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 curious or not happy is not funny and vice versa.
If someone is not creative or not tall then someone is humble and vice versa.
Everyone who is either rich or not generous is funny or not curious and vice versa.
Everyone who is both not quiet and not humble is either funny or creative.
If paul is both brave and not old then someone is happy and vice versa.
Everyone who is not calm or not brave is curious.
If fred is both tall and old then someone is both patient and not brave and vice versa.
If paul is strong then someone is quiet or not calm and vice versa.
If someone is not funny then someone is either not tall or funny and vice versa.
Everyone who is kind or quiet is quiet.
Everyone who is funny is both not wise and generous and vice versa.
If mary is not kind then someone is both calm and not quiet and vice versa.
If someone is either creative or not creative then mary is both not humble and curious.
Everyone who is either not rich or strong is both kind and wise and vice versa.
Everyone who is quiet is both tall and not calm.
Everyone who is both rich and happy is both not rich and kind.
Someone is either curious or old.
John is either quiet or not old.
Someone is either calm or not humble.
John is either not happy or not calm.
Alice is old.
Someone is tall.
Someone is either not quiet or old. | Mary is kind. | contradiction | (![X]:((~curious(X)|~happy(X))<=>~funny(X)))&
((?[X]:((~creative(X)|~tall(X))))<=>(?[X]:(humble(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(funny(X)|~curious(X))))&
(![X]:((~quiet(X)&~humble(X))=>(funny(X)<~>creative(X))))&
(((brave(paul)&~old(paul)))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)|~brave(X))=>curious(X)))&
(((tall(fred)&old(fred)))<=>(?[X]:((patient(X)&~brave(X)))))&
((strong(paul))<=>(?[X]:((quiet(X)|~calm(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((~tall(X)<~>funny(X)))))&
(![X]:((kind(X)|quiet(X))=>quiet(X)))&
(![X]:(funny(X)<=>(~wise(X)&generous(X))))&
((~kind(mary))<=>(?[X]:((calm(X)&~quiet(X)))))&
((?[X]:((creative(X)<~>~creative(X))))=>((~humble(mary)&curious(mary))))&
(![X]:((~rich(X)<~>strong(X))<=>(kind(X)&wise(X))))&
(![X]:(quiet(X)=>(tall(X)&~calm(X))))&
(![X]:((rich(X)&happy(X))=>(~rich(X)&kind(X))))&
(?[X]:((curious(X)<~>old(X))))&
((quiet(john)<~>~old(john)))&
(?[X]:((calm(X)<~>~humble(X))))&
((~happy(john)<~>~calm(john)))&
(old(alice))&
(?[X]:(tall(X)))&
(?[X]:((~quiet(X)<~>old(X)))) | kind(mary) | [
"p0",
"p2",
"p5",
"p10",
"p11",
"p14",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 5199553403201521831455405
% SZS output start Proof for 5199553403201521831455405
1. ! [X0] : ((~happy(X0) | ~curious(X0)) <=> ~funny(X0)) [input p0]
3. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (~curious(X0) | funny(X0))) [input p2]
6. ! [X0] : ((~brave(X0) | ~calm(X0)) => curious(X0)) [input p5]
11. ! [X0] : (funny(X0) <=> (generous(X0) & ~wise(X0))) [input p10]
12. ~kind(mary) <=> ? [X0] : (~quiet(X0) & calm(X0)) [input p11]
15. ! [X0] : (quiet(X0) => (~calm(X0) & tall(X0))) [input p14]
16. ! [X0] : ((happy(X0) & rich(X0)) => (kind(X0) & ~rich(X0))) [input p15]
20. ~happy(john) <~> ~calm(john) [input p19]
24. kind(mary) [input hypothesis]
29. ! [X0] : (curious(X0) | (brave(X0) & calm(X0))) [ennf transformation 6]
32. ! [X0] : ((~calm(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 15]
33. ! [X0] : ((kind(X0) & ~rich(X0)) | (~happy(X0) | ~rich(X0))) [ennf transformation 16]
34. ! [X0] : ((kind(X0) & ~rich(X0)) | ~happy(X0) | ~rich(X0)) [flattening 33]
35. ! [X0] : (((~happy(X0) | ~curious(X0)) | funny(X0)) & (~funny(X0) | (happy(X0) & curious(X0)))) [nnf transformation 1]
36. ! [X0] : ((~happy(X0) | ~curious(X0) | funny(X0)) & (~funny(X0) | (happy(X0) & curious(X0)))) [flattening 35]
42. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (curious(X0) & ~funny(X0))) & ((~curious(X0) | funny(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 3]
43. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (curious(X0) & ~funny(X0))) & (~curious(X0) | funny(X0) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 42]
64. ! [X0] : ((funny(X0) | (~generous(X0) | wise(X0))) & ((generous(X0) & ~wise(X0)) | ~funny(X0))) [nnf transformation 11]
65. ! [X0] : ((funny(X0) | ~generous(X0) | wise(X0)) & ((generous(X0) & ~wise(X0)) | ~funny(X0))) [flattening 64]
66. (~kind(mary) | ! [X0] : (quiet(X0) | ~calm(X0))) & (? [X0] : (~quiet(X0) & calm(X0)) | kind(mary)) [nnf transformation 12]
67. (~kind(mary) | ! [X0] : (quiet(X0) | ~calm(X0))) & (? [X1] : (~quiet(X1) & calm(X1)) | kind(mary)) [rectify 66]
68. ? [X1] : (~quiet(X1) & calm(X1)) => (~quiet(sK7) & calm(sK7)) [choice axiom]
69. (~kind(mary) | ! [X0] : (quiet(X0) | ~calm(X0))) & ((~quiet(sK7) & calm(sK7)) | kind(mary)) [skolemisation 67,68]
80. (calm(john) | happy(john)) & (~calm(john) | ~happy(john)) [nnf transformation 20]
88. ~happy(X0) | ~curious(X0) | funny(X0) [cnf transformation 36]
94. ~generous(X0) | rich(X0) | ~funny(X0) [cnf transformation 43]
103. calm(X0) | curious(X0) [cnf transformation 29]
119. ~funny(X0) | generous(X0) [cnf transformation 65]
123. ~kind(mary) | quiet(X0) | ~calm(X0) [cnf transformation 69]
135. ~calm(X0) | ~quiet(X0) [cnf transformation 32]
136. ~rich(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 34]
145. calm(john) | happy(john) [cnf transformation 80]
150. kind(mary) [cnf transformation 24]
151. ~rich(X0) | ~happy(X0) [duplicate literal removal 136]
268. 27 <=> ! [X0] : (quiet(X0) | ~calm(X0)) [avatar definition]
269. quiet(X0) | ~calm(X0) <- (27) [avatar component clause 268]
271. 28 <=> kind(mary) [avatar definition]
274. 27 | ~28 [avatar split clause 123,271,268]
331. 40 <=> happy(john) [avatar definition]
333. happy(john) <- (40) [avatar component clause 331]
335. 41 <=> calm(john) [avatar definition]
336. ~calm(john) <- (~41) [avatar component clause 335]
337. calm(john) <- (41) [avatar component clause 335]
338. 40 | 41 [avatar split clause 145,335,331]
350. 28 [avatar split clause 150,271]
351. ~calm(X0) <- (27) [subsumption resolution 269,135]
355. curious(john) <- (~41) [resolution 103,336]
360. ~curious(john) | funny(john) <- (40) [resolution 88,333]
362. funny(john) <- (40, ~41) [subsumption resolution 360,355]
364. generous(john) <- (40, ~41) [resolution 362,119]
371. rich(john) | ~funny(john) <- (40, ~41) [resolution 364,94]
372. rich(john) <- (40, ~41) [subsumption resolution 371,362]
380. ~happy(john) <- (40, ~41) [resolution 372,151]
381. $false <- (40, ~41) [subsumption resolution 380,333]
382. ~40 | 41 [avatar contradiction clause 381]
383. $false <- (27, 41) [subsumption resolution 337,351]
384. ~27 | ~41 [avatar contradiction clause 383]
385. $false [avatar sat refutation 274,338,350,382,384]
% SZS output end Proof for 5199553403201521831455405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is either rich or strong. If someone is not generous or tall then someone is kind and vice versa. Everyone who is both not quiet and not kind is not calm or patient and vice versa. Everyone who is both brave and not kind is not tall or not humble and vice versa. If someone is either funny or old then someone is both generous and not funny and vice versa. If susan is not patient then fred is either not old or humble. If mary is both rich and brave then john is not curious or old. If mary is not generous then someone is quiet or creative. Everyone who is either funny or strong is calm or kind. Everyone who is both not generous and not strong is both not rich and tall. If someone is both wise and not old then susan is not calm and vice versa. Everyone who is kind or old is quiet or not old. If lucy is happy then susan is brave or creative and vice versa. Everyone who is both happy and rich is creative or not generous. If someone is not wise or not creative then lucy is brave. Everyone who is curious or not kind is either happy or wise. Someone is not happy or rich. Mary is not strong or not calm. Fred is either funny or not tall. Someone is either not rich or not wise. Someone is happy. Alice is quiet. Susan is not rich. Alice is both creative and not curious. | Alice is not patient. | entailment | (![X]:((~patient(X)|~calm(X))=>(rich(X)<~>strong(X))))&
((?[X]:((~generous(X)|tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)&~kind(X))<=>(~calm(X)|patient(X))))&
(![X]:((brave(X)&~kind(X))<=>(~tall(X)|~humble(X))))&
((?[X]:((funny(X)<~>old(X))))<=>(?[X]:((generous(X)&~funny(X)))))&
((~patient(susan))=>((~old(fred)<~>humble(fred))))&
(((rich(mary)&brave(mary)))=>((~curious(john)|old(john))))&
((~generous(mary))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:((funny(X)<~>strong(X))=>(calm(X)|kind(X))))&
(![X]:((~generous(X)&~strong(X))=>(~rich(X)&tall(X))))&
((?[X]:((wise(X)&~old(X))))<=>(~calm(susan)))&
(![X]:((kind(X)|old(X))=>(quiet(X)|~old(X))))&
((happy(lucy))<=>((brave(susan)|creative(susan))))&
(![X]:((happy(X)&rich(X))=>(creative(X)|~generous(X))))&
((?[X]:((~wise(X)|~creative(X))))=>(brave(lucy)))&
(![X]:((curious(X)|~kind(X))=>(happy(X)<~>wise(X))))&
(?[X]:((~happy(X)|rich(X))))&
((~strong(mary)|~calm(mary)))&
((funny(fred)<~>~tall(fred)))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(happy(X)))&
(quiet(alice))&
(~rich(susan))&
((creative(alice)&~curious(alice))) | ~patient(alice) | [
"p2",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 8008779087108852717336722
% SZS output start Proof for 8008779087108852717336722
3. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> (patient(X0) | ~calm(X0))) [input p2]
22. quiet(alice) [input p21]
25. patient(alice) [input hypothesis]
50. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (kind(X0) | quiet(X0)))) [nnf transformation 3]
51. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | kind(X0) | quiet(X0))) [flattening 50]
87. ~quiet(X0) | ~patient(X0) [cnf transformation 51]
128. quiet(alice) [cnf transformation 22]
131. patient(alice) [cnf transformation 25]
301. ~patient(alice) [resolution 87,128]
302. $false [subsumption resolution 301,131]
% SZS output end Proof for 8008779087108852717336722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not quiet is either old or strong and vice versa. If alice is both creative and curious then susan is either rich or quiet. Everyone who is happy is not quiet or old and vice versa. Everyone who is either brave or patient is both generous and not happy. If someone is calm then someone is not humble or not funny and vice versa. Everyone who is both old and not funny is strong or not happy and vice versa. Everyone who is not rich or not quiet is wise. Everyone who is calm or not quiet is not wise or not rich and vice versa. If lucy is either not generous or not quiet then fred is not calm. Everyone who is happy or not brave is not rich or not humble and vice versa. If alice is not calm then paul is not brave or curious. Everyone who is tall or generous is creative or not wise. Everyone who is generous is not kind or not old and vice versa. Everyone who is both not strong and humble is either patient or not kind and vice versa. Everyone who is either brave or not wise is humble or not funny and vice versa. Everyone who is generous is not calm and vice versa. Someone is both not funny and calm. Susan is not calm. Someone is kind or not generous. Alice is rich. Fred is brave. Someone is either creative or calm. Lucy is either not creative or not patient. | Fred is not kind. | entailment | (![X]:((generous(X)&~quiet(X))<=>(old(X)<~>strong(X))))&
(((creative(alice)&curious(alice)))=>((rich(susan)<~>quiet(susan))))&
(![X]:(happy(X)<=>(~quiet(X)|old(X))))&
(![X]:((brave(X)<~>patient(X))=>(generous(X)&~happy(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((old(X)&~funny(X))<=>(strong(X)|~happy(X))))&
(![X]:((~rich(X)|~quiet(X))=>wise(X)))&
(![X]:((calm(X)|~quiet(X))<=>(~wise(X)|~rich(X))))&
(((~generous(lucy)<~>~quiet(lucy)))=>(~calm(fred)))&
(![X]:((happy(X)|~brave(X))<=>(~rich(X)|~humble(X))))&
((~calm(alice))=>((~brave(paul)|curious(paul))))&
(![X]:((tall(X)|generous(X))=>(creative(X)|~wise(X))))&
(![X]:(generous(X)<=>(~kind(X)|~old(X))))&
(![X]:((~strong(X)&humble(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((brave(X)<~>~wise(X))<=>(humble(X)|~funny(X))))&
(![X]:(generous(X)<=>~calm(X)))&
(?[X]:((~funny(X)&calm(X))))&
(~calm(susan))&
(?[X]:((kind(X)|~generous(X))))&
(rich(alice))&
(brave(fred))&
(?[X]:((creative(X)<~>calm(X))))&
((~creative(lucy)<~>~patient(lucy))) | ~kind(fred) | [
"p0",
"p2",
"p3",
"p5",
"p12",
"p13",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 1793216468247277510747843
% SZS output start Proof for 1793216468247277510747843
1. ! [X0] : ((~quiet(X0) & generous(X0)) <=> (old(X0) <~> strong(X0))) [input p0]
3. ! [X0] : (happy(X0) <=> (old(X0) | ~quiet(X0))) [input p2]
4. ! [X0] : ((brave(X0) <~> patient(X0)) => (~happy(X0) & generous(X0))) [input p3]
6. ! [X0] : ((~funny(X0) & old(X0)) <=> (~happy(X0) | strong(X0))) [input p5]
13. ! [X0] : (generous(X0) <=> (~old(X0) | ~kind(X0))) [input p12]
14. ! [X0] : ((humble(X0) & ~strong(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p13]
16. ! [X0] : (generous(X0) <=> ~calm(X0)) [input p15]
21. brave(fred) [input p20]
24. kind(fred) [input hypothesis]
29. ! [X0] : ((~happy(X0) & generous(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 4]
36. ! [X0] : (((~quiet(X0) & generous(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (quiet(X0) | ~generous(X0)))) [nnf transformation 1]
37. ! [X0] : (((~quiet(X0) & generous(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | quiet(X0) | ~generous(X0))) [flattening 36]
39. ! [X0] : ((happy(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | ~happy(X0))) [nnf transformation 3]
40. ! [X0] : ((happy(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | ~happy(X0))) [flattening 39]
41. ! [X0] : ((~happy(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 29]
47. ! [X0] : (((~funny(X0) & old(X0)) | (happy(X0) & ~strong(X0))) & ((~happy(X0) | strong(X0)) | (funny(X0) | ~old(X0)))) [nnf transformation 6]
48. ! [X0] : (((~funny(X0) & old(X0)) | (happy(X0) & ~strong(X0))) & (~happy(X0) | strong(X0) | funny(X0) | ~old(X0))) [flattening 47]
54. ! [X0] : ((generous(X0) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | ~generous(X0))) [nnf transformation 13]
55. ! [X0] : ((generous(X0) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | ~generous(X0))) [flattening 54]
56. ! [X0] : (((humble(X0) & ~strong(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~humble(X0) | strong(X0)))) [nnf transformation 14]
57. ! [X0] : (((humble(X0) & ~strong(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ~humble(X0) | strong(X0))) [flattening 56]
60. ! [X0] : ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0))) [nnf transformation 16]
69. ~generous(X0) | old(X0) | quiet(X0) | strong(X0) [cnf transformation 37]
71. ~old(X0) | strong(X0) | generous(X0) [cnf transformation 37]
77. ~happy(X0) | ~quiet(X0) | old(X0) [cnf transformation 40]
79. ~old(X0) | happy(X0) [cnf transformation 40]
82. ~brave(X0) | patient(X0) | ~happy(X0) [cnf transformation 41]
89. old(X0) | happy(X0) [cnf transformation 48]
106. ~kind(X0) | ~old(X0) | ~generous(X0) [cnf transformation 55]
108. old(X0) | generous(X0) [cnf transformation 55]
111. ~kind(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 57]
121. ~calm(X0) | ~generous(X0) [cnf transformation 60]
122. calm(X0) | generous(X0) [cnf transformation 60]
128. brave(fred) [cnf transformation 21]
133. kind(fred) [cnf transformation 24]
176. happy(X0) [subsumption resolution 89,79]
189. 13 <=> calm(fred) [avatar definition]
190. calm(fred) <- (13) [avatar component clause 189]
191. ~calm(fred) <- (~13) [avatar component clause 189]
234. generous(fred) <- (~13) [resolution 122,191]
237. strong(X0) | generous(X0) | generous(X0) [resolution 71,108]
238. strong(X0) | generous(X0) [duplicate literal removal 237]
245. ~quiet(X1) | old(X1) [resolution 77,176]
252. patient(fred) | ~happy(fred) [resolution 82,128]
253. patient(fred) [subsumption resolution 252,176]
267. ~old(fred) | ~generous(fred) [resolution 106,133]
270. ~old(fred) <- (~13) [subsumption resolution 267,234]
281. ~strong(fred) | ~patient(fred) [resolution 111,133]
284. ~strong(fred) [subsumption resolution 281,253]
306. generous(fred) [resolution 284,238]
346. old(fred) | quiet(fred) | strong(fred) <- (~13) [resolution 69,234]
350. quiet(fred) | strong(fred) <- (~13) [subsumption resolution 346,270]
351. quiet(fred) <- (~13) [subsumption resolution 350,284]
371. old(fred) <- (~13) [resolution 351,245]
375. $false <- (~13) [subsumption resolution 371,270]
376. 13 [avatar contradiction clause 375]
378. 30 <=> generous(fred) [avatar definition]
379. generous(fred) <- (30) [avatar component clause 378]
386. 30 [avatar split clause 306,378]
392. ~generous(fred) <- (13) [resolution 190,121]
393. $false <- (13, 30) [subsumption resolution 392,379]
394. ~13 | ~30 [avatar contradiction clause 393]
395. $false [avatar sat refutation 376,386,394]
% SZS output end Proof for 1793216468247277510747843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is either happy or not calm and vice versa. If someone is not strong then someone is either curious or patient. If fred is either not old or not brave then someone is either not calm or kind. If someone is not patient then someone is both not wise and kind. Everyone who is tall is funny and vice versa. Everyone who is patient or not rich is not patient or rich. If someone is both wise and not strong then someone is not generous or calm. If someone is funny then john is not brave or patient and vice versa. Everyone who is not strong is both not generous and calm and vice versa. If someone is not brave or strong then susan is not humble or not tall. Everyone who is either happy or not humble is humble. Everyone who is either not old or creative is not quiet. If paul is funny then someone is not patient or not rich and vice versa. If someone is both calm and not creative then someone is rich or not happy and vice versa. If someone is patient or strong then paul is either generous or not rich. If someone is either not patient or not old then someone is both not rich and not funny. Susan is either humble or old. Fred is not kind. Paul is either not humble or not quiet. Someone is kind or not wise. Someone is both funny and patient. Paul is both creative and wise. Someone is not funny or not rich. Susan is either not humble or not calm. | Susan is humble. | entailment | (![X]:(~old(X)<=>(happy(X)<~>~calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((curious(X)<~>patient(X)))))&
(((~old(fred)<~>~brave(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:(tall(X)<=>funny(X)))&
(![X]:((patient(X)|~rich(X))=>(~patient(X)|rich(X))))&
((?[X]:((wise(X)&~strong(X))))=>(?[X]:((~generous(X)|calm(X)))))&
((?[X]:(funny(X)))<=>((~brave(john)|patient(john))))&
(![X]:(~strong(X)<=>(~generous(X)&calm(X))))&
((?[X]:((~brave(X)|strong(X))))=>((~humble(susan)|~tall(susan))))&
(![X]:((happy(X)<~>~humble(X))=>humble(X)))&
(![X]:((~old(X)<~>creative(X))=>~quiet(X)))&
((funny(paul))<=>(?[X]:((~patient(X)|~rich(X)))))&
((?[X]:((calm(X)&~creative(X))))<=>(?[X]:((rich(X)|~happy(X)))))&
((?[X]:((patient(X)|strong(X))))=>((generous(paul)<~>~rich(paul))))&
((?[X]:((~patient(X)<~>~old(X))))=>(?[X]:((~rich(X)&~funny(X)))))&
((humble(susan)<~>old(susan)))&
(~kind(fred))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((funny(X)&patient(X))))&
((creative(paul)&wise(paul)))&
(?[X]:((~funny(X)|~rich(X))))&
((~humble(susan)<~>~calm(susan))) | humble(susan) | [
"p0",
"p10",
"p16",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 6735245525811500419832559
% SZS output start Proof for 6735245525811500419832559
1. ! [X0] : (~old(X0) <=> (happy(X0) <~> ~calm(X0))) [input p0]
11. ! [X0] : ((happy(X0) <~> ~humble(X0)) => humble(X0)) [input p10]
17. humble(susan) <~> old(susan) [input p16]
24. ~humble(susan) <~> ~calm(susan) [input p23]
25. ~humble(susan) [input hypothesis]
41. ! [X0] : (humble(X0) | (happy(X0) <=> ~humble(X0))) [ennf transformation 11]
45. ! [X0] : ((~old(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | old(X0))) [nnf transformation 1]
66. ! [X0] : (humble(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) [nnf transformation 41]
82. (~old(susan) | ~humble(susan)) & (old(susan) | humble(susan)) [nnf transformation 17]
90. (calm(susan) | humble(susan)) & (~calm(susan) | ~humble(susan)) [nnf transformation 24]
93. ~calm(X0) | ~old(X0) | ~happy(X0) [cnf transformation 45]
116. humble(X0) | happy(X0) | humble(X0) [cnf transformation 66]
135. old(susan) | humble(susan) [cnf transformation 82]
147. calm(susan) | humble(susan) [cnf transformation 90]
148. ~humble(susan) [cnf transformation 25]
149. humble(X0) | happy(X0) [duplicate literal removal 116]
232. 19 <=> humble(susan) [avatar definition]
234. ~humble(susan) <- (~19) [avatar component clause 232]
323. 39 <=> old(susan) [avatar definition]
324. old(susan) <- (39) [avatar component clause 323]
327. 19 | 39 [avatar split clause 135,323,232]
357. 46 <=> calm(susan) [avatar definition]
359. calm(susan) <- (46) [avatar component clause 357]
360. 19 | 46 [avatar split clause 147,357,232]
362. ~19 [avatar split clause 148,232]
372. happy(susan) <- (~19) [resolution 149,234]
389. ~old(susan) | ~happy(susan) <- (46) [resolution 93,359]
392. ~happy(susan) <- (39, 46) [subsumption resolution 389,324]
393. $false <- (~19, 39, 46) [subsumption resolution 392,372]
394. 19 | ~39 | ~46 [avatar contradiction clause 393]
395. $false [avatar sat refutation 327,360,362,394]
% SZS output end Proof for 6735245525811500419832559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not humble is not old or brave and vice versa.
If someone is not creative then someone is either not patient or humble and vice versa.
If paul is not humble then someone is not funny or rich and vice versa.
Everyone who is curious or not happy is not kind or not brave.
If someone is both old and not generous then susan is both not old and funny.
If fred is either not rich or not old then someone is either not patient or strong and vice versa.
Everyone who is strong or creative is wise and vice versa.
If someone is either not tall or calm then mary is quiet and vice versa.
If someone is either not strong or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Everyone who is either not brave or calm is either rich or not funny.
If paul is both funny and not old then someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise.
Paul is both old and calm.
Someone is rich.
Lucy is both calm and wise.
Paul is both not kind and quiet.
Fred is either quiet or rich. | Mary is brave. | contradiction | (![X]:((wise(X)&~humble(X))<=>(~old(X)|brave(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~patient(X)<~>humble(X)))))&
((~humble(paul))<=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((curious(X)|~happy(X))=>(~kind(X)|~brave(X))))&
((?[X]:((old(X)&~generous(X))))=>((~old(susan)&funny(susan))))&
(((~rich(fred)<~>~old(fred)))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((strong(X)|creative(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>calm(X))=>(rich(X)<~>~funny(X))))&
(((funny(paul)&~old(paul)))=>(?[X]:((curious(X)|~calm(X)))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
((old(paul)&calm(paul)))&
(?[X]:(rich(X)))&
((calm(lucy)&wise(lucy)))&
((~kind(paul)&quiet(paul)))&
((quiet(fred)<~>rich(fred))) | brave(mary) | [
"p0",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 267620476583898794998916
% SZS output start Proof for 267620476583898794998916
1. ! [X0] : ((~humble(X0) & wise(X0)) <=> (brave(X0) | ~old(X0))) [input p0]
12. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p11]
25. brave(mary) [input hypothesis]
38. ! [X0] : (((~humble(X0) & wise(X0)) | (~brave(X0) & old(X0))) & ((brave(X0) | ~old(X0)) | (humble(X0) | ~wise(X0)))) [nnf transformation 1]
39. ! [X0] : (((~humble(X0) & wise(X0)) | (~brave(X0) & old(X0))) & (brave(X0) | ~old(X0) | humble(X0) | ~wise(X0))) [flattening 38]
66. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 12]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 66]
86. ~brave(X0) | wise(X0) [cnf transformation 39]
88. ~brave(X0) | ~humble(X0) [cnf transformation 39]
130. ~wise(X0) | humble(X0) [cnf transformation 67]
156. brave(mary) [cnf transformation 25]
376. wise(mary) [resolution 86,156]
381. ~humble(mary) [resolution 88,156]
389. humble(mary) [resolution 130,376]
390. $false [subsumption resolution 389,381]
% SZS output end Proof for 267620476583898794998916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and tall then someone is either brave or humble and vice versa. If alice is both funny and not brave then fred is not strong or not rich. Everyone who is either calm or quiet is not generous or quiet and vice versa. Everyone who is not wise or not quiet is both not brave and wise and vice versa. Everyone who is kind or quiet is not quiet or tall. Everyone who is quiet is both not creative and not calm and vice versa. If alice is not kind then alice is both not kind and calm and vice versa. Everyone who is both not happy and not patient is either not kind or not humble and vice versa. Everyone who is generous or kind is creative and vice versa. Everyone who is either not funny or not generous is not wise or funny. If paul is either strong or brave then someone is both brave and quiet and vice versa. If someone is both rich and not calm then someone is either curious or funny and vice versa. Everyone who is either humble or patient is either not funny or curious. If someone is both humble and not happy then susan is both humble and curious. Everyone who is not calm is both not quiet and not generous. If someone is quiet then someone is not calm or not rich. Someone is calm. Lucy is not funny or not old. Fred is either quiet or old. Someone is not happy. Someone is either quiet or calm. Someone is not creative or generous. Paul is both not generous and not happy. | Lucy is not wise. | contradiction | ((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>humble(X)))))&
(((funny(alice)&~brave(alice)))=>((~strong(fred)|~rich(fred))))&
(![X]:((calm(X)<~>quiet(X))<=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)&wise(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((humble(X)&~happy(X))))=>((humble(susan)&curious(susan))))&
(![X]:(~calm(X)=>(~quiet(X)&~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|~rich(X)))))&
(?[X]:(calm(X)))&
((~funny(lucy)|~old(lucy)))&
((quiet(fred)<~>old(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((quiet(X)<~>calm(X))))&
(?[X]:((~creative(X)|generous(X))))&
((~generous(paul)&~happy(paul))) | ~wise(lucy) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 8648647138098604174707116
% SZS output start Proof for 8648647138098604174707116
4. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (wise(X0) & ~brave(X0))) [input p3]
24. ~wise(lucy) [input hypothesis]
45. ! [X0] : (((~quiet(X0) | ~wise(X0)) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | (quiet(X0) & wise(X0)))) [nnf transformation 4]
46. ! [X0] : ((~quiet(X0) | ~wise(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | (quiet(X0) & wise(X0)))) [flattening 45]
94. wise(X0) | wise(X0) [cnf transformation 46]
147. ~wise(lucy) [cnf transformation 24]
150. wise(X0) [duplicate literal removal 94]
298. $false [subsumption resolution 147,150]
% SZS output end Proof for 8648647138098604174707116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is generous then someone is either calm or patient and vice versa. Everyone who is either strong or not wise is not humble. Everyone who is not generous or rich is not rich or not wise. If john is calm then someone is old. Everyone who is either patient or not happy is either not tall or not brave and vice versa. If someone is both not wise and curious then fred is patient. If lucy is both rich and not brave then someone is generous and vice versa. Everyone who is either not humble or not wise is either calm or quiet and vice versa. If lucy is either creative or strong then paul is strong or not calm and vice versa. Everyone who is not tall is both tall and kind and vice versa. Everyone who is funny is both brave and tall and vice versa. Everyone who is both not quiet and not brave is both not kind and not happy. If alice is both not humble and not tall then lucy is calm or not calm. Everyone who is calm is quiet and vice versa. If someone is both curious and kind then someone is not humble or rich. Everyone who is either not tall or brave is both old and kind and vice versa. Paul is calm or rich. Someone is not brave or tall. Someone is not rich or brave. John is old. Someone is both not calm and not rich. Someone is happy or creative. Someone is not patient or not happy. John is not generous. | Paul is not calm. | neutral | ((generous(lucy))<=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:((strong(X)<~>~wise(X))=>~humble(X)))&
(![X]:((~generous(X)|rich(X))=>(~rich(X)|~wise(X))))&
((calm(john))=>(?[X]:(old(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(~tall(X)<~>~brave(X))))&
((?[X]:((~wise(X)&curious(X))))=>(patient(fred)))&
(((rich(lucy)&~brave(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(calm(X)<~>quiet(X))))&
(((creative(lucy)<~>strong(lucy)))<=>((strong(paul)|~calm(paul))))&
(![X]:(~tall(X)<=>(tall(X)&kind(X))))&
(![X]:(funny(X)<=>(brave(X)&tall(X))))&
(![X]:((~quiet(X)&~brave(X))=>(~kind(X)&~happy(X))))&
(((~humble(alice)&~tall(alice)))=>((calm(lucy)|~calm(lucy))))&
(![X]:(calm(X)<=>quiet(X)))&
((?[X]:((curious(X)&kind(X))))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:((~tall(X)<~>brave(X))<=>(old(X)&kind(X))))&
((calm(paul)|rich(paul)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~rich(X)|brave(X))))&
(old(john))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((happy(X)|creative(X))))&
(?[X]:((~patient(X)|~happy(X))))&
(~generous(john)) | ~calm(paul) | []
| null | 0 |
Everyone who is both not old and calm is generous or calm and vice versa. If someone is both rich and not kind then mary is kind or not strong. Everyone who is either funny or not rich is old or generous. If someone is either happy or not patient then fred is not kind and vice versa. Everyone who is either not wise or happy is calm or old. If someone is either not patient or old then lucy is not tall or not old and vice versa. If fred is humble or calm then someone is not kind or tall. Everyone who is either not humble or not wise is humble. Everyone who is brave or funny is either funny or rich. If someone is either happy or not patient then paul is both patient and not rich. Everyone who is both not happy and not patient is not curious or funny and vice versa. Everyone who is both not calm and not strong is both not tall and brave and vice versa. Everyone who is either not old or not kind is not quiet. If john is both not strong and strong then someone is not wise and vice versa. If fred is strong or tall then john is both not old and rich and vice versa. Everyone who is humble or kind is happy. Alice is not rich. Alice is not kind. Susan is wise. Someone is not brave. John is either kind or wise. Someone is quiet or wise. | Paul is wise. | entailment | (![X]:((~old(X)&calm(X))<=>(generous(X)|calm(X))))&
((?[X]:((rich(X)&~kind(X))))=>((kind(mary)|~strong(mary))))&
(![X]:((funny(X)<~>~rich(X))=>(old(X)|generous(X))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(~kind(fred)))&
(![X]:((~wise(X)<~>happy(X))=>(calm(X)|old(X))))&
((?[X]:((~patient(X)<~>old(X))))<=>((~tall(lucy)|~old(lucy))))&
(((humble(fred)|calm(fred)))=>(?[X]:((~kind(X)|tall(X)))))&
(![X]:((~humble(X)<~>~wise(X))=>humble(X)))&
(![X]:((brave(X)|funny(X))=>(funny(X)<~>rich(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>((patient(paul)&~rich(paul))))&
(![X]:((~happy(X)&~patient(X))<=>(~curious(X)|funny(X))))&
(![X]:((~calm(X)&~strong(X))<=>(~tall(X)&brave(X))))&
(![X]:((~old(X)<~>~kind(X))=>~quiet(X)))&
(((~strong(john)&strong(john)))<=>(?[X]:(~wise(X))))&
(((strong(fred)|tall(fred)))<=>((~old(john)&rich(john))))&
(![X]:((humble(X)|kind(X))=>happy(X)))&
(~rich(alice))&
(~kind(alice))&
(wise(susan))&
(?[X]:(~brave(X)))&
((kind(john)<~>wise(john)))&
(?[X]:((quiet(X)|wise(X)))) | wise(paul) | [
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 6577647475058082629376267
% SZS output start Proof for 6577647475058082629376267
14. (strong(john) & ~strong(john)) <=> ? [X0] : ~wise(X0) [input p13]
23. ~wise(paul) [input hypothesis]
59. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (~strong(john) | strong(john))) [nnf transformation 14]
60. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ~strong(john) | strong(john)) [flattening 59]
61. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ~strong(john) | strong(john)) [rectify 60]
62. ? [X1] : ~wise(X1) => ~wise(sK3) [choice axiom]
63. ((strong(john) & ~strong(john)) | ! [X0] : wise(X0)) & (~wise(sK3) | ~strong(john) | strong(john)) [skolemisation 61,62]
115. ~strong(john) | wise(X0) [cnf transformation 63]
116. strong(john) | wise(X0) [cnf transformation 63]
131. ~wise(paul) [cnf transformation 23]
227. 21 <=> ! [X0] : wise(X0) [avatar definition]
228. wise(X0) <- (21) [avatar component clause 227]
230. 22 <=> strong(john) [avatar definition]
233. 21 | 22 [avatar split clause 116,230,227]
234. 21 | ~22 [avatar split clause 115,230,227]
275. $false <- (21) [resolution 228,131]
276. ~21 [avatar contradiction clause 275]
277. $false [avatar sat refutation 233,234,276]
% SZS output end Proof for 6577647475058082629376267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is both humble and generous and vice versa.
If fred is not kind or curious then someone is happy or not calm.
Everyone who is curious or happy is not humble.
If john is kind or not humble then paul is either funny or not rich and vice versa.
Everyone who is either wise or not calm is brave and vice versa.
Everyone who is happy or funny is strong or tall.
Everyone who is either not creative or generous is either not funny or not calm.
Everyone who is either strong or generous is either kind or not brave and vice versa.
Everyone who is not rich or creative is both not quiet and not generous.
Everyone who is either not creative or not humble is either funny or not rich and vice versa.
If lucy is rich then someone is both not creative and not kind.
Everyone who is happy is either kind or not kind and vice versa.
Everyone who is both not calm and not patient is generous or strong and vice versa.
If someone is rich or kind then someone is not kind or not happy and vice versa.
If susan is happy then fred is tall or not kind and vice versa.
John is wise.
Alice is either not brave or old.
Someone is either not funny or not curious.
Someone is both curious and old.
Someone is either not generous or rich.
Someone is either quiet or strong.
Someone is either not rich or not funny.
Alice is both kind and not generous. | Paul is quiet. | contradiction | ((?[X]:(~patient(X)))<=>(?[X]:((humble(X)&generous(X)))))&
(((~kind(fred)|curious(fred)))=>(?[X]:((happy(X)|~calm(X)))))&
(![X]:((curious(X)|happy(X))=>~humble(X)))&
(((kind(john)|~humble(john)))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)|funny(X))=>(strong(X)|tall(X))))&
(![X]:((~creative(X)<~>generous(X))=>(~funny(X)<~>~calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~rich(X)|creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~creative(X)<~>~humble(X))<=>(funny(X)<~>~rich(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:(happy(X)<=>(kind(X)<~>~kind(X))))&
(![X]:((~calm(X)&~patient(X))<=>(generous(X)|strong(X))))&
((?[X]:((rich(X)|kind(X))))<=>(?[X]:((~kind(X)|~happy(X)))))&
((happy(susan))<=>((tall(fred)|~kind(fred))))&
(wise(john))&
((~brave(alice)<~>old(alice)))&
(?[X]:((~funny(X)<~>~curious(X))))&
(?[X]:((curious(X)&old(X))))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~rich(X)<~>~funny(X))))&
((kind(alice)&~generous(alice))) | quiet(paul) | [
"p2",
"p3",
"p8",
"p9",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 1690262070210581915763828
% SZS output start Proof for 1690262070210581915763828
3. ! [X0] : ((happy(X0) | curious(X0)) => ~humble(X0)) [input p2]
4. (~humble(john) | kind(john)) <=> (funny(paul) <~> ~rich(paul)) [input p3]
9. ! [X0] : ((creative(X0) | ~rich(X0)) => (~generous(X0) & ~quiet(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> ~humble(X0)) <=> (funny(X0) <~> ~rich(X0))) [input p9]
12. ! [X0] : (happy(X0) <=> (kind(X0) <~> ~kind(X0))) [input p11]
24. quiet(paul) [input hypothesis]
28. ! [X0] : (~humble(X0) | (~happy(X0) & ~curious(X0))) [ennf transformation 3]
32. ! [X0] : ((~generous(X0) & ~quiet(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 9]
41. ((~humble(john) | kind(john)) | ((funny(paul) | rich(paul)) & (~rich(paul) | ~funny(paul)))) & (((rich(paul) | ~funny(paul)) & (~rich(paul) | funny(paul))) | (humble(john) & ~kind(john))) [nnf transformation 4]
42. (~humble(john) | kind(john) | ((funny(paul) | rich(paul)) & (~rich(paul) | ~funny(paul)))) & (((rich(paul) | ~funny(paul)) & (~rich(paul) | funny(paul))) | (humble(john) & ~kind(john))) [flattening 41]
46. ! [X0] : ((((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0)))) & (((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0))))) [nnf transformation 10]
49. ! [X0] : ((happy(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~happy(X0))) [nnf transformation 12]
80. ~happy(X0) | ~humble(X0) [cnf transformation 28]
82. ~rich(paul) | funny(paul) | humble(john) [cnf transformation 42]
105. ~quiet(X0) | rich(X0) [cnf transformation 32]
106. ~quiet(X0) | ~creative(X0) [cnf transformation 32]
115. ~rich(X0) | creative(X0) | humble(X0) | ~funny(X0) [cnf transformation 46]
121. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 49]
122. happy(X0) | kind(X0) | kind(X0) [cnf transformation 49]
150. quiet(paul) [cnf transformation 24]
151. happy(X0) | ~kind(X0) [duplicate literal removal 121]
152. happy(X0) | kind(X0) [duplicate literal removal 122]
193. 10 <=> rich(paul) [avatar definition]
195. rich(paul) <- (10) [avatar component clause 193]
197. 11 <=> funny(paul) [avatar definition]
205. 13 <=> humble(john) [avatar definition]
206. humble(john) <- (13) [avatar component clause 205]
212. 13 | 11 | ~10 [avatar split clause 82,193,197,205]
228. happy(X0) [subsumption resolution 151,152]
315. ~humble(X0) [resolution 80,228]
316. rich(paul) [resolution 105,150]
320. 10 [avatar split clause 316,193]
321. ~creative(paul) [resolution 106,150]
475. creative(paul) | humble(paul) | ~funny(paul) <- (10) [resolution 115,195]
479. humble(paul) | ~funny(paul) <- (10) [subsumption resolution 475,321]
480. ~funny(paul) <- (10) [subsumption resolution 479,315]
497. ~11 | ~10 [avatar split clause 480,193,197]
508. $false <- (13) [subsumption resolution 206,315]
509. ~13 [avatar contradiction clause 508]
510. $false [avatar sat refutation 212,320,497,509]
% SZS output end Proof for 1690262070210581915763828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not creative or not kind then alice is both not curious and not tall.
If someone is both funny and not creative then susan is creative or not creative.
Everyone who is not creative or humble is humble and vice versa.
Everyone who is both curious and not calm is either not happy or happy and vice versa.
If someone is brave or patient then lucy is not calm and vice versa.
If paul is either funny or tall then someone is either calm or not happy and vice versa.
Everyone who is both strong and generous is both curious and not wise.
Everyone who is either humble or not rich is both strong and old and vice versa.
If someone is not tall then someone is both not kind and not patient and vice versa.
Everyone who is either not quiet or not kind is not funny and vice versa.
If mary is not calm then susan is not brave.
If mary is either humble or patient then paul is not happy.
Everyone who is either not brave or not wise is both strong and calm and vice versa.
If someone is not brave then someone is either wise or not brave.
Everyone who is quiet is patient.
If someone is tall then susan is wise.
Someone is both curious and not calm.
Lucy is both not happy and not humble.
John is not rich or old.
Someone is happy.
Alice is funny or not humble.
Fred is either not happy or kind.
Lucy is not funny. | John is old. | neutral | ((?[X]:((~creative(X)<~>~kind(X))))=>((~curious(alice)&~tall(alice))))&
((?[X]:((funny(X)&~creative(X))))=>((creative(susan)|~creative(susan))))&
(![X]:((~creative(X)|humble(X))<=>humble(X)))&
(![X]:((curious(X)&~calm(X))<=>(~happy(X)<~>happy(X))))&
((?[X]:((brave(X)|patient(X))))<=>(~calm(lucy)))&
(((funny(paul)<~>tall(paul)))<=>(?[X]:((calm(X)<~>~happy(X)))))&
(![X]:((strong(X)&generous(X))=>(curious(X)&~wise(X))))&
(![X]:((humble(X)<~>~rich(X))<=>(strong(X)&old(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>~funny(X)))&
((~calm(mary))=>(~brave(susan)))&
(((humble(mary)<~>patient(mary)))=>(~happy(paul)))&
(![X]:((~brave(X)<~>~wise(X))<=>(strong(X)&calm(X))))&
((?[X]:(~brave(X)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:(quiet(X)=>patient(X)))&
((?[X]:(tall(X)))=>(wise(susan)))&
(?[X]:((curious(X)&~calm(X))))&
((~happy(lucy)&~humble(lucy)))&
((~rich(john)|old(john)))&
(?[X]:(happy(X)))&
((funny(alice)|~humble(alice)))&
((~happy(fred)<~>kind(fred)))&
(~funny(lucy)) | old(john) | []
| null | 0 |
Everyone who is rich is either wise or rich and vice versa. If someone is both curious and rich then someone is either strong or not tall and vice versa. Everyone who is either not quiet or curious is old or not brave. Everyone who is creative or not calm is not generous and vice versa. Everyone who is both not kind and not humble is either not funny or old. Everyone who is either curious or not happy is tall or happy and vice versa. Everyone who is either quiet or not wise is either not curious or not kind. Everyone who is not wise or brave is not strong. Everyone who is either not tall or humble is happy and vice versa. Everyone who is wise or not quiet is not humble and vice versa. Everyone who is either not wise or not brave is either not brave or not strong and vice versa. Everyone who is not humble is not wise or not funny. Everyone who is not generous is both not humble and not old and vice versa. If mary is both not generous and not old then someone is not brave and vice versa. If john is either not old or strong then fred is both strong and quiet. Everyone who is wise or kind is not tall or not brave and vice versa. Fred is both rich and not strong. Someone is not curious. Paul is either not funny or humble. Someone is not humble or not rich. Someone is not brave. Paul is either wise or not old. Someone is both quiet and old. Fred is either not happy or funny. | Mary is humble. | contradiction | (![X]:(rich(X)<=>(wise(X)<~>rich(X))))&
((?[X]:((curious(X)&rich(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((~quiet(X)<~>curious(X))=>(old(X)|~brave(X))))&
(![X]:((creative(X)|~calm(X))<=>~generous(X)))&
(![X]:((~kind(X)&~humble(X))=>(~funny(X)<~>old(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(tall(X)|happy(X))))&
(![X]:((quiet(X)<~>~wise(X))=>(~curious(X)<~>~kind(X))))&
(![X]:((~wise(X)|brave(X))=>~strong(X)))&
(![X]:((~tall(X)<~>humble(X))<=>happy(X)))&
(![X]:((wise(X)|~quiet(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:(~humble(X)=>(~wise(X)|~funny(X))))&
(![X]:(~generous(X)<=>(~humble(X)&~old(X))))&
(((~generous(mary)&~old(mary)))<=>(?[X]:(~brave(X))))&
(((~old(john)<~>strong(john)))=>((strong(fred)&quiet(fred))))&
(![X]:((wise(X)|kind(X))<=>(~tall(X)|~brave(X))))&
((rich(fred)&~strong(fred)))&
(?[X]:(~curious(X)))&
((~funny(paul)<~>humble(paul)))&
(?[X]:((~humble(X)|~rich(X))))&
(?[X]:(~brave(X)))&
((wise(paul)<~>~old(paul)))&
(?[X]:((quiet(X)&old(X))))&
((~happy(fred)<~>funny(fred))) | humble(mary) | [
"p12",
"p13",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 5120188989759957079419824
% SZS output start Proof for 5120188989759957079419824
13. ! [X0] : (~generous(X0) <=> (~old(X0) & ~humble(X0))) [input p12]
14. (~old(mary) & ~generous(mary)) <=> ? [X0] : ~brave(X0) [input p13]
21. ? [X0] : ~brave(X0) [input p20]
25. humble(mary) [input hypothesis]
53. ! [X0] : ((~generous(X0) | (old(X0) | humble(X0))) & ((~old(X0) & ~humble(X0)) | generous(X0))) [nnf transformation 13]
54. ! [X0] : ((~generous(X0) | old(X0) | humble(X0)) & ((~old(X0) & ~humble(X0)) | generous(X0))) [flattening 53]
55. ((~old(mary) & ~generous(mary)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (old(mary) | generous(mary))) [nnf transformation 14]
56. ((~old(mary) & ~generous(mary)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | old(mary) | generous(mary)) [flattening 55]
57. ((~old(mary) & ~generous(mary)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | old(mary) | generous(mary)) [rectify 56]
58. ? [X1] : ~brave(X1) => ~brave(sK2) [choice axiom]
59. ((~old(mary) & ~generous(mary)) | ! [X0] : brave(X0)) & (~brave(sK2) | old(mary) | generous(mary)) [skolemisation 57,58]
68. ? [X0] : ~brave(X0) => ~brave(sK5) [choice axiom]
69. ~brave(sK5) [skolemisation 21,68]
119. ~humble(X0) | generous(X0) [cnf transformation 54]
123. ~generous(mary) | brave(X0) [cnf transformation 59]
139. ~brave(sK5) [cnf transformation 69]
146. humble(mary) [cnf transformation 25]
193. 8 <=> ! [X0] : brave(X0) [avatar definition]
194. brave(X0) <- (8) [avatar component clause 193]
201. 10 <=> generous(mary) [avatar definition]
204. 8 | ~10 [avatar split clause 123,201,193]
257. generous(mary) [resolution 119,146]
260. 10 [avatar split clause 257,201]
261. $false <- (8) [resolution 194,139]
265. ~8 [avatar contradiction clause 261]
266. $false [avatar sat refutation 204,260,265]
% SZS output end Proof for 5120188989759957079419824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and curious is humble and vice versa.
Everyone who is both not tall and humble is not rich or not generous and vice versa.
If mary is both happy and not old then someone is not humble.
If someone is happy then susan is both not curious and not generous.
Everyone who is generous or not brave is either not wise or tall.
If john is not patient then someone is either rich or kind.
Everyone who is either rich or humble is generous.
Everyone who is quiet is either happy or not tall and vice versa.
If someone is both not generous and brave then someone is tall and vice versa.
If susan is brave or not rich then paul is not quiet or generous and vice versa.
Everyone who is either not creative or curious is not kind.
Everyone who is not happy is both not curious and not tall and vice versa.
Everyone who is both not creative and brave is calm or tall and vice versa.
Everyone who is patient or wise is quiet and vice versa.
If lucy is old then someone is either not patient or not tall and vice versa.
Everyone who is calm is both wise and not funny.
Paul is either not funny or not rich.
Fred is both not humble and creative.
Someone is both not humble and rich.
Susan is both brave and not happy.
Someone is either creative or not wise.
Paul is either old or funny.
Someone is not wise. | Lucy is tall. | contradiction | (![X]:((humble(X)&curious(X))<=>humble(X)))&
(![X]:((~tall(X)&humble(X))<=>(~rich(X)|~generous(X))))&
(((happy(mary)&~old(mary)))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))=>((~curious(susan)&~generous(susan))))&
(![X]:((generous(X)|~brave(X))=>(~wise(X)<~>tall(X))))&
((~patient(john))=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((rich(X)<~>humble(X))=>generous(X)))&
(![X]:(quiet(X)<=>(happy(X)<~>~tall(X))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:(tall(X))))&
(((brave(susan)|~rich(susan)))<=>((~quiet(paul)|generous(paul))))&
(![X]:((~creative(X)<~>curious(X))=>~kind(X)))&
(![X]:(~happy(X)<=>(~curious(X)&~tall(X))))&
(![X]:((~creative(X)&brave(X))<=>(calm(X)|tall(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
((old(lucy))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:(calm(X)=>(wise(X)&~funny(X))))&
((~funny(paul)<~>~rich(paul)))&
((~humble(fred)&creative(fred)))&
(?[X]:((~humble(X)&rich(X))))&
((brave(susan)&~happy(susan)))&
(?[X]:((creative(X)<~>~wise(X))))&
((old(paul)<~>funny(paul)))&
(?[X]:(~wise(X))) | tall(lucy) | [
"p0",
"p1",
"p3",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 4853138409719745436129623
% SZS output start Proof for 4853138409719745436129623
1. ! [X0] : ((curious(X0) & humble(X0)) <=> humble(X0)) [input p0]
2. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (~generous(X0) | ~rich(X0))) [input p1]
4. ? [X0] : happy(X0) => (~generous(susan) & ~curious(susan)) [input p3]
12. ! [X0] : (~happy(X0) <=> (~tall(X0) & ~curious(X0))) [input p11]
24. tall(lucy) [input hypothesis]
28. (~generous(susan) & ~curious(susan)) | ! [X0] : ~happy(X0) [ennf transformation 4]
34. ! [X0] : (((curious(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | (~curious(X0) | ~humble(X0)))) [nnf transformation 1]
35. ! [X0] : (((curious(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | ~curious(X0) | ~humble(X0))) [flattening 34]
36. ! [X0] : (((humble(X0) & ~tall(X0)) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 2]
37. ! [X0] : (((humble(X0) & ~tall(X0)) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ~humble(X0) | tall(X0))) [flattening 36]
54. ! [X0] : ((~happy(X0) | (tall(X0) | curious(X0))) & ((~tall(X0) & ~curious(X0)) | happy(X0))) [nnf transformation 12]
55. ! [X0] : ((~happy(X0) | tall(X0) | curious(X0)) & ((~tall(X0) & ~curious(X0)) | happy(X0))) [flattening 54]
75. ~humble(X0) | curious(X0) [cnf transformation 35]
80. generous(X0) | humble(X0) [cnf transformation 37]
82. ~curious(susan) | ~happy(X0) [cnf transformation 28]
83. ~generous(susan) | ~happy(X0) [cnf transformation 28]
106. ~tall(X0) | happy(X0) [cnf transformation 55]
135. tall(lucy) [cnf transformation 24]
150. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
151. ~happy(X0) <- (4) [avatar component clause 150]
153. 5 <=> generous(susan) [avatar definition]
155. ~generous(susan) <- (~5) [avatar component clause 153]
156. 4 | ~5 [avatar split clause 83,153,150]
158. 6 <=> curious(susan) [avatar definition]
160. ~curious(susan) <- (~6) [avatar component clause 158]
161. 4 | ~6 [avatar split clause 82,158,150]
274. humble(susan) <- (~5) [resolution 80,155]
276. curious(susan) <- (~5) [resolution 274,75]
277. $false <- (~5, ~6) [subsumption resolution 276,160]
278. 5 | 6 [avatar contradiction clause 277]
280. happy(lucy) [resolution 106,135]
281. $false <- (4) [subsumption resolution 280,151]
282. ~4 [avatar contradiction clause 281]
283. $false [avatar sat refutation 156,161,278,282]
% SZS output end Proof for 4853138409719745436129623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not patient is not calm and vice versa.
Everyone who is happy or not brave is kind and vice versa.
If someone is calm or funny then someone is both not creative and creative.
If someone is both kind and brave then someone is either not wise or not creative.
If susan is either not rich or not strong then someone is either not old or not funny.
If susan is not happy or not humble then someone is old or happy and vice versa.
Everyone who is not wise is not quiet or kind.
If paul is kind then someone is creative and vice versa.
Everyone who is either not rich or not kind is either not happy or funny.
Everyone who is not wise or old is calm or kind.
Everyone who is both tall and curious is tall or humble.
If alice is both creative and curious then someone is not funny or not creative and vice versa.
Everyone who is not humble is both patient and not wise and vice versa.
Everyone who is not quiet or strong is either rich or funny.
If someone is both not old and rich then alice is either kind or old.
If alice is not quiet then someone is both humble and not kind and vice versa.
Someone is either not funny or not strong.
Someone is both creative and rich.
Someone is not kind.
John is not brave or not generous.
Mary is not calm or tall.
Someone is happy.
Fred is not wise or patient.
Alice is strong. | Alice is not funny. | entailment | (![X]:((kind(X)<~>~patient(X))<=>~calm(X)))&
(![X]:((happy(X)|~brave(X))<=>kind(X)))&
((?[X]:((calm(X)|funny(X))))=>(?[X]:((~creative(X)&creative(X)))))&
((?[X]:((kind(X)&brave(X))))=>(?[X]:((~wise(X)<~>~creative(X)))))&
(((~rich(susan)<~>~strong(susan)))=>(?[X]:((~old(X)<~>~funny(X)))))&
(((~happy(susan)|~humble(susan)))<=>(?[X]:((old(X)|happy(X)))))&
(![X]:(~wise(X)=>(~quiet(X)|kind(X))))&
((kind(paul))<=>(?[X]:(creative(X))))&
(![X]:((~rich(X)<~>~kind(X))=>(~happy(X)<~>funny(X))))&
(![X]:((~wise(X)|old(X))=>(calm(X)|kind(X))))&
(![X]:((tall(X)&curious(X))=>(tall(X)|humble(X))))&
(((creative(alice)&curious(alice)))<=>(?[X]:((~funny(X)|~creative(X)))))&
(![X]:(~humble(X)<=>(patient(X)&~wise(X))))&
(![X]:((~quiet(X)|strong(X))=>(rich(X)<~>funny(X))))&
((?[X]:((~old(X)&rich(X))))=>((kind(alice)<~>old(alice))))&
((~quiet(alice))<=>(?[X]:((humble(X)&~kind(X)))))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:(~kind(X)))&
((~brave(john)|~generous(john)))&
((~calm(mary)|tall(mary)))&
(?[X]:(happy(X)))&
((~wise(fred)|patient(fred)))&
(strong(alice)) | ~funny(alice) | [
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 2400793926249314482294511
% SZS output start Proof for 2400793926249314482294511
3. ? [X0] : (funny(X0) | calm(X0)) => ? [X0] : (creative(X0) & ~creative(X0)) [input p2]
25. funny(alice) [input hypothesis]
26. ? [X0] : (funny(X0) | calm(X0)) => ? [X1] : (creative(X1) & ~creative(X1)) [rectify 3]
29. ? [X1] : (creative(X1) & ~creative(X1)) | ! [X0] : (~funny(X0) & ~calm(X0)) [ennf transformation 26]
44. ? [X0] : (creative(X0) & ~creative(X0)) | ! [X1] : (~funny(X1) & ~calm(X1)) [rectify 29]
45. ? [X0] : (creative(X0) & ~creative(X0)) => (creative(sK0) & ~creative(sK0)) [choice axiom]
46. (creative(sK0) & ~creative(sK0)) | ! [X1] : (~funny(X1) & ~calm(X1)) [skolemisation 44,45]
94. ~creative(sK0) | ~funny(X1) [cnf transformation 46]
96. creative(sK0) | ~funny(X1) [cnf transformation 46]
143. funny(alice) [cnf transformation 25]
145. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
146. ~funny(X1) <- (1) [avatar component clause 145]
148. 2 <=> creative(sK0) [avatar definition]
151. 1 | 2 [avatar split clause 96,148,145]
156. 1 | ~2 [avatar split clause 94,148,145]
328. $false <- (1) [resolution 146,143]
329. ~1 [avatar contradiction clause 328]
330. $false [avatar sat refutation 151,156,329]
% SZS output end Proof for 2400793926249314482294511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or old is tall or creative and vice versa. Everyone who is humble or not calm is humble. Everyone who is either not old or not curious is not humble. If susan is not brave or not generous then alice is both not tall and calm. Everyone who is both patient and brave is patient or not humble and vice versa. If someone is either happy or quiet then lucy is both not curious and not humble and vice versa. Everyone who is both kind and not wise is generous or not tall and vice versa. Everyone who is not funny is both not curious and tall. If fred is either creative or wise then susan is both not old and curious. If paul is both not old and not funny then lucy is not creative. If someone is either not patient or wise then paul is curious or not calm and vice versa. If someone is either not calm or generous then someone is either not generous or creative. Everyone who is either patient or rich is happy or 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 not quiet. Paul is not old. Alice is both not quiet and patient. Lucy is not generous or quiet. Fred is not quiet. Susan is not generous. John is both not generous and not humble. Someone is both generous and not old. | Paul is patient. | neutral | (![X]:((~wise(X)|old(X))<=>(tall(X)|creative(X))))&
(![X]:((humble(X)|~calm(X))=>humble(X)))&
(![X]:((~old(X)<~>~curious(X))=>~humble(X)))&
(((~brave(susan)|~generous(susan)))=>((~tall(alice)&calm(alice))))&
(![X]:((patient(X)&brave(X))<=>(patient(X)|~humble(X))))&
((?[X]:((happy(X)<~>quiet(X))))<=>((~curious(lucy)&~humble(lucy))))&
(![X]:((kind(X)&~wise(X))<=>(generous(X)|~tall(X))))&
(![X]:(~funny(X)=>(~curious(X)&tall(X))))&
(((creative(fred)<~>wise(fred)))=>((~old(susan)&curious(susan))))&
(((~old(paul)&~funny(paul)))=>(~creative(lucy)))&
((?[X]:((~patient(X)<~>wise(X))))<=>((curious(paul)|~calm(paul))))&
((?[X]:((~calm(X)<~>generous(X))))=>(?[X]:((~generous(X)<~>creative(X)))))&
(![X]:((patient(X)<~>rich(X))=>(happy(X)|~old(X))))&
(((~kind(lucy)|~patient(lucy)))=>(?[X]:((~happy(X)|~strong(X)))))&
(((~quiet(fred)|~patient(fred)))<=>((~patient(paul)<~>~quiet(paul))))&
(![X]:(tall(X)=>strong(X)))&
(?[X]:(~quiet(X)))&
(~old(paul))&
((~quiet(alice)&patient(alice)))&
((~generous(lucy)|quiet(lucy)))&
(~quiet(fred))&
(~generous(susan))&
((~generous(john)&~humble(john)))&
(?[X]:((generous(X)&~old(X)))) | patient(paul) | []
| null | 0 |
Everyone who is patient or kind is not generous. Everyone who is calm is both tall and rich. Everyone who is not quiet or not patient is either not strong or happy. If susan is either happy or creative then john is both curious and not humble and vice versa. Everyone who is both happy and not happy is either not tall or curious and vice versa. Everyone who is curious is not wise and vice versa. Everyone who is not kind or not old is not humble or rich. Everyone who is either rich or humble is funny and vice versa. If someone is either curious or funny then alice is both wise and not humble and vice versa. Everyone who is both funny and not old is either creative or humble. If someone is not creative or strong then susan is calm or happy. If fred is either not tall or happy then fred is either old or funny. Everyone who is not tall is either not quiet or tall. Everyone who is both not calm and funny is both not old and not curious and vice versa. If someone is not brave then john is not brave and vice versa. Everyone who is humble is not rich. Alice is not patient or tall. Fred is either tall or not calm. Someone is either not kind or calm. Susan is both not happy and creative. Fred is either kind or not calm. Someone is not wise or not humble. Paul is not wise. | Paul is calm. | contradiction | (![X]:((patient(X)|kind(X))=>~generous(X)))&
(![X]:(calm(X)=>(tall(X)&rich(X))))&
(![X]:((~quiet(X)|~patient(X))=>(~strong(X)<~>happy(X))))&
(((happy(susan)<~>creative(susan)))<=>((curious(john)&~humble(john))))&
(![X]:((happy(X)&~happy(X))<=>(~tall(X)<~>curious(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((~kind(X)|~old(X))=>(~humble(X)|rich(X))))&
(![X]:((rich(X)<~>humble(X))<=>funny(X)))&
((?[X]:((curious(X)<~>funny(X))))<=>((wise(alice)&~humble(alice))))&
(![X]:((funny(X)&~old(X))=>(creative(X)<~>humble(X))))&
((?[X]:((~creative(X)|strong(X))))=>((calm(susan)|happy(susan))))&
(((~tall(fred)<~>happy(fred)))=>((old(fred)<~>funny(fred))))&
(![X]:(~tall(X)=>(~quiet(X)<~>tall(X))))&
(![X]:((~calm(X)&funny(X))<=>(~old(X)&~curious(X))))&
((?[X]:(~brave(X)))<=>(~brave(john)))&
(![X]:(humble(X)=>~rich(X)))&
((~patient(alice)|tall(alice)))&
((tall(fred)<~>~calm(fred)))&
(?[X]:((~kind(X)<~>calm(X))))&
((~happy(susan)&creative(susan)))&
((kind(fred)<~>~calm(fred)))&
(?[X]:((~wise(X)|~humble(X))))&
(~wise(paul)) | calm(paul) | [
"p1",
"p4",
"p5",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4148467591474436613377179
% SZS output start Proof for 4148467591474436613377179
2. ! [X0] : (calm(X0) => (rich(X0) & tall(X0))) [input p1]
5. ! [X0] : ((~happy(X0) & happy(X0)) <=> (~tall(X0) <~> curious(X0))) [input p4]
6. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p5]
23. ~wise(paul) [input p22]
24. calm(paul) [input hypothesis]
26. ! [X0] : ((rich(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 2]
40. ! [X0] : (((~happy(X0) & happy(X0)) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0)))) & (((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | (happy(X0) | ~happy(X0)))) [nnf transformation 5]
41. ! [X0] : (((~happy(X0) & happy(X0)) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0)))) & (((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | happy(X0) | ~happy(X0))) [flattening 40]
42. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 6]
65. ~calm(X0) | tall(X0) [cnf transformation 26]
80. happy(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 41]
82. ~happy(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 41]
84. wise(X0) | curious(X0) [cnf transformation 42]
124. ~wise(paul) [cnf transformation 23]
125. calm(paul) [cnf transformation 24]
149. ~curious(X0) | ~tall(X0) [subsumption resolution 80,82]
265. tall(paul) [resolution 65,125]
271. curious(paul) [resolution 84,124]
275. ~tall(paul) [resolution 149,271]
277. $false [subsumption resolution 275,265]
% SZS output end Proof for 4148467591474436613377179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and not old then someone is not funny.
If someone is both not generous and not creative then mary is both funny and not wise and vice versa.
Everyone who is funny is either old or not calm and vice versa.
If someone is both calm and rich then fred is either not kind or funny and vice versa.
Everyone who is both strong and not quiet is either strong or funny.
If someone is not generous then someone is both not quiet and happy.
If someone is not creative then someone is curious and vice versa.
If someone is both not kind and not humble then lucy is either kind or not strong and vice versa.
If someone is not generous then someone is not patient or strong and vice versa.
Everyone who is both rich and patient is both strong and not patient.
Everyone who is both tall and not quiet is both not patient and patient and vice versa.
If mary is either not wise or old then mary is either not happy or rich.
If someone is humble or happy then mary is not brave.
Everyone who is not creative is both not kind and patient.
Everyone who is not rich is either not brave or creative and vice versa.
Everyone who is tall or quiet is creative or not humble and vice versa.
Paul is both happy and rich.
Someone is curious.
Fred is both tall and kind.
Someone is both quiet and not curious.
Someone is either not calm or not strong.
John is both rich and not tall.
Alice is either not generous or funny.
Susan is either not kind or not funny. | John is not quiet. | contradiction | ((?[X]:((patient(X)&~old(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~generous(X)&~creative(X))))<=>((funny(mary)&~wise(mary))))&
(![X]:(funny(X)<=>(old(X)<~>~calm(X))))&
((?[X]:((calm(X)&rich(X))))<=>((~kind(fred)<~>funny(fred))))&
(![X]:((strong(X)&~quiet(X))=>(strong(X)<~>funny(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:(curious(X))))&
((?[X]:((~kind(X)&~humble(X))))<=>((kind(lucy)<~>~strong(lucy))))&
((?[X]:(~generous(X)))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((rich(X)&patient(X))=>(strong(X)&~patient(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~patient(X)&patient(X))))&
(((~wise(mary)<~>old(mary)))=>((~happy(mary)<~>rich(mary))))&
((?[X]:((humble(X)|happy(X))))=>(~brave(mary)))&
(![X]:(~creative(X)=>(~kind(X)&patient(X))))&
(![X]:(~rich(X)<=>(~brave(X)<~>creative(X))))&
(![X]:((tall(X)|quiet(X))<=>(creative(X)|~humble(X))))&
((happy(paul)&rich(paul)))&
(?[X]:(curious(X)))&
((tall(fred)&kind(fred)))&
(?[X]:((quiet(X)&~curious(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
((rich(john)&~tall(john)))&
((~generous(alice)<~>funny(alice)))&
((~kind(susan)<~>~funny(susan))) | ~quiet(john) | [
"p9",
"p10",
"p13",
"p15",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 3685694532233201956953308
% SZS output start Proof for 3685694532233201956953308
10. ! [X0] : ((patient(X0) & rich(X0)) => (~patient(X0) & strong(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) & tall(X0)) <=> (patient(X0) & ~patient(X0))) [input p10]
14. ! [X0] : (~creative(X0) => (patient(X0) & ~kind(X0))) [input p13]
16. ! [X0] : ((quiet(X0) | tall(X0)) <=> (~humble(X0) | creative(X0))) [input p15]
22. ~tall(john) & rich(john) [input p21]
25. ~quiet(john) [input hypothesis]
34. ! [X0] : ((~patient(X0) & strong(X0)) | (~patient(X0) | ~rich(X0))) [ennf transformation 10]
35. ! [X0] : ((~patient(X0) & strong(X0)) | ~patient(X0) | ~rich(X0)) [flattening 34]
38. ! [X0] : ((patient(X0) & ~kind(X0)) | creative(X0)) [ennf transformation 14]
70. ! [X0] : (((~quiet(X0) & tall(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (quiet(X0) | ~tall(X0)))) [nnf transformation 11]
71. ! [X0] : (((~quiet(X0) & tall(X0)) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | quiet(X0) | ~tall(X0))) [flattening 70]
74. ! [X0] : (((quiet(X0) | tall(X0)) | (humble(X0) & ~creative(X0))) & ((~humble(X0) | creative(X0)) | (~quiet(X0) & ~tall(X0)))) [nnf transformation 16]
75. ! [X0] : ((quiet(X0) | tall(X0) | (humble(X0) & ~creative(X0))) & (~humble(X0) | creative(X0) | (~quiet(X0) & ~tall(X0)))) [flattening 74]
116. ~patient(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 35]
117. ~patient(X0) | quiet(X0) | ~tall(X0) [cnf transformation 71]
118. ~tall(X0) | quiet(X0) | patient(X0) [cnf transformation 71]
128. creative(X0) | patient(X0) [cnf transformation 38]
135. quiet(X0) | tall(X0) | ~creative(X0) [cnf transformation 75]
146. rich(john) [cnf transformation 22]
152. ~quiet(john) [cnf transformation 25]
153. ~rich(X0) | ~patient(X0) [duplicate literal removal 116]
286. ~tall(X0) | quiet(X0) [subsumption resolution 117,118]
316. ~creative(X0) | quiet(X0) [subsumption resolution 135,286]
360. ~patient(john) [resolution 153,146]
466. 58 <=> creative(john) [avatar definition]
467. ~creative(john) <- (~58) [avatar component clause 466]
468. creative(john) <- (58) [avatar component clause 466]
494. quiet(john) <- (58) [resolution 468,316]
495. $false <- (58) [subsumption resolution 494,152]
496. ~58 [avatar contradiction clause 495]
500. patient(john) <- (~58) [resolution 467,128]
501. $false <- (~58) [subsumption resolution 500,360]
502. 58 [avatar contradiction clause 501]
503. $false [avatar sat refutation 496,502]
% SZS output end Proof for 3685694532233201956953308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both old and happy and vice versa. Everyone who is creative is either generous or not creative. Everyone who is not patient or not old is not humble and vice versa. If someone is both rich and not strong then mary is old or calm and vice versa. Everyone who is either not curious or strong is not old. If susan is not wise then someone is not patient or calm and vice versa. Everyone who is either not strong or strong is not humble or not wise. Everyone who is both not tall and creative is both wise and curious and vice versa. If susan is kind or not old then someone is happy and vice versa. Everyone who is not generous or funny is either funny or brave and vice versa. Everyone who is creative is both wise and not patient and vice versa. If fred is both old and creative then alice is not calm or generous and vice versa. If john is either not humble or not patient then fred is not patient and vice versa. Everyone who is not old is generous. If someone is both patient and brave then alice is not creative or generous and vice versa. Everyone who is both curious and not kind is either rich or not old. Someone is old or patient. Mary is funny or not generous. Someone is not creative or not humble. Alice is both funny and rich. Alice is kind or not brave. Someone is either generous or not quiet. John is both not generous and not humble. Someone is both humble and not quiet. | Susan is happy. | entailment | (![X]:(~wise(X)<=>(old(X)&happy(X))))&
(![X]:(creative(X)=>(generous(X)<~>~creative(X))))&
(![X]:((~patient(X)|~old(X))<=>~humble(X)))&
((?[X]:((rich(X)&~strong(X))))<=>((old(mary)|calm(mary))))&
(![X]:((~curious(X)<~>strong(X))=>~old(X)))&
((~wise(susan))<=>(?[X]:((~patient(X)|calm(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(~humble(X)|~wise(X))))&
(![X]:((~tall(X)&creative(X))<=>(wise(X)&curious(X))))&
(((kind(susan)|~old(susan)))<=>(?[X]:(happy(X))))&
(![X]:((~generous(X)|funny(X))<=>(funny(X)<~>brave(X))))&
(![X]:(creative(X)<=>(wise(X)&~patient(X))))&
(((old(fred)&creative(fred)))<=>((~calm(alice)|generous(alice))))&
(((~humble(john)<~>~patient(john)))<=>(~patient(fred)))&
(![X]:(~old(X)=>generous(X)))&
((?[X]:((patient(X)&brave(X))))<=>((~creative(alice)|generous(alice))))&
(![X]:((curious(X)&~kind(X))=>(rich(X)<~>~old(X))))&
(?[X]:((old(X)|patient(X))))&
((funny(mary)|~generous(mary)))&
(?[X]:((~creative(X)|~humble(X))))&
((funny(alice)&rich(alice)))&
((kind(alice)|~brave(alice)))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~generous(john)&~humble(john)))&
(?[X]:((humble(X)&~quiet(X)))) | happy(susan) | [
"p0",
"p5",
"p12",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 219706806523372808122002
% SZS output start Proof for 219706806523372808122002
1. ! [X0] : (~wise(X0) <=> (happy(X0) & old(X0))) [input p0]
6. ~wise(susan) <=> ? [X0] : (calm(X0) | ~patient(X0)) [input p5]
13. (~humble(john) <~> ~patient(john)) <=> ~patient(fred) [input p12]
23. ~humble(john) & ~generous(john) [input p22]
25. ~happy(susan) [input hypothesis]
33. ! [X0] : ((~wise(X0) | (~happy(X0) | ~old(X0))) & ((happy(X0) & old(X0)) | wise(X0))) [nnf transformation 1]
34. ! [X0] : ((~wise(X0) | ~happy(X0) | ~old(X0)) & ((happy(X0) & old(X0)) | wise(X0))) [flattening 33]
44. (~wise(susan) | ! [X0] : (~calm(X0) & patient(X0))) & (? [X0] : (calm(X0) | ~patient(X0)) | wise(susan)) [nnf transformation 6]
45. (~wise(susan) | ! [X0] : (~calm(X0) & patient(X0))) & (? [X1] : (calm(X1) | ~patient(X1)) | wise(susan)) [rectify 44]
46. ? [X1] : (calm(X1) | ~patient(X1)) => (calm(sK1) | ~patient(sK1)) [choice axiom]
47. (~wise(susan) | ! [X0] : (~calm(X0) & patient(X0))) & ((calm(sK1) | ~patient(sK1)) | wise(susan)) [skolemisation 45,46]
62. (((patient(john) | humble(john)) & (~patient(john) | ~humble(john))) | patient(fred)) & (~patient(fred) | ((~humble(john) | patient(john)) & (~patient(john) | humble(john)))) [nnf transformation 13]
79. happy(X0) | wise(X0) [cnf transformation 34]
94. ~wise(susan) | patient(X0) [cnf transformation 47]
119. ~patient(fred) | ~patient(john) | humble(john) [cnf transformation 62]
140. ~humble(john) [cnf transformation 23]
143. ~happy(susan) [cnf transformation 25]
177. 7 <=> wise(susan) [avatar definition]
179. ~wise(susan) <- (~7) [avatar component clause 177]
182. 8 <=> ! [X0] : patient(X0) [avatar definition]
183. patient(X0) <- (8) [avatar component clause 182]
184. 8 | ~7 [avatar split clause 94,177,182]
236. 19 <=> patient(fred) [avatar definition]
237. ~patient(fred) <- (~19) [avatar component clause 236]
240. 20 <=> patient(john) [avatar definition]
241. ~patient(john) <- (~20) [avatar component clause 240]
246. 21 <=> humble(john) [avatar definition]
250. 21 | ~20 | ~19 [avatar split clause 119,236,240,246]
313. ~21 [avatar split clause 140,246]
315. wise(susan) [resolution 79,143]
317. $false <- (~7) [subsumption resolution 315,179]
318. 7 [avatar contradiction clause 317]
322. $false <- (8, ~20) [resolution 183,241]
323. ~8 | 20 [avatar contradiction clause 322]
325. $false <- (8, ~19) [subsumption resolution 237,183]
326. ~8 | 19 [avatar contradiction clause 325]
327. $false [avatar sat refutation 184,250,313,318,323,326]
% SZS output end Proof for 219706806523372808122002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not calm or not humble and vice versa. Everyone who is not patient is both curious and not happy. Everyone who is not quiet is both not strong and not patient. Everyone who is not quiet or not happy is either not patient or not happy and vice versa. Everyone who is both strong and not happy is either brave or not strong. Everyone who is both not calm and strong is either happy or not calm and vice versa. Everyone who is both tall and calm is both not brave and not kind. If susan is strong then someone is both not strong and not curious and vice versa. Everyone who is not strong is humble and vice versa. If paul is both happy and not humble then alice is both quiet and curious. Everyone who is calm or brave is either calm or not happy. Everyone who is tall is both generous and not rich. If paul is both curious and not funny then someone is not strong and vice versa. Everyone who is not old is either not patient or funny. Everyone who is funny is not quiet. If fred is either rich or happy then someone is both kind and rich and vice versa. Someone is either old or wise. Someone is wise or not patient. Fred is not old or not brave. Mary is not curious or quiet. Someone is patient or not generous. Alice is not creative. | Fred is old. | entailment | (![X]:(~brave(X)<=>(~calm(X)|~humble(X))))&
(![X]:(~patient(X)=>(curious(X)&~happy(X))))&
(![X]:(~quiet(X)=>(~strong(X)&~patient(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:((strong(X)&~happy(X))=>(brave(X)<~>~strong(X))))&
(![X]:((~calm(X)&strong(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((tall(X)&calm(X))=>(~brave(X)&~kind(X))))&
((strong(susan))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:(~strong(X)<=>humble(X)))&
(((happy(paul)&~humble(paul)))=>((quiet(alice)&curious(alice))))&
(![X]:((calm(X)|brave(X))=>(calm(X)<~>~happy(X))))&
(![X]:(tall(X)=>(generous(X)&~rich(X))))&
(((curious(paul)&~funny(paul)))<=>(?[X]:(~strong(X))))&
(![X]:(~old(X)=>(~patient(X)<~>funny(X))))&
(![X]:(funny(X)=>~quiet(X)))&
(((rich(fred)<~>happy(fred)))<=>(?[X]:((kind(X)&rich(X)))))&
(?[X]:((old(X)<~>wise(X))))&
(?[X]:((wise(X)|~patient(X))))&
((~old(fred)|~brave(fred)))&
((~curious(mary)|quiet(mary)))&
(?[X]:((patient(X)|~generous(X))))&
(~creative(alice)) | old(fred) | [
"p1",
"p2",
"p3",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8918935026794299007644448
% SZS output start Proof for 8918935026794299007644448
2. ! [X0] : (~patient(X0) => (~happy(X0) & curious(X0))) [input p1]
3. ! [X0] : (~quiet(X0) => (~patient(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (~patient(X0) <~> ~happy(X0))) [input p3]
14. ! [X0] : (~old(X0) => (~patient(X0) <~> funny(X0))) [input p13]
15. ! [X0] : (funny(X0) => ~quiet(X0)) [input p14]
23. ~old(fred) [input hypothesis]
28. ! [X0] : ((~happy(X0) & curious(X0)) | patient(X0)) [ennf transformation 2]
29. ! [X0] : ((~patient(X0) & ~strong(X0)) | quiet(X0)) [ennf transformation 3]
35. ! [X0] : ((~patient(X0) <~> funny(X0)) | old(X0)) [ennf transformation 14]
36. ! [X0] : (~quiet(X0) | ~funny(X0)) [ennf transformation 15]
39. ! [X0] : (((~happy(X0) | ~quiet(X0)) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (happy(X0) & quiet(X0)))) [nnf transformation 4]
40. ! [X0] : ((~happy(X0) | ~quiet(X0) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | (happy(X0) & quiet(X0)))) [flattening 39]
55. ! [X0] : (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | old(X0)) [nnf transformation 35]
69. ~happy(X0) | patient(X0) [cnf transformation 28]
71. ~patient(X0) | quiet(X0) [cnf transformation 29]
75. happy(X0) | patient(X0) | happy(X0) [cnf transformation 40]
100. funny(X0) | ~patient(X0) | old(X0) [cnf transformation 55]
102. ~funny(X0) | ~quiet(X0) [cnf transformation 36]
114. ~old(fred) [cnf transformation 23]
119. happy(X0) | patient(X0) [duplicate literal removal 75]
121. patient(X0) [subsumption resolution 119,69]
180. old(X0) | funny(X0) [subsumption resolution 100,121]
231. quiet(X0) [resolution 71,121]
239. funny(fred) [resolution 180,114]
240. ~quiet(fred) [resolution 239,102]
241. $false [subsumption resolution 240,231]
% SZS output end Proof for 8918935026794299007644448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not quiet or brave.
Everyone who is both generous and not generous is either not calm or curious.
Everyone who is brave or curious is wise or not strong.
Everyone who is funny or happy is either rich or tall and vice versa.
Everyone who is kind or not humble is not humble and vice versa.
Everyone who is either not happy or not rich is either brave or happy and vice versa.
If someone is both not wise and not strong then paul is both wise and tall and vice versa.
Everyone who is either brave or not creative is either not rich or not wise and vice versa.
Everyone who is either curious or old is creative and vice versa.
Everyone who is rich is either not kind or curious and vice versa.
Everyone who is either not wise or curious is either not happy or quiet and vice versa.
Everyone who is not quiet is quiet or not humble and vice versa.
Everyone who is either not tall or creative is either generous or quiet and vice versa.
If paul is both not generous and not wise then someone is both curious and creative and vice versa.
Everyone who is not creative or calm is not calm or humble and vice versa.
Everyone who is either humble or calm is not humble or kind.
Someone is either not patient or curious.
Paul is both strong and not quiet.
Fred is calm or not rich.
Someone is generous.
John is not strong or not creative.
Alice is patient or not rich.
Someone is either not kind or funny. | John is not funny. | neutral | (![X]:(~calm(X)=>(~quiet(X)|brave(X))))&
(![X]:((generous(X)&~generous(X))=>(~calm(X)<~>curious(X))))&
(![X]:((brave(X)|curious(X))=>(wise(X)|~strong(X))))&
(![X]:((funny(X)|happy(X))<=>(rich(X)<~>tall(X))))&
(![X]:((kind(X)|~humble(X))<=>~humble(X)))&
(![X]:((~happy(X)<~>~rich(X))<=>(brave(X)<~>happy(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>((wise(paul)&tall(paul))))&
(![X]:((brave(X)<~>~creative(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((curious(X)<~>old(X))<=>creative(X)))&
(![X]:(rich(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:(~quiet(X)<=>(quiet(X)|~humble(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(generous(X)<~>quiet(X))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:((~creative(X)|calm(X))<=>(~calm(X)|humble(X))))&
(![X]:((humble(X)<~>calm(X))=>(~humble(X)|kind(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
((strong(paul)&~quiet(paul)))&
((calm(fred)|~rich(fred)))&
(?[X]:(generous(X)))&
((~strong(john)|~creative(john)))&
((patient(alice)|~rich(alice)))&
(?[X]:((~kind(X)<~>funny(X)))) | ~funny(john) | []
| null | 0 |
Everyone who is both not brave and funny is quiet and vice versa.
Everyone who is rich or not patient is not patient or creative and vice versa.
If alice is either not patient or humble then alice is not creative or not generous.
Everyone who is either calm or creative is both not patient and not curious and vice versa.
If lucy is not kind or not patient then alice is not rich and vice versa.
Everyone who is either not rich or happy is not wise or quiet and vice versa.
If paul is not creative or not humble then mary is both not happy and brave.
If lucy is either not humble or funny then john is creative or not tall and vice versa.
If someone is happy then susan is both calm and rich and vice versa.
If someone is both not happy and generous then someone is either kind or not curious and vice versa.
Everyone who is happy or generous is not strong or kind.
Everyone who is either creative or not rich is either not humble or not wise.
If lucy is both not wise and curious then someone is both not calm and kind.
If someone is either not calm or rich then alice is wise or not generous and vice versa.
If someone is not rich or curious then alice is either brave or funny and vice versa.
Everyone who is not humble is both humble and not patient and vice versa.
John is either rich or brave.
Alice is both strong and not generous.
Mary is either not tall or funny.
Lucy is not generous or brave.
John is curious or not curious.
Someone is either not strong or curious.
Fred is not quiet.
Paul is both not creative and not kind. | Paul is not rich. | entailment | (![X]:((~brave(X)&funny(X))<=>quiet(X)))&
(![X]:((rich(X)|~patient(X))<=>(~patient(X)|creative(X))))&
(((~patient(alice)<~>humble(alice)))=>((~creative(alice)|~generous(alice))))&
(![X]:((calm(X)<~>creative(X))<=>(~patient(X)&~curious(X))))&
(((~kind(lucy)|~patient(lucy)))<=>(~rich(alice)))&
(![X]:((~rich(X)<~>happy(X))<=>(~wise(X)|quiet(X))))&
(((~creative(paul)|~humble(paul)))=>((~happy(mary)&brave(mary))))&
(((~humble(lucy)<~>funny(lucy)))<=>((creative(john)|~tall(john))))&
((?[X]:(happy(X)))<=>((calm(susan)&rich(susan))))&
((?[X]:((~happy(X)&generous(X))))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((happy(X)|generous(X))=>(~strong(X)|kind(X))))&
(![X]:((creative(X)<~>~rich(X))=>(~humble(X)<~>~wise(X))))&
(((~wise(lucy)&curious(lucy)))=>(?[X]:((~calm(X)&kind(X)))))&
((?[X]:((~calm(X)<~>rich(X))))<=>((wise(alice)|~generous(alice))))&
((?[X]:((~rich(X)|curious(X))))<=>((brave(alice)<~>funny(alice))))&
(![X]:(~humble(X)<=>(humble(X)&~patient(X))))&
((rich(john)<~>brave(john)))&
((strong(alice)&~generous(alice)))&
((~tall(mary)<~>funny(mary)))&
((~generous(lucy)|brave(lucy)))&
((curious(john)|~curious(john)))&
(?[X]:((~strong(X)<~>curious(X))))&
(~quiet(fred))&
((~creative(paul)&~kind(paul))) | ~rich(paul) | [
"p1",
"p15",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 8797226846921653270687772
% SZS output start Proof for 8797226846921653270687772
2. ! [X0] : ((~patient(X0) | rich(X0)) <=> (creative(X0) | ~patient(X0))) [input p1]
16. ! [X0] : (~humble(X0) <=> (~patient(X0) & humble(X0))) [input p15]
24. ~kind(paul) & ~creative(paul) [input p23]
25. rich(paul) [input hypothesis]
37. ! [X0] : (((~patient(X0) | rich(X0)) | (~creative(X0) & patient(X0))) & ((creative(X0) | ~patient(X0)) | (patient(X0) & ~rich(X0)))) [nnf transformation 2]
38. ! [X0] : ((~patient(X0) | rich(X0) | (~creative(X0) & patient(X0))) & (creative(X0) | ~patient(X0) | (patient(X0) & ~rich(X0)))) [flattening 37]
70. ! [X0] : ((~humble(X0) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | humble(X0))) [nnf transformation 16]
71. ! [X0] : ((~humble(X0) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | humble(X0))) [flattening 70]
80. ~patient(X0) | creative(X0) | ~rich(X0) [cnf transformation 38]
140. humble(X0) | humble(X0) [cnf transformation 71]
142. ~humble(X0) | patient(X0) | ~humble(X0) [cnf transformation 71]
154. ~creative(paul) [cnf transformation 24]
156. rich(paul) [cnf transformation 25]
157. humble(X0) [duplicate literal removal 140]
158. ~humble(X0) | patient(X0) [duplicate literal removal 142]
202. 10 <=> creative(paul) [avatar definition]
203. ~creative(paul) <- (~10) [avatar component clause 202]
393. ~10 [avatar split clause 154,202]
396. patient(X0) [resolution 158,157]
402. ~rich(X0) | creative(X0) [resolution 80,396]
405. creative(paul) [resolution 402,156]
408. $false <- (~10) [subsumption resolution 405,203]
409. 10 [avatar contradiction clause 408]
412. $false [avatar sat refutation 393,409]
% SZS output end Proof for 8797226846921653270687772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not rich is both not strong and not curious.
Everyone who is both not generous and not tall is humble or not humble.
Everyone who is not strong or generous is both funny and old and vice versa.
If paul is either not calm or tall then alice is both patient and strong and vice versa.
Everyone who is either not strong or not happy is not generous.
If paul is old or not quiet then fred is not creative.
Everyone who is not quiet is not curious and vice versa.
Everyone who is either not kind or not funny is either not curious or not quiet and vice versa.
Everyone who is both not creative and not funny is either not kind or strong.
If john is not humble or rich then alice is either old or patient.
If fred is either creative or not brave then mary is both generous and patient.
Everyone who is both old and not patient is not funny.
If fred is both kind and not curious then someone is either patient or not rich.
Everyone who is either not wise or not funny is either wise or creative.
If someone is patient then someone is old.
Everyone who is either not old or not patient is both generous and not rich.
Fred is either tall or creative.
Lucy is not quiet.
Someone is not wise or rich.
Mary is not strong.
Alice is not quiet.
Susan is not old or not happy.
Someone is either quiet or not patient.
Alice is not creative. | Alice is not curious. | entailment | (![X]:((~curious(X)&~rich(X))=>(~strong(X)&~curious(X))))&
(![X]:((~generous(X)&~tall(X))=>(humble(X)|~humble(X))))&
(![X]:((~strong(X)|generous(X))<=>(funny(X)&old(X))))&
(((~calm(paul)<~>tall(paul)))<=>((patient(alice)&strong(alice))))&
(![X]:((~strong(X)<~>~happy(X))=>~generous(X)))&
(((old(paul)|~quiet(paul)))=>(~creative(fred)))&
(![X]:(~quiet(X)<=>~curious(X)))&
(![X]:((~kind(X)<~>~funny(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:((~creative(X)&~funny(X))=>(~kind(X)<~>strong(X))))&
(((~humble(john)|rich(john)))=>((old(alice)<~>patient(alice))))&
(((creative(fred)<~>~brave(fred)))=>((generous(mary)&patient(mary))))&
(![X]:((old(X)&~patient(X))=>~funny(X)))&
(((kind(fred)&~curious(fred)))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((~wise(X)<~>~funny(X))=>(wise(X)<~>creative(X))))&
((?[X]:(patient(X)))=>(?[X]:(old(X))))&
(![X]:((~old(X)<~>~patient(X))=>(generous(X)&~rich(X))))&
((tall(fred)<~>creative(fred)))&
(~quiet(lucy))&
(?[X]:((~wise(X)|rich(X))))&
(~strong(mary))&
(~quiet(alice))&
((~old(susan)|~happy(susan)))&
(?[X]:((quiet(X)<~>~patient(X))))&
(~creative(alice)) | ~curious(alice) | [
"p6",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 950309755923166501812969
% SZS output start Proof for 950309755923166501812969
7. ! [X0] : (~quiet(X0) <=> ~curious(X0)) [input p6]
21. ~quiet(alice) [input p20]
25. curious(alice) [input hypothesis]
49. ! [X0] : ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))) [nnf transformation 7]
86. ~curious(X0) | quiet(X0) [cnf transformation 49]
123. ~quiet(alice) [cnf transformation 21]
128. curious(alice) [cnf transformation 25]
267. quiet(alice) [resolution 86,128]
268. $false [subsumption resolution 267,123]
% SZS output end Proof for 950309755923166501812969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not brave is both not humble and curious and vice versa.
If susan is either funny or not strong then john is not quiet or strong and vice versa.
If someone is curious or old then lucy is both rich and not creative.
If fred is not funny then lucy is either not old or curious and vice versa.
Everyone who is either not generous or not curious is not calm or not wise.
If fred is humble then someone is calm.
If susan is tall or strong then paul is not old or creative and vice versa.
If lucy is not wise then someone is either tall or not creative and vice versa.
If susan is either not rich or not patient then susan is curious.
If someone is both not rich and not happy then mary is strong.
If someone is brave then someone is not curious.
Everyone who is tall or not old is rich or not patient.
Everyone who is either not wise or not strong is both rich and not creative and vice versa.
Everyone who is either not strong or not brave is both not funny and brave and vice versa.
Everyone who is not calm or tall is not funny.
Everyone who is either quiet or not strong is patient or humble and vice versa.
Someone is not tall or humble.
Someone is quiet or happy.
Lucy is either not tall or not wise.
John is creative.
Lucy is either not calm or quiet.
John is not humble. | Lucy is quiet. | contradiction | (![X]:((quiet(X)|~brave(X))<=>(~humble(X)&curious(X))))&
(((funny(susan)<~>~strong(susan)))<=>((~quiet(john)|strong(john))))&
((?[X]:((curious(X)|old(X))))=>((rich(lucy)&~creative(lucy))))&
((~funny(fred))<=>((~old(lucy)<~>curious(lucy))))&
(![X]:((~generous(X)<~>~curious(X))=>(~calm(X)|~wise(X))))&
((humble(fred))=>(?[X]:(calm(X))))&
(((tall(susan)|strong(susan)))<=>((~old(paul)|creative(paul))))&
((~wise(lucy))<=>(?[X]:((tall(X)<~>~creative(X)))))&
(((~rich(susan)<~>~patient(susan)))=>(curious(susan)))&
((?[X]:((~rich(X)&~happy(X))))=>(strong(mary)))&
((?[X]:(brave(X)))=>(?[X]:(~curious(X))))&
(![X]:((tall(X)|~old(X))=>(rich(X)|~patient(X))))&
(![X]:((~wise(X)<~>~strong(X))<=>(rich(X)&~creative(X))))&
(![X]:((~strong(X)<~>~brave(X))<=>(~funny(X)&brave(X))))&
(![X]:((~calm(X)|tall(X))=>~funny(X)))&
(![X]:((quiet(X)<~>~strong(X))<=>(patient(X)|humble(X))))&
(?[X]:((~tall(X)|humble(X))))&
(?[X]:((quiet(X)|happy(X))))&
((~tall(lucy)<~>~wise(lucy)))&
(creative(john))&
((~calm(lucy)<~>quiet(lucy)))&
(~humble(john)) | quiet(lucy) | [
"p0",
"p2",
"p7",
"p12",
"p13",
"p14",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 6238235594571688336115856
% SZS output start Proof for 6238235594571688336115856
1. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (curious(X0) & ~humble(X0))) [input p0]
3. ? [X0] : (old(X0) | curious(X0)) => (~creative(lucy) & rich(lucy)) [input p2]
8. ~wise(lucy) <=> ? [X0] : (tall(X0) <~> ~creative(X0)) [input p7]
13. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~creative(X0) & rich(X0))) [input p12]
14. ! [X0] : ((~strong(X0) <~> ~brave(X0)) <=> (brave(X0) & ~funny(X0))) [input p13]
15. ! [X0] : ((tall(X0) | ~calm(X0)) => ~funny(X0)) [input p14]
19. ~tall(lucy) <~> ~wise(lucy) [input p18]
23. quiet(lucy) [input hypothesis]
27. (~creative(lucy) & rich(lucy)) | ! [X0] : (~old(X0) & ~curious(X0)) [ennf transformation 3]
35. ! [X0] : (~funny(X0) | (~tall(X0) & calm(X0))) [ennf transformation 15]
36. ! [X0] : (((~brave(X0) | quiet(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (brave(X0) & ~quiet(X0)))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | quiet(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (brave(X0) & ~quiet(X0)))) [flattening 36]
46. (~wise(lucy) | ! [X0] : ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (? [X0] : ((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | wise(lucy)) [nnf transformation 8]
47. (~wise(lucy) | ! [X0] : ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (? [X1] : ((creative(X1) | ~tall(X1)) & (~creative(X1) | tall(X1))) | wise(lucy)) [rectify 46]
48. ? [X1] : ((creative(X1) | ~tall(X1)) & (~creative(X1) | tall(X1))) => ((creative(sK1) | ~tall(sK1)) & (~creative(sK1) | tall(sK1))) [choice axiom]
49. (~wise(lucy) | ! [X0] : ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(sK1) | ~tall(sK1)) & (~creative(sK1) | tall(sK1))) | wise(lucy)) [skolemisation 47,48]
54. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (creative(X0) | ~rich(X0))) & ((~creative(X0) & rich(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 13]
55. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | creative(X0) | ~rich(X0)) & ((~creative(X0) & rich(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [flattening 54]
56. ! [X0] : ((((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (~brave(X0) | funny(X0))) & ((brave(X0) & ~funny(X0)) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))))) [nnf transformation 14]
57. ! [X0] : ((((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | ~brave(X0) | funny(X0)) & ((brave(X0) & ~funny(X0)) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0))))) [flattening 56]
62. (wise(lucy) | tall(lucy)) & (~wise(lucy) | ~tall(lucy)) [nnf transformation 19]
66. ~quiet(X0) | curious(X0) [cnf transformation 37]
75. rich(lucy) | ~curious(X0) [cnf transformation 27]
77. ~creative(lucy) | ~curious(X0) [cnf transformation 27]
93. ~wise(lucy) | tall(X0) | creative(X0) [cnf transformation 49]
104. ~rich(X0) | wise(X0) | creative(X0) | strong(X0) [cnf transformation 55]
108. brave(X0) | ~strong(X0) | brave(X0) [cnf transformation 57]
109. ~brave(X0) | ~strong(X0) | ~brave(X0) | funny(X0) [cnf transformation 57]
112. ~tall(X0) | ~funny(X0) [cnf transformation 35]
120. ~wise(lucy) | ~tall(lucy) [cnf transformation 62]
121. wise(lucy) | tall(lucy) [cnf transformation 62]
126. quiet(lucy) [cnf transformation 23]
127. ~strong(X0) | brave(X0) [duplicate literal removal 108]
128. ~strong(X0) | ~brave(X0) | funny(X0) [duplicate literal removal 109]
155. 6 <=> creative(lucy) [avatar definition]
157. ~creative(lucy) <- (~6) [avatar component clause 155]
160. 7 <=> ! [X0] : ~curious(X0) [avatar definition]
161. ~curious(X0) <- (7) [avatar component clause 160]
162. 7 | ~6 [avatar split clause 77,155,160]
164. 8 <=> rich(lucy) [avatar definition]
166. rich(lucy) <- (8) [avatar component clause 164]
168. 7 | 8 [avatar split clause 75,164,160]
211. 17 <=> ! [X0] : (tall(X0) | creative(X0)) [avatar definition]
212. tall(X0) | creative(X0) <- (17) [avatar component clause 211]
214. 18 <=> wise(lucy) [avatar definition]
216. ~wise(lucy) <- (~18) [avatar component clause 214]
217. 17 | ~18 [avatar split clause 93,214,211]
266. 29 <=> tall(lucy) [avatar definition]
267. ~tall(lucy) <- (~29) [avatar component clause 266]
268. tall(lucy) <- (29) [avatar component clause 266]
269. 29 | 18 [avatar split clause 121,214,266]
270. ~29 | ~18 [avatar split clause 120,214,266]
276. 31 <=> quiet(lucy) [avatar definition]
277. quiet(lucy) <- (31) [avatar component clause 276]
281. 31 [avatar split clause 126,276]
282. curious(lucy) <- (31) [resolution 66,277]
285. $false <- (7, 31) [subsumption resolution 282,161]
286. ~7 | ~31 [avatar contradiction clause 285]
295. creative(lucy) <- (17, ~29) [resolution 212,267]
297. $false <- (~6, 17, ~29) [subsumption resolution 295,157]
298. 6 | ~17 | 29 [avatar contradiction clause 297]
299. ~funny(lucy) <- (29) [resolution 268,112]
331. wise(lucy) | creative(lucy) | strong(lucy) <- (8) [resolution 104,166]
332. creative(lucy) | strong(lucy) <- (8, ~18) [subsumption resolution 331,216]
333. strong(lucy) <- (~6, 8, ~18) [subsumption resolution 332,157]
335. ~brave(lucy) | funny(lucy) <- (~6, 8, ~18) [resolution 333,128]
338. brave(lucy) <- (~6, 8, ~18) [resolution 333,127]
340. ~brave(lucy) <- (~6, 8, ~18, 29) [subsumption resolution 335,299]
341. $false <- (~6, 8, ~18, 29) [subsumption resolution 338,340]
342. 6 | ~8 | 18 | ~29 [avatar contradiction clause 341]
343. $false [avatar sat refutation 162,168,217,269,270,281,286,298,342]
% SZS output end Proof for 6238235594571688336115856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or calm and vice versa.
Everyone who is kind or not calm is both wise and funny.
Everyone who is not kind is generous.
Everyone who is either brave or happy is not old or funny and vice versa.
If lucy is either not creative or calm then susan is not creative or not generous.
Everyone who is wise is not funny and vice versa.
If john is generous or not happy then fred is not quiet and vice versa.
If someone is both not kind and not tall then alice is not calm or not humble and vice versa.
Everyone who is either tall or generous is either wise or kind and vice versa.
Everyone who is not kind or creative is not patient or funny.
If someone is generous or curious then mary is wise.
If lucy is not tall then someone is either not happy or not curious.
If someone is not calm or not funny then someone is either not quiet or creative and vice versa.
Everyone who is both not calm and kind is wise.
Someone is both creative and brave.
Lucy is both not strong and not creative.
Someone is curious or funny.
Susan is either funny or not strong.
Paul is rich or tall.
Lucy is either humble or not creative. | Mary is not tall. | entailment | (![X]:(~humble(X)<=>(kind(X)|calm(X))))&
(![X]:((kind(X)|~calm(X))=>(wise(X)&funny(X))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((brave(X)<~>happy(X))<=>(~old(X)|funny(X))))&
(((~creative(lucy)<~>calm(lucy)))=>((~creative(susan)|~generous(susan))))&
(![X]:(wise(X)<=>~funny(X)))&
(((generous(john)|~happy(john)))<=>(~quiet(fred)))&
((?[X]:((~kind(X)&~tall(X))))<=>((~calm(alice)|~humble(alice))))&
(![X]:((tall(X)<~>generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~kind(X)|creative(X))=>(~patient(X)|funny(X))))&
((?[X]:((generous(X)|curious(X))))=>(wise(mary)))&
((~tall(lucy))=>(?[X]:((~happy(X)<~>~curious(X)))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(![X]:((~calm(X)&kind(X))=>wise(X)))&
(?[X]:((creative(X)&brave(X))))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((curious(X)|funny(X))))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)|tall(paul)))&
((humble(lucy)<~>~creative(lucy))) | ~tall(mary) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p8",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 1547147243366329547893043
% SZS output start Proof for 1547147243366329547893043
1. ! [X0] : (~humble(X0) <=> (calm(X0) | kind(X0))) [input p0]
2. ! [X0] : ((~calm(X0) | kind(X0)) => (funny(X0) & wise(X0))) [input p1]
3. ! [X0] : (~kind(X0) => generous(X0)) [input p2]
6. ! [X0] : (wise(X0) <=> ~funny(X0)) [input p5]
8. ? [X0] : (~tall(X0) & ~kind(X0)) <=> (~humble(alice) | ~calm(alice)) [input p7]
9. ! [X0] : ((tall(X0) <~> generous(X0)) <=> (wise(X0) <~> kind(X0))) [input p8]
11. ? [X0] : (curious(X0) | generous(X0)) => wise(mary) [input p10]
21. tall(mary) [input hypothesis]
25. ! [X0] : ((funny(X0) & wise(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 2]
26. ! [X0] : (generous(X0) | kind(X0)) [ennf transformation 3]
29. wise(mary) | ! [X0] : (~curious(X0) & ~generous(X0)) [ennf transformation 11]
33. ! [X0] : ((~humble(X0) | (~calm(X0) & ~kind(X0))) & ((calm(X0) | kind(X0)) | humble(X0))) [nnf transformation 1]
34. ! [X0] : ((~humble(X0) | (~calm(X0) & ~kind(X0))) & (calm(X0) | kind(X0) | humble(X0))) [flattening 33]
38. ! [X0] : ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))) [nnf transformation 6]
41. (? [X0] : (~tall(X0) & ~kind(X0)) | (humble(alice) & calm(alice))) & ((~humble(alice) | ~calm(alice)) | ! [X0] : (tall(X0) | kind(X0))) [nnf transformation 8]
42. (? [X0] : (~tall(X0) & ~kind(X0)) | (humble(alice) & calm(alice))) & (~humble(alice) | ~calm(alice) | ! [X0] : (tall(X0) | kind(X0))) [flattening 41]
43. (? [X0] : (~tall(X0) & ~kind(X0)) | (humble(alice) & calm(alice))) & (~humble(alice) | ~calm(alice) | ! [X1] : (tall(X1) | kind(X1))) [rectify 42]
44. ? [X0] : (~tall(X0) & ~kind(X0)) => (~tall(sK0) & ~kind(sK0)) [choice axiom]
45. ((~tall(sK0) & ~kind(sK0)) | (humble(alice) & calm(alice))) & (~humble(alice) | ~calm(alice) | ! [X1] : (tall(X1) | kind(X1))) [skolemisation 43,44]
46. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 9]
63. ~calm(X0) | ~humble(X0) [cnf transformation 34]
65. wise(X0) | calm(X0) [cnf transformation 25]
66. ~kind(X0) | funny(X0) [cnf transformation 25]
67. funny(X0) | calm(X0) [cnf transformation 25]
68. generous(X0) | kind(X0) [cnf transformation 26]
77. ~funny(X0) | ~wise(X0) [cnf transformation 38]
84. ~kind(sK0) | humble(alice) [cnf transformation 45]
93. ~generous(X0) | ~tall(X0) | kind(X0) | ~wise(X0) [cnf transformation 46]
95. wise(mary) | ~generous(X0) [cnf transformation 29]
115. tall(mary) [cnf transformation 21]
150. 8 <=> humble(alice) [avatar definition]
152. humble(alice) <- (8) [avatar component clause 150]
164. 11 <=> kind(sK0) [avatar definition]
166. ~kind(sK0) <- (~11) [avatar component clause 164]
167. 8 | ~11 [avatar split clause 84,164,150]
169. ~tall(X0) | kind(X0) | ~wise(X0) [subsumption resolution 93,68]
177. 13 <=> wise(mary) [avatar definition]
179. wise(mary) <- (13) [avatar component clause 177]
182. 14 <=> ! [X0] : ~generous(X0) [avatar definition]
183. ~generous(X0) <- (14) [avatar component clause 182]
184. 14 | 13 [avatar split clause 95,177,182]
228. 25 <=> ! [X3] : calm(X3) [avatar definition]
229. calm(X3) <- (25) [avatar component clause 228]
261. ~wise(X0) | calm(X0) [resolution 77,67]
262. calm(X0) [subsumption resolution 261,65]
263. 25 [avatar split clause 262,228]
265. ~humble(X0) <- (25) [resolution 229,63]
274. kind(mary) | ~wise(mary) [resolution 169,115]
276. kind(mary) <- (13) [subsumption resolution 274,179]
287. funny(mary) <- (13) [resolution 276,66]
301. ~wise(mary) <- (13) [resolution 287,77]
311. $false <- (13) [subsumption resolution 301,179]
312. ~13 [avatar contradiction clause 311]
326. kind(X0) <- (14) [resolution 183,68]
340. $false <- (~11, 14) [resolution 326,166]
344. 11 | ~14 [avatar contradiction clause 340]
346. $false <- (8, 25) [subsumption resolution 152,265]
347. ~8 | ~25 [avatar contradiction clause 346]
348. $false [avatar sat refutation 167,184,263,312,344,347]
% SZS output end Proof for 1547147243366329547893043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not calm and not rich then someone is not strong or quiet and vice versa.
Everyone who is not calm or not creative is not tall.
Everyone who is wise is either not strong or calm.
Everyone who is not brave or creative is either humble or not creative.
If someone is not funny then john is humble or tall and vice versa.
Everyone who is both rich and not creative is funny or not tall.
If someone is quiet then lucy is tall.
Everyone who is not calm is not quiet or happy.
Everyone who is tall is curious and vice versa.
Everyone who is either tall or humble is curious and vice versa.
If paul is not happy or wise then paul is either humble or not strong and vice versa.
If lucy is either not kind or not funny then fred is both wise and not rich and vice versa.
If john is both not strong and strong then someone is both happy and not happy.
If susan is creative then paul is both not humble and calm and vice versa.
Everyone who is either humble or not happy is both not generous and not old.
If someone is not wise or funny then someone is not tall and vice versa.
Someone is calm.
Fred is either calm or not humble.
Someone is generous.
John is both wise and not quiet. | Lucy is not rich. | neutral | (((~calm(fred)&~rich(fred)))<=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:((~calm(X)|~creative(X))=>~tall(X)))&
(![X]:(wise(X)=>(~strong(X)<~>calm(X))))&
(![X]:((~brave(X)|creative(X))=>(humble(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>((humble(john)|tall(john))))&
(![X]:((rich(X)&~creative(X))=>(funny(X)|~tall(X))))&
((?[X]:(quiet(X)))=>(tall(lucy)))&
(![X]:(~calm(X)=>(~quiet(X)|happy(X))))&
(![X]:(tall(X)<=>curious(X)))&
(![X]:((tall(X)<~>humble(X))<=>curious(X)))&
(((~happy(paul)|wise(paul)))<=>((humble(paul)<~>~strong(paul))))&
(((~kind(lucy)<~>~funny(lucy)))<=>((wise(fred)&~rich(fred))))&
(((~strong(john)&strong(john)))=>(?[X]:((happy(X)&~happy(X)))))&
((creative(susan))<=>((~humble(paul)&calm(paul))))&
(![X]:((humble(X)<~>~happy(X))=>(~generous(X)&~old(X))))&
((?[X]:((~wise(X)|funny(X))))<=>(?[X]:(~tall(X))))&
(?[X]:(calm(X)))&
((calm(fred)<~>~humble(fred)))&
(?[X]:(generous(X)))&
((wise(john)&~quiet(john))) | ~rich(lucy) | []
| null | 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 5511613620452556255800998
% SZS output start Proof for 5511613620452556255800998
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 5511613620452556255800998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not happy is rich.
Everyone who is not quiet is wise.
If john is generous or not rich then mary is either quiet or patient.
If someone is not quiet or strong then john is old or not wise.
If someone is quiet or patient then paul is not humble and vice versa.
If someone is both humble and happy then someone is both curious and not patient and vice versa.
Everyone who is both not strong and humble is both not creative and curious and vice versa.
If someone is old or kind then someone is both not brave and not creative and vice versa.
Everyone who is both funny and calm is not humble and vice versa.
If someone is either not brave or not tall then alice is not quiet or brave.
Everyone who is not curious is both calm and not strong and vice versa.
Everyone who is calm or creative is quiet or strong.
Everyone who is both not brave and tall is either creative or brave and vice versa.
Everyone who is quiet or humble is both not calm and not tall and vice versa.
Everyone who is both kind and humble is either not curious or not tall.
Susan is both not old and not kind.
Someone is not humble or patient. | Alice is curious. | entailment | (![X]:((creative(X)|~happy(X))=>rich(X)))&
(![X]:(~quiet(X)=>wise(X)))&
(((generous(john)|~rich(john)))=>((quiet(mary)<~>patient(mary))))&
((?[X]:((~quiet(X)|strong(X))))=>((old(john)|~wise(john))))&
((?[X]:((quiet(X)|patient(X))))<=>(~humble(paul)))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~strong(X)&humble(X))<=>(~creative(X)&curious(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((funny(X)&calm(X))<=>~humble(X)))&
((?[X]:((~brave(X)<~>~tall(X))))=>((~quiet(alice)|brave(alice))))&
(![X]:(~curious(X)<=>(calm(X)&~strong(X))))&
(![X]:((calm(X)|creative(X))=>(quiet(X)|strong(X))))&
(![X]:((~brave(X)&tall(X))<=>(creative(X)<~>brave(X))))&
(![X]:((quiet(X)|humble(X))<=>(~calm(X)&~tall(X))))&
(![X]:((kind(X)&humble(X))=>(~curious(X)<~>~tall(X))))&
((~old(susan)&~kind(susan)))&
(?[X]:((~humble(X)|patient(X)))) | curious(alice) | [
"p10",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 7864675393858781452634310
% SZS output start Proof for 7864675393858781452634310
11. ! [X0] : (~curious(X0) <=> (~strong(X0) & calm(X0))) [input p10]
12. ! [X0] : ((creative(X0) | calm(X0)) => (strong(X0) | quiet(X0))) [input p11]
14. ! [X0] : ((humble(X0) | quiet(X0)) <=> (~tall(X0) & ~calm(X0))) [input p13]
18. ~curious(alice) [input hypothesis]
29. ! [X0] : ((strong(X0) | quiet(X0)) | (~creative(X0) & ~calm(X0))) [ennf transformation 12]
30. ! [X0] : (strong(X0) | quiet(X0) | (~creative(X0) & ~calm(X0))) [flattening 29]
52. ! [X0] : ((~curious(X0) | (strong(X0) | ~calm(X0))) & ((~strong(X0) & calm(X0)) | curious(X0))) [nnf transformation 11]
53. ! [X0] : ((~curious(X0) | strong(X0) | ~calm(X0)) & ((~strong(X0) & calm(X0)) | curious(X0))) [flattening 52]
56. ! [X0] : (((humble(X0) | quiet(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 14]
57. ! [X0] : ((humble(X0) | quiet(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (~humble(X0) & ~quiet(X0)))) [flattening 56]
85. calm(X0) | curious(X0) [cnf transformation 53]
86. ~strong(X0) | curious(X0) [cnf transformation 53]
88. ~calm(X0) | quiet(X0) | strong(X0) [cnf transformation 30]
96. ~calm(X0) | ~quiet(X0) [cnf transformation 57]
106. ~curious(alice) [cnf transformation 18]
233. ~quiet(X0) | curious(X0) [resolution 96,85]
283. quiet(X0) | strong(X0) | curious(X0) [resolution 88,85]
285. strong(X0) | curious(X0) [subsumption resolution 283,233]
286. curious(X0) [subsumption resolution 285,86]
288. $false [resolution 286,106]
% SZS output end Proof for 7864675393858781452634310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either kind or not creative then susan is both generous and not rich. Everyone who is rich or strong is not calm. Everyone who is both generous and curious is kind or funny and vice versa. Everyone who is not patient or not strong is wise or not tall and vice versa. If someone is either generous or not tall then someone is curious or not patient. Everyone who is funny or not calm is both not brave and curious and vice versa. If susan is rich then someone is old or kind. If fred is both not old and rich then someone is both not kind and wise and vice versa. If someone is not curious then someone is creative or rich and vice versa. Everyone who is not rich or not curious is tall. If susan is either wise or generous then lucy is either not funny or tall and vice versa. Everyone who is not patient or not humble is either creative or tall and vice versa. Everyone who is both humble and strong is both humble and not patient and vice versa. Everyone who is either humble or quiet is both not funny and not kind. Everyone who is tall or rich is both not patient and not happy. Alice is both not happy and funny. Someone is funny. Susan is not patient or kind. Someone is not humble or not curious. Someone is either brave or tall. | Susan is tall. | entailment | ((?[X]:((kind(X)<~>~creative(X))))=>((generous(susan)&~rich(susan))))&
(![X]:((rich(X)|strong(X))=>~calm(X)))&
(![X]:((generous(X)&curious(X))<=>(kind(X)|funny(X))))&
(![X]:((~patient(X)|~strong(X))<=>(wise(X)|~tall(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((funny(X)|~calm(X))<=>(~brave(X)&curious(X))))&
((rich(susan))=>(?[X]:((old(X)|kind(X)))))&
(((~old(fred)&rich(fred)))<=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((~rich(X)|~curious(X))=>tall(X)))&
(((wise(susan)<~>generous(susan)))<=>((~funny(lucy)<~>tall(lucy))))&
(![X]:((~patient(X)|~humble(X))<=>(creative(X)<~>tall(X))))&
(![X]:((humble(X)&strong(X))<=>(humble(X)&~patient(X))))&
(![X]:((humble(X)<~>quiet(X))=>(~funny(X)&~kind(X))))&
(![X]:((tall(X)|rich(X))=>(~patient(X)&~happy(X))))&
((~happy(alice)&funny(alice)))&
(?[X]:(funny(X)))&
((~patient(susan)|kind(susan)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:((brave(X)<~>tall(X)))) | tall(susan) | [
"p0",
"p2",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8176661643716267063365712
% SZS output start Proof for 8176661643716267063365712
1. ? [X0] : (kind(X0) <~> ~creative(X0)) => (~rich(susan) & generous(susan)) [input p0]
3. ! [X0] : ((curious(X0) & generous(X0)) <=> (funny(X0) | kind(X0))) [input p2]
9. ? [X0] : ~curious(X0) <=> ? [X0] : (rich(X0) | creative(X0)) [input p8]
10. ! [X0] : ((~curious(X0) | ~rich(X0)) => tall(X0)) [input p9]
12. ! [X0] : ((~humble(X0) | ~patient(X0)) <=> (creative(X0) <~> tall(X0))) [input p11]
15. ! [X0] : ((rich(X0) | tall(X0)) => (~happy(X0) & ~patient(X0))) [input p14]
21. ~tall(susan) [input hypothesis]
23. ? [X0] : ~curious(X0) <=> ? [X1] : (rich(X1) | creative(X1)) [rectify 9]
25. ! [X0] : ((rich(X0) | tall(X0)) => ~patient(X0)) [pure predicate removal 15]
26. (~rich(susan) & generous(susan)) | ! [X0] : (kind(X0) <=> ~creative(X0)) [ennf transformation 1]
30. ! [X0] : (tall(X0) | (curious(X0) & rich(X0))) [ennf transformation 10]
32. ! [X0] : (~patient(X0) | (~rich(X0) & ~tall(X0))) [ennf transformation 25]
33. (~rich(susan) & generous(susan)) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))) [nnf transformation 26]
34. ! [X0] : (((curious(X0) & generous(X0)) | (~funny(X0) & ~kind(X0))) & ((funny(X0) | kind(X0)) | (~curious(X0) | ~generous(X0)))) [nnf transformation 3]
35. ! [X0] : (((curious(X0) & generous(X0)) | (~funny(X0) & ~kind(X0))) & (funny(X0) | kind(X0) | ~curious(X0) | ~generous(X0))) [flattening 34]
51. (? [X0] : ~curious(X0) | ! [X1] : (~rich(X1) & ~creative(X1))) & (? [X1] : (rich(X1) | creative(X1)) | ! [X0] : curious(X0)) [nnf transformation 23]
52. (? [X0] : ~curious(X0) | ! [X1] : (~rich(X1) & ~creative(X1))) & (? [X2] : (rich(X2) | creative(X2)) | ! [X3] : curious(X3)) [rectify 51]
53. ? [X0] : ~curious(X0) => ~curious(sK3) [choice axiom]
54. ? [X2] : (rich(X2) | creative(X2)) => (rich(sK4) | creative(sK4)) [choice axiom]
55. (~curious(sK3) | ! [X1] : (~rich(X1) & ~creative(X1))) & ((rich(sK4) | creative(sK4)) | ! [X3] : curious(X3)) [skolemisation 52,54,53]
57. ! [X0] : (((~humble(X0) | ~patient(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (humble(X0) & patient(X0)))) [nnf transformation 12]
58. ! [X0] : ((~humble(X0) | ~patient(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (humble(X0) & patient(X0)))) [flattening 57]
72. ~rich(susan) | kind(X0) | creative(X0) [cnf transformation 33]
78. ~kind(X0) | curious(X0) [cnf transformation 35]
98. ~curious(sK3) | ~rich(X1) [cnf transformation 55]
99. tall(X0) | rich(X0) [cnf transformation 30]
100. tall(X0) | curious(X0) [cnf transformation 30]
111. ~tall(X0) | ~creative(X0) | patient(X0) [cnf transformation 58]
123. ~tall(X0) | ~patient(X0) [cnf transformation 32]
124. ~patient(X0) | ~rich(X0) [cnf transformation 32]
131. ~tall(susan) [cnf transformation 21]
133. 1 <=> ! [X0] : (kind(X0) | creative(X0)) [avatar definition]
134. creative(X0) | kind(X0) <- (1) [avatar component clause 133]
136. 2 <=> rich(susan) [avatar definition]
137. rich(susan) <- (2) [avatar component clause 136]
139. 1 | ~2 [avatar split clause 72,136,133]
199. 16 <=> ! [X1] : ~rich(X1) [avatar definition]
200. ~rich(X1) <- (16) [avatar component clause 199]
202. 17 <=> curious(sK3) [avatar definition]
204. ~curious(sK3) <- (~17) [avatar component clause 202]
205. 16 | ~17 [avatar split clause 98,202,199]
211. 19 <=> ! [X3] : curious(X3) [avatar definition]
212. curious(X3) <- (19) [avatar component clause 211]
270. $false <- (~17, 19) [subsumption resolution 204,212]
271. 17 | ~19 [avatar contradiction clause 270]
284. rich(susan) [resolution 99,131]
293. 2 [avatar split clause 284,136]
303. ~patient(X1) | rich(X1) [resolution 123,99]
305. ~patient(X1) [subsumption resolution 303,124]
335. ~creative(X1) | patient(X1) | curious(X1) [resolution 111,100]
339. ~creative(X1) | curious(X1) [subsumption resolution 335,305]
408. curious(X0) | kind(X0) <- (1) [resolution 339,134]
412. curious(X0) <- (1) [subsumption resolution 408,78]
413. 19 | ~1 [avatar split clause 412,133,211]
414. $false <- (2, 16) [resolution 200,137]
417. ~2 | ~16 [avatar contradiction clause 414]
418. $false [avatar sat refutation 139,205,271,293,413,417]
% SZS output end Proof for 8176661643716267063365712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not wise then paul is either not kind or wise and vice versa. Everyone who is not funny or not humble is not creative or wise and vice versa. Everyone who is not happy is not creative or funny. Everyone who is not funny is patient or not kind. If someone is not generous then fred is rich. If someone is both not patient and tall then mary is both not humble and not generous. Everyone who is not calm or rich is both funny and not quiet and vice versa. Everyone who is funny is not quiet and vice versa. If someone is both strong and quiet then someone is not old and vice versa. Everyone who is both not creative and creative is tall and vice versa. If alice is creative or not tall then someone is both old and not humble and vice versa. Everyone who is not strong is both not tall and not humble and vice versa. Everyone who is either not quiet or not happy is rich or happy. Everyone who is not calm or not old is both wise and tall. If someone is both strong and not patient then john is either not quiet or not creative and vice versa. If fred is either funny or not creative then someone is both not calm and funny. Someone is either not generous or generous. Someone is either tall or quiet. Alice is tall or generous. Paul is rich. John is not tall. Mary is not quiet or brave. Someone is not funny or not brave. | John is calm. | entailment | ((?[X]:((~happy(X)|~wise(X))))<=>((~kind(paul)<~>wise(paul))))&
(![X]:((~funny(X)|~humble(X))<=>(~creative(X)|wise(X))))&
(![X]:(~happy(X)=>(~creative(X)|funny(X))))&
(![X]:(~funny(X)=>(patient(X)|~kind(X))))&
((?[X]:(~generous(X)))=>(rich(fred)))&
((?[X]:((~patient(X)&tall(X))))=>((~humble(mary)&~generous(mary))))&
(![X]:((~calm(X)|rich(X))<=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>~quiet(X)))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&creative(X))<=>tall(X)))&
(((creative(alice)|~tall(alice)))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(rich(X)|happy(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)&tall(X))))&
((?[X]:((strong(X)&~patient(X))))<=>((~quiet(john)<~>~creative(john))))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:((~calm(X)&funny(X)))))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
((tall(alice)|generous(alice)))&
(rich(paul))&
(~tall(john))&
((~quiet(mary)|brave(mary)))&
(?[X]:((~funny(X)|~brave(X)))) | calm(john) | [
"p9",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 859966553524862797396834
% SZS output start Proof for 859966553524862797396834
10. ! [X0] : ((creative(X0) & ~creative(X0)) <=> tall(X0)) [input p9]
14. ! [X0] : ((~old(X0) | ~calm(X0)) => (tall(X0) & wise(X0))) [input p13]
24. ~calm(john) [input hypothesis]
34. ! [X0] : ((tall(X0) & wise(X0)) | (old(X0) & calm(X0))) [ennf transformation 14]
50. ! [X0] : (((creative(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 10]
51. ! [X0] : (((creative(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | ~creative(X0) | creative(X0))) [flattening 50]
101. ~creative(X0) | ~tall(X0) [cnf transformation 51]
102. creative(X0) | ~tall(X0) [cnf transformation 51]
115. tall(X0) | calm(X0) [cnf transformation 34]
136. ~calm(john) [cnf transformation 24]
208. ~tall(X0) [subsumption resolution 101,102]
215. calm(X0) [subsumption resolution 115,208]
279. $false [subsumption resolution 136,215]
% SZS output end Proof for 859966553524862797396834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is not funny and vice versa.
If someone is calm or brave then someone is not curious or not calm and vice versa.
Everyone who is not quiet is either not wise or not patient and vice versa.
Everyone who is happy or curious is either curious or not wise and vice versa.
Everyone who is either not calm or strong is tall or curious and vice versa.
If paul is either not old or not humble then someone is both not happy and not generous and vice versa.
Everyone who is rich is happy or not rich and vice versa.
If someone is brave or kind then mary is both funny and not patient and vice versa.
If lucy is not brave or not kind then someone is both creative and rich.
Everyone who is generous or kind is either not rich or not strong and vice versa.
If someone is either humble or not quiet then someone is patient or old.
If someone is both not tall and not strong then someone is not tall.
Everyone who is rich or funny is not happy or calm and vice versa.
Everyone who is either not strong or curious is either not quiet or not curious.
Everyone who is kind or not kind is kind.
Everyone who is humble is calm or kind and vice versa.
Someone is creative.
Fred is either not strong or creative.
Fred is brave.
Someone is not generous or not brave.
Someone is not humble or happy. | Fred is not patient. | entailment | (![X]:(patient(X)<=>~funny(X)))&
((?[X]:((calm(X)|brave(X))))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>~patient(X))))&
(![X]:((happy(X)|curious(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>strong(X))<=>(tall(X)|curious(X))))&
(((~old(paul)<~>~humble(paul)))<=>(?[X]:((~happy(X)&~generous(X)))))&
(![X]:(rich(X)<=>(happy(X)|~rich(X))))&
((?[X]:((brave(X)|kind(X))))<=>((funny(mary)&~patient(mary))))&
(((~brave(lucy)|~kind(lucy)))=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((generous(X)|kind(X))<=>(~rich(X)<~>~strong(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((patient(X)|old(X)))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:(~tall(X))))&
(![X]:((rich(X)|funny(X))<=>(~happy(X)|calm(X))))&
(![X]:((~strong(X)<~>curious(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((kind(X)|~kind(X))=>kind(X)))&
(![X]:(humble(X)<=>(calm(X)|kind(X))))&
(?[X]:(creative(X)))&
((~strong(fred)<~>creative(fred)))&
(brave(fred))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((~humble(X)|happy(X)))) | ~patient(fred) | [
"p2",
"p3",
"p4",
"p6",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8732015299694576682109630
% SZS output start Proof for 8732015299694576682109630
3. ! [X0] : (~quiet(X0) <=> (~wise(X0) <~> ~patient(X0))) [input p2]
4. ! [X0] : ((curious(X0) | happy(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p3]
5. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> (curious(X0) | tall(X0))) [input p4]
7. ! [X0] : (rich(X0) <=> (~rich(X0) | happy(X0))) [input p6]
10. ! [X0] : ((kind(X0) | generous(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p9]
13. ! [X0] : ((funny(X0) | rich(X0)) <=> (calm(X0) | ~happy(X0))) [input p12]
14. ! [X0] : ((~strong(X0) <~> curious(X0)) => (~quiet(X0) <~> ~curious(X0))) [input p13]
15. ! [X0] : ((~kind(X0) | kind(X0)) => kind(X0)) [input p14]
22. patient(fred) [input hypothesis]
29. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) | (~strong(X0) <=> curious(X0))) [ennf transformation 14]
30. ! [X0] : (kind(X0) | (kind(X0) & ~kind(X0))) [ennf transformation 15]
37. ! [X0] : ((~quiet(X0) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) & (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | quiet(X0))) [nnf transformation 3]
38. ! [X0] : (((curious(X0) | happy(X0)) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | (~curious(X0) & ~happy(X0)))) [nnf transformation 4]
39. ! [X0] : ((curious(X0) | happy(X0) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | (~curious(X0) & ~happy(X0)))) [flattening 38]
40. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~curious(X0) & ~tall(X0))) & ((curious(X0) | tall(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 5]
41. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~curious(X0) & ~tall(X0))) & (curious(X0) | tall(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [flattening 40]
46. ! [X0] : ((rich(X0) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | ~rich(X0))) [nnf transformation 7]
47. ! [X0] : ((rich(X0) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | ~rich(X0))) [flattening 46]
55. ! [X0] : (((kind(X0) | generous(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~kind(X0) & ~generous(X0)))) [nnf transformation 10]
56. ! [X0] : ((kind(X0) | generous(X0) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~kind(X0) & ~generous(X0)))) [flattening 55]
64. ! [X0] : (((funny(X0) | rich(X0)) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | (~funny(X0) & ~rich(X0)))) [nnf transformation 13]
65. ! [X0] : ((funny(X0) | rich(X0) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | (~funny(X0) & ~rich(X0)))) [flattening 64]
66. ! [X0] : (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) [nnf transformation 29]
84. ~quiet(X0) | ~patient(X0) | wise(X0) [cnf transformation 37]
86. ~happy(X0) | curious(X0) | ~wise(X0) [cnf transformation 39]
95. ~curious(X0) | ~calm(X0) | strong(X0) [cnf transformation 41]
104. ~rich(X0) | happy(X0) | ~rich(X0) [cnf transformation 47]
106. rich(X0) | rich(X0) [cnf transformation 47]
117. ~strong(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 56]
125. calm(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 65]
131. curious(X0) | quiet(X0) | curious(X0) | strong(X0) [cnf transformation 66]
134. kind(X0) | kind(X0) [cnf transformation 30]
144. patient(fred) [cnf transformation 22]
145. kind(X0) [duplicate literal removal 134]
147. strong(X0) | quiet(X0) | curious(X0) [duplicate literal removal 131]
148. ~rich(X0) | happy(X0) [duplicate literal removal 104]
149. rich(X0) [duplicate literal removal 106]
153. 1 <=> ! [X1] : calm(X1) [avatar definition]
154. calm(X1) <- (1) [avatar component clause 153]
209. happy(X0) [subsumption resolution 148,149]
250. ~kind(X0) | ~strong(X0) [subsumption resolution 117,149]
277. calm(X0) | ~rich(X0) [subsumption resolution 125,209]
278. calm(X0) [subsumption resolution 277,149]
279. 1 [avatar split clause 278,153]
282. 28 <=> strong(fred) [avatar definition]
283. ~strong(fred) <- (~28) [avatar component clause 282]
284. strong(fred) <- (28) [avatar component clause 282]
306. ~strong(X0) [resolution 250,145]
313. ~wise(X0) | curious(X0) [resolution 86,209]
315. quiet(fred) | curious(fred) <- (~28) [resolution 147,283]
320. 32 <=> curious(fred) [avatar definition]
321. ~curious(fred) <- (~32) [avatar component clause 320]
322. curious(fred) <- (32) [avatar component clause 320]
324. 33 <=> quiet(fred) [avatar definition]
326. quiet(fred) <- (33) [avatar component clause 324]
327. 32 | 33 | 28 [avatar split clause 315,282,324,320]
328. $false <- (28) [subsumption resolution 284,306]
329. ~28 [avatar contradiction clause 328]
332. ~calm(fred) | strong(fred) <- (32) [resolution 322,95]
334. strong(fred) <- (1, 32) [subsumption resolution 332,154]
335. $false <- (1, 32) [subsumption resolution 334,306]
336. ~1 | ~32 [avatar contradiction clause 335]
343. ~patient(fred) | wise(fred) <- (33) [resolution 326,84]
344. wise(fred) <- (33) [subsumption resolution 343,144]
347. curious(fred) <- (33) [resolution 344,313]
350. $false <- (~32, 33) [subsumption resolution 347,321]
351. 32 | ~33 [avatar contradiction clause 350]
352. $false [avatar sat refutation 279,327,329,336,351]
% SZS output end Proof for 8732015299694576682109630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either strong or not old.
Everyone who is both not generous and creative is both creative and not wise and vice versa.
If alice is either strong or not calm then someone is either not curious or not tall.
Everyone who is either humble or not rich is both rich and not old and vice versa.
Everyone who is either quiet or not funny is generous.
Everyone who is either generous or brave is either not happy or generous.
Everyone who is strong or kind is both wise and not calm.
Everyone who is both humble and not patient is both rich and not funny.
If susan is either not old or not humble then someone is both strong and not creative and vice versa.
If alice is both rich and not happy then susan is funny.
Everyone who is not funny or tall is quiet and vice versa.
If someone is both patient and tall then lucy is either not old or humble and vice versa.
Everyone who is both not happy and quiet is not calm or kind.
Everyone who is both not tall and not creative is both kind and not rich.
Everyone who is calm or old is both strong and not wise and vice versa.
If someone is both curious and calm then paul is not funny.
Fred is either happy or not calm.
Mary is funny or not funny.
Someone is either not patient or not strong.
Someone is both not happy and not wise.
Someone is not brave or not rich.
Fred is both not kind and humble. | Paul is old. | contradiction | (![X]:(old(X)=>(strong(X)<~>~old(X))))&
(![X]:((~generous(X)&creative(X))<=>(creative(X)&~wise(X))))&
(((strong(alice)<~>~calm(alice)))=>(?[X]:((~curious(X)<~>~tall(X)))))&
(![X]:((humble(X)<~>~rich(X))<=>(rich(X)&~old(X))))&
(![X]:((quiet(X)<~>~funny(X))=>generous(X)))&
(![X]:((generous(X)<~>brave(X))=>(~happy(X)<~>generous(X))))&
(![X]:((strong(X)|kind(X))=>(wise(X)&~calm(X))))&
(![X]:((humble(X)&~patient(X))=>(rich(X)&~funny(X))))&
(((~old(susan)<~>~humble(susan)))<=>(?[X]:((strong(X)&~creative(X)))))&
(((rich(alice)&~happy(alice)))=>(funny(susan)))&
(![X]:((~funny(X)|tall(X))<=>quiet(X)))&
((?[X]:((patient(X)&tall(X))))<=>((~old(lucy)<~>humble(lucy))))&
(![X]:((~happy(X)&quiet(X))=>(~calm(X)|kind(X))))&
(![X]:((~tall(X)&~creative(X))=>(kind(X)&~rich(X))))&
(![X]:((calm(X)|old(X))<=>(strong(X)&~wise(X))))&
((?[X]:((curious(X)&calm(X))))=>(~funny(paul)))&
((happy(fred)<~>~calm(fred)))&
((funny(mary)|~funny(mary)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:((~happy(X)&~wise(X))))&
(?[X]:((~brave(X)|~rich(X))))&
((~kind(fred)&humble(fred))) | old(paul) | [
"p0",
"p6",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8584865385970977886659415
% SZS output start Proof for 8584865385970977886659415
1. ! [X0] : (old(X0) => (strong(X0) <~> ~old(X0))) [input p0]
7. ! [X0] : ((kind(X0) | strong(X0)) => (~calm(X0) & wise(X0))) [input p6]
15. ! [X0] : ((old(X0) | calm(X0)) <=> (~wise(X0) & strong(X0))) [input p14]
23. old(paul) [input hypothesis]
24. ! [X0] : ((strong(X0) <~> ~old(X0)) | ~old(X0)) [ennf transformation 1]
28. ! [X0] : ((~calm(X0) & wise(X0)) | (~kind(X0) & ~strong(X0))) [ennf transformation 7]
38. ! [X0] : (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ~old(X0)) [nnf transformation 24]
58. ! [X0] : (((old(X0) | calm(X0)) | (wise(X0) | ~strong(X0))) & ((~wise(X0) & strong(X0)) | (~old(X0) & ~calm(X0)))) [nnf transformation 15]
59. ! [X0] : ((old(X0) | calm(X0) | wise(X0) | ~strong(X0)) & ((~wise(X0) & strong(X0)) | (~old(X0) & ~calm(X0)))) [flattening 58]
68. ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 38]
90. ~strong(X0) | wise(X0) [cnf transformation 28]
118. ~wise(X0) | ~old(X0) [cnf transformation 59]
131. old(paul) [cnf transformation 23]
136. ~old(X0) | strong(X0) [duplicate literal removal 68]
248. strong(paul) [resolution 136,131]
249. wise(paul) [resolution 248,90]
256. ~old(paul) [resolution 249,118]
258. $false [subsumption resolution 256,131]
% SZS output end Proof for 8584865385970977886659415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not kind or quiet.
If alice is both kind and wise then someone is not rich or old and vice versa.
Everyone who is not generous or tall is not wise or curious.
If someone is both not kind and wise then someone is wise or not generous and vice versa.
Everyone who is not kind is both not generous and strong.
If fred is both funny and not brave then someone is either not happy or creative.
Everyone who is both quiet and not curious is either humble or calm and vice versa.
If mary is not curious then alice is old or quiet and vice versa.
Everyone who is both kind and creative is kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Everyone who is either not old or not funny is either strong or humble and vice versa.
If paul is both not humble and not old then lucy is patient or not tall and vice versa.
Everyone who is either kind or creative is either old or not tall and vice versa.
Everyone who is not creative is either not creative or creative and vice versa.
If someone is rich then fred is either not curious or brave.
Someone is either not generous or not calm.
Mary is wise.
Someone is not brave or wise.
Someone is brave or not quiet.
Alice is generous or patient.
Someone is strong or humble.
Someone is either strong or quiet. | Paul is not strong. | contradiction | (![X]:(~quiet(X)=>(~kind(X)<~>quiet(X))))&
(((kind(alice)&wise(alice)))<=>(?[X]:((~rich(X)|old(X)))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>creative(X))))&
((?[X]:(rich(X)))=>((~curious(fred)<~>brave(fred))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(wise(mary))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice)))&
(?[X]:((strong(X)|humble(X))))&
(?[X]:((strong(X)<~>quiet(X)))) | ~strong(paul) | [
"p4",
"p8",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2758537287604881936576067
% SZS output start Proof for 2758537287604881936576067
5. ! [X0] : (~kind(X0) => (strong(X0) & ~generous(X0))) [input p4]
9. ! [X0] : ((creative(X0) & kind(X0)) <=> kind(X0)) [input p8]
15. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> creative(X0))) [input p14]
24. ~strong(paul) [input hypothesis]
29. ! [X0] : ((strong(X0) & ~generous(X0)) | kind(X0)) [ennf transformation 5]
52. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) | ~kind(X0)))) [nnf transformation 9]
53. ! [X0] : (((creative(X0) & kind(X0)) | ~kind(X0)) & (kind(X0) | ~creative(X0) | ~kind(X0))) [flattening 52]
63. ! [X0] : ((~creative(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 15]
92. strong(X0) | kind(X0) [cnf transformation 29]
106. ~kind(X0) | creative(X0) [cnf transformation 53]
140. ~creative(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 63]
152. ~strong(paul) [cnf transformation 24]
156. ~creative(X0) [duplicate literal removal 140]
352. kind(paul) [resolution 92,152]
355. creative(paul) [resolution 106,352]
360. $false [subsumption resolution 355,156]
% SZS output end Proof for 2758537287604881936576067
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not curious is not funny.
If paul is not quiet then someone is either not wise or not calm.
Everyone who is not calm or not kind is rich and vice versa.
If someone is both happy and funny then lucy is both not strong and rich.
Everyone who is both generous and kind is not brave and vice versa.
If mary is kind or wise then susan is either not calm or humble and vice versa.
Everyone who is both not old and old is both quiet and creative.
If john is both not calm and brave then someone is not creative.
If alice is both not creative and tall then someone is both quiet and brave.
Everyone who is both not quiet and not tall is not old and vice versa.
Everyone who is not happy or happy is patient or creative.
Everyone who is either not funny or kind is either calm or creative and vice versa.
If someone is not calm then lucy is either not quiet or curious and vice versa.
Everyone who is either rich or not happy is both not tall and wise and vice versa.
Everyone who is calm or creative is both happy and generous and vice versa.
If someone is patient or not brave then someone is either rich or tall and vice versa.
Susan is both not old and happy.
Someone is either not tall or not old.
Paul is wise.
Someone is both not tall and brave.
Lucy is not strong.
Mary is not happy.
Someone is not wise or brave.
Someone is either brave or humble. | Mary is calm. | contradiction | (![X]:((old(X)<~>~curious(X))=>~funny(X)))&
((~quiet(paul))=>(?[X]:((~wise(X)<~>~calm(X)))))&
(![X]:((~calm(X)|~kind(X))<=>rich(X)))&
((?[X]:((happy(X)&funny(X))))=>((~strong(lucy)&rich(lucy))))&
(![X]:((generous(X)&kind(X))<=>~brave(X)))&
(((kind(mary)|wise(mary)))<=>((~calm(susan)<~>humble(susan))))&
(![X]:((~old(X)&old(X))=>(quiet(X)&creative(X))))&
(((~calm(john)&brave(john)))=>(?[X]:(~creative(X))))&
(((~creative(alice)&tall(alice)))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((~quiet(X)&~tall(X))<=>~old(X)))&
(![X]:((~happy(X)|happy(X))=>(patient(X)|creative(X))))&
(![X]:((~funny(X)<~>kind(X))<=>(calm(X)<~>creative(X))))&
((?[X]:(~calm(X)))<=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((rich(X)<~>~happy(X))<=>(~tall(X)&wise(X))))&
(![X]:((calm(X)|creative(X))<=>(happy(X)&generous(X))))&
((?[X]:((patient(X)|~brave(X))))<=>(?[X]:((rich(X)<~>tall(X)))))&
((~old(susan)&happy(susan)))&
(?[X]:((~tall(X)<~>~old(X))))&
(wise(paul))&
(?[X]:((~tall(X)&brave(X))))&
(~strong(lucy))&
(~happy(mary))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((brave(X)<~>humble(X)))) | calm(mary) | [
"p14",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 3004896818068752762464584
% SZS output start Proof for 3004896818068752762464584
15. ! [X0] : ((creative(X0) | calm(X0)) <=> (generous(X0) & happy(X0))) [input p14]
22. ~happy(mary) [input p21]
25. calm(mary) [input hypothesis]
63. ! [X0] : (((creative(X0) | calm(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~creative(X0) & ~calm(X0)))) [nnf transformation 15]
64. ! [X0] : ((creative(X0) | calm(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | (~creative(X0) & ~calm(X0)))) [flattening 63]
125. ~calm(X0) | happy(X0) [cnf transformation 64]
143. ~happy(mary) [cnf transformation 22]
147. calm(mary) [cnf transformation 25]
300. happy(mary) [resolution 125,147]
301. $false [subsumption resolution 300,143]
% SZS output end Proof for 3004896818068752762464584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or kind is either generous or not patient and vice versa.
If someone is generous or not humble then mary is both kind and not happy and vice versa.
If susan is either not tall or creative then someone is either not old or humble.
Everyone who is not generous or happy is not brave and vice versa.
If john is both generous and happy then someone is either quiet or not calm and vice versa.
Everyone who is either not generous or not funny is funny and vice versa.
Everyone who is curious or not old is rich and vice versa.
Everyone who is both not tall and not quiet is not humble and vice versa.
Everyone who is not tall or brave is either wise or not brave and vice versa.
Everyone who is either creative or not humble is both not humble and not wise.
Everyone who is both calm and not tall is patient and vice versa.
If someone is not happy or rich then someone is brave and vice versa.
If alice is not wise or rich then someone is either funny or not happy.
If lucy is either old or quiet then paul is not strong or not quiet.
If someone is both not happy and strong then someone is either not wise or not rich and vice versa.
Someone is not generous.
Mary is humble.
Mary is both humble and not brave.
Someone is either tall or not creative.
Someone is either curious or strong.
Lucy is not funny or generous. | Paul is not kind. | neutral | (![X]:((strong(X)<~>kind(X))<=>(generous(X)<~>~patient(X))))&
((?[X]:((generous(X)|~humble(X))))<=>((kind(mary)&~happy(mary))))&
(((~tall(susan)<~>creative(susan)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~generous(X)|happy(X))<=>~brave(X)))&
(((generous(john)&happy(john)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~generous(X)<~>~funny(X))<=>funny(X)))&
(![X]:((curious(X)|~old(X))<=>rich(X)))&
(![X]:((~tall(X)&~quiet(X))<=>~humble(X)))&
(![X]:((~tall(X)|brave(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((creative(X)<~>~humble(X))=>(~humble(X)&~wise(X))))&
(![X]:((calm(X)&~tall(X))<=>patient(X)))&
((?[X]:((~happy(X)|rich(X))))<=>(?[X]:(brave(X))))&
(((~wise(alice)|rich(alice)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(((old(lucy)<~>quiet(lucy)))=>((~strong(paul)|~quiet(paul))))&
((?[X]:((~happy(X)&strong(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(?[X]:(~generous(X)))&
(humble(mary))&
((humble(mary)&~brave(mary)))&
(?[X]:((tall(X)<~>~creative(X))))&
(?[X]:((curious(X)<~>strong(X))))&
((~funny(lucy)|generous(lucy))) | ~kind(paul) | []
| null | 0 |
Everyone who is either not brave or not strong is either funny or happy and vice versa.
Everyone who is not rich or not funny is either not kind or quiet and vice versa.
If mary is happy then alice is not kind or kind.
If john is both not humble and not patient then susan is not curious or curious and vice versa.
If alice is not generous then someone is both not curious and patient.
Everyone who is kind is either not curious or not old and vice versa.
If someone is not old then mary is not strong or kind and vice versa.
Everyone who is not strong is either kind or not kind.
Everyone who is not brave or not funny is either old or not kind and vice versa.
Everyone who is quiet or not old is not happy or not creative.
Everyone who is both not generous and not old is both not patient and not funny.
If fred is not patient then someone is creative or happy.
If someone is both not generous and wise then mary is either curious or brave and vice versa.
Everyone who is creative is both rich and not rich and vice versa.
If mary is old or quiet then someone is both strong and not happy.
If someone is either happy or not curious then someone is both not curious and not quiet.
Susan is both not old and not creative.
Someone is either patient or brave.
Mary is tall.
Alice is both not humble and funny.
Mary is not happy or not wise.
Someone is either not old or patient.
Someone is happy or not strong. | Alice is humble. | contradiction | (![X]:((~brave(X)<~>~strong(X))<=>(funny(X)<~>happy(X))))&
(![X]:((~rich(X)|~funny(X))<=>(~kind(X)<~>quiet(X))))&
((happy(mary))=>((~kind(alice)|kind(alice))))&
(((~humble(john)&~patient(john)))<=>((~curious(susan)|curious(susan))))&
((~generous(alice))=>(?[X]:((~curious(X)&patient(X)))))&
(![X]:(kind(X)<=>(~curious(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>((~strong(mary)|kind(mary))))&
(![X]:(~strong(X)=>(kind(X)<~>~kind(X))))&
(![X]:((~brave(X)|~funny(X))<=>(old(X)<~>~kind(X))))&
(![X]:((quiet(X)|~old(X))=>(~happy(X)|~creative(X))))&
(![X]:((~generous(X)&~old(X))=>(~patient(X)&~funny(X))))&
((~patient(fred))=>(?[X]:((creative(X)|happy(X)))))&
((?[X]:((~generous(X)&wise(X))))<=>((curious(mary)<~>brave(mary))))&
(![X]:(creative(X)<=>(rich(X)&~rich(X))))&
(((old(mary)|quiet(mary)))=>(?[X]:((strong(X)&~happy(X)))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~curious(X)&~quiet(X)))))&
((~old(susan)&~creative(susan)))&
(?[X]:((patient(X)<~>brave(X))))&
(tall(mary))&
((~humble(alice)&funny(alice)))&
((~happy(mary)|~wise(mary)))&
(?[X]:((~old(X)<~>patient(X))))&
(?[X]:((happy(X)|~strong(X)))) | humble(alice) | [
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7429859358799359015612440
% SZS output start Proof for 7429859358799359015612440
20. funny(alice) & ~humble(alice) [input p19]
24. humble(alice) [input hypothesis]
139. ~humble(alice) [cnf transformation 20]
145. humble(alice) [cnf transformation 24]
309. $false [subsumption resolution 145,139]
% SZS output end Proof for 7429859358799359015612440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not rich is not brave and vice versa. Everyone who is rich or creative is not strong or not rich and vice versa. Everyone who is either not old or patient is not strong. If fred is not generous or curious then mary is not calm or generous. Everyone who is either kind or not kind is both happy and not kind and vice versa. Everyone who is curious is either not happy or brave. If someone is both wise and not creative then alice is either happy or not calm. If someone is either calm or humble then mary is not kind and vice versa. If someone is either not curious or not humble then someone is either humble or happy. If someone is either not humble or kind then someone is not wise. Everyone who is not strong or not quiet is creative and vice versa. Everyone who is not generous or not tall is not kind and vice versa. Everyone who is either not patient or not creative is both creative and not generous and vice versa. If paul is rich then someone is both not strong and not generous and vice versa. Someone is either patient or not funny. Someone is not kind or brave. Paul is either not wise or quiet. Susan is calm. Paul is not kind or humble. Mary is both creative and happy. Alice is both generous and old. | Susan is not wise. | neutral | (![X]:((~calm(X)|~rich(X))<=>~brave(X)))&
(![X]:((rich(X)|creative(X))<=>(~strong(X)|~rich(X))))&
(![X]:((~old(X)<~>patient(X))=>~strong(X)))&
(((~generous(fred)|curious(fred)))=>((~calm(mary)|generous(mary))))&
(![X]:((kind(X)<~>~kind(X))<=>(happy(X)&~kind(X))))&
(![X]:(curious(X)=>(~happy(X)<~>brave(X))))&
((?[X]:((wise(X)&~creative(X))))=>((happy(alice)<~>~calm(alice))))&
((?[X]:((calm(X)<~>humble(X))))<=>(~kind(mary)))&
((?[X]:((~curious(X)<~>~humble(X))))=>(?[X]:((humble(X)<~>happy(X)))))&
((?[X]:((~humble(X)<~>kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)|~quiet(X))<=>creative(X)))&
(![X]:((~generous(X)|~tall(X))<=>~kind(X)))&
(![X]:((~patient(X)<~>~creative(X))<=>(creative(X)&~generous(X))))&
((rich(paul))<=>(?[X]:((~strong(X)&~generous(X)))))&
(?[X]:((patient(X)<~>~funny(X))))&
(?[X]:((~kind(X)|brave(X))))&
((~wise(paul)<~>quiet(paul)))&
(calm(susan))&
((~kind(paul)|humble(paul)))&
((creative(mary)&happy(mary)))&
((generous(alice)&old(alice))) | ~wise(susan) | []
| null | 0 |
If paul is both quiet and not old then someone is not patient or not brave and vice versa.
Everyone who is both curious and not tall is either funny or quiet.
If someone is either happy or rich then john is either creative or curious.
If susan is both not curious and not calm then someone is tall or not quiet and vice versa.
Everyone who is either not patient or not rich is not rich or not strong and vice versa.
Everyone who is either not generous or not old is both brave and generous and vice versa.
Everyone who is not wise or not brave is both not patient and not humble and vice versa.
If someone is both not humble and not kind then fred is not quiet or old and vice versa.
If someone is rich or not calm then fred is either not humble or old and vice versa.
Everyone who is generous or humble is either not funny or patient and vice versa.
If someone is old then someone is both brave and not old.
If someone is both happy and wise then someone is both not generous and funny.
If alice is either humble or funny then alice is quiet or kind.
Everyone who is not curious or not quiet is not strong and vice versa.
Everyone who is not creative is both not patient and happy and vice versa.
Everyone who is rich or happy is not creative or kind and vice versa.
Someone is funny or not creative.
Alice is patient.
Someone is curious.
Fred is tall.
Fred is kind.
Alice is not strong.
Alice is not rich or not old. | Susan is not curious. | entailment | (((quiet(paul)&~old(paul)))<=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((curious(X)&~tall(X))=>(funny(X)<~>quiet(X))))&
((?[X]:((happy(X)<~>rich(X))))=>((creative(john)<~>curious(john))))&
(((~curious(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~quiet(X)))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~rich(X)|~strong(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(brave(X)&generous(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~quiet(fred)|old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>((~humble(fred)<~>old(fred))))&
(![X]:((generous(X)|humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((humble(alice)<~>funny(alice)))=>((quiet(alice)|kind(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(![X]:((rich(X)|happy(X))<=>(~creative(X)|kind(X))))&
(?[X]:((funny(X)|~creative(X))))&
(patient(alice))&
(?[X]:(curious(X)))&
(tall(fred))&
(kind(fred))&
(~strong(alice))&
((~rich(alice)|~old(alice))) | ~curious(susan) | [
"p3",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 8109517098885376816159184
% SZS output start Proof for 8109517098885376816159184
4. (~calm(susan) & ~curious(susan)) <=> ? [X0] : (~quiet(X0) | tall(X0)) [input p3]
20. tall(fred) [input p19]
24. curious(susan) [input hypothesis]
41. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X0] : (~quiet(X0) | tall(X0)) | (calm(susan) | curious(susan))) [nnf transformation 4]
42. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X0] : (~quiet(X0) | tall(X0)) | calm(susan) | curious(susan)) [flattening 41]
43. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & (? [X1] : (~quiet(X1) | tall(X1)) | calm(susan) | curious(susan)) [rectify 42]
44. ? [X1] : (~quiet(X1) | tall(X1)) => (~quiet(sK1) | tall(sK1)) [choice axiom]
45. ((~calm(susan) & ~curious(susan)) | ! [X0] : (quiet(X0) & ~tall(X0))) & ((~quiet(sK1) | tall(sK1)) | calm(susan) | curious(susan)) [skolemisation 43,44]
92. ~curious(susan) | ~tall(X0) [cnf transformation 45]
149. tall(fred) [cnf transformation 20]
153. curious(susan) [cnf transformation 24]
212. 13 <=> ! [X0] : ~tall(X0) [avatar definition]
213. ~tall(X0) <- (13) [avatar component clause 212]
216. 14 <=> curious(susan) [avatar definition]
220. 13 | ~14 [avatar split clause 92,216,212]
341. 14 [avatar split clause 153,216]
342. $false <- (13) [resolution 213,149]
343. ~13 [avatar contradiction clause 342]
344. $false [avatar sat refutation 220,341,343]
% SZS output end Proof for 8109517098885376816159184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not kind and curious. If someone is not creative or strong then someone is both wise and not brave and vice versa. Everyone who is kind is both funny and quiet. Everyone who is both not happy and happy is not generous or happy and vice versa. If someone is not kind or tall then alice is both not funny and curious. If someone is either not patient or funny then paul is both not funny and not curious. Everyone who is both patient and quiet is either kind or wise and vice versa. If someone is either wise or happy then alice is not tall. If paul is not creative then mary is wise and vice versa. Everyone who is not curious or not tall is both strong and not curious. If alice is not brave or not strong then john is not kind and vice versa. If alice is tall then lucy is either not brave or patient. If someone is humble or kind then someone is both not patient and wise and vice versa. Everyone who is funny or not brave is old or not creative and vice versa. Everyone who is either not generous or not tall is both brave and not brave. Everyone who is either brave or not kind is strong and vice versa. Someone is not strong or patient. Someone is not funny or creative. Someone is not happy. | Paul is tall. | entailment | (![X]:(~kind(X)=>(~kind(X)&curious(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(kind(X)=>(funny(X)&quiet(X))))&
(![X]:((~happy(X)&happy(X))<=>(~generous(X)|happy(X))))&
((?[X]:((~kind(X)|tall(X))))=>((~funny(alice)&curious(alice))))&
((?[X]:((~patient(X)<~>funny(X))))=>((~funny(paul)&~curious(paul))))&
(![X]:((patient(X)&quiet(X))<=>(kind(X)<~>wise(X))))&
((?[X]:((wise(X)<~>happy(X))))=>(~tall(alice)))&
((~creative(paul))<=>(wise(mary)))&
(![X]:((~curious(X)|~tall(X))=>(strong(X)&~curious(X))))&
(((~brave(alice)|~strong(alice)))<=>(~kind(john)))&
((tall(alice))=>((~brave(lucy)<~>patient(lucy))))&
((?[X]:((humble(X)|kind(X))))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((funny(X)|~brave(X))<=>(old(X)|~creative(X))))&
(![X]:((~generous(X)<~>~tall(X))=>(brave(X)&~brave(X))))&
(![X]:((brave(X)<~>~kind(X))<=>strong(X)))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:(~happy(X))) | tall(paul) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p9",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 719862247511882500120358
% SZS output start Proof for 719862247511882500120358
1. ! [X0] : (~kind(X0) => (curious(X0) & ~kind(X0))) [input p0]
2. ? [X0] : (strong(X0) | ~creative(X0)) <=> ? [X0] : (~brave(X0) & wise(X0)) [input p1]
3. ! [X0] : (kind(X0) => (quiet(X0) & funny(X0))) [input p2]
4. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (happy(X0) | ~generous(X0))) [input p3]
5. ? [X0] : (tall(X0) | ~kind(X0)) => (curious(alice) & ~funny(alice)) [input p4]
6. ? [X0] : (~patient(X0) <~> funny(X0)) => (~curious(paul) & ~funny(paul)) [input p5]
8. ? [X0] : (wise(X0) <~> happy(X0)) => ~tall(alice) [input p7]
10. ! [X0] : ((~tall(X0) | ~curious(X0)) => (~curious(X0) & strong(X0))) [input p9]
17. ? [X0] : (patient(X0) | ~strong(X0)) [input p16]
20. ~tall(paul) [input hypothesis]
21. ? [X0] : (strong(X0) | ~creative(X0)) <=> ? [X1] : (~brave(X1) & wise(X1)) [rectify 2]
23. ! [X0] : ((curious(X0) & ~kind(X0)) | kind(X0)) [ennf transformation 1]
24. ! [X0] : ((quiet(X0) & funny(X0)) | ~kind(X0)) [ennf transformation 3]
25. (curious(alice) & ~funny(alice)) | ! [X0] : (~tall(X0) & kind(X0)) [ennf transformation 5]
26. (~curious(paul) & ~funny(paul)) | ! [X0] : (~patient(X0) <=> funny(X0)) [ennf transformation 6]
27. ~tall(alice) | ! [X0] : (wise(X0) <=> happy(X0)) [ennf transformation 8]
28. ! [X0] : ((~curious(X0) & strong(X0)) | (tall(X0) & curious(X0))) [ennf transformation 10]
31. (? [X0] : (strong(X0) | ~creative(X0)) | ! [X1] : (brave(X1) | ~wise(X1))) & (? [X1] : (~brave(X1) & wise(X1)) | ! [X0] : (~strong(X0) & creative(X0))) [nnf transformation 21]
32. (? [X0] : (strong(X0) | ~creative(X0)) | ! [X1] : (brave(X1) | ~wise(X1))) & (? [X2] : (~brave(X2) & wise(X2)) | ! [X3] : (~strong(X3) & creative(X3))) [rectify 31]
33. ? [X0] : (strong(X0) | ~creative(X0)) => (strong(sK0) | ~creative(sK0)) [choice axiom]
34. ? [X2] : (~brave(X2) & wise(X2)) => (~brave(sK1) & wise(sK1)) [choice axiom]
35. ((strong(sK0) | ~creative(sK0)) | ! [X1] : (brave(X1) | ~wise(X1))) & ((~brave(sK1) & wise(sK1)) | ! [X3] : (~strong(X3) & creative(X3))) [skolemisation 32,34,33]
36. ! [X0] : (((happy(X0) & ~happy(X0)) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 4]
37. ! [X0] : (((happy(X0) & ~happy(X0)) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | ~happy(X0) | happy(X0))) [flattening 36]
38. (~curious(paul) & ~funny(paul)) | ! [X0] : ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0))) [nnf transformation 26]
41. ~tall(alice) | ! [X0] : ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))) [nnf transformation 27]
55. ? [X0] : (patient(X0) | ~strong(X0)) => (patient(sK4) | ~strong(sK4)) [choice axiom]
56. patient(sK4) | ~strong(sK4) [skolemisation 17,55]
62. curious(X0) | kind(X0) [cnf transformation 23]
64. wise(sK1) | ~strong(X3) [cnf transformation 35]
68. ~kind(X0) | funny(X0) [cnf transformation 24]
72. ~happy(X0) | ~happy(X0) [cnf transformation 37]
77. curious(alice) | kind(X0) [cnf transformation 25]
78. curious(alice) | ~tall(X0) [cnf transformation 25]
80. ~funny(paul) | ~patient(X0) | ~funny(X0) [cnf transformation 38]
89. ~tall(alice) | happy(X0) | ~wise(X0) [cnf transformation 41]
94. tall(X0) | strong(X0) [cnf transformation 28]
96. ~curious(X0) | tall(X0) [cnf transformation 28]
119. patient(sK4) | ~strong(sK4) [cnf transformation 56]
122. ~tall(paul) [cnf transformation 20]
124. ~happy(X0) [duplicate literal removal 72]
138. 4 <=> ! [X3] : ~strong(X3) [avatar definition]
139. ~strong(X3) <- (4) [avatar component clause 138]
150. 7 <=> wise(sK1) [avatar definition]
152. wise(sK1) <- (7) [avatar component clause 150]
153. 4 | 7 [avatar split clause 64,150,138]
156. 8 <=> ! [X0] : ~tall(X0) [avatar definition]
157. ~tall(X0) <- (8) [avatar component clause 156]
159. 9 <=> curious(alice) [avatar definition]
161. curious(alice) <- (9) [avatar component clause 159]
162. 8 | 9 [avatar split clause 78,159,156]
164. 10 <=> ! [X0] : kind(X0) [avatar definition]
165. kind(X0) <- (10) [avatar component clause 164]
166. 10 | 9 [avatar split clause 77,159,164]
174. 12 <=> ! [X0] : (~patient(X0) | ~funny(X0)) [avatar definition]
175. ~patient(X0) | ~funny(X0) <- (12) [avatar component clause 174]
177. 13 <=> curious(paul) [avatar definition]
178. curious(paul) <- (13) [avatar component clause 177]
179. ~curious(paul) <- (~13) [avatar component clause 177]
186. 15 <=> funny(paul) [avatar definition]
188. ~funny(paul) <- (~15) [avatar component clause 186]
189. 12 | ~15 [avatar split clause 80,186,174]
193. ~tall(alice) | ~wise(X0) [subsumption resolution 89,124]
195. 16 <=> ! [X0] : ~wise(X0) [avatar definition]
196. ~wise(X0) <- (16) [avatar component clause 195]
198. 17 <=> tall(alice) [avatar definition]
200. ~tall(alice) <- (~17) [avatar component clause 198]
201. 16 | ~17 [avatar split clause 193,198,195]
270. 32 <=> strong(sK4) [avatar definition]
272. ~strong(sK4) <- (~32) [avatar component clause 270]
274. 33 <=> patient(sK4) [avatar definition]
276. patient(sK4) <- (33) [avatar component clause 274]
277. ~32 | 33 [avatar split clause 119,274,270]
289. kind(paul) <- (~13) [resolution 62,179]
290. funny(paul) <- (~13) [resolution 68,289]
291. $false <- (~13, ~15) [subsumption resolution 290,188]
292. 13 | 15 [avatar contradiction clause 291]
296. strong(paul) [resolution 94,122]
298. $false <- (4) [subsumption resolution 296,139]
299. ~4 [avatar contradiction clause 298]
302. $false <- (7, 16) [resolution 196,152]
307. ~7 | ~16 [avatar contradiction clause 302]
310. tall(alice) <- (9) [resolution 96,161]
311. tall(paul) <- (13) [resolution 96,178]
313. $false <- (9, ~17) [subsumption resolution 310,200]
314. ~9 | 17 [avatar contradiction clause 313]
315. $false <- (13) [subsumption resolution 311,122]
316. ~13 [avatar contradiction clause 315]
317. strong(X0) <- (8) [resolution 157,94]
321. funny(X1) <- (10) [resolution 165,68]
324. $false <- (8, ~32) [resolution 317,272]
325. ~8 | 32 [avatar contradiction clause 324]
326. ~funny(sK4) <- (12, 33) [resolution 276,175]
327. $false <- (10, 12, 33) [subsumption resolution 326,321]
328. ~10 | ~12 | ~33 [avatar contradiction clause 327]
329. $false [avatar sat refutation 153,162,166,189,201,277,292,299,307,314,316,325,328]
% SZS output end Proof for 719862247511882500120358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not old is both not quiet and rich and vice versa. Everyone who is not humble or not happy is strong or funny. Everyone who is both calm and funny is happy or strong and vice versa. Everyone who is both not tall and not wise is not old or funny and vice versa. If paul is both not kind and not humble then someone is not calm. If someone is not calm then someone is both humble and quiet and vice versa. Everyone who is humble is not quiet. Everyone who is not humble is not brave. If someone is not curious or not calm then someone is not happy and vice versa. If someone is both not funny and curious then susan is strong or not calm and vice versa. If someone is either not funny or not curious then someone is either humble or creative. Everyone who is creative is both not wise and generous and vice versa. Everyone who is calm or not wise is not brave or quiet. If someone is both not funny and creative then fred is patient or not calm and vice versa. Everyone who is humble or not kind is not brave. Mary is not curious. Someone is not creative. Someone is not old or not brave. Someone is either not patient or not wise. Someone is not generous or not kind. | Paul is tall. | contradiction | (![X]:((old(X)&~old(X))<=>(~quiet(X)&rich(X))))&
(![X]:((~humble(X)|~happy(X))=>(strong(X)|funny(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)|strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~old(X)|funny(X))))&
(((~kind(paul)&~humble(paul)))=>(?[X]:(~calm(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:(humble(X)=>~quiet(X)))&
(![X]:(~humble(X)=>~brave(X)))&
((?[X]:((~curious(X)|~calm(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((strong(susan)|~calm(susan))))&
((?[X]:((~funny(X)<~>~curious(X))))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:(creative(X)<=>(~wise(X)&generous(X))))&
(![X]:((calm(X)|~wise(X))=>(~brave(X)|quiet(X))))&
((?[X]:((~funny(X)&creative(X))))<=>((patient(fred)|~calm(fred))))&
(![X]:((humble(X)|~kind(X))=>~brave(X)))&
(~curious(mary))&
(?[X]:(~creative(X)))&
(?[X]:((~old(X)|~brave(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((~generous(X)|~kind(X)))) | tall(paul) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 6706331994045739071756077
% SZS output start Proof for 6706331994045739071756077
2. ! [X0] : ((~happy(X0) | ~humble(X0)) => (funny(X0) | strong(X0))) [input p1]
3. ! [X0] : ((funny(X0) & calm(X0)) <=> (strong(X0) | happy(X0))) [input p2]
4. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (funny(X0) | ~old(X0))) [input p3]
6. ? [X0] : ~calm(X0) <=> ? [X0] : (quiet(X0) & humble(X0)) [input p5]
7. ! [X0] : (humble(X0) => ~quiet(X0)) [input p6]
21. tall(paul) [input hypothesis]
22. ? [X0] : ~calm(X0) <=> ? [X1] : (quiet(X1) & humble(X1)) [rectify 6]
29. ! [X0] : ((funny(X0) | strong(X0)) | (happy(X0) & humble(X0))) [ennf transformation 2]
30. ! [X0] : (funny(X0) | strong(X0) | (happy(X0) & humble(X0))) [flattening 29]
33. ! [X0] : (~quiet(X0) | ~humble(X0)) [ennf transformation 7]
37. ! [X0] : (((funny(X0) & calm(X0)) | (~strong(X0) & ~happy(X0))) & ((strong(X0) | happy(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 3]
38. ! [X0] : (((funny(X0) & calm(X0)) | (~strong(X0) & ~happy(X0))) & (strong(X0) | happy(X0) | ~funny(X0) | ~calm(X0))) [flattening 37]
39. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | (wise(X0) | tall(X0)))) [nnf transformation 4]
40. ! [X0] : (((~wise(X0) & ~tall(X0)) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | wise(X0) | tall(X0))) [flattening 39]
43. (? [X0] : ~calm(X0) | ! [X1] : (~quiet(X1) | ~humble(X1))) & (? [X1] : (quiet(X1) & humble(X1)) | ! [X0] : calm(X0)) [nnf transformation 22]
44. (? [X0] : ~calm(X0) | ! [X1] : (~quiet(X1) | ~humble(X1))) & (? [X2] : (quiet(X2) & humble(X2)) | ! [X3] : calm(X3)) [rectify 43]
45. ? [X0] : ~calm(X0) => ~calm(sK1) [choice axiom]
46. ? [X2] : (quiet(X2) & humble(X2)) => (quiet(sK2) & humble(sK2)) [choice axiom]
47. (~calm(sK1) | ! [X1] : (~quiet(X1) | ~humble(X1))) & ((quiet(sK2) & humble(sK2)) | ! [X3] : calm(X3)) [skolemisation 44,46,45]
81. funny(X0) | strong(X0) | happy(X0) [cnf transformation 30]
82. strong(X0) | happy(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 38]
85. ~happy(X0) | funny(X0) [cnf transformation 38]
86. ~strong(X0) | funny(X0) [cnf transformation 38]
89. ~tall(X0) | ~funny(X0) [cnf transformation 40]
93. humble(sK2) | calm(X3) [cnf transformation 47]
94. quiet(sK2) | calm(X3) [cnf transformation 47]
96. ~quiet(X0) | ~humble(X0) [cnf transformation 33]
122. tall(paul) [cnf transformation 21]
124. ~calm(X0) | happy(X0) | strong(X0) [subsumption resolution 82,81]
139. 4 <=> ! [X1] : (~quiet(X1) | ~humble(X1)) [avatar definition]
140. ~humble(X1) | ~quiet(X1) <- (4) [avatar component clause 139]
147. 6 <=> ! [X3] : calm(X3) [avatar definition]
148. calm(X3) <- (6) [avatar component clause 147]
150. 7 <=> quiet(sK2) [avatar definition]
152. quiet(sK2) <- (7) [avatar component clause 150]
153. 6 | 7 [avatar split clause 94,150,147]
155. 8 <=> humble(sK2) [avatar definition]
157. humble(sK2) <- (8) [avatar component clause 155]
158. 6 | 8 [avatar split clause 93,155,147]
159. 4 [avatar split clause 96,139]
266. ~funny(paul) [resolution 89,122]
269. ~quiet(sK2) <- (4, 8) [resolution 140,157]
270. $false <- (4, 7, 8) [subsumption resolution 269,152]
271. ~4 | ~7 | ~8 [avatar contradiction clause 270]
326. strong(X0) | happy(X0) <- (6) [resolution 124,148]
343. happy(X0) | funny(X0) <- (6) [resolution 326,86]
346. funny(X0) <- (6) [subsumption resolution 343,85]
384. $false <- (6) [resolution 346,266]
385. ~6 [avatar contradiction clause 384]
387. $false [avatar sat refutation 153,158,159,271,385]
% SZS output end Proof for 6706331994045739071756077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not old is both rich and not wise and vice versa.
If john is not brave or not kind then alice is either not humble or not kind.
Everyone who is humble or creative is either not humble or brave.
Everyone who is not creative or creative is funny.
If someone is patient then someone is both not curious and not generous and vice versa.
If someone is both brave and not old then someone is kind or not strong.
If someone is both old and not funny then someone is rich and vice versa.
Everyone who is both not strong and not wise is both not wise and not calm.
Everyone who is not calm is not quiet or old and vice versa.
Everyone who is patient is either not old or not wise and vice versa.
If lucy is both old and not tall then alice is either not curious or curious and vice versa.
Everyone who is rich or quiet is not generous.
Everyone who is both rich and not happy is curious and vice versa.
Everyone who is quiet is either not funny or not calm.
Everyone who is both curious and not patient is either kind or strong.
Everyone who is both patient and not old is patient or not old and vice versa.
Someone is brave.
John is both not tall and old.
Susan is not humble or not quiet.
Someone is calm or not patient.
Someone is either not patient or not kind.
Someone is both not quiet and creative. | Susan is not calm. | entailment | (![X]:((~wise(X)|~old(X))<=>(rich(X)&~wise(X))))&
(((~brave(john)|~kind(john)))=>((~humble(alice)<~>~kind(alice))))&
(![X]:((humble(X)|creative(X))=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|creative(X))=>funny(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((~strong(X)&~wise(X))=>(~wise(X)&~calm(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|old(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~wise(X))))&
(((old(lucy)&~tall(lucy)))<=>((~curious(alice)<~>curious(alice))))&
(![X]:((rich(X)|quiet(X))=>~generous(X)))&
(![X]:((rich(X)&~happy(X))<=>curious(X)))&
(![X]:(quiet(X)=>(~funny(X)<~>~calm(X))))&
(![X]:((curious(X)&~patient(X))=>(kind(X)<~>strong(X))))&
(![X]:((patient(X)&~old(X))<=>(patient(X)|~old(X))))&
(?[X]:(brave(X)))&
((~tall(john)&old(john)))&
((~humble(susan)|~quiet(susan)))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&creative(X)))) | ~calm(susan) | [
"p3",
"p8",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 322980791740443088410687
% SZS output start Proof for 322980791740443088410687
4. ! [X0] : ((creative(X0) | ~creative(X0)) => funny(X0)) [input p3]
9. ! [X0] : (~calm(X0) <=> (old(X0) | ~quiet(X0))) [input p8]
14. ! [X0] : (quiet(X0) => (~funny(X0) <~> ~calm(X0))) [input p13]
23. calm(susan) [input hypothesis]
29. ! [X0] : (funny(X0) | (~creative(X0) & creative(X0))) [ennf transformation 4]
34. ! [X0] : ((~funny(X0) <~> ~calm(X0)) | ~quiet(X0)) [ennf transformation 14]
54. ! [X0] : ((~calm(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | calm(X0))) [nnf transformation 9]
55. ! [X0] : ((~calm(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | calm(X0))) [flattening 54]
61. ! [X0] : (((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | ~quiet(X0)) [nnf transformation 34]
87. funny(X0) | creative(X0) [cnf transformation 29]
88. funny(X0) | ~creative(X0) [cnf transformation 29]
99. ~calm(X0) | quiet(X0) [cnf transformation 55]
116. ~calm(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 61]
134. calm(susan) [cnf transformation 23]
160. funny(X0) [subsumption resolution 87,88]
214. ~calm(X0) | ~quiet(X0) [subsumption resolution 116,160]
215. ~calm(X0) [subsumption resolution 214,99]
239. $false [subsumption resolution 134,215]
% SZS output end Proof for 322980791740443088410687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is quiet or not strong and vice versa.
If mary is both not rich and not funny then mary is either calm or strong.
Everyone who is either not humble or brave is brave.
If someone is wise or not happy then someone is tall and vice versa.
Everyone who is not funny or not quiet is quiet and vice versa.
Everyone who is both curious and creative is not happy or not tall and vice versa.
Everyone who is both old and not old is either not strong or not funny and vice versa.
Everyone who is not generous is happy or not happy.
Everyone who is both not creative and not generous is not creative and vice versa.
Everyone who is either wise or rich is either quiet or kind and vice versa.
If alice is either kind or not rich then fred is not generous or calm.
Everyone who is either not kind or not quiet is both quiet and not creative and vice versa.
Everyone who is both not strong and not rich is either creative or not brave.
Everyone who is happy or patient is either not strong or old.
If someone is not creative then someone is both generous and tall and vice versa.
Everyone who is patient or not generous is either funny or humble and vice versa.
Someone is generous.
Someone is not generous.
Someone is either not funny or not wise.
Someone is either happy or calm.
Someone is quiet or not creative.
Someone is both calm and not brave. | Fred is not curious. | contradiction | (![X]:(old(X)<=>(quiet(X)|~strong(X))))&
(((~rich(mary)&~funny(mary)))=>((calm(mary)<~>strong(mary))))&
(![X]:((~humble(X)<~>brave(X))=>brave(X)))&
((?[X]:((wise(X)|~happy(X))))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)|~quiet(X))<=>quiet(X)))&
(![X]:((curious(X)&creative(X))<=>(~happy(X)|~tall(X))))&
(![X]:((old(X)&~old(X))<=>(~strong(X)<~>~funny(X))))&
(![X]:(~generous(X)=>(happy(X)|~happy(X))))&
(![X]:((~creative(X)&~generous(X))<=>~creative(X)))&
(![X]:((wise(X)<~>rich(X))<=>(quiet(X)<~>kind(X))))&
(((kind(alice)<~>~rich(alice)))=>((~generous(fred)|calm(fred))))&
(![X]:((~kind(X)<~>~quiet(X))<=>(quiet(X)&~creative(X))))&
(![X]:((~strong(X)&~rich(X))=>(creative(X)<~>~brave(X))))&
(![X]:((happy(X)|patient(X))=>(~strong(X)<~>old(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((patient(X)|~generous(X))<=>(funny(X)<~>humble(X))))&
(?[X]:(generous(X)))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((happy(X)<~>calm(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((calm(X)&~brave(X)))) | ~curious(fred) | [
"p0",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 3531943955070333300537214
% SZS output start Proof for 3531943955070333300537214
1. ! [X0] : (old(X0) <=> (~strong(X0) | quiet(X0))) [input p0]
5. ! [X0] : ((~quiet(X0) | ~funny(X0)) <=> quiet(X0)) [input p4]
6. ! [X0] : ((creative(X0) & curious(X0)) <=> (~tall(X0) | ~happy(X0))) [input p5]
7. ! [X0] : ((~old(X0) & old(X0)) <=> (~strong(X0) <~> ~funny(X0))) [input p6]
14. ! [X0] : ((patient(X0) | happy(X0)) => (~strong(X0) <~> old(X0))) [input p13]
23. ~curious(fred) [input hypothesis]
35. ! [X0] : ((~strong(X0) <~> old(X0)) | (~patient(X0) & ~happy(X0))) [ennf transformation 14]
36. ! [X0] : ((old(X0) | (strong(X0) & ~quiet(X0))) & ((~strong(X0) | quiet(X0)) | ~old(X0))) [nnf transformation 1]
37. ! [X0] : ((old(X0) | (strong(X0) & ~quiet(X0))) & (~strong(X0) | quiet(X0) | ~old(X0))) [flattening 36]
45. ! [X0] : (((~quiet(X0) | ~funny(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & funny(X0)))) [nnf transformation 5]
46. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & funny(X0)))) [flattening 45]
47. ! [X0] : (((creative(X0) & curious(X0)) | (tall(X0) & happy(X0))) & ((~tall(X0) | ~happy(X0)) | (~creative(X0) | ~curious(X0)))) [nnf transformation 6]
48. ! [X0] : (((creative(X0) & curious(X0)) | (tall(X0) & happy(X0))) & (~tall(X0) | ~happy(X0) | ~creative(X0) | ~curious(X0))) [flattening 47]
49. ! [X0] : (((~old(X0) & old(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | (old(X0) | ~old(X0)))) [nnf transformation 7]
50. ! [X0] : (((~old(X0) & old(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | old(X0) | ~old(X0))) [flattening 49]
58. ! [X0] : (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (~patient(X0) & ~happy(X0))) [nnf transformation 35]
82. strong(X0) | old(X0) [cnf transformation 37]
91. quiet(X0) | quiet(X0) [cnf transformation 46]
92. ~quiet(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 46]
94. curious(X0) | happy(X0) [cnf transformation 48]
101. old(X0) | ~strong(X0) | funny(X0) [cnf transformation 50]
103. ~old(X0) | ~strong(X0) | funny(X0) [cnf transformation 50]
128. ~old(X0) | strong(X0) | ~happy(X0) [cnf transformation 58]
148. ~curious(fred) [cnf transformation 23]
151. quiet(X0) [duplicate literal removal 91]
152. ~funny(X0) | ~quiet(X0) [duplicate literal removal 92]
197. ~strong(X0) | funny(X0) [subsumption resolution 101,103]
223. ~happy(X0) | strong(X0) [subsumption resolution 128,82]
270. happy(fred) [resolution 94,148]
287. strong(fred) [resolution 223,270]
289. funny(fred) [resolution 287,197]
300. ~quiet(fred) [resolution 289,152]
301. $false [subsumption resolution 300,151]
% SZS output end Proof for 3531943955070333300537214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then lucy is not quiet.
Everyone who is both brave and rich is calm or not patient.
Everyone who is both calm and curious is either not patient or rich.
Everyone who is both humble and not tall is quiet and vice versa.
If someone is not strong then someone is both quiet and not rich and vice versa.
Everyone who is old is not wise or patient.
If someone is both not happy and curious then someone is happy or not wise.
If mary is both rich and not old then susan is quiet or not patient.
Everyone who is either not patient or not funny is old.
Everyone who is both happy and funny is either generous or creative and vice versa.
If someone is either not strong or wise then someone is rich or not rich.
Everyone who is kind is both generous and not happy.
If someone is both quiet and brave then someone is not calm and vice versa.
Everyone who is either not kind or tall is calm.
Everyone who is not wise is either rich or not strong and vice versa.
Fred is both not kind and not funny.
Someone is either not old or happy.
Lucy is wise.
John is rich or not brave.
Mary is either patient or not rich.
Someone is both generous and not quiet.
Mary is funny or happy.
Someone is not generous. | Mary is funny. | neutral | ((patient(john))=>(~quiet(lucy)))&
(![X]:((brave(X)&rich(X))=>(calm(X)|~patient(X))))&
(![X]:((calm(X)&curious(X))=>(~patient(X)<~>rich(X))))&
(![X]:((humble(X)&~tall(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:(old(X)=>(~wise(X)|patient(X))))&
((?[X]:((~happy(X)&curious(X))))=>(?[X]:((happy(X)|~wise(X)))))&
(((rich(mary)&~old(mary)))=>((quiet(susan)|~patient(susan))))&
(![X]:((~patient(X)<~>~funny(X))=>old(X)))&
(![X]:((happy(X)&funny(X))<=>(generous(X)<~>creative(X))))&
((?[X]:((~strong(X)<~>wise(X))))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:(kind(X)=>(generous(X)&~happy(X))))&
((?[X]:((quiet(X)&brave(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)<~>tall(X))=>calm(X)))&
(![X]:(~wise(X)<=>(rich(X)<~>~strong(X))))&
((~kind(fred)&~funny(fred)))&
(?[X]:((~old(X)<~>happy(X))))&
(wise(lucy))&
((rich(john)|~brave(john)))&
((patient(mary)<~>~rich(mary)))&
(?[X]:((generous(X)&~quiet(X))))&
((funny(mary)|happy(mary)))&
(?[X]:(~generous(X))) | funny(mary) | []
| null | 0 |
If lucy is kind then someone is not happy.
If lucy is not rich then someone is both not brave and not generous and vice versa.
If susan is old then alice is old or humble and vice versa.
Everyone who is either tall or humble is not patient and vice versa.
Everyone who is not happy or wise is not funny.
Everyone who is either creative or kind is quiet.
If paul is not happy or not tall then someone is not kind or not wise.
If someone is both not humble and old then lucy is either brave or not wise.
Everyone who is not rich is either rich or patient and vice versa.
If someone is wise or calm then fred is generous and vice versa.
Everyone who is both not calm and humble is not rich or happy.
Everyone who is generous is happy.
If alice is either patient or not curious then someone is patient and vice versa.
Everyone who is humble is both not patient and humble and vice versa.
If susan is not happy then paul is both not rich and not patient and vice versa.
If someone is patient or not old then someone is either not curious or generous and vice versa.
Someone is either wise or not calm.
Someone is both not funny and not tall.
Lucy is both not creative and brave.
Susan is old or rich.
Someone is not curious.
Someone is either funny or kind. | Fred is not patient. | contradiction | ((kind(lucy))=>(?[X]:(~happy(X))))&
((~rich(lucy))<=>(?[X]:((~brave(X)&~generous(X)))))&
((old(susan))<=>((old(alice)|humble(alice))))&
(![X]:((tall(X)<~>humble(X))<=>~patient(X)))&
(![X]:((~happy(X)|wise(X))=>~funny(X)))&
(![X]:((creative(X)<~>kind(X))=>quiet(X)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~kind(X)|~wise(X)))))&
((?[X]:((~humble(X)&old(X))))=>((brave(lucy)<~>~wise(lucy))))&
(![X]:(~rich(X)<=>(rich(X)<~>patient(X))))&
((?[X]:((wise(X)|calm(X))))<=>(generous(fred)))&
(![X]:((~calm(X)&humble(X))=>(~rich(X)|happy(X))))&
(![X]:(generous(X)=>happy(X)))&
(((patient(alice)<~>~curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:(humble(X)<=>(~patient(X)&humble(X))))&
((~happy(susan))<=>((~rich(paul)&~patient(paul))))&
((?[X]:((patient(X)|~old(X))))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(?[X]:((wise(X)<~>~calm(X))))&
(?[X]:((~funny(X)&~tall(X))))&
((~creative(lucy)&brave(lucy)))&
((old(susan)|rich(susan)))&
(?[X]:(~curious(X)))&
(?[X]:((funny(X)<~>kind(X)))) | ~patient(fred) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 3803380676403994227870920
% SZS output start Proof for 3803380676403994227870920
9. ! [X0] : (~rich(X0) <=> (rich(X0) <~> patient(X0))) [input p8]
23. ~patient(fred) [input hypothesis]
46. ! [X0] : ((~rich(X0) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | rich(X0))) [nnf transformation 9]
91. patient(X0) | rich(X0) | rich(X0) [cnf transformation 46]
93. ~rich(X0) | patient(X0) | ~rich(X0) [cnf transformation 46]
125. ~patient(fred) [cnf transformation 23]
126. patient(X0) | rich(X0) [duplicate literal removal 91]
127. ~rich(X0) | patient(X0) [duplicate literal removal 93]
201. patient(X0) [subsumption resolution 126,127]
270. $false [subsumption resolution 125,201]
% SZS output end Proof for 3803380676403994227870920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then fred is not generous or not brave and vice versa.
Everyone who is not strong is both not rich and not old and vice versa.
If someone is not generous or not quiet then someone is both not creative and not funny and vice versa.
Everyone who is not generous is both generous and not quiet and vice versa.
Everyone who is both kind and humble is not creative and vice versa.
If lucy is either not curious or not old then fred is patient or not strong.
Everyone who is happy is either patient or curious and vice versa.
Everyone who is both creative and not humble is either wise or kind and vice versa.
Everyone who is calm or not curious is not patient.
Everyone who is both wise and happy is funny or not happy.
Everyone who is both humble and not happy is curious or not calm and vice versa.
If someone is not creative or patient then someone is either not funny or rich and vice versa.
Everyone who is wise or not strong is both not strong and kind.
If someone is both not brave and tall then someone is not happy and vice versa.
If someone is not happy or not tall then fred is either tall or not rich and vice versa.
If john is both not wise and curious then someone is rich or not calm and vice versa.
Paul is either wise or patient.
Someone is either tall or not funny.
Someone is either creative or kind.
Mary is either humble or tall.
Someone is both not curious and not strong.
Someone is creative.
Someone is both rich and not wise. | Paul is not humble. | contradiction | ((?[X]:(~kind(X)))<=>((~generous(fred)|~brave(fred))))&
(![X]:(~strong(X)<=>(~rich(X)&~old(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:(~generous(X)<=>(generous(X)&~quiet(X))))&
(![X]:((kind(X)&humble(X))<=>~creative(X)))&
(((~curious(lucy)<~>~old(lucy)))=>((patient(fred)|~strong(fred))))&
(![X]:(happy(X)<=>(patient(X)<~>curious(X))))&
(![X]:((creative(X)&~humble(X))<=>(wise(X)<~>kind(X))))&
(![X]:((calm(X)|~curious(X))=>~patient(X)))&
(![X]:((wise(X)&happy(X))=>(funny(X)|~happy(X))))&
(![X]:((humble(X)&~happy(X))<=>(curious(X)|~calm(X))))&
((?[X]:((~creative(X)|patient(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((wise(X)|~strong(X))=>(~strong(X)&kind(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~happy(X)|~tall(X))))<=>((tall(fred)<~>~rich(fred))))&
(((~wise(john)&curious(john)))<=>(?[X]:((rich(X)|~calm(X)))))&
((wise(paul)<~>patient(paul)))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((humble(mary)<~>tall(mary)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:(creative(X)))&
(?[X]:((rich(X)&~wise(X)))) | ~humble(paul) | [
"p4",
"p6",
"p7",
"p8",
"p10",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8456987080684228822584852
% SZS output start Proof for 8456987080684228822584852
5. ! [X0] : ((humble(X0) & kind(X0)) <=> ~creative(X0)) [input p4]
7. ! [X0] : (happy(X0) <=> (patient(X0) <~> curious(X0))) [input p6]
8. ! [X0] : ((~humble(X0) & creative(X0)) <=> (wise(X0) <~> kind(X0))) [input p7]
9. ! [X0] : ((~curious(X0) | calm(X0)) => ~patient(X0)) [input p8]
11. ! [X0] : ((~happy(X0) & humble(X0)) <=> (~calm(X0) | curious(X0))) [input p10]
13. ! [X0] : ((~strong(X0) | wise(X0)) => (kind(X0) & ~strong(X0))) [input p12]
17. wise(paul) <~> patient(paul) [input p16]
24. ~humble(paul) [input hypothesis]
30. ! [X0] : (~patient(X0) | (curious(X0) & ~calm(X0))) [ennf transformation 9]
33. ! [X0] : ((kind(X0) & ~strong(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 13]
48. ! [X0] : (((humble(X0) & kind(X0)) | creative(X0)) & (~creative(X0) | (~humble(X0) | ~kind(X0)))) [nnf transformation 5]
49. ! [X0] : (((humble(X0) & kind(X0)) | creative(X0)) & (~creative(X0) | ~humble(X0) | ~kind(X0))) [flattening 48]
51. ! [X0] : ((happy(X0) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0)))) & (((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | ~happy(X0))) [nnf transformation 7]
52. ! [X0] : (((~humble(X0) & creative(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (humble(X0) | ~creative(X0)))) [nnf transformation 8]
53. ! [X0] : (((~humble(X0) & creative(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | humble(X0) | ~creative(X0))) [flattening 52]
54. ! [X0] : (((~happy(X0) & humble(X0)) | (calm(X0) & ~curious(X0))) & ((~calm(X0) | curious(X0)) | (happy(X0) | ~humble(X0)))) [nnf transformation 11]
55. ! [X0] : (((~happy(X0) & humble(X0)) | (calm(X0) & ~curious(X0))) & (~calm(X0) | curious(X0) | happy(X0) | ~humble(X0))) [flattening 54]
75. (~patient(paul) | ~wise(paul)) & (patient(paul) | wise(paul)) [nnf transformation 17]
105. humble(X0) | creative(X0) [cnf transformation 49]
110. ~patient(X0) | curious(X0) | happy(X0) [cnf transformation 51]
113. ~kind(X0) | ~wise(X0) | humble(X0) | ~creative(X0) [cnf transformation 53]
119. ~patient(X0) | curious(X0) [cnf transformation 30]
122. ~curious(X0) | humble(X0) [cnf transformation 55]
124. ~happy(X0) | ~curious(X0) [cnf transformation 55]
134. ~wise(X0) | kind(X0) [cnf transformation 33]
150. patient(paul) | wise(paul) [cnf transformation 75]
163. ~humble(paul) [cnf transformation 24]
235. ~wise(X0) | ~kind(X0) | humble(X0) [subsumption resolution 113,105]
345. 40 <=> wise(paul) [avatar definition]
346. wise(paul) <- (40) [avatar component clause 345]
349. 41 <=> patient(paul) [avatar definition]
350. patient(paul) <- (41) [avatar component clause 349]
353. 40 | 41 [avatar split clause 150,349,345]
393. kind(paul) <- (40) [resolution 134,346]
477. 54 <=> happy(paul) [avatar definition]
478. happy(paul) <- (54) [avatar component clause 477]
479. ~happy(paul) <- (~54) [avatar component clause 477]
488. ~kind(paul) | humble(paul) <- (40) [resolution 235,346]
490. humble(paul) <- (40) [subsumption resolution 488,393]
491. $false <- (40) [subsumption resolution 490,163]
492. ~40 [avatar contradiction clause 491]
494. curious(paul) | happy(paul) <- (41) [resolution 350,110]
495. curious(paul) <- (41) [resolution 350,119]
496. curious(paul) <- (41, ~54) [subsumption resolution 494,479]
525. humble(paul) <- (41, ~54) [resolution 496,122]
526. $false <- (41, ~54) [subsumption resolution 525,163]
527. ~41 | 54 [avatar contradiction clause 526]
531. ~curious(paul) <- (54) [resolution 478,124]
535. $false <- (41, 54) [subsumption resolution 531,495]
536. ~41 | ~54 [avatar contradiction clause 535]
537. $false [avatar sat refutation 353,492,527,536]
% SZS output end Proof for 8456987080684228822584852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not old is curious and vice versa.
Everyone who is creative or not kind is wise or not generous.
Everyone who is not patient is patient or not brave and vice versa.
If someone is both not rich and not brave then someone is not rich and vice versa.
If someone is brave or not kind then someone is not funny or not curious.
If someone is both not kind and not rich then mary is either not wise or old.
If someone is wise then someone is either not generous or curious.
If someone is not patient then someone is both not quiet and curious.
Everyone who is both creative and calm is not happy or tall and vice versa.
Everyone who is wise or not calm is both not strong and not tall.
Everyone who is not tall or tall is either calm or old.
Everyone who is both wise and creative is not wise and vice versa.
Everyone who is both not calm and not old is not rich.
If paul is both not creative and humble then someone is both calm and not brave and vice versa.
If mary is both not wise and not generous then alice is old and vice versa.
Everyone who is both not curious and generous is both curious and brave and vice versa.
Fred is not old.
Alice is not kind.
Someone is not calm or brave.
Someone is either not quiet or not generous.
Mary is either curious or not humble. | Paul is not old. | neutral | (![X]:((tall(X)|~old(X))<=>curious(X)))&
(![X]:((creative(X)|~kind(X))=>(wise(X)|~generous(X))))&
(![X]:(~patient(X)<=>(patient(X)|~brave(X))))&
((?[X]:((~rich(X)&~brave(X))))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|~kind(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
((?[X]:((~kind(X)&~rich(X))))=>((~wise(mary)<~>old(mary))))&
((?[X]:(wise(X)))=>(?[X]:((~generous(X)<~>curious(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~quiet(X)&curious(X)))))&
(![X]:((creative(X)&calm(X))<=>(~happy(X)|tall(X))))&
(![X]:((wise(X)|~calm(X))=>(~strong(X)&~tall(X))))&
(![X]:((~tall(X)|tall(X))=>(calm(X)<~>old(X))))&
(![X]:((wise(X)&creative(X))<=>~wise(X)))&
(![X]:((~calm(X)&~old(X))=>~rich(X)))&
(((~creative(paul)&humble(paul)))<=>(?[X]:((calm(X)&~brave(X)))))&
(((~wise(mary)&~generous(mary)))<=>(old(alice)))&
(![X]:((~curious(X)&generous(X))<=>(curious(X)&brave(X))))&
(~old(fred))&
(~kind(alice))&
(?[X]:((~calm(X)|brave(X))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((curious(mary)<~>~humble(mary))) | ~old(paul) | []
| null | 0 |
Everyone who is rich is either quiet or not humble. If someone is not quiet then someone is both rich and not wise and vice versa. Everyone who is both humble and not happy is funny. If fred is curious or calm then fred is both not happy and not funny. Everyone who is both not patient and not wise is not rich. If someone is wise then paul is not generous or strong and vice versa. Everyone who is either not strong or not patient is both not rich and not calm and vice versa. If someone is both creative and rich then someone is either not humble or brave and vice versa. Everyone who is not generous or happy is not happy and vice versa. Everyone who is not creative is either not strong or creative. Everyone who is patient or calm is not humble. If fred is either not quiet or kind then someone is not rich. Everyone who is either not patient or not strong is either kind or not tall. Everyone who is both not curious and not brave is not generous and vice versa. If paul is both not tall and old then susan is either quiet or not calm and vice versa. If someone is both happy and not rich then someone is tall or not patient. Someone is either not calm or curious. Paul is funny or calm. Someone is either creative or humble. Someone is happy or not brave. Someone is not brave. John is both funny and calm. Someone is either not calm or quiet. Someone is not old. | Fred is not brave. | entailment | (![X]:(rich(X)=>(quiet(X)<~>~humble(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((rich(X)&~wise(X)))))&
(![X]:((humble(X)&~happy(X))=>funny(X)))&
(((curious(fred)|calm(fred)))=>((~happy(fred)&~funny(fred))))&
(![X]:((~patient(X)&~wise(X))=>~rich(X)))&
((?[X]:(wise(X)))<=>((~generous(paul)|strong(paul))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~rich(X)&~calm(X))))&
((?[X]:((creative(X)&rich(X))))<=>(?[X]:((~humble(X)<~>brave(X)))))&
(![X]:((~generous(X)|happy(X))<=>~happy(X)))&
(![X]:(~creative(X)=>(~strong(X)<~>creative(X))))&
(![X]:((patient(X)|calm(X))=>~humble(X)))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:(~rich(X))))&
(![X]:((~patient(X)<~>~strong(X))=>(kind(X)<~>~tall(X))))&
(![X]:((~curious(X)&~brave(X))<=>~generous(X)))&
(((~tall(paul)&old(paul)))<=>((quiet(susan)<~>~calm(susan))))&
((?[X]:((happy(X)&~rich(X))))=>(?[X]:((tall(X)|~patient(X)))))&
(?[X]:((~calm(X)<~>curious(X))))&
((funny(paul)|calm(paul)))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:((happy(X)|~brave(X))))&
(?[X]:(~brave(X)))&
((funny(john)&calm(john)))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:(~old(X))) | ~brave(fred) | [
"p8",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8565936145932211844572371
% SZS output start Proof for 8565936145932211844572371
9. ! [X0] : ((happy(X0) | ~generous(X0)) <=> ~happy(X0)) [input p8]
14. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> ~generous(X0)) [input p13]
25. brave(fred) [input hypothesis]
58. ! [X0] : (((happy(X0) | ~generous(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) & generous(X0)))) [nnf transformation 9]
59. ! [X0] : ((happy(X0) | ~generous(X0) | happy(X0)) & (~happy(X0) | (~happy(X0) & generous(X0)))) [flattening 58]
65. ! [X0] : (((~brave(X0) & ~curious(X0)) | generous(X0)) & (~generous(X0) | (brave(X0) | curious(X0)))) [nnf transformation 14]
66. ! [X0] : (((~brave(X0) & ~curious(X0)) | generous(X0)) & (~generous(X0) | brave(X0) | curious(X0))) [flattening 65]
114. ~happy(X0) | ~happy(X0) [cnf transformation 59]
115. happy(X0) | ~generous(X0) | happy(X0) [cnf transformation 59]
128. ~brave(X0) | generous(X0) [cnf transformation 66]
148. brave(fred) [cnf transformation 25]
150. ~happy(X0) [duplicate literal removal 114]
151. ~generous(X0) | happy(X0) [duplicate literal removal 115]
322. generous(fred) [resolution 128,148]
323. happy(fred) [resolution 151,322]
324. $false [subsumption resolution 323,150]
% SZS output end Proof for 8565936145932211844572371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not funny or funny then mary is both quiet and strong.
Everyone who is both not funny and not creative is not tall or not old and vice versa.
If alice is either not brave or not funny then someone is generous and vice versa.
Everyone who is both not generous and tall is both not creative and not old.
Everyone who is generous or not calm is not rich or not old.
Everyone who is both happy and rich is either not calm or not wise and vice versa.
Everyone who is both brave and happy is either brave or not old and vice versa.
Everyone who is both happy and patient is rich.
If fred is creative then someone is rich and vice versa.
If paul is either not curious or funny then someone is either kind or not old.
If someone is not creative or curious then paul is either humble or not curious and vice versa.
If someone is both not patient and not funny then fred is not kind.
Everyone who is funny is either quiet or not humble.
Everyone who is not wise is not creative.
John is not humble or not happy.
Someone is either not brave or calm.
Someone is both not funny and not creative.
Lucy is not rich.
Someone is both generous and not brave.
Someone is calm.
Someone is both not generous and curious.
Fred is not patient. | Mary is not patient. | neutral | (((~funny(paul)<~>funny(paul)))=>((quiet(mary)&strong(mary))))&
(![X]:((~funny(X)&~creative(X))<=>(~tall(X)|~old(X))))&
(((~brave(alice)<~>~funny(alice)))<=>(?[X]:(generous(X))))&
(![X]:((~generous(X)&tall(X))=>(~creative(X)&~old(X))))&
(![X]:((generous(X)|~calm(X))=>(~rich(X)|~old(X))))&
(![X]:((happy(X)&rich(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((brave(X)&happy(X))<=>(brave(X)<~>~old(X))))&
(![X]:((happy(X)&patient(X))=>rich(X)))&
((creative(fred))<=>(?[X]:(rich(X))))&
(((~curious(paul)<~>funny(paul)))=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~creative(X)|curious(X))))<=>((humble(paul)<~>~curious(paul))))&
((?[X]:((~patient(X)&~funny(X))))=>(~kind(fred)))&
(![X]:(funny(X)=>(quiet(X)<~>~humble(X))))&
(![X]:(~wise(X)=>~creative(X)))&
((~humble(john)|~happy(john)))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(~rich(lucy))&
(?[X]:((generous(X)&~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((~generous(X)&curious(X))))&
(~patient(fred)) | ~patient(mary) | []
| null | 0 |
Everyone who is both not humble and not old is not patient or quiet and vice versa.
If alice is both not strong and not quiet then someone is either not brave or not strong and vice versa.
Everyone who is both happy and kind is both not wise and not old and vice versa.
Everyone who is either kind or not rich is happy.
Everyone who is curious is old or not funny.
Everyone who is either not funny or brave is either not humble or not tall and vice versa.
If fred is quiet or not humble then someone is curious or not generous and vice versa.
Everyone who is both not happy and not brave is both not tall and patient.
Everyone who is not humble is both kind and not happy and vice versa.
Everyone who is tall or not old is both happy and not old.
Everyone who is both not tall and not kind is strong.
Everyone who is both quiet and brave is both old and not creative.
Everyone who is either not humble or funny is either not patient or patient and vice versa.
Everyone who is not creative is both not tall and not brave and vice versa.
If john is not wise then someone is either tall or generous.
Everyone who is both calm and strong is not brave and vice versa.
Someone is not tall.
Lucy is both not old and not brave.
John is both not happy and not curious.
Someone is not quiet.
Susan is either not strong or brave.
Someone is calm. | Fred is not brave. | neutral | (![X]:((~humble(X)&~old(X))<=>(~patient(X)|quiet(X))))&
(((~strong(alice)&~quiet(alice)))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:((happy(X)&kind(X))<=>(~wise(X)&~old(X))))&
(![X]:((kind(X)<~>~rich(X))=>happy(X)))&
(![X]:(curious(X)=>(old(X)|~funny(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(~humble(X)<~>~tall(X))))&
(((quiet(fred)|~humble(fred)))<=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((~happy(X)&~brave(X))=>(~tall(X)&patient(X))))&
(![X]:(~humble(X)<=>(kind(X)&~happy(X))))&
(![X]:((tall(X)|~old(X))=>(happy(X)&~old(X))))&
(![X]:((~tall(X)&~kind(X))=>strong(X)))&
(![X]:((quiet(X)&brave(X))=>(old(X)&~creative(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(~patient(X)<~>patient(X))))&
(![X]:(~creative(X)<=>(~tall(X)&~brave(X))))&
((~wise(john))=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((calm(X)&strong(X))<=>~brave(X)))&
(?[X]:(~tall(X)))&
((~old(lucy)&~brave(lucy)))&
((~happy(john)&~curious(john)))&
(?[X]:(~quiet(X)))&
((~strong(susan)<~>brave(susan)))&
(?[X]:(calm(X))) | ~brave(fred) | []
| null | 0 |
Everyone who is both not curious and happy is either strong or not rich and vice versa.
Everyone who is not rich or humble is both curious and humble.
If paul is either humble or not funny then someone is both calm and quiet and vice versa.
Everyone who is both curious and not curious is either rich or not wise and vice versa.
Everyone who is not wise or not funny is either creative or not patient and vice versa.
Everyone who is both not calm and not brave is humble or kind and vice versa.
Everyone who is kind or calm is not calm or not creative.
Everyone who is both not funny and not rich is both calm and not old and vice versa.
Everyone who is either not generous or not brave is both humble and happy and vice versa.
Everyone who is not old or rich is curious.
If someone is either humble or not curious then lucy is both not humble and creative.
If alice is not funny or not wise then alice is strong or old and vice versa.
Everyone who is not old is either not brave or not generous and vice versa.
If someone is not rich then mary is not curious or creative.
Everyone who is not brave or brave is not humble or happy and vice versa.
Someone is either humble or not quiet.
Lucy is either old or generous.
Paul is both generous and not quiet.
Someone is not curious or brave.
Mary is either rich or not patient.
Mary is not funny. | Alice is not generous. | neutral | (![X]:((~curious(X)&happy(X))<=>(strong(X)<~>~rich(X))))&
(![X]:((~rich(X)|humble(X))=>(curious(X)&humble(X))))&
(((humble(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)&quiet(X)))))&
(![X]:((curious(X)&~curious(X))<=>(rich(X)<~>~wise(X))))&
(![X]:((~wise(X)|~funny(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((~calm(X)&~brave(X))<=>(humble(X)|kind(X))))&
(![X]:((kind(X)|calm(X))=>(~calm(X)|~creative(X))))&
(![X]:((~funny(X)&~rich(X))<=>(calm(X)&~old(X))))&
(![X]:((~generous(X)<~>~brave(X))<=>(humble(X)&happy(X))))&
(![X]:((~old(X)|rich(X))=>curious(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>((~humble(lucy)&creative(lucy))))&
(((~funny(alice)|~wise(alice)))<=>((strong(alice)|old(alice))))&
(![X]:(~old(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:(~rich(X)))=>((~curious(mary)|creative(mary))))&
(![X]:((~brave(X)|brave(X))<=>(~humble(X)|happy(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
((old(lucy)<~>generous(lucy)))&
((generous(paul)&~quiet(paul)))&
(?[X]:((~curious(X)|brave(X))))&
((rich(mary)<~>~patient(mary)))&
(~funny(mary)) | ~generous(alice) | []
| null | 0 |
If someone is creative or not strong then paul is not creative and vice versa. If someone is not brave then paul is not rich or not kind and vice versa. Everyone who is both curious and creative is quiet. If fred is kind or not calm then someone is both not creative and not strong and vice versa. Everyone who is either not strong or not curious is both wise and generous and vice versa. If someone is either not funny or not humble then someone is either old or kind and vice versa. If someone is either curious or not brave then someone is either patient or not creative. Everyone who is both not funny and tall is both not generous and not brave. Everyone who is both not calm and not curious is either wise or strong. If someone is not funny or happy then someone is both not creative and old. Everyone who is either not rich or humble is either old or not strong and vice versa. If someone is both not curious and funny then alice is wise or not quiet. If someone is not humble or wise then fred is either happy or rich and vice versa. If someone is not creative then someone is not brave. If susan is tall or wise then someone is both not funny and not strong. Everyone who is either not tall or not funny is both not generous and funny and vice versa. Someone is happy or not humble. Mary is both curious and not generous. Someone is both rich and tall. Someone is both funny and not kind. Paul is both curious and wise. Paul is not old. Alice is not happy. Someone is rich. | Mary is not tall. | entailment | ((?[X]:((creative(X)|~strong(X))))<=>(~creative(paul)))&
((?[X]:(~brave(X)))<=>((~rich(paul)|~kind(paul))))&
(![X]:((curious(X)&creative(X))=>quiet(X)))&
(((kind(fred)|~calm(fred)))<=>(?[X]:((~creative(X)&~strong(X)))))&
(![X]:((~strong(X)<~>~curious(X))<=>(wise(X)&generous(X))))&
((?[X]:((~funny(X)<~>~humble(X))))<=>(?[X]:((old(X)<~>kind(X)))))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((~funny(X)&tall(X))=>(~generous(X)&~brave(X))))&
(![X]:((~calm(X)&~curious(X))=>(wise(X)<~>strong(X))))&
((?[X]:((~funny(X)|happy(X))))=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((~rich(X)<~>humble(X))<=>(old(X)<~>~strong(X))))&
((?[X]:((~curious(X)&funny(X))))=>((wise(alice)|~quiet(alice))))&
((?[X]:((~humble(X)|wise(X))))<=>((happy(fred)<~>rich(fred))))&
((?[X]:(~creative(X)))=>(?[X]:(~brave(X))))&
(((tall(susan)|wise(susan)))=>(?[X]:((~funny(X)&~strong(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(~generous(X)&funny(X))))&
(?[X]:((happy(X)|~humble(X))))&
((curious(mary)&~generous(mary)))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((funny(X)&~kind(X))))&
((curious(paul)&wise(paul)))&
(~old(paul))&
(~happy(alice))&
(?[X]:(rich(X))) | ~tall(mary) | [
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7105592436964808226874514
% SZS output start Proof for 7105592436964808226874514
16. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> (funny(X0) & ~generous(X0))) [input p15]
18. ~generous(mary) & curious(mary) [input p17]
25. tall(mary) [input hypothesis]
81. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 16]
82. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [flattening 81]
152. funny(X0) | ~tall(X0) | funny(X0) [cnf transformation 82]
153. ~funny(X0) | ~tall(X0) | ~funny(X0) | generous(X0) [cnf transformation 82]
157. ~generous(mary) [cnf transformation 18]
167. tall(mary) [cnf transformation 25]
168. ~tall(X0) | funny(X0) [duplicate literal removal 152]
169. ~tall(X0) | ~funny(X0) | generous(X0) [duplicate literal removal 153]
385. funny(mary) [resolution 168,167]
450. ~funny(mary) | generous(mary) [resolution 169,167]
452. generous(mary) [subsumption resolution 450,385]
453. $false [subsumption resolution 452,157]
% SZS output end Proof for 7105592436964808226874514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny then someone is not generous and vice versa.
Everyone who is brave is not generous.
If alice is both not patient and not strong then someone is quiet and vice versa.
Everyone who is kind is not creative and vice versa.
If someone is both not old and not patient then mary is old.
If someone is not funny or creative then someone is calm and vice versa.
Everyone who is not funny or not patient is both creative and not tall.
Everyone who is not generous is either rich or not wise and vice versa.
Everyone who is not quiet or happy is not funny or generous and vice versa.
Everyone who is both rich and not patient is both not tall and rich.
Everyone who is not kind is not old.
Everyone who is either not creative or not kind is both curious and not funny.
If someone is both rich and old then alice is either not happy or curious.
If someone is both not creative and funny then someone is rich or old.
Everyone who is either tall or humble is funny or not generous and vice versa.
If lucy is both not creative and not quiet then paul is either not old or not tall and vice versa.
Someone is wise.
Someone is not quiet or not patient.
Susan is not funny or not strong.
Lucy is not creative or not funny.
Fred is both not tall and not humble.
Susan is either not brave or tall. | Lucy is quiet. | contradiction | ((funny(alice))<=>(?[X]:(~generous(X))))&
(![X]:(brave(X)=>~generous(X)))&
(((~patient(alice)&~strong(alice)))<=>(?[X]:(quiet(X))))&
(![X]:(kind(X)<=>~creative(X)))&
((?[X]:((~old(X)&~patient(X))))=>(old(mary)))&
((?[X]:((~funny(X)|creative(X))))<=>(?[X]:(calm(X))))&
(![X]:((~funny(X)|~patient(X))=>(creative(X)&~tall(X))))&
(![X]:(~generous(X)<=>(rich(X)<~>~wise(X))))&
(![X]:((~quiet(X)|happy(X))<=>(~funny(X)|generous(X))))&
(![X]:((rich(X)&~patient(X))=>(~tall(X)&rich(X))))&
(![X]:(~kind(X)=>~old(X)))&
(![X]:((~creative(X)<~>~kind(X))=>(curious(X)&~funny(X))))&
((?[X]:((rich(X)&old(X))))=>((~happy(alice)<~>curious(alice))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:((rich(X)|old(X)))))&
(![X]:((tall(X)<~>humble(X))<=>(funny(X)|~generous(X))))&
(((~creative(lucy)&~quiet(lucy)))<=>((~old(paul)<~>~tall(paul))))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|~patient(X))))&
((~funny(susan)|~strong(susan)))&
((~creative(lucy)|~funny(lucy)))&
((~tall(fred)&~humble(fred)))&
((~brave(susan)<~>tall(susan))) | quiet(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 8751983003235394188592539
% SZS output start Proof for 8751983003235394188592539
3. (~strong(alice) & ~patient(alice)) <=> ? [X0] : quiet(X0) [input p2]
4. ! [X0] : (kind(X0) <=> ~creative(X0)) [input p3]
5. ? [X0] : (~patient(X0) & ~old(X0)) => old(mary) [input p4]
7. ! [X0] : ((~patient(X0) | ~funny(X0)) => (~tall(X0) & creative(X0))) [input p6]
11. ! [X0] : (~kind(X0) => ~old(X0)) [input p10]
12. ! [X0] : ((~creative(X0) <~> ~kind(X0)) => (~funny(X0) & curious(X0))) [input p11]
23. quiet(lucy) [input hypothesis]
27. old(mary) | ! [X0] : (patient(X0) | old(X0)) [ennf transformation 5]
28. ! [X0] : ((~tall(X0) & creative(X0)) | (patient(X0) & funny(X0))) [ennf transformation 7]
31. ! [X0] : (~old(X0) | kind(X0)) [ennf transformation 11]
32. ! [X0] : ((~funny(X0) & curious(X0)) | (~creative(X0) <=> ~kind(X0))) [ennf transformation 12]
39. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | (strong(alice) | patient(alice))) [nnf transformation 3]
40. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | strong(alice) | patient(alice)) [flattening 39]
41. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | strong(alice) | patient(alice)) [rectify 40]
42. ? [X1] : quiet(X1) => quiet(sK1) [choice axiom]
43. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (quiet(sK1) | strong(alice) | patient(alice)) [skolemisation 41,42]
44. ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))) [nnf transformation 4]
53. ! [X0] : ((~funny(X0) & curious(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) [nnf transformation 32]
71. ~patient(alice) | ~quiet(X0) [cnf transformation 43]
73. ~creative(X0) | ~kind(X0) [cnf transformation 44]
74. creative(X0) | kind(X0) [cnf transformation 44]
75. old(mary) | patient(X0) | old(X0) [cnf transformation 27]
79. creative(X0) | funny(X0) [cnf transformation 28]
93. ~old(X0) | kind(X0) [cnf transformation 31]
96. ~funny(X0) | ~kind(X0) | creative(X0) [cnf transformation 53]
121. quiet(lucy) [cnf transformation 23]
136. 4 <=> ! [X0] : ~quiet(X0) [avatar definition]
137. ~quiet(X0) <- (4) [avatar component clause 136]
144. 6 <=> patient(alice) [avatar definition]
146. ~patient(alice) <- (~6) [avatar component clause 144]
147. 4 | ~6 [avatar split clause 71,144,136]
154. 8 <=> ! [X0] : (patient(X0) | old(X0)) [avatar definition]
155. old(X0) | patient(X0) <- (8) [avatar component clause 154]
157. 9 <=> old(mary) [avatar definition]
159. old(mary) <- (9) [avatar component clause 157]
160. 8 | 9 [avatar split clause 75,157,154]
186. ~funny(X0) | creative(X0) [subsumption resolution 96,74]
187. creative(X0) [subsumption resolution 186,79]
213. 21 <=> quiet(lucy) [avatar definition]
214. quiet(lucy) <- (21) [avatar component clause 213]
251. 21 [avatar split clause 121,213]
252. $false <- (4, 21) [resolution 214,137]
253. ~4 | ~21 [avatar contradiction clause 252]
254. ~kind(X0) [resolution 73,187]
259. patient(X0) | kind(X0) <- (8) [resolution 155,93]
260. patient(X0) <- (8) [subsumption resolution 259,254]
269. $false <- (~6, 8) [resolution 260,146]
272. 6 | ~8 [avatar contradiction clause 269]
273. kind(mary) <- (9) [resolution 159,93]
274. $false <- (9) [subsumption resolution 273,254]
275. ~9 [avatar contradiction clause 274]
276. $false [avatar sat refutation 147,160,251,253,272,275]
% SZS output end Proof for 8751983003235394188592539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or curious is kind.
Everyone who is not humble or curious is generous.
Everyone who is not quiet is not strong and vice versa.
Everyone who is not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
Everyone who is patient or not tall is patient or funny.
If someone is either curious or not funny then susan is either not quiet or not old and vice versa.
If someone is strong then someone is not funny and vice versa.
If someone is either not happy or creative then susan is not wise or generous and vice versa.
If someone is both tall and not curious then someone is not tall and vice versa.
Everyone who is either creative or not tall is humble or not creative.
If paul is not generous then someone is not old.
Everyone who is both creative and not quiet is either not old or creative and vice versa.
Paul is strong.
Mary is either strong or not quiet.
Susan is calm or not brave.
Mary is either calm or not quiet.
Lucy is either wise or creative. | Lucy is not curious. | contradiction | (![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![X]:(~happy(X)<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)|~tall(X))=>(patient(X)|funny(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~quiet(susan)<~>~old(susan))))&
((?[X]:(strong(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~wise(susan)|generous(susan))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>~tall(X))=>(humble(X)|~creative(X))))&
((~generous(paul))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>creative(X))))&
(strong(paul))&
((strong(mary)<~>~quiet(mary)))&
((calm(susan)|~brave(susan)))&
((calm(mary)<~>~quiet(mary)))&
((wise(lucy)<~>creative(lucy))) | ~curious(lucy) | [
"p5",
"p7",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 6775695226423590696569258
% SZS output start Proof for 6775695226423590696569258
6. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p5]
8. ! [X0] : ((old(X0) | ~calm(X0)) => (~patient(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | patient(X0)) => (funny(X0) | patient(X0))) [input p8]
13. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X0] : ~tall(X0) [input p12]
22. ~curious(lucy) [input hypothesis]
24. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X1] : ~tall(X1) [rectify 13]
33. ! [X0] : ((~patient(X0) <~> tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 8]
34. ! [X0] : ((funny(X0) | patient(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 9]
35. ! [X0] : (funny(X0) | patient(X0) | (tall(X0) & ~patient(X0))) [flattening 34]
42. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 6]
43. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 42]
46. ! [X0] : (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 33]
61. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (curious(X0) | ~tall(X0))) [nnf transformation 24]
62. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (curious(X3) | ~tall(X3))) [rectify 61]
63. ? [X0] : (~curious(X0) & tall(X0)) => (~curious(sK6) & tall(sK6)) [choice axiom]
64. ? [X2] : ~tall(X2) => ~tall(sK7) [choice axiom]
65. ((~curious(sK6) & tall(sK6)) | ! [X1] : tall(X1)) & (~tall(sK7) | ! [X3] : (curious(X3) | ~tall(X3))) [skolemisation 62,64,63]
84. ~funny(X0) | ~funny(X0) [cnf transformation 43]
85. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 43]
88. ~patient(X0) | tall(X0) | calm(X0) [cnf transformation 46]
93. funny(X0) | patient(X0) | tall(X0) [cnf transformation 35]
110. ~tall(sK7) | curious(X3) | ~tall(X3) [cnf transformation 65]
111. tall(sK6) | tall(X1) [cnf transformation 65]
112. ~curious(sK6) | tall(X1) [cnf transformation 65]
127. ~curious(lucy) [cnf transformation 22]
130. ~funny(X0) [duplicate literal removal 84]
131. ~calm(X0) | funny(X0) [duplicate literal removal 85]
156. tall(X0) | patient(X0) [subsumption resolution 93,130]
175. 9 <=> ! [X1] : curious(X1) [avatar definition]
176. curious(X1) <- (9) [avatar component clause 175]
210. 16 <=> ! [X1] : tall(X1) [avatar definition]
211. tall(X1) <- (16) [avatar component clause 210]
213. 17 <=> curious(sK6) [avatar definition]
215. ~curious(sK6) <- (~17) [avatar component clause 213]
216. 16 | ~17 [avatar split clause 112,213,210]
218. 18 <=> tall(sK6) [avatar definition]
220. tall(sK6) <- (18) [avatar component clause 218]
221. 16 | 18 [avatar split clause 111,218,210]
223. 19 <=> ! [X3] : (curious(X3) | ~tall(X3)) [avatar definition]
224. ~tall(X3) | curious(X3) <- (19) [avatar component clause 223]
226. 20 <=> tall(sK7) [avatar definition]
228. ~tall(sK7) <- (~20) [avatar component clause 226]
229. 19 | ~20 [avatar split clause 110,226,223]
301. curious(X0) <- (16, 19) [resolution 224,211]
304. 9 | ~16 | ~19 [avatar split clause 301,223,210,175]
307. $false <- (9) [resolution 176,127]
312. ~9 [avatar contradiction clause 307]
313. curious(sK6) <- (18, 19) [resolution 220,224]
315. $false <- (~17, 18, 19) [subsumption resolution 313,215]
316. 17 | ~18 | ~19 [avatar contradiction clause 315]
317. patient(sK7) <- (~20) [resolution 228,156]
334. tall(sK7) | calm(sK7) <- (~20) [resolution 317,88]
336. calm(sK7) <- (~20) [subsumption resolution 334,228]
345. funny(sK7) <- (~20) [resolution 336,131]
347. $false <- (~20) [subsumption resolution 345,130]
348. 20 [avatar contradiction clause 347]
349. $false [avatar sat refutation 216,221,229,304,312,316,348]
% SZS output end Proof for 6775695226423590696569258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either happy or funny then someone is either kind or not patient. If someone is wise or generous then someone is both patient and not generous and vice versa. Everyone who is either strong or not strong is kind and vice versa. Everyone who is both not brave and old is not generous or not brave and vice versa. If john is rich then someone is either not creative or not happy. Everyone who is tall or funny is either not old or kind. Everyone who is quiet or patient is funny. If paul is happy or not calm then susan is calm and vice versa. Everyone who is creative is not curious or curious and vice versa. Everyone who is not strong is generous or curious. Everyone who is either not humble or funny is both old and not quiet and vice versa. Everyone who is both wise and not kind is curious and vice versa. Everyone who is either not rich or not curious is both patient and humble and vice versa. Everyone who is not patient or not humble is both not strong and tall. Everyone who is either generous or not patient is not patient. If someone is either patient or not old then someone is not generous or calm. Alice is not curious. Alice is either not curious or not quiet. Paul is both rich and funny. Paul is old. Someone is either not creative or wise. Someone is not calm or not humble. | Alice is not humble. | entailment | (((happy(susan)<~>funny(susan)))=>(?[X]:((kind(X)<~>~patient(X)))))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:((strong(X)<~>~strong(X))<=>kind(X)))&
(![X]:((~brave(X)&old(X))<=>(~generous(X)|~brave(X))))&
((rich(john))=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:((tall(X)|funny(X))=>(~old(X)<~>kind(X))))&
(![X]:((quiet(X)|patient(X))=>funny(X)))&
(((happy(paul)|~calm(paul)))<=>(calm(susan)))&
(![X]:(creative(X)<=>(~curious(X)|curious(X))))&
(![X]:(~strong(X)=>(generous(X)|curious(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(old(X)&~quiet(X))))&
(![X]:((wise(X)&~kind(X))<=>curious(X)))&
(![X]:((~rich(X)<~>~curious(X))<=>(patient(X)&humble(X))))&
(![X]:((~patient(X)|~humble(X))=>(~strong(X)&tall(X))))&
(![X]:((generous(X)<~>~patient(X))=>~patient(X)))&
((?[X]:((patient(X)<~>~old(X))))=>(?[X]:((~generous(X)|calm(X)))))&
(~curious(alice))&
((~curious(alice)<~>~quiet(alice)))&
((rich(paul)&funny(paul)))&
(old(paul))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((~calm(X)|~humble(X)))) | ~humble(alice) | [
"p2",
"p6",
"p10",
"p11",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 562980168640587340061
% SZS output start Proof for 562980168640587340061
3. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> kind(X0)) [input p2]
7. ! [X0] : ((patient(X0) | quiet(X0)) => funny(X0)) [input p6]
11. ! [X0] : ((~humble(X0) <~> funny(X0)) <=> (~quiet(X0) & old(X0))) [input p10]
12. ! [X0] : ((~kind(X0) & wise(X0)) <=> curious(X0)) [input p11]
18. ~curious(alice) <~> ~quiet(alice) [input p17]
23. humble(alice) [input hypothesis]
29. ! [X0] : (funny(X0) | (~patient(X0) & ~quiet(X0))) [ennf transformation 7]
43. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~kind(X0)) & (kind(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 3]
54. ! [X0] : ((((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (quiet(X0) | ~old(X0))) & ((~quiet(X0) & old(X0)) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0))))) [nnf transformation 11]
55. ! [X0] : ((((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | quiet(X0) | ~old(X0)) & ((~quiet(X0) & old(X0)) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0))))) [flattening 54]
56. ! [X0] : (((~kind(X0) & wise(X0)) | ~curious(X0)) & (curious(X0) | (kind(X0) | ~wise(X0)))) [nnf transformation 12]
57. ! [X0] : (((~kind(X0) & wise(X0)) | ~curious(X0)) & (curious(X0) | kind(X0) | ~wise(X0))) [flattening 56]
65. (quiet(alice) | curious(alice)) & (~quiet(alice) | ~curious(alice)) [nnf transformation 18]
80. kind(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 43]
81. kind(X0) | strong(X0) | strong(X0) [cnf transformation 43]
95. ~quiet(X0) | funny(X0) [cnf transformation 29]
107. ~quiet(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 55]
112. ~kind(X0) | ~curious(X0) [cnf transformation 57]
129. quiet(alice) | curious(alice) [cnf transformation 65]
136. humble(alice) [cnf transformation 23]
138. kind(X0) | ~strong(X0) [duplicate literal removal 80]
139. strong(X0) | kind(X0) [duplicate literal removal 81]
190. kind(X0) [subsumption resolution 138,139]
225. ~humble(X0) | ~quiet(X0) [subsumption resolution 107,95]
227. ~curious(X0) [subsumption resolution 112,190]
247. quiet(alice) [subsumption resolution 129,227]
272. ~quiet(alice) [resolution 225,136]
274. $false [subsumption resolution 272,247]
% SZS output end Proof for 562980168640587340061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is 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 happy. | entailment | (![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)))) | ~happy(fred) | [
"p0",
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 4397220796460143357458165
% SZS output start Proof for 4397220796460143357458165
1. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~happy(X0) <~> generous(X0))) [input p0]
3. ! [X0] : ((~happy(X0) & ~humble(X0)) <=> (generous(X0) | kind(X0))) [input p2]
22. happy(fred) [input hypothesis]
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. generous(X0) | ~happy(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]
87. ~happy(X0) | ~generous(X0) [cnf transformation 40]
131. happy(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]
279. generous(fred) [resolution 134,131]
280. $false [subsumption resolution 279,148]
% SZS output end Proof for 4397220796460143357458165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not calm is either calm or creative and vice versa.
Everyone who is humble or not curious is both quiet and not tall.
Everyone who is both not funny and not kind is both curious and not funny and vice versa.
If someone is wise then john is rich or not rich and vice versa.
Everyone who is not kind or not patient is both not wise and rich and vice versa.
If someone is both wise and happy then lucy is either not tall or old.
If someone is not funny then someone is both not strong and curious.
If susan is generous or humble then john is not patient.
Everyone who is not calm or calm is either not quiet or not strong.
Everyone who is not patient or funny is calm or old.
If john is not creative then susan is funny.
Everyone who is not calm or not brave is not patient or not kind and vice versa.
Everyone who is not tall is either not old or not rich.
If susan is either not calm or not quiet then someone is strong and vice versa.
If fred is either old or not old then paul is brave.
Everyone who is either funny or brave is both not patient and not brave and vice versa.
Someone is either creative or not tall.
Fred is creative.
Someone is not curious.
Mary is tall.
Someone is both not curious and creative.
Someone is not generous.
Lucy is old.
Susan is either rich or not kind. | Paul is creative. | entailment | (![X]:((~brave(X)<~>~calm(X))<=>(calm(X)<~>creative(X))))&
(![X]:((humble(X)|~curious(X))=>(quiet(X)&~tall(X))))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)&~funny(X))))&
((?[X]:(wise(X)))<=>((rich(john)|~rich(john))))&
(![X]:((~kind(X)|~patient(X))<=>(~wise(X)&rich(X))))&
((?[X]:((wise(X)&happy(X))))=>((~tall(lucy)<~>old(lucy))))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)&curious(X)))))&
(((generous(susan)|humble(susan)))=>(~patient(john)))&
(![X]:((~calm(X)|calm(X))=>(~quiet(X)<~>~strong(X))))&
(![X]:((~patient(X)|funny(X))=>(calm(X)|old(X))))&
((~creative(john))=>(funny(susan)))&
(![X]:((~calm(X)|~brave(X))<=>(~patient(X)|~kind(X))))&
(![X]:(~tall(X)=>(~old(X)<~>~rich(X))))&
(((~calm(susan)<~>~quiet(susan)))<=>(?[X]:(strong(X))))&
(((old(fred)<~>~old(fred)))=>(brave(paul)))&
(![X]:((funny(X)<~>brave(X))<=>(~patient(X)&~brave(X))))&
(?[X]:((creative(X)<~>~tall(X))))&
(creative(fred))&
(?[X]:(~curious(X)))&
(tall(mary))&
(?[X]:((~curious(X)&creative(X))))&
(?[X]:(~generous(X)))&
(old(lucy))&
((rich(susan)<~>~kind(susan))) | creative(paul) | [
"p0",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2931789030185603721871561
% SZS output start Proof for 2931789030185603721871561
1. ! [X0] : ((~brave(X0) <~> ~calm(X0)) <=> (calm(X0) <~> creative(X0))) [input p0]
15. (old(fred) <~> ~old(fred)) => brave(paul) [input p14]
25. ~creative(paul) [input hypothesis]
39. brave(paul) | (old(fred) <=> ~old(fred)) [ennf transformation 15]
40. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [nnf transformation 1]
61. brave(paul) | ((old(fred) | old(fred)) & (~old(fred) | ~old(fred))) [nnf transformation 39]
73. creative(X0) | calm(X0) | ~brave(X0) | calm(X0) [cnf transformation 40]
76. ~calm(X0) | ~brave(X0) | creative(X0) | ~calm(X0) [cnf transformation 40]
113. brave(paul) | ~old(fred) | ~old(fred) [cnf transformation 61]
114. brave(paul) | old(fred) | old(fred) [cnf transformation 61]
131. ~creative(paul) [cnf transformation 25]
134. brave(paul) | ~old(fred) [duplicate literal removal 113]
135. brave(paul) | old(fred) [duplicate literal removal 114]
136. creative(X0) | calm(X0) | ~brave(X0) [duplicate literal removal 73]
138. ~calm(X0) | ~brave(X0) | creative(X0) [duplicate literal removal 76]
141. ~brave(X0) | creative(X0) [subsumption resolution 136,138]
196. 12 <=> old(fred) [avatar definition]
200. 13 <=> brave(paul) [avatar definition]
202. brave(paul) <- (13) [avatar component clause 200]
203. 12 | 13 [avatar split clause 135,200,196]
204. ~12 | 13 [avatar split clause 134,200,196]
224. creative(paul) <- (13) [resolution 141,202]
225. $false <- (13) [subsumption resolution 224,131]
226. ~13 [avatar contradiction clause 225]
227. $false [avatar sat refutation 203,204,226]
% SZS output end Proof for 2931789030185603721871561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not kind then someone is either not curious or quiet.
Everyone who is calm is either curious or calm and vice versa.
Everyone who is either not creative or not kind is both patient and humble and vice versa.
Everyone who is both not calm and not kind is both old and happy and vice versa.
If susan is strong then someone is brave.
Everyone who is not funny or strong is both not tall and brave and vice versa.
If someone is not brave or not kind then fred is either happy or tall and vice versa.
If susan is not brave then someone is funny and vice versa.
Everyone who is either wise or happy is not quiet or creative and vice versa.
Everyone who is creative or curious is curious.
If susan is both creative and not quiet then alice is either not kind or not generous and vice versa.
If susan is not generous then paul is not funny.
If alice is not humble or not quiet then someone is tall or not calm and vice versa.
If someone is creative then lucy is either not strong or happy and vice versa.
If paul is not old or not calm then someone is wise.
Everyone who is both not rich and humble is not calm or kind.
Fred is either not tall or creative.
John is both not calm and not funny.
Paul is either rich or patient.
Lucy is both happy and not curious.
Someone is both not rich and not creative.
Alice is not generous. | John is not quiet. | neutral | ((?[X]:((creative(X)<~>~kind(X))))=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:(calm(X)<=>(curious(X)<~>calm(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(patient(X)&humble(X))))&
(![X]:((~calm(X)&~kind(X))<=>(old(X)&happy(X))))&
((strong(susan))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)|strong(X))<=>(~tall(X)&brave(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>((happy(fred)<~>tall(fred))))&
((~brave(susan))<=>(?[X]:(funny(X))))&
(![X]:((wise(X)<~>happy(X))<=>(~quiet(X)|creative(X))))&
(![X]:((creative(X)|curious(X))=>curious(X)))&
(((creative(susan)&~quiet(susan)))<=>((~kind(alice)<~>~generous(alice))))&
((~generous(susan))=>(~funny(paul)))&
(((~humble(alice)|~quiet(alice)))<=>(?[X]:((tall(X)|~calm(X)))))&
((?[X]:(creative(X)))<=>((~strong(lucy)<~>happy(lucy))))&
(((~old(paul)|~calm(paul)))=>(?[X]:(wise(X))))&
(![X]:((~rich(X)&humble(X))=>(~calm(X)|kind(X))))&
((~tall(fred)<~>creative(fred)))&
((~calm(john)&~funny(john)))&
((rich(paul)<~>patient(paul)))&
((happy(lucy)&~curious(lucy)))&
(?[X]:((~rich(X)&~creative(X))))&
(~generous(alice)) | ~quiet(john) | []
| null | 0 |
Everyone who is either tall or rich is either not wise or wise and vice versa.
If alice is either wise or not patient then someone is happy.
Everyone who is not tall is either kind or not strong.
Everyone who is kind or not creative is either not kind or not tall.
Everyone who is both not quiet and strong is not happy.
If someone is either not curious or brave then someone is not patient or not humble.
If someone is not calm or wise then john is both not wise and funny and vice versa.
If mary is brave or creative then lucy is not funny or calm.
Everyone who is funny is both not humble and funny and vice versa.
Everyone who is wise is either not generous or funny and vice versa.
Everyone who is both brave and happy is not rich or patient.
If someone is both not generous and not old then someone is both not quiet and not wise.
If mary is not calm or patient then someone is not happy or not patient and vice versa.
Everyone who is creative or not humble is generous or not wise and vice versa.
If alice is rich or not generous then mary is not brave.
If someone is quiet then someone is not humble.
Mary is both calm and not happy.
Susan is both old and brave.
Someone is patient.
Someone is not kind or old.
Alice is either not kind or old.
Someone is both patient and funny.
Mary is both humble and wise.
Paul is not humble or not patient. | Mary is generous. | contradiction | (![X]:((tall(X)<~>rich(X))<=>(~wise(X)<~>wise(X))))&
(((wise(alice)<~>~patient(alice)))=>(?[X]:(happy(X))))&
(![X]:(~tall(X)=>(kind(X)<~>~strong(X))))&
(![X]:((kind(X)|~creative(X))=>(~kind(X)<~>~tall(X))))&
(![X]:((~quiet(X)&strong(X))=>~happy(X)))&
((?[X]:((~curious(X)<~>brave(X))))=>(?[X]:((~patient(X)|~humble(X)))))&
((?[X]:((~calm(X)|wise(X))))<=>((~wise(john)&funny(john))))&
(((brave(mary)|creative(mary)))=>((~funny(lucy)|calm(lucy))))&
(![X]:(funny(X)<=>(~humble(X)&funny(X))))&
(![X]:(wise(X)<=>(~generous(X)<~>funny(X))))&
(![X]:((brave(X)&happy(X))=>(~rich(X)|patient(X))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((~quiet(X)&~wise(X)))))&
(((~calm(mary)|patient(mary)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((creative(X)|~humble(X))<=>(generous(X)|~wise(X))))&
(((rich(alice)|~generous(alice)))=>(~brave(mary)))&
((?[X]:(quiet(X)))=>(?[X]:(~humble(X))))&
((calm(mary)&~happy(mary)))&
((old(susan)&brave(susan)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)|old(X))))&
((~kind(alice)<~>old(alice)))&
(?[X]:((patient(X)&funny(X))))&
((humble(mary)&wise(mary)))&
((~humble(paul)|~patient(paul))) | generous(mary) | [
"p8",
"p9",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4648993296589127728617036
% SZS output start Proof for 4648993296589127728617036
9. ! [X0] : (funny(X0) <=> (funny(X0) & ~humble(X0))) [input p8]
10. ! [X0] : (wise(X0) <=> (~generous(X0) <~> funny(X0))) [input p9]
23. wise(mary) & humble(mary) [input p22]
25. generous(mary) [input hypothesis]
57. ! [X0] : ((funny(X0) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | ~funny(X0))) [nnf transformation 9]
58. ! [X0] : ((funny(X0) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | ~funny(X0))) [flattening 57]
59. ! [X0] : ((wise(X0) | ((~generous(X0) | ~funny(X0)) & (funny(X0) | generous(X0)))) & (((~funny(X0) | generous(X0)) & (funny(X0) | ~generous(X0))) | ~wise(X0))) [nnf transformation 10]
106. ~funny(X0) | ~humble(X0) [cnf transformation 58]
109. ~generous(X0) | funny(X0) | ~wise(X0) [cnf transformation 59]
137. humble(mary) [cnf transformation 23]
138. wise(mary) [cnf transformation 23]
140. generous(mary) [cnf transformation 25]
322. funny(mary) | ~wise(mary) [resolution 109,140]
323. funny(mary) [subsumption resolution 322,138]
336. ~humble(mary) [resolution 323,106]
337. $false [subsumption resolution 336,137]
% SZS output end Proof for 4648993296589127728617036
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is not creative and vice versa. Everyone who is not patient or not rich is quiet or not old and vice versa. If someone is either quiet or curious then someone is either not old or calm and vice versa. Everyone who is either not happy or curious is not old. Everyone who is both not brave and curious is either not funny or funny and vice versa. Everyone who is both happy and not quiet is both not brave and not humble and vice versa. If someone is either kind or not old then lucy is happy and vice versa. Everyone who is either kind or not curious is not calm and vice versa. Everyone who is kind is either creative or not curious. If susan is both generous and not curious then someone is not funny or not old. If someone is not happy then someone is either not happy or not funny. Everyone who is either old or not humble is funny or quiet and vice versa. If lucy is both calm and not old then susan is either creative or quiet. Everyone who is not wise or not patient is funny or not wise and vice versa. Everyone who is both not kind and not patient is both quiet and generous. If someone is humble or not calm then paul is creative or not tall. Someone is both not tall and humble. Lucy is both not generous and not creative. John is creative or happy. Alice is not funny. Someone is not quiet or calm. | Alice is humble. | entailment | (![X]:(curious(X)<=>~creative(X)))&
(![X]:((~patient(X)|~rich(X))<=>(quiet(X)|~old(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~happy(X)<~>curious(X))=>~old(X)))&
(![X]:((~brave(X)&curious(X))<=>(~funny(X)<~>funny(X))))&
(![X]:((happy(X)&~quiet(X))<=>(~brave(X)&~humble(X))))&
((?[X]:((kind(X)<~>~old(X))))<=>(happy(lucy)))&
(![X]:((kind(X)<~>~curious(X))<=>~calm(X)))&
(![X]:(kind(X)=>(creative(X)<~>~curious(X))))&
(((generous(susan)&~curious(susan)))=>(?[X]:((~funny(X)|~old(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((~happy(X)<~>~funny(X)))))&
(![X]:((old(X)<~>~humble(X))<=>(funny(X)|quiet(X))))&
(((calm(lucy)&~old(lucy)))=>((creative(susan)<~>quiet(susan))))&
(![X]:((~wise(X)|~patient(X))<=>(funny(X)|~wise(X))))&
(![X]:((~kind(X)&~patient(X))=>(quiet(X)&generous(X))))&
((?[X]:((humble(X)|~calm(X))))=>((creative(paul)|~tall(paul))))&
(?[X]:((~tall(X)&humble(X))))&
((~generous(lucy)&~creative(lucy)))&
((creative(john)|happy(john)))&
(~funny(alice))&
(?[X]:((~quiet(X)|calm(X)))) | humble(alice) | [
"p3",
"p4",
"p5",
"p11",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 3016377800755611175174656
% SZS output start Proof for 3016377800755611175174656
4. ! [X0] : ((~happy(X0) <~> curious(X0)) => ~old(X0)) [input p3]
5. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (~funny(X0) <~> funny(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) & happy(X0)) <=> (~humble(X0) & ~brave(X0))) [input p5]
12. ! [X0] : ((old(X0) <~> ~humble(X0)) <=> (quiet(X0) | funny(X0))) [input p11]
20. ~funny(alice) [input p19]
22. ~humble(alice) [input hypothesis]
27. ! [X0] : (~old(X0) | (~happy(X0) <=> curious(X0))) [ennf transformation 4]
44. ! [X0] : (~old(X0) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0)))) [nnf transformation 27]
45. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (~curious(X0) | brave(X0)))) [nnf transformation 5]
46. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~curious(X0) | brave(X0))) [flattening 45]
47. ! [X0] : (((~quiet(X0) & happy(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (quiet(X0) | ~happy(X0)))) [nnf transformation 6]
48. ! [X0] : (((~quiet(X0) & happy(X0)) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | quiet(X0) | ~happy(X0))) [flattening 47]
61. ! [X0] : ((((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (~quiet(X0) & ~funny(X0))) & ((quiet(X0) | funny(X0)) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))))) [nnf transformation 12]
62. ! [X0] : ((((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (~quiet(X0) & ~funny(X0))) & (quiet(X0) | funny(X0) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0))))) [flattening 61]
85. ~happy(X0) | ~old(X0) | ~curious(X0) [cnf transformation 44]
88. ~brave(X0) | funny(X0) | funny(X0) [cnf transformation 46]
89. ~brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
90. curious(X0) | funny(X0) | funny(X0) [cnf transformation 46]
91. curious(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
94. happy(X0) | humble(X0) | brave(X0) [cnf transformation 48]
95. ~quiet(X0) | humble(X0) | brave(X0) [cnf transformation 48]
110. quiet(X0) | funny(X0) | old(X0) | humble(X0) [cnf transformation 62]
127. ~funny(alice) [cnf transformation 20]
129. ~humble(alice) [cnf transformation 22]
130. ~brave(X0) | funny(X0) [duplicate literal removal 88]
131. ~funny(X0) | ~brave(X0) [duplicate literal removal 89]
132. curious(X0) | funny(X0) [duplicate literal removal 90]
133. ~funny(X0) | curious(X0) [duplicate literal removal 91]
170. curious(X0) [subsumption resolution 132,133]
171. ~brave(X0) [subsumption resolution 130,131]
172. ~quiet(X0) | humble(X0) [subsumption resolution 95,171]
173. humble(X0) | happy(X0) [subsumption resolution 94,171]
213. humble(X0) | old(X0) | funny(X0) [subsumption resolution 110,172]
264. happy(alice) [resolution 173,129]
356. ~old(alice) | ~curious(alice) [resolution 264,85]
357. ~old(alice) [subsumption resolution 356,170]
433. old(alice) | funny(alice) [resolution 213,129]
437. funny(alice) [subsumption resolution 433,357]
438. $false [subsumption resolution 437,127]
% SZS output end Proof for 3016377800755611175174656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then alice is not creative.
If someone is both wise and tall then mary is either not curious or humble.
Everyone who is both not tall and kind is wise.
If someone is both quiet and funny then mary is either not wise or not strong.
If someone is kind or not old then mary is either creative or brave and vice versa.
Everyone who is not kind is both creative and not creative.
Everyone who is creative or tall is both happy and not generous.
Everyone who is not wise or not patient is happy or not humble and vice versa.
Everyone who is either not tall or not happy is not wise or not patient.
Everyone who is brave is either curious or patient.
Everyone who is either not strong or old is both patient and generous.
If fred is either not strong or tall then susan is curious.
Everyone who is either curious or brave is both not curious and generous and vice versa.
Everyone who is quiet is either brave or not patient.
Everyone who is not wise is not happy and vice versa.
If someone is not humble or not kind then alice is happy or old and vice versa.
Someone is both not old and quiet.
Lucy is either not old or not creative.
Someone is not brave.
Someone is either old or brave.
Someone is either not calm or rich.
Fred is curious or tall. | Mary is not creative. | neutral | ((?[X]:(~funny(X)))=>(~creative(alice)))&
((?[X]:((wise(X)&tall(X))))=>((~curious(mary)<~>humble(mary))))&
(![X]:((~tall(X)&kind(X))=>wise(X)))&
((?[X]:((quiet(X)&funny(X))))=>((~wise(mary)<~>~strong(mary))))&
((?[X]:((kind(X)|~old(X))))<=>((creative(mary)<~>brave(mary))))&
(![X]:(~kind(X)=>(creative(X)&~creative(X))))&
(![X]:((creative(X)|tall(X))=>(happy(X)&~generous(X))))&
(![X]:((~wise(X)|~patient(X))<=>(happy(X)|~humble(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(~wise(X)|~patient(X))))&
(![X]:(brave(X)=>(curious(X)<~>patient(X))))&
(![X]:((~strong(X)<~>old(X))=>(patient(X)&generous(X))))&
(((~strong(fred)<~>tall(fred)))=>(curious(susan)))&
(![X]:((curious(X)<~>brave(X))<=>(~curious(X)&generous(X))))&
(![X]:(quiet(X)=>(brave(X)<~>~patient(X))))&
(![X]:(~wise(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~kind(X))))<=>((happy(alice)|old(alice))))&
(?[X]:((~old(X)&quiet(X))))&
((~old(lucy)<~>~creative(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)<~>brave(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
((curious(fred)|tall(fred))) | ~creative(mary) | []
| null | 0 |
Everyone who is both not calm and not patient is not quiet. Everyone who is not funny is not patient or not old and vice versa. If paul is not old or patient then lucy is rich or funny. Everyone who is not wise is both rich and brave. Everyone who is either not humble or not old is either not strong or wise and vice versa. If fred is not generous or quiet then paul is both not happy and not kind. If someone is either not old or not brave then someone is curious or rich and vice versa. Everyone who is either wise or not generous is happy. If someone is either not happy or quiet then someone is either calm or not generous and vice versa. If susan is not curious or not patient then john is either not creative or humble. Everyone who is not patient or creative is both creative and not generous and vice versa. Everyone who is quiet is either not strong or brave and vice versa. Everyone who is not wise or not tall is not curious and vice versa. Everyone who is funny is quiet or creative and vice versa. Everyone who is both calm and not generous is both creative and not rich and vice versa. If lucy is both tall and generous then fred is brave. Someone is either strong or not wise. Alice is both generous and not kind. Susan is either tall or curious. Someone is not kind or happy. Mary is happy or generous. Someone is both calm and not generous. Someone is not funny or not calm. Alice is not wise. | Fred is not curious. | neutral | (![X]:((~calm(X)&~patient(X))=>~quiet(X)))&
(![X]:(~funny(X)<=>(~patient(X)|~old(X))))&
(((~old(paul)|patient(paul)))=>((rich(lucy)|funny(lucy))))&
(![X]:(~wise(X)=>(rich(X)&brave(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(~strong(X)<~>wise(X))))&
(((~generous(fred)|quiet(fred)))=>((~happy(paul)&~kind(paul))))&
((?[X]:((~old(X)<~>~brave(X))))<=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((wise(X)<~>~generous(X))=>happy(X)))&
((?[X]:((~happy(X)<~>quiet(X))))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(((~curious(susan)|~patient(susan)))=>((~creative(john)<~>humble(john))))&
(![X]:((~patient(X)|creative(X))<=>(creative(X)&~generous(X))))&
(![X]:(quiet(X)<=>(~strong(X)<~>brave(X))))&
(![X]:((~wise(X)|~tall(X))<=>~curious(X)))&
(![X]:(funny(X)<=>(quiet(X)|creative(X))))&
(![X]:((calm(X)&~generous(X))<=>(creative(X)&~rich(X))))&
(((tall(lucy)&generous(lucy)))=>(brave(fred)))&
(?[X]:((strong(X)<~>~wise(X))))&
((generous(alice)&~kind(alice)))&
((tall(susan)<~>curious(susan)))&
(?[X]:((~kind(X)|happy(X))))&
((happy(mary)|generous(mary)))&
(?[X]:((calm(X)&~generous(X))))&
(?[X]:((~funny(X)|~calm(X))))&
(~wise(alice)) | ~curious(fred) | []
| null | 0 |
Everyone who is funny is rich or calm and vice versa.
If mary is both quiet and not tall then someone is kind and vice versa.
Everyone who is creative is not tall or not rich and vice versa.
If mary is quiet or funny then john is creative.
If fred is curious or not kind then someone is both not old and kind.
If someone is calm or generous then alice is either rich or not brave and vice versa.
Everyone who is both quiet and not happy is both kind and not rich and vice versa.
Everyone who is both not patient and not calm is not calm or funny and vice versa.
Everyone who is both calm and not old is both humble and tall.
Everyone who is either not calm or not rich is both happy and not tall and vice versa.
Everyone who is humble is not curious or old.
If alice is not humble then someone is quiet.
Everyone who is both not curious and not humble is not old.
If fred is humble or kind then susan is either wise or not calm.
If someone is either not generous or not strong then mary is either creative or not calm.
If lucy is patient then paul is old or not patient.
Paul is either not happy or brave.
Lucy is not patient.
Someone is not tall or not calm.
Paul is not generous.
Someone is not wise.
Susan is both humble and not wise. | Fred is patient. | contradiction | (![X]:(funny(X)<=>(rich(X)|calm(X))))&
(((quiet(mary)&~tall(mary)))<=>(?[X]:(kind(X))))&
(![X]:(creative(X)<=>(~tall(X)|~rich(X))))&
(((quiet(mary)|funny(mary)))=>(creative(john)))&
(((curious(fred)|~kind(fred)))=>(?[X]:((~old(X)&kind(X)))))&
((?[X]:((calm(X)|generous(X))))<=>((rich(alice)<~>~brave(alice))))&
(![X]:((quiet(X)&~happy(X))<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)&~calm(X))<=>(~calm(X)|funny(X))))&
(![X]:((calm(X)&~old(X))=>(humble(X)&tall(X))))&
(![X]:((~calm(X)<~>~rich(X))<=>(happy(X)&~tall(X))))&
(![X]:(humble(X)=>(~curious(X)|old(X))))&
((~humble(alice))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)&~humble(X))=>~old(X)))&
(((humble(fred)|kind(fred)))=>((wise(susan)<~>~calm(susan))))&
((?[X]:((~generous(X)<~>~strong(X))))=>((creative(mary)<~>~calm(mary))))&
((patient(lucy))=>((old(paul)|~patient(paul))))&
((~happy(paul)<~>brave(paul)))&
(~patient(lucy))&
(?[X]:((~tall(X)|~calm(X))))&
(~generous(paul))&
(?[X]:(~wise(X)))&
((humble(susan)&~wise(susan))) | patient(fred) | [
"p0",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 801349089210255070794284
% SZS output start Proof for 801349089210255070794284
1. ! [X0] : (funny(X0) <=> (calm(X0) | rich(X0))) [input p0]
8. ! [X0] : ((~calm(X0) & ~patient(X0)) <=> (funny(X0) | ~calm(X0))) [input p7]
23. patient(fred) [input hypothesis]
37. ! [X0] : ((funny(X0) | (~calm(X0) & ~rich(X0))) & ((calm(X0) | rich(X0)) | ~funny(X0))) [nnf transformation 1]
38. ! [X0] : ((funny(X0) | (~calm(X0) & ~rich(X0))) & (calm(X0) | rich(X0) | ~funny(X0))) [flattening 37]
54. ! [X0] : (((~calm(X0) & ~patient(X0)) | (~funny(X0) & calm(X0))) & ((funny(X0) | ~calm(X0)) | (calm(X0) | patient(X0)))) [nnf transformation 8]
55. ! [X0] : (((~calm(X0) & ~patient(X0)) | (~funny(X0) & calm(X0))) & (funny(X0) | ~calm(X0) | calm(X0) | patient(X0))) [flattening 54]
69. ~calm(X0) | funny(X0) [cnf transformation 38]
93. ~patient(X0) | calm(X0) [cnf transformation 55]
96. ~calm(X0) | ~funny(X0) [cnf transformation 55]
125. patient(fred) [cnf transformation 23]
197. 16 <=> ! [X1] : ~calm(X1) [avatar definition]
198. ~calm(X1) <- (16) [avatar component clause 197]
202. ~calm(X0) [subsumption resolution 96,69]
203. 16 [avatar split clause 202,197]
296. calm(fred) [resolution 93,125]
297. $false <- (16) [subsumption resolution 296,198]
298. ~16 [avatar contradiction clause 297]
299. $false [avatar sat refutation 203,298]
% SZS output end Proof for 801349089210255070794284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not brave is either tall or not quiet.
Everyone who is not wise or not funny is generous or not quiet and vice versa.
Everyone who is generous is not wise.
Everyone who is either funny or not tall is kind or curious.
Everyone who is funny or strong is brave.
Everyone who is not patient is calm or not calm.
Everyone who is not strong or not tall is rich or creative and vice versa.
Everyone who is not kind is both wise and generous and vice versa.
If mary is not kind or calm then someone is either not humble or tall.
Everyone who is either old or generous is either not calm or not creative and vice versa.
Everyone who is not patient or patient is both tall and not humble and vice versa.
Everyone who is not tall or kind is not happy and vice versa.
Everyone who is not curious or happy is both strong and not tall.
If someone is brave then someone is both humble and not old.
Everyone who is not rich is not calm.
Everyone who is both not wise and not quiet is either not brave or not kind.
Susan is not brave.
Susan is either not generous or quiet.
John is calm or not wise.
Lucy is not quiet or kind.
Someone is calm.
Someone is both not old and not happy. | Mary is brave. | contradiction | (![X]:((~strong(X)|~brave(X))=>(tall(X)<~>~quiet(X))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)|~quiet(X))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:((funny(X)<~>~tall(X))=>(kind(X)|curious(X))))&
(![X]:((funny(X)|strong(X))=>brave(X)))&
(![X]:(~patient(X)=>(calm(X)|~calm(X))))&
(![X]:((~strong(X)|~tall(X))<=>(rich(X)|creative(X))))&
(![X]:(~kind(X)<=>(wise(X)&generous(X))))&
(((~kind(mary)|calm(mary)))=>(?[X]:((~humble(X)<~>tall(X)))))&
(![X]:((old(X)<~>generous(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~patient(X)|patient(X))<=>(tall(X)&~humble(X))))&
(![X]:((~tall(X)|kind(X))<=>~happy(X)))&
(![X]:((~curious(X)|happy(X))=>(strong(X)&~tall(X))))&
((?[X]:(brave(X)))=>(?[X]:((humble(X)&~old(X)))))&
(![X]:(~rich(X)=>~calm(X)))&
(![X]:((~wise(X)&~quiet(X))=>(~brave(X)<~>~kind(X))))&
(~brave(susan))&
((~generous(susan)<~>quiet(susan)))&
((calm(john)|~wise(john)))&
((~quiet(lucy)|kind(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)&~happy(X)))) | brave(mary) | [
"p10",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 2703334688296717509348792
% SZS output start Proof for 2703334688296717509348792
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~humble(X0) & tall(X0))) [input p10]
14. ? [X0] : brave(X0) => ? [X0] : (~old(X0) & humble(X0)) [input p13]
23. brave(mary) [input hypothesis]
24. ? [X0] : brave(X0) => ? [X1] : (~old(X1) & humble(X1)) [rectify 14]
37. ? [X1] : (~old(X1) & humble(X1)) | ! [X0] : ~brave(X0) [ennf transformation 24]
52. ! [X0] : (((patient(X0) | ~patient(X0)) | (humble(X0) | ~tall(X0))) & ((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
53. ! [X0] : ((patient(X0) | ~patient(X0) | humble(X0) | ~tall(X0)) & ((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0)))) [flattening 52]
54. ? [X0] : (~old(X0) & humble(X0)) | ! [X1] : ~brave(X1) [rectify 37]
55. ? [X0] : (~old(X0) & humble(X0)) => (~old(sK1) & humble(sK1)) [choice axiom]
56. (~old(sK1) & humble(sK1)) | ! [X1] : ~brave(X1) [skolemisation 54,55]
96. ~humble(X0) | patient(X0) [cnf transformation 53]
97. ~humble(X0) | ~patient(X0) [cnf transformation 53]
102. humble(sK1) | ~brave(X1) [cnf transformation 56]
115. brave(mary) [cnf transformation 23]
136. ~humble(X0) [subsumption resolution 96,97]
141. 5 <=> ! [X1] : ~brave(X1) [avatar definition]
142. ~brave(X1) <- (5) [avatar component clause 141]
148. ~brave(X1) [subsumption resolution 102,136]
149. 5 [avatar split clause 148,141]
181. $false <- (5) [resolution 142,115]
182. ~5 [avatar contradiction clause 181]
183. $false [avatar sat refutation 149,182]
% SZS output end Proof for 2703334688296717509348792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not tall or tall then alice is not kind and vice versa. Everyone who is humble is not kind or not humble and vice versa. If someone is either tall or not generous then someone is wise or not calm and vice versa. If susan is not quiet or not kind then john is creative or not wise. Everyone who is rich is both rich and tall. If someone is not patient then john is not quiet or curious. If someone is both not happy and tall then alice is either not creative or generous. Everyone who is both not creative and old is not brave or not creative. Everyone who is not calm or not curious is both generous and not old and vice versa. Everyone who is not curious is either not creative or not brave. If alice is either wise or not calm then someone is creative and vice versa. If someone is both not rich and not kind then someone is not old. Everyone who is not wise or strong is both not kind and not generous and vice versa. Everyone who is either curious or not happy is not happy or calm and vice versa. If mary is either humble or calm then susan is both calm and not patient and vice versa. Everyone who is not curious or brave is kind. Someone is either brave or not kind. Someone is not wise. Fred is either calm or not rich. Lucy is either not tall or old. Someone is both rich and old. Paul is not calm or not old. Someone is not quiet or not humble. Paul is not rich or not patient. | Paul is old. | contradiction | (((~tall(lucy)<~>tall(lucy)))<=>(~kind(alice)))&
(![X]:(humble(X)<=>(~kind(X)|~humble(X))))&
((?[X]:((tall(X)<~>~generous(X))))<=>(?[X]:((wise(X)|~calm(X)))))&
(((~quiet(susan)|~kind(susan)))=>((creative(john)|~wise(john))))&
(![X]:(rich(X)=>(rich(X)&tall(X))))&
((?[X]:(~patient(X)))=>((~quiet(john)|curious(john))))&
((?[X]:((~happy(X)&tall(X))))=>((~creative(alice)<~>generous(alice))))&
(![X]:((~creative(X)&old(X))=>(~brave(X)|~creative(X))))&
(![X]:((~calm(X)|~curious(X))<=>(generous(X)&~old(X))))&
(![X]:(~curious(X)=>(~creative(X)<~>~brave(X))))&
(((wise(alice)<~>~calm(alice)))<=>(?[X]:(creative(X))))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:(~old(X))))&
(![X]:((~wise(X)|strong(X))<=>(~kind(X)&~generous(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(~happy(X)|calm(X))))&
(((humble(mary)<~>calm(mary)))<=>((calm(susan)&~patient(susan))))&
(![X]:((~curious(X)|brave(X))=>kind(X)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:(~wise(X)))&
((calm(fred)<~>~rich(fred)))&
((~tall(lucy)<~>old(lucy)))&
(?[X]:((rich(X)&old(X))))&
((~calm(paul)|~old(paul)))&
(?[X]:((~quiet(X)|~humble(X))))&
((~rich(paul)|~patient(paul))) | old(paul) | [
"p8",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 5693736456872514134493234
% SZS output start Proof for 5693736456872514134493234
9. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (~old(X0) & generous(X0))) [input p8]
22. ~old(paul) | ~calm(paul) [input p21]
25. old(paul) [input hypothesis]
48. ! [X0] : (((~curious(X0) | ~calm(X0)) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | (curious(X0) & calm(X0)))) [nnf transformation 9]
49. ! [X0] : ((~curious(X0) | ~calm(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | (curious(X0) & calm(X0)))) [flattening 48]
98. ~old(X0) | calm(X0) [cnf transformation 49]
136. ~old(paul) | ~calm(paul) [cnf transformation 22]
139. old(paul) [cnf transformation 25]
297. ~old(paul) [subsumption resolution 136,98]
308. $false [subsumption resolution 139,297]
% SZS output end Proof for 5693736456872514134493234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not curious is both not curious and not brave and vice versa.
If fred is either quiet or old then someone is not generous and vice versa.
Everyone who is not strong is both not happy and not rich and vice versa.
If fred is both creative and not happy then someone is either calm or old.
If someone is both not old and old then someone is both humble and not quiet and vice versa.
If susan is not brave or curious then someone is not happy and vice versa.
If lucy is both not kind and not patient then someone is both wise and not wise and vice versa.
If susan is kind or not strong then susan is not wise.
Everyone who is not rich is brave and vice versa.
Everyone who is not wise is either not brave or strong.
Everyone who is both patient and calm is not calm or rich and vice versa.
Everyone who is wise is both not quiet and tall and vice versa.
Everyone who is happy or not tall is either not rich or not strong and vice versa.
If paul is either not strong or curious then someone is not calm or happy.
If paul is both curious and humble then mary is humble or not tall.
Someone is strong or not generous.
Fred is either kind or not creative.
Lucy is generous.
Someone is not old or not wise.
Alice is humble or generous.
Someone is not rich or not brave. | Fred is tall. | entailment | (![X]:((~wise(X)|~curious(X))<=>(~curious(X)&~brave(X))))&
(((quiet(fred)<~>old(fred)))<=>(?[X]:(~generous(X))))&
(![X]:(~strong(X)<=>(~happy(X)&~rich(X))))&
(((creative(fred)&~happy(fred)))=>(?[X]:((calm(X)<~>old(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((humble(X)&~quiet(X)))))&
(((~brave(susan)|curious(susan)))<=>(?[X]:(~happy(X))))&
(((~kind(lucy)&~patient(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(((kind(susan)|~strong(susan)))=>(~wise(susan)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:(~wise(X)=>(~brave(X)<~>strong(X))))&
(![X]:((patient(X)&calm(X))<=>(~calm(X)|rich(X))))&
(![X]:(wise(X)<=>(~quiet(X)&tall(X))))&
(![X]:((happy(X)|~tall(X))<=>(~rich(X)<~>~strong(X))))&
(((~strong(paul)<~>curious(paul)))=>(?[X]:((~calm(X)|happy(X)))))&
(((curious(paul)&humble(paul)))=>((humble(mary)|~tall(mary))))&
(?[X]:((strong(X)|~generous(X))))&
((kind(fred)<~>~creative(fred)))&
(generous(lucy))&
(?[X]:((~old(X)|~wise(X))))&
((humble(alice)|generous(alice)))&
(?[X]:((~rich(X)|~brave(X)))) | tall(fred) | [
"p0",
"p2",
"p9",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 512120795839825867080621
% SZS output start Proof for 512120795839825867080621
1. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> (~brave(X0) & ~curious(X0))) [input p0]
3. ! [X0] : (~strong(X0) <=> (~rich(X0) & ~happy(X0))) [input p2]
10. ! [X0] : (~wise(X0) => (~brave(X0) <~> strong(X0))) [input p9]
12. ! [X0] : (wise(X0) <=> (tall(X0) & ~quiet(X0))) [input p11]
13. ! [X0] : ((~tall(X0) | happy(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p12]
22. ~tall(fred) [input hypothesis]
27. ! [X0] : ((~brave(X0) <~> strong(X0)) | wise(X0)) [ennf transformation 10]
31. ! [X0] : (((~curious(X0) | ~wise(X0)) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | (curious(X0) & wise(X0)))) [nnf transformation 1]
32. ! [X0] : ((~curious(X0) | ~wise(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | (curious(X0) & wise(X0)))) [flattening 31]
37. ! [X0] : ((~strong(X0) | (rich(X0) | happy(X0))) & ((~rich(X0) & ~happy(X0)) | strong(X0))) [nnf transformation 3]
38. ! [X0] : ((~strong(X0) | rich(X0) | happy(X0)) & ((~rich(X0) & ~happy(X0)) | strong(X0))) [flattening 37]
58. ! [X0] : (((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | wise(X0)) [nnf transformation 27]
61. ! [X0] : ((wise(X0) | (~tall(X0) | quiet(X0))) & ((tall(X0) & ~quiet(X0)) | ~wise(X0))) [nnf transformation 12]
62. ! [X0] : ((wise(X0) | ~tall(X0) | quiet(X0)) & ((tall(X0) & ~quiet(X0)) | ~wise(X0))) [flattening 61]
63. ! [X0] : (((~tall(X0) | happy(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (tall(X0) & ~happy(X0)))) [nnf transformation 13]
64. ! [X0] : ((~tall(X0) | happy(X0) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (tall(X0) & ~happy(X0)))) [flattening 63]
77. ~brave(X0) | wise(X0) [cnf transformation 32]
85. ~rich(X0) | strong(X0) [cnf transformation 38]
105. ~strong(X0) | brave(X0) | wise(X0) [cnf transformation 58]
112. ~wise(X0) | tall(X0) [cnf transformation 62]
117. strong(X0) | rich(X0) | tall(X0) [cnf transformation 64]
130. ~tall(fred) [cnf transformation 22]
221. ~strong(X0) | wise(X0) [subsumption resolution 105,77]
223. tall(X0) | strong(X0) [subsumption resolution 117,85]
297. strong(fred) [resolution 223,130]
299. wise(fred) [resolution 297,221]
303. tall(fred) [resolution 299,112]
304. $false [subsumption resolution 303,130]
% SZS output end Proof for 512120795839825867080621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not funny is either not wise or creative.
If someone is either not humble or calm then someone is quiet and vice versa.
Everyone who is not rich or old is both not kind and strong.
If someone is strong then someone is either patient or not quiet and vice versa.
Everyone who is not humble is creative.
If mary is funny then someone is both not curious and patient and vice versa.
If paul is either patient or not kind then someone is both strong and humble.
Everyone who is both funny and not curious is either not tall or tall and vice versa.
Everyone who is not funny is both old and not calm.
If alice is rich then john is both wise and not wise.
If fred is both not old and creative then someone is old and vice versa.
If fred is not patient then john is not kind and vice versa.
Everyone who is either humble or not creative is happy or not brave and vice versa.
If john is both quiet and not brave then paul is not strong and vice versa.
Everyone who is not patient is either creative or not quiet and vice versa.
If fred is either not tall or not patient then someone is both not rich and not funny and vice versa.
Susan is both patient and quiet.
Someone is old.
Lucy is both wise and not generous.
Someone is both not kind and not patient.
Someone is both wise and not creative.
Paul is either happy or not patient.
Someone is either quiet or not wise. | Alice is not strong. | contradiction | (![X]:((happy(X)&~funny(X))=>(~wise(X)<~>creative(X))))&
((?[X]:((~humble(X)<~>calm(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~rich(X)|old(X))=>(~kind(X)&strong(X))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:(~humble(X)=>creative(X)))&
((funny(mary))<=>(?[X]:((~curious(X)&patient(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((funny(X)&~curious(X))<=>(~tall(X)<~>tall(X))))&
(![X]:(~funny(X)=>(old(X)&~calm(X))))&
((rich(alice))=>((wise(john)&~wise(john))))&
(((~old(fred)&creative(fred)))<=>(?[X]:(old(X))))&
((~patient(fred))<=>(~kind(john)))&
(![X]:((humble(X)<~>~creative(X))<=>(happy(X)|~brave(X))))&
(((quiet(john)&~brave(john)))<=>(~strong(paul)))&
(![X]:(~patient(X)<=>(creative(X)<~>~quiet(X))))&
(((~tall(fred)<~>~patient(fred)))<=>(?[X]:((~rich(X)&~funny(X)))))&
((patient(susan)&quiet(susan)))&
(?[X]:(old(X)))&
((wise(lucy)&~generous(lucy)))&
(?[X]:((~kind(X)&~patient(X))))&
(?[X]:((wise(X)&~creative(X))))&
((happy(paul)<~>~patient(paul)))&
(?[X]:((quiet(X)<~>~wise(X)))) | ~strong(alice) | [
"p2",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 8288698342573010058910048
% SZS output start Proof for 8288698342573010058910048
3. ! [X0] : ((old(X0) | ~rich(X0)) => (strong(X0) & ~kind(X0))) [input p2]
10. rich(alice) => (~wise(john) & wise(john)) [input p9]
24. ~strong(alice) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~kind(X0)) | (~old(X0) & rich(X0))) [ennf transformation 3]
34. (~wise(john) & wise(john)) | ~rich(alice) [ennf transformation 10]
88. strong(X0) | rich(X0) [cnf transformation 30]
110. wise(john) | ~rich(alice) [cnf transformation 34]
111. ~wise(john) | ~rich(alice) [cnf transformation 34]
148. ~strong(alice) [cnf transformation 24]
244. 21 <=> rich(alice) [avatar definition]
246. ~rich(alice) <- (~21) [avatar component clause 244]
248. 22 <=> wise(john) [avatar definition]
251. ~21 | ~22 [avatar split clause 111,248,244]
252. ~21 | 22 [avatar split clause 110,248,244]
339. rich(alice) [resolution 88,148]
340. $false <- (~21) [subsumption resolution 339,246]
341. 21 [avatar contradiction clause 340]
342. $false [avatar sat refutation 251,252,341]
% SZS output end Proof for 8288698342573010058910048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or curious then mary is brave.
Everyone who is not rich or patient is strong or wise and vice versa.
Everyone who is not rich or kind is calm or happy.
If lucy is both creative and not strong then lucy is both creative and quiet.
Everyone who is both not happy and happy is not humble or not generous.
Everyone who is either calm or not brave is not creative and vice versa.
If someone is not creative or wise then someone is both brave and funny and vice versa.
If susan is old then alice is not kind.
Everyone who is either not kind or not creative is both not calm and wise and vice versa.
Everyone who is either brave or creative is either brave or old.
If someone is strong then mary is both not calm and quiet and vice versa.
Everyone who is either brave or patient is both creative and quiet.
If paul is both kind and not curious then someone is curious or funny and vice versa.
Everyone who is either not creative or not wise is not kind and vice versa.
Everyone who is not rich or happy is either not funny or not strong and vice versa.
Everyone who is both wise and curious is both not quiet and curious.
John is either not creative or not rich.
Someone is both not happy and funny.
Someone is not rich.
Someone is both tall and funny.
Fred is both not funny and curious.
Someone is either generous or creative.
Someone is not quiet. | Fred is not old. | entailment | ((?[X]:((~humble(X)|curious(X))))=>(brave(mary)))&
(![X]:((~rich(X)|patient(X))<=>(strong(X)|wise(X))))&
(![X]:((~rich(X)|kind(X))=>(calm(X)|happy(X))))&
(((creative(lucy)&~strong(lucy)))=>((creative(lucy)&quiet(lucy))))&
(![X]:((~happy(X)&happy(X))=>(~humble(X)|~generous(X))))&
(![X]:((calm(X)<~>~brave(X))<=>~creative(X)))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((brave(X)&funny(X)))))&
((old(susan))=>(~kind(alice)))&
(![X]:((~kind(X)<~>~creative(X))<=>(~calm(X)&wise(X))))&
(![X]:((brave(X)<~>creative(X))=>(brave(X)<~>old(X))))&
((?[X]:(strong(X)))<=>((~calm(mary)&quiet(mary))))&
(![X]:((brave(X)<~>patient(X))=>(creative(X)&quiet(X))))&
(((kind(paul)&~curious(paul)))<=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~creative(X)<~>~wise(X))<=>~kind(X)))&
(![X]:((~rich(X)|happy(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)&curious(X))=>(~quiet(X)&curious(X))))&
((~creative(john)<~>~rich(john)))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:(~rich(X)))&
(?[X]:((tall(X)&funny(X))))&
((~funny(fred)&curious(fred)))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:(~quiet(X))) | ~old(fred) | [
"p0",
"p1",
"p5",
"p8",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3242630359148457217695071
% SZS output start Proof for 3242630359148457217695071
1. ? [X0] : (curious(X0) | ~humble(X0)) => brave(mary) [input p0]
2. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (wise(X0) | strong(X0))) [input p1]
6. ! [X0] : ((calm(X0) <~> ~brave(X0)) <=> ~creative(X0)) [input p5]
9. ! [X0] : ((~kind(X0) <~> ~creative(X0)) <=> (wise(X0) & ~calm(X0))) [input p8]
10. ! [X0] : ((brave(X0) <~> creative(X0)) => (brave(X0) <~> old(X0))) [input p9]
11. ? [X0] : strong(X0) <=> (quiet(mary) & ~calm(mary)) [input p10]
12. ! [X0] : ((brave(X0) <~> patient(X0)) => (quiet(X0) & creative(X0))) [input p11]
14. ! [X0] : ((~creative(X0) <~> ~wise(X0)) <=> ~kind(X0)) [input p13]
15. ! [X0] : ((happy(X0) | ~rich(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p14]
16. ! [X0] : ((curious(X0) & wise(X0)) => (curious(X0) & ~quiet(X0))) [input p15]
21. curious(fred) & ~funny(fred) [input p20]
24. old(fred) [input hypothesis]
27. brave(mary) | ! [X0] : (~curious(X0) & humble(X0)) [ennf transformation 1]
35. ! [X0] : ((brave(X0) <~> old(X0)) | (brave(X0) <=> creative(X0))) [ennf transformation 10]
36. ! [X0] : ((quiet(X0) & creative(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 12]
37. ! [X0] : ((curious(X0) & ~quiet(X0)) | (~curious(X0) | ~wise(X0))) [ennf transformation 16]
38. ! [X0] : ((curious(X0) & ~quiet(X0)) | ~curious(X0) | ~wise(X0)) [flattening 37]
39. ! [X0] : (((patient(X0) | ~rich(X0)) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 2]
40. ! [X0] : ((patient(X0) | ~rich(X0) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | (~patient(X0) & rich(X0)))) [flattening 39]
41. ! [X0] : ((((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | creative(X0)) & (~creative(X0) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0))))) [nnf transformation 6]
47. ! [X0] : ((((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | (~wise(X0) | calm(X0))) & ((wise(X0) & ~calm(X0)) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))))) [nnf transformation 9]
48. ! [X0] : ((((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | ~wise(X0) | calm(X0)) & ((wise(X0) & ~calm(X0)) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))))) [flattening 47]
49. ! [X0] : (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0)))) [nnf transformation 35]
50. (? [X0] : strong(X0) | (~quiet(mary) | calm(mary))) & ((quiet(mary) & ~calm(mary)) | ! [X0] : ~strong(X0)) [nnf transformation 11]
51. (? [X0] : strong(X0) | ~quiet(mary) | calm(mary)) & ((quiet(mary) & ~calm(mary)) | ! [X0] : ~strong(X0)) [flattening 50]
52. (? [X0] : strong(X0) | ~quiet(mary) | calm(mary)) & ((quiet(mary) & ~calm(mary)) | ! [X1] : ~strong(X1)) [rectify 51]
53. ? [X0] : strong(X0) => strong(sK2) [choice axiom]
54. (strong(sK2) | ~quiet(mary) | calm(mary)) & ((quiet(mary) & ~calm(mary)) | ! [X1] : ~strong(X1)) [skolemisation 52,53]
55. ! [X0] : ((quiet(X0) & creative(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 36]
61. ! [X0] : ((((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | kind(X0)) & (~kind(X0) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0))))) [nnf transformation 14]
62. ! [X0] : (((happy(X0) | ~rich(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (~happy(X0) & rich(X0)))) [nnf transformation 15]
63. ! [X0] : ((happy(X0) | ~rich(X0) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (~happy(X0) & rich(X0)))) [flattening 62]
77. brave(mary) | ~curious(X0) [cnf transformation 27]
81. ~wise(X0) | ~rich(X0) | patient(X0) [cnf transformation 40]
87. ~creative(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 41]
89. ~brave(X0) | calm(X0) | creative(X0) [cnf transformation 41]
99. ~creative(X0) | wise(X0) | kind(X0) [cnf transformation 48]
100. ~kind(X0) | wise(X0) | creative(X0) [cnf transformation 48]
101. ~creative(X0) | ~kind(X0) | ~wise(X0) | calm(X0) [cnf transformation 48]
102. ~wise(X0) | kind(X0) | creative(X0) | calm(X0) [cnf transformation 48]
105. ~old(X0) | ~brave(X0) | creative(X0) | ~brave(X0) [cnf transformation 49]
107. ~calm(mary) | ~strong(X1) [cnf transformation 54]
113. ~patient(X0) | brave(X0) | quiet(X0) [cnf transformation 55]
119. ~kind(X0) | ~wise(X0) | creative(X0) [cnf transformation 61]
120. ~kind(X0) | ~creative(X0) | wise(X0) [cnf transformation 61]
121. ~wise(X0) | ~creative(X0) | kind(X0) [cnf transformation 61]
122. wise(X0) | creative(X0) | kind(X0) [cnf transformation 61]
125. funny(X0) | strong(X0) | rich(X0) [cnf transformation 63]
129. ~quiet(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 38]
137. ~funny(fred) [cnf transformation 21]
138. curious(fred) [cnf transformation 21]
142. old(fred) [cnf transformation 24]
144. ~old(X0) | ~brave(X0) | creative(X0) [duplicate literal removal 105]
146. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
147. ~curious(X0) <- (1) [avatar component clause 146]
149. 2 <=> brave(mary) [avatar definition]
151. brave(mary) <- (2) [avatar component clause 149]
152. 1 | 2 [avatar split clause 77,149,146]
210. 16 <=> calm(mary) [avatar definition]
211. ~calm(mary) <- (~16) [avatar component clause 210]
223. 19 <=> ! [X1] : ~strong(X1) [avatar definition]
224. ~strong(X1) <- (19) [avatar component clause 223]
226. 19 | ~16 [avatar split clause 107,210,223]
251. kind(X0) | wise(X0) [subsumption resolution 122,99]
252. ~creative(X0) | kind(X0) [subsumption resolution 121,251]
253. ~creative(X0) | wise(X0) [subsumption resolution 120,99]
254. ~kind(X0) | creative(X0) [subsumption resolution 119,100]
297. creative(X0) | wise(X0) [resolution 254,251]
298. wise(X0) [subsumption resolution 297,253]
347. ~rich(X0) | patient(X0) [resolution 298,81]
380. $false <- (1) [resolution 147,138]
383. ~1 [avatar contradiction clause 380]
392. calm(mary) | creative(mary) <- (2) [resolution 89,151]
394. creative(mary) <- (2, ~16) [subsumption resolution 392,211]
423. kind(mary) <- (2, ~16) [resolution 394,252]
475. strong(fred) | rich(fred) [resolution 125,137]
480. 51 <=> rich(fred) [avatar definition]
482. rich(fred) <- (51) [avatar component clause 480]
484. 52 <=> strong(fred) [avatar definition]
486. strong(fred) <- (52) [avatar component clause 484]
487. 51 | 52 [avatar split clause 475,484,480]
509. ~brave(fred) | creative(fred) [resolution 144,142]
511. 55 <=> creative(fred) [avatar definition]
513. creative(fred) <- (55) [avatar component clause 511]
515. 56 <=> brave(fred) [avatar definition]
517. ~brave(fred) <- (~56) [avatar component clause 515]
518. 55 | ~56 [avatar split clause 509,515,511]
520. ~kind(mary) | ~wise(mary) | calm(mary) <- (2, ~16) [resolution 101,394]
521. ~wise(mary) | calm(mary) <- (2, ~16) [subsumption resolution 520,423]
522. calm(mary) <- (2, ~16) [subsumption resolution 521,298]
523. $false <- (2, ~16) [subsumption resolution 522,211]
524. ~2 | 16 [avatar contradiction clause 523]
553. kind(X0) | creative(X0) | calm(X0) [resolution 102,298]
555. creative(X0) | calm(X0) [subsumption resolution 553,254]
629. patient(fred) <- (51) [resolution 347,482]
649. calm(X4) | ~kind(X4) | ~wise(X4) | calm(X4) [resolution 555,101]
651. calm(X6) | kind(X6) [resolution 555,252]
660. calm(X4) | ~kind(X4) | ~wise(X4) [duplicate literal removal 649]
662. ~kind(X4) | calm(X4) [subsumption resolution 660,298]
663. calm(X6) [subsumption resolution 651,662]
664. brave(fred) | quiet(fred) <- (51) [resolution 629,113]
667. quiet(fred) <- (51, ~56) [subsumption resolution 664,517]
670. ~brave(fred) | ~calm(fred) <- (55) [resolution 513,87]
707. ~curious(fred) | ~wise(fred) <- (51, ~56) [resolution 667,129]
708. ~wise(fred) <- (51, ~56) [subsumption resolution 707,138]
709. $false <- (51, ~56) [subsumption resolution 708,298]
710. ~51 | 56 [avatar contradiction clause 709]
711. ~brave(fred) <- (55) [subsumption resolution 670,663]
712. ~56 | ~55 [avatar split clause 711,511,515]
718. $false <- (19, 52) [subsumption resolution 486,224]
719. ~19 | ~52 [avatar contradiction clause 718]
720. $false [avatar sat refutation 152,226,383,487,518,524,710,712,719]
% SZS output end Proof for 3242630359148457217695071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is not kind and vice versa.
Everyone who is either not brave or not creative is not tall and vice versa.
Everyone who is either happy or not patient is not generous or not kind and vice versa.
Everyone who is either rich or not curious is not happy and vice versa.
Everyone who is generous is generous or not happy.
Everyone who is either rich or patient is both strong and not curious.
Everyone who is both not patient and not curious is either not funny or not calm and vice versa.
If john is either not rich or generous then fred is both wise and not creative.
If mary is wise or not quiet then someone is not kind.
If john is both not generous and curious then someone is not curious and vice versa.
Everyone who is both quiet and not rich is both wise and quiet.
If lucy is calm then someone is kind or humble.
If susan is both not old and old then fred is brave or old and vice versa.
Everyone who is either not wise or wise is not old or not patient.
If alice is either patient or not happy then someone is humble.
Lucy is either generous or not quiet.
Lucy is wise or generous.
Someone is either not happy or not strong.
Someone is either not funny or not old.
Someone is both not strong and calm. | Alice is patient. | entailment | (![X]:(~rich(X)<=>~kind(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>~tall(X)))&
(![X]:((happy(X)<~>~patient(X))<=>(~generous(X)|~kind(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~happy(X)))&
(![X]:(generous(X)=>(generous(X)|~happy(X))))&
(![X]:((rich(X)<~>patient(X))=>(strong(X)&~curious(X))))&
(![X]:((~patient(X)&~curious(X))<=>(~funny(X)<~>~calm(X))))&
(((~rich(john)<~>generous(john)))=>((wise(fred)&~creative(fred))))&
(((wise(mary)|~quiet(mary)))=>(?[X]:(~kind(X))))&
(((~generous(john)&curious(john)))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)&~rich(X))=>(wise(X)&quiet(X))))&
((calm(lucy))=>(?[X]:((kind(X)|humble(X)))))&
(((~old(susan)&old(susan)))<=>((brave(fred)|old(fred))))&
(![X]:((~wise(X)<~>wise(X))=>(~old(X)|~patient(X))))&
(((patient(alice)<~>~happy(alice)))=>(?[X]:(humble(X))))&
((generous(lucy)<~>~quiet(lucy)))&
((wise(lucy)|generous(lucy)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:((~strong(X)&calm(X)))) | patient(alice) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 1109246720155996272434741
% SZS output start Proof for 1109246720155996272434741
1. ! [X0] : (~rich(X0) <=> ~kind(X0)) [input p0]
3. ! [X0] : ((happy(X0) <~> ~patient(X0)) <=> (~kind(X0) | ~generous(X0))) [input p2]
4. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> ~happy(X0)) [input p3]
6. ! [X0] : ((rich(X0) <~> patient(X0)) => (~curious(X0) & strong(X0))) [input p5]
10. (curious(john) & ~generous(john)) <=> ? [X0] : ~curious(X0) [input p9]
21. ~patient(alice) [input hypothesis]
27. ! [X0] : ((~curious(X0) & strong(X0)) | (rich(X0) <=> patient(X0))) [ennf transformation 6]
34. ! [X0] : ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0))) [nnf transformation 1]
35. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [nnf transformation 3]
36. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [flattening 35]
37. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | happy(X0)) & (~happy(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 4]
38. ! [X0] : ((~curious(X0) & strong(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) [nnf transformation 27]
44. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~curious(john) | generous(john))) [nnf transformation 10]
45. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~curious(john) | generous(john)) [flattening 44]
46. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~curious(john) | generous(john)) [rectify 45]
47. ? [X1] : ~curious(X1) => ~curious(sK1) [choice axiom]
48. ((curious(john) & ~generous(john)) | ! [X0] : curious(X0)) & (~curious(sK1) | ~curious(john) | generous(john)) [skolemisation 46,47]
61. ~kind(X0) | rich(X0) [cnf transformation 34]
62. ~rich(X0) | kind(X0) [cnf transformation 34]
64. ~generous(X0) | ~kind(X0) | happy(X0) | patient(X0) [cnf transformation 36]
65. ~patient(X0) | happy(X0) | generous(X0) [cnf transformation 36]
66. ~patient(X0) | happy(X0) | kind(X0) [cnf transformation 36]
67. ~happy(X0) | patient(X0) | generous(X0) [cnf transformation 36]
68. ~happy(X0) | patient(X0) | kind(X0) [cnf transformation 36]
69. ~curious(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 37]
71. ~curious(X0) | rich(X0) | happy(X0) [cnf transformation 37]
76. ~curious(X0) | patient(X0) | ~rich(X0) [cnf transformation 38]
77. ~curious(X0) | rich(X0) | ~patient(X0) [cnf transformation 38]
89. ~generous(john) | curious(X0) [cnf transformation 48]
90. curious(john) | curious(X0) [cnf transformation 48]
109. ~patient(alice) [cnf transformation 21]
113. 1 <=> generous(john) [avatar definition]
115. ~generous(john) <- (~1) [avatar component clause 113]
117. 2 <=> rich(john) [avatar definition]
141. 7 <=> ! [X0] : curious(X0) [avatar definition]
142. curious(X0) <- (7) [avatar component clause 141]
144. 8 <=> curious(john) [avatar definition]
146. curious(john) <- (8) [avatar component clause 144]
147. 7 | 8 [avatar split clause 90,144,141]
148. 7 | ~1 [avatar split clause 89,113,141]
230. 23 <=> patient(john) [avatar definition]
231. ~patient(john) <- (~23) [avatar component clause 230]
232. patient(john) <- (23) [avatar component clause 230]
235. 24 <=> happy(john) [avatar definition]
237. happy(john) <- (24) [avatar component clause 235]
309. happy(john) | kind(john) <- (23) [resolution 232,66]
310. happy(john) | generous(john) <- (23) [resolution 232,65]
391. 31 <=> kind(john) [avatar definition]
392. ~kind(john) <- (~31) [avatar component clause 391]
393. kind(john) <- (31) [avatar component clause 391]
394. 31 | 24 | ~23 [avatar split clause 309,230,235,391]
395. happy(john) <- (~1, 23) [subsumption resolution 310,115]
396. 24 | 1 | ~23 [avatar split clause 395,230,113,235]
398. rich(john) | ~patient(john) <- (8) [resolution 146,77]
399. patient(john) | ~rich(john) <- (8) [resolution 146,76]
400. rich(john) | happy(john) <- (8) [resolution 146,71]
401. ~happy(john) | ~rich(john) <- (8) [resolution 146,69]
405. ~2 | ~24 | ~8 [avatar split clause 401,144,235,117]
406. ~23 | 2 | ~8 [avatar split clause 398,144,117,230]
407. ~2 | 23 | ~8 [avatar split clause 399,144,230,117]
408. 24 | 2 | ~8 [avatar split clause 400,144,117,235]
414. ~patient(X0) | rich(X0) <- (7) [resolution 142,77]
415. ~rich(X1) | patient(X1) <- (7) [resolution 142,76]
416. happy(X2) | rich(X2) <- (7) [resolution 142,71]
417. ~happy(X3) | ~rich(X3) <- (7) [resolution 142,69]
478. rich(john) <- (31) [resolution 393,61]
485. rich(X1) | patient(X1) | kind(X1) <- (7) [resolution 416,68]
486. rich(X2) | patient(X2) | generous(X2) <- (7) [resolution 416,67]
490. patient(X1) | kind(X1) <- (7) [subsumption resolution 485,62]
491. generous(X2) | patient(X2) <- (7) [subsumption resolution 486,415]
523. kind(X0) | rich(X0) <- (7) [resolution 490,414]
531. kind(X0) <- (7) [subsumption resolution 523,62]
537. patient(X0) | ~kind(X0) | happy(X0) | patient(X0) <- (7) [resolution 491,64]
539. patient(X0) | ~kind(X0) | happy(X0) <- (7) [duplicate literal removal 537]
540. patient(X0) | happy(X0) <- (7) [subsumption resolution 539,531]
548. rich(X0) <- (7) [resolution 531,61]
571. happy(alice) <- (7) [resolution 540,109]
576. ~rich(alice) <- (7) [resolution 571,417]
580. $false <- (7) [subsumption resolution 576,548]
581. ~7 [avatar contradiction clause 580]
582. 2 | ~31 [avatar split clause 478,391,117]
606. patient(john) | kind(john) <- (24) [resolution 237,68]
608. kind(john) <- (~23, 24) [subsumption resolution 606,231]
609. $false <- (~23, 24, ~31) [subsumption resolution 608,392]
610. 23 | ~24 | 31 [avatar contradiction clause 609]
614. $false [avatar sat refutation 147,148,394,396,405,406,407,408,581,582,610]
% SZS output end Proof for 1109246720155996272434741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not creative is happy or not patient and vice versa.
Everyone who is not wise is both patient and not funny and vice versa.
Everyone who is brave is both not creative and not humble and vice versa.
Everyone who is strong or not kind is either not calm or patient.
If someone is wise or not brave then lucy is not calm and vice versa.
Everyone who is both curious and creative is either wise or not wise and vice versa.
If lucy is patient or not curious then lucy is both rich and curious and vice versa.
Everyone who is strong or not rich is both old and tall.
If fred is both patient and strong then john is curious or not kind.
If paul is not tall or not old then someone is either not wise or calm and vice versa.
Everyone who is either not wise or not funny is both not brave and humble.
Everyone who is not brave is either not curious or generous and vice versa.
Everyone who is either strong or not tall is not quiet or not kind and vice versa.
Everyone who is patient is either not funny or not curious and vice versa.
If someone is both not old and funny then someone is either kind or quiet.
Someone is generous.
Alice is either not curious or old.
Paul is either humble or tall.
Paul is either rich or not brave.
Someone is not rich.
Alice is rich or not creative. | Paul is not old. | contradiction | (![X]:((humble(X)<~>~creative(X))<=>(happy(X)|~patient(X))))&
(![X]:(~wise(X)<=>(patient(X)&~funny(X))))&
(![X]:(brave(X)<=>(~creative(X)&~humble(X))))&
(![X]:((strong(X)|~kind(X))=>(~calm(X)<~>patient(X))))&
((?[X]:((wise(X)|~brave(X))))<=>(~calm(lucy)))&
(![X]:((curious(X)&creative(X))<=>(wise(X)<~>~wise(X))))&
(((patient(lucy)|~curious(lucy)))<=>((rich(lucy)&curious(lucy))))&
(![X]:((strong(X)|~rich(X))=>(old(X)&tall(X))))&
(((patient(fred)&strong(fred)))=>((curious(john)|~kind(john))))&
(((~tall(paul)|~old(paul)))<=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((~wise(X)<~>~funny(X))=>(~brave(X)&humble(X))))&
(![X]:(~brave(X)<=>(~curious(X)<~>generous(X))))&
(![X]:((strong(X)<~>~tall(X))<=>(~quiet(X)|~kind(X))))&
(![X]:(patient(X)<=>(~funny(X)<~>~curious(X))))&
((?[X]:((~old(X)&funny(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
(?[X]:(generous(X)))&
((~curious(alice)<~>old(alice)))&
((humble(paul)<~>tall(paul)))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(~rich(X)))&
((rich(alice)|~creative(alice))) | ~old(paul) | [
"p2",
"p5",
"p7",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 645989048765198341901906
% SZS output start Proof for 645989048765198341901906
3. ! [X0] : (brave(X0) <=> (~humble(X0) & ~creative(X0))) [input p2]
6. ! [X0] : ((creative(X0) & curious(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p5]
8. ! [X0] : ((~rich(X0) | strong(X0)) => (tall(X0) & old(X0))) [input p7]
19. rich(paul) <~> ~brave(paul) [input p18]
22. ~old(paul) [input hypothesis]
25. ! [X0] : ((tall(X0) & old(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 8]
34. ! [X0] : ((brave(X0) | (humble(X0) | creative(X0))) & ((~humble(X0) & ~creative(X0)) | ~brave(X0))) [nnf transformation 3]
35. ! [X0] : ((brave(X0) | humble(X0) | creative(X0)) & ((~humble(X0) & ~creative(X0)) | ~brave(X0))) [flattening 34]
41. ! [X0] : (((creative(X0) & curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (~creative(X0) | ~curious(X0)))) [nnf transformation 6]
42. ! [X0] : (((creative(X0) & curious(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~creative(X0) | ~curious(X0))) [flattening 41]
63. (brave(paul) | ~rich(paul)) & (~brave(paul) | rich(paul)) [nnf transformation 19]
75. ~brave(X0) | ~creative(X0) [cnf transformation 35]
89. creative(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 42]
90. creative(X0) | wise(X0) | wise(X0) [cnf transformation 42]
97. old(X0) | rich(X0) [cnf transformation 25]
133. brave(paul) | ~rich(paul) [cnf transformation 63]
136. ~old(paul) [cnf transformation 22]
141. creative(X0) | ~wise(X0) [duplicate literal removal 89]
142. creative(X0) | wise(X0) [duplicate literal removal 90]
164. creative(X0) [subsumption resolution 141,142]
185. 10 <=> old(paul) [avatar definition]
187. ~old(paul) <- (~10) [avatar component clause 185]
232. 18 <=> rich(paul) [avatar definition]
236. 19 <=> brave(paul) [avatar definition]
238. brave(paul) <- (19) [avatar component clause 236]
239. ~18 | 19 [avatar split clause 133,236,232]
242. ~10 [avatar split clause 136,185]
244. rich(paul) <- (~10) [resolution 97,187]
247. 18 | 10 [avatar split clause 244,185,232]
249. ~creative(paul) <- (19) [resolution 238,75]
250. $false <- (19) [subsumption resolution 249,164]
251. ~19 [avatar contradiction clause 250]
252. $false [avatar sat refutation 239,242,247,251]
% SZS output end Proof for 645989048765198341901906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or not brave then someone is not patient and vice versa.
If fred is not strong then alice is not patient and vice versa.
Everyone who is brave is patient or not wise and vice versa.
If susan is not quiet then someone is rich or generous and vice versa.
Everyone who is both not calm and not creative is old.
Everyone who is both not old and not wise is not brave and vice versa.
Everyone who is curious is both creative and not wise.
Everyone who is both not creative and not generous is calm or kind and vice versa.
If john is either not strong or patient then someone is not old.
Everyone who is not happy is either brave or not creative.
If alice is both old and not old then fred is not creative or not strong and vice versa.
Everyone who is quiet or tall is not creative or happy.
Everyone who is brave is generous and vice versa.
Everyone who is not patient is either kind or calm.
If someone is not generous then someone is both humble and not old and vice versa.
If fred is patient or not kind then someone is either not wise or happy and vice versa.
Fred is both patient and not tall.
Susan is not curious or tall.
Someone is not funny.
Paul is quiet. | Susan is humble. | contradiction | ((?[X]:((old(X)|~brave(X))))<=>(?[X]:(~patient(X))))&
((~strong(fred))<=>(~patient(alice)))&
(![X]:(brave(X)<=>(patient(X)|~wise(X))))&
((~quiet(susan))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((~calm(X)&~creative(X))=>old(X)))&
(![X]:((~old(X)&~wise(X))<=>~brave(X)))&
(![X]:(curious(X)=>(creative(X)&~wise(X))))&
(![X]:((~creative(X)&~generous(X))<=>(calm(X)|kind(X))))&
(((~strong(john)<~>patient(john)))=>(?[X]:(~old(X))))&
(![X]:(~happy(X)=>(brave(X)<~>~creative(X))))&
(((old(alice)&~old(alice)))<=>((~creative(fred)|~strong(fred))))&
(![X]:((quiet(X)|tall(X))=>(~creative(X)|happy(X))))&
(![X]:(brave(X)<=>generous(X)))&
(![X]:(~patient(X)=>(kind(X)<~>calm(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((humble(X)&~old(X)))))&
(((patient(fred)|~kind(fred)))<=>(?[X]:((~wise(X)<~>happy(X)))))&
((patient(fred)&~tall(fred)))&
((~curious(susan)|tall(susan)))&
(?[X]:(~funny(X)))&
(quiet(paul)) | humble(susan) | [
"p0",
"p2",
"p5",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 252533139317706669923296
% SZS output start Proof for 252533139317706669923296
1. ? [X0] : (~brave(X0) | old(X0)) <=> ? [X0] : ~patient(X0) [input p0]
3. ! [X0] : (brave(X0) <=> (~wise(X0) | patient(X0))) [input p2]
6. ! [X0] : ((~wise(X0) & ~old(X0)) <=> ~brave(X0)) [input p5]
8. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> (kind(X0) | calm(X0))) [input p7]
13. ! [X0] : (brave(X0) <=> generous(X0)) [input p12]
14. ! [X0] : (~patient(X0) => (kind(X0) <~> calm(X0))) [input p13]
15. ? [X0] : ~generous(X0) <=> ? [X0] : (~old(X0) & humble(X0)) [input p14]
21. humble(susan) [input hypothesis]
22. ? [X0] : (~brave(X0) | old(X0)) <=> ? [X1] : ~patient(X1) [rectify 1]
23. ? [X0] : ~generous(X0) <=> ? [X1] : (~old(X1) & humble(X1)) [rectify 15]
35. ! [X0] : ((kind(X0) <~> calm(X0)) | patient(X0)) [ennf transformation 14]
36. (? [X0] : (~brave(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 22]
37. (? [X0] : (~brave(X0) | old(X0)) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : (brave(X3) & ~old(X3))) [rectify 36]
38. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK0) | old(sK0)) [choice axiom]
39. ? [X2] : ~patient(X2) => ~patient(sK1) [choice axiom]
40. ((~brave(sK0) | old(sK0)) | ! [X1] : patient(X1)) & (~patient(sK1) | ! [X3] : (brave(X3) & ~old(X3))) [skolemisation 37,39,38]
42. ! [X0] : ((brave(X0) | (wise(X0) & ~patient(X0))) & ((~wise(X0) | patient(X0)) | ~brave(X0))) [nnf transformation 3]
43. ! [X0] : ((brave(X0) | (wise(X0) & ~patient(X0))) & (~wise(X0) | patient(X0) | ~brave(X0))) [flattening 42]
48. ! [X0] : (((~wise(X0) & ~old(X0)) | brave(X0)) & (~brave(X0) | (wise(X0) | old(X0)))) [nnf transformation 6]
49. ! [X0] : (((~wise(X0) & ~old(X0)) | brave(X0)) & (~brave(X0) | wise(X0) | old(X0))) [flattening 48]
50. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~kind(X0) & ~calm(X0))) & ((kind(X0) | calm(X0)) | (generous(X0) | creative(X0)))) [nnf transformation 8]
51. ! [X0] : (((~generous(X0) & ~creative(X0)) | (~kind(X0) & ~calm(X0))) & (kind(X0) | calm(X0) | generous(X0) | creative(X0))) [flattening 50]
58. ! [X0] : ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0))) [nnf transformation 13]
59. ! [X0] : (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | patient(X0)) [nnf transformation 35]
60. (? [X0] : ~generous(X0) | ! [X1] : (old(X1) | ~humble(X1))) & (? [X1] : (~old(X1) & humble(X1)) | ! [X0] : generous(X0)) [nnf transformation 23]
61. (? [X0] : ~generous(X0) | ! [X1] : (old(X1) | ~humble(X1))) & (? [X2] : (~old(X2) & humble(X2)) | ! [X3] : generous(X3)) [rectify 60]
62. ? [X0] : ~generous(X0) => ~generous(sK4) [choice axiom]
63. ? [X2] : (~old(X2) & humble(X2)) => (~old(sK5) & humble(sK5)) [choice axiom]
64. (~generous(sK4) | ! [X1] : (old(X1) | ~humble(X1))) & ((~old(sK5) & humble(sK5)) | ! [X3] : generous(X3)) [skolemisation 61,63,62]
70. ~patient(sK1) | ~old(X3) [cnf transformation 40]
77. wise(X0) | brave(X0) [cnf transformation 43]
84. ~wise(X0) | brave(X0) [cnf transformation 49]
88. ~calm(X0) | ~generous(X0) [cnf transformation 51]
89. ~kind(X0) | ~generous(X0) [cnf transformation 51]
100. ~brave(X0) | generous(X0) [cnf transformation 58]
102. kind(X0) | calm(X0) | patient(X0) [cnf transformation 59]
106. ~generous(sK4) | old(X1) | ~humble(X1) [cnf transformation 64]
115. humble(susan) [cnf transformation 21]
117. 1 <=> ! [X1] : patient(X1) [avatar definition]
118. patient(X1) <- (1) [avatar component clause 117]
129. 4 <=> ! [X3] : brave(X3) [avatar definition]
130. brave(X3) <- (4) [avatar component clause 129]
132. 5 <=> patient(sK1) [avatar definition]
134. ~patient(sK1) <- (~5) [avatar component clause 132]
137. 6 <=> ! [X3] : ~old(X3) [avatar definition]
138. ~old(X3) <- (6) [avatar component clause 137]
139. 6 | ~5 [avatar split clause 70,132,137]
171. brave(X0) [subsumption resolution 84,77]
172. 4 [avatar split clause 171,129]
201. 19 <=> ! [X1] : (old(X1) | ~humble(X1)) [avatar definition]
202. ~humble(X1) | old(X1) <- (19) [avatar component clause 201]
204. 20 <=> generous(sK4) [avatar definition]
206. ~generous(sK4) <- (~20) [avatar component clause 204]
207. 19 | ~20 [avatar split clause 106,204,201]
209. 21 <=> ! [X3] : generous(X3) [avatar definition]
210. generous(X3) <- (21) [avatar component clause 209]
250. $false <- (~20, 21) [subsumption resolution 206,210]
251. 20 | ~21 [avatar contradiction clause 250]
254. $false <- (1, ~5) [resolution 134,118]
255. ~1 | 5 [avatar contradiction clause 254]
261. generous(X0) <- (4) [resolution 100,130]
264. old(susan) <- (19) [resolution 202,115]
289. calm(X0) | patient(X0) | ~generous(X0) [resolution 102,89]
291. calm(X0) | patient(X0) <- (21) [subsumption resolution 289,210]
302. patient(X0) | ~generous(X0) <- (21) [resolution 291,88]
304. patient(X0) <- (21) [subsumption resolution 302,210]
305. 1 | ~21 [avatar split clause 304,209,117]
308. $false <- (6, 19) [resolution 138,264]
313. ~6 | ~19 [avatar contradiction clause 308]
314. 21 | ~4 [avatar split clause 261,129,209]
315. $false [avatar sat refutation 139,172,207,251,255,305,313,314]
% SZS output end Proof for 252533139317706669923296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is brave and vice versa.
If someone is not kind then someone is happy.
If someone is both strong and creative then mary is not generous or not funny and vice versa.
Everyone who is not patient is not wise and vice versa.
If someone is both not kind and not humble then paul is not strong and vice versa.
Everyone who is not old is either tall or not tall.
If john is either not rich or rich then lucy is not brave and vice versa.
If paul is not funny or not patient then john is either strong or not happy.
If someone is not quiet or not rich then fred is either not brave or not curious and vice versa.
Everyone who is patient is rich or funny and vice versa.
Everyone who is not kind or not curious is either not old or not brave and vice versa.
If someone is creative or not funny then someone is not old or curious and vice versa.
Everyone who is either old or curious is patient.
If paul is not creative or old then susan is both not humble and wise and vice versa.
Everyone who is strong or not curious is either calm or curious and vice versa.
If someone is strong or rich then john is either not wise or not funny and vice versa.
Susan is both not humble and not brave.
Paul is either funny or brave.
Someone is either not calm or quiet.
Someone is wise.
Fred is both not calm and not tall.
Someone is both humble and strong.
Fred is either strong or not strong.
Someone is both not calm and not creative. | Susan is not patient. | contradiction | (![X]:(~kind(X)<=>brave(X)))&
((?[X]:(~kind(X)))=>(?[X]:(happy(X))))&
((?[X]:((strong(X)&creative(X))))<=>((~generous(mary)|~funny(mary))))&
(![X]:(~patient(X)<=>~wise(X)))&
((?[X]:((~kind(X)&~humble(X))))<=>(~strong(paul)))&
(![X]:(~old(X)=>(tall(X)<~>~tall(X))))&
(((~rich(john)<~>rich(john)))<=>(~brave(lucy)))&
(((~funny(paul)|~patient(paul)))=>((strong(john)<~>~happy(john))))&
((?[X]:((~quiet(X)|~rich(X))))<=>((~brave(fred)<~>~curious(fred))))&
(![X]:(patient(X)<=>(rich(X)|funny(X))))&
(![X]:((~kind(X)|~curious(X))<=>(~old(X)<~>~brave(X))))&
((?[X]:((creative(X)|~funny(X))))<=>(?[X]:((~old(X)|curious(X)))))&
(![X]:((old(X)<~>curious(X))=>patient(X)))&
(((~creative(paul)|old(paul)))<=>((~humble(susan)&wise(susan))))&
(![X]:((strong(X)|~curious(X))<=>(calm(X)<~>curious(X))))&
((?[X]:((strong(X)|rich(X))))<=>((~wise(john)<~>~funny(john))))&
((~humble(susan)&~brave(susan)))&
((funny(paul)<~>brave(paul)))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:(wise(X)))&
((~calm(fred)&~tall(fred)))&
(?[X]:((humble(X)&strong(X))))&
((strong(fred)<~>~strong(fred)))&
(?[X]:((~calm(X)&~creative(X)))) | ~patient(susan) | [
"p0",
"p10",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 5427924510173737796829706
% SZS output start Proof for 5427924510173737796829706
1. ! [X0] : (~kind(X0) <=> brave(X0)) [input p0]
11. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (~old(X0) <~> ~brave(X0))) [input p10]
13. ! [X0] : ((old(X0) <~> curious(X0)) => patient(X0)) [input p12]
17. ~brave(susan) & ~humble(susan) [input p16]
25. ~patient(susan) [input hypothesis]
31. ! [X0] : (patient(X0) | (old(X0) <=> curious(X0))) [ennf transformation 13]
32. ! [X0] : ((~kind(X0) | ~brave(X0)) & (brave(X0) | kind(X0))) [nnf transformation 1]
55. ! [X0] : (((~curious(X0) | ~kind(X0)) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (curious(X0) & kind(X0)))) [nnf transformation 11]
56. ! [X0] : ((~curious(X0) | ~kind(X0) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (curious(X0) & kind(X0)))) [flattening 55]
62. ! [X0] : (patient(X0) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) [nnf transformation 31]
82. brave(X0) | kind(X0) [cnf transformation 32]
83. ~brave(X0) | ~kind(X0) [cnf transformation 32]
114. ~brave(X0) | ~old(X0) | kind(X0) [cnf transformation 56]
117. curious(X0) | old(X0) | brave(X0) [cnf transformation 56]
119. ~curious(X0) | ~kind(X0) | ~old(X0) | brave(X0) [cnf transformation 56]
124. ~old(X0) | curious(X0) | patient(X0) [cnf transformation 62]
125. ~curious(X0) | old(X0) | patient(X0) [cnf transformation 62]
144. ~brave(susan) [cnf transformation 17]
158. ~patient(susan) [cnf transformation 25]
271. ~curious(X0) | ~old(X0) | brave(X0) [subsumption resolution 119,82]
272. ~old(X0) | ~brave(X0) [subsumption resolution 114,83]
423. old(X0) | patient(X0) | old(X0) | brave(X0) [resolution 125,117]
427. old(X0) | patient(X0) | brave(X0) [duplicate literal removal 423]
493. patient(X0) | brave(X0) | curious(X0) | patient(X0) [resolution 427,124]
499. curious(X0) | brave(X0) | patient(X0) [duplicate literal removal 493]
545. brave(X0) | patient(X0) | ~old(X0) | brave(X0) [resolution 499,271]
549. brave(X0) | patient(X0) | ~old(X0) [duplicate literal removal 545]
550. ~old(X0) | patient(X0) [subsumption resolution 549,272]
554. patient(X0) | patient(X0) | brave(X0) [resolution 550,427]
555. patient(X0) | brave(X0) [duplicate literal removal 554]
556. brave(susan) [resolution 555,158]
559. $false [subsumption resolution 556,144]
% SZS output end Proof for 5427924510173737796829706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not rich is either not kind or kind. If fred is both creative and not humble then someone is curious or patient and vice versa. Everyone who is both not funny and not strong is patient or curious and vice versa. If someone is both wise and calm then fred is both patient and not brave. If john is not humble or not quiet then someone is either not kind or old. Everyone who is both not humble and creative is either not funny or not patient and vice versa. If someone is both not happy and not calm then mary is quiet or patient and vice versa. If someone is not humble then fred is not kind or generous and vice versa. Everyone who is both not creative and not rich is curious or rich. Everyone who is not calm or not brave is either not rich or rich and vice versa. Everyone who is not humble is either brave or calm and vice versa. If fred is both not tall and calm then someone is both patient and not creative. Everyone who is either funny or not humble is strong or not patient and vice versa. Everyone who is either humble or not strong is humble and vice versa. Everyone who is both curious and not generous is either not quiet or rich and vice versa. If lucy is either not quiet or curious then mary is both not creative and not calm. Fred is quiet or not tall. Lucy is either not creative or not generous. Someone is not quiet. Someone is rich or not brave. Alice is not patient. | Lucy is not patient. | entailment | (![X]:((old(X)|~rich(X))=>(~kind(X)<~>kind(X))))&
(((creative(fred)&~humble(fred)))<=>(?[X]:((curious(X)|patient(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(patient(X)|curious(X))))&
((?[X]:((wise(X)&calm(X))))=>((patient(fred)&~brave(fred))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~humble(X)&creative(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>((quiet(mary)|patient(mary))))&
((?[X]:(~humble(X)))<=>((~kind(fred)|generous(fred))))&
(![X]:((~creative(X)&~rich(X))=>(curious(X)|rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~rich(X)<~>rich(X))))&
(![X]:(~humble(X)<=>(brave(X)<~>calm(X))))&
(((~tall(fred)&calm(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(strong(X)|~patient(X))))&
(![X]:((humble(X)<~>~strong(X))<=>humble(X)))&
(![X]:((curious(X)&~generous(X))<=>(~quiet(X)<~>rich(X))))&
(((~quiet(lucy)<~>curious(lucy)))=>((~creative(mary)&~calm(mary))))&
((quiet(fred)|~tall(fred)))&
((~creative(lucy)<~>~generous(lucy)))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|~brave(X))))&
(~patient(alice)) | ~patient(lucy) | [
"p2",
"p5",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 496924812331211056521467
% SZS output start Proof for 496924812331211056521467
3. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (curious(X0) | patient(X0))) [input p2]
6. ! [X0] : ((creative(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p5]
13. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~patient(X0) | strong(X0))) [input p12]
22. patient(lucy) [input hypothesis]
37. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 3]
38. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | strong(X0) | funny(X0))) [flattening 37]
42. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | (~creative(X0) | humble(X0)))) [nnf transformation 6]
43. ! [X0] : (((creative(X0) & ~humble(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | ~creative(X0) | humble(X0))) [flattening 42]
59. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 13]
60. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 59]
80. ~funny(X0) | ~patient(X0) [cnf transformation 38]
82. ~strong(X0) | ~patient(X0) [cnf transformation 38]
90. ~humble(X0) | ~patient(X0) | funny(X0) [cnf transformation 43]
91. ~humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 43]
116. ~patient(X0) | strong(X0) | funny(X0) | humble(X0) [cnf transformation 60]
118. ~humble(X0) | funny(X0) | patient(X0) [cnf transformation 60]
120. humble(X0) | ~funny(X0) | patient(X0) [cnf transformation 60]
141. patient(lucy) [cnf transformation 22]
148. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
149. ~patient(X0) <- (1) [avatar component clause 148]
196. ~humble(X0) | ~funny(X0) [subsumption resolution 91,80]
197. ~humble(X0) | ~patient(X0) [subsumption resolution 90,80]
261. ~funny(X0) | patient(X0) [subsumption resolution 120,196]
262. ~funny(X0) [subsumption resolution 261,80]
263. ~humble(X0) | patient(X0) [subsumption resolution 118,262]
264. ~humble(X0) [subsumption resolution 263,197]
265. ~patient(X0) | strong(X0) | humble(X0) [subsumption resolution 116,262]
266. ~patient(X0) | strong(X0) [subsumption resolution 265,264]
267. ~patient(X0) [subsumption resolution 266,82]
268. 1 [avatar split clause 267,148]
314. $false <- (1) [resolution 149,141]
315. ~1 [avatar contradiction clause 314]
316. $false [avatar sat refutation 268,315]
% SZS output end Proof for 496924812331211056521467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not happy then someone is either curious or not generous and vice versa.
If someone is either old or not funny then paul is either not humble or not rich and vice versa.
If someone is both not patient and calm then someone is not brave or kind and vice versa.
Everyone who is not quiet is not funny or not brave and vice versa.
Everyone who is both quiet and humble is either old or not calm and vice versa.
If someone is both not wise and not strong then someone is creative and vice versa.
Everyone who is not kind or not calm is both not happy and not humble.
If paul is both not patient and not funny then john is old.
If someone is not curious then paul is not strong or not tall.
Everyone who is both not kind and not calm is either kind or not strong and vice versa.
Everyone who is tall is not happy.
If someone is funny or strong then fred is either not kind or happy.
Everyone who is wise or tall is both generous and not generous.
If fred is humble or not creative then fred is calm or not generous.
If alice is either not rich or funny then someone is both funny and humble and vice versa.
Everyone who is humble is old or quiet and vice versa.
Someone is both not brave and funny.
Susan is both quiet and creative.
Someone is kind.
Someone is quiet or calm.
Someone is not quiet or humble.
Susan is both generous and brave.
Someone is not creative. | Paul is not calm. | contradiction | ((?[X]:((~kind(X)|~happy(X))))<=>(?[X]:((curious(X)<~>~generous(X)))))&
((?[X]:((old(X)<~>~funny(X))))<=>((~humble(paul)<~>~rich(paul))))&
((?[X]:((~patient(X)&calm(X))))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:(~quiet(X)<=>(~funny(X)|~brave(X))))&
(![X]:((quiet(X)&humble(X))<=>(old(X)<~>~calm(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>(?[X]:(creative(X))))&
(![X]:((~kind(X)|~calm(X))=>(~happy(X)&~humble(X))))&
(((~patient(paul)&~funny(paul)))=>(old(john)))&
((?[X]:(~curious(X)))=>((~strong(paul)|~tall(paul))))&
(![X]:((~kind(X)&~calm(X))<=>(kind(X)<~>~strong(X))))&
(![X]:(tall(X)=>~happy(X)))&
((?[X]:((funny(X)|strong(X))))=>((~kind(fred)<~>happy(fred))))&
(![X]:((wise(X)|tall(X))=>(generous(X)&~generous(X))))&
(((humble(fred)|~creative(fred)))=>((calm(fred)|~generous(fred))))&
(((~rich(alice)<~>funny(alice)))<=>(?[X]:((funny(X)&humble(X)))))&
(![X]:(humble(X)<=>(old(X)|quiet(X))))&
(?[X]:((~brave(X)&funny(X))))&
((quiet(susan)&creative(susan)))&
(?[X]:(kind(X)))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:((~quiet(X)|humble(X))))&
((generous(susan)&brave(susan)))&
(?[X]:(~creative(X))) | ~calm(paul) | [
"p4",
"p6",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3913978018536249264324493
% SZS output start Proof for 3913978018536249264324493
5. ! [X0] : ((humble(X0) & quiet(X0)) <=> (old(X0) <~> ~calm(X0))) [input p4]
7. ! [X0] : ((~calm(X0) | ~kind(X0)) => (~humble(X0) & ~happy(X0))) [input p6]
16. ! [X0] : (humble(X0) <=> (quiet(X0) | old(X0))) [input p15]
24. ~calm(paul) [input hypothesis]
31. ! [X0] : ((~humble(X0) & ~happy(X0)) | (calm(X0) & kind(X0))) [ennf transformation 7]
54. ! [X0] : (((humble(X0) & quiet(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | (~humble(X0) | ~quiet(X0)))) [nnf transformation 5]
55. ! [X0] : (((humble(X0) & quiet(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0)))) & (((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | ~humble(X0) | ~quiet(X0))) [flattening 54]
68. ! [X0] : ((humble(X0) | (~quiet(X0) & ~old(X0))) & ((quiet(X0) | old(X0)) | ~humble(X0))) [nnf transformation 16]
69. ! [X0] : ((humble(X0) | (~quiet(X0) & ~old(X0))) & (quiet(X0) | old(X0) | ~humble(X0))) [flattening 68]
107. calm(X0) | old(X0) | humble(X0) [cnf transformation 55]
114. ~humble(X0) | calm(X0) [cnf transformation 31]
137. ~old(X0) | humble(X0) [cnf transformation 69]
149. ~calm(paul) [cnf transformation 24]
191. 10 <=> humble(paul) [avatar definition]
192. humble(paul) <- (10) [avatar component clause 191]
400. old(paul) | humble(paul) [resolution 107,149]
408. humble(paul) [subsumption resolution 400,137]
409. 10 [avatar split clause 408,191]
410. calm(paul) <- (10) [resolution 192,114]
412. $false <- (10) [subsumption resolution 410,149]
413. ~10 [avatar contradiction clause 412]
414. $false [avatar sat refutation 409,413]
% SZS output end Proof for 3913978018536249264324493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is not patient or not happy and vice versa.
If mary is not quiet then alice is both kind and not quiet and vice versa.
If someone is not kind then lucy is generous or not patient and vice versa.
If someone is either calm or creative then susan is quiet and vice versa.
Everyone who is either rich or not humble is quiet or creative.
Everyone who is not brave is either not calm or patient and vice versa.
Everyone who is both not happy and brave is patient or humble.
If someone is both not humble and tall then mary is not creative or creative and vice versa.
Everyone who is both brave and not kind is either not patient or creative and vice versa.
If someone is generous or not wise then susan is both not brave and tall and vice versa.
If someone is not rich or tall then fred is both generous and not tall and vice versa.
If mary is generous or creative then someone is patient.
If susan is brave or patient then paul is either strong or not happy.
If mary is not brave or not generous then lucy is curious or generous and vice versa.
If someone is both not generous and not happy then someone is either not strong or happy.
If someone is not calm or not funny then someone is both brave and not patient.
Lucy is kind or not generous.
Someone is either not strong or calm.
Someone is not happy or not quiet.
Someone is either not curious or not creative.
Alice is wise.
Lucy is not rich or quiet.
Someone is tall.
Someone is either not generous or not funny. | Susan is quiet. | entailment | (![X]:(creative(X)<=>(~patient(X)|~happy(X))))&
((~quiet(mary))<=>((kind(alice)&~quiet(alice))))&
((?[X]:(~kind(X)))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((calm(X)<~>creative(X))))<=>(quiet(susan)))&
(![X]:((rich(X)<~>~humble(X))=>(quiet(X)|creative(X))))&
(![X]:(~brave(X)<=>(~calm(X)<~>patient(X))))&
(![X]:((~happy(X)&brave(X))=>(patient(X)|humble(X))))&
((?[X]:((~humble(X)&tall(X))))<=>((~creative(mary)|creative(mary))))&
(![X]:((brave(X)&~kind(X))<=>(~patient(X)<~>creative(X))))&
((?[X]:((generous(X)|~wise(X))))<=>((~brave(susan)&tall(susan))))&
((?[X]:((~rich(X)|tall(X))))<=>((generous(fred)&~tall(fred))))&
(((generous(mary)|creative(mary)))=>(?[X]:(patient(X))))&
(((brave(susan)|patient(susan)))=>((strong(paul)<~>~happy(paul))))&
(((~brave(mary)|~generous(mary)))<=>((curious(lucy)|generous(lucy))))&
((?[X]:((~generous(X)&~happy(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((~calm(X)|~funny(X))))=>(?[X]:((brave(X)&~patient(X)))))&
((kind(lucy)|~generous(lucy)))&
(?[X]:((~strong(X)<~>calm(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
(wise(alice))&
((~rich(lucy)|quiet(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((~generous(X)<~>~funny(X)))) | quiet(susan) | [
"p0",
"p3",
"p5",
"p8",
"p9",
"p10",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 8264424264325150287595741
% SZS output start Proof for 8264424264325150287595741
1. ! [X0] : (creative(X0) <=> (~happy(X0) | ~patient(X0))) [input p0]
4. ? [X0] : (calm(X0) <~> creative(X0)) <=> quiet(susan) [input p3]
6. ! [X0] : (~brave(X0) <=> (~calm(X0) <~> patient(X0))) [input p5]
9. ! [X0] : ((~kind(X0) & brave(X0)) <=> (~patient(X0) <~> creative(X0))) [input p8]
10. ? [X0] : (~wise(X0) | generous(X0)) <=> (tall(susan) & ~brave(susan)) [input p9]
11. ? [X0] : (tall(X0) | ~rich(X0)) <=> (~tall(fred) & generous(fred)) [input p10]
23. ? [X0] : tall(X0) [input p22]
25. ~quiet(susan) [input hypothesis]
36. ! [X0] : ((creative(X0) | (happy(X0) & patient(X0))) & ((~happy(X0) | ~patient(X0)) | ~creative(X0))) [nnf transformation 1]
37. ! [X0] : ((creative(X0) | (happy(X0) & patient(X0))) & (~happy(X0) | ~patient(X0) | ~creative(X0))) [flattening 36]
45. (? [X0] : ((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ~quiet(susan)) & (quiet(susan) | ! [X0] : ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) [nnf transformation 4]
46. (? [X0] : ((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ~quiet(susan)) & (quiet(susan) | ! [X1] : ((calm(X1) | ~creative(X1)) & (creative(X1) | ~calm(X1)))) [rectify 45]
47. ? [X0] : ((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) => ((~creative(sK1) | ~calm(sK1)) & (creative(sK1) | calm(sK1))) [choice axiom]
48. (((~creative(sK1) | ~calm(sK1)) & (creative(sK1) | calm(sK1))) | ~quiet(susan)) & (quiet(susan) | ! [X1] : ((calm(X1) | ~creative(X1)) & (creative(X1) | ~calm(X1)))) [skolemisation 46,47]
50. ! [X0] : ((~brave(X0) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | brave(X0))) [nnf transformation 6]
56. ! [X0] : (((~kind(X0) & brave(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (kind(X0) | ~brave(X0)))) [nnf transformation 9]
57. ! [X0] : (((~kind(X0) & brave(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | kind(X0) | ~brave(X0))) [flattening 56]
58. (? [X0] : (~wise(X0) | generous(X0)) | (~tall(susan) | brave(susan))) & ((tall(susan) & ~brave(susan)) | ! [X0] : (wise(X0) & ~generous(X0))) [nnf transformation 10]
59. (? [X0] : (~wise(X0) | generous(X0)) | ~tall(susan) | brave(susan)) & ((tall(susan) & ~brave(susan)) | ! [X0] : (wise(X0) & ~generous(X0))) [flattening 58]
60. (? [X0] : (~wise(X0) | generous(X0)) | ~tall(susan) | brave(susan)) & ((tall(susan) & ~brave(susan)) | ! [X1] : (wise(X1) & ~generous(X1))) [rectify 59]
61. ? [X0] : (~wise(X0) | generous(X0)) => (~wise(sK3) | generous(sK3)) [choice axiom]
62. ((~wise(sK3) | generous(sK3)) | ~tall(susan) | brave(susan)) & ((tall(susan) & ~brave(susan)) | ! [X1] : (wise(X1) & ~generous(X1))) [skolemisation 60,61]
63. (? [X0] : (tall(X0) | ~rich(X0)) | (tall(fred) | ~generous(fred))) & ((~tall(fred) & generous(fred)) | ! [X0] : (~tall(X0) & rich(X0))) [nnf transformation 11]
64. (? [X0] : (tall(X0) | ~rich(X0)) | tall(fred) | ~generous(fred)) & ((~tall(fred) & generous(fred)) | ! [X0] : (~tall(X0) & rich(X0))) [flattening 63]
65. (? [X0] : (tall(X0) | ~rich(X0)) | tall(fred) | ~generous(fred)) & ((~tall(fred) & generous(fred)) | ! [X1] : (~tall(X1) & rich(X1))) [rectify 64]
66. ? [X0] : (tall(X0) | ~rich(X0)) => (tall(sK4) | ~rich(sK4)) [choice axiom]
67. ((tall(sK4) | ~rich(sK4)) | tall(fred) | ~generous(fred)) & ((~tall(fred) & generous(fred)) | ! [X1] : (~tall(X1) & rich(X1))) [skolemisation 65,66]
88. ? [X0] : tall(X0) => tall(sK11) [choice axiom]
89. tall(sK11) [skolemisation 23,88]
94. patient(X0) | creative(X0) [cnf transformation 37]
102. quiet(susan) | creative(X1) | ~calm(X1) [cnf transformation 48]
103. quiet(susan) | calm(X1) | ~creative(X1) [cnf transformation 48]
108. ~calm(X0) | patient(X0) | brave(X0) [cnf transformation 50]
109. ~patient(X0) | calm(X0) | brave(X0) [cnf transformation 50]
121. ~patient(X0) | brave(X0) | ~creative(X0) [cnf transformation 57]
124. ~brave(susan) | ~generous(X1) [cnf transformation 62]
130. generous(fred) | ~tall(X1) [cnf transformation 67]
158. tall(sK11) [cnf transformation 89]
161. ~quiet(susan) [cnf transformation 25]
196. 8 <=> quiet(susan) [avatar definition]
210. 11 <=> ! [X1] : (calm(X1) | ~creative(X1)) [avatar definition]
211. ~creative(X1) | calm(X1) <- (11) [avatar component clause 210]
212. 11 | 8 [avatar split clause 103,196,210]
214. 12 <=> ! [X1] : (creative(X1) | ~calm(X1)) [avatar definition]
215. ~calm(X1) | creative(X1) <- (12) [avatar component clause 214]
216. 12 | 8 [avatar split clause 102,196,214]
236. 16 <=> brave(susan) [avatar definition]
237. ~brave(susan) <- (~16) [avatar component clause 236]
257. 21 <=> ! [X1] : ~generous(X1) [avatar definition]
258. ~generous(X1) <- (21) [avatar component clause 257]
261. 21 | ~16 [avatar split clause 124,236,257]
263. 22 <=> generous(fred) [avatar definition]
264. generous(fred) <- (22) [avatar component clause 263]
280. 26 <=> ! [X1] : ~tall(X1) [avatar definition]
281. ~tall(X1) <- (26) [avatar component clause 280]
287. 26 | 22 [avatar split clause 130,263,280]
300. 30 <=> patient(susan) [avatar definition]
301. patient(susan) <- (30) [avatar component clause 300]
302. ~patient(susan) <- (~30) [avatar component clause 300]
411. ~8 [avatar split clause 161,196]
418. creative(susan) <- (~30) [resolution 94,302]
423. calm(susan) <- (11, ~30) [resolution 211,418]
432. calm(X0) | brave(X0) | creative(X0) [resolution 109,94]
442. brave(X0) | creative(X0) <- (12) [subsumption resolution 432,215]
465. patient(susan) | brave(susan) <- (11, ~30) [resolution 423,108]
467. brave(susan) <- (11, ~30) [subsumption resolution 465,302]
468. $false <- (11, ~16, ~30) [subsumption resolution 467,237]
469. ~11 | 16 | 30 [avatar contradiction clause 468]
470. brave(susan) | ~creative(susan) <- (30) [resolution 301,121]
484. brave(susan) <- (12, 30) [subsumption resolution 470,442]
485. 16 | ~12 | ~30 [avatar split clause 484,300,214,236]
492. $false <- (21, 22) [resolution 258,264]
495. ~21 | ~22 [avatar contradiction clause 492]
496. $false <- (26) [resolution 281,158]
501. ~26 [avatar contradiction clause 496]
502. $false [avatar sat refutation 212,216,261,287,411,469,485,495,501]
% SZS output end Proof for 8264424264325150287595741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and happy is either funny or generous and vice versa.
If john is not quiet or not tall then susan is either kind or not kind.
Everyone who is not funny is not brave or funny and vice versa.
If lucy is both kind and not funny then someone is both generous and kind and vice versa.
Everyone who is not tall is not patient or funny and vice versa.
Everyone who is quiet or not strong is old.
If someone is either not curious or not calm then fred is creative.
Everyone who is both not calm and calm is tall and vice versa.
If fred is both not brave and funny then someone is old or patient and vice versa.
If paul is not curious then someone is both tall and not patient.
If someone is both kind and quiet then someone is not old or quiet.
If lucy is either generous or not happy then someone is both not calm and not creative and vice versa.
If mary is not rich then susan is quiet or not patient.
Everyone who is not curious or not creative is either not kind or tall and vice versa.
If lucy is wise then mary is kind.
Lucy is either funny or not quiet.
Someone is humble or not old.
Paul is either humble or not tall.
Someone is not kind or not humble.
Paul is not strong or kind.
John is curious.
Someone is not happy or not rich. | Lucy is not tall. | entailment | (![X]:((brave(X)&happy(X))<=>(funny(X)<~>generous(X))))&
(((~quiet(john)|~tall(john)))=>((kind(susan)<~>~kind(susan))))&
(![X]:(~funny(X)<=>(~brave(X)|funny(X))))&
(((kind(lucy)&~funny(lucy)))<=>(?[X]:((generous(X)&kind(X)))))&
(![X]:(~tall(X)<=>(~patient(X)|funny(X))))&
(![X]:((quiet(X)|~strong(X))=>old(X)))&
((?[X]:((~curious(X)<~>~calm(X))))=>(creative(fred)))&
(![X]:((~calm(X)&calm(X))<=>tall(X)))&
(((~brave(fred)&funny(fred)))<=>(?[X]:((old(X)|patient(X)))))&
((~curious(paul))=>(?[X]:((tall(X)&~patient(X)))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((~old(X)|quiet(X)))))&
(((generous(lucy)<~>~happy(lucy)))<=>(?[X]:((~calm(X)&~creative(X)))))&
((~rich(mary))=>((quiet(susan)|~patient(susan))))&
(![X]:((~curious(X)|~creative(X))<=>(~kind(X)<~>tall(X))))&
((wise(lucy))=>(kind(mary)))&
((funny(lucy)<~>~quiet(lucy)))&
(?[X]:((humble(X)|~old(X))))&
((humble(paul)<~>~tall(paul)))&
(?[X]:((~kind(X)|~humble(X))))&
((~strong(paul)|kind(paul)))&
(curious(john))&
(?[X]:((~happy(X)|~rich(X)))) | ~tall(lucy) | [
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 485904584514925569396996
% SZS output start Proof for 485904584514925569396996
8. ! [X0] : ((calm(X0) & ~calm(X0)) <=> tall(X0)) [input p7]
23. tall(lucy) [input hypothesis]
46. ! [X0] : (((calm(X0) & ~calm(X0)) | ~tall(X0)) & (tall(X0) | (~calm(X0) | calm(X0)))) [nnf transformation 8]
47. ! [X0] : (((calm(X0) & ~calm(X0)) | ~tall(X0)) & (tall(X0) | ~calm(X0) | calm(X0))) [flattening 46]
97. ~calm(X0) | ~tall(X0) [cnf transformation 47]
98. calm(X0) | ~tall(X0) [cnf transformation 47]
129. tall(lucy) [cnf transformation 23]
166. ~tall(X0) [subsumption resolution 97,98]
227. $false [subsumption resolution 129,166]
% SZS output end Proof for 485904584514925569396996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not generous is patient or curious.
Everyone who is both not brave and generous is not rich and vice versa.
Everyone who is wise is both old and tall.
Everyone who is both quiet and not happy is either not creative or rich.
Everyone who is both generous and humble is either not wise or wise and vice versa.
If someone is both not brave and generous then fred is either not wise or not quiet and vice versa.
Everyone who is not curious or strong is both patient and not curious and vice versa.
Everyone who is not curious or not calm is both not quiet and not brave and vice versa.
If alice is not tall then lucy is not rich or not tall.
If someone is brave or not humble then john is patient.
Everyone who is not kind is not tall or happy.
If someone is either brave or calm then mary is both tall and not happy.
Everyone who is both not quiet and humble is tall or not humble and vice versa.
If mary is either not patient or not funny then someone is rich and vice versa.
If susan is generous then mary is either happy or kind and vice versa.
If someone is both not funny and not creative then paul is both brave and creative.
Someone is either tall or kind.
Alice is either quiet or not quiet.
Susan is not tall.
Someone is not wise or quiet.
Susan is either curious or patient.
Someone is either not old or not calm.
John is both not wise and not funny.
Someone is funny. | Susan is not humble. | contradiction | (![X]:((quiet(X)<~>~generous(X))=>(patient(X)|curious(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
(![X]:(wise(X)=>(old(X)&tall(X))))&
(![X]:((quiet(X)&~happy(X))=>(~creative(X)<~>rich(X))))&
(![X]:((generous(X)&humble(X))<=>(~wise(X)<~>wise(X))))&
((?[X]:((~brave(X)&generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((~curious(X)|strong(X))<=>(patient(X)&~curious(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&~brave(X))))&
((~tall(alice))=>((~rich(lucy)|~tall(lucy))))&
((?[X]:((brave(X)|~humble(X))))=>(patient(john)))&
(![X]:(~kind(X)=>(~tall(X)|happy(X))))&
((?[X]:((brave(X)<~>calm(X))))=>((tall(mary)&~happy(mary))))&
(![X]:((~quiet(X)&humble(X))<=>(tall(X)|~humble(X))))&
(((~patient(mary)<~>~funny(mary)))<=>(?[X]:(rich(X))))&
((generous(susan))<=>((happy(mary)<~>kind(mary))))&
((?[X]:((~funny(X)&~creative(X))))=>((brave(paul)&creative(paul))))&
(?[X]:((tall(X)<~>kind(X))))&
((quiet(alice)<~>~quiet(alice)))&
(~tall(susan))&
(?[X]:((~wise(X)|quiet(X))))&
((curious(susan)<~>patient(susan)))&
(?[X]:((~old(X)<~>~calm(X))))&
((~wise(john)&~funny(john)))&
(?[X]:(funny(X))) | ~humble(susan) | [
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 8138483470341352983709447
% SZS output start Proof for 8138483470341352983709447
5. ! [X0] : ((humble(X0) & generous(X0)) <=> (~wise(X0) <~> wise(X0))) [input p4]
25. ~humble(susan) [input hypothesis]
42. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~humble(X0) | ~generous(X0)))) [nnf transformation 5]
43. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~humble(X0) | ~generous(X0))) [flattening 42]
85. humble(X0) | wise(X0) | wise(X0) [cnf transformation 43]
86. humble(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 43]
139. ~humble(susan) [cnf transformation 25]
144. humble(X0) | wise(X0) [duplicate literal removal 85]
145. humble(X0) | ~wise(X0) [duplicate literal removal 86]
146. humble(X0) [subsumption resolution 144,145]
282. $false [subsumption resolution 139,146]
% SZS output end Proof for 8138483470341352983709447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either quiet or generous then john is not strong.
Everyone who is both not creative and old is not strong or old.
If someone is either calm or quiet then alice is not strong or not calm and vice versa.
If someone is both not old and patient then paul is both not quiet and not patient and vice versa.
Everyone who is not calm is either brave or not happy and vice versa.
Everyone who is either creative or not rich is humble and vice versa.
Everyone who is both creative and not creative is not happy or not quiet.
If fred is both tall and not tall then paul is both curious and happy and vice versa.
Everyone who is kind is not humble or not old and vice versa.
If alice is not strong or calm then someone is both not funny and not old and vice versa.
If john is either calm or funny then susan is both not wise and strong and vice versa.
Everyone who is rich is curious.
If susan is both happy and not happy then someone is tall or rich.
If someone is either humble or happy then alice is not calm or wise and vice versa.
Everyone who is both not rich and not funny is either wise or not calm.
Everyone who is both calm and not kind is not funny or old and vice versa.
Susan is both kind and not quiet.
Someone is not old or not funny.
Someone is both rich and not happy.
Someone is not tall.
Someone is quiet or funny.
Lucy is either quiet or old.
Mary is not humble.
Someone is both calm and not creative. | Lucy is not funny. | neutral | (((quiet(paul)<~>generous(paul)))=>(~strong(john)))&
(![X]:((~creative(X)&old(X))=>(~strong(X)|old(X))))&
((?[X]:((calm(X)<~>quiet(X))))<=>((~strong(alice)|~calm(alice))))&
((?[X]:((~old(X)&patient(X))))<=>((~quiet(paul)&~patient(paul))))&
(![X]:(~calm(X)<=>(brave(X)<~>~happy(X))))&
(![X]:((creative(X)<~>~rich(X))<=>humble(X)))&
(![X]:((creative(X)&~creative(X))=>(~happy(X)|~quiet(X))))&
(((tall(fred)&~tall(fred)))<=>((curious(paul)&happy(paul))))&
(![X]:(kind(X)<=>(~humble(X)|~old(X))))&
(((~strong(alice)|calm(alice)))<=>(?[X]:((~funny(X)&~old(X)))))&
(((calm(john)<~>funny(john)))<=>((~wise(susan)&strong(susan))))&
(![X]:(rich(X)=>curious(X)))&
(((happy(susan)&~happy(susan)))=>(?[X]:((tall(X)|rich(X)))))&
((?[X]:((humble(X)<~>happy(X))))<=>((~calm(alice)|wise(alice))))&
(![X]:((~rich(X)&~funny(X))=>(wise(X)<~>~calm(X))))&
(![X]:((calm(X)&~kind(X))<=>(~funny(X)|old(X))))&
((kind(susan)&~quiet(susan)))&
(?[X]:((~old(X)|~funny(X))))&
(?[X]:((rich(X)&~happy(X))))&
(?[X]:(~tall(X)))&
(?[X]:((quiet(X)|funny(X))))&
((quiet(lucy)<~>old(lucy)))&
(~humble(mary))&
(?[X]:((calm(X)&~creative(X)))) | ~funny(lucy) | []
| null | 0 |
Everyone who is both old and strong is not creative or creative.
If someone is both not brave and curious then someone is either not happy or creative and vice versa.
Everyone who is both funny and kind is not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Everyone who is happy or not funny is both not strong and not happy and vice versa.
Everyone who is both brave and not generous is both curious and quiet and vice versa.
If someone is both not curious and not wise then paul is wise or patient.
If alice is rich then someone is either funny or brave and vice versa.
If someone is patient or not funny then someone is not humble or not happy.
If mary is brave or generous then mary is not humble.
Everyone who is either kind or quiet is strong and vice versa.
Everyone who is tall or wise is not quiet or happy and vice versa.
Everyone who is not strong or not creative is either curious or not funny and vice versa.
Everyone who is both not happy and not brave is not tall.
If mary is strong then mary is not creative or not brave and vice versa.
Mary is either not happy or wise.
Someone is either humble or tall.
Someone is both old and not funny.
Lucy is either patient or not happy.
Paul is either not happy or old. | Alice is not rich. | contradiction | (![X]:((old(X)&strong(X))=>(~creative(X)|creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((funny(X)&kind(X))=>~strong(X)))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(![X]:((happy(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~generous(X))<=>(curious(X)&quiet(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(paul)|patient(paul))))&
((rich(alice))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
(((brave(mary)|generous(mary)))=>(~humble(mary)))&
(![X]:((kind(X)<~>quiet(X))<=>strong(X)))&
(![X]:((tall(X)|wise(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~strong(X)|~creative(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&~brave(X))=>~tall(X)))&
((strong(mary))<=>((~creative(mary)|~brave(mary))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((old(X)&~funny(X))))&
((patient(lucy)<~>~happy(lucy)))&
((~happy(paul)<~>old(paul))) | ~rich(alice) | [
"p1",
"p5",
"p8",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 614407297134559039731327
% SZS output start Proof for 614407297134559039731327
2. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X0] : (~happy(X0) <~> creative(X0)) [input p1]
6. ! [X0] : ((~funny(X0) | happy(X0)) <=> (~happy(X0) & ~strong(X0))) [input p5]
9. rich(alice) <=> ? [X0] : (funny(X0) <~> brave(X0)) [input p8]
14. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p13]
16. strong(mary) <=> (~brave(mary) | ~creative(mary)) [input p15]
22. ~rich(alice) [input hypothesis]
23. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X1] : (~happy(X1) <~> creative(X1)) [rectify 2]
35. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X1] : ((~creative(X1) | happy(X1)) & (creative(X1) | ~happy(X1))) | ! [X0] : (~curious(X0) | brave(X0))) [nnf transformation 23]
36. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) | ! [X3] : (~curious(X3) | brave(X3))) [rectify 35]
37. ? [X0] : (curious(X0) & ~brave(X0)) => (curious(sK0) & ~brave(sK0)) [choice axiom]
38. ? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) => ((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) [choice axiom]
39. ((curious(sK0) & ~brave(sK0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) | ! [X3] : (~curious(X3) | brave(X3))) [skolemisation 36,38,37]
44. ! [X0] : (((~funny(X0) | happy(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~funny(X0) | happy(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [flattening 44]
48. (rich(alice) | ! [X0] : ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (? [X0] : ((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | ~rich(alice)) [nnf transformation 9]
49. (rich(alice) | ! [X0] : ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (? [X1] : ((~brave(X1) | ~funny(X1)) & (brave(X1) | funny(X1))) | ~rich(alice)) [rectify 48]
50. ? [X1] : ((~brave(X1) | ~funny(X1)) & (brave(X1) | funny(X1))) => ((~brave(sK2) | ~funny(sK2)) & (brave(sK2) | funny(sK2))) [choice axiom]
51. (rich(alice) | ! [X0] : ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) & (((~brave(sK2) | ~funny(sK2)) & (brave(sK2) | funny(sK2))) | ~rich(alice)) [skolemisation 49,50]
58. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 14]
59. ! [X0] : ((~creative(X0) | ~strong(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [flattening 58]
60. (strong(mary) | (brave(mary) & creative(mary))) & ((~brave(mary) | ~creative(mary)) | ~strong(mary)) [nnf transformation 16]
61. (strong(mary) | (brave(mary) & creative(mary))) & (~brave(mary) | ~creative(mary) | ~strong(mary)) [flattening 60]
73. ~brave(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
75. curious(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
89. ~strong(X0) | funny(X0) [cnf transformation 45]
90. ~happy(X0) | ~happy(X0) [cnf transformation 45]
92. ~funny(X0) | happy(X0) | happy(X0) | strong(X0) [cnf transformation 45]
100. rich(alice) | brave(X0) | ~funny(X0) [cnf transformation 51]
101. rich(alice) | funny(X0) | ~brave(X0) [cnf transformation 51]
116. funny(X0) | ~curious(X0) | strong(X0) [cnf transformation 59]
121. ~brave(mary) | ~creative(mary) | ~strong(mary) [cnf transformation 61]
123. strong(mary) | brave(mary) [cnf transformation 61]
134. ~rich(alice) [cnf transformation 22]
135. ~happy(X0) [duplicate literal removal 90]
136. ~funny(X0) | happy(X0) | strong(X0) [duplicate literal removal 92]
143. 2 <=> curious(sK0) [avatar definition]
145. curious(sK0) <- (2) [avatar component clause 143]
148. 3 <=> ! [X1] : (creative(X1) | happy(X1)) [avatar definition]
149. creative(X1) | happy(X1) <- (3) [avatar component clause 148]
150. 3 | 2 [avatar split clause 75,143,148]
152. 4 <=> brave(sK0) [avatar definition]
156. 3 | ~4 [avatar split clause 73,152,148]
204. 15 <=> ! [X0] : (funny(X0) | ~brave(X0)) [avatar definition]
205. ~brave(X0) | funny(X0) <- (15) [avatar component clause 204]
207. 16 <=> rich(alice) [avatar definition]
210. 15 | 16 [avatar split clause 101,207,204]
212. 17 <=> ! [X0] : (brave(X0) | ~funny(X0)) [avatar definition]
213. ~funny(X0) | brave(X0) <- (17) [avatar component clause 212]
214. 17 | 16 [avatar split clause 100,207,212]
235. 22 <=> brave(mary) [avatar definition]
236. brave(mary) <- (22) [avatar component clause 235]
242. ~curious(X0) | funny(X0) [subsumption resolution 116,89]
245. 23 <=> strong(mary) [avatar definition]
246. ~strong(mary) <- (~23) [avatar component clause 245]
247. strong(mary) <- (23) [avatar component clause 245]
248. 22 | 23 [avatar split clause 123,245,235]
250. 24 <=> creative(mary) [avatar definition]
251. ~creative(mary) <- (~24) [avatar component clause 250]
254. ~23 | ~24 | ~22 [avatar split clause 121,235,250,245]
268. ~16 [avatar split clause 134,207]
269. funny(mary) <- (23) [resolution 89,247]
271. brave(mary) <- (17, 23) [resolution 213,269]
272. 22 | ~17 | ~23 [avatar split clause 271,245,212,235]
273. funny(mary) <- (15, 22) [resolution 236,205]
275. funny(sK0) <- (2) [resolution 242,145]
277. brave(sK0) <- (2, 17) [resolution 275,213]
280. 4 | ~2 | ~17 [avatar split clause 277,212,143,152]
281. creative(X1) <- (3) [subsumption resolution 149,135]
284. $false <- (3, ~24) [resolution 281,251]
285. ~3 | 24 [avatar contradiction clause 284]
330. happy(mary) | strong(mary) <- (15, 22) [resolution 273,136]
334. strong(mary) <- (15, 22) [subsumption resolution 330,135]
335. $false <- (15, 22, ~23) [subsumption resolution 334,246]
336. ~15 | ~22 | 23 [avatar contradiction clause 335]
338. $false [avatar sat refutation 150,156,210,214,248,254,268,272,280,285,336]
% SZS output end Proof for 614407297134559039731327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is wise then someone is not generous or not humble.
Everyone who is both not wise and happy is either not kind or not curious and vice versa.
If lucy is both patient and not old then someone is either kind or not quiet and vice versa.
If someone is both strong and not generous then someone is not rich and vice versa.
Everyone who is calm or creative is both not curious and not happy and vice versa.
If someone is brave or creative then someone is kind and vice versa.
Everyone who is not happy or not funny is both not kind and creative and vice versa.
If john is not wise then someone is happy.
If mary is both not kind and wise then paul is both not creative and calm and vice versa.
If lucy is kind then susan is patient and vice versa.
Everyone who is not patient is not curious.
Everyone who is either curious or wise is kind or not rich and vice versa.
If susan is both not old and rich then paul is both not curious and not happy.
If someone is quiet or not strong then someone is generous.
Everyone who is either not patient or not kind is not brave.
If lucy is either not generous or funny then paul is patient.
Susan is either not creative or quiet.
Someone is both not creative and not humble.
Mary is both not rich and happy.
Susan is both not curious and strong.
Someone is either kind or not curious.
Someone is not rich or strong.
Someone is either happy or not generous.
Paul is both strong and old. | Lucy is creative. | contradiction | ((wise(paul))=>(?[X]:((~generous(X)|~humble(X)))))&
(![X]:((~wise(X)&happy(X))<=>(~kind(X)<~>~curious(X))))&
(((patient(lucy)&~old(lucy)))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
((?[X]:((strong(X)&~generous(X))))<=>(?[X]:(~rich(X))))&
(![X]:((calm(X)|creative(X))<=>(~curious(X)&~happy(X))))&
((?[X]:((brave(X)|creative(X))))<=>(?[X]:(kind(X))))&
(![X]:((~happy(X)|~funny(X))<=>(~kind(X)&creative(X))))&
((~wise(john))=>(?[X]:(happy(X))))&
(((~kind(mary)&wise(mary)))<=>((~creative(paul)&calm(paul))))&
((kind(lucy))<=>(patient(susan)))&
(![X]:(~patient(X)=>~curious(X)))&
(![X]:((curious(X)<~>wise(X))<=>(kind(X)|~rich(X))))&
(((~old(susan)&rich(susan)))=>((~curious(paul)&~happy(paul))))&
((?[X]:((quiet(X)|~strong(X))))=>(?[X]:(generous(X))))&
(![X]:((~patient(X)<~>~kind(X))=>~brave(X)))&
(((~generous(lucy)<~>funny(lucy)))=>(patient(paul)))&
((~creative(susan)<~>quiet(susan)))&
(?[X]:((~creative(X)&~humble(X))))&
((~rich(mary)&happy(mary)))&
((~curious(susan)&strong(susan)))&
(?[X]:((kind(X)<~>~curious(X))))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
((strong(paul)&old(paul))) | creative(lucy) | [
"p1",
"p5",
"p6",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 2318597834433897474194583
% SZS output start Proof for 2318597834433897474194583
2. ! [X0] : ((happy(X0) & ~wise(X0)) <=> (~kind(X0) <~> ~curious(X0))) [input p1]
6. ? [X0] : (creative(X0) | brave(X0)) <=> ? [X0] : kind(X0) [input p5]
7. ! [X0] : ((~funny(X0) | ~happy(X0)) <=> (creative(X0) & ~kind(X0))) [input p6]
12. ! [X0] : ((curious(X0) <~> wise(X0)) <=> (~rich(X0) | kind(X0))) [input p11]
25. creative(lucy) [input hypothesis]
27. ? [X0] : (creative(X0) | brave(X0)) <=> ? [X1] : kind(X1) [rectify 6]
38. ! [X0] : (((happy(X0) & ~wise(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (~happy(X0) | wise(X0)))) [nnf transformation 2]
39. ! [X0] : (((happy(X0) & ~wise(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ~happy(X0) | wise(X0))) [flattening 38]
52. (? [X0] : (creative(X0) | brave(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (~creative(X0) & ~brave(X0))) [nnf transformation 27]
53. (? [X0] : (creative(X0) | brave(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (~creative(X3) & ~brave(X3))) [rectify 52]
54. ? [X0] : (creative(X0) | brave(X0)) => (creative(sK3) | brave(sK3)) [choice axiom]
55. ? [X2] : kind(X2) => kind(sK4) [choice axiom]
56. ((creative(sK3) | brave(sK3)) | ! [X1] : ~kind(X1)) & (kind(sK4) | ! [X3] : (~creative(X3) & ~brave(X3))) [skolemisation 53,55,54]
57. ! [X0] : (((~funny(X0) | ~happy(X0)) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | (funny(X0) & happy(X0)))) [nnf transformation 7]
58. ! [X0] : ((~funny(X0) | ~happy(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | (funny(X0) & happy(X0)))) [flattening 57]
64. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 12]
65. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [flattening 64]
82. ~curious(X0) | ~kind(X0) | ~happy(X0) | wise(X0) [cnf transformation 39]
84. ~curious(X0) | ~wise(X0) | kind(X0) [cnf transformation 39]
85. ~kind(X0) | ~wise(X0) | curious(X0) [cnf transformation 39]
103. kind(sK4) | ~creative(X3) [cnf transformation 56]
105. ~kind(X0) | happy(X0) [cnf transformation 58]
120. wise(X0) | curious(X0) | ~kind(X0) [cnf transformation 65]
122. ~wise(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 65]
146. creative(lucy) [cnf transformation 25]
209. 15 <=> ! [X3] : ~creative(X3) [avatar definition]
210. ~creative(X3) <- (15) [avatar component clause 209]
212. 16 <=> kind(sK4) [avatar definition]
214. kind(sK4) <- (16) [avatar component clause 212]
215. 15 | 16 [avatar split clause 103,212,209]
259. ~curious(X0) | ~wise(X0) [subsumption resolution 122,84]
260. ~kind(X0) | curious(X0) [subsumption resolution 120,85]
352. happy(sK4) <- (16) [resolution 105,214]
358. curious(sK4) <- (16) [resolution 260,214]
359. ~wise(sK4) <- (16) [resolution 358,259]
429. ~kind(sK4) | ~happy(sK4) | wise(sK4) <- (16) [resolution 82,358]
431. ~happy(sK4) | wise(sK4) <- (16) [subsumption resolution 429,214]
432. wise(sK4) <- (16) [subsumption resolution 431,352]
433. $false <- (16) [subsumption resolution 432,359]
434. ~16 [avatar contradiction clause 433]
438. $false <- (15) [resolution 210,146]
440. ~15 [avatar contradiction clause 438]
441. $false [avatar sat refutation 215,434,440]
% SZS output end Proof for 2318597834433897474194583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old or creative then someone is both not creative and quiet and vice versa.
If alice is both old and brave then john is either tall or humble.
If fred is not patient or not strong then lucy is not patient and vice versa.
Everyone who is both not rich and not calm is both creative and patient and vice versa.
If someone is kind or old then someone is quiet or strong.
If lucy is not tall then someone is both quiet and old and vice versa.
Everyone who is both wise and humble is generous and vice versa.
Everyone who is either quiet or tall is both rich and kind and vice versa.
If someone is both not kind and rich then john is both tall and strong and vice versa.
Everyone who is not curious is either not curious or not generous and vice versa.
Everyone who is tall or not quiet is brave.
If someone is not calm or not patient then susan is generous or not old and vice versa.
Everyone who is quiet is patient or not kind and vice versa.
If someone is either calm or humble then someone is either happy or quiet and vice versa.
If mary is both not generous and quiet then someone is either not creative or kind.
Everyone who is both tall and not humble is kind or not rich and vice versa.
Mary is generous.
Mary is both generous and not creative.
John is not creative.
Someone is not creative.
Susan is strong or funny.
Someone is either old or happy.
Someone is either not kind or not calm. | Lucy is old. | contradiction | (((old(lucy)|creative(lucy)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(((old(alice)&brave(alice)))=>((tall(john)<~>humble(john))))&
(((~patient(fred)|~strong(fred)))<=>(~patient(lucy)))&
(![X]:((~rich(X)&~calm(X))<=>(creative(X)&patient(X))))&
((?[X]:((kind(X)|old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((~tall(lucy))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((wise(X)&humble(X))<=>generous(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(rich(X)&kind(X))))&
((?[X]:((~kind(X)&rich(X))))<=>((tall(john)&strong(john))))&
(![X]:(~curious(X)<=>(~curious(X)<~>~generous(X))))&
(![X]:((tall(X)|~quiet(X))=>brave(X)))&
((?[X]:((~calm(X)|~patient(X))))<=>((generous(susan)|~old(susan))))&
(![X]:(quiet(X)<=>(patient(X)|~kind(X))))&
((?[X]:((calm(X)<~>humble(X))))<=>(?[X]:((happy(X)<~>quiet(X)))))&
(((~generous(mary)&quiet(mary)))=>(?[X]:((~creative(X)<~>kind(X)))))&
(![X]:((tall(X)&~humble(X))<=>(kind(X)|~rich(X))))&
(generous(mary))&
((generous(mary)&~creative(mary)))&
(~creative(john))&
(?[X]:(~creative(X)))&
((strong(susan)|funny(susan)))&
(?[X]:((old(X)<~>happy(X))))&
(?[X]:((~kind(X)<~>~calm(X)))) | old(lucy) | [
"p5",
"p6",
"p7",
"p9",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 3510580873848551271815701
% SZS output start Proof for 3510580873848551271815701
6. ~tall(lucy) <=> ? [X0] : (old(X0) & quiet(X0)) [input p5]
7. ! [X0] : ((humble(X0) & wise(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (kind(X0) & rich(X0))) [input p7]
10. ! [X0] : (~curious(X0) <=> (~curious(X0) <~> ~generous(X0))) [input p9]
13. ! [X0] : (quiet(X0) <=> (~kind(X0) | patient(X0))) [input p12]
16. ! [X0] : ((~humble(X0) & tall(X0)) <=> (~rich(X0) | kind(X0))) [input p15]
24. old(lucy) [input hypothesis]
47. (~tall(lucy) | ! [X0] : (~old(X0) | ~quiet(X0))) & (? [X0] : (old(X0) & quiet(X0)) | tall(lucy)) [nnf transformation 6]
48. (~tall(lucy) | ! [X0] : (~old(X0) | ~quiet(X0))) & (? [X1] : (old(X1) & quiet(X1)) | tall(lucy)) [rectify 47]
49. ? [X1] : (old(X1) & quiet(X1)) => (old(sK2) & quiet(sK2)) [choice axiom]
50. (~tall(lucy) | ! [X0] : (~old(X0) | ~quiet(X0))) & ((old(sK2) & quiet(sK2)) | tall(lucy)) [skolemisation 48,49]
51. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) | ~wise(X0)))) [nnf transformation 7]
52. ! [X0] : (((humble(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | ~humble(X0) | ~wise(X0))) [flattening 51]
53. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (~kind(X0) | ~rich(X0))) & ((kind(X0) & rich(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 8]
54. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | ~kind(X0) | ~rich(X0)) & ((kind(X0) & rich(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [flattening 53]
60. ! [X0] : ((~curious(X0) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) & (((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | curious(X0))) [nnf transformation 10]
66. ! [X0] : ((quiet(X0) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | ~quiet(X0))) [nnf transformation 13]
67. ! [X0] : ((quiet(X0) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | ~quiet(X0))) [flattening 66]
76. ! [X0] : (((~humble(X0) & tall(X0)) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 16]
77. ! [X0] : (((~humble(X0) & tall(X0)) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | humble(X0) | ~tall(X0))) [flattening 76]
104. ~tall(lucy) | ~old(X0) | ~quiet(X0) [cnf transformation 50]
107. ~generous(X0) | humble(X0) [cnf transformation 52]
110. ~quiet(X0) | tall(X0) | kind(X0) [cnf transformation 54]
119. generous(X0) | curious(X0) | curious(X0) [cnf transformation 60]
121. ~curious(X0) | ~curious(X0) | generous(X0) [cnf transformation 60]
130. kind(X0) | quiet(X0) [cnf transformation 67]
142. ~kind(X0) | tall(X0) [cnf transformation 77]
144. ~kind(X0) | ~humble(X0) [cnf transformation 77]
155. old(lucy) [cnf transformation 24]
156. generous(X0) | curious(X0) [duplicate literal removal 119]
157. ~curious(X0) | generous(X0) [duplicate literal removal 121]
162. 2 <=> old(lucy) [avatar definition]
164. old(lucy) <- (2) [avatar component clause 162]
216. 13 <=> ! [X1] : ~old(X1) [avatar definition]
217. ~old(X1) <- (13) [avatar component clause 216]
232. 17 <=> ! [X0] : (~old(X0) | ~quiet(X0)) [avatar definition]
233. ~quiet(X0) | ~old(X0) <- (17) [avatar component clause 232]
235. 18 <=> tall(lucy) [avatar definition]
237. ~tall(lucy) <- (~18) [avatar component clause 235]
238. 17 | ~18 [avatar split clause 104,235,232]
268. generous(X0) [subsumption resolution 156,157]
340. 2 [avatar split clause 155,162]
342. humble(X0) [resolution 107,268]
352. ~humble(X0) | quiet(X0) [resolution 144,130]
355. quiet(X0) [subsumption resolution 352,342]
360. ~old(X0) <- (17) [resolution 233,355]
364. 13 | ~17 [avatar split clause 360,232,216]
365. $false <- (2, 13) [resolution 217,164]
368. ~2 | ~13 [avatar contradiction clause 365]
398. tall(X0) | kind(X0) [resolution 110,355]
402. tall(X0) [subsumption resolution 398,142]
405. $false <- (~18) [resolution 402,237]
406. 18 [avatar contradiction clause 405]
407. $false [avatar sat refutation 238,340,364,368,406]
% SZS output end Proof for 3510580873848551271815701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and strong is calm or old and vice versa.
If alice is strong then paul is curious or not brave.
If someone is strong or not calm then paul is not kind.
Everyone who is creative or not happy is old.
Everyone who is strong is wise or quiet and vice versa.
Everyone who is both strong and not calm is funny and vice versa.
Everyone who is both tall and not creative is happy and vice versa.
Everyone who is strong or not happy is either funny or not tall.
Everyone who is either not patient or not strong is calm or strong and vice versa.
Everyone who is either tall or kind is both not wise and not humble and vice versa.
If someone is both curious and not humble then john is either humble or not strong and vice versa.
Everyone who is creative or not calm is either humble or not humble.
If paul is not creative or not tall then someone is rich or patient.
Everyone who is either strong or quiet is either quiet or old and vice versa.
If someone is either wise or creative then someone is either generous or not wise.
Lucy is strong.
Alice is either not rich or kind.
Mary is curious or strong.
Fred is brave or not happy.
John is either curious or not rich.
Fred is quiet or not humble.
Someone is either curious or not funny.
Alice is not funny or brave. | Mary is not happy. | neutral | (![X]:((~rich(X)&strong(X))<=>(calm(X)|old(X))))&
((strong(alice))=>((curious(paul)|~brave(paul))))&
((?[X]:((strong(X)|~calm(X))))=>(~kind(paul)))&
(![X]:((creative(X)|~happy(X))=>old(X)))&
(![X]:(strong(X)<=>(wise(X)|quiet(X))))&
(![X]:((strong(X)&~calm(X))<=>funny(X)))&
(![X]:((tall(X)&~creative(X))<=>happy(X)))&
(![X]:((strong(X)|~happy(X))=>(funny(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>~strong(X))<=>(calm(X)|strong(X))))&
(![X]:((tall(X)<~>kind(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((curious(X)&~humble(X))))<=>((humble(john)<~>~strong(john))))&
(![X]:((creative(X)|~calm(X))=>(humble(X)<~>~humble(X))))&
(((~creative(paul)|~tall(paul)))=>(?[X]:((rich(X)|patient(X)))))&
(![X]:((strong(X)<~>quiet(X))<=>(quiet(X)<~>old(X))))&
((?[X]:((wise(X)<~>creative(X))))=>(?[X]:((generous(X)<~>~wise(X)))))&
(strong(lucy))&
((~rich(alice)<~>kind(alice)))&
((curious(mary)|strong(mary)))&
((brave(fred)|~happy(fred)))&
((curious(john)<~>~rich(john)))&
((quiet(fred)|~humble(fred)))&
(?[X]:((curious(X)<~>~funny(X))))&
((~funny(alice)|brave(alice))) | ~happy(mary) | []
| null | 0 |
Everyone who is patient is either not rich or not brave.
Everyone who is both old and wise is creative or not curious and vice versa.
If mary is not tall then susan is both creative and not old and vice versa.
Everyone who is rich or strong is both strong and not brave.
Everyone who is not strong or not tall is either not brave or tall and vice versa.
Everyone who is either funny or not curious is patient and vice versa.
If someone is tall or not happy then paul is brave.
Everyone who is either rich or not old is either quiet or not curious.
If someone is quiet then someone is both patient and not strong and vice versa.
If lucy is both not generous and not humble then someone is either generous or kind and vice versa.
Everyone who is humble or not happy is old.
Everyone who is either creative or not funny is not happy or not wise and vice versa.
Everyone who is both funny and happy is either curious or brave and vice versa.
If paul is brave then someone is both happy and old.
If lucy is not calm or curious then someone is either rich or humble.
John is not generous.
Someone is not rich or not curious.
Someone is both not humble and not creative.
Someone is either wise or humble.
Someone is both strong and not calm.
Paul is tall.
Someone is brave or not wise.
Alice is both not brave and funny. | John is kind. | neutral | (![X]:(patient(X)=>(~rich(X)<~>~brave(X))))&
(![X]:((old(X)&wise(X))<=>(creative(X)|~curious(X))))&
((~tall(mary))<=>((creative(susan)&~old(susan))))&
(![X]:((rich(X)|strong(X))=>(strong(X)&~brave(X))))&
(![X]:((~strong(X)|~tall(X))<=>(~brave(X)<~>tall(X))))&
(![X]:((funny(X)<~>~curious(X))<=>patient(X)))&
((?[X]:((tall(X)|~happy(X))))=>(brave(paul)))&
(![X]:((rich(X)<~>~old(X))=>(quiet(X)<~>~curious(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((patient(X)&~strong(X)))))&
(((~generous(lucy)&~humble(lucy)))<=>(?[X]:((generous(X)<~>kind(X)))))&
(![X]:((humble(X)|~happy(X))=>old(X)))&
(![X]:((creative(X)<~>~funny(X))<=>(~happy(X)|~wise(X))))&
(![X]:((funny(X)&happy(X))<=>(curious(X)<~>brave(X))))&
((brave(paul))=>(?[X]:((happy(X)&old(X)))))&
(((~calm(lucy)|curious(lucy)))=>(?[X]:((rich(X)<~>humble(X)))))&
(~generous(john))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:((strong(X)&~calm(X))))&
(tall(paul))&
(?[X]:((brave(X)|~wise(X))))&
((~brave(alice)&funny(alice))) | kind(john) | []
| null | 0 |
Everyone who is tall or rich is either not patient or not humble and vice versa.
Everyone who is either not patient or strong is happy and vice versa.
Everyone who is both generous and quiet is not brave or not rich.
Everyone who is not kind or old is tall.
If someone is either not quiet or not strong then someone is both happy and not happy and vice versa.
If lucy is creative or curious then someone is both not generous and happy and vice versa.
Everyone who is both creative and rich is not rich or creative and vice versa.
If someone is not creative or not old then fred is funny.
Everyone who is both calm and funny is either not funny or creative and vice versa.
If someone is curious or humble then lucy is brave or not wise and vice versa.
Everyone who is quiet or not humble is either kind or calm.
If susan is either old or not patient then fred is either quiet or not funny and vice versa.
Everyone who is either old or not humble is not quiet or quiet.
Everyone who is humble is both calm and tall and vice versa.
If someone is quiet then susan is not strong or not happy and vice versa.
If alice is strong then mary is either not patient or not quiet.
Susan is not rich or funny.
Susan is either funny or not quiet.
Someone is either rich or not generous.
Mary is either strong or not patient.
Someone is both generous and funny.
Someone is both happy and not humble.
Someone is both humble and kind. | Susan is not strong. | contradiction | (![X]:((tall(X)|rich(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>strong(X))<=>happy(X)))&
(![X]:((generous(X)&quiet(X))=>(~brave(X)|~rich(X))))&
(![X]:((~kind(X)|old(X))=>tall(X)))&
((?[X]:((~quiet(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~happy(X)))))&
(((creative(lucy)|curious(lucy)))<=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((creative(X)&rich(X))<=>(~rich(X)|creative(X))))&
((?[X]:((~creative(X)|~old(X))))=>(funny(fred)))&
(![X]:((calm(X)&funny(X))<=>(~funny(X)<~>creative(X))))&
((?[X]:((curious(X)|humble(X))))<=>((brave(lucy)|~wise(lucy))))&
(![X]:((quiet(X)|~humble(X))=>(kind(X)<~>calm(X))))&
(((old(susan)<~>~patient(susan)))<=>((quiet(fred)<~>~funny(fred))))&
(![X]:((old(X)<~>~humble(X))=>(~quiet(X)|quiet(X))))&
(![X]:(humble(X)<=>(calm(X)&tall(X))))&
((?[X]:(quiet(X)))<=>((~strong(susan)|~happy(susan))))&
((strong(alice))=>((~patient(mary)<~>~quiet(mary))))&
((~rich(susan)|funny(susan)))&
((funny(susan)<~>~quiet(susan)))&
(?[X]:((rich(X)<~>~generous(X))))&
((strong(mary)<~>~patient(mary)))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((happy(X)&~humble(X))))&
(?[X]:((humble(X)&kind(X)))) | ~strong(susan) | [
"p4",
"p6",
"p16",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7896365645840674471834333
% SZS output start Proof for 7896365645840674471834333
5. ? [X0] : (~quiet(X0) <~> ~strong(X0)) <=> ? [X0] : (~happy(X0) & happy(X0)) [input p4]
7. ! [X0] : ((rich(X0) & creative(X0)) <=> (creative(X0) | ~rich(X0))) [input p6]
17. funny(susan) | ~rich(susan) [input p16]
18. funny(susan) <~> ~quiet(susan) [input p17]
24. ~strong(susan) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> ~strong(X0)) <=> ? [X1] : (~happy(X1) & happy(X1)) [rectify 5]
37. (? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X1] : (~happy(X1) & happy(X1)) | ! [X0] : ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) [nnf transformation 25]
38. (? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X2] : (~happy(X2) & happy(X2)) | ! [X3] : ((~quiet(X3) | strong(X3)) & (~strong(X3) | quiet(X3)))) [rectify 37]
39. ? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) => ((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) [choice axiom]
40. ? [X2] : (~happy(X2) & happy(X2)) => (~happy(sK1) & happy(sK1)) [choice axiom]
41. (((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) | ! [X1] : (happy(X1) | ~happy(X1))) & ((~happy(sK1) & happy(sK1)) | ! [X3] : ((~quiet(X3) | strong(X3)) & (~strong(X3) | quiet(X3)))) [skolemisation 38,40,39]
47. ! [X0] : (((rich(X0) & creative(X0)) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 7]
48. ! [X0] : (((rich(X0) & creative(X0)) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | ~rich(X0) | ~creative(X0))) [flattening 47]
67. (quiet(susan) | ~funny(susan)) & (~quiet(susan) | funny(susan)) [nnf transformation 18]
92. happy(sK1) | ~quiet(X3) | strong(X3) [cnf transformation 41]
94. ~happy(sK1) | ~quiet(X3) | strong(X3) [cnf transformation 41]
105. rich(X0) | rich(X0) [cnf transformation 48]
141. funny(susan) | ~rich(susan) [cnf transformation 17]
143. quiet(susan) | ~funny(susan) [cnf transformation 67]
154. ~strong(susan) [cnf transformation 24]
158. rich(X0) [duplicate literal removal 105]
160. 1 <=> ! [X3] : (~quiet(X3) | strong(X3)) [avatar definition]
161. ~quiet(X3) | strong(X3) <- (1) [avatar component clause 160]
163. 2 <=> happy(sK1) [avatar definition]
166. 1 | ~2 [avatar split clause 94,163,160]
171. 1 | 2 [avatar split clause 92,163,160]
266. 23 <=> strong(susan) [avatar definition]
267. ~strong(susan) <- (~23) [avatar component clause 266]
288. funny(susan) [subsumption resolution 141,158]
289. quiet(susan) [subsumption resolution 143,288]
297. ~23 [avatar split clause 154,266]
307. strong(susan) <- (1) [resolution 161,289]
308. $false <- (1, ~23) [subsumption resolution 307,267]
309. ~1 | 23 [avatar contradiction clause 308]
310. $false [avatar sat refutation 166,171,297,309]
% SZS output end Proof for 7896365645840674471834333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is not rich or not creative.
Everyone who is either not kind or humble is either not creative or kind.
If susan is not tall then alice is both old and tall and vice versa.
Everyone who is either quiet or patient is both quiet and kind and vice versa.
If someone is not creative then lucy is humble.
If mary is both not calm and not rich then susan is strong.
Everyone who is not old or not kind is both not generous and wise and vice versa.
If susan is either curious or not strong then lucy is not strong or not rich and vice versa.
Everyone who is both not generous and not humble is either not brave or old.
If someone is not kind then someone is generous or creative.
Everyone who is both happy and old is not generous or generous.
Everyone who is not patient or brave is curious or kind and vice versa.
If someone is either not patient or not tall then alice is creative or happy and vice versa.
Everyone who is not calm is both generous and not wise and vice versa.
Everyone who is not humble or wise is not wise or not brave and vice versa.
Everyone who is both not kind and wise is both brave and not creative.
Fred is not wise.
Mary is either happy or quiet.
Someone is both not funny and curious.
Someone is tall or not wise.
Susan is either not rich or not brave.
Fred is strong or not funny.
Someone is not curious or rich.
Mary is either brave or not quiet. | Fred is kind. | entailment | ((~funny(mary))=>(?[X]:((~rich(X)|~creative(X)))))&
(![X]:((~kind(X)<~>humble(X))=>(~creative(X)<~>kind(X))))&
((~tall(susan))<=>((old(alice)&tall(alice))))&
(![X]:((quiet(X)<~>patient(X))<=>(quiet(X)&kind(X))))&
((?[X]:(~creative(X)))=>(humble(lucy)))&
(((~calm(mary)&~rich(mary)))=>(strong(susan)))&
(![X]:((~old(X)|~kind(X))<=>(~generous(X)&wise(X))))&
(((curious(susan)<~>~strong(susan)))<=>((~strong(lucy)|~rich(lucy))))&
(![X]:((~generous(X)&~humble(X))=>(~brave(X)<~>old(X))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((happy(X)&old(X))=>(~generous(X)|generous(X))))&
(![X]:((~patient(X)|brave(X))<=>(curious(X)|kind(X))))&
((?[X]:((~patient(X)<~>~tall(X))))<=>((creative(alice)|happy(alice))))&
(![X]:(~calm(X)<=>(generous(X)&~wise(X))))&
(![X]:((~humble(X)|wise(X))<=>(~wise(X)|~brave(X))))&
(![X]:((~kind(X)&wise(X))=>(brave(X)&~creative(X))))&
(~wise(fred))&
((happy(mary)<~>quiet(mary)))&
(?[X]:((~funny(X)&curious(X))))&
(?[X]:((tall(X)|~wise(X))))&
((~rich(susan)<~>~brave(susan)))&
((strong(fred)|~funny(fred)))&
(?[X]:((~curious(X)|rich(X))))&
((brave(mary)<~>~quiet(mary))) | kind(fred) | [
"p6",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 1149424201355992603732807
% SZS output start Proof for 1149424201355992603732807
7. ! [X0] : ((~kind(X0) | ~old(X0)) <=> (wise(X0) & ~generous(X0))) [input p6]
15. ! [X0] : ((wise(X0) | ~humble(X0)) <=> (~brave(X0) | ~wise(X0))) [input p14]
16. ! [X0] : ((wise(X0) & ~kind(X0)) => (~creative(X0) & brave(X0))) [input p15]
25. ~kind(fred) [input hypothesis]
40. ! [X0] : ((~creative(X0) & brave(X0)) | (~wise(X0) | kind(X0))) [ennf transformation 16]
41. ! [X0] : ((~creative(X0) & brave(X0)) | ~wise(X0) | kind(X0)) [flattening 40]
49. ! [X0] : (((~kind(X0) | ~old(X0)) | (~wise(X0) | generous(X0))) & ((wise(X0) & ~generous(X0)) | (kind(X0) & old(X0)))) [nnf transformation 7]
50. ! [X0] : ((~kind(X0) | ~old(X0) | ~wise(X0) | generous(X0)) & ((wise(X0) & ~generous(X0)) | (kind(X0) & old(X0)))) [flattening 49]
64. ! [X0] : (((wise(X0) | ~humble(X0)) | (brave(X0) & wise(X0))) & ((~brave(X0) | ~wise(X0)) | (~wise(X0) & humble(X0)))) [nnf transformation 15]
65. ! [X0] : ((wise(X0) | ~humble(X0) | (brave(X0) & wise(X0))) & (~brave(X0) | ~wise(X0) | (~wise(X0) & humble(X0)))) [flattening 64]
94. wise(X0) | kind(X0) [cnf transformation 50]
118. ~brave(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 65]
121. brave(X0) | ~wise(X0) | kind(X0) [cnf transformation 41]
135. ~kind(fred) [cnf transformation 25]
136. ~brave(X0) | ~wise(X0) [duplicate literal removal 118]
211. 15 <=> ! [X1] : kind(X1) [avatar definition]
212. kind(X1) <- (15) [avatar component clause 211]
251. ~wise(X0) | kind(X0) [subsumption resolution 121,136]
252. kind(X0) [subsumption resolution 251,94]
253. 15 [avatar split clause 252,211]
307. $false <- (15) [resolution 212,135]
308. ~15 [avatar contradiction clause 307]
309. $false [avatar sat refutation 253,308]
% SZS output end Proof for 1149424201355992603732807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or old is either not creative or not wise. If someone is patient or not kind then lucy is not patient and vice versa. If someone is either old or quiet then susan is not brave or not kind and vice versa. Everyone who is both patient and not funny is either not funny or not calm and vice versa. If paul is not calm then paul is curious or patient and vice versa. Everyone who is kind is curious or not old. If someone is either kind or curious then john is both not tall and calm. Everyone who is not rich or not quiet is creative or not wise. Everyone who is either curious or not humble is both generous and happy and vice versa. Everyone who is not patient or patient is both calm and not generous. If someone is strong or not kind then someone is not humble or strong and vice versa. Everyone who is both not old and funny is both not creative and humble and vice versa. Everyone who is both not curious and wise is either not humble or not brave. Everyone who is either not humble or not curious is wise. Everyone who is old or happy is not old. Everyone who is not humble is old or not old. John is both kind and happy. Someone is both wise and curious. Someone is either strong or patient. Someone is either not wise or patient. Someone is happy or creative. Someone is both not generous and not tall. Susan is not generous or not old. | Lucy is calm. | entailment | (![X]:((~rich(X)<~>old(X))=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(~patient(lucy)))&
((?[X]:((old(X)<~>quiet(X))))<=>((~brave(susan)|~kind(susan))))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)<~>~calm(X))))&
((~calm(paul))<=>((curious(paul)|patient(paul))))&
(![X]:(kind(X)=>(curious(X)|~old(X))))&
((?[X]:((kind(X)<~>curious(X))))=>((~tall(john)&calm(john))))&
(![X]:((~rich(X)|~quiet(X))=>(creative(X)|~wise(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(generous(X)&happy(X))))&
(![X]:((~patient(X)|patient(X))=>(calm(X)&~generous(X))))&
((?[X]:((strong(X)|~kind(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
(![X]:((~old(X)&funny(X))<=>(~creative(X)&humble(X))))&
(![X]:((~curious(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(![X]:((old(X)|happy(X))=>~old(X)))&
(![X]:(~humble(X)=>(old(X)|~old(X))))&
((kind(john)&happy(john)))&
(?[X]:((wise(X)&curious(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
(?[X]:((happy(X)|creative(X))))&
(?[X]:((~generous(X)&~tall(X))))&
((~generous(susan)|~old(susan))) | calm(lucy) | [
"p3",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 506688538516224134907741
% SZS output start Proof for 506688538516224134907741
4. ! [X0] : ((~funny(X0) & patient(X0)) <=> (~funny(X0) <~> ~calm(X0))) [input p3]
10. ! [X0] : ((patient(X0) | ~patient(X0)) => (~generous(X0) & calm(X0))) [input p9]
24. ~calm(lucy) [input hypothesis]
34. ! [X0] : ((~generous(X0) & calm(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 10]
51. ! [X0] : (((~funny(X0) & patient(X0)) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0)))) & (((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | (funny(X0) | ~patient(X0)))) [nnf transformation 4]
52. ! [X0] : (((~funny(X0) & patient(X0)) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0)))) & (((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | funny(X0) | ~patient(X0))) [flattening 51]
93. calm(X0) | funny(X0) | funny(X0) | ~patient(X0) [cnf transformation 52]
97. ~funny(X0) | ~funny(X0) | calm(X0) [cnf transformation 52]
112. calm(X0) | patient(X0) [cnf transformation 34]
142. ~calm(lucy) [cnf transformation 24]
144. calm(X0) | funny(X0) | ~patient(X0) [duplicate literal removal 93]
145. ~funny(X0) | calm(X0) [duplicate literal removal 97]
195. calm(X0) | ~patient(X0) [subsumption resolution 144,145]
221. calm(X0) [subsumption resolution 112,195]
277. $false [subsumption resolution 142,221]
% SZS output end Proof for 506688538516224134907741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not creative is rich and vice versa.
If paul is either wise or brave then paul is not creative or calm and vice versa.
Everyone who is either patient or funny is both not generous and funny and vice versa.
If someone is not humble or kind then someone is either not patient or curious.
Everyone who is not happy or not quiet is old.
Everyone who is not rich or not creative is funny or creative and vice versa.
Everyone who is both not calm and not quiet is both old and not generous.
If someone is both tall and humble then lucy is both rich and not strong.
If susan is curious then lucy is either funny or not happy and vice versa.
If alice is either not wise or curious then someone is either patient or strong and vice versa.
If someone is both not generous and not tall then someone is both not old and tall.
If someone is generous then paul is not brave.
If lucy is both brave and generous then someone is either curious or patient and vice versa.
Everyone who is either not strong or curious is both not rich and creative and vice versa.
Everyone who is either not funny or old is both not creative and funny and vice versa.
Everyone who is not tall or kind is both kind and brave and vice versa.
Someone is patient.
Alice is strong.
Mary is either quiet or not funny.
Someone is both rich and strong.
John is either not patient or generous.
Someone is either not rich or not humble.
Someone is not generous or rich.
John is rich. | Paul is brave. | contradiction | (![X]:((~generous(X)&~creative(X))<=>rich(X)))&
(((wise(paul)<~>brave(paul)))<=>((~creative(paul)|calm(paul))))&
(![X]:((patient(X)<~>funny(X))<=>(~generous(X)&funny(X))))&
((?[X]:((~humble(X)|kind(X))))=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((~happy(X)|~quiet(X))=>old(X)))&
(![X]:((~rich(X)|~creative(X))<=>(funny(X)|creative(X))))&
(![X]:((~calm(X)&~quiet(X))=>(old(X)&~generous(X))))&
((?[X]:((tall(X)&humble(X))))=>((rich(lucy)&~strong(lucy))))&
((curious(susan))<=>((funny(lucy)<~>~happy(lucy))))&
(((~wise(alice)<~>curious(alice)))<=>(?[X]:((patient(X)<~>strong(X)))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(generous(X)))=>(~brave(paul)))&
(((brave(lucy)&generous(lucy)))<=>(?[X]:((curious(X)<~>patient(X)))))&
(![X]:((~strong(X)<~>curious(X))<=>(~rich(X)&creative(X))))&
(![X]:((~funny(X)<~>old(X))<=>(~creative(X)&funny(X))))&
(![X]:((~tall(X)|kind(X))<=>(kind(X)&brave(X))))&
(?[X]:(patient(X)))&
(strong(alice))&
((quiet(mary)<~>~funny(mary)))&
(?[X]:((rich(X)&strong(X))))&
((~patient(john)<~>generous(john)))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((~generous(X)|rich(X))))&
(rich(john)) | brave(paul) | [
"p2",
"p11",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 425403222295331309488525
% SZS output start Proof for 425403222295331309488525
3. ! [X0] : ((patient(X0) <~> funny(X0)) <=> (funny(X0) & ~generous(X0))) [input p2]
12. ? [X0] : generous(X0) => ~brave(paul) [input p11]
17. ? [X0] : patient(X0) [input p16]
25. brave(paul) [input hypothesis]
34. ~brave(paul) | ! [X0] : ~generous(X0) [ennf transformation 12]
39. ! [X0] : ((((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0))))) [flattening 39]
66. ? [X0] : patient(X0) => patient(sK4) [choice axiom]
67. patient(sK4) [skolemisation 17,66]
88. funny(X0) | funny(X0) | ~patient(X0) [cnf transformation 40]
91. ~funny(X0) | ~patient(X0) | ~funny(X0) | generous(X0) [cnf transformation 40]
120. ~brave(paul) | ~generous(X0) [cnf transformation 34]
144. patient(sK4) [cnf transformation 67]
156. brave(paul) [cnf transformation 25]
161. ~patient(X0) | funny(X0) [duplicate literal removal 88]
162. ~funny(X0) | ~patient(X0) | generous(X0) [duplicate literal removal 91]
172. 3 <=> brave(paul) [avatar definition]
276. 24 <=> ! [X0] : ~generous(X0) [avatar definition]
277. ~generous(X0) <- (24) [avatar component clause 276]
278. 24 | ~3 [avatar split clause 120,172,276]
341. 3 [avatar split clause 156,172]
352. funny(sK4) [resolution 161,144]
441. ~patient(sK4) | generous(sK4) [resolution 162,352]
444. generous(sK4) [subsumption resolution 441,144]
445. $false <- (24) [subsumption resolution 444,277]
446. ~24 [avatar contradiction clause 445]
450. $false [avatar sat refutation 278,341,446]
% SZS output end Proof for 425403222295331309488525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not wise is either not creative or funny and vice versa.
If someone is tall then lucy is not rich and vice versa.
Everyone who is both creative and not tall is not quiet or not generous.
If susan is both happy and not tall then alice is rich and vice versa.
If someone is not creative or not wise then lucy is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
Everyone who is either funny or creative is both rich and humble and vice versa.
If mary is not generous or not rich then someone is wise.
Someone is not old or not generous.
Alice is not generous or not kind.
Someone is not humble. | Susan is not kind. | entailment | (![X]:((~kind(X)&~wise(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:(tall(X)))<=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
(((~generous(mary)|~rich(mary)))=>(?[X]:(wise(X))))&
(?[X]:((~old(X)|~generous(X))))&
((~generous(alice)|~kind(alice)))&
(?[X]:(~humble(X))) | ~kind(susan) | [
"p0",
"p8",
"p10",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2410701698477735190837325
% SZS output start Proof for 2410701698477735190837325
1. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~creative(X0) <~> funny(X0))) [input p0]
9. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (~strong(X0) & ~rich(X0))) [input p8]
11. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p10]
13. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p12]
14. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p13]
15. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (humble(X0) & rich(X0))) [input p14]
20. kind(susan) [input hypothesis]
26. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 11]
29. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (wise(X0) | kind(X0)))) [nnf transformation 1]
30. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | wise(X0) | kind(X0))) [flattening 29]
42. ! [X0] : (((~happy(X0) | ~funny(X0)) | (strong(X0) | rich(X0))) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 9]
43. ! [X0] : ((~happy(X0) | ~funny(X0) | strong(X0) | rich(X0)) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [flattening 42]
47. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 13]
48. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 47]
49. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 14]
50. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 49]
51. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 15]
52. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 51]
61. ~kind(X0) | funny(X0) | creative(X0) [cnf transformation 30]
62. ~funny(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 30]
86. ~rich(X0) | funny(X0) [cnf transformation 43]
87. ~rich(X0) | happy(X0) [cnf transformation 43]
95. ~happy(X0) | funny(X0) [cnf transformation 26]
96. ~old(X0) | ~happy(X0) [cnf transformation 26]
102. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 48]
110. ~brave(X0) | old(X0) | ~kind(X0) [cnf transformation 50]
111. ~funny(X0) | creative(X0) | rich(X0) [cnf transformation 52]
112. rich(X0) | funny(X0) | ~creative(X0) [cnf transformation 52]
122. kind(susan) [cnf transformation 20]
146. 6 <=> happy(susan) [avatar definition]
148. happy(susan) <- (6) [avatar component clause 146]
189. ~happy(X0) | brave(X0) [subsumption resolution 102,95]
192. ~creative(X0) | funny(X0) [subsumption resolution 112,86]
225. funny(susan) | creative(susan) [resolution 61,122]
226. funny(susan) [subsumption resolution 225,192]
227. ~creative(susan) | ~kind(susan) [resolution 62,226]
228. ~creative(susan) [subsumption resolution 227,122]
304. creative(susan) | rich(susan) [resolution 111,226]
307. rich(susan) [subsumption resolution 304,228]
315. happy(susan) [resolution 307,87]
319. 6 [avatar split clause 315,146]
322. brave(susan) <- (6) [resolution 148,189]
378. old(susan) | ~kind(susan) <- (6) [resolution 322,110]
382. old(susan) <- (6) [subsumption resolution 378,122]
527. ~happy(susan) <- (6) [resolution 382,96]
528. $false <- (6) [subsumption resolution 527,148]
529. ~6 [avatar contradiction clause 528]
530. $false [avatar sat refutation 319,529]
% SZS output end Proof for 2410701698477735190837325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not quiet is curious and vice versa.
If alice is either not happy or not rich then susan is both not patient and kind.
Everyone who is wise or not patient is both kind and generous.
Everyone who is either not tall or rich is both not generous and calm.
If someone is strong then someone is wise and vice versa.
Everyone who is both wise and creative is either not happy or not rich and vice versa.
Everyone who is not curious is old.
Everyone who is both wise and tall is not humble or curious and vice versa.
Everyone who is both not rich and funny is not quiet.
If alice is both not kind and quiet then alice is not rich or humble.
Everyone who is either strong or wise is either not calm or not old and vice versa.
Everyone who is not old or rich is wise or not curious and vice versa.
If susan is happy or tall then paul is generous or wise.
If fred is not quiet then susan is curious or not quiet.
Everyone who is both not patient and not old is either not tall or not generous.
Everyone who is not kind is both not quiet and not calm.
Paul is both not rich and not brave.
Someone is rich or not wise.
Someone is both rich and kind.
Fred is either not wise or tall.
Someone is kind or strong.
Alice is either funny or wise.
Alice is strong. | Paul is not generous. | contradiction | (![X]:((humble(X)<~>~quiet(X))<=>curious(X)))&
(((~happy(alice)<~>~rich(alice)))=>((~patient(susan)&kind(susan))))&
(![X]:((wise(X)|~patient(X))=>(kind(X)&generous(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~generous(X)&calm(X))))&
((?[X]:(strong(X)))<=>(?[X]:(wise(X))))&
(![X]:((wise(X)&creative(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:(~curious(X)=>old(X)))&
(![X]:((wise(X)&tall(X))<=>(~humble(X)|curious(X))))&
(![X]:((~rich(X)&funny(X))=>~quiet(X)))&
(((~kind(alice)&quiet(alice)))=>((~rich(alice)|humble(alice))))&
(![X]:((strong(X)<~>wise(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((~old(X)|rich(X))<=>(wise(X)|~curious(X))))&
(((happy(susan)|tall(susan)))=>((generous(paul)|wise(paul))))&
((~quiet(fred))=>((curious(susan)|~quiet(susan))))&
(![X]:((~patient(X)&~old(X))=>(~tall(X)<~>~generous(X))))&
(![X]:(~kind(X)=>(~quiet(X)&~calm(X))))&
((~rich(paul)&~brave(paul)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((rich(X)&kind(X))))&
((~wise(fred)<~>tall(fred)))&
(?[X]:((kind(X)|strong(X))))&
((funny(alice)<~>wise(alice)))&
(strong(alice)) | ~generous(paul) | [
"p2",
"p6",
"p7",
"p11",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8969594287484094829212903
% SZS output start Proof for 8969594287484094829212903
3. ! [X0] : ((~patient(X0) | wise(X0)) => (generous(X0) & kind(X0))) [input p2]
7. ! [X0] : (~curious(X0) => old(X0)) [input p6]
8. ! [X0] : ((tall(X0) & wise(X0)) <=> (curious(X0) | ~humble(X0))) [input p7]
12. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~curious(X0) | wise(X0))) [input p11]
17. ~brave(paul) & ~rich(paul) [input p16]
24. ~generous(paul) [input hypothesis]
26. ~rich(paul) [pure predicate removal 17]
29. ! [X0] : ((~patient(X0) | wise(X0)) => generous(X0)) [pure predicate removal 3]
34. ! [X0] : (generous(X0) | (patient(X0) & ~wise(X0))) [ennf transformation 29]
36. ! [X0] : (old(X0) | curious(X0)) [ennf transformation 7]
55. ! [X0] : (((tall(X0) & wise(X0)) | (~curious(X0) & humble(X0))) & ((curious(X0) | ~humble(X0)) | (~tall(X0) | ~wise(X0)))) [nnf transformation 8]
56. ! [X0] : (((tall(X0) & wise(X0)) | (~curious(X0) & humble(X0))) & (curious(X0) | ~humble(X0) | ~tall(X0) | ~wise(X0))) [flattening 55]
58. ! [X0] : (((rich(X0) | ~old(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 12]
59. ! [X0] : ((rich(X0) | ~old(X0) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | (~rich(X0) & old(X0)))) [flattening 58]
73. ~wise(X0) | generous(X0) [cnf transformation 34]
87. old(X0) | curious(X0) [cnf transformation 36]
90. ~curious(X0) | wise(X0) [cnf transformation 56]
105. rich(X0) | ~old(X0) | curious(X0) [cnf transformation 59]
111. ~rich(paul) [cnf transformation 26]
119. ~generous(paul) [cnf transformation 24]
150. rich(X0) | curious(X0) [subsumption resolution 105,87]
157. 9 <=> generous(paul) [avatar definition]
158. ~generous(paul) <- (~9) [avatar component clause 157]
210. ~9 [avatar split clause 119,157]
223. curious(paul) [resolution 150,111]
225. wise(paul) [resolution 223,90]
240. generous(paul) [resolution 225,73]
241. $false <- (~9) [subsumption resolution 240,158]
242. 9 [avatar contradiction clause 241]
243. $false [avatar sat refutation 210,242]
% SZS output end Proof for 8969594287484094829212903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not curious is curious.
If someone is either rich or funny then someone is both humble and creative and vice versa.
If john is both not generous and generous then someone is either humble or tall.
Everyone who is not kind or creative is not calm or old and vice versa.
If alice is funny or kind then alice is not quiet or quiet and vice versa.
Everyone who is both quiet and rich is both curious and kind.
Everyone who is not tall or creative is creative and vice versa.
If paul is either happy or not wise then someone is humble and vice versa.
If lucy is either not funny or not strong then someone is either not curious or not rich and vice versa.
Everyone who is curious is both not patient and not curious and vice versa.
If someone is not happy then someone is wise or creative and vice versa.
Everyone who is both wise and not funny is rich or not happy and vice versa.
If someone is old or not brave then susan is both humble and not quiet and vice versa.
If mary is not calm or humble then someone is brave or not funny and vice versa.
Everyone who is either not tall or quiet is either not curious or not quiet and vice versa.
Fred is either curious or not calm.
Someone is calm or tall.
Fred is either quiet or not patient.
Someone is either not brave or not calm.
Someone is brave or creative. | Susan is curious. | contradiction | (![X]:((~happy(X)<~>~curious(X))=>curious(X)))&
((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((humble(X)&creative(X)))))&
(((~generous(john)&generous(john)))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~calm(X)|old(X))))&
(((funny(alice)|kind(alice)))<=>((~quiet(alice)|quiet(alice))))&
(![X]:((quiet(X)&rich(X))=>(curious(X)&kind(X))))&
(![X]:((~tall(X)|creative(X))<=>creative(X)))&
(((happy(paul)<~>~wise(paul)))<=>(?[X]:(humble(X))))&
(((~funny(lucy)<~>~strong(lucy)))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>(~patient(X)&~curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)&~funny(X))<=>(rich(X)|~happy(X))))&
((?[X]:((old(X)|~brave(X))))<=>((humble(susan)&~quiet(susan))))&
(((~calm(mary)|humble(mary)))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~curious(X)<~>~quiet(X))))&
((curious(fred)<~>~calm(fred)))&
(?[X]:((calm(X)|tall(X))))&
((quiet(fred)<~>~patient(fred)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((brave(X)|creative(X)))) | curious(susan) | [
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 1869222417505195095619975
% SZS output start Proof for 1869222417505195095619975
10. ! [X0] : (curious(X0) <=> (~curious(X0) & ~patient(X0))) [input p9]
21. curious(susan) [input hypothesis]
52. ! [X0] : ((curious(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [nnf transformation 10]
53. ! [X0] : ((curious(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [flattening 52]
117. ~curious(X0) | ~curious(X0) [cnf transformation 53]
152. curious(susan) [cnf transformation 21]
157. ~curious(X0) [duplicate literal removal 117]
364. $false [subsumption resolution 152,157]
% SZS output end Proof for 1869222417505195095619975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If susan is tall then john is either not humble or not wise.
Everyone who is either not creative or quiet is not rich or not generous.
If someone is happy then alice is happy or not curious.
Everyone who is not tall or happy is creative and vice versa.
Everyone who is funny is not curious.
If someone is either happy or not generous then someone is brave or calm and vice versa.
Everyone who is either not creative or strong is curious and vice versa.
If someone is generous or not tall then alice is not creative.
If someone is both not happy and not tall then someone is patient and vice versa.
If lucy is funny or generous then someone is not creative.
If someone is not rich then someone is both not tall and tall.
Everyone who is either not creative or not happy is not happy or strong and vice versa.
If someone is both not creative and not funny then someone is either not wise or creative and vice versa.
If john is not strong then someone is rich or patient and vice versa.
If someone is not tall or not quiet then someone is not rich.
Someone is either humble or not quiet.
Someone is not wise.
Alice is both tall and creative.
Someone is either brave or funny.
Someone is both creative and tall.
Someone is not kind.
Someone is either wise or rich. | Susan is not calm. | entailment | ((tall(susan))=>((~humble(john)<~>~wise(john))))&
(![X]:((~creative(X)<~>quiet(X))=>(~rich(X)|~generous(X))))&
((?[X]:(happy(X)))=>((happy(alice)|~curious(alice))))&
(![X]:((~tall(X)|happy(X))<=>creative(X)))&
(![X]:(funny(X)=>~curious(X)))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~creative(X)<~>strong(X))<=>curious(X)))&
((?[X]:((generous(X)|~tall(X))))=>(~creative(alice)))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:(patient(X))))&
(((funny(lucy)|generous(lucy)))=>(?[X]:(~creative(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~tall(X)&tall(X)))))&
(![X]:((~creative(X)<~>~happy(X))<=>(~happy(X)|strong(X))))&
((?[X]:((~creative(X)&~funny(X))))<=>(?[X]:((~wise(X)<~>creative(X)))))&
((~strong(john))<=>(?[X]:((rich(X)|patient(X)))))&
((?[X]:((~tall(X)|~quiet(X))))=>(?[X]:(~rich(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:(~wise(X)))&
((tall(alice)&creative(alice)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)<~>rich(X)))) | ~calm(susan) | [
"p3",
"p5",
"p7",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 8341706676608924003211630
% SZS output start Proof for 8341706676608924003211630
4. ! [X0] : ((happy(X0) | ~tall(X0)) <=> creative(X0)) [input p3]
6. ? [X0] : (happy(X0) <~> ~generous(X0)) <=> ? [X0] : (calm(X0) | brave(X0)) [input p5]
8. ? [X0] : (~tall(X0) | generous(X0)) => ~creative(alice) [input p7]
12. ! [X0] : ((~creative(X0) <~> ~happy(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
23. calm(susan) [input hypothesis]
24. ? [X0] : (happy(X0) <~> ~generous(X0)) <=> ? [X1] : (calm(X1) | brave(X1)) [rectify 6]
38. ~creative(alice) | ! [X0] : (tall(X0) & ~generous(X0)) [ennf transformation 8]
44. ! [X0] : (((happy(X0) | ~tall(X0)) | ~creative(X0)) & (creative(X0) | (~happy(X0) & tall(X0)))) [nnf transformation 4]
45. ! [X0] : ((happy(X0) | ~tall(X0) | ~creative(X0)) & (creative(X0) | (~happy(X0) & tall(X0)))) [flattening 44]
46. (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ! [X1] : (~calm(X1) & ~brave(X1))) & (? [X1] : (calm(X1) | brave(X1)) | ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) [nnf transformation 24]
47. (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ! [X1] : (~calm(X1) & ~brave(X1))) & (? [X2] : (calm(X2) | brave(X2)) | ! [X3] : ((happy(X3) | generous(X3)) & (~generous(X3) | ~happy(X3)))) [rectify 46]
48. ? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) => ((generous(sK0) | ~happy(sK0)) & (~generous(sK0) | happy(sK0))) [choice axiom]
49. ? [X2] : (calm(X2) | brave(X2)) => (calm(sK1) | brave(sK1)) [choice axiom]
50. (((generous(sK0) | ~happy(sK0)) & (~generous(sK0) | happy(sK0))) | ! [X1] : (~calm(X1) & ~brave(X1))) & ((calm(sK1) | brave(sK1)) | ! [X3] : ((happy(X3) | generous(X3)) & (~generous(X3) | ~happy(X3)))) [skolemisation 47,49,48]
62. ! [X0] : ((((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0))))) [nnf transformation 12]
63. ! [X0] : ((((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0))))) [flattening 62]
95. ~happy(X0) | creative(X0) [cnf transformation 45]
96. ~creative(X0) | ~tall(X0) | happy(X0) [cnf transformation 45]
103. generous(sK0) | ~happy(sK0) | ~calm(X1) [cnf transformation 50]
106. ~creative(alice) | ~generous(X0) [cnf transformation 38]
107. ~creative(alice) | tall(X0) [cnf transformation 38]
119. happy(X0) | creative(X0) | happy(X0) [cnf transformation 63]
143. calm(susan) [cnf transformation 23]
145. happy(X0) | creative(X0) [duplicate literal removal 119]
173. 7 <=> ! [X1] : ~calm(X1) [avatar definition]
174. ~calm(X1) <- (7) [avatar component clause 173]
176. 8 <=> happy(sK0) [avatar definition]
178. ~happy(sK0) <- (~8) [avatar component clause 176]
180. 9 <=> generous(sK0) [avatar definition]
182. generous(sK0) <- (9) [avatar component clause 180]
183. 7 | ~8 | 9 [avatar split clause 103,180,176,173]
207. 15 <=> ! [X0] : tall(X0) [avatar definition]
208. tall(X0) <- (15) [avatar component clause 207]
210. 16 <=> creative(alice) [avatar definition]
212. ~creative(alice) <- (~16) [avatar component clause 210]
213. 15 | ~16 [avatar split clause 107,210,207]
215. 17 <=> ! [X0] : ~generous(X0) [avatar definition]
216. ~generous(X0) <- (17) [avatar component clause 215]
217. 17 | ~16 [avatar split clause 106,210,215]
263. creative(X0) [subsumption resolution 145,95]
338. $false <- (~16) [subsumption resolution 212,263]
339. 16 [avatar contradiction clause 338]
351. ~tall(X1) | happy(X1) [resolution 96,263]
352. happy(X1) <- (15) [subsumption resolution 351,208]
353. $false <- (~8, 15) [resolution 352,178]
355. 8 | ~15 [avatar contradiction clause 353]
356. $false <- (9, 17) [subsumption resolution 182,216]
357. ~9 | ~17 [avatar contradiction clause 356]
358. $false <- (7) [resolution 174,143]
359. ~7 [avatar contradiction clause 358]
360. $false [avatar sat refutation 183,213,217,339,355,357,359]
% SZS output end Proof for 8341706676608924003211630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and not humble then someone is not happy or not creative.
If lucy is not curious then someone is calm or rich and vice versa.
Everyone who is tall is brave.
If paul is either creative or tall then fred is both not happy and old.
If someone is patient or not happy then someone is not kind and vice versa.
Everyone who is funny or not quiet is strong or happy and vice versa.
If someone is wise or not strong then someone is both calm and patient and vice versa.
If john is not calm then someone is both tall and not old and vice versa.
If someone is either strong or not rich then someone is either not creative or kind.
If lucy is both not kind and quiet then john is rich or not humble and vice versa.
Everyone who is both kind and not generous is funny or not calm.
If someone is not creative then someone is both funny and not patient and vice versa.
Everyone who is not humble is old or not old and vice versa.
Everyone who is both not humble and brave is not calm or not tall and vice versa.
If susan is not tall or tall then someone is both funny and not kind and vice versa.
Everyone who is curious is not humble or brave.
Someone is not rich or not old.
Someone is not happy.
Fred is either patient or not wise.
John is not quiet or funny.
Someone is either not wise or not humble.
Fred is not rich. | Susan is patient. | neutral | ((?[X]:((rich(X)&~humble(X))))=>(?[X]:((~happy(X)|~creative(X)))))&
((~curious(lucy))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(tall(X)=>brave(X)))&
(((creative(paul)<~>tall(paul)))=>((~happy(fred)&old(fred))))&
((?[X]:((patient(X)|~happy(X))))<=>(?[X]:(~kind(X))))&
(![X]:((funny(X)|~quiet(X))<=>(strong(X)|happy(X))))&
((?[X]:((wise(X)|~strong(X))))<=>(?[X]:((calm(X)&patient(X)))))&
((~calm(john))<=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((strong(X)<~>~rich(X))))=>(?[X]:((~creative(X)<~>kind(X)))))&
(((~kind(lucy)&quiet(lucy)))<=>((rich(john)|~humble(john))))&
(![X]:((kind(X)&~generous(X))=>(funny(X)|~calm(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:(~humble(X)<=>(old(X)|~old(X))))&
(![X]:((~humble(X)&brave(X))<=>(~calm(X)|~tall(X))))&
(((~tall(susan)|tall(susan)))<=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:(curious(X)=>(~humble(X)|brave(X))))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:(~happy(X)))&
((patient(fred)<~>~wise(fred)))&
((~quiet(john)|funny(john)))&
(?[X]:((~wise(X)<~>~humble(X))))&
(~rich(fred)) | patient(susan) | []
| null | 0 |
If alice is both not kind and not humble then someone is both strong and not tall and vice versa.
If lucy is old then someone is either old or not calm.
Everyone who is not funny or humble is happy or generous and vice versa.
If someone is humble or not brave then someone is not wise or not happy.
Everyone who is both not humble and kind is curious.
Everyone who is not quiet is both rich and kind.
Everyone who is either kind or not kind is both calm and generous and vice versa.
If lucy is both not rich and not generous then someone is tall or not humble.
Everyone who is either not funny or quiet is generous and vice versa.
If someone is both not wise and tall then someone is both not humble and not curious.
If someone is not kind or not strong then fred is both not brave and not wise and vice versa.
If someone is not old then someone is either strong or patient and vice versa.
If someone is not calm then someone is both not creative and quiet.
Everyone who is not old is not happy or not rich and vice versa.
If someone is not quiet then alice is not happy or calm and vice versa.
Everyone who is not rich is not brave and vice versa.
Someone is either generous or not funny.
Alice is either funny or not curious.
Someone is either tall or rich.
Lucy is either quiet or humble.
Susan is not wise.
Someone is not old.
Someone is not calm or not quiet.
Someone is patient. | Lucy is not generous. | contradiction | (((~kind(alice)&~humble(alice)))<=>(?[X]:((strong(X)&~tall(X)))))&
((old(lucy))=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((~funny(X)|humble(X))<=>(happy(X)|generous(X))))&
((?[X]:((humble(X)|~brave(X))))=>(?[X]:((~wise(X)|~happy(X)))))&
(![X]:((~humble(X)&kind(X))=>curious(X)))&
(![X]:(~quiet(X)=>(rich(X)&kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(calm(X)&generous(X))))&
(((~rich(lucy)&~generous(lucy)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~funny(X)<~>quiet(X))<=>generous(X)))&
((?[X]:((~wise(X)&tall(X))))=>(?[X]:((~humble(X)&~curious(X)))))&
((?[X]:((~kind(X)|~strong(X))))<=>((~brave(fred)&~wise(fred))))&
((?[X]:(~old(X)))<=>(?[X]:((strong(X)<~>patient(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:(~old(X)<=>(~happy(X)|~rich(X))))&
((?[X]:(~quiet(X)))<=>((~happy(alice)|calm(alice))))&
(![X]:(~rich(X)<=>~brave(X)))&
(?[X]:((generous(X)<~>~funny(X))))&
((funny(alice)<~>~curious(alice)))&
(?[X]:((tall(X)<~>rich(X))))&
((quiet(lucy)<~>humble(lucy)))&
(~wise(susan))&
(?[X]:(~old(X)))&
(?[X]:((~calm(X)|~quiet(X))))&
(?[X]:(patient(X))) | ~generous(lucy) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 7308769166514128511128225
% SZS output start Proof for 7308769166514128511128225
7. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> (generous(X0) & calm(X0))) [input p6]
25. ~generous(lucy) [input hypothesis]
53. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 7]
54. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [flattening 53]
113. generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 54]
114. generous(X0) | kind(X0) | kind(X0) [cnf transformation 54]
154. ~generous(lucy) [cnf transformation 25]
157. generous(X0) | ~kind(X0) [duplicate literal removal 113]
158. generous(X0) | kind(X0) [duplicate literal removal 114]
212. generous(X0) [subsumption resolution 157,158]
314. $false [subsumption resolution 154,212]
% SZS output end Proof for 7308769166514128511128225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is both not patient and not curious. Everyone who is either humble or generous is not funny and vice versa. Everyone who is not patient is both kind and rich and vice versa. Everyone who is either old or not happy is generous. If someone is both not quiet and not old then fred is wise or not patient and vice versa. Everyone who is both not old and not curious is not humble and vice versa. If someone is either wise or not rich then susan is happy or calm and vice versa. Everyone who is strong is rich and vice versa. Everyone who is both humble and not calm is not curious and vice versa. Everyone who is both tall and old is humble. Everyone who is not kind is either strong or not rich and vice versa. Everyone who is either rich or strong is both patient and not funny and vice versa. If alice is generous then someone is either generous or not wise. If mary is calm or not happy then someone is creative or not generous and vice versa. If lucy is both quiet and kind then john is not old. Everyone who is generous or not humble is strong or not humble. Paul is not calm. Someone is not wise or curious. Someone is not humble or not brave. Someone is creative or not quiet. Susan is either not quiet or not kind. Lucy is not tall. | Alice is not funny. | contradiction | (![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
(![X]:((humble(X)<~>generous(X))<=>~funny(X)))&
(![X]:(~patient(X)<=>(kind(X)&rich(X))))&
(![X]:((old(X)<~>~happy(X))=>generous(X)))&
((?[X]:((~quiet(X)&~old(X))))<=>((wise(fred)|~patient(fred))))&
(![X]:((~old(X)&~curious(X))<=>~humble(X)))&
((?[X]:((wise(X)<~>~rich(X))))<=>((happy(susan)|calm(susan))))&
(![X]:(strong(X)<=>rich(X)))&
(![X]:((humble(X)&~calm(X))<=>~curious(X)))&
(![X]:((tall(X)&old(X))=>humble(X)))&
(![X]:(~kind(X)<=>(strong(X)<~>~rich(X))))&
(![X]:((rich(X)<~>strong(X))<=>(patient(X)&~funny(X))))&
((generous(alice))=>(?[X]:((generous(X)<~>~wise(X)))))&
(((calm(mary)|~happy(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((quiet(lucy)&kind(lucy)))=>(~old(john)))&
(![X]:((generous(X)|~humble(X))=>(strong(X)|~humble(X))))&
(~calm(paul))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((creative(X)|~quiet(X))))&
((~quiet(susan)<~>~kind(susan)))&
(~tall(lucy)) | ~funny(alice) | [
"p2",
"p7",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 4710926746852888059850205
% SZS output start Proof for 4710926746852888059850205
3. ! [X0] : (~patient(X0) <=> (rich(X0) & kind(X0))) [input p2]
8. ! [X0] : (strong(X0) <=> rich(X0)) [input p7]
11. ! [X0] : (~kind(X0) <=> (strong(X0) <~> ~rich(X0))) [input p10]
12. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (~funny(X0) & patient(X0))) [input p11]
23. ~funny(alice) [input hypothesis]
35. ! [X0] : ((~patient(X0) | (~rich(X0) | ~kind(X0))) & ((rich(X0) & kind(X0)) | patient(X0))) [nnf transformation 3]
36. ! [X0] : ((~patient(X0) | ~rich(X0) | ~kind(X0)) & ((rich(X0) & kind(X0)) | patient(X0))) [flattening 35]
50. ! [X0] : ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))) [nnf transformation 8]
53. ! [X0] : ((~kind(X0) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0)))) & (((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | kind(X0))) [nnf transformation 11]
54. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 12]
55. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [flattening 54]
75. kind(X0) | patient(X0) [cnf transformation 36]
76. rich(X0) | patient(X0) [cnf transformation 36]
94. ~strong(X0) | rich(X0) [cnf transformation 50]
95. ~rich(X0) | strong(X0) [cnf transformation 50]
101. ~kind(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 53]
102. ~kind(X0) | strong(X0) | rich(X0) [cnf transformation 53]
107. strong(X0) | rich(X0) | funny(X0) | ~patient(X0) [cnf transformation 55]
108. ~strong(X0) | ~rich(X0) | funny(X0) | ~patient(X0) [cnf transformation 55]
123. ~funny(alice) [cnf transformation 23]
178. ~kind(X0) | strong(X0) [subsumption resolution 102,95]
179. ~kind(X0) | ~strong(X0) [subsumption resolution 101,94]
180. ~kind(X0) [subsumption resolution 179,178]
181. ~strong(X0) | funny(X0) | ~patient(X0) [subsumption resolution 108,94]
182. strong(X0) | rich(X0) | funny(X0) [subsumption resolution 107,76]
183. strong(X0) | funny(X0) [subsumption resolution 182,95]
244. patient(X0) [resolution 75,180]
320. funny(X0) | ~patient(X0) | funny(X0) [resolution 181,183]
323. funny(X0) | ~patient(X0) [duplicate literal removal 320]
324. funny(X0) [subsumption resolution 323,244]
328. $false [resolution 324,123]
% SZS output end Proof for 4710926746852888059850205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not brave is either happy or not wise and vice versa. If someone is both not kind and not happy then lucy is kind or not creative and vice versa. Everyone who is either wise or kind is not old or not funny. Everyone who is not creative or not happy is generous. Everyone who is either humble or old is both not curious and not humble and vice versa. Everyone who is patient or not generous is rich. Everyone who is either generous or rich is generous and vice versa. Everyone who is not humble is both happy and strong and vice versa. If someone is not wise then fred is both happy and not happy. If someone is tall then lucy is not generous or not patient and vice versa. If someone is not kind then someone is quiet or generous. If fred is brave or not kind then mary is humble. If someone is either not strong or strong then someone is not tall or strong and vice versa. If someone is both happy and not calm then lucy is not creative or strong. Everyone who is either not curious or not strong is calm or not quiet. If susan is wise or not old then someone is curious or rich. Susan is not old. Someone is strong or funny. Alice is both funny and old. Susan is calm or not happy. Alice is not tall or rich. Someone is not strong or not tall. | Lucy is kind. | neutral | (![X]:((~kind(X)<~>~brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~kind(X)&~happy(X))))<=>((kind(lucy)|~creative(lucy))))&
(![X]:((wise(X)<~>kind(X))=>(~old(X)|~funny(X))))&
(![X]:((~creative(X)|~happy(X))=>generous(X)))&
(![X]:((humble(X)<~>old(X))<=>(~curious(X)&~humble(X))))&
(![X]:((patient(X)|~generous(X))=>rich(X)))&
(![X]:((generous(X)<~>rich(X))<=>generous(X)))&
(![X]:(~humble(X)<=>(happy(X)&strong(X))))&
((?[X]:(~wise(X)))=>((happy(fred)&~happy(fred))))&
((?[X]:(tall(X)))<=>((~generous(lucy)|~patient(lucy))))&
((?[X]:(~kind(X)))=>(?[X]:((quiet(X)|generous(X)))))&
(((brave(fred)|~kind(fred)))=>(humble(mary)))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~tall(X)|strong(X)))))&
((?[X]:((happy(X)&~calm(X))))=>((~creative(lucy)|strong(lucy))))&
(![X]:((~curious(X)<~>~strong(X))=>(calm(X)|~quiet(X))))&
(((wise(susan)|~old(susan)))=>(?[X]:((curious(X)|rich(X)))))&
(~old(susan))&
(?[X]:((strong(X)|funny(X))))&
((funny(alice)&old(alice)))&
((calm(susan)|~happy(susan)))&
((~tall(alice)|rich(alice)))&
(?[X]:((~strong(X)|~tall(X)))) | kind(lucy) | []
| null | 0 |
If someone is either not calm or tall then lucy is either brave or humble and vice versa.
If someone is both not generous and quiet then lucy is both humble and not creative.
If lucy is either tall or rich then fred is kind or tall.
If lucy is not quiet then john is both not happy and not old.
If someone is happy then someone is both kind and not kind and vice versa.
If susan is both old and not creative then someone is not brave and vice versa.
Everyone who is curious is either curious or quiet.
If john is either funny or not kind then someone is not funny or brave.
Everyone who is curious is not wise or not creative and vice versa.
If mary is not patient or not curious then someone is both creative and not patient.
If someone is both not rich and quiet then john is old and vice versa.
If someone is not patient or funny then john is not humble or wise.
If john is rich then mary is both generous and humble.
If someone is either curious or not old then someone is not wise and vice versa.
If alice is either not strong or strong then fred is both not happy and rich and vice versa.
Everyone who is both not generous and funny is both creative and not brave and vice versa.
Someone is not kind.
Alice is calm.
Mary is not brave.
Susan is either calm or not happy.
Alice is not quiet or not creative.
Someone is either not quiet or patient.
Paul is not quiet or not rich. | Susan is creative. | contradiction | ((?[X]:((~calm(X)<~>tall(X))))<=>((brave(lucy)<~>humble(lucy))))&
((?[X]:((~generous(X)&quiet(X))))=>((humble(lucy)&~creative(lucy))))&
(((tall(lucy)<~>rich(lucy)))=>((kind(fred)|tall(fred))))&
((~quiet(lucy))=>((~happy(john)&~old(john))))&
((?[X]:(happy(X)))<=>(?[X]:((kind(X)&~kind(X)))))&
(((old(susan)&~creative(susan)))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>(curious(X)<~>quiet(X))))&
(((funny(john)<~>~kind(john)))=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:(curious(X)<=>(~wise(X)|~creative(X))))&
(((~patient(mary)|~curious(mary)))=>(?[X]:((creative(X)&~patient(X)))))&
((?[X]:((~rich(X)&quiet(X))))<=>(old(john)))&
((?[X]:((~patient(X)|funny(X))))=>((~humble(john)|wise(john))))&
((rich(john))=>((generous(mary)&humble(mary))))&
((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:(~wise(X))))&
(((~strong(alice)<~>strong(alice)))<=>((~happy(fred)&rich(fred))))&
(![X]:((~generous(X)&funny(X))<=>(creative(X)&~brave(X))))&
(?[X]:(~kind(X)))&
(calm(alice))&
(~brave(mary))&
((calm(susan)<~>~happy(susan)))&
((~quiet(alice)|~creative(alice)))&
(?[X]:((~quiet(X)<~>patient(X))))&
((~quiet(paul)|~rich(paul))) | creative(susan) | [
"p5",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7890249272103607040196182
% SZS output start Proof for 7890249272103607040196182
6. (~creative(susan) & old(susan)) <=> ? [X0] : ~brave(X0) [input p5]
19. ~brave(mary) [input p18]
24. creative(susan) [input hypothesis]
47. ((~creative(susan) & old(susan)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (creative(susan) | ~old(susan))) [nnf transformation 6]
48. ((~creative(susan) & old(susan)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | creative(susan) | ~old(susan)) [flattening 47]
49. ((~creative(susan) & old(susan)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | creative(susan) | ~old(susan)) [rectify 48]
50. ? [X1] : ~brave(X1) => ~brave(sK3) [choice axiom]
51. ((~creative(susan) & old(susan)) | ! [X0] : brave(X0)) & (~brave(sK3) | creative(susan) | ~old(susan)) [skolemisation 49,50]
98. ~creative(susan) | brave(X0) [cnf transformation 51]
133. ~brave(mary) [cnf transformation 19]
140. creative(susan) [cnf transformation 24]
227. 18 <=> ! [X0] : brave(X0) [avatar definition]
228. brave(X0) <- (18) [avatar component clause 227]
230. 19 <=> creative(susan) [avatar definition]
233. 18 | ~19 [avatar split clause 98,230,227]
405. 19 [avatar split clause 140,230]
408. $false <- (18) [resolution 228,133]
409. ~18 [avatar contradiction clause 408]
410. $false [avatar sat refutation 233,405,409]
% SZS output end Proof for 7890249272103607040196182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise then fred is both curious and brave and vice versa.
Everyone who is not tall or quiet is either kind or happy and vice versa.
Everyone who is not patient or not strong is not curious and vice versa.
Everyone who is generous or calm is either not old or not strong.
Everyone who is both not humble and generous is strong and vice versa.
If fred is either not rich or not funny then paul is either kind or creative and vice versa.
If someone is both not kind and not creative then paul is not humble and vice versa.
If someone is curious then someone is generous or curious.
Everyone who is not old or tall is not wise or not patient.
Everyone who is wise or funny is either old or not patient.
Everyone who is not humble is not creative or old and vice versa.
Everyone who is wise or strong is either calm or not happy and vice versa.
Everyone who is not patient is both strong and not rich and vice versa.
Everyone who is funny or not wise is both not tall and humble.
Everyone who is not calm or not strong is both strong and humble and vice versa.
If paul is either not humble or not generous then someone is either patient or not rich and vice versa.
Someone is quiet.
Someone is not brave or curious.
Susan is either rich or not funny. | Fred is rich. | contradiction | ((?[X]:(~wise(X)))<=>((curious(fred)&brave(fred))))&
(![X]:((~tall(X)|quiet(X))<=>(kind(X)<~>happy(X))))&
(![X]:((~patient(X)|~strong(X))<=>~curious(X)))&
(![X]:((generous(X)|calm(X))=>(~old(X)<~>~strong(X))))&
(![X]:((~humble(X)&generous(X))<=>strong(X)))&
(((~rich(fred)<~>~funny(fred)))<=>((kind(paul)<~>creative(paul))))&
((?[X]:((~kind(X)&~creative(X))))<=>(~humble(paul)))&
((?[X]:(curious(X)))=>(?[X]:((generous(X)|curious(X)))))&
(![X]:((~old(X)|tall(X))=>(~wise(X)|~patient(X))))&
(![X]:((wise(X)|funny(X))=>(old(X)<~>~patient(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
(![X]:((wise(X)|strong(X))<=>(calm(X)<~>~happy(X))))&
(![X]:(~patient(X)<=>(strong(X)&~rich(X))))&
(![X]:((funny(X)|~wise(X))=>(~tall(X)&humble(X))))&
(![X]:((~calm(X)|~strong(X))<=>(strong(X)&humble(X))))&
(((~humble(paul)<~>~generous(paul)))<=>(?[X]:((patient(X)<~>~rich(X)))))&
(?[X]:(quiet(X)))&
(?[X]:((~brave(X)|curious(X))))&
((rich(susan)<~>~funny(susan))) | rich(fred) | [
"p3",
"p4",
"p8",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3422862516879105934793133
% SZS output start Proof for 3422862516879105934793133
4. ! [X0] : ((calm(X0) | generous(X0)) => (~old(X0) <~> ~strong(X0))) [input p3]
5. ! [X0] : ((generous(X0) & ~humble(X0)) <=> strong(X0)) [input p4]
9. ! [X0] : ((tall(X0) | ~old(X0)) => (~patient(X0) | ~wise(X0))) [input p8]
13. ! [X0] : (~patient(X0) <=> (~rich(X0) & strong(X0))) [input p12]
14. ! [X0] : ((~wise(X0) | funny(X0)) => (humble(X0) & ~tall(X0))) [input p13]
15. ! [X0] : ((~strong(X0) | ~calm(X0)) <=> (humble(X0) & strong(X0))) [input p14]
20. rich(fred) [input hypothesis]
22. ! [X0] : ((~old(X0) <~> ~strong(X0)) | (~calm(X0) & ~generous(X0))) [ennf transformation 4]
24. ! [X0] : ((~patient(X0) | ~wise(X0)) | (~tall(X0) & old(X0))) [ennf transformation 9]
25. ! [X0] : (~patient(X0) | ~wise(X0) | (~tall(X0) & old(X0))) [flattening 24]
27. ! [X0] : ((humble(X0) & ~tall(X0)) | (wise(X0) & ~funny(X0))) [ennf transformation 14]
37. ! [X0] : (((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (~calm(X0) & ~generous(X0))) [nnf transformation 22]
38. ! [X0] : (((generous(X0) & ~humble(X0)) | ~strong(X0)) & (strong(X0) | (~generous(X0) | humble(X0)))) [nnf transformation 5]
39. ! [X0] : (((generous(X0) & ~humble(X0)) | ~strong(X0)) & (strong(X0) | ~generous(X0) | humble(X0))) [flattening 38]
53. ! [X0] : ((~patient(X0) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | patient(X0))) [nnf transformation 13]
54. ! [X0] : ((~patient(X0) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | patient(X0))) [flattening 53]
55. ! [X0] : (((~strong(X0) | ~calm(X0)) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | (strong(X0) & calm(X0)))) [nnf transformation 15]
56. ! [X0] : ((~strong(X0) | ~calm(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | (strong(X0) & calm(X0)))) [flattening 55]
78. ~old(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 37]
83. ~humble(X0) | ~strong(X0) [cnf transformation 39]
84. ~strong(X0) | generous(X0) [cnf transformation 39]
97. ~patient(X0) | ~wise(X0) | old(X0) [cnf transformation 25]
113. ~rich(X0) | patient(X0) [cnf transformation 54]
118. humble(X0) | wise(X0) [cnf transformation 27]
120. strong(X0) | strong(X0) [cnf transformation 56]
136. rich(fred) [cnf transformation 20]
137. strong(X0) [duplicate literal removal 120]
153. 4 <=> ! [X1] : wise(X1) [avatar definition]
154. wise(X1) <- (4) [avatar component clause 153]
166. 7 <=> rich(fred) [avatar definition]
168. rich(fred) <- (7) [avatar component clause 166]
258. 7 [avatar split clause 136,166]
264. generous(X0) [resolution 84,137]
266. patient(fred) <- (7) [resolution 113,168]
269. wise(X2) | ~strong(X2) [resolution 118,83]
320. ~wise(fred) | old(fred) <- (7) [resolution 97,266]
321. old(fred) <- (4, 7) [subsumption resolution 320,154]
323. ~strong(fred) | ~generous(fred) <- (4, 7) [resolution 321,78]
328. ~generous(fred) <- (4, 7) [subsumption resolution 323,137]
329. $false <- (4, 7) [subsumption resolution 328,264]
330. ~4 | ~7 [avatar contradiction clause 329]
340. wise(X2) [subsumption resolution 269,137]
341. 4 [avatar split clause 340,153]
342. $false [avatar sat refutation 258,330,341]
% SZS output end Proof for 3422862516879105934793133
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not patient is generous and vice versa.
Everyone who is both patient and happy is old.
If someone is not wise or not calm then someone is both brave and strong and vice versa.
Everyone who is not patient is both rich and not calm and vice versa.
Everyone who is humble or not creative is wise or not tall and vice versa.
If someone is either not creative or not strong then mary is either curious or not tall and vice versa.
If mary is funny then someone is not humble or old.
If lucy is curious or not humble then someone is both not creative and tall.
If paul is calm or not humble then someone is wise or not humble.
Everyone who is kind is old or patient.
Everyone who is strong is both not old and not brave.
If alice is both happy and not curious then lucy is not creative.
Everyone who is either not tall or rich is humble or patient.
If susan is either funny or strong then someone is both old and not creative and vice versa.
If fred is not funny then someone is not generous or generous and vice versa.
Everyone who is either not strong or not creative is either curious or creative and vice versa.
Someone is both not quiet and humble.
Mary is happy.
Lucy is old.
Someone is either not rich or not humble.
Alice is not creative or not quiet.
Someone is strong or brave. | Alice is not creative. | neutral | (![X]:((strong(X)|~patient(X))<=>generous(X)))&
(![X]:((patient(X)&happy(X))=>old(X)))&
((?[X]:((~wise(X)|~calm(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:(~patient(X)<=>(rich(X)&~calm(X))))&
(![X]:((humble(X)|~creative(X))<=>(wise(X)|~tall(X))))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((curious(mary)<~>~tall(mary))))&
((funny(mary))=>(?[X]:((~humble(X)|old(X)))))&
(((curious(lucy)|~humble(lucy)))=>(?[X]:((~creative(X)&tall(X)))))&
(((calm(paul)|~humble(paul)))=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:(kind(X)=>(old(X)|patient(X))))&
(![X]:(strong(X)=>(~old(X)&~brave(X))))&
(((happy(alice)&~curious(alice)))=>(~creative(lucy)))&
(![X]:((~tall(X)<~>rich(X))=>(humble(X)|patient(X))))&
(((funny(susan)<~>strong(susan)))<=>(?[X]:((old(X)&~creative(X)))))&
((~funny(fred))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((~strong(X)<~>~creative(X))<=>(curious(X)<~>creative(X))))&
(?[X]:((~quiet(X)&humble(X))))&
(happy(mary))&
(old(lucy))&
(?[X]:((~rich(X)<~>~humble(X))))&
((~creative(alice)|~quiet(alice)))&
(?[X]:((strong(X)|brave(X)))) | ~creative(alice) | []
| null | 0 |
Everyone who is creative is both not calm and humble and vice versa.
Everyone who is kind or creative is not funny.
If susan is either old or not wise then lucy is not calm or generous.
If lucy is not strong then mary is both curious and not quiet.
Everyone who is not rich or old is creative and vice versa.
Everyone who is either not wise or humble is either humble or rich and vice versa.
If lucy is either not old or not patient then alice is not strong or humble.
Everyone who is either not patient or funny is funny and vice versa.
If someone is both kind and old then lucy is both wise and not strong and vice versa.
If john is either not calm or not humble then lucy is not generous or not calm.
If someone is both kind and not kind then paul is either not quiet or happy and vice versa.
Everyone who is either not rich or not happy is not generous.
Everyone who is either strong or calm is strong or not wise and vice versa.
If fred is both not funny and happy then paul is not quiet or kind.
If someone is both rich and not patient then susan is either not generous or not funny.
Everyone who is rich is either not calm or rich and vice versa.
Someone is not brave.
Lucy is curious or not funny.
Lucy is not old or not tall.
Fred is not funny or not happy.
Paul is either calm or strong.
Someone is either not brave or not wise. | Susan is humble. | neutral | (![X]:(creative(X)<=>(~calm(X)&humble(X))))&
(![X]:((kind(X)|creative(X))=>~funny(X)))&
(((old(susan)<~>~wise(susan)))=>((~calm(lucy)|generous(lucy))))&
((~strong(lucy))=>((curious(mary)&~quiet(mary))))&
(![X]:((~rich(X)|old(X))<=>creative(X)))&
(![X]:((~wise(X)<~>humble(X))<=>(humble(X)<~>rich(X))))&
(((~old(lucy)<~>~patient(lucy)))=>((~strong(alice)|humble(alice))))&
(![X]:((~patient(X)<~>funny(X))<=>funny(X)))&
((?[X]:((kind(X)&old(X))))<=>((wise(lucy)&~strong(lucy))))&
(((~calm(john)<~>~humble(john)))=>((~generous(lucy)|~calm(lucy))))&
((?[X]:((kind(X)&~kind(X))))<=>((~quiet(paul)<~>happy(paul))))&
(![X]:((~rich(X)<~>~happy(X))=>~generous(X)))&
(![X]:((strong(X)<~>calm(X))<=>(strong(X)|~wise(X))))&
(((~funny(fred)&happy(fred)))=>((~quiet(paul)|kind(paul))))&
((?[X]:((rich(X)&~patient(X))))=>((~generous(susan)<~>~funny(susan))))&
(![X]:(rich(X)<=>(~calm(X)<~>rich(X))))&
(?[X]:(~brave(X)))&
((curious(lucy)|~funny(lucy)))&
((~old(lucy)|~tall(lucy)))&
((~funny(fred)|~happy(fred)))&
((calm(paul)<~>strong(paul)))&
(?[X]:((~brave(X)<~>~wise(X)))) | humble(susan) | []
| null | 0 |
Everyone who is both tall and curious is not kind and vice versa.
Everyone who is both not tall and rich is old and vice versa.
Everyone who is either not old or not kind is both kind and not patient and vice versa.
Everyone who is both creative and not kind is either not tall or rich.
Everyone who is both not rich and not humble is not generous.
Everyone who is brave or not funny is kind or funny and vice versa.
Everyone who is kind or not humble is either wise or not creative.
If someone is both not calm and not funny then lucy is calm or not kind.
Everyone who is not generous or tall is curious and vice versa.
If someone is both not brave and funny then someone is either patient or creative and vice versa.
Everyone who is funny or not happy is funny and vice versa.
Everyone who is both generous and patient is kind or not tall.
Everyone who is not calm is not brave or humble and vice versa.
Everyone who is creative or not happy is funny.
Everyone who is generous or not wise is not calm or rich and vice versa.
If someone is generous or not happy then susan is either funny or not happy.
Someone is either quiet or not quiet.
John is not creative or not kind.
Lucy is strong.
John is either strong or tall.
Susan is either rich or funny.
Fred is quiet.
Someone is both old and not calm.
Someone is both not funny and quiet. | John is brave. | neutral | (![X]:((tall(X)&curious(X))<=>~kind(X)))&
(![X]:((~tall(X)&rich(X))<=>old(X)))&
(![X]:((~old(X)<~>~kind(X))<=>(kind(X)&~patient(X))))&
(![X]:((creative(X)&~kind(X))=>(~tall(X)<~>rich(X))))&
(![X]:((~rich(X)&~humble(X))=>~generous(X)))&
(![X]:((brave(X)|~funny(X))<=>(kind(X)|funny(X))))&
(![X]:((kind(X)|~humble(X))=>(wise(X)<~>~creative(X))))&
((?[X]:((~calm(X)&~funny(X))))=>((calm(lucy)|~kind(lucy))))&
(![X]:((~generous(X)|tall(X))<=>curious(X)))&
((?[X]:((~brave(X)&funny(X))))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((funny(X)|~happy(X))<=>funny(X)))&
(![X]:((generous(X)&patient(X))=>(kind(X)|~tall(X))))&
(![X]:(~calm(X)<=>(~brave(X)|humble(X))))&
(![X]:((creative(X)|~happy(X))=>funny(X)))&
(![X]:((generous(X)|~wise(X))<=>(~calm(X)|rich(X))))&
((?[X]:((generous(X)|~happy(X))))=>((funny(susan)<~>~happy(susan))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
((~creative(john)|~kind(john)))&
(strong(lucy))&
((strong(john)<~>tall(john)))&
((rich(susan)<~>funny(susan)))&
(quiet(fred))&
(?[X]:((old(X)&~calm(X))))&
(?[X]:((~funny(X)&quiet(X)))) | brave(john) | []
| null | 0 |
If someone is either wise or not strong then someone is both not tall and brave and vice versa.
If someone is humble or quiet then mary is either not curious or tall and vice versa.
If fred is brave or not old then fred is strong.
If someone is brave or not happy then someone is either humble or not calm and vice versa.
Everyone who is either not humble or rich is both calm and strong and vice versa.
If someone is wise then lucy is either not calm or not old and vice versa.
Everyone who is either not generous or not quiet is either brave or not quiet and vice versa.
If someone is not quiet or wise then mary is either kind or tall.
If alice is not patient or not happy then john is brave and vice versa.
Everyone who is not calm is both not strong and not wise and vice versa.
If someone is not patient then fred is either not quiet or wise.
Everyone who is kind or generous is not rich or wise.
If fred is either not patient or not funny then someone is wise and vice versa.
Everyone who is either not tall or not strong is both not creative and calm.
Everyone who is both tall and calm is not tall or not funny and vice versa.
Someone is either not curious or not rich.
Someone is either humble or not patient.
Lucy is kind.
Someone is not wise.
Paul is not old.
Lucy is old or funny.
Someone is not patient or not curious.
Susan is not curious or not patient. | Fred is wise. | contradiction | ((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((~tall(X)&brave(X)))))&
((?[X]:((humble(X)|quiet(X))))<=>((~curious(mary)<~>tall(mary))))&
(((brave(fred)|~old(fred)))=>(strong(fred)))&
((?[X]:((brave(X)|~happy(X))))<=>(?[X]:((humble(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>rich(X))<=>(calm(X)&strong(X))))&
((?[X]:(wise(X)))<=>((~calm(lucy)<~>~old(lucy))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(brave(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)|wise(X))))=>((kind(mary)<~>tall(mary))))&
(((~patient(alice)|~happy(alice)))<=>(brave(john)))&
(![X]:(~calm(X)<=>(~strong(X)&~wise(X))))&
((?[X]:(~patient(X)))=>((~quiet(fred)<~>wise(fred))))&
(![X]:((kind(X)|generous(X))=>(~rich(X)|wise(X))))&
(((~patient(fred)<~>~funny(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~creative(X)&calm(X))))&
(![X]:((tall(X)&calm(X))<=>(~tall(X)|~funny(X))))&
(?[X]:((~curious(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
(kind(lucy))&
(?[X]:(~wise(X)))&
(~old(paul))&
((old(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|~curious(X))))&
((~curious(susan)|~patient(susan))) | wise(fred) | [
"p5",
"p9",
"p13",
"p14",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 7962179977750314899975157
% SZS output start Proof for 7962179977750314899975157
6. ? [X0] : wise(X0) <=> (~calm(lucy) <~> ~old(lucy)) [input p5]
10. ! [X0] : (~calm(X0) <=> (~wise(X0) & ~strong(X0))) [input p9]
14. ! [X0] : ((~tall(X0) <~> ~strong(X0)) => (calm(X0) & ~creative(X0))) [input p13]
15. ! [X0] : ((calm(X0) & tall(X0)) <=> (~funny(X0) | ~tall(X0))) [input p14]
21. funny(lucy) | old(lucy) [input p20]
24. wise(fred) [input hypothesis]
27. ! [X0] : ((~tall(X0) <~> ~strong(X0)) => calm(X0)) [pure predicate removal 14]
33. ! [X0] : (calm(X0) | (~tall(X0) <=> ~strong(X0))) [ennf transformation 27]
50. (? [X0] : wise(X0) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X0] : ~wise(X0)) [nnf transformation 6]
51. (? [X0] : wise(X0) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X1] : ~wise(X1)) [rectify 50]
52. ? [X0] : wise(X0) => wise(sK5) [choice axiom]
53. (wise(sK5) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X1] : ~wise(X1)) [skolemisation 51,52]
58. ! [X0] : ((~calm(X0) | (wise(X0) | strong(X0))) & ((~wise(X0) & ~strong(X0)) | calm(X0))) [nnf transformation 10]
59. ! [X0] : ((~calm(X0) | wise(X0) | strong(X0)) & ((~wise(X0) & ~strong(X0)) | calm(X0))) [flattening 58]
65. ! [X0] : (calm(X0) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 33]
66. ! [X0] : (((calm(X0) & tall(X0)) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | (~calm(X0) | ~tall(X0)))) [nnf transformation 15]
67. ! [X0] : (((calm(X0) & tall(X0)) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | ~calm(X0) | ~tall(X0))) [flattening 66]
104. ~old(lucy) | ~calm(lucy) | ~wise(X1) [cnf transformation 53]
123. ~strong(X0) | calm(X0) [cnf transformation 59]
135. calm(X0) | ~tall(X0) | strong(X0) [cnf transformation 65]
136. ~funny(X0) | ~tall(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 67]
137. tall(X0) | tall(X0) [cnf transformation 67]
139. calm(X0) | tall(X0) [cnf transformation 67]
148. funny(lucy) | old(lucy) [cnf transformation 21]
151. wise(fred) [cnf transformation 24]
152. ~funny(X0) | ~tall(X0) | ~calm(X0) [duplicate literal removal 136]
153. tall(X0) [duplicate literal removal 137]
266. 25 <=> old(lucy) [avatar definition]
270. 26 <=> calm(lucy) [avatar definition]
272. ~calm(lucy) <- (~26) [avatar component clause 270]
280. 28 <=> ! [X1] : ~wise(X1) [avatar definition]
281. ~wise(X1) <- (28) [avatar component clause 280]
283. 28 | ~26 | ~25 [avatar split clause 104,266,270,280]
320. 36 <=> wise(fred) [avatar definition]
321. wise(fred) <- (36) [avatar component clause 320]
341. calm(X0) | ~tall(X0) [subsumption resolution 135,123]
342. calm(X0) [subsumption resolution 139,341]
343. ~funny(X0) | ~calm(X0) [subsumption resolution 152,153]
344. ~funny(X0) [subsumption resolution 343,342]
365. old(lucy) [subsumption resolution 148,344]
366. 25 [avatar split clause 365,266]
385. 36 [avatar split clause 151,320]
391. $false <- (28, 36) [resolution 321,281]
392. ~28 | ~36 [avatar contradiction clause 391]
393. $false <- (~26) [subsumption resolution 272,342]
394. 26 [avatar contradiction clause 393]
395. $false [avatar sat refutation 283,366,385,392,394]
% SZS output end Proof for 7962179977750314899975157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is calm or not brave. If fred is both not kind and not brave then alice is not tall or tall. If someone is both not quiet and kind then someone is strong. Everyone who is not strong or not rich is calm and vice versa. If mary is both not wise and not creative then mary is patient and vice versa. Everyone who is generous or not kind is both not curious and quiet. Everyone who is not brave or kind is strong or kind. Everyone who is not patient is not brave or wise. If someone is either not patient or humble then someone is patient and vice versa. If someone is not calm or kind then someone is either not kind or wise and vice versa. If john is either calm or not rich then lucy is curious and vice versa. Everyone who is either curious or quiet is both not creative and happy and vice versa. Everyone who is both not funny and not old is not rich or quiet and vice versa. Everyone who is not tall or creative is humble and vice versa. Everyone who is both not humble and patient is kind. If someone is not strong then someone is both curious and wise and vice versa. Mary is both quiet and happy. Alice is either not generous or curious. Susan is not happy or not calm. Mary is curious or wise. Someone is either funny or not wise. John is not funny or rich. Paul is either not calm or not patient. | Susan is not humble. | neutral | (![X]:(~humble(X)=>(calm(X)|~brave(X))))&
(((~kind(fred)&~brave(fred)))=>((~tall(alice)|tall(alice))))&
((?[X]:((~quiet(X)&kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|~rich(X))<=>calm(X)))&
(((~wise(mary)&~creative(mary)))<=>(patient(mary)))&
(![X]:((generous(X)|~kind(X))=>(~curious(X)&quiet(X))))&
(![X]:((~brave(X)|kind(X))=>(strong(X)|kind(X))))&
(![X]:(~patient(X)=>(~brave(X)|wise(X))))&
((?[X]:((~patient(X)<~>humble(X))))<=>(?[X]:(patient(X))))&
((?[X]:((~calm(X)|kind(X))))<=>(?[X]:((~kind(X)<~>wise(X)))))&
(((calm(john)<~>~rich(john)))<=>(curious(lucy)))&
(![X]:((curious(X)<~>quiet(X))<=>(~creative(X)&happy(X))))&
(![X]:((~funny(X)&~old(X))<=>(~rich(X)|quiet(X))))&
(![X]:((~tall(X)|creative(X))<=>humble(X)))&
(![X]:((~humble(X)&patient(X))=>kind(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((curious(X)&wise(X)))))&
((quiet(mary)&happy(mary)))&
((~generous(alice)<~>curious(alice)))&
((~happy(susan)|~calm(susan)))&
((curious(mary)|wise(mary)))&
(?[X]:((funny(X)<~>~wise(X))))&
((~funny(john)|rich(john)))&
((~calm(paul)<~>~patient(paul))) | ~humble(susan) | []
| null | 0 |
If lucy is not old or not wise then alice is creative.
Everyone who is both creative and tall is kind and vice versa.
If someone is either not brave or rich then fred is not wise and vice versa.
Everyone who is either curious or not creative is kind or happy.
If someone is both not rich and patient then someone is both not creative and not tall and vice versa.
Everyone who is both not tall and not brave is both not kind and not tall and vice versa.
Everyone who is both patient and curious is either not calm or happy and vice versa.
Everyone who is not happy or curious is either old or not wise and vice versa.
If mary is either not strong or humble then someone is not wise or tall.
Everyone who is both not creative and not kind is humble or generous and vice versa.
If someone is either wise or quiet then someone is tall and vice versa.
Everyone who is kind or not creative is both not quiet and generous and vice versa.
Everyone who is not wise or not old is not generous.
Everyone who is not rich or not curious is not wise.
If alice is not kind or not curious then someone is either humble or strong and vice versa.
Lucy is either not funny or old.
John is not patient.
John is humble or not funny.
Someone is not calm.
Susan is either tall or brave.
Someone is calm.
Someone is funny. | Susan is creative. | contradiction | (((~old(lucy)|~wise(lucy)))=>(creative(alice)))&
(![X]:((creative(X)&tall(X))<=>kind(X)))&
((?[X]:((~brave(X)<~>rich(X))))<=>(~wise(fred)))&
(![X]:((curious(X)<~>~creative(X))=>(kind(X)|happy(X))))&
((?[X]:((~rich(X)&patient(X))))<=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~tall(X)&~brave(X))<=>(~kind(X)&~tall(X))))&
(![X]:((patient(X)&curious(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~happy(X)|curious(X))<=>(old(X)<~>~wise(X))))&
(((~strong(mary)<~>humble(mary)))=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:((~creative(X)&~kind(X))<=>(humble(X)|generous(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)|~creative(X))<=>(~quiet(X)&generous(X))))&
(![X]:((~wise(X)|~old(X))=>~generous(X)))&
(![X]:((~rich(X)|~curious(X))=>~wise(X)))&
(((~kind(alice)|~curious(alice)))<=>(?[X]:((humble(X)<~>strong(X)))))&
((~funny(lucy)<~>old(lucy)))&
(~patient(john))&
((humble(john)|~funny(john)))&
(?[X]:(~calm(X)))&
((tall(susan)<~>brave(susan)))&
(?[X]:(calm(X)))&
(?[X]:(funny(X))) | creative(susan) | [
"p1",
"p5",
"p9",
"p11",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 4106901373410393173453759
% SZS output start Proof for 4106901373410393173453759
2. ! [X0] : ((tall(X0) & creative(X0)) <=> kind(X0)) [input p1]
6. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (~tall(X0) & ~kind(X0))) [input p5]
10. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (generous(X0) | humble(X0))) [input p9]
12. ! [X0] : ((~creative(X0) | kind(X0)) <=> (generous(X0) & ~quiet(X0))) [input p11]
20. tall(susan) <~> brave(susan) [input p19]
23. creative(susan) [input hypothesis]
32. ! [X0] : (((tall(X0) & creative(X0)) | ~kind(X0)) & (kind(X0) | (~tall(X0) | ~creative(X0)))) [nnf transformation 2]
33. ! [X0] : (((tall(X0) & creative(X0)) | ~kind(X0)) & (kind(X0) | ~tall(X0) | ~creative(X0))) [flattening 32]
44. ! [X0] : (((~brave(X0) & ~tall(X0)) | (tall(X0) | kind(X0))) & ((~tall(X0) & ~kind(X0)) | (brave(X0) | tall(X0)))) [nnf transformation 6]
45. ! [X0] : (((~brave(X0) & ~tall(X0)) | tall(X0) | kind(X0)) & ((~tall(X0) & ~kind(X0)) | brave(X0) | tall(X0))) [flattening 44]
53. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 10]
54. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | kind(X0) | creative(X0))) [flattening 53]
60. ! [X0] : (((~creative(X0) | kind(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (creative(X0) & ~kind(X0)))) [nnf transformation 12]
61. ! [X0] : ((~creative(X0) | kind(X0) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | (creative(X0) & ~kind(X0)))) [flattening 60]
70. (~brave(susan) | ~tall(susan)) & (brave(susan) | tall(susan)) [nnf transformation 20]
77. ~tall(X0) | kind(X0) | ~creative(X0) [cnf transformation 33]
79. ~kind(X0) | tall(X0) [cnf transformation 33]
93. ~brave(X0) | tall(X0) | kind(X0) [cnf transformation 45]
112. ~generous(X0) | ~kind(X0) [cnf transformation 54]
119. generous(X0) | ~kind(X0) [cnf transformation 61]
137. brave(susan) | tall(susan) [cnf transformation 70]
138. ~brave(susan) | ~tall(susan) [cnf transformation 70]
141. creative(susan) [cnf transformation 23]
205. ~brave(X0) | tall(X0) [subsumption resolution 93,79]
250. ~kind(X0) [subsumption resolution 119,112]
284. ~brave(susan) [subsumption resolution 138,205]
285. tall(susan) [subsumption resolution 137,284]
301. kind(susan) | ~creative(susan) [resolution 77,285]
303. ~creative(susan) [subsumption resolution 301,250]
304. $false [subsumption resolution 303,141]
% SZS output end Proof for 4106901373410393173453759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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