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
|
|---|---|---|---|---|---|---|---|
Everyone who is not wise or old is tall or not old and vice versa.
Everyone who is either humble or not funny is both not brave and not wise and vice versa.
If someone is both not tall and not brave then john is not kind or brave and vice versa.
Everyone who is either creative or funny is strong and vice versa.
If someone is both strong and not old then someone is both not humble and not strong.
If fred is both not rich and generous then someone is not wise or not kind.
If fred is both brave and not curious then alice is tall.
If lucy is either humble or happy then paul is both not humble and not kind.
Everyone who is not wise or not tall is either tall or wise and vice versa.
If someone is generous or not old then mary is creative and vice versa.
Everyone who is both generous and humble is either creative or not funny and vice versa.
If someone is rich or not wise then paul is not old.
If lucy is not kind or not patient then someone is not happy or not strong.
If fred is not quiet or not patient then paul is either not patient or not quiet and vice versa.
Everyone who is tall is strong.
Someone is happy or not wise.
Susan is either generous or rich.
Alice is generous or calm.
Someone is either patient or tall.
Lucy is not wise or not funny.
Someone is either not quiet or not wise. | Mary is funny. | contradiction | (![X]:((~wise(X)|old(X))<=>(tall(X)|~old(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(~brave(X)&~wise(X))))&
((?[X]:((~tall(X)&~brave(X))))<=>((~kind(john)|brave(john))))&
(![X]:((creative(X)<~>funny(X))<=>strong(X)))&
((?[X]:((strong(X)&~old(X))))=>(?[X]:((~humble(X)&~strong(X)))))&
(((~rich(fred)&generous(fred)))=>(?[X]:((~wise(X)|~kind(X)))))&
(((brave(fred)&~curious(fred)))=>(tall(alice)))&
(((humble(lucy)<~>happy(lucy)))=>((~humble(paul)&~kind(paul))))&
(![X]:((~wise(X)|~tall(X))<=>(tall(X)<~>wise(X))))&
((?[X]:((generous(X)|~old(X))))<=>(creative(mary)))&
(![X]:((generous(X)&humble(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((rich(X)|~wise(X))))=>(~old(paul)))&
(((~kind(lucy)|~patient(lucy)))=>(?[X]:((~happy(X)|~strong(X)))))&
(((~quiet(fred)|~patient(fred)))<=>((~patient(paul)<~>~quiet(paul))))&
(![X]:(tall(X)=>strong(X)))&
(?[X]:((happy(X)|~wise(X))))&
((generous(susan)<~>rich(susan)))&
((generous(alice)|calm(alice)))&
(?[X]:((patient(X)<~>tall(X))))&
((~wise(lucy)|~funny(lucy)))&
(?[X]:((~quiet(X)<~>~wise(X)))) | funny(mary) | [
"p0",
"p1",
"p2",
"p3",
"p8",
"p9",
"p10",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8706961918949570195484726
% SZS output start Proof for 8706961918949570195484726
1. ! [X0] : ((old(X0) | ~wise(X0)) <=> (~old(X0) | tall(X0))) [input p0]
2. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~wise(X0) & ~brave(X0))) [input p1]
3. ? [X0] : (~brave(X0) & ~tall(X0)) <=> (brave(john) | ~kind(john)) [input p2]
4. ! [X0] : ((creative(X0) <~> funny(X0)) <=> strong(X0)) [input p3]
9. ! [X0] : ((~tall(X0) | ~wise(X0)) <=> (tall(X0) <~> wise(X0))) [input p8]
10. ? [X0] : (~old(X0) | generous(X0)) <=> creative(mary) [input p9]
11. ! [X0] : ((humble(X0) & generous(X0)) <=> (creative(X0) <~> ~funny(X0))) [input p10]
12. ? [X0] : (~wise(X0) | rich(X0)) => ~old(paul) [input p11]
15. ! [X0] : (tall(X0) => strong(X0)) [input p14]
17. generous(susan) <~> rich(susan) [input p16]
22. funny(mary) [input hypothesis]
30. ~old(paul) | ! [X0] : (wise(X0) & ~rich(X0)) [ennf transformation 12]
32. ! [X0] : (strong(X0) | ~tall(X0)) [ennf transformation 15]
33. ! [X0] : (((old(X0) | ~wise(X0)) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | (~old(X0) & wise(X0)))) [nnf transformation 1]
34. ! [X0] : ((old(X0) | ~wise(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | (~old(X0) & wise(X0)))) [flattening 33]
35. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 2]
36. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 35]
37. (? [X0] : (~brave(X0) & ~tall(X0)) | (~brave(john) & kind(john))) & ((brave(john) | ~kind(john)) | ! [X0] : (brave(X0) | tall(X0))) [nnf transformation 3]
38. (? [X0] : (~brave(X0) & ~tall(X0)) | (~brave(john) & kind(john))) & (brave(john) | ~kind(john) | ! [X0] : (brave(X0) | tall(X0))) [flattening 37]
39. (? [X0] : (~brave(X0) & ~tall(X0)) | (~brave(john) & kind(john))) & (brave(john) | ~kind(john) | ! [X1] : (brave(X1) | tall(X1))) [rectify 38]
40. ? [X0] : (~brave(X0) & ~tall(X0)) => (~brave(sK0) & ~tall(sK0)) [choice axiom]
41. ((~brave(sK0) & ~tall(sK0)) | (~brave(john) & kind(john))) & (brave(john) | ~kind(john) | ! [X1] : (brave(X1) | tall(X1))) [skolemisation 39,40]
42. ! [X0] : ((((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ~strong(X0)) & (strong(X0) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0))))) [nnf transformation 4]
49. ! [X0] : (((~tall(X0) | ~wise(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (tall(X0) & wise(X0)))) [nnf transformation 9]
50. ! [X0] : ((~tall(X0) | ~wise(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (tall(X0) & wise(X0)))) [flattening 49]
51. (? [X0] : (~old(X0) | generous(X0)) | ~creative(mary)) & (creative(mary) | ! [X0] : (old(X0) & ~generous(X0))) [nnf transformation 10]
52. (? [X0] : (~old(X0) | generous(X0)) | ~creative(mary)) & (creative(mary) | ! [X1] : (old(X1) & ~generous(X1))) [rectify 51]
53. ? [X0] : (~old(X0) | generous(X0)) => (~old(sK3) | generous(sK3)) [choice axiom]
54. ((~old(sK3) | generous(sK3)) | ~creative(mary)) & (creative(mary) | ! [X1] : (old(X1) & ~generous(X1))) [skolemisation 52,53]
55. ! [X0] : (((humble(X0) & generous(X0)) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0)))) & (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~humble(X0) | ~generous(X0)))) [nnf transformation 11]
56. ! [X0] : (((humble(X0) & generous(X0)) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0)))) & (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ~humble(X0) | ~generous(X0))) [flattening 55]
63. (~rich(susan) | ~generous(susan)) & (rich(susan) | generous(susan)) [nnf transformation 17]
71. ~old(X0) | tall(X0) | ~old(X0) [cnf transformation 34]
73. old(X0) | ~wise(X0) | old(X0) [cnf transformation 34]
74. ~brave(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 36]
80. brave(john) | ~kind(john) | brave(X1) | tall(X1) [cnf transformation 41]
81. ~tall(sK0) | kind(john) [cnf transformation 41]
82. ~tall(sK0) | ~brave(john) [cnf transformation 41]
88. ~strong(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 42]
97. wise(X0) | tall(X0) | tall(X0) [cnf transformation 50]
102. creative(mary) | ~generous(X1) [cnf transformation 54]
103. creative(mary) | old(X1) [cnf transformation 54]
109. ~creative(X0) | ~funny(X0) | humble(X0) [cnf transformation 56]
111. ~old(paul) | ~rich(X0) [cnf transformation 30]
121. ~tall(X0) | strong(X0) [cnf transformation 32]
123. rich(susan) | generous(susan) [cnf transformation 63]
130. funny(mary) [cnf transformation 22]
132. tall(X0) | wise(X0) [duplicate literal removal 97]
135. ~old(X0) | tall(X0) [duplicate literal removal 71]
136. ~wise(X0) | old(X0) [duplicate literal removal 73]
138. 1 <=> brave(john) [avatar definition]
147. 3 <=> kind(john) [avatar definition]
152. 4 <=> tall(sK0) [avatar definition]
154. ~tall(sK0) <- (~4) [avatar component clause 152]
155. ~1 | ~4 [avatar split clause 82,152,138]
156. 3 | ~4 [avatar split clause 81,152,147]
158. 5 <=> ! [X1] : (brave(X1) | tall(X1)) [avatar definition]
159. brave(X1) | tall(X1) <- (5) [avatar component clause 158]
160. 5 | ~3 | 1 [avatar split clause 80,138,147,158]
212. 17 <=> creative(mary) [avatar definition]
213. creative(mary) <- (17) [avatar component clause 212]
225. 20 <=> ! [X1] : old(X1) [avatar definition]
226. old(X1) <- (20) [avatar component clause 225]
227. 20 | 17 [avatar split clause 103,212,225]
229. 21 <=> ! [X1] : ~generous(X1) [avatar definition]
230. ~generous(X1) <- (21) [avatar component clause 229]
231. 21 | 17 [avatar split clause 102,212,229]
236. 23 <=> old(paul) [avatar definition]
238. ~old(paul) <- (~23) [avatar component clause 236]
241. 24 <=> ! [X0] : ~rich(X0) [avatar definition]
242. ~rich(X0) <- (24) [avatar component clause 241]
243. 24 | ~23 [avatar split clause 111,236,241]
294. 35 <=> generous(susan) [avatar definition]
295. generous(susan) <- (35) [avatar component clause 294]
298. 36 <=> rich(susan) [avatar definition]
299. rich(susan) <- (36) [avatar component clause 298]
302. 35 | 36 [avatar split clause 123,298,294]
332. wise(sK0) <- (~4) [resolution 132,154]
335. old(sK0) <- (~4) [resolution 136,332]
337. tall(sK0) <- (~4) [resolution 335,135]
338. $false <- (~4) [subsumption resolution 337,154]
339. 4 [avatar contradiction clause 338]
344. ~funny(X0) | ~humble(X0) | tall(X0) <- (5) [resolution 74,159]
352. 43 <=> humble(mary) [avatar definition]
353. humble(mary) <- (43) [avatar component clause 352]
354. ~humble(mary) <- (~43) [avatar component clause 352]
431. ~funny(mary) | humble(mary) <- (17) [resolution 109,213]
432. humble(mary) <- (17) [subsumption resolution 431,130]
433. $false <- (17, ~43) [subsumption resolution 432,354]
434. ~17 | 43 [avatar contradiction clause 433]
436. 55 <=> strong(mary) [avatar definition]
438. strong(mary) <- (55) [avatar component clause 436]
447. $false <- (20, ~23) [resolution 226,238]
449. ~20 | 23 [avatar contradiction clause 447]
544. ~humble(mary) | tall(mary) <- (5) [resolution 344,130]
546. tall(mary) <- (5, 43) [subsumption resolution 544,353]
570. strong(mary) <- (5, 43) [resolution 546,121]
571. 55 | ~5 | ~43 [avatar split clause 570,352,158,436]
572. ~creative(mary) | ~funny(mary) <- (55) [resolution 438,88]
577. ~creative(mary) <- (55) [subsumption resolution 572,130]
578. ~17 | ~55 [avatar split clause 577,436,212]
592. $false <- (21, 35) [resolution 230,295]
595. ~21 | ~35 [avatar contradiction clause 592]
596. $false <- (24, 36) [subsumption resolution 299,242]
597. ~24 | ~36 [avatar contradiction clause 596]
598. $false [avatar sat refutation 155,156,160,227,231,243,302,339,434,449,571,578,595,597]
% SZS output end Proof for 8706961918949570195484726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old then paul is not wise or humble and vice versa.
If fred is not generous or not quiet then john is either strong or funny and vice versa.
Everyone who is either kind or humble is both not creative and not strong and vice versa.
If fred is not brave then lucy is both not old and patient and vice versa.
If john is creative or not strong then john is happy or not strong and vice versa.
Everyone who is not creative or not humble is either not funny or not wise and vice versa.
If alice is both not strong and brave then lucy is either not kind or patient.
If fred is both wise and not generous then someone is both brave and rich and vice versa.
Everyone who is both not happy and not quiet is both not curious and not calm and vice versa.
Everyone who is not humble is generous or not curious.
Everyone who is not strong is either not funny or wise.
Everyone who is rich or brave is either not creative or rich and vice versa.
If lucy is not curious then lucy is wise and vice versa.
If john is not curious then someone is not kind or not humble.
If someone is either not generous or not funny then someone is both not creative and not tall.
Everyone who is either not kind or not humble is not old.
Someone is not generous or funny.
Someone is kind or funny.
Someone is either rich or strong.
Someone is either not happy or not calm.
Paul is not generous or funny.
Someone is not wise or not quiet.
Susan is either not calm or patient.
Alice is both strong and not old. | Alice is tall. | neutral | ((~old(alice))<=>((~wise(paul)|humble(paul))))&
(((~generous(fred)|~quiet(fred)))<=>((strong(john)<~>funny(john))))&
(![X]:((kind(X)<~>humble(X))<=>(~creative(X)&~strong(X))))&
((~brave(fred))<=>((~old(lucy)&patient(lucy))))&
(((creative(john)|~strong(john)))<=>((happy(john)|~strong(john))))&
(![X]:((~creative(X)|~humble(X))<=>(~funny(X)<~>~wise(X))))&
(((~strong(alice)&brave(alice)))=>((~kind(lucy)<~>patient(lucy))))&
(((wise(fred)&~generous(fred)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(~curious(X)&~calm(X))))&
(![X]:(~humble(X)=>(generous(X)|~curious(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>wise(X))))&
(![X]:((rich(X)|brave(X))<=>(~creative(X)<~>rich(X))))&
((~curious(lucy))<=>(wise(lucy)))&
((~curious(john))=>(?[X]:((~kind(X)|~humble(X)))))&
((?[X]:((~generous(X)<~>~funny(X))))=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~kind(X)<~>~humble(X))=>~old(X)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~happy(X)<~>~calm(X))))&
((~generous(paul)|funny(paul)))&
(?[X]:((~wise(X)|~quiet(X))))&
((~calm(susan)<~>patient(susan)))&
((strong(alice)&~old(alice))) | tall(alice) | [] | null | 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa.
If susan is both creative and kind then someone is not patient.
Everyone who is both not humble and not happy is kind or generous and vice versa.
Everyone who is not rich is generous.
If fred is not rich or quiet then someone is either not tall or generous.
Everyone who is not brave is either not quiet or old and vice versa.
If someone is not patient or funny then mary is both not humble and not funny and vice versa.
Everyone who is not tall is either humble or not tall.
If someone is both humble and not kind then someone is either calm or strong.
If lucy is brave or not old then someone is both wise and not wise and vice versa.
Everyone who is not kind is happy or funny.
Everyone who is both funny and old is both not curious and not calm and vice versa.
If someone is rich or funny then john is creative or not calm.
Everyone who is humble is both not funny and not old.
Everyone who is quiet is both not humble and wise and vice versa.
Fred is not humble or brave.
Someone is either brave or not curious.
Someone is strong.
Someone is either tall or not creative.
Someone is creative or humble.
Someone is kind or tall. | Fred is not kind. | contradiction | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
(((creative(susan)&kind(susan)))=>(?[X]:(~patient(X))))&
(![X]:((~humble(X)&~happy(X))<=>(kind(X)|generous(X))))&
(![X]:(~rich(X)=>generous(X)))&
(((~rich(fred)|quiet(fred)))=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(~quiet(X)<~>old(X))))&
((?[X]:((~patient(X)|funny(X))))<=>((~humble(mary)&~funny(mary))))&
(![X]:(~tall(X)=>(humble(X)<~>~tall(X))))&
((?[X]:((humble(X)&~kind(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(((brave(lucy)|~old(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~kind(X)=>(happy(X)|funny(X))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
((~humble(fred)|brave(fred)))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:(strong(X)))&
(?[X]:((tall(X)<~>~creative(X))))&
(?[X]:((creative(X)|humble(X))))&
(?[X]:((kind(X)|tall(X)))) | ~kind(fred) | [
"p0",
"p2",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5247188397431036195615531
% SZS output start Proof for 5247188397431036195615531
1. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~happy(X0) <~> generous(X0))) [input p0]
3. ! [X0] : ((~happy(X0) & ~humble(X0)) <=> (generous(X0) | kind(X0))) [input p2]
11. ! [X0] : (~kind(X0) => (funny(X0) | happy(X0))) [input p10]
14. ! [X0] : (humble(X0) => (~old(X0) & ~funny(X0))) [input p13]
22. ~kind(fred) [input hypothesis]
30. ! [X0] : ((funny(X0) | happy(X0)) | kind(X0)) [ennf transformation 11]
31. ! [X0] : (funny(X0) | happy(X0) | kind(X0)) [flattening 30]
34. ! [X0] : ((~old(X0) & ~funny(X0)) | ~humble(X0)) [ennf transformation 14]
35. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 1]
36. ! [X0] : ((funny(X0) | ~funny(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [flattening 35]
39. ! [X0] : (((~happy(X0) & ~humble(X0)) | (~generous(X0) & ~kind(X0))) & ((generous(X0) | kind(X0)) | (happy(X0) | humble(X0)))) [nnf transformation 3]
40. ! [X0] : (((~happy(X0) & ~humble(X0)) | (~generous(X0) & ~kind(X0))) & (generous(X0) | kind(X0) | happy(X0) | humble(X0))) [flattening 39]
76. generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 36]
77. ~happy(X0) | generous(X0) | ~funny(X0) [cnf transformation 36]
78. ~generous(X0) | happy(X0) | funny(X0) [cnf transformation 36]
79. ~generous(X0) | happy(X0) | ~funny(X0) [cnf transformation 36]
83. generous(X0) | kind(X0) | happy(X0) | humble(X0) [cnf transformation 40]
87. ~happy(X0) | ~generous(X0) [cnf transformation 40]
111. kind(X0) | happy(X0) | funny(X0) [cnf transformation 31]
118. ~humble(X0) | ~funny(X0) [cnf transformation 34]
131. ~kind(fred) [cnf transformation 22]
133. ~generous(X0) | happy(X0) [subsumption resolution 78,79]
134. ~happy(X0) | generous(X0) [subsumption resolution 76,77]
148. ~generous(X0) [subsumption resolution 87,133]
149. humble(X0) | happy(X0) | kind(X0) [subsumption resolution 83,148]
292. 31 <=> happy(fred) [avatar definition]
294. happy(fred) <- (31) [avatar component clause 292]
326. happy(X1) | kind(X1) | ~funny(X1) [resolution 149,118]
330. kind(X1) | happy(X1) [subsumption resolution 326,111]
331. happy(fred) [resolution 330,131]
333. 31 [avatar split clause 331,292]
335. generous(fred) <- (31) [resolution 294,134]
339. $false <- (31) [subsumption resolution 335,148]
340. ~31 [avatar contradiction clause 339]
341. $false [avatar sat refutation 333,340]
% SZS output end Proof for 5247188397431036195615531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not old is both old and curious.
If someone is humble or rich then mary is wise and vice versa.
Everyone who is either not kind or happy is brave.
Everyone who is calm is brave or not strong and vice versa.
If john is both happy and funny then someone is strong or not generous and vice versa.
Everyone who is not strong or kind is both old and happy and vice versa.
Everyone who is not humble or not happy is funny and vice versa.
If lucy is either tall or not creative then susan is calm.
If someone is creative or not kind then someone is patient or generous and vice versa.
Everyone who is either not calm or happy is both calm and wise and vice versa.
Everyone who is not happy is either not curious or not kind and vice versa.
Everyone who is calm is not calm or wise and vice versa.
If alice is brave or curious then someone is both creative and tall.
If someone is either old or wise then john is humble and vice versa.
Everyone who is both kind and not quiet is old or not patient and vice versa.
If someone is either tall or wise then someone is either not strong or not quiet.
Mary is brave or funny.
Someone is either not strong or not brave.
Someone is not patient or strong.
Someone is both funny and not creative.
John is either not strong or creative.
Mary is not curious or funny. | Mary is not old. | contradiction | (![X]:((humble(X)<~>~old(X))=>(old(X)&curious(X))))&
((?[X]:((humble(X)|rich(X))))<=>(wise(mary)))&
(![X]:((~kind(X)<~>happy(X))=>brave(X)))&
(![X]:(calm(X)<=>(brave(X)|~strong(X))))&
(((happy(john)&funny(john)))<=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((~strong(X)|kind(X))<=>(old(X)&happy(X))))&
(![X]:((~humble(X)|~happy(X))<=>funny(X)))&
(((tall(lucy)<~>~creative(lucy)))=>(calm(susan)))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~calm(X)<~>happy(X))<=>(calm(X)&wise(X))))&
(![X]:(~happy(X)<=>(~curious(X)<~>~kind(X))))&
(![X]:(calm(X)<=>(~calm(X)|wise(X))))&
(((brave(alice)|curious(alice)))=>(?[X]:((creative(X)&tall(X)))))&
((?[X]:((old(X)<~>wise(X))))<=>(humble(john)))&
(![X]:((kind(X)&~quiet(X))<=>(old(X)|~patient(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((brave(mary)|funny(mary)))&
(?[X]:((~strong(X)<~>~brave(X))))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((funny(X)&~creative(X))))&
((~strong(john)<~>creative(john)))&
((~curious(mary)|funny(mary))) | ~old(mary) | [
"p4",
"p5",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3637236363664439552966680
% SZS output start Proof for 3637236363664439552966680
5. (funny(john) & happy(john)) <=> ? [X0] : (~generous(X0) | strong(X0)) [input p4]
6. ! [X0] : ((kind(X0) | ~strong(X0)) <=> (happy(X0) & old(X0))) [input p5]
7. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> funny(X0)) [input p6]
12. ! [X0] : (calm(X0) <=> (wise(X0) | ~calm(X0))) [input p11]
14. ? [X0] : (old(X0) <~> wise(X0)) <=> humble(john) [input p13]
23. ~old(mary) [input hypothesis]
39. ((funny(john) & happy(john)) | ! [X0] : (generous(X0) & ~strong(X0))) & (? [X0] : (~generous(X0) | strong(X0)) | (~funny(john) | ~happy(john))) [nnf transformation 5]
40. ((funny(john) & happy(john)) | ! [X0] : (generous(X0) & ~strong(X0))) & (? [X0] : (~generous(X0) | strong(X0)) | ~funny(john) | ~happy(john)) [flattening 39]
41. ((funny(john) & happy(john)) | ! [X0] : (generous(X0) & ~strong(X0))) & (? [X1] : (~generous(X1) | strong(X1)) | ~funny(john) | ~happy(john)) [rectify 40]
42. ? [X1] : (~generous(X1) | strong(X1)) => (~generous(sK1) | strong(sK1)) [choice axiom]
43. ((funny(john) & happy(john)) | ! [X0] : (generous(X0) & ~strong(X0))) & ((~generous(sK1) | strong(sK1)) | ~funny(john) | ~happy(john)) [skolemisation 41,42]
44. ! [X0] : (((kind(X0) | ~strong(X0)) | (~happy(X0) | ~old(X0))) & ((happy(X0) & old(X0)) | (~kind(X0) & strong(X0)))) [nnf transformation 6]
45. ! [X0] : ((kind(X0) | ~strong(X0) | ~happy(X0) | ~old(X0)) & ((happy(X0) & old(X0)) | (~kind(X0) & strong(X0)))) [flattening 44]
46. ! [X0] : (((~happy(X0) | ~humble(X0)) | ~funny(X0)) & (funny(X0) | (happy(X0) & humble(X0)))) [nnf transformation 7]
47. ! [X0] : ((~happy(X0) | ~humble(X0) | ~funny(X0)) & (funny(X0) | (happy(X0) & humble(X0)))) [flattening 46]
57. ! [X0] : ((calm(X0) | (~wise(X0) & calm(X0))) & ((wise(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 12]
58. ! [X0] : ((calm(X0) | (~wise(X0) & calm(X0))) & (wise(X0) | ~calm(X0) | ~calm(X0))) [flattening 57]
61. (? [X0] : ((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | ~humble(john)) & (humble(john) | ! [X0] : ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0)))) [nnf transformation 14]
62. (? [X0] : ((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | ~humble(john)) & (humble(john) | ! [X1] : ((old(X1) | ~wise(X1)) & (wise(X1) | ~old(X1)))) [rectify 61]
63. ? [X0] : ((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) => ((~wise(sK5) | ~old(sK5)) & (wise(sK5) | old(sK5))) [choice axiom]
64. (((~wise(sK5) | ~old(sK5)) & (wise(sK5) | old(sK5))) | ~humble(john)) & (humble(john) | ! [X1] : ((old(X1) | ~wise(X1)) & (wise(X1) | ~old(X1)))) [skolemisation 62,63]
92. happy(john) | ~strong(X0) [cnf transformation 43]
94. funny(john) | ~strong(X0) [cnf transformation 43]
96. strong(X0) | old(X0) [cnf transformation 45]
103. ~funny(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 47]
120. wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 58]
121. calm(X0) | calm(X0) [cnf transformation 58]
128. humble(john) | old(X1) | ~wise(X1) [cnf transformation 64]
149. ~old(mary) [cnf transformation 23]
150. wise(X0) | ~calm(X0) [duplicate literal removal 120]
151. calm(X0) [duplicate literal removal 121]
180. 7 <=> funny(john) [avatar definition]
182. funny(john) <- (7) [avatar component clause 180]
185. 8 <=> ! [X0] : ~strong(X0) [avatar definition]
186. ~strong(X0) <- (8) [avatar component clause 185]
187. 8 | 7 [avatar split clause 94,180,185]
189. 9 <=> happy(john) [avatar definition]
191. happy(john) <- (9) [avatar component clause 189]
193. 8 | 9 [avatar split clause 92,189,185]
251. wise(X0) [subsumption resolution 150,151]
274. 27 <=> humble(john) [avatar definition]
275. humble(john) <- (27) [avatar component clause 274]
282. humble(john) | old(X1) [subsumption resolution 128,251]
284. 29 <=> ! [X1] : old(X1) [avatar definition]
285. old(X1) <- (29) [avatar component clause 284]
286. 29 | 27 [avatar split clause 282,274,284]
353. $false <- (29) [resolution 285,149]
356. ~29 [avatar contradiction clause 353]
363. old(X0) <- (8) [resolution 96,186]
365. 29 | ~8 [avatar split clause 363,185,284]
416. ~humble(john) | ~happy(john) <- (7) [resolution 103,182]
428. ~happy(john) <- (7, 27) [subsumption resolution 416,275]
429. $false <- (7, 9, 27) [subsumption resolution 428,191]
430. ~7 | ~9 | ~27 [avatar contradiction clause 429]
431. $false [avatar sat refutation 187,193,286,356,365,430]
% SZS output end Proof for 3637236363664439552966680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or not funny then mary is either calm or generous.
Everyone who is not brave or not happy is not old or not tall.
Everyone who is strong is patient or not curious.
Everyone who is not humble is creative and vice versa.
Everyone who is rich is either calm or not wise.
If alice is not patient then someone is both not rich and not generous.
If someone is funny then someone is not old or patient.
Everyone who is not patient is both rich and not funny.
If someone is either not creative or not funny then susan is not brave and vice versa.
If someone is both not wise and not patient then someone is not calm or not strong.
Everyone who is not happy is both brave and not brave and vice versa.
If someone is both old and curious then someone is calm.
Everyone who is humble is not rich and vice versa.
If paul is either strong or not rich then john is either not calm or happy.
Everyone who is both not generous and not happy is strong or kind and vice versa.
If someone is not rich or brave then lucy is both calm and patient.
Paul is either kind or not humble.
Alice is both tall and brave.
Paul is curious or not calm.
Someone is both not creative and not rich.
Someone is either patient or generous.
Alice is not quiet.
Someone is either not wise or not curious. | Lucy is not strong. | entailment | ((?[X]:((old(X)<~>~funny(X))))=>((calm(mary)<~>generous(mary))))&
(![X]:((~brave(X)|~happy(X))=>(~old(X)|~tall(X))))&
(![X]:(strong(X)=>(patient(X)|~curious(X))))&
(![X]:(~humble(X)<=>creative(X)))&
(![X]:(rich(X)=>(calm(X)<~>~wise(X))))&
((~patient(alice))=>(?[X]:((~rich(X)&~generous(X)))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)|patient(X)))))&
(![X]:(~patient(X)=>(rich(X)&~funny(X))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(~brave(susan)))&
((?[X]:((~wise(X)&~patient(X))))=>(?[X]:((~calm(X)|~strong(X)))))&
(![X]:(~happy(X)<=>(brave(X)&~brave(X))))&
((?[X]:((old(X)&curious(X))))=>(?[X]:(calm(X))))&
(![X]:(humble(X)<=>~rich(X)))&
(((strong(paul)<~>~rich(paul)))=>((~calm(john)<~>happy(john))))&
(![X]:((~generous(X)&~happy(X))<=>(strong(X)|kind(X))))&
((?[X]:((~rich(X)|brave(X))))=>((calm(lucy)&patient(lucy))))&
((kind(paul)<~>~humble(paul)))&
((tall(alice)&brave(alice)))&
((curious(paul)|~calm(paul)))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:((patient(X)<~>generous(X))))&
(~quiet(alice))&
(?[X]:((~wise(X)<~>~curious(X)))) | ~strong(lucy) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4593868232177960356947009
% SZS output start Proof for 4593868232177960356947009
11. ! [X0] : (~happy(X0) <=> (~brave(X0) & brave(X0))) [input p10]
15. ! [X0] : ((~happy(X0) & ~generous(X0)) <=> (kind(X0) | strong(X0))) [input p14]
24. strong(lucy) [input hypothesis]
57. ! [X0] : ((~happy(X0) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | happy(X0))) [nnf transformation 11]
58. ! [X0] : ((~happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | happy(X0))) [flattening 57]
64. ! [X0] : (((~happy(X0) & ~generous(X0)) | (~kind(X0) & ~strong(X0))) & ((kind(X0) | strong(X0)) | (happy(X0) | generous(X0)))) [nnf transformation 15]
65. ! [X0] : (((~happy(X0) & ~generous(X0)) | (~kind(X0) & ~strong(X0))) & (kind(X0) | strong(X0) | happy(X0) | generous(X0))) [flattening 64]
96. brave(X0) | happy(X0) [cnf transformation 58]
97. ~brave(X0) | happy(X0) [cnf transformation 58]
109. ~happy(X0) | ~strong(X0) [cnf transformation 65]
126. strong(lucy) [cnf transformation 24]
205. happy(X0) [subsumption resolution 96,97]
231. ~strong(X0) [subsumption resolution 109,205]
280. $false [subsumption resolution 126,231]
% SZS output end Proof for 4593868232177960356947009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not brave is either patient or not humble.
Everyone who is not rich or strong is both calm and quiet.
Everyone who is both old and creative is either not tall or tall and vice versa.
Everyone who is either not kind or not humble is quiet and vice versa.
Everyone who is brave is both curious and not generous.
Everyone who is funny or not brave is either old or not brave.
If someone is not wise or humble then someone is creative.
If someone is both not tall and not creative then someone is either wise or happy.
Everyone who is both curious and not humble is either not wise or rich.
Everyone who is both not wise and old is not old or generous.
Everyone who is either quiet or kind is rich and vice versa.
If someone is not happy or not old then someone is both not generous and kind and vice versa.
If someone is tall then paul is either wise or old and vice versa.
If someone is either kind or quiet then lucy is not funny or wise.
Everyone who is rich is either calm or tall and vice versa.
Someone is not brave or old.
Alice is both not quiet and not generous.
Someone is either not generous or not kind.
Someone is funny.
Someone is either patient or quiet. | Alice is tall. | contradiction | (![X]:((rich(X)|~brave(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)|strong(X))=>(calm(X)&quiet(X))))&
(![X]:((old(X)&creative(X))<=>(~tall(X)<~>tall(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>quiet(X)))&
(![X]:(brave(X)=>(curious(X)&~generous(X))))&
(![X]:((funny(X)|~brave(X))=>(old(X)<~>~brave(X))))&
((?[X]:((~wise(X)|humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~tall(X)&~creative(X))))=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((curious(X)&~humble(X))=>(~wise(X)<~>rich(X))))&
(![X]:((~wise(X)&old(X))=>(~old(X)|generous(X))))&
(![X]:((quiet(X)<~>kind(X))<=>rich(X)))&
((?[X]:((~happy(X)|~old(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
((?[X]:(tall(X)))<=>((wise(paul)<~>old(paul))))&
((?[X]:((kind(X)<~>quiet(X))))=>((~funny(lucy)|wise(lucy))))&
(![X]:(rich(X)<=>(calm(X)<~>tall(X))))&
(?[X]:((~brave(X)|old(X))))&
((~quiet(alice)&~generous(alice)))&
(?[X]:((~generous(X)<~>~kind(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)<~>quiet(X)))) | tall(alice) | [
"p2",
"p4",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3446853367653253219332079
% SZS output start Proof for 3446853367653253219332079
3. ! [X0] : ((creative(X0) & old(X0)) <=> (~tall(X0) <~> tall(X0))) [input p2]
5. ! [X0] : (brave(X0) => (~generous(X0) & curious(X0))) [input p4]
6. ! [X0] : ((~brave(X0) | funny(X0)) => (old(X0) <~> ~brave(X0))) [input p5]
10. ! [X0] : ((old(X0) & ~wise(X0)) => (generous(X0) | ~old(X0))) [input p9]
13. ? [X0] : tall(X0) <=> (wise(paul) <~> old(paul)) [input p12]
21. tall(alice) [input hypothesis]
28. ! [X0] : ((~generous(X0) & curious(X0)) | ~brave(X0)) [ennf transformation 5]
29. ! [X0] : ((old(X0) <~> ~brave(X0)) | (brave(X0) & ~funny(X0))) [ennf transformation 6]
34. ! [X0] : ((generous(X0) | ~old(X0)) | (~old(X0) | wise(X0))) [ennf transformation 10]
35. ! [X0] : (generous(X0) | ~old(X0) | ~old(X0) | wise(X0)) [flattening 34]
39. ! [X0] : (((creative(X0) & old(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | (~creative(X0) | ~old(X0)))) [nnf transformation 3]
40. ! [X0] : (((creative(X0) & old(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ~creative(X0) | ~old(X0))) [flattening 39]
42. ! [X0] : (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | (brave(X0) & ~funny(X0))) [nnf transformation 29]
57. (? [X0] : tall(X0) | ((wise(paul) | ~old(paul)) & (old(paul) | ~wise(paul)))) & (((~old(paul) | ~wise(paul)) & (old(paul) | wise(paul))) | ! [X0] : ~tall(X0)) [nnf transformation 13]
58. (? [X0] : tall(X0) | ((wise(paul) | ~old(paul)) & (old(paul) | ~wise(paul)))) & (((~old(paul) | ~wise(paul)) & (old(paul) | wise(paul))) | ! [X1] : ~tall(X1)) [rectify 57]
59. ? [X0] : tall(X0) => tall(sK4) [choice axiom]
60. (tall(sK4) | ((wise(paul) | ~old(paul)) & (old(paul) | ~wise(paul)))) & (((~old(paul) | ~wise(paul)) & (old(paul) | wise(paul))) | ! [X1] : ~tall(X1)) [skolemisation 58,59]
81. old(X0) | tall(X0) | tall(X0) [cnf transformation 40]
82. old(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 40]
90. ~generous(X0) | ~brave(X0) [cnf transformation 28]
94. brave(X0) | ~old(X0) | brave(X0) [cnf transformation 42]
101. generous(X0) | ~old(X0) | ~old(X0) | wise(X0) [cnf transformation 35]
112. ~old(paul) | ~wise(paul) | ~tall(X1) [cnf transformation 60]
129. tall(alice) [cnf transformation 21]
130. generous(X0) | ~old(X0) | wise(X0) [duplicate literal removal 101]
131. brave(X0) | ~old(X0) [duplicate literal removal 94]
132. old(X0) | tall(X0) [duplicate literal removal 81]
133. ~tall(X0) | old(X0) [duplicate literal removal 82]
137. old(X0) [subsumption resolution 132,133]
138. brave(X0) [subsumption resolution 131,137]
139. wise(X0) | generous(X0) [subsumption resolution 130,137]
166. 6 <=> wise(paul) [avatar definition]
167. ~wise(paul) <- (~6) [avatar component clause 166]
174. ~wise(paul) | ~tall(X1) [subsumption resolution 112,137]
176. 8 <=> ! [X1] : ~tall(X1) [avatar definition]
177. ~tall(X1) <- (8) [avatar component clause 176]
178. 8 | ~6 [avatar split clause 174,166,176]
231. generous(paul) <- (~6) [resolution 139,167]
232. ~brave(paul) <- (~6) [resolution 231,90]
233. $false <- (~6) [subsumption resolution 232,138]
234. 6 [avatar contradiction clause 233]
235. $false <- (8) [resolution 177,129]
238. ~8 [avatar contradiction clause 235]
239. $false [avatar sat refutation 178,234,238]
% SZS output end Proof for 3446853367653253219332079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not wise.
If someone is either not patient or old then someone is not rich and vice versa.
Everyone who is either not brave or kind is either patient or generous and vice versa.
If someone is either brave or not brave then fred is either not patient or rich and vice versa.
If susan is either not brave or not wise then john is both not humble and humble.
Everyone who is both old and calm is either not rich or strong.
If someone is not tall or not creative then someone is both not patient and not old and vice versa.
If john is both strong and patient then someone is not calm or not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Everyone who is not tall or not quiet is not old or generous.
John is not funny.
John is not old.
Someone is patient.
Someone is either not strong or not wise. | Alice is generous. | contradiction | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(patient(X)<~>generous(X))))&
((?[X]:((brave(X)<~>~brave(X))))<=>((~patient(fred)<~>rich(fred))))&
(((~brave(susan)<~>~wise(susan)))=>((~humble(john)&humble(john))))&
(![X]:((old(X)&calm(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(~funny(john))&
(~old(john))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)<~>~wise(X)))) | generous(alice) | [
"p0",
"p1",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2445321386826730055470178
% SZS output start Proof for 2445321386826730055470178
1. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (rich(X0) & wise(X0))) [input p0]
2. ~creative(alice) <=> ? [X0] : generous(X0) [input p1]
4. ? [X0] : (~patient(X0) <~> old(X0)) <=> ? [X0] : ~rich(X0) [input p3]
9. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X0] : (~old(X0) & ~patient(X0)) [input p8]
21. generous(alice) [input hypothesis]
22. ? [X0] : (~patient(X0) <~> old(X0)) <=> ? [X1] : ~rich(X1) [rectify 4]
23. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X1] : (~old(X1) & ~patient(X1)) [rectify 9]
35. ! [X0] : (((strong(X0) | ~strong(X0)) | (~rich(X0) | ~wise(X0))) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((strong(X0) | ~strong(X0) | ~rich(X0) | ~wise(X0)) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [flattening 35]
37. (~creative(alice) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | creative(alice)) [nnf transformation 2]
38. (~creative(alice) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | creative(alice)) [rectify 37]
39. ? [X1] : generous(X1) => generous(sK0) [choice axiom]
40. (~creative(alice) | ! [X0] : ~generous(X0)) & (generous(sK0) | creative(alice)) [skolemisation 38,39]
41. (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) [nnf transformation 22]
42. (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : ((~patient(X3) | ~old(X3)) & (old(X3) | patient(X3)))) [rectify 41]
43. ? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) => ((~old(sK1) | patient(sK1)) & (old(sK1) | ~patient(sK1))) [choice axiom]
44. ? [X2] : ~rich(X2) => ~rich(sK2) [choice axiom]
45. (((~old(sK1) | patient(sK1)) & (old(sK1) | ~patient(sK1))) | ! [X1] : rich(X1)) & (~rich(sK2) | ! [X3] : ((~patient(X3) | ~old(X3)) & (old(X3) | patient(X3)))) [skolemisation 42,44,43]
53. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (old(X1) | patient(X1))) & (? [X1] : (~old(X1) & ~patient(X1)) | ! [X0] : (creative(X0) & tall(X0))) [nnf transformation 23]
54. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (old(X1) | patient(X1))) & (? [X2] : (~old(X2) & ~patient(X2)) | ! [X3] : (creative(X3) & tall(X3))) [rectify 53]
55. ? [X0] : (~creative(X0) | ~tall(X0)) => (~creative(sK4) | ~tall(sK4)) [choice axiom]
56. ? [X2] : (~old(X2) & ~patient(X2)) => (~old(sK5) & ~patient(sK5)) [choice axiom]
57. ((~creative(sK4) | ~tall(sK4)) | ! [X1] : (old(X1) | patient(X1))) & ((~old(sK5) & ~patient(sK5)) | ! [X3] : (creative(X3) & tall(X3))) [skolemisation 54,56,55]
80. rich(X0) | strong(X0) [cnf transformation 36]
81. ~strong(X0) | rich(X0) [cnf transformation 36]
84. ~creative(alice) | ~generous(X0) [cnf transformation 40]
86. ~rich(sK2) | old(X3) | patient(X3) [cnf transformation 45]
113. ~patient(sK5) | creative(X3) [cnf transformation 57]
115. ~old(sK5) | creative(X3) [cnf transformation 57]
140. generous(alice) [cnf transformation 21]
145. rich(X0) [subsumption resolution 80,81]
148. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
149. ~generous(X0) <- (1) [avatar component clause 148]
151. 2 <=> creative(alice) [avatar definition]
153. ~creative(alice) <- (~2) [avatar component clause 151]
154. 1 | ~2 [avatar split clause 84,151,148]
162. old(X3) | patient(X3) [subsumption resolution 86,145]
191. 9 <=> ! [X3] : creative(X3) [avatar definition]
192. creative(X3) <- (9) [avatar component clause 191]
194. 10 <=> old(sK5) [avatar definition]
196. ~old(sK5) <- (~10) [avatar component clause 194]
197. 9 | ~10 [avatar split clause 115,194,191]
203. 12 <=> patient(sK5) [avatar definition]
205. ~patient(sK5) <- (~12) [avatar component clause 203]
206. 9 | ~12 [avatar split clause 113,203,191]
284. patient(sK5) <- (~10) [resolution 162,196]
287. $false <- (~10, ~12) [subsumption resolution 284,205]
288. 10 | 12 [avatar contradiction clause 287]
289. $false <- (~2, 9) [resolution 192,153]
290. 2 | ~9 [avatar contradiction clause 289]
291. $false <- (1) [resolution 149,140]
294. ~1 [avatar contradiction clause 291]
295. $false [avatar sat refutation 154,197,206,288,290,294]
% SZS output end Proof for 2445321386826730055470178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is happy and vice versa.
If someone is both happy and funny then mary is either humble or not creative and vice versa.
If mary is both not funny and not brave then fred is not wise or brave.
Everyone who is either not funny or patient is both kind and not curious.
If someone is both not wise and generous then someone is not brave and vice versa.
Everyone who is not calm or not wise is not generous or not happy and vice versa.
If someone is both humble and old then someone is either curious or not old.
Everyone who is not calm is both calm and not calm and vice versa.
Everyone who is not brave or not patient is not wise.
Everyone who is either not quiet or humble is either not humble or wise.
Everyone who is both not funny and not old is wise or old.
Everyone who is not kind or not curious is not happy and vice versa.
If someone is either not humble or not generous then fred is either tall or calm and vice versa.
Everyone who is not calm or not rich is tall or humble and vice versa.
Everyone who is both not curious and tall is not kind.
Everyone who is either not creative or old is creative or funny.
Someone is wise or not wise.
Someone is both not creative and not patient.
Someone is funny or curious.
John is strong or not creative.
Paul is either not humble or not wise.
John is wise.
Susan is both curious and funny.
Someone is not quiet or funny. | Fred is calm. | entailment | (![X]:(~humble(X)<=>happy(X)))&
((?[X]:((happy(X)&funny(X))))<=>((humble(mary)<~>~creative(mary))))&
(((~funny(mary)&~brave(mary)))=>((~wise(fred)|brave(fred))))&
(![X]:((~funny(X)<~>patient(X))=>(kind(X)&~curious(X))))&
((?[X]:((~wise(X)&generous(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~calm(X)|~wise(X))<=>(~generous(X)|~happy(X))))&
((?[X]:((humble(X)&old(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:(~calm(X)<=>(calm(X)&~calm(X))))&
(![X]:((~brave(X)|~patient(X))=>~wise(X)))&
(![X]:((~quiet(X)<~>humble(X))=>(~humble(X)<~>wise(X))))&
(![X]:((~funny(X)&~old(X))=>(wise(X)|old(X))))&
(![X]:((~kind(X)|~curious(X))<=>~happy(X)))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~calm(X)|~rich(X))<=>(tall(X)|humble(X))))&
(![X]:((~curious(X)&tall(X))=>~kind(X)))&
(![X]:((~creative(X)<~>old(X))=>(creative(X)|funny(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((~creative(X)&~patient(X))))&
(?[X]:((funny(X)|curious(X))))&
((strong(john)|~creative(john)))&
((~humble(paul)<~>~wise(paul)))&
(wise(john))&
((curious(susan)&funny(susan)))&
(?[X]:((~quiet(X)|funny(X)))) | calm(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 228207453943447123536021
% SZS output start Proof for 228207453943447123536021
8. ! [X0] : (~calm(X0) <=> (~calm(X0) & calm(X0))) [input p7]
25. ~calm(fred) [input hypothesis]
58. ! [X0] : ((~calm(X0) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | calm(X0))) [nnf transformation 8]
59. ! [X0] : ((~calm(X0) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | calm(X0))) [flattening 58]
101. calm(X0) | calm(X0) [cnf transformation 59]
139. ~calm(fred) [cnf transformation 25]
144. calm(X0) [duplicate literal removal 101]
278. $false [subsumption resolution 139,144]
% SZS output end Proof for 228207453943447123536021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not old then fred is not calm or not humble and vice versa.
Everyone who is not calm is not creative.
If someone is both kind and strong then paul is not creative and vice versa.
Everyone who is brave or happy is either not kind or curious and vice versa.
If someone is either not quiet or humble then someone is not curious and vice versa.
If someone is both brave and not funny then someone is funny and vice versa.
Everyone who is either not generous or tall is either not calm or not old.
If someone is not quiet or not generous then alice is not quiet and vice versa.
Everyone who is brave is either kind or creative.
If susan is not creative or quiet then someone is either not calm or curious.
If someone is not creative then john is old and vice versa.
Everyone who is not old is not wise or old.
If someone is either not calm or not tall then someone is either not creative or creative and vice versa.
Everyone who is calm or rich is both not patient and quiet and vice versa.
Everyone who is calm is not strong and vice versa.
Everyone who is either quiet or creative is not curious and vice versa.
Someone is either not brave or not humble.
Someone is either not creative or not wise.
Someone is not generous.
Someone is either not patient or not wise.
Someone is either patient or not humble.
Susan is not strong or not curious.
Paul is either not calm or not tall. | Susan is not quiet. | contradiction | ((~old(susan))<=>((~calm(fred)|~humble(fred))))&
(![X]:(~calm(X)=>~creative(X)))&
((?[X]:((kind(X)&strong(X))))<=>(~creative(paul)))&
(![X]:((brave(X)|happy(X))<=>(~kind(X)<~>curious(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)&~funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~generous(X)<~>tall(X))=>(~calm(X)<~>~old(X))))&
((?[X]:((~quiet(X)|~generous(X))))<=>(~quiet(alice)))&
(![X]:(brave(X)=>(kind(X)<~>creative(X))))&
(((~creative(susan)|quiet(susan)))=>(?[X]:((~calm(X)<~>curious(X)))))&
((?[X]:(~creative(X)))<=>(old(john)))&
(![X]:(~old(X)=>(~wise(X)|old(X))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:((calm(X)|rich(X))<=>(~patient(X)&quiet(X))))&
(![X]:(calm(X)<=>~strong(X)))&
(![X]:((quiet(X)<~>creative(X))<=>~curious(X)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((patient(X)<~>~humble(X))))&
((~strong(susan)|~curious(susan)))&
((~calm(paul)<~>~tall(paul))) | ~quiet(susan) | [
"p1",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5506863752038205515666391
% SZS output start Proof for 5506863752038205515666391
2. ! [X0] : (~calm(X0) => ~creative(X0)) [input p1]
14. ! [X0] : ((rich(X0) | calm(X0)) <=> (quiet(X0) & ~patient(X0))) [input p13]
15. ! [X0] : (calm(X0) <=> ~strong(X0)) [input p14]
16. ! [X0] : ((quiet(X0) <~> creative(X0)) <=> ~curious(X0)) [input p15]
22. ~curious(susan) | ~strong(susan) [input p21]
24. ~quiet(susan) [input hypothesis]
28. ! [X0] : (~creative(X0) | calm(X0)) [ennf transformation 2]
70. ! [X0] : (((rich(X0) | calm(X0)) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 14]
71. ! [X0] : ((rich(X0) | calm(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 70]
72. ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))) [nnf transformation 15]
73. ! [X0] : ((((~creative(X0) | ~quiet(X0)) & (creative(X0) | quiet(X0))) | curious(X0)) & (~curious(X0) | ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))))) [nnf transformation 16]
92. ~creative(X0) | calm(X0) [cnf transformation 28]
135. ~calm(X0) | quiet(X0) [cnf transformation 71]
138. ~strong(X0) | ~calm(X0) [cnf transformation 72]
139. strong(X0) | calm(X0) [cnf transformation 72]
142. quiet(X0) | creative(X0) | curious(X0) [cnf transformation 73]
153. ~curious(susan) | ~strong(susan) [cnf transformation 22]
156. ~quiet(susan) [cnf transformation 24]
263. 24 <=> quiet(susan) [avatar definition]
265. ~quiet(susan) <- (~24) [avatar component clause 263]
276. 27 <=> creative(susan) [avatar definition]
278. creative(susan) <- (27) [avatar component clause 276]
351. 42 <=> strong(susan) [avatar definition]
352. strong(susan) <- (42) [avatar component clause 351]
353. ~strong(susan) <- (~42) [avatar component clause 351]
355. 43 <=> curious(susan) [avatar definition]
357. ~curious(susan) <- (~43) [avatar component clause 355]
358. ~42 | ~43 [avatar split clause 153,355,351]
369. ~24 [avatar split clause 156,263]
397. calm(susan) <- (~42) [resolution 139,353]
430. quiet(susan) <- (~42) [resolution 397,135]
431. $false <- (~24, ~42) [subsumption resolution 430,265]
432. 24 | 42 [avatar contradiction clause 431]
433. ~calm(susan) <- (42) [resolution 352,138]
473. creative(susan) | curious(susan) <- (~24) [resolution 142,265]
477. creative(susan) <- (~24, ~43) [subsumption resolution 473,357]
478. 27 | 24 | 43 [avatar split clause 477,355,263,276]
497. calm(susan) <- (27) [resolution 278,92]
498. $false <- (27, 42) [subsumption resolution 497,433]
499. ~27 | ~42 [avatar contradiction clause 498]
500. $false [avatar sat refutation 358,369,432,478,499]
% SZS output end Proof for 5506863752038205515666391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is creative then someone is not strong and vice versa.
If paul is either tall or not old then someone is not curious or kind and vice versa.
If paul is both not funny and not calm then mary is either not curious or strong.
Everyone who is funny is creative and vice versa.
Everyone who is rich or not rich is both wise and tall and vice versa.
If someone is patient then someone is either not strong or not calm and vice versa.
If lucy is funny then someone is curious.
If someone is wise then someone is both not curious and not funny and vice versa.
Everyone who is either not happy or not kind is both not kind and rich.
Everyone who is either quiet or happy is old or not quiet.
Everyone who is either old or not generous is strong and vice versa.
If lucy is either rich or not curious then alice is either not rich or not creative.
If someone is either not happy or not humble then paul is patient.
Everyone who is both strong and happy is not happy.
Everyone who is both not old and not tall is not quiet.
Everyone who is calm or kind is either not patient or funny and vice versa.
Fred is generous.
Fred is both not brave and not humble.
Someone is either not calm or not humble.
Someone is generous.
Lucy is both not humble and not kind.
Alice is brave or wise.
Lucy is either strong or brave.
Alice is either not generous or not humble. | Alice is not wise. | contradiction | ((creative(susan))<=>(?[X]:(~strong(X))))&
(((tall(paul)<~>~old(paul)))<=>(?[X]:((~curious(X)|kind(X)))))&
(((~funny(paul)&~calm(paul)))=>((~curious(mary)<~>strong(mary))))&
(![X]:(funny(X)<=>creative(X)))&
(![X]:((rich(X)|~rich(X))<=>(wise(X)&tall(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
((funny(lucy))=>(?[X]:(curious(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>(~kind(X)&rich(X))))&
(![X]:((quiet(X)<~>happy(X))=>(old(X)|~quiet(X))))&
(![X]:((old(X)<~>~generous(X))<=>strong(X)))&
(((rich(lucy)<~>~curious(lucy)))=>((~rich(alice)<~>~creative(alice))))&
((?[X]:((~happy(X)<~>~humble(X))))=>(patient(paul)))&
(![X]:((strong(X)&happy(X))=>~happy(X)))&
(![X]:((~old(X)&~tall(X))=>~quiet(X)))&
(![X]:((calm(X)|kind(X))<=>(~patient(X)<~>funny(X))))&
(generous(fred))&
((~brave(fred)&~humble(fred)))&
(?[X]:((~calm(X)<~>~humble(X))))&
(?[X]:(generous(X)))&
((~humble(lucy)&~kind(lucy)))&
((brave(alice)|wise(alice)))&
((strong(lucy)<~>brave(lucy)))&
((~generous(alice)<~>~humble(alice))) | ~wise(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8111907260090456936331237
% SZS output start Proof for 8111907260090456936331237
5. ! [X0] : ((~rich(X0) | rich(X0)) <=> (tall(X0) & wise(X0))) [input p4]
25. ~wise(alice) [input hypothesis]
50. ! [X0] : (((~rich(X0) | rich(X0)) | (~tall(X0) | ~wise(X0))) & ((tall(X0) & wise(X0)) | (rich(X0) & ~rich(X0)))) [nnf transformation 5]
51. ! [X0] : ((~rich(X0) | rich(X0) | ~tall(X0) | ~wise(X0)) & ((tall(X0) & wise(X0)) | (rich(X0) & ~rich(X0)))) [flattening 50]
90. wise(X0) | ~rich(X0) [cnf transformation 51]
91. wise(X0) | rich(X0) [cnf transformation 51]
140. ~wise(alice) [cnf transformation 25]
204. wise(X0) [subsumption resolution 90,91]
303. $false [subsumption resolution 140,204]
% SZS output end Proof for 8111907260090456936331237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is humble then someone is both patient and kind.
If paul is both not patient and kind then susan is either not tall or not patient and vice versa.
Everyone who is funny or not curious is funny and vice versa.
If someone is calm then someone is patient and vice versa.
Everyone who is both not patient and wise is both not old and not kind and vice versa.
If someone is either calm or not patient then someone is not funny or kind.
Everyone who is not humble is both old and not creative and vice versa.
Everyone who is both rich and not brave is either not rich or not funny and vice versa.
If someone is old or not quiet then someone is both not brave and funny and vice versa.
If someone is either calm or quiet then someone is either kind or not old and vice versa.
Everyone who is not quiet or not calm is both not quiet and not strong and vice versa.
Everyone who is both not rich and generous is curious.
If someone is both not kind and tall then susan is creative and vice versa.
If someone is patient or strong then susan is either not patient or kind.
If john is not tall or strong then alice is both wise and brave.
Everyone who is both not funny and patient is both quiet and kind.
Someone is both strong and quiet.
Paul is both quiet and not patient.
Someone is both not happy and not curious.
John is either kind or tall.
Susan is either calm or not curious.
Lucy is not rich or not strong.
Fred is humble. | Paul is not wise. | entailment | ((humble(john))=>(?[X]:((patient(X)&kind(X)))))&
(((~patient(paul)&kind(paul)))<=>((~tall(susan)<~>~patient(susan))))&
(![X]:((funny(X)|~curious(X))<=>funny(X)))&
((?[X]:(calm(X)))<=>(?[X]:(patient(X))))&
(![X]:((~patient(X)&wise(X))<=>(~old(X)&~kind(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>(?[X]:((~funny(X)|kind(X)))))&
(![X]:(~humble(X)<=>(old(X)&~creative(X))))&
(![X]:((rich(X)&~brave(X))<=>(~rich(X)<~>~funny(X))))&
((?[X]:((old(X)|~quiet(X))))<=>(?[X]:((~brave(X)&funny(X)))))&
((?[X]:((calm(X)<~>quiet(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:((~quiet(X)|~calm(X))<=>(~quiet(X)&~strong(X))))&
(![X]:((~rich(X)&generous(X))=>curious(X)))&
((?[X]:((~kind(X)&tall(X))))<=>(creative(susan)))&
((?[X]:((patient(X)|strong(X))))=>((~patient(susan)<~>kind(susan))))&
(((~tall(john)|strong(john)))=>((wise(alice)&brave(alice))))&
(![X]:((~funny(X)&patient(X))=>(quiet(X)&kind(X))))&
(?[X]:((strong(X)&quiet(X))))&
((quiet(paul)&~patient(paul)))&
(?[X]:((~happy(X)&~curious(X))))&
((kind(john)<~>tall(john)))&
((calm(susan)<~>~curious(susan)))&
((~rich(lucy)|~strong(lucy)))&
(humble(fred)) | ~wise(paul) | [
"p4",
"p7",
"p8",
"p9",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9053953634755240271460493
% SZS output start Proof for 9053953634755240271460493
5. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (~kind(X0) & ~old(X0))) [input p4]
8. ! [X0] : ((~brave(X0) & rich(X0)) <=> (~rich(X0) <~> ~funny(X0))) [input p7]
9. ? [X0] : (~quiet(X0) | old(X0)) <=> ? [X0] : (funny(X0) & ~brave(X0)) [input p8]
10. ? [X0] : (calm(X0) <~> quiet(X0)) <=> ? [X0] : (kind(X0) <~> ~old(X0)) [input p9]
11. ! [X0] : ((~calm(X0) | ~quiet(X0)) <=> (~strong(X0) & ~quiet(X0))) [input p10]
18. ~patient(paul) & quiet(paul) [input p17]
24. wise(paul) [input hypothesis]
27. ? [X0] : (~quiet(X0) | old(X0)) <=> ? [X1] : (funny(X1) & ~brave(X1)) [rectify 9]
28. ? [X0] : (calm(X0) <~> quiet(X0)) <=> ? [X1] : (kind(X1) <~> ~old(X1)) [rectify 10]
48. ! [X0] : (((wise(X0) & ~patient(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~wise(X0) | patient(X0)))) [nnf transformation 5]
49. ! [X0] : (((wise(X0) & ~patient(X0)) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ~wise(X0) | patient(X0))) [flattening 48]
56. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (brave(X0) | ~rich(X0)))) [nnf transformation 8]
57. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | brave(X0) | ~rich(X0))) [flattening 56]
58. (? [X0] : (~quiet(X0) | old(X0)) | ! [X1] : (~funny(X1) | brave(X1))) & (? [X1] : (funny(X1) & ~brave(X1)) | ! [X0] : (quiet(X0) & ~old(X0))) [nnf transformation 27]
59. (? [X0] : (~quiet(X0) | old(X0)) | ! [X1] : (~funny(X1) | brave(X1))) & (? [X2] : (funny(X2) & ~brave(X2)) | ! [X3] : (quiet(X3) & ~old(X3))) [rectify 58]
60. ? [X0] : (~quiet(X0) | old(X0)) => (~quiet(sK4) | old(sK4)) [choice axiom]
61. ? [X2] : (funny(X2) & ~brave(X2)) => (funny(sK5) & ~brave(sK5)) [choice axiom]
62. ((~quiet(sK4) | old(sK4)) | ! [X1] : (~funny(X1) | brave(X1))) & ((funny(sK5) & ~brave(sK5)) | ! [X3] : (quiet(X3) & ~old(X3))) [skolemisation 59,61,60]
63. (? [X0] : ((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (? [X1] : ((old(X1) | ~kind(X1)) & (~old(X1) | kind(X1))) | ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0)))) [nnf transformation 28]
64. (? [X0] : ((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (? [X2] : ((old(X2) | ~kind(X2)) & (~old(X2) | kind(X2))) | ! [X3] : ((calm(X3) | ~quiet(X3)) & (quiet(X3) | ~calm(X3)))) [rectify 63]
65. ? [X0] : ((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) => ((~quiet(sK6) | ~calm(sK6)) & (quiet(sK6) | calm(sK6))) [choice axiom]
66. ? [X2] : ((old(X2) | ~kind(X2)) & (~old(X2) | kind(X2))) => ((old(sK7) | ~kind(sK7)) & (~old(sK7) | kind(sK7))) [choice axiom]
67. (((~quiet(sK6) | ~calm(sK6)) & (quiet(sK6) | calm(sK6))) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (((old(sK7) | ~kind(sK7)) & (~old(sK7) | kind(sK7))) | ! [X3] : ((calm(X3) | ~quiet(X3)) & (quiet(X3) | ~calm(X3)))) [skolemisation 64,66,65]
68. ! [X0] : (((~calm(X0) | ~quiet(X0)) | (strong(X0) | quiet(X0))) & ((~strong(X0) & ~quiet(X0)) | (calm(X0) & quiet(X0)))) [nnf transformation 11]
69. ! [X0] : ((~calm(X0) | ~quiet(X0) | strong(X0) | quiet(X0)) & ((~strong(X0) & ~quiet(X0)) | (calm(X0) & quiet(X0)))) [flattening 68]
95. ~wise(X0) | ~kind(X0) | patient(X0) [cnf transformation 49]
103. ~funny(X0) | ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 57]
105. rich(X0) | ~funny(X0) | rich(X0) [cnf transformation 57]
109. ~brave(sK5) | ~old(X3) [cnf transformation 62]
110. ~brave(sK5) | quiet(X3) [cnf transformation 62]
111. funny(sK5) | ~old(X3) [cnf transformation 62]
112. funny(sK5) | quiet(X3) [cnf transformation 62]
121. ~quiet(sK6) | ~calm(sK6) | kind(X1) | old(X1) [cnf transformation 67]
123. ~quiet(X0) | calm(X0) [cnf transformation 69]
143. ~patient(paul) [cnf transformation 18]
151. wise(paul) [cnf transformation 24]
152. ~funny(X0) | ~rich(X0) | brave(X0) [duplicate literal removal 103]
153. ~funny(X0) | rich(X0) [duplicate literal removal 105]
183. 7 <=> patient(paul) [avatar definition]
185. ~patient(paul) <- (~7) [avatar component clause 183]
222. ~funny(X0) | brave(X0) [subsumption resolution 152,153]
224. 16 <=> ! [X3] : quiet(X3) [avatar definition]
225. quiet(X3) <- (16) [avatar component clause 224]
227. 17 <=> funny(sK5) [avatar definition]
229. funny(sK5) <- (17) [avatar component clause 227]
230. 16 | 17 [avatar split clause 112,227,224]
232. 18 <=> ! [X3] : ~old(X3) [avatar definition]
233. ~old(X3) <- (18) [avatar component clause 232]
234. 18 | 17 [avatar split clause 111,227,232]
236. 19 <=> brave(sK5) [avatar definition]
238. ~brave(sK5) <- (~19) [avatar component clause 236]
239. 16 | ~19 [avatar split clause 110,236,224]
240. 18 | ~19 [avatar split clause 109,236,232]
242. 20 <=> ! [X1] : (kind(X1) | old(X1)) [avatar definition]
243. kind(X1) | old(X1) <- (20) [avatar component clause 242]
245. 21 <=> calm(sK6) [avatar definition]
247. ~calm(sK6) <- (~21) [avatar component clause 245]
249. 22 <=> quiet(sK6) [avatar definition]
251. ~quiet(sK6) <- (~22) [avatar component clause 249]
252. 20 | ~21 | ~22 [avatar split clause 121,249,245,242]
260. 24 <=> ! [X3] : (calm(X3) | ~quiet(X3)) [avatar definition]
261. ~quiet(X3) | calm(X3) <- (24) [avatar component clause 260]
277. 24 [avatar split clause 123,260]
327. ~7 [avatar split clause 143,183]
366. brave(sK5) <- (17) [resolution 222,229]
369. $false <- (17, ~19) [subsumption resolution 366,238]
370. ~17 | 19 [avatar contradiction clause 369]
371. $false <- (16, ~22) [resolution 225,251]
372. ~16 | 22 [avatar contradiction clause 371]
378. calm(X0) <- (16, 24) [resolution 261,225]
381. $false <- (16, ~21, 24) [resolution 378,247]
382. ~16 | 21 | ~24 [avatar contradiction clause 381]
384. kind(X1) <- (18, 20) [subsumption resolution 243,233]
397. ~kind(paul) | patient(paul) [resolution 95,151]
399. patient(paul) <- (18, 20) [subsumption resolution 397,384]
400. $false <- (~7, 18, 20) [subsumption resolution 399,185]
401. 7 | ~18 | ~20 [avatar contradiction clause 400]
403. $false [avatar sat refutation 230,234,239,240,252,277,327,370,372,382,401]
% SZS output end Proof for 9053953634755240271460493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or curious is wise or generous.
If lucy is funny or old then someone is quiet and vice versa.
If someone is brave or not patient then alice is patient or not kind.
If someone is either happy or not kind then someone is either not tall or tall and vice versa.
Everyone who is calm or not generous is curious or not funny.
Everyone who is both not rich and funny is happy or not kind.
If someone is both tall and not tall then someone is old or not rich and vice versa.
If mary is both strong and rich then john is either not tall or not rich.
If paul is not rich then mary is not curious.
Everyone who is not wise is either not calm or funny.
Everyone who is patient is either happy or brave.
Everyone who is patient is not wise and vice versa.
Everyone who is not patient or not creative is either wise or not creative.
If someone is calm or patient then someone is either creative or not calm and vice versa.
Everyone who is both not calm and not rich is not calm and vice versa.
If lucy is not patient then fred is happy and vice versa.
Mary is not creative.
Someone is quiet.
Someone is not rich or strong.
Someone is old or happy.
Someone is both patient and not kind.
Susan is not patient.
Susan is not tall. | Alice is not kind. | neutral | (![X]:((kind(X)<~>curious(X))=>(wise(X)|generous(X))))&
(((funny(lucy)|old(lucy)))<=>(?[X]:(quiet(X))))&
((?[X]:((brave(X)|~patient(X))))=>((patient(alice)|~kind(alice))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((calm(X)|~generous(X))=>(curious(X)|~funny(X))))&
(![X]:((~rich(X)&funny(X))=>(happy(X)|~kind(X))))&
((?[X]:((tall(X)&~tall(X))))<=>(?[X]:((old(X)|~rich(X)))))&
(((strong(mary)&rich(mary)))=>((~tall(john)<~>~rich(john))))&
((~rich(paul))=>(~curious(mary)))&
(![X]:(~wise(X)=>(~calm(X)<~>funny(X))))&
(![X]:(patient(X)=>(happy(X)<~>brave(X))))&
(![X]:(patient(X)<=>~wise(X)))&
(![X]:((~patient(X)|~creative(X))=>(wise(X)<~>~creative(X))))&
((?[X]:((calm(X)|patient(X))))<=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((~calm(X)&~rich(X))<=>~calm(X)))&
((~patient(lucy))<=>(happy(fred)))&
(~creative(mary))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((old(X)|happy(X))))&
(?[X]:((patient(X)&~kind(X))))&
(~patient(susan))&
(~tall(susan)) | ~kind(alice) | [] | null | 0 |
If someone is both not creative and generous then alice is both tall and not old.
Everyone who is rich or wise is not kind and vice versa.
Everyone who is both generous and not old is not patient or happy and vice versa.
Everyone who is both not curious and not rich is both not rich and not calm.
Everyone who is funny or old is rich and vice versa.
If someone is happy then someone is either curious or not creative.
Everyone who is both brave and not humble is both old and happy and vice versa.
If lucy is old then fred is not creative or wise and vice versa.
Everyone who is both kind and not kind is both not wise and happy and vice versa.
Everyone who is tall is not quiet and vice versa.
Everyone who is happy is tall.
Everyone who is both rich and humble is not creative or not generous and vice versa.
Everyone who is both generous and not creative is both patient and rich and vice versa.
Everyone who is not kind is not rich or humble and vice versa.
If fred is calm then alice is happy and vice versa.
Lucy is humble or quiet.
Lucy is either not tall or not creative.
Paul is not brave.
Susan is not wise or creative.
Someone is either not happy or humble.
Mary is humble or not generous.
Someone is both not quiet and not happy. | Susan is tall. | neutral | ((?[X]:((~creative(X)&generous(X))))=>((tall(alice)&~old(alice))))&
(![X]:((rich(X)|wise(X))<=>~kind(X)))&
(![X]:((generous(X)&~old(X))<=>(~patient(X)|happy(X))))&
(![X]:((~curious(X)&~rich(X))=>(~rich(X)&~calm(X))))&
(![X]:((funny(X)|old(X))<=>rich(X)))&
((?[X]:(happy(X)))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((brave(X)&~humble(X))<=>(old(X)&happy(X))))&
((old(lucy))<=>((~creative(fred)|wise(fred))))&
(![X]:((kind(X)&~kind(X))<=>(~wise(X)&happy(X))))&
(![X]:(tall(X)<=>~quiet(X)))&
(![X]:(happy(X)=>tall(X)))&
(![X]:((rich(X)&humble(X))<=>(~creative(X)|~generous(X))))&
(![X]:((generous(X)&~creative(X))<=>(patient(X)&rich(X))))&
(![X]:(~kind(X)<=>(~rich(X)|humble(X))))&
((calm(fred))<=>(happy(alice)))&
((humble(lucy)|quiet(lucy)))&
((~tall(lucy)<~>~creative(lucy)))&
(~brave(paul))&
((~wise(susan)|creative(susan)))&
(?[X]:((~happy(X)<~>humble(X))))&
((humble(mary)|~generous(mary)))&
(?[X]:((~quiet(X)&~happy(X)))) | tall(susan) | [] | null | 0 |
Everyone who is not patient is either not creative or creative.
Everyone who is either funny or not brave is both not wise and kind.
Everyone who is both calm and brave is curious or humble and vice versa.
Everyone who is both curious and not quiet is either tall or not patient and vice versa.
If someone is not curious or humble then someone is either happy or humble.
Everyone who is both not curious and curious is either happy or humble.
Everyone who is not brave is both brave and not strong.
Everyone who is funny is both rich and not kind and vice versa.
If someone is both not kind and not creative then mary is not humble.
Everyone who is either generous or not brave is both generous and not curious.
If someone is not patient or creative then someone is quiet or generous and vice versa.
If fred is patient or not quiet then paul is not quiet or funny and vice versa.
Everyone who is creative or not calm is both generous and old.
Everyone who is curious or not funny is happy or wise.
Everyone who is quiet is not kind or not quiet and vice versa.
If mary is not creative or kind then alice is both not tall and not kind.
Someone is not creative or happy.
Mary is not generous.
Someone is not curious or wise.
Someone is kind or not tall.
Lucy is not wise.
John is either humble or tall.
Mary is either kind or brave.
Someone is both not happy and quiet. | Paul is rich. | contradiction | (![X]:(~patient(X)=>(~creative(X)<~>creative(X))))&
(![X]:((funny(X)<~>~brave(X))=>(~wise(X)&kind(X))))&
(![X]:((calm(X)&brave(X))<=>(curious(X)|humble(X))))&
(![X]:((curious(X)&~quiet(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:((~curious(X)|humble(X))))=>(?[X]:((happy(X)<~>humble(X)))))&
(![X]:((~curious(X)&curious(X))=>(happy(X)<~>humble(X))))&
(![X]:(~brave(X)=>(brave(X)&~strong(X))))&
(![X]:(funny(X)<=>(rich(X)&~kind(X))))&
((?[X]:((~kind(X)&~creative(X))))=>(~humble(mary)))&
(![X]:((generous(X)<~>~brave(X))=>(generous(X)&~curious(X))))&
((?[X]:((~patient(X)|creative(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(((patient(fred)|~quiet(fred)))<=>((~quiet(paul)|funny(paul))))&
(![X]:((creative(X)|~calm(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|~funny(X))=>(happy(X)|wise(X))))&
(![X]:(quiet(X)<=>(~kind(X)|~quiet(X))))&
(((~creative(mary)|kind(mary)))=>((~tall(alice)&~kind(alice))))&
(?[X]:((~creative(X)|happy(X))))&
(~generous(mary))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:((kind(X)|~tall(X))))&
(~wise(lucy))&
((humble(john)<~>tall(john)))&
((kind(mary)<~>brave(mary)))&
(?[X]:((~happy(X)&quiet(X)))) | rich(paul) | [
"p1",
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3926023799840689490197257
% SZS output start Proof for 3926023799840689490197257
2. ! [X0] : ((funny(X0) <~> ~brave(X0)) => (kind(X0) & ~wise(X0))) [input p1]
7. ! [X0] : (~brave(X0) => (~strong(X0) & brave(X0))) [input p6]
8. ! [X0] : (funny(X0) <=> (~kind(X0) & rich(X0))) [input p7]
15. ! [X0] : (quiet(X0) <=> (~quiet(X0) | ~kind(X0))) [input p14]
25. rich(paul) [input hypothesis]
29. ! [X0] : (~brave(X0) => brave(X0)) [pure predicate removal 7]
31. ! [X0] : ((kind(X0) & ~wise(X0)) | (funny(X0) <=> ~brave(X0))) [ennf transformation 2]
35. ! [X0] : (brave(X0) | brave(X0)) [ennf transformation 29]
43. ! [X0] : ((kind(X0) & ~wise(X0)) | ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0)))) [nnf transformation 31]
53. ! [X0] : ((funny(X0) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | ~funny(X0))) [nnf transformation 8]
54. ! [X0] : ((funny(X0) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | ~funny(X0))) [flattening 53]
63. ! [X0] : ((quiet(X0) | (quiet(X0) & kind(X0))) & ((~quiet(X0) | ~kind(X0)) | ~quiet(X0))) [nnf transformation 15]
64. ! [X0] : ((quiet(X0) | (quiet(X0) & kind(X0))) & (~quiet(X0) | ~kind(X0) | ~quiet(X0))) [flattening 63]
79. ~brave(X0) | kind(X0) | ~funny(X0) [cnf transformation 43]
98. brave(X0) | brave(X0) [cnf transformation 35]
101. ~rich(X0) | kind(X0) | funny(X0) [cnf transformation 54]
119. ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 64]
121. quiet(X0) | quiet(X0) [cnf transformation 64]
137. rich(paul) [cnf transformation 25]
138. ~quiet(X0) | ~kind(X0) [duplicate literal removal 119]
139. quiet(X0) [duplicate literal removal 121]
141. brave(X0) [duplicate literal removal 98]
221. ~kind(X0) [subsumption resolution 138,139]
268. kind(X0) | ~funny(X0) [resolution 79,141]
269. ~funny(X0) [subsumption resolution 268,221]
313. kind(paul) | funny(paul) [resolution 101,137]
314. funny(paul) [subsumption resolution 313,221]
317. $false [subsumption resolution 314,269]
% SZS output end Proof for 3926023799840689490197257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not rich is both generous and humble. Everyone who is either not patient or patient is not funny or generous and vice versa. If john is either generous or calm then fred is both not strong and not calm. Everyone who is either patient or tall is either not strong or old. Everyone who is old or not wise is either quiet or patient and vice versa. Everyone who is humble or rich is both rich and kind. Everyone who is both not quiet and not wise is not funny or not strong and vice versa. If someone is either not old or not humble then paul is tall or happy and vice versa. If someone is wise then fred is wise or not creative. If someone is not calm then lucy is both not tall and not rich and vice versa. Everyone who is both not brave and rich is not quiet and vice versa. Everyone who is both quiet and not brave is either rich or not funny and vice versa. Everyone who is old is calm or not happy and vice versa. Everyone who is both strong and not calm is either kind or happy and vice versa. Everyone who is both curious and not tall is not rich or quiet and vice versa. If paul is funny then someone is both not old and old and vice versa. Alice is either brave or not funny. Someone is either not happy or not generous. Susan is patient. Someone is both brave and not humble. Someone is either not humble or not curious. Someone is generous. | Susan is funny. | contradiction | (![X]:((quiet(X)<~>~rich(X))=>(generous(X)&humble(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(~funny(X)|generous(X))))&
(((generous(john)<~>calm(john)))=>((~strong(fred)&~calm(fred))))&
(![X]:((patient(X)<~>tall(X))=>(~strong(X)<~>old(X))))&
(![X]:((old(X)|~wise(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((humble(X)|rich(X))=>(rich(X)&kind(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(~funny(X)|~strong(X))))&
((?[X]:((~old(X)<~>~humble(X))))<=>((tall(paul)|happy(paul))))&
((?[X]:(wise(X)))=>((wise(fred)|~creative(fred))))&
((?[X]:(~calm(X)))<=>((~tall(lucy)&~rich(lucy))))&
(![X]:((~brave(X)&rich(X))<=>~quiet(X)))&
(![X]:((quiet(X)&~brave(X))<=>(rich(X)<~>~funny(X))))&
(![X]:(old(X)<=>(calm(X)|~happy(X))))&
(![X]:((strong(X)&~calm(X))<=>(kind(X)<~>happy(X))))&
(![X]:((curious(X)&~tall(X))<=>(~rich(X)|quiet(X))))&
((funny(paul))<=>(?[X]:((~old(X)&old(X)))))&
((brave(alice)<~>~funny(alice)))&
(?[X]:((~happy(X)<~>~generous(X))))&
(patient(susan))&
(?[X]:((brave(X)&~humble(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:(generous(X))) | funny(susan) | [
"p3",
"p4",
"p6",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 453075430361186653173698
% SZS output start Proof for 453075430361186653173698
4. ! [X0] : ((patient(X0) <~> tall(X0)) => (~strong(X0) <~> old(X0))) [input p3]
5. ! [X0] : ((~wise(X0) | old(X0)) <=> (quiet(X0) <~> patient(X0))) [input p4]
7. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (~strong(X0) | ~funny(X0))) [input p6]
11. ! [X0] : ((rich(X0) & ~brave(X0)) <=> ~quiet(X0)) [input p10]
12. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (rich(X0) <~> ~funny(X0))) [input p11]
15. ! [X0] : ((~tall(X0) & curious(X0)) <=> (quiet(X0) | ~rich(X0))) [input p14]
19. patient(susan) [input p18]
23. funny(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) <~> old(X0)) | (patient(X0) <=> tall(X0))) [ennf transformation 4]
33. ! [X0] : (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) [nnf transformation 27]
34. ! [X0] : (((~wise(X0) | old(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (wise(X0) & ~old(X0)))) [nnf transformation 5]
35. ! [X0] : ((~wise(X0) | old(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (wise(X0) & ~old(X0)))) [flattening 34]
36. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 7]
37. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | wise(X0) | quiet(X0))) [flattening 36]
48. ! [X0] : (((rich(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | (~rich(X0) | brave(X0)))) [nnf transformation 11]
49. ! [X0] : (((rich(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | ~rich(X0) | brave(X0))) [flattening 48]
50. ! [X0] : (((~brave(X0) & quiet(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 12]
51. ! [X0] : (((~brave(X0) & quiet(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | brave(X0) | ~quiet(X0))) [flattening 50]
56. ! [X0] : (((~tall(X0) & curious(X0)) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | (tall(X0) | ~curious(X0)))) [nnf transformation 15]
57. ! [X0] : (((~tall(X0) & curious(X0)) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | tall(X0) | ~curious(X0))) [flattening 56]
87. ~strong(X0) | old(X0) | tall(X0) | ~patient(X0) [cnf transformation 33]
93. ~old(X0) | ~quiet(X0) | ~patient(X0) [cnf transformation 35]
102. ~quiet(X0) | funny(X0) [cnf transformation 37]
103. ~quiet(X0) | strong(X0) [cnf transformation 37]
115. ~rich(X0) | ~quiet(X0) | brave(X0) [cnf transformation 49]
117. rich(X0) | quiet(X0) [cnf transformation 49]
118. ~funny(X0) | rich(X0) | brave(X0) | ~quiet(X0) [cnf transformation 51]
120. quiet(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 51]
122. ~brave(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 51]
136. ~tall(X0) | rich(X0) [cnf transformation 57]
145. patient(susan) [cnf transformation 19]
151. funny(susan) [cnf transformation 23]
221. ~funny(X0) | quiet(X0) [subsumption resolution 120,117]
222. rich(X0) | brave(X0) | ~quiet(X0) [subsumption resolution 118,102]
223. ~quiet(X0) | brave(X0) [subsumption resolution 222,115]
281. quiet(susan) [resolution 221,151]
285. strong(susan) [resolution 281,103]
289. brave(susan) [resolution 223,281]
345. ~funny(susan) | ~rich(susan) [resolution 122,289]
347. ~rich(susan) [subsumption resolution 345,151]
478. old(susan) | tall(susan) | ~patient(susan) [resolution 87,285]
493. old(susan) | tall(susan) [subsumption resolution 478,145]
495. 46 <=> tall(susan) [avatar definition]
497. tall(susan) <- (46) [avatar component clause 495]
499. 47 <=> old(susan) [avatar definition]
501. old(susan) <- (47) [avatar component clause 499]
502. 46 | 47 [avatar split clause 493,499,495]
772. rich(susan) <- (46) [resolution 497,136]
775. $false <- (46) [subsumption resolution 772,347]
776. ~46 [avatar contradiction clause 775]
785. ~quiet(susan) | ~patient(susan) <- (47) [resolution 501,93]
787. ~patient(susan) <- (47) [subsumption resolution 785,281]
788. $false <- (47) [subsumption resolution 787,145]
789. ~47 [avatar contradiction clause 788]
790. $false [avatar sat refutation 502,776,789]
% SZS output end Proof for 453075430361186653173698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa.
If susan is both creative and kind then someone is not patient.
Everyone who is both not humble and not happy is kind or generous and vice versa.
Everyone who is not rich is not curious or not rich.
Everyone who is both not wise and calm is not tall or quiet and vice versa.
Everyone who is not brave is either not quiet or old and vice versa.
If someone is not patient or funny then mary is both not humble and not funny and vice versa.
Everyone who is not tall is either humble or not tall.
If someone is both humble and not kind then someone is either calm or strong.
If lucy is brave or not old then someone is both wise and not wise and vice versa.
Everyone who is not kind is happy or funny.
Everyone who is both funny and old is both not curious and not calm and vice versa.
If someone is rich or funny then john is creative or not calm.
Everyone who is humble is both not funny and not old.
Fred is not humble or brave.
Someone is either brave or not curious.
Someone is strong.
Someone is either tall or not creative.
Someone is creative or humble.
Someone is kind or tall. | Susan is not old. | neutral | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
(((creative(susan)&kind(susan)))=>(?[X]:(~patient(X))))&
(![X]:((~humble(X)&~happy(X))<=>(kind(X)|generous(X))))&
(![X]:(~rich(X)=>(~curious(X)|~rich(X))))&
(![X]:((~wise(X)&calm(X))<=>(~tall(X)|quiet(X))))&
(![X]:(~brave(X)<=>(~quiet(X)<~>old(X))))&
((?[X]:((~patient(X)|funny(X))))<=>((~humble(mary)&~funny(mary))))&
(![X]:(~tall(X)=>(humble(X)<~>~tall(X))))&
((?[X]:((humble(X)&~kind(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(((brave(lucy)|~old(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~kind(X)=>(happy(X)|funny(X))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
((~humble(fred)|brave(fred)))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:(strong(X)))&
(?[X]:((tall(X)<~>~creative(X))))&
(?[X]:((creative(X)|humble(X))))&
(?[X]:((kind(X)|tall(X)))) | ~old(susan) | [] | null | 0 |
If john is not brave then someone is either brave or not funny and vice versa.
Everyone who is not brave or not rich is rich and vice versa.
Everyone who is either curious or not patient is not strong and vice versa.
Everyone who is both not wise and not happy is either quiet or funny and vice versa.
Everyone who is not quiet or humble is both not patient and patient and vice versa.
If someone is either funny or not old then someone is either not wise or not patient and vice versa.
If someone is not humble or not generous then someone is calm and vice versa.
If lucy is not tall or generous then mary is not creative or not strong.
If someone is both not funny and not rich then susan is brave.
If fred is not generous or not curious then mary is not rich.
If lucy is patient or kind then john is not patient.
Everyone who is either curious or not wise is both generous and calm and vice versa.
If someone is either happy or patient then alice is brave or curious.
If john is either tall or happy then susan is either not quiet or rich and vice versa.
If alice is not kind or not rich then lucy is both not kind and funny and vice versa.
Someone is both wise and patient.
Mary is patient.
Someone is wise or not humble.
Fred is either not tall or not generous.
Paul is rich or not creative.
Someone is calm or brave. | John is brave. | contradiction | ((~brave(john))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((~brave(X)|~rich(X))<=>rich(X)))&
(![X]:((curious(X)<~>~patient(X))<=>~strong(X)))&
(![X]:((~wise(X)&~happy(X))<=>(quiet(X)<~>funny(X))))&
(![X]:((~quiet(X)|humble(X))<=>(~patient(X)&patient(X))))&
((?[X]:((funny(X)<~>~old(X))))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(calm(X))))&
(((~tall(lucy)|generous(lucy)))=>((~creative(mary)|~strong(mary))))&
((?[X]:((~funny(X)&~rich(X))))=>(brave(susan)))&
(((~generous(fred)|~curious(fred)))=>(~rich(mary)))&
(((patient(lucy)|kind(lucy)))=>(~patient(john)))&
(![X]:((curious(X)<~>~wise(X))<=>(generous(X)&calm(X))))&
((?[X]:((happy(X)<~>patient(X))))=>((brave(alice)|curious(alice))))&
(((tall(john)<~>happy(john)))<=>((~quiet(susan)<~>rich(susan))))&
(((~kind(alice)|~rich(alice)))<=>((~kind(lucy)&funny(lucy))))&
(?[X]:((wise(X)&patient(X))))&
(patient(mary))&
(?[X]:((wise(X)|~humble(X))))&
((~tall(fred)<~>~generous(fred)))&
((rich(paul)|~creative(paul)))&
(?[X]:((calm(X)|brave(X)))) | brave(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5156856633494575000310852
% SZS output start Proof for 5156856633494575000310852
2. ! [X0] : ((~rich(X0) | ~brave(X0)) <=> rich(X0)) [input p1]
22. brave(john) [input hypothesis]
38. ! [X0] : (((~rich(X0) | ~brave(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) & brave(X0)))) [nnf transformation 2]
39. ! [X0] : ((~rich(X0) | ~brave(X0) | ~rich(X0)) & (rich(X0) | (rich(X0) & brave(X0)))) [flattening 38]
72. rich(X0) | rich(X0) [cnf transformation 39]
73. ~rich(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 39]
129. brave(john) [cnf transformation 22]
130. rich(X0) [duplicate literal removal 72]
131. ~rich(X0) | ~brave(X0) [duplicate literal removal 73]
136. 2 <=> brave(john) [avatar definition]
137. brave(john) <- (2) [avatar component clause 136]
270. 2 [avatar split clause 129,136]
271. ~brave(X0) [resolution 131,130]
272. $false <- (2) [resolution 271,137]
275. ~2 [avatar contradiction clause 272]
276. $false [avatar sat refutation 270,275]
% SZS output end Proof for 5156856633494575000310852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not kind is both not generous and not wise.
Everyone who is not calm or not strong is either kind or not curious.
Everyone who is both not calm and not patient is either brave or calm.
Everyone who is both calm and curious is wise.
Everyone who is brave is both not calm and happy.
If someone is not rich then someone is not happy or quiet.
Everyone who is both not kind and old is either not generous or not curious.
If someone is both not strong and funny then someone is either kind or not strong.
Everyone who is either not wise or old is not old.
If fred is either quiet or not wise then lucy is both not funny and rich and vice versa.
Everyone who is either patient or not tall is happy or not happy.
If someone is calm or kind then alice is both kind and not old.
Everyone who is not patient or humble is either not creative or not brave.
Everyone who is both not brave and not happy is not old or strong and vice versa.
Everyone who is rich or patient is both not humble and not kind.
If someone is both not kind and generous then alice is curious or calm and vice versa.
Mary is both not generous and rich.
Someone is both humble and wise.
Someone is both tall and happy.
Someone is old.
John is both not happy and not curious.
Fred is not curious or strong.
Lucy is not creative or humble.
Alice is not brave. | Lucy is funny. | neutral | (![X]:((curious(X)<~>~kind(X))=>(~generous(X)&~wise(X))))&
(![X]:((~calm(X)|~strong(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~calm(X)&~patient(X))=>(brave(X)<~>calm(X))))&
(![X]:((calm(X)&curious(X))=>wise(X)))&
(![X]:(brave(X)=>(~calm(X)&happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((~kind(X)&old(X))=>(~generous(X)<~>~curious(X))))&
((?[X]:((~strong(X)&funny(X))))=>(?[X]:((kind(X)<~>~strong(X)))))&
(![X]:((~wise(X)<~>old(X))=>~old(X)))&
(((quiet(fred)<~>~wise(fred)))<=>((~funny(lucy)&rich(lucy))))&
(![X]:((patient(X)<~>~tall(X))=>(happy(X)|~happy(X))))&
((?[X]:((calm(X)|kind(X))))=>((kind(alice)&~old(alice))))&
(![X]:((~patient(X)|humble(X))=>(~creative(X)<~>~brave(X))))&
(![X]:((~brave(X)&~happy(X))<=>(~old(X)|strong(X))))&
(![X]:((rich(X)|patient(X))=>(~humble(X)&~kind(X))))&
((?[X]:((~kind(X)&generous(X))))<=>((curious(alice)|calm(alice))))&
((~generous(mary)&rich(mary)))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:(old(X)))&
((~happy(john)&~curious(john)))&
((~curious(fred)|strong(fred)))&
((~creative(lucy)|humble(lucy)))&
(~brave(alice)) | funny(lucy) | [] | null | 0 |
Everyone who is both creative and not rich is funny or not curious. If fred is brave or not brave then john is both funny and old. Everyone who is wise or not generous is either not curious or not quiet and vice versa. Everyone who is not old is kind. Everyone who is not calm is not wise or quiet and vice versa. Everyone who is not kind is both wise and not rich and vice versa. Everyone who is either calm or curious is both not strong and not patient and vice versa. If susan is kind then someone is brave and vice versa. Everyone who is rich or kind is either not generous or wise and vice versa. If someone is both not brave and generous then someone is humble. Everyone who is either quiet or not generous is not brave or not patient and vice versa. If someone is both not tall and not rich then someone is curious. If someone is not happy or quiet then someone is both not generous and not happy and vice versa. Everyone who is calm or quiet is either not old or happy and vice versa. Everyone who is either funny or calm is both curious and not generous and vice versa. Everyone who is not humble or not kind is either old or not quiet and vice versa. Someone is both happy and creative. Someone is calm or not rich. Alice is quiet. Paul is not funny. John is rich. Someone is patient. Someone is not brave or happy. Alice is both old and not patient. | Paul is quiet. | entailment | (![X]:((creative(X)&~rich(X))=>(funny(X)|~curious(X))))&
(((brave(fred)|~brave(fred)))=>((funny(john)&old(john))))&
(![X]:((wise(X)|~generous(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~calm(X)<=>(~wise(X)|quiet(X))))&
(![X]:(~kind(X)<=>(wise(X)&~rich(X))))&
(![X]:((calm(X)<~>curious(X))<=>(~strong(X)&~patient(X))))&
((kind(susan))<=>(?[X]:(brave(X))))&
(![X]:((rich(X)|kind(X))<=>(~generous(X)<~>wise(X))))&
((?[X]:((~brave(X)&generous(X))))=>(?[X]:(humble(X))))&
(![X]:((quiet(X)<~>~generous(X))<=>(~brave(X)|~patient(X))))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:(curious(X))))&
((?[X]:((~happy(X)|quiet(X))))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~old(X)<~>happy(X))))&
(![X]:((funny(X)<~>calm(X))<=>(curious(X)&~generous(X))))&
(![X]:((~humble(X)|~kind(X))<=>(old(X)<~>~quiet(X))))&
(?[X]:((happy(X)&creative(X))))&
(?[X]:((calm(X)|~rich(X))))&
(quiet(alice))&
(~funny(paul))&
(rich(john))&
(?[X]:(patient(X)))&
(?[X]:((~brave(X)|happy(X))))&
((old(alice)&~patient(alice))) | quiet(paul) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6559057566134653146947744
% SZS output start Proof for 6559057566134653146947744
3. ! [X0] : ((~generous(X0) | wise(X0)) <=> (~curious(X0) <~> ~quiet(X0))) [input p2]
4. ! [X0] : (~old(X0) => kind(X0)) [input p3]
5. ! [X0] : (~calm(X0) <=> (quiet(X0) | ~wise(X0))) [input p4]
6. ! [X0] : (~kind(X0) <=> (~rich(X0) & wise(X0))) [input p5]
9. ! [X0] : ((kind(X0) | rich(X0)) <=> (~generous(X0) <~> wise(X0))) [input p8]
15. ! [X0] : ((funny(X0) <~> calm(X0)) <=> (~generous(X0) & curious(X0))) [input p14]
16. ! [X0] : ((~kind(X0) | ~humble(X0)) <=> (old(X0) <~> ~quiet(X0))) [input p15]
20. ~funny(paul) [input p19]
25. ~quiet(paul) [input hypothesis]
33. ! [X0] : (kind(X0) | old(X0)) [ennf transformation 4]
35. ! [X0] : (((~generous(X0) | wise(X0)) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (generous(X0) & ~wise(X0)))) [nnf transformation 3]
36. ! [X0] : ((~generous(X0) | wise(X0) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (generous(X0) & ~wise(X0)))) [flattening 35]
37. ! [X0] : ((~calm(X0) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | calm(X0))) [nnf transformation 5]
38. ! [X0] : ((~calm(X0) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | calm(X0))) [flattening 37]
39. ! [X0] : ((~kind(X0) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | kind(X0))) [nnf transformation 6]
40. ! [X0] : ((~kind(X0) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | kind(X0))) [flattening 39]
47. ! [X0] : (((kind(X0) | rich(X0)) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (~kind(X0) & ~rich(X0)))) [nnf transformation 9]
48. ! [X0] : ((kind(X0) | rich(X0) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (~kind(X0) & ~rich(X0)))) [flattening 47]
61. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [flattening 61]
63. ! [X0] : (((~kind(X0) | ~humble(X0)) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (kind(X0) & humble(X0)))) [nnf transformation 16]
64. ! [X0] : ((~kind(X0) | ~humble(X0) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (kind(X0) & humble(X0)))) [flattening 63]
81. quiet(X0) | curious(X0) | generous(X0) [cnf transformation 36]
84. kind(X0) | old(X0) [cnf transformation 33]
85. ~wise(X0) | quiet(X0) | calm(X0) [cnf transformation 38]
86. ~calm(X0) | wise(X0) [cnf transformation 38]
88. kind(X0) | wise(X0) [cnf transformation 40]
89. ~rich(X0) | kind(X0) [cnf transformation 40]
100. wise(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 48]
102. ~kind(X0) | generous(X0) | ~wise(X0) [cnf transformation 48]
104. kind(X0) | rich(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 48]
126. ~calm(X0) | funny(X0) | ~generous(X0) [cnf transformation 62]
127. ~curious(X0) | funny(X0) | generous(X0) | calm(X0) [cnf transformation 62]
132. quiet(X0) | ~old(X0) | kind(X0) [cnf transformation 64]
139. ~funny(paul) [cnf transformation 20]
145. ~quiet(paul) [cnf transformation 25]
175. kind(X0) | ~generous(X0) | ~wise(X0) [subsumption resolution 104,89]
176. ~generous(X0) | kind(X0) [subsumption resolution 175,88]
177. ~generous(X0) | wise(X0) [subsumption resolution 100,176]
217. kind(X0) | quiet(X0) [subsumption resolution 132,84]
260. curious(paul) | generous(paul) [resolution 81,145]
265. 23 <=> generous(paul) [avatar definition]
266. ~generous(paul) <- (~23) [avatar component clause 265]
267. generous(paul) <- (23) [avatar component clause 265]
269. 24 <=> curious(paul) [avatar definition]
271. curious(paul) <- (24) [avatar component clause 269]
272. 23 | 24 [avatar split clause 260,269,265]
306. ~wise(X0) | generous(X0) | quiet(X0) [resolution 102,217]
654. funny(paul) | generous(paul) | calm(paul) <- (24) [resolution 127,271]
656. generous(paul) | calm(paul) <- (24) [subsumption resolution 654,139]
657. calm(paul) <- (~23, 24) [subsumption resolution 656,266]
842. wise(paul) <- (~23, 24) [resolution 657,86]
1133. generous(paul) | quiet(paul) <- (~23, 24) [resolution 842,306]
1141. quiet(paul) <- (~23, 24) [subsumption resolution 1133,266]
1142. $false <- (~23, 24) [subsumption resolution 1141,145]
1143. 23 | ~24 [avatar contradiction clause 1142]
1148. 97 <=> calm(paul) [avatar definition]
1149. ~calm(paul) <- (~97) [avatar component clause 1148]
1150. calm(paul) <- (97) [avatar component clause 1148]
1151. 97 | 23 | ~24 [avatar split clause 656,269,265,1148]
1156. wise(paul) <- (23) [resolution 267,177]
1182. funny(paul) | ~generous(paul) <- (97) [resolution 1150,126]
1185. ~generous(paul) <- (97) [subsumption resolution 1182,139]
1186. $false <- (23, 97) [subsumption resolution 1185,267]
1187. ~23 | ~97 [avatar contradiction clause 1186]
1189. quiet(paul) | calm(paul) <- (23) [resolution 1156,85]
1198. calm(paul) <- (23) [subsumption resolution 1189,145]
1199. $false <- (23, ~97) [subsumption resolution 1198,1149]
1200. ~23 | 97 [avatar contradiction clause 1199]
1201. $false [avatar sat refutation 272,1143,1151,1187,1200]
% SZS output end Proof for 6559057566134653146947744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not patient is either humble or patient and vice versa.
Everyone who is humble is calm and vice versa.
Everyone who is both not kind and not quiet is not creative or not happy and vice versa.
If someone is not curious or not strong then someone is either not calm or not humble and vice versa.
If paul is tall or old then someone is both tall and not kind and vice versa.
If mary is brave or funny then susan is both not tall and patient and vice versa.
If someone is either strong or creative then john is not patient.
Everyone who is not tall or humble is either not patient or tall and vice versa.
Everyone who is either not old or not happy is not creative.
Everyone who is quiet is not happy.
If someone is not creative then someone is both not old and happy.
Everyone who is rich or not strong is either not tall or not patient and vice versa.
Everyone who is not tall is either kind or patient.
If someone is either humble or generous then lucy is either wise or not tall and vice versa.
Everyone who is not curious is either not calm or calm.
Mary is curious or tall.
Fred is curious or not old.
Someone is curious.
Someone is patient.
Alice is either calm or tall.
Susan is wise.
Mary is either curious or wise. | Paul is generous. | neutral | (![X]:((~strong(X)<~>~patient(X))<=>(humble(X)<~>patient(X))))&
(![X]:(humble(X)<=>calm(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~curious(X)|~strong(X))))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(((tall(paul)|old(paul)))<=>(?[X]:((tall(X)&~kind(X)))))&
(((brave(mary)|funny(mary)))<=>((~tall(susan)&patient(susan))))&
((?[X]:((strong(X)<~>creative(X))))=>(~patient(john)))&
(![X]:((~tall(X)|humble(X))<=>(~patient(X)<~>tall(X))))&
(![X]:((~old(X)<~>~happy(X))=>~creative(X)))&
(![X]:(quiet(X)=>~happy(X)))&
((?[X]:(~creative(X)))=>(?[X]:((~old(X)&happy(X)))))&
(![X]:((rich(X)|~strong(X))<=>(~tall(X)<~>~patient(X))))&
(![X]:(~tall(X)=>(kind(X)<~>patient(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>((wise(lucy)<~>~tall(lucy))))&
(![X]:(~curious(X)=>(~calm(X)<~>calm(X))))&
((curious(mary)|tall(mary)))&
((curious(fred)|~old(fred)))&
(?[X]:(curious(X)))&
(?[X]:(patient(X)))&
((calm(alice)<~>tall(alice)))&
(wise(susan))&
((curious(mary)<~>wise(mary))) | generous(paul) | [] | null | 0 |
If alice is either strong or not kind then john is not calm and vice versa. Everyone who is not brave is not kind or not humble and vice versa. Everyone who is funny is strong or rich and vice versa. If lucy is old or happy then susan is kind and vice versa. Everyone who is not curious is not strong and vice versa. Everyone who is wise or not humble is not creative and vice versa. Everyone who is either not brave or patient is quiet and vice versa. If lucy is not brave or strong then someone is both humble and brave. Everyone who is both tall and not tall is humble. If someone is old then someone is brave or strong and vice versa. Everyone who is both not quiet and kind is either quiet or patient and vice versa. If alice is humble or curious then lucy is both not humble and tall. Everyone who is either brave or not rich is both not tall and funny and vice versa. Everyone who is brave or kind is generous. Everyone who is both not brave and brave is not wise. If susan is either creative or not tall then paul is not funny or strong. Fred is both tall and not old. Susan is not curious or not brave. Alice is not tall or not quiet. Susan is wise. Someone is either brave or generous. Fred is not strong or not generous. Someone is curious. | Lucy is happy. | neutral | (((strong(alice)<~>~kind(alice)))<=>(~calm(john)))&
(![X]:(~brave(X)<=>(~kind(X)|~humble(X))))&
(![X]:(funny(X)<=>(strong(X)|rich(X))))&
(((old(lucy)|happy(lucy)))<=>(kind(susan)))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:((wise(X)|~humble(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>patient(X))<=>quiet(X)))&
(((~brave(lucy)|strong(lucy)))=>(?[X]:((humble(X)&brave(X)))))&
(![X]:((tall(X)&~tall(X))=>humble(X)))&
((?[X]:(old(X)))<=>(?[X]:((brave(X)|strong(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(quiet(X)<~>patient(X))))&
(((humble(alice)|curious(alice)))=>((~humble(lucy)&tall(lucy))))&
(![X]:((brave(X)<~>~rich(X))<=>(~tall(X)&funny(X))))&
(![X]:((brave(X)|kind(X))=>generous(X)))&
(![X]:((~brave(X)&brave(X))=>~wise(X)))&
(((creative(susan)<~>~tall(susan)))=>((~funny(paul)|strong(paul))))&
((tall(fred)&~old(fred)))&
((~curious(susan)|~brave(susan)))&
((~tall(alice)|~quiet(alice)))&
(wise(susan))&
(?[X]:((brave(X)<~>generous(X))))&
((~strong(fred)|~generous(fred)))&
(?[X]:(curious(X))) | happy(lucy) | [] | null | 0 |
Everyone who is either happy or not brave is tall or not calm.
Everyone who is both patient and not old is not patient or not calm and vice versa.
If alice is tall or kind then someone is either calm or patient.
Everyone who is not quiet or funny is either funny or calm and vice versa.
If susan is not rich then paul is either patient or curious and vice versa.
If someone is old or tall then someone is both humble and not creative and vice versa.
If someone is either not generous or brave then susan is not humble and vice versa.
If someone is either not old or not creative then someone is not quiet.
If paul is not generous then someone is not patient or calm.
If someone is both curious and kind then susan is not tall.
Everyone who is curious or kind is either happy or not happy.
If someone is not quiet then susan is both quiet and not happy and vice versa.
Everyone who is rich or not generous is either not calm or not strong.
If susan is not brave then someone is curious.
If fred is not rich then someone is not tall or not happy and vice versa.
If someone is either not rich or curious then someone is either patient or not strong.
Someone is both old and rich.
Someone is both funny and not old.
Paul is patient or not calm.
John is either not patient or not curious.
Susan is not brave.
Fred is either kind or not patient.
Someone is either not humble or rich.
Paul is both curious and not creative. | Susan is old. | contradiction | (![X]:((happy(X)<~>~brave(X))=>(tall(X)|~calm(X))))&
(![X]:((patient(X)&~old(X))<=>(~patient(X)|~calm(X))))&
(((tall(alice)|kind(alice)))=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:((~quiet(X)|funny(X))<=>(funny(X)<~>calm(X))))&
((~rich(susan))<=>((patient(paul)<~>curious(paul))))&
((?[X]:((old(X)|tall(X))))<=>(?[X]:((humble(X)&~creative(X)))))&
((?[X]:((~generous(X)<~>brave(X))))<=>(~humble(susan)))&
((?[X]:((~old(X)<~>~creative(X))))=>(?[X]:(~quiet(X))))&
((~generous(paul))=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:((curious(X)&kind(X))))=>(~tall(susan)))&
(![X]:((curious(X)|kind(X))=>(happy(X)<~>~happy(X))))&
((?[X]:(~quiet(X)))<=>((quiet(susan)&~happy(susan))))&
(![X]:((rich(X)|~generous(X))=>(~calm(X)<~>~strong(X))))&
((~brave(susan))=>(?[X]:(curious(X))))&
((~rich(fred))<=>(?[X]:((~tall(X)|~happy(X)))))&
((?[X]:((~rich(X)<~>curious(X))))=>(?[X]:((patient(X)<~>~strong(X)))))&
(?[X]:((old(X)&rich(X))))&
(?[X]:((funny(X)&~old(X))))&
((patient(paul)|~calm(paul)))&
((~patient(john)<~>~curious(john)))&
(~brave(susan))&
((kind(fred)<~>~patient(fred)))&
(?[X]:((~humble(X)<~>rich(X))))&
((curious(paul)&~creative(paul))) | old(susan) | [
"p1",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 345464689000271177283506
% SZS output start Proof for 345464689000271177283506
2. ! [X0] : ((~old(X0) & patient(X0)) <=> (~calm(X0) | ~patient(X0))) [input p1]
4. ! [X0] : ((funny(X0) | ~quiet(X0)) <=> (funny(X0) <~> calm(X0))) [input p3]
12. ? [X0] : ~quiet(X0) <=> (~happy(susan) & quiet(susan)) [input p11]
25. old(susan) [input hypothesis]
40. ! [X0] : (((~old(X0) & patient(X0)) | (calm(X0) & patient(X0))) & ((~calm(X0) | ~patient(X0)) | (old(X0) | ~patient(X0)))) [nnf transformation 2]
41. ! [X0] : (((~old(X0) & patient(X0)) | (calm(X0) & patient(X0))) & (~calm(X0) | ~patient(X0) | old(X0) | ~patient(X0))) [flattening 40]
45. ! [X0] : (((funny(X0) | ~quiet(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0)))) & (((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | (~funny(X0) & quiet(X0)))) [nnf transformation 4]
46. ! [X0] : ((funny(X0) | ~quiet(X0) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0)))) & (((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | (~funny(X0) & quiet(X0)))) [flattening 45]
64. (? [X0] : ~quiet(X0) | (happy(susan) | ~quiet(susan))) & ((~happy(susan) & quiet(susan)) | ! [X0] : quiet(X0)) [nnf transformation 12]
65. (? [X0] : ~quiet(X0) | happy(susan) | ~quiet(susan)) & ((~happy(susan) & quiet(susan)) | ! [X0] : quiet(X0)) [flattening 64]
66. (? [X0] : ~quiet(X0) | happy(susan) | ~quiet(susan)) & ((~happy(susan) & quiet(susan)) | ! [X1] : quiet(X1)) [rectify 65]
67. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
68. (~quiet(sK6) | happy(susan) | ~quiet(susan)) & ((~happy(susan) & quiet(susan)) | ! [X1] : quiet(X1)) [skolemisation 66,67]
95. ~old(X0) | calm(X0) [cnf transformation 41]
103. ~calm(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
105. funny(X0) | ~quiet(X0) | funny(X0) | ~calm(X0) [cnf transformation 46]
127. quiet(susan) | quiet(X1) [cnf transformation 68]
156. old(susan) [cnf transformation 25]
157. ~funny(X0) | ~calm(X0) [duplicate literal removal 103]
158. ~quiet(X0) | funny(X0) | ~calm(X0) [duplicate literal removal 105]
273. 25 <=> quiet(susan) [avatar definition]
274. quiet(susan) <- (25) [avatar component clause 273]
275. ~quiet(susan) <- (~25) [avatar component clause 273]
286. 28 <=> ! [X1] : quiet(X1) [avatar definition]
287. quiet(X1) <- (28) [avatar component clause 286]
289. 28 | 25 [avatar split clause 127,273,286]
355. calm(susan) [resolution 95,156]
387. funny(susan) | ~calm(susan) <- (25) [resolution 158,274]
388. funny(susan) <- (25) [subsumption resolution 387,355]
412. ~calm(susan) <- (25) [resolution 388,157]
413. $false <- (25) [subsumption resolution 412,355]
414. ~25 [avatar contradiction clause 413]
415. $false <- (~25, 28) [subsumption resolution 275,287]
416. 25 | ~28 [avatar contradiction clause 415]
417. $false [avatar sat refutation 289,414,416]
% SZS output end Proof for 345464689000271177283506
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not patient or not strong then someone is either brave or humble and vice versa. If someone is either creative or not quiet then someone is not humble or not wise and vice versa. If someone is rich then susan is either tall or kind and vice versa. If alice is both creative and not creative then john is not kind or not rich and vice versa. If someone is both not old and patient then alice is not creative and vice versa. Everyone who is not rich is funny. Everyone who is either funny or happy is quiet or not strong. Everyone who is either creative or not humble is not tall or not rich and vice versa. Everyone who is not kind is humble. If someone is creative or humble then mary is quiet. If mary is not wise then mary is either not humble or old and vice versa. If fred is both not happy and not kind then someone is either not wise or not humble and vice versa. Everyone who is both not tall and kind is either not strong or patient and vice versa. Everyone who is brave is either not rich or not kind. If someone is both not rich and wise then mary is kind and vice versa. If someone is not happy or tall then someone is both not rich and not happy. Fred is not curious or not quiet. Someone is both old and quiet. Someone is either patient or not quiet. Someone is not old or not wise. Someone is not strong or not wise. John is both humble and curious. Mary is rich. Someone is both funny and not creative. | Mary is old. | neutral | (((~patient(alice)<~>~strong(alice)))<=>(?[X]:((brave(X)<~>humble(X)))))&
((?[X]:((creative(X)<~>~quiet(X))))<=>(?[X]:((~humble(X)|~wise(X)))))&
((?[X]:(rich(X)))<=>((tall(susan)<~>kind(susan))))&
(((creative(alice)&~creative(alice)))<=>((~kind(john)|~rich(john))))&
((?[X]:((~old(X)&patient(X))))<=>(~creative(alice)))&
(![X]:(~rich(X)=>funny(X)))&
(![X]:((funny(X)<~>happy(X))=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)<~>~humble(X))<=>(~tall(X)|~rich(X))))&
(![X]:(~kind(X)=>humble(X)))&
((?[X]:((creative(X)|humble(X))))=>(quiet(mary)))&
((~wise(mary))<=>((~humble(mary)<~>old(mary))))&
(((~happy(fred)&~kind(fred)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~tall(X)&kind(X))<=>(~strong(X)<~>patient(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~kind(X))))&
((?[X]:((~rich(X)&wise(X))))<=>(kind(mary)))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:((~rich(X)&~happy(X)))))&
((~curious(fred)|~quiet(fred)))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:((~old(X)|~wise(X))))&
(?[X]:((~strong(X)|~wise(X))))&
((humble(john)&curious(john)))&
(rich(mary))&
(?[X]:((funny(X)&~creative(X)))) | old(mary) | [] | null | 0 |
If fred is humble or not kind then lucy is happy and vice versa. Everyone who is not strong is either not quiet or happy. Everyone who is both not curious and brave is not creative or not curious. If fred is both strong and not kind then mary is not quiet or not funny. Everyone who is either curious or not patient is curious or not wise and vice versa. If fred is quiet then susan is either not happy or not tall and vice versa. Everyone who is curious or not old is both rich and not funny. Everyone who is either not old or creative is old or not wise. If paul is both brave and not generous then someone is either not funny or not humble. If susan is rich or creative then someone is not strong or not kind. Everyone who is not strong or brave is strong and vice versa. If someone is either not patient or not generous then someone is not patient. Everyone who is not quiet or strong is both not humble and not creative and vice versa. Everyone who is both kind and wise is either not creative or not patient. Everyone who is not quiet is calm or funny and vice versa. Everyone who is not old is both not creative and not calm and vice versa. Lucy is calm. Someone is generous or not generous. Someone is either not generous or not strong. Mary is not tall or creative. Paul is curious or not funny. Someone is quiet or not strong. | Paul is not brave. | contradiction | (((humble(fred)|~kind(fred)))<=>(happy(lucy)))&
(![X]:(~strong(X)=>(~quiet(X)<~>happy(X))))&
(![X]:((~curious(X)&brave(X))=>(~creative(X)|~curious(X))))&
(((strong(fred)&~kind(fred)))=>((~quiet(mary)|~funny(mary))))&
(![X]:((curious(X)<~>~patient(X))<=>(curious(X)|~wise(X))))&
((quiet(fred))<=>((~happy(susan)<~>~tall(susan))))&
(![X]:((curious(X)|~old(X))=>(rich(X)&~funny(X))))&
(![X]:((~old(X)<~>creative(X))=>(old(X)|~wise(X))))&
(((brave(paul)&~generous(paul)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((rich(susan)|creative(susan)))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((~strong(X)|brave(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(~patient(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~humble(X)&~creative(X))))&
(![X]:((kind(X)&wise(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(~quiet(X)<=>(calm(X)|funny(X))))&
(![X]:(~old(X)<=>(~creative(X)&~calm(X))))&
(calm(lucy))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((~generous(X)<~>~strong(X))))&
((~tall(mary)|creative(mary)))&
((curious(paul)|~funny(paul)))&
(?[X]:((quiet(X)|~strong(X)))) | ~brave(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7550184614351976304357071
% SZS output start Proof for 7550184614351976304357071
11. ! [X0] : ((brave(X0) | ~strong(X0)) <=> strong(X0)) [input p10]
23. ~brave(paul) [input hypothesis]
51. ! [X0] : (((brave(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (~brave(X0) & strong(X0)))) [nnf transformation 11]
52. ! [X0] : ((brave(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (~brave(X0) & strong(X0)))) [flattening 51]
98. strong(X0) | strong(X0) [cnf transformation 52]
100. brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 52]
123. ~brave(paul) [cnf transformation 23]
124. strong(X0) [duplicate literal removal 98]
125. ~strong(X0) | brave(X0) [duplicate literal removal 100]
175. 10 <=> brave(paul) [avatar definition]
177. ~brave(paul) <- (~10) [avatar component clause 175]
229. ~10 [avatar split clause 123,175]
234. brave(X0) [resolution 125,124]
235. $false <- (~10) [resolution 234,177]
237. 10 [avatar contradiction clause 235]
238. $false [avatar sat refutation 229,237]
% SZS output end Proof for 7550184614351976304357071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is both not kind and not quiet. Everyone who is both humble and not quiet is either not humble or not strong and vice versa. If alice is either humble or not kind then alice is not patient. If someone is either curious or happy then mary is both not strong and kind. Everyone who is either funny or wise is not rich. Everyone who is tall is either wise or not funny and vice versa. Everyone who is both brave and kind is both not curious and wise. If someone is either rich or not wise then someone is wise and vice versa. If john is not creative or not generous then someone is either wise or old and vice versa. If someone is either kind or curious then lucy is either wise or not rich and vice versa. Everyone who is not happy or humble is both not strong and not wise and vice versa. Everyone who is either brave or creative is either not rich or rich and vice versa. Everyone who is humble is either not wise or not curious and vice versa. If someone is both not brave and kind then someone is humble. If alice is either not humble or not generous then someone is either creative or generous and vice versa. Everyone who is generous is both not strong and not brave. Someone is creative. Someone is humble. Someone is both quiet and curious. Fred is either not patient or not generous. Mary is creative or patient. Alice is either not wise or not funny. Susan is either not quiet or not old. | Lucy is generous. | neutral | (![X]:(~rich(X)=>(~kind(X)&~quiet(X))))&
(![X]:((humble(X)&~quiet(X))<=>(~humble(X)<~>~strong(X))))&
(((humble(alice)<~>~kind(alice)))=>(~patient(alice)))&
((?[X]:((curious(X)<~>happy(X))))=>((~strong(mary)&kind(mary))))&
(![X]:((funny(X)<~>wise(X))=>~rich(X)))&
(![X]:(tall(X)<=>(wise(X)<~>~funny(X))))&
(![X]:((brave(X)&kind(X))=>(~curious(X)&wise(X))))&
((?[X]:((rich(X)<~>~wise(X))))<=>(?[X]:(wise(X))))&
(((~creative(john)|~generous(john)))<=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((kind(X)<~>curious(X))))<=>((wise(lucy)<~>~rich(lucy))))&
(![X]:((~happy(X)|humble(X))<=>(~strong(X)&~wise(X))))&
(![X]:((brave(X)<~>creative(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(humble(X)<=>(~wise(X)<~>~curious(X))))&
((?[X]:((~brave(X)&kind(X))))=>(?[X]:(humble(X))))&
(((~humble(alice)<~>~generous(alice)))<=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:(generous(X)=>(~strong(X)&~brave(X))))&
(?[X]:(creative(X)))&
(?[X]:(humble(X)))&
(?[X]:((quiet(X)&curious(X))))&
((~patient(fred)<~>~generous(fred)))&
((creative(mary)|patient(mary)))&
((~wise(alice)<~>~funny(alice)))&
((~quiet(susan)<~>~old(susan))) | generous(lucy) | [] | null | 0 |
If john is patient then susan is either not rich or strong and vice versa.
If lucy is either funny or not patient then john is either not calm or not old and vice versa.
Everyone who is both not patient and not tall is both not curious and not quiet.
Everyone who is old or kind is both rich and strong.
Everyone who is humble or generous is either quiet or not patient and vice versa.
Everyone who is both calm and not tall is either happy or funny.
If lucy is both not strong and happy then someone is not calm.
If mary is not patient or humble then lucy is either not generous or not creative and vice versa.
Everyone who is either funny or tall is not wise and vice versa.
If someone is quiet or not happy then someone is not strong.
Everyone who is either not wise or patient is funny or curious and vice versa.
If john is not wise or quiet then someone is either kind or funny.
Everyone who is either creative or old is both curious and not old and vice versa.
Everyone who is either happy or not calm is either creative or kind and vice versa.
Everyone who is both tall and not curious is rich and vice versa.
Everyone who is curious is both old and not wise and vice versa.
John is both not calm and brave.
Someone is either not creative or curious.
Someone is both humble and not quiet.
Someone is either generous or not funny.
Paul is either not brave or humble.
Paul is either wise or not kind.
Paul is both brave and strong. | Susan is not happy. | neutral | ((patient(john))<=>((~rich(susan)<~>strong(susan))))&
(((funny(lucy)<~>~patient(lucy)))<=>((~calm(john)<~>~old(john))))&
(![X]:((~patient(X)&~tall(X))=>(~curious(X)&~quiet(X))))&
(![X]:((old(X)|kind(X))=>(rich(X)&strong(X))))&
(![X]:((humble(X)|generous(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((calm(X)&~tall(X))=>(happy(X)<~>funny(X))))&
(((~strong(lucy)&happy(lucy)))=>(?[X]:(~calm(X))))&
(((~patient(mary)|humble(mary)))<=>((~generous(lucy)<~>~creative(lucy))))&
(![X]:((funny(X)<~>tall(X))<=>~wise(X)))&
((?[X]:((quiet(X)|~happy(X))))=>(?[X]:(~strong(X))))&
(![X]:((~wise(X)<~>patient(X))<=>(funny(X)|curious(X))))&
(((~wise(john)|quiet(john)))=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:((creative(X)<~>old(X))<=>(curious(X)&~old(X))))&
(![X]:((happy(X)<~>~calm(X))<=>(creative(X)<~>kind(X))))&
(![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:(curious(X)<=>(old(X)&~wise(X))))&
((~calm(john)&brave(john)))&
(?[X]:((~creative(X)<~>curious(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((generous(X)<~>~funny(X))))&
((~brave(paul)<~>humble(paul)))&
((wise(paul)<~>~kind(paul)))&
((brave(paul)&strong(paul))) | ~happy(susan) | [] | null | 0 |
Everyone who is both brave and not humble is both not generous and not old.
If lucy is both rich and quiet then someone is patient.
If paul is not generous then alice is either not happy or tall and vice versa.
Everyone who is either not rich or rich is both calm and not humble and vice versa.
If fred is either not creative or not patient then susan is either humble or not generous and vice versa.
If john is humble or not generous then someone is strong and vice versa.
Everyone who is either patient or not patient is both creative and calm and vice versa.
Everyone who is both not quiet and rich is either kind or not rich.
If lucy is kind or quiet then someone is wise.
If paul is either not old or happy then john is kind or not funny and vice versa.
Everyone who is not humble is both patient and not happy.
Everyone who is not brave or not tall is either not happy or happy and vice versa.
Everyone who is funny is both humble and not creative.
Everyone who is either not patient or brave is either rich or calm.
If alice is either happy or curious then someone is both not tall and happy.
Everyone who is either not generous or funny is not strong.
Someone is either tall or brave.
Someone is old.
Fred is wise or generous.
Someone is both not generous and wise.
Someone is either generous or not curious.
Alice is tall.
Alice is kind.
Lucy is curious. | Alice is not funny. | entailment | (![X]:((brave(X)&~humble(X))=>(~generous(X)&~old(X))))&
(((rich(lucy)&quiet(lucy)))=>(?[X]:(patient(X))))&
((~generous(paul))<=>((~happy(alice)<~>tall(alice))))&
(![X]:((~rich(X)<~>rich(X))<=>(calm(X)&~humble(X))))&
(((~creative(fred)<~>~patient(fred)))<=>((humble(susan)<~>~generous(susan))))&
(((humble(john)|~generous(john)))<=>(?[X]:(strong(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(creative(X)&calm(X))))&
(![X]:((~quiet(X)&rich(X))=>(kind(X)<~>~rich(X))))&
(((kind(lucy)|quiet(lucy)))=>(?[X]:(wise(X))))&
(((~old(paul)<~>happy(paul)))<=>((kind(john)|~funny(john))))&
(![X]:(~humble(X)=>(patient(X)&~happy(X))))&
(![X]:((~brave(X)|~tall(X))<=>(~happy(X)<~>happy(X))))&
(![X]:(funny(X)=>(humble(X)&~creative(X))))&
(![X]:((~patient(X)<~>brave(X))=>(rich(X)<~>calm(X))))&
(((happy(alice)<~>curious(alice)))=>(?[X]:((~tall(X)&happy(X)))))&
(![X]:((~generous(X)<~>funny(X))=>~strong(X)))&
(?[X]:((tall(X)<~>brave(X))))&
(?[X]:(old(X)))&
((wise(fred)|generous(fred)))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(tall(alice))&
(kind(alice))&
(curious(lucy)) | ~funny(alice) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6395692542162366638135440
% SZS output start Proof for 6395692542162366638135440
7. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (calm(X0) & creative(X0))) [input p6]
13. ! [X0] : (funny(X0) => (~creative(X0) & humble(X0))) [input p12]
25. funny(alice) [input hypothesis]
36. ! [X0] : ((~creative(X0) & humble(X0)) | ~funny(X0)) [ennf transformation 13]
51. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 7]
52. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 51]
97. creative(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 52]
98. creative(X0) | patient(X0) | patient(X0) [cnf transformation 52]
120. ~creative(X0) | ~funny(X0) [cnf transformation 36]
140. funny(alice) [cnf transformation 25]
144. creative(X0) | ~patient(X0) [duplicate literal removal 97]
145. creative(X0) | patient(X0) [duplicate literal removal 98]
217. creative(X0) [subsumption resolution 144,145]
243. ~funny(X0) [subsumption resolution 120,217]
269. $false [subsumption resolution 140,243]
% SZS output end Proof for 6395692542162366638135440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or humble is not calm or not generous.
Everyone who is kind or tall is not creative or not calm.
If mary is not wise or not creative then someone is not rich.
Everyone who is both not wise and not rich is funny and vice versa.
Everyone who is either generous or not old is both not humble and old.
If mary is either not strong or not generous then paul is either generous or wise.
If john is not generous or wise then someone is both not quiet and not strong and vice versa.
Everyone who is both kind and not quiet is both not kind and funny.
Everyone who is either old or not curious is strong.
If paul is both not strong and generous then john is not strong or not wise and vice versa.
Everyone who is either calm or not calm is both not tall and curious and vice versa.
If paul is both kind and not quiet then someone is not rich and vice versa.
If fred is either tall or not calm then someone is both old and not tall and vice versa.
Everyone who is both not quiet and strong is both not curious and not brave.
Everyone who is creative is both not calm and not patient and vice versa.
Everyone who is generous is kind or not humble and vice versa.
Fred is not kind.
John is brave or strong.
Someone is either not patient or rich.
Mary is either not quiet or quiet.
John is not patient or not creative.
Paul is both creative and not generous.
Someone is not funny.
Lucy is both patient and not funny. | Lucy is not tall. | entailment | (![X]:((calm(X)<~>humble(X))=>(~calm(X)|~generous(X))))&
(![X]:((kind(X)|tall(X))=>(~creative(X)|~calm(X))))&
(((~wise(mary)|~creative(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~rich(X))<=>funny(X)))&
(![X]:((generous(X)<~>~old(X))=>(~humble(X)&old(X))))&
(((~strong(mary)<~>~generous(mary)))=>((generous(paul)<~>wise(paul))))&
(((~generous(john)|wise(john)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((kind(X)&~quiet(X))=>(~kind(X)&funny(X))))&
(![X]:((old(X)<~>~curious(X))=>strong(X)))&
(((~strong(paul)&generous(paul)))<=>((~strong(john)|~wise(john))))&
(![X]:((calm(X)<~>~calm(X))<=>(~tall(X)&curious(X))))&
(((kind(paul)&~quiet(paul)))<=>(?[X]:(~rich(X))))&
(((tall(fred)<~>~calm(fred)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~curious(X)&~brave(X))))&
(![X]:(creative(X)<=>(~calm(X)&~patient(X))))&
(![X]:(generous(X)<=>(kind(X)|~humble(X))))&
(~kind(fred))&
((brave(john)|strong(john)))&
(?[X]:((~patient(X)<~>rich(X))))&
((~quiet(mary)<~>quiet(mary)))&
((~patient(john)|~creative(john)))&
((creative(paul)&~generous(paul)))&
(?[X]:(~funny(X)))&
((patient(lucy)&~funny(lucy))) | ~tall(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4835054932722374621188796
% SZS output start Proof for 4835054932722374621188796
11. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> (curious(X0) & ~tall(X0))) [input p10]
25. tall(lucy) [input hypothesis]
53. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | (~curious(X0) | tall(X0))) & ((curious(X0) & ~tall(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 11]
54. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ~curious(X0) | tall(X0)) & ((curious(X0) & ~tall(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [flattening 53]
105. ~tall(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 54]
106. ~tall(X0) | calm(X0) | calm(X0) [cnf transformation 54]
140. tall(lucy) [cnf transformation 25]
141. ~tall(X0) | ~calm(X0) [duplicate literal removal 105]
142. ~tall(X0) | calm(X0) [duplicate literal removal 106]
220. ~tall(X0) [subsumption resolution 141,142]
267. $false [subsumption resolution 140,220]
% SZS output end Proof for 4835054932722374621188796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and wise is both not kind and patient. If someone is quiet then someone is both creative and not funny. Everyone who is curious or funny is both curious and not creative and vice versa. If susan is tall then alice is both quiet and tall and vice versa. If someone is not patient or strong then someone is both not patient and not strong and vice versa. Everyone who is happy or not tall is quiet or not quiet. If someone is both quiet and not creative then someone is brave or not happy and vice versa. Everyone who is either brave or humble is both not calm and happy and vice versa. Everyone who is both not creative and curious is not old or happy and vice versa. Everyone who is either creative or funny is funny and vice versa. Everyone who is either not rich or creative is both not patient and not humble and vice versa. If john is not wise or generous then someone is both not funny and not kind. If someone is not old or not curious then fred is either strong or not rich. If alice is both not tall and not humble then susan is either humble or not quiet and vice versa. Everyone who is not humble is either funny or not creative. Everyone who is humble or not quiet is not strong or rich and vice versa. Someone is not patient or not kind. Someone is either strong or kind. Alice is both not creative and strong. Fred is either wise or not rich. Mary is either rich or not brave. | Susan is not rich. | neutral | (![X]:((brave(X)&wise(X))=>(~kind(X)&patient(X))))&
((?[X]:(quiet(X)))=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:((curious(X)|funny(X))<=>(curious(X)&~creative(X))))&
((tall(susan))<=>((quiet(alice)&tall(alice))))&
((?[X]:((~patient(X)|strong(X))))<=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:((happy(X)|~tall(X))=>(quiet(X)|~quiet(X))))&
((?[X]:((quiet(X)&~creative(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)&happy(X))))&
(![X]:((~creative(X)&curious(X))<=>(~old(X)|happy(X))))&
(![X]:((creative(X)<~>funny(X))<=>funny(X)))&
(![X]:((~rich(X)<~>creative(X))<=>(~patient(X)&~humble(X))))&
(((~wise(john)|generous(john)))=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((~old(X)|~curious(X))))=>((strong(fred)<~>~rich(fred))))&
(((~tall(alice)&~humble(alice)))<=>((humble(susan)<~>~quiet(susan))))&
(![X]:(~humble(X)=>(funny(X)<~>~creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~strong(X)|rich(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((strong(X)<~>kind(X))))&
((~creative(alice)&strong(alice)))&
((wise(fred)<~>~rich(fred)))&
((rich(mary)<~>~brave(mary))) | ~rich(susan) | [] | null | 0 |
If alice is not quiet or funny then mary is not patient and vice versa.
Everyone who is not patient or old is rich or happy.
Everyone who is tall is either happy or not creative and vice versa.
Everyone who is rich is either tall or humble.
If fred is brave then someone is not happy.
If someone is not old or not kind then alice is both patient and wise.
Everyone who is both old and happy is either not curious or brave.
Everyone who is not humble or not strong is not patient and vice versa.
Everyone who is not tall or not calm is curious.
If paul is either happy or old then lucy is both not patient and tall and vice versa.
If paul is not creative then someone is not humble or kind.
If paul is rich or generous then fred is both not humble and not generous.
Everyone who is wise is calm.
If lucy is tall or not strong then someone is not humble or not generous.
Everyone who is not generous is creative or tall.
If john is not happy or not tall then alice is either not patient or not strong and vice versa.
Someone is either not strong or happy.
Someone is either creative or rich.
John is both not strong and not patient.
Lucy is wise or not patient.
Someone is either not rich or happy.
Paul is curious or quiet.
Paul is quiet or not funny. | Fred is not strong. | neutral | (((~quiet(alice)|funny(alice)))<=>(~patient(mary)))&
(![X]:((~patient(X)|old(X))=>(rich(X)|happy(X))))&
(![X]:(tall(X)<=>(happy(X)<~>~creative(X))))&
(![X]:(rich(X)=>(tall(X)<~>humble(X))))&
((brave(fred))=>(?[X]:(~happy(X))))&
((?[X]:((~old(X)|~kind(X))))=>((patient(alice)&wise(alice))))&
(![X]:((old(X)&happy(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~humble(X)|~strong(X))<=>~patient(X)))&
(![X]:((~tall(X)|~calm(X))=>curious(X)))&
(((happy(paul)<~>old(paul)))<=>((~patient(lucy)&tall(lucy))))&
((~creative(paul))=>(?[X]:((~humble(X)|kind(X)))))&
(((rich(paul)|generous(paul)))=>((~humble(fred)&~generous(fred))))&
(![X]:(wise(X)=>calm(X)))&
(((tall(lucy)|~strong(lucy)))=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:(~generous(X)=>(creative(X)|tall(X))))&
(((~happy(john)|~tall(john)))<=>((~patient(alice)<~>~strong(alice))))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:((creative(X)<~>rich(X))))&
((~strong(john)&~patient(john)))&
((wise(lucy)|~patient(lucy)))&
(?[X]:((~rich(X)<~>happy(X))))&
((curious(paul)|quiet(paul)))&
((quiet(paul)|~funny(paul))) | ~strong(fred) | [] | null | 0 |
Everyone who is not quiet is either not quiet or calm.
Everyone who is not creative or brave is either happy or not happy and vice versa.
If someone is not brave or rich then fred is strong and vice versa.
Everyone who is kind or not quiet is either rich or curious and vice versa.
If fred is either tall or strong then someone is both rich and humble.
Everyone who is both patient and not rich is generous or not calm and vice versa.
If susan is creative then someone is both old and humble.
If someone is quiet then lucy is not rich or not strong.
Everyone who is both not patient and not old is either not curious or curious and vice versa.
If someone is both wise and not happy then someone is both rich and not kind.
If mary is both funny and creative then alice is not funny.
If someone is curious or patient then john is either humble or not rich.
Everyone who is either creative or not quiet is either not creative or not humble.
Everyone who is not creative or rich is not funny.
Everyone who is brave or quiet is both not creative and quiet.
If someone is brave or creative then someone is either not happy or not old and vice versa.
John is not happy.
Fred is not tall.
Lucy is tall or not rich.
Lucy is not calm or not kind.
Lucy is patient or not wise.
Someone is not generous. | John is not quiet. | contradiction | (![X]:(~quiet(X)=>(~quiet(X)<~>calm(X))))&
(![X]:((~creative(X)|brave(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:((~brave(X)|rich(X))))<=>(strong(fred)))&
(![X]:((kind(X)|~quiet(X))<=>(rich(X)<~>curious(X))))&
(((tall(fred)<~>strong(fred)))=>(?[X]:((rich(X)&humble(X)))))&
(![X]:((patient(X)&~rich(X))<=>(generous(X)|~calm(X))))&
((creative(susan))=>(?[X]:((old(X)&humble(X)))))&
((?[X]:(quiet(X)))=>((~rich(lucy)|~strong(lucy))))&
(![X]:((~patient(X)&~old(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((wise(X)&~happy(X))))=>(?[X]:((rich(X)&~kind(X)))))&
(((funny(mary)&creative(mary)))=>(~funny(alice)))&
((?[X]:((curious(X)|patient(X))))=>((humble(john)<~>~rich(john))))&
(![X]:((creative(X)<~>~quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((~creative(X)|rich(X))=>~funny(X)))&
(![X]:((brave(X)|quiet(X))=>(~creative(X)&quiet(X))))&
((?[X]:((brave(X)|creative(X))))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(~happy(john))&
(~tall(fred))&
((tall(lucy)|~rich(lucy)))&
((~calm(lucy)|~kind(lucy)))&
((patient(lucy)|~wise(lucy)))&
(?[X]:(~generous(X))) | ~quiet(john) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8818609179135769182674432
% SZS output start Proof for 8818609179135769182674432
1. ! [X0] : (~quiet(X0) => (~quiet(X0) <~> calm(X0))) [input p0]
6. ! [X0] : ((~rich(X0) & patient(X0)) <=> (~calm(X0) | generous(X0))) [input p5]
9. ! [X0] : ((~old(X0) & ~patient(X0)) <=> (~curious(X0) <~> curious(X0))) [input p8]
23. ~quiet(john) [input hypothesis]
30. ! [X0] : ((~quiet(X0) <~> calm(X0)) | quiet(X0)) [ennf transformation 1]
38. ! [X0] : (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | quiet(X0)) [nnf transformation 30]
50. ! [X0] : (((~rich(X0) & patient(X0)) | (calm(X0) & ~generous(X0))) & ((~calm(X0) | generous(X0)) | (rich(X0) | ~patient(X0)))) [nnf transformation 6]
51. ! [X0] : (((~rich(X0) & patient(X0)) | (calm(X0) & ~generous(X0))) & (~calm(X0) | generous(X0) | rich(X0) | ~patient(X0))) [flattening 50]
54. ! [X0] : (((~old(X0) & ~patient(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | (old(X0) | patient(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~patient(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | old(X0) | patient(X0))) [flattening 54]
66. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
88. patient(X0) | calm(X0) [cnf transformation 51]
96. ~patient(X0) | curious(X0) | curious(X0) [cnf transformation 55]
97. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 55]
123. ~quiet(john) [cnf transformation 23]
126. ~patient(X0) | curious(X0) [duplicate literal removal 96]
127. ~patient(X0) | ~curious(X0) [duplicate literal removal 97]
132. ~calm(X0) | quiet(X0) [duplicate literal removal 66]
198. ~patient(X0) [subsumption resolution 126,127]
251. calm(X0) [resolution 88,198]
260. quiet(X0) [resolution 132,251]
261. $false [resolution 260,123]
% SZS output end Proof for 8818609179135769182674432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or creative is either wise or not patient and vice versa.
Everyone who is both curious and happy is both not funny and not quiet and vice versa.
If paul is both not happy and not quiet then john is both not humble and not kind.
Everyone who is not creative or not tall is funny.
Everyone who is not calm is old or happy and vice versa.
If someone is either not curious or not patient then paul is not old.
Everyone who is either curious or not tall is both brave and old and vice versa.
If someone is both happy and quiet then john is either not wise or not happy.
If john is either humble or brave then someone is not funny and vice versa.
Everyone who is both wise and brave is creative or calm and vice versa.
Everyone who is not rich or not patient is not rich or creative and vice versa.
Everyone who is either patient or wise is both not generous and tall.
Everyone who is either generous or calm is either not quiet or strong and vice versa.
Everyone who is calm or not wise is rich or not strong.
Everyone who is both old and not quiet is patient and vice versa.
Everyone who is both curious and rich is both patient and not quiet.
Someone is wise.
Someone is not happy or curious.
Someone is wise or not generous.
Someone is both happy and not strong.
Someone is both not rich and not happy.
Someone is not wise.
Someone is either not strong or quiet. | Paul is creative. | neutral | (![X]:((~calm(X)<~>creative(X))<=>(wise(X)<~>~patient(X))))&
(![X]:((curious(X)&happy(X))<=>(~funny(X)&~quiet(X))))&
(((~happy(paul)&~quiet(paul)))=>((~humble(john)&~kind(john))))&
(![X]:((~creative(X)|~tall(X))=>funny(X)))&
(![X]:(~calm(X)<=>(old(X)|happy(X))))&
((?[X]:((~curious(X)<~>~patient(X))))=>(~old(paul)))&
(![X]:((curious(X)<~>~tall(X))<=>(brave(X)&old(X))))&
((?[X]:((happy(X)&quiet(X))))=>((~wise(john)<~>~happy(john))))&
(((humble(john)<~>brave(john)))<=>(?[X]:(~funny(X))))&
(![X]:((wise(X)&brave(X))<=>(creative(X)|calm(X))))&
(![X]:((~rich(X)|~patient(X))<=>(~rich(X)|creative(X))))&
(![X]:((patient(X)<~>wise(X))=>(~generous(X)&tall(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~quiet(X)<~>strong(X))))&
(![X]:((calm(X)|~wise(X))=>(rich(X)|~strong(X))))&
(![X]:((old(X)&~quiet(X))<=>patient(X)))&
(![X]:((curious(X)&rich(X))=>(patient(X)&~quiet(X))))&
(?[X]:(wise(X)))&
(?[X]:((~happy(X)|curious(X))))&
(?[X]:((wise(X)|~generous(X))))&
(?[X]:((happy(X)&~strong(X))))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~strong(X)<~>quiet(X)))) | creative(paul) | [] | null | 0 |
If someone is not funny or rich then someone is either not generous or brave and vice versa. If someone is both old and not creative then someone is both quiet and happy and vice versa. Everyone who is old or quiet is either kind or creative and vice versa. Everyone who is patient or not quiet is both creative and not quiet and vice versa. If someone is either humble or not calm then mary is not humble. Everyone who is not happy or not curious is either tall or not humble and vice versa. Everyone who is either happy or not brave is kind. Everyone who is both creative and strong is both old and calm and vice versa. Everyone who is either kind or creative is not quiet and vice versa. If someone is not happy or quiet then someone is old. If lucy is either not strong or not tall then someone is curious. If someone is not kind then susan is either not humble or not brave and vice versa. If fred is either happy or not tall then fred is creative or not wise and vice versa. If someone is either not strong or old then paul is either not rich or tall and vice versa. Everyone who is tall or not strong is not old or brave. Lucy is not curious. Alice is either not creative or not calm. Someone is either not quiet or wise. Lucy is not patient. Someone is either not wise or calm. Someone is either rich or tall. Susan is either brave or patient. | Fred is not creative. | contradiction | ((?[X]:((~funny(X)|rich(X))))<=>(?[X]:((~generous(X)<~>brave(X)))))&
((?[X]:((old(X)&~creative(X))))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((old(X)|quiet(X))<=>(kind(X)<~>creative(X))))&
(![X]:((patient(X)|~quiet(X))<=>(creative(X)&~quiet(X))))&
((?[X]:((humble(X)<~>~calm(X))))=>(~humble(mary)))&
(![X]:((~happy(X)|~curious(X))<=>(tall(X)<~>~humble(X))))&
(![X]:((happy(X)<~>~brave(X))=>kind(X)))&
(![X]:((creative(X)&strong(X))<=>(old(X)&calm(X))))&
(![X]:((kind(X)<~>creative(X))<=>~quiet(X)))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:(old(X))))&
(((~strong(lucy)<~>~tall(lucy)))=>(?[X]:(curious(X))))&
((?[X]:(~kind(X)))<=>((~humble(susan)<~>~brave(susan))))&
(((happy(fred)<~>~tall(fred)))<=>((creative(fred)|~wise(fred))))&
((?[X]:((~strong(X)<~>old(X))))<=>((~rich(paul)<~>tall(paul))))&
(![X]:((tall(X)|~strong(X))=>(~old(X)|brave(X))))&
(~curious(lucy))&
((~creative(alice)<~>~calm(alice)))&
(?[X]:((~quiet(X)<~>wise(X))))&
(~patient(lucy))&
(?[X]:((~wise(X)<~>calm(X))))&
(?[X]:((rich(X)<~>tall(X))))&
((brave(susan)<~>patient(susan))) | ~creative(fred) | [
"p2",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6656422647226994506289939
% SZS output start Proof for 6656422647226994506289939
3. ! [X0] : ((quiet(X0) | old(X0)) <=> (kind(X0) <~> creative(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) | patient(X0)) <=> (~quiet(X0) & creative(X0))) [input p3]
9. ! [X0] : ((kind(X0) <~> creative(X0)) <=> ~quiet(X0)) [input p8]
23. ~creative(fred) [input hypothesis]
43. ! [X0] : (((quiet(X0) | old(X0)) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | (~quiet(X0) & ~old(X0)))) [nnf transformation 3]
44. ! [X0] : ((quiet(X0) | old(X0) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0)))) & (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | (~quiet(X0) & ~old(X0)))) [flattening 43]
45. ! [X0] : (((~quiet(X0) | patient(X0)) | (quiet(X0) | ~creative(X0))) & ((~quiet(X0) & creative(X0)) | (quiet(X0) & ~patient(X0)))) [nnf transformation 4]
46. ! [X0] : ((~quiet(X0) | patient(X0) | quiet(X0) | ~creative(X0)) & ((~quiet(X0) & creative(X0)) | (quiet(X0) & ~patient(X0)))) [flattening 45]
53. ! [X0] : ((((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | quiet(X0)) & (~quiet(X0) | ((kind(X0) | ~creative(X0)) & (creative(X0) | ~kind(X0))))) [nnf transformation 9]
92. creative(X0) | kind(X0) | ~quiet(X0) [cnf transformation 44]
94. ~creative(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 44]
98. quiet(X0) | creative(X0) [cnf transformation 46]
116. ~quiet(X0) | creative(X0) | ~kind(X0) [cnf transformation 53]
117. ~quiet(X0) | kind(X0) | ~creative(X0) [cnf transformation 53]
119. ~creative(X0) | ~kind(X0) | quiet(X0) [cnf transformation 53]
156. ~creative(fred) [cnf transformation 23]
229. ~kind(X0) | quiet(X0) [subsumption resolution 119,98]
230. ~quiet(X0) | kind(X0) [subsumption resolution 117,92]
231. ~quiet(X0) | ~kind(X0) [subsumption resolution 116,94]
232. ~kind(X0) [subsumption resolution 231,229]
285. 29 <=> creative(fred) [avatar definition]
287. ~creative(fred) <- (~29) [avatar component clause 285]
369. ~29 [avatar split clause 156,285]
372. kind(X0) | creative(X0) [resolution 230,98]
373. creative(X0) [subsumption resolution 372,232]
374. $false <- (~29) [resolution 373,287]
375. 29 [avatar contradiction clause 374]
376. $false [avatar sat refutation 369,375]
% SZS output end Proof for 6656422647226994506289939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or calm is both not creative and rich and vice versa.
If someone is not generous then paul is humble or patient and vice versa.
Everyone who is not happy is not strong and vice versa.
Everyone who is calm is both calm and not strong.
Everyone who is either kind or tall is not quiet or not old.
If mary is curious or not kind then john is not quiet or wise and vice versa.
Everyone who is not kind or not tall is both not generous and happy and vice versa.
If someone is either not curious or not brave then someone is not quiet or not happy and vice versa.
Everyone who is rich is not humble or not calm and vice versa.
Everyone who is strong is not curious or kind and vice versa.
Everyone who is happy or curious is both old and not calm and vice versa.
Everyone who is humble is not strong.
Everyone who is both not happy and not humble is not tall and vice versa.
If john is not brave or generous then someone is either tall or creative.
Everyone who is not calm or wise is either not generous or kind.
Everyone who is both brave and strong is not funny or tall and vice versa.
Someone is either calm or funny.
Someone is not curious or not humble.
Fred is both not kind and patient.
Paul is wise.
Fred is either creative or not generous.
Susan is not quiet.
Mary is either quiet or not rich. | Fred is happy. | entailment | (![X]:((~quiet(X)<~>calm(X))<=>(~creative(X)&rich(X))))&
((?[X]:(~generous(X)))<=>((humble(paul)|patient(paul))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(calm(X)=>(calm(X)&~strong(X))))&
(![X]:((kind(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(((curious(mary)|~kind(mary)))<=>((~quiet(john)|wise(john))))&
(![X]:((~kind(X)|~tall(X))<=>(~generous(X)&happy(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)|~happy(X)))))&
(![X]:(rich(X)<=>(~humble(X)|~calm(X))))&
(![X]:(strong(X)<=>(~curious(X)|kind(X))))&
(![X]:((happy(X)|curious(X))<=>(old(X)&~calm(X))))&
(![X]:(humble(X)=>~strong(X)))&
(![X]:((~happy(X)&~humble(X))<=>~tall(X)))&
(((~brave(john)|generous(john)))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))=>(~generous(X)<~>kind(X))))&
(![X]:((brave(X)&strong(X))<=>(~funny(X)|tall(X))))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~curious(X)|~humble(X))))&
((~kind(fred)&patient(fred)))&
(wise(paul))&
((creative(fred)<~>~generous(fred)))&
(~quiet(susan))&
((quiet(mary)<~>~rich(mary))) | happy(fred) | [
"p2",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 761605106260253304983447
% SZS output start Proof for 761605106260253304983447
3. ! [X0] : (~happy(X0) <=> ~strong(X0)) [input p2]
7. ! [X0] : ((~tall(X0) | ~kind(X0)) <=> (happy(X0) & ~generous(X0))) [input p6]
13. ! [X0] : ((~humble(X0) & ~happy(X0)) <=> ~tall(X0)) [input p12]
16. ! [X0] : ((strong(X0) & brave(X0)) <=> (tall(X0) | ~funny(X0))) [input p15]
24. ~happy(fred) [input hypothesis]
39. ! [X0] : ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))) [nnf transformation 3]
43. ! [X0] : (((~tall(X0) | ~kind(X0)) | (~happy(X0) | generous(X0))) & ((happy(X0) & ~generous(X0)) | (tall(X0) & kind(X0)))) [nnf transformation 7]
44. ! [X0] : ((~tall(X0) | ~kind(X0) | ~happy(X0) | generous(X0)) & ((happy(X0) & ~generous(X0)) | (tall(X0) & kind(X0)))) [flattening 43]
56. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (humble(X0) | happy(X0)))) [nnf transformation 13]
57. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | humble(X0) | happy(X0))) [flattening 56]
62. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 16]
63. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~strong(X0) | ~brave(X0))) [flattening 62]
80. ~strong(X0) | happy(X0) [cnf transformation 39]
93. happy(X0) | tall(X0) [cnf transformation 44]
114. ~happy(X0) | tall(X0) [cnf transformation 57]
128. strong(X0) | ~tall(X0) [cnf transformation 63]
140. ~happy(fred) [cnf transformation 24]
180. 9 <=> ! [X1] : happy(X1) [avatar definition]
181. happy(X1) <- (9) [avatar component clause 180]
213. tall(X0) [subsumption resolution 114,93]
231. strong(X0) [subsumption resolution 128,213]
274. happy(X0) [resolution 80,231]
275. 9 [avatar split clause 274,180]
276. $false <- (9) [resolution 181,140]
277. ~9 [avatar contradiction clause 276]
278. $false [avatar sat refutation 275,277]
% SZS output end Proof for 761605106260253304983447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If susan is either tall or quiet then susan is both old and patient and vice versa.
If someone is not kind or rich then someone is both generous and not generous and vice versa.
Everyone who is curious is wise.
Everyone who is quiet or not kind is not quiet.
If fred is both not funny and quiet then susan is not generous.
Everyone who is happy is brave or old and vice versa.
If someone is not old or funny then someone is not tall or not curious.
Everyone who is not calm or creative is both not curious and not wise.
Everyone who is both wise and not humble is strong or happy.
Everyone who is calm is patient or happy and vice versa.
If someone is happy then someone is not calm and vice versa.
If someone is not brave then alice is either kind or calm.
Everyone who is either kind or not brave is either old or not wise.
Everyone who is either not rich or happy is not tall and vice versa.
If mary is both creative and generous then john is funny or not funny and vice versa.
Everyone who is both calm and not creative is either not wise or funny.
Someone is calm.
Someone is not wise or generous.
Lucy is either tall or not generous.
Susan is either brave or strong.
Someone is both patient and curious.
Lucy is both not funny and not patient. | Alice is not curious. | entailment | (((tall(susan)<~>quiet(susan)))<=>((old(susan)&patient(susan))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:(curious(X)=>wise(X)))&
(![X]:((quiet(X)|~kind(X))=>~quiet(X)))&
(((~funny(fred)&quiet(fred)))=>(~generous(susan)))&
(![X]:(happy(X)<=>(brave(X)|old(X))))&
((?[X]:((~old(X)|funny(X))))=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~calm(X)|creative(X))=>(~curious(X)&~wise(X))))&
(![X]:((wise(X)&~humble(X))=>(strong(X)|happy(X))))&
(![X]:(calm(X)<=>(patient(X)|happy(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~calm(X))))&
((?[X]:(~brave(X)))=>((kind(alice)<~>calm(alice))))&
(![X]:((kind(X)<~>~brave(X))=>(old(X)<~>~wise(X))))&
(![X]:((~rich(X)<~>happy(X))<=>~tall(X)))&
(((creative(mary)&generous(mary)))<=>((funny(john)|~funny(john))))&
(![X]:((calm(X)&~creative(X))=>(~wise(X)<~>funny(X))))&
(?[X]:(calm(X)))&
(?[X]:((~wise(X)|generous(X))))&
((tall(lucy)<~>~generous(lucy)))&
((brave(susan)<~>strong(susan)))&
(?[X]:((patient(X)&curious(X))))&
((~funny(lucy)&~patient(lucy))) | ~curious(alice) | [
"p1",
"p5",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2672859171569125848506446
% SZS output start Proof for 2672859171569125848506446
2. ? [X0] : (rich(X0) | ~kind(X0)) <=> ? [X0] : (~generous(X0) & generous(X0)) [input p1]
6. ! [X0] : (happy(X0) <=> (old(X0) | brave(X0))) [input p5]
8. ! [X0] : ((creative(X0) | ~calm(X0)) => (~wise(X0) & ~curious(X0))) [input p7]
10. ! [X0] : (calm(X0) <=> (happy(X0) | patient(X0))) [input p9]
11. ? [X0] : happy(X0) <=> ? [X0] : ~calm(X0) [input p10]
12. ? [X0] : ~brave(X0) => (kind(alice) <~> calm(alice)) [input p11]
23. curious(alice) [input hypothesis]
24. ? [X0] : (rich(X0) | ~kind(X0)) <=> ? [X1] : (~generous(X1) & generous(X1)) [rectify 2]
26. ? [X0] : happy(X0) <=> ? [X1] : ~calm(X1) [rectify 11]
33. ! [X0] : ((~wise(X0) & ~curious(X0)) | (~creative(X0) & calm(X0))) [ennf transformation 8]
34. (kind(alice) <~> calm(alice)) | ! [X0] : brave(X0) [ennf transformation 12]
40. (? [X0] : (rich(X0) | ~kind(X0)) | ! [X1] : (generous(X1) | ~generous(X1))) & (? [X1] : (~generous(X1) & generous(X1)) | ! [X0] : (~rich(X0) & kind(X0))) [nnf transformation 24]
41. (? [X0] : (rich(X0) | ~kind(X0)) | ! [X1] : (generous(X1) | ~generous(X1))) & (? [X2] : (~generous(X2) & generous(X2)) | ! [X3] : (~rich(X3) & kind(X3))) [rectify 40]
42. ? [X0] : (rich(X0) | ~kind(X0)) => (rich(sK0) | ~kind(sK0)) [choice axiom]
43. ? [X2] : (~generous(X2) & generous(X2)) => (~generous(sK1) & generous(sK1)) [choice axiom]
44. ((rich(sK0) | ~kind(sK0)) | ! [X1] : (generous(X1) | ~generous(X1))) & ((~generous(sK1) & generous(sK1)) | ! [X3] : (~rich(X3) & kind(X3))) [skolemisation 41,43,42]
45. ! [X0] : ((happy(X0) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ~happy(X0))) [nnf transformation 6]
46. ! [X0] : ((happy(X0) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ~happy(X0))) [flattening 45]
50. ! [X0] : ((calm(X0) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | ~calm(X0))) [nnf transformation 10]
51. ! [X0] : ((calm(X0) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | ~calm(X0))) [flattening 50]
52. (? [X0] : happy(X0) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : ~happy(X0)) [nnf transformation 26]
53. (? [X0] : happy(X0) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : ~happy(X3)) [rectify 52]
54. ? [X0] : happy(X0) => happy(sK3) [choice axiom]
55. ? [X2] : ~calm(X2) => ~calm(sK4) [choice axiom]
56. (happy(sK3) | ! [X1] : calm(X1)) & (~calm(sK4) | ! [X3] : ~happy(X3)) [skolemisation 53,55,54]
57. ((~calm(alice) | ~kind(alice)) & (calm(alice) | kind(alice))) | ! [X0] : brave(X0) [nnf transformation 34]
77. generous(sK1) | kind(X3) [cnf transformation 44]
79. ~generous(sK1) | kind(X3) [cnf transformation 44]
87. ~brave(X0) | happy(X0) [cnf transformation 46]
91. ~curious(X0) | calm(X0) [cnf transformation 33]
97. ~happy(X0) | calm(X0) [cnf transformation 51]
98. ~calm(sK4) | ~happy(X3) [cnf transformation 56]
101. ~calm(alice) | ~kind(alice) | brave(X0) [cnf transformation 57]
127. curious(alice) [cnf transformation 23]
155. 6 <=> generous(sK1) [avatar definition]
160. 7 <=> ! [X3] : kind(X3) [avatar definition]
161. kind(X3) <- (7) [avatar component clause 160]
162. 7 | ~6 [avatar split clause 79,155,160]
164. 7 | 6 [avatar split clause 77,155,160]
182. 12 <=> ! [X1] : calm(X1) [avatar definition]
183. calm(X1) <- (12) [avatar component clause 182]
190. 14 <=> ! [X3] : ~happy(X3) [avatar definition]
191. ~happy(X3) <- (14) [avatar component clause 190]
193. 15 <=> calm(sK4) [avatar definition]
195. ~calm(sK4) <- (~15) [avatar component clause 193]
196. 14 | ~15 [avatar split clause 98,193,190]
198. 16 <=> ! [X0] : brave(X0) [avatar definition]
199. brave(X0) <- (16) [avatar component clause 198]
201. 17 <=> kind(alice) [avatar definition]
203. ~kind(alice) <- (~17) [avatar component clause 201]
205. 18 <=> calm(alice) [avatar definition]
208. 16 | ~17 | ~18 [avatar split clause 101,205,201,198]
257. $false <- (12, ~15) [resolution 195,183]
258. ~12 | 15 [avatar contradiction clause 257]
261. happy(X0) <- (16) [resolution 87,199]
264. calm(alice) [resolution 91,127]
265. 18 [avatar split clause 264,205]
272. calm(X0) <- (16) [resolution 97,261]
273. 12 | ~16 [avatar split clause 272,198,182]
274. $false <- (7, ~17) [subsumption resolution 203,161]
275. ~7 | 17 [avatar contradiction clause 274]
278. happy(X0) <- (16) [resolution 199,87]
279. $false <- (14, 16) [subsumption resolution 278,191]
280. ~14 | ~16 [avatar contradiction clause 279]
281. $false [avatar sat refutation 162,164,196,208,258,265,273,275,280]
% SZS output end Proof for 2672859171569125848506446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or generous then paul is tall or not strong and vice versa.
Everyone who is both not tall and not patient is both not generous and not brave.
If someone is curious then susan is either not strong or not old.
If someone is brave then alice is either creative or generous and vice versa.
Everyone who is not old or not brave is not patient or not strong.
If someone is either not humble or generous then susan is either not wise or kind and vice versa.
If someone is not curious then someone is humble and vice versa.
Everyone who is not kind is either not patient or strong.
If john is either brave or not curious then lucy is wise.
Everyone who is both humble and not strong is either not curious or humble and vice versa.
Everyone who is both old and curious is tall or patient and vice versa.
If someone is tall or happy then someone is both humble and tall.
If fred is brave or strong then fred is not tall or not strong.
Everyone who is both not strong and not creative is either wise or quiet.
Everyone who is either not strong or not brave is not brave or not old and vice versa.
If mary is not creative or humble then someone is not strong and vice versa.
Alice is either not brave or not humble.
Fred is generous or funny.
Lucy is brave or quiet.
Someone is either patient or not happy.
Someone is either not old or rich.
John is tall or creative. | Lucy is not happy. | entailment | ((?[X]:((humble(X)<~>generous(X))))<=>((tall(paul)|~strong(paul))))&
(![X]:((~tall(X)&~patient(X))=>(~generous(X)&~brave(X))))&
((?[X]:(curious(X)))=>((~strong(susan)<~>~old(susan))))&
((?[X]:(brave(X)))<=>((creative(alice)<~>generous(alice))))&
(![X]:((~old(X)|~brave(X))=>(~patient(X)|~strong(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>((~wise(susan)<~>kind(susan))))&
((?[X]:(~curious(X)))<=>(?[X]:(humble(X))))&
(![X]:(~kind(X)=>(~patient(X)<~>strong(X))))&
(((brave(john)<~>~curious(john)))=>(wise(lucy)))&
(![X]:((humble(X)&~strong(X))<=>(~curious(X)<~>humble(X))))&
(![X]:((old(X)&curious(X))<=>(tall(X)|patient(X))))&
((?[X]:((tall(X)|happy(X))))=>(?[X]:((humble(X)&tall(X)))))&
(((brave(fred)|strong(fred)))=>((~tall(fred)|~strong(fred))))&
(![X]:((~strong(X)&~creative(X))=>(wise(X)<~>quiet(X))))&
(![X]:((~strong(X)<~>~brave(X))<=>(~brave(X)|~old(X))))&
(((~creative(mary)|humble(mary)))<=>(?[X]:(~strong(X))))&
((~brave(alice)<~>~humble(alice)))&
((generous(fred)|funny(fred)))&
((brave(lucy)|quiet(lucy)))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((tall(john)|creative(john))) | ~happy(lucy) | [
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2963885842314759905487773
% SZS output start Proof for 2963885842314759905487773
10. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~curious(X0) <~> humble(X0))) [input p9]
11. ! [X0] : ((curious(X0) & old(X0)) <=> (patient(X0) | tall(X0))) [input p10]
12. ? [X0] : (happy(X0) | tall(X0)) => ? [X0] : (tall(X0) & humble(X0)) [input p11]
15. ! [X0] : ((~strong(X0) <~> ~brave(X0)) <=> (~old(X0) | ~brave(X0))) [input p14]
23. happy(lucy) [input hypothesis]
25. ? [X0] : (happy(X0) | tall(X0)) => ? [X1] : (tall(X1) & humble(X1)) [rectify 12]
34. ? [X1] : (tall(X1) & humble(X1)) | ! [X0] : (~happy(X0) & ~tall(X0)) [ennf transformation 25]
60. ! [X0] : (((~strong(X0) & humble(X0)) | ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0)))) & (((~humble(X0) | curious(X0)) & (humble(X0) | ~curious(X0))) | (strong(X0) | ~humble(X0)))) [nnf transformation 10]
61. ! [X0] : (((~strong(X0) & humble(X0)) | ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0)))) & (((~humble(X0) | curious(X0)) & (humble(X0) | ~curious(X0))) | strong(X0) | ~humble(X0))) [flattening 60]
62. ! [X0] : (((curious(X0) & old(X0)) | (~patient(X0) & ~tall(X0))) & ((patient(X0) | tall(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 11]
63. ! [X0] : (((curious(X0) & old(X0)) | (~patient(X0) & ~tall(X0))) & (patient(X0) | tall(X0) | ~curious(X0) | ~old(X0))) [flattening 62]
64. ? [X0] : (tall(X0) & humble(X0)) | ! [X1] : (~happy(X1) & ~tall(X1)) [rectify 34]
65. ? [X0] : (tall(X0) & humble(X0)) => (tall(sK5) & humble(sK5)) [choice axiom]
66. (tall(sK5) & humble(sK5)) | ! [X1] : (~happy(X1) & ~tall(X1)) [skolemisation 64,65]
68. ! [X0] : ((((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))))) [nnf transformation 15]
69. ! [X0] : ((((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))))) [flattening 68]
117. ~curious(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 61]
119. ~tall(X0) | old(X0) [cnf transformation 63]
121. ~tall(X0) | curious(X0) [cnf transformation 63]
124. humble(sK5) | ~happy(X1) [cnf transformation 66]
126. tall(sK5) | ~happy(X1) [cnf transformation 66]
131. ~old(X0) | ~brave(X0) | ~brave(X0) | strong(X0) [cnf transformation 69]
135. brave(X0) | strong(X0) | brave(X0) [cnf transformation 69]
148. happy(lucy) [cnf transformation 23]
149. ~old(X0) | ~brave(X0) | strong(X0) [duplicate literal removal 131]
150. brave(X0) | strong(X0) [duplicate literal removal 135]
276. 27 <=> ! [X1] : ~happy(X1) [avatar definition]
277. ~happy(X1) <- (27) [avatar component clause 276]
279. 28 <=> tall(sK5) [avatar definition]
281. tall(sK5) <- (28) [avatar component clause 279]
282. 27 | 28 [avatar split clause 126,279,276]
288. 30 <=> humble(sK5) [avatar definition]
290. humble(sK5) <- (30) [avatar component clause 288]
291. 27 | 30 [avatar split clause 124,288,276]
307. ~old(X0) | strong(X0) [subsumption resolution 149,150]
378. $false <- (27) [resolution 277,148]
379. ~27 [avatar contradiction clause 378]
384. old(sK5) <- (28) [resolution 119,281]
386. curious(sK5) <- (28) [resolution 121,281]
391. strong(sK5) <- (28) [resolution 307,384]
539. ~strong(sK5) | ~humble(sK5) <- (28) [resolution 117,386]
541. ~humble(sK5) <- (28) [subsumption resolution 539,391]
542. $false <- (28, 30) [subsumption resolution 541,290]
543. ~28 | ~30 [avatar contradiction clause 542]
544. $false [avatar sat refutation 282,291,379,543]
% SZS output end Proof for 2963885842314759905487773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and creative is curious or happy. Everyone who is either not calm or not patient is both not rich and not old. Everyone who is strong is not rich or not funny and vice versa. Everyone who is both humble and not humble is funny or creative and vice versa. Everyone who is not quiet is either wise or tall. If someone is both not creative and not strong then paul is both not creative and not quiet. Everyone who is strong is either not strong or not happy. Everyone who is either not tall or not strong is happy. Everyone who is happy or generous is either generous or not calm and vice versa. Everyone who is not happy is tall. Everyone who is not old or funny is either not generous or happy. If someone is wise or kind then someone is strong or not strong. If susan is creative then paul is both kind and not strong. Everyone who is either calm or not quiet is kind or not kind. Everyone who is both not old and creative is either kind or not wise. Someone is humble or wise. Someone is either not humble or not wise. Someone is wise. Lucy is wise or patient. Someone is both not old and tall. Someone is not curious. Susan is either not rich or creative. | Lucy is not old. | neutral | (![X]:((humble(X)&creative(X))=>(curious(X)|happy(X))))&
(![X]:((~calm(X)<~>~patient(X))=>(~rich(X)&~old(X))))&
(![X]:(strong(X)<=>(~rich(X)|~funny(X))))&
(![X]:((humble(X)&~humble(X))<=>(funny(X)|creative(X))))&
(![X]:(~quiet(X)=>(wise(X)<~>tall(X))))&
((?[X]:((~creative(X)&~strong(X))))=>((~creative(paul)&~quiet(paul))))&
(![X]:(strong(X)=>(~strong(X)<~>~happy(X))))&
(![X]:((~tall(X)<~>~strong(X))=>happy(X)))&
(![X]:((happy(X)|generous(X))<=>(generous(X)<~>~calm(X))))&
(![X]:(~happy(X)=>tall(X)))&
(![X]:((~old(X)|funny(X))=>(~generous(X)<~>happy(X))))&
((?[X]:((wise(X)|kind(X))))=>(?[X]:((strong(X)|~strong(X)))))&
((creative(susan))=>((kind(paul)&~strong(paul))))&
(![X]:((calm(X)<~>~quiet(X))=>(kind(X)|~kind(X))))&
(![X]:((~old(X)&creative(X))=>(kind(X)<~>~wise(X))))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:(wise(X)))&
((wise(lucy)|patient(lucy)))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:(~curious(X)))&
((~rich(susan)<~>creative(susan))) | ~old(lucy) | [] | null | 0 |
If susan is either brave or tall then someone is not rich.
If fred is kind or not curious then fred is both not funny and not rich.
Everyone who is quiet is both not wise and funny and vice versa.
If susan is either funny or old then someone is either not funny or not creative and vice versa.
If someone is either rich or not generous then susan is either not funny or kind.
Everyone who is not old is not wise.
Everyone who is either not brave or not rich is strong or not patient and vice versa.
Everyone who is not creative or not old is both creative and not patient.
Everyone who is funny or creative is not kind or funny and vice versa.
If someone is happy or not creative then john is either humble or rich.
Everyone who is not old is either not patient or not happy and vice versa.
If someone is not old or generous then alice is not generous and vice versa.
Everyone who is both tall and not generous is brave and vice versa.
Everyone who is both not brave and kind is quiet or humble.
If someone is not curious or curious then someone is not rich or not curious.
Everyone who is both generous and patient is not humble and vice versa.
Susan is quiet or not old.
Someone is not happy or not kind.
Someone is not wise or not patient.
Alice is not happy or happy.
Susan is either not wise or not generous.
Someone is both kind and not humble.
Someone is either not creative or not curious. | Fred is not brave. | neutral | (((brave(susan)<~>tall(susan)))=>(?[X]:(~rich(X))))&
(((kind(fred)|~curious(fred)))=>((~funny(fred)&~rich(fred))))&
(![X]:(quiet(X)<=>(~wise(X)&funny(X))))&
(((funny(susan)<~>old(susan)))<=>(?[X]:((~funny(X)<~>~creative(X)))))&
((?[X]:((rich(X)<~>~generous(X))))=>((~funny(susan)<~>kind(susan))))&
(![X]:(~old(X)=>~wise(X)))&
(![X]:((~brave(X)<~>~rich(X))<=>(strong(X)|~patient(X))))&
(![X]:((~creative(X)|~old(X))=>(creative(X)&~patient(X))))&
(![X]:((funny(X)|creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((happy(X)|~creative(X))))=>((humble(john)<~>rich(john))))&
(![X]:(~old(X)<=>(~patient(X)<~>~happy(X))))&
((?[X]:((~old(X)|generous(X))))<=>(~generous(alice)))&
(![X]:((tall(X)&~generous(X))<=>brave(X)))&
(![X]:((~brave(X)&kind(X))=>(quiet(X)|humble(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((generous(X)&patient(X))<=>~humble(X)))&
((quiet(susan)|~old(susan)))&
(?[X]:((~happy(X)|~kind(X))))&
(?[X]:((~wise(X)|~patient(X))))&
((~happy(alice)|happy(alice)))&
((~wise(susan)<~>~generous(susan)))&
(?[X]:((kind(X)&~humble(X))))&
(?[X]:((~creative(X)<~>~curious(X)))) | ~brave(fred) | [] | null | 0 |
Everyone who is both not rich and not generous is not happy and vice versa. If john is either calm or humble then fred is not wise or not rich and vice versa. If someone is either not curious or not generous then someone is either creative or not patient. Everyone who is either not quiet or quiet is rich or brave and vice versa. If mary is calm or not rich then mary is not quiet and vice versa. If someone is either not brave or calm then mary is both rich and not humble and vice versa. If someone is either not old or creative then someone is either not old or strong. Everyone who is either not patient or brave is not patient or calm and vice versa. Everyone who is both not generous and patient is both happy and not curious. If mary is not curious then mary is both not kind and kind and vice versa. Everyone who is either kind or not funny is not wise. If someone is either not creative or not happy then someone is funny. Everyone who is both not old and not patient is both not humble and curious and vice versa. If mary is tall then mary is either happy or quiet and vice versa. If someone is both not happy and not tall then someone is both not wise and old and vice versa. If someone is either generous or brave then someone is not rich and vice versa. Someone is quiet. Fred is either curious or not strong. Someone is either not calm or wise. Mary is kind. Alice is either old or not generous. Someone is wise. Someone is brave. Someone is both not rich and happy. | Fred is happy. | entailment | (![X]:((~rich(X)&~generous(X))<=>~happy(X)))&
(((calm(john)<~>humble(john)))<=>((~wise(fred)|~rich(fred))))&
((?[X]:((~curious(X)<~>~generous(X))))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(rich(X)|brave(X))))&
(((calm(mary)|~rich(mary)))<=>(~quiet(mary)))&
((?[X]:((~brave(X)<~>calm(X))))<=>((rich(mary)&~humble(mary))))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((~old(X)<~>strong(X)))))&
(![X]:((~patient(X)<~>brave(X))<=>(~patient(X)|calm(X))))&
(![X]:((~generous(X)&patient(X))=>(happy(X)&~curious(X))))&
((~curious(mary))<=>((~kind(mary)&kind(mary))))&
(![X]:((kind(X)<~>~funny(X))=>~wise(X)))&
((?[X]:((~creative(X)<~>~happy(X))))=>(?[X]:(funny(X))))&
(![X]:((~old(X)&~patient(X))<=>(~humble(X)&curious(X))))&
((tall(mary))<=>((happy(mary)<~>quiet(mary))))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:((~wise(X)&old(X)))))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:(~rich(X))))&
(?[X]:(quiet(X)))&
((curious(fred)<~>~strong(fred)))&
(?[X]:((~calm(X)<~>wise(X))))&
(kind(mary))&
((old(alice)<~>~generous(alice)))&
(?[X]:(wise(X)))&
(?[X]:(brave(X)))&
(?[X]:((~rich(X)&happy(X)))) | happy(fred) | [
"p0",
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6709543573508839384806273
% SZS output start Proof for 6709543573508839384806273
1. ! [X0] : ((~generous(X0) & ~rich(X0)) <=> ~happy(X0)) [input p0]
4. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> (brave(X0) | rich(X0))) [input p3]
8. ! [X0] : ((~patient(X0) <~> brave(X0)) <=> (calm(X0) | ~patient(X0))) [input p7]
9. ! [X0] : ((patient(X0) & ~generous(X0)) => (~curious(X0) & happy(X0))) [input p8]
25. ~happy(fred) [input hypothesis]
33. ! [X0] : ((~curious(X0) & happy(X0)) | (~patient(X0) | generous(X0))) [ennf transformation 9]
34. ! [X0] : ((~curious(X0) & happy(X0)) | ~patient(X0) | generous(X0)) [flattening 33]
37. ! [X0] : (((~generous(X0) & ~rich(X0)) | happy(X0)) & (~happy(X0) | (generous(X0) | rich(X0)))) [nnf transformation 1]
38. ! [X0] : (((~generous(X0) & ~rich(X0)) | happy(X0)) & (~happy(X0) | generous(X0) | rich(X0))) [flattening 37]
45. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 4]
46. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [flattening 45]
58. ! [X0] : ((((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | (~calm(X0) & patient(X0))) & ((calm(X0) | ~patient(X0)) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0))))) [nnf transformation 8]
59. ! [X0] : ((((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | (~calm(X0) & patient(X0))) & (calm(X0) | ~patient(X0) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0))))) [flattening 58]
94. ~rich(X0) | happy(X0) [cnf transformation 38]
95. ~generous(X0) | happy(X0) [cnf transformation 38]
106. brave(X0) | rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 46]
107. brave(X0) | rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 46]
129. ~brave(X0) | patient(X0) | patient(X0) [cnf transformation 59]
131. happy(X0) | ~patient(X0) | generous(X0) [cnf transformation 34]
168. ~happy(fred) [cnf transformation 25]
170. ~brave(X0) | patient(X0) [duplicate literal removal 129]
171. brave(X0) | rich(X0) | quiet(X0) [duplicate literal removal 106]
172. ~quiet(X0) | rich(X0) | brave(X0) [duplicate literal removal 107]
213. brave(X0) | rich(X0) [subsumption resolution 171,172]
272. ~patient(X0) | happy(X0) [subsumption resolution 131,95]
408. patient(X0) | rich(X0) [resolution 213,170]
531. rich(X3) | happy(X3) [resolution 408,272]
532. happy(X3) [subsumption resolution 531,94]
537. $false [resolution 532,168]
% SZS output end Proof for 6709543573508839384806273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm is not wise or not quiet.
If someone is not happy then someone is either tall or strong and vice versa.
Everyone who is either calm or creative is brave or strong.
Everyone who is curious or quiet is not brave.
If someone is creative or rich then someone is tall and vice versa.
If someone is not wise then someone is tall or not brave.
If susan is quiet then john is either rich or funny and vice versa.
Everyone who is both not calm and not happy is generous or calm and vice versa.
Everyone who is curious is not patient.
Everyone who is not funny or tall is not strong or creative and vice versa.
Everyone who is strong or curious is either calm or not generous and vice versa.
If mary is not strong then fred is both not generous and calm and vice versa.
Everyone who is tall or not brave is not creative or strong.
If someone is either not old or old then someone is not curious and vice versa.
Everyone who is humble or curious is not old or rich and vice versa.
Everyone who is either generous or not generous is either quiet or not brave and vice versa.
Someone is not tall.
Someone is either not wise or not patient.
Someone is not quiet or not wise.
Someone is either strong or kind.
Someone is funny or not kind.
Fred is not calm or happy. | Mary is not curious. | neutral | (![X]:(~calm(X)=>(~wise(X)|~quiet(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:((calm(X)<~>creative(X))=>(brave(X)|strong(X))))&
(![X]:((curious(X)|quiet(X))=>~brave(X)))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:(tall(X))))&
((?[X]:(~wise(X)))=>(?[X]:((tall(X)|~brave(X)))))&
((quiet(susan))<=>((rich(john)<~>funny(john))))&
(![X]:((~calm(X)&~happy(X))<=>(generous(X)|calm(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((~funny(X)|tall(X))<=>(~strong(X)|creative(X))))&
(![X]:((strong(X)|curious(X))<=>(calm(X)<~>~generous(X))))&
((~strong(mary))<=>((~generous(fred)&calm(fred))))&
(![X]:((tall(X)|~brave(X))=>(~creative(X)|strong(X))))&
((?[X]:((~old(X)<~>old(X))))<=>(?[X]:(~curious(X))))&
(![X]:((humble(X)|curious(X))<=>(~old(X)|rich(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(quiet(X)<~>~brave(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~quiet(X)|~wise(X))))&
(?[X]:((strong(X)<~>kind(X))))&
(?[X]:((funny(X)|~kind(X))))&
((~calm(fred)|happy(fred))) | ~curious(mary) | [] | null | 0 |
Everyone who is either not wise or not strong is either not calm or funny and vice versa. Everyone who is either not wise or patient is patient or not creative and vice versa. Everyone who is curious is brave and vice versa. Everyone who is either strong or calm is either not funny or quiet and vice versa. Everyone who is not rich is not old or tall. Everyone who is either humble or creative is not wise or generous. If someone is either quiet or creative then paul is both not kind and not humble. Everyone who is curious or not humble is both not funny and not happy. If someone is not happy then susan is not rich. Everyone who is both quiet and strong is creative or not rich. Everyone who is quiet is not kind. Everyone who is either not kind or kind is either patient or not tall and vice versa. Everyone who is happy is either kind or not creative and vice versa. Everyone who is quiet is both rich and not calm and vice versa. If lucy is either patient or not curious then susan is both curious and not tall. If someone is both tall and not strong then john is not rich and vice versa. Someone is either kind or creative. John is brave or not funny. John is wise. Alice is not curious. Someone is not tall. Someone is not funny or not rich. | Paul is humble. | neutral | (![X]:((~wise(X)<~>~strong(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((~wise(X)<~>patient(X))<=>(patient(X)|~creative(X))))&
(![X]:(curious(X)<=>brave(X)))&
(![X]:((strong(X)<~>calm(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:(~rich(X)=>(~old(X)|tall(X))))&
(![X]:((humble(X)<~>creative(X))=>(~wise(X)|generous(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>((~kind(paul)&~humble(paul))))&
(![X]:((curious(X)|~humble(X))=>(~funny(X)&~happy(X))))&
((?[X]:(~happy(X)))=>(~rich(susan)))&
(![X]:((quiet(X)&strong(X))=>(creative(X)|~rich(X))))&
(![X]:(quiet(X)=>~kind(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(patient(X)<~>~tall(X))))&
(![X]:(happy(X)<=>(kind(X)<~>~creative(X))))&
(![X]:(quiet(X)<=>(rich(X)&~calm(X))))&
(((patient(lucy)<~>~curious(lucy)))=>((curious(susan)&~tall(susan))))&
((?[X]:((tall(X)&~strong(X))))<=>(~rich(john)))&
(?[X]:((kind(X)<~>creative(X))))&
((brave(john)|~funny(john)))&
(wise(john))&
(~curious(alice))&
(?[X]:(~tall(X)))&
(?[X]:((~funny(X)|~rich(X)))) | humble(paul) | [] | null | 0 |
If paul is both not patient and happy then someone is not creative. If someone is both not quiet and patient then john is either not generous or not creative. Everyone who is old is not humble and vice versa. Everyone who is strong or not old is tall and vice versa. Everyone who is not wise or kind is either not humble or not calm. If fred is either not curious or wise then susan is either not calm or not quiet and vice versa. Everyone who is either funny or quiet is not quiet and vice versa. If someone is both not creative and kind then susan is both not calm and quiet and vice versa. Everyone who is wise or not patient is either funny or not strong and vice versa. If someone is strong or patient then someone is calm. If someone is not strong then john is rich or happy. If someone is not humble or not old then susan is either old or not patient. Everyone who is not patient or not wise is not brave or not patient and vice versa. If alice is curious then someone is calm and vice versa. Everyone who is both generous and not brave is both tall and not rich and vice versa. Everyone who is both wise and not quiet is tall. Fred is humble. Someone is both not brave and humble. Someone is either not quiet or not humble. John is not generous or happy. Lucy is not rich. Susan is generous. Someone is not happy or patient. Someone is both not kind and not tall. | Susan is strong. | entailment | (((~patient(paul)&happy(paul)))=>(?[X]:(~creative(X))))&
((?[X]:((~quiet(X)&patient(X))))=>((~generous(john)<~>~creative(john))))&
(![X]:(old(X)<=>~humble(X)))&
(![X]:((strong(X)|~old(X))<=>tall(X)))&
(![X]:((~wise(X)|kind(X))=>(~humble(X)<~>~calm(X))))&
(((~curious(fred)<~>wise(fred)))<=>((~calm(susan)<~>~quiet(susan))))&
(![X]:((funny(X)<~>quiet(X))<=>~quiet(X)))&
((?[X]:((~creative(X)&kind(X))))<=>((~calm(susan)&quiet(susan))))&
(![X]:((wise(X)|~patient(X))<=>(funny(X)<~>~strong(X))))&
((?[X]:((strong(X)|patient(X))))=>(?[X]:(calm(X))))&
((?[X]:(~strong(X)))=>((rich(john)|happy(john))))&
((?[X]:((~humble(X)|~old(X))))=>((old(susan)<~>~patient(susan))))&
(![X]:((~patient(X)|~wise(X))<=>(~brave(X)|~patient(X))))&
((curious(alice))<=>(?[X]:(calm(X))))&
(![X]:((generous(X)&~brave(X))<=>(tall(X)&~rich(X))))&
(![X]:((wise(X)&~quiet(X))=>tall(X)))&
(humble(fred))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((~generous(john)|happy(john)))&
(~rich(lucy))&
(generous(susan))&
(?[X]:((~happy(X)|patient(X))))&
(?[X]:((~kind(X)&~tall(X)))) | strong(susan) | [
"p2",
"p3",
"p6",
"p8",
"p11",
"p12",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4352203152381213775433476
% SZS output start Proof for 4352203152381213775433476
3. ! [X0] : (old(X0) <=> ~humble(X0)) [input p2]
4. ! [X0] : ((~old(X0) | strong(X0)) <=> tall(X0)) [input p3]
7. ! [X0] : ((funny(X0) <~> quiet(X0)) <=> ~quiet(X0)) [input p6]
9. ! [X0] : ((~patient(X0) | wise(X0)) <=> (funny(X0) <~> ~strong(X0))) [input p8]
12. ? [X0] : (~old(X0) | ~humble(X0)) => (old(susan) <~> ~patient(susan)) [input p11]
13. ! [X0] : ((~wise(X0) | ~patient(X0)) <=> (~patient(X0) | ~brave(X0))) [input p12]
15. ! [X0] : ((~brave(X0) & generous(X0)) <=> (~rich(X0) & tall(X0))) [input p14]
18. ? [X0] : (humble(X0) & ~brave(X0)) [input p17]
22. generous(susan) [input p21]
25. ~strong(susan) [input hypothesis]
34. (old(susan) <~> ~patient(susan)) | ! [X0] : (old(X0) & humble(X0)) [ennf transformation 12]
40. ! [X0] : ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))) [nnf transformation 3]
41. ! [X0] : (((~old(X0) | strong(X0)) | ~tall(X0)) & (tall(X0) | (old(X0) & ~strong(X0)))) [nnf transformation 4]
42. ! [X0] : ((~old(X0) | strong(X0) | ~tall(X0)) & (tall(X0) | (old(X0) & ~strong(X0)))) [flattening 41]
45. ! [X0] : ((((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | quiet(X0)) & (~quiet(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0))))) [nnf transformation 7]
51. ! [X0] : (((~patient(X0) | wise(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (patient(X0) & ~wise(X0)))) [nnf transformation 9]
52. ! [X0] : ((~patient(X0) | wise(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (patient(X0) & ~wise(X0)))) [flattening 51]
56. ((patient(susan) | ~old(susan)) & (~patient(susan) | old(susan))) | ! [X0] : (old(X0) & humble(X0)) [nnf transformation 34]
57. ! [X0] : (((~wise(X0) | ~patient(X0)) | (patient(X0) & brave(X0))) & ((~patient(X0) | ~brave(X0)) | (wise(X0) & patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((~wise(X0) | ~patient(X0) | (patient(X0) & brave(X0))) & (~patient(X0) | ~brave(X0) | (wise(X0) & patient(X0)))) [flattening 57]
63. ! [X0] : (((~brave(X0) & generous(X0)) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | (brave(X0) | ~generous(X0)))) [nnf transformation 15]
64. ! [X0] : (((~brave(X0) & generous(X0)) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | brave(X0) | ~generous(X0))) [flattening 63]
65. ? [X0] : (humble(X0) & ~brave(X0)) => (humble(sK4) & ~brave(sK4)) [choice axiom]
66. humble(sK4) & ~brave(sK4) [skolemisation 18,65]
77. ~humble(X0) | ~old(X0) [cnf transformation 40]
81. ~tall(X0) | strong(X0) | ~old(X0) [cnf transformation 42]
95. ~quiet(X0) | funny(X0) | ~quiet(X0) [cnf transformation 45]
96. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 45]
104. strong(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 52]
105. strong(X0) | ~funny(X0) | patient(X0) [cnf transformation 52]
112. ~patient(susan) | old(susan) | old(X0) [cnf transformation 56]
116. ~brave(X0) | ~patient(X0) | wise(X0) [cnf transformation 58]
121. ~generous(X0) | brave(X0) | tall(X0) [cnf transformation 64]
128. humble(sK4) [cnf transformation 66]
133. generous(susan) [cnf transformation 22]
137. ~strong(susan) [cnf transformation 25]
138. ~quiet(X0) | funny(X0) [duplicate literal removal 95]
139. funny(X0) | quiet(X0) [duplicate literal removal 96]
190. funny(X0) [subsumption resolution 138,139]
207. strong(X0) | patient(X0) [subsumption resolution 105,190]
208. ~wise(X0) | strong(X0) [subsumption resolution 104,190]
234. 20 <=> ! [X0] : old(X0) [avatar definition]
235. old(X0) <- (20) [avatar component clause 234]
237. 21 <=> old(susan) [avatar definition]
238. old(susan) <- (21) [avatar component clause 237]
241. 22 <=> patient(susan) [avatar definition]
242. ~patient(susan) <- (~22) [avatar component clause 241]
243. patient(susan) <- (22) [avatar component clause 241]
249. 20 | 21 | ~22 [avatar split clause 112,241,237,234]
289. ~old(sK4) [resolution 77,128]
293. patient(susan) [resolution 207,137]
296. $false <- (~22) [subsumption resolution 293,242]
297. 22 [avatar contradiction clause 296]
331. 35 <=> wise(susan) [avatar definition]
332. ~wise(susan) <- (~35) [avatar component clause 331]
333. wise(susan) <- (35) [avatar component clause 331]
354. $false <- (20) [resolution 235,289]
357. ~20 [avatar contradiction clause 354]
367. brave(susan) | tall(susan) [resolution 121,133]
369. 39 <=> tall(susan) [avatar definition]
371. tall(susan) <- (39) [avatar component clause 369]
373. 40 <=> brave(susan) [avatar definition]
375. brave(susan) <- (40) [avatar component clause 373]
376. 39 | 40 [avatar split clause 367,373,369]
382. strong(susan) <- (35) [resolution 333,208]
383. $false <- (35) [subsumption resolution 382,137]
384. ~35 [avatar contradiction clause 383]
387. strong(susan) | ~old(susan) <- (39) [resolution 371,81]
388. ~old(susan) <- (39) [subsumption resolution 387,137]
389. $false <- (21, 39) [subsumption resolution 388,238]
390. ~21 | ~39 [avatar contradiction clause 389]
394. ~patient(susan) | wise(susan) <- (40) [resolution 375,116]
395. wise(susan) <- (22, 40) [subsumption resolution 394,243]
396. $false <- (22, ~35, 40) [subsumption resolution 395,332]
397. ~22 | 35 | ~40 [avatar contradiction clause 396]
398. $false [avatar sat refutation 249,297,357,376,384,390,397]
% SZS output end Proof for 4352203152381213775433476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or not patient is either brave or not brave and vice versa. If susan is both generous and strong then someone is wise or not quiet. Everyone who is both humble and not humble is both not humble and calm and vice versa. If someone is humble or not humble then someone is rich. If someone is strong or old then someone is not wise. Everyone who is not patient is not funny and vice versa. Everyone who is creative or not tall is either not old or quiet. If lucy is either not strong or old then john is both old and brave and vice versa. If someone is quiet or funny then someone is humble or tall. If alice is not quiet then someone is both not happy and not patient and vice versa. If someone is not humble then someone is either not wise or not strong and vice versa. If someone is not wise or not tall then susan is not tall. Everyone who is both not funny and brave is not funny and vice versa. If mary is both not quiet and patient then alice is curious or not humble and vice versa. If mary is either not brave or not calm then someone is both curious and not old. Everyone who is not tall or quiet is not funny or wise. Someone is not patient. Someone is happy or generous. Someone is either not strong or creative. John is both not wise and curious. Someone is not brave or patient. Someone is either funny or strong. | Mary is not rich. | neutral | (![X]:((~generous(X)<~>~patient(X))<=>(brave(X)<~>~brave(X))))&
(((generous(susan)&strong(susan)))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((humble(X)&~humble(X))<=>(~humble(X)&calm(X))))&
((?[X]:((humble(X)|~humble(X))))=>(?[X]:(rich(X))))&
((?[X]:((strong(X)|old(X))))=>(?[X]:(~wise(X))))&
(![X]:(~patient(X)<=>~funny(X)))&
(![X]:((creative(X)|~tall(X))=>(~old(X)<~>quiet(X))))&
(((~strong(lucy)<~>old(lucy)))<=>((old(john)&brave(john))))&
((?[X]:((quiet(X)|funny(X))))=>(?[X]:((humble(X)|tall(X)))))&
((~quiet(alice))<=>(?[X]:((~happy(X)&~patient(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
((?[X]:((~wise(X)|~tall(X))))=>(~tall(susan)))&
(![X]:((~funny(X)&brave(X))<=>~funny(X)))&
(((~quiet(mary)&patient(mary)))<=>((curious(alice)|~humble(alice))))&
(((~brave(mary)<~>~calm(mary)))=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((~tall(X)|quiet(X))=>(~funny(X)|wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((~strong(X)<~>creative(X))))&
((~wise(john)&curious(john)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((funny(X)<~>strong(X)))) | ~rich(mary) | [] | null | 0 |
Everyone who is either humble or strong is either calm or kind.
Everyone who is tall is not patient or not old and vice versa.
If fred is both not curious and not rich then john is not old and vice versa.
Everyone who is not brave or strong is either not kind or not generous and vice versa.
If lucy is both not humble and humble then alice is both not happy and not rich and vice versa.
Everyone who is curious is funny and vice versa.
Everyone who is either rich or humble is kind or not humble.
If john is both not strong and not kind then someone is not strong and vice versa.
If paul is either not calm or creative then fred is either not curious or not generous and vice versa.
Everyone who is rich or not wise is old and vice versa.
If alice is not generous then fred is not kind or not generous.
If someone is old then someone is either patient or not funny.
Everyone who is either old or not happy is not humble or calm and vice versa.
Everyone who is not calm or wise is either not kind or rich and vice versa.
If someone is brave or not brave then lucy is both strong and not funny.
If susan is generous or old then fred is either brave or not creative.
Someone is happy or not brave.
Someone is not quiet or not brave.
Alice is happy.
Paul is either not generous or patient.
Someone is not generous.
Someone is either not patient or not happy.
Someone is brave or not happy.
Someone is not old or not brave. | Lucy is not funny. | entailment | (![X]:((humble(X)<~>strong(X))=>(calm(X)<~>kind(X))))&
(![X]:(tall(X)<=>(~patient(X)|~old(X))))&
(((~curious(fred)&~rich(fred)))<=>(~old(john)))&
(![X]:((~brave(X)|strong(X))<=>(~kind(X)<~>~generous(X))))&
(((~humble(lucy)&humble(lucy)))<=>((~happy(alice)&~rich(alice))))&
(![X]:(curious(X)<=>funny(X)))&
(![X]:((rich(X)<~>humble(X))=>(kind(X)|~humble(X))))&
(((~strong(john)&~kind(john)))<=>(?[X]:(~strong(X))))&
(((~calm(paul)<~>creative(paul)))<=>((~curious(fred)<~>~generous(fred))))&
(![X]:((rich(X)|~wise(X))<=>old(X)))&
((~generous(alice))=>((~kind(fred)|~generous(fred))))&
((?[X]:(old(X)))=>(?[X]:((patient(X)<~>~funny(X)))))&
(![X]:((old(X)<~>~happy(X))<=>(~humble(X)|calm(X))))&
(![X]:((~calm(X)|wise(X))<=>(~kind(X)<~>rich(X))))&
((?[X]:((brave(X)|~brave(X))))=>((strong(lucy)&~funny(lucy))))&
(((generous(susan)|old(susan)))=>((brave(fred)<~>~creative(fred))))&
(?[X]:((happy(X)|~brave(X))))&
(?[X]:((~quiet(X)|~brave(X))))&
(happy(alice))&
((~generous(paul)<~>patient(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((~patient(X)<~>~happy(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((~old(X)|~brave(X)))) | ~funny(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 925692508385426128281989
% SZS output start Proof for 925692508385426128281989
15. ? [X0] : (~brave(X0) | brave(X0)) => (~funny(lucy) & strong(lucy)) [input p14]
25. funny(lucy) [input hypothesis]
34. (~funny(lucy) & strong(lucy)) | ! [X0] : (brave(X0) & ~brave(X0)) [ennf transformation 15]
126. ~funny(lucy) | ~brave(X0) [cnf transformation 34]
127. ~funny(lucy) | brave(X0) [cnf transformation 34]
141. funny(lucy) [cnf transformation 25]
233. 19 <=> ! [X0] : brave(X0) [avatar definition]
234. brave(X0) <- (19) [avatar component clause 233]
236. 20 <=> funny(lucy) [avatar definition]
239. 19 | ~20 [avatar split clause 127,236,233]
241. 21 <=> ! [X0] : ~brave(X0) [avatar definition]
242. ~brave(X0) <- (21) [avatar component clause 241]
243. 21 | ~20 [avatar split clause 126,236,241]
318. 20 [avatar split clause 141,236]
319. $false <- (19, 21) [subsumption resolution 234,242]
320. ~19 | ~21 [avatar contradiction clause 319]
321. $false [avatar sat refutation 239,243,318,320]
% SZS output end Proof for 925692508385426128281989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not funny is happy and vice versa. If someone is not humble then someone is both not generous and not calm and vice versa. Everyone who is not generous or not tall is tall and vice versa. Everyone who is either happy or not humble is both not tall and not curious. If susan is not patient then alice is either rich or not tall. If alice is both old and not calm then someone is either strong or funny and vice versa. Everyone who is either creative or happy is either not brave or not calm. If someone is rich then someone is either not old or calm and vice versa. If someone is not strong then mary is either curious or not funny. Everyone who is both not curious and wise is funny and vice versa. Everyone who is either not happy or not quiet is either generous or not patient. If someone is not generous or not calm then fred is both not quiet and funny and vice versa. Everyone who is patient or happy is both patient and humble and vice versa. If someone is not old then someone is either humble or funny. Everyone who is not wise or not kind is not kind and vice versa. Someone is either not tall or not kind. Lucy is not patient. Alice is either strong or not creative. Fred is not quiet or strong. | Alice is happy. | contradiction | (![X]:((~humble(X)|~funny(X))<=>happy(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:((~generous(X)|~tall(X))<=>tall(X)))&
(![X]:((happy(X)<~>~humble(X))=>(~tall(X)&~curious(X))))&
((~patient(susan))=>((rich(alice)<~>~tall(alice))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((creative(X)<~>happy(X))=>(~brave(X)<~>~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
((?[X]:(~strong(X)))=>((curious(mary)<~>~funny(mary))))&
(![X]:((~curious(X)&wise(X))<=>funny(X)))&
(![X]:((~happy(X)<~>~quiet(X))=>(generous(X)<~>~patient(X))))&
((?[X]:((~generous(X)|~calm(X))))<=>((~quiet(fred)&funny(fred))))&
(![X]:((patient(X)|happy(X))<=>(patient(X)&humble(X))))&
((?[X]:(~old(X)))=>(?[X]:((humble(X)<~>funny(X)))))&
(![X]:((~wise(X)|~kind(X))<=>~kind(X)))&
(?[X]:((~tall(X)<~>~kind(X))))&
(~patient(lucy))&
((strong(alice)<~>~creative(alice)))&
((~quiet(fred)|strong(fred))) | happy(alice) | [
"p2",
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7782891139940966167635343
% SZS output start Proof for 7782891139940966167635343
3. ! [X0] : ((~tall(X0) | ~generous(X0)) <=> tall(X0)) [input p2]
4. ! [X0] : ((happy(X0) <~> ~humble(X0)) => (~curious(X0) & ~tall(X0))) [input p3]
13. ! [X0] : ((happy(X0) | patient(X0)) <=> (humble(X0) & patient(X0))) [input p12]
20. happy(alice) [input hypothesis]
24. ! [X0] : ((~curious(X0) & ~tall(X0)) | (happy(X0) <=> ~humble(X0))) [ennf transformation 4]
37. ! [X0] : (((~tall(X0) | ~generous(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) & generous(X0)))) [nnf transformation 3]
38. ! [X0] : ((~tall(X0) | ~generous(X0) | ~tall(X0)) & (tall(X0) | (tall(X0) & generous(X0)))) [flattening 37]
39. ! [X0] : ((~curious(X0) & ~tall(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) [nnf transformation 24]
61. ! [X0] : (((happy(X0) | patient(X0)) | (~humble(X0) | ~patient(X0))) & ((humble(X0) & patient(X0)) | (~happy(X0) & ~patient(X0)))) [nnf transformation 13]
62. ! [X0] : ((happy(X0) | patient(X0) | ~humble(X0) | ~patient(X0)) & ((humble(X0) & patient(X0)) | (~happy(X0) & ~patient(X0)))) [flattening 61]
80. tall(X0) | tall(X0) [cnf transformation 38]
82. ~tall(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 39]
119. humble(X0) | ~happy(X0) [cnf transformation 62]
132. happy(alice) [cnf transformation 20]
133. tall(X0) [duplicate literal removal 80]
156. ~humble(X0) | ~happy(X0) [subsumption resolution 82,133]
260. ~happy(X0) [subsumption resolution 119,156]
290. $false [subsumption resolution 132,260]
% SZS output end Proof for 7782891139940966167635343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or generous then someone is both not brave and not strong and vice versa. If susan is funny or brave then someone is not patient. Everyone who is not strong is both tall and not calm and vice versa. If alice is not happy or tall then someone is not kind or not calm. Everyone who is not rich is either patient or old. If lucy is calm then john is not strong or strong and vice versa. Everyone who is happy or creative is either not humble or not generous. Everyone who is either tall or not strong is both not funny and quiet and vice versa. Everyone who is both quiet and brave is not tall and vice versa. If fred is not curious or not tall then someone is patient and vice versa. If susan is either not kind or quiet then someone is both not quiet and patient. Everyone who is either not curious or not wise is both strong and not quiet and vice versa. If lucy is both not calm and not kind then someone is happy or not rich and vice versa. If someone is patient then paul is not wise and vice versa. If mary is rich then someone is either not funny or patient and vice versa. Everyone who is not strong or not humble is not brave and vice versa. Mary is either not humble or brave. Fred is curious. Someone is both not old and calm. Someone is not wise. Someone is calm. Someone is kind or not strong. Lucy is quiet or humble. | Susan is not happy. | entailment | ((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:((~brave(X)&~strong(X)))))&
(((funny(susan)|brave(susan)))=>(?[X]:(~patient(X))))&
(![X]:(~strong(X)<=>(tall(X)&~calm(X))))&
(((~happy(alice)|tall(alice)))=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:(~rich(X)=>(patient(X)<~>old(X))))&
((calm(lucy))<=>((~strong(john)|strong(john))))&
(![X]:((happy(X)|creative(X))=>(~humble(X)<~>~generous(X))))&
(![X]:((tall(X)<~>~strong(X))<=>(~funny(X)&quiet(X))))&
(![X]:((quiet(X)&brave(X))<=>~tall(X)))&
(((~curious(fred)|~tall(fred)))<=>(?[X]:(patient(X))))&
(((~kind(susan)<~>quiet(susan)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>(strong(X)&~quiet(X))))&
(((~calm(lucy)&~kind(lucy)))<=>(?[X]:((happy(X)|~rich(X)))))&
((?[X]:(patient(X)))<=>(~wise(paul)))&
((rich(mary))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~strong(X)|~humble(X))<=>~brave(X)))&
((~humble(mary)<~>brave(mary)))&
(curious(fred))&
(?[X]:((~old(X)&calm(X))))&
(?[X]:(~wise(X)))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)|~strong(X))))&
((quiet(lucy)|humble(lucy))) | ~happy(susan) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2485893779926233616717509
% SZS output start Proof for 2485893779926233616717509
6. calm(lucy) <=> (strong(john) | ~strong(john)) [input p5]
13. (~kind(lucy) & ~calm(lucy)) <=> ? [X0] : (~rich(X0) | happy(X0)) [input p12]
24. happy(susan) [input hypothesis]
44. (calm(lucy) | (~strong(john) & strong(john))) & ((strong(john) | ~strong(john)) | ~calm(lucy)) [nnf transformation 6]
45. (calm(lucy) | (~strong(john) & strong(john))) & (strong(john) | ~strong(john) | ~calm(lucy)) [flattening 44]
61. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X0] : (~rich(X0) | happy(X0)) | (kind(lucy) | calm(lucy))) [nnf transformation 13]
62. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X0] : (~rich(X0) | happy(X0)) | kind(lucy) | calm(lucy)) [flattening 61]
63. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X1] : (~rich(X1) | happy(X1)) | kind(lucy) | calm(lucy)) [rectify 62]
64. ? [X1] : (~rich(X1) | happy(X1)) => (~rich(sK6) | happy(sK6)) [choice axiom]
65. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & ((~rich(sK6) | happy(sK6)) | kind(lucy) | calm(lucy)) [skolemisation 63,64]
101. calm(lucy) | strong(john) [cnf transformation 45]
102. calm(lucy) | ~strong(john) [cnf transformation 45]
128. ~calm(lucy) | ~happy(X0) [cnf transformation 65]
150. happy(susan) [cnf transformation 24]
215. 15 <=> strong(john) [avatar definition]
219. 16 <=> calm(lucy) [avatar definition]
222. ~15 | 16 [avatar split clause 102,219,215]
223. 15 | 16 [avatar split clause 101,219,215]
273. 27 <=> ! [X0] : ~happy(X0) [avatar definition]
274. ~happy(X0) <- (27) [avatar component clause 273]
277. 27 | ~16 [avatar split clause 128,219,273]
348. $false <- (27) [resolution 274,150]
349. ~27 [avatar contradiction clause 348]
350. $false [avatar sat refutation 222,223,277,349]
% SZS output end Proof for 2485893779926233616717509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or curious then someone is not kind and vice versa. Everyone who is creative or not tall is both kind and creative. Everyone who is not creative is creative or rich. Everyone who is either patient or funny is not brave or not happy. Everyone who is either not generous or brave is not old or not happy and vice versa. Everyone who is not quiet is happy. Everyone who is either not funny or not old is wise or rich. Everyone who is not quiet or not old is both kind and not happy and vice versa. Everyone who is humble or not old is not humble or not funny. Everyone who is not happy or not strong is either not humble or not brave and vice versa. Everyone who is creative or quiet is either humble or not strong and vice versa. Everyone who is wise is creative or not funny. If mary is either not quiet or brave then mary is both not old and not tall and vice versa. Everyone who is wise or not quiet is either not creative or not wise and vice versa. If someone is not wise then someone is calm and vice versa. If someone is creative or rich then someone is creative or patient and vice versa. Alice is not humble or not rich. Someone is not curious. John is either not quiet or humble. Someone is either not generous or kind. Paul is either not happy or not tall. Someone is either not creative or calm. Someone is not brave. Lucy is either not calm or humble. | Lucy is rich. | entailment | ((?[X]:((humble(X)<~>curious(X))))<=>(?[X]:(~kind(X))))&
(![X]:((creative(X)|~tall(X))=>(kind(X)&creative(X))))&
(![X]:(~creative(X)=>(creative(X)|rich(X))))&
(![X]:((patient(X)<~>funny(X))=>(~brave(X)|~happy(X))))&
(![X]:((~generous(X)<~>brave(X))<=>(~old(X)|~happy(X))))&
(![X]:(~quiet(X)=>happy(X)))&
(![X]:((~funny(X)<~>~old(X))=>(wise(X)|rich(X))))&
(![X]:((~quiet(X)|~old(X))<=>(kind(X)&~happy(X))))&
(![X]:((humble(X)|~old(X))=>(~humble(X)|~funny(X))))&
(![X]:((~happy(X)|~strong(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:((creative(X)|quiet(X))<=>(humble(X)<~>~strong(X))))&
(![X]:(wise(X)=>(creative(X)|~funny(X))))&
(((~quiet(mary)<~>brave(mary)))<=>((~old(mary)&~tall(mary))))&
(![X]:((wise(X)|~quiet(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(calm(X))))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((creative(X)|patient(X)))))&
((~humble(alice)|~rich(alice)))&
(?[X]:(~curious(X)))&
((~quiet(john)<~>humble(john)))&
(?[X]:((~generous(X)<~>kind(X))))&
((~happy(paul)<~>~tall(paul)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:(~brave(X)))&
((~calm(lucy)<~>humble(lucy))) | rich(lucy) | [
"p2",
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 549108971854694318223543
% SZS output start Proof for 549108971854694318223543
3. ! [X0] : (~creative(X0) => (rich(X0) | creative(X0))) [input p2]
6. ! [X0] : (~quiet(X0) => happy(X0)) [input p5]
8. ! [X0] : ((~old(X0) | ~quiet(X0)) <=> (~happy(X0) & kind(X0))) [input p7]
14. ! [X0] : ((~quiet(X0) | wise(X0)) <=> (~creative(X0) <~> ~wise(X0))) [input p13]
25. ~rich(lucy) [input hypothesis]
30. ! [X0] : ((rich(X0) | creative(X0)) | creative(X0)) [ennf transformation 3]
31. ! [X0] : (rich(X0) | creative(X0) | creative(X0)) [flattening 30]
34. ! [X0] : (happy(X0) | quiet(X0)) [ennf transformation 6]
50. ! [X0] : (((~old(X0) | ~quiet(X0)) | (happy(X0) | ~kind(X0))) & ((~happy(X0) & kind(X0)) | (old(X0) & quiet(X0)))) [nnf transformation 8]
51. ! [X0] : ((~old(X0) | ~quiet(X0) | happy(X0) | ~kind(X0)) & ((~happy(X0) & kind(X0)) | (old(X0) & quiet(X0)))) [flattening 50]
58. ! [X0] : (((~quiet(X0) | wise(X0)) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) & (((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | (quiet(X0) & ~wise(X0)))) [nnf transformation 14]
59. ! [X0] : ((~quiet(X0) | wise(X0) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) & (((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | (quiet(X0) & ~wise(X0)))) [flattening 58]
91. rich(X0) | creative(X0) | creative(X0) [cnf transformation 31]
100. quiet(X0) | happy(X0) [cnf transformation 34]
105. ~happy(X0) | quiet(X0) [cnf transformation 51]
129. ~wise(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 59]
134. ~quiet(X0) | wise(X0) | ~creative(X0) | wise(X0) [cnf transformation 59]
154. ~rich(lucy) [cnf transformation 25]
155. ~wise(X0) | ~creative(X0) [duplicate literal removal 129]
156. ~quiet(X0) | wise(X0) | ~creative(X0) [duplicate literal removal 134]
158. rich(X0) | creative(X0) [duplicate literal removal 91]
185. quiet(X0) [subsumption resolution 105,100]
206. wise(X0) | ~creative(X0) [subsumption resolution 156,185]
207. ~creative(X0) [subsumption resolution 155,206]
280. creative(lucy) [resolution 158,154]
283. $false [subsumption resolution 280,207]
% SZS output end Proof for 549108971854694318223543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is not funny then someone is both not patient and not tall and vice versa. Everyone who is either curious or strong is both not strong and not generous and vice versa. Everyone who is both not curious and not creative is not strong or humble and vice versa. If someone is not curious or creative then fred is both kind and wise. If someone is both not tall and wise then someone is rich and vice versa. Everyone who is not curious is either wise or not patient and vice versa. If someone is both rich and not patient then someone is old. If lucy is not brave or patient then lucy is not generous. Everyone who is either not wise or rich is both not kind and not curious. Everyone who is both kind and curious is not curious or old. Everyone who is both kind and happy is either generous or not strong and vice versa. Everyone who is not wise is either not kind or wise and vice versa. Everyone who is either old or not calm is not strong and vice versa. If alice is either funny or curious then fred is not tall or not quiet. If paul is both not curious and not wise then alice is strong. Everyone who is both wise and curious is either old or curious and vice versa. Fred is either old or tall. Alice is either tall or not calm. Someone is both wise and not old. Someone is tall or not funny. Someone is either not curious or not old. Someone is not quiet. | Lucy is not curious. | contradiction | ((~funny(mary))<=>(?[X]:((~patient(X)&~tall(X)))))&
(![X]:((curious(X)<~>strong(X))<=>(~strong(X)&~generous(X))))&
(![X]:((~curious(X)&~creative(X))<=>(~strong(X)|humble(X))))&
((?[X]:((~curious(X)|creative(X))))=>((kind(fred)&wise(fred))))&
((?[X]:((~tall(X)&wise(X))))<=>(?[X]:(rich(X))))&
(![X]:(~curious(X)<=>(wise(X)<~>~patient(X))))&
((?[X]:((rich(X)&~patient(X))))=>(?[X]:(old(X))))&
(((~brave(lucy)|patient(lucy)))=>(~generous(lucy)))&
(![X]:((~wise(X)<~>rich(X))=>(~kind(X)&~curious(X))))&
(![X]:((kind(X)&curious(X))=>(~curious(X)|old(X))))&
(![X]:((kind(X)&happy(X))<=>(generous(X)<~>~strong(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>wise(X))))&
(![X]:((old(X)<~>~calm(X))<=>~strong(X)))&
(((funny(alice)<~>curious(alice)))=>((~tall(fred)|~quiet(fred))))&
(((~curious(paul)&~wise(paul)))=>(strong(alice)))&
(![X]:((wise(X)&curious(X))<=>(old(X)<~>curious(X))))&
((old(fred)<~>tall(fred)))&
((tall(alice)<~>~calm(alice)))&
(?[X]:((wise(X)&~old(X))))&
(?[X]:((tall(X)|~funny(X))))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:(~quiet(X))) | ~curious(lucy) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4353790368103508512739813
% SZS output start Proof for 4353790368103508512739813
4. ? [X0] : (creative(X0) | ~curious(X0)) => (wise(fred) & kind(fred)) [input p3]
12. ! [X0] : (~wise(X0) <=> (~kind(X0) <~> wise(X0))) [input p11]
23. ~curious(lucy) [input hypothesis]
29. (wise(fred) & kind(fred)) | ! [X0] : (~creative(X0) & curious(X0)) [ennf transformation 4]
57. ! [X0] : ((~wise(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0)))) & (((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | wise(X0))) [nnf transformation 12]
84. kind(fred) | curious(X0) [cnf transformation 29]
108. wise(X0) | ~kind(X0) | wise(X0) [cnf transformation 57]
111. ~wise(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 57]
132. ~curious(lucy) [cnf transformation 23]
135. wise(X0) | ~kind(X0) [duplicate literal removal 108]
136. ~wise(X0) | ~kind(X0) [duplicate literal removal 111]
167. 7 <=> ! [X0] : curious(X0) [avatar definition]
168. curious(X0) <- (7) [avatar component clause 167]
171. 8 <=> kind(fred) [avatar definition]
173. kind(fred) <- (8) [avatar component clause 171]
175. 7 | 8 [avatar split clause 84,171,167]
214. ~kind(X0) [subsumption resolution 135,136]
260. $false <- (7) [resolution 168,132]
261. ~7 [avatar contradiction clause 260]
262. $false <- (8) [subsumption resolution 173,214]
263. ~8 [avatar contradiction clause 262]
264. $false [avatar sat refutation 175,261,263]
% SZS output end Proof for 4353790368103508512739813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and calm is both humble and not humble and vice versa. Everyone who is either not brave or kind is both not wise and not strong and vice versa. If john is not wise or not quiet then someone is wise and vice versa. If someone is both not wise and generous then lucy is old. If john is either not old or strong then lucy is both wise and calm. If someone is not tall or tall then someone is happy or humble and vice versa. Everyone who is both not wise and creative is either curious or rich and vice versa. Everyone who is either not tall or quiet is either not tall or not wise and vice versa. Everyone who is both funny and not rich is either not funny or rich and vice versa. Everyone who is creative or funny is not quiet or not happy. Everyone who is tall is both not strong and quiet and vice versa. If susan is quiet then someone is calm and vice versa. If someone is both not kind and curious then someone is either generous or not curious. If someone is not rich then paul is either creative or not patient. Everyone who is either not happy or generous is curious or strong. Everyone who is both not patient and generous is not creative. John is funny or strong. Lucy is either old or funny. Someone is either not brave or not funny. Someone is both not patient and happy. Someone is brave or not strong. Fred is wise. Alice is not kind or wise. | Susan is curious. | entailment | (![X]:((~funny(X)&calm(X))<=>(humble(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~wise(X)&~strong(X))))&
(((~wise(john)|~quiet(john)))<=>(?[X]:(wise(X))))&
((?[X]:((~wise(X)&generous(X))))=>(old(lucy)))&
(((~old(john)<~>strong(john)))=>((wise(lucy)&calm(lucy))))&
((?[X]:((~tall(X)|tall(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((~wise(X)&creative(X))<=>(curious(X)<~>rich(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)<~>~wise(X))))&
(![X]:((funny(X)&~rich(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((creative(X)|funny(X))=>(~quiet(X)|~happy(X))))&
(![X]:(tall(X)<=>(~strong(X)&quiet(X))))&
((quiet(susan))<=>(?[X]:(calm(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:(~rich(X)))=>((creative(paul)<~>~patient(paul))))&
(![X]:((~happy(X)<~>generous(X))=>(curious(X)|strong(X))))&
(![X]:((~patient(X)&generous(X))=>~creative(X)))&
((funny(john)|strong(john)))&
((old(lucy)<~>funny(lucy)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(?[X]:((~patient(X)&happy(X))))&
(?[X]:((brave(X)|~strong(X))))&
(wise(fred))&
((~kind(alice)|wise(alice))) | curious(susan) | [
"p0",
"p6",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4996352585248759651358822
% SZS output start Proof for 4996352585248759651358822
1. ! [X0] : ((calm(X0) & ~funny(X0)) <=> (~humble(X0) & humble(X0))) [input p0]
7. ! [X0] : ((creative(X0) & ~wise(X0)) <=> (curious(X0) <~> rich(X0))) [input p6]
8. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (~tall(X0) <~> ~wise(X0))) [input p7]
9. ! [X0] : ((~rich(X0) & funny(X0)) <=> (~funny(X0) <~> rich(X0))) [input p8]
12. quiet(susan) <=> ? [X0] : calm(X0) [input p11]
24. ~curious(susan) [input hypothesis]
37. ! [X0] : (((calm(X0) & ~funny(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (~calm(X0) | funny(X0)))) [nnf transformation 1]
38. ! [X0] : (((calm(X0) & ~funny(X0)) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ~calm(X0) | funny(X0))) [flattening 37]
52. ! [X0] : (((creative(X0) & ~wise(X0)) | ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0)))) & (((~rich(X0) | ~curious(X0)) & (rich(X0) | curious(X0))) | (~creative(X0) | wise(X0)))) [nnf transformation 7]
53. ! [X0] : (((creative(X0) & ~wise(X0)) | ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0)))) & (((~rich(X0) | ~curious(X0)) & (rich(X0) | curious(X0))) | ~creative(X0) | wise(X0))) [flattening 52]
54. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0)))) & (((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 8]
55. ! [X0] : (((~rich(X0) & funny(X0)) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | (rich(X0) | ~funny(X0)))) [nnf transformation 9]
56. ! [X0] : (((~rich(X0) & funny(X0)) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | rich(X0) | ~funny(X0))) [flattening 55]
59. (quiet(susan) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~quiet(susan)) [nnf transformation 12]
60. (quiet(susan) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~quiet(susan)) [rectify 59]
61. ? [X1] : calm(X1) => calm(sK3) [choice axiom]
62. (quiet(susan) | ! [X0] : ~calm(X0)) & (calm(sK3) | ~quiet(susan)) [skolemisation 60,61]
77. humble(X0) | ~calm(X0) | funny(X0) [cnf transformation 38]
78. ~humble(X0) | ~calm(X0) | funny(X0) [cnf transformation 38]
102. ~rich(X0) | curious(X0) | ~wise(X0) [cnf transformation 53]
107. wise(X0) | tall(X0) | quiet(X0) | tall(X0) [cnf transformation 54]
110. quiet(X0) | ~tall(X0) | ~tall(X0) | wise(X0) [cnf transformation 54]
113. rich(X0) | ~funny(X0) | rich(X0) | ~funny(X0) [cnf transformation 56]
115. funny(X0) | rich(X0) | funny(X0) [cnf transformation 56]
118. ~rich(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 56]
124. calm(sK3) | ~quiet(susan) [cnf transformation 62]
143. ~curious(susan) [cnf transformation 24]
144. rich(X0) | ~funny(X0) [duplicate literal removal 113]
145. rich(X0) | funny(X0) [duplicate literal removal 115]
146. ~rich(X0) | ~funny(X0) [duplicate literal removal 118]
148. wise(X0) | tall(X0) | quiet(X0) [duplicate literal removal 107]
149. quiet(X0) | ~tall(X0) | wise(X0) [duplicate literal removal 110]
151. ~calm(X0) | funny(X0) [subsumption resolution 77,78]
214. quiet(X0) | wise(X0) [subsumption resolution 148,149]
216. rich(X0) [subsumption resolution 144,145]
221. 16 <=> quiet(susan) [avatar definition]
222. ~quiet(susan) <- (~16) [avatar component clause 221]
226. 17 <=> calm(sK3) [avatar definition]
228. calm(sK3) <- (17) [avatar component clause 226]
229. ~16 | 17 [avatar split clause 124,226,221]
283. ~funny(X1) [resolution 146,216]
331. funny(sK3) <- (17) [resolution 228,151]
332. $false <- (17) [subsumption resolution 331,283]
333. ~17 [avatar contradiction clause 332]
334. wise(susan) <- (~16) [resolution 222,214]
346. curious(X0) | ~wise(X0) | funny(X0) [resolution 102,145]
348. ~wise(X0) | curious(X0) [subsumption resolution 346,283]
360. curious(susan) <- (~16) [resolution 348,334]
363. $false <- (~16) [subsumption resolution 360,143]
364. 16 [avatar contradiction clause 363]
365. $false [avatar sat refutation 229,333,364]
% SZS output end Proof for 4996352585248759651358822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is strong or curious.
If susan is not tall then someone is either not humble or brave.
Everyone who is creative or not humble is either not kind or strong.
If paul is either not rich or humble then someone is either creative or tall and vice versa.
If paul is not rich then someone is tall.
Everyone who is funny or calm is either not humble or not strong.
If paul is both patient and not humble then paul is both old and not strong.
If someone is both funny and strong then fred is not patient or old and vice versa.
Everyone who is both not happy and quiet is not happy.
Everyone who is patient is either rich or not humble.
Everyone who is not calm or kind is either not kind or brave.
Everyone who is not calm is either brave or not quiet and vice versa.
If someone is both happy and humble then paul is brave.
Everyone who is quiet or not calm is not humble and vice versa.
If john is both not calm and curious then alice is either kind or tall.
Everyone who is not strong is not humble or not brave.
John is creative or not rich.
Mary is funny or not rich.
Alice is not wise or not quiet.
Someone is both not creative and happy.
Someone is not funny or not generous.
Lucy is generous.
Mary is not wise.
Fred is not brave. | Mary is not humble. | entailment | (![X]:(~curious(X)=>(strong(X)|curious(X))))&
((~tall(susan))=>(?[X]:((~humble(X)<~>brave(X)))))&
(![X]:((creative(X)|~humble(X))=>(~kind(X)<~>strong(X))))&
(((~rich(paul)<~>humble(paul)))<=>(?[X]:((creative(X)<~>tall(X)))))&
((~rich(paul))=>(?[X]:(tall(X))))&
(![X]:((funny(X)|calm(X))=>(~humble(X)<~>~strong(X))))&
(((patient(paul)&~humble(paul)))=>((old(paul)&~strong(paul))))&
((?[X]:((funny(X)&strong(X))))<=>((~patient(fred)|old(fred))))&
(![X]:((~happy(X)&quiet(X))=>~happy(X)))&
(![X]:(patient(X)=>(rich(X)<~>~humble(X))))&
(![X]:((~calm(X)|kind(X))=>(~kind(X)<~>brave(X))))&
(![X]:(~calm(X)<=>(brave(X)<~>~quiet(X))))&
((?[X]:((happy(X)&humble(X))))=>(brave(paul)))&
(![X]:((quiet(X)|~calm(X))<=>~humble(X)))&
(((~calm(john)&curious(john)))=>((kind(alice)<~>tall(alice))))&
(![X]:(~strong(X)=>(~humble(X)|~brave(X))))&
((creative(john)|~rich(john)))&
((funny(mary)|~rich(mary)))&
((~wise(alice)|~quiet(alice)))&
(?[X]:((~creative(X)&happy(X))))&
(?[X]:((~funny(X)|~generous(X))))&
(generous(lucy))&
(~wise(mary))&
(~brave(fred)) | ~humble(mary) | [
"p5",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8612271316347060053329359
% SZS output start Proof for 8612271316347060053329359
6. ! [X0] : ((calm(X0) | funny(X0)) => (~humble(X0) <~> ~strong(X0))) [input p5]
12. ! [X0] : (~calm(X0) <=> (brave(X0) <~> ~quiet(X0))) [input p11]
14. ! [X0] : ((~calm(X0) | quiet(X0)) <=> ~humble(X0)) [input p13]
16. ! [X0] : (~strong(X0) => (~brave(X0) | ~humble(X0))) [input p15]
25. humble(mary) [input hypothesis]
33. ! [X0] : ((~humble(X0) <~> ~strong(X0)) | (~calm(X0) & ~funny(X0))) [ennf transformation 6]
43. ! [X0] : ((~brave(X0) | ~humble(X0)) | strong(X0)) [ennf transformation 16]
44. ! [X0] : (~brave(X0) | ~humble(X0) | strong(X0)) [flattening 43]
55. ! [X0] : (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~calm(X0) & ~funny(X0))) [nnf transformation 33]
63. ! [X0] : ((~calm(X0) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) & (((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | calm(X0))) [nnf transformation 12]
64. ! [X0] : (((~calm(X0) | quiet(X0)) | humble(X0)) & (~humble(X0) | (calm(X0) & ~quiet(X0)))) [nnf transformation 14]
65. ! [X0] : ((~calm(X0) | quiet(X0) | humble(X0)) & (~humble(X0) | (calm(X0) & ~quiet(X0)))) [flattening 64]
88. ~calm(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 55]
108. ~calm(X0) | brave(X0) | quiet(X0) [cnf transformation 63]
110. ~quiet(X0) | ~humble(X0) [cnf transformation 65]
111. ~humble(X0) | calm(X0) [cnf transformation 65]
115. ~brave(X0) | ~humble(X0) | strong(X0) [cnf transformation 44]
123. humble(mary) [cnf transformation 25]
266. calm(mary) [resolution 111,123]
294. ~humble(mary) | ~strong(mary) [resolution 88,266]
296. ~strong(mary) [subsumption resolution 294,123]
320. brave(mary) | quiet(mary) [resolution 108,266]
324. 37 <=> quiet(mary) [avatar definition]
326. quiet(mary) <- (37) [avatar component clause 324]
328. 38 <=> brave(mary) [avatar definition]
330. brave(mary) <- (38) [avatar component clause 328]
331. 37 | 38 [avatar split clause 320,328,324]
344. ~humble(mary) <- (37) [resolution 326,110]
347. $false <- (37) [subsumption resolution 344,123]
348. ~37 [avatar contradiction clause 347]
354. ~humble(mary) | strong(mary) <- (38) [resolution 330,115]
357. strong(mary) <- (38) [subsumption resolution 354,123]
358. $false <- (38) [subsumption resolution 357,296]
359. ~38 [avatar contradiction clause 358]
360. $false [avatar sat refutation 331,348,359]
% SZS output end Proof for 8612271316347060053329359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If mary is calm or creative then someone is not quiet.
If mary is curious or not humble then someone is happy and vice versa.
If lucy is both not generous and patient then someone is both not creative and not calm and vice versa.
If alice is both quiet and calm then someone is not rich.
If someone is old or not humble then lucy is brave or rich and vice versa.
Everyone who is kind is both generous and not curious.
Everyone who is both old and patient is humble.
Everyone who is both old and curious is happy.
Everyone who is kind is not curious.
Everyone who is humble is not calm and vice versa.
If alice is both curious and not creative then fred is strong or not patient.
If mary is either patient or not creative then fred is humble and vice versa.
Everyone who is tall or not quiet is humble and vice versa.
Everyone who is curious or not wise is either not calm or humble and vice versa.
If someone is either not curious or not wise then someone is either not calm or not creative and vice versa.
If alice is happy then john is either not old or generous.
John is both not strong and creative.
John is generous or not creative.
Someone is both not creative and not kind.
Someone is not tall or funny.
Mary is not creative or not strong.
Someone is both not quiet and generous.
Paul is either happy or not patient. | Alice is creative. | neutral | (((calm(mary)|creative(mary)))=>(?[X]:(~quiet(X))))&
(((curious(mary)|~humble(mary)))<=>(?[X]:(happy(X))))&
(((~generous(lucy)&patient(lucy)))<=>(?[X]:((~creative(X)&~calm(X)))))&
(((quiet(alice)&calm(alice)))=>(?[X]:(~rich(X))))&
((?[X]:((old(X)|~humble(X))))<=>((brave(lucy)|rich(lucy))))&
(![X]:(kind(X)=>(generous(X)&~curious(X))))&
(![X]:((old(X)&patient(X))=>humble(X)))&
(![X]:((old(X)&curious(X))=>happy(X)))&
(![X]:(kind(X)=>~curious(X)))&
(![X]:(humble(X)<=>~calm(X)))&
(((curious(alice)&~creative(alice)))=>((strong(fred)|~patient(fred))))&
(((patient(mary)<~>~creative(mary)))<=>(humble(fred)))&
(![X]:((tall(X)|~quiet(X))<=>humble(X)))&
(![X]:((curious(X)|~wise(X))<=>(~calm(X)<~>humble(X))))&
((?[X]:((~curious(X)<~>~wise(X))))<=>(?[X]:((~calm(X)<~>~creative(X)))))&
((happy(alice))=>((~old(john)<~>generous(john))))&
((~strong(john)&creative(john)))&
((generous(john)|~creative(john)))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:((~tall(X)|funny(X))))&
((~creative(mary)|~strong(mary)))&
(?[X]:((~quiet(X)&generous(X))))&
((happy(paul)<~>~patient(paul))) | creative(alice) | [] | null | 0 |
Everyone who is funny or not humble is tall and vice versa.
Everyone who is both quiet and calm is not happy or not brave.
If someone is both not strong and not patient then someone is not quiet or rich.
If mary is either tall or not creative then someone is not old.
Everyone who is not quiet is either not brave or not old and vice versa.
If paul is not humble then someone is both quiet and not curious and vice versa.
If paul is curious then someone is both not patient and not quiet.
If alice is either old or quiet then someone is either patient or not tall and vice versa.
If fred is not curious or not wise then lucy is funny and vice versa.
Everyone who is strong or not kind is either not generous or not creative and vice versa.
If someone is either brave or humble then alice is either tall or not kind.
Everyone who is both old and humble is not curious or not happy and vice versa.
Everyone who is not brave is either not kind or humble.
If lucy is either strong or calm then john is either rich or not brave and vice versa.
Everyone who is not happy is both tall and kind.
Everyone who is not funny or patient is either not humble or not patient.
Someone is either calm or not happy.
Someone is not curious.
Fred is generous or not wise.
Someone is both not funny and calm.
Mary is either not funny or generous.
Paul is either patient or creative.
Someone is rich or not brave.
Someone is generous or not rich. | Alice is not brave. | entailment | (![X]:((funny(X)|~humble(X))<=>tall(X)))&
(![X]:((quiet(X)&calm(X))=>(~happy(X)|~brave(X))))&
((?[X]:((~strong(X)&~patient(X))))=>(?[X]:((~quiet(X)|rich(X)))))&
(((tall(mary)<~>~creative(mary)))=>(?[X]:(~old(X))))&
(![X]:(~quiet(X)<=>(~brave(X)<~>~old(X))))&
((~humble(paul))<=>(?[X]:((quiet(X)&~curious(X)))))&
((curious(paul))=>(?[X]:((~patient(X)&~quiet(X)))))&
(((old(alice)<~>quiet(alice)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(((~curious(fred)|~wise(fred)))<=>(funny(lucy)))&
(![X]:((strong(X)|~kind(X))<=>(~generous(X)<~>~creative(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((tall(alice)<~>~kind(alice))))&
(![X]:((old(X)&humble(X))<=>(~curious(X)|~happy(X))))&
(![X]:(~brave(X)=>(~kind(X)<~>humble(X))))&
(((strong(lucy)<~>calm(lucy)))<=>((rich(john)<~>~brave(john))))&
(![X]:(~happy(X)=>(tall(X)&kind(X))))&
(![X]:((~funny(X)|patient(X))=>(~humble(X)<~>~patient(X))))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:(~curious(X)))&
((generous(fred)|~wise(fred)))&
(?[X]:((~funny(X)&calm(X))))&
((~funny(mary)<~>generous(mary)))&
((patient(paul)<~>creative(paul)))&
(?[X]:((rich(X)|~brave(X))))&
(?[X]:((generous(X)|~rich(X)))) | ~brave(alice) | [
"p0",
"p4",
"p7",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4257523424323521044265900
% SZS output start Proof for 4257523424323521044265900
1. ! [X0] : ((~humble(X0) | funny(X0)) <=> tall(X0)) [input p0]
5. ! [X0] : (~quiet(X0) <=> (~brave(X0) <~> ~old(X0))) [input p4]
8. (old(alice) <~> quiet(alice)) <=> ? [X0] : (patient(X0) <~> ~tall(X0)) [input p7]
16. ! [X0] : ((patient(X0) | ~funny(X0)) => (~humble(X0) <~> ~patient(X0))) [input p15]
20. ? [X0] : (calm(X0) & ~funny(X0)) [input p19]
25. brave(alice) [input hypothesis]
35. ! [X0] : ((~humble(X0) <~> ~patient(X0)) | (~patient(X0) & funny(X0))) [ennf transformation 16]
36. ! [X0] : (((~humble(X0) | funny(X0)) | ~tall(X0)) & (tall(X0) | (humble(X0) & ~funny(X0)))) [nnf transformation 1]
37. ! [X0] : ((~humble(X0) | funny(X0) | ~tall(X0)) & (tall(X0) | (humble(X0) & ~funny(X0)))) [flattening 36]
44. ! [X0] : ((~quiet(X0) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | quiet(X0))) [nnf transformation 5]
51. (((~quiet(alice) | ~old(alice)) & (quiet(alice) | old(alice))) | ! [X0] : ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (? [X0] : ((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | ((old(alice) | ~quiet(alice)) & (quiet(alice) | ~old(alice)))) [nnf transformation 8]
52. (((~quiet(alice) | ~old(alice)) & (quiet(alice) | old(alice))) | ! [X0] : ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (? [X1] : ((tall(X1) | ~patient(X1)) & (~tall(X1) | patient(X1))) | ((old(alice) | ~quiet(alice)) & (quiet(alice) | ~old(alice)))) [rectify 51]
53. ? [X1] : ((tall(X1) | ~patient(X1)) & (~tall(X1) | patient(X1))) => ((tall(sK4) | ~patient(sK4)) & (~tall(sK4) | patient(sK4))) [choice axiom]
54. (((~quiet(alice) | ~old(alice)) & (quiet(alice) | old(alice))) | ! [X0] : ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (((tall(sK4) | ~patient(sK4)) & (~tall(sK4) | patient(sK4))) | ((old(alice) | ~quiet(alice)) & (quiet(alice) | ~old(alice)))) [skolemisation 52,53]
64. ! [X0] : (((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | (~patient(X0) & funny(X0))) [nnf transformation 35]
70. ? [X0] : (calm(X0) & ~funny(X0)) => (calm(sK7) & ~funny(sK7)) [choice axiom]
71. calm(sK7) & ~funny(sK7) [skolemisation 20,70]
79. tall(X0) | humble(X0) [cnf transformation 37]
80. ~tall(X0) | funny(X0) | ~humble(X0) [cnf transformation 37]
85. ~old(X0) | ~brave(X0) | quiet(X0) [cnf transformation 44]
88. ~brave(X0) | ~quiet(X0) | old(X0) [cnf transformation 44]
98. quiet(alice) | old(alice) | ~tall(X0) | ~patient(X0) [cnf transformation 54]
99. quiet(alice) | old(alice) | patient(X0) | tall(X0) [cnf transformation 54]
100. ~quiet(alice) | ~old(alice) | ~tall(X0) | ~patient(X0) [cnf transformation 54]
101. ~quiet(alice) | ~old(alice) | patient(X0) | tall(X0) [cnf transformation 54]
133. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 64]
134. patient(X0) | humble(X0) | funny(X0) [cnf transformation 64]
140. ~funny(sK7) [cnf transformation 71]
148. brave(alice) [cnf transformation 25]
149. ~patient(X0) | ~humble(X0) [duplicate literal removal 133]
209. 14 <=> ! [X0] : (patient(X0) | tall(X0)) [avatar definition]
210. patient(X0) | tall(X0) <- (14) [avatar component clause 209]
212. 15 <=> old(alice) [avatar definition]
213. old(alice) <- (15) [avatar component clause 212]
216. 16 <=> quiet(alice) [avatar definition]
218. ~quiet(alice) <- (~16) [avatar component clause 216]
219. 14 | ~15 | ~16 [avatar split clause 101,216,212,209]
221. 17 <=> ! [X0] : (~tall(X0) | ~patient(X0)) [avatar definition]
222. ~patient(X0) | ~tall(X0) <- (17) [avatar component clause 221]
223. 17 | ~15 | ~16 [avatar split clause 100,216,212,221]
224. 14 | 15 | 16 [avatar split clause 99,216,212,209]
225. 17 | 15 | 16 [avatar split clause 98,216,212,221]
374. ~brave(alice) | quiet(alice) <- (15) [resolution 85,213]
376. quiet(alice) <- (15) [subsumption resolution 374,148]
377. $false <- (15, ~16) [subsumption resolution 376,218]
378. ~15 | 16 [avatar contradiction clause 377]
411. ~quiet(alice) | old(alice) [resolution 88,148]
431. tall(X0) | ~humble(X0) <- (14) [resolution 210,149]
435. tall(X0) <- (14) [subsumption resolution 431,79]
446. 15 | ~16 [avatar split clause 411,216,212]
451. funny(X0) | ~humble(X0) <- (14) [resolution 435,80]
482. humble(X0) | funny(X0) | ~tall(X0) <- (17) [resolution 134,222]
487. humble(X0) | funny(X0) <- (14, 17) [subsumption resolution 482,435]
488. funny(X0) <- (14, 17) [subsumption resolution 487,451]
489. $false <- (14, 17) [resolution 488,140]
493. ~14 | ~17 [avatar contradiction clause 489]
494. $false [avatar sat refutation 219,223,224,225,378,446,493]
% SZS output end Proof for 4257523424323521044265900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not calm is both not wise and not brave and vice versa.
Everyone who is both quiet and not patient is either happy or not generous.
Everyone who is creative or funny is not tall.
Everyone who is not kind or calm is either not patient or not creative.
If fred is not quiet or generous then someone is old or not curious.
If someone is both strong and not patient then someone is rich or patient and vice versa.
Everyone who is both humble and old is both brave and not generous and vice versa.
If paul is both not generous and brave then someone is tall or happy and vice versa.
If alice is both patient and not brave then lucy is not rich or quiet and vice versa.
If someone is either not funny or strong then someone is both wise and not curious and vice versa.
Everyone who is not tall is both old and not patient.
Everyone who is humble or not humble is not calm and vice versa.
Everyone who is both not wise and not calm is not kind or not calm.
If paul is generous then someone is not curious.
If someone is not kind or funny then someone is both patient and happy and vice versa.
Fred is old or curious.
John is either not rich or brave.
Mary is old or not creative.
Susan is not strong or generous. | Lucy is tall. | contradiction | (![X]:((~humble(X)|~calm(X))<=>(~wise(X)&~brave(X))))&
(![X]:((quiet(X)&~patient(X))=>(happy(X)<~>~generous(X))))&
(![X]:((creative(X)|funny(X))=>~tall(X)))&
(![X]:((~kind(X)|calm(X))=>(~patient(X)<~>~creative(X))))&
(((~quiet(fred)|generous(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:((strong(X)&~patient(X))))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:((humble(X)&old(X))<=>(brave(X)&~generous(X))))&
(((~generous(paul)&brave(paul)))<=>(?[X]:((tall(X)|happy(X)))))&
(((patient(alice)&~brave(alice)))<=>((~rich(lucy)|quiet(lucy))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:(~tall(X)=>(old(X)&~patient(X))))&
(![X]:((humble(X)|~humble(X))<=>~calm(X)))&
(![X]:((~wise(X)&~calm(X))=>(~kind(X)|~calm(X))))&
((generous(paul))=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)|funny(X))))<=>(?[X]:((patient(X)&happy(X)))))&
((old(fred)|curious(fred)))&
((~rich(john)<~>brave(john)))&
((old(mary)|~creative(mary)))&
((~strong(susan)|generous(susan))) | tall(lucy) | [
"p0",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3942114357498302914891027
% SZS output start Proof for 3942114357498302914891027
1. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (~brave(X0) & ~wise(X0))) [input p0]
8. (brave(paul) & ~generous(paul)) <=> ? [X0] : (happy(X0) | tall(X0)) [input p7]
12. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~calm(X0)) [input p11]
20. tall(lucy) [input hypothesis]
33. ! [X0] : (((~calm(X0) | ~humble(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 1]
34. ! [X0] : ((~calm(X0) | ~humble(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [flattening 33]
46. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | (~brave(paul) | generous(paul))) [nnf transformation 8]
47. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | ~brave(paul) | generous(paul)) [flattening 46]
48. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X1] : (happy(X1) | tall(X1)) | ~brave(paul) | generous(paul)) [rectify 47]
49. ? [X1] : (happy(X1) | tall(X1)) => (happy(sK3) | tall(sK3)) [choice axiom]
50. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & ((happy(sK3) | tall(sK3)) | ~brave(paul) | generous(paul)) [skolemisation 48,49]
58. ! [X0] : (((~humble(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 12]
59. ! [X0] : ((~humble(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [flattening 58]
71. ~brave(X0) | calm(X0) [cnf transformation 34]
95. brave(paul) | ~tall(X0) [cnf transformation 50]
110. ~calm(X0) | ~humble(X0) [cnf transformation 59]
111. ~calm(X0) | humble(X0) [cnf transformation 59]
125. tall(lucy) [cnf transformation 20]
178. 13 <=> brave(paul) [avatar definition]
180. brave(paul) <- (13) [avatar component clause 178]
183. 14 <=> ! [X0] : ~tall(X0) [avatar definition]
184. ~tall(X0) <- (14) [avatar component clause 183]
185. 14 | 13 [avatar split clause 95,178,183]
253. ~calm(X0) [subsumption resolution 110,111]
338. $false <- (14) [resolution 184,125]
339. ~14 [avatar contradiction clause 338]
343. calm(paul) <- (13) [resolution 71,180]
344. $false <- (13) [subsumption resolution 343,253]
345. ~13 [avatar contradiction clause 344]
346. $false [avatar sat refutation 185,339,345]
% SZS output end Proof for 3942114357498302914891027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is both quiet and old and vice versa.
If someone is kind or not patient then lucy is quiet and vice versa.
Everyone who is both generous and not generous is either not wise or not old.
Everyone who is strong or brave is either not old or brave and vice versa.
If mary is curious or not wise then someone is both strong and not generous.
If susan is either not rich or not creative then lucy is not tall or happy.
If someone is funny then someone is either not curious or not generous and vice versa.
Everyone who is wise or not brave is both not tall and not quiet and vice versa.
Everyone who is either curious or old is either not wise or tall and vice versa.
If paul is both happy and not quiet then paul is both not funny and not creative.
Everyone who is either not calm or not wise is not patient.
If lucy is either kind or not generous then someone is both generous and not curious.
If someone is both happy and tall then someone is both creative and not curious.
Everyone who is not calm is either brave or not humble.
If someone is both curious and not creative then someone is either happy or not brave.
Everyone who is old or tall is both not quiet and not humble.
Someone is either not strong or old.
Someone is not brave.
Someone is both not quiet and strong.
Someone is both creative and rich.
Paul is curious.
Someone is either calm or not funny. | Mary is kind. | contradiction | ((?[X]:(~wise(X)))<=>(?[X]:((quiet(X)&old(X)))))&
((?[X]:((kind(X)|~patient(X))))<=>(quiet(lucy)))&
(![X]:((generous(X)&~generous(X))=>(~wise(X)<~>~old(X))))&
(![X]:((strong(X)|brave(X))<=>(~old(X)<~>brave(X))))&
(((curious(mary)|~wise(mary)))=>(?[X]:((strong(X)&~generous(X)))))&
(((~rich(susan)<~>~creative(susan)))=>((~tall(lucy)|happy(lucy))))&
((?[X]:(funny(X)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(![X]:((wise(X)|~brave(X))<=>(~tall(X)&~quiet(X))))&
(![X]:((curious(X)<~>old(X))<=>(~wise(X)<~>tall(X))))&
(((happy(paul)&~quiet(paul)))=>((~funny(paul)&~creative(paul))))&
(![X]:((~calm(X)<~>~wise(X))=>~patient(X)))&
(((kind(lucy)<~>~generous(lucy)))=>(?[X]:((generous(X)&~curious(X)))))&
((?[X]:((happy(X)&tall(X))))=>(?[X]:((creative(X)&~curious(X)))))&
(![X]:(~calm(X)=>(brave(X)<~>~humble(X))))&
((?[X]:((curious(X)&~creative(X))))=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((old(X)|tall(X))=>(~quiet(X)&~humble(X))))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:((creative(X)&rich(X))))&
(curious(paul))&
(?[X]:((calm(X)<~>~funny(X)))) | kind(mary) | [
"p1",
"p3",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6298355736026495185434411
% SZS output start Proof for 6298355736026495185434411
2. ? [X0] : (~patient(X0) | kind(X0)) <=> quiet(lucy) [input p1]
4. ! [X0] : ((brave(X0) | strong(X0)) <=> (~old(X0) <~> brave(X0))) [input p3]
8. ! [X0] : ((~brave(X0) | wise(X0)) <=> (~quiet(X0) & ~tall(X0))) [input p7]
16. ! [X0] : ((tall(X0) | old(X0)) => (~humble(X0) & ~quiet(X0))) [input p15]
23. kind(mary) [input hypothesis]
40. ! [X0] : ((~humble(X0) & ~quiet(X0)) | (~tall(X0) & ~old(X0))) [ennf transformation 16]
46. (? [X0] : (~patient(X0) | kind(X0)) | ~quiet(lucy)) & (quiet(lucy) | ! [X0] : (patient(X0) & ~kind(X0))) [nnf transformation 2]
47. (? [X0] : (~patient(X0) | kind(X0)) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : (patient(X1) & ~kind(X1))) [rectify 46]
48. ? [X0] : (~patient(X0) | kind(X0)) => (~patient(sK2) | kind(sK2)) [choice axiom]
49. ((~patient(sK2) | kind(sK2)) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : (patient(X1) & ~kind(X1))) [skolemisation 47,48]
51. ! [X0] : (((brave(X0) | strong(X0)) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0)))) & (((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | (~brave(X0) & ~strong(X0)))) [nnf transformation 4]
52. ! [X0] : ((brave(X0) | strong(X0) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0)))) & (((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | (~brave(X0) & ~strong(X0)))) [flattening 51]
61. ! [X0] : (((~brave(X0) | wise(X0)) | (quiet(X0) | tall(X0))) & ((~quiet(X0) & ~tall(X0)) | (brave(X0) & ~wise(X0)))) [nnf transformation 8]
62. ! [X0] : ((~brave(X0) | wise(X0) | quiet(X0) | tall(X0)) & ((~quiet(X0) & ~tall(X0)) | (brave(X0) & ~wise(X0)))) [flattening 61]
91. quiet(lucy) | ~kind(X1) [cnf transformation 49]
99. ~brave(X0) | old(X0) | ~brave(X0) [cnf transformation 52]
115. ~quiet(X0) | brave(X0) [cnf transformation 62]
139. ~quiet(X0) | ~old(X0) [cnf transformation 40]
153. kind(mary) [cnf transformation 23]
154. ~brave(X0) | old(X0) [duplicate literal removal 99]
157. 1 <=> ! [X1] : (~old(X1) | ~quiet(X1)) [avatar definition]
158. ~old(X1) | ~quiet(X1) <- (1) [avatar component clause 157]
178. 6 <=> quiet(lucy) [avatar definition]
179. quiet(lucy) <- (6) [avatar component clause 178]
195. 10 <=> ! [X1] : ~kind(X1) [avatar definition]
196. ~kind(X1) <- (10) [avatar component clause 195]
197. 10 | 6 [avatar split clause 91,178,195]
329. 1 [avatar split clause 139,157]
357. $false <- (10) [resolution 196,153]
358. ~10 [avatar contradiction clause 357]
362. brave(lucy) <- (6) [resolution 115,179]
364. old(lucy) <- (6) [resolution 154,362]
366. ~quiet(lucy) <- (1, 6) [resolution 158,364]
369. $false <- (1, 6) [subsumption resolution 366,179]
370. ~1 | ~6 [avatar contradiction clause 369]
371. $false [avatar sat refutation 197,329,358,370]
% SZS output end Proof for 6298355736026495185434411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is brave then someone is either humble or not tall and vice versa.
If alice is rich or wise then john is funny.
Everyone who is either not tall or quiet is creative and vice versa.
If someone is not creative then paul is not tall.
Everyone who is not wise or strong is either not generous or patient and vice versa.
Everyone who is not old is curious or not humble and vice versa.
If mary is either quiet or old then someone is both brave and generous.
If alice is both not generous and not rich then someone is either strong or not brave and vice versa.
Everyone who is either not happy or brave is curious or creative and vice versa.
If someone is both not wise and rich then someone is humble and vice versa.
Everyone who is either patient or kind is calm and vice versa.
Everyone who is both not creative and wise is not brave or rich and vice versa.
Everyone who is not funny or wise is both quiet and not kind and vice versa.
Everyone who is either not curious or happy is either humble or not generous.
If someone is not wise or brave then lucy is not humble and vice versa.
If someone is both strong and quiet then susan is calm and vice versa.
Someone is tall or not brave.
John is either calm or not strong.
Lucy is both not funny and wise.
Someone is not kind or not calm.
Someone is not humble or old.
Someone is not creative or tall.
Fred is not quiet or creative.
Alice is wise or not kind. | Susan is kind. | neutral | ((brave(paul))<=>(?[X]:((humble(X)<~>~tall(X)))))&
(((rich(alice)|wise(alice)))=>(funny(john)))&
(![X]:((~tall(X)<~>quiet(X))<=>creative(X)))&
((?[X]:(~creative(X)))=>(~tall(paul)))&
(![X]:((~wise(X)|strong(X))<=>(~generous(X)<~>patient(X))))&
(![X]:(~old(X)<=>(curious(X)|~humble(X))))&
(((quiet(mary)<~>old(mary)))=>(?[X]:((brave(X)&generous(X)))))&
(((~generous(alice)&~rich(alice)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(curious(X)|creative(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>calm(X)))&
(![X]:((~creative(X)&wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~funny(X)|wise(X))<=>(quiet(X)&~kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~generous(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~humble(lucy)))&
((?[X]:((strong(X)&quiet(X))))<=>(calm(susan)))&
(?[X]:((tall(X)|~brave(X))))&
((calm(john)<~>~strong(john)))&
((~funny(lucy)&wise(lucy)))&
(?[X]:((~kind(X)|~calm(X))))&
(?[X]:((~humble(X)|old(X))))&
(?[X]:((~creative(X)|tall(X))))&
((~quiet(fred)|creative(fred)))&
((wise(alice)|~kind(alice))) | kind(susan) | [] | null | 0 |
If someone is both not funny and not kind then someone is not humble or not quiet.
If john is not funny then fred is either not generous or generous.
Everyone who is either not brave or not tall is either not brave or kind.
Everyone who is not tall is both funny and not tall and vice versa.
Everyone who is not old is kind or tall and vice versa.
If mary is not humble then someone is kind.
Everyone who is either calm or not patient is either old or funny.
Everyone who is brave is not tall and vice versa.
If mary is humble then john is either wise or not happy.
Everyone who is not kind or not tall is either humble or not patient and vice versa.
Everyone who is both quiet and not happy is happy or curious and vice versa.
Everyone who is calm is both curious and wise.
Everyone who is either tall or not creative is both quiet and rich.
Everyone who is either not strong or generous is both not generous and not humble.
Everyone who is both happy and not strong is both kind and calm and vice versa.
If someone is happy or not funny then someone is both calm and quiet and vice versa.
Someone is either quiet or old.
Susan is not strong.
Someone is either creative or not funny.
Someone is not kind.
John is curious.
Paul is either calm or creative.
Someone is not tall.
Mary is creative. | Fred is not happy. | entailment | ((?[X]:((~funny(X)&~kind(X))))=>(?[X]:((~humble(X)|~quiet(X)))))&
((~funny(john))=>((~generous(fred)<~>generous(fred))))&
(![X]:((~brave(X)<~>~tall(X))=>(~brave(X)<~>kind(X))))&
(![X]:(~tall(X)<=>(funny(X)&~tall(X))))&
(![X]:(~old(X)<=>(kind(X)|tall(X))))&
((~humble(mary))=>(?[X]:(kind(X))))&
(![X]:((calm(X)<~>~patient(X))=>(old(X)<~>funny(X))))&
(![X]:(brave(X)<=>~tall(X)))&
((humble(mary))=>((wise(john)<~>~happy(john))))&
(![X]:((~kind(X)|~tall(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((quiet(X)&~happy(X))<=>(happy(X)|curious(X))))&
(![X]:(calm(X)=>(curious(X)&wise(X))))&
(![X]:((tall(X)<~>~creative(X))=>(quiet(X)&rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>(~generous(X)&~humble(X))))&
(![X]:((happy(X)&~strong(X))<=>(kind(X)&calm(X))))&
((?[X]:((happy(X)|~funny(X))))<=>(?[X]:((calm(X)&quiet(X)))))&
(?[X]:((quiet(X)<~>old(X))))&
(~strong(susan))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:(~kind(X)))&
(curious(john))&
((calm(paul)<~>creative(paul)))&
(?[X]:(~tall(X)))&
(creative(mary)) | ~happy(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6607246373410227909293410
% SZS output start Proof for 6607246373410227909293410
11. ! [X0] : ((~happy(X0) & quiet(X0)) <=> (curious(X0) | happy(X0))) [input p10]
25. happy(fred) [input hypothesis]
54. ! [X0] : (((~happy(X0) & quiet(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (happy(X0) | ~quiet(X0)))) [nnf transformation 11]
55. ! [X0] : (((~happy(X0) & quiet(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | happy(X0) | ~quiet(X0))) [flattening 54]
107. ~happy(X0) | ~happy(X0) [cnf transformation 55]
137. happy(fred) [cnf transformation 25]
140. ~happy(X0) [duplicate literal removal 107]
228. $false [subsumption resolution 137,140]
% SZS output end Proof for 6607246373410227909293410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not rich is creative.
If paul is either strong or patient then paul is both not creative and funny and vice versa.
If paul is either strong or wise then mary is curious.
If fred is both not old and not strong then someone is not kind or not tall.
Everyone who is not funny is not old or happy.
If someone is either humble or not kind then paul is both curious and humble and vice versa.
Everyone who is both not old and curious is wise and vice versa.
If someone is not creative or kind then lucy is both creative and not patient.
If someone is quiet or creative then someone is either not kind or not curious and vice versa.
Everyone who is either not funny or not curious is both not brave and not patient.
Everyone who is brave is not kind.
Everyone who is not old or not wise is both not curious and funny and vice versa.
If someone is not brave then mary is both not wise and old.
Everyone who is either wise or not patient is not strong and vice versa.
Everyone who is both curious and not funny is either old or funny.
Fred is not curious or not rich.
Someone is both tall and calm.
John is either calm or brave.
Susan is both generous and not calm.
Someone is not curious. | Lucy is not patient. | entailment | (![X]:((~kind(X)<~>~rich(X))=>creative(X)))&
(((strong(paul)<~>patient(paul)))<=>((~creative(paul)&funny(paul))))&
(((strong(paul)<~>wise(paul)))=>(curious(mary)))&
(((~old(fred)&~strong(fred)))=>(?[X]:((~kind(X)|~tall(X)))))&
(![X]:(~funny(X)=>(~old(X)|happy(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((curious(paul)&humble(paul))))&
(![X]:((~old(X)&curious(X))<=>wise(X)))&
((?[X]:((~creative(X)|kind(X))))=>((creative(lucy)&~patient(lucy))))&
((?[X]:((quiet(X)|creative(X))))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
(![X]:((~funny(X)<~>~curious(X))=>(~brave(X)&~patient(X))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((~old(X)|~wise(X))<=>(~curious(X)&funny(X))))&
((?[X]:(~brave(X)))=>((~wise(mary)&old(mary))))&
(![X]:((wise(X)<~>~patient(X))<=>~strong(X)))&
(![X]:((curious(X)&~funny(X))=>(old(X)<~>funny(X))))&
((~curious(fred)|~rich(fred)))&
(?[X]:((tall(X)&calm(X))))&
((calm(john)<~>brave(john)))&
((generous(susan)&~calm(susan)))&
(?[X]:(~curious(X))) | ~patient(lucy) | [
"p6",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6198242093668361963624572
% SZS output start Proof for 6198242093668361963624572
7. ! [X0] : ((curious(X0) & ~old(X0)) <=> wise(X0)) [input p6]
8. ? [X0] : (kind(X0) | ~creative(X0)) => (~patient(lucy) & creative(lucy)) [input p7]
9. ? [X0] : (creative(X0) | quiet(X0)) <=> ? [X0] : (~kind(X0) <~> ~curious(X0)) [input p8]
12. ! [X0] : ((~wise(X0) | ~old(X0)) <=> (funny(X0) & ~curious(X0))) [input p11]
21. patient(lucy) [input hypothesis]
22. ? [X0] : (creative(X0) | quiet(X0)) <=> ? [X1] : (~kind(X1) <~> ~curious(X1)) [rectify 9]
29. (~patient(lucy) & creative(lucy)) | ! [X0] : (~kind(X0) & creative(X0)) [ennf transformation 8]
46. ! [X0] : (((curious(X0) & ~old(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) | old(X0)))) [nnf transformation 7]
47. ! [X0] : (((curious(X0) & ~old(X0)) | ~wise(X0)) & (wise(X0) | ~curious(X0) | old(X0))) [flattening 46]
48. (? [X0] : (creative(X0) | quiet(X0)) | ! [X1] : ((~kind(X1) | curious(X1)) & (~curious(X1) | kind(X1)))) & (? [X1] : ((curious(X1) | kind(X1)) & (~curious(X1) | ~kind(X1))) | ! [X0] : (~creative(X0) & ~quiet(X0))) [nnf transformation 22]
49. (? [X0] : (creative(X0) | quiet(X0)) | ! [X1] : ((~kind(X1) | curious(X1)) & (~curious(X1) | kind(X1)))) & (? [X2] : ((curious(X2) | kind(X2)) & (~curious(X2) | ~kind(X2))) | ! [X3] : (~creative(X3) & ~quiet(X3))) [rectify 48]
50. ? [X0] : (creative(X0) | quiet(X0)) => (creative(sK2) | quiet(sK2)) [choice axiom]
51. ? [X2] : ((curious(X2) | kind(X2)) & (~curious(X2) | ~kind(X2))) => ((curious(sK3) | kind(sK3)) & (~curious(sK3) | ~kind(sK3))) [choice axiom]
52. ((creative(sK2) | quiet(sK2)) | ! [X1] : ((~kind(X1) | curious(X1)) & (~curious(X1) | kind(X1)))) & (((curious(sK3) | kind(sK3)) & (~curious(sK3) | ~kind(sK3))) | ! [X3] : (~creative(X3) & ~quiet(X3))) [skolemisation 49,51,50]
54. ! [X0] : (((~wise(X0) | ~old(X0)) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | (wise(X0) & old(X0)))) [nnf transformation 12]
55. ! [X0] : ((~wise(X0) | ~old(X0) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | (wise(X0) & old(X0)))) [flattening 54]
81. ~old(X0) | ~wise(X0) [cnf transformation 47]
85. ~patient(lucy) | creative(X0) [cnf transformation 29]
86. ~patient(lucy) | ~kind(X0) [cnf transformation 29]
90. curious(sK3) | kind(sK3) | ~creative(X3) [cnf transformation 52]
98. ~curious(X0) | old(X0) [cnf transformation 55]
99. ~curious(X0) | wise(X0) [cnf transformation 55]
118. patient(lucy) [cnf transformation 21]
198. 17 <=> ! [X0] : ~kind(X0) [avatar definition]
199. ~kind(X0) <- (17) [avatar component clause 198]
201. 18 <=> patient(lucy) [avatar definition]
204. 17 | ~18 [avatar split clause 86,201,198]
206. 19 <=> ! [X0] : creative(X0) [avatar definition]
207. creative(X0) <- (19) [avatar component clause 206]
208. 19 | ~18 [avatar split clause 85,201,206]
232. 25 <=> ! [X3] : ~creative(X3) [avatar definition]
233. ~creative(X3) <- (25) [avatar component clause 232]
235. 26 <=> kind(sK3) [avatar definition]
237. kind(sK3) <- (26) [avatar component clause 235]
239. 27 <=> curious(sK3) [avatar definition]
241. curious(sK3) <- (27) [avatar component clause 239]
242. 25 | 26 | 27 [avatar split clause 90,239,235,232]
281. 18 [avatar split clause 118,201]
282. $false <- (17, 26) [resolution 237,199]
283. ~17 | ~26 [avatar contradiction clause 282]
288. old(sK3) <- (27) [resolution 98,241]
290. wise(sK3) <- (27) [resolution 99,241]
308. ~wise(sK3) <- (27) [resolution 288,81]
309. $false <- (27) [subsumption resolution 308,290]
310. ~27 [avatar contradiction clause 309]
311. $false <- (19, 25) [subsumption resolution 233,207]
312. ~19 | ~25 [avatar contradiction clause 311]
313. $false [avatar sat refutation 204,208,242,281,283,310,312]
% SZS output end Proof for 6198242093668361963624572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or happy then alice is both not brave and not tall.
If alice is kind then fred is not kind or not funny and vice versa.
Everyone who is both not rich and not curious is not quiet or not curious and vice versa.
Everyone who is patient is either not kind or not quiet and vice versa.
Everyone who is patient or old is either not rich or not kind.
If someone is either brave or not generous then someone is either generous or not calm.
Everyone who is either creative or calm is patient or not generous and vice versa.
If someone is both not generous and not old then mary is either not humble or not wise.
If someone is not funny or rich then lucy is either humble or funny and vice versa.
Everyone who is generous or not patient is either not quiet or quiet and vice versa.
Everyone who is both kind and not calm is not kind or brave.
If alice is both not creative and not happy then someone is either not strong or not rich.
If someone is rich or not generous then paul is both wise and not old and vice versa.
Everyone who is not quiet or creative is either not brave or not wise and vice versa.
Everyone who is both not patient and quiet is not strong and vice versa.
Someone is rich or not calm.
Someone is both strong and not creative.
Someone is both not patient and creative.
Someone is not rich or tall.
John is either not wise or tall.
Paul is either not kind or not old.
Fred is funny.
Someone is not tall. | Lucy is calm. | neutral | ((?[X]:((~wise(X)<~>happy(X))))=>((~brave(alice)&~tall(alice))))&
((kind(alice))<=>((~kind(fred)|~funny(fred))))&
(![X]:((~rich(X)&~curious(X))<=>(~quiet(X)|~curious(X))))&
(![X]:(patient(X)<=>(~kind(X)<~>~quiet(X))))&
(![X]:((patient(X)|old(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((brave(X)<~>~generous(X))))=>(?[X]:((generous(X)<~>~calm(X)))))&
(![X]:((creative(X)<~>calm(X))<=>(patient(X)|~generous(X))))&
((?[X]:((~generous(X)&~old(X))))=>((~humble(mary)<~>~wise(mary))))&
((?[X]:((~funny(X)|rich(X))))<=>((humble(lucy)<~>funny(lucy))))&
(![X]:((generous(X)|~patient(X))<=>(~quiet(X)<~>quiet(X))))&
(![X]:((kind(X)&~calm(X))=>(~kind(X)|brave(X))))&
(((~creative(alice)&~happy(alice)))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((?[X]:((rich(X)|~generous(X))))<=>((wise(paul)&~old(paul))))&
(![X]:((~quiet(X)|creative(X))<=>(~brave(X)<~>~wise(X))))&
(![X]:((~patient(X)&quiet(X))<=>~strong(X)))&
(?[X]:((rich(X)|~calm(X))))&
(?[X]:((strong(X)&~creative(X))))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((~rich(X)|tall(X))))&
((~wise(john)<~>tall(john)))&
((~kind(paul)<~>~old(paul)))&
(funny(fred))&
(?[X]:(~tall(X))) | calm(lucy) | [] | null | 0 |
If someone is not strong or not calm then someone is either quiet or not quiet and vice versa. Everyone who is both not creative and strong is either not strong or not happy. Everyone who is either not strong or not funny is not wise and vice versa. If alice is either not happy or not brave then alice is both kind and calm and vice versa. Everyone who is either not wise or not funny is both not funny and wise and vice versa. If mary is strong or humble then lucy is both strong and happy and vice versa. Everyone who is not strong is kind. Everyone who is either not kind or wise is both curious and not wise. If someone is either brave or kind then susan is either generous or patient and vice versa. Everyone who is both not creative and old is not humble and vice versa. If someone is both generous and not wise then someone is not happy or curious and vice versa. Everyone who is not patient or not quiet is not patient or not wise and vice versa. If john is brave or not kind then john is calm and vice versa. Everyone who is both humble and calm is either quiet or not creative. If fred is curious or patient then someone is both tall and generous. Fred is not creative. Fred is wise or not old. Alice is both not quiet and patient. Alice is not happy. Someone is both generous and not creative. Susan is not creative. Someone is either not patient or not creative. | Fred is tall. | neutral | ((?[X]:((~strong(X)|~calm(X))))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~creative(X)&strong(X))=>(~strong(X)<~>~happy(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>~wise(X)))&
(((~happy(alice)<~>~brave(alice)))<=>((kind(alice)&calm(alice))))&
(![X]:((~wise(X)<~>~funny(X))<=>(~funny(X)&wise(X))))&
(((strong(mary)|humble(mary)))<=>((strong(lucy)&happy(lucy))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((~kind(X)<~>wise(X))=>(curious(X)&~wise(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>((generous(susan)<~>patient(susan))))&
(![X]:((~creative(X)&old(X))<=>~humble(X)))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:((~patient(X)|~quiet(X))<=>(~patient(X)|~wise(X))))&
(((brave(john)|~kind(john)))<=>(calm(john)))&
(![X]:((humble(X)&calm(X))=>(quiet(X)<~>~creative(X))))&
(((curious(fred)|patient(fred)))=>(?[X]:((tall(X)&generous(X)))))&
(~creative(fred))&
((wise(fred)|~old(fred)))&
((~quiet(alice)&patient(alice)))&
(~happy(alice))&
(?[X]:((generous(X)&~creative(X))))&
(~creative(susan))&
(?[X]:((~patient(X)<~>~creative(X)))) | tall(fred) | [] | null | 0 |
Everyone who is calm or not old is not generous.
Everyone who is either not old or curious is old or not strong and vice versa.
Everyone who is both happy and not old is not rich or not generous.
If mary is patient or humble then alice is not rich or not wise and vice versa.
If someone is both happy and not kind then fred is either happy or not kind.
If someone is not quiet then someone is either generous or tall.
If someone is either not quiet or strong then someone is not calm and vice versa.
If someone is both not rich and not patient then susan is kind and vice versa.
If someone is not calm or not old then someone is patient or not tall and vice versa.
If mary is curious or rich then someone is both calm and not humble.
Everyone who is both not calm and not brave is brave and vice versa.
Everyone who is old is rich or generous and vice versa.
If someone is funny then someone is either not tall or curious.
If lucy is not quiet then someone is either strong or tall and vice versa.
If susan is either strong or not wise then someone is calm or tall.
Everyone who is either not quiet or not generous is not funny or not quiet and vice versa.
Lucy is both humble and not patient.
Someone is not humble or not calm.
Someone is not curious.
Someone is wise or not funny. | Susan is tall. | contradiction | (![X]:((calm(X)|~old(X))=>~generous(X)))&
(![X]:((~old(X)<~>curious(X))<=>(old(X)|~strong(X))))&
(![X]:((happy(X)&~old(X))=>(~rich(X)|~generous(X))))&
(((patient(mary)|humble(mary)))<=>((~rich(alice)|~wise(alice))))&
((?[X]:((happy(X)&~kind(X))))=>((happy(fred)<~>~kind(fred))))&
((?[X]:(~quiet(X)))=>(?[X]:((generous(X)<~>tall(X)))))&
((?[X]:((~quiet(X)<~>strong(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((~rich(X)&~patient(X))))<=>(kind(susan)))&
((?[X]:((~calm(X)|~old(X))))<=>(?[X]:((patient(X)|~tall(X)))))&
(((curious(mary)|rich(mary)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:((~calm(X)&~brave(X))<=>brave(X)))&
(![X]:(old(X)<=>(rich(X)|generous(X))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((~quiet(lucy))<=>(?[X]:((strong(X)<~>tall(X)))))&
(((strong(susan)<~>~wise(susan)))=>(?[X]:((calm(X)|tall(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~funny(X)|~quiet(X))))&
((humble(lucy)&~patient(lucy)))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:(~curious(X)))&
(?[X]:((wise(X)|~funny(X)))) | tall(susan) | [
"p0",
"p5",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1302527042886094916207701
% SZS output start Proof for 1302527042886094916207701
1. ! [X0] : ((~old(X0) | calm(X0)) => ~generous(X0)) [input p0]
6. ? [X0] : ~quiet(X0) => ? [X0] : (generous(X0) <~> tall(X0)) [input p5]
7. ? [X0] : (~quiet(X0) <~> strong(X0)) <=> ? [X0] : ~calm(X0) [input p6]
11. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> brave(X0)) [input p10]
14. ~quiet(lucy) <=> ? [X0] : (strong(X0) <~> tall(X0)) [input p13]
16. ! [X0] : ((~quiet(X0) <~> ~generous(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p15]
21. tall(susan) [input hypothesis]
22. ? [X0] : ~quiet(X0) => ? [X1] : (generous(X1) <~> tall(X1)) [rectify 6]
23. ? [X0] : (~quiet(X0) <~> strong(X0)) <=> ? [X1] : ~calm(X1) [rectify 7]
26. ! [X0] : (~generous(X0) | (old(X0) & ~calm(X0))) [ennf transformation 1]
30. ? [X1] : (generous(X1) <~> tall(X1)) | ! [X0] : quiet(X0) [ennf transformation 22]
39. ? [X1] : ((~tall(X1) | ~generous(X1)) & (tall(X1) | generous(X1))) | ! [X0] : quiet(X0) [nnf transformation 30]
40. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | ! [X1] : quiet(X1) [rectify 39]
41. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) => ((~tall(sK0) | ~generous(sK0)) & (tall(sK0) | generous(sK0))) [choice axiom]
42. ((~tall(sK0) | ~generous(sK0)) & (tall(sK0) | generous(sK0))) | ! [X1] : quiet(X1) [skolemisation 40,41]
43. (? [X0] : ((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) [nnf transformation 23]
44. (? [X0] : ((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : ((~quiet(X3) | ~strong(X3)) & (strong(X3) | quiet(X3)))) [rectify 43]
45. ? [X0] : ((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) => ((~strong(sK1) | quiet(sK1)) & (strong(sK1) | ~quiet(sK1))) [choice axiom]
46. ? [X2] : ~calm(X2) => ~calm(sK2) [choice axiom]
47. (((~strong(sK1) | quiet(sK1)) & (strong(sK1) | ~quiet(sK1))) | ! [X1] : calm(X1)) & (~calm(sK2) | ! [X3] : ((~quiet(X3) | ~strong(X3)) & (strong(X3) | quiet(X3)))) [skolemisation 44,46,45]
59. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | calm(X0)))) [nnf transformation 11]
60. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | calm(X0))) [flattening 59]
67. (~quiet(lucy) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (? [X0] : ((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | quiet(lucy)) [nnf transformation 14]
68. (~quiet(lucy) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (? [X1] : ((~tall(X1) | ~strong(X1)) & (tall(X1) | strong(X1))) | quiet(lucy)) [rectify 67]
69. ? [X1] : ((~tall(X1) | ~strong(X1)) & (tall(X1) | strong(X1))) => ((~tall(sK8) | ~strong(sK8)) & (tall(sK8) | strong(sK8))) [choice axiom]
70. (~quiet(lucy) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (((~tall(sK8) | ~strong(sK8)) & (tall(sK8) | strong(sK8))) | quiet(lucy)) [skolemisation 68,69]
74. ! [X0] : ((((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0))))) [nnf transformation 16]
75. ! [X0] : ((((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0))))) [flattening 74]
82. ~generous(X0) | ~calm(X0) [cnf transformation 26]
97. tall(sK0) | generous(sK0) | quiet(X1) [cnf transformation 42]
100. ~calm(sK2) | ~quiet(X3) | ~strong(X3) [cnf transformation 47]
114. brave(X0) | brave(X0) | calm(X0) [cnf transformation 60]
116. ~brave(X0) | ~brave(X0) [cnf transformation 60]
125. ~quiet(lucy) | strong(X0) | ~tall(X0) [cnf transformation 70]
133. generous(X0) | quiet(X0) | quiet(X0) [cnf transformation 75]
139. tall(susan) [cnf transformation 21]
141. quiet(X0) | generous(X0) [duplicate literal removal 133]
142. brave(X0) | calm(X0) [duplicate literal removal 114]
143. ~brave(X0) [duplicate literal removal 116]
181. 8 <=> ! [X1] : quiet(X1) [avatar definition]
182. quiet(X1) <- (8) [avatar component clause 181]
184. 9 <=> generous(sK0) [avatar definition]
185. generous(sK0) <- (9) [avatar component clause 184]
186. ~generous(sK0) <- (~9) [avatar component clause 184]
188. 10 <=> tall(sK0) [avatar definition]
189. tall(sK0) <- (10) [avatar component clause 188]
192. 8 | 9 | 10 [avatar split clause 97,188,184,181]
194. 11 <=> ! [X1] : calm(X1) [avatar definition]
195. calm(X1) <- (11) [avatar component clause 194]
207. 14 <=> ! [X3] : (~quiet(X3) | ~strong(X3)) [avatar definition]
208. ~quiet(X3) | ~strong(X3) <- (14) [avatar component clause 207]
210. 15 <=> calm(sK2) [avatar definition]
212. ~calm(sK2) <- (~15) [avatar component clause 210]
213. 14 | ~15 [avatar split clause 100,210,207]
285. calm(X0) [subsumption resolution 142,143]
286. 11 [avatar split clause 285,194]
301. 35 <=> ! [X0] : (strong(X0) | ~tall(X0)) [avatar definition]
302. ~tall(X0) | strong(X0) <- (35) [avatar component clause 301]
304. 36 <=> quiet(lucy) [avatar definition]
306. ~quiet(lucy) <- (~36) [avatar component clause 304]
307. 35 | ~36 [avatar split clause 125,304,301]
327. 41 <=> strong(susan) [avatar definition]
328. ~strong(susan) <- (~41) [avatar component clause 327]
329. strong(susan) <- (41) [avatar component clause 327]
359. $false <- (11, ~15) [resolution 212,195]
360. ~11 | 15 [avatar contradiction clause 359]
364. strong(susan) <- (35) [resolution 302,139]
365. $false <- (35, ~41) [subsumption resolution 364,328]
366. ~35 | 41 [avatar contradiction clause 365]
372. ~calm(sK0) <- (9) [resolution 185,82]
373. $false <- (9, 11) [subsumption resolution 372,195]
374. ~9 | ~11 [avatar contradiction clause 373]
375. generous(lucy) <- (~36) [resolution 306,141]
377. ~strong(X0) | generous(X0) <- (14) [resolution 208,141]
379. ~calm(lucy) <- (~36) [resolution 375,82]
380. $false <- (11, ~36) [subsumption resolution 379,195]
381. ~11 | 36 [avatar contradiction clause 380]
386. strong(sK0) <- (10, 35) [resolution 302,189]
396. generous(sK0) <- (10, 14, 35) [resolution 377,386]
397. $false <- (~9, 10, 14, 35) [subsumption resolution 396,186]
398. 9 | ~10 | ~14 | ~35 [avatar contradiction clause 397]
399. ~strong(X0) <- (8, 14) [resolution 182,208]
400. $false <- (8, 14, 41) [resolution 399,329]
401. ~8 | ~14 | ~41 [avatar contradiction clause 400]
402. $false [avatar sat refutation 192,213,286,307,360,366,374,381,398,401]
% SZS output end Proof for 1302527042886094916207701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not rich then someone is curious.
If someone is either not kind or old then someone is either curious or not generous.
If lucy is happy or kind then someone is calm or not happy and vice versa.
If someone is not creative then lucy is either not humble or not calm.
If someone is creative then someone is either tall or not calm.
Everyone who is either happy or generous is not kind and vice versa.
If fred is both not quiet and not creative then paul is tall.
Everyone who is calm is both kind and not patient and vice versa.
Everyone who is either old or not happy is not strong.
Everyone who is wise or not funny is both not old and not quiet.
If someone is not creative or not old then someone is both creative and kind and vice versa.
Everyone who is both not kind and calm is patient and vice versa.
If susan is not curious then someone is kind and vice versa.
Everyone who is patient or not kind is either not old or not rich.
If paul is both not tall and not old then someone is both generous and wise and vice versa.
John is not humble or creative.
Someone is both not funny and not brave.
Someone is patient or tall.
Someone is both not old and not funny.
Someone is both wise and not calm.
Susan is both not creative and not humble.
Susan is tall.
Someone is both strong and not rich. | Lucy is patient. | contradiction | ((?[X]:((strong(X)&~rich(X))))=>(?[X]:(curious(X))))&
((?[X]:((~kind(X)<~>old(X))))=>(?[X]:((curious(X)<~>~generous(X)))))&
(((happy(lucy)|kind(lucy)))<=>(?[X]:((calm(X)|~happy(X)))))&
((?[X]:(~creative(X)))=>((~humble(lucy)<~>~calm(lucy))))&
((?[X]:(creative(X)))=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:((happy(X)<~>generous(X))<=>~kind(X)))&
(((~quiet(fred)&~creative(fred)))=>(tall(paul)))&
(![X]:(calm(X)<=>(kind(X)&~patient(X))))&
(![X]:((old(X)<~>~happy(X))=>~strong(X)))&
(![X]:((wise(X)|~funny(X))=>(~old(X)&~quiet(X))))&
((?[X]:((~creative(X)|~old(X))))<=>(?[X]:((creative(X)&kind(X)))))&
(![X]:((~kind(X)&calm(X))<=>patient(X)))&
((~curious(susan))<=>(?[X]:(kind(X))))&
(![X]:((patient(X)|~kind(X))=>(~old(X)<~>~rich(X))))&
(((~tall(paul)&~old(paul)))<=>(?[X]:((generous(X)&wise(X)))))&
((~humble(john)|creative(john)))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((wise(X)&~calm(X))))&
((~creative(susan)&~humble(susan)))&
(tall(susan))&
(?[X]:((strong(X)&~rich(X)))) | patient(lucy) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 717301310596058514023949
% SZS output start Proof for 717301310596058514023949
8. ! [X0] : (calm(X0) <=> (~patient(X0) & kind(X0))) [input p7]
12. ! [X0] : ((calm(X0) & ~kind(X0)) <=> patient(X0)) [input p11]
24. patient(lucy) [input hypothesis]
57. ! [X0] : ((calm(X0) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ~calm(X0))) [nnf transformation 8]
58. ! [X0] : ((calm(X0) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ~calm(X0))) [flattening 57]
65. ! [X0] : (((calm(X0) & ~kind(X0)) | ~patient(X0)) & (patient(X0) | (~calm(X0) | kind(X0)))) [nnf transformation 12]
66. ! [X0] : (((calm(X0) & ~kind(X0)) | ~patient(X0)) & (patient(X0) | ~calm(X0) | kind(X0))) [flattening 65]
106. ~patient(X0) | ~calm(X0) [cnf transformation 58]
121. calm(X0) | ~patient(X0) [cnf transformation 66]
144. patient(lucy) [cnf transformation 24]
263. ~patient(X0) [subsumption resolution 121,106]
306. $false [subsumption resolution 144,263]
% SZS output end Proof for 717301310596058514023949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not wise is kind or not tall and vice versa.
Everyone who is either generous or tall is either curious or wise.
If someone is both not generous and kind then someone is creative or not calm and vice versa.
Everyone who is either not old or patient is not rich and vice versa.
Everyone who is either not strong or not calm is either not wise or happy.
If mary is both not patient and not quiet then someone is both happy and rich.
If someone is both tall and humble then someone is not rich or curious.
Everyone who is both wise and not brave is either not happy or wise and vice versa.
If paul is not funny or not calm then alice is either not patient or not brave and vice versa.
Everyone who is both not quiet and rich is both not brave and not funny.
Everyone who is either not wise or not strong is not happy or not wise and vice versa.
Everyone who is not brave is either not strong or not happy and vice versa.
If someone is not happy or not curious then someone is not tall or not calm and vice versa.
If alice is either happy or wise then susan is either happy or funny.
If someone is either not kind or generous then lucy is not rich or brave.
Everyone who is not kind or not humble is both not happy and strong and vice versa.
Lucy is not old or wise.
Mary is quiet or happy.
John is either creative or happy.
Someone is not patient or not happy.
Fred is not generous. | Fred is strong. | entailment | (![X]:((rich(X)&~wise(X))<=>(kind(X)|~tall(X))))&
(![X]:((generous(X)<~>tall(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~generous(X)&kind(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~old(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~strong(X)<~>~calm(X))=>(~wise(X)<~>happy(X))))&
(((~patient(mary)&~quiet(mary)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((tall(X)&humble(X))))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((wise(X)&~brave(X))<=>(~happy(X)<~>wise(X))))&
(((~funny(paul)|~calm(paul)))<=>((~patient(alice)<~>~brave(alice))))&
(![X]:((~quiet(X)&rich(X))=>(~brave(X)&~funny(X))))&
(![X]:((~wise(X)<~>~strong(X))<=>(~happy(X)|~wise(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~happy(X))))&
((?[X]:((~happy(X)|~curious(X))))<=>(?[X]:((~tall(X)|~calm(X)))))&
(((happy(alice)<~>wise(alice)))=>((happy(susan)<~>funny(susan))))&
((?[X]:((~kind(X)<~>generous(X))))=>((~rich(lucy)|brave(lucy))))&
(![X]:((~kind(X)|~humble(X))<=>(~happy(X)&strong(X))))&
((~old(lucy)|wise(lucy)))&
((quiet(mary)|happy(mary)))&
((creative(john)<~>happy(john)))&
(?[X]:((~patient(X)|~happy(X))))&
(~generous(fred)) | strong(fred) | [
"p0",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7268138824069949229699095
% SZS output start Proof for 7268138824069949229699095
1. ! [X0] : ((~wise(X0) & rich(X0)) <=> (~tall(X0) | kind(X0))) [input p0]
11. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~wise(X0) | ~happy(X0))) [input p10]
16. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (strong(X0) & ~happy(X0))) [input p15]
22. ~strong(fred) [input hypothesis]
35. ! [X0] : (((~wise(X0) & rich(X0)) | (tall(X0) & ~kind(X0))) & ((~tall(X0) | kind(X0)) | (wise(X0) | ~rich(X0)))) [nnf transformation 1]
36. ! [X0] : (((~wise(X0) & rich(X0)) | (tall(X0) & ~kind(X0))) & (~tall(X0) | kind(X0) | wise(X0) | ~rich(X0))) [flattening 35]
52. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (wise(X0) & happy(X0))) & ((~wise(X0) | ~happy(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 11]
53. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (wise(X0) & happy(X0))) & (~wise(X0) | ~happy(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [flattening 52]
62. ! [X0] : (((~humble(X0) | ~kind(X0)) | (~strong(X0) | happy(X0))) & ((strong(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 16]
63. ! [X0] : ((~humble(X0) | ~kind(X0) | ~strong(X0) | happy(X0)) & ((strong(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [flattening 62]
70. ~kind(X0) | ~wise(X0) [cnf transformation 36]
107. strong(X0) | wise(X0) | wise(X0) [cnf transformation 53]
124. strong(X0) | kind(X0) [cnf transformation 63]
132. ~strong(fred) [cnf transformation 22]
134. strong(X0) | wise(X0) [duplicate literal removal 107]
311. kind(fred) [resolution 124,132]
312. ~wise(fred) [resolution 311,70]
314. wise(fred) [resolution 134,132]
315. $false [subsumption resolution 314,312]
% SZS output end Proof for 7268138824069949229699095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If john is creative or not brave then someone is both strong and curious.
If someone is both patient and not wise then fred is not humble or not funny and vice versa.
If susan is both not rich and old then someone is not funny and vice versa.
Everyone who is both strong and funny is both creative and not humble.
If susan is both not patient and not calm then lucy is either not humble or not creative.
If paul is both not wise and not generous then someone is either not rich or not calm.
Everyone who is calm or funny is both not brave and rich and vice versa.
Everyone who is either not generous or not strong is both patient and not creative.
Everyone who is rich is not patient or not rich and vice versa.
If someone is not humble then someone is either not calm or humble and vice versa.
If someone is not tall or not kind then someone is either happy or not happy.
Everyone who is not strong or strong is both quiet and wise.
If someone is wise then alice is happy and vice versa.
If someone is creative then john is either old or not tall and vice versa.
Someone is not brave.
Someone is strong or not old.
Someone is not old.
Mary is creative.
Someone is either rich or old.
Mary is either happy or humble.
Someone is either not kind or not patient. | Fred is not strong. | entailment | (((creative(john)|~brave(john)))=>(?[X]:((strong(X)&curious(X)))))&
((?[X]:((patient(X)&~wise(X))))<=>((~humble(fred)|~funny(fred))))&
(((~rich(susan)&old(susan)))<=>(?[X]:(~funny(X))))&
(![X]:((strong(X)&funny(X))=>(creative(X)&~humble(X))))&
(((~patient(susan)&~calm(susan)))=>((~humble(lucy)<~>~creative(lucy))))&
(((~wise(paul)&~generous(paul)))=>(?[X]:((~rich(X)<~>~calm(X)))))&
(![X]:((calm(X)|funny(X))<=>(~brave(X)&rich(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(patient(X)&~creative(X))))&
(![X]:(rich(X)<=>(~patient(X)|~rich(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:((~strong(X)|strong(X))=>(quiet(X)&wise(X))))&
((?[X]:(wise(X)))<=>(happy(alice)))&
((?[X]:(creative(X)))<=>((old(john)<~>~tall(john))))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)|~old(X))))&
(?[X]:(~old(X)))&
(creative(mary))&
(?[X]:((rich(X)<~>old(X))))&
((happy(mary)<~>humble(mary)))&
(?[X]:((~kind(X)<~>~patient(X)))) | ~strong(fred) | [
"p1",
"p2",
"p3",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5511613620452556255242462
% SZS output start Proof for 5511613620452556255242462
2. ? [X0] : (~wise(X0) & patient(X0)) <=> (~funny(fred) | ~humble(fred)) [input p1]
3. (old(susan) & ~rich(susan)) <=> ? [X0] : ~funny(X0) [input p2]
4. ! [X0] : ((funny(X0) & strong(X0)) => (~humble(X0) & creative(X0))) [input p3]
9. ! [X0] : (rich(X0) <=> (~rich(X0) | ~patient(X0))) [input p8]
12. ! [X0] : ((strong(X0) | ~strong(X0)) => (wise(X0) & quiet(X0))) [input p11]
22. strong(fred) [input hypothesis]
25. ! [X0] : ((strong(X0) | ~strong(X0)) => wise(X0)) [pure predicate removal 12]
28. ! [X0] : ((~humble(X0) & creative(X0)) | (~funny(X0) | ~strong(X0))) [ennf transformation 4]
29. ! [X0] : ((~humble(X0) & creative(X0)) | ~funny(X0) | ~strong(X0)) [flattening 28]
36. ! [X0] : (wise(X0) | (~strong(X0) & strong(X0))) [ennf transformation 25]
39. (? [X0] : (~wise(X0) & patient(X0)) | (funny(fred) & humble(fred))) & ((~funny(fred) | ~humble(fred)) | ! [X0] : (wise(X0) | ~patient(X0))) [nnf transformation 2]
40. (? [X0] : (~wise(X0) & patient(X0)) | (funny(fred) & humble(fred))) & (~funny(fred) | ~humble(fred) | ! [X0] : (wise(X0) | ~patient(X0))) [flattening 39]
41. (? [X0] : (~wise(X0) & patient(X0)) | (funny(fred) & humble(fred))) & (~funny(fred) | ~humble(fred) | ! [X1] : (wise(X1) | ~patient(X1))) [rectify 40]
42. ? [X0] : (~wise(X0) & patient(X0)) => (~wise(sK1) & patient(sK1)) [choice axiom]
43. ((~wise(sK1) & patient(sK1)) | (funny(fred) & humble(fred))) & (~funny(fred) | ~humble(fred) | ! [X1] : (wise(X1) | ~patient(X1))) [skolemisation 41,42]
44. ((old(susan) & ~rich(susan)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | (~old(susan) | rich(susan))) [nnf transformation 3]
45. ((old(susan) & ~rich(susan)) | ! [X0] : funny(X0)) & (? [X0] : ~funny(X0) | ~old(susan) | rich(susan)) [flattening 44]
46. ((old(susan) & ~rich(susan)) | ! [X0] : funny(X0)) & (? [X1] : ~funny(X1) | ~old(susan) | rich(susan)) [rectify 45]
47. ? [X1] : ~funny(X1) => ~funny(sK2) [choice axiom]
48. ((old(susan) & ~rich(susan)) | ! [X0] : funny(X0)) & (~funny(sK2) | ~old(susan) | rich(susan)) [skolemisation 46,47]
56. ! [X0] : ((rich(X0) | (rich(X0) & patient(X0))) & ((~rich(X0) | ~patient(X0)) | ~rich(X0))) [nnf transformation 9]
57. ! [X0] : ((rich(X0) | (rich(X0) & patient(X0))) & (~rich(X0) | ~patient(X0) | ~rich(X0))) [flattening 56]
93. ~wise(sK1) | humble(fred) [cnf transformation 43]
96. ~rich(susan) | funny(X0) [cnf transformation 48]
99. ~funny(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 29]
115. rich(X0) | rich(X0) [cnf transformation 57]
124. wise(X0) | strong(X0) [cnf transformation 36]
125. ~strong(X0) | wise(X0) [cnf transformation 36]
142. strong(fred) [cnf transformation 22]
144. rich(X0) [duplicate literal removal 115]
164. 5 <=> wise(sK1) [avatar definition]
166. ~wise(sK1) <- (~5) [avatar component clause 164]
169. 6 <=> humble(fred) [avatar definition]
171. humble(fred) <- (6) [avatar component clause 169]
172. 6 | ~5 [avatar split clause 93,164,169]
184. 9 <=> ! [X0] : funny(X0) [avatar definition]
185. funny(X0) <- (9) [avatar component clause 184]
192. 11 <=> rich(susan) [avatar definition]
194. ~rich(susan) <- (~11) [avatar component clause 192]
195. 9 | ~11 [avatar split clause 96,192,184]
263. wise(X0) [subsumption resolution 124,125]
307. $false <- (~5) [subsumption resolution 166,263]
308. 5 [avatar contradiction clause 307]
318. ~humble(X0) | ~strong(X0) <- (9) [resolution 99,185]
329. ~strong(fred) <- (6, 9) [resolution 318,171]
330. $false <- (6, 9) [subsumption resolution 329,142]
331. ~6 | ~9 [avatar contradiction clause 330]
332. $false <- (~11) [subsumption resolution 194,144]
333. 11 [avatar contradiction clause 332]
334. $false [avatar sat refutation 172,195,308,331,333]
% SZS output end Proof for 5511613620452556255242462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or not curious then someone is not brave. If someone is either not generous or not funny then someone is either not patient or patient and vice versa. Everyone who is not funny is not tall and vice versa. Everyone who is either curious or not creative is either not strong or calm. If fred is either happy or old then alice is not curious or strong and vice versa. Everyone who is creative is not tall. If someone is wise or not rich then someone is either not funny or not humble and vice versa. If alice is old or tall then lucy is tall or not wise and vice versa. Everyone who is old or not old is rich or not wise. If someone is quiet then fred is either not rich or calm and vice versa. Everyone who is both quiet and kind is curious or not curious and vice versa. Everyone who is not strong is either not funny or kind. If someone is both not kind and not funny then lucy is not rich or old. Everyone who is either wise or humble is kind and vice versa. If susan is both happy and not creative then someone is both humble and not wise and vice versa. Everyone who is creative or kind is either funny or wise. Paul is curious or happy. Someone is not old or not curious. Someone is either not kind or not patient. Mary is either old or not generous. Someone is happy. Mary is either not calm or not wise. Someone is either rich or happy. John is old. | Susan is tall. | entailment | ((?[X]:((old(X)<~>~curious(X))))=>(?[X]:(~brave(X))))&
((?[X]:((~generous(X)<~>~funny(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:(~funny(X)<=>~tall(X)))&
(![X]:((curious(X)<~>~creative(X))=>(~strong(X)<~>calm(X))))&
(((happy(fred)<~>old(fred)))<=>((~curious(alice)|strong(alice))))&
(![X]:(creative(X)=>~tall(X)))&
((?[X]:((wise(X)|~rich(X))))<=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((old(alice)|tall(alice)))<=>((tall(lucy)|~wise(lucy))))&
(![X]:((old(X)|~old(X))=>(rich(X)|~wise(X))))&
((?[X]:(quiet(X)))<=>((~rich(fred)<~>calm(fred))))&
(![X]:((quiet(X)&kind(X))<=>(curious(X)|~curious(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>kind(X))))&
((?[X]:((~kind(X)&~funny(X))))=>((~rich(lucy)|old(lucy))))&
(![X]:((wise(X)<~>humble(X))<=>kind(X)))&
(((happy(susan)&~creative(susan)))<=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:((creative(X)|kind(X))=>(funny(X)<~>wise(X))))&
((curious(paul)|happy(paul)))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((~kind(X)<~>~patient(X))))&
((old(mary)<~>~generous(mary)))&
(?[X]:(happy(X)))&
((~calm(mary)<~>~wise(mary)))&
(?[X]:((rich(X)<~>happy(X))))&
(old(john)) | tall(susan) | [
"p2",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 490318809630983644351238
% SZS output start Proof for 490318809630983644351238
3. ! [X0] : (~funny(X0) <=> ~tall(X0)) [input p2]
7. ? [X0] : (~rich(X0) | wise(X0)) <=> ? [X0] : (~funny(X0) <~> ~humble(X0)) [input p6]
11. ! [X0] : ((kind(X0) & quiet(X0)) <=> (~curious(X0) | curious(X0))) [input p10]
14. ! [X0] : ((wise(X0) <~> humble(X0)) <=> kind(X0)) [input p13]
16. ! [X0] : ((kind(X0) | creative(X0)) => (funny(X0) <~> wise(X0))) [input p15]
25. ~tall(susan) [input hypothesis]
28. ? [X0] : (~rich(X0) | wise(X0)) <=> ? [X1] : (~funny(X1) <~> ~humble(X1)) [rectify 7]
37. ! [X0] : ((funny(X0) <~> wise(X0)) | (~kind(X0) & ~creative(X0))) [ennf transformation 16]
43. ! [X0] : ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0))) [nnf transformation 3]
47. (? [X0] : (~rich(X0) | wise(X0)) | ! [X1] : ((~funny(X1) | humble(X1)) & (~humble(X1) | funny(X1)))) & (? [X1] : ((humble(X1) | funny(X1)) & (~humble(X1) | ~funny(X1))) | ! [X0] : (rich(X0) & ~wise(X0))) [nnf transformation 28]
48. (? [X0] : (~rich(X0) | wise(X0)) | ! [X1] : ((~funny(X1) | humble(X1)) & (~humble(X1) | funny(X1)))) & (? [X2] : ((humble(X2) | funny(X2)) & (~humble(X2) | ~funny(X2))) | ! [X3] : (rich(X3) & ~wise(X3))) [rectify 47]
49. ? [X0] : (~rich(X0) | wise(X0)) => (~rich(sK2) | wise(sK2)) [choice axiom]
50. ? [X2] : ((humble(X2) | funny(X2)) & (~humble(X2) | ~funny(X2))) => ((humble(sK3) | funny(sK3)) & (~humble(sK3) | ~funny(sK3))) [choice axiom]
51. ((~rich(sK2) | wise(sK2)) | ! [X1] : ((~funny(X1) | humble(X1)) & (~humble(X1) | funny(X1)))) & (((humble(sK3) | funny(sK3)) & (~humble(sK3) | ~funny(sK3))) | ! [X3] : (rich(X3) & ~wise(X3))) [skolemisation 48,50,49]
58. ! [X0] : (((kind(X0) & quiet(X0)) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | (~kind(X0) | ~quiet(X0)))) [nnf transformation 11]
59. ! [X0] : (((kind(X0) & quiet(X0)) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ~kind(X0) | ~quiet(X0))) [flattening 58]
61. ! [X0] : ((((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | ~kind(X0)) & (kind(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0))))) [nnf transformation 14]
67. ! [X0] : (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | (~kind(X0) & ~creative(X0))) [nnf transformation 37]
89. ~funny(X0) | tall(X0) [cnf transformation 43]
101. ~humble(sK3) | ~funny(sK3) | ~wise(X3) [cnf transformation 51]
103. humble(sK3) | funny(sK3) | ~wise(X3) [cnf transformation 51]
120. kind(X0) | ~curious(X0) [cnf transformation 59]
121. kind(X0) | curious(X0) [cnf transformation 59]
127. humble(X0) | wise(X0) | ~kind(X0) [cnf transformation 61]
128. ~humble(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 61]
134. wise(X0) | funny(X0) | ~kind(X0) [cnf transformation 67]
136. ~wise(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 67]
149. ~tall(susan) [cnf transformation 25]
214. 14 <=> funny(sK3) [avatar definition]
216. funny(sK3) <- (14) [avatar component clause 214]
218. 15 <=> humble(sK3) [avatar definition]
219. ~humble(sK3) <- (~15) [avatar component clause 218]
220. humble(sK3) <- (15) [avatar component clause 218]
223. 16 <=> ! [X3] : ~wise(X3) [avatar definition]
224. ~wise(X3) <- (16) [avatar component clause 223]
225. 16 | 14 | 15 [avatar split clause 103,218,214,223]
227. 16 | ~14 | ~15 [avatar split clause 101,218,214,223]
268. kind(X0) [subsumption resolution 120,121]
271. ~humble(X0) | ~wise(X0) [subsumption resolution 128,268]
272. humble(X0) | wise(X0) [subsumption resolution 127,268]
298. ~wise(X0) | ~funny(X0) [subsumption resolution 136,268]
299. wise(X0) | funny(X0) [subsumption resolution 134,268]
362. wise(sK3) <- (~15) [resolution 219,272]
368. ~funny(sK3) <- (~15) [resolution 362,298]
370. $false <- (14, ~15) [subsumption resolution 368,216]
371. ~14 | 15 [avatar contradiction clause 370]
372. ~wise(sK3) <- (15) [resolution 220,271]
379. funny(sK3) <- (15) [resolution 372,299]
382. 14 | ~15 [avatar split clause 379,218,214]
395. funny(X0) <- (16) [resolution 224,299]
406. tall(X1) <- (16) [resolution 395,89]
456. $false <- (16) [resolution 406,149]
457. ~16 [avatar contradiction clause 456]
460. $false [avatar sat refutation 225,227,371,382,457]
% SZS output end Proof for 490318809630983644351238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not wise is not humble or not brave and vice versa.
If mary is both not patient and not funny then paul is old.
If someone is funny then john is not brave or not generous and vice versa.
If someone is both not curious and patient then paul is either not generous or not patient.
If someone is either not strong or humble then someone is both not creative and kind.
If someone is not happy then someone is not kind and vice versa.
Everyone who is not wise or not calm is rich or not humble and vice versa.
Everyone who is both rich and not old is either not strong or quiet.
Everyone who is both patient and not quiet is not old and vice versa.
If someone is patient or humble then lucy is either not rich or humble.
If someone is not brave or generous then mary is both not kind and happy.
Everyone who is both kind and not kind is not calm or not generous and vice versa.
If someone is brave or old then someone is calm or not humble and vice versa.
Everyone who is either not quiet or not kind is quiet and vice versa.
If mary is both not humble and curious then someone is creative or not generous and vice versa.
Everyone who is humble is brave or not humble.
Someone is not kind.
John is either not kind or brave.
Alice is creative.
Alice is either calm or not tall.
Someone is tall or calm.
Someone is creative. | Alice is strong. | neutral | (![X]:((~tall(X)<~>~wise(X))<=>(~humble(X)|~brave(X))))&
(((~patient(mary)&~funny(mary)))=>(old(paul)))&
((?[X]:(funny(X)))<=>((~brave(john)|~generous(john))))&
((?[X]:((~curious(X)&patient(X))))=>((~generous(paul)<~>~patient(paul))))&
((?[X]:((~strong(X)<~>humble(X))))=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)|~calm(X))<=>(rich(X)|~humble(X))))&
(![X]:((rich(X)&~old(X))=>(~strong(X)<~>quiet(X))))&
(![X]:((patient(X)&~quiet(X))<=>~old(X)))&
((?[X]:((patient(X)|humble(X))))=>((~rich(lucy)<~>humble(lucy))))&
((?[X]:((~brave(X)|generous(X))))=>((~kind(mary)&happy(mary))))&
(![X]:((kind(X)&~kind(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((brave(X)|old(X))))<=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>quiet(X)))&
(((~humble(mary)&curious(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:(humble(X)=>(brave(X)|~humble(X))))&
(?[X]:(~kind(X)))&
((~kind(john)<~>brave(john)))&
(creative(alice))&
((calm(alice)<~>~tall(alice)))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:(creative(X))) | strong(alice) | [] | null | 0 |
Everyone who is either calm or not curious is creative or wise and vice versa. If someone is either not patient or not funny then someone is not tall or quiet and vice versa. Everyone who is both kind and not rich is not rich. Everyone who is both not creative and not curious is not patient and vice versa. Everyone who is generous is either curious or not calm and vice versa. Everyone who is either humble or not patient is humble and vice versa. If someone is both not generous and old then alice is both tall and not strong and vice versa. If fred is old then alice is not strong and vice versa. If someone is both not happy and brave then someone is both not curious and not calm. If someone is patient or happy then someone is either not strong or not humble and vice versa. If someone is not funny or not tall then someone is both not curious and rich. Everyone who is both not kind and quiet is either not humble or not wise. If fred is rich then susan is both not funny and brave. Everyone who is quiet or curious is both not strong and wise. Everyone who is both tall and kind is both humble and not calm and vice versa. If mary is both not quiet and not strong then someone is either not wise or happy and vice versa. Someone is both not calm and strong. Someone is both patient and creative. Paul is tall or kind. Someone is either old or not brave. Mary is not wise or not generous. Alice is strong. Someone is not funny or strong. | Susan is brave. | neutral | (![X]:((calm(X)<~>~curious(X))<=>(creative(X)|wise(X))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((~tall(X)|quiet(X)))))&
(![X]:((kind(X)&~rich(X))=>~rich(X)))&
(![X]:((~creative(X)&~curious(X))<=>~patient(X)))&
(![X]:(generous(X)<=>(curious(X)<~>~calm(X))))&
(![X]:((humble(X)<~>~patient(X))<=>humble(X)))&
((?[X]:((~generous(X)&old(X))))<=>((tall(alice)&~strong(alice))))&
((old(fred))<=>(~strong(alice)))&
((?[X]:((~happy(X)&brave(X))))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((patient(X)|happy(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
((?[X]:((~funny(X)|~tall(X))))=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((~kind(X)&quiet(X))=>(~humble(X)<~>~wise(X))))&
((rich(fred))=>((~funny(susan)&brave(susan))))&
(![X]:((quiet(X)|curious(X))=>(~strong(X)&wise(X))))&
(![X]:((tall(X)&kind(X))<=>(humble(X)&~calm(X))))&
(((~quiet(mary)&~strong(mary)))<=>(?[X]:((~wise(X)<~>happy(X)))))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:((patient(X)&creative(X))))&
((tall(paul)|kind(paul)))&
(?[X]:((old(X)<~>~brave(X))))&
((~wise(mary)|~generous(mary)))&
(strong(alice))&
(?[X]:((~funny(X)|strong(X)))) | brave(susan) | [] | null | 0 |
If mary is kind then lucy is both generous and quiet and vice versa.
Everyone who is either not wise or old is not calm or not curious and vice versa.
If someone is funny or not wise then lucy is either quiet or not old and vice versa.
Everyone who is not creative is not curious or generous and vice versa.
If alice is not kind then someone is generous or kind.
Everyone who is both kind and calm is curious and vice versa.
If someone is both patient and strong then someone is both not humble and patient.
Everyone who is generous is both not calm and quiet.
Everyone who is not curious is not brave.
Everyone who is wise or strong is either humble or creative.
Everyone who is not strong is both creative and not quiet and vice versa.
Everyone who is not rich or rich is either not rich or not kind and vice versa.
Everyone who is either not funny or not patient is either not wise or not rich and vice versa.
Everyone who is either happy or quiet is both happy and tall and vice versa.
If someone is either not kind or not old then lucy is not funny and vice versa.
Everyone who is both not tall and not funny is either curious or not patient and vice versa.
Alice is not tall or quiet.
Someone is both happy and quiet.
Someone is calm or creative.
Someone is either not patient or strong.
Alice is patient or not happy.
Someone is not strong or not rich.
John is strong or not funny.
Someone is patient or kind. | Alice is not strong. | neutral | ((kind(mary))<=>((generous(lucy)&quiet(lucy))))&
(![X]:((~wise(X)<~>old(X))<=>(~calm(X)|~curious(X))))&
((?[X]:((funny(X)|~wise(X))))<=>((quiet(lucy)<~>~old(lucy))))&
(![X]:(~creative(X)<=>(~curious(X)|generous(X))))&
((~kind(alice))=>(?[X]:((generous(X)|kind(X)))))&
(![X]:((kind(X)&calm(X))<=>curious(X)))&
((?[X]:((patient(X)&strong(X))))=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(generous(X)=>(~calm(X)&quiet(X))))&
(![X]:(~curious(X)=>~brave(X)))&
(![X]:((wise(X)|strong(X))=>(humble(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~rich(X)|rich(X))<=>(~rich(X)<~>~kind(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((happy(X)<~>quiet(X))<=>(happy(X)&tall(X))))&
((?[X]:((~kind(X)<~>~old(X))))<=>(~funny(lucy)))&
(![X]:((~tall(X)&~funny(X))<=>(curious(X)<~>~patient(X))))&
((~tall(alice)|quiet(alice)))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((~patient(X)<~>strong(X))))&
((patient(alice)|~happy(alice)))&
(?[X]:((~strong(X)|~rich(X))))&
((strong(john)|~funny(john)))&
(?[X]:((patient(X)|kind(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is both curious and not kind is not funny and vice versa. If someone is not patient then someone is rich or happy. Everyone who is not happy or not rich is kind or calm and vice versa. Everyone who is not generous or not humble is not calm or not rich and vice versa. If someone is not kind then someone is not generous and vice versa. If someone is either not kind or not rich then mary is both not brave and not humble. Everyone who is both humble and not curious is not generous or not calm and vice versa. Everyone who is not curious is old or not kind and vice versa. Everyone who is not humble is strong. If john is either not creative or not kind then fred is both not quiet and old. Everyone who is not happy or patient is generous. Everyone who is both rich and patient is not kind or not wise and vice versa. Everyone who is not strong or not brave is both funny and wise. If someone is brave then susan is not wise and vice versa. Everyone who is not curious is both not brave and not funny and vice versa. Someone is not kind or not tall. John is either happy or not calm. Someone is not old or humble. Mary is happy or not kind. Someone is either funny or not humble. Someone is not old or not calm. Paul is not old or not calm. | John is not rich. | entailment | (![X]:((curious(X)&~kind(X))<=>~funny(X)))&
((?[X]:(~patient(X)))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~happy(X)|~rich(X))<=>(kind(X)|calm(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~calm(X)|~rich(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(~generous(X))))&
((?[X]:((~kind(X)<~>~rich(X))))=>((~brave(mary)&~humble(mary))))&
(![X]:((humble(X)&~curious(X))<=>(~generous(X)|~calm(X))))&
(![X]:(~curious(X)<=>(old(X)|~kind(X))))&
(![X]:(~humble(X)=>strong(X)))&
(((~creative(john)<~>~kind(john)))=>((~quiet(fred)&old(fred))))&
(![X]:((~happy(X)|patient(X))=>generous(X)))&
(![X]:((rich(X)&patient(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~strong(X)|~brave(X))=>(funny(X)&wise(X))))&
((?[X]:(brave(X)))<=>(~wise(susan)))&
(![X]:(~curious(X)<=>(~brave(X)&~funny(X))))&
(?[X]:((~kind(X)|~tall(X))))&
((happy(john)<~>~calm(john)))&
(?[X]:((~old(X)|humble(X))))&
((happy(mary)|~kind(mary)))&
(?[X]:((funny(X)<~>~humble(X))))&
(?[X]:((~old(X)|~calm(X))))&
((~old(paul)|~calm(paul))) | ~rich(john) | [
"p0",
"p2",
"p4",
"p6",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5669085894072752470911839
% SZS output start Proof for 5669085894072752470911839
1. ! [X0] : ((~kind(X0) & curious(X0)) <=> ~funny(X0)) [input p0]
3. ! [X0] : ((~rich(X0) | ~happy(X0)) <=> (calm(X0) | kind(X0))) [input p2]
5. ? [X0] : ~kind(X0) <=> ? [X0] : ~generous(X0) [input p4]
7. ! [X0] : ((~curious(X0) & humble(X0)) <=> (~calm(X0) | ~generous(X0))) [input p6]
15. ! [X0] : (~curious(X0) <=> (~funny(X0) & ~brave(X0))) [input p14]
17. happy(john) <~> ~calm(john) [input p16]
23. rich(john) [input hypothesis]
25. ? [X0] : ~kind(X0) <=> ? [X1] : ~generous(X1) [rectify 5]
35. ! [X0] : (((~kind(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | (kind(X0) | ~curious(X0)))) [nnf transformation 1]
36. ! [X0] : (((~kind(X0) & curious(X0)) | funny(X0)) & (~funny(X0) | kind(X0) | ~curious(X0))) [flattening 35]
40. ! [X0] : (((~rich(X0) | ~happy(X0)) | (~calm(X0) & ~kind(X0))) & ((calm(X0) | kind(X0)) | (rich(X0) & happy(X0)))) [nnf transformation 3]
41. ! [X0] : ((~rich(X0) | ~happy(X0) | (~calm(X0) & ~kind(X0))) & (calm(X0) | kind(X0) | (rich(X0) & happy(X0)))) [flattening 40]
44. (? [X0] : ~kind(X0) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : kind(X0)) [nnf transformation 25]
45. (? [X0] : ~kind(X0) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : kind(X3)) [rectify 44]
46. ? [X0] : ~kind(X0) => ~kind(sK1) [choice axiom]
47. ? [X2] : ~generous(X2) => ~generous(sK2) [choice axiom]
48. (~kind(sK1) | ! [X1] : generous(X1)) & (~generous(sK2) | ! [X3] : kind(X3)) [skolemisation 45,47,46]
50. ! [X0] : (((~curious(X0) & humble(X0)) | (calm(X0) & generous(X0))) & ((~calm(X0) | ~generous(X0)) | (curious(X0) | ~humble(X0)))) [nnf transformation 7]
51. ! [X0] : (((~curious(X0) & humble(X0)) | (calm(X0) & generous(X0))) & (~calm(X0) | ~generous(X0) | curious(X0) | ~humble(X0))) [flattening 50]
61. ! [X0] : ((~curious(X0) | (funny(X0) | brave(X0))) & ((~funny(X0) & ~brave(X0)) | curious(X0))) [nnf transformation 15]
62. ! [X0] : ((~curious(X0) | funny(X0) | brave(X0)) & ((~funny(X0) & ~brave(X0)) | curious(X0))) [flattening 61]
63. (calm(john) | ~happy(john)) & (~calm(john) | happy(john)) [nnf transformation 17]
72. funny(X0) | curious(X0) [cnf transformation 36]
77. ~happy(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 41]
83. ~generous(sK2) | kind(X3) [cnf transformation 48]
92. ~curious(X0) | generous(X0) [cnf transformation 51]
93. ~curious(X0) | calm(X0) [cnf transformation 51]
111. ~funny(X0) | curious(X0) [cnf transformation 62]
113. ~calm(john) | happy(john) [cnf transformation 63]
121. rich(john) [cnf transformation 23]
135. 4 <=> ! [X1] : generous(X1) [avatar definition]
136. generous(X1) <- (4) [avatar component clause 135]
143. 6 <=> ! [X3] : kind(X3) [avatar definition]
144. kind(X3) <- (6) [avatar component clause 143]
146. 7 <=> generous(sK2) [avatar definition]
148. ~generous(sK2) <- (~7) [avatar component clause 146]
149. 6 | ~7 [avatar split clause 83,146,143]
196. curious(X0) [subsumption resolution 111,72]
198. 18 <=> happy(john) [avatar definition]
199. happy(john) <- (18) [avatar component clause 198]
202. 19 <=> calm(john) [avatar definition]
203. ~calm(john) <- (~19) [avatar component clause 202]
206. 18 | ~19 [avatar split clause 113,202,198]
258. generous(X0) [resolution 92,196]
259. 4 [avatar split clause 258,135]
260. $false <- (4, ~7) [resolution 136,148]
261. ~4 | 7 [avatar contradiction clause 260]
269. calm(X0) [resolution 93,196]
272. $false <- (~19) [resolution 269,203]
275. 19 [avatar contradiction clause 272]
286. ~rich(john) | ~kind(john) <- (18) [resolution 77,199]
288. ~kind(john) <- (18) [subsumption resolution 286,121]
289. $false <- (6, 18) [subsumption resolution 288,144]
290. ~6 | ~18 [avatar contradiction clause 289]
291. $false [avatar sat refutation 149,206,259,261,275,290]
% SZS output end Proof for 5669085894072752470911839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is calm or not old.
If fred is not creative or not old then someone is strong and vice versa.
Everyone who is creative or not brave is not kind.
Everyone who is both rich and calm is either brave or rich.
If someone is both wise and rich then susan is both not creative and quiet.
Everyone who is not rich or strong is happy and vice versa.
Everyone who is either rich or not brave is either tall or humble and vice versa.
If someone is both not wise and not humble then someone is not patient or not rich and vice versa.
Everyone who is both generous and not tall is either kind or brave and vice versa.
If fred is either not generous or not happy then mary is not wise and vice versa.
If paul is both not creative and patient then someone is brave or not curious and vice versa.
If paul is strong or brave then someone is either not wise or not generous.
Everyone who is not brave or generous is either not old or not funny and vice versa.
If mary is both tall and old then paul is not kind or creative.
Everyone who is not tall or calm is both humble and kind and vice versa.
If someone is curious then someone is either not funny or not strong and vice versa.
Alice is both not curious and quiet.
Someone is either creative or not calm.
Someone is both wise and not old.
Paul is either kind or not kind.
John is both not strong and not rich.
Someone is either generous or not rich.
Someone is not patient or not rich.
Someone is humble. | John is not tall. | contradiction | (![X]:(~humble(X)=>(calm(X)|~old(X))))&
(((~creative(fred)|~old(fred)))<=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~brave(X))=>~kind(X)))&
(![X]:((rich(X)&calm(X))=>(brave(X)<~>rich(X))))&
((?[X]:((wise(X)&rich(X))))=>((~creative(susan)&quiet(susan))))&
(![X]:((~rich(X)|strong(X))<=>happy(X)))&
(![X]:((rich(X)<~>~brave(X))<=>(tall(X)<~>humble(X))))&
((?[X]:((~wise(X)&~humble(X))))<=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((generous(X)&~tall(X))<=>(kind(X)<~>brave(X))))&
(((~generous(fred)<~>~happy(fred)))<=>(~wise(mary)))&
(((~creative(paul)&patient(paul)))<=>(?[X]:((brave(X)|~curious(X)))))&
(((strong(paul)|brave(paul)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~old(X)<~>~funny(X))))&
(((tall(mary)&old(mary)))=>((~kind(paul)|creative(paul))))&
(![X]:((~tall(X)|calm(X))<=>(humble(X)&kind(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~funny(X)<~>~strong(X)))))&
((~curious(alice)&quiet(alice)))&
(?[X]:((creative(X)<~>~calm(X))))&
(?[X]:((wise(X)&~old(X))))&
((kind(paul)<~>~kind(paul)))&
((~strong(john)&~rich(john)))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:((~patient(X)|~rich(X))))&
(?[X]:(humble(X))) | ~tall(john) | [
"p2",
"p6",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3357232163722673632309232
% SZS output start Proof for 3357232163722673632309232
3. ! [X0] : ((~brave(X0) | creative(X0)) => ~kind(X0)) [input p2]
7. ! [X0] : ((rich(X0) <~> ~brave(X0)) <=> (tall(X0) <~> humble(X0))) [input p6]
15. ! [X0] : ((calm(X0) | ~tall(X0)) <=> (kind(X0) & humble(X0))) [input p14]
21. ~rich(john) & ~strong(john) [input p20]
25. ~tall(john) [input hypothesis]
32. ! [X0] : (~kind(X0) | (brave(X0) & ~creative(X0))) [ennf transformation 3]
47. ! [X0] : ((((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0))))) [nnf transformation 7]
66. ! [X0] : (((calm(X0) | ~tall(X0)) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | (~calm(X0) & tall(X0)))) [nnf transformation 15]
67. ! [X0] : ((calm(X0) | ~tall(X0) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | (~calm(X0) & tall(X0)))) [flattening 66]
91. ~kind(X0) | brave(X0) [cnf transformation 32]
103. ~brave(X0) | rich(X0) | tall(X0) | ~humble(X0) [cnf transformation 47]
137. tall(X0) | humble(X0) [cnf transformation 67]
139. tall(X0) | kind(X0) [cnf transformation 67]
154. ~rich(john) [cnf transformation 21]
159. ~tall(john) [cnf transformation 25]
354. humble(john) [resolution 137,159]
355. kind(john) [resolution 139,159]
356. brave(john) [resolution 355,91]
429. rich(john) | tall(john) | ~humble(john) [resolution 103,356]
431. tall(john) | ~humble(john) [subsumption resolution 429,154]
432. ~humble(john) [subsumption resolution 431,159]
433. $false [subsumption resolution 432,354]
% SZS output end Proof for 3357232163722673632309232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and funny then someone is both not rich and not calm.
If susan is both patient and kind then john is both not strong and not curious.
If someone is either brave or tall then susan is brave or wise and vice versa.
If someone is happy then someone is not generous or not wise and vice versa.
Everyone who is both not humble and tall is not rich and vice versa.
Everyone who is either not kind or wise is humble or calm.
Everyone who is both creative and not patient is either not humble or not funny.
If someone is not wise then alice is both not creative and not happy and vice versa.
If someone is either not happy or not kind then mary is creative.
Everyone who is either calm or quiet is both generous and not kind and vice versa.
Everyone who is either not kind or happy is wise and vice versa.
If mary is both calm and not strong then someone is either not old or old.
Everyone who is both quiet and not calm is either brave or not kind and vice versa.
If paul is not generous or kind then someone is happy and vice versa.
If someone is both patient and not kind then someone is both wise and patient and vice versa.
Everyone who is either calm or patient is not funny or not quiet and vice versa.
Fred is tall.
Someone is not patient or funny.
Someone is humble.
Someone is either rich or wise.
Lucy is both generous and not wise.
Paul is both humble and not wise.
Someone is not quiet or patient.
Paul is both not brave and tall. | Paul is humble. | entailment | ((?[X]:((tall(X)&funny(X))))=>(?[X]:((~rich(X)&~calm(X)))))&
(((patient(susan)&kind(susan)))=>((~strong(john)&~curious(john))))&
((?[X]:((brave(X)<~>tall(X))))<=>((brave(susan)|wise(susan))))&
((?[X]:(happy(X)))<=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((~humble(X)&tall(X))<=>~rich(X)))&
(![X]:((~kind(X)<~>wise(X))=>(humble(X)|calm(X))))&
(![X]:((creative(X)&~patient(X))=>(~humble(X)<~>~funny(X))))&
((?[X]:(~wise(X)))<=>((~creative(alice)&~happy(alice))))&
((?[X]:((~happy(X)<~>~kind(X))))=>(creative(mary)))&
(![X]:((calm(X)<~>quiet(X))<=>(generous(X)&~kind(X))))&
(![X]:((~kind(X)<~>happy(X))<=>wise(X)))&
(((calm(mary)&~strong(mary)))=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((quiet(X)&~calm(X))<=>(brave(X)<~>~kind(X))))&
(((~generous(paul)|kind(paul)))<=>(?[X]:(happy(X))))&
((?[X]:((patient(X)&~kind(X))))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((calm(X)<~>patient(X))<=>(~funny(X)|~quiet(X))))&
(tall(fred))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:(humble(X)))&
(?[X]:((rich(X)<~>wise(X))))&
((generous(lucy)&~wise(lucy)))&
((humble(paul)&~wise(paul)))&
(?[X]:((~quiet(X)|patient(X))))&
((~brave(paul)&tall(paul))) | humble(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 184152818287709843248054
% SZS output start Proof for 184152818287709843248054
22. ~wise(paul) & humble(paul) [input p21]
25. ~humble(paul) [input hypothesis]
154. humble(paul) [cnf transformation 22]
159. ~humble(paul) [cnf transformation 25]
335. $false [subsumption resolution 159,154]
% SZS output end Proof for 184152818287709843248054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and creative is both not happy and wise and vice versa.
If susan is wise or old then mary is generous or funny and vice versa.
Everyone who is not rich or not kind is either patient or not kind and vice versa.
If paul is both funny and not happy then someone is calm and vice versa.
Everyone who is both brave and strong is brave or not happy and vice versa.
Everyone who is quiet is both not patient and not kind and vice versa.
Everyone who is either patient or rich is either curious or not rich and vice versa.
Everyone who is either not humble or not old is either patient or old and vice versa.
Everyone who is calm or humble is both strong and generous.
If someone is both old and not creative then someone is not old and vice versa.
Everyone who is either not kind or not rich is either not generous or not old.
Everyone who is old or not generous is old or humble and vice versa.
If lucy is both tall and not humble then someone is kind and vice versa.
If susan is either not generous or curious then someone is both wise and kind.
Everyone who is old or brave is either brave or not humble.
Susan is not quiet or brave.
Someone is both not old and wise.
Someone is not rich or wise.
Susan is not rich or rich. | Susan is rich. | entailment | (![X]:((~wise(X)&creative(X))<=>(~happy(X)&wise(X))))&
(((wise(susan)|old(susan)))<=>((generous(mary)|funny(mary))))&
(![X]:((~rich(X)|~kind(X))<=>(patient(X)<~>~kind(X))))&
(((funny(paul)&~happy(paul)))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)&strong(X))<=>(brave(X)|~happy(X))))&
(![X]:(quiet(X)<=>(~patient(X)&~kind(X))))&
(![X]:((patient(X)<~>rich(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(patient(X)<~>old(X))))&
(![X]:((calm(X)|humble(X))=>(strong(X)&generous(X))))&
((?[X]:((old(X)&~creative(X))))<=>(?[X]:(~old(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~generous(X)<~>~old(X))))&
(![X]:((old(X)|~generous(X))<=>(old(X)|humble(X))))&
(((tall(lucy)&~humble(lucy)))<=>(?[X]:(kind(X))))&
(((~generous(susan)<~>curious(susan)))=>(?[X]:((wise(X)&kind(X)))))&
(![X]:((old(X)|brave(X))=>(brave(X)<~>~humble(X))))&
((~quiet(susan)|brave(susan)))&
(?[X]:((~old(X)&wise(X))))&
(?[X]:((~rich(X)|wise(X))))&
((~rich(susan)|rich(susan))) | rich(susan) | [
"p2",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 135311165005310064495903
% SZS output start Proof for 135311165005310064495903
3. ! [X0] : ((~kind(X0) | ~rich(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p2]
6. ! [X0] : (quiet(X0) <=> (~kind(X0) & ~patient(X0))) [input p5]
7. ! [X0] : ((patient(X0) <~> rich(X0)) <=> (curious(X0) <~> ~rich(X0))) [input p6]
8. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (patient(X0) <~> old(X0))) [input p7]
9. ! [X0] : ((humble(X0) | calm(X0)) => (generous(X0) & strong(X0))) [input p8]
11. ! [X0] : ((~kind(X0) <~> ~rich(X0)) => (~generous(X0) <~> ~old(X0))) [input p10]
12. ! [X0] : ((~generous(X0) | old(X0)) <=> (humble(X0) | old(X0))) [input p11]
15. ! [X0] : ((brave(X0) | old(X0)) => (brave(X0) <~> ~humble(X0))) [input p14]
16. brave(susan) | ~quiet(susan) [input p15]
20. ~rich(susan) [input hypothesis]
22. ! [X0] : ((~kind(X0) & ~patient(X0)) => quiet(X0)) [unused predicate definition removal 6]
23. ! [X0] : (quiet(X0) | (kind(X0) | patient(X0))) [ennf transformation 22]
24. ! [X0] : (quiet(X0) | kind(X0) | patient(X0)) [flattening 23]
25. ! [X0] : ((generous(X0) & strong(X0)) | (~humble(X0) & ~calm(X0))) [ennf transformation 9]
26. ! [X0] : ((~generous(X0) <~> ~old(X0)) | (~kind(X0) <=> ~rich(X0))) [ennf transformation 11]
28. ! [X0] : ((brave(X0) <~> ~humble(X0)) | (~brave(X0) & ~old(X0))) [ennf transformation 15]
33. ! [X0] : (((~kind(X0) | ~rich(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (kind(X0) & rich(X0)))) [nnf transformation 3]
34. ! [X0] : ((~kind(X0) | ~rich(X0) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (kind(X0) & rich(X0)))) [flattening 33]
42. ! [X0] : ((((~rich(X0) | ~patient(X0)) & (rich(X0) | patient(X0))) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0))))) [nnf transformation 7]
43. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 8]
49. ! [X0] : (((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) [nnf transformation 26]
50. ! [X0] : (((~generous(X0) | old(X0)) | (~humble(X0) & ~old(X0))) & ((humble(X0) | old(X0)) | (generous(X0) & ~old(X0)))) [nnf transformation 12]
51. ! [X0] : ((~generous(X0) | old(X0) | (~humble(X0) & ~old(X0))) & (humble(X0) | old(X0) | (generous(X0) & ~old(X0)))) [flattening 50]
60. ! [X0] : (((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (~brave(X0) & ~old(X0))) [nnf transformation 28]
73. ~kind(X0) | patient(X0) | rich(X0) [cnf transformation 34]
76. kind(X0) | ~patient(X0) | kind(X0) [cnf transformation 34]
87. quiet(X0) | kind(X0) | patient(X0) [cnf transformation 24]
89. ~rich(X0) | curious(X0) | patient(X0) | ~rich(X0) [cnf transformation 42]
90. rich(X0) | ~curious(X0) | rich(X0) | ~patient(X0) [cnf transformation 42]
93. rich(X0) | patient(X0) | curious(X0) | rich(X0) [cnf transformation 42]
94. ~rich(X0) | ~patient(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 42]
97. old(X0) | patient(X0) | ~humble(X0) | old(X0) [cnf transformation 43]
98. ~old(X0) | ~patient(X0) | ~old(X0) | humble(X0) [cnf transformation 43]
101. ~old(X0) | ~humble(X0) | patient(X0) | ~old(X0) [cnf transformation 43]
102. old(X0) | humble(X0) | old(X0) | ~patient(X0) [cnf transformation 43]
107. ~humble(X0) | generous(X0) [cnf transformation 25]
112. ~kind(X0) | ~generous(X0) | ~old(X0) | rich(X0) [cnf transformation 49]
118. ~generous(X0) | old(X0) | ~humble(X0) [cnf transformation 51]
126. ~humble(X0) | brave(X0) | ~old(X0) [cnf transformation 60]
129. humble(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
130. brave(susan) | ~quiet(susan) [cnf transformation 16]
135. ~rich(susan) [cnf transformation 20]
136. ~brave(X0) | humble(X0) [duplicate literal removal 129]
137. old(X0) | patient(X0) | ~humble(X0) [duplicate literal removal 97]
138. ~old(X0) | ~patient(X0) | humble(X0) [duplicate literal removal 98]
139. ~humble(X0) | ~old(X0) | patient(X0) [duplicate literal removal 101]
140. ~patient(X0) | humble(X0) | old(X0) [duplicate literal removal 102]
141. ~rich(X0) | curious(X0) | patient(X0) [duplicate literal removal 89]
142. rich(X0) | ~curious(X0) | ~patient(X0) [duplicate literal removal 90]
143. curious(X0) | patient(X0) | rich(X0) [duplicate literal removal 93]
144. ~curious(X0) | ~patient(X0) | ~rich(X0) [duplicate literal removal 94]
145. ~patient(X0) | kind(X0) [duplicate literal removal 76]
158. 3 <=> old(susan) [avatar definition]
160. old(susan) <- (3) [avatar component clause 158]
187. quiet(X0) | kind(X0) [subsumption resolution 87,145]
188. ~curious(X0) | ~patient(X0) [subsumption resolution 142,144]
189. curious(X0) | patient(X0) [subsumption resolution 141,143]
190. ~patient(X0) | humble(X0) [subsumption resolution 138,140]
191. ~humble(X0) | patient(X0) [subsumption resolution 137,139]
213. ~humble(X0) | old(X0) [subsumption resolution 118,107]
234. 18 <=> curious(susan) [avatar definition]
235. curious(susan) <- (18) [avatar component clause 234]
236. ~curious(susan) <- (~18) [avatar component clause 234]
238. 19 <=> generous(susan) [avatar definition]
239. generous(susan) <- (19) [avatar component clause 238]
253. ~humble(X0) | brave(X0) [subsumption resolution 126,213]
255. 22 <=> quiet(susan) [avatar definition]
257. ~quiet(susan) <- (~22) [avatar component clause 255]
259. 23 <=> brave(susan) [avatar definition]
261. brave(susan) <- (23) [avatar component clause 259]
262. ~22 | 23 [avatar split clause 130,259,255]
279. kind(susan) <- (~22) [resolution 187,257]
282. ~patient(susan) <- (18) [resolution 188,235]
293. patient(susan) | rich(susan) <- (~22) [resolution 73,279]
303. rich(susan) <- (18, ~22) [subsumption resolution 293,282]
304. $false <- (18, ~22) [subsumption resolution 303,135]
305. ~18 | 22 [avatar contradiction clause 304]
311. humble(susan) <- (23) [resolution 261,136]
332. patient(susan) <- (23) [resolution 311,191]
333. generous(susan) <- (23) [resolution 311,107]
338. $false <- (18, 23) [subsumption resolution 332,282]
339. ~18 | ~23 [avatar contradiction clause 338]
342. 19 | ~23 [avatar split clause 333,259,238]
344. patient(susan) <- (~18) [resolution 236,189]
368. humble(susan) <- (~18) [resolution 344,190]
369. kind(susan) <- (~18) [resolution 344,145]
394. brave(susan) <- (~18) [resolution 368,253]
395. old(susan) <- (~18) [resolution 368,213]
399. 23 | 18 [avatar split clause 394,234,259]
402. 3 | 18 [avatar split clause 395,234,158]
406. ~generous(susan) | ~old(susan) | rich(susan) <- (~18) [resolution 369,112]
408. ~old(susan) | rich(susan) <- (~18, 19) [subsumption resolution 406,239]
409. rich(susan) <- (3, ~18, 19) [subsumption resolution 408,160]
410. $false <- (3, ~18, 19) [subsumption resolution 409,135]
411. ~3 | 18 | ~19 [avatar contradiction clause 410]
412. $false [avatar sat refutation 262,305,339,342,399,402,411]
% SZS output end Proof for 135311165005310064495903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both happy and not happy then mary is both not rich and not calm and vice versa.
Everyone who is both not wise and generous is both not generous and old and vice versa.
Everyone who is quiet is either not generous or not calm and vice versa.
If fred is either not rich or not kind then susan is both old and not old and vice versa.
If someone is either happy or not curious then someone is both not brave and brave.
If someone is not curious or creative then someone is not creative.
If someone is happy or not calm then susan is not quiet and vice versa.
Everyone who is both strong and rich is not calm or quiet and vice versa.
Everyone who is quiet or tall is not rich or not brave.
Everyone who is both calm and old is wise or curious and vice versa.
If someone is tall then john is both strong and not wise.
Everyone who is either strong or not generous is not wise and vice versa.
If someone is both not tall and not old then mary is rich or not generous and vice versa.
If alice is either strong or not funny then someone is either not humble or patient and vice versa.
Everyone who is old or rich is both not humble and not creative.
Everyone who is not funny is both strong and not happy.
Someone is both not tall and happy.
Mary is not calm or patient.
Someone is either old or curious.
Someone is either not wise or calm.
Someone is either not curious or not patient.
Someone is brave.
Someone is not rich.
Someone is both patient and not happy. | Mary is humble. | contradiction | (((happy(mary)&~happy(mary)))<=>((~rich(mary)&~calm(mary))))&
(![X]:((~wise(X)&generous(X))<=>(~generous(X)&old(X))))&
(![X]:(quiet(X)<=>(~generous(X)<~>~calm(X))))&
(((~rich(fred)<~>~kind(fred)))<=>((old(susan)&~old(susan))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&brave(X)))))&
((?[X]:((~curious(X)|creative(X))))=>(?[X]:(~creative(X))))&
((?[X]:((happy(X)|~calm(X))))<=>(~quiet(susan)))&
(![X]:((strong(X)&rich(X))<=>(~calm(X)|quiet(X))))&
(![X]:((quiet(X)|tall(X))=>(~rich(X)|~brave(X))))&
(![X]:((calm(X)&old(X))<=>(wise(X)|curious(X))))&
((?[X]:(tall(X)))=>((strong(john)&~wise(john))))&
(![X]:((strong(X)<~>~generous(X))<=>~wise(X)))&
((?[X]:((~tall(X)&~old(X))))<=>((rich(mary)|~generous(mary))))&
(((strong(alice)<~>~funny(alice)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:((old(X)|rich(X))=>(~humble(X)&~creative(X))))&
(![X]:(~funny(X)=>(strong(X)&~happy(X))))&
(?[X]:((~tall(X)&happy(X))))&
((~calm(mary)|patient(mary)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((~wise(X)<~>calm(X))))&
(?[X]:((~curious(X)<~>~patient(X))))&
(?[X]:(brave(X)))&
(?[X]:(~rich(X)))&
(?[X]:((patient(X)&~happy(X)))) | humble(mary) | [
"p1",
"p7",
"p9",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7567348044684181596530412
% SZS output start Proof for 7567348044684181596530412
2. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (old(X0) & ~generous(X0))) [input p1]
8. ! [X0] : ((rich(X0) & strong(X0)) <=> (quiet(X0) | ~calm(X0))) [input p7]
10. ! [X0] : ((old(X0) & calm(X0)) <=> (curious(X0) | wise(X0))) [input p9]
12. ! [X0] : ((strong(X0) <~> ~generous(X0)) <=> ~wise(X0)) [input p11]
14. (strong(alice) <~> ~funny(alice)) <=> ? [X0] : (~humble(X0) <~> patient(X0)) [input p13]
16. ! [X0] : (~funny(X0) => (~happy(X0) & strong(X0))) [input p15]
18. patient(mary) | ~calm(mary) [input p17]
25. humble(mary) [input hypothesis]
35. ! [X0] : ((~happy(X0) & strong(X0)) | funny(X0)) [ennf transformation 16]
38. ! [X0] : (((generous(X0) & ~wise(X0)) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | (~generous(X0) | wise(X0)))) [nnf transformation 2]
39. ! [X0] : (((generous(X0) & ~wise(X0)) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | ~generous(X0) | wise(X0))) [flattening 38]
51. ! [X0] : (((rich(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~rich(X0) | ~strong(X0)))) [nnf transformation 8]
52. ! [X0] : (((rich(X0) & strong(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~rich(X0) | ~strong(X0))) [flattening 51]
53. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & ~wise(X0))) & ((curious(X0) | wise(X0)) | (~old(X0) | ~calm(X0)))) [nnf transformation 10]
54. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & ~wise(X0))) & (curious(X0) | wise(X0) | ~old(X0) | ~calm(X0))) [flattening 53]
55. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | wise(X0)) & (~wise(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [nnf transformation 12]
61. (((funny(alice) | ~strong(alice)) & (~funny(alice) | strong(alice))) | ! [X0] : ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) & (? [X0] : ((~patient(X0) | humble(X0)) & (patient(X0) | ~humble(X0))) | ((strong(alice) | funny(alice)) & (~funny(alice) | ~strong(alice)))) [nnf transformation 14]
62. (((funny(alice) | ~strong(alice)) & (~funny(alice) | strong(alice))) | ! [X0] : ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) & (? [X1] : ((~patient(X1) | humble(X1)) & (patient(X1) | ~humble(X1))) | ((strong(alice) | funny(alice)) & (~funny(alice) | ~strong(alice)))) [rectify 61]
63. ? [X1] : ((~patient(X1) | humble(X1)) & (patient(X1) | ~humble(X1))) => ((~patient(sK3) | humble(sK3)) & (patient(sK3) | ~humble(sK3))) [choice axiom]
64. (((funny(alice) | ~strong(alice)) & (~funny(alice) | strong(alice))) | ! [X0] : ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) & (((~patient(sK3) | humble(sK3)) & (patient(sK3) | ~humble(sK3))) | ((strong(alice) | funny(alice)) & (~funny(alice) | ~strong(alice)))) [skolemisation 62,63]
86. ~generous(X0) | ~generous(X0) | wise(X0) [cnf transformation 39]
89. generous(X0) | ~old(X0) | generous(X0) [cnf transformation 39]
108. strong(X0) | calm(X0) [cnf transformation 52]
115. ~wise(X0) | calm(X0) [cnf transformation 54]
117. ~wise(X0) | old(X0) [cnf transformation 54]
121. ~wise(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 55]
124. generous(X0) | ~strong(X0) | wise(X0) [cnf transformation 55]
135. ~funny(alice) | strong(alice) | ~humble(X0) | ~patient(X0) [cnf transformation 64]
140. funny(X0) | strong(X0) [cnf transformation 35]
144. patient(mary) | ~calm(mary) [cnf transformation 18]
155. humble(mary) [cnf transformation 25]
156. ~generous(X0) | wise(X0) [duplicate literal removal 86]
157. ~old(X0) | generous(X0) [duplicate literal removal 89]
163. 2 <=> calm(mary) [avatar definition]
164. ~calm(mary) <- (~2) [avatar component clause 163]
216. 13 <=> ! [X1] : calm(X1) [avatar definition]
217. calm(X1) <- (13) [avatar component clause 216]
237. ~strong(X0) | wise(X0) [subsumption resolution 124,156]
238. ~strong(X0) | ~generous(X0) [subsumption resolution 121,237]
260. 22 <=> ! [X0] : (~humble(X0) | ~patient(X0)) [avatar definition]
261. ~patient(X0) | ~humble(X0) <- (22) [avatar component clause 260]
263. 23 <=> strong(alice) [avatar definition]
264. strong(alice) <- (23) [avatar component clause 263]
265. ~strong(alice) <- (~23) [avatar component clause 263]
267. 24 <=> funny(alice) [avatar definition]
268. ~funny(alice) <- (~24) [avatar component clause 267]
275. 22 | 23 | ~24 [avatar split clause 135,267,263,260]
290. 28 <=> patient(mary) [avatar definition]
292. patient(mary) <- (28) [avatar component clause 290]
293. ~2 | 28 [avatar split clause 144,290,163]
322. strong(alice) <- (~24) [resolution 140,268]
323. $false <- (~23, ~24) [subsumption resolution 322,265]
324. 23 | 24 [avatar contradiction clause 323]
336. wise(X0) | calm(X0) [resolution 237,108]
337. wise(alice) <- (23) [resolution 237,264]
338. calm(X0) [subsumption resolution 336,115]
339. 13 [avatar split clause 338,216]
353. old(alice) <- (23) [resolution 337,117]
356. ~generous(alice) <- (23) [resolution 238,264]
369. generous(alice) <- (23) [resolution 353,157]
370. $false <- (23) [subsumption resolution 369,356]
371. ~23 [avatar contradiction clause 370]
377. ~humble(mary) <- (22, 28) [resolution 261,292]
378. $false <- (22, 28) [subsumption resolution 377,155]
379. ~22 | ~28 [avatar contradiction clause 378]
381. $false <- (~2, 13) [subsumption resolution 164,217]
382. 2 | ~13 [avatar contradiction clause 381]
383. $false [avatar sat refutation 275,293,324,339,371,379,382]
% SZS output end Proof for 7567348044684181596530412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or old is not quiet or kind.
Everyone who is both not generous and not wise is either not old or not curious and vice versa.
Everyone who is not happy is kind or humble and vice versa.
Everyone who is happy or wise is brave or curious.
If paul is not brave then lucy is both not old and not funny and vice versa.
Everyone who is either not happy or not rich is not patient.
If someone is tall then someone is either happy or rich and vice versa.
Everyone who is not strong or not kind is both not quiet and rich and vice versa.
Everyone who is both curious and not patient is not rich.
Everyone who is not patient or not funny is both old and not patient.
Everyone who is both patient and not generous is either not kind or not funny.
Everyone who is curious or tall is not rich and vice versa.
Everyone who is both curious and strong is both patient and not funny.
Everyone who is both wise and not humble is both generous and not brave and vice versa.
Everyone who is not old is both not quiet and not brave.
Everyone who is both not calm and not generous is either not calm or not brave.
Someone is both happy and not wise.
Someone is both humble and not generous.
Alice is patient.
Someone is either not happy or not kind.
Fred is creative.
Lucy is either old or creative.
John is either not kind or not humble.
Someone is either not strong or not old. | Lucy is wise. | contradiction | (![X]:((~curious(X)<~>old(X))=>(~quiet(X)|kind(X))))&
(![X]:((~generous(X)&~wise(X))<=>(~old(X)<~>~curious(X))))&
(![X]:(~happy(X)<=>(kind(X)|humble(X))))&
(![X]:((happy(X)|wise(X))=>(brave(X)|curious(X))))&
((~brave(paul))<=>((~old(lucy)&~funny(lucy))))&
(![X]:((~happy(X)<~>~rich(X))=>~patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((happy(X)<~>rich(X)))))&
(![X]:((~strong(X)|~kind(X))<=>(~quiet(X)&rich(X))))&
(![X]:((curious(X)&~patient(X))=>~rich(X)))&
(![X]:((~patient(X)|~funny(X))=>(old(X)&~patient(X))))&
(![X]:((patient(X)&~generous(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((curious(X)|tall(X))<=>~rich(X)))&
(![X]:((curious(X)&strong(X))=>(patient(X)&~funny(X))))&
(![X]:((wise(X)&~humble(X))<=>(generous(X)&~brave(X))))&
(![X]:(~old(X)=>(~quiet(X)&~brave(X))))&
(![X]:((~calm(X)&~generous(X))=>(~calm(X)<~>~brave(X))))&
(?[X]:((happy(X)&~wise(X))))&
(?[X]:((humble(X)&~generous(X))))&
(patient(alice))&
(?[X]:((~happy(X)<~>~kind(X))))&
(creative(fred))&
((old(lucy)<~>creative(lucy)))&
((~kind(john)<~>~humble(john)))&
(?[X]:((~strong(X)<~>~old(X)))) | wise(lucy) | [
"p1",
"p3",
"p7",
"p8",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7332706727128591043429070
% SZS output start Proof for 7332706727128591043429070
2. ! [X0] : ((~wise(X0) & ~generous(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p1]
4. ! [X0] : ((wise(X0) | happy(X0)) => (curious(X0) | brave(X0))) [input p3]
8. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (rich(X0) & ~quiet(X0))) [input p7]
9. ! [X0] : ((~patient(X0) & curious(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~patient(X0) & old(X0))) [input p9]
12. ! [X0] : ((tall(X0) | curious(X0)) <=> ~rich(X0)) [input p11]
13. ! [X0] : ((strong(X0) & curious(X0)) => (~funny(X0) & patient(X0))) [input p12]
15. ! [X0] : (~old(X0) => (~brave(X0) & ~quiet(X0))) [input p14]
25. wise(lucy) [input hypothesis]
29. ! [X0] : ((curious(X0) | brave(X0)) | (~wise(X0) & ~happy(X0))) [ennf transformation 4]
30. ! [X0] : (curious(X0) | brave(X0) | (~wise(X0) & ~happy(X0))) [flattening 29]
32. ! [X0] : (~rich(X0) | (patient(X0) | ~curious(X0))) [ennf transformation 9]
33. ! [X0] : (~rich(X0) | patient(X0) | ~curious(X0)) [flattening 32]
34. ! [X0] : ((~patient(X0) & old(X0)) | (funny(X0) & patient(X0))) [ennf transformation 10]
37. ! [X0] : ((~funny(X0) & patient(X0)) | (~strong(X0) | ~curious(X0))) [ennf transformation 13]
38. ! [X0] : ((~funny(X0) & patient(X0)) | ~strong(X0) | ~curious(X0)) [flattening 37]
39. ! [X0] : ((~brave(X0) & ~quiet(X0)) | old(X0)) [ennf transformation 15]
43. ! [X0] : (((~wise(X0) & ~generous(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (wise(X0) | generous(X0)))) [nnf transformation 2]
44. ! [X0] : (((~wise(X0) & ~generous(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | wise(X0) | generous(X0))) [flattening 43]
55. ! [X0] : (((~kind(X0) | ~strong(X0)) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [nnf transformation 8]
56. ! [X0] : ((~kind(X0) | ~strong(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | (kind(X0) & strong(X0)))) [flattening 55]
58. ! [X0] : (((tall(X0) | curious(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [nnf transformation 12]
59. ! [X0] : ((tall(X0) | curious(X0) | rich(X0)) & (~rich(X0) | (~tall(X0) & ~curious(X0)))) [flattening 58]
82. ~wise(X0) | ~old(X0) | curious(X0) [cnf transformation 44]
87. ~wise(X0) | brave(X0) | curious(X0) [cnf transformation 30]
99. strong(X0) | rich(X0) [cnf transformation 56]
102. ~rich(X0) | patient(X0) | ~curious(X0) [cnf transformation 33]
104. funny(X0) | old(X0) [cnf transformation 34]
106. ~patient(X0) | funny(X0) [cnf transformation 34]
109. ~rich(X0) | ~curious(X0) [cnf transformation 59]
112. ~strong(X0) | patient(X0) | ~curious(X0) [cnf transformation 38]
113. ~strong(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 38]
119. ~brave(X0) | old(X0) [cnf transformation 39]
136. wise(lucy) [cnf transformation 25]
139. 1 <=> old(lucy) [avatar definition]
140. ~old(lucy) <- (~1) [avatar component clause 139]
141. old(lucy) <- (1) [avatar component clause 139]
143. 2 <=> funny(lucy) [avatar definition]
144. ~funny(lucy) <- (~2) [avatar component clause 143]
145. funny(lucy) <- (2) [avatar component clause 143]
220. old(lucy) <- (~2) [resolution 104,144]
223. 1 | 2 [avatar split clause 220,143,139]
236. ~old(lucy) | curious(lucy) [resolution 82,136]
237. curious(lucy) <- (1) [subsumption resolution 236,141]
246. brave(lucy) | curious(lucy) [resolution 87,136]
263. patient(X0) | ~curious(X0) | rich(X0) [resolution 112,99]
273. ~curious(X0) | patient(X0) [subsumption resolution 263,102]
275. ~funny(X0) | ~curious(X0) | rich(X0) [resolution 113,99]
316. patient(lucy) <- (1) [resolution 273,237]
331. funny(lucy) <- (1) [resolution 316,106]
334. 2 | ~1 [avatar split clause 331,139,143]
360. ~funny(X0) | ~curious(X0) [subsumption resolution 275,109]
478. ~curious(lucy) <- (2) [resolution 360,145]
483. brave(lucy) <- (2) [subsumption resolution 246,478]
484. ~old(lucy) <- (2) [subsumption resolution 236,478]
485. ~1 | ~2 [avatar split clause 484,143,139]
487. old(lucy) <- (2) [resolution 483,119]
490. $false <- (~1, 2) [subsumption resolution 487,140]
491. 1 | ~2 [avatar contradiction clause 490]
492. $false [avatar sat refutation 223,334,485,491]
% SZS output end Proof for 7332706727128591043429070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is rich and vice versa.
If someone is kind then someone is calm or not strong.
If alice is tall then someone is either not calm or not rich and vice versa.
Everyone who is both funny and wise is either not old or calm and vice versa.
If someone is not curious then someone is not wise.
If someone is not wise or tall then john is either not wise or not creative.
Everyone who is rich is happy and vice versa.
If fred is not curious then alice is either strong or not funny.
Everyone who is either not happy or not quiet is either curious or quiet.
Everyone who is happy or rich is old.
If lucy is either happy or funny then lucy is either strong or old and vice versa.
If mary is both funny and not creative then someone is either not generous or rich.
If alice is not funny then lucy is creative or not happy and vice versa.
Everyone who is not kind or tall is both not strong and not wise.
Everyone who is kind is both curious and creative and vice versa.
Everyone who is both generous and not brave is happy or not calm.
Paul is either not calm or not happy.
Someone is brave.
Paul is curious or not generous.
Lucy is patient.
Someone is both not quiet and curious.
John is both not wise and not calm.
Lucy is humble. | Alice is not tall. | contradiction | (![X]:(~old(X)<=>rich(X)))&
((?[X]:(kind(X)))=>(?[X]:((calm(X)|~strong(X)))))&
((tall(alice))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
(![X]:((funny(X)&wise(X))<=>(~old(X)<~>calm(X))))&
((?[X]:(~curious(X)))=>(?[X]:(~wise(X))))&
((?[X]:((~wise(X)|tall(X))))=>((~wise(john)<~>~creative(john))))&
(![X]:(rich(X)<=>happy(X)))&
((~curious(fred))=>((strong(alice)<~>~funny(alice))))&
(![X]:((~happy(X)<~>~quiet(X))=>(curious(X)<~>quiet(X))))&
(![X]:((happy(X)|rich(X))=>old(X)))&
(((happy(lucy)<~>funny(lucy)))<=>((strong(lucy)<~>old(lucy))))&
(((funny(mary)&~creative(mary)))=>(?[X]:((~generous(X)<~>rich(X)))))&
((~funny(alice))<=>((creative(lucy)|~happy(lucy))))&
(![X]:((~kind(X)|tall(X))=>(~strong(X)&~wise(X))))&
(![X]:(kind(X)<=>(curious(X)&creative(X))))&
(![X]:((generous(X)&~brave(X))=>(happy(X)|~calm(X))))&
((~calm(paul)<~>~happy(paul)))&
(?[X]:(brave(X)))&
((curious(paul)|~generous(paul)))&
(patient(lucy))&
(?[X]:((~quiet(X)&curious(X))))&
((~wise(john)&~calm(john)))&
(humble(lucy)) | ~tall(alice) | [
"p0",
"p2",
"p6",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5231225828370790191215713
% SZS output start Proof for 5231225828370790191215713
1. ! [X0] : (~old(X0) <=> rich(X0)) [input p0]
3. tall(alice) <=> ? [X0] : (~calm(X0) <~> ~rich(X0)) [input p2]
7. ! [X0] : (rich(X0) <=> happy(X0)) [input p6]
10. ! [X0] : ((rich(X0) | happy(X0)) => old(X0)) [input p9]
17. ~calm(paul) <~> ~happy(paul) [input p16]
24. ~tall(alice) [input hypothesis]
36. ! [X0] : (old(X0) | (~rich(X0) & ~happy(X0))) [ennf transformation 10]
40. ! [X0] : ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))) [nnf transformation 1]
44. (tall(alice) | ! [X0] : ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (? [X0] : ((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | ~tall(alice)) [nnf transformation 3]
45. (tall(alice) | ! [X0] : ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (? [X1] : ((rich(X1) | calm(X1)) & (~rich(X1) | ~calm(X1))) | ~tall(alice)) [rectify 44]
46. ? [X1] : ((rich(X1) | calm(X1)) & (~rich(X1) | ~calm(X1))) => ((rich(sK1) | calm(sK1)) & (~rich(sK1) | ~calm(sK1))) [choice axiom]
47. (tall(alice) | ! [X0] : ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (((rich(sK1) | calm(sK1)) & (~rich(sK1) | ~calm(sK1))) | ~tall(alice)) [skolemisation 45,46]
54. ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0))) [nnf transformation 7]
65. (happy(paul) | calm(paul)) & (~happy(paul) | ~calm(paul)) [nnf transformation 17]
69. ~rich(X0) | ~old(X0) [cnf transformation 40]
74. tall(alice) | ~calm(X0) | rich(X0) [cnf transformation 47]
87. ~happy(X0) | rich(X0) [cnf transformation 54]
95. old(X0) | ~rich(X0) [cnf transformation 36]
117. happy(paul) | calm(paul) [cnf transformation 65]
123. ~tall(alice) [cnf transformation 24]
139. 4 <=> ! [X0] : (~calm(X0) | rich(X0)) [avatar definition]
140. ~calm(X0) | rich(X0) <- (4) [avatar component clause 139]
142. 5 <=> tall(alice) [avatar definition]
145. 4 | 5 [avatar split clause 74,142,139]
200. ~rich(X0) [subsumption resolution 95,69]
249. 26 <=> calm(paul) [avatar definition]
251. calm(paul) <- (26) [avatar component clause 249]
253. 27 <=> happy(paul) [avatar definition]
255. happy(paul) <- (27) [avatar component clause 253]
256. 26 | 27 [avatar split clause 117,253,249]
268. ~5 [avatar split clause 123,142]
269. ~calm(X0) <- (4) [subsumption resolution 140,200]
270. $false <- (4, 26) [resolution 269,251]
271. ~4 | ~26 [avatar contradiction clause 270]
277. rich(paul) <- (27) [resolution 87,255]
279. $false <- (27) [subsumption resolution 277,200]
280. ~27 [avatar contradiction clause 279]
283. $false [avatar sat refutation 145,256,268,271,280]
% SZS output end Proof for 5231225828370790191215713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either funny or not generous and vice versa. If someone is brave then someone is both generous and not funny. Everyone who is strong or old is curious or humble. If someone is both wise and not quiet then someone is not funny or not generous and vice versa. Everyone who is not kind or not humble is curious and vice versa. Everyone who is not wise or not calm is both wise and not rich. Everyone who is either strong or generous is wise or not curious and vice versa. Everyone who is both wise and not strong is either not patient or quiet and vice versa. Everyone who is tall is not patient or not brave. If someone is not strong then lucy is funny. Everyone who is tall or not rich is not kind. If fred is both creative and not curious then someone is not happy or strong. Everyone who is both not brave and kind is either patient or not brave. Everyone who is both not rich and patient is both wise and not brave. Everyone who is both funny and calm is both curious and not brave. If fred is quiet then someone is tall. Someone is both not calm and creative. Someone is both generous and curious. Paul is either not humble or tall. Someone is strong or not rich. Someone is both not strong and not kind. Susan is either calm or not generous. Someone is both funny and calm. | Fred is creative. | neutral | (![X]:(happy(X)<=>(funny(X)<~>~generous(X))))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((strong(X)|old(X))=>(curious(X)|humble(X))))&
((?[X]:((wise(X)&~quiet(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:((~kind(X)|~humble(X))<=>curious(X)))&
(![X]:((~wise(X)|~calm(X))=>(wise(X)&~rich(X))))&
(![X]:((strong(X)<~>generous(X))<=>(wise(X)|~curious(X))))&
(![X]:((wise(X)&~strong(X))<=>(~patient(X)<~>quiet(X))))&
(![X]:(tall(X)=>(~patient(X)|~brave(X))))&
((?[X]:(~strong(X)))=>(funny(lucy)))&
(![X]:((tall(X)|~rich(X))=>~kind(X)))&
(((creative(fred)&~curious(fred)))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~brave(X)&kind(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)&patient(X))=>(wise(X)&~brave(X))))&
(![X]:((funny(X)&calm(X))=>(curious(X)&~brave(X))))&
((quiet(fred))=>(?[X]:(tall(X))))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((generous(X)&curious(X))))&
((~humble(paul)<~>tall(paul)))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((~strong(X)&~kind(X))))&
((calm(susan)<~>~generous(susan)))&
(?[X]:((funny(X)&calm(X)))) | creative(fred) | [] | null | 0 |
Everyone who is tall is not rich.
Everyone who is quiet or old is either happy or not strong and vice versa.
Everyone who is both not patient and not creative is not rich and vice versa.
If lucy is either happy or generous then someone is patient or not curious.
Everyone who is strong or tall is old.
If lucy is either not funny or kind then fred is calm and vice versa.
Everyone who is both calm and happy is either not old or not quiet.
Everyone who is not patient or tall is either not old or not rich and vice versa.
Everyone who is not old is strong and vice versa.
If mary is either not happy or not wise then someone is not tall and vice versa.
Everyone who is either not creative or old is generous or brave.
Everyone who is funny or not creative is both generous and quiet.
If susan is both brave and generous then fred is not curious or tall and vice versa.
If john is not patient or creative then mary is both strong and curious and vice versa.
If mary is both not patient and rich then susan is either not kind or not tall.
Everyone who is either not brave or not curious is humble.
Lucy is both brave and creative.
Someone is both not tall and not rich.
Fred is brave.
Susan is either not happy or not patient.
Alice is funny.
Paul is both not kind and not brave.
Someone is wise or happy. | Susan is curious. | neutral | (![X]:(tall(X)=>~rich(X)))&
(![X]:((quiet(X)|old(X))<=>(happy(X)<~>~strong(X))))&
(![X]:((~patient(X)&~creative(X))<=>~rich(X)))&
(((happy(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)|~curious(X)))))&
(![X]:((strong(X)|tall(X))=>old(X)))&
(((~funny(lucy)<~>kind(lucy)))<=>(calm(fred)))&
(![X]:((calm(X)&happy(X))=>(~old(X)<~>~quiet(X))))&
(![X]:((~patient(X)|tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(~old(X)<=>strong(X)))&
(((~happy(mary)<~>~wise(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((~creative(X)<~>old(X))=>(generous(X)|brave(X))))&
(![X]:((funny(X)|~creative(X))=>(generous(X)&quiet(X))))&
(((brave(susan)&generous(susan)))<=>((~curious(fred)|tall(fred))))&
(((~patient(john)|creative(john)))<=>((strong(mary)&curious(mary))))&
(((~patient(mary)&rich(mary)))=>((~kind(susan)<~>~tall(susan))))&
(![X]:((~brave(X)<~>~curious(X))=>humble(X)))&
((brave(lucy)&creative(lucy)))&
(?[X]:((~tall(X)&~rich(X))))&
(brave(fred))&
((~happy(susan)<~>~patient(susan)))&
(funny(alice))&
((~kind(paul)&~brave(paul)))&
(?[X]:((wise(X)|happy(X)))) | curious(susan) | [] | null | 0 |
If susan is both old and not wise then paul is either wise or brave. If mary is both rich and not funny then someone is either not funny or generous and vice versa. Everyone who is either not old or kind is both not rich and not humble. If someone is not patient or not rich then someone is both funny and not wise. Everyone who is patient is either brave or kind. Everyone who is either not kind or happy is both kind and funny and vice versa. Everyone who is not quiet is quiet. If someone is humble or not happy then someone is both tall and calm. If susan is creative or rich then someone is either happy or funny. Everyone who is not rich or not patient is both kind and wise. If lucy is both not funny and not strong then someone is rich and vice versa. Everyone who is creative is either tall or not generous and vice versa. Everyone who is not calm is tall or not calm. Everyone who is not quiet is not brave. Everyone who is quiet is both not calm and not curious and vice versa. Someone is not old or humble. Someone is either not tall or not creative. | Lucy is generous. | neutral | (((old(susan)&~wise(susan)))=>((wise(paul)<~>brave(paul))))&
(((rich(mary)&~funny(mary)))<=>(?[X]:((~funny(X)<~>generous(X)))))&
(![X]:((~old(X)<~>kind(X))=>(~rich(X)&~humble(X))))&
((?[X]:((~patient(X)|~rich(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:(patient(X)=>(brave(X)<~>kind(X))))&
(![X]:((~kind(X)<~>happy(X))<=>(kind(X)&funny(X))))&
(![X]:(~quiet(X)=>quiet(X)))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:((tall(X)&calm(X)))))&
(((creative(susan)|rich(susan)))=>(?[X]:((happy(X)<~>funny(X)))))&
(![X]:((~rich(X)|~patient(X))=>(kind(X)&wise(X))))&
(((~funny(lucy)&~strong(lucy)))<=>(?[X]:(rich(X))))&
(![X]:(creative(X)<=>(tall(X)<~>~generous(X))))&
(![X]:(~calm(X)=>(tall(X)|~calm(X))))&
(![X]:(~quiet(X)=>~brave(X)))&
(![X]:(quiet(X)<=>(~calm(X)&~curious(X))))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((~tall(X)<~>~creative(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is quiet or not strong is both kind and not funny and vice versa.
Everyone who is either patient or rich is not happy or kind.
Everyone who is both not wise and not brave is happy and vice versa.
Everyone who is both not kind and rich is humble.
Everyone who is generous is wise.
Everyone who is both quiet and humble is quiet or strong and vice versa.
Everyone who is kind or tall is both strong and generous.
Everyone who is either curious or not funny is either not brave or strong and vice versa.
If someone is both not creative and curious then mary is generous or calm and vice versa.
Everyone who is both not calm and strong is either wise or kind and vice versa.
Everyone who is both not calm and rich is not generous.
Everyone who is either creative or tall is either patient or not funny.
Everyone who is not rich or not humble is not patient or not rich.
Everyone who is both not strong and rich is either not kind or wise.
If someone is either not creative or not patient then someone is not humble or not generous and vice versa.
Someone is old.
Mary is curious or old.
Fred is not kind or creative.
Someone is either not quiet or kind.
Someone is both generous and not creative. | Fred is old. | neutral | (![X]:((quiet(X)|~strong(X))<=>(kind(X)&~funny(X))))&
(![X]:((patient(X)<~>rich(X))=>(~happy(X)|kind(X))))&
(![X]:((~wise(X)&~brave(X))<=>happy(X)))&
(![X]:((~kind(X)&rich(X))=>humble(X)))&
(![X]:(generous(X)=>wise(X)))&
(![X]:((quiet(X)&humble(X))<=>(quiet(X)|strong(X))))&
(![X]:((kind(X)|tall(X))=>(strong(X)&generous(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(~brave(X)<~>strong(X))))&
((?[X]:((~creative(X)&curious(X))))<=>((generous(mary)|calm(mary))))&
(![X]:((~calm(X)&strong(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~calm(X)&rich(X))=>~generous(X)))&
(![X]:((creative(X)<~>tall(X))=>(patient(X)<~>~funny(X))))&
(![X]:((~rich(X)|~humble(X))=>(~patient(X)|~rich(X))))&
(![X]:((~strong(X)&rich(X))=>(~kind(X)<~>wise(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(?[X]:(old(X)))&
((curious(mary)|old(mary)))&
((~kind(fred)|creative(fred)))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:((generous(X)&~creative(X)))) | old(fred) | [] | null | 0 |
If someone is both not funny and not patient then someone is not strong.
If alice is either strong or not generous then someone is not generous or humble.
Everyone who is both not generous and creative is not strong or not curious.
If paul is not old or creative then lucy is not creative.
Everyone who is either not rich or not funny is either not generous or wise.
If someone is old then lucy is curious or not generous.
Everyone who is not old or not generous is both old and not creative and vice versa.
If john is either tall or not brave then fred is both brave and not calm.
Everyone who is happy or funny is patient or not rich and vice versa.
If mary is happy or not funny then susan is not old or humble.
Everyone who is both humble and wise is wise or tall.
If someone is not wise then susan is either curious or humble.
Everyone who is not rich is either funny or strong.
If lucy is not rich then paul is not strong or not generous and vice versa.
Everyone who is either humble or calm is brave.
Everyone who is both not funny and calm is not kind and vice versa.
Someone is calm or not strong.
Fred is either not tall or not humble.
Someone is either not curious or humble.
Mary is not kind.
Someone is either not patient or not creative.
Someone is strong or not kind.
Someone is calm. | Paul is not generous. | neutral | ((?[X]:((~funny(X)&~patient(X))))=>(?[X]:(~strong(X))))&
(((strong(alice)<~>~generous(alice)))=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~generous(X)&creative(X))=>(~strong(X)|~curious(X))))&
(((~old(paul)|creative(paul)))=>(~creative(lucy)))&
(![X]:((~rich(X)<~>~funny(X))=>(~generous(X)<~>wise(X))))&
((?[X]:(old(X)))=>((curious(lucy)|~generous(lucy))))&
(![X]:((~old(X)|~generous(X))<=>(old(X)&~creative(X))))&
(((tall(john)<~>~brave(john)))=>((brave(fred)&~calm(fred))))&
(![X]:((happy(X)|funny(X))<=>(patient(X)|~rich(X))))&
(((happy(mary)|~funny(mary)))=>((~old(susan)|humble(susan))))&
(![X]:((humble(X)&wise(X))=>(wise(X)|tall(X))))&
((?[X]:(~wise(X)))=>((curious(susan)<~>humble(susan))))&
(![X]:(~rich(X)=>(funny(X)<~>strong(X))))&
((~rich(lucy))<=>((~strong(paul)|~generous(paul))))&
(![X]:((humble(X)<~>calm(X))=>brave(X)))&
(![X]:((~funny(X)&calm(X))<=>~kind(X)))&
(?[X]:((calm(X)|~strong(X))))&
((~tall(fred)<~>~humble(fred)))&
(?[X]:((~curious(X)<~>humble(X))))&
(~kind(mary))&
(?[X]:((~patient(X)<~>~creative(X))))&
(?[X]:((strong(X)|~kind(X))))&
(?[X]:(calm(X))) | ~generous(paul) | [] | null | 0 |
Everyone who is rich is not wise or funny and vice versa.
If someone is not tall then someone is both patient and not creative and vice versa.
Everyone who is creative or humble is both not brave and not patient.
If someone is not rich then alice is not quiet or calm.
Everyone who is both funny and humble is both humble and not quiet and vice versa.
Everyone who is either humble or not patient is not generous or curious.
Everyone who is both kind and generous is not funny or not tall and vice versa.
If susan is either rich or not calm then mary is tall or not humble.
If someone is tall or not humble then lucy is rich.
If paul is either happy or generous then someone is both patient and humble and vice versa.
If someone is not patient then john is both humble and not funny and vice versa.
If lucy is not happy then someone is generous.
Everyone who is not happy or creative is brave or not quiet.
Everyone who is not brave is both not happy and strong.
Everyone who is both not happy and not brave is strong and vice versa.
Susan is not curious or generous.
Someone is either tall or humble.
Someone is kind or not brave.
John is not wise.
Someone is calm or curious. | John is rich. | entailment | (![X]:(rich(X)<=>(~wise(X)|funny(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((creative(X)|humble(X))=>(~brave(X)&~patient(X))))&
((?[X]:(~rich(X)))=>((~quiet(alice)|calm(alice))))&
(![X]:((funny(X)&humble(X))<=>(humble(X)&~quiet(X))))&
(![X]:((humble(X)<~>~patient(X))=>(~generous(X)|curious(X))))&
(![X]:((kind(X)&generous(X))<=>(~funny(X)|~tall(X))))&
(((rich(susan)<~>~calm(susan)))=>((tall(mary)|~humble(mary))))&
((?[X]:((tall(X)|~humble(X))))=>(rich(lucy)))&
(((happy(paul)<~>generous(paul)))<=>(?[X]:((patient(X)&humble(X)))))&
((?[X]:(~patient(X)))<=>((humble(john)&~funny(john))))&
((~happy(lucy))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)|creative(X))=>(brave(X)|~quiet(X))))&
(![X]:(~brave(X)=>(~happy(X)&strong(X))))&
(![X]:((~happy(X)&~brave(X))<=>strong(X)))&
((~curious(susan)|generous(susan)))&
(?[X]:((tall(X)<~>humble(X))))&
(?[X]:((kind(X)|~brave(X))))&
(~wise(john))&
(?[X]:((calm(X)|curious(X)))) | rich(john) | [
"p0",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7968042590372141721585930
% SZS output start Proof for 7968042590372141721585930
1. ! [X0] : (rich(X0) <=> (funny(X0) | ~wise(X0))) [input p0]
19. ~wise(john) [input p18]
21. ~rich(john) [input hypothesis]
37. ! [X0] : ((rich(X0) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | ~rich(X0))) [nnf transformation 1]
38. ! [X0] : ((rich(X0) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | ~rich(X0))) [flattening 37]
69. wise(X0) | rich(X0) [cnf transformation 38]
114. ~wise(john) [cnf transformation 19]
116. ~rich(john) [cnf transformation 21]
267. rich(john) [resolution 69,114]
268. $false [subsumption resolution 267,116]
% SZS output end Proof for 7968042590372141721585930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or happy is both calm and not quiet. Everyone who is not humble is not wise and vice versa. If someone is both curious and not patient then mary is either not rich or happy. Everyone who is either not strong or not curious is humble or not curious and vice versa. If someone is happy or not generous then someone is both not brave and brave. Everyone who is either not patient or not strong is both quiet and happy. Everyone who is either creative or not happy is not generous and vice versa. If someone is both not quiet and not happy then john is either creative or quiet and vice versa. If fred is happy then someone is both not calm and not generous. Everyone who is patient is both not curious and not strong and vice versa. If susan is not wise then someone is not wise or strong and vice versa. Everyone who is either not quiet or not kind is strong or curious and vice versa. Everyone who is either not humble or old is humble. If susan is calm then susan is not patient. If alice is not kind or not brave then someone is happy or not tall and vice versa. Fred is either kind or not tall. Someone is not calm or brave. Mary is either wise or not curious. | Fred is not kind. | contradiction | (![X]:((~patient(X)|happy(X))=>(calm(X)&~quiet(X))))&
(![X]:(~humble(X)<=>~wise(X)))&
((?[X]:((curious(X)&~patient(X))))=>((~rich(mary)<~>happy(mary))))&
(![X]:((~strong(X)<~>~curious(X))<=>(humble(X)|~curious(X))))&
((?[X]:((happy(X)|~generous(X))))=>(?[X]:((~brave(X)&brave(X)))))&
(![X]:((~patient(X)<~>~strong(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)<~>~happy(X))<=>~generous(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((creative(john)<~>quiet(john))))&
((happy(fred))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:(patient(X)<=>(~curious(X)&~strong(X))))&
((~wise(susan))<=>(?[X]:((~wise(X)|strong(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(strong(X)|curious(X))))&
(![X]:((~humble(X)<~>old(X))=>humble(X)))&
((calm(susan))=>(~patient(susan)))&
(((~kind(alice)|~brave(alice)))<=>(?[X]:((happy(X)|~tall(X)))))&
((kind(fred)<~>~tall(fred)))&
(?[X]:((~calm(X)|brave(X))))&
((wise(mary)<~>~curious(mary))) | ~kind(fred) | [
"p0",
"p3",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5608074702042986869780101
% SZS output start Proof for 5608074702042986869780101
1. ! [X0] : ((happy(X0) | ~patient(X0)) => (~quiet(X0) & calm(X0))) [input p0]
4. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> (~curious(X0) | humble(X0))) [input p3]
6. ! [X0] : ((~patient(X0) <~> ~strong(X0)) => (happy(X0) & quiet(X0))) [input p5]
10. ! [X0] : (patient(X0) <=> (~strong(X0) & ~curious(X0))) [input p9]
12. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> (curious(X0) | strong(X0))) [input p11]
19. ~kind(fred) [input hypothesis]
21. ! [X0] : ((~quiet(X0) & calm(X0)) | (~happy(X0) & patient(X0))) [ennf transformation 1]
24. ! [X0] : ((happy(X0) & quiet(X0)) | (~patient(X0) <=> ~strong(X0))) [ennf transformation 6]
30. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 4]
31. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [flattening 30]
35. ! [X0] : ((happy(X0) & quiet(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) [nnf transformation 24]
43. ! [X0] : ((patient(X0) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | ~patient(X0))) [nnf transformation 10]
44. ! [X0] : ((patient(X0) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | ~patient(X0))) [flattening 43]
49. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 12]
50. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [flattening 49]
63. ~quiet(X0) | patient(X0) [cnf transformation 21]
74. curious(X0) | strong(X0) | curious(X0) [cnf transformation 31]
79. quiet(X0) | ~strong(X0) | patient(X0) [cnf transformation 35]
95. ~curious(X0) | ~patient(X0) [cnf transformation 44]
96. ~strong(X0) | ~patient(X0) [cnf transformation 44]
106. ~curious(X0) | quiet(X0) | kind(X0) [cnf transformation 50]
119. ~kind(fred) [cnf transformation 19]
122. strong(X0) | curious(X0) [duplicate literal removal 74]
151. ~strong(X0) | patient(X0) [subsumption resolution 79,63]
191. ~strong(X0) [subsumption resolution 96,151]
239. 25 <=> kind(fred) [avatar definition]
241. ~kind(fred) <- (~25) [avatar component clause 239]
267. ~25 [avatar split clause 119,239]
271. curious(X0) [resolution 122,191]
273. ~patient(X0) [resolution 271,95]
301. kind(X0) | quiet(X0) [resolution 106,271]
302. quiet(fred) <- (~25) [resolution 301,241]
305. patient(fred) <- (~25) [resolution 302,63]
306. $false <- (~25) [subsumption resolution 305,273]
307. 25 [avatar contradiction clause 306]
308. $false [avatar sat refutation 267,307]
% SZS output end Proof for 5608074702042986869780101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both happy and calm.
Everyone who is not brave or tall is both creative and wise.
Everyone who is both not creative and rich is creative or not funny and vice versa.
If someone is both not patient and strong then susan is both calm and not quiet and vice versa.
If someone is both patient and not humble then someone is either not patient or rich and vice versa.
If someone is either not strong or not creative then alice is not tall or not happy.
Everyone who is happy or strong is both not patient and calm and vice versa.
Everyone who is not brave is both not curious and not creative and vice versa.
If someone is both rich and happy then someone is both curious and rich and vice versa.
If susan is either not wise or not old then someone is funny or old.
Everyone who is either not calm or not wise is curious and vice versa.
Everyone who is either humble or funny is either not old or not patient and vice versa.
If someone is either not brave or not rich then susan is both kind and wise.
Lucy is not generous.
John is not wise.
Someone is not tall or not old.
Someone is either rich or creative. | Alice is not humble. | neutral | (![X]:((strong(X)|~happy(X))=>(happy(X)&calm(X))))&
(![X]:((~brave(X)|tall(X))=>(creative(X)&wise(X))))&
(![X]:((~creative(X)&rich(X))<=>(creative(X)|~funny(X))))&
((?[X]:((~patient(X)&strong(X))))<=>((calm(susan)&~quiet(susan))))&
((?[X]:((patient(X)&~humble(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((~strong(X)<~>~creative(X))))=>((~tall(alice)|~happy(alice))))&
(![X]:((happy(X)|strong(X))<=>(~patient(X)&calm(X))))&
(![X]:(~brave(X)<=>(~curious(X)&~creative(X))))&
((?[X]:((rich(X)&happy(X))))<=>(?[X]:((curious(X)&rich(X)))))&
(((~wise(susan)<~>~old(susan)))=>(?[X]:((funny(X)|old(X)))))&
(![X]:((~calm(X)<~>~wise(X))<=>curious(X)))&
(![X]:((humble(X)<~>funny(X))<=>(~old(X)<~>~patient(X))))&
((?[X]:((~brave(X)<~>~rich(X))))=>((kind(susan)&wise(susan))))&
(~generous(lucy))&
(~wise(john))&
(?[X]:((~tall(X)|~old(X))))&
(?[X]:((rich(X)<~>creative(X)))) | ~humble(alice) | [] | null | 0 |
If lucy is not funny then mary is either not calm or quiet.
Everyone who is both old and not quiet is not calm.
If john is creative then someone is both not curious and not patient and vice versa.
If susan is both not strong and not calm then someone is tall or not brave and vice versa.
Everyone who is either not brave or not happy is either funny or happy.
If john is both not calm and not tall then john is both humble and wise and vice versa.
Everyone who is both brave and not generous is wise.
If someone is both not strong and humble then someone is not strong or not kind and vice versa.
Everyone who is both patient and humble is not patient and vice versa.
Everyone who is not happy or humble is wise.
Everyone who is either brave or not quiet is not brave and vice versa.
If someone is both kind and not generous then lucy is both not generous and not rich and vice versa.
If someone is both not creative and not quiet then someone is either not brave or curious and vice versa.
If someone is not humble then lucy is both wise and generous and vice versa.
If mary is either wise or strong then john is not creative.
Someone is not humble or not happy.
Someone is both not rich and not humble.
Someone is not funny or not kind.
Alice is either not wise or generous.
Alice is wise or not curious.
Paul is not funny or not calm.
John is strong. | John is brave. | entailment | ((~funny(lucy))=>((~calm(mary)<~>quiet(mary))))&
(![X]:((old(X)&~quiet(X))=>~calm(X)))&
((creative(john))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((~strong(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((~brave(X)<~>~happy(X))=>(funny(X)<~>happy(X))))&
(((~calm(john)&~tall(john)))<=>((humble(john)&wise(john))))&
(![X]:((brave(X)&~generous(X))=>wise(X)))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((patient(X)&humble(X))<=>~patient(X)))&
(![X]:((~happy(X)|humble(X))=>wise(X)))&
(![X]:((brave(X)<~>~quiet(X))<=>~brave(X)))&
((?[X]:((kind(X)&~generous(X))))<=>((~generous(lucy)&~rich(lucy))))&
((?[X]:((~creative(X)&~quiet(X))))<=>(?[X]:((~brave(X)<~>curious(X)))))&
((?[X]:(~humble(X)))<=>((wise(lucy)&generous(lucy))))&
(((wise(mary)<~>strong(mary)))=>(~creative(john)))&
(?[X]:((~humble(X)|~happy(X))))&
(?[X]:((~rich(X)&~humble(X))))&
(?[X]:((~funny(X)|~kind(X))))&
((~wise(alice)<~>generous(alice)))&
((wise(alice)|~curious(alice)))&
((~funny(paul)|~calm(paul)))&
(strong(john)) | brave(john) | [
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6053303912821664042359835
% SZS output start Proof for 6053303912821664042359835
4. (~calm(susan) & ~strong(susan)) <=> ? [X0] : (~brave(X0) | tall(X0)) [input p3]
8. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X0] : (~kind(X0) | ~strong(X0)) [input p7]
9. ! [X0] : ((humble(X0) & patient(X0)) <=> ~patient(X0)) [input p8]
23. ~brave(john) [input hypothesis]
24. ? [X0] : (humble(X0) & ~strong(X0)) <=> ? [X1] : (~kind(X1) | ~strong(X1)) [rectify 8]
38. ((~calm(susan) & ~strong(susan)) | ! [X0] : (brave(X0) & ~tall(X0))) & (? [X0] : (~brave(X0) | tall(X0)) | (calm(susan) | strong(susan))) [nnf transformation 4]
39. ((~calm(susan) & ~strong(susan)) | ! [X0] : (brave(X0) & ~tall(X0))) & (? [X0] : (~brave(X0) | tall(X0)) | calm(susan) | strong(susan)) [flattening 38]
40. ((~calm(susan) & ~strong(susan)) | ! [X0] : (brave(X0) & ~tall(X0))) & (? [X1] : (~brave(X1) | tall(X1)) | calm(susan) | strong(susan)) [rectify 39]
41. ? [X1] : (~brave(X1) | tall(X1)) => (~brave(sK1) | tall(sK1)) [choice axiom]
42. ((~calm(susan) & ~strong(susan)) | ! [X0] : (brave(X0) & ~tall(X0))) & ((~brave(sK1) | tall(sK1)) | calm(susan) | strong(susan)) [skolemisation 40,41]
46. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : (kind(X1) & strong(X1))) & (? [X1] : (~kind(X1) | ~strong(X1)) | ! [X0] : (~humble(X0) | strong(X0))) [nnf transformation 24]
47. (? [X0] : (humble(X0) & ~strong(X0)) | ! [X1] : (kind(X1) & strong(X1))) & (? [X2] : (~kind(X2) | ~strong(X2)) | ! [X3] : (~humble(X3) | strong(X3))) [rectify 46]
48. ? [X0] : (humble(X0) & ~strong(X0)) => (humble(sK2) & ~strong(sK2)) [choice axiom]
49. ? [X2] : (~kind(X2) | ~strong(X2)) => (~kind(sK3) | ~strong(sK3)) [choice axiom]
50. ((humble(sK2) & ~strong(sK2)) | ! [X1] : (kind(X1) & strong(X1))) & ((~kind(sK3) | ~strong(sK3)) | ! [X3] : (~humble(X3) | strong(X3))) [skolemisation 47,49,48]
51. ! [X0] : (((humble(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | (~humble(X0) | ~patient(X0)))) [nnf transformation 9]
52. ! [X0] : (((humble(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | ~humble(X0) | ~patient(X0))) [flattening 51]
84. ~strong(susan) | brave(X0) [cnf transformation 42]
99. humble(sK2) | strong(X1) [cnf transformation 50]
101. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 52]
102. patient(X0) | patient(X0) [cnf transformation 52]
134. ~brave(john) [cnf transformation 23]
137. ~patient(X0) | ~humble(X0) [duplicate literal removal 101]
138. patient(X0) [duplicate literal removal 102]
174. 8 <=> ! [X0] : brave(X0) [avatar definition]
175. brave(X0) <- (8) [avatar component clause 174]
186. 11 <=> strong(susan) [avatar definition]
188. ~strong(susan) <- (~11) [avatar component clause 186]
189. 8 | ~11 [avatar split clause 84,186,174]
224. 19 <=> humble(sK2) [avatar definition]
226. humble(sK2) <- (19) [avatar component clause 224]
229. 20 <=> ! [X1] : strong(X1) [avatar definition]
230. strong(X1) <- (20) [avatar component clause 229]
231. 20 | 19 [avatar split clause 99,224,229]
250. ~humble(X0) [subsumption resolution 137,138]
348. $false <- (19) [subsumption resolution 226,250]
349. ~19 [avatar contradiction clause 348]
352. $false <- (~11, 20) [resolution 230,188]
353. 11 | ~20 [avatar contradiction clause 352]
354. $false <- (8) [resolution 175,134]
357. ~8 [avatar contradiction clause 354]
358. $false [avatar sat refutation 189,231,349,353,357]
% SZS output end Proof for 6053303912821664042359835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not funny then someone is not patient or not generous and vice versa.
If someone is both calm and not old then john is both not calm and not rich.
Everyone who is quiet or not wise is either wise or patient and vice versa.
If john is tall then someone is tall or not creative.
If someone is happy or wise then fred is not calm and vice versa.
Everyone who is not quiet is either not tall or not calm and vice versa.
Everyone who is patient is both not old and generous.
Everyone who is both happy and funny is either funny or not kind and vice versa.
Everyone who is either calm or not funny is either rich or curious and vice versa.
Everyone who is not kind is rich.
If someone is creative then someone is old or not calm and vice versa.
If lucy is either strong or not kind then someone is funny and vice versa.
Everyone who is generous or not tall is either quiet or wise and vice versa.
Everyone who is both not wise and wise is both curious and not quiet.
Everyone who is funny or kind is both curious and not strong and vice versa.
Someone is both not old and funny.
Someone is curious.
Someone is either not curious or not happy.
Mary is either not old or old.
Someone is not quiet.
Susan is rich or curious. | John is not curious. | contradiction | ((~funny(fred))<=>(?[X]:((~patient(X)|~generous(X)))))&
((?[X]:((calm(X)&~old(X))))=>((~calm(john)&~rich(john))))&
(![X]:((quiet(X)|~wise(X))<=>(wise(X)<~>patient(X))))&
((tall(john))=>(?[X]:((tall(X)|~creative(X)))))&
((?[X]:((happy(X)|wise(X))))<=>(~calm(fred)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:(patient(X)=>(~old(X)&generous(X))))&
(![X]:((happy(X)&funny(X))<=>(funny(X)<~>~kind(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(rich(X)<~>curious(X))))&
(![X]:(~kind(X)=>rich(X)))&
((?[X]:(creative(X)))<=>(?[X]:((old(X)|~calm(X)))))&
(((strong(lucy)<~>~kind(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((generous(X)|~tall(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((~wise(X)&wise(X))=>(curious(X)&~quiet(X))))&
(![X]:((funny(X)|kind(X))<=>(curious(X)&~strong(X))))&
(?[X]:((~old(X)&funny(X))))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)<~>~happy(X))))&
((~old(mary)<~>old(mary)))&
(?[X]:(~quiet(X)))&
((rich(susan)|curious(susan))) | ~curious(john) | [
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8237740528708141432579686
% SZS output start Proof for 8237740528708141432579686
8. ! [X0] : ((funny(X0) & happy(X0)) <=> (funny(X0) <~> ~kind(X0))) [input p7]
15. ! [X0] : ((kind(X0) | funny(X0)) <=> (~strong(X0) & curious(X0))) [input p14]
22. ~curious(john) [input hypothesis]
43. ! [X0] : (((funny(X0) & happy(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) & (((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (~funny(X0) | ~happy(X0)))) [nnf transformation 8]
44. ! [X0] : (((funny(X0) & happy(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) & (((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ~funny(X0) | ~happy(X0))) [flattening 43]
57. ! [X0] : (((kind(X0) | funny(X0)) | (strong(X0) | ~curious(X0))) & ((~strong(X0) & curious(X0)) | (~kind(X0) & ~funny(X0)))) [nnf transformation 15]
58. ! [X0] : ((kind(X0) | funny(X0) | strong(X0) | ~curious(X0)) & ((~strong(X0) & curious(X0)) | (~kind(X0) & ~funny(X0)))) [flattening 57]
95. funny(X0) | funny(X0) | kind(X0) [cnf transformation 44]
120. ~funny(X0) | curious(X0) [cnf transformation 58]
121. ~kind(X0) | curious(X0) [cnf transformation 58]
134. ~curious(john) [cnf transformation 22]
136. kind(X0) | funny(X0) [duplicate literal removal 95]
277. funny(X0) | curious(X0) [resolution 136,121]
278. curious(X0) [subsumption resolution 277,120]
280. $false [resolution 278,134]
% SZS output end Proof for 8237740528708141432579686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not strong or strong then lucy is both not brave and not tall and vice versa.
Everyone who is not patient or brave is quiet and vice versa.
Everyone who is both humble and rich is both not generous and not calm and vice versa.
Everyone who is either brave or not calm is brave.
Everyone who is either not humble or not calm is both wise and humble.
Everyone who is either not humble or not old is kind or calm and vice versa.
Everyone who is not rich or not happy is quiet and vice versa.
If someone is either not old or not brave then someone is both rich and not curious.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
Alice is tall or not creative.
Alice is not creative or not strong.
Someone is both not strong and tall.
Mary is either not patient or tall.
Paul is not creative or not wise.
John is not wise.
Someone is kind or not generous.
Someone is curious or not wise. | John is not creative. | entailment | (((~strong(mary)|strong(mary)))<=>((~brave(lucy)&~tall(lucy))))&
(![X]:((~patient(X)|brave(X))<=>quiet(X)))&
(![X]:((humble(X)&rich(X))<=>(~generous(X)&~calm(X))))&
(![X]:((brave(X)<~>~calm(X))=>brave(X)))&
(![X]:((~humble(X)<~>~calm(X))=>(wise(X)&humble(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(kind(X)|calm(X))))&
(![X]:((~rich(X)|~happy(X))<=>quiet(X)))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:((rich(X)&~curious(X)))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
((tall(alice)|~creative(alice)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((~strong(X)&tall(X))))&
((~patient(mary)<~>tall(mary)))&
((~creative(paul)|~wise(paul)))&
(~wise(john))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((curious(X)|~wise(X)))) | ~creative(john) | [
"p2",
"p4",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6393591728045442712585407
% SZS output start Proof for 6393591728045442712585407
3. ! [X0] : ((rich(X0) & humble(X0)) <=> (~calm(X0) & ~generous(X0))) [input p2]
5. ! [X0] : ((~humble(X0) <~> ~calm(X0)) => (humble(X0) & wise(X0))) [input p4]
10. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> (~creative(X0) <~> wise(X0))) [input p9]
22. ~wise(john) [input p21]
25. creative(john) [input hypothesis]
30. ! [X0] : ((humble(X0) & wise(X0)) | (~humble(X0) <=> ~calm(X0))) [ennf transformation 5]
40. ! [X0] : (((rich(X0) & humble(X0)) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((rich(X0) & humble(X0)) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~rich(X0) | ~humble(X0))) [flattening 40]
43. ! [X0] : ((humble(X0) & wise(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 30]
55. ! [X0] : (((~calm(X0) | ~rich(X0)) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (calm(X0) & rich(X0)))) [nnf transformation 10]
56. ! [X0] : ((~calm(X0) | ~rich(X0) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (calm(X0) & rich(X0)))) [flattening 55]
88. ~calm(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 41]
95. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 43]
112. ~creative(X0) | wise(X0) | rich(X0) [cnf transformation 56]
113. ~creative(X0) | wise(X0) | calm(X0) [cnf transformation 56]
140. ~wise(john) [cnf transformation 22]
143. creative(john) [cnf transformation 25]
144. ~calm(X0) | humble(X0) [duplicate literal removal 95]
367. wise(john) | rich(john) [resolution 112,143]
368. rich(john) [subsumption resolution 367,140]
370. wise(john) | calm(john) [resolution 113,143]
371. calm(john) [subsumption resolution 370,140]
372. ~rich(john) | ~humble(john) [resolution 371,88]
373. humble(john) [resolution 371,144]
374. ~humble(john) [subsumption resolution 372,368]
375. $false [subsumption resolution 373,374]
% SZS output end Proof for 6393591728045442712585407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or not wise then someone is both tall and not funny and vice versa.
Everyone who is not kind or wise is not patient or not strong and vice versa.
If someone is not old or tall then john is either strong or brave and vice versa.
Everyone who is either not funny or not calm is both old and not creative and vice versa.
Everyone who is not patient is either creative or old and vice versa.
If john is funny or not kind then john is either rich or not old and vice versa.
Everyone who is not creative is both quiet and funny.
If lucy is rich or wise then someone is not rich.
If john is either not funny or tall then susan is funny and vice versa.
If fred is strong then john is either kind or wise.
If fred is not tall or not patient then alice is not kind.
Everyone who is funny or happy is not curious or happy and vice versa.
Everyone who is both not curious and not rich is strong.
If someone is wise then john is not patient or not kind and vice versa.
Everyone who is either quiet or not strong is either happy or not funny and vice versa.
Everyone who is not brave is both not happy and not kind.
Someone is not tall or rich.
John is either tall or rich.
Alice is either curious or patient.
Alice is either creative or strong.
John is calm.
John is either funny or not funny.
Someone is both brave and not kind. | Susan is curious. | neutral | ((?[X]:((patient(X)<~>~wise(X))))<=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:((~kind(X)|wise(X))<=>(~patient(X)|~strong(X))))&
((?[X]:((~old(X)|tall(X))))<=>((strong(john)<~>brave(john))))&
(![X]:((~funny(X)<~>~calm(X))<=>(old(X)&~creative(X))))&
(![X]:(~patient(X)<=>(creative(X)<~>old(X))))&
(((funny(john)|~kind(john)))<=>((rich(john)<~>~old(john))))&
(![X]:(~creative(X)=>(quiet(X)&funny(X))))&
(((rich(lucy)|wise(lucy)))=>(?[X]:(~rich(X))))&
(((~funny(john)<~>tall(john)))<=>(funny(susan)))&
((strong(fred))=>((kind(john)<~>wise(john))))&
(((~tall(fred)|~patient(fred)))=>(~kind(alice)))&
(![X]:((funny(X)|happy(X))<=>(~curious(X)|happy(X))))&
(![X]:((~curious(X)&~rich(X))=>strong(X)))&
((?[X]:(wise(X)))<=>((~patient(john)|~kind(john))))&
(![X]:((quiet(X)<~>~strong(X))<=>(happy(X)<~>~funny(X))))&
(![X]:(~brave(X)=>(~happy(X)&~kind(X))))&
(?[X]:((~tall(X)|rich(X))))&
((tall(john)<~>rich(john)))&
((curious(alice)<~>patient(alice)))&
((creative(alice)<~>strong(alice)))&
(calm(john))&
((funny(john)<~>~funny(john)))&
(?[X]:((brave(X)&~kind(X)))) | curious(susan) | [] | null | 0 |
Everyone who is funny is calm or not kind and vice versa.
Everyone who is not old or not humble is both old and not patient and vice versa.
Everyone who is humble is curious or not curious and vice versa.
Everyone who is quiet or not funny is both calm and not tall.
Everyone who is humble is not brave and vice versa.
Everyone who is both not happy and strong is quiet.
Everyone who is either happy or generous is strong.
If someone is both not happy and not brave then fred is both not happy and rich and vice versa.
Everyone who is either not patient or not calm is both not kind and wise.
If someone is both humble and strong then alice is either old or not funny and vice versa.
Everyone who is either funny or not generous is both brave and not brave and vice versa.
Everyone who is not kind or happy is both not tall and happy and vice versa.
If someone is rich then susan is either patient or brave and vice versa.
Everyone who is not strong or happy is old and vice versa.
If someone is not brave then someone is happy and vice versa.
If mary is not rich or generous then someone is both creative and not old and vice versa.
Someone is either strong or curious.
Susan is not strong.
Someone is either patient or wise.
Someone is both wise and quiet.
Someone is not funny or patient.
Susan is either calm or not curious.
Someone is either kind or not happy.
Someone is strong or wise. | Mary is not old. | contradiction | (![X]:(funny(X)<=>(calm(X)|~kind(X))))&
(![X]:((~old(X)|~humble(X))<=>(old(X)&~patient(X))))&
(![X]:(humble(X)<=>(curious(X)|~curious(X))))&
(![X]:((quiet(X)|~funny(X))=>(calm(X)&~tall(X))))&
(![X]:(humble(X)<=>~brave(X)))&
(![X]:((~happy(X)&strong(X))=>quiet(X)))&
(![X]:((happy(X)<~>generous(X))=>strong(X)))&
((?[X]:((~happy(X)&~brave(X))))<=>((~happy(fred)&rich(fred))))&
(![X]:((~patient(X)<~>~calm(X))=>(~kind(X)&wise(X))))&
((?[X]:((humble(X)&strong(X))))<=>((old(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>~generous(X))<=>(brave(X)&~brave(X))))&
(![X]:((~kind(X)|happy(X))<=>(~tall(X)&happy(X))))&
((?[X]:(rich(X)))<=>((patient(susan)<~>brave(susan))))&
(![X]:((~strong(X)|happy(X))<=>old(X)))&
((?[X]:(~brave(X)))<=>(?[X]:(happy(X))))&
(((~rich(mary)|generous(mary)))<=>(?[X]:((creative(X)&~old(X)))))&
(?[X]:((strong(X)<~>curious(X))))&
(~strong(susan))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:((wise(X)&quiet(X))))&
(?[X]:((~funny(X)|patient(X))))&
((calm(susan)<~>~curious(susan)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((strong(X)|wise(X)))) | ~old(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1159574384354866636859491
% SZS output start Proof for 1159574384354866636859491
2. ! [X0] : ((~humble(X0) | ~old(X0)) <=> (~patient(X0) & old(X0))) [input p1]
25. ~old(mary) [input hypothesis]
34. ! [X0] : (((~humble(X0) | ~old(X0)) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | (humble(X0) & old(X0)))) [nnf transformation 2]
35. ! [X0] : ((~humble(X0) | ~old(X0) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | (humble(X0) & old(X0)))) [flattening 34]
89. old(X0) | old(X0) [cnf transformation 35]
158. ~old(mary) [cnf transformation 25]
159. old(X0) [duplicate literal removal 89]
248. $false [subsumption resolution 158,159]
% SZS output end Proof for 1159574384354866636859491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not creative and not tall then paul is not kind or kind and vice versa. If someone is either rich or not creative then fred is not tall or not happy and vice versa. If someone is brave then someone is calm and vice versa. If alice is both not wise and not quiet then someone is both calm and not old and vice versa. Everyone who is wise or not patient is either not happy or rich and vice versa. Everyone who is not kind is either wise or creative. Everyone who is calm is not old and vice versa. Everyone who is both wise and not humble is not quiet or not kind. Everyone who is quiet or humble is not funny or not old. If paul is not strong then someone is either not happy or old. If susan is not brave or wise then someone is not calm and vice versa. Everyone who is both rich and not humble is not funny. If susan is either kind or wise then someone is not curious. Everyone who is not rich is not old or curious and vice versa. Everyone who is not wise or creative is both not curious and quiet. If lucy is kind or not kind then mary is not funny and vice versa. Fred is kind or creative. Fred is both not quiet and tall. Susan is both not curious and not happy. Susan is creative or rich. Someone is either happy or funny. Paul is not rich or not funny. John is both not tall and not creative. | Fred is creative. | contradiction | (((~creative(lucy)&~tall(lucy)))<=>((~kind(paul)|kind(paul))))&
((?[X]:((rich(X)<~>~creative(X))))<=>((~tall(fred)|~happy(fred))))&
((?[X]:(brave(X)))<=>(?[X]:(calm(X))))&
(((~wise(alice)&~quiet(alice)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((wise(X)|~patient(X))<=>(~happy(X)<~>rich(X))))&
(![X]:(~kind(X)=>(wise(X)<~>creative(X))))&
(![X]:(calm(X)<=>~old(X)))&
(![X]:((wise(X)&~humble(X))=>(~quiet(X)|~kind(X))))&
(![X]:((quiet(X)|humble(X))=>(~funny(X)|~old(X))))&
((~strong(paul))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~brave(susan)|wise(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((rich(X)&~humble(X))=>~funny(X)))&
(((kind(susan)<~>wise(susan)))=>(?[X]:(~curious(X))))&
(![X]:(~rich(X)<=>(~old(X)|curious(X))))&
(![X]:((~wise(X)|creative(X))=>(~curious(X)&quiet(X))))&
(((kind(lucy)|~kind(lucy)))<=>(~funny(mary)))&
((kind(fred)|creative(fred)))&
((~quiet(fred)&tall(fred)))&
((~curious(susan)&~happy(susan)))&
((creative(susan)|rich(susan)))&
(?[X]:((happy(X)<~>funny(X))))&
((~rich(paul)|~funny(paul)))&
((~tall(john)&~creative(john))) | creative(fred) | [
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 613074927454404689317365
% SZS output start Proof for 613074927454404689317365
15. ! [X0] : ((creative(X0) | ~wise(X0)) => (quiet(X0) & ~curious(X0))) [input p14]
18. tall(fred) & ~quiet(fred) [input p17]
24. creative(fred) [input hypothesis]
35. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 15]
114. ~creative(X0) | quiet(X0) [cnf transformation 35]
119. ~quiet(fred) [cnf transformation 18]
129. creative(fred) [cnf transformation 24]
256. 28 <=> creative(fred) [avatar definition]
258. creative(fred) <- (28) [avatar component clause 256]
289. 28 [avatar split clause 129,256]
294. quiet(fred) <- (28) [resolution 114,258]
296. $false <- (28) [subsumption resolution 294,119]
297. ~28 [avatar contradiction clause 296]
298. $false [avatar sat refutation 289,297]
% SZS output end Proof for 613074927454404689317365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not humble and brave then lucy is both quiet and rich and vice versa. If someone is both humble and old then lucy is tall or old and vice versa. If john is either wise or curious then alice is not funny or curious. If someone is not happy or happy then someone is both not kind and rich and vice versa. If someone is either kind or humble then someone is not quiet and vice versa. If susan is both brave and generous then someone is both not old and not patient. Everyone who is not calm or rich is happy or not quiet and vice versa. Everyone who is brave or not calm is either not happy or generous and vice versa. Everyone who is humble or not brave is quiet and vice versa. Everyone who is either creative or wise is either not tall or tall. Everyone who is not happy or not rich is not strong or strong and vice versa. Everyone who is both not tall and happy is not tall or old and vice versa. Everyone who is either not calm or happy is rich or strong and vice versa. Everyone who is brave or strong is tall. If someone is tall then someone is either not creative or curious and vice versa. If alice is both not calm and kind then someone is either not funny or not patient. Paul is not tall. Someone is both not old and creative. Lucy is not generous or funny. Someone is not quiet or happy. Someone is both patient and not creative. Susan is funny or not brave. John is not strong or generous. Someone is both not humble and creative. | Paul is generous. | entailment | (((~humble(paul)&brave(paul)))<=>((quiet(lucy)&rich(lucy))))&
((?[X]:((humble(X)&old(X))))<=>((tall(lucy)|old(lucy))))&
(((wise(john)<~>curious(john)))=>((~funny(alice)|curious(alice))))&
((?[X]:((~happy(X)|happy(X))))<=>(?[X]:((~kind(X)&rich(X)))))&
((?[X]:((kind(X)<~>humble(X))))<=>(?[X]:(~quiet(X))))&
(((brave(susan)&generous(susan)))=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:((~calm(X)|rich(X))<=>(happy(X)|~quiet(X))))&
(![X]:((brave(X)|~calm(X))<=>(~happy(X)<~>generous(X))))&
(![X]:((humble(X)|~brave(X))<=>quiet(X)))&
(![X]:((creative(X)<~>wise(X))=>(~tall(X)<~>tall(X))))&
(![X]:((~happy(X)|~rich(X))<=>(~strong(X)|strong(X))))&
(![X]:((~tall(X)&happy(X))<=>(~tall(X)|old(X))))&
(![X]:((~calm(X)<~>happy(X))<=>(rich(X)|strong(X))))&
(![X]:((brave(X)|strong(X))=>tall(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(((~calm(alice)&kind(alice)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
(~tall(paul))&
(?[X]:((~old(X)&creative(X))))&
((~generous(lucy)|funny(lucy)))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:((patient(X)&~creative(X))))&
((funny(susan)|~brave(susan)))&
((~strong(john)|generous(john)))&
(?[X]:((~humble(X)&creative(X)))) | generous(paul) | [
"p6",
"p7",
"p10",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 889904213760256739283980
% SZS output start Proof for 889904213760256739283980
7. ! [X0] : ((rich(X0) | ~calm(X0)) <=> (~quiet(X0) | happy(X0))) [input p6]
8. ! [X0] : ((~calm(X0) | brave(X0)) <=> (~happy(X0) <~> generous(X0))) [input p7]
11. ! [X0] : ((~rich(X0) | ~happy(X0)) <=> (strong(X0) | ~strong(X0))) [input p10]
12. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (old(X0) | ~tall(X0))) [input p11]
13. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> (strong(X0) | rich(X0))) [input p12]
17. ~tall(paul) [input p16]
25. ~generous(paul) [input hypothesis]
57. ! [X0] : (((rich(X0) | ~calm(X0)) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | (~rich(X0) & calm(X0)))) [nnf transformation 7]
58. ! [X0] : ((rich(X0) | ~calm(X0) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | (~rich(X0) & calm(X0)))) [flattening 57]
59. ! [X0] : (((~calm(X0) | brave(X0)) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (calm(X0) & ~brave(X0)))) [nnf transformation 8]
60. ! [X0] : ((~calm(X0) | brave(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (calm(X0) & ~brave(X0)))) [flattening 59]
64. ! [X0] : (((~rich(X0) | ~happy(X0)) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | (rich(X0) & happy(X0)))) [nnf transformation 11]
65. ! [X0] : ((~rich(X0) | ~happy(X0) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | (rich(X0) & happy(X0)))) [flattening 64]
66. ! [X0] : (((happy(X0) & ~tall(X0)) | (~old(X0) & tall(X0))) & ((old(X0) | ~tall(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 12]
67. ! [X0] : (((happy(X0) & ~tall(X0)) | (~old(X0) & tall(X0))) & (old(X0) | ~tall(X0) | ~happy(X0) | tall(X0))) [flattening 66]
68. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~strong(X0) & ~rich(X0))) & ((strong(X0) | rich(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 13]
69. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~strong(X0) & ~rich(X0))) & (strong(X0) | rich(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [flattening 68]
110. ~calm(X0) | rich(X0) | ~happy(X0) [cnf transformation 58]
113. ~happy(X0) | generous(X0) | calm(X0) [cnf transformation 60]
127. ~rich(X0) | ~happy(X0) | strong(X0) [cnf transformation 65]
128. ~strong(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 65]
132. happy(X0) | tall(X0) [cnf transformation 67]
136. happy(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 69]
148. ~tall(paul) [cnf transformation 17]
159. ~generous(paul) [cnf transformation 25]
283. ~happy(X0) | ~rich(X0) [subsumption resolution 127,128]
284. ~calm(X0) | ~rich(X0) [subsumption resolution 136,283]
442. 52 <=> calm(paul) [avatar definition]
444. calm(paul) <- (52) [avatar component clause 442]
446. 53 <=> happy(paul) [avatar definition]
447. ~happy(paul) <- (~53) [avatar component clause 446]
448. happy(paul) <- (53) [avatar component clause 446]
467. generous(paul) | calm(paul) <- (53) [resolution 448,113]
470. calm(paul) <- (53) [subsumption resolution 467,159]
471. 52 | ~53 [avatar split clause 470,446,442]
472. tall(paul) <- (~53) [resolution 447,132]
473. $false <- (~53) [subsumption resolution 472,148]
474. 53 [avatar contradiction clause 473]
478. rich(paul) | ~happy(paul) <- (52) [resolution 444,110]
479. ~rich(paul) <- (52) [resolution 444,284]
485. 56 <=> rich(paul) [avatar definition]
489. rich(paul) <- (52, 53) [subsumption resolution 478,448]
490. 56 | ~52 | ~53 [avatar split clause 489,446,442,485]
491. ~56 | ~52 [avatar split clause 479,442,485]
492. $false [avatar sat refutation 471,474,490,491]
% SZS output end Proof for 889904213760256739283980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or calm is either not wise or brave.
Everyone who is both not quiet and funny is curious.
Everyone who is strong is humble and vice versa.
If alice is quiet or generous then lucy is both rich and wise.
Everyone who is both not kind and happy is both not old and not brave and vice versa.
If paul is not tall then fred is either kind or not calm.
Everyone who is either not humble or not happy is rich or not rich.
Everyone who is strong is both not old and not funny and vice versa.
If someone is creative or quiet then someone is old or funny.
Everyone who is either not patient or not tall is not brave and vice versa.
Everyone who is quiet is either humble or calm.
Everyone who is not strong or generous is not tall.
If someone is either not humble or not kind then someone is not brave.
Everyone who is brave or not humble is both quiet and strong and vice versa.
Everyone who is both tall and calm is kind or tall.
Everyone who is patient or creative is not strong.
Someone is not rich.
Someone is either not calm or funny.
Fred is both not kind and not curious.
Susan is not calm or not curious. | Susan is not calm. | neutral | (![X]:((~happy(X)|calm(X))=>(~wise(X)<~>brave(X))))&
(![X]:((~quiet(X)&funny(X))=>curious(X)))&
(![X]:(strong(X)<=>humble(X)))&
(((quiet(alice)|generous(alice)))=>((rich(lucy)&wise(lucy))))&
(![X]:((~kind(X)&happy(X))<=>(~old(X)&~brave(X))))&
((~tall(paul))=>((kind(fred)<~>~calm(fred))))&
(![X]:((~humble(X)<~>~happy(X))=>(rich(X)|~rich(X))))&
(![X]:(strong(X)<=>(~old(X)&~funny(X))))&
((?[X]:((creative(X)|quiet(X))))=>(?[X]:((old(X)|funny(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>~brave(X)))&
(![X]:(quiet(X)=>(humble(X)<~>calm(X))))&
(![X]:((~strong(X)|generous(X))=>~tall(X)))&
((?[X]:((~humble(X)<~>~kind(X))))=>(?[X]:(~brave(X))))&
(![X]:((brave(X)|~humble(X))<=>(quiet(X)&strong(X))))&
(![X]:((tall(X)&calm(X))=>(kind(X)|tall(X))))&
(![X]:((patient(X)|creative(X))=>~strong(X)))&
(?[X]:(~rich(X)))&
(?[X]:((~calm(X)<~>funny(X))))&
((~kind(fred)&~curious(fred)))&
((~calm(susan)|~curious(susan))) | ~calm(susan) | [] | null | 0 |
Everyone who is either not tall or not wise is not humble or not brave and vice versa.
If mary is both not patient and not funny then paul is old.
If someone is funny then john is not brave or not generous and vice versa.
If someone is both not curious and patient then paul is either not generous or not patient.
If someone is either not strong or humble then someone is both not creative and kind.
If someone is not happy then someone is not kind and vice versa.
Everyone who is not wise or not calm is rich or not humble and vice versa.
Everyone who is both rich and not old is either not strong or quiet.
Everyone who is both patient and not quiet is not old and vice versa.
If someone is patient or humble then lucy is either not rich or humble.
If someone is not brave or generous then mary is both not kind and happy.
Everyone who is both kind and not kind is not calm or not generous and vice versa.
If someone is brave or old then someone is calm or not humble and vice versa.
Everyone who is either not quiet or not kind is quiet and vice versa.
If mary is both not humble and curious then someone is creative or not generous and vice versa.
Everyone who is humble is brave or not humble.
Someone is not kind.
John is either not kind or brave.
Alice is creative.
Alice is either calm or not tall.
Someone is tall or calm.
Someone is creative. | Alice is strong. | neutral | (![X]:((~tall(X)<~>~wise(X))<=>(~humble(X)|~brave(X))))&
(((~patient(mary)&~funny(mary)))=>(old(paul)))&
((?[X]:(funny(X)))<=>((~brave(john)|~generous(john))))&
((?[X]:((~curious(X)&patient(X))))=>((~generous(paul)<~>~patient(paul))))&
((?[X]:((~strong(X)<~>humble(X))))=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)|~calm(X))<=>(rich(X)|~humble(X))))&
(![X]:((rich(X)&~old(X))=>(~strong(X)<~>quiet(X))))&
(![X]:((patient(X)&~quiet(X))<=>~old(X)))&
((?[X]:((patient(X)|humble(X))))=>((~rich(lucy)<~>humble(lucy))))&
((?[X]:((~brave(X)|generous(X))))=>((~kind(mary)&happy(mary))))&
(![X]:((kind(X)&~kind(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((brave(X)|old(X))))<=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>quiet(X)))&
(((~humble(mary)&curious(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:(humble(X)=>(brave(X)|~humble(X))))&
(?[X]:(~kind(X)))&
((~kind(john)<~>brave(john)))&
(creative(alice))&
((calm(alice)<~>~tall(alice)))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:(creative(X))) | strong(alice) | [] | null | 0 |
If someone is either quiet or not creative then john is not brave. Everyone who is brave or not kind is both old and not creative. If someone is either not creative or humble then mary is generous and vice versa. If fred is both not strong and brave then someone is not rich and vice versa. Everyone who is either quiet or kind is both patient and curious. If fred is both not brave and generous then mary is either funny or old. Everyone who is not happy or not wise is wise and vice versa. If fred is not wise or not tall then someone is not patient or quiet and vice versa. If lucy is strong or not happy then fred is both old and not curious and vice versa. Everyone who is not calm is both wise and not rich. Everyone who is either not quiet or funny is patient. If mary is both not calm and not creative then alice is tall or not patient and vice versa. If someone is either not strong or not rich then mary is both not generous and not tall and vice versa. If someone is either brave or strong then someone is both not rich and not curious. If susan is either old or not funny then someone is rich or not kind and vice versa. If someone is both funny and strong then someone is old and vice versa. Someone is kind or calm. Someone is not rich. Alice is quiet. Someone is either funny or not old. Fred is not kind. Someone is both not calm and not happy. Someone is either quiet or not humble. | Fred is wise. | entailment | ((?[X]:((quiet(X)<~>~creative(X))))=>(~brave(john)))&
(![X]:((brave(X)|~kind(X))=>(old(X)&~creative(X))))&
((?[X]:((~creative(X)<~>humble(X))))<=>(generous(mary)))&
(((~strong(fred)&brave(fred)))<=>(?[X]:(~rich(X))))&
(![X]:((quiet(X)<~>kind(X))=>(patient(X)&curious(X))))&
(((~brave(fred)&generous(fred)))=>((funny(mary)<~>old(mary))))&
(![X]:((~happy(X)|~wise(X))<=>wise(X)))&
(((~wise(fred)|~tall(fred)))<=>(?[X]:((~patient(X)|quiet(X)))))&
(((strong(lucy)|~happy(lucy)))<=>((old(fred)&~curious(fred))))&
(![X]:(~calm(X)=>(wise(X)&~rich(X))))&
(![X]:((~quiet(X)<~>funny(X))=>patient(X)))&
(((~calm(mary)&~creative(mary)))<=>((tall(alice)|~patient(alice))))&
((?[X]:((~strong(X)<~>~rich(X))))<=>((~generous(mary)&~tall(mary))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~rich(X)&~curious(X)))))&
(((old(susan)<~>~funny(susan)))<=>(?[X]:((rich(X)|~kind(X)))))&
((?[X]:((funny(X)&strong(X))))<=>(?[X]:(old(X))))&
(?[X]:((kind(X)|calm(X))))&
(?[X]:(~rich(X)))&
(quiet(alice))&
(?[X]:((funny(X)<~>~old(X))))&
(~kind(fred))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((quiet(X)<~>~humble(X)))) | wise(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 940562702219537558496034
% SZS output start Proof for 940562702219537558496034
7. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> wise(X0)) [input p6]
24. ~wise(fred) [input hypothesis]
47. ! [X0] : (((~wise(X0) | ~happy(X0)) | ~wise(X0)) & (wise(X0) | (wise(X0) & happy(X0)))) [nnf transformation 7]
48. ! [X0] : ((~wise(X0) | ~happy(X0) | ~wise(X0)) & (wise(X0) | (wise(X0) & happy(X0)))) [flattening 47]
109. wise(X0) | wise(X0) [cnf transformation 48]
158. ~wise(fred) [cnf transformation 24]
159. wise(X0) [duplicate literal removal 109]
412. $false [subsumption resolution 158,159]
% SZS output end Proof for 940562702219537558496034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is creative. Everyone who is not rich is not calm or not patient and vice versa. Everyone who is not curious is either kind or not creative and vice versa. If john is either not generous or not curious then someone is either generous or rich and vice versa. If alice is both calm and not quiet then alice is both not kind and not rich. Everyone who is both happy and humble is not happy or brave and vice versa. Everyone who is not kind or happy is not funny and vice versa. If mary is both not rich and not creative then someone is rich. Everyone who is tall is not curious or brave and vice versa. Everyone who is either rich or not quiet is both patient and not calm. Everyone who is both curious and quiet is curious or not calm and vice versa. If paul is creative or not quiet then someone is wise or calm and vice versa. If someone is both not brave and not patient then john is both generous and not generous. Everyone who is not funny is generous or not funny. Everyone who is not patient or kind is both not strong and not humble and vice versa. Everyone who is strong is funny or wise. Alice is not generous. Someone is either happy or not kind. Someone is either not creative or quiet. Fred is not wise. Someone is brave or not kind. Someone is old or brave. Alice is rich or not rich. Susan is both creative and happy. | Susan is humble. | neutral | (![X]:(kind(X)=>creative(X)))&
(![X]:(~rich(X)<=>(~calm(X)|~patient(X))))&
(![X]:(~curious(X)<=>(kind(X)<~>~creative(X))))&
(((~generous(john)<~>~curious(john)))<=>(?[X]:((generous(X)<~>rich(X)))))&
(((calm(alice)&~quiet(alice)))=>((~kind(alice)&~rich(alice))))&
(![X]:((happy(X)&humble(X))<=>(~happy(X)|brave(X))))&
(![X]:((~kind(X)|happy(X))<=>~funny(X)))&
(((~rich(mary)&~creative(mary)))=>(?[X]:(rich(X))))&
(![X]:(tall(X)<=>(~curious(X)|brave(X))))&
(![X]:((rich(X)<~>~quiet(X))=>(patient(X)&~calm(X))))&
(![X]:((curious(X)&quiet(X))<=>(curious(X)|~calm(X))))&
(((creative(paul)|~quiet(paul)))<=>(?[X]:((wise(X)|calm(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((generous(john)&~generous(john))))&
(![X]:(~funny(X)=>(generous(X)|~funny(X))))&
(![X]:((~patient(X)|kind(X))<=>(~strong(X)&~humble(X))))&
(![X]:(strong(X)=>(funny(X)|wise(X))))&
(~generous(alice))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:((~creative(X)<~>quiet(X))))&
(~wise(fred))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((old(X)|brave(X))))&
((rich(alice)|~rich(alice)))&
((creative(susan)&happy(susan))) | humble(susan) | [] | null | 0 |
Everyone who is either humble or rich is not strong.
If john is not old then someone is both not rich and curious and vice versa.
If susan is old then someone is not strong or not patient and vice versa.
If someone is either not patient or not wise then someone is not kind or not wise.
Everyone who is either old or brave is both happy and not brave and vice versa.
Everyone who is either kind or calm is both not tall and not humble and vice versa.
Everyone who is not humble is either not kind or kind.
If mary is either rich or tall then someone is either not old or not calm and vice versa.
Everyone who is both not humble and not creative is either not curious or not patient.
Everyone who is old or rich is not rich or strong and vice versa.
If alice is both old and not generous then someone is both old and not creative.
Everyone who is not quiet or patient is not patient.
Everyone who is funny is wise.
If someone is either not patient or wise then someone is both not quiet and not old.
If mary is both not curious and tall then someone is old or wise and vice versa.
Everyone who is not curious is funny and vice versa.
Mary is not brave or creative.
Someone is both not strong and not curious.
Someone is either funny or calm.
Someone is not creative.
Fred is either calm or not funny.
Someone is creative or calm.
Lucy is wise.
Someone is either not happy or humble. | Mary is funny. | entailment | (![X]:((humble(X)<~>rich(X))=>~strong(X)))&
((~old(john))<=>(?[X]:((~rich(X)&curious(X)))))&
((old(susan))<=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~patient(X)<~>~wise(X))))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((old(X)<~>brave(X))<=>(happy(X)&~brave(X))))&
(![X]:((kind(X)<~>calm(X))<=>(~tall(X)&~humble(X))))&
(![X]:(~humble(X)=>(~kind(X)<~>kind(X))))&
(((rich(mary)<~>tall(mary)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((~humble(X)&~creative(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((old(X)|rich(X))<=>(~rich(X)|strong(X))))&
(((old(alice)&~generous(alice)))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~quiet(X)|patient(X))=>~patient(X)))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~curious(mary)&tall(mary)))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
((~brave(mary)|creative(mary)))&
(?[X]:((~strong(X)&~curious(X))))&
(?[X]:((funny(X)<~>calm(X))))&
(?[X]:(~creative(X)))&
((calm(fred)<~>~funny(fred)))&
(?[X]:((creative(X)|calm(X))))&
(wise(lucy))&
(?[X]:((~happy(X)<~>humble(X)))) | funny(mary) | [
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2189491437979988579693086
% SZS output start Proof for 2189491437979988579693086
15. (tall(mary) & ~curious(mary)) <=> ? [X0] : (wise(X0) | old(X0)) [input p14]
16. ! [X0] : (~curious(X0) <=> funny(X0)) [input p15]
23. wise(lucy) [input p22]
25. ~funny(mary) [input hypothesis]
66. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | (~tall(mary) | curious(mary))) [nnf transformation 15]
67. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | ~tall(mary) | curious(mary)) [flattening 66]
68. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X1] : (wise(X1) | old(X1)) | ~tall(mary) | curious(mary)) [rectify 67]
69. ? [X1] : (wise(X1) | old(X1)) => (wise(sK5) | old(sK5)) [choice axiom]
70. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & ((wise(sK5) | old(sK5)) | ~tall(mary) | curious(mary)) [skolemisation 68,69]
71. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 16]
132. ~curious(mary) | ~wise(X0) [cnf transformation 70]
135. funny(X0) | curious(X0) [cnf transformation 71]
146. wise(lucy) [cnf transformation 23]
149. ~funny(mary) [cnf transformation 25]
256. 23 <=> ! [X0] : ~wise(X0) [avatar definition]
257. ~wise(X0) <- (23) [avatar component clause 256]
264. 25 <=> curious(mary) [avatar definition]
266. ~curious(mary) <- (~25) [avatar component clause 264]
267. 23 | ~25 [avatar split clause 132,264,256]
329. $false <- (23) [resolution 257,146]
330. ~23 [avatar contradiction clause 329]
332. curious(mary) [resolution 135,149]
335. $false <- (~25) [subsumption resolution 332,266]
336. 25 [avatar contradiction clause 335]
337. $false [avatar sat refutation 267,330,336]
% SZS output end Proof for 2189491437979988579693086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not kind or generous then someone is not happy or old. If someone is both not humble and funny then paul is either not calm or not wise. Everyone who is brave or rich is not humble and vice versa. If someone is rich or not calm then someone is not patient or not generous. Everyone who is both tall and not rich is not creative or not funny and vice versa. Everyone who is humble or not generous is both rich and not kind and vice versa. If paul is kind or not quiet then paul is quiet and vice versa. If someone is brave or quiet then alice is not kind or curious and vice versa. If someone is either not kind or strong then someone is not kind. If mary is generous then alice is either not brave or tall. If paul is generous or not generous then fred is both not patient and not old. Everyone who is both humble and wise is curious or funny and vice versa. If someone is tall or strong then someone is not creative and vice versa. Everyone who is not strong is either not creative or not curious. Everyone who is both strong and tall is either not rich or not wise. Everyone who is not strong or kind is kind or strong. Someone is not happy. Paul is brave or patient. Someone is either strong or old. Someone is either curious or not old. Someone is either quiet or old. | Paul is not calm. | neutral | (((~kind(lucy)<~>generous(lucy)))=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:((~humble(X)&funny(X))))=>((~calm(paul)<~>~wise(paul))))&
(![X]:((brave(X)|rich(X))<=>~humble(X)))&
((?[X]:((rich(X)|~calm(X))))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((tall(X)&~rich(X))<=>(~creative(X)|~funny(X))))&
(![X]:((humble(X)|~generous(X))<=>(rich(X)&~kind(X))))&
(((kind(paul)|~quiet(paul)))<=>(quiet(paul)))&
((?[X]:((brave(X)|quiet(X))))<=>((~kind(alice)|curious(alice))))&
((?[X]:((~kind(X)<~>strong(X))))=>(?[X]:(~kind(X))))&
((generous(mary))=>((~brave(alice)<~>tall(alice))))&
(((generous(paul)|~generous(paul)))=>((~patient(fred)&~old(fred))))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|funny(X))))&
((?[X]:((tall(X)|strong(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(~creative(X)<~>~curious(X))))&
(![X]:((strong(X)&tall(X))=>(~rich(X)<~>~wise(X))))&
(![X]:((~strong(X)|kind(X))=>(kind(X)|strong(X))))&
(?[X]:(~happy(X)))&
((brave(paul)|patient(paul)))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((quiet(X)<~>old(X)))) | ~calm(paul) | [] | null | 0 |
If alice is humble or not humble then someone is strong or humble.
If paul is either patient or not rich then paul is both calm and funny.
Everyone who is either brave or quiet is either not tall or not happy.
If john is both not kind and not strong then someone is strong or brave and vice versa.
Everyone who is generous is either kind or not quiet.
Everyone who is both happy and tall is both kind and generous.
If someone is either calm or tall then mary is both calm and quiet and vice versa.
If someone is both calm and not funny then alice is generous or patient.
If someone is not humble then lucy is both rich and not wise.
Everyone who is funny or not calm is not creative or creative.
If susan is not funny or not old then someone is not wise or happy and vice versa.
Everyone who is both not happy and wise is not humble or creative.
Everyone who is rich is both not humble and not tall.
Everyone who is either not quiet or not curious is not funny.
If paul is both curious and brave then someone is not tall or happy and vice versa.
Everyone who is quiet is both not generous and not calm and vice versa.
Susan is either humble or not funny.
Fred is either calm or patient.
Someone is both wise and not humble.
Lucy is both kind and not generous.
Someone is not patient or calm.
Someone is not creative.
Fred is not wise.
Someone is calm or strong. | Lucy is calm. | contradiction | (((humble(alice)|~humble(alice)))=>(?[X]:((strong(X)|humble(X)))))&
(((patient(paul)<~>~rich(paul)))=>((calm(paul)&funny(paul))))&
(![X]:((brave(X)<~>quiet(X))=>(~tall(X)<~>~happy(X))))&
(((~kind(john)&~strong(john)))<=>(?[X]:((strong(X)|brave(X)))))&
(![X]:(generous(X)=>(kind(X)<~>~quiet(X))))&
(![X]:((happy(X)&tall(X))=>(kind(X)&generous(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>((calm(mary)&quiet(mary))))&
((?[X]:((calm(X)&~funny(X))))=>((generous(alice)|patient(alice))))&
((?[X]:(~humble(X)))=>((rich(lucy)&~wise(lucy))))&
(![X]:((funny(X)|~calm(X))=>(~creative(X)|creative(X))))&
(((~funny(susan)|~old(susan)))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~happy(X)&wise(X))=>(~humble(X)|creative(X))))&
(![X]:(rich(X)=>(~humble(X)&~tall(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>~funny(X)))&
(((curious(paul)&brave(paul)))<=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:(quiet(X)<=>(~generous(X)&~calm(X))))&
((humble(susan)<~>~funny(susan)))&
((calm(fred)<~>patient(fred)))&
(?[X]:((wise(X)&~humble(X))))&
((kind(lucy)&~generous(lucy)))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:(~creative(X)))&
(~wise(fred))&
(?[X]:((calm(X)|strong(X)))) | calm(lucy) | [
"p6",
"p8",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3145382530988915991446620
% SZS output start Proof for 3145382530988915991446620
7. ? [X0] : (calm(X0) <~> tall(X0)) <=> (quiet(mary) & calm(mary)) [input p6]
9. ? [X0] : ~humble(X0) => (~wise(lucy) & rich(lucy)) [input p8]
13. ! [X0] : (rich(X0) => (~tall(X0) & ~humble(X0))) [input p12]
16. ! [X0] : (quiet(X0) <=> (~calm(X0) & ~generous(X0))) [input p15]
19. ? [X0] : (~humble(X0) & wise(X0)) [input p18]
25. calm(lucy) [input hypothesis]
34. (~wise(lucy) & rich(lucy)) | ! [X0] : humble(X0) [ennf transformation 9]
39. ! [X0] : ((~tall(X0) & ~humble(X0)) | ~rich(X0)) [ennf transformation 13]
51. (? [X0] : ((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~quiet(mary) | ~calm(mary))) & ((quiet(mary) & calm(mary)) | ! [X0] : ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0)))) [nnf transformation 7]
52. (? [X0] : ((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | ~quiet(mary) | ~calm(mary)) & ((quiet(mary) & calm(mary)) | ! [X0] : ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0)))) [flattening 51]
53. (? [X0] : ((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | ~quiet(mary) | ~calm(mary)) & ((quiet(mary) & calm(mary)) | ! [X1] : ((calm(X1) | ~tall(X1)) & (tall(X1) | ~calm(X1)))) [rectify 52]
54. ? [X0] : ((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) => ((~tall(sK2) | ~calm(sK2)) & (tall(sK2) | calm(sK2))) [choice axiom]
55. (((~tall(sK2) | ~calm(sK2)) & (tall(sK2) | calm(sK2))) | ~quiet(mary) | ~calm(mary)) & ((quiet(mary) & calm(mary)) | ! [X1] : ((calm(X1) | ~tall(X1)) & (tall(X1) | ~calm(X1)))) [skolemisation 53,54]
67. ! [X0] : ((quiet(X0) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | ~quiet(X0))) [nnf transformation 16]
68. ! [X0] : ((quiet(X0) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~quiet(X0))) [flattening 67]
71. ? [X0] : (~humble(X0) & wise(X0)) => (~humble(sK5) & wise(sK5)) [choice axiom]
72. ~humble(sK5) & wise(sK5) [skolemisation 19,71]
98. calm(mary) | tall(X1) | ~calm(X1) [cnf transformation 55]
100. quiet(mary) | tall(X1) | ~calm(X1) [cnf transformation 55]
105. rich(lucy) | humble(X0) [cnf transformation 34]
115. ~tall(X0) | ~rich(X0) [cnf transformation 39]
124. ~quiet(X0) | ~calm(X0) [cnf transformation 68]
131. ~humble(sK5) [cnf transformation 72]
138. calm(lucy) [cnf transformation 25]
201. 14 <=> calm(mary) [avatar definition]
202. calm(mary) <- (14) [avatar component clause 201]
205. 15 <=> quiet(mary) [avatar definition]
206. quiet(mary) <- (15) [avatar component clause 205]
223. 19 <=> ! [X1] : (tall(X1) | ~calm(X1)) [avatar definition]
224. ~calm(X1) | tall(X1) <- (19) [avatar component clause 223]
225. 19 | 15 [avatar split clause 100,205,223]
227. 19 | 14 [avatar split clause 98,201,223]
241. 23 <=> ! [X0] : humble(X0) [avatar definition]
242. humble(X0) <- (23) [avatar component clause 241]
249. 25 <=> rich(lucy) [avatar definition]
251. rich(lucy) <- (25) [avatar component clause 249]
252. 23 | 25 [avatar split clause 105,249,241]
343. $false <- (23) [resolution 242,131]
344. ~23 [avatar contradiction clause 343]
352. ~calm(mary) <- (15) [resolution 124,206]
353. $false <- (14, 15) [subsumption resolution 352,202]
354. ~14 | ~15 [avatar contradiction clause 353]
360. tall(lucy) <- (19) [resolution 224,138]
372. ~rich(lucy) <- (19) [resolution 360,115]
373. $false <- (19, 25) [subsumption resolution 372,251]
374. ~19 | ~25 [avatar contradiction clause 373]
375. $false [avatar sat refutation 225,227,252,344,354,374]
% SZS output end Proof for 3145382530988915991446620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble and calm is old. If mary is either quiet or not generous then john is both strong and not old and vice versa. If lucy is either strong or wise then someone is both curious and not quiet and vice versa. Everyone who is either not generous or quiet is not happy. Everyone who is not creative is both quiet and not quiet and vice versa. Everyone who is not curious or generous is either kind or rich and vice versa. If someone is both not kind and not generous then mary is either rich or brave. Everyone who is not patient is funny or rich. If lucy is either happy or old then susan is either not old or wise and vice versa. If someone is not patient or not funny then alice is either not rich or strong. Everyone who is rich is not rich or patient and vice versa. If paul is either funny or generous then lucy is funny or not quiet. Everyone who is quiet or old is both not funny and not kind and vice versa. Everyone who is happy or patient is either humble or old and vice versa. If someone is curious or tall then paul is both not quiet and quiet. Everyone who is brave is both not funny and patient and vice versa. Someone is not funny. Someone is either humble or not patient. Someone is either patient or happy. Paul is creative or patient. John is not brave or not curious. Someone is quiet or not calm. | Susan is not old. | neutral | (![X]:((~humble(X)&calm(X))=>old(X)))&
(((quiet(mary)<~>~generous(mary)))<=>((strong(john)&~old(john))))&
(((strong(lucy)<~>wise(lucy)))<=>(?[X]:((curious(X)&~quiet(X)))))&
(![X]:((~generous(X)<~>quiet(X))=>~happy(X)))&
(![X]:(~creative(X)<=>(quiet(X)&~quiet(X))))&
(![X]:((~curious(X)|generous(X))<=>(kind(X)<~>rich(X))))&
((?[X]:((~kind(X)&~generous(X))))=>((rich(mary)<~>brave(mary))))&
(![X]:(~patient(X)=>(funny(X)|rich(X))))&
(((happy(lucy)<~>old(lucy)))<=>((~old(susan)<~>wise(susan))))&
((?[X]:((~patient(X)|~funny(X))))=>((~rich(alice)<~>strong(alice))))&
(![X]:(rich(X)<=>(~rich(X)|patient(X))))&
(((funny(paul)<~>generous(paul)))=>((funny(lucy)|~quiet(lucy))))&
(![X]:((quiet(X)|old(X))<=>(~funny(X)&~kind(X))))&
(![X]:((happy(X)|patient(X))<=>(humble(X)<~>old(X))))&
((?[X]:((curious(X)|tall(X))))=>((~quiet(paul)&quiet(paul))))&
(![X]:(brave(X)<=>(~funny(X)&patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((humble(X)<~>~patient(X))))&
(?[X]:((patient(X)<~>happy(X))))&
((creative(paul)|patient(paul)))&
((~brave(john)|~curious(john)))&
(?[X]:((quiet(X)|~calm(X)))) | ~old(susan) | [] | null | 0 |
If someone is either not generous or not patient then someone is either not calm or calm. If someone is either calm or tall then someone is both not calm and patient and vice versa. If someone is either generous or tall then someone is both not brave and kind and vice versa. If alice is not happy or not rich then susan is happy. Everyone who is both generous and humble is both not quiet and not rich. If someone is rich then john is not tall or not generous and vice versa. Everyone who is not curious is happy or not quiet and vice versa. If alice is strong or generous then susan is either not rich or not curious and vice versa. If alice is not humble then paul is not quiet or not strong. If someone is either not patient or curious then john is not brave. If someone is both not creative and not calm then someone is both not generous and not curious and vice versa. If john is not kind or old then fred is happy or not quiet and vice versa. If someone is not quiet or not creative then someone is not old or curious. If alice is either quiet or not patient then someone is quiet or generous and vice versa. Everyone who is both not quiet and not humble is quiet or curious and vice versa. If fred is both not wise and not old then someone is both not tall and quiet. Lucy is either curious or calm. Someone is not old. John is both not rich and generous. Paul is tall. Someone is not brave. John is either calm or not brave. Someone is not rich or strong. Alice is either not creative or generous. | Susan is not quiet. | entailment | ((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:((~calm(X)&patient(X)))))&
((?[X]:((generous(X)<~>tall(X))))<=>(?[X]:((~brave(X)&kind(X)))))&
(((~happy(alice)|~rich(alice)))=>(happy(susan)))&
(![X]:((generous(X)&humble(X))=>(~quiet(X)&~rich(X))))&
((?[X]:(rich(X)))<=>((~tall(john)|~generous(john))))&
(![X]:(~curious(X)<=>(happy(X)|~quiet(X))))&
(((strong(alice)|generous(alice)))<=>((~rich(susan)<~>~curious(susan))))&
((~humble(alice))=>((~quiet(paul)|~strong(paul))))&
((?[X]:((~patient(X)<~>curious(X))))=>(~brave(john)))&
((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((~generous(X)&~curious(X)))))&
(((~kind(john)|old(john)))<=>((happy(fred)|~quiet(fred))))&
((?[X]:((~quiet(X)|~creative(X))))=>(?[X]:((~old(X)|curious(X)))))&
(((quiet(alice)<~>~patient(alice)))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(quiet(X)|curious(X))))&
(((~wise(fred)&~old(fred)))=>(?[X]:((~tall(X)&quiet(X)))))&
((curious(lucy)<~>calm(lucy)))&
(?[X]:(~old(X)))&
((~rich(john)&generous(john)))&
(tall(paul))&
(?[X]:(~brave(X)))&
((calm(john)<~>~brave(john)))&
(?[X]:((~rich(X)|strong(X))))&
((~creative(alice)<~>generous(alice))) | ~quiet(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7720094841334670137351394
% SZS output start Proof for 7720094841334670137351394
15. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (curious(X0) | quiet(X0))) [input p14]
25. quiet(susan) [input hypothesis]
78. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 15]
79. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | humble(X0) | quiet(X0))) [flattening 78]
141. ~quiet(X0) | ~quiet(X0) [cnf transformation 79]
157. quiet(susan) [cnf transformation 25]
159. ~quiet(X0) [duplicate literal removal 141]
376. 49 <=> ! [X0] : ~quiet(X0) [avatar definition]
377. ~quiet(X0) <- (49) [avatar component clause 376]
392. 49 [avatar split clause 159,376]
423. $false <- (49) [resolution 377,157]
424. ~49 [avatar contradiction clause 423]
425. $false [avatar sat refutation 392,424]
% SZS output end Proof for 7720094841334670137351394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either brave or patient and vice versa.
If paul is both quiet and rich then someone is not curious.
If someone is not wise or kind then someone is not humble.
If someone is both not happy and not funny then someone is both wise and not kind and vice versa.
If mary is not happy then alice is either not tall or humble.
Everyone who is either quiet or kind is not wise and vice versa.
If paul is not curious or funny then someone is not quiet and vice versa.
Everyone who is happy is both creative and not strong and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Someone is tall.
Alice is brave.
Someone is generous.
Alice is either creative or not generous.
Fred is happy or not humble.
Mary is funny or not wise.
Someone is not curious.
Mary is both not wise and kind. | Mary is brave. | contradiction | (![X]:(~kind(X)<=>(brave(X)<~>patient(X))))&
(((quiet(paul)&rich(paul)))=>(?[X]:(~curious(X))))&
((?[X]:((~wise(X)|kind(X))))=>(?[X]:(~humble(X))))&
((?[X]:((~happy(X)&~funny(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
((~happy(mary))=>((~tall(alice)<~>humble(alice))))&
(![X]:((quiet(X)<~>kind(X))<=>~wise(X)))&
(((~curious(paul)|funny(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)<=>(creative(X)&~strong(X))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(?[X]:(tall(X)))&
(brave(alice))&
(?[X]:(generous(X)))&
((creative(alice)<~>~generous(alice)))&
((happy(fred)|~humble(fred)))&
((funny(mary)|~wise(mary)))&
(?[X]:(~curious(X)))&
((~wise(mary)&kind(mary))) | brave(mary) | [
"p0",
"p5",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1094006252025084209958143
% SZS output start Proof for 1094006252025084209958143
1. ! [X0] : (~kind(X0) <=> (brave(X0) <~> patient(X0))) [input p0]
6. ! [X0] : ((quiet(X0) <~> kind(X0)) <=> ~wise(X0)) [input p5]
16. ! [X0] : ((wise(X0) | patient(X0)) <=> quiet(X0)) [input p15]
24. kind(mary) & ~wise(mary) [input p23]
25. brave(mary) [input hypothesis]
38. ! [X0] : ((~kind(X0) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | kind(X0))) [nnf transformation 1]
50. ! [X0] : ((((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | wise(X0)) & (~wise(X0) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))))) [nnf transformation 6]
67. ! [X0] : (((wise(X0) | patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [nnf transformation 16]
68. ! [X0] : ((wise(X0) | patient(X0) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [flattening 67]
78. ~brave(X0) | patient(X0) | ~kind(X0) [cnf transformation 38]
92. ~quiet(X0) | ~kind(X0) | wise(X0) [cnf transformation 50]
117. ~patient(X0) | quiet(X0) [cnf transformation 68]
128. ~wise(mary) [cnf transformation 24]
129. kind(mary) [cnf transformation 24]
130. brave(mary) [cnf transformation 25]
306. 40 <=> wise(mary) [avatar definition]
308. ~wise(mary) <- (~40) [avatar component clause 306]
310. ~40 [avatar split clause 128,306]
318. patient(mary) | ~kind(mary) [resolution 78,130]
328. patient(mary) [subsumption resolution 318,129]
333. quiet(mary) [resolution 328,117]
346. ~kind(mary) | wise(mary) [resolution 92,333]
348. wise(mary) [subsumption resolution 346,129]
349. $false <- (~40) [subsumption resolution 348,308]
350. 40 [avatar contradiction clause 349]
351. $false [avatar sat refutation 310,350]
% SZS output end Proof for 1094006252025084209958143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not generous or funny then someone is either rich or quiet and vice versa. Everyone who is not tall or not humble is either not curious or quiet. Everyone who is old is not quiet. If lucy is either quiet or tall then someone is both tall and strong and vice versa. If lucy is either not old or quiet then someone is both not quiet and humble. Everyone who is either not brave or not old is both not humble and brave and vice versa. Everyone who is happy is either not happy or quiet and vice versa. If john is wise or calm then someone is either quiet or wise. If mary is both brave and not wise then john is creative and vice versa. If someone is not generous then alice is not funny. Everyone who is calm or humble is strong or not tall. Everyone who is not tall is rich. If someone is either not humble or kind then susan is both not generous and not humble. If lucy is either funny or kind then fred is both humble and not wise. Everyone who is both not quiet and not kind is both creative and not tall. If someone is not creative then someone is either funny or strong. Mary is wise. John is not happy. Someone is either not patient or creative. Paul is not brave. Mary is not rich. Someone is either not quiet or brave. Someone is either not happy or calm. Someone is happy or not generous. | John is not quiet. | contradiction | (((~generous(susan)<~>funny(susan)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(![X]:((~tall(X)|~humble(X))=>(~curious(X)<~>quiet(X))))&
(![X]:(old(X)=>~quiet(X)))&
(((quiet(lucy)<~>tall(lucy)))<=>(?[X]:((tall(X)&strong(X)))))&
(((~old(lucy)<~>quiet(lucy)))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~brave(X)<~>~old(X))<=>(~humble(X)&brave(X))))&
(![X]:(happy(X)<=>(~happy(X)<~>quiet(X))))&
(((wise(john)|calm(john)))=>(?[X]:((quiet(X)<~>wise(X)))))&
(((brave(mary)&~wise(mary)))<=>(creative(john)))&
((?[X]:(~generous(X)))=>(~funny(alice)))&
(![X]:((calm(X)|humble(X))=>(strong(X)|~tall(X))))&
(![X]:(~tall(X)=>rich(X)))&
((?[X]:((~humble(X)<~>kind(X))))=>((~generous(susan)&~humble(susan))))&
(((funny(lucy)<~>kind(lucy)))=>((humble(fred)&~wise(fred))))&
(![X]:((~quiet(X)&~kind(X))=>(creative(X)&~tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((funny(X)<~>strong(X)))))&
(wise(mary))&
(~happy(john))&
(?[X]:((~patient(X)<~>creative(X))))&
(~brave(paul))&
(~rich(mary))&
(?[X]:((~quiet(X)<~>brave(X))))&
(?[X]:((~happy(X)<~>calm(X))))&
(?[X]:((happy(X)|~generous(X)))) | ~quiet(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5868208868754473805769957
% SZS output start Proof for 5868208868754473805769957
7. ! [X0] : (happy(X0) <=> (~happy(X0) <~> quiet(X0))) [input p6]
25. ~quiet(john) [input hypothesis]
54. ! [X0] : ((happy(X0) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | ~happy(X0))) [nnf transformation 7]
106. quiet(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 54]
108. happy(X0) | quiet(X0) | happy(X0) [cnf transformation 54]
144. ~quiet(john) [cnf transformation 25]
145. quiet(X0) | ~happy(X0) [duplicate literal removal 106]
146. happy(X0) | quiet(X0) [duplicate literal removal 108]
218. quiet(X0) [subsumption resolution 145,146]
336. $false [subsumption resolution 144,218]
% SZS output end Proof for 5868208868754473805769957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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