X))))&
(![X]:((~calm(X)|rich(X))=>~patient(X)))&
(((wise(mary)<~>~creative(mary)))<=>((humble(paul)|~curious(paul))))&
(?[X]:((~humble(X)|happy(X))))&
((~old(alice)|~wise(alice)))&
(?[X]:((~old(X)|~wise(X))))&
((~rich(lucy)<~>~calm(lucy)))&
(brave(mary))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:(happy(X))) | ~calm(mary) | [
"p0",
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8434081004970839311637964
% SZS output start Proof for 8434081004970839311637964
1. ! [X0] : ((creative(X0) | ~curious(X0)) => (rich(X0) & wise(X0))) [input p0]
3. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~rich(X0) <~> curious(X0))) [input p2]
6. ? [X0] : calm(X0) <=> (rich(lucy) & patient(lucy)) [input p5]
14. ! [X0] : ((rich(X0) | ~calm(X0)) => ~patient(X0)) [input p13]
23. calm(mary) [input hypothesis]
29. ! [X0] : ((rich(X0) & wise(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 1]
34. ! [X0] : (~patient(X0) | (~rich(X0) & calm(X0))) [ennf transformation 14]
40. ! [X0] : (((~happy(X0) | curious(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (happy(X0) & ~curious(X0)))) [nnf transformation 3]
41. ! [X0] : ((~happy(X0) | curious(X0) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (happy(X0) & ~curious(X0)))) [flattening 40]
46. (? [X0] : calm(X0) | (~rich(lucy) | ~patient(lucy))) & ((rich(lucy) & patient(lucy)) | ! [X0] : ~calm(X0)) [nnf transformation 6]
47. (? [X0] : calm(X0) | ~rich(lucy) | ~patient(lucy)) & ((rich(lucy) & patient(lucy)) | ! [X0] : ~calm(X0)) [flattening 46]
48. (? [X0] : calm(X0) | ~rich(lucy) | ~patient(lucy)) & ((rich(lucy) & patient(lucy)) | ! [X1] : ~calm(X1)) [rectify 47]
49. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
50. (calm(sK2) | ~rich(lucy) | ~patient(lucy)) & ((rich(lucy) & patient(lucy)) | ! [X1] : ~calm(X1)) [skolemisation 48,49]
81. rich(X0) | curious(X0) [cnf transformation 29]
90. ~curious(X0) | rich(X0) | ~curious(X0) [cnf transformation 41]
97. patient(lucy) | ~calm(X1) [cnf transformation 50]
134. ~patient(X0) | ~rich(X0) [cnf transformation 34]
147. calm(mary) [cnf transformation 23]
150. ~curious(X0) | rich(X0) [duplicate literal removal 90]
177. rich(X0) [subsumption resolution 150,81]
197. 10 <=> patient(lucy) [avatar definition]
198. patient(lucy) <- (10) [avatar component clause 197]
206. 12 <=> ! [X1] : ~calm(X1) [avatar definition]
207. ~calm(X1) <- (12) [avatar component clause 206]
208. 12 | 10 [avatar split clause 97,197,206]
263. ~patient(X0) [subsumption resolution 134,177]
298. $false <- (10) [subsumption resolution 198,263]
299. ~10 [avatar contradiction clause 298]
302. $false <- (12) [resolution 207,147]
305. ~12 [avatar contradiction clause 302]
306. $false [avatar sat refutation 208,299,305]
% SZS output end Proof for 8434081004970839311637964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not tall and not patient then someone is either wise or not wise and vice versa.
If paul is both strong and rich then someone is both curious and not kind and vice versa.
If lucy is both curious and not funny then susan is either not generous or happy.
Everyone who is not tall or kind is both not calm and quiet.
If someone is both old and creative then someone is both not calm and strong and vice versa.
Everyone who is tall is not quiet.
Everyone who is not patient or funny is brave or not patient and vice versa.
Everyone who is either not rich or not strong is not tall or quiet.
Everyone who is old or creative is not tall.
Everyone who is not patient or not curious is either not rich or not humble and vice versa.
Everyone who is either rich or not calm is not wise and vice versa.
Everyone who is not old is both not happy and not funny and vice versa.
Everyone who is both not rich and not quiet is rich and vice versa.
Everyone who is kind or not curious is either not generous or not patient.
If someone is not funny or old then someone is either generous or not curious.
Everyone who is curious or not quiet is not calm or not happy and vice versa.
Fred is both brave and not strong.
Someone is either old or calm.
Someone is both not calm and old.
Paul is funny.
Paul is not calm.
Someone is strong.
Fred is either creative or strong. | Paul is not kind. | contradiction | (((~tall(fred)&~patient(fred)))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(((strong(paul)&rich(paul)))<=>(?[X]:((curious(X)&~kind(X)))))&
(((curious(lucy)&~funny(lucy)))=>((~generous(susan)<~>happy(susan))))&
(![X]:((~tall(X)|kind(X))=>(~calm(X)&quiet(X))))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((~patient(X)|funny(X))<=>(brave(X)|~patient(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(~tall(X)|quiet(X))))&
(![X]:((old(X)|creative(X))=>~tall(X)))&
(![X]:((~patient(X)|~curious(X))<=>(~rich(X)<~>~humble(X))))&
(![X]:((rich(X)<~>~calm(X))<=>~wise(X)))&
(![X]:(~old(X)<=>(~happy(X)&~funny(X))))&
(![X]:((~rich(X)&~quiet(X))<=>rich(X)))&
(![X]:((kind(X)|~curious(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(~calm(X)|~happy(X))))&
((brave(fred)&~strong(fred)))&
(?[X]:((old(X)<~>calm(X))))&
(?[X]:((~calm(X)&old(X))))&
(funny(paul))&
(~calm(paul))&
(?[X]:(strong(X)))&
((creative(fred)<~>strong(fred))) | ~kind(paul) | [
"p1",
"p3",
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5395377982199839319419139
% SZS output start Proof for 5395377982199839319419139
2. (rich(paul) & strong(paul)) <=> ? [X0] : (~kind(X0) & curious(X0)) [input p1]
4. ! [X0] : ((kind(X0) | ~tall(X0)) => (quiet(X0) & ~calm(X0))) [input p3]
6. ! [X0] : (tall(X0) => ~quiet(X0)) [input p5]
13. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> rich(X0)) [input p12]
16. ! [X0] : ((~quiet(X0) | curious(X0)) <=> (~happy(X0) | ~calm(X0))) [input p15]
24. ~kind(paul) [input hypothesis]
29. ! [X0] : ((quiet(X0) & ~calm(X0)) | (~kind(X0) & tall(X0))) [ennf transformation 4]
30. ! [X0] : (~quiet(X0) | ~tall(X0)) [ennf transformation 6]
41. ((rich(paul) & strong(paul)) | ! [X0] : (kind(X0) | ~curious(X0))) & (? [X0] : (~kind(X0) & curious(X0)) | (~rich(paul) | ~strong(paul))) [nnf transformation 2]
42. ((rich(paul) & strong(paul)) | ! [X0] : (kind(X0) | ~curious(X0))) & (? [X0] : (~kind(X0) & curious(X0)) | ~rich(paul) | ~strong(paul)) [flattening 41]
43. ((rich(paul) & strong(paul)) | ! [X0] : (kind(X0) | ~curious(X0))) & (? [X1] : (~kind(X1) & curious(X1)) | ~rich(paul) | ~strong(paul)) [rectify 42]
44. ? [X1] : (~kind(X1) & curious(X1)) => (~kind(sK1) & curious(sK1)) [choice axiom]
45. ((rich(paul) & strong(paul)) | ! [X0] : (kind(X0) | ~curious(X0))) & ((~kind(sK1) & curious(sK1)) | ~rich(paul) | ~strong(paul)) [skolemisation 43,44]
60. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | (quiet(X0) | rich(X0)))) [nnf transformation 13]
61. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | quiet(X0) | rich(X0))) [flattening 60]
67. ! [X0] : (((~quiet(X0) | curious(X0)) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | (quiet(X0) & ~curious(X0)))) [nnf transformation 16]
68. ! [X0] : ((~quiet(X0) | curious(X0) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | (quiet(X0) & ~curious(X0)))) [flattening 67]
86. rich(paul) | kind(X0) | ~curious(X0) [cnf transformation 45]
89. ~calm(X0) | tall(X0) [cnf transformation 29]
97. ~quiet(X0) | ~tall(X0) [cnf transformation 30]
119. rich(X0) | quiet(X0) | rich(X0) [cnf transformation 61]
120. ~rich(X0) | ~rich(X0) [cnf transformation 61]
132. ~quiet(X0) | curious(X0) | calm(X0) [cnf transformation 68]
145. ~kind(paul) [cnf transformation 24]
146. rich(X0) | quiet(X0) [duplicate literal removal 119]
147. ~rich(X0) [duplicate literal removal 120]
171. 5 <=> ! [X0] : (kind(X0) | ~curious(X0)) [avatar definition]
172. ~curious(X0) | kind(X0) <- (5) [avatar component clause 171]
174. 6 <=> rich(paul) [avatar definition]
176. rich(paul) <- (6) [avatar component clause 174]
177. 5 | 6 [avatar split clause 86,174,171]
239. quiet(X0) [subsumption resolution 146,147]
259. calm(X0) | curious(X0) [subsumption resolution 132,239]
272. ~tall(X1) [resolution 97,239]
293. curious(X1) | tall(X1) [resolution 259,89]
298. curious(X1) [subsumption resolution 293,272]
301. kind(X0) <- (5) [resolution 298,172]
305. $false <- (5) [resolution 301,145]
307. ~5 [avatar contradiction clause 305]
308. $false <- (6) [subsumption resolution 176,147]
309. ~6 [avatar contradiction clause 308]
310. $false [avatar sat refutation 177,307,309]
% SZS output end Proof for 5395377982199839319419139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and not rich then paul is either creative or quiet and vice versa.
Everyone who is either not kind or wise is not old.
Everyone who is both funny and not wise is either not wise or rich.
If paul is generous or not wise then alice is either kind or wise and vice versa.
If mary is either tall or old then fred is humble and vice versa.
If mary is not wise or old then alice is both not strong and humble.
If someone is kind or not tall then fred is happy or humble and vice versa.
Everyone who is either patient or wise is both tall and not tall.
Everyone who is both not calm and curious is both not brave and not rich and vice versa.
If someone is not patient then someone is both not calm and calm and vice versa.
Everyone who is either brave or not quiet is not rich.
Everyone who is either not creative or curious is not curious and vice versa.
Everyone who is not brave or generous is either creative or happy and vice versa.
If fred is happy or not tall then someone is both curious and not creative and vice versa.
If lucy is both rich and brave then someone is not quiet or wise and vice versa.
Everyone who is either wise or brave is humble or strong.
Fred is both not happy and not calm.
Someone is not humble or wise.
Someone is both patient and not curious.
Mary is both curious and quiet.
Someone is generous or not curious.
Lucy is not old or not tall.
Susan is quiet or not wise. | Fred is not wise. | contradiction | ((?[X]:((kind(X)&~rich(X))))<=>((creative(paul)<~>quiet(paul))))&
(![X]:((~kind(X)<~>wise(X))=>~old(X)))&
(![X]:((funny(X)&~wise(X))=>(~wise(X)<~>rich(X))))&
(((generous(paul)|~wise(paul)))<=>((kind(alice)<~>wise(alice))))&
(((tall(mary)<~>old(mary)))<=>(humble(fred)))&
(((~wise(mary)|old(mary)))=>((~strong(alice)&humble(alice))))&
((?[X]:((kind(X)|~tall(X))))<=>((happy(fred)|humble(fred))))&
(![X]:((patient(X)<~>wise(X))=>(tall(X)&~tall(X))))&
(![X]:((~calm(X)&curious(X))<=>(~brave(X)&~rich(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~calm(X)&calm(X)))))&
(![X]:((brave(X)<~>~quiet(X))=>~rich(X)))&
(![X]:((~creative(X)<~>curious(X))<=>~curious(X)))&
(![X]:((~brave(X)|generous(X))<=>(creative(X)<~>happy(X))))&
(((happy(fred)|~tall(fred)))<=>(?[X]:((curious(X)&~creative(X)))))&
(((rich(lucy)&brave(lucy)))<=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:((wise(X)<~>brave(X))=>(humble(X)|strong(X))))&
((~happy(fred)&~calm(fred)))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((patient(X)&~curious(X))))&
((curious(mary)&quiet(mary)))&
(?[X]:((generous(X)|~curious(X))))&
((~old(lucy)|~tall(lucy)))&
((quiet(susan)|~wise(susan))) | ~wise(fred) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 912972214431710622546887
% SZS output start Proof for 912972214431710622546887
8. ! [X0] : ((patient(X0) <~> wise(X0)) => (~tall(X0) & tall(X0))) [input p7]
10. ? [X0] : ~patient(X0) <=> ? [X0] : (calm(X0) & ~calm(X0)) [input p9]
24. ~wise(fred) [input hypothesis]
25. ? [X0] : ~patient(X0) <=> ? [X1] : (calm(X1) & ~calm(X1)) [rectify 10]
29. ! [X0] : ((~tall(X0) & tall(X0)) | (patient(X0) <=> wise(X0))) [ennf transformation 8]
46. ! [X0] : ((~tall(X0) & tall(X0)) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) [nnf transformation 29]
49. (? [X0] : ~patient(X0) | ! [X1] : (~calm(X1) | calm(X1))) & (? [X1] : (calm(X1) & ~calm(X1)) | ! [X0] : patient(X0)) [nnf transformation 25]
50. (? [X0] : ~patient(X0) | ! [X1] : (~calm(X1) | calm(X1))) & (? [X2] : (calm(X2) & ~calm(X2)) | ! [X3] : patient(X3)) [rectify 49]
51. ? [X0] : ~patient(X0) => ~patient(sK2) [choice axiom]
52. ? [X2] : (calm(X2) & ~calm(X2)) => (calm(sK3) & ~calm(sK3)) [choice axiom]
53. (~patient(sK2) | ! [X1] : (~calm(X1) | calm(X1))) & ((calm(sK3) & ~calm(sK3)) | ! [X3] : patient(X3)) [skolemisation 50,52,51]
101. tall(X0) | wise(X0) | ~patient(X0) [cnf transformation 46]
103. ~tall(X0) | wise(X0) | ~patient(X0) [cnf transformation 46]
109. ~calm(sK3) | patient(X3) [cnf transformation 53]
110. calm(sK3) | patient(X3) [cnf transformation 53]
146. ~wise(fred) [cnf transformation 24]
251. ~patient(X0) | wise(X0) [subsumption resolution 101,103]
253. 21 <=> ! [X3] : patient(X3) [avatar definition]
254. patient(X3) <- (21) [avatar component clause 253]
256. 22 <=> calm(sK3) [avatar definition]
259. 21 | 22 [avatar split clause 110,256,253]
260. 21 | ~22 [avatar split clause 109,256,253]
358. wise(X0) <- (21) [resolution 251,254]
367. $false <- (21) [resolution 358,146]
371. ~21 [avatar contradiction clause 367]
372. $false [avatar sat refutation 259,260,371]
% SZS output end Proof for 912972214431710622546887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not curious then someone is both happy and not creative and vice versa.
Everyone who is either not humble or not calm is both happy and not quiet and vice versa.
If alice is both quiet and not curious then someone is both kind and humble.
If paul is both not brave and kind then alice is both not generous and not calm.
Everyone who is calm or not funny is either tall or not old and vice versa.
Everyone who is either rich or not rich is either generous or curious and vice versa.
Everyone who is kind or rich is rich and vice versa.
If someone is both not kind and tall then someone is both patient and not wise.
Everyone who is both strong and rich is either not happy or generous.
If someone is either not quiet or not creative then susan is creative.
If someone is patient or happy then someone is either not curious or not generous and vice versa.
If someone is rich then fred is both not generous and funny and vice versa.
If john is creative or not humble then lucy is not quiet and vice versa.
If someone is not strong then paul is both not patient and wise.
If someone is curious then mary is either happy or not happy and vice versa.
If someone is both funny and not calm then lucy is either not generous or not calm.
John is both patient and humble.
Mary is either not kind or old.
Lucy is either quiet or not kind.
Susan is either wise or not strong.
Someone is rich.
Susan is wise.
Someone is generous.
Mary is both not quiet and not creative. | Mary is funny. | neutral | ((~curious(lucy))<=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>(happy(X)&~quiet(X))))&
(((quiet(alice)&~curious(alice)))=>(?[X]:((kind(X)&humble(X)))))&
(((~brave(paul)&kind(paul)))=>((~generous(alice)&~calm(alice))))&
(![X]:((calm(X)|~funny(X))<=>(tall(X)<~>~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(generous(X)<~>curious(X))))&
(![X]:((kind(X)|rich(X))<=>rich(X)))&
((?[X]:((~kind(X)&tall(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((strong(X)&rich(X))=>(~happy(X)<~>generous(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>(creative(susan)))&
((?[X]:((patient(X)|happy(X))))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:(rich(X)))<=>((~generous(fred)&funny(fred))))&
(((creative(john)|~humble(john)))<=>(~quiet(lucy)))&
((?[X]:(~strong(X)))=>((~patient(paul)&wise(paul))))&
((?[X]:(curious(X)))<=>((happy(mary)<~>~happy(mary))))&
((?[X]:((funny(X)&~calm(X))))=>((~generous(lucy)<~>~calm(lucy))))&
((patient(john)&humble(john)))&
((~kind(mary)<~>old(mary)))&
((quiet(lucy)<~>~kind(lucy)))&
((wise(susan)<~>~strong(susan)))&
(?[X]:(rich(X)))&
(wise(susan))&
(?[X]:(generous(X)))&
((~quiet(mary)&~creative(mary))) | funny(mary) | [] | null | 0 |
Everyone who is both not rich and not generous is not generous or rich.
If someone is not curious or not kind then alice is curious.
If mary is both quiet and wise then someone is either patient or not curious and vice versa.
If someone is patient or old then someone is both not rich and brave.
Everyone who is not patient is either calm or rich.
If john is either not funny or funny then someone is generous.
Everyone who is creative is generous or not curious.
Everyone who is calm is both not brave and not rich.
Everyone who is not funny is both quiet and not calm and vice versa.
If someone is curious then someone is either humble or not wise and vice versa.
If lucy is both patient and not generous then someone is not old.
Everyone who is creative is curious or not rich and vice versa.
Everyone who is both not humble and not patient is creative.
If someone is either tall or not curious then fred is not generous.
Everyone who is either not quiet or not generous is both creative and kind.
Everyone who is both kind and not calm is either rich or not brave and vice versa.
Fred is kind or generous.
Fred is happy or rich.
Susan is both not kind and rich.
Paul is not patient.
Paul is either patient or not funny.
Someone is funny.
John is either not curious or patient.
John is both rich and not wise. | Mary is not funny. | entailment | (![X]:((~rich(X)&~generous(X))=>(~generous(X)|rich(X))))&
((?[X]:((~curious(X)|~kind(X))))=>(curious(alice)))&
(((quiet(mary)&wise(mary)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
((?[X]:((patient(X)|old(X))))=>(?[X]:((~rich(X)&brave(X)))))&
(![X]:(~patient(X)=>(calm(X)<~>rich(X))))&
(((~funny(john)<~>funny(john)))=>(?[X]:(generous(X))))&
(![X]:(creative(X)=>(generous(X)|~curious(X))))&
(![X]:(calm(X)=>(~brave(X)&~rich(X))))&
(![X]:(~funny(X)<=>(quiet(X)&~calm(X))))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)<~>~wise(X)))))&
(((patient(lucy)&~generous(lucy)))=>(?[X]:(~old(X))))&
(![X]:(creative(X)<=>(curious(X)|~rich(X))))&
(![X]:((~humble(X)&~patient(X))=>creative(X)))&
((?[X]:((tall(X)<~>~curious(X))))=>(~generous(fred)))&
(![X]:((~quiet(X)<~>~generous(X))=>(creative(X)&kind(X))))&
(![X]:((kind(X)&~calm(X))<=>(rich(X)<~>~brave(X))))&
((kind(fred)|generous(fred)))&
((happy(fred)|rich(fred)))&
((~kind(susan)&rich(susan)))&
(~patient(paul))&
((patient(paul)<~>~funny(paul)))&
(?[X]:(funny(X)))&
((~curious(john)<~>patient(john)))&
((rich(john)&~wise(john))) | ~funny(mary) | [
"p2",
"p7",
"p8",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2722757156860889934304559
% SZS output start Proof for 2722757156860889934304559
3. (wise(mary) & quiet(mary)) <=> ? [X0] : (patient(X0) <~> ~curious(X0)) [input p2]
8. ! [X0] : (calm(X0) => (~rich(X0) & ~brave(X0))) [input p7]
9. ! [X0] : (~funny(X0) <=> (~calm(X0) & quiet(X0))) [input p8]
16. ! [X0] : ((~calm(X0) & kind(X0)) <=> (rich(X0) <~> ~brave(X0))) [input p15]
23. ~curious(john) <~> patient(john) [input p22]
25. funny(mary) [input hypothesis]
39. ! [X0] : ((~rich(X0) & ~brave(X0)) | ~calm(X0)) [ennf transformation 8]
44. ((wise(mary) & quiet(mary)) | ! [X0] : ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (? [X0] : ((curious(X0) | ~patient(X0)) & (~curious(X0) | patient(X0))) | (~wise(mary) | ~quiet(mary))) [nnf transformation 3]
45. ((wise(mary) & quiet(mary)) | ! [X0] : ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (? [X0] : ((curious(X0) | ~patient(X0)) & (~curious(X0) | patient(X0))) | ~wise(mary) | ~quiet(mary)) [flattening 44]
46. ((wise(mary) & quiet(mary)) | ! [X0] : ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (? [X1] : ((curious(X1) | ~patient(X1)) & (~curious(X1) | patient(X1))) | ~wise(mary) | ~quiet(mary)) [rectify 45]
47. ? [X1] : ((curious(X1) | ~patient(X1)) & (~curious(X1) | patient(X1))) => ((curious(sK0) | ~patient(sK0)) & (~curious(sK0) | patient(sK0))) [choice axiom]
48. ((wise(mary) & quiet(mary)) | ! [X0] : ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (((curious(sK0) | ~patient(sK0)) & (~curious(sK0) | patient(sK0))) | ~wise(mary) | ~quiet(mary)) [skolemisation 46,47]
56. ! [X0] : ((~funny(X0) | (calm(X0) | ~quiet(X0))) & ((~calm(X0) & quiet(X0)) | funny(X0))) [nnf transformation 9]
57. ! [X0] : ((~funny(X0) | calm(X0) | ~quiet(X0)) & ((~calm(X0) & quiet(X0)) | funny(X0))) [flattening 56]
67. ! [X0] : (((~calm(X0) & kind(X0)) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | (calm(X0) | ~kind(X0)))) [nnf transformation 16]
68. ! [X0] : (((~calm(X0) & kind(X0)) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | calm(X0) | ~kind(X0))) [flattening 67]
72. (~patient(john) | curious(john)) & (patient(john) | ~curious(john)) [nnf transformation 23]
78. quiet(mary) | ~curious(X0) | ~patient(X0) [cnf transformation 48]
79. quiet(mary) | patient(X0) | curious(X0) [cnf transformation 48]
89. ~calm(X0) | ~brave(X0) [cnf transformation 39]
90. ~calm(X0) | ~rich(X0) [cnf transformation 39]
93. ~funny(X0) | calm(X0) | ~quiet(X0) [cnf transformation 57]
113. ~calm(X0) | rich(X0) | brave(X0) [cnf transformation 68]
121. patient(john) | ~curious(john) [cnf transformation 72]
122. ~patient(john) | curious(john) [cnf transformation 72]
125. funny(mary) [cnf transformation 25]
142. 4 <=> ! [X0] : (patient(X0) | curious(X0)) [avatar definition]
143. patient(X0) | curious(X0) <- (4) [avatar component clause 142]
150. 6 <=> ! [X0] : (~curious(X0) | ~patient(X0)) [avatar definition]
151. ~patient(X0) | ~curious(X0) <- (6) [avatar component clause 150]
154. 7 <=> quiet(mary) [avatar definition]
157. 4 | 7 [avatar split clause 79,154,142]
158. 6 | 7 [avatar split clause 78,154,150]
229. ~calm(X0) | brave(X0) [subsumption resolution 113,90]
230. ~calm(X0) [subsumption resolution 229,89]
240. 25 <=> curious(john) [avatar definition]
241. ~curious(john) <- (~25) [avatar component clause 240]
242. curious(john) <- (25) [avatar component clause 240]
244. 26 <=> patient(john) [avatar definition]
245. patient(john) <- (26) [avatar component clause 244]
246. ~patient(john) <- (~26) [avatar component clause 244]
247. 25 | ~26 [avatar split clause 122,244,240]
248. ~25 | 26 [avatar split clause 121,244,240]
268. calm(mary) | ~quiet(mary) [resolution 93,125]
271. ~quiet(mary) [subsumption resolution 268,230]
274. ~7 [avatar split clause 271,154]
283. curious(john) <- (4, ~26) [resolution 143,246]
285. $false <- (4, ~25, ~26) [subsumption resolution 283,241]
286. ~4 | 25 | 26 [avatar contradiction clause 285]
293. ~curious(john) <- (6, 26) [resolution 151,245]
294. $false <- (6, 25, 26) [subsumption resolution 293,242]
295. ~6 | ~25 | ~26 [avatar contradiction clause 294]
296. $false [avatar sat refutation 157,158,247,248,274,286,295]
% SZS output end Proof for 2722757156860889934304559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and happy then someone is not strong.
If alice is either funny or curious then mary is curious.
Everyone who is brave or kind is strong or happy and vice versa.
Everyone who is not humble or not tall is either not generous or not creative and vice versa.
Everyone who is both wise and not funny is both curious and not old and vice versa.
If john is both wise and not happy then alice is not funny or old and vice versa.
Everyone who is both not curious and tall is both funny and old and vice versa.
If someone is either not quiet or not humble then someone is either kind or creative.
If mary is funny then someone is both creative and quiet and vice versa.
Everyone who is either not patient or rich is both kind and calm and vice versa.
If someone is either humble or not humble then someone is either not humble or not creative.
If lucy is both not curious and not patient then someone is not brave or not funny.
Everyone who is either not wise or wise is not generous and vice versa.
Everyone who is not tall is either not humble or kind and vice versa.
Everyone who is not quiet or brave is both not curious and not strong.
Everyone who is kind is either not tall or not kind and vice versa.
Someone is both not calm and not happy.
Someone is either not calm or not tall.
Someone is both not curious and brave.
Someone is both humble and brave.
Alice is both rich and not happy.
Someone is brave.
Paul is not curious. | John is humble. | neutral | ((?[X]:((tall(X)&happy(X))))=>(?[X]:(~strong(X))))&
(((funny(alice)<~>curious(alice)))=>(curious(mary)))&
(![X]:((brave(X)|kind(X))<=>(strong(X)|happy(X))))&
(![X]:((~humble(X)|~tall(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:((wise(X)&~funny(X))<=>(curious(X)&~old(X))))&
(((wise(john)&~happy(john)))<=>((~funny(alice)|old(alice))))&
(![X]:((~curious(X)&tall(X))<=>(funny(X)&old(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((kind(X)<~>creative(X)))))&
((funny(mary))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~patient(X)<~>rich(X))<=>(kind(X)&calm(X))))&
((?[X]:((humble(X)<~>~humble(X))))=>(?[X]:((~humble(X)<~>~creative(X)))))&
(((~curious(lucy)&~patient(lucy)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~generous(X)))&
(![X]:(~tall(X)<=>(~humble(X)<~>kind(X))))&
(![X]:((~quiet(X)|brave(X))=>(~curious(X)&~strong(X))))&
(![X]:(kind(X)<=>(~tall(X)<~>~kind(X))))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((humble(X)&brave(X))))&
((rich(alice)&~happy(alice)))&
(?[X]:(brave(X)))&
(~curious(paul)) | humble(john) | [] | null | 0 |
Everyone who is strong is both not brave and not humble.
Everyone who is not calm is not funny.
Everyone who is not strong is both not brave and not calm and vice versa.
If alice is not rich then someone is either not happy or not quiet.
If someone is not kind then mary is not kind.
If mary is not wise or not generous then someone is either humble or not wise.
Everyone who is either rich or not wise is both tall and not generous.
Everyone who is both not patient and not wise is either generous or not wise.
If someone is either not funny or not happy then someone is not quiet or humble.
Everyone who is either not old or not brave is not creative or curious.
Everyone who is both not tall and not humble is either calm or not rich and vice versa.
Everyone who is not generous or not happy is both not rich and quiet.
If alice is generous or brave then someone is both quiet and tall and vice versa.
If mary is not calm then someone is humble or not generous and vice versa.
Everyone who is happy is both funny and rich and vice versa.
Everyone who is not strong or not creative is either funny or brave and vice versa.
Mary is quiet or not brave.
Someone is either not brave or not tall.
Susan is not old.
Someone is either brave or wise.
Fred is funny or tall.
John is both generous and creative. | John is not tall. | contradiction | (![X]:(strong(X)=>(~brave(X)&~humble(X))))&
(![X]:(~calm(X)=>~funny(X)))&
(![X]:(~strong(X)<=>(~brave(X)&~calm(X))))&
((~rich(alice))=>(?[X]:((~happy(X)<~>~quiet(X)))))&
((?[X]:(~kind(X)))=>(~kind(mary)))&
(((~wise(mary)|~generous(mary)))=>(?[X]:((humble(X)<~>~wise(X)))))&
(![X]:((rich(X)<~>~wise(X))=>(tall(X)&~generous(X))))&
(![X]:((~patient(X)&~wise(X))=>(generous(X)<~>~wise(X))))&
((?[X]:((~funny(X)<~>~happy(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~creative(X)|curious(X))))&
(![X]:((~tall(X)&~humble(X))<=>(calm(X)<~>~rich(X))))&
(![X]:((~generous(X)|~happy(X))=>(~rich(X)&quiet(X))))&
(((generous(alice)|brave(alice)))<=>(?[X]:((quiet(X)&tall(X)))))&
((~calm(mary))<=>(?[X]:((humble(X)|~generous(X)))))&
(![X]:(happy(X)<=>(funny(X)&rich(X))))&
(![X]:((~strong(X)|~creative(X))<=>(funny(X)<~>brave(X))))&
((quiet(mary)|~brave(mary)))&
(?[X]:((~brave(X)<~>~tall(X))))&
(~old(susan))&
(?[X]:((brave(X)<~>wise(X))))&
((funny(fred)|tall(fred)))&
((generous(john)&creative(john))) | ~tall(john) | [
"p0",
"p1",
"p2",
"p10",
"p11",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7623675538074302718889036
% SZS output start Proof for 7623675538074302718889036
1. ! [X0] : (strong(X0) => (~humble(X0) & ~brave(X0))) [input p0]
2. ! [X0] : (~calm(X0) => ~funny(X0)) [input p1]
3. ! [X0] : (~strong(X0) <=> (~calm(X0) & ~brave(X0))) [input p2]
11. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> (calm(X0) <~> ~rich(X0))) [input p10]
12. ! [X0] : ((~happy(X0) | ~generous(X0)) => (quiet(X0) & ~rich(X0))) [input p11]
14. ~calm(mary) <=> ? [X0] : (~generous(X0) | humble(X0)) [input p13]
15. ! [X0] : (happy(X0) <=> (rich(X0) & funny(X0))) [input p14]
16. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (funny(X0) <~> brave(X0))) [input p15]
22. creative(john) & generous(john) [input p21]
23. ~tall(john) [input hypothesis]
28. ! [X0] : ((~humble(X0) & ~brave(X0)) | ~strong(X0)) [ennf transformation 1]
29. ! [X0] : (~funny(X0) | calm(X0)) [ennf transformation 2]
35. ! [X0] : ((quiet(X0) & ~rich(X0)) | (happy(X0) & generous(X0))) [ennf transformation 12]
36. ! [X0] : ((~strong(X0) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | strong(X0))) [nnf transformation 3]
37. ! [X0] : ((~strong(X0) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | strong(X0))) [flattening 36]
49. ! [X0] : (((~humble(X0) & ~tall(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (humble(X0) | tall(X0)))) [nnf transformation 11]
50. ! [X0] : (((~humble(X0) & ~tall(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | humble(X0) | tall(X0))) [flattening 49]
56. (~calm(mary) | ! [X0] : (generous(X0) & ~humble(X0))) & (? [X0] : (~generous(X0) | humble(X0)) | calm(mary)) [nnf transformation 14]
57. (~calm(mary) | ! [X0] : (generous(X0) & ~humble(X0))) & (? [X1] : (~generous(X1) | humble(X1)) | calm(mary)) [rectify 56]
58. ? [X1] : (~generous(X1) | humble(X1)) => (~generous(sK4) | humble(sK4)) [choice axiom]
59. (~calm(mary) | ! [X0] : (generous(X0) & ~humble(X0))) & ((~generous(sK4) | humble(sK4)) | calm(mary)) [skolemisation 57,58]
60. ! [X0] : ((happy(X0) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ~happy(X0))) [nnf transformation 15]
61. ! [X0] : ((happy(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ~happy(X0))) [flattening 60]
62. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 16]
63. ! [X0] : ((~creative(X0) | ~strong(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (creative(X0) & strong(X0)))) [flattening 62]
70. ~brave(X0) | ~strong(X0) [cnf transformation 28]
72. ~funny(X0) | calm(X0) [cnf transformation 29]
73. ~brave(X0) | strong(X0) [cnf transformation 37]
74. ~calm(X0) | strong(X0) [cnf transformation 37]
75. ~strong(X0) | calm(X0) | brave(X0) [cnf transformation 37]
90. ~calm(X0) | rich(X0) | humble(X0) | tall(X0) [cnf transformation 50]
96. ~rich(X0) | happy(X0) [cnf transformation 35]
105. ~calm(mary) | ~humble(X0) [cnf transformation 59]
107. funny(X0) | ~happy(X0) [cnf transformation 61]
110. brave(X0) | funny(X0) | strong(X0) [cnf transformation 63]
114. ~creative(X0) | ~strong(X0) | brave(X0) | ~funny(X0) [cnf transformation 63]
123. creative(john) [cnf transformation 22]
124. ~tall(john) [cnf transformation 23]
125. ~strong(X0) | calm(X0) [subsumption resolution 75,70]
126. ~brave(X0) [subsumption resolution 73,70]
182. 13 <=> ! [X1] : (~happy(X1) | funny(X1)) [avatar definition]
183. ~happy(X1) | funny(X1) <- (13) [avatar component clause 182]
208. 19 <=> calm(mary) [avatar definition]
210. ~calm(mary) <- (~19) [avatar component clause 208]
213. 20 <=> ! [X0] : ~humble(X0) [avatar definition]
214. ~humble(X0) <- (20) [avatar component clause 213]
215. 20 | ~19 [avatar split clause 105,208,213]
225. 13 [avatar split clause 107,182]
226. ~creative(X0) | ~strong(X0) | ~funny(X0) [subsumption resolution 114,126]
228. funny(X0) | strong(X0) [subsumption resolution 110,126]
256. strong(X0) | calm(X0) [resolution 228,72]
257. calm(X0) [subsumption resolution 256,125]
258. $false <- (~19) [resolution 257,210]
259. strong(X0) [resolution 257,74]
260. 19 [avatar contradiction clause 258]
284. 28 <=> rich(john) [avatar definition]
286. rich(john) <- (28) [avatar component clause 284]
313. ~strong(john) | ~funny(john) [resolution 226,123]
315. ~funny(john) [subsumption resolution 313,259]
321. rich(X0) | humble(X0) | tall(X0) [resolution 90,257]
329. tall(X0) | rich(X0) <- (20) [subsumption resolution 321,214]
346. rich(john) <- (20) [resolution 329,124]
352. 28 | ~20 [avatar split clause 346,213,284]
356. happy(john) <- (28) [resolution 286,96]
358. funny(john) <- (13, 28) [resolution 356,183]
360. $false <- (13, 28) [subsumption resolution 358,315]
361. ~13 | ~28 [avatar contradiction clause 360]
362. $false [avatar sat refutation 215,225,260,352,361]
% SZS output end Proof for 7623675538074302718889036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is both old and not generous.
Everyone who is not funny is both curious and not humble and vice versa.
If lucy is either old or not calm then susan is either not quiet or calm.
If someone is old or not rich then someone is both not quiet and not tall.
If someone is both not patient and tall then fred is not generous or not wise.
Everyone who is not patient is either rich or not patient and vice versa.
If someone is both generous and strong then susan is not quiet and vice versa.
Everyone who is either funny or calm is both tall and not old and vice versa.
If someone is not wise or calm then alice is not strong and vice versa.
Everyone who is not funny or not patient is curious or not brave and vice versa.
If paul is both generous and not rich then someone is both not creative and not rich.
If susan is not happy then someone is curious.
Everyone who is calm or brave is either not patient or rich and vice versa.
Everyone who is both not curious and not wise is kind or not rich and vice versa.
If someone is both not old and not tall then alice is either funny or not wise and vice versa.
Paul is not creative.
John is either funny or not calm.
Alice is not rich or old.
Alice is not quiet.
Lucy is either not wise or not generous. | Fred is curious. | contradiction | (![X]:(happy(X)=>(old(X)&~generous(X))))&
(![X]:(~funny(X)<=>(curious(X)&~humble(X))))&
(((old(lucy)<~>~calm(lucy)))=>((~quiet(susan)<~>calm(susan))))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((~quiet(X)&~tall(X)))))&
((?[X]:((~patient(X)&tall(X))))=>((~generous(fred)|~wise(fred))))&
(![X]:(~patient(X)<=>(rich(X)<~>~patient(X))))&
((?[X]:((generous(X)&strong(X))))<=>(~quiet(susan)))&
(![X]:((funny(X)<~>calm(X))<=>(tall(X)&~old(X))))&
((?[X]:((~wise(X)|calm(X))))<=>(~strong(alice)))&
(![X]:((~funny(X)|~patient(X))<=>(curious(X)|~brave(X))))&
(((generous(paul)&~rich(paul)))=>(?[X]:((~creative(X)&~rich(X)))))&
((~happy(susan))=>(?[X]:(curious(X))))&
(![X]:((calm(X)|brave(X))<=>(~patient(X)<~>rich(X))))&
(![X]:((~curious(X)&~wise(X))<=>(kind(X)|~rich(X))))&
((?[X]:((~old(X)&~tall(X))))<=>((funny(alice)<~>~wise(alice))))&
(~creative(paul))&
((funny(john)<~>~calm(john)))&
((~rich(alice)|old(alice)))&
(~quiet(alice))&
((~wise(lucy)<~>~generous(lucy))) | curious(fred) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3011365547521958421617327
% SZS output start Proof for 3011365547521958421617327
6. ! [X0] : (~patient(X0) <=> (rich(X0) <~> ~patient(X0))) [input p5]
14. ! [X0] : ((~wise(X0) & ~curious(X0)) <=> (~rich(X0) | kind(X0))) [input p13]
21. curious(fred) [input hypothesis]
39. ! [X0] : ((~patient(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) & (((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | patient(X0))) [nnf transformation 6]
58. ! [X0] : (((~wise(X0) & ~curious(X0)) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | (wise(X0) | curious(X0)))) [nnf transformation 14]
59. ! [X0] : (((~wise(X0) & ~curious(X0)) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | wise(X0) | curious(X0))) [flattening 58]
81. patient(X0) | ~rich(X0) | patient(X0) [cnf transformation 39]
82. ~patient(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 39]
110. ~curious(X0) | rich(X0) [cnf transformation 59]
125. curious(fred) [cnf transformation 21]
126. patient(X0) | ~rich(X0) [duplicate literal removal 81]
127. ~patient(X0) | ~rich(X0) [duplicate literal removal 82]
178. ~rich(X0) [subsumption resolution 126,127]
227. ~curious(X0) [subsumption resolution 110,178]
260. $false [subsumption resolution 125,227]
% SZS output end Proof for 3011365547521958421617327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or kind then someone is quiet or not rich. Everyone who is either not rich or not creative is not creative and vice versa. If someone is not tall or not brave then someone is both not brave and not humble and vice versa. If susan is not old or wise then someone is not quiet or funny. If lucy is not tall or creative then someone is either not wise or not curious and vice versa. If someone is not funny or not rich then someone is both old and tall. If someone is creative or old then fred is not calm and vice versa. Everyone who is either not generous or curious is not kind or funny and vice versa. Everyone who is either patient or not generous is not tall. Everyone who is brave is tall or rich and vice versa. Everyone who is strong is calm and vice versa. Everyone who is not humble is both brave and patient and vice versa. If lucy is both not humble and not calm then paul is old or not strong and vice versa. If susan is not brave then someone is not humble or rich. If someone is either not quiet or calm then someone is either not old or creative. Everyone who is creative is creative or not quiet. Someone is happy or not funny. Someone is both not calm and funny. Someone is not old. Someone is not patient or curious. Someone is not brave or strong. John is not tall or old. | Lucy is not creative. | neutral | ((?[X]:((quiet(X)|kind(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((~rich(X)<~>~creative(X))<=>~creative(X)))&
((?[X]:((~tall(X)|~brave(X))))<=>(?[X]:((~brave(X)&~humble(X)))))&
(((~old(susan)|wise(susan)))=>(?[X]:((~quiet(X)|funny(X)))))&
(((~tall(lucy)|creative(lucy)))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
((?[X]:((~funny(X)|~rich(X))))=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((creative(X)|old(X))))<=>(~calm(fred)))&
(![X]:((~generous(X)<~>curious(X))<=>(~kind(X)|funny(X))))&
(![X]:((patient(X)<~>~generous(X))=>~tall(X)))&
(![X]:(brave(X)<=>(tall(X)|rich(X))))&
(![X]:(strong(X)<=>calm(X)))&
(![X]:(~humble(X)<=>(brave(X)&patient(X))))&
(((~humble(lucy)&~calm(lucy)))<=>((old(paul)|~strong(paul))))&
((~brave(susan))=>(?[X]:((~humble(X)|rich(X)))))&
((?[X]:((~quiet(X)<~>calm(X))))=>(?[X]:((~old(X)<~>creative(X)))))&
(![X]:(creative(X)=>(creative(X)|~quiet(X))))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((~calm(X)&funny(X))))&
(?[X]:(~old(X)))&
(?[X]:((~patient(X)|curious(X))))&
(?[X]:((~brave(X)|strong(X))))&
((~tall(john)|old(john))) | ~creative(lucy) | [] | null | 0 |
Everyone who is both not wise and not quiet is both not calm and not creative.
Everyone who is both wise and not happy is either tall or not humble and vice versa.
If someone is tall then someone is either calm or funny.
Everyone who is both generous and not strong is both not strong and rich and vice versa.
Everyone who is both not wise and wise is tall or happy.
If someone is both old and humble then fred is either quiet or strong and vice versa.
Everyone who is not curious is either not calm or brave.
Everyone who is kind is both quiet and not curious.
Everyone who is wise is not tall or curious and vice versa.
Everyone who is not brave or kind is not calm or wise.
If someone is wise then someone is generous or not brave and vice versa.
If paul is either not calm or not brave then someone is either not curious or not patient.
If susan is either not old or not curious then someone is not creative and vice versa.
If someone is not strong then someone is both calm and not rich.
If someone is brave or not rich then john is both old and not old.
Everyone who is not funny or not rich is not generous and vice versa.
Someone is both not curious and tall.
Someone is either not happy or not generous.
Someone is either not generous or not tall.
John is not happy or not curious.
Someone is both kind and generous.
Someone is either wise or funny.
Someone is both curious and wise. | Fred is brave. | contradiction | (![X]:((~wise(X)&~quiet(X))=>(~calm(X)&~creative(X))))&
(![X]:((wise(X)&~happy(X))<=>(tall(X)<~>~humble(X))))&
((?[X]:(tall(X)))=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((generous(X)&~strong(X))<=>(~strong(X)&rich(X))))&
(![X]:((~wise(X)&wise(X))=>(tall(X)|happy(X))))&
((?[X]:((old(X)&humble(X))))<=>((quiet(fred)<~>strong(fred))))&
(![X]:(~curious(X)=>(~calm(X)<~>brave(X))))&
(![X]:(kind(X)=>(quiet(X)&~curious(X))))&
(![X]:(wise(X)<=>(~tall(X)|curious(X))))&
(![X]:((~brave(X)|kind(X))=>(~calm(X)|wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:((generous(X)|~brave(X)))))&
(((~calm(paul)<~>~brave(paul)))=>(?[X]:((~curious(X)<~>~patient(X)))))&
(((~old(susan)<~>~curious(susan)))<=>(?[X]:(~creative(X))))&
((?[X]:(~strong(X)))=>(?[X]:((calm(X)&~rich(X)))))&
((?[X]:((brave(X)|~rich(X))))=>((old(john)&~old(john))))&
(![X]:((~funny(X)|~rich(X))<=>~generous(X)))&
(?[X]:((~curious(X)&tall(X))))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~generous(X)<~>~tall(X))))&
((~happy(john)|~curious(john)))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:((wise(X)<~>funny(X))))&
(?[X]:((curious(X)&wise(X)))) | brave(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6950989693727344004471334
% SZS output start Proof for 6950989693727344004471334
15. ? [X0] : (~rich(X0) | brave(X0)) => (~old(john) & old(john)) [input p14]
24. brave(fred) [input hypothesis]
39. (~old(john) & old(john)) | ! [X0] : (rich(X0) & ~brave(X0)) [ennf transformation 15]
130. old(john) | ~brave(X0) [cnf transformation 39]
132. ~old(john) | ~brave(X0) [cnf transformation 39]
150. brave(fred) [cnf transformation 24]
269. 27 <=> old(john) [avatar definition]
274. 28 <=> ! [X0] : ~brave(X0) [avatar definition]
275. ~brave(X0) <- (28) [avatar component clause 274]
276. 28 | ~27 [avatar split clause 132,269,274]
278. 28 | 27 [avatar split clause 130,269,274]
320. $false <- (28) [resolution 275,150]
321. ~28 [avatar contradiction clause 320]
322. $false [avatar sat refutation 276,278,321]
% SZS output end Proof for 6950989693727344004471334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not funny is either not kind or not funny.
Everyone who is both not funny and not tall is both quiet and not curious.
Everyone who is either not humble or humble is old and vice versa.
Everyone who is not creative or not funny is either not funny or funny.
Everyone who is curious is creative or wise.
If someone is either not brave or not happy then mary is either not calm or not rich.
Everyone who is not patient is either not brave or generous.
Everyone who is kind or funny is wise or not strong and vice versa.
If fred is both not curious and kind then susan is strong or not calm.
Everyone who is brave is wise and vice versa.
If someone is not rich or humble then someone is not happy and vice versa.
Everyone who is not generous or not kind is either not curious or rich.
Everyone who is both rich and funny is not curious or not happy.
If paul is both not strong and not old then someone is both not creative and kind and vice versa.
Everyone who is happy or wise is not happy or rich and vice versa.
Everyone who is old or tall is not happy.
Someone is not tall.
Someone is either not rich or not wise.
Alice is quiet.
Susan is not rich.
Alice is both creative and not curious.
Someone is wise or strong.
Alice is both funny and not kind. | Susan is not calm. | neutral | (![X]:((~old(X)<~>~funny(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((~funny(X)&~tall(X))=>(quiet(X)&~curious(X))))&
(![X]:((~humble(X)<~>humble(X))<=>old(X)))&
(![X]:((~creative(X)|~funny(X))=>(~funny(X)<~>funny(X))))&
(![X]:(curious(X)=>(creative(X)|wise(X))))&
((?[X]:((~brave(X)<~>~happy(X))))=>((~calm(mary)<~>~rich(mary))))&
(![X]:(~patient(X)=>(~brave(X)<~>generous(X))))&
(![X]:((kind(X)|funny(X))<=>(wise(X)|~strong(X))))&
(((~curious(fred)&kind(fred)))=>((strong(susan)|~calm(susan))))&
(![X]:(brave(X)<=>wise(X)))&
((?[X]:((~rich(X)|humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~generous(X)|~kind(X))=>(~curious(X)<~>rich(X))))&
(![X]:((rich(X)&funny(X))=>(~curious(X)|~happy(X))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((happy(X)|wise(X))<=>(~happy(X)|rich(X))))&
(![X]:((old(X)|tall(X))=>~happy(X)))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)<~>~wise(X))))&
(quiet(alice))&
(~rich(susan))&
((creative(alice)&~curious(alice)))&
(?[X]:((wise(X)|strong(X))))&
((funny(alice)&~kind(alice))) | ~calm(susan) | [] | null | 0 |
If someone is both rich and not generous then someone is wise and vice versa. If alice is both brave and not creative then john is calm. Everyone who is both not old and old is both humble and tall. If lucy is generous or not calm then someone is both strong and rich. Everyone who is both patient and curious is either not calm or rich. Everyone who is not quiet or not curious is either quiet or tall. Everyone who is both not old and creative is not strong and vice versa. Everyone who is both not wise and generous is patient. If paul is not patient or old then someone is curious. Everyone who is not calm or not tall is kind. If someone is both brave and tall then someone is not brave. Everyone who is generous is both not old and happy. Everyone who is both curious and not old is strong and vice versa. If paul is strong then someone is either not brave or not kind and vice versa. If susan is happy or not kind then someone is either kind or not old and vice versa. If someone is both not curious and not happy then someone is wise. John is patient or funny. Someone is not humble or curious. Lucy is not curious or tall. Someone is both brave and not patient. Someone is both not patient and not kind. Someone is not creative. Paul is either not calm or not curious. Someone is not calm. | Paul is not old. | entailment | ((?[X]:((rich(X)&~generous(X))))<=>(?[X]:(wise(X))))&
(((brave(alice)&~creative(alice)))=>(calm(john)))&
(![X]:((~old(X)&old(X))=>(humble(X)&tall(X))))&
(((generous(lucy)|~calm(lucy)))=>(?[X]:((strong(X)&rich(X)))))&
(![X]:((patient(X)&curious(X))=>(~calm(X)<~>rich(X))))&
(![X]:((~quiet(X)|~curious(X))=>(quiet(X)<~>tall(X))))&
(![X]:((~old(X)&creative(X))<=>~strong(X)))&
(![X]:((~wise(X)&generous(X))=>patient(X)))&
(((~patient(paul)|old(paul)))=>(?[X]:(curious(X))))&
(![X]:((~calm(X)|~tall(X))=>kind(X)))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:(~brave(X))))&
(![X]:(generous(X)=>(~old(X)&happy(X))))&
(![X]:((curious(X)&~old(X))<=>strong(X)))&
((strong(paul))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(((happy(susan)|~kind(susan)))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~curious(X)&~happy(X))))=>(?[X]:(wise(X))))&
((patient(john)|funny(john)))&
(?[X]:((~humble(X)|curious(X))))&
((~curious(lucy)|tall(lucy)))&
(?[X]:((brave(X)&~patient(X))))&
(?[X]:((~patient(X)&~kind(X))))&
(?[X]:(~creative(X)))&
((~calm(paul)<~>~curious(paul)))&
(?[X]:(~calm(X))) | ~old(paul) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2813424228660010164534154
% SZS output start Proof for 2813424228660010164534154
7. ! [X0] : ((creative(X0) & ~old(X0)) <=> ~strong(X0)) [input p6]
13. ! [X0] : ((~old(X0) & curious(X0)) <=> strong(X0)) [input p12]
25. old(paul) [input hypothesis]
54. ! [X0] : (((creative(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | (~creative(X0) | old(X0)))) [nnf transformation 7]
55. ! [X0] : (((creative(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | ~creative(X0) | old(X0))) [flattening 54]
61. ! [X0] : (((~old(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | (old(X0) | ~curious(X0)))) [nnf transformation 13]
62. ! [X0] : (((~old(X0) & curious(X0)) | ~strong(X0)) & (strong(X0) | old(X0) | ~curious(X0))) [flattening 61]
103. ~old(X0) | strong(X0) [cnf transformation 55]
115. ~old(X0) | ~strong(X0) [cnf transformation 62]
137. old(paul) [cnf transformation 25]
215. ~old(X0) [subsumption resolution 115,103]
296. $false [subsumption resolution 137,215]
% SZS output end Proof for 2813424228660010164534154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not brave or not rich then susan is generous and vice versa. Everyone who is both wise and funny is both strong and wise and vice versa. Everyone who is not rich is either not curious or quiet. If someone is calm then alice is both not calm and not quiet. Everyone who is not happy is not rich and vice versa. If mary is either strong or old then someone is not happy. If someone is funny then john is not brave or quiet and vice versa. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Everyone who is happy is both generous and kind and vice versa. Everyone who is both not generous and not calm is either not happy or not rich. Mary is not patient or humble. Someone is not kind. Someone is not wise. Someone is either old or not rich. Alice is both not curious and happy. Someone is kind. Someone is not funny. | John is calm. | neutral | ((?[X]:((~brave(X)|~rich(X))))<=>(generous(susan)))&
(![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(![X]:(happy(X)<=>(generous(X)&kind(X))))&
(![X]:((~generous(X)&~calm(X))=>(~happy(X)<~>~rich(X))))&
((~patient(mary)|humble(mary)))&
(?[X]:(~kind(X)))&
(?[X]:(~wise(X)))&
(?[X]:((old(X)<~>~rich(X))))&
((~curious(alice)&happy(alice)))&
(?[X]:(kind(X)))&
(?[X]:(~funny(X))) | calm(john) | [] | null | 0 |
Everyone who is either strong or not generous is both creative and generous and vice versa. Everyone who is both not funny and not happy is both not rich and tall and vice versa. Everyone who is humble or curious is both patient and wise and vice versa. Everyone who is either generous or not wise is either strong or funny and vice versa. Everyone who is either not brave or not tall is not brave. If john is either humble or quiet then susan is rich or not old. Everyone who is not brave or not humble is tall or happy. Everyone who is brave is either brave or not rich. If john is generous then lucy is not quiet. Everyone who is either quiet or not quiet is both not old and rich and vice versa. Everyone who is not curious is both not funny and not brave. Everyone who is not wise is both tall and wise and vice versa. Everyone who is not wise is either creative or not funny. If someone is both not wise and not patient then someone is wise or kind. If someone is both patient and not strong then mary is not quiet and vice versa. Everyone who is not generous or rich is either not calm or not strong. John is either not patient or not generous. Someone is patient. Alice is not rich or not tall. Someone is happy or old. Someone is not brave or not rich. Susan is curious or not old. | Mary is not quiet. | neutral | (![X]:((strong(X)<~>~generous(X))<=>(creative(X)&generous(X))))&
(![X]:((~funny(X)&~happy(X))<=>(~rich(X)&tall(X))))&
(![X]:((humble(X)|curious(X))<=>(patient(X)&wise(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(strong(X)<~>funny(X))))&
(![X]:((~brave(X)<~>~tall(X))=>~brave(X)))&
(((humble(john)<~>quiet(john)))=>((rich(susan)|~old(susan))))&
(![X]:((~brave(X)|~humble(X))=>(tall(X)|happy(X))))&
(![X]:(brave(X)=>(brave(X)<~>~rich(X))))&
((generous(john))=>(~quiet(lucy)))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~old(X)&rich(X))))&
(![X]:(~curious(X)=>(~funny(X)&~brave(X))))&
(![X]:(~wise(X)<=>(tall(X)&wise(X))))&
(![X]:(~wise(X)=>(creative(X)<~>~funny(X))))&
((?[X]:((~wise(X)&~patient(X))))=>(?[X]:((wise(X)|kind(X)))))&
((?[X]:((patient(X)&~strong(X))))<=>(~quiet(mary)))&
(![X]:((~generous(X)|rich(X))=>(~calm(X)<~>~strong(X))))&
((~patient(john)<~>~generous(john)))&
(?[X]:(patient(X)))&
((~rich(alice)|~tall(alice)))&
(?[X]:((happy(X)|old(X))))&
(?[X]:((~brave(X)|~rich(X))))&
((curious(susan)|~old(susan))) | ~quiet(mary) | [] | null | 0 |
If mary is either not calm or not creative then someone is generous or not funny.
If someone is not curious then susan is not happy or not curious and vice versa.
Everyone who is either strong or not humble is either not funny or not humble.
If someone is wise or kind then fred is not patient and vice versa.
If someone is not strong or happy then fred is either calm or not kind and vice versa.
Everyone who is either humble or not strong is not strong or not kind.
If someone is either quiet or patient then someone is not happy or strong and vice versa.
Everyone who is not rich or calm is both creative and not tall and vice versa.
Everyone who is either calm or tall is not old or funny and vice versa.
Everyone who is either not brave or not rich is both not quiet and patient and vice versa.
If john is not creative then lucy is not patient and vice versa.
Everyone who is calm or curious is creative and vice versa.
Everyone who is kind is either strong or kind and vice versa.
Everyone who is not calm or not tall is either old or not quiet.
Everyone who is not calm or tall is both not tall and generous and vice versa.
If susan is not tall then john is both old and curious.
Mary is not happy or generous.
Mary is not generous or strong.
Alice is brave or not patient.
Alice is patient or not happy.
Mary is not rich.
Someone is wise.
Paul is both wise and not humble. | Paul is not generous. | entailment | (((~calm(mary)<~>~creative(mary)))=>(?[X]:((generous(X)|~funny(X)))))&
((?[X]:(~curious(X)))<=>((~happy(susan)|~curious(susan))))&
(![X]:((strong(X)<~>~humble(X))=>(~funny(X)<~>~humble(X))))&
((?[X]:((wise(X)|kind(X))))<=>(~patient(fred)))&
((?[X]:((~strong(X)|happy(X))))<=>((calm(fred)<~>~kind(fred))))&
(![X]:((humble(X)<~>~strong(X))=>(~strong(X)|~kind(X))))&
((?[X]:((quiet(X)<~>patient(X))))<=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~rich(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~old(X)|funny(X))))&
(![X]:((~brave(X)<~>~rich(X))<=>(~quiet(X)&patient(X))))&
((~creative(john))<=>(~patient(lucy)))&
(![X]:((calm(X)|curious(X))<=>creative(X)))&
(![X]:(kind(X)<=>(strong(X)<~>kind(X))))&
(![X]:((~calm(X)|~tall(X))=>(old(X)<~>~quiet(X))))&
(![X]:((~calm(X)|tall(X))<=>(~tall(X)&generous(X))))&
((~tall(susan))=>((old(john)&curious(john))))&
((~happy(mary)|generous(mary)))&
((~generous(mary)|strong(mary)))&
((brave(alice)|~patient(alice)))&
((patient(alice)|~happy(alice)))&
(~rich(mary))&
(?[X]:(wise(X)))&
((wise(paul)&~humble(paul))) | ~generous(paul) | [
"p2",
"p7",
"p8",
"p12",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2021219476924174192107856
% SZS output start Proof for 2021219476924174192107856
3. ! [X0] : ((strong(X0) <~> ~humble(X0)) => (~funny(X0) <~> ~humble(X0))) [input p2]
8. ! [X0] : ((calm(X0) | ~rich(X0)) <=> (~tall(X0) & creative(X0))) [input p7]
9. ! [X0] : ((calm(X0) <~> tall(X0)) <=> (funny(X0) | ~old(X0))) [input p8]
13. ! [X0] : (kind(X0) <=> (strong(X0) <~> kind(X0))) [input p12]
15. ! [X0] : ((tall(X0) | ~calm(X0)) <=> (generous(X0) & ~tall(X0))) [input p14]
23. ~humble(paul) & wise(paul) [input p22]
24. generous(paul) [input hypothesis]
27. ! [X0] : ((~funny(X0) <~> ~humble(X0)) | (strong(X0) <=> ~humble(X0))) [ennf transformation 3]
40. ! [X0] : (((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) [nnf transformation 27]
55. ! [X0] : (((calm(X0) | ~rich(X0)) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | (~calm(X0) & rich(X0)))) [nnf transformation 8]
56. ! [X0] : ((calm(X0) | ~rich(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | (~calm(X0) & rich(X0)))) [flattening 55]
57. ! [X0] : ((((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0))))) [nnf transformation 9]
58. ! [X0] : ((((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0))))) [flattening 57]
64. ! [X0] : ((kind(X0) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | ~kind(X0))) [nnf transformation 13]
66. ! [X0] : (((tall(X0) | ~calm(X0)) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | (~tall(X0) & calm(X0)))) [nnf transformation 15]
67. ! [X0] : ((tall(X0) | ~calm(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | (~tall(X0) & calm(X0)))) [flattening 66]
78. humble(X0) | funny(X0) | strong(X0) | humble(X0) [cnf transformation 40]
99. ~tall(X0) | ~calm(X0) [cnf transformation 56]
104. ~funny(X0) | calm(X0) | tall(X0) [cnf transformation 58]
119. ~kind(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 64]
120. kind(X0) | kind(X0) | ~strong(X0) [cnf transformation 64]
127. ~tall(X0) | ~tall(X0) [cnf transformation 67]
130. tall(X0) | ~calm(X0) | ~generous(X0) | tall(X0) [cnf transformation 67]
140. ~humble(paul) [cnf transformation 23]
141. generous(paul) [cnf transformation 24]
142. ~tall(X0) [duplicate literal removal 127]
143. tall(X0) | ~calm(X0) | ~generous(X0) [duplicate literal removal 130]
144. ~kind(X0) | ~strong(X0) [duplicate literal removal 119]
145. ~strong(X0) | kind(X0) [duplicate literal removal 120]
148. humble(X0) | funny(X0) | strong(X0) [duplicate literal removal 78]
235. 20 <=> ! [X1] : ~strong(X1) [avatar definition]
236. ~strong(X1) <- (20) [avatar component clause 235]
280. ~strong(X0) [subsumption resolution 144,145]
281. 20 [avatar split clause 280,235]
282. ~generous(X0) | ~calm(X0) [subsumption resolution 143,99]
325. ~calm(paul) [resolution 282,141]
368. funny(paul) | strong(paul) [resolution 148,140]
370. funny(paul) <- (20) [subsumption resolution 368,236]
371. calm(paul) | tall(paul) <- (20) [resolution 370,104]
372. tall(paul) <- (20) [subsumption resolution 371,325]
373. $false <- (20) [subsumption resolution 372,142]
374. ~20 [avatar contradiction clause 373]
375. $false [avatar sat refutation 281,374]
% SZS output end Proof for 2021219476924174192107856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or old then alice is either patient or brave and vice versa.
Everyone who is creative is either not tall or old.
Everyone who is both kind and not funny is not kind or strong and vice versa.
Everyone who is wise or not strong is both creative and not quiet and vice versa.
If susan is both not wise and wise then someone is both not rich and not generous and vice versa.
Everyone who is strong is not old or rich.
Everyone who is kind or not generous is either not patient or not rich and vice versa.
Everyone who is not rich is not funny or tall.
Everyone who is kind is either happy or wise and vice versa.
Everyone who is quiet or not humble is either not creative or not happy and vice versa.
Everyone who is either not strong or not happy is humble.
Everyone who is patient or not kind is not humble or not rich and vice versa.
Everyone who is both not brave and tall is not tall or not calm and vice versa.
If fred is either calm or patient then alice is not strong.
Everyone who is both not brave and humble is quiet and vice versa.
If someone is patient then alice is both tall and not funny and vice versa.
Lucy is both not creative and not humble.
Paul is either patient or happy.
Paul is both creative and tall.
Someone is either not strong or not creative.
John is both old and tall.
Someone is tall.
Susan is either happy or not brave. | Fred is happy. | neutral | ((?[X]:((calm(X)|old(X))))<=>((patient(alice)<~>brave(alice))))&
(![X]:(creative(X)=>(~tall(X)<~>old(X))))&
(![X]:((kind(X)&~funny(X))<=>(~kind(X)|strong(X))))&
(![X]:((wise(X)|~strong(X))<=>(creative(X)&~quiet(X))))&
(((~wise(susan)&wise(susan)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:(strong(X)=>(~old(X)|rich(X))))&
(![X]:((kind(X)|~generous(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:(~rich(X)=>(~funny(X)|tall(X))))&
(![X]:(kind(X)<=>(happy(X)<~>wise(X))))&
(![X]:((quiet(X)|~humble(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:((~strong(X)<~>~happy(X))=>humble(X)))&
(![X]:((patient(X)|~kind(X))<=>(~humble(X)|~rich(X))))&
(![X]:((~brave(X)&tall(X))<=>(~tall(X)|~calm(X))))&
(((calm(fred)<~>patient(fred)))=>(~strong(alice)))&
(![X]:((~brave(X)&humble(X))<=>quiet(X)))&
((?[X]:(patient(X)))<=>((tall(alice)&~funny(alice))))&
((~creative(lucy)&~humble(lucy)))&
((patient(paul)<~>happy(paul)))&
((creative(paul)&tall(paul)))&
(?[X]:((~strong(X)<~>~creative(X))))&
((old(john)&tall(john)))&
(?[X]:(tall(X)))&
((happy(susan)<~>~brave(susan))) | happy(fred) | [] | null | 0 |
If someone is rich or not strong then someone is either not patient or not calm and vice versa.
Everyone who is tall or old is not rich or not strong and vice versa.
If alice is not rich or happy then mary is both creative and funny and vice versa.
Everyone who is wise is either not wise or patient.
Everyone who is both curious and not rich is both not humble and happy.
If alice is humble then lucy is happy or calm.
Everyone who is both wise and not tall is both patient and strong and vice versa.
Everyone who is either not quiet or not wise is old or not strong and vice versa.
Everyone who is generous or tall is either not quiet or not calm and vice versa.
If alice is both rich and curious then someone is both not kind and humble.
If susan is either not wise or not generous then susan is funny and vice versa.
If someone is either not old or not calm then someone is both happy and brave and vice versa.
If someone is curious then fred is both calm and rich and vice versa.
If someone is either quiet or not quiet then someone is not strong or wise and vice versa.
Everyone who is humble or rich is not patient.
If mary is not generous then someone is not happy or strong.
Someone is funny.
Mary is kind.
John is not curious.
Paul is either wise or calm.
Someone is quiet.
Mary is either quiet or humble.
Alice is either generous or old.
Fred is kind. | Mary is not wise. | entailment | ((?[X]:((rich(X)|~strong(X))))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
(![X]:((tall(X)|old(X))<=>(~rich(X)|~strong(X))))&
(((~rich(alice)|happy(alice)))<=>((creative(mary)&funny(mary))))&
(![X]:(wise(X)=>(~wise(X)<~>patient(X))))&
(![X]:((curious(X)&~rich(X))=>(~humble(X)&happy(X))))&
((humble(alice))=>((happy(lucy)|calm(lucy))))&
(![X]:((wise(X)&~tall(X))<=>(patient(X)&strong(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(old(X)|~strong(X))))&
(![X]:((generous(X)|tall(X))<=>(~quiet(X)<~>~calm(X))))&
(((rich(alice)&curious(alice)))=>(?[X]:((~kind(X)&humble(X)))))&
(((~wise(susan)<~>~generous(susan)))<=>(funny(susan)))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:((happy(X)&brave(X)))))&
((?[X]:(curious(X)))<=>((calm(fred)&rich(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))<=>(?[X]:((~strong(X)|wise(X)))))&
(![X]:((humble(X)|rich(X))=>~patient(X)))&
((~generous(mary))=>(?[X]:((~happy(X)|strong(X)))))&
(?[X]:(funny(X)))&
(kind(mary))&
(~curious(john))&
((wise(paul)<~>calm(paul)))&
(?[X]:(quiet(X)))&
((quiet(mary)<~>humble(mary)))&
((generous(alice)<~>old(alice)))&
(kind(fred)) | ~wise(mary) | [
"p1",
"p3",
"p6",
"p7",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8058352838054989695727447
% SZS output start Proof for 8058352838054989695727447
2. ! [X0] : ((old(X0) | tall(X0)) <=> (~strong(X0) | ~rich(X0))) [input p1]
4. ! [X0] : (wise(X0) => (~wise(X0) <~> patient(X0))) [input p3]
7. ! [X0] : ((~tall(X0) & wise(X0)) <=> (strong(X0) & patient(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) <~> ~wise(X0)) <=> (~strong(X0) | old(X0))) [input p7]
15. ! [X0] : ((rich(X0) | humble(X0)) => ~patient(X0)) [input p14]
22. quiet(mary) <~> humble(mary) [input p21]
25. wise(mary) [input hypothesis]
29. ! [X0] : ((~wise(X0) <~> patient(X0)) | ~wise(X0)) [ennf transformation 4]
36. ! [X0] : (~patient(X0) | (~rich(X0) & ~humble(X0))) [ennf transformation 15]
43. ! [X0] : (((old(X0) | tall(X0)) | (strong(X0) & rich(X0))) & ((~strong(X0) | ~rich(X0)) | (~old(X0) & ~tall(X0)))) [nnf transformation 2]
44. ! [X0] : ((old(X0) | tall(X0) | (strong(X0) & rich(X0))) & (~strong(X0) | ~rich(X0) | (~old(X0) & ~tall(X0)))) [flattening 43]
47. ! [X0] : (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | ~wise(X0)) [nnf transformation 29]
48. ! [X0] : (((~tall(X0) & wise(X0)) | (~strong(X0) | ~patient(X0))) & ((strong(X0) & patient(X0)) | (tall(X0) | ~wise(X0)))) [nnf transformation 7]
49. ! [X0] : (((~tall(X0) & wise(X0)) | ~strong(X0) | ~patient(X0)) & ((strong(X0) & patient(X0)) | tall(X0) | ~wise(X0))) [flattening 48]
50. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [nnf transformation 8]
51. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [flattening 50]
79. (~humble(mary) | ~quiet(mary)) & (humble(mary) | quiet(mary)) [nnf transformation 22]
89. old(X0) | tall(X0) | rich(X0) [cnf transformation 44]
96. patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 47]
104. ~tall(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 49]
107. ~quiet(X0) | ~wise(X0) | ~old(X0) [cnf transformation 51]
108. ~quiet(X0) | ~wise(X0) | strong(X0) [cnf transformation 51]
138. ~humble(X0) | ~patient(X0) [cnf transformation 36]
139. ~patient(X0) | ~rich(X0) [cnf transformation 36]
147. humble(mary) | quiet(mary) [cnf transformation 79]
152. wise(mary) [cnf transformation 25]
155. ~wise(X0) | patient(X0) [duplicate literal removal 96]
343. 42 <=> quiet(mary) [avatar definition]
344. quiet(mary) <- (42) [avatar component clause 343]
347. 43 <=> humble(mary) [avatar definition]
348. humble(mary) <- (43) [avatar component clause 347]
351. 42 | 43 [avatar split clause 147,347,343]
363. patient(mary) [resolution 155,152]
365. ~rich(mary) [resolution 363,139]
397. 49 <=> strong(mary) [avatar definition]
398. ~strong(mary) <- (~49) [avatar component clause 397]
401. 50 <=> tall(mary) [avatar definition]
402. ~tall(mary) <- (~50) [avatar component clause 401]
403. tall(mary) <- (50) [avatar component clause 401]
428. ~strong(mary) | ~patient(mary) <- (50) [resolution 104,403]
438. ~strong(mary) <- (50) [subsumption resolution 428,363]
439. ~49 | ~50 [avatar split clause 438,401,397]
453. ~wise(mary) | strong(mary) <- (42) [resolution 108,344]
459. strong(mary) <- (42) [subsumption resolution 453,152]
460. $false <- (42, ~49) [subsumption resolution 459,398]
461. ~42 | 49 [avatar contradiction clause 460]
463. ~patient(mary) <- (43) [resolution 348,138]
464. $false <- (43) [subsumption resolution 463,363]
465. ~43 [avatar contradiction clause 464]
467. ~wise(mary) | ~old(mary) <- (42) [resolution 344,107]
468. ~old(mary) <- (42) [subsumption resolution 467,152]
520. tall(mary) | rich(mary) <- (42) [resolution 468,89]
521. rich(mary) <- (42, ~50) [subsumption resolution 520,402]
522. $false <- (42, ~50) [subsumption resolution 521,365]
523. ~42 | 50 [avatar contradiction clause 522]
524. $false [avatar sat refutation 351,439,461,465,523]
% SZS output end Proof for 8058352838054989695727447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not curious is funny or kind and vice versa.
Everyone who is both old and humble is either not wise or not happy and vice versa.
Everyone who is not kind or not curious is both strong and not funny and vice versa.
If someone is either not funny or not creative then someone is both not tall and not humble and vice versa.
Everyone who is patient or brave is calm or creative and vice versa.
Everyone who is funny or quiet is brave.
Everyone who is either not curious or not generous is either not patient or not quiet.
Everyone who is either not rich or not funny is both not happy and not strong.
If paul is calm then lucy is either curious or humble.
Everyone who is humble is old and vice versa.
If someone is both rich and old then someone is both not curious and not happy.
If lucy is both not tall and not rich then fred is either creative or curious.
Everyone who is not rich is tall and vice versa.
If someone is not rich or humble then someone is humble or old.
If someone is both brave and not rich then john is either calm or not strong and vice versa.
Everyone who is both not patient and not creative is either wise or strong.
Someone is not happy.
Paul is wise or not old.
Someone is not creative or not calm.
Someone is calm.
Mary is not calm.
Someone is not calm.
Someone is both brave and not funny. | John is strong. | entailment | (![X]:((~wise(X)&~curious(X))<=>(funny(X)|kind(X))))&
(![X]:((old(X)&humble(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((~kind(X)|~curious(X))<=>(strong(X)&~funny(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:((~tall(X)&~humble(X)))))&
(![X]:((patient(X)|brave(X))<=>(calm(X)|creative(X))))&
(![X]:((funny(X)|quiet(X))=>brave(X)))&
(![X]:((~curious(X)<~>~generous(X))=>(~patient(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(~happy(X)&~strong(X))))&
((calm(paul))=>((curious(lucy)<~>humble(lucy))))&
(![X]:(humble(X)<=>old(X)))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((~curious(X)&~happy(X)))))&
(((~tall(lucy)&~rich(lucy)))=>((creative(fred)<~>curious(fred))))&
(![X]:(~rich(X)<=>tall(X)))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:((humble(X)|old(X)))))&
((?[X]:((brave(X)&~rich(X))))<=>((calm(john)<~>~strong(john))))&
(![X]:((~patient(X)&~creative(X))=>(wise(X)<~>strong(X))))&
(?[X]:(~happy(X)))&
((wise(paul)|~old(paul)))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:(calm(X)))&
(~calm(mary))&
(?[X]:(~calm(X)))&
(?[X]:((brave(X)&~funny(X)))) | strong(john) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8018399633776560621899847
% SZS output start Proof for 8018399633776560621899847
1. ! [X0] : ((~curious(X0) & ~wise(X0)) <=> (kind(X0) | funny(X0))) [input p0]
3. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (~funny(X0) & strong(X0))) [input p2]
24. ~strong(john) [input hypothesis]
38. ! [X0] : (((~curious(X0) & ~wise(X0)) | (~kind(X0) & ~funny(X0))) & ((kind(X0) | funny(X0)) | (curious(X0) | wise(X0)))) [nnf transformation 1]
39. ! [X0] : (((~curious(X0) & ~wise(X0)) | (~kind(X0) & ~funny(X0))) & (kind(X0) | funny(X0) | curious(X0) | wise(X0))) [flattening 38]
42. ! [X0] : (((~curious(X0) | ~kind(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (curious(X0) & kind(X0)))) [nnf transformation 3]
43. ! [X0] : ((~curious(X0) | ~kind(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (curious(X0) & kind(X0)))) [flattening 42]
82. ~kind(X0) | ~curious(X0) [cnf transformation 39]
89. strong(X0) | kind(X0) [cnf transformation 43]
90. strong(X0) | curious(X0) [cnf transformation 43]
142. ~strong(john) [cnf transformation 24]
234. 20 <=> strong(john) [avatar definition]
235. ~strong(john) <- (~20) [avatar component clause 234]
276. ~20 [avatar split clause 142,234]
281. kind(john) <- (~20) [resolution 89,235]
282. ~curious(john) <- (~20) [resolution 281,82]
284. curious(john) <- (~20) [resolution 90,235]
285. $false <- (~20) [subsumption resolution 284,282]
286. 20 [avatar contradiction clause 285]
287. $false [avatar sat refutation 276,286]
% SZS output end Proof for 8018399633776560621899847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not humble is patient or not generous and vice versa.
Everyone who is humble or kind is both calm and tall and vice versa.
Everyone who is both generous and not brave is either creative or not creative and vice versa.
If someone is either calm or wise then fred is both rich and not curious.
Everyone who is both not rich and not quiet is strong or not creative and vice versa.
If mary is not tall or funny then susan is both not happy and kind and vice versa.
Everyone who is humble is both rich and patient.
If someone is both not tall and not patient then someone is both curious and not rich and vice versa.
Everyone who is old or not calm is both not calm and humble.
Everyone who is both old and not curious is happy or not rich and vice versa.
If fred is both old and kind then someone is both tall and not brave.
Everyone who is either not old or rich is not kind or not rich and vice versa.
If susan is not wise then lucy is either calm or not curious and vice versa.
Everyone who is either not creative or not curious is patient.
Everyone who is rich is creative or not happy.
If mary is brave then someone is either strong or happy and vice versa.
Fred is either tall or not wise.
Someone is either rich or happy.
Alice is either creative or not generous.
Someone is both kind and not wise.
Someone is either not generous or not quiet.
Fred is rich.
Someone is old or rich.
Someone is strong or not old. | Fred is wise. | entailment | (![X]:((funny(X)<~>~humble(X))<=>(patient(X)|~generous(X))))&
(![X]:((humble(X)|kind(X))<=>(calm(X)&tall(X))))&
(![X]:((generous(X)&~brave(X))<=>(creative(X)<~>~creative(X))))&
((?[X]:((calm(X)<~>wise(X))))=>((rich(fred)&~curious(fred))))&
(![X]:((~rich(X)&~quiet(X))<=>(strong(X)|~creative(X))))&
(((~tall(mary)|funny(mary)))<=>((~happy(susan)&kind(susan))))&
(![X]:(humble(X)=>(rich(X)&patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((old(X)|~calm(X))=>(~calm(X)&humble(X))))&
(![X]:((old(X)&~curious(X))<=>(happy(X)|~rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(~kind(X)|~rich(X))))&
((~wise(susan))<=>((calm(lucy)<~>~curious(lucy))))&
(![X]:((~creative(X)<~>~curious(X))=>patient(X)))&
(![X]:(rich(X)=>(creative(X)|~happy(X))))&
((brave(mary))<=>(?[X]:((strong(X)<~>happy(X)))))&
((tall(fred)<~>~wise(fred)))&
(?[X]:((rich(X)<~>happy(X))))&
((creative(alice)<~>~generous(alice)))&
(?[X]:((kind(X)&~wise(X))))&
(?[X]:((~generous(X)<~>~quiet(X))))&
(rich(fred))&
(?[X]:((old(X)|rich(X))))&
(?[X]:((strong(X)|~old(X)))) | wise(fred) | [
"p1",
"p8",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6647375479741293217324343
% SZS output start Proof for 6647375479741293217324343
2. ! [X0] : ((kind(X0) | humble(X0)) <=> (tall(X0) & calm(X0))) [input p1]
9. ! [X0] : ((~calm(X0) | old(X0)) => (humble(X0) & ~calm(X0))) [input p8]
10. ! [X0] : ((~curious(X0) & old(X0)) <=> (~rich(X0) | happy(X0))) [input p9]
12. ! [X0] : ((~old(X0) <~> rich(X0)) <=> (~rich(X0) | ~kind(X0))) [input p11]
17. tall(fred) <~> ~wise(fred) [input p16]
25. ~wise(fred) [input hypothesis]
29. ! [X0] : ((humble(X0) & ~calm(X0)) | (calm(X0) & ~old(X0))) [ennf transformation 9]
37. ! [X0] : (((kind(X0) | humble(X0)) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | (~kind(X0) & ~humble(X0)))) [nnf transformation 2]
38. ! [X0] : ((kind(X0) | humble(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | (~kind(X0) & ~humble(X0)))) [flattening 37]
51. ! [X0] : (((~curious(X0) & old(X0)) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | (curious(X0) | ~old(X0)))) [nnf transformation 10]
52. ! [X0] : (((~curious(X0) & old(X0)) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | curious(X0) | ~old(X0))) [flattening 51]
55. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [nnf transformation 12]
56. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [flattening 55]
63. (wise(fred) | ~tall(fred)) & (~wise(fred) | tall(fred)) [nnf transformation 17]
83. ~humble(X0) | calm(X0) [cnf transformation 38]
86. ~kind(X0) | tall(X0) [cnf transformation 38]
114. ~calm(X0) | ~old(X0) [cnf transformation 29]
117. humble(X0) | calm(X0) [cnf transformation 29]
120. old(X0) | rich(X0) [cnf transformation 52]
129. ~rich(X0) | old(X0) | kind(X0) [cnf transformation 56]
143. wise(fred) | ~tall(fred) [cnf transformation 63]
155. ~wise(fred) [cnf transformation 25]
229. calm(X0) [subsumption resolution 117,83]
230. ~old(X0) [subsumption resolution 114,229]
232. rich(X0) [subsumption resolution 120,230]
234. old(X0) | kind(X0) [subsumption resolution 129,232]
235. kind(X0) [subsumption resolution 234,230]
251. 17 <=> tall(fred) [avatar definition]
253. ~tall(fred) <- (~17) [avatar component clause 251]
255. 18 <=> wise(fred) [avatar definition]
258. ~17 | 18 [avatar split clause 143,255,251]
262. ~18 [avatar split clause 155,255]
264. tall(X0) [resolution 86,235]
266. $false <- (~17) [resolution 264,253]
267. 17 [avatar contradiction clause 266]
269. $false [avatar sat refutation 258,262,267]
% SZS output end Proof for 6647375479741293217324343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and patient is both curious and happy and vice versa.
Everyone who is not wise or not humble is not rich or patient.
If someone is both not curious and generous then john is calm or not strong.
If mary is not calm or not wise then someone is quiet or old and vice versa.
Everyone who is either not funny or not strong is not quiet.
Everyone who is not old is not quiet or generous and vice versa.
Everyone who is funny or not brave is creative or wise and vice versa.
If susan is either not rich or funny then alice is not strong or old.
If alice is both old and creative then someone is humble.
If alice is kind then susan is both calm and curious and vice versa.
If mary is not funny or not strong then someone is not generous or old and vice versa.
If lucy is not calm then mary is both not generous and tall.
If someone is either not strong or generous then someone is old or not tall and vice versa.
Everyone who is not happy is patient.
If someone is both not kind and not funny then john is calm or strong.
If susan is either not funny or not generous then someone is not wise.
Alice is either not kind or patient.
Someone is either strong or wise.
Paul is both calm and not quiet.
Someone is both not tall and humble.
Someone is not brave or curious.
Someone is both strong and not wise.
Someone is not quiet or tall.
John is generous or rich. | Susan is funny. | neutral | (![X]:((generous(X)&patient(X))<=>(curious(X)&happy(X))))&
(![X]:((~wise(X)|~humble(X))=>(~rich(X)|patient(X))))&
((?[X]:((~curious(X)&generous(X))))=>((calm(john)|~strong(john))))&
(((~calm(mary)|~wise(mary)))<=>(?[X]:((quiet(X)|old(X)))))&
(![X]:((~funny(X)<~>~strong(X))=>~quiet(X)))&
(![X]:(~old(X)<=>(~quiet(X)|generous(X))))&
(![X]:((funny(X)|~brave(X))<=>(creative(X)|wise(X))))&
(((~rich(susan)<~>funny(susan)))=>((~strong(alice)|old(alice))))&
(((old(alice)&creative(alice)))=>(?[X]:(humble(X))))&
((kind(alice))<=>((calm(susan)&curious(susan))))&
(((~funny(mary)|~strong(mary)))<=>(?[X]:((~generous(X)|old(X)))))&
((~calm(lucy))=>((~generous(mary)&tall(mary))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)|~tall(X)))))&
(![X]:(~happy(X)=>patient(X)))&
((?[X]:((~kind(X)&~funny(X))))=>((calm(john)|strong(john))))&
(((~funny(susan)<~>~generous(susan)))=>(?[X]:(~wise(X))))&
((~kind(alice)<~>patient(alice)))&
(?[X]:((strong(X)<~>wise(X))))&
((calm(paul)&~quiet(paul)))&
(?[X]:((~tall(X)&humble(X))))&
(?[X]:((~brave(X)|curious(X))))&
(?[X]:((strong(X)&~wise(X))))&
(?[X]:((~quiet(X)|tall(X))))&
((generous(john)|rich(john))) | funny(susan) | [] | null | 0 |
Everyone who is either quiet or patient is either quiet or not strong and vice versa. If someone is both brave and not humble then alice is both not strong and not happy and vice versa. Everyone who is either curious or not tall is not brave and vice versa. Everyone who is tall is either not kind or kind. Everyone who is happy or not funny is not tall or not humble and vice versa. If someone is rich then someone is not funny. If paul is both curious and not quiet then someone is not wise or rich and vice versa. Everyone who is both not brave and tall is either not patient or strong and vice versa. If someone is both calm and not brave then someone is calm or brave and vice versa. Everyone who is either not patient or not rich is not wise or not strong. If someone is not happy then someone is not humble or brave and vice versa. Everyone who is not kind or kind is not brave and vice versa. If someone is not happy or funny then lucy is not happy. If someone is not strong then someone is not brave. Everyone who is not curious or tall is not brave. Paul is old. Someone is either old or not patient. Mary is not funny. Someone is old or not patient. Someone is not patient. | Lucy is rich. | contradiction | (![X]:((quiet(X)<~>patient(X))<=>(quiet(X)<~>~strong(X))))&
((?[X]:((brave(X)&~humble(X))))<=>((~strong(alice)&~happy(alice))))&
(![X]:((curious(X)<~>~tall(X))<=>~brave(X)))&
(![X]:(tall(X)=>(~kind(X)<~>kind(X))))&
(![X]:((happy(X)|~funny(X))<=>(~tall(X)|~humble(X))))&
((?[X]:(rich(X)))=>(?[X]:(~funny(X))))&
(((curious(paul)&~quiet(paul)))<=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:((~brave(X)&tall(X))<=>(~patient(X)<~>strong(X))))&
((?[X]:((calm(X)&~brave(X))))<=>(?[X]:((calm(X)|brave(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>(~wise(X)|~strong(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~humble(X)|brave(X)))))&
(![X]:((~kind(X)|kind(X))<=>~brave(X)))&
((?[X]:((~happy(X)|funny(X))))=>(~happy(lucy)))&
((?[X]:(~strong(X)))=>(?[X]:(~brave(X))))&
(![X]:((~curious(X)|tall(X))=>~brave(X)))&
(old(paul))&
(?[X]:((old(X)<~>~patient(X))))&
(~funny(mary))&
(?[X]:((old(X)|~patient(X))))&
(?[X]:(~patient(X))) | rich(lucy) | [
"p0",
"p2",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6240509761881742765871467
% SZS output start Proof for 6240509761881742765871467
1. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (quiet(X0) <~> ~strong(X0))) [input p0]
3. ! [X0] : ((curious(X0) <~> ~tall(X0)) <=> ~brave(X0)) [input p2]
7. (~quiet(paul) & curious(paul)) <=> ? [X0] : (rich(X0) | ~wise(X0)) [input p6]
8. ! [X0] : ((tall(X0) & ~brave(X0)) <=> (~patient(X0) <~> strong(X0))) [input p7]
12. ! [X0] : ((kind(X0) | ~kind(X0)) <=> ~brave(X0)) [input p11]
21. rich(lucy) [input hypothesis]
33. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0)))) & (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 1]
39. ! [X0] : ((((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | brave(X0)) & (~brave(X0) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0))))) [nnf transformation 3]
46. ((~quiet(paul) & curious(paul)) | ! [X0] : (~rich(X0) & wise(X0))) & (? [X0] : (rich(X0) | ~wise(X0)) | (quiet(paul) | ~curious(paul))) [nnf transformation 7]
47. ((~quiet(paul) & curious(paul)) | ! [X0] : (~rich(X0) & wise(X0))) & (? [X0] : (rich(X0) | ~wise(X0)) | quiet(paul) | ~curious(paul)) [flattening 46]
48. ((~quiet(paul) & curious(paul)) | ! [X0] : (~rich(X0) & wise(X0))) & (? [X1] : (rich(X1) | ~wise(X1)) | quiet(paul) | ~curious(paul)) [rectify 47]
49. ? [X1] : (rich(X1) | ~wise(X1)) => (rich(sK2) | ~wise(sK2)) [choice axiom]
50. ((~quiet(paul) & curious(paul)) | ! [X0] : (~rich(X0) & wise(X0))) & ((rich(sK2) | ~wise(sK2)) | quiet(paul) | ~curious(paul)) [skolemisation 48,49]
51. ! [X0] : (((tall(X0) & ~brave(X0)) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) & (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | (~tall(X0) | brave(X0)))) [nnf transformation 8]
52. ! [X0] : (((tall(X0) & ~brave(X0)) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) & (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | ~tall(X0) | brave(X0))) [flattening 51]
64. ! [X0] : (((kind(X0) | ~kind(X0)) | brave(X0)) & (~brave(X0) | (~kind(X0) & kind(X0)))) [nnf transformation 12]
65. ! [X0] : ((kind(X0) | ~kind(X0) | brave(X0)) & (~brave(X0) | (~kind(X0) & kind(X0)))) [flattening 64]
77. ~strong(X0) | quiet(X0) | quiet(X0) | ~patient(X0) [cnf transformation 33]
78. strong(X0) | ~quiet(X0) | patient(X0) | ~quiet(X0) [cnf transformation 33]
81. patient(X0) | quiet(X0) | quiet(X0) | strong(X0) [cnf transformation 33]
82. ~patient(X0) | ~quiet(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 33]
91. ~curious(X0) | tall(X0) | brave(X0) [cnf transformation 39]
101. curious(paul) | ~rich(X0) [cnf transformation 50]
104. strong(X0) | ~patient(X0) | ~tall(X0) | brave(X0) [cnf transformation 52]
105. ~strong(X0) | patient(X0) | ~tall(X0) | brave(X0) [cnf transformation 52]
120. ~brave(X0) | kind(X0) [cnf transformation 65]
121. ~kind(X0) | ~brave(X0) [cnf transformation 65]
134. rich(lucy) [cnf transformation 21]
135. ~strong(X0) | quiet(X0) | ~patient(X0) [duplicate literal removal 77]
136. strong(X0) | ~quiet(X0) | patient(X0) [duplicate literal removal 78]
137. strong(X0) | quiet(X0) | patient(X0) [duplicate literal removal 81]
138. ~strong(X0) | ~quiet(X0) | ~patient(X0) [duplicate literal removal 82]
139. strong(X0) | patient(X0) [subsumption resolution 136,137]
140. ~strong(X0) | ~patient(X0) [subsumption resolution 135,138]
165. 6 <=> ! [X1] : ~rich(X1) [avatar definition]
166. ~rich(X1) <- (6) [avatar component clause 165]
182. 10 <=> curious(paul) [avatar definition]
184. curious(paul) <- (10) [avatar component clause 182]
185. 6 | 10 [avatar split clause 101,182,165]
196. ~tall(X0) | patient(X0) | brave(X0) [subsumption resolution 105,139]
197. ~tall(X0) | strong(X0) | brave(X0) [subsumption resolution 104,196]
199. 13 <=> ! [X1] : ~brave(X1) [avatar definition]
200. ~brave(X1) <- (13) [avatar component clause 199]
250. ~brave(X0) [subsumption resolution 120,121]
251. 13 [avatar split clause 250,199]
290. $false <- (6) [resolution 166,134]
291. ~6 [avatar contradiction clause 290]
296. tall(paul) | brave(paul) <- (10) [resolution 91,184]
297. tall(paul) <- (10, 13) [subsumption resolution 296,200]
321. patient(paul) | brave(paul) <- (10, 13) [resolution 196,297]
322. patient(paul) <- (10, 13) [subsumption resolution 321,200]
323. strong(paul) | brave(paul) <- (10, 13) [resolution 197,297]
324. strong(paul) <- (10, 13) [subsumption resolution 323,200]
326. ~patient(paul) <- (10, 13) [resolution 324,140]
327. $false <- (10, 13) [subsumption resolution 326,322]
328. ~10 | ~13 [avatar contradiction clause 327]
329. $false [avatar sat refutation 185,251,291,328]
% SZS output end Proof for 6240509761881742765871467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is both curious and not brave.
Everyone who is funny or quiet is not quiet and vice versa.
If someone is calm or generous then paul is quiet and vice versa.
If someone is not generous or brave then john is either kind or not quiet and vice versa.
Everyone who is both humble and happy is not rich.
Everyone who is old is not strong or not happy.
Everyone who is not happy is either rich or happy and vice versa.
Everyone who is creative or humble is not old or not creative and vice versa.
Everyone who is both old and funny is both not strong and rich.
If lucy is either happy or not wise then someone is wise or not curious and vice versa.
Everyone who is wise is both happy and not creative.
If paul is not strong or brave then someone is humble or tall.
If susan is patient or strong then someone is not strong and vice versa.
Everyone who is either not old or not funny is either not humble or funny.
Everyone who is either not generous or brave is patient and vice versa.
Mary is either not tall or curious.
Alice is either not humble or not patient.
Someone is not funny or humble.
Lucy is either patient or not calm. | Mary is happy. | contradiction | (![X]:((curious(X)|kind(X))=>(curious(X)&~brave(X))))&
(![X]:((funny(X)|quiet(X))<=>~quiet(X)))&
((?[X]:((calm(X)|generous(X))))<=>(quiet(paul)))&
((?[X]:((~generous(X)|brave(X))))<=>((kind(john)<~>~quiet(john))))&
(![X]:((humble(X)&happy(X))=>~rich(X)))&
(![X]:(old(X)=>(~strong(X)|~happy(X))))&
(![X]:(~happy(X)<=>(rich(X)<~>happy(X))))&
(![X]:((creative(X)|humble(X))<=>(~old(X)|~creative(X))))&
(![X]:((old(X)&funny(X))=>(~strong(X)&rich(X))))&
(((happy(lucy)<~>~wise(lucy)))<=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:(wise(X)=>(happy(X)&~creative(X))))&
(((~strong(paul)|brave(paul)))=>(?[X]:((humble(X)|tall(X)))))&
(((patient(susan)|strong(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>~funny(X))=>(~humble(X)<~>funny(X))))&
(![X]:((~generous(X)<~>brave(X))<=>patient(X)))&
((~tall(mary)<~>curious(mary)))&
((~humble(alice)<~>~patient(alice)))&
(?[X]:((~funny(X)|humble(X))))&
((patient(lucy)<~>~calm(lucy))) | happy(mary) | [
"p1",
"p4",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8689502498950536373534265
% SZS output start Proof for 8689502498950536373534265
2. ! [X0] : ((quiet(X0) | funny(X0)) <=> ~quiet(X0)) [input p1]
5. ! [X0] : ((happy(X0) & humble(X0)) => ~rich(X0)) [input p4]
7. ! [X0] : (~happy(X0) <=> (rich(X0) <~> happy(X0))) [input p6]
8. ! [X0] : ((humble(X0) | creative(X0)) <=> (~creative(X0) | ~old(X0))) [input p7]
14. ! [X0] : ((~old(X0) <~> ~funny(X0)) => (~humble(X0) <~> funny(X0))) [input p13]
20. happy(mary) [input hypothesis]
22. ! [X0] : (~rich(X0) | (~happy(X0) | ~humble(X0))) [ennf transformation 5]
23. ! [X0] : (~rich(X0) | ~happy(X0) | ~humble(X0)) [flattening 22]
30. ! [X0] : ((~humble(X0) <~> funny(X0)) | (~old(X0) <=> ~funny(X0))) [ennf transformation 14]
31. ! [X0] : (((quiet(X0) | funny(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 2]
32. ! [X0] : ((quiet(X0) | funny(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [flattening 31]
41. ! [X0] : ((~happy(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | happy(X0))) [nnf transformation 7]
42. ! [X0] : (((humble(X0) | creative(X0)) | (creative(X0) & old(X0))) & ((~creative(X0) | ~old(X0)) | (~humble(X0) & ~creative(X0)))) [nnf transformation 8]
43. ! [X0] : ((humble(X0) | creative(X0) | (creative(X0) & old(X0))) & (~creative(X0) | ~old(X0) | (~humble(X0) & ~creative(X0)))) [flattening 42]
55. ! [X0] : (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0)))) [nnf transformation 30]
67. ~quiet(X0) | ~quiet(X0) [cnf transformation 32]
68. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 32]
78. ~rich(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 23]
80. happy(X0) | rich(X0) | happy(X0) [cnf transformation 41]
83. ~happy(X0) | rich(X0) | ~happy(X0) [cnf transformation 41]
84. ~creative(X0) | ~old(X0) | ~creative(X0) [cnf transformation 43]
87. humble(X0) | creative(X0) | creative(X0) [cnf transformation 43]
105. ~funny(X0) | humble(X0) | ~funny(X0) | old(X0) [cnf transformation 55]
118. happy(mary) [cnf transformation 20]
120. ~funny(X0) | humble(X0) | old(X0) [duplicate literal removal 105]
121. ~creative(X0) | ~old(X0) [duplicate literal removal 84]
122. creative(X0) | humble(X0) [duplicate literal removal 87]
123. happy(X0) | rich(X0) [duplicate literal removal 80]
124. ~happy(X0) | rich(X0) [duplicate literal removal 83]
125. ~quiet(X0) [duplicate literal removal 67]
126. quiet(X0) | funny(X0) [duplicate literal removal 68]
141. rich(X0) [subsumption resolution 123,124]
240. ~old(X0) | humble(X0) [resolution 122,121]
242. funny(X0) [resolution 126,125]
249. ~happy(X0) | ~humble(X0) [resolution 78,141]
255. humble(X0) | old(X0) [resolution 120,242]
256. humble(X0) [subsumption resolution 255,240]
257. ~humble(mary) [resolution 249,118]
258. $false [subsumption resolution 257,256]
% SZS output end Proof for 8689502498950536373534265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then lucy is either old or kind. If someone is both not happy and curious then fred is not generous or old. Everyone who is rich is both not brave and not kind. Everyone who is not strong or not calm is curious or not rich. Everyone who is not rich is both funny and old and vice versa. If alice is not old or not funny then lucy is strong or humble. If paul is kind then paul is not generous and vice versa. If someone is not patient or not calm then paul is either patient or funny and vice versa. Everyone who is not patient or calm is not wise and vice versa. Everyone who is either not happy or wise is both not generous and not old and vice versa. Everyone who is not patient or rich is not old and vice versa. Everyone who is not calm or not rich is creative and vice versa. Everyone who is either not curious or calm is wise. Everyone who is not happy is curious and vice versa. If someone is not kind then fred is both not wise and not patient and vice versa. If mary is both not curious and not brave then someone is not generous and vice versa. Susan is both not generous and not tall. Alice is either not funny or not brave. John is either curious or calm. Someone is either generous or not quiet. Someone is tall or calm. Someone is quiet or old. Alice is quiet or wise. Someone is both wise and not generous. | Mary is not calm. | contradiction | ((?[X]:(generous(X)))=>((old(lucy)<~>kind(lucy))))&
((?[X]:((~happy(X)&curious(X))))=>((~generous(fred)|old(fred))))&
(![X]:(rich(X)=>(~brave(X)&~kind(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)|~rich(X))))&
(![X]:(~rich(X)<=>(funny(X)&old(X))))&
(((~old(alice)|~funny(alice)))=>((strong(lucy)|humble(lucy))))&
((kind(paul))<=>(~generous(paul)))&
((?[X]:((~patient(X)|~calm(X))))<=>((patient(paul)<~>funny(paul))))&
(![X]:((~patient(X)|calm(X))<=>~wise(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(~generous(X)&~old(X))))&
(![X]:((~patient(X)|rich(X))<=>~old(X)))&
(![X]:((~calm(X)|~rich(X))<=>creative(X)))&
(![X]:((~curious(X)<~>calm(X))=>wise(X)))&
(![X]:(~happy(X)<=>curious(X)))&
((?[X]:(~kind(X)))<=>((~wise(fred)&~patient(fred))))&
(((~curious(mary)&~brave(mary)))<=>(?[X]:(~generous(X))))&
((~generous(susan)&~tall(susan)))&
((~funny(alice)<~>~brave(alice)))&
((curious(john)<~>calm(john)))&
(?[X]:((generous(X)<~>~quiet(X))))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((quiet(X)|old(X))))&
((quiet(alice)|wise(alice)))&
(?[X]:((wise(X)&~generous(X)))) | ~calm(mary) | [
"p3",
"p4",
"p9",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 120886538309945456231213
% SZS output start Proof for 120886538309945456231213
4. ! [X0] : ((~calm(X0) | ~strong(X0)) => (~rich(X0) | curious(X0))) [input p3]
5. ! [X0] : (~rich(X0) <=> (old(X0) & funny(X0))) [input p4]
10. ! [X0] : ((~happy(X0) <~> wise(X0)) <=> (~old(X0) & ~generous(X0))) [input p9]
13. ! [X0] : ((~curious(X0) <~> calm(X0)) => wise(X0)) [input p12]
14. ! [X0] : (~happy(X0) <=> curious(X0)) [input p13]
16. (~brave(mary) & ~curious(mary)) <=> ? [X0] : ~generous(X0) [input p15]
17. ~tall(susan) & ~generous(susan) [input p16]
25. ~calm(mary) [input hypothesis]
27. ! [X0] : (~calm(X0) => (~rich(X0) | curious(X0))) [pure predicate removal 4]
32. ! [X0] : ((~rich(X0) | curious(X0)) | calm(X0)) [ennf transformation 27]
33. ! [X0] : (~rich(X0) | curious(X0) | calm(X0)) [flattening 32]
34. ! [X0] : (wise(X0) | (~curious(X0) <=> calm(X0))) [ennf transformation 13]
36. ! [X0] : ((~rich(X0) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | rich(X0))) [nnf transformation 5]
37. ! [X0] : ((~rich(X0) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | rich(X0))) [flattening 36]
45. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [nnf transformation 10]
46. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [flattening 45]
49. ! [X0] : (wise(X0) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) [nnf transformation 34]
50. ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 14]
56. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (brave(mary) | curious(mary))) [nnf transformation 16]
57. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | brave(mary) | curious(mary)) [flattening 56]
58. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | brave(mary) | curious(mary)) [rectify 57]
59. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
60. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (~generous(sK2) | brave(mary) | curious(mary)) [skolemisation 58,59]
77. ~rich(X0) | curious(X0) | calm(X0) [cnf transformation 33]
79. rich(X0) | old(X0) [cnf transformation 37]
95. ~wise(X0) | ~happy(X0) | ~old(X0) [cnf transformation 46]
101. wise(X0) | calm(X0) | curious(X0) [cnf transformation 49]
103. curious(X0) | happy(X0) [cnf transformation 50]
109. ~curious(mary) | generous(X0) [cnf transformation 60]
111. ~generous(susan) [cnf transformation 17]
124. ~calm(mary) [cnf transformation 25]
209. 19 <=> ! [X0] : generous(X0) [avatar definition]
210. generous(X0) <- (19) [avatar component clause 209]
217. 21 <=> curious(mary) [avatar definition]
220. 19 | ~21 [avatar split clause 109,217,209]
290. curious(X0) | calm(X0) | old(X0) [resolution 77,79]
351. calm(X0) | curious(X0) | ~happy(X0) | ~old(X0) [resolution 101,95]
364. calm(X0) | curious(X0) | ~old(X0) [subsumption resolution 351,103]
365. calm(X0) | curious(X0) [subsumption resolution 364,290]
392. curious(mary) [resolution 365,124]
397. 21 [avatar split clause 392,217]
400. $false <- (19) [resolution 210,111]
407. ~19 [avatar contradiction clause 400]
409. $false [avatar sat refutation 220,397,407]
% SZS output end Proof for 120886538309945456231213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or humble then someone is both not brave and humble.
Everyone who is not tall is humble or kind and vice versa.
Everyone who is both not kind and brave is not wise.
Everyone who is either not curious or not creative is not strong.
Everyone who is either not happy or not kind is creative or not kind and vice versa.
Everyone who is wise is either humble or happy.
Everyone who is either wise or calm is both not curious and not wise and vice versa.
Everyone who is either not old or not funny is both not calm and funny and vice versa.
If someone is curious then someone is either not calm or tall.
Everyone who is either not patient or quiet is not generous.
Everyone who is not kind or rich is both not tall and not old and vice versa.
If alice is patient or calm then fred is both not happy and funny.
Everyone who is either quiet or not old is both creative and not wise and vice versa.
Everyone who is both brave and old is either strong or curious and vice versa.
If someone is either tall or quiet then paul is kind or humble and vice versa.
If someone is not curious or not patient then someone is both patient and not strong and vice versa.
Someone is both funny and not quiet.
Someone is not wise.
John is either calm or not strong.
Someone is both brave and kind.
Someone is humble or brave.
Lucy is curious.
Fred is not generous. | Alice is not curious. | neutral | ((?[X]:((brave(X)<~>humble(X))))=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:(~tall(X)<=>(humble(X)|kind(X))))&
(![X]:((~kind(X)&brave(X))=>~wise(X)))&
(![X]:((~curious(X)<~>~creative(X))=>~strong(X)))&
(![X]:((~happy(X)<~>~kind(X))<=>(creative(X)|~kind(X))))&
(![X]:(wise(X)=>(humble(X)<~>happy(X))))&
(![X]:((wise(X)<~>calm(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~calm(X)&funny(X))))&
((?[X]:(curious(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((~patient(X)<~>quiet(X))=>~generous(X)))&
(![X]:((~kind(X)|rich(X))<=>(~tall(X)&~old(X))))&
(((patient(alice)|calm(alice)))=>((~happy(fred)&funny(fred))))&
(![X]:((quiet(X)<~>~old(X))<=>(creative(X)&~wise(X))))&
(![X]:((brave(X)&old(X))<=>(strong(X)<~>curious(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((kind(paul)|humble(paul))))&
((?[X]:((~curious(X)|~patient(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:(~wise(X)))&
((calm(john)<~>~strong(john)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)|brave(X))))&
(curious(lucy))&
(~generous(fred)) | ~curious(alice) | [] | null | 0 |
If paul is either curious or kind then someone is either not old or old.
If someone is not old or not tall then someone is wise and vice versa.
Everyone who is quiet or strong is not brave.
If lucy is rich then john is either happy or not patient and vice versa.
Everyone who is not brave is either not patient or not creative and vice versa.
If alice is humble or not tall then fred is not patient and vice versa.
Everyone who is generous or patient is humble.
If john is both not brave and not tall then someone is both funny and not creative and vice versa.
If someone is patient or not wise then someone is either not creative or rich and vice versa.
If mary is not calm then alice is either not brave or calm.
Everyone who is calm or curious is not patient or not quiet and vice versa.
If paul is both not happy and curious then someone is humble and vice versa.
If paul is not funny or not patient then fred is not wise and vice versa.
Everyone who is quiet is both wise and brave and vice versa.
Everyone who is not curious or kind is both quiet and humble and vice versa.
Everyone who is either not calm or happy is humble or happy.
Someone is either funny or not humble.
Susan is not happy.
Mary is either not rich or not patient.
Mary is either not wise or kind.
Someone is either funny or not kind.
Someone is both not funny and not strong.
Someone is either not kind or not rich.
Someone is either old or creative. | Susan is quiet. | contradiction | (((curious(paul)<~>kind(paul)))=>(?[X]:((~old(X)<~>old(X)))))&
((?[X]:((~old(X)|~tall(X))))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|strong(X))=>~brave(X)))&
((rich(lucy))<=>((happy(john)<~>~patient(john))))&
(![X]:(~brave(X)<=>(~patient(X)<~>~creative(X))))&
(((humble(alice)|~tall(alice)))<=>(~patient(fred)))&
(![X]:((generous(X)|patient(X))=>humble(X)))&
(((~brave(john)&~tall(john)))<=>(?[X]:((funny(X)&~creative(X)))))&
((?[X]:((patient(X)|~wise(X))))<=>(?[X]:((~creative(X)<~>rich(X)))))&
((~calm(mary))=>((~brave(alice)<~>calm(alice))))&
(![X]:((calm(X)|curious(X))<=>(~patient(X)|~quiet(X))))&
(((~happy(paul)&curious(paul)))<=>(?[X]:(humble(X))))&
(((~funny(paul)|~patient(paul)))<=>(~wise(fred)))&
(![X]:(quiet(X)<=>(wise(X)&brave(X))))&
(![X]:((~curious(X)|kind(X))<=>(quiet(X)&humble(X))))&
(![X]:((~calm(X)<~>happy(X))=>(humble(X)|happy(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(~happy(susan))&
((~rich(mary)<~>~patient(mary)))&
((~wise(mary)<~>kind(mary)))&
(?[X]:((funny(X)<~>~kind(X))))&
(?[X]:((~funny(X)&~strong(X))))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:((old(X)<~>creative(X)))) | quiet(susan) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6230510410648343728365378
% SZS output start Proof for 6230510410648343728365378
3. ! [X0] : ((strong(X0) | quiet(X0)) => ~brave(X0)) [input p2]
14. ! [X0] : (quiet(X0) <=> (brave(X0) & wise(X0))) [input p13]
25. quiet(susan) [input hypothesis]
29. ! [X0] : (quiet(X0) => ~brave(X0)) [pure predicate removal 3]
32. ! [X0] : (~brave(X0) | ~quiet(X0)) [ennf transformation 29]
69. ! [X0] : ((quiet(X0) | (~brave(X0) | ~wise(X0))) & ((brave(X0) & wise(X0)) | ~quiet(X0))) [nnf transformation 14]
70. ! [X0] : ((quiet(X0) | ~brave(X0) | ~wise(X0)) & ((brave(X0) & wise(X0)) | ~quiet(X0))) [flattening 69]
97. ~brave(X0) | ~quiet(X0) [cnf transformation 32]
133. brave(X0) | ~quiet(X0) [cnf transformation 70]
156. quiet(susan) [cnf transformation 25]
318. ~quiet(X0) [subsumption resolution 133,97]
354. $false [subsumption resolution 156,318]
% SZS output end Proof for 6230510410648343728365378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or not brave then someone is not calm or not humble.
Everyone who is not patient is both curious and not quiet.
Everyone who is both not curious and not quiet is not tall.
Everyone who is both not quiet and kind is both strong and tall.
Everyone who is not happy or not old is either old or not calm.
Everyone who is either funny or tall is either quiet or generous and vice versa.
Everyone who is both calm and not brave is patient or not tall and vice versa.
Everyone who is humble or wise is generous and vice versa.
If someone is not quiet or not kind then someone is not happy.
Everyone who is either not old or not happy is brave or generous and vice versa.
If susan is curious or not patient then fred is not funny and vice versa.
Everyone who is not tall is calm and vice versa.
If mary is not curious then someone is generous or kind and vice versa.
Everyone who is both kind and not humble is not creative or not strong and vice versa.
If someone is both not funny and not rich then mary is either patient or tall and vice versa.
If susan is not curious or kind then fred is either not curious or not old and vice versa.
Alice is not creative or not rich.
John is either curious or not patient.
Mary is both not funny and not kind.
Paul is both not funny and tall.
Someone is both generous and not creative.
Someone is humble.
John is not funny or not wise.
Someone is either not funny or not wise. | Lucy is not funny. | neutral | (((~patient(lucy)<~>~brave(lucy)))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:(~patient(X)=>(curious(X)&~quiet(X))))&
(![X]:((~curious(X)&~quiet(X))=>~tall(X)))&
(![X]:((~quiet(X)&kind(X))=>(strong(X)&tall(X))))&
(![X]:((~happy(X)|~old(X))=>(old(X)<~>~calm(X))))&
(![X]:((funny(X)<~>tall(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((calm(X)&~brave(X))<=>(patient(X)|~tall(X))))&
(![X]:((humble(X)|wise(X))<=>generous(X)))&
((?[X]:((~quiet(X)|~kind(X))))=>(?[X]:(~happy(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(brave(X)|generous(X))))&
(((curious(susan)|~patient(susan)))<=>(~funny(fred)))&
(![X]:(~tall(X)<=>calm(X)))&
((~curious(mary))<=>(?[X]:((generous(X)|kind(X)))))&
(![X]:((kind(X)&~humble(X))<=>(~creative(X)|~strong(X))))&
((?[X]:((~funny(X)&~rich(X))))<=>((patient(mary)<~>tall(mary))))&
(((~curious(susan)|kind(susan)))<=>((~curious(fred)<~>~old(fred))))&
((~creative(alice)|~rich(alice)))&
((curious(john)<~>~patient(john)))&
((~funny(mary)&~kind(mary)))&
((~funny(paul)&tall(paul)))&
(?[X]:((generous(X)&~creative(X))))&
(?[X]:(humble(X)))&
((~funny(john)|~wise(john)))&
(?[X]:((~funny(X)<~>~wise(X)))) | ~funny(lucy) | [] | null | 0 |
If lucy is both calm and strong then someone is humble. If susan is both brave and calm then someone is not curious and vice versa. Everyone who is not rich is tall and vice versa. If fred is not rich or not patient then someone is both humble and curious and vice versa. If someone is either creative or not rich then mary is both kind and not calm and vice versa. Everyone who is either quiet or not creative is not curious. Everyone who is either rich or curious is both humble and tall. If lucy is quiet or not old then someone is either calm or not rich and vice versa. Everyone who is happy is both not funny and calm. If someone is both not generous and not humble then someone is both not funny and curious and vice versa. If someone is either patient or rich then someone is both rich and not old. If mary is not calm or not tall then mary is both calm and not curious. Everyone who is either not rich or strong is both generous and quiet and vice versa. If paul is not happy then someone is not generous. If fred is happy or not strong then someone is not funny and vice versa. If someone is both not curious and not creative then someone is either quiet or rich. Someone is both calm and not kind. Lucy is patient. John is both creative and curious. Alice is brave. Someone is both generous and not funny. Fred is not tall. John is curious or not quiet. Someone is both kind and not creative. | John is not tall. | contradiction | (((calm(lucy)&strong(lucy)))=>(?[X]:(humble(X))))&
(((brave(susan)&calm(susan)))<=>(?[X]:(~curious(X))))&
(![X]:(~rich(X)<=>tall(X)))&
(((~rich(fred)|~patient(fred)))<=>(?[X]:((humble(X)&curious(X)))))&
((?[X]:((creative(X)<~>~rich(X))))<=>((kind(mary)&~calm(mary))))&
(![X]:((quiet(X)<~>~creative(X))=>~curious(X)))&
(![X]:((rich(X)<~>curious(X))=>(humble(X)&tall(X))))&
(((quiet(lucy)|~old(lucy)))<=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:(happy(X)=>(~funny(X)&calm(X))))&
((?[X]:((~generous(X)&~humble(X))))<=>(?[X]:((~funny(X)&curious(X)))))&
((?[X]:((patient(X)<~>rich(X))))=>(?[X]:((rich(X)&~old(X)))))&
(((~calm(mary)|~tall(mary)))=>((calm(mary)&~curious(mary))))&
(![X]:((~rich(X)<~>strong(X))<=>(generous(X)&quiet(X))))&
((~happy(paul))=>(?[X]:(~generous(X))))&
(((happy(fred)|~strong(fred)))<=>(?[X]:(~funny(X))))&
((?[X]:((~curious(X)&~creative(X))))=>(?[X]:((quiet(X)<~>rich(X)))))&
(?[X]:((calm(X)&~kind(X))))&
(patient(lucy))&
((creative(john)&curious(john)))&
(brave(alice))&
(?[X]:((generous(X)&~funny(X))))&
(~tall(fred))&
((curious(john)|~quiet(john)))&
(?[X]:((kind(X)&~creative(X)))) | ~tall(john) | [
"p2",
"p4",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 830328260052507677556336
% SZS output start Proof for 830328260052507677556336
3. ! [X0] : (~rich(X0) <=> tall(X0)) [input p2]
5. ? [X0] : (creative(X0) <~> ~rich(X0)) <=> (~calm(mary) & kind(mary)) [input p4]
12. (~tall(mary) | ~calm(mary)) => (~curious(mary) & calm(mary)) [input p11]
19. curious(john) & creative(john) [input p18]
25. ~tall(john) [input hypothesis]
35. (~curious(mary) & calm(mary)) | (tall(mary) & calm(mary)) [ennf transformation 12]
45. ! [X0] : ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0))) [nnf transformation 3]
51. (? [X0] : ((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | (calm(mary) | ~kind(mary))) & ((~calm(mary) & kind(mary)) | ! [X0] : ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 5]
52. (? [X0] : ((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | calm(mary) | ~kind(mary)) & ((~calm(mary) & kind(mary)) | ! [X0] : ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [flattening 51]
53. (? [X0] : ((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | calm(mary) | ~kind(mary)) & ((~calm(mary) & kind(mary)) | ! [X1] : ((creative(X1) | rich(X1)) & (~rich(X1) | ~creative(X1)))) [rectify 52]
54. ? [X0] : ((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) => ((rich(sK3) | ~creative(sK3)) & (~rich(sK3) | creative(sK3))) [choice axiom]
55. (((rich(sK3) | ~creative(sK3)) & (~rich(sK3) | creative(sK3))) | calm(mary) | ~kind(mary)) & ((~calm(mary) & kind(mary)) | ! [X1] : ((creative(X1) | rich(X1)) & (~rich(X1) | ~creative(X1)))) [skolemisation 53,54]
95. tall(X0) | rich(X0) [cnf transformation 45]
104. ~calm(mary) | ~rich(X1) | ~creative(X1) [cnf transformation 55]
130. calm(mary) | calm(mary) [cnf transformation 35]
149. creative(john) [cnf transformation 19]
158. ~tall(john) [cnf transformation 25]
159. calm(mary) [duplicate literal removal 130]
220. 14 <=> calm(mary) [avatar definition]
238. 18 <=> ! [X1] : (~rich(X1) | ~creative(X1)) [avatar definition]
239. ~creative(X1) | ~rich(X1) <- (18) [avatar component clause 238]
240. 18 | ~14 [avatar split clause 104,220,238]
322. 14 [avatar split clause 159,220]
366. rich(john) [resolution 95,158]
371. ~rich(john) <- (18) [resolution 239,149]
373. $false <- (18) [subsumption resolution 371,366]
374. ~18 [avatar contradiction clause 373]
375. $false [avatar sat refutation 240,322,374]
% SZS output end Proof for 830328260052507677556336
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or rich is both not strong and strong and vice versa.
Everyone who is not tall or tall is not wise or not rich and vice versa.
If mary is happy or tall then someone is both generous and wise.
If someone is wise or not tall then someone is either humble or not creative and vice versa.
If someone is patient or happy then fred is not strong.
Everyone who is both tall and not generous is calm.
If someone is not wise or creative then someone is patient and vice versa.
Everyone who is not strong or not generous is both kind and not rich and vice versa.
Everyone who is either not patient or not happy is not strong or patient and vice versa.
Everyone who is funny is not quiet or not kind.
Everyone who is either not strong or not generous is humble.
Everyone who is either not curious or curious is not happy and vice versa.
Everyone who is both not happy and curious is both curious and not tall and vice versa.
Everyone who is either strong or generous is not calm.
If paul is funny or humble then fred is either rich or kind.
Paul is humble.
Someone is not curious.
John is not old or rich.
Someone is both not old and kind.
Someone is either not wise or quiet.
Someone is either not rich or brave.
Someone is calm.
John is either not old or rich. | Paul is not patient. | neutral | (![X]:((brave(X)|rich(X))<=>(~strong(X)&strong(X))))&
(![X]:((~tall(X)|tall(X))<=>(~wise(X)|~rich(X))))&
(((happy(mary)|tall(mary)))=>(?[X]:((generous(X)&wise(X)))))&
((?[X]:((wise(X)|~tall(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((?[X]:((patient(X)|happy(X))))=>(~strong(fred)))&
(![X]:((tall(X)&~generous(X))=>calm(X)))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~strong(X)|~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(![X]:(funny(X)=>(~quiet(X)|~kind(X))))&
(![X]:((~strong(X)<~>~generous(X))=>humble(X)))&
(![X]:((~curious(X)<~>curious(X))<=>~happy(X)))&
(![X]:((~happy(X)&curious(X))<=>(curious(X)&~tall(X))))&
(![X]:((strong(X)<~>generous(X))=>~calm(X)))&
(((funny(paul)|humble(paul)))=>((rich(fred)<~>kind(fred))))&
(humble(paul))&
(?[X]:(~curious(X)))&
((~old(john)|rich(john)))&
(?[X]:((~old(X)&kind(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>rich(john))) | ~patient(paul) | [] | null | 0 |
If someone is creative then mary is not patient or not creative.
Everyone who is not tall is not creative.
Everyone who is not brave is not rich or not brave and vice versa.
Everyone who is not quiet or not creative is rich or not happy.
If someone is strong or not wise then someone is either not curious or not tall.
Everyone who is happy is either brave or kind and vice versa.
Everyone who is either patient or humble is either rich or not funny.
Everyone who is either happy or not creative is either calm or patient.
Everyone who is both strong and not rich is both generous and not funny.
If susan is strong then someone is both happy and calm and vice versa.
Everyone who is strong or old is not old or kind and vice versa.
Everyone who is both not curious and quiet is not calm.
Everyone who is either not funny or not humble is happy.
Everyone who is either calm or brave is calm or not funny.
Everyone who is funny or not creative is not kind.
If paul is strong or calm then someone is both not humble and quiet.
Someone is either wise or not creative.
Someone is generous or happy.
Someone is not curious.
Fred is not creative or curious.
Someone is not tall.
Someone is brave or not quiet.
Mary is humble. | Mary is funny. | neutral | ((?[X]:(creative(X)))=>((~patient(mary)|~creative(mary))))&
(![X]:(~tall(X)=>~creative(X)))&
(![X]:(~brave(X)<=>(~rich(X)|~brave(X))))&
(![X]:((~quiet(X)|~creative(X))=>(rich(X)|~happy(X))))&
((?[X]:((strong(X)|~wise(X))))=>(?[X]:((~curious(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>(brave(X)<~>kind(X))))&
(![X]:((patient(X)<~>humble(X))=>(rich(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~creative(X))=>(calm(X)<~>patient(X))))&
(![X]:((strong(X)&~rich(X))=>(generous(X)&~funny(X))))&
((strong(susan))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((strong(X)|old(X))<=>(~old(X)|kind(X))))&
(![X]:((~curious(X)&quiet(X))=>~calm(X)))&
(![X]:((~funny(X)<~>~humble(X))=>happy(X)))&
(![X]:((calm(X)<~>brave(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|~creative(X))=>~kind(X)))&
(((strong(paul)|calm(paul)))=>(?[X]:((~humble(X)&quiet(X)))))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((generous(X)|happy(X))))&
(?[X]:(~curious(X)))&
((~creative(fred)|curious(fred)))&
(?[X]:(~tall(X)))&
(?[X]:((brave(X)|~quiet(X))))&
(humble(mary)) | funny(mary) | [] | null | 0 |
Everyone who is both quiet and not creative is strong.
If someone is old then someone is not generous or calm.
Everyone who is not humble or old is old and vice versa.
Everyone who is either not tall or not brave is either wise or not old.
If someone is both not happy and not old then someone is not generous or patient and vice versa.
If alice is both strong and not funny then susan is rich.
Everyone who is both not funny and not happy is both tall and funny.
Everyone who is either tall or not brave is either not tall or old.
If fred is either not generous or brave then someone is not generous.
Everyone who is not patient is old or not patient.
Everyone who is either not happy or creative is tall and vice versa.
Everyone who is quiet is both not curious and patient and vice versa.
If mary is both rich and old then someone is either strong or not brave.
Everyone who is either patient or not kind is both not curious and strong.
Everyone who is not happy is either not generous or not happy.
Everyone who is both not tall and funny is either tall or not humble and vice versa.
Someone is happy.
Someone is not happy.
Someone is both funny and wise.
Someone is either funny or not quiet.
John is either not wise or creative.
Lucy is not happy.
Someone is not kind or brave. | Susan is generous. | entailment | (![X]:((quiet(X)&~creative(X))=>strong(X)))&
((?[X]:(old(X)))=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:((~humble(X)|old(X))<=>old(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(wise(X)<~>~old(X))))&
((?[X]:((~happy(X)&~old(X))))<=>(?[X]:((~generous(X)|patient(X)))))&
(((strong(alice)&~funny(alice)))=>(rich(susan)))&
(![X]:((~funny(X)&~happy(X))=>(tall(X)&funny(X))))&
(![X]:((tall(X)<~>~brave(X))=>(~tall(X)<~>old(X))))&
(((~generous(fred)<~>brave(fred)))=>(?[X]:(~generous(X))))&
(![X]:(~patient(X)=>(old(X)|~patient(X))))&
(![X]:((~happy(X)<~>creative(X))<=>tall(X)))&
(![X]:(quiet(X)<=>(~curious(X)&patient(X))))&
(((rich(mary)&old(mary)))=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((patient(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(![X]:(~happy(X)=>(~generous(X)<~>~happy(X))))&
(![X]:((~tall(X)&funny(X))<=>(tall(X)<~>~humble(X))))&
(?[X]:(happy(X)))&
(?[X]:(~happy(X)))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:((funny(X)<~>~quiet(X))))&
((~wise(john)<~>creative(john)))&
(~happy(lucy))&
(?[X]:((~kind(X)|brave(X)))) | generous(susan) | [
"p2",
"p4",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7615572715713425037389255
% SZS output start Proof for 7615572715713425037389255
3. ! [X0] : ((old(X0) | ~humble(X0)) <=> old(X0)) [input p2]
5. ? [X0] : (~old(X0) & ~happy(X0)) <=> ? [X0] : (patient(X0) | ~generous(X0)) [input p4]
7. ! [X0] : ((~happy(X0) & ~funny(X0)) => (funny(X0) & tall(X0))) [input p6]
16. ! [X0] : ((funny(X0) & ~tall(X0)) <=> (tall(X0) <~> ~humble(X0))) [input p15]
24. ~generous(susan) [input hypothesis]
26. ? [X0] : (~old(X0) & ~happy(X0)) <=> ? [X1] : (patient(X1) | ~generous(X1)) [rectify 5]
33. ! [X0] : ((funny(X0) & tall(X0)) | (happy(X0) | funny(X0))) [ennf transformation 7]
34. ! [X0] : ((funny(X0) & tall(X0)) | happy(X0) | funny(X0)) [flattening 33]
43. ! [X0] : (((old(X0) | ~humble(X0)) | ~old(X0)) & (old(X0) | (~old(X0) & humble(X0)))) [nnf transformation 3]
44. ! [X0] : ((old(X0) | ~humble(X0) | ~old(X0)) & (old(X0) | (~old(X0) & humble(X0)))) [flattening 43]
46. (? [X0] : (~old(X0) & ~happy(X0)) | ! [X1] : (~patient(X1) & generous(X1))) & (? [X1] : (patient(X1) | ~generous(X1)) | ! [X0] : (old(X0) | happy(X0))) [nnf transformation 26]
47. (? [X0] : (~old(X0) & ~happy(X0)) | ! [X1] : (~patient(X1) & generous(X1))) & (? [X2] : (patient(X2) | ~generous(X2)) | ! [X3] : (old(X3) | happy(X3))) [rectify 46]
48. ? [X0] : (~old(X0) & ~happy(X0)) => (~old(sK0) & ~happy(sK0)) [choice axiom]
49. ? [X2] : (patient(X2) | ~generous(X2)) => (patient(sK1) | ~generous(sK1)) [choice axiom]
50. ((~old(sK0) & ~happy(sK0)) | ! [X1] : (~patient(X1) & generous(X1))) & ((patient(sK1) | ~generous(sK1)) | ! [X3] : (old(X3) | happy(X3))) [skolemisation 47,49,48]
63. ! [X0] : (((funny(X0) & ~tall(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) & (((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | (~funny(X0) | tall(X0)))) [nnf transformation 16]
64. ! [X0] : (((funny(X0) & ~tall(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) & (((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | ~funny(X0) | tall(X0))) [flattening 63]
78. humble(X0) | old(X0) [cnf transformation 44]
86. ~happy(sK0) | generous(X1) [cnf transformation 50]
88. ~old(sK0) | generous(X1) [cnf transformation 50]
92. funny(X0) | happy(X0) | funny(X0) [cnf transformation 34]
115. ~humble(X0) | tall(X0) | ~funny(X0) | tall(X0) [cnf transformation 64]
117. ~tall(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 64]
131. ~generous(susan) [cnf transformation 24]
132. ~humble(X0) | tall(X0) | ~funny(X0) [duplicate literal removal 115]
133. ~tall(X0) | ~humble(X0) [duplicate literal removal 117]
137. funny(X0) | happy(X0) [duplicate literal removal 92]
142. 2 <=> old(sK0) [avatar definition]
147. 3 <=> ! [X1] : generous(X1) [avatar definition]
148. generous(X1) <- (3) [avatar component clause 147]
149. 3 | ~2 [avatar split clause 88,142,147]
151. 4 <=> happy(sK0) [avatar definition]
153. ~happy(sK0) <- (~4) [avatar component clause 151]
155. 3 | ~4 [avatar split clause 86,151,147]
157. 5 <=> ! [X3] : (old(X3) | happy(X3)) [avatar definition]
158. happy(X3) | old(X3) <- (5) [avatar component clause 157]
213. ~funny(X0) | ~humble(X0) [subsumption resolution 132,133]
248. ~humble(X0) | happy(X0) [resolution 213,137]
412. happy(X0) | old(X0) [resolution 248,78]
414. 5 [avatar split clause 412,157]
421. old(sK0) <- (~4, 5) [resolution 158,153]
429. 2 | 4 | ~5 [avatar split clause 421,157,151,142]
442. $false <- (3) [resolution 148,131]
447. ~3 [avatar contradiction clause 442]
448. $false [avatar sat refutation 149,155,414,429,447]
% SZS output end Proof for 7615572715713425037389255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong is either wise or not generous. If mary is both old and not creative then someone is both not happy and not wise and vice versa. Everyone who is brave is both not rich and not wise and vice versa. Everyone who is kind is creative or generous. Everyone who is either not wise or not calm is kind and vice versa. Everyone who is either not patient or creative is either brave or humble. Everyone who is both funny and quiet is either creative or kind. Everyone who is not calm is not tall or strong and vice versa. If lucy is not brave then someone is both not quiet and humble and vice versa. If susan is either not tall or not old then susan is happy or tall. If susan is both funny and not funny then someone is either not tall or humble. Everyone who is either rich or not patient is either not funny or tall and vice versa. If someone is either not quiet or not humble then someone is either humble or happy. Everyone who is not humble is not quiet or not patient. If someone is wise or kind then susan is not old. Everyone who is both generous and funny is both not old and not rich. Someone is not generous. Fred is tall or not creative. Someone is both not calm and patient. Someone is either not happy or calm. Someone is either not rich or not happy. Someone is either humble or not wise. Someone is either not calm or brave. Susan is both not wise and happy. | Susan is not happy. | contradiction | (![X]:((~wise(X)|~strong(X))=>(wise(X)<~>~generous(X))))&
(((old(mary)&~creative(mary)))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:(brave(X)<=>(~rich(X)&~wise(X))))&
(![X]:(kind(X)=>(creative(X)|generous(X))))&
(![X]:((~wise(X)<~>~calm(X))<=>kind(X)))&
(![X]:((~patient(X)<~>creative(X))=>(brave(X)<~>humble(X))))&
(![X]:((funny(X)&quiet(X))=>(creative(X)<~>kind(X))))&
(![X]:(~calm(X)<=>(~tall(X)|strong(X))))&
((~brave(lucy))<=>(?[X]:((~quiet(X)&humble(X)))))&
(((~tall(susan)<~>~old(susan)))=>((happy(susan)|tall(susan))))&
(((funny(susan)&~funny(susan)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((rich(X)<~>~patient(X))<=>(~funny(X)<~>tall(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((humble(X)<~>happy(X)))))&
(![X]:(~humble(X)=>(~quiet(X)|~patient(X))))&
((?[X]:((wise(X)|kind(X))))=>(~old(susan)))&
(![X]:((generous(X)&funny(X))=>(~old(X)&~rich(X))))&
(?[X]:(~generous(X)))&
((tall(fred)|~creative(fred)))&
(?[X]:((~calm(X)&patient(X))))&
(?[X]:((~happy(X)<~>calm(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((~calm(X)<~>brave(X))))&
((~wise(susan)&happy(susan))) | ~happy(susan) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4533448985486802353530027
% SZS output start Proof for 4533448985486802353530027
24. happy(susan) & ~wise(susan) [input p23]
25. ~happy(susan) [input hypothesis]
147. happy(susan) [cnf transformation 24]
148. ~happy(susan) [cnf transformation 25]
197. 11 <=> happy(susan) [avatar definition]
277. 11 [avatar split clause 147,197]
278. ~11 [avatar split clause 148,197]
279. $false [avatar sat refutation 277,278]
% SZS output end Proof for 4533448985486802353530027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and happy is happy or wise and vice versa. If alice is tall or not rich then someone is either not brave or not wise and vice versa. If paul is both brave and tall then someone is both happy and not curious and vice versa. If susan is not old then fred is not wise or not old. Everyone who is either humble or rich is not quiet and vice versa. If someone is both not rich and brave then someone is old or rich. Everyone who is not calm or patient is strong or not happy. Everyone who is either wise or kind is either patient or brave. If someone is not funny then paul is not tall and vice versa. Everyone who is calm is creative. If someone is not tall or not curious then someone is strong and vice versa. If someone is strong or quiet then someone is generous or old. Everyone who is either not creative or rich is both not quiet and calm. Everyone who is not humble or not rich is both generous and quiet and vice versa. Everyone who is either patient or funny is either strong or tall and vice versa. Everyone who is brave is not quiet and vice versa. Mary is not creative or generous. Mary is calm or not happy. Someone is rich or not tall. Someone is not patient or quiet. Paul is strong or not creative. Mary is not kind or calm. Someone is humble or not funny. | Fred is humble. | neutral | (![X]:((patient(X)&happy(X))<=>(happy(X)|wise(X))))&
(((tall(alice)|~rich(alice)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(((brave(paul)&tall(paul)))<=>(?[X]:((happy(X)&~curious(X)))))&
((~old(susan))=>((~wise(fred)|~old(fred))))&
(![X]:((humble(X)<~>rich(X))<=>~quiet(X)))&
((?[X]:((~rich(X)&brave(X))))=>(?[X]:((old(X)|rich(X)))))&
(![X]:((~calm(X)|patient(X))=>(strong(X)|~happy(X))))&
(![X]:((wise(X)<~>kind(X))=>(patient(X)<~>brave(X))))&
((?[X]:(~funny(X)))<=>(~tall(paul)))&
(![X]:(calm(X)=>creative(X)))&
((?[X]:((~tall(X)|~curious(X))))<=>(?[X]:(strong(X))))&
((?[X]:((strong(X)|quiet(X))))=>(?[X]:((generous(X)|old(X)))))&
(![X]:((~creative(X)<~>rich(X))=>(~quiet(X)&calm(X))))&
(![X]:((~humble(X)|~rich(X))<=>(generous(X)&quiet(X))))&
(![X]:((patient(X)<~>funny(X))<=>(strong(X)<~>tall(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
((~creative(mary)|generous(mary)))&
((calm(mary)|~happy(mary)))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:((~patient(X)|quiet(X))))&
((strong(paul)|~creative(paul)))&
((~kind(mary)|calm(mary)))&
(?[X]:((humble(X)|~funny(X)))) | humble(fred) | [] | null | 0 |
If someone is either generous or brave then john is both not tall and not quiet and vice versa. Everyone who is both not patient and wise is not happy. If paul is either not funny or calm then susan is calm. Everyone who is either not kind or humble is both not quiet and not patient. If someone is either not kind or tall then fred is happy or quiet and vice versa. If susan is not brave then someone is either not wise or old and vice versa. Everyone who is either wise or not calm is either brave or old. If someone is both not tall and not old then paul is curious and vice versa. Everyone who is not tall or not humble is both tall and quiet. If someone is both not happy and not brave then someone is either humble or not funny. If someone is strong or funny then someone is both not strong and not happy. If someone is either creative or patient then someone is strong. If fred is both not generous and not old then someone is not kind or quiet. Everyone who is both not calm and strong is either tall or kind and vice versa. If alice is curious then john is brave. If mary is both strong and not tall then someone is patient. John is both creative and not humble. Alice is either not happy or tall. Fred is patient or not old. Someone is either brave or patient. Alice is quiet. Someone is either not patient or not quiet. Mary is either not curious or humble. Someone is patient. | Paul is curious. | contradiction | ((?[X]:((generous(X)<~>brave(X))))<=>((~tall(john)&~quiet(john))))&
(![X]:((~patient(X)&wise(X))=>~happy(X)))&
(((~funny(paul)<~>calm(paul)))=>(calm(susan)))&
(![X]:((~kind(X)<~>humble(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((~kind(X)<~>tall(X))))<=>((happy(fred)|quiet(fred))))&
((~brave(susan))<=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:((wise(X)<~>~calm(X))=>(brave(X)<~>old(X))))&
((?[X]:((~tall(X)&~old(X))))<=>(curious(paul)))&
(![X]:((~tall(X)|~humble(X))=>(tall(X)&quiet(X))))&
((?[X]:((~happy(X)&~brave(X))))=>(?[X]:((humble(X)<~>~funny(X)))))&
((?[X]:((strong(X)|funny(X))))=>(?[X]:((~strong(X)&~happy(X)))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(strong(X))))&
(((~generous(fred)&~old(fred)))=>(?[X]:((~kind(X)|quiet(X)))))&
(![X]:((~calm(X)&strong(X))<=>(tall(X)<~>kind(X))))&
((curious(alice))=>(brave(john)))&
(((strong(mary)&~tall(mary)))=>(?[X]:(patient(X))))&
((creative(john)&~humble(john)))&
((~happy(alice)<~>tall(alice)))&
((patient(fred)|~old(fred)))&
(?[X]:((brave(X)<~>patient(X))))&
(quiet(alice))&
(?[X]:((~patient(X)<~>~quiet(X))))&
((~curious(mary)<~>humble(mary)))&
(?[X]:(patient(X))) | curious(paul) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 908026622517282573852382
% SZS output start Proof for 908026622517282573852382
8. ? [X0] : (~old(X0) & ~tall(X0)) <=> curious(paul) [input p7]
9. ! [X0] : ((~humble(X0) | ~tall(X0)) => (quiet(X0) & tall(X0))) [input p8]
25. curious(paul) [input hypothesis]
34. ! [X0] : ((quiet(X0) & tall(X0)) | (humble(X0) & tall(X0))) [ennf transformation 9]
60. (? [X0] : (~old(X0) & ~tall(X0)) | ~curious(paul)) & (curious(paul) | ! [X0] : (old(X0) | tall(X0))) [nnf transformation 8]
61. (? [X0] : (~old(X0) & ~tall(X0)) | ~curious(paul)) & (curious(paul) | ! [X1] : (old(X1) | tall(X1))) [rectify 60]
62. ? [X0] : (~old(X0) & ~tall(X0)) => (~old(sK3) & ~tall(sK3)) [choice axiom]
63. ((~old(sK3) & ~tall(sK3)) | ~curious(paul)) & (curious(paul) | ! [X1] : (old(X1) | tall(X1))) [skolemisation 61,62]
119. ~tall(sK3) | ~curious(paul) [cnf transformation 63]
121. tall(X0) | tall(X0) [cnf transformation 34]
155. curious(paul) [cnf transformation 25]
156. tall(X0) [duplicate literal removal 121]
250. 21 <=> curious(paul) [avatar definition]
259. 23 <=> tall(sK3) [avatar definition]
261. ~tall(sK3) <- (~23) [avatar component clause 259]
262. ~21 | ~23 [avatar split clause 119,259,250]
375. 21 [avatar split clause 155,250]
376. $false <- (~23) [subsumption resolution 261,156]
377. 23 [avatar contradiction clause 376]
382. $false [avatar sat refutation 262,375,377]
% SZS output end Proof for 908026622517282573852382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is wise or old and vice versa. Everyone who is wise or strong is either not happy or not tall. Everyone who is not old or not strong is wise or not rich. Everyone who is both rich and kind is not calm. Everyone who is both happy and funny is not rich or not funny and vice versa. If lucy is both not humble and curious then paul is creative. Everyone who is either funny or brave is not rich or happy and vice versa. Everyone who is both kind and not old is not happy and vice versa. If lucy is humble or not wise then someone is not tall or kind and vice versa. Everyone who is either not creative or not tall is tall or not tall and vice versa. If someone is not generous then someone is humble and vice versa. If someone is either humble or generous then someone is either calm or not strong and vice versa. If mary is not happy then someone is not happy or not funny and vice versa. Everyone who is tall or quiet is either funny or generous. If alice is not calm then alice is either not generous or not wise and vice versa. Everyone who is brave or creative is both kind and brave. Someone is quiet. Someone is tall or not kind. Mary is either strong or happy. Lucy is both kind and quiet. Fred is not brave. Paul is quiet or not happy. Someone is either happy or humble. Paul is not curious. | Alice is generous. | contradiction | (![X]:(funny(X)<=>(wise(X)|old(X))))&
(![X]:((wise(X)|strong(X))=>(~happy(X)<~>~tall(X))))&
(![X]:((~old(X)|~strong(X))=>(wise(X)|~rich(X))))&
(![X]:((rich(X)&kind(X))=>~calm(X)))&
(![X]:((happy(X)&funny(X))<=>(~rich(X)|~funny(X))))&
(((~humble(lucy)&curious(lucy)))=>(creative(paul)))&
(![X]:((funny(X)<~>brave(X))<=>(~rich(X)|happy(X))))&
(![X]:((kind(X)&~old(X))<=>~happy(X)))&
(((humble(lucy)|~wise(lucy)))<=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:((~creative(X)<~>~tall(X))<=>(tall(X)|~tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(humble(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>(?[X]:((calm(X)<~>~strong(X)))))&
((~happy(mary))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((tall(X)|quiet(X))=>(funny(X)<~>generous(X))))&
((~calm(alice))<=>((~generous(alice)<~>~wise(alice))))&
(![X]:((brave(X)|creative(X))=>(kind(X)&brave(X))))&
(?[X]:(quiet(X)))&
(?[X]:((tall(X)|~kind(X))))&
((strong(mary)<~>happy(mary)))&
((kind(lucy)&quiet(lucy)))&
(~brave(fred))&
((quiet(paul)|~happy(paul)))&
(?[X]:((happy(X)<~>humble(X))))&
(~curious(paul)) | generous(alice) | [
"p0",
"p1",
"p4",
"p6",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4580911672030734155734027
% SZS output start Proof for 4580911672030734155734027
1. ! [X0] : (funny(X0) <=> (old(X0) | wise(X0))) [input p0]
2. ! [X0] : ((strong(X0) | wise(X0)) => (~happy(X0) <~> ~tall(X0))) [input p1]
5. ! [X0] : ((funny(X0) & happy(X0)) <=> (~funny(X0) | ~rich(X0))) [input p4]
7. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (happy(X0) | ~rich(X0))) [input p6]
8. ! [X0] : ((~old(X0) & kind(X0)) <=> ~happy(X0)) [input p7]
10. ! [X0] : ((~creative(X0) <~> ~tall(X0)) <=> (~tall(X0) | tall(X0))) [input p9]
14. ! [X0] : ((quiet(X0) | tall(X0)) => (funny(X0) <~> generous(X0))) [input p13]
16. ! [X0] : ((creative(X0) | brave(X0)) => (brave(X0) & kind(X0))) [input p15]
25. generous(alice) [input hypothesis]
30. ! [X0] : ((~happy(X0) <~> ~tall(X0)) | (~strong(X0) & ~wise(X0))) [ennf transformation 2]
35. ! [X0] : ((funny(X0) <~> generous(X0)) | (~quiet(X0) & ~tall(X0))) [ennf transformation 14]
36. ! [X0] : ((brave(X0) & kind(X0)) | (~creative(X0) & ~brave(X0))) [ennf transformation 16]
37. ! [X0] : ((funny(X0) | (~old(X0) & ~wise(X0))) & ((old(X0) | wise(X0)) | ~funny(X0))) [nnf transformation 1]
38. ! [X0] : ((funny(X0) | (~old(X0) & ~wise(X0))) & (old(X0) | wise(X0) | ~funny(X0))) [flattening 37]
39. ! [X0] : (((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (~strong(X0) & ~wise(X0))) [nnf transformation 30]
40. ! [X0] : (((funny(X0) & happy(X0)) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 5]
41. ! [X0] : (((funny(X0) & happy(X0)) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | ~funny(X0) | ~happy(X0))) [flattening 40]
42. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 7]
43. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [flattening 42]
44. ! [X0] : (((~old(X0) & kind(X0)) | happy(X0)) & (~happy(X0) | (old(X0) | ~kind(X0)))) [nnf transformation 8]
45. ! [X0] : (((~old(X0) & kind(X0)) | happy(X0)) & (~happy(X0) | old(X0) | ~kind(X0))) [flattening 44]
51. ! [X0] : ((((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0))))) [nnf transformation 10]
52. ! [X0] : ((((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0))))) [flattening 51]
67. ! [X0] : (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~quiet(X0) & ~tall(X0))) [nnf transformation 35]
77. ~funny(X0) | wise(X0) | old(X0) [cnf transformation 38]
82. ~wise(X0) | happy(X0) | tall(X0) [cnf transformation 39]
91. funny(X0) | funny(X0) [cnf transformation 41]
97. ~brave(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 43]
100. ~old(X0) | happy(X0) [cnf transformation 45]
110. tall(X0) | creative(X0) | tall(X0) [cnf transformation 52]
126. ~generous(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 67]
135. ~creative(X0) | brave(X0) [cnf transformation 36]
146. generous(alice) [cnf transformation 25]
150. creative(X0) | tall(X0) [duplicate literal removal 110]
152. funny(X0) [duplicate literal removal 91]
154. ~brave(X0) | ~happy(X0) [subsumption resolution 97,152]
251. ~generous(X0) | ~tall(X0) [subsumption resolution 126,152]
253. 22 <=> wise(alice) [avatar definition]
255. wise(alice) <- (22) [avatar component clause 253]
257. 23 <=> generous(alice) [avatar definition]
258. generous(alice) <- (23) [avatar component clause 257]
302. 23 [avatar split clause 146,257]
311. brave(X1) | tall(X1) [resolution 150,135]
317. ~tall(alice) <- (23) [resolution 251,258]
318. old(X0) | wise(X0) [resolution 77,152]
321. ~happy(X1) | tall(X1) [resolution 311,154]
370. happy(X0) | wise(X0) [resolution 318,100]
432. tall(X0) | wise(X0) [resolution 370,321]
453. wise(alice) <- (23) [resolution 432,317]
459. 22 | ~23 [avatar split clause 453,257,253]
460. happy(alice) | tall(alice) <- (22) [resolution 255,82]
462. happy(alice) <- (22, 23) [subsumption resolution 460,317]
473. tall(alice) <- (22, 23) [resolution 462,321]
474. $false <- (22, 23) [subsumption resolution 473,317]
475. ~22 | ~23 [avatar contradiction clause 474]
476. $false [avatar sat refutation 302,459,475]
% SZS output end Proof for 4580911672030734155734027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both old and not creative. Everyone who is old or humble is creative. Everyone who is old or patient is both not old and not strong. Everyone who is not strong or not happy is both not happy and kind. Everyone who is not kind or generous is calm and vice versa. If john is both not quiet and tall then someone is tall or humble and vice versa. Everyone who is curious or quiet is both funny and rich. Everyone who is not patient is both not old and funny and vice versa. Everyone who is not curious or calm is both not humble and kind and vice versa. If john is humble then alice is either not rich or not quiet. If john is both creative and funny then susan is either not quiet or brave and vice versa. If mary is kind then paul is creative or curious and vice versa. Everyone who is both not generous and not kind is both not happy and not creative. If fred is both old and not humble then someone is either old or not tall and vice versa. Everyone who is quiet is both humble and not creative and vice versa. If paul is not creative or not strong then someone is strong and vice versa. John is not patient or humble. John is brave or not funny. Someone is not old. Lucy is both not old and not rich. Someone is brave. Lucy is patient or calm. | John is not humble. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>creative(X)))&
(![X]:((old(X)|patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
((~patient(john)|humble(john)))&
((brave(john)|~funny(john)))&
(?[X]:(~old(X)))&
((~old(lucy)&~rich(lucy)))&
(?[X]:(brave(X)))&
((patient(lucy)|calm(lucy))) | ~humble(john) | [
"p0",
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5491016329423642630600609
% SZS output start Proof for 5491016329423642630600609
1. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~creative(X0) & old(X0))) [input p0]
3. ! [X0] : ((patient(X0) | old(X0)) => (~strong(X0) & ~old(X0))) [input p2]
7. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p6]
9. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p8]
23. humble(john) [input hypothesis]
24. ! [X0] : ((~creative(X0) & old(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 1]
26. ! [X0] : ((~strong(X0) & ~old(X0)) | (~patient(X0) & ~old(X0))) [ennf transformation 3]
28. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 7]
32. ! [X0] : ((~creative(X0) & old(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 24]
42. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 9]
43. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 42]
66. ~funny(X0) | ~curious(X0) | old(X0) [cnf transformation 32]
71. ~old(X0) | ~old(X0) [cnf transformation 26]
87. ~curious(X0) | funny(X0) [cnf transformation 28]
94. ~humble(X0) | curious(X0) [cnf transformation 43]
131. humble(john) [cnf transformation 23]
132. ~old(X0) [duplicate literal removal 71]
165. 7 <=> humble(john) [avatar definition]
166. humble(john) <- (7) [avatar component clause 165]
188. 12 <=> funny(john) [avatar definition]
190. funny(john) <- (12) [avatar component clause 188]
256. 7 [avatar split clause 131,165]
266. curious(john) <- (7) [resolution 94,166]
268. funny(john) <- (7) [resolution 266,87]
271. 12 | ~7 [avatar split clause 268,165,188]
291. ~curious(john) | old(john) <- (12) [resolution 66,190]
294. old(john) <- (7, 12) [subsumption resolution 291,266]
295. $false <- (7, 12) [subsumption resolution 294,132]
296. ~7 | ~12 [avatar contradiction clause 295]
299. $false [avatar sat refutation 256,271,296]
% SZS output end Proof for 5491016329423642630600609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is brave or funny.
Everyone who is either creative or not funny is either not generous or not calm.
Everyone who is not creative is humble and vice versa.
Everyone who is not creative is rich or funny and vice versa.
Everyone who is not humble or not funny is both tall and not funny and vice versa.
Everyone who is either not generous or humble is both not kind and not tall and vice versa.
If someone is kind or not creative then fred is both humble and not rich.
Everyone who is wise is generous or not calm and vice versa.
If someone is not kind or strong then susan is not rich.
If lucy is both not calm and patient then susan is not brave or patient.
Everyone who is both not brave and not rich is not curious or not creative and vice versa.
Everyone who is not quiet is not funny or old and vice versa.
Everyone who is both not wise and kind is tall.
Everyone who is both not patient and old is either funny or strong and vice versa.
If john is either not humble or not quiet then alice is either tall or not brave and vice versa.
Everyone who is either kind or not patient is both funny and not wise and vice versa.
John is not tall or not rich.
John is not generous.
Someone is kind or not calm.
Lucy is either funny or not strong.
Someone is both old and not rich.
Fred is either wise or not generous.
Someone is not generous or funny. | Fred is funny. | entailment | (![X]:(~quiet(X)=>(brave(X)|funny(X))))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)<~>~calm(X))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:(~creative(X)<=>(rich(X)|funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(tall(X)&~funny(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((kind(X)|~creative(X))))=>((humble(fred)&~rich(fred))))&
(![X]:(wise(X)<=>(generous(X)|~calm(X))))&
((?[X]:((~kind(X)|strong(X))))=>(~rich(susan)))&
(((~calm(lucy)&patient(lucy)))=>((~brave(susan)|patient(susan))))&
(![X]:((~brave(X)&~rich(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|old(X))))&
(![X]:((~wise(X)&kind(X))=>tall(X)))&
(![X]:((~patient(X)&old(X))<=>(funny(X)<~>strong(X))))&
(((~humble(john)<~>~quiet(john)))<=>((tall(alice)<~>~brave(alice))))&
(![X]:((kind(X)<~>~patient(X))<=>(funny(X)&~wise(X))))&
((~tall(john)|~rich(john)))&
(~generous(john))&
(?[X]:((kind(X)|~calm(X))))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((old(X)&~rich(X))))&
((wise(fred)<~>~generous(fred)))&
(?[X]:((~generous(X)|funny(X)))) | funny(fred) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1596748595082104429118865
% SZS output start Proof for 1596748595082104429118865
1. ! [X0] : (~quiet(X0) => (funny(X0) | brave(X0))) [input p0]
3. ! [X0] : (~creative(X0) <=> humble(X0)) [input p2]
5. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~funny(X0) & tall(X0))) [input p4]
6. ! [X0] : ((~generous(X0) <~> humble(X0)) <=> (~tall(X0) & ~kind(X0))) [input p5]
7. ? [X0] : (~creative(X0) | kind(X0)) => (~rich(fred) & humble(fred)) [input p6]
11. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> (~creative(X0) | ~curious(X0))) [input p10]
12. ! [X0] : (~quiet(X0) <=> (old(X0) | ~funny(X0))) [input p11]
18. ~generous(john) [input p17]
24. ~funny(fred) [input hypothesis]
25. ! [X0] : ((funny(X0) | brave(X0)) | quiet(X0)) [ennf transformation 1]
26. ! [X0] : (funny(X0) | brave(X0) | quiet(X0)) [flattening 25]
28. (~rich(fred) & humble(fred)) | ! [X0] : (creative(X0) & ~kind(X0)) [ennf transformation 7]
35. ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))) [nnf transformation 3]
38. ! [X0] : (((~funny(X0) | ~humble(X0)) | (funny(X0) | ~tall(X0))) & ((~funny(X0) & tall(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 5]
39. ! [X0] : ((~funny(X0) | ~humble(X0) | funny(X0) | ~tall(X0)) & ((~funny(X0) & tall(X0)) | (funny(X0) & humble(X0)))) [flattening 38]
40. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (tall(X0) | kind(X0))) & ((~tall(X0) & ~kind(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [nnf transformation 6]
41. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | tall(X0) | kind(X0)) & ((~tall(X0) & ~kind(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [flattening 40]
44. ! [X0] : (((~rich(X0) & ~brave(X0)) | (creative(X0) & curious(X0))) & ((~creative(X0) | ~curious(X0)) | (rich(X0) | brave(X0)))) [nnf transformation 11]
45. ! [X0] : (((~rich(X0) & ~brave(X0)) | (creative(X0) & curious(X0))) & (~creative(X0) | ~curious(X0) | rich(X0) | brave(X0))) [flattening 44]
46. ! [X0] : ((~quiet(X0) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | quiet(X0))) [nnf transformation 12]
47. ! [X0] : ((~quiet(X0) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | quiet(X0))) [flattening 46]
61. funny(X0) | brave(X0) | quiet(X0) [cnf transformation 26]
67. ~humble(X0) | ~creative(X0) [cnf transformation 35]
71. tall(X0) | humble(X0) [cnf transformation 39]
78. ~tall(X0) | humble(X0) | generous(X0) [cnf transformation 41]
83. humble(fred) | creative(X0) [cnf transformation 28]
94. ~brave(X0) | creative(X0) [cnf transformation 45]
98. ~quiet(X0) | funny(X0) [cnf transformation 47]
122. ~generous(john) [cnf transformation 18]
131. ~funny(fred) [cnf transformation 24]
133. humble(X0) | generous(X0) [subsumption resolution 78,71]
135. 1 <=> ! [X0] : creative(X0) [avatar definition]
136. creative(X0) <- (1) [avatar component clause 135]
147. 4 <=> humble(fred) [avatar definition]
149. humble(fred) <- (4) [avatar component clause 147]
150. 1 | 4 [avatar split clause 83,147,135]
192. 14 <=> humble(john) [avatar definition]
193. ~humble(john) <- (~14) [avatar component clause 192]
194. humble(john) <- (14) [avatar component clause 192]
245. ~creative(fred) <- (4) [resolution 67,149]
258. generous(john) <- (~14) [resolution 133,193]
260. $false <- (~14) [subsumption resolution 258,122]
261. 14 [avatar contradiction clause 260]
262. ~creative(john) <- (14) [resolution 194,67]
265. brave(fred) | quiet(fred) [resolution 61,131]
268. 24 <=> quiet(fred) [avatar definition]
270. quiet(fred) <- (24) [avatar component clause 268]
272. 25 <=> brave(fred) [avatar definition]
274. brave(fred) <- (25) [avatar component clause 272]
275. 24 | 25 [avatar split clause 265,272,268]
288. funny(fred) <- (24) [resolution 270,98]
289. $false <- (24) [subsumption resolution 288,131]
290. ~24 [avatar contradiction clause 289]
303. creative(fred) <- (25) [resolution 274,94]
305. $false <- (4, 25) [subsumption resolution 303,245]
306. ~4 | ~25 [avatar contradiction clause 305]
307. $false <- (1, 14) [resolution 136,262]
309. ~1 | ~14 [avatar contradiction clause 307]
310. $false [avatar sat refutation 150,261,275,290,306,309]
% SZS output end Proof for 1596748595082104429118865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not creative or patient then lucy is either strong or not brave and vice versa. Everyone who is old is not humble and vice versa. If someone is either not wise or not funny then susan is both not creative and creative. Everyone who is not patient is curious or not curious. Everyone who is rich is old and vice versa. If alice is not curious or old then someone is both calm and not strong. If john is both not quiet and humble then paul is either quiet or not creative. If someone is both humble and not quiet then someone is not creative or creative. Everyone who is not old is both calm and not funny. Everyone who is both old and not patient is either happy or not curious. Everyone who is old or funny is both not happy and not patient. If john is either humble or not rich then someone is both not kind and tall. If susan is not wise then john is generous or funny and vice versa. If someone is either happy or not generous then john is not funny or wise and vice versa. If alice is either rich or not quiet then someone is not strong. Everyone who is calm or not happy is curious and vice versa. John is not happy. John is not patient. Someone is not curious or not brave. Someone is curious or quiet. Lucy is either not curious or kind. | John is not kind. | neutral | (((~creative(fred)<~>patient(fred)))<=>((strong(lucy)<~>~brave(lucy))))&
(![X]:(old(X)<=>~humble(X)))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~creative(susan)&creative(susan))))&
(![X]:(~patient(X)=>(curious(X)|~curious(X))))&
(![X]:(rich(X)<=>old(X)))&
(((~curious(alice)|old(alice)))=>(?[X]:((calm(X)&~strong(X)))))&
(((~quiet(john)&humble(john)))=>((quiet(paul)<~>~creative(paul))))&
((?[X]:((humble(X)&~quiet(X))))=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:(~old(X)=>(calm(X)&~funny(X))))&
(![X]:((old(X)&~patient(X))=>(happy(X)<~>~curious(X))))&
(![X]:((old(X)|funny(X))=>(~happy(X)&~patient(X))))&
(((humble(john)<~>~rich(john)))=>(?[X]:((~kind(X)&tall(X)))))&
((~wise(susan))<=>((generous(john)|funny(john))))&
((?[X]:((happy(X)<~>~generous(X))))<=>((~funny(john)|wise(john))))&
(((rich(alice)<~>~quiet(alice)))=>(?[X]:(~strong(X))))&
(![X]:((calm(X)|~happy(X))<=>curious(X)))&
(~happy(john))&
(~patient(john))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((~curious(lucy)<~>kind(lucy))) | ~kind(john) | [] | null | 0 |
If alice is not curious then mary is funny.
If someone is not kind or wise then someone is both not strong and generous.
If someone is either not rich or strong then paul is either not tall or funny.
Everyone who is tall or not old is both not wise and not old.
If paul is either not rich or not quiet then someone is both not brave and not curious.
If someone is both old and not happy then lucy is not old or generous.
Everyone who is not old or not brave is not calm.
Everyone who is brave is either brave or not wise.
Everyone who is not tall or quiet is both rich and not curious and vice versa.
If lucy is either not patient or not generous then someone is not rich and vice versa.
Everyone who is not wise is both not wise and brave and vice versa.
If someone is not calm then paul is both not humble and creative.
Everyone who is either tall or funny is either patient or not calm and vice versa.
Everyone who is both not humble and patient is not calm or generous.
If paul is either not old or quiet then someone is kind or not creative.
Someone is rich or not brave.
Someone is either funny or not strong.
Someone is happy or not creative.
Someone is quiet or not old.
Someone is not funny.
Someone is not funny or not happy. | Alice is tall. | contradiction | ((~curious(alice))=>(funny(mary)))&
((?[X]:((~kind(X)|wise(X))))=>(?[X]:((~strong(X)&generous(X)))))&
((?[X]:((~rich(X)<~>strong(X))))=>((~tall(paul)<~>funny(paul))))&
(![X]:((tall(X)|~old(X))=>(~wise(X)&~old(X))))&
(((~rich(paul)<~>~quiet(paul)))=>(?[X]:((~brave(X)&~curious(X)))))&
((?[X]:((old(X)&~happy(X))))=>((~old(lucy)|generous(lucy))))&
(![X]:((~old(X)|~brave(X))=>~calm(X)))&
(![X]:(brave(X)=>(brave(X)<~>~wise(X))))&
(![X]:((~tall(X)|quiet(X))<=>(rich(X)&~curious(X))))&
(((~patient(lucy)<~>~generous(lucy)))<=>(?[X]:(~rich(X))))&
(![X]:(~wise(X)<=>(~wise(X)&brave(X))))&
((?[X]:(~calm(X)))=>((~humble(paul)&creative(paul))))&
(![X]:((tall(X)<~>funny(X))<=>(patient(X)<~>~calm(X))))&
(![X]:((~humble(X)&patient(X))=>(~calm(X)|generous(X))))&
(((~old(paul)<~>quiet(paul)))=>(?[X]:((kind(X)|~creative(X)))))&
(?[X]:((rich(X)|~brave(X))))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~funny(X)|~happy(X)))) | tall(alice) | [
"p3",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8729753339650104412461754
% SZS output start Proof for 8729753339650104412461754
4. ! [X0] : ((~old(X0) | tall(X0)) => (~old(X0) & ~wise(X0))) [input p3]
8. ! [X0] : (brave(X0) => (brave(X0) <~> ~wise(X0))) [input p7]
11. ! [X0] : (~wise(X0) <=> (brave(X0) & ~wise(X0))) [input p10]
22. tall(alice) [input hypothesis]
29. ! [X0] : ((~old(X0) & ~wise(X0)) | (old(X0) & ~tall(X0))) [ennf transformation 4]
34. ! [X0] : ((brave(X0) <~> ~wise(X0)) | ~brave(X0)) [ennf transformation 8]
45. ! [X0] : (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ~brave(X0)) [nnf transformation 34]
52. ! [X0] : ((~wise(X0) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | wise(X0))) [nnf transformation 11]
53. ! [X0] : ((~wise(X0) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | wise(X0))) [flattening 52]
75. ~tall(X0) | ~wise(X0) [cnf transformation 29]
87. wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 45]
98. brave(X0) | wise(X0) [cnf transformation 53]
118. tall(alice) [cnf transformation 22]
119. wise(X0) | ~brave(X0) [duplicate literal removal 87]
207. wise(X0) [subsumption resolution 98,119]
269. ~wise(alice) [resolution 75,118]
270. $false [subsumption resolution 269,207]
% SZS output end Proof for 8729753339650104412461754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or calm is both not generous and quiet and vice versa. If someone is both not tall and quiet then someone is either wise or tall and vice versa. Everyone who is creative or not strong is not kind and vice versa. If mary is humble then someone is both creative and not rich. Everyone who is happy or not curious is either not strong or patient and vice versa. If someone is strong or wise then someone is both old and not funny. Everyone who is not generous or not patient is either rich or not kind and vice versa. If fred is not creative or not old then someone is both not quiet and not kind. Everyone who is either wise or strong is both calm and curious. If paul is happy or not patient then susan is not generous and vice versa. If john is generous then someone is either not rich or not strong. If someone is both not humble and creative then lucy is either not happy or not wise. Everyone who is either not humble or humble is both patient and happy and vice versa. If paul is tall then someone is humble and vice versa. If susan is funny then fred is tall or not generous. Everyone who is strong or not patient is not calm and vice versa. John is both happy and tall. Alice is rich or not quiet. Someone is either not strong or happy. Someone is not rich or old. Someone is not old. Someone is funny or wise. Alice is either not wise or not old. | Lucy is not wise. | contradiction | (![X]:((funny(X)|calm(X))<=>(~generous(X)&quiet(X))))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:((wise(X)<~>tall(X)))))&
(![X]:((creative(X)|~strong(X))<=>~kind(X)))&
((humble(mary))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((happy(X)|~curious(X))<=>(~strong(X)<~>patient(X))))&
((?[X]:((strong(X)|wise(X))))=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((~generous(X)|~patient(X))<=>(rich(X)<~>~kind(X))))&
(((~creative(fred)|~old(fred)))=>(?[X]:((~quiet(X)&~kind(X)))))&
(![X]:((wise(X)<~>strong(X))=>(calm(X)&curious(X))))&
(((happy(paul)|~patient(paul)))<=>(~generous(susan)))&
((generous(john))=>(?[X]:((~rich(X)<~>~strong(X)))))&
((?[X]:((~humble(X)&creative(X))))=>((~happy(lucy)<~>~wise(lucy))))&
(![X]:((~humble(X)<~>humble(X))<=>(patient(X)&happy(X))))&
((tall(paul))<=>(?[X]:(humble(X))))&
((funny(susan))=>((tall(fred)|~generous(fred))))&
(![X]:((strong(X)|~patient(X))<=>~calm(X)))&
((happy(john)&tall(john)))&
((rich(alice)|~quiet(alice)))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:((~rich(X)|old(X))))&
(?[X]:(~old(X)))&
(?[X]:((funny(X)|wise(X))))&
((~wise(alice)<~>~old(alice))) | ~wise(lucy) | [
"p4",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7845531020111385177512351
% SZS output start Proof for 7845531020111385177512351
5. ! [X0] : ((~curious(X0) | happy(X0)) <=> (~strong(X0) <~> patient(X0))) [input p4]
9. ! [X0] : ((wise(X0) <~> strong(X0)) => (curious(X0) & calm(X0))) [input p8]
13. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (happy(X0) & patient(X0))) [input p12]
16. ! [X0] : ((~patient(X0) | strong(X0)) <=> ~calm(X0)) [input p15]
24. ~wise(lucy) [input hypothesis]
30. ! [X0] : ((curious(X0) & calm(X0)) | (wise(X0) <=> strong(X0))) [ennf transformation 9]
46. ! [X0] : (((~curious(X0) | happy(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (curious(X0) & ~happy(X0)))) [nnf transformation 5]
47. ! [X0] : ((~curious(X0) | happy(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (curious(X0) & ~happy(X0)))) [flattening 46]
55. ! [X0] : ((curious(X0) & calm(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0)))) [nnf transformation 30]
62. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 13]
63. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 62]
68. ! [X0] : (((~patient(X0) | strong(X0)) | calm(X0)) & (~calm(X0) | (patient(X0) & ~strong(X0)))) [nnf transformation 16]
69. ! [X0] : ((~patient(X0) | strong(X0) | calm(X0)) & (~calm(X0) | (patient(X0) & ~strong(X0)))) [flattening 68]
98. ~patient(X0) | strong(X0) | ~happy(X0) [cnf transformation 47]
117. ~strong(X0) | wise(X0) | calm(X0) [cnf transformation 55]
127. patient(X0) | humble(X0) | humble(X0) [cnf transformation 63]
128. patient(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 63]
129. happy(X0) | humble(X0) | humble(X0) [cnf transformation 63]
130. happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 63]
136. ~strong(X0) | ~calm(X0) [cnf transformation 69]
149. ~wise(lucy) [cnf transformation 24]
150. patient(X0) | humble(X0) [duplicate literal removal 127]
151. ~humble(X0) | patient(X0) [duplicate literal removal 128]
152. happy(X0) | humble(X0) [duplicate literal removal 129]
153. ~humble(X0) | happy(X0) [duplicate literal removal 130]
274. 27 <=> wise(lucy) [avatar definition]
275. ~wise(lucy) <- (~27) [avatar component clause 274]
279. happy(X0) [subsumption resolution 152,153]
280. patient(X0) [subsumption resolution 150,151]
346. ~27 [avatar split clause 149,274]
392. strong(X0) | ~happy(X0) [resolution 98,280]
393. strong(X0) [subsumption resolution 392,279]
397. ~calm(X2) [resolution 393,136]
407. wise(X0) | calm(X0) [resolution 117,393]
411. wise(X0) [subsumption resolution 407,397]
418. $false <- (~27) [resolution 411,275]
422. 27 [avatar contradiction clause 418]
423. $false [avatar sat refutation 346,422]
% SZS output end Proof for 7845531020111385177512351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not humble then paul is not curious and vice versa.
Everyone who is both old and not old is not brave and vice versa.
If someone is both not kind and funny then susan is both kind and tall and vice versa.
If someone is not quiet or not brave then fred is patient.
If alice is patient or not tall then someone is both not curious and not rich and vice versa.
Everyone who is both not curious and creative is not calm or not rich and vice versa.
If someone is either humble or not rich then susan is not patient and vice versa.
If someone is not quiet or generous then alice is not happy or wise.
Everyone who is humble is calm.
Everyone who is patient is both strong and old.
If someone is both quiet and not quiet then someone is both wise and not curious and vice versa.
If susan is either strong or patient then john is calm.
If someone is both tall and not happy then alice is either not brave or not curious.
If someone is strong then someone is not funny.
Everyone who is not happy is both not creative and patient and vice versa.
Everyone who is both creative and not funny is both patient and not calm and vice versa.
Someone is not strong or not creative.
Someone is either kind or not strong.
John is not wise.
Fred is either happy or strong.
Someone is both not tall and not quiet.
Mary is creative or not creative.
Lucy is strong or creative.
Fred is either not kind or calm. | Fred is creative. | contradiction | ((~humble(alice))<=>(~curious(paul)))&
(![X]:((old(X)&~old(X))<=>~brave(X)))&
((?[X]:((~kind(X)&funny(X))))<=>((kind(susan)&tall(susan))))&
((?[X]:((~quiet(X)|~brave(X))))=>(patient(fred)))&
(((patient(alice)|~tall(alice)))<=>(?[X]:((~curious(X)&~rich(X)))))&
(![X]:((~curious(X)&creative(X))<=>(~calm(X)|~rich(X))))&
((?[X]:((humble(X)<~>~rich(X))))<=>(~patient(susan)))&
((?[X]:((~quiet(X)|generous(X))))=>((~happy(alice)|wise(alice))))&
(![X]:(humble(X)=>calm(X)))&
(![X]:(patient(X)=>(strong(X)&old(X))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(((strong(susan)<~>patient(susan)))=>(calm(john)))&
((?[X]:((tall(X)&~happy(X))))=>((~brave(alice)<~>~curious(alice))))&
((?[X]:(strong(X)))=>(?[X]:(~funny(X))))&
(![X]:(~happy(X)<=>(~creative(X)&patient(X))))&
(![X]:((creative(X)&~funny(X))<=>(patient(X)&~calm(X))))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((kind(X)<~>~strong(X))))&
(~wise(john))&
((happy(fred)<~>strong(fred)))&
(?[X]:((~tall(X)&~quiet(X))))&
((creative(mary)|~creative(mary)))&
((strong(lucy)|creative(lucy)))&
((~kind(fred)<~>calm(fred))) | creative(fred) | [
"p3",
"p9",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5544485740430371181254740
% SZS output start Proof for 5544485740430371181254740
4. ? [X0] : (~brave(X0) | ~quiet(X0)) => patient(fred) [input p3]
10. ! [X0] : (patient(X0) => (old(X0) & strong(X0))) [input p9]
15. ! [X0] : (~happy(X0) <=> (patient(X0) & ~creative(X0))) [input p14]
20. happy(fred) <~> strong(fred) [input p19]
21. ? [X0] : (~quiet(X0) & ~tall(X0)) [input p20]
25. creative(fred) [input hypothesis]
29. patient(fred) | ! [X0] : (brave(X0) & quiet(X0)) [ennf transformation 4]
33. ! [X0] : ((old(X0) & strong(X0)) | ~patient(X0)) [ennf transformation 10]
66. ! [X0] : ((~happy(X0) | (~patient(X0) | creative(X0))) & ((patient(X0) & ~creative(X0)) | happy(X0))) [nnf transformation 15]
67. ! [X0] : ((~happy(X0) | ~patient(X0) | creative(X0)) & ((patient(X0) & ~creative(X0)) | happy(X0))) [flattening 66]
75. (~strong(fred) | ~happy(fred)) & (strong(fred) | happy(fred)) [nnf transformation 20]
76. ? [X0] : (~quiet(X0) & ~tall(X0)) => (~quiet(sK8) & ~tall(sK8)) [choice axiom]
77. ~quiet(sK8) & ~tall(sK8) [skolemisation 21,76]
88. patient(fred) | quiet(X0) [cnf transformation 29]
106. ~patient(X0) | strong(X0) [cnf transformation 33]
117. ~creative(X0) | happy(X0) [cnf transformation 67]
129. ~strong(fred) | ~happy(fred) [cnf transformation 75]
131. ~quiet(sK8) [cnf transformation 77]
136. creative(fred) [cnf transformation 25]
172. 8 <=> ! [X0] : quiet(X0) [avatar definition]
173. quiet(X0) <- (8) [avatar component clause 172]
175. 9 <=> patient(fred) [avatar definition]
177. patient(fred) <- (9) [avatar component clause 175]
178. 8 | 9 [avatar split clause 88,175,172]
289. 34 <=> happy(fred) [avatar definition]
291. ~happy(fred) <- (~34) [avatar component clause 289]
293. 35 <=> strong(fred) [avatar definition]
296. ~34 | ~35 [avatar split clause 129,293,289]
317. $false <- (8) [resolution 173,131]
318. ~8 [avatar contradiction clause 317]
321. strong(fred) <- (9) [resolution 106,177]
324. 35 | ~9 [avatar split clause 321,175,293]
326. happy(fred) [resolution 117,136]
328. $false <- (~34) [subsumption resolution 326,291]
329. 34 [avatar contradiction clause 328]
330. $false [avatar sat refutation 178,296,318,324,329]
% SZS output end Proof for 5544485740430371181254740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or calm is either not old or old and vice versa.
If someone is both not strong and not kind then mary is both not funny and not wise.
If someone is happy then susan is not brave.
If mary is either not tall or not quiet then lucy is not creative and vice versa.
Everyone who is not quiet or not calm is calm and vice versa.
Everyone who is both not rich and not wise is not rich and vice versa.
Everyone who is generous or rich is either old or not patient and vice versa.
Everyone who is either not brave or not curious is not kind.
Everyone who is either patient or curious is not quiet or not happy.
Everyone who is not creative is curious and vice versa.
Everyone who is rich is both happy and not tall and vice versa.
Everyone who is not happy or not brave is not quiet.
If someone is not calm or brave then someone is not quiet.
Everyone who is both generous and funny is both tall and not funny and vice versa.
If someone is not tall or not happy then someone is not strong or brave.
If someone is either not rich or rich then someone is either calm or not creative and vice versa.
John is both not quiet and brave.
Someone is either kind or not kind.
Susan is creative.
Someone is calm or rich.
Susan is both not rich and not quiet.
Someone is both calm and funny. | John is kind. | contradiction | (![X]:((curious(X)<~>calm(X))<=>(~old(X)<~>old(X))))&
((?[X]:((~strong(X)&~kind(X))))=>((~funny(mary)&~wise(mary))))&
((?[X]:(happy(X)))=>(~brave(susan)))&
(((~tall(mary)<~>~quiet(mary)))<=>(~creative(lucy)))&
(![X]:((~quiet(X)|~calm(X))<=>calm(X)))&
(![X]:((~rich(X)&~wise(X))<=>~rich(X)))&
(![X]:((generous(X)|rich(X))<=>(old(X)<~>~patient(X))))&
(![X]:((~brave(X)<~>~curious(X))=>~kind(X)))&
(![X]:((patient(X)<~>curious(X))=>(~quiet(X)|~happy(X))))&
(![X]:(~creative(X)<=>curious(X)))&
(![X]:(rich(X)<=>(happy(X)&~tall(X))))&
(![X]:((~happy(X)|~brave(X))=>~quiet(X)))&
((?[X]:((~calm(X)|brave(X))))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)&funny(X))<=>(tall(X)&~funny(X))))&
((?[X]:((~tall(X)|~happy(X))))=>(?[X]:((~strong(X)|brave(X)))))&
((?[X]:((~rich(X)<~>rich(X))))<=>(?[X]:((calm(X)<~>~creative(X)))))&
((~quiet(john)&brave(john)))&
(?[X]:((kind(X)<~>~kind(X))))&
(creative(susan))&
(?[X]:((calm(X)|rich(X))))&
((~rich(susan)&~quiet(susan)))&
(?[X]:((calm(X)&funny(X)))) | kind(john) | [
"p0",
"p4",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6498777421283658910614750
% SZS output start Proof for 6498777421283658910614750
1. ! [X0] : ((curious(X0) <~> calm(X0)) <=> (~old(X0) <~> old(X0))) [input p0]
5. ! [X0] : ((~calm(X0) | ~quiet(X0)) <=> calm(X0)) [input p4]
8. ! [X0] : ((~brave(X0) <~> ~curious(X0)) => ~kind(X0)) [input p7]
17. brave(john) & ~quiet(john) [input p16]
23. kind(john) [input hypothesis]
29. ! [X0] : (~kind(X0) | (~brave(X0) <=> ~curious(X0))) [ennf transformation 8]
35. ! [X0] : ((((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0))))) [nnf transformation 1]
37. ! [X0] : (((~calm(X0) | ~quiet(X0)) | ~calm(X0)) & (calm(X0) | (calm(X0) & quiet(X0)))) [nnf transformation 5]
38. ! [X0] : ((~calm(X0) | ~quiet(X0) | ~calm(X0)) & (calm(X0) | (calm(X0) & quiet(X0)))) [flattening 37]
43. ! [X0] : (~kind(X0) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) [nnf transformation 29]
74. ~calm(X0) | ~curious(X0) | old(X0) | old(X0) [cnf transformation 35]
75. ~calm(X0) | ~curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 35]
84. calm(X0) | calm(X0) [cnf transformation 38]
96. ~brave(X0) | ~kind(X0) | curious(X0) [cnf transformation 43]
123. brave(john) [cnf transformation 17]
132. kind(john) [cnf transformation 23]
139. calm(X0) [duplicate literal removal 84]
143. ~calm(X0) | ~curious(X0) | old(X0) [duplicate literal removal 74]
144. ~calm(X0) | ~curious(X0) | ~old(X0) [duplicate literal removal 75]
145. ~calm(X0) | ~curious(X0) [subsumption resolution 143,144]
226. ~curious(X0) [resolution 145,139]
229. ~kind(john) | curious(john) [resolution 96,123]
230. curious(john) [subsumption resolution 229,132]
231. $false [subsumption resolution 230,226]
% SZS output end Proof for 6498777421283658910614750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not old and not patient then lucy is not wise. If alice is either not strong or not happy then alice is creative or not strong and vice versa. If susan is funny or old then lucy is not humble or tall and vice versa. If alice is both not patient and not calm then alice is either not rich or not creative. If someone is both curious and not happy then someone is not generous or patient and vice versa. Everyone who is patient or not creative is brave or not quiet. If someone is both calm and not humble then someone is tall or quiet. Everyone who is both quiet and not calm is not rich. Everyone who is either not patient or funny is not happy and vice versa. Everyone who is tall or curious is not rich or not strong. Everyone who is old is not tall or kind and vice versa. Everyone who is not rich is generous or not kind. Everyone who is both not quiet and humble is strong or funny. If lucy is both funny and generous then mary is not strong. If someone is either generous or happy then someone is both not calm and quiet. Everyone who is not quiet or not funny is brave or not creative. Someone is both humble and calm. Mary is either brave or generous. Someone is either not rich or not funny. Mary is either not generous or not kind. Alice is both not happy and not calm. Someone is not happy. Someone is not funny. Someone is both humble and kind. | Alice is happy. | contradiction | (((~old(fred)&~patient(fred)))=>(~wise(lucy)))&
(((~strong(alice)<~>~happy(alice)))<=>((creative(alice)|~strong(alice))))&
(((funny(susan)|old(susan)))<=>((~humble(lucy)|tall(lucy))))&
(((~patient(alice)&~calm(alice)))=>((~rich(alice)<~>~creative(alice))))&
((?[X]:((curious(X)&~happy(X))))<=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((patient(X)|~creative(X))=>(brave(X)|~quiet(X))))&
((?[X]:((calm(X)&~humble(X))))=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:((quiet(X)&~calm(X))=>~rich(X)))&
(![X]:((~patient(X)<~>funny(X))<=>~happy(X)))&
(![X]:((tall(X)|curious(X))=>(~rich(X)|~strong(X))))&
(![X]:(old(X)<=>(~tall(X)|kind(X))))&
(![X]:(~rich(X)=>(generous(X)|~kind(X))))&
(![X]:((~quiet(X)&humble(X))=>(strong(X)|funny(X))))&
(((funny(lucy)&generous(lucy)))=>(~strong(mary)))&
((?[X]:((generous(X)<~>happy(X))))=>(?[X]:((~calm(X)&quiet(X)))))&
(![X]:((~quiet(X)|~funny(X))=>(brave(X)|~creative(X))))&
(?[X]:((humble(X)&calm(X))))&
((brave(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((~generous(mary)<~>~kind(mary)))&
((~happy(alice)&~calm(alice)))&
(?[X]:(~happy(X)))&
(?[X]:(~funny(X)))&
(?[X]:((humble(X)&kind(X)))) | happy(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4381499288601206427996568
% SZS output start Proof for 4381499288601206427996568
21. ~calm(alice) & ~happy(alice) [input p20]
25. happy(alice) [input hypothesis]
128. ~happy(alice) [cnf transformation 21]
134. happy(alice) [cnf transformation 25]
142. 2 <=> happy(alice) [avatar definition]
287. ~2 [avatar split clause 128,142]
288. 2 [avatar split clause 134,142]
289. $false [avatar sat refutation 287,288]
% SZS output end Proof for 4381499288601206427996568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not strong is not happy or not creative and vice versa.
If someone is both kind and old then someone is both happy and old.
Everyone who is not rich is strong and vice versa.
If someone is wise then someone is either tall or not calm and vice versa.
Everyone who is kind is both not wise and calm and vice versa.
Everyone who is both not happy and not wise is both not quiet and tall and vice versa.
Everyone who is either not brave or not old is both quiet and wise.
If someone is both strong and humble then someone is not creative or old and vice versa.
Everyone who is both not patient and not happy is quiet or old and vice versa.
If susan is not generous or creative then mary is not rich or not brave.
Everyone who is both brave and strong is both not curious and brave.
Everyone who is both not curious and not happy is both not kind and not calm.
If someone is either creative or not calm then someone is wise and vice versa.
Everyone who is strong is either happy or brave and vice versa.
Everyone who is not generous or not strong is not curious.
Everyone who is kind or not rich is happy and vice versa.
Paul is both kind and humble.
Someone is not humble.
John is both strong and not rich.
Paul is either quiet or humble.
Paul is either humble or quiet.
Paul is humble. | Mary is not brave. | entailment | (![X]:((funny(X)|~strong(X))<=>(~happy(X)|~creative(X))))&
((?[X]:((kind(X)&old(X))))=>(?[X]:((happy(X)&old(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
((?[X]:(wise(X)))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:(kind(X)<=>(~wise(X)&calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>(~quiet(X)&tall(X))))&
(![X]:((~brave(X)<~>~old(X))=>(quiet(X)&wise(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(quiet(X)|old(X))))&
(((~generous(susan)|creative(susan)))=>((~rich(mary)|~brave(mary))))&
(![X]:((brave(X)&strong(X))=>(~curious(X)&brave(X))))&
(![X]:((~curious(X)&~happy(X))=>(~kind(X)&~calm(X))))&
((?[X]:((creative(X)<~>~calm(X))))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>(happy(X)<~>brave(X))))&
(![X]:((~generous(X)|~strong(X))=>~curious(X)))&
(![X]:((kind(X)|~rich(X))<=>happy(X)))&
((kind(paul)&humble(paul)))&
(?[X]:(~humble(X)))&
((strong(john)&~rich(john)))&
((quiet(paul)<~>humble(paul)))&
((humble(paul)<~>quiet(paul)))&
(humble(paul)) | ~brave(mary) | [
"p2",
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7116212096173579704983824
% SZS output start Proof for 7116212096173579704983824
3. ! [X0] : (~rich(X0) <=> strong(X0)) [input p2]
7. ! [X0] : ((~brave(X0) <~> ~old(X0)) => (wise(X0) & quiet(X0))) [input p6]
9. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (old(X0) | quiet(X0))) [input p8]
14. ! [X0] : (strong(X0) <=> (happy(X0) <~> brave(X0))) [input p13]
16. ! [X0] : ((~rich(X0) | kind(X0)) <=> happy(X0)) [input p15]
23. brave(mary) [input hypothesis]
31. ! [X0] : ((wise(X0) & quiet(X0)) | (~brave(X0) <=> ~old(X0))) [ennf transformation 7]
44. ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))) [nnf transformation 3]
54. ! [X0] : ((wise(X0) & quiet(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) [nnf transformation 31]
60. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 9]
61. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | happy(X0) | patient(X0))) [flattening 60]
67. ! [X0] : ((strong(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~strong(X0))) [nnf transformation 14]
68. ! [X0] : (((~rich(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((~rich(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [flattening 68]
81. ~rich(X0) | ~strong(X0) [cnf transformation 44]
94. ~brave(X0) | quiet(X0) | old(X0) [cnf transformation 54]
105. ~quiet(X0) | ~happy(X0) [cnf transformation 61]
106. ~old(X0) | ~happy(X0) [cnf transformation 61]
119. ~brave(X0) | happy(X0) | strong(X0) [cnf transformation 67]
122. rich(X0) | happy(X0) [cnf transformation 69]
134. brave(mary) [cnf transformation 23]
208. 18 <=> rich(mary) [avatar definition]
209. rich(mary) <- (18) [avatar component clause 208]
210. ~rich(mary) <- (~18) [avatar component clause 208]
212. 19 <=> brave(mary) [avatar definition]
213. brave(mary) <- (19) [avatar component clause 212]
239. 19 [avatar split clause 134,212]
256. happy(mary) <- (~18) [resolution 122,210]
324. quiet(mary) | old(mary) <- (19) [resolution 94,213]
326. 35 <=> old(mary) [avatar definition]
328. old(mary) <- (35) [avatar component clause 326]
330. 36 <=> quiet(mary) [avatar definition]
332. quiet(mary) <- (36) [avatar component clause 330]
333. 35 | 36 | ~19 [avatar split clause 324,212,330,326]
339. ~happy(mary) <- (36) [resolution 332,105]
340. $false <- (~18, 36) [subsumption resolution 339,256]
341. 18 | ~36 [avatar contradiction clause 340]
343. ~strong(mary) <- (18) [resolution 209,81]
364. happy(mary) | strong(mary) <- (19) [resolution 119,213]
365. strong(mary) <- (19, 36) [subsumption resolution 364,339]
366. $false <- (18, 19, 36) [subsumption resolution 365,343]
367. ~18 | ~19 | ~36 [avatar contradiction clause 366]
368. happy(mary) <- (18, 19) [subsumption resolution 364,343]
377. ~happy(mary) <- (35) [resolution 328,106]
378. $false <- (18, 19, 35) [subsumption resolution 377,368]
379. ~18 | ~19 | ~35 [avatar contradiction clause 378]
381. happy(mary) <- (~18) [resolution 210,122]
383. $false <- (~18, 35) [subsumption resolution 381,377]
384. 18 | ~35 [avatar contradiction clause 383]
385. $false [avatar sat refutation 239,333,341,367,379,384]
% SZS output end Proof for 7116212096173579704983824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or funny is both not generous and quiet and vice versa.
Everyone who is both rich and not creative is funny.
Everyone who is not brave or curious is not strong.
If john is both brave and not funny then someone is either calm or kind.
If john is wise then someone is both rich and kind.
If someone is either not kind or humble then someone is rich or not old and vice versa.
Everyone who is generous is curious and vice versa.
Everyone who is both not rich and strong is kind or curious.
If someone is curious or quiet then john is either curious or not curious.
If paul is both old and not generous then susan is both patient and not kind.
Everyone who is not old is generous or happy and vice versa.
If someone is not quiet then someone is either not humble or not creative.
If someone is not happy or not strong then someone is not humble and vice versa.
Everyone who is not rich is either quiet or patient and vice versa.
Everyone who is not curious or curious is both kind and not wise.
If someone is either not funny or not tall then lucy is both creative and not strong and vice versa.
Someone is either not strong or creative.
Fred is either quiet or happy.
Someone is quiet.
Someone is both humble and not wise.
Susan is creative or not funny.
Paul is either not quiet or not patient.
Someone is either old or not happy.
Alice is both not curious and kind. | Fred is wise. | contradiction | (![X]:((humble(X)<~>funny(X))<=>(~generous(X)&quiet(X))))&
(![X]:((rich(X)&~creative(X))=>funny(X)))&
(![X]:((~brave(X)|curious(X))=>~strong(X)))&
(((brave(john)&~funny(john)))=>(?[X]:((calm(X)<~>kind(X)))))&
((wise(john))=>(?[X]:((rich(X)&kind(X)))))&
((?[X]:((~kind(X)<~>humble(X))))<=>(?[X]:((rich(X)|~old(X)))))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~rich(X)&strong(X))=>(kind(X)|curious(X))))&
((?[X]:((curious(X)|quiet(X))))=>((curious(john)<~>~curious(john))))&
(((old(paul)&~generous(paul)))=>((patient(susan)&~kind(susan))))&
(![X]:(~old(X)<=>(generous(X)|happy(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~humble(X)<~>~creative(X)))))&
((?[X]:((~happy(X)|~strong(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~rich(X)<=>(quiet(X)<~>patient(X))))&
(![X]:((~curious(X)|curious(X))=>(kind(X)&~wise(X))))&
((?[X]:((~funny(X)<~>~tall(X))))<=>((creative(lucy)&~strong(lucy))))&
(?[X]:((~strong(X)<~>creative(X))))&
((quiet(fred)<~>happy(fred)))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)&~wise(X))))&
((creative(susan)|~funny(susan)))&
((~quiet(paul)<~>~patient(paul)))&
(?[X]:((old(X)<~>~happy(X))))&
((~curious(alice)&kind(alice))) | wise(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 599847029853104491142663
% SZS output start Proof for 599847029853104491142663
15. ! [X0] : ((curious(X0) | ~curious(X0)) => (~wise(X0) & kind(X0))) [input p14]
25. wise(fred) [input hypothesis]
41. ! [X0] : ((~wise(X0) & kind(X0)) | (~curious(X0) & curious(X0))) [ennf transformation 15]
127. ~wise(X0) | curious(X0) [cnf transformation 41]
128. ~wise(X0) | ~curious(X0) [cnf transformation 41]
149. wise(fred) [cnf transformation 25]
272. ~wise(X0) [subsumption resolution 127,128]
343. $false [subsumption resolution 149,272]
% SZS output end Proof for 599847029853104491142663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative. | 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)))) | creative(fred) | [
"p2",
"p3",
"p4",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6133267216332680988763048
% SZS output start Proof for 6133267216332680988763048
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. creative(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]
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]
118. ~creative(X0) | ~wise(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]
146. creative(sK9) | wise(X1) [cnf transformation 79]
165. creative(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]
351. 40 | 41 [avatar split clause 146,348,345]
418. ~wise(sK2) <- (11) [resolution 100,214]
419. $false <- (11, 40) [subsumption resolution 418,346]
420. ~11 | ~40 [avatar contradiction clause 419]
424. calm(fred) [resolution 103,165]
425. calm(sK9) <- (41) [resolution 103,350]
428. ~happy(fred) <- (13) [resolution 223,424]
431. wise(fred) <- (13) [resolution 428,101]
441. ~wise(fred) | brave(fred) [resolution 118,165]
442. ~wise(sK9) | brave(sK9) <- (41) [resolution 118,350]
451. wise(sK9) | ~brave(sK9) <- (41) [resolution 120,350]
455. happy(fred) | ~brave(fred) [resolution 139,424]
457. happy(sK9) | ~brave(sK9) <- (41) [resolution 139,425]
459. ~brave(fred) <- (13) [subsumption resolution 455,428]
467. ~wise(fred) <- (13) [subsumption resolution 441,459]
470. $false <- (13) [subsumption resolution 431,467]
471. ~13 [avatar contradiction clause 470]
488. 58 <=> brave(sK9) [avatar definition]
492. 59 <=> wise(sK9) [avatar definition]
493. wise(sK9) <- (59) [avatar component clause 492]
494. ~wise(sK9) <- (~59) [avatar component clause 492]
495. 58 | ~59 | ~41 [avatar split clause 442,348,492,488]
497. ~58 | 59 | ~41 [avatar split clause 451,348,492,488]
499. 60 <=> happy(sK9) [avatar definition]
500. ~happy(sK9) <- (~60) [avatar component clause 499]
501. happy(sK9) <- (60) [avatar component clause 499]
502. ~58 | 60 | ~41 [avatar split clause 457,348,499,488]
523. ~happy(sK9) | brave(sK9) <- (41) [resolution 141,425]
622. wise(sK9) <- (~60) [resolution 500,101]
623. $false <- (~59, ~60) [subsumption resolution 622,494]
624. 59 | 60 [avatar contradiction clause 623]
625. 58 | ~60 | ~41 [avatar split clause 523,348,499,488]
644. ~wise(sK9) <- (60) [resolution 501,100]
645. $false <- (59, 60) [subsumption resolution 644,493]
646. ~59 | ~60 [avatar contradiction clause 645]
647. $false [avatar sat refutation 215,224,225,351,420,471,495,497,502,624,625,646]
% SZS output end Proof for 6133267216332680988763048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both tall and happy is both calm and wise and vice versa.
Everyone who is not creative is either funny or happy.
If john is both not kind and not wise then fred is both calm and brave and vice versa.
Everyone who is both tall and brave is both rich and not brave and vice versa.
If someone is either not strong or tall then someone is kind.
Everyone who is either not wise or not creative is not happy or not calm and vice versa.
Everyone who is both not funny and not strong is curious and vice versa.
If someone is both not humble and not happy then someone is not happy.
If someone is kind then john is not brave or creative.
Everyone who is both creative and not creative is creative or not tall and vice versa.
If fred is not brave or calm then someone is either calm or strong.
If someone is either not brave or not kind then someone is not quiet and vice versa.
If someone is not creative then alice is either not quiet or not creative.
If mary is both not generous and old then paul is humble or not curious and vice versa.
Alice is humble.
Someone is either not kind or not patient.
Lucy is not patient or not strong. | Paul is not rich. | entailment | (![X]:((tall(X)&happy(X))<=>(calm(X)&wise(X))))&
(![X]:(~creative(X)=>(funny(X)<~>happy(X))))&
(((~kind(john)&~wise(john)))<=>((calm(fred)&brave(fred))))&
(![X]:((tall(X)&brave(X))<=>(rich(X)&~brave(X))))&
((?[X]:((~strong(X)<~>tall(X))))=>(?[X]:(kind(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(~happy(X)|~calm(X))))&
(![X]:((~funny(X)&~strong(X))<=>curious(X)))&
((?[X]:((~humble(X)&~happy(X))))=>(?[X]:(~happy(X))))&
((?[X]:(kind(X)))=>((~brave(john)|creative(john))))&
(![X]:((creative(X)&~creative(X))<=>(creative(X)|~tall(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:((calm(X)<~>strong(X)))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(~creative(X)))=>((~quiet(alice)<~>~creative(alice))))&
(((~generous(mary)&old(mary)))<=>((humble(paul)|~curious(paul))))&
(humble(alice))&
(?[X]:((~kind(X)<~>~patient(X))))&
((~patient(lucy)|~strong(lucy))) | ~rich(paul) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6200115145460176296304954
% SZS output start Proof for 6200115145460176296304954
4. ! [X0] : ((brave(X0) & tall(X0)) <=> (~brave(X0) & rich(X0))) [input p3]
10. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~tall(X0) | creative(X0))) [input p9]
18. rich(paul) [input hypothesis]
34. ! [X0] : (((brave(X0) & tall(X0)) | (brave(X0) | ~rich(X0))) & ((~brave(X0) & rich(X0)) | (~brave(X0) | ~tall(X0)))) [nnf transformation 4]
35. ! [X0] : (((brave(X0) & tall(X0)) | brave(X0) | ~rich(X0)) & ((~brave(X0) & rich(X0)) | ~brave(X0) | ~tall(X0))) [flattening 34]
47. ! [X0] : (((~creative(X0) & creative(X0)) | (tall(X0) & ~creative(X0))) & ((~tall(X0) | creative(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 10]
48. ! [X0] : (((~creative(X0) & creative(X0)) | (tall(X0) & ~creative(X0))) & (~tall(X0) | creative(X0) | creative(X0) | ~creative(X0))) [flattening 47]
74. ~brave(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 35]
76. brave(X0) | brave(X0) | ~rich(X0) [cnf transformation 35]
92. creative(X0) | tall(X0) [cnf transformation 48]
93. ~creative(X0) | ~creative(X0) [cnf transformation 48]
114. rich(paul) [cnf transformation 18]
116. ~creative(X0) [duplicate literal removal 93]
117. ~brave(X0) | ~tall(X0) [duplicate literal removal 74]
118. ~rich(X0) | brave(X0) [duplicate literal removal 76]
172. tall(X0) [subsumption resolution 92,116]
262. brave(paul) [resolution 118,114]
263. ~tall(paul) [resolution 262,117]
264. $false [subsumption resolution 263,172]
% SZS output end Proof for 6200115145460176296304954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is tall then john is both not rich and tall.
If someone is either calm or funny then someone is not kind or not creative and vice versa.
Everyone who is kind is both not generous and humble.
Everyone who is both generous and tall is either funny or strong and vice versa.
Everyone who is not calm or patient is both creative and not wise.
Everyone who is curious is either not tall or strong and vice versa.
Everyone who is both quiet and not brave is either not happy or old.
Everyone who is not strong is either strong or tall and vice versa.
Everyone who is funny is either rich or creative and vice versa.
If someone is not rich then mary is rich or not tall.
Everyone who is not happy or not generous is either not rich or not funny and vice versa.
If susan is either old or generous then someone is both not calm and not quiet and vice versa.
Everyone who is not strong or kind is wise or generous.
If someone is both not creative and wise then someone is not rich and vice versa.
If someone is both wise and not calm then mary is both old and rich and vice versa.
Someone is both old and brave.
Someone is either not humble or not funny.
John is both quiet and not kind.
Paul is either not strong or calm.
Someone is not calm or kind.
Mary is brave or patient.
Lucy is not happy or not calm.
Alice is both not quiet and calm. | Alice is not strong. | neutral | ((tall(john))=>((~rich(john)&tall(john))))&
((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((~kind(X)|~creative(X)))))&
(![X]:(kind(X)=>(~generous(X)&humble(X))))&
(![X]:((generous(X)&tall(X))<=>(funny(X)<~>strong(X))))&
(![X]:((~calm(X)|patient(X))=>(creative(X)&~wise(X))))&
(![X]:(curious(X)<=>(~tall(X)<~>strong(X))))&
(![X]:((quiet(X)&~brave(X))=>(~happy(X)<~>old(X))))&
(![X]:(~strong(X)<=>(strong(X)<~>tall(X))))&
(![X]:(funny(X)<=>(rich(X)<~>creative(X))))&
((?[X]:(~rich(X)))=>((rich(mary)|~tall(mary))))&
(![X]:((~happy(X)|~generous(X))<=>(~rich(X)<~>~funny(X))))&
(((old(susan)<~>generous(susan)))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:((~strong(X)|kind(X))=>(wise(X)|generous(X))))&
((?[X]:((~creative(X)&wise(X))))<=>(?[X]:(~rich(X))))&
((?[X]:((wise(X)&~calm(X))))<=>((old(mary)&rich(mary))))&
(?[X]:((old(X)&brave(X))))&
(?[X]:((~humble(X)<~>~funny(X))))&
((quiet(john)&~kind(john)))&
((~strong(paul)<~>calm(paul)))&
(?[X]:((~calm(X)|kind(X))))&
((brave(mary)|patient(mary)))&
((~happy(lucy)|~calm(lucy)))&
((~quiet(alice)&calm(alice))) | ~strong(alice) | [] | null | 0 |
Everyone who is not quiet or creative is not calm or generous and vice versa. Everyone who is either patient or not humble is both strong and calm. If someone is both wise and humble then john is not strong or creative and vice versa. Everyone who is both humble and not wise is both rich and calm and vice versa. If susan is both quiet and creative then susan is patient. Everyone who is both not funny and not creative is either not creative or not generous and vice versa. Everyone who is both not creative and quiet is not quiet and vice versa. Everyone who is not funny is curious and vice versa. Everyone who is either not old or strong is either old or not calm. Everyone who is not kind or curious is both not brave and not kind. If paul is humble or happy then someone is both kind and old. If lucy is both not generous and generous then paul is both kind and not creative. Everyone who is both calm and patient is not calm or funny. If someone is both old and not curious then someone is either not funny or not rich and vice versa. If someone is not happy or not wise then alice is both tall and generous. Someone is curious or brave. Someone is both humble and funny. Someone is calm or wise. Alice is not humble. Someone is not calm. Mary is not funny. | Alice is not curious. | neutral | (![X]:((~quiet(X)|creative(X))<=>(~calm(X)|generous(X))))&
(![X]:((patient(X)<~>~humble(X))=>(strong(X)&calm(X))))&
((?[X]:((wise(X)&humble(X))))<=>((~strong(john)|creative(john))))&
(![X]:((humble(X)&~wise(X))<=>(rich(X)&calm(X))))&
(((quiet(susan)&creative(susan)))=>(patient(susan)))&
(![X]:((~funny(X)&~creative(X))<=>(~creative(X)<~>~generous(X))))&
(![X]:((~creative(X)&quiet(X))<=>~quiet(X)))&
(![X]:(~funny(X)<=>curious(X)))&
(![X]:((~old(X)<~>strong(X))=>(old(X)<~>~calm(X))))&
(![X]:((~kind(X)|curious(X))=>(~brave(X)&~kind(X))))&
(((humble(paul)|happy(paul)))=>(?[X]:((kind(X)&old(X)))))&
(((~generous(lucy)&generous(lucy)))=>((kind(paul)&~creative(paul))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)|funny(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|~wise(X))))=>((tall(alice)&generous(alice))))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:((humble(X)&funny(X))))&
(?[X]:((calm(X)|wise(X))))&
(~humble(alice))&
(?[X]:(~calm(X)))&
(~funny(mary)) | ~curious(alice) | [] | null | 0 |
Everyone who is both not curious and rich is either strong or not generous and vice versa. If someone is both rich and not calm then lucy is either strong or curious. If mary is not wise then someone is not tall or kind. Everyone who is not humble is tall or not happy. If someone is both strong and quiet then susan is happy and vice versa. Everyone who is quiet is not wise or not rich. Everyone who is both not rich and tall is not generous. Everyone who is brave is patient and vice versa. Everyone who is either patient or not strong is both not calm and brave and vice versa. Everyone who is not strong is kind or not calm and vice versa. If susan is old or not tall then someone is quiet. If someone is both quiet and happy then fred is happy or generous and vice versa. Everyone who is not wise or not rich is both not happy and not brave. Everyone who is either not curious or not brave is curious or funny and vice versa. Everyone who is not curious or not calm is not calm and vice versa. Everyone who is either rich or curious is brave or not quiet and vice versa. Paul is both not humble and not generous. Someone is either not funny or not wise. Someone is either not brave or not funny. Alice is both calm and not tall. Susan is not funny or funny. Someone is both not tall and not wise. | Mary is not patient. | entailment | (![X]:((~curious(X)&rich(X))<=>(strong(X)<~>~generous(X))))&
((?[X]:((rich(X)&~calm(X))))=>((strong(lucy)<~>curious(lucy))))&
((~wise(mary))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:(~humble(X)=>(tall(X)|~happy(X))))&
((?[X]:((strong(X)&quiet(X))))<=>(happy(susan)))&
(![X]:(quiet(X)=>(~wise(X)|~rich(X))))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X)))) | ~patient(mary) | [
"p7",
"p8",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7321450377144408843834886
% SZS output start Proof for 7321450377144408843834886
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
14. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p14]
23. patient(mary) [input hypothesis]
44. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 8]
45. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 9]
46. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 45]
47. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 47]
56. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 14]
57. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 56]
58. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 15]
59. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 58]
85. ~brave(X0) | patient(X0) [cnf transformation 44]
86. ~patient(X0) | brave(X0) [cnf transformation 44]
92. strong(X0) | ~patient(X0) | ~brave(X0) | calm(X0) [cnf transformation 46]
95. ~strong(X0) | calm(X0) [cnf transformation 48]
108. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
112. ~calm(X0) | curious(X0) [cnf transformation 59]
132. patient(mary) [cnf transformation 23]
134. ~brave(X0) | ~curious(X0) [duplicate literal removal 108]
179. ~brave(X0) | strong(X0) | calm(X0) [subsumption resolution 92,85]
228. brave(mary) [resolution 86,132]
244. ~curious(mary) [resolution 134,228]
382. strong(mary) | calm(mary) [resolution 179,228]
418. calm(mary) [subsumption resolution 382,95]
446. curious(mary) [resolution 418,112]
448. $false [subsumption resolution 446,244]
% SZS output end Proof for 7321450377144408843834886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not funny or generous and vice versa. Everyone who is tall is both not kind and wise and vice versa. Everyone who is either not strong or kind is both old and not humble. Everyone who is either humble or generous is happy and vice versa. If someone is funny or kind then fred is either not generous or not humble and vice versa. If fred is strong or not generous then lucy is happy or not quiet. If john is both creative and quiet then susan is curious or patient and vice versa. If paul is not curious or generous then john is both not generous and not rich and vice versa. Everyone who is tall or old is old and vice versa. If mary is both not generous and not patient then paul is wise or generous. Everyone who is funny is either tall or strong and vice versa. Everyone who is not calm is not patient or happy. If john is not calm or quiet then someone is either old or not old. Everyone who is patient is both brave and quiet and vice versa. Everyone who is quiet is funny or rich and vice versa. Everyone who is both not kind and old is either patient or not brave and vice versa. Someone is either creative or not calm. Mary is old or not quiet. Someone is not quiet. John is both not generous and not tall. Someone is either not patient or not generous. Someone is both not brave and not curious. Someone is both not brave and humble. Someone is not patient. | Fred is quiet. | neutral | (![X]:(humble(X)<=>(~funny(X)|generous(X))))&
(![X]:(tall(X)<=>(~kind(X)&wise(X))))&
(![X]:((~strong(X)<~>kind(X))=>(old(X)&~humble(X))))&
(![X]:((humble(X)<~>generous(X))<=>happy(X)))&
((?[X]:((funny(X)|kind(X))))<=>((~generous(fred)<~>~humble(fred))))&
(((strong(fred)|~generous(fred)))=>((happy(lucy)|~quiet(lucy))))&
(((creative(john)&quiet(john)))<=>((curious(susan)|patient(susan))))&
(((~curious(paul)|generous(paul)))<=>((~generous(john)&~rich(john))))&
(![X]:((tall(X)|old(X))<=>old(X)))&
(((~generous(mary)&~patient(mary)))=>((wise(paul)|generous(paul))))&
(![X]:(funny(X)<=>(tall(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~patient(X)|happy(X))))&
(((~calm(john)|quiet(john)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:(patient(X)<=>(brave(X)&quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(patient(X)<~>~brave(X))))&
(?[X]:((creative(X)<~>~calm(X))))&
((old(mary)|~quiet(mary)))&
(?[X]:(~quiet(X)))&
((~generous(john)&~tall(john)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((~brave(X)&~curious(X))))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:(~patient(X))) | quiet(fred) | [] | null | 0 |
Everyone who is not wise or brave is brave. Everyone who is either calm or creative is wise. If susan is happy or wise then susan is either tall or strong and vice versa. Everyone who is rich is not brave and vice versa. If someone is creative then someone is humble and vice versa. If someone is kind then someone is either not happy or happy and vice versa. Everyone who is rich or calm is not calm and vice versa. If paul is either not wise or generous then paul is strong or not strong. If alice is both humble and curious then someone is not funny and vice versa. If someone is old then mary is either not brave or calm and vice versa. If susan is either not calm or patient then someone is both creative and old and vice versa. Everyone who is humble is not quiet or not creative. Everyone who is not calm or old is happy. If paul is not brave then someone is either not calm or strong. Everyone who is not quiet or old is wise or calm. If john is brave then mary is both humble and creative and vice versa. Fred is both not tall and patient. Someone is either happy or not curious. Fred is generous. Paul is not rich or old. Someone is quiet or patient. | Alice is humble. | neutral | (![X]:((~wise(X)|brave(X))=>brave(X)))&
(![X]:((calm(X)<~>creative(X))=>wise(X)))&
(((happy(susan)|wise(susan)))<=>((tall(susan)<~>strong(susan))))&
(![X]:(rich(X)<=>~brave(X)))&
((?[X]:(creative(X)))<=>(?[X]:(humble(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((rich(X)|calm(X))<=>~calm(X)))&
(((~wise(paul)<~>generous(paul)))=>((strong(paul)|~strong(paul))))&
(((humble(alice)&curious(alice)))<=>(?[X]:(~funny(X))))&
((?[X]:(old(X)))<=>((~brave(mary)<~>calm(mary))))&
(((~calm(susan)<~>patient(susan)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:(humble(X)=>(~quiet(X)|~creative(X))))&
(![X]:((~calm(X)|old(X))=>happy(X)))&
((~brave(paul))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((~quiet(X)|old(X))=>(wise(X)|calm(X))))&
((brave(john))<=>((humble(mary)&creative(mary))))&
((~tall(fred)&patient(fred)))&
(?[X]:((happy(X)<~>~curious(X))))&
(generous(fred))&
((~rich(paul)|old(paul)))&
(?[X]:((quiet(X)|patient(X)))) | humble(alice) | [] | null | 0 |
Everyone who is creative or not curious is both not old and not generous and vice versa. Everyone who is both calm and not patient is both not patient and not wise. Everyone who is either old or humble is either not creative or happy. If someone is generous or not calm then paul is calm. Everyone who is either not brave or not rich is not funny and vice versa. Everyone who is funny is tall and vice versa. If alice is not wise or strong then paul is both not patient and quiet. If lucy is both tall and funny then lucy is both patient and curious. Everyone who is old or funny is both not creative and brave and vice versa. Everyone who is generous or quiet is both quiet and calm. If mary is not curious or not happy then someone is both not old and happy and vice versa. Everyone who is not rich or not tall is either not kind or not happy and vice versa. Everyone who is both not patient and not humble is either curious or strong and vice versa. If someone is both not old and creative then someone is not curious and vice versa. If someone is both generous and kind then fred is not wise. Everyone who is not kind is either not tall or calm and vice versa. Alice is not strong. Lucy is either quiet or not patient. Susan is not kind. Someone is both funny and happy. Susan is either not funny or not quiet. Someone is either not generous or humble. John is either not calm or not rich. Someone is either not old or humble. | Fred is not happy. | neutral | (![X]:((creative(X)|~curious(X))<=>(~old(X)&~generous(X))))&
(![X]:((calm(X)&~patient(X))=>(~patient(X)&~wise(X))))&
(![X]:((old(X)<~>humble(X))=>(~creative(X)<~>happy(X))))&
((?[X]:((generous(X)|~calm(X))))=>(calm(paul)))&
(![X]:((~brave(X)<~>~rich(X))<=>~funny(X)))&
(![X]:(funny(X)<=>tall(X)))&
(((~wise(alice)|strong(alice)))=>((~patient(paul)&quiet(paul))))&
(((tall(lucy)&funny(lucy)))=>((patient(lucy)&curious(lucy))))&
(![X]:((old(X)|funny(X))<=>(~creative(X)&brave(X))))&
(![X]:((generous(X)|quiet(X))=>(quiet(X)&calm(X))))&
(((~curious(mary)|~happy(mary)))<=>(?[X]:((~old(X)&happy(X)))))&
(![X]:((~rich(X)|~tall(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((~patient(X)&~humble(X))<=>(curious(X)<~>strong(X))))&
((?[X]:((~old(X)&creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((generous(X)&kind(X))))=>(~wise(fred)))&
(![X]:(~kind(X)<=>(~tall(X)<~>calm(X))))&
(~strong(alice))&
((quiet(lucy)<~>~patient(lucy)))&
(~kind(susan))&
(?[X]:((funny(X)&happy(X))))&
((~funny(susan)<~>~quiet(susan)))&
(?[X]:((~generous(X)<~>humble(X))))&
((~calm(john)<~>~rich(john)))&
(?[X]:((~old(X)<~>humble(X)))) | ~happy(fred) | [] | null | 0 |
Everyone who is either wise or not old is both not curious and not kind and vice versa.
Everyone who is calm is not brave.
If someone is happy or not calm then someone is humble.
Everyone who is humble or wise is both not happy and not brave and vice versa.
Everyone who is either generous or quiet is old or not strong.
Everyone who is either not curious or not brave is not humble or not happy and vice versa.
Everyone who is both patient and not curious is not tall and vice versa.
Everyone who is humble is not quiet.
Everyone who is not wise is either generous or not quiet and vice versa.
Everyone who is happy or brave is not creative.
Everyone who is curious or not strong is either not happy or patient.
If fred is not calm then someone is not brave and vice versa.
Everyone who is old or not brave is not funny and vice versa.
Everyone who is either rich or tall is either strong or not rich and vice versa.
Everyone who is either not happy or not creative is both not tall and funny and vice versa.
Everyone who is creative is rich or happy and vice versa.
Susan is either tall or happy.
Susan is both brave and not funny.
Lucy is not calm or patient.
Paul is generous.
Someone is either rich or not creative. | Susan is quiet. | neutral | (![X]:((wise(X)<~>~old(X))<=>(~curious(X)&~kind(X))))&
(![X]:(calm(X)=>~brave(X)))&
((?[X]:((happy(X)|~calm(X))))=>(?[X]:(humble(X))))&
(![X]:((humble(X)|wise(X))<=>(~happy(X)&~brave(X))))&
(![X]:((generous(X)<~>quiet(X))=>(old(X)|~strong(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(~humble(X)|~happy(X))))&
(![X]:((patient(X)&~curious(X))<=>~tall(X)))&
(![X]:(humble(X)=>~quiet(X)))&
(![X]:(~wise(X)<=>(generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|brave(X))=>~creative(X)))&
(![X]:((curious(X)|~strong(X))=>(~happy(X)<~>patient(X))))&
((~calm(fred))<=>(?[X]:(~brave(X))))&
(![X]:((old(X)|~brave(X))<=>~funny(X)))&
(![X]:((rich(X)<~>tall(X))<=>(strong(X)<~>~rich(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(~tall(X)&funny(X))))&
(![X]:(creative(X)<=>(rich(X)|happy(X))))&
((tall(susan)<~>happy(susan)))&
((brave(susan)&~funny(susan)))&
((~calm(lucy)|patient(lucy)))&
(generous(paul))&
(?[X]:((rich(X)<~>~creative(X)))) | quiet(susan) | [] | null | 0 |
Everyone who is both brave and not creative is strong and vice versa.
If someone is either not creative or not wise then mary is both not generous and strong and vice versa.
If lucy is either not calm or not tall then alice is not brave or not wise and vice versa.
Everyone who is kind or strong is either not wise or not humble and vice versa.
Everyone who is either not humble or not kind is not funny.
Everyone who is not wise is not calm or not patient and vice versa.
If someone is both rich and kind then someone is not strong.
Everyone who is both funny and quiet is funny or not curious and vice versa.
Everyone who is both not tall and creative is not patient or funny.
Everyone who is both kind and not creative is both not generous and not patient.
Everyone who is not strong or old is not brave and vice versa.
Everyone who is both not happy and curious is rich and vice versa.
Everyone who is both patient and quiet is kind or not strong.
Everyone who is both calm and rich is funny and vice versa.
If fred is curious or patient then lucy is both calm and not strong.
Everyone who is not humble or generous is not old or not curious.
Someone is funny or tall.
Mary is both not humble and calm.
Alice is either creative or not wise.
Fred is quiet or not calm.
Paul is generous or rich.
Paul is not rich or not curious.
Fred is both not funny and not quiet. | Alice is patient. | neutral | (![X]:((brave(X)&~creative(X))<=>strong(X)))&
((?[X]:((~creative(X)<~>~wise(X))))<=>((~generous(mary)&strong(mary))))&
(((~calm(lucy)<~>~tall(lucy)))<=>((~brave(alice)|~wise(alice))))&
(![X]:((kind(X)|strong(X))<=>(~wise(X)<~>~humble(X))))&
(![X]:((~humble(X)<~>~kind(X))=>~funny(X)))&
(![X]:(~wise(X)<=>(~calm(X)|~patient(X))))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:(~strong(X))))&
(![X]:((funny(X)&quiet(X))<=>(funny(X)|~curious(X))))&
(![X]:((~tall(X)&creative(X))=>(~patient(X)|funny(X))))&
(![X]:((kind(X)&~creative(X))=>(~generous(X)&~patient(X))))&
(![X]:((~strong(X)|old(X))<=>~brave(X)))&
(![X]:((~happy(X)&curious(X))<=>rich(X)))&
(![X]:((patient(X)&quiet(X))=>(kind(X)|~strong(X))))&
(![X]:((calm(X)&rich(X))<=>funny(X)))&
(((curious(fred)|patient(fred)))=>((calm(lucy)&~strong(lucy))))&
(![X]:((~humble(X)|generous(X))=>(~old(X)|~curious(X))))&
(?[X]:((funny(X)|tall(X))))&
((~humble(mary)&calm(mary)))&
((creative(alice)<~>~wise(alice)))&
((quiet(fred)|~calm(fred)))&
((generous(paul)|rich(paul)))&
((~rich(paul)|~curious(paul)))&
((~funny(fred)&~quiet(fred))) | patient(alice) | [] | null | 0 |
Everyone who is both brave and not creative is either curious or kind and vice versa.
Everyone who is wise or not curious is both not creative and not patient.
If someone is both not rich and not old then someone is either rich or curious.
Everyone who is both humble and creative is not quiet or kind and vice versa.
Everyone who is humble is wise.
Everyone who is both not happy and not funny is both not strong and happy.
Everyone who is not wise is not brave or happy and vice versa.
Everyone who is strong is either funny or curious.
If susan is not wise or not strong then fred is strong and vice versa.
Everyone who is not calm or funny is not funny and vice versa.
Everyone who is either not kind or not tall is either rich or not patient and vice versa.
Everyone who is both happy and not kind is either not strong or not old and vice versa.
If someone is both not patient and old then fred is both not curious and humble and vice versa.
If someone is both not strong and not funny then someone is brave and vice versa.
Everyone who is not funny or curious is not brave or tall and vice versa.
Someone is either kind or patient.
Susan is not patient or not creative.
Someone is either patient or not patient.
Alice is not quiet or not kind.
Susan is either not rich or not quiet. | Susan is strong. | entailment | (![X]:((brave(X)&~creative(X))<=>(curious(X)<~>kind(X))))&
(![X]:((wise(X)|~curious(X))=>(~creative(X)&~patient(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((humble(X)&creative(X))<=>(~quiet(X)|kind(X))))&
(![X]:(humble(X)=>wise(X)))&
(![X]:((~happy(X)&~funny(X))=>(~strong(X)&happy(X))))&
(![X]:(~wise(X)<=>(~brave(X)|happy(X))))&
(![X]:(strong(X)=>(funny(X)<~>curious(X))))&
(((~wise(susan)|~strong(susan)))<=>(strong(fred)))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(![X]:((~kind(X)<~>~tall(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((happy(X)&~kind(X))<=>(~strong(X)<~>~old(X))))&
((?[X]:((~patient(X)&old(X))))<=>((~curious(fred)&humble(fred))))&
((?[X]:((~strong(X)&~funny(X))))<=>(?[X]:(brave(X))))&
(![X]:((~funny(X)|curious(X))<=>(~brave(X)|tall(X))))&
(?[X]:((kind(X)<~>patient(X))))&
((~patient(susan)|~creative(susan)))&
(?[X]:((patient(X)<~>~patient(X))))&
((~quiet(alice)|~kind(alice)))&
((~rich(susan)<~>~quiet(susan))) | strong(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5369095715030632775598770
% SZS output start Proof for 5369095715030632775598770
1. ! [X0] : ((~creative(X0) & brave(X0)) <=> (curious(X0) <~> kind(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | wise(X0)) => (~patient(X0) & ~creative(X0))) [input p1]
4. ! [X0] : ((creative(X0) & humble(X0)) <=> (kind(X0) | ~quiet(X0))) [input p3]
5. ! [X0] : (humble(X0) => wise(X0)) [input p4]
6. ! [X0] : ((~funny(X0) & ~happy(X0)) => (happy(X0) & ~strong(X0))) [input p5]
7. ! [X0] : (~wise(X0) <=> (happy(X0) | ~brave(X0))) [input p6]
10. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p9]
11. ! [X0] : ((~kind(X0) <~> ~tall(X0)) <=> (rich(X0) <~> ~patient(X0))) [input p10]
12. ! [X0] : ((~kind(X0) & happy(X0)) <=> (~strong(X0) <~> ~old(X0))) [input p11]
13. ? [X0] : (old(X0) & ~patient(X0)) <=> (humble(fred) & ~curious(fred)) [input p12]
15. ! [X0] : ((curious(X0) | ~funny(X0)) <=> (tall(X0) | ~brave(X0))) [input p14]
20. ~rich(susan) <~> ~quiet(susan) [input p19]
21. ~strong(susan) [input hypothesis]
24. ! [X0] : ((~patient(X0) & ~creative(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 2]
26. ! [X0] : (wise(X0) | ~humble(X0)) [ennf transformation 5]
27. ! [X0] : ((happy(X0) & ~strong(X0)) | (funny(X0) | happy(X0))) [ennf transformation 6]
28. ! [X0] : ((happy(X0) & ~strong(X0)) | funny(X0) | happy(X0)) [flattening 27]
30. ! [X0] : (((~creative(X0) & brave(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (creative(X0) | ~brave(X0)))) [nnf transformation 1]
31. ! [X0] : (((~creative(X0) & brave(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0)))) & (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | creative(X0) | ~brave(X0))) [flattening 30]
36. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | (~creative(X0) | ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : (((creative(X0) & humble(X0)) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ~creative(X0) | ~humble(X0))) [flattening 36]
38. ! [X0] : ((~wise(X0) | (~happy(X0) & brave(X0))) & ((happy(X0) | ~brave(X0)) | wise(X0))) [nnf transformation 7]
39. ! [X0] : ((~wise(X0) | (~happy(X0) & brave(X0))) & (happy(X0) | ~brave(X0) | wise(X0))) [flattening 38]
43. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 10]
44. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 43]
45. ! [X0] : ((((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) & (((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0))))) [nnf transformation 11]
46. ! [X0] : (((~kind(X0) & happy(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (kind(X0) | ~happy(X0)))) [nnf transformation 12]
47. ! [X0] : (((~kind(X0) & happy(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | kind(X0) | ~happy(X0))) [flattening 46]
48. (? [X0] : (old(X0) & ~patient(X0)) | (~humble(fred) | curious(fred))) & ((humble(fred) & ~curious(fred)) | ! [X0] : (~old(X0) | patient(X0))) [nnf transformation 13]
49. (? [X0] : (old(X0) & ~patient(X0)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X0] : (~old(X0) | patient(X0))) [flattening 48]
50. (? [X0] : (old(X0) & ~patient(X0)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X1] : (~old(X1) | patient(X1))) [rectify 49]
51. ? [X0] : (old(X0) & ~patient(X0)) => (old(sK1) & ~patient(sK1)) [choice axiom]
52. ((old(sK1) & ~patient(sK1)) | ~humble(fred) | curious(fred)) & ((humble(fred) & ~curious(fred)) | ! [X1] : (~old(X1) | patient(X1))) [skolemisation 50,51]
58. ! [X0] : (((curious(X0) | ~funny(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (~curious(X0) & funny(X0)))) [nnf transformation 15]
59. ! [X0] : ((curious(X0) | ~funny(X0) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | (~curious(X0) & funny(X0)))) [flattening 58]
66. (quiet(susan) | rich(susan)) & (~quiet(susan) | ~rich(susan)) [nnf transformation 20]
69. ~curious(X0) | kind(X0) | brave(X0) [cnf transformation 31]
76. ~patient(X0) | curious(X0) [cnf transformation 24]
80. quiet(X0) | humble(X0) [cnf transformation 37]
81. ~kind(X0) | humble(X0) [cnf transformation 37]
84. ~humble(X0) | wise(X0) [cnf transformation 26]
86. happy(X0) | funny(X0) | happy(X0) [cnf transformation 28]
89. ~happy(X0) | ~wise(X0) [cnf transformation 39]
96. ~funny(X0) | ~funny(X0) [cnf transformation 44]
98. ~tall(X0) | rich(X0) | ~patient(X0) | kind(X0) [cnf transformation 45]
107. ~happy(X0) | strong(X0) | kind(X0) | old(X0) [cnf transformation 47]
113. humble(fred) | ~old(X1) | patient(X1) [cnf transformation 52]
119. tall(X0) | ~brave(X0) | funny(X0) [cnf transformation 59]
129. ~quiet(susan) | ~rich(susan) [cnf transformation 66]
131. ~strong(susan) [cnf transformation 21]
132. ~funny(X0) [duplicate literal removal 96]
134. funny(X0) | happy(X0) [duplicate literal removal 86]
153. 5 <=> wise(susan) [avatar definition]
154. wise(susan) <- (5) [avatar component clause 153]
157. 6 <=> strong(susan) [avatar definition]
159. ~strong(susan) <- (~6) [avatar component clause 157]
168. 8 <=> humble(fred) [avatar definition]
169. humble(fred) <- (8) [avatar component clause 168]
182. 11 <=> ! [X1] : (~old(X1) | patient(X1)) [avatar definition]
183. ~old(X1) | patient(X1) <- (11) [avatar component clause 182]
184. 11 | 8 [avatar split clause 113,168,182]
203. ~brave(X0) | tall(X0) [subsumption resolution 119,132]
215. 18 <=> patient(susan) [avatar definition]
216. patient(susan) <- (18) [avatar component clause 215]
233. 22 <=> rich(susan) [avatar definition]
234. ~rich(susan) <- (~22) [avatar component clause 233]
237. 23 <=> quiet(susan) [avatar definition]
238. ~quiet(susan) <- (~23) [avatar component clause 237]
241. ~22 | ~23 [avatar split clause 129,237,233]
242. ~6 [avatar split clause 131,157]
247. humble(susan) <- (~23) [resolution 80,238]
256. wise(fred) <- (8) [resolution 84,169]
257. wise(susan) <- (~23) [resolution 84,247]
259. 5 | 23 [avatar split clause 257,237,153]
268. happy(X0) [resolution 134,132]
270. ~wise(X0) [resolution 268,89]
274. 24 <=> brave(susan) [avatar definition]
276. brave(susan) <- (24) [avatar component clause 274]
278. 25 <=> kind(susan) [avatar definition]
279. ~kind(susan) <- (~25) [avatar component clause 278]
280. kind(susan) <- (25) [avatar component clause 278]
288. $false <- (8) [resolution 270,256]
289. ~8 [avatar contradiction clause 288]
431. strong(X0) | kind(X0) | old(X0) [resolution 107,268]
432. kind(susan) | old(susan) <- (~6) [resolution 431,159]
443. 39 <=> old(susan) [avatar definition]
445. old(susan) <- (39) [avatar component clause 443]
446. 39 | 25 | 6 [avatar split clause 432,157,278,443]
471. 42 <=> curious(susan) [avatar definition]
472. curious(susan) <- (42) [avatar component clause 471]
483. 43 <=> humble(susan) [avatar definition]
484. humble(susan) <- (43) [avatar component clause 483]
495. patient(susan) <- (11, 39) [resolution 445,183]
498. 18 | ~11 | ~39 [avatar split clause 495,443,182,215]
500. curious(susan) <- (18) [resolution 216,76]
502. 42 | ~18 [avatar split clause 500,215,471]
510. kind(susan) | brave(susan) <- (42) [resolution 472,69]
511. brave(susan) <- (~25, 42) [subsumption resolution 510,279]
514. 24 | 25 | ~42 [avatar split clause 511,471,278,274]
517. tall(susan) <- (24) [resolution 276,203]
521. rich(susan) | ~patient(susan) | kind(susan) <- (24) [resolution 517,98]
522. ~patient(susan) | kind(susan) <- (~22, 24) [subsumption resolution 521,234]
526. 25 | ~18 | 22 | ~24 [avatar split clause 522,274,233,215,278]
533. $false <- (5) [subsumption resolution 154,270]
534. ~5 [avatar contradiction clause 533]
541. humble(susan) <- (25) [resolution 280,81]
542. 43 | ~25 [avatar split clause 541,278,483]
543. wise(susan) <- (43) [resolution 484,84]
544. $false <- (43) [subsumption resolution 543,270]
545. ~43 [avatar contradiction clause 544]
546. $false [avatar sat refutation 184,241,242,259,289,446,498,502,514,526,534,542,545]
% SZS output end Proof for 5369095715030632775598770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or brave is both curious and not brave and vice versa.
Everyone who is both not kind and patient is rich and vice versa.
If someone is not patient then someone is not patient or creative.
Everyone who is both not patient and curious is not tall or not quiet and vice versa.
Everyone who is not funny is either old or not generous.
Everyone who is both not humble and not wise is not calm and vice versa.
Everyone who is either humble or not rich is both generous and not wise and vice versa.
Everyone who is either not strong or not humble is either strong or quiet and vice versa.
If someone is curious then someone is humble or wise and vice versa.
Everyone who is not happy or not tall is either not wise or not funny.
If someone is either not humble or not rich then john is both rich and not patient.
Everyone who is either not creative or old is either not wise or not tall.
If someone is not generous then someone is not happy or generous.
If john is either not funny or not humble then susan is both not quiet and creative and vice versa.
If susan is quiet or not old then john is not quiet and vice versa.
Someone is both curious and not happy.
Someone is brave or rich.
Someone is both strong and not creative.
Someone is either not generous or funny.
Mary is either rich or not quiet.
Someone is both funny and generous. | Susan is wise. | contradiction | (![X]:((kind(X)|brave(X))<=>(curious(X)&~brave(X))))&
(![X]:((~kind(X)&patient(X))<=>rich(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~patient(X)|creative(X)))))&
(![X]:((~patient(X)&curious(X))<=>(~tall(X)|~quiet(X))))&
(![X]:(~funny(X)=>(old(X)<~>~generous(X))))&
(![X]:((~humble(X)&~wise(X))<=>~calm(X)))&
(![X]:((humble(X)<~>~rich(X))<=>(generous(X)&~wise(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)|wise(X)))))&
(![X]:((~happy(X)|~tall(X))=>(~wise(X)<~>~funny(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>((rich(john)&~patient(john))))&
(![X]:((~creative(X)<~>old(X))=>(~wise(X)<~>~tall(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~happy(X)|generous(X)))))&
(((~funny(john)<~>~humble(john)))<=>((~quiet(susan)&creative(susan))))&
(((quiet(susan)|~old(susan)))<=>(~quiet(john)))&
(?[X]:((curious(X)&~happy(X))))&
(?[X]:((brave(X)|rich(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((~generous(X)<~>funny(X))))&
((rich(mary)<~>~quiet(mary)))&
(?[X]:((funny(X)&generous(X)))) | wise(susan) | [
"p1",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7245460834626466819756743
% SZS output start Proof for 7245460834626466819756743
2. ! [X0] : ((patient(X0) & ~kind(X0)) <=> rich(X0)) [input p1]
7. ! [X0] : ((humble(X0) <~> ~rich(X0)) <=> (~wise(X0) & generous(X0))) [input p6]
11. ? [X0] : (~humble(X0) <~> ~rich(X0)) => (~patient(john) & rich(john)) [input p10]
22. wise(susan) [input hypothesis]
29. (~patient(john) & rich(john)) | ! [X0] : (~humble(X0) <=> ~rich(X0)) [ennf transformation 11]
34. ! [X0] : (((patient(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | (~patient(X0) | kind(X0)))) [nnf transformation 2]
35. ! [X0] : (((patient(X0) & ~kind(X0)) | ~rich(X0)) & (rich(X0) | ~patient(X0) | kind(X0))) [flattening 34]
42. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [nnf transformation 7]
43. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [flattening 42]
51. (~patient(john) & rich(john)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))) [nnf transformation 29]
79. ~rich(X0) | patient(X0) [cnf transformation 35]
90. ~wise(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 43]
91. ~wise(X0) | humble(X0) | rich(X0) [cnf transformation 43]
109. rich(john) | ~rich(X0) | humble(X0) [cnf transformation 51]
110. rich(john) | ~humble(X0) | rich(X0) [cnf transformation 51]
111. ~patient(john) | ~rich(X0) | humble(X0) [cnf transformation 51]
112. ~patient(john) | ~humble(X0) | rich(X0) [cnf transformation 51]
138. wise(susan) [cnf transformation 22]
184. 10 <=> ! [X0] : (~humble(X0) | rich(X0)) [avatar definition]
185. ~humble(X0) | rich(X0) <- (10) [avatar component clause 184]
187. 11 <=> patient(john) [avatar definition]
190. 10 | ~11 [avatar split clause 112,187,184]
192. 12 <=> ! [X0] : (~rich(X0) | humble(X0)) [avatar definition]
193. ~rich(X0) | humble(X0) <- (12) [avatar component clause 192]
194. 12 | ~11 [avatar split clause 111,187,192]
196. 13 <=> rich(john) [avatar definition]
198. rich(john) <- (13) [avatar component clause 196]
199. 10 | 13 [avatar split clause 110,196,184]
200. 12 | 13 [avatar split clause 109,196,192]
319. patient(john) <- (13) [resolution 198,79]
323. 11 | ~13 [avatar split clause 319,196,187]
362. ~rich(susan) | ~humble(susan) [resolution 90,138]
366. humble(susan) | rich(susan) [resolution 91,138]
374. rich(susan) <- (10) [subsumption resolution 366,185]
375. ~humble(susan) <- (10) [subsumption resolution 362,374]
474. humble(susan) <- (10, 12) [resolution 374,193]
477. $false <- (10, 12) [subsumption resolution 474,375]
478. ~10 | ~12 [avatar contradiction clause 477]
479. $false [avatar sat refutation 190,194,199,200,323,478]
% SZS output end Proof for 7245460834626466819756743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or not strong then alice is both happy and not kind.
If someone is both not strong and not brave then someone is either not creative or brave and vice versa.
Everyone who is both not tall and not old is either not creative or brave.
Everyone who is either humble or generous is not wise or funny.
Everyone who is not kind or rich is both rich and calm and vice versa.
If paul is either not old or not patient then fred is both not wise and not creative.
Everyone who is not funny or generous is either rich or not brave and vice versa.
If susan is both not rich and happy then someone is not creative.
Everyone who is either kind or not strong is both not creative and not calm and vice versa.
If someone is both not creative and not old then someone is not old and vice versa.
Everyone who is either not creative or creative is strong or humble and vice versa.
If alice is tall or not patient then lucy is either generous or creative and vice versa.
Everyone who is not kind is not brave and vice versa.
Everyone who is both strong and not curious is not generous or not funny and vice versa.
If paul is old or patient then mary is both not strong and patient and vice versa.
Everyone who is both not generous and brave is either not creative or curious.
Someone is curious.
Susan is not generous.
Someone is wise or strong.
Someone is creative.
Fred is either quiet or not tall.
Someone is patient or not generous.
Someone is both not wise and not curious. | Alice is strong. | entailment | ((?[X]:((calm(X)<~>~strong(X))))=>((happy(alice)&~kind(alice))))&
((?[X]:((~strong(X)&~brave(X))))<=>(?[X]:((~creative(X)<~>brave(X)))))&
(![X]:((~tall(X)&~old(X))=>(~creative(X)<~>brave(X))))&
(![X]:((humble(X)<~>generous(X))=>(~wise(X)|funny(X))))&
(![X]:((~kind(X)|rich(X))<=>(rich(X)&calm(X))))&
(((~old(paul)<~>~patient(paul)))=>((~wise(fred)&~creative(fred))))&
(![X]:((~funny(X)|generous(X))<=>(rich(X)<~>~brave(X))))&
(((~rich(susan)&happy(susan)))=>(?[X]:(~creative(X))))&
(![X]:((kind(X)<~>~strong(X))<=>(~creative(X)&~calm(X))))&
((?[X]:((~creative(X)&~old(X))))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(strong(X)|humble(X))))&
(((tall(alice)|~patient(alice)))<=>((generous(lucy)<~>creative(lucy))))&
(![X]:(~kind(X)<=>~brave(X)))&
(![X]:((strong(X)&~curious(X))<=>(~generous(X)|~funny(X))))&
(((old(paul)|patient(paul)))<=>((~strong(mary)&patient(mary))))&
(![X]:((~generous(X)&brave(X))=>(~creative(X)<~>curious(X))))&
(?[X]:(curious(X)))&
(~generous(susan))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:(creative(X)))&
((quiet(fred)<~>~tall(fred)))&
(?[X]:((patient(X)|~generous(X))))&
(?[X]:((~wise(X)&~curious(X)))) | strong(alice) | [
"p0",
"p1",
"p4",
"p8",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 240561817958795006196964
% SZS output start Proof for 240561817958795006196964
1. ? [X0] : (calm(X0) <~> ~strong(X0)) => (~kind(alice) & happy(alice)) [input p0]
2. ? [X0] : (~brave(X0) & ~strong(X0)) <=> ? [X0] : (~creative(X0) <~> brave(X0)) [input p1]
5. ! [X0] : ((rich(X0) | ~kind(X0)) <=> (calm(X0) & rich(X0))) [input p4]
9. ! [X0] : ((kind(X0) <~> ~strong(X0)) <=> (~calm(X0) & ~creative(X0))) [input p8]
13. ! [X0] : (~kind(X0) <=> ~brave(X0)) [input p12]
20. ? [X0] : creative(X0) [input p19]
24. ~strong(alice) [input hypothesis]
25. ? [X0] : (~brave(X0) & ~strong(X0)) <=> ? [X1] : (~creative(X1) <~> brave(X1)) [rectify 2]
27. (~kind(alice) & happy(alice)) | ! [X0] : (calm(X0) <=> ~strong(X0)) [ennf transformation 1]
37. (~kind(alice) & happy(alice)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))) [nnf transformation 27]
38. (? [X0] : (~brave(X0) & ~strong(X0)) | ! [X1] : ((~creative(X1) | ~brave(X1)) & (brave(X1) | creative(X1)))) & (? [X1] : ((~brave(X1) | creative(X1)) & (brave(X1) | ~creative(X1))) | ! [X0] : (brave(X0) | strong(X0))) [nnf transformation 25]
39. (? [X0] : (~brave(X0) & ~strong(X0)) | ! [X1] : ((~creative(X1) | ~brave(X1)) & (brave(X1) | creative(X1)))) & (? [X2] : ((~brave(X2) | creative(X2)) & (brave(X2) | ~creative(X2))) | ! [X3] : (brave(X3) | strong(X3))) [rectify 38]
40. ? [X0] : (~brave(X0) & ~strong(X0)) => (~brave(sK0) & ~strong(sK0)) [choice axiom]
41. ? [X2] : ((~brave(X2) | creative(X2)) & (brave(X2) | ~creative(X2))) => ((~brave(sK1) | creative(sK1)) & (brave(sK1) | ~creative(sK1))) [choice axiom]
42. ((~brave(sK0) & ~strong(sK0)) | ! [X1] : ((~creative(X1) | ~brave(X1)) & (brave(X1) | creative(X1)))) & (((~brave(sK1) | creative(sK1)) & (brave(sK1) | ~creative(sK1))) | ! [X3] : (brave(X3) | strong(X3))) [skolemisation 39,41,40]
45. ! [X0] : (((rich(X0) | ~kind(X0)) | (~calm(X0) | ~rich(X0))) & ((calm(X0) & rich(X0)) | (~rich(X0) & kind(X0)))) [nnf transformation 5]
46. ! [X0] : ((rich(X0) | ~kind(X0) | ~calm(X0) | ~rich(X0)) & ((calm(X0) & rich(X0)) | (~rich(X0) & kind(X0)))) [flattening 45]
52. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (calm(X0) | creative(X0))) & ((~calm(X0) & ~creative(X0)) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [nnf transformation 9]
53. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | calm(X0) | creative(X0)) & ((~calm(X0) & ~creative(X0)) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [flattening 52]
63. ! [X0] : ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0))) [nnf transformation 13]
73. ? [X0] : creative(X0) => creative(sK7) [choice axiom]
74. creative(sK7) [skolemisation 20,73]
82. ~kind(alice) | ~strong(X0) | ~calm(X0) [cnf transformation 37]
87. ~strong(sK0) | ~creative(X1) | ~brave(X1) [cnf transformation 42]
89. ~brave(sK0) | ~creative(X1) | ~brave(X1) [cnf transformation 42]
96. kind(X0) | calm(X0) [cnf transformation 46]
110. ~creative(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 53]
113. ~calm(X0) | kind(X0) | strong(X0) [cnf transformation 53]
132. ~kind(X0) | brave(X0) [cnf transformation 63]
148. creative(sK7) [cnf transformation 74]
154. ~strong(alice) [cnf transformation 24]
161. 2 <=> kind(alice) [avatar definition]
163. ~kind(alice) <- (~2) [avatar component clause 161]
166. 3 <=> ! [X0] : (~strong(X0) | ~calm(X0)) [avatar definition]
167. ~strong(X0) | ~calm(X0) <- (3) [avatar component clause 166]
168. 3 | ~2 [avatar split clause 82,161,166]
176. 5 <=> ! [X1] : (~creative(X1) | ~brave(X1)) [avatar definition]
177. ~creative(X1) | ~brave(X1) <- (5) [avatar component clause 176]
179. 6 <=> brave(sK0) [avatar definition]
181. ~brave(sK0) <- (~6) [avatar component clause 179]
182. 5 | ~6 [avatar split clause 89,179,176]
188. 8 <=> strong(sK0) [avatar definition]
190. ~strong(sK0) <- (~8) [avatar component clause 188]
191. 5 | ~8 [avatar split clause 87,188,176]
194. 9 <=> ! [X3] : (brave(X3) | strong(X3)) [avatar definition]
195. brave(X3) | strong(X3) <- (9) [avatar component clause 194]
240. kind(X0) | strong(X0) [subsumption resolution 113,96]
335. strong(alice) <- (~2) [resolution 240,163]
336. strong(X0) | brave(X0) [resolution 240,132]
337. $false <- (~2) [subsumption resolution 335,154]
338. 2 [avatar contradiction clause 337]
339. 9 [avatar split clause 336,194]
347. strong(sK0) <- (~6, 9) [resolution 195,181]
350. $false <- (~6, ~8, 9) [subsumption resolution 347,190]
351. 6 | 8 | ~9 [avatar contradiction clause 350]
353. ~brave(sK7) <- (5) [resolution 177,148]
401. strong(sK7) <- (5, 9) [resolution 353,195]
405. ~strong(sK7) | ~kind(sK7) [resolution 110,148]
408. ~kind(sK7) <- (5, 9) [subsumption resolution 405,401]
472. calm(sK7) <- (5, 9) [resolution 408,96]
716. ~calm(sK7) <- (3, 5, 9) [resolution 401,167]
717. $false <- (3, 5, 9) [subsumption resolution 716,472]
718. ~3 | ~5 | ~9 [avatar contradiction clause 717]
719. $false [avatar sat refutation 168,182,191,338,339,351,718]
% SZS output end Proof for 240561817958795006196964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not brave then someone is both not humble and not generous.
Everyone who is not quiet is both brave and not patient.
If someone is not funny or funny then mary is not brave and vice versa.
Everyone who is either not funny or brave is both patient and wise.
Everyone who is either funny or not rich is both not patient and not happy and vice versa.
If someone is either not humble or brave then someone is creative or not generous and vice versa.
Everyone who is generous or old is either old or brave and vice versa.
If lucy is not old then john is patient and vice versa.
If susan is either strong or not quiet then someone is both not humble and generous.
If someone is either brave or not old then someone is not curious.
If someone is either not patient or not rich then alice is not happy and vice versa.
If fred is not wise then someone is wise.
If mary is calm or not quiet then lucy is patient or not tall.
Everyone who is funny or quiet is both not funny and not strong.
Everyone who is not creative or not calm is not quiet or quiet.
Everyone who is both not wise and not funny is not rich.
Someone is both generous and wise.
Susan is not curious or not kind.
Someone is not generous.
Fred is both not happy and not funny.
Someone is not brave.
Someone is rich.
Someone is not patient or not brave. | Mary is rich. | entailment | ((?[X]:((humble(X)&~brave(X))))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:(~quiet(X)=>(brave(X)&~patient(X))))&
((?[X]:((~funny(X)|funny(X))))<=>(~brave(mary)))&
(![X]:((~funny(X)<~>brave(X))=>(patient(X)&wise(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(~patient(X)&~happy(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((generous(X)|old(X))<=>(old(X)<~>brave(X))))&
((~old(lucy))<=>(patient(john)))&
(((strong(susan)<~>~quiet(susan)))=>(?[X]:((~humble(X)&generous(X)))))&
((?[X]:((brave(X)<~>~old(X))))=>(?[X]:(~curious(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(~happy(alice)))&
((~wise(fred))=>(?[X]:(wise(X))))&
(((calm(mary)|~quiet(mary)))=>((patient(lucy)|~tall(lucy))))&
(![X]:((funny(X)|quiet(X))=>(~funny(X)&~strong(X))))&
(![X]:((~creative(X)|~calm(X))=>(~quiet(X)|quiet(X))))&
(![X]:((~wise(X)&~funny(X))=>~rich(X)))&
(?[X]:((generous(X)&wise(X))))&
((~curious(susan)|~kind(susan)))&
(?[X]:(~generous(X)))&
((~happy(fred)&~funny(fred)))&
(?[X]:(~brave(X)))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)|~brave(X)))) | rich(mary) | [
"p1",
"p2",
"p3",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1395294168492486493156273
% SZS output start Proof for 1395294168492486493156273
2. ! [X0] : (~quiet(X0) => (~patient(X0) & brave(X0))) [input p1]
3. ? [X0] : (funny(X0) | ~funny(X0)) <=> ~brave(mary) [input p2]
4. ! [X0] : ((~funny(X0) <~> brave(X0)) => (wise(X0) & patient(X0))) [input p3]
5. ! [X0] : ((funny(X0) <~> ~rich(X0)) <=> (~happy(X0) & ~patient(X0))) [input p4]
14. ! [X0] : ((quiet(X0) | funny(X0)) => (~strong(X0) & ~funny(X0))) [input p13]
24. ~rich(mary) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> brave(X0)) => patient(X0)) [pure predicate removal 4]
37. ! [X0] : ((~patient(X0) & brave(X0)) | quiet(X0)) [ennf transformation 2]
38. ! [X0] : (patient(X0) | (~funny(X0) <=> brave(X0))) [ennf transformation 33]
40. ! [X0] : ((~strong(X0) & ~funny(X0)) | (~quiet(X0) & ~funny(X0))) [ennf transformation 14]
46. (? [X0] : (funny(X0) | ~funny(X0)) | brave(mary)) & (~brave(mary) | ! [X0] : (~funny(X0) & funny(X0))) [nnf transformation 3]
47. (? [X0] : (funny(X0) | ~funny(X0)) | brave(mary)) & (~brave(mary) | ! [X1] : (~funny(X1) & funny(X1))) [rectify 46]
48. ? [X0] : (funny(X0) | ~funny(X0)) => (funny(sK1) | ~funny(sK1)) [choice axiom]
49. ((funny(sK1) | ~funny(sK1)) | brave(mary)) & (~brave(mary) | ! [X1] : (~funny(X1) & funny(X1))) [skolemisation 47,48]
50. ! [X0] : (patient(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) [nnf transformation 38]
51. ! [X0] : ((((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | (happy(X0) | patient(X0))) & ((~happy(X0) & ~patient(X0)) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0))))) [nnf transformation 5]
52. ! [X0] : ((((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | happy(X0) | patient(X0)) & ((~happy(X0) & ~patient(X0)) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0))))) [flattening 51]
80. quiet(X0) | brave(X0) [cnf transformation 37]
82. ~brave(mary) | funny(X1) [cnf transformation 49]
85. funny(X0) | brave(X0) | patient(X0) [cnf transformation 50]
88. ~patient(X0) | funny(X0) | rich(X0) [cnf transformation 52]
115. ~funny(X0) | ~funny(X0) [cnf transformation 40]
116. ~funny(X0) | ~quiet(X0) [cnf transformation 40]
127. ~rich(mary) [cnf transformation 24]
128. ~funny(X0) [duplicate literal removal 115]
145. 4 <=> ! [X1] : ~funny(X1) [avatar definition]
146. ~funny(X1) <- (4) [avatar component clause 145]
148. 5 <=> brave(mary) [avatar definition]
153. 6 <=> ! [X1] : funny(X1) [avatar definition]
154. funny(X1) <- (6) [avatar component clause 153]
155. 6 | ~5 [avatar split clause 82,148,153]
242. 4 [avatar split clause 128,145]
255. brave(X0) | patient(X0) | ~quiet(X0) [resolution 85,116]
266. patient(X0) | brave(X0) [subsumption resolution 255,80]
283. brave(X0) | funny(X0) | rich(X0) [resolution 266,88]
287. rich(X0) | brave(X0) <- (4) [subsumption resolution 283,146]
337. brave(mary) <- (4) [resolution 287,127]
342. 5 | ~4 [avatar split clause 337,145,148]
343. $false <- (4, 6) [subsumption resolution 154,146]
344. ~4 | ~6 [avatar contradiction clause 343]
345. $false [avatar sat refutation 155,242,342,344]
% SZS output end Proof for 1395294168492486493156273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.