premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is both calm and not happy is either not wise or funny.
Everyone who is either old or wise is not wise or generous and vice versa.
Everyone who is happy or curious is both strong and not curious and vice versa.
Everyone who is patient or funny is both humble and not wise and vice versa.
If someone is wise or humble then someone is either not old or brave and vice versa.
Everyone who is generous or not generous is not funny or not humble.
If paul is either funny or not wise then someone is not rich and vice versa.
Everyone who is both generous and strong is both not quiet and strong and vice versa.
Everyone who is either not creative or patient is not old.
Everyone who is not tall is both not humble and humble and vice versa.
Everyone who is both not brave and brave is humble or not curious.
If susan is both not creative and not old then someone is not quiet or not tall.
Everyone who is both not rich and funny is old or not humble and vice versa.
If someone is not generous then paul is strong.
If someone is wise or generous then fred is either not wise or kind and vice versa.
Everyone who is either humble or kind is both not brave and not kind and vice versa.
Alice is either not strong or not generous.
Someone is not patient.
Fred is either quiet or not generous.
Someone is either rich or kind.
Alice is not old.
Someone is not quiet.
Paul is not brave or not funny. | Fred is not strong. | entailment | (![X]:((calm(X)&~happy(X))=>(~wise(X)<~>funny(X))))&
(![X]:((old(X)<~>wise(X))<=>(~wise(X)|generous(X))))&
(![X]:((happy(X)|curious(X))<=>(strong(X)&~curious(X))))&
(![X]:((patient(X)|funny(X))<=>(humble(X)&~wise(X))))&
((?[X]:((wise(X)|humble(X))))<=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((generous(X)|~generous(X))=>(~funny(X)|~humble(X))))&
(((funny(paul)<~>~wise(paul)))<=>(?[X]:(~rich(X))))&
(![X]:((generous(X)&strong(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~creative(X)<~>patient(X))=>~old(X)))&
(![X]:(~tall(X)<=>(~humble(X)&humble(X))))&
(![X]:((~brave(X)&brave(X))=>(humble(X)|~curious(X))))&
(((~creative(susan)&~old(susan)))=>(?[X]:((~quiet(X)|~tall(X)))))&
(![X]:((~rich(X)&funny(X))<=>(old(X)|~humble(X))))&
((?[X]:(~generous(X)))=>(strong(paul)))&
((?[X]:((wise(X)|generous(X))))<=>((~wise(fred)<~>kind(fred))))&
(![X]:((humble(X)<~>kind(X))<=>(~brave(X)&~kind(X))))&
((~strong(alice)<~>~generous(alice)))&
(?[X]:(~patient(X)))&
((quiet(fred)<~>~generous(fred)))&
(?[X]:((rich(X)<~>kind(X))))&
(~old(alice))&
(?[X]:(~quiet(X)))&
((~brave(paul)|~funny(paul))) | ~strong(fred) | [
"p1",
"p3",
"p5",
"p7",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2887833247337844919808813
% SZS output start Proof for 2887833247337844919808813
2. ! [X0] : ((old(X0) <~> wise(X0)) <=> (generous(X0) | ~wise(X0))) [input p1]
4. ! [X0] : ((funny(X0) | patient(X0)) <=> (~wise(X0) & humble(X0))) [input p3]
6. ! [X0] : ((~generous(X0) | generous(X0)) => (~humble(X0) | ~funny(X0))) [input p5]
8. ! [X0] : ((strong(X0) & generous(X0)) <=> (strong(X0) & ~quiet(X0))) [input p7]
13. ! [X0] : ((funny(X0) & ~rich(X0)) <=> (~humble(X0) | old(X0))) [input p12]
19. quiet(fred) <~> ~generous(fred) [input p18]
24. strong(fred) [input hypothesis]
28. ! [X0] : ((~humble(X0) | ~funny(X0)) | (generous(X0) & ~generous(X0))) [ennf transformation 6]
29. ! [X0] : (~humble(X0) | ~funny(X0) | (generous(X0) & ~generous(X0))) [flattening 28]
37. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [flattening 37]
41. ! [X0] : (((funny(X0) | patient(X0)) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | (~funny(X0) & ~patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((funny(X0) | patient(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | (~funny(X0) & ~patient(X0)))) [flattening 41]
52. ! [X0] : (((strong(X0) & generous(X0)) | (~strong(X0) | quiet(X0))) & ((strong(X0) & ~quiet(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 8]
53. ! [X0] : (((strong(X0) & generous(X0)) | ~strong(X0) | quiet(X0)) & ((strong(X0) & ~quiet(X0)) | ~strong(X0) | ~generous(X0))) [flattening 52]
57. ! [X0] : (((funny(X0) & ~rich(X0)) | (humble(X0) & ~old(X0))) & ((~humble(X0) | old(X0)) | (~funny(X0) | rich(X0)))) [nnf transformation 13]
58. ! [X0] : (((funny(X0) & ~rich(X0)) | (humble(X0) & ~old(X0))) & (~humble(X0) | old(X0) | ~funny(X0) | rich(X0))) [flattening 57]
68. (generous(fred) | ~quiet(fred)) & (~generous(fred) | quiet(fred)) [nnf transformation 19]
75. generous(X0) | ~wise(X0) | old(X0) | ~wise(X0) [cnf transformation 38]
76. wise(X0) | old(X0) | wise(X0) [cnf transformation 38]
86. ~funny(X0) | humble(X0) [cnf transformation 42]
96. ~humble(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 29]
97. ~humble(X0) | ~funny(X0) | generous(X0) [cnf transformation 29]
102. ~quiet(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 53]
115. funny(X0) | ~old(X0) [cnf transformation 58]
133. ~generous(fred) | quiet(fred) [cnf transformation 68]
140. strong(fred) [cnf transformation 24]
145. generous(X0) | ~wise(X0) | old(X0) [duplicate literal removal 75]
146. old(X0) | wise(X0) [duplicate literal removal 76]
147. generous(X0) | old(X0) [subsumption resolution 145,146]
182. ~funny(X0) | generous(X0) [subsumption resolution 97,86]
183. ~funny(X0) | ~generous(X0) [subsumption resolution 96,86]
184. ~funny(X0) [subsumption resolution 183,182]
216. ~old(X0) [subsumption resolution 115,184]
262. 24 <=> quiet(fred) [avatar definition]
263. quiet(fred) <- (24) [avatar component clause 262]
266. 25 <=> generous(fred) [avatar definition]
267. ~generous(fred) <- (~25) [avatar component clause 266]
268. generous(fred) <- (25) [avatar component clause 266]
270. 24 | ~25 [avatar split clause 133,266,262]
291. old(fred) <- (~25) [resolution 147,267]
294. $false <- (~25) [subsumption resolution 291,216]
295. 25 [avatar contradiction clause 294]
303. ~strong(fred) | ~generous(fred) <- (24) [resolution 102,263]
304. ~generous(fred) <- (24) [subsumption resolution 303,140]
305. $false <- (24, 25) [subsumption resolution 304,268]
306. ~24 | ~25 [avatar contradiction clause 305]
307. $false [avatar sat refutation 270,295,306]
% SZS output end Proof for 2887833247337844919808813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or generous is both wise and curious.
If fred is either not calm or tall then fred is generous or strong.
Everyone who is both tall and curious is either patient or not humble.
If lucy is either creative or not creative then paul is funny or happy and vice versa.
Everyone who is both tall and humble is patient or calm.
If someone is either not quiet or not brave then someone is not humble and vice versa.
If someone is funny then mary is not generous.
If someone is both not old and not rich then someone is either strong or curious.
Everyone who is both not tall and not brave is not funny or not brave and vice versa.
If mary is strong then someone is brave.
If someone is both patient and not old then alice is both wise and happy and vice versa.
If someone is both not brave and not generous then john is both not strong and tall.
If someone is not rich then someone is both funny and curious.
If mary is not wise then someone is either not tall or curious and vice versa.
If someone is both humble and not creative then someone is not tall.
If susan is not rich or not generous then someone is humble or kind and vice versa.
Someone is brave or not quiet.
John is not creative or brave.
Someone is not old.
Mary is either not happy or not wise.
Someone is either not calm or kind.
Susan is generous or old.
Someone is not curious or generous.
Someone is not generous. | Mary is generous. | contradiction | (![X]:((~quiet(X)<~>generous(X))=>(wise(X)&curious(X))))&
(((~calm(fred)<~>tall(fred)))=>((generous(fred)|strong(fred))))&
(![X]:((tall(X)&curious(X))=>(patient(X)<~>~humble(X))))&
(((creative(lucy)<~>~creative(lucy)))<=>((funny(paul)|happy(paul))))&
(![X]:((tall(X)&humble(X))=>(patient(X)|calm(X))))&
((?[X]:((~quiet(X)<~>~brave(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(funny(X)))=>(~generous(mary)))&
((?[X]:((~old(X)&~rich(X))))=>(?[X]:((strong(X)<~>curious(X)))))&
(![X]:((~tall(X)&~brave(X))<=>(~funny(X)|~brave(X))))&
((strong(mary))=>(?[X]:(brave(X))))&
((?[X]:((patient(X)&~old(X))))<=>((wise(alice)&happy(alice))))&
((?[X]:((~brave(X)&~generous(X))))=>((~strong(john)&tall(john))))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)&curious(X)))))&
((~wise(mary))<=>(?[X]:((~tall(X)<~>curious(X)))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:(~tall(X))))&
(((~rich(susan)|~generous(susan)))<=>(?[X]:((humble(X)|kind(X)))))&
(?[X]:((brave(X)|~quiet(X))))&
((~creative(john)|brave(john)))&
(?[X]:(~old(X)))&
((~happy(mary)<~>~wise(mary)))&
(?[X]:((~calm(X)<~>kind(X))))&
((generous(susan)|old(susan)))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:(~generous(X))) | generous(mary) | [
"p6",
"p8",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 228954137170577899251599
% SZS output start Proof for 228954137170577899251599
7. ? [X0] : funny(X0) => ~generous(mary) [input p6]
9. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (~brave(X0) | ~funny(X0))) [input p8]
12. ? [X0] : (~generous(X0) & ~brave(X0)) => (tall(john) & ~strong(john)) [input p11]
24. ? [X0] : ~generous(X0) [input p23]
25. generous(mary) [input hypothesis]
37. ~generous(mary) | ! [X0] : ~funny(X0) [ennf transformation 7]
40. (tall(john) & ~strong(john)) | ! [X0] : (generous(X0) | brave(X0)) [ennf transformation 12]
57. ! [X0] : (((~brave(X0) & ~tall(X0)) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | (brave(X0) | tall(X0)))) [nnf transformation 9]
58. ! [X0] : (((~brave(X0) & ~tall(X0)) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | brave(X0) | tall(X0))) [flattening 57]
91. ? [X0] : ~generous(X0) => ~generous(sK13) [choice axiom]
92. ~generous(sK13) [skolemisation 24,91]
112. ~generous(mary) | ~funny(X0) [cnf transformation 37]
116. ~tall(X0) | funny(X0) [cnf transformation 58]
118. ~brave(X0) | funny(X0) [cnf transformation 58]
126. tall(john) | generous(X0) | brave(X0) [cnf transformation 40]
147. ~generous(sK13) [cnf transformation 92]
148. generous(mary) [cnf transformation 25]
209. 14 <=> ! [X0] : ~funny(X0) [avatar definition]
210. ~funny(X0) <- (14) [avatar component clause 209]
212. 15 <=> generous(mary) [avatar definition]
215. 14 | ~15 [avatar split clause 112,212,209]
262. 26 <=> ! [X0] : (generous(X0) | brave(X0)) [avatar definition]
263. brave(X0) | generous(X0) <- (26) [avatar component clause 262]
265. 27 <=> tall(john) [avatar definition]
267. tall(john) <- (27) [avatar component clause 265]
268. 26 | 27 [avatar split clause 126,265,262]
391. 15 [avatar split clause 148,212]
397. generous(X0) | funny(X0) <- (26) [resolution 263,118]
398. generous(X0) <- (14, 26) [subsumption resolution 397,210]
405. $false <- (14, 26) [resolution 398,147]
406. ~14 | ~26 [avatar contradiction clause 405]
409. funny(john) <- (27) [resolution 267,116]
413. $false <- (14, 27) [subsumption resolution 409,210]
414. ~14 | ~27 [avatar contradiction clause 413]
415. $false [avatar sat refutation 215,268,391,406,414]
% SZS output end Proof for 228954137170577899251599
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and not old then john is both quiet and wise.
If mary is not rich or not quiet then susan is either not humble or happy.
If someone is both curious and not strong then someone is kind.
Everyone who is not generous or patient is both wise and not wise and vice versa.
If someone is quiet or rich then someone is either curious or not rich and vice versa.
If someone is either not patient or not tall then someone is either not rich or creative and vice versa.
Everyone who is either not brave or strong is not quiet or patient and vice versa.
Everyone who is not tall is either not patient or calm.
If someone is both old and humble then susan is not wise or not old and vice versa.
If someone is both old and not old then someone is either not humble or kind and vice versa.
If someone is both not brave and not funny then susan is not brave or strong and vice versa.
Everyone who is either happy or not brave is humble or not happy and vice versa.
If john is both not rich and not happy then someone is not wise and vice versa.
If lucy is both not happy and old then someone is happy or not creative.
Everyone who is not patient is both happy and creative.
Everyone who is creative or old is not humble.
Susan is either wise or not creative.
Someone is quiet or not brave.
Someone is either quiet or not quiet. | Susan is not kind. | contradiction | ((?[X]:((~tall(X)&~old(X))))=>((quiet(john)&wise(john))))&
(((~rich(mary)|~quiet(mary)))=>((~humble(susan)<~>happy(susan))))&
((?[X]:((curious(X)&~strong(X))))=>(?[X]:(kind(X))))&
(![X]:((~generous(X)|patient(X))<=>(wise(X)&~wise(X))))&
((?[X]:((quiet(X)|rich(X))))<=>(?[X]:((curious(X)<~>~rich(X)))))&
((?[X]:((~patient(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(~quiet(X)|patient(X))))&
(![X]:(~tall(X)=>(~patient(X)<~>calm(X))))&
((?[X]:((old(X)&humble(X))))<=>((~wise(susan)|~old(susan))))&
((?[X]:((old(X)&~old(X))))<=>(?[X]:((~humble(X)<~>kind(X)))))&
((?[X]:((~brave(X)&~funny(X))))<=>((~brave(susan)|strong(susan))))&
(![X]:((happy(X)<~>~brave(X))<=>(humble(X)|~happy(X))))&
(((~rich(john)&~happy(john)))<=>(?[X]:(~wise(X))))&
(((~happy(lucy)&old(lucy)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:(~patient(X)=>(happy(X)&creative(X))))&
(![X]:((creative(X)|old(X))=>~humble(X)))&
((wise(susan)<~>~creative(susan)))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((quiet(X)<~>~quiet(X)))) | ~kind(susan) | [
"p3",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3419093512915607874942779
% SZS output start Proof for 3419093512915607874942779
4. ! [X0] : ((patient(X0) | ~generous(X0)) <=> (~wise(X0) & wise(X0))) [input p3]
10. ? [X0] : (~old(X0) & old(X0)) <=> ? [X0] : (~humble(X0) <~> kind(X0)) [input p9]
15. ! [X0] : (~patient(X0) => (creative(X0) & happy(X0))) [input p14]
16. ! [X0] : ((old(X0) | creative(X0)) => ~humble(X0)) [input p15]
20. ~kind(susan) [input hypothesis]
24. ? [X0] : (~old(X0) & old(X0)) <=> ? [X1] : (~humble(X1) <~> kind(X1)) [rectify 10]
31. ! [X0] : ((creative(X0) & happy(X0)) | patient(X0)) [ennf transformation 15]
32. ! [X0] : (~humble(X0) | (~old(X0) & ~creative(X0))) [ennf transformation 16]
37. ! [X0] : (((patient(X0) | ~generous(X0)) | (wise(X0) | ~wise(X0))) & ((~wise(X0) & wise(X0)) | (~patient(X0) & generous(X0)))) [nnf transformation 4]
38. ! [X0] : ((patient(X0) | ~generous(X0) | wise(X0) | ~wise(X0)) & ((~wise(X0) & wise(X0)) | (~patient(X0) & generous(X0)))) [flattening 37]
57. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (? [X1] : ((~kind(X1) | humble(X1)) & (kind(X1) | ~humble(X1))) | ! [X0] : (old(X0) | ~old(X0))) [nnf transformation 24]
58. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (? [X2] : ((~kind(X2) | humble(X2)) & (kind(X2) | ~humble(X2))) | ! [X3] : (old(X3) | ~old(X3))) [rectify 57]
59. ? [X0] : (~old(X0) & old(X0)) => (~old(sK6) & old(sK6)) [choice axiom]
60. ? [X2] : ((~kind(X2) | humble(X2)) & (kind(X2) | ~humble(X2))) => ((~kind(sK7) | humble(sK7)) & (kind(sK7) | ~humble(sK7))) [choice axiom]
61. ((~old(sK6) & old(sK6)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (((~kind(sK7) | humble(sK7)) & (kind(sK7) | ~humble(sK7))) | ! [X3] : (old(X3) | ~old(X3))) [skolemisation 58,60,59]
90. wise(X0) | ~patient(X0) [cnf transformation 38]
92. ~wise(X0) | ~patient(X0) [cnf transformation 38]
123. old(sK6) | kind(X1) | humble(X1) [cnf transformation 61]
125. ~old(sK6) | kind(X1) | humble(X1) [cnf transformation 61]
143. creative(X0) | patient(X0) [cnf transformation 31]
144. ~humble(X0) | ~creative(X0) [cnf transformation 32]
151. ~kind(susan) [cnf transformation 20]
195. ~patient(X0) [subsumption resolution 90,92]
291. 30 <=> old(sK6) [avatar definition]
296. 31 <=> ! [X1] : (kind(X1) | humble(X1)) [avatar definition]
297. kind(X1) | humble(X1) <- (31) [avatar component clause 296]
298. 31 | ~30 [avatar split clause 125,291,296]
300. 31 | 30 [avatar split clause 123,291,296]
361. creative(X0) [subsumption resolution 143,195]
364. ~humble(X0) [subsumption resolution 144,361]
378. kind(X1) <- (31) [subsumption resolution 297,364]
393. $false <- (31) [resolution 378,151]
394. ~31 [avatar contradiction clause 393]
395. $false [avatar sat refutation 298,300,394]
% SZS output end Proof for 3419093512915607874942779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and happy is both not old and curious.
If someone is both not wise and old then lucy is both not strong and not rich and vice versa.
Everyone who is not happy or creative is both not tall and funny.
Everyone who is not old or not humble is both kind and not curious.
If john is not old then lucy is both not patient and old.
Everyone who is wise or not rich is both not rich and not old.
Everyone who is not wise is humble or not kind and vice versa.
If alice is either not wise or curious then someone is not old and vice versa.
If alice is both not kind and not humble then mary is tall.
If fred is patient or not funny then someone is either happy or curious and vice versa.
If someone is not creative then mary is either calm or not kind.
If someone is both not tall and patient then someone is both not curious and not old.
Lucy is generous.
Someone is either not creative or not curious.
Alice is not quiet or not calm.
Mary is either not patient or not creative.
Someone is not rich. | Fred is not strong. | neutral | (![X]:((~wise(X)&happy(X))=>(~old(X)&curious(X))))&
((?[X]:((~wise(X)&old(X))))<=>((~strong(lucy)&~rich(lucy))))&
(![X]:((~happy(X)|creative(X))=>(~tall(X)&funny(X))))&
(![X]:((~old(X)|~humble(X))=>(kind(X)&~curious(X))))&
((~old(john))=>((~patient(lucy)&old(lucy))))&
(![X]:((wise(X)|~rich(X))=>(~rich(X)&~old(X))))&
(![X]:(~wise(X)<=>(humble(X)|~kind(X))))&
(((~wise(alice)<~>curious(alice)))<=>(?[X]:(~old(X))))&
(((~kind(alice)&~humble(alice)))=>(tall(mary)))&
(((patient(fred)|~funny(fred)))<=>(?[X]:((happy(X)<~>curious(X)))))&
((?[X]:(~creative(X)))=>((calm(mary)<~>~kind(mary))))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(generous(lucy))&
(?[X]:((~creative(X)<~>~curious(X))))&
((~quiet(alice)|~calm(alice)))&
((~patient(mary)<~>~creative(mary)))&
(?[X]:(~rich(X))) | ~strong(fred) | [] | null | 0 |
Everyone who is both rich and curious is both not calm and humble.
If susan is not tall then someone is either humble or not tall and vice versa.
Everyone who is kind is either generous or patient and vice versa.
Everyone who is humble or creative is both calm and not humble and vice versa.
If someone is both humble and creative then someone is wise and vice versa.
Everyone who is strong is wise and vice versa.
Everyone who is either not humble or not rich is not happy.
If fred is kind then alice is creative or happy.
If mary is not brave then someone is rich and vice versa.
If fred is quiet then mary is generous or humble and vice versa.
Everyone who is curious is not kind and vice versa.
Everyone who is not creative or not happy is both not rich and calm and vice versa.
If alice is patient then someone is not generous and vice versa.
If mary is either tall or not quiet then fred is curious or not quiet.
Everyone who is not humble is either not quiet or not patient.
Everyone who is either not creative or patient is both tall and generous.
John is either rich or not rich.
Lucy is both tall and patient.
Someone is not curious.
Mary is not patient.
Someone is quiet. | Susan is strong. | contradiction | (![X]:((rich(X)&curious(X))=>(~calm(X)&humble(X))))&
((~tall(susan))<=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:(kind(X)<=>(generous(X)<~>patient(X))))&
(![X]:((humble(X)|creative(X))<=>(calm(X)&~humble(X))))&
((?[X]:((humble(X)&creative(X))))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>wise(X)))&
(![X]:((~humble(X)<~>~rich(X))=>~happy(X)))&
((kind(fred))=>((creative(alice)|happy(alice))))&
((~brave(mary))<=>(?[X]:(rich(X))))&
((quiet(fred))<=>((generous(mary)|humble(mary))))&
(![X]:(curious(X)<=>~kind(X)))&
(![X]:((~creative(X)|~happy(X))<=>(~rich(X)&calm(X))))&
((patient(alice))<=>(?[X]:(~generous(X))))&
(((tall(mary)<~>~quiet(mary)))=>((curious(fred)|~quiet(fred))))&
(![X]:(~humble(X)=>(~quiet(X)<~>~patient(X))))&
(![X]:((~creative(X)<~>patient(X))=>(tall(X)&generous(X))))&
((rich(john)<~>~rich(john)))&
((tall(lucy)&patient(lucy)))&
(?[X]:(~curious(X)))&
(~patient(mary))&
(?[X]:(quiet(X))) | strong(susan) | [
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4832501501788520935541989
% SZS output start Proof for 4832501501788520935541989
4. ! [X0] : ((creative(X0) | humble(X0)) <=> (~humble(X0) & calm(X0))) [input p3]
5. ? [X0] : (creative(X0) & humble(X0)) <=> ? [X0] : wise(X0) [input p4]
6. ! [X0] : (strong(X0) <=> wise(X0)) [input p5]
22. strong(susan) [input hypothesis]
23. ? [X0] : (creative(X0) & humble(X0)) <=> ? [X1] : wise(X1) [rectify 5]
24. ! [X0] : (strong(X0) => wise(X0)) [unused predicate definition removal 6]
27. ! [X0] : (wise(X0) | ~strong(X0)) [ennf transformation 24]
40. ! [X0] : (((creative(X0) | humble(X0)) | (humble(X0) | ~calm(X0))) & ((~humble(X0) & calm(X0)) | (~creative(X0) & ~humble(X0)))) [nnf transformation 4]
41. ! [X0] : ((creative(X0) | humble(X0) | humble(X0) | ~calm(X0)) & ((~humble(X0) & calm(X0)) | (~creative(X0) & ~humble(X0)))) [flattening 40]
42. (? [X0] : (creative(X0) & humble(X0)) | ! [X1] : ~wise(X1)) & (? [X1] : wise(X1) | ! [X0] : (~creative(X0) | ~humble(X0))) [nnf transformation 23]
43. (? [X0] : (creative(X0) & humble(X0)) | ! [X1] : ~wise(X1)) & (? [X2] : wise(X2) | ! [X3] : (~creative(X3) | ~humble(X3))) [rectify 42]
44. ? [X0] : (creative(X0) & humble(X0)) => (creative(sK1) & humble(sK1)) [choice axiom]
45. ? [X2] : wise(X2) => wise(sK2) [choice axiom]
46. ((creative(sK1) & humble(sK1)) | ! [X1] : ~wise(X1)) & (wise(sK2) | ! [X3] : (~creative(X3) | ~humble(X3))) [skolemisation 43,45,44]
81. ~humble(X0) | ~humble(X0) [cnf transformation 41]
85. humble(sK1) | ~wise(X1) [cnf transformation 46]
87. ~strong(X0) | wise(X0) [cnf transformation 27]
120. strong(susan) [cnf transformation 22]
121. ~humble(X0) [duplicate literal removal 81]
146. 6 <=> ! [X1] : ~wise(X1) [avatar definition]
147. ~wise(X1) <- (6) [avatar component clause 146]
153. ~wise(X1) [subsumption resolution 85,121]
154. 6 [avatar split clause 153,146]
229. wise(susan) [resolution 87,120]
230. $false <- (6) [subsumption resolution 229,147]
231. ~6 [avatar contradiction clause 230]
232. $false [avatar sat refutation 154,231]
% SZS output end Proof for 4832501501788520935541989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not curious then john is not quiet. Everyone who is creative or humble is either generous or curious. Everyone who is not humble or not calm is brave or creative and vice versa. Everyone who is both not tall and tall is either not rich or not strong and vice versa. If alice is both patient and humble then someone is both kind and not curious and vice versa. Everyone who is not strong is either not humble or not patient and vice versa. If someone is both generous and not wise then someone is either strong or not rich and vice versa. If paul is brave or not wise then someone is both not happy and not calm and vice versa. If someone is quiet then john is funny or not patient. If someone is calm or not patient then susan is both not wise and not brave. If someone is either humble or creative then john is wise and vice versa. Everyone who is rich or not quiet is both humble and not quiet. Everyone who is not old is both brave and not old. If someone is funny or not creative then fred is strong or kind and vice versa. If someone is tall or calm then someone is not patient or not humble and vice versa. Everyone who is both not patient and funny is kind or not generous and vice versa. John is kind. Mary is either wise or calm. Paul is generous or not calm. Alice is patient or not wise. Susan is either not strong or curious. Fred is curious. Lucy is both not calm and creative. Mary is either humble or not wise. | Fred is not funny. | contradiction | ((?[X]:((~rich(X)|~curious(X))))=>(~quiet(john)))&
(![X]:((creative(X)|humble(X))=>(generous(X)<~>curious(X))))&
(![X]:((~humble(X)|~calm(X))<=>(brave(X)|creative(X))))&
(![X]:((~tall(X)&tall(X))<=>(~rich(X)<~>~strong(X))))&
(((patient(alice)&humble(alice)))<=>(?[X]:((kind(X)&~curious(X)))))&
(![X]:(~strong(X)<=>(~humble(X)<~>~patient(X))))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(((brave(paul)|~wise(paul)))<=>(?[X]:((~happy(X)&~calm(X)))))&
((?[X]:(quiet(X)))=>((funny(john)|~patient(john))))&
((?[X]:((calm(X)|~patient(X))))=>((~wise(susan)&~brave(susan))))&
((?[X]:((humble(X)<~>creative(X))))<=>(wise(john)))&
(![X]:((rich(X)|~quiet(X))=>(humble(X)&~quiet(X))))&
(![X]:(~old(X)=>(brave(X)&~old(X))))&
((?[X]:((funny(X)|~creative(X))))<=>((strong(fred)|kind(fred))))&
((?[X]:((tall(X)|calm(X))))<=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:((~patient(X)&funny(X))<=>(kind(X)|~generous(X))))&
(kind(john))&
((wise(mary)<~>calm(mary)))&
((generous(paul)|~calm(paul)))&
((patient(alice)|~wise(alice)))&
((~strong(susan)<~>curious(susan)))&
(curious(fred))&
((~calm(lucy)&creative(lucy)))&
((humble(mary)<~>~wise(mary))) | ~funny(fred) | [
"p1",
"p3",
"p11",
"p13",
"p15",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8482308811330133054258054
% SZS output start Proof for 8482308811330133054258054
2. ! [X0] : ((humble(X0) | creative(X0)) => (generous(X0) <~> curious(X0))) [input p1]
4. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p3]
12. ! [X0] : ((~quiet(X0) | rich(X0)) => (~quiet(X0) & humble(X0))) [input p11]
14. ? [X0] : (~creative(X0) | funny(X0)) <=> (kind(fred) | strong(fred)) [input p13]
16. ! [X0] : ((funny(X0) & ~patient(X0)) <=> (~generous(X0) | kind(X0))) [input p15]
17. kind(john) [input p16]
22. curious(fred) [input p21]
25. ~funny(fred) [input hypothesis]
29. ! [X0] : ((generous(X0) <~> curious(X0)) | (~humble(X0) & ~creative(X0))) [ennf transformation 2]
33. ! [X0] : ((~quiet(X0) & humble(X0)) | (quiet(X0) & ~rich(X0))) [ennf transformation 12]
35. ! [X0] : (((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (~humble(X0) & ~creative(X0))) [nnf transformation 29]
38. ! [X0] : (((tall(X0) & ~tall(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~tall(X0) | tall(X0)))) [nnf transformation 4]
39. ! [X0] : (((tall(X0) & ~tall(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | ~tall(X0) | tall(X0))) [flattening 38]
60. (? [X0] : (~creative(X0) | funny(X0)) | (~kind(fred) & ~strong(fred))) & ((kind(fred) | strong(fred)) | ! [X0] : (creative(X0) & ~funny(X0))) [nnf transformation 14]
61. (? [X0] : (~creative(X0) | funny(X0)) | (~kind(fred) & ~strong(fred))) & (kind(fred) | strong(fred) | ! [X0] : (creative(X0) & ~funny(X0))) [flattening 60]
62. (? [X0] : (~creative(X0) | funny(X0)) | (~kind(fred) & ~strong(fred))) & (kind(fred) | strong(fred) | ! [X1] : (creative(X1) & ~funny(X1))) [rectify 61]
63. ? [X0] : (~creative(X0) | funny(X0)) => (~creative(sK5) | funny(sK5)) [choice axiom]
64. ((~creative(sK5) | funny(sK5)) | (~kind(fred) & ~strong(fred))) & (kind(fred) | strong(fred) | ! [X1] : (creative(X1) & ~funny(X1))) [skolemisation 62,63]
70. ! [X0] : (((funny(X0) & ~patient(X0)) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | (~funny(X0) | patient(X0)))) [nnf transformation 16]
71. ! [X0] : (((funny(X0) & ~patient(X0)) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | ~funny(X0) | patient(X0))) [flattening 70]
80. ~generous(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 35]
87. ~tall(X0) | ~strong(X0) | rich(X0) [cnf transformation 39]
89. tall(X0) | ~strong(X0) | rich(X0) [cnf transformation 39]
119. ~rich(X0) | humble(X0) [cnf transformation 33]
125. kind(fred) | strong(fred) | ~funny(X1) [cnf transformation 64]
136. ~kind(X0) | funny(X0) [cnf transformation 71]
137. funny(X0) | generous(X0) [cnf transformation 71]
138. kind(john) [cnf transformation 17]
145. curious(fred) [cnf transformation 22]
150. ~funny(fred) [cnf transformation 25]
164. ~strong(X0) | rich(X0) [subsumption resolution 87,89]
287. 30 <=> kind(fred) [avatar definition]
288. kind(fred) <- (30) [avatar component clause 287]
300. 33 <=> strong(fred) [avatar definition]
301. strong(fred) <- (33) [avatar component clause 300]
309. 35 <=> ! [X1] : ~funny(X1) [avatar definition]
310. ~funny(X1) <- (35) [avatar component clause 309]
311. 35 | 33 | 30 [avatar split clause 125,287,300,309]
407. funny(john) [resolution 136,138]
409. funny(fred) <- (30) [resolution 136,288]
410. $false <- (30) [subsumption resolution 409,150]
411. ~30 [avatar contradiction clause 410]
421. $false <- (35) [subsumption resolution 407,310]
422. ~35 [avatar contradiction clause 421]
426. generous(fred) [resolution 137,150]
427. rich(fred) <- (33) [resolution 164,301]
447. humble(fred) <- (33) [resolution 427,119]
503. ~curious(fred) | ~humble(fred) [resolution 80,426]
504. ~humble(fred) [subsumption resolution 503,145]
505. $false <- (33) [subsumption resolution 504,447]
506. ~33 [avatar contradiction clause 505]
507. $false [avatar sat refutation 311,411,422,506]
% SZS output end Proof for 8482308811330133054258054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and rich then susan is both old and kind.
Everyone who is humble is either not brave or not rich and vice versa.
Everyone who is generous or not funny is not old and vice versa.
If someone is rich or kind then alice is both curious and humble.
Everyone who is strong is both rich and not old and vice versa.
If susan is not curious or brave then someone is both wise and not quiet.
Everyone who is either not humble or rich is patient or wise.
If someone is both quiet and not tall then someone is kind and vice versa.
If paul is creative or not quiet then someone is wise or calm and vice versa.
If someone is both not brave and not patient then john is both generous and not generous.
Everyone who is not funny is generous or not funny.
Everyone who is not patient or kind is both not strong and not humble and vice versa.
Everyone who is strong is funny or wise.
Everyone who is funny or not strong is happy or quiet.
Everyone who is old or kind is funny.
Everyone who is both not wise and not kind is not old and vice versa.
Someone is funny.
Mary is either quiet or not generous.
Susan is either not creative or not strong.
John is happy or not patient.
Fred is not funny.
Alice is both happy and not wise.
Paul is generous or not old.
Someone is wise. | Mary is generous. | neutral | ((?[X]:((creative(X)&rich(X))))=>((old(susan)&kind(susan))))&
(![X]:(humble(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((generous(X)|~funny(X))<=>~old(X)))&
((?[X]:((rich(X)|kind(X))))=>((curious(alice)&humble(alice))))&
(![X]:(strong(X)<=>(rich(X)&~old(X))))&
(((~curious(susan)|brave(susan)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(patient(X)|wise(X))))&
((?[X]:((quiet(X)&~tall(X))))<=>(?[X]:(kind(X))))&
(((creative(paul)|~quiet(paul)))<=>(?[X]:((wise(X)|calm(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((generous(john)&~generous(john))))&
(![X]:(~funny(X)=>(generous(X)|~funny(X))))&
(![X]:((~patient(X)|kind(X))<=>(~strong(X)&~humble(X))))&
(![X]:(strong(X)=>(funny(X)|wise(X))))&
(![X]:((funny(X)|~strong(X))=>(happy(X)|quiet(X))))&
(![X]:((old(X)|kind(X))=>funny(X)))&
(![X]:((~wise(X)&~kind(X))<=>~old(X)))&
(?[X]:(funny(X)))&
((quiet(mary)<~>~generous(mary)))&
((~creative(susan)<~>~strong(susan)))&
((happy(john)|~patient(john)))&
(~funny(fred))&
((happy(alice)&~wise(alice)))&
((generous(paul)|~old(paul)))&
(?[X]:(wise(X))) | generous(mary) | [] | null | 0 |
If lucy is either creative or not funny then john is either not strong or patient and vice versa.
Everyone who is funny or patient is not calm.
If fred is both not strong and rich then fred is not creative and vice versa.
Everyone who is wise or not humble is either not happy or calm and vice versa.
If paul is both funny and generous then fred is either not creative or not calm and vice versa.
Everyone who is either not patient or not funny is both curious and not patient.
Everyone who is both not rich and generous is either generous or not humble and vice versa.
Everyone who is either funny or calm is not kind or calm and vice versa.
If someone is both wise and not old then someone is not creative or not rich and vice versa.
If john is both not brave and brave then someone is wise and vice versa.
If susan is either not creative or humble then alice is not old.
Everyone who is both brave and not wise is either generous or not quiet.
Everyone who is either not quiet or not kind is calm.
Everyone who is either not strong or not curious is either tall or generous and vice versa.
If someone is either wise or strong then paul is calm and vice versa.
If paul is either not old or not happy then someone is either not quiet or not funny and vice versa.
Someone is either patient or strong.
Someone is either curious or rich.
Mary is funny or brave.
Someone is either strong or not happy.
Paul is not calm or not kind.
Paul is not kind or rich.
Mary is both not funny and not strong.
Susan is not brave or calm. | Fred is not patient. | entailment | (((creative(lucy)<~>~funny(lucy)))<=>((~strong(john)<~>patient(john))))&
(![X]:((funny(X)|patient(X))=>~calm(X)))&
(((~strong(fred)&rich(fred)))<=>(~creative(fred)))&
(![X]:((wise(X)|~humble(X))<=>(~happy(X)<~>calm(X))))&
(((funny(paul)&generous(paul)))<=>((~creative(fred)<~>~calm(fred))))&
(![X]:((~patient(X)<~>~funny(X))=>(curious(X)&~patient(X))))&
(![X]:((~rich(X)&generous(X))<=>(generous(X)<~>~humble(X))))&
(![X]:((funny(X)<~>calm(X))<=>(~kind(X)|calm(X))))&
((?[X]:((wise(X)&~old(X))))<=>(?[X]:((~creative(X)|~rich(X)))))&
(((~brave(john)&brave(john)))<=>(?[X]:(wise(X))))&
(((~creative(susan)<~>humble(susan)))=>(~old(alice)))&
(![X]:((brave(X)&~wise(X))=>(generous(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>calm(X)))&
(![X]:((~strong(X)<~>~curious(X))<=>(tall(X)<~>generous(X))))&
((?[X]:((wise(X)<~>strong(X))))<=>(calm(paul)))&
(((~old(paul)<~>~happy(paul)))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(?[X]:((patient(X)<~>strong(X))))&
(?[X]:((curious(X)<~>rich(X))))&
((funny(mary)|brave(mary)))&
(?[X]:((strong(X)<~>~happy(X))))&
((~calm(paul)|~kind(paul)))&
((~kind(paul)|rich(paul)))&
((~funny(mary)&~strong(mary)))&
((~brave(susan)|calm(susan))) | ~patient(fred) | [
"p1",
"p2",
"p4",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5793365219085755344338554
% SZS output start Proof for 5793365219085755344338554
2. ! [X0] : ((patient(X0) | funny(X0)) => ~calm(X0)) [input p1]
3. (rich(fred) & ~strong(fred)) <=> ~creative(fred) [input p2]
5. (generous(paul) & funny(paul)) <=> (~creative(fred) <~> ~calm(fred)) [input p4]
9. ? [X0] : (~old(X0) & wise(X0)) <=> ? [X0] : (~rich(X0) | ~creative(X0)) [input p8]
10. (brave(john) & ~brave(john)) <=> ? [X0] : wise(X0) [input p9]
15. ? [X0] : (wise(X0) <~> strong(X0)) <=> calm(paul) [input p14]
25. patient(fred) [input hypothesis]
26. ? [X0] : (~old(X0) & wise(X0)) <=> ? [X1] : (~rich(X1) | ~creative(X1)) [rectify 9]
27. ! [X0] : (~calm(X0) | (~patient(X0) & ~funny(X0))) [ennf transformation 2]
34. ((rich(fred) & ~strong(fred)) | creative(fred)) & (~creative(fred) | (~rich(fred) | strong(fred))) [nnf transformation 3]
35. ((rich(fred) & ~strong(fred)) | creative(fred)) & (~creative(fred) | ~rich(fred) | strong(fred)) [flattening 34]
38. ((generous(paul) & funny(paul)) | ((~creative(fred) | calm(fred)) & (~calm(fred) | creative(fred)))) & (((calm(fred) | creative(fred)) & (~calm(fred) | ~creative(fred))) | (~generous(paul) | ~funny(paul))) [nnf transformation 5]
39. ((generous(paul) & funny(paul)) | ((~creative(fred) | calm(fred)) & (~calm(fred) | creative(fred)))) & (((calm(fred) | creative(fred)) & (~calm(fred) | ~creative(fred))) | ~generous(paul) | ~funny(paul)) [flattening 38]
45. (? [X0] : (~old(X0) & wise(X0)) | ! [X1] : (rich(X1) & creative(X1))) & (? [X1] : (~rich(X1) | ~creative(X1)) | ! [X0] : (old(X0) | ~wise(X0))) [nnf transformation 26]
46. (? [X0] : (~old(X0) & wise(X0)) | ! [X1] : (rich(X1) & creative(X1))) & (? [X2] : (~rich(X2) | ~creative(X2)) | ! [X3] : (old(X3) | ~wise(X3))) [rectify 45]
47. ? [X0] : (~old(X0) & wise(X0)) => (~old(sK0) & wise(sK0)) [choice axiom]
48. ? [X2] : (~rich(X2) | ~creative(X2)) => (~rich(sK1) | ~creative(sK1)) [choice axiom]
49. ((~old(sK0) & wise(sK0)) | ! [X1] : (rich(X1) & creative(X1))) & ((~rich(sK1) | ~creative(sK1)) | ! [X3] : (old(X3) | ~wise(X3))) [skolemisation 46,48,47]
50. ((brave(john) & ~brave(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (~brave(john) | brave(john))) [nnf transformation 10]
51. ((brave(john) & ~brave(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | ~brave(john) | brave(john)) [flattening 50]
52. ((brave(john) & ~brave(john)) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | ~brave(john) | brave(john)) [rectify 51]
53. ? [X1] : wise(X1) => wise(sK2) [choice axiom]
54. ((brave(john) & ~brave(john)) | ! [X0] : ~wise(X0)) & (wise(sK2) | ~brave(john) | brave(john)) [skolemisation 52,53]
59. (? [X0] : ((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | ~calm(paul)) & (calm(paul) | ! [X0] : ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0)))) [nnf transformation 15]
60. (? [X0] : ((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | ~calm(paul)) & (calm(paul) | ! [X1] : ((wise(X1) | ~strong(X1)) & (strong(X1) | ~wise(X1)))) [rectify 59]
61. ? [X0] : ((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) => ((~strong(sK3) | ~wise(sK3)) & (strong(sK3) | wise(sK3))) [choice axiom]
62. (((~strong(sK3) | ~wise(sK3)) & (strong(sK3) | wise(sK3))) | ~calm(paul)) & (calm(paul) | ! [X1] : ((wise(X1) | ~strong(X1)) & (strong(X1) | ~wise(X1)))) [skolemisation 60,61]
84. ~calm(X0) | ~funny(X0) [cnf transformation 27]
85. ~calm(X0) | ~patient(X0) [cnf transformation 27]
86. ~creative(fred) | ~rich(fred) | strong(fred) [cnf transformation 35]
98. funny(paul) | ~creative(fred) | calm(fred) [cnf transformation 39]
118. wise(sK0) | creative(X1) [cnf transformation 49]
119. wise(sK0) | rich(X1) [cnf transformation 49]
123. ~brave(john) | ~wise(X0) [cnf transformation 54]
124. brave(john) | ~wise(X0) [cnf transformation 54]
140. calm(paul) | wise(X1) | ~strong(X1) [cnf transformation 62]
163. patient(fred) [cnf transformation 25]
194. 5 <=> creative(fred) [avatar definition]
195. ~creative(fred) <- (~5) [avatar component clause 194]
198. 6 <=> rich(fred) [avatar definition]
199. ~rich(fred) <- (~6) [avatar component clause 198]
203. 7 <=> strong(fred) [avatar definition]
204. strong(fred) <- (7) [avatar component clause 203]
207. 7 | ~6 | ~5 [avatar split clause 86,194,198,203]
209. 8 <=> calm(fred) [avatar definition]
211. calm(fred) <- (8) [avatar component clause 209]
219. 10 <=> funny(paul) [avatar definition]
222. 8 | ~5 | 10 [avatar split clause 98,219,194,209]
229. 11 <=> ! [X1] : rich(X1) [avatar definition]
230. rich(X1) <- (11) [avatar component clause 229]
237. 13 <=> ! [X1] : creative(X1) [avatar definition]
238. creative(X1) <- (13) [avatar component clause 237]
241. 14 <=> wise(sK0) [avatar definition]
243. wise(sK0) <- (14) [avatar component clause 241]
244. 11 | 14 [avatar split clause 119,241,229]
245. 13 | 14 [avatar split clause 118,241,237]
259. 18 <=> ! [X0] : ~wise(X0) [avatar definition]
260. ~wise(X0) <- (18) [avatar component clause 259]
262. 19 <=> brave(john) [avatar definition]
265. 18 | 19 [avatar split clause 124,262,259]
266. 18 | ~19 [avatar split clause 123,262,259]
282. 23 <=> calm(paul) [avatar definition]
283. calm(paul) <- (23) [avatar component clause 282]
296. 26 <=> ! [X1] : (wise(X1) | ~strong(X1)) [avatar definition]
297. wise(X1) | ~strong(X1) <- (26) [avatar component clause 296]
298. 26 | 23 [avatar split clause 140,282,296]
392. $false <- (14, 18) [subsumption resolution 243,260]
393. ~14 | ~18 [avatar contradiction clause 392]
395. $false <- (~5, 13) [resolution 238,195]
396. 5 | ~13 [avatar contradiction clause 395]
398. $false <- (~6, 11) [subsumption resolution 199,230]
399. 6 | ~11 [avatar contradiction clause 398]
409. ~funny(paul) <- (23) [resolution 84,283]
410. ~patient(fred) <- (8) [resolution 85,211]
412. $false <- (8) [subsumption resolution 410,163]
413. ~8 [avatar contradiction clause 412]
414. ~10 | ~23 [avatar split clause 409,282,219]
415. ~strong(X1) <- (18, 26) [subsumption resolution 297,260]
416. $false <- (7, 18, 26) [resolution 415,204]
419. ~7 | ~18 | ~26 [avatar contradiction clause 416]
420. $false [avatar sat refutation 207,222,244,245,265,266,298,393,396,399,413,414,419]
% SZS output end Proof for 5793365219085755344338554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not funny and vice versa. Everyone who is generous is tall and vice versa. If fred is not brave then someone is either creative or not happy and vice versa. If paul is both not strong and not old then someone is not tall or not brave and vice versa. Everyone who is not rich is strong and vice versa. If alice is both not creative and not wise then alice is not rich or humble and vice versa. If someone is calm or happy then fred is either not wise or not generous. Everyone who is both not wise and not kind is quiet and vice versa. If fred is not wise or not humble then alice is either strong or patient. Everyone who is both not patient and tall is both not curious and not calm. If someone is not happy then paul is both rich and not happy. If someone is either not brave or not strong then someone is rich or quiet. Everyone who is both not quiet and strong is not brave or creative and vice versa. Everyone who is brave or not quiet is not wise. Everyone who is either happy or not brave is both not curious and quiet. If someone is not brave then alice is both not happy and wise and vice versa. Fred is rich or not generous. Someone is generous. Lucy is not curious or not tall. Susan is both not generous and humble. Someone is either creative or not creative. Someone is not kind or not generous. | Alice is not calm. | neutral | (![X]:(~wise(X)<=>~funny(X)))&
(![X]:(generous(X)<=>tall(X)))&
((~brave(fred))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
(((~creative(alice)&~wise(alice)))<=>((~rich(alice)|humble(alice))))&
((?[X]:((calm(X)|happy(X))))=>((~wise(fred)<~>~generous(fred))))&
(![X]:((~wise(X)&~kind(X))<=>quiet(X)))&
(((~wise(fred)|~humble(fred)))=>((strong(alice)<~>patient(alice))))&
(![X]:((~patient(X)&tall(X))=>(~curious(X)&~calm(X))))&
((?[X]:(~happy(X)))=>((rich(paul)&~happy(paul))))&
((?[X]:((~brave(X)<~>~strong(X))))=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~brave(X)|creative(X))))&
(![X]:((brave(X)|~quiet(X))=>~wise(X)))&
(![X]:((happy(X)<~>~brave(X))=>(~curious(X)&quiet(X))))&
((?[X]:(~brave(X)))<=>((~happy(alice)&wise(alice))))&
((rich(fred)|~generous(fred)))&
(?[X]:(generous(X)))&
((~curious(lucy)|~tall(lucy)))&
((~generous(susan)&humble(susan)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:((~kind(X)|~generous(X)))) | ~calm(alice) | [] | null | 0 |
Everyone who is both old and not quiet is both not humble and not old. Everyone who is humble or not strong is wise or not old. If lucy is both strong and not old then someone is both funny and not funny and vice versa. If mary is rich or not tall then fred is brave and vice versa. Everyone who is brave or not humble is curious. Everyone who is either not kind or patient is tall or brave and vice versa. If someone is not funny or patient then fred is both not calm and strong. Everyone who is generous or not funny is either quiet or not kind. If someone is either not happy or not strong then someone is not generous. Everyone who is either not tall or patient is patient and vice versa. If someone is both not funny and not calm then alice is not humble and vice versa. Everyone who is either generous or happy is not wise or happy and vice versa. Everyone who is creative or tall is both patient and old. Everyone who is both not calm and funny is both not old and generous. Everyone who is humble is both kind and happy. Someone is both funny and rich. Someone is happy or wise. Mary is not wise or funny. Someone is not happy. Someone is humble or rich. Someone is either not brave or generous. Susan is either strong or not kind. | Susan is not brave. | neutral | (![X]:((old(X)&~quiet(X))=>(~humble(X)&~old(X))))&
(![X]:((humble(X)|~strong(X))=>(wise(X)|~old(X))))&
(((strong(lucy)&~old(lucy)))<=>(?[X]:((funny(X)&~funny(X)))))&
(((rich(mary)|~tall(mary)))<=>(brave(fred)))&
(![X]:((brave(X)|~humble(X))=>curious(X)))&
(![X]:((~kind(X)<~>patient(X))<=>(tall(X)|brave(X))))&
((?[X]:((~funny(X)|patient(X))))=>((~calm(fred)&strong(fred))))&
(![X]:((generous(X)|~funny(X))=>(quiet(X)<~>~kind(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)<~>patient(X))<=>patient(X)))&
((?[X]:((~funny(X)&~calm(X))))<=>(~humble(alice)))&
(![X]:((generous(X)<~>happy(X))<=>(~wise(X)|happy(X))))&
(![X]:((creative(X)|tall(X))=>(patient(X)&old(X))))&
(![X]:((~calm(X)&funny(X))=>(~old(X)&generous(X))))&
(![X]:(humble(X)=>(kind(X)&happy(X))))&
(?[X]:((funny(X)&rich(X))))&
(?[X]:((happy(X)|wise(X))))&
((~wise(mary)|funny(mary)))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)|rich(X))))&
(?[X]:((~brave(X)<~>generous(X))))&
((strong(susan)<~>~kind(susan))) | ~brave(susan) | [] | null | 0 |
If someone is both humble and funny then someone is calm or old. If someone is either not humble or not quiet then lucy is either not creative or kind. Everyone who is both old and tall is either not kind or quiet and vice versa. Everyone who is patient is old or not patient and vice versa. Everyone who is both quiet and calm is both not brave and not happy. Everyone who is either creative or old is not old. Everyone who is both not creative and curious is either humble or not curious and vice versa. If lucy is not humble then paul is not kind or not creative. If someone is either humble or not calm then someone is not curious and vice versa. Everyone who is generous is both not generous and funny. If fred is creative or not happy then lucy is not curious or not humble and vice versa. If someone is humble then mary is both not calm and curious and vice versa. Everyone who is not funny is brave. Everyone who is either not brave or not rich is both not patient and not generous. Everyone who is both tall and not brave is not tall and vice versa. Everyone who is not creative or wise is calm or rich and vice versa. Susan is not patient or not humble. Someone is both brave and not kind. Someone is strong. Someone is either creative or not kind. Alice is not kind. Someone is either not happy or not funny. | Fred is quiet. | neutral | ((?[X]:((humble(X)&funny(X))))=>(?[X]:((calm(X)|old(X)))))&
((?[X]:((~humble(X)<~>~quiet(X))))=>((~creative(lucy)<~>kind(lucy))))&
(![X]:((old(X)&tall(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:(patient(X)<=>(old(X)|~patient(X))))&
(![X]:((quiet(X)&calm(X))=>(~brave(X)&~happy(X))))&
(![X]:((creative(X)<~>old(X))=>~old(X)))&
(![X]:((~creative(X)&curious(X))<=>(humble(X)<~>~curious(X))))&
((~humble(lucy))=>((~kind(paul)|~creative(paul))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:(~curious(X))))&
(![X]:(generous(X)=>(~generous(X)&funny(X))))&
(((creative(fred)|~happy(fred)))<=>((~curious(lucy)|~humble(lucy))))&
((?[X]:(humble(X)))<=>((~calm(mary)&curious(mary))))&
(![X]:(~funny(X)=>brave(X)))&
(![X]:((~brave(X)<~>~rich(X))=>(~patient(X)&~generous(X))))&
(![X]:((tall(X)&~brave(X))<=>~tall(X)))&
(![X]:((~creative(X)|wise(X))<=>(calm(X)|rich(X))))&
((~patient(susan)|~humble(susan)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:(strong(X)))&
(?[X]:((creative(X)<~>~kind(X))))&
(~kind(alice))&
(?[X]:((~happy(X)<~>~funny(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is happy or not patient is either not funny or creative and vice versa. Everyone who is not creative or not happy is wise and vice versa. Everyone who is generous or not creative is both calm and quiet and vice versa. Everyone who is either kind or creative is not brave or calm and vice versa. Everyone who is humble is either not humble or humble and vice versa. Everyone who is either old or strong is both not rich and not happy. Everyone who is not calm or not funny is either not happy or wise. If someone is either brave or calm then susan is both not quiet and not wise. If someone is either quiet or not generous then someone is not tall or quiet. If someone is not creative then someone is both not funny and brave and vice versa. Everyone who is not funny is both tall and not calm. If mary is not generous then susan is not curious. Everyone who is rich or generous is quiet. If mary is not old or quiet then someone is not tall and vice versa. If mary is either rich or not curious then someone is either not humble or funny. Everyone who is not calm or brave is either not funny or happy and vice versa. Paul is not old. Susan is brave or strong. Someone is old or generous. Someone is either rich or not generous. Someone is quiet. Alice is not happy. | Susan is not brave. | contradiction | (![X]:((happy(X)|~patient(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~creative(X)|~happy(X))<=>wise(X)))&
(![X]:((generous(X)|~creative(X))<=>(calm(X)&quiet(X))))&
(![X]:((kind(X)<~>creative(X))<=>(~brave(X)|calm(X))))&
(![X]:(humble(X)<=>(~humble(X)<~>humble(X))))&
(![X]:((old(X)<~>strong(X))=>(~rich(X)&~happy(X))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)<~>wise(X))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(((~old(mary)|quiet(mary)))<=>(?[X]:(~tall(X))))&
(((rich(mary)<~>~curious(mary)))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|brave(X))<=>(~funny(X)<~>happy(X))))&
(~old(paul))&
((brave(susan)|strong(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:(quiet(X)))&
(~happy(alice)) | ~brave(susan) | [
"p1",
"p6",
"p7",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3509283272427330659179111
% SZS output start Proof for 3509283272427330659179111
2. ! [X0] : ((~happy(X0) | ~creative(X0)) <=> wise(X0)) [input p1]
7. ! [X0] : ((~funny(X0) | ~calm(X0)) => (~happy(X0) <~> wise(X0))) [input p6]
8. ? [X0] : (brave(X0) <~> calm(X0)) => (~wise(susan) & ~quiet(susan)) [input p7]
11. ! [X0] : (~funny(X0) => (~calm(X0) & tall(X0))) [input p10]
16. ! [X0] : ((brave(X0) | ~calm(X0)) <=> (~funny(X0) <~> happy(X0))) [input p15]
22. ~happy(alice) [input p21]
23. ~brave(susan) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> wise(X0)) | (funny(X0) & calm(X0))) [ennf transformation 7]
28. (~wise(susan) & ~quiet(susan)) | ! [X0] : (brave(X0) <=> calm(X0)) [ennf transformation 8]
30. ! [X0] : ((~calm(X0) & tall(X0)) | funny(X0)) [ennf transformation 11]
36. ! [X0] : (((~happy(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [flattening 36]
44. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (funny(X0) & calm(X0))) [nnf transformation 27]
45. (~wise(susan) & ~quiet(susan)) | ! [X0] : ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))) [nnf transformation 28]
63. ! [X0] : (((brave(X0) | ~calm(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [nnf transformation 16]
64. ! [X0] : ((brave(X0) | ~calm(X0) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [flattening 63]
79. wise(X0) | happy(X0) [cnf transformation 37]
100. wise(X0) | ~happy(X0) | calm(X0) [cnf transformation 44]
102. ~wise(X0) | happy(X0) | calm(X0) [cnf transformation 44]
107. ~wise(susan) | brave(X0) | ~calm(X0) [cnf transformation 45]
114. ~calm(X0) | funny(X0) [cnf transformation 30]
126. happy(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 64]
127. ~happy(X0) | funny(X0) | calm(X0) [cnf transformation 64]
130. brave(X0) | ~calm(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 64]
137. ~happy(alice) [cnf transformation 22]
138. ~brave(susan) [cnf transformation 23]
146. calm(X0) | happy(X0) [subsumption resolution 102,79]
148. calm(X0) | wise(X0) [subsumption resolution 100,146]
150. 1 <=> ! [X0] : (brave(X0) | ~calm(X0)) [avatar definition]
151. ~calm(X0) | brave(X0) <- (1) [avatar component clause 150]
153. 2 <=> wise(susan) [avatar definition]
156. 1 | ~2 [avatar split clause 107,153,150]
249. ~calm(X0) | brave(X0) | ~happy(X0) [subsumption resolution 130,114]
252. funny(X0) | calm(X0) [subsumption resolution 127,146]
253. funny(X0) [subsumption resolution 252,114]
254. ~brave(X0) | happy(X0) [subsumption resolution 126,253]
256. 23 <=> brave(susan) [avatar definition]
257. ~brave(susan) <- (~23) [avatar component clause 256]
283. ~23 [avatar split clause 138,256]
317. brave(X0) | ~happy(X0) | wise(X0) [resolution 249,148]
320. brave(X0) | wise(X0) [subsumption resolution 317,79]
321. wise(susan) <- (~23) [resolution 320,257]
326. 2 | 23 [avatar split clause 321,256,153]
338. brave(X1) | happy(X1) <- (1) [resolution 151,146]
340. happy(X1) <- (1) [subsumption resolution 338,254]
341. $false <- (1) [resolution 340,137]
346. ~1 [avatar contradiction clause 341]
347. $false [avatar sat refutation 156,283,326,346]
% SZS output end Proof for 3509283272427330659179111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not kind or old. Everyone who is both curious and not strong is both not generous and not tall. If someone is both generous and patient then someone is not calm. Everyone who is both creative and humble is either wise or not creative. Everyone who is both happy and brave is not tall or quiet and vice versa. Everyone who is brave is calm or humble. Everyone who is either funny or not calm is humble or curious. Everyone who is not calm or not tall is rich and vice versa. If someone is not wise or happy then alice is both brave and wise and vice versa. If someone is either wise or patient then someone is not patient or not kind. If someone is generous or not generous then john is quiet. Everyone who is both not wise and not rich is not kind or not creative and vice versa. If john is not strong then someone is either quiet or humble and vice versa. Everyone who is both kind and not curious is either not rich or not curious. If someone is quiet or not creative then someone is not calm. Someone is either not quiet or not rich. John is old or strong. Alice is both not strong and not patient. Someone is both not wise and not brave. Alice is rich or humble. | John is wise. | neutral | (![X]:(wise(X)=>(~kind(X)<~>old(X))))&
(![X]:((curious(X)&~strong(X))=>(~generous(X)&~tall(X))))&
((?[X]:((generous(X)&patient(X))))=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&humble(X))=>(wise(X)<~>~creative(X))))&
(![X]:((happy(X)&brave(X))<=>(~tall(X)|quiet(X))))&
(![X]:(brave(X)=>(calm(X)|humble(X))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((~calm(X)|~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)|happy(X))))<=>((brave(alice)&wise(alice))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(quiet(john)))&
(![X]:((~wise(X)&~rich(X))<=>(~kind(X)|~creative(X))))&
((~strong(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((kind(X)&~curious(X))=>(~rich(X)<~>~curious(X))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:(~calm(X))))&
(?[X]:((~quiet(X)<~>~rich(X))))&
((old(john)|strong(john)))&
((~strong(alice)&~patient(alice)))&
(?[X]:((~wise(X)&~brave(X))))&
((rich(alice)|humble(alice))) | wise(john) | [] | null | 0 |
Everyone who is calm is both not rich and not strong.
Everyone who is happy is either tall or not creative and vice versa.
Everyone who is both not tall and kind is both not patient and tall.
If someone is not wise or funny then someone is both quiet and not rich.
Everyone who is both not humble and patient is both patient and wise.
Everyone who is not rich is either quiet or patient and vice versa.
Everyone who is not generous is both calm and not tall and vice versa.
Everyone who is not patient or wise is both not old and happy.
If someone is creative then john is not patient or brave and vice versa.
Everyone who is either not tall or wise is both rich and not curious and vice versa.
Everyone who is curious is not calm or not humble and vice versa.
If john is both not happy and patient then someone is either not strong or not wise and vice versa.
If someone is both funny and patient then mary is kind.
Everyone who is not rich or not strong is both funny and old and vice versa.
Mary is not humble.
Mary is both quiet and strong.
Someone is either not patient or not rich.
Someone is either calm or quiet.
Someone is both patient and wise.
Alice is either brave or not happy. | John is not rich. | contradiction | (![X]:(calm(X)=>(~rich(X)&~strong(X))))&
(![X]:(happy(X)<=>(tall(X)<~>~creative(X))))&
(![X]:((~tall(X)&kind(X))=>(~patient(X)&tall(X))))&
((?[X]:((~wise(X)|funny(X))))=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:((~humble(X)&patient(X))=>(patient(X)&wise(X))))&
(![X]:(~rich(X)<=>(quiet(X)<~>patient(X))))&
(![X]:(~generous(X)<=>(calm(X)&~tall(X))))&
(![X]:((~patient(X)|wise(X))=>(~old(X)&happy(X))))&
((?[X]:(creative(X)))<=>((~patient(john)|brave(john))))&
(![X]:((~tall(X)<~>wise(X))<=>(rich(X)&~curious(X))))&
(![X]:(curious(X)<=>(~calm(X)|~humble(X))))&
(((~happy(john)&patient(john)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
((?[X]:((funny(X)&patient(X))))=>(kind(mary)))&
(![X]:((~rich(X)|~strong(X))<=>(funny(X)&old(X))))&
(~humble(mary))&
((quiet(mary)&strong(mary)))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((patient(X)&wise(X))))&
((brave(alice)<~>~happy(alice))) | ~rich(john) | [
"p3",
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5333360048856223692231985
% SZS output start Proof for 5333360048856223692231985
4. ? [X0] : (funny(X0) | ~wise(X0)) => ? [X0] : (~rich(X0) & quiet(X0)) [input p3]
6. ! [X0] : (~rich(X0) <=> (quiet(X0) <~> patient(X0))) [input p5]
8. ! [X0] : ((wise(X0) | ~patient(X0)) => (happy(X0) & ~old(X0))) [input p7]
14. ! [X0] : ((~strong(X0) | ~rich(X0)) <=> (old(X0) & funny(X0))) [input p13]
21. ~rich(john) [input hypothesis]
22. ? [X0] : (funny(X0) | ~wise(X0)) => ? [X1] : (~rich(X1) & quiet(X1)) [rectify 4]
26. ? [X1] : (~rich(X1) & quiet(X1)) | ! [X0] : (~funny(X0) & wise(X0)) [ennf transformation 22]
29. ! [X0] : ((happy(X0) & ~old(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 8]
32. ? [X0] : (~rich(X0) & quiet(X0)) | ! [X1] : (~funny(X1) & wise(X1)) [rectify 26]
33. ? [X0] : (~rich(X0) & quiet(X0)) => (~rich(sK0) & quiet(sK0)) [choice axiom]
34. (~rich(sK0) & quiet(sK0)) | ! [X1] : (~funny(X1) & wise(X1)) [skolemisation 32,33]
35. ! [X0] : ((~rich(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | rich(X0))) [nnf transformation 6]
50. ! [X0] : (((~strong(X0) | ~rich(X0)) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | (strong(X0) & rich(X0)))) [nnf transformation 14]
51. ! [X0] : ((~strong(X0) | ~rich(X0) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | (strong(X0) & rich(X0)))) [flattening 50]
70. quiet(sK0) | ~funny(X1) [cnf transformation 34]
72. ~rich(sK0) | ~funny(X1) [cnf transformation 34]
76. ~quiet(X0) | ~patient(X0) | rich(X0) [cnf transformation 35]
77. ~quiet(X0) | patient(X0) | ~rich(X0) [cnf transformation 35]
79. ~old(X0) | patient(X0) [cnf transformation 29]
102. funny(X0) | rich(X0) [cnf transformation 51]
104. old(X0) | rich(X0) [cnf transformation 51]
118. ~rich(john) [cnf transformation 21]
121. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
122. ~funny(X1) <- (1) [avatar component clause 121]
124. 2 <=> rich(sK0) [avatar definition]
127. 1 | ~2 [avatar split clause 72,124,121]
133. 4 <=> quiet(sK0) [avatar definition]
135. quiet(sK0) <- (4) [avatar component clause 133]
136. 1 | 4 [avatar split clause 70,133,121]
224. patient(X1) | rich(X1) [resolution 104,79]
310. ~patient(sK0) | rich(sK0) <- (4) [resolution 76,135]
329. patient(sK0) | ~rich(sK0) <- (4) [resolution 77,135]
455. patient(sK0) <- (4) [subsumption resolution 329,224]
456. rich(sK0) <- (4) [subsumption resolution 310,455]
457. 2 | ~4 [avatar split clause 456,133,124]
459. rich(X1) <- (1) [resolution 122,102]
484. $false <- (1) [resolution 459,118]
485. ~1 [avatar contradiction clause 484]
486. $false [avatar sat refutation 127,136,457,485]
% SZS output end Proof for 5333360048856223692231985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or funny then someone is either not tall or not old and vice versa.
If mary is both not kind and curious then fred is brave.
If susan is either not wise or brave then alice is quiet or not humble and vice versa.
Everyone who is happy or generous is quiet or patient and vice versa.
Everyone who is generous is strong or humble and vice versa.
If mary is not wise or not funny then someone is either creative or not generous.
Everyone who is calm is not patient or not quiet.
Everyone who is either wise or funny is either happy or not rich and vice versa.
Everyone who is not generous is not wise or not happy and vice versa.
Everyone who is either not creative or not wise is not tall or not humble.
If someone is curious or wise then susan is tall or not humble.
If someone is either quiet or not generous then lucy is not humble or tall.
If someone is not humble then susan is not brave.
Everyone who is not wise is strong or not rich and vice versa.
If paul is patient or not funny then john is either not tall or not wise and vice versa.
If alice is either not kind or strong then someone is either not wise or not generous.
Someone is both calm and patient.
Alice is not creative.
Someone is kind or not patient.
Someone is both not funny and not old.
Fred is either quiet or not quiet.
Susan is brave or strong.
Lucy is not quiet or brave.
Fred is either rich or not generous. | Fred is not wise. | contradiction | ((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(((~kind(mary)&curious(mary)))=>(brave(fred)))&
(((~wise(susan)<~>brave(susan)))<=>((quiet(alice)|~humble(alice))))&
(![X]:((happy(X)|generous(X))<=>(quiet(X)|patient(X))))&
(![X]:(generous(X)<=>(strong(X)|humble(X))))&
(((~wise(mary)|~funny(mary)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(calm(X)=>(~patient(X)|~quiet(X))))&
(![X]:((wise(X)<~>funny(X))<=>(happy(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~wise(X)|~happy(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~tall(X)|~humble(X))))&
((?[X]:((curious(X)|wise(X))))=>((tall(susan)|~humble(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>((~humble(lucy)|tall(lucy))))&
((?[X]:(~humble(X)))=>(~brave(susan)))&
(![X]:(~wise(X)<=>(strong(X)|~rich(X))))&
(((patient(paul)|~funny(paul)))<=>((~tall(john)<~>~wise(john))))&
(((~kind(alice)<~>strong(alice)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(?[X]:((calm(X)&patient(X))))&
(~creative(alice))&
(?[X]:((kind(X)|~patient(X))))&
(?[X]:((~funny(X)&~old(X))))&
((quiet(fred)<~>~quiet(fred)))&
((brave(susan)|strong(susan)))&
((~quiet(lucy)|brave(lucy)))&
((rich(fred)<~>~generous(fred))) | ~wise(fred) | [
"p4",
"p8",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4181524337533452673968039
% SZS output start Proof for 4181524337533452673968039
5. ! [X0] : (generous(X0) <=> (humble(X0) | strong(X0))) [input p4]
9. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~wise(X0))) [input p8]
13. ? [X0] : ~humble(X0) => ~brave(susan) [input p12]
14. ! [X0] : (~wise(X0) <=> (~rich(X0) | strong(X0))) [input p13]
22. strong(susan) | brave(susan) [input p21]
25. ~wise(fred) [input hypothesis]
38. ~brave(susan) | ! [X0] : humble(X0) [ennf transformation 13]
49. ! [X0] : ((generous(X0) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ~generous(X0))) [nnf transformation 5]
50. ! [X0] : ((generous(X0) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ~generous(X0))) [flattening 49]
55. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 9]
56. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | generous(X0))) [flattening 55]
59. ! [X0] : ((~wise(X0) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | wise(X0))) [nnf transformation 14]
60. ! [X0] : ((~wise(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | wise(X0))) [flattening 59]
93. ~strong(X0) | generous(X0) [cnf transformation 50]
94. ~humble(X0) | generous(X0) [cnf transformation 50]
109. ~generous(X0) | wise(X0) [cnf transformation 56]
116. ~brave(susan) | humble(X0) [cnf transformation 38]
118. ~strong(X0) | ~wise(X0) [cnf transformation 60]
138. strong(susan) | brave(susan) [cnf transformation 22]
142. ~wise(fred) [cnf transformation 25]
184. 10 <=> wise(susan) [avatar definition]
185. ~wise(susan) <- (~10) [avatar component clause 184]
188. 11 <=> brave(susan) [avatar definition]
250. 24 <=> ! [X0] : humble(X0) [avatar definition]
251. humble(X0) <- (24) [avatar component clause 250]
252. 24 | ~11 [avatar split clause 116,188,250]
309. 35 <=> strong(susan) [avatar definition]
311. strong(susan) <- (35) [avatar component clause 309]
312. 11 | 35 [avatar split clause 138,309,188]
327. 39 <=> generous(fred) [avatar definition]
328. ~generous(fred) <- (~39) [avatar component clause 327]
329. generous(fred) <- (39) [avatar component clause 327]
339. generous(X0) <- (24) [resolution 94,251]
342. $false <- (24, ~39) [resolution 339,328]
344. ~24 | 39 [avatar contradiction clause 342]
348. generous(susan) <- (35) [resolution 311,93]
359. ~wise(susan) <- (35) [resolution 118,311]
364. ~10 | ~35 [avatar split clause 359,309,184]
367. wise(susan) <- (35) [resolution 348,109]
368. $false <- (~10, 35) [subsumption resolution 367,185]
369. 10 | ~35 [avatar contradiction clause 368]
377. wise(fred) <- (39) [resolution 329,109]
378. $false <- (39) [subsumption resolution 377,142]
379. ~39 [avatar contradiction clause 378]
380. $false [avatar sat refutation 252,312,344,364,369,379]
% SZS output end Proof for 4181524337533452673968039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not kind and not tall then someone is funny.
If someone is both not kind and not humble then lucy is old or wise.
If lucy is either happy or rich then someone is not quiet.
Everyone who is both not happy and not tall is either not generous or not rich and vice versa.
Everyone who is not rich or brave is rich and vice versa.
If paul is generous then someone is old.
Everyone who is not calm or not old is not kind.
If someone is both not curious and not old then someone is not kind and vice versa.
Everyone who is both tall and not strong is not calm and vice versa.
Everyone who is curious is either not humble or not tall.
Everyone who is not tall is either not kind or not curious.
Everyone who is generous is either not patient or curious.
If alice is both not happy and not kind then john is quiet or not creative.
Everyone who is not funny is creative or not tall.
Everyone who is not wise or not strong is both not creative and humble.
Everyone who is not calm is either rich or not strong and vice versa.
Alice is not kind or not wise.
Mary is not wise.
Lucy is both funny and wise. | John is old. | entailment | (((~kind(paul)&~tall(paul)))=>(?[X]:(funny(X))))&
((?[X]:((~kind(X)&~humble(X))))=>((old(lucy)|wise(lucy))))&
(((happy(lucy)<~>rich(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)&~tall(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((~rich(X)|brave(X))<=>rich(X)))&
((generous(paul))=>(?[X]:(old(X))))&
(![X]:((~calm(X)|~old(X))=>~kind(X)))&
((?[X]:((~curious(X)&~old(X))))<=>(?[X]:(~kind(X))))&
(![X]:((tall(X)&~strong(X))<=>~calm(X)))&
(![X]:(curious(X)=>(~humble(X)<~>~tall(X))))&
(![X]:(~tall(X)=>(~kind(X)<~>~curious(X))))&
(![X]:(generous(X)=>(~patient(X)<~>curious(X))))&
(((~happy(alice)&~kind(alice)))=>((quiet(john)|~creative(john))))&
(![X]:(~funny(X)=>(creative(X)|~tall(X))))&
(![X]:((~wise(X)|~strong(X))=>(~creative(X)&humble(X))))&
(![X]:(~calm(X)<=>(rich(X)<~>~strong(X))))&
((~kind(alice)|~wise(alice)))&
(~wise(mary))&
((funny(lucy)&wise(lucy))) | old(john) | [
"p4",
"p6",
"p7",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 375283968783809618035960
% SZS output start Proof for 375283968783809618035960
5. ! [X0] : ((brave(X0) | ~rich(X0)) <=> rich(X0)) [input p4]
7. ! [X0] : ((~old(X0) | ~calm(X0)) => ~kind(X0)) [input p6]
8. ? [X0] : (~old(X0) & ~curious(X0)) <=> ? [X0] : ~kind(X0) [input p7]
9. ! [X0] : ((~strong(X0) & tall(X0)) <=> ~calm(X0)) [input p8]
11. ! [X0] : (~tall(X0) => (~kind(X0) <~> ~curious(X0))) [input p10]
16. ! [X0] : (~calm(X0) <=> (rich(X0) <~> ~strong(X0))) [input p15]
20. ~old(john) [input hypothesis]
21. ? [X0] : (~old(X0) & ~curious(X0)) <=> ? [X1] : ~kind(X1) [rectify 8]
31. ! [X0] : (~kind(X0) | (old(X0) & calm(X0))) [ennf transformation 7]
33. ! [X0] : ((~kind(X0) <~> ~curious(X0)) | tall(X0)) [ennf transformation 11]
38. ! [X0] : (((brave(X0) | ~rich(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) & rich(X0)))) [nnf transformation 5]
39. ! [X0] : ((brave(X0) | ~rich(X0) | ~rich(X0)) & (rich(X0) | (~brave(X0) & rich(X0)))) [flattening 38]
42. (? [X0] : (~old(X0) & ~curious(X0)) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : (old(X0) | curious(X0))) [nnf transformation 21]
43. (? [X0] : (~old(X0) & ~curious(X0)) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : (old(X3) | curious(X3))) [rectify 42]
44. ? [X0] : (~old(X0) & ~curious(X0)) => (~old(sK1) & ~curious(sK1)) [choice axiom]
45. ? [X2] : ~kind(X2) => ~kind(sK2) [choice axiom]
46. ((~old(sK1) & ~curious(sK1)) | ! [X1] : kind(X1)) & (~kind(sK2) | ! [X3] : (old(X3) | curious(X3))) [skolemisation 43,45,44]
47. ! [X0] : (((~strong(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | (strong(X0) | ~tall(X0)))) [nnf transformation 9]
48. ! [X0] : (((~strong(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | strong(X0) | ~tall(X0))) [flattening 47]
50. ! [X0] : (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | tall(X0)) [nnf transformation 33]
52. ! [X0] : ((~calm(X0) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | calm(X0))) [nnf transformation 16]
60. rich(X0) | rich(X0) [cnf transformation 39]
65. ~kind(X0) | old(X0) [cnf transformation 31]
67. ~curious(sK1) | kind(X1) [cnf transformation 46]
68. ~old(sK1) | kind(X1) [cnf transformation 46]
69. ~calm(X0) | strong(X0) | ~tall(X0) [cnf transformation 48]
71. ~strong(X0) | calm(X0) [cnf transformation 48]
75. curious(X0) | kind(X0) | tall(X0) [cnf transformation 50]
81. strong(X0) | ~rich(X0) | calm(X0) [cnf transformation 52]
82. ~calm(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 52]
87. ~old(john) [cnf transformation 20]
88. rich(X0) [duplicate literal removal 60]
112. 6 <=> ! [X1] : kind(X1) [avatar definition]
113. kind(X1) <- (6) [avatar component clause 112]
115. 7 <=> old(sK1) [avatar definition]
118. 6 | ~7 [avatar split clause 68,115,112]
120. 8 <=> curious(sK1) [avatar definition]
122. ~curious(sK1) <- (~8) [avatar component clause 120]
123. 6 | ~8 [avatar split clause 67,120,112]
132. ~calm(X0) | ~strong(X0) [subsumption resolution 82,88]
133. ~strong(X0) [subsumption resolution 132,71]
134. ~rich(X0) | calm(X0) [subsumption resolution 81,133]
135. calm(X0) [subsumption resolution 134,88]
155. strong(X1) | ~tall(X1) [resolution 69,135]
156. ~tall(X1) [subsumption resolution 155,133]
157. kind(sK1) | tall(sK1) <- (~8) [resolution 75,122]
163. kind(sK1) <- (~8) [subsumption resolution 157,156]
164. old(sK1) <- (~8) [resolution 163,65]
168. 7 | 8 [avatar split clause 164,120,115]
170. old(X0) <- (6) [resolution 113,65]
180. $false <- (6) [resolution 170,87]
181. ~6 [avatar contradiction clause 180]
182. $false [avatar sat refutation 118,123,168,181]
% SZS output end Proof for 375283968783809618035960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient then john is either not kind or not creative.
Everyone who is not tall is generous or kind.
Everyone who is both patient and generous is happy or wise and vice versa.
Everyone who is not brave or not tall is happy and vice versa.
Everyone who is not old or not quiet is both not curious and tall and vice versa.
If someone is wise then fred is either not creative or rich.
Everyone who is either kind or funny is not brave.
Everyone who is both generous and not patient is rich and vice versa.
Everyone who is rich is not happy and vice versa.
If someone is not generous then someone is not kind.
Everyone who is patient is brave.
Everyone who is brave is wise or not curious.
If someone is both brave and funny then fred is not patient and vice versa.
Everyone who is either strong or not patient is both patient and strong.
If alice is not happy then someone is not old or tall and vice versa.
Everyone who is both strong and not calm is not funny and vice versa.
Someone is either not kind or not old.
Someone is both patient and generous.
Someone is patient.
Paul is wise or not calm.
John is either patient or not funny.
Someone is wise.
Mary is happy. | Alice is patient. | contradiction | ((~patient(paul))=>((~kind(john)<~>~creative(john))))&
(![X]:(~tall(X)=>(generous(X)|kind(X))))&
(![X]:((patient(X)&generous(X))<=>(happy(X)|wise(X))))&
(![X]:((~brave(X)|~tall(X))<=>happy(X)))&
(![X]:((~old(X)|~quiet(X))<=>(~curious(X)&tall(X))))&
((?[X]:(wise(X)))=>((~creative(fred)<~>rich(fred))))&
(![X]:((kind(X)<~>funny(X))=>~brave(X)))&
(![X]:((generous(X)&~patient(X))<=>rich(X)))&
(![X]:(rich(X)<=>~happy(X)))&
((?[X]:(~generous(X)))=>(?[X]:(~kind(X))))&
(![X]:(patient(X)=>brave(X)))&
(![X]:(brave(X)=>(wise(X)|~curious(X))))&
((?[X]:((brave(X)&funny(X))))<=>(~patient(fred)))&
(![X]:((strong(X)<~>~patient(X))=>(patient(X)&strong(X))))&
((~happy(alice))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((strong(X)&~calm(X))<=>~funny(X)))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:((patient(X)&generous(X))))&
(?[X]:(patient(X)))&
((wise(paul)|~calm(paul)))&
((patient(john)<~>~funny(john)))&
(?[X]:(wise(X)))&
(happy(mary)) | patient(alice) | [
"p2",
"p3",
"p7",
"p8",
"p10",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4518686270603141222539239
% SZS output start Proof for 4518686270603141222539239
3. ! [X0] : ((generous(X0) & patient(X0)) <=> (wise(X0) | happy(X0))) [input p2]
4. ! [X0] : ((~tall(X0) | ~brave(X0)) <=> happy(X0)) [input p3]
8. ! [X0] : ((~patient(X0) & generous(X0)) <=> rich(X0)) [input p7]
9. ! [X0] : (rich(X0) <=> ~happy(X0)) [input p8]
11. ! [X0] : (patient(X0) => brave(X0)) [input p10]
13. ? [X0] : (funny(X0) & brave(X0)) <=> ~patient(fred) [input p12]
15. ~happy(alice) <=> ? [X0] : (tall(X0) | ~old(X0)) [input p14]
21. patient(john) <~> ~funny(john) [input p20]
24. patient(alice) [input hypothesis]
32. ! [X0] : (brave(X0) | ~patient(X0)) [ennf transformation 11]
37. ! [X0] : (((generous(X0) & patient(X0)) | (~wise(X0) & ~happy(X0))) & ((wise(X0) | happy(X0)) | (~generous(X0) | ~patient(X0)))) [nnf transformation 3]
38. ! [X0] : (((generous(X0) & patient(X0)) | (~wise(X0) & ~happy(X0))) & (wise(X0) | happy(X0) | ~generous(X0) | ~patient(X0))) [flattening 37]
39. ! [X0] : (((~tall(X0) | ~brave(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & brave(X0)))) [nnf transformation 4]
40. ! [X0] : ((~tall(X0) | ~brave(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & brave(X0)))) [flattening 39]
45. ! [X0] : (((~patient(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | (patient(X0) | ~generous(X0)))) [nnf transformation 8]
46. ! [X0] : (((~patient(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | patient(X0) | ~generous(X0))) [flattening 45]
47. ! [X0] : ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))) [nnf transformation 9]
51. (? [X0] : (funny(X0) & brave(X0)) | patient(fred)) & (~patient(fred) | ! [X0] : (~funny(X0) | ~brave(X0))) [nnf transformation 13]
52. (? [X0] : (funny(X0) & brave(X0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~funny(X1) | ~brave(X1))) [rectify 51]
53. ? [X0] : (funny(X0) & brave(X0)) => (funny(sK1) & brave(sK1)) [choice axiom]
54. ((funny(sK1) & brave(sK1)) | patient(fred)) & (~patient(fred) | ! [X1] : (~funny(X1) | ~brave(X1))) [skolemisation 52,53]
56. (~happy(alice) | ! [X0] : (~tall(X0) & old(X0))) & (? [X0] : (tall(X0) | ~old(X0)) | happy(alice)) [nnf transformation 15]
57. (~happy(alice) | ! [X0] : (~tall(X0) & old(X0))) & (? [X1] : (tall(X1) | ~old(X1)) | happy(alice)) [rectify 56]
58. ? [X1] : (tall(X1) | ~old(X1)) => (tall(sK2) | ~old(sK2)) [choice axiom]
59. (~happy(alice) | ! [X0] : (~tall(X0) & old(X0))) & ((tall(sK2) | ~old(sK2)) | happy(alice)) [skolemisation 57,58]
69. (funny(john) | ~patient(john)) & (~funny(john) | patient(john)) [nnf transformation 21]
76. ~happy(X0) | patient(X0) [cnf transformation 38]
81. happy(X0) | tall(X0) [cnf transformation 40]
94. ~rich(X0) | ~patient(X0) [cnf transformation 46]
95. ~rich(X0) | ~happy(X0) [cnf transformation 47]
96. rich(X0) | happy(X0) [cnf transformation 47]
98. ~patient(X0) | brave(X0) [cnf transformation 32]
100. ~patient(fred) | ~funny(X1) | ~brave(X1) [cnf transformation 54]
109. ~happy(alice) | ~tall(X0) [cnf transformation 59]
120. funny(john) | ~patient(john) [cnf transformation 69]
123. patient(alice) [cnf transformation 24]
148. 6 <=> rich(fred) [avatar definition]
149. rich(fred) <- (6) [avatar component clause 148]
150. ~rich(fred) <- (~6) [avatar component clause 148]
162. 9 <=> patient(fred) [avatar definition]
163. ~patient(fred) <- (~9) [avatar component clause 162]
176. 12 <=> ! [X1] : (~funny(X1) | ~brave(X1)) [avatar definition]
177. ~funny(X1) | ~brave(X1) <- (12) [avatar component clause 176]
178. 12 | ~9 [avatar split clause 100,162,176]
180. 13 <=> ! [X0] : ~tall(X0) [avatar definition]
181. ~tall(X0) <- (13) [avatar component clause 180]
183. 14 <=> happy(alice) [avatar definition]
186. 13 | ~14 [avatar split clause 109,183,180]
217. 21 <=> patient(john) [avatar definition]
219. ~patient(john) <- (~21) [avatar component clause 217]
221. 22 <=> funny(john) [avatar definition]
223. funny(john) <- (22) [avatar component clause 221]
224. ~21 | 22 [avatar split clause 120,221,217]
236. tall(X1) | patient(X1) [resolution 81,76]
238. happy(fred) <- (~6) [resolution 96,150]
240. ~patient(X1) | happy(X1) [resolution 96,94]
250. patient(fred) <- (~6) [resolution 238,76]
251. $false <- (~6, ~9) [subsumption resolution 250,163]
252. 6 | 9 [avatar contradiction clause 251]
255. ~happy(fred) <- (6) [resolution 149,95]
258. tall(fred) <- (6) [resolution 255,81]
379. happy(alice) [resolution 240,123]
389. 14 [avatar split clause 379,183]
395. patient(X0) <- (13) [resolution 181,236]
396. $false <- (6, 13) [resolution 181,258]
397. ~6 | ~13 [avatar contradiction clause 396]
425. brave(X1) <- (13) [resolution 395,98]
426. $false <- (13, ~21) [resolution 395,219]
427. ~13 | 21 [avatar contradiction clause 426]
429. ~brave(john) <- (12, 22) [resolution 223,177]
431. $false <- (12, 13, 22) [subsumption resolution 429,425]
432. ~12 | ~13 | ~22 [avatar contradiction clause 431]
433. $false [avatar sat refutation 178,186,224,252,389,397,427,432]
% SZS output end Proof for 4518686270603141222539239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either rich or generous then someone is not brave and vice versa. If someone is not calm or not patient then someone is both calm and not curious and vice versa. Everyone who is wise or not creative is both happy and patient and vice versa. If someone is both not generous and not old then someone is both strong and patient. If someone is either not rich or calm then someone is both patient and rich. Everyone who is strong is either not quiet or funny and vice versa. If someone is not curious then someone is both wise and not wise. Everyone who is not funny is either wise or not wise and vice versa. Everyone who is both not wise and not kind is either humble or not rich. Everyone who is both not brave and not patient is both rich and not kind and vice versa. Everyone who is not old or kind is funny or happy. If paul is generous or rich then mary is both curious and quiet and vice versa. Everyone who is not kind or not tall is both tall and not brave. Everyone who is either not humble or not strong is not curious or not patient and vice versa. If someone is generous then lucy is not happy or creative and vice versa. If someone is not patient then paul is either not happy or strong and vice versa. Paul is rich. Mary is not humble or not kind. Paul is both calm and patient. Mary is either patient or not patient. John is not funny or not rich. | Mary is generous. | neutral | (((rich(john)<~>generous(john)))<=>(?[X]:(~brave(X))))&
((?[X]:((~calm(X)|~patient(X))))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((wise(X)|~creative(X))<=>(happy(X)&patient(X))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((strong(X)&patient(X)))))&
((?[X]:((~rich(X)<~>calm(X))))=>(?[X]:((patient(X)&rich(X)))))&
(![X]:(strong(X)<=>(~quiet(X)<~>funny(X))))&
((?[X]:(~curious(X)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~funny(X)<=>(wise(X)<~>~wise(X))))&
(![X]:((~wise(X)&~kind(X))=>(humble(X)<~>~rich(X))))&
(![X]:((~brave(X)&~patient(X))<=>(rich(X)&~kind(X))))&
(![X]:((~old(X)|kind(X))=>(funny(X)|happy(X))))&
(((generous(paul)|rich(paul)))<=>((curious(mary)&quiet(mary))))&
(![X]:((~kind(X)|~tall(X))=>(tall(X)&~brave(X))))&
(![X]:((~humble(X)<~>~strong(X))<=>(~curious(X)|~patient(X))))&
((?[X]:(generous(X)))<=>((~happy(lucy)|creative(lucy))))&
((?[X]:(~patient(X)))<=>((~happy(paul)<~>strong(paul))))&
(rich(paul))&
((~humble(mary)|~kind(mary)))&
((calm(paul)&patient(paul)))&
((patient(mary)<~>~patient(mary)))&
((~funny(john)|~rich(john))) | generous(mary) | [] | null | 0 |
If mary is creative then someone is both not rich and creative and vice versa. If someone is both not generous and not wise then john is strong. If someone is not kind or rich then someone is not happy and vice versa. Everyone who is either not patient or not creative is rich or not humble. Everyone who is old or brave is both creative and calm and vice versa. Everyone who is both humble and not calm is both wise and kind and vice versa. Everyone who is strong or not kind is kind or curious and vice versa. Everyone who is not tall is creative or not rich and vice versa. If susan is either calm or generous then susan is both not happy and not old. If paul is not strong or brave then paul is old and vice versa. Everyone who is both not calm and quiet is both not creative and not funny. If someone is rich or not happy then john is not calm and vice versa. Everyone who is either happy or calm is not funny or not strong and vice versa. Everyone who is both kind and not curious is either quiet or creative and vice versa. Everyone who is both creative and not old is both humble and not happy. Everyone who is both patient and not creative is either not brave or not creative and vice versa. Fred is both curious and brave. Someone is both rich and curious. Someone is both creative and patient. Fred is curious or not patient. Lucy is rich. Someone is either old or generous. Someone is both not curious and not brave. | Susan is not happy. | neutral | ((creative(mary))<=>(?[X]:((~rich(X)&creative(X)))))&
((?[X]:((~generous(X)&~wise(X))))=>(strong(john)))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)<~>~creative(X))=>(rich(X)|~humble(X))))&
(![X]:((old(X)|brave(X))<=>(creative(X)&calm(X))))&
(![X]:((humble(X)&~calm(X))<=>(wise(X)&kind(X))))&
(![X]:((strong(X)|~kind(X))<=>(kind(X)|curious(X))))&
(![X]:(~tall(X)<=>(creative(X)|~rich(X))))&
(((calm(susan)<~>generous(susan)))=>((~happy(susan)&~old(susan))))&
(((~strong(paul)|brave(paul)))<=>(old(paul)))&
(![X]:((~calm(X)&quiet(X))=>(~creative(X)&~funny(X))))&
((?[X]:((rich(X)|~happy(X))))<=>(~calm(john)))&
(![X]:((happy(X)<~>calm(X))<=>(~funny(X)|~strong(X))))&
(![X]:((kind(X)&~curious(X))<=>(quiet(X)<~>creative(X))))&
(![X]:((creative(X)&~old(X))=>(humble(X)&~happy(X))))&
(![X]:((patient(X)&~creative(X))<=>(~brave(X)<~>~creative(X))))&
((curious(fred)&brave(fred)))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((creative(X)&patient(X))))&
((curious(fred)|~patient(fred)))&
(rich(lucy))&
(?[X]:((old(X)<~>generous(X))))&
(?[X]:((~curious(X)&~brave(X)))) | ~happy(susan) | [] | null | 0 |
If someone is either strong or old then alice is calm and vice versa. Everyone who is either kind or funny is both curious and tall and vice versa. Everyone who is both not old and generous is curious or not wise and vice versa. Everyone who is strong is happy and vice versa. If john is both curious and rich then fred is not patient or calm. If someone is both not patient and tall then john is both not wise and humble. If someone is not tall or wise then lucy is both curious and not curious and vice versa. Everyone who is either not old or calm is both not curious and humble and vice versa. If paul is creative or not kind then someone is either rich or not tall and vice versa. Everyone who is patient is both not funny and not quiet and vice versa. Everyone who is humble is wise or tall and vice versa. Everyone who is both curious and not kind is either not creative or not tall and vice versa. Everyone who is both brave and not strong is either happy or generous and vice versa. Everyone who is funny or humble is either humble or not kind. If susan is either not happy or not strong then susan is old or curious. If paul is either quiet or patient then fred is either not strong or not creative and vice versa. Someone is not happy. Someone is both quiet and brave. Mary is either not funny or tall. John is humble. Someone is kind or not quiet. Susan is not quiet. | Alice is brave. | neutral | ((?[X]:((strong(X)<~>old(X))))<=>(calm(alice)))&
(![X]:((kind(X)<~>funny(X))<=>(curious(X)&tall(X))))&
(![X]:((~old(X)&generous(X))<=>(curious(X)|~wise(X))))&
(![X]:(strong(X)<=>happy(X)))&
(((curious(john)&rich(john)))=>((~patient(fred)|calm(fred))))&
((?[X]:((~patient(X)&tall(X))))=>((~wise(john)&humble(john))))&
((?[X]:((~tall(X)|wise(X))))<=>((curious(lucy)&~curious(lucy))))&
(![X]:((~old(X)<~>calm(X))<=>(~curious(X)&humble(X))))&
(((creative(paul)|~kind(paul)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(patient(X)<=>(~funny(X)&~quiet(X))))&
(![X]:(humble(X)<=>(wise(X)|tall(X))))&
(![X]:((curious(X)&~kind(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((brave(X)&~strong(X))<=>(happy(X)<~>generous(X))))&
(![X]:((funny(X)|humble(X))=>(humble(X)<~>~kind(X))))&
(((~happy(susan)<~>~strong(susan)))=>((old(susan)|curious(susan))))&
(((quiet(paul)<~>patient(paul)))<=>((~strong(fred)<~>~creative(fred))))&
(?[X]:(~happy(X)))&
(?[X]:((quiet(X)&brave(X))))&
((~funny(mary)<~>tall(mary)))&
(humble(john))&
(?[X]:((kind(X)|~quiet(X))))&
(~quiet(susan)) | brave(alice) | [] | null | 0 |
Everyone who is old is either not happy or not kind and vice versa.
Everyone who is curious is both not strong and humble.
Everyone who is not brave is humble and vice versa.
Everyone who is both not kind and not happy is both not curious and not patient and vice versa.
Everyone who is not creative or rich is not old and vice versa.
Everyone who is not kind or tall is both calm and not curious and vice versa.
Everyone who is not rich is not happy or rich and vice versa.
Everyone who is both not tall and humble is both not old and quiet and vice versa.
If someone is either not wise or creative then someone is both not funny and not kind.
Everyone who is not creative is both calm and not wise.
Everyone who is both generous and not wise is either not kind or not rich.
If someone is calm or not funny then john is both not rich and wise.
Everyone who is both creative and humble is not kind or quiet and vice versa.
Everyone who is kind or not quiet is tall or not humble.
Everyone who is either wise or old is not quiet.
If someone is tall then lucy is both brave and not patient and vice versa.
Paul is both not wise and patient.
Someone is not humble.
Someone is either generous or not happy.
Fred is either rich or funny.
Someone is quiet or not happy.
Susan is not strong or wise. | Lucy is brave. | entailment | (![X]:(old(X)<=>(~happy(X)<~>~kind(X))))&
(![X]:(curious(X)=>(~strong(X)&humble(X))))&
(![X]:(~brave(X)<=>humble(X)))&
(![X]:((~kind(X)&~happy(X))<=>(~curious(X)&~patient(X))))&
(![X]:((~creative(X)|rich(X))<=>~old(X)))&
(![X]:((~kind(X)|tall(X))<=>(calm(X)&~curious(X))))&
(![X]:(~rich(X)<=>(~happy(X)|rich(X))))&
(![X]:((~tall(X)&humble(X))<=>(~old(X)&quiet(X))))&
((?[X]:((~wise(X)<~>creative(X))))=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:(~creative(X)=>(calm(X)&~wise(X))))&
(![X]:((generous(X)&~wise(X))=>(~kind(X)<~>~rich(X))))&
((?[X]:((calm(X)|~funny(X))))=>((~rich(john)&wise(john))))&
(![X]:((creative(X)&humble(X))<=>(~kind(X)|quiet(X))))&
(![X]:((kind(X)|~quiet(X))=>(tall(X)|~humble(X))))&
(![X]:((wise(X)<~>old(X))=>~quiet(X)))&
((?[X]:(tall(X)))<=>((brave(lucy)&~patient(lucy))))&
((~wise(paul)&patient(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((generous(X)<~>~happy(X))))&
((rich(fred)<~>funny(fred)))&
(?[X]:((quiet(X)|~happy(X))))&
((~strong(susan)|wise(susan))) | brave(lucy) | [
"p0",
"p2",
"p4",
"p6",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8949198396946888226798152
% SZS output start Proof for 8949198396946888226798152
1. ! [X0] : (old(X0) <=> (~happy(X0) <~> ~kind(X0))) [input p0]
3. ! [X0] : (~brave(X0) <=> humble(X0)) [input p2]
5. ! [X0] : ((rich(X0) | ~creative(X0)) <=> ~old(X0)) [input p4]
7. ! [X0] : (~rich(X0) <=> (rich(X0) | ~happy(X0))) [input p6]
8. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (quiet(X0) & ~old(X0))) [input p7]
13. ! [X0] : ((humble(X0) & creative(X0)) <=> (quiet(X0) | ~kind(X0))) [input p12]
16. ? [X0] : tall(X0) <=> (~patient(lucy) & brave(lucy)) [input p15]
23. ~brave(lucy) [input hypothesis]
36. ! [X0] : ((old(X0) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | ~old(X0))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0))) [nnf transformation 3]
40. ! [X0] : (((rich(X0) | ~creative(X0)) | old(X0)) & (~old(X0) | (~rich(X0) & creative(X0)))) [nnf transformation 5]
41. ! [X0] : ((rich(X0) | ~creative(X0) | old(X0)) & (~old(X0) | (~rich(X0) & creative(X0)))) [flattening 40]
44. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & ((rich(X0) | ~happy(X0)) | rich(X0))) [nnf transformation 7]
45. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & (rich(X0) | ~happy(X0) | rich(X0))) [flattening 44]
46. ! [X0] : (((humble(X0) & ~tall(X0)) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 8]
47. ! [X0] : (((humble(X0) & ~tall(X0)) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | ~humble(X0) | tall(X0))) [flattening 46]
53. ! [X0] : (((humble(X0) & creative(X0)) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | (~humble(X0) | ~creative(X0)))) [nnf transformation 13]
54. ! [X0] : (((humble(X0) & creative(X0)) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | ~humble(X0) | ~creative(X0))) [flattening 53]
56. (? [X0] : tall(X0) | (patient(lucy) | ~brave(lucy))) & ((~patient(lucy) & brave(lucy)) | ! [X0] : ~tall(X0)) [nnf transformation 16]
57. (? [X0] : tall(X0) | patient(lucy) | ~brave(lucy)) & ((~patient(lucy) & brave(lucy)) | ! [X0] : ~tall(X0)) [flattening 56]
58. (? [X0] : tall(X0) | patient(lucy) | ~brave(lucy)) & ((~patient(lucy) & brave(lucy)) | ! [X1] : ~tall(X1)) [rectify 57]
59. ? [X0] : tall(X0) => tall(sK1) [choice axiom]
60. (tall(sK1) | patient(lucy) | ~brave(lucy)) & ((~patient(lucy) & brave(lucy)) | ! [X1] : ~tall(X1)) [skolemisation 58,59]
71. ~kind(X0) | old(X0) | happy(X0) [cnf transformation 36]
74. brave(X0) | humble(X0) [cnf transformation 37]
82. ~creative(X0) | rich(X0) | old(X0) [cnf transformation 41]
88. rich(X0) | ~happy(X0) | rich(X0) [cnf transformation 45]
90. ~rich(X0) | ~rich(X0) [cnf transformation 45]
91. ~humble(X0) | ~old(X0) | tall(X0) [cnf transformation 47]
108. creative(X0) | kind(X0) [cnf transformation 54]
110. humble(X0) | kind(X0) [cnf transformation 54]
116. brave(lucy) | ~tall(X1) [cnf transformation 60]
127. ~brave(lucy) [cnf transformation 23]
128. rich(X0) | ~happy(X0) [duplicate literal removal 88]
129. ~rich(X0) [duplicate literal removal 90]
130. ~happy(X0) [subsumption resolution 128,129]
163. 8 <=> brave(lucy) [avatar definition]
165. ~brave(lucy) <- (~8) [avatar component clause 163]
176. 11 <=> ! [X1] : ~tall(X1) [avatar definition]
177. ~tall(X1) <- (11) [avatar component clause 176]
179. 11 | 8 [avatar split clause 116,163,176]
182. ~8 [avatar split clause 127,163]
183. humble(lucy) <- (~8) [resolution 74,165]
216. rich(X0) | old(X0) | kind(X0) [resolution 82,108]
219. old(X0) | kind(X0) [subsumption resolution 216,129]
220. ~old(lucy) | tall(lucy) <- (~8) [resolution 91,183]
221. ~old(X0) | tall(X0) | kind(X0) [resolution 91,110]
222. ~old(lucy) <- (~8, 11) [subsumption resolution 220,177]
223. ~old(X0) | kind(X0) <- (11) [subsumption resolution 221,177]
224. kind(X0) <- (11) [subsumption resolution 223,219]
227. old(X1) | happy(X1) <- (11) [resolution 224,71]
230. old(X1) <- (11) [subsumption resolution 227,130]
246. $false <- (~8, 11) [resolution 230,222]
247. 8 | ~11 [avatar contradiction clause 246]
248. $false [avatar sat refutation 179,182,247]
% SZS output end Proof for 8949198396946888226798152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is either not wise or not calm. Everyone who is happy or not strong is not tall or not happy and vice versa. Everyone who is both not old and not patient is creative or generous. If john is not patient then someone is kind or not strong. Everyone who is creative is not curious. Everyone who is both not brave and not happy is not wise or wise and vice versa. Everyone who is not happy or not old is not wise or not patient. Everyone who is either not strong or not humble is creative and vice versa. Everyone who is not curious is both not tall and not humble and vice versa. Everyone who is brave or not tall is both not generous and calm and vice versa. Everyone who is either humble or not tall is either wise or creative. If alice is either kind or creative then susan is humble and vice versa. Everyone who is not calm is either patient or not strong and vice versa. If alice is not quiet or not happy then someone is not calm or not happy. Everyone who is both not strong and not wise is funny and vice versa. If paul is either generous or not humble then john is either humble or not humble. Someone is happy or generous. Someone is either generous or not tall. Susan is old. Someone is both not kind and old. Someone is wise. Someone is both not strong and not old. Someone is not strong. | Alice is tall. | entailment | (![X]:(strong(X)=>(~wise(X)<~>~calm(X))))&
(![X]:((happy(X)|~strong(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~old(X)&~patient(X))=>(creative(X)|generous(X))))&
((~patient(john))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:(creative(X)=>~curious(X)))&
(![X]:((~brave(X)&~happy(X))<=>(~wise(X)|wise(X))))&
(![X]:((~happy(X)|~old(X))=>(~wise(X)|~patient(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>creative(X)))&
(![X]:(~curious(X)<=>(~tall(X)&~humble(X))))&
(![X]:((brave(X)|~tall(X))<=>(~generous(X)&calm(X))))&
(![X]:((humble(X)<~>~tall(X))=>(wise(X)<~>creative(X))))&
(((kind(alice)<~>creative(alice)))<=>(humble(susan)))&
(![X]:(~calm(X)<=>(patient(X)<~>~strong(X))))&
(((~quiet(alice)|~happy(alice)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~strong(X)&~wise(X))<=>funny(X)))&
(((generous(paul)<~>~humble(paul)))=>((humble(john)<~>~humble(john))))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((generous(X)<~>~tall(X))))&
(old(susan))&
(?[X]:((~kind(X)&old(X))))&
(?[X]:(wise(X)))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:(~strong(X))) | tall(alice) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1465556613352494495827518
% SZS output start Proof for 1465556613352494495827518
2. ! [X0] : ((~strong(X0) | happy(X0)) <=> (~happy(X0) | ~tall(X0))) [input p1]
5. ! [X0] : (creative(X0) => ~curious(X0)) [input p4]
6. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (wise(X0) | ~wise(X0))) [input p5]
7. ! [X0] : ((~old(X0) | ~happy(X0)) => (~patient(X0) | ~wise(X0))) [input p6]
8. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> creative(X0)) [input p7]
9. ! [X0] : (~curious(X0) <=> (~humble(X0) & ~tall(X0))) [input p8]
10. ! [X0] : ((~tall(X0) | brave(X0)) <=> (calm(X0) & ~generous(X0))) [input p9]
11. ! [X0] : ((humble(X0) <~> ~tall(X0)) => (wise(X0) <~> creative(X0))) [input p10]
13. ! [X0] : (~calm(X0) <=> (patient(X0) <~> ~strong(X0))) [input p12]
24. ~tall(alice) [input hypothesis]
25. ! [X0] : (~curious(X0) => (~humble(X0) & ~tall(X0))) [unused predicate definition removal 9]
31. ! [X0] : (~curious(X0) | ~creative(X0)) [ennf transformation 5]
32. ! [X0] : ((~patient(X0) | ~wise(X0)) | (old(X0) & happy(X0))) [ennf transformation 7]
33. ! [X0] : (~patient(X0) | ~wise(X0) | (old(X0) & happy(X0))) [flattening 32]
34. ! [X0] : ((~humble(X0) & ~tall(X0)) | curious(X0)) [ennf transformation 25]
35. ! [X0] : ((wise(X0) <~> creative(X0)) | (humble(X0) <=> ~tall(X0))) [ennf transformation 11]
39. ! [X0] : (((~strong(X0) | happy(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (strong(X0) & ~happy(X0)))) [nnf transformation 2]
40. ! [X0] : ((~strong(X0) | happy(X0) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | (strong(X0) & ~happy(X0)))) [flattening 39]
43. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 6]
44. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | happy(X0) | brave(X0))) [flattening 43]
45. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~creative(X0)) & (creative(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 8]
46. ! [X0] : (((~tall(X0) | brave(X0)) | (~calm(X0) | generous(X0))) & ((calm(X0) & ~generous(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 10]
47. ! [X0] : ((~tall(X0) | brave(X0) | ~calm(X0) | generous(X0)) & ((calm(X0) & ~generous(X0)) | (tall(X0) & ~brave(X0)))) [flattening 46]
48. ! [X0] : (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) [nnf transformation 35]
50. ! [X0] : ((~calm(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | calm(X0))) [nnf transformation 13]
72. ~strong(X0) | happy(X0) | happy(X0) [cnf transformation 40]
75. ~curious(X0) | ~creative(X0) [cnf transformation 31]
79. ~happy(X0) | wise(X0) [cnf transformation 44]
80. ~happy(X0) | ~wise(X0) [cnf transformation 44]
81. ~patient(X0) | ~wise(X0) | happy(X0) [cnf transformation 33]
83. ~humble(X0) | creative(X0) | strong(X0) [cnf transformation 45]
86. ~creative(X0) | strong(X0) | humble(X0) [cnf transformation 45]
88. ~humble(X0) | curious(X0) [cnf transformation 34]
92. tall(X0) | calm(X0) [cnf transformation 47]
95. humble(X0) | wise(X0) | creative(X0) | tall(X0) [cnf transformation 48]
105. ~calm(X0) | patient(X0) | strong(X0) [cnf transformation 50]
121. ~tall(alice) [cnf transformation 24]
123. ~strong(X0) | happy(X0) [duplicate literal removal 72]
137. ~happy(X0) [subsumption resolution 79,80]
139. ~patient(X0) | ~wise(X0) [subsumption resolution 81,137]
150. 6 <=> creative(alice) [avatar definition]
151. creative(alice) <- (6) [avatar component clause 150]
152. ~creative(alice) <- (~6) [avatar component clause 150]
169. calm(alice) [resolution 92,121]
178. 9 <=> strong(alice) [avatar definition]
179. strong(alice) <- (9) [avatar component clause 178]
180. ~strong(alice) <- (~9) [avatar component clause 178]
182. 10 <=> wise(alice) [avatar definition]
184. ~wise(alice) <- (~10) [avatar component clause 182]
198. patient(alice) | strong(alice) [resolution 105,169]
200. patient(alice) <- (~9) [subsumption resolution 198,180]
218. ~wise(alice) <- (~9) [resolution 200,139]
224. ~10 | 9 [avatar split clause 218,178,182]
228. wise(X2) | creative(X2) | tall(X2) | creative(X2) | strong(X2) [resolution 95,83]
230. creative(X2) | wise(X2) | tall(X2) | strong(X2) [duplicate literal removal 228]
287. wise(alice) | tall(alice) | strong(alice) <- (~6) [resolution 230,152]
293. tall(alice) | strong(alice) <- (~6, ~10) [subsumption resolution 287,184]
294. strong(alice) <- (~6, ~10) [subsumption resolution 293,121]
295. $false <- (~6, ~9, ~10) [subsumption resolution 294,180]
296. 6 | 9 | 10 [avatar contradiction clause 295]
298. strong(alice) | humble(alice) <- (6) [resolution 151,86]
300. humble(alice) <- (6, ~9) [subsumption resolution 298,180]
305. curious(alice) <- (6, ~9) [resolution 300,88]
306. ~creative(alice) <- (6, ~9) [resolution 305,75]
307. $false <- (6, ~9) [subsumption resolution 306,151]
308. ~6 | 9 [avatar contradiction clause 307]
322. happy(alice) <- (9) [resolution 179,123]
323. $false <- (9) [subsumption resolution 322,137]
324. ~9 [avatar contradiction clause 323]
325. $false [avatar sat refutation 224,296,308,324]
% SZS output end Proof for 1465556613352494495827518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not patient and vice versa.
If someone is either rich or brave then alice is both not funny and curious and vice versa.
If someone is brave or not tall then lucy is either patient or rich and vice versa.
Everyone who is not strong or kind is either not humble or not old and vice versa.
If john is brave then lucy is not calm and vice versa.
If someone is not patient then someone is either tall or not happy.
Everyone who is either not quiet or not creative is both humble and creative.
If paul is either not curious or not happy then mary is either funny or strong and vice versa.
Everyone who is both patient and funny is both not rich and tall.
If someone is funny or tall then mary is both rich and not humble and vice versa.
Everyone who is not old is not humble or not strong and vice versa.
If fred is either not old or strong then john is quiet.
Everyone who is both quiet and not kind is either not wise or rich.
Everyone who is either rich or not curious is humble or happy.
Everyone who is strong is either curious or rich and vice versa.
Everyone who is rich is not tall or calm.
Someone is both old and patient.
Someone is either not calm or kind.
Someone is either happy or calm.
Paul is either not quiet or tall.
Someone is creative.
Mary is not tall or not humble.
Paul is not brave or not creative.
Someone is rich. | Paul is brave. | neutral | (![X]:(~calm(X)<=>~patient(X)))&
((?[X]:((rich(X)<~>brave(X))))<=>((~funny(alice)&curious(alice))))&
((?[X]:((brave(X)|~tall(X))))<=>((patient(lucy)<~>rich(lucy))))&
(![X]:((~strong(X)|kind(X))<=>(~humble(X)<~>~old(X))))&
((brave(john))<=>(~calm(lucy)))&
((?[X]:(~patient(X)))=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:((~quiet(X)<~>~creative(X))=>(humble(X)&creative(X))))&
(((~curious(paul)<~>~happy(paul)))<=>((funny(mary)<~>strong(mary))))&
(![X]:((patient(X)&funny(X))=>(~rich(X)&tall(X))))&
((?[X]:((funny(X)|tall(X))))<=>((rich(mary)&~humble(mary))))&
(![X]:(~old(X)<=>(~humble(X)|~strong(X))))&
(((~old(fred)<~>strong(fred)))=>(quiet(john)))&
(![X]:((quiet(X)&~kind(X))=>(~wise(X)<~>rich(X))))&
(![X]:((rich(X)<~>~curious(X))=>(humble(X)|happy(X))))&
(![X]:(strong(X)<=>(curious(X)<~>rich(X))))&
(![X]:(rich(X)=>(~tall(X)|calm(X))))&
(?[X]:((old(X)&patient(X))))&
(?[X]:((~calm(X)<~>kind(X))))&
(?[X]:((happy(X)<~>calm(X))))&
((~quiet(paul)<~>tall(paul)))&
(?[X]:(creative(X)))&
((~tall(mary)|~humble(mary)))&
((~brave(paul)|~creative(paul)))&
(?[X]:(rich(X))) | brave(paul) | [] | null | 0 |
If someone is both not calm and not rich then paul is either not old or funny and vice versa. If someone is not quiet then alice is happy or not patient and vice versa. Everyone who is either not funny or not brave is not calm or not quiet and vice versa. Everyone who is tall or funny is both not calm and not patient. Everyone who is both quiet and not funny is both not rich and not funny and vice versa. Everyone who is both wise and tall is both not calm and not kind and vice versa. If someone is not tall then someone is both not wise and humble. Everyone who is not creative is not brave or funny and vice versa. Everyone who is either kind or quiet is not brave or quiet and vice versa. Everyone who is both not happy and not old is not happy. Everyone who is both not brave and not strong is calm. Everyone who is wise is either not patient or kind. Everyone who is either not rich or not brave is kind or not quiet and vice versa. Everyone who is patient or generous is not curious or not brave. Everyone who is funny is creative. If susan is either not old or not funny then mary is either not happy or not tall. Paul is not wise or patient. Alice is either not wise or kind. John is both quiet and happy. Lucy is either not humble or not quiet. John is not generous. | John is curious. | neutral | ((?[X]:((~calm(X)&~rich(X))))<=>((~old(paul)<~>funny(paul))))&
((?[X]:(~quiet(X)))<=>((happy(alice)|~patient(alice))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~calm(X)|~quiet(X))))&
(![X]:((tall(X)|funny(X))=>(~calm(X)&~patient(X))))&
(![X]:((quiet(X)&~funny(X))<=>(~rich(X)&~funny(X))))&
(![X]:((wise(X)&tall(X))<=>(~calm(X)&~kind(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:(~creative(X)<=>(~brave(X)|funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>(~brave(X)|quiet(X))))&
(![X]:((~happy(X)&~old(X))=>~happy(X)))&
(![X]:((~brave(X)&~strong(X))=>calm(X)))&
(![X]:(wise(X)=>(~patient(X)<~>kind(X))))&
(![X]:((~rich(X)<~>~brave(X))<=>(kind(X)|~quiet(X))))&
(![X]:((patient(X)|generous(X))=>(~curious(X)|~brave(X))))&
(![X]:(funny(X)=>creative(X)))&
(((~old(susan)<~>~funny(susan)))=>((~happy(mary)<~>~tall(mary))))&
((~wise(paul)|patient(paul)))&
((~wise(alice)<~>kind(alice)))&
((quiet(john)&happy(john)))&
((~humble(lucy)<~>~quiet(lucy)))&
(~generous(john)) | curious(john) | [] | null | 0 |
Everyone who is both not strong and not happy is both curious and not curious and vice versa. Everyone who is happy or curious is old and vice versa. Everyone who is either strong or not rich is generous or humble and vice versa. If someone is either not rich or curious then someone is either calm or not kind and vice versa. Everyone who is both not calm and not tall is both quiet and not brave and vice versa. Everyone who is not generous is both not strong and not generous. If someone is rich then someone is both brave and creative and vice versa. Everyone who is not calm or not happy is curious. If john is curious then john is both not funny and strong and vice versa. Everyone who is either not old or old is both strong and generous and vice versa. Everyone who is creative is generous or strong. Everyone who is both funny and not tall is both wise and brave. If john is either not curious or not humble then someone is strong. Everyone who is not patient is brave or wise and vice versa. If mary is both creative and quiet then susan is either calm or not quiet. Everyone who is either funny or calm is both not old and tall. Fred is creative or humble. Susan is both not humble and not tall. Susan is not wise. Someone is not brave or creative. Someone is both not kind and patient. Someone is both patient and not kind. | Mary is funny. | neutral | (![X]:((~strong(X)&~happy(X))<=>(curious(X)&~curious(X))))&
(![X]:((happy(X)|curious(X))<=>old(X)))&
(![X]:((strong(X)<~>~rich(X))<=>(generous(X)|humble(X))))&
((?[X]:((~rich(X)<~>curious(X))))<=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((~calm(X)&~tall(X))<=>(quiet(X)&~brave(X))))&
(![X]:(~generous(X)=>(~strong(X)&~generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((~calm(X)|~happy(X))=>curious(X)))&
((curious(john))<=>((~funny(john)&strong(john))))&
(![X]:((~old(X)<~>old(X))<=>(strong(X)&generous(X))))&
(![X]:(creative(X)=>(generous(X)|strong(X))))&
(![X]:((funny(X)&~tall(X))=>(wise(X)&brave(X))))&
(((~curious(john)<~>~humble(john)))=>(?[X]:(strong(X))))&
(![X]:(~patient(X)<=>(brave(X)|wise(X))))&
(((creative(mary)&quiet(mary)))=>((calm(susan)<~>~quiet(susan))))&
(![X]:((funny(X)<~>calm(X))=>(~old(X)&tall(X))))&
((creative(fred)|humble(fred)))&
((~humble(susan)&~tall(susan)))&
(~wise(susan))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:((patient(X)&~kind(X)))) | funny(mary) | [] | null | 0 |
Everyone who is either old or humble is both not funny and not brave.
If someone is not old then susan is not happy and vice versa.
Everyone who is both generous and not quiet is either old or quiet.
Everyone who is quiet is not wise.
Everyone who is both not humble and kind is both not wise and strong and vice versa.
Everyone who is both not tall and calm is not happy or patient and vice versa.
If someone is not strong or humble then someone is either not happy or not humble.
Everyone who is not humble is happy or not generous.
If john is either strong or not kind then someone is either not quiet or not brave and vice versa.
If someone is not curious then fred is happy or not rich and vice versa.
Everyone who is both not happy and strong is not funny and vice versa.
If mary is not strong then someone is wise or quiet.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
Someone is calm or not rich.
Mary is not old or wise.
Someone is not old or not rich.
Someone is creative or not happy.
Someone is calm.
Someone is not calm or not brave.
Fred is not wise. | John is not humble. | neutral | (![X]:((old(X)<~>humble(X))=>(~funny(X)&~brave(X))))&
((?[X]:(~old(X)))<=>(~happy(susan)))&
(![X]:((generous(X)&~quiet(X))=>(old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>~wise(X)))&
(![X]:((~humble(X)&kind(X))<=>(~wise(X)&strong(X))))&
(![X]:((~tall(X)&calm(X))<=>(~happy(X)|patient(X))))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((~happy(X)<~>~humble(X)))))&
(![X]:(~humble(X)=>(happy(X)|~generous(X))))&
(((strong(john)<~>~kind(john)))<=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:(~curious(X)))<=>((happy(fred)|~rich(fred))))&
(![X]:((~happy(X)&strong(X))<=>~funny(X)))&
((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(?[X]:((calm(X)|~rich(X))))&
((~old(mary)|wise(mary)))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:((creative(X)|~happy(X))))&
(?[X]:(calm(X)))&
(?[X]:((~calm(X)|~brave(X))))&
(~wise(fred)) | ~humble(john) | [] | null | 0 |
Everyone who is either humble or old is patient or rich and vice versa.
If someone is calm or quiet then someone is humble or tall and vice versa.
Everyone who is not curious or calm is both quiet and happy.
Everyone who is either patient or not happy is not generous or strong and vice versa.
Everyone who is either funny or not humble is rich.
If someone is not strong then someone is not quiet or old and vice versa.
If john is either not strong or rich then someone is old and vice versa.
Everyone who is both generous and not old is both not humble and not generous and vice versa.
If paul is both calm and not calm then someone is not calm.
If someone is either generous or not quiet then susan is creative.
If lucy is not quiet or not generous then someone is not funny or not humble.
If fred is either strong or quiet then someone is either not strong or not patient.
If someone is both funny and not humble then someone is either humble or generous.
If lucy is generous then someone is both calm and funny.
Everyone who is not strong is strong.
If someone is tall or not calm then susan is not patient or old and vice versa.
Someone is not patient or patient.
Someone is both not curious and not old.
Lucy is not patient or creative.
Susan is not rich.
Someone is both not generous and not brave.
Someone is either patient or rich.
Someone is not funny or not strong. | John is not patient. | contradiction | (![X]:((humble(X)<~>old(X))<=>(patient(X)|rich(X))))&
((?[X]:((calm(X)|quiet(X))))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((~curious(X)|calm(X))=>(quiet(X)&happy(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(~generous(X)|strong(X))))&
(![X]:((funny(X)<~>~humble(X))=>rich(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~quiet(X)|old(X)))))&
(((~strong(john)<~>rich(john)))<=>(?[X]:(old(X))))&
(![X]:((generous(X)&~old(X))<=>(~humble(X)&~generous(X))))&
(((calm(paul)&~calm(paul)))=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)<~>~quiet(X))))=>(creative(susan)))&
(((~quiet(lucy)|~generous(lucy)))=>(?[X]:((~funny(X)|~humble(X)))))&
(((strong(fred)<~>quiet(fred)))=>(?[X]:((~strong(X)<~>~patient(X)))))&
((?[X]:((funny(X)&~humble(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
((generous(lucy))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:(~strong(X)=>strong(X)))&
((?[X]:((tall(X)|~calm(X))))<=>((~patient(susan)|old(susan))))&
(?[X]:((~patient(X)|patient(X))))&
(?[X]:((~curious(X)&~old(X))))&
((~patient(lucy)|creative(lucy)))&
(~rich(susan))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:((~funny(X)|~strong(X)))) | ~patient(john) | [
"p0",
"p5",
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7219711795631759093934253
% SZS output start Proof for 7219711795631759093934253
1. ! [X0] : ((humble(X0) <~> old(X0)) <=> (rich(X0) | patient(X0))) [input p0]
6. ? [X0] : ~strong(X0) <=> ? [X0] : (old(X0) | ~quiet(X0)) [input p5]
7. (~strong(john) <~> rich(john)) <=> ? [X0] : old(X0) [input p6]
8. ! [X0] : ((~old(X0) & generous(X0)) <=> (~generous(X0) & ~humble(X0))) [input p7]
15. ! [X0] : (~strong(X0) => strong(X0)) [input p14]
24. ~patient(john) [input hypothesis]
26. ? [X0] : ~strong(X0) <=> ? [X1] : (old(X1) | ~quiet(X1)) [rectify 6]
39. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 15]
40. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 40]
50. (? [X0] : ~strong(X0) | ! [X1] : (~old(X1) & quiet(X1))) & (? [X1] : (old(X1) | ~quiet(X1)) | ! [X0] : strong(X0)) [nnf transformation 26]
51. (? [X0] : ~strong(X0) | ! [X1] : (~old(X1) & quiet(X1))) & (? [X2] : (old(X2) | ~quiet(X2)) | ! [X3] : strong(X3)) [rectify 50]
52. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
53. ? [X2] : (old(X2) | ~quiet(X2)) => (old(sK3) | ~quiet(sK3)) [choice axiom]
54. (~strong(sK2) | ! [X1] : (~old(X1) & quiet(X1))) & ((old(sK3) | ~quiet(sK3)) | ! [X3] : strong(X3)) [skolemisation 51,53,52]
55. (((~rich(john) | strong(john)) & (rich(john) | ~strong(john))) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ((~strong(john) | ~rich(john)) & (rich(john) | strong(john)))) [nnf transformation 7]
56. (((~rich(john) | strong(john)) & (rich(john) | ~strong(john))) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ((~strong(john) | ~rich(john)) & (rich(john) | strong(john)))) [rectify 55]
57. ? [X1] : old(X1) => old(sK4) [choice axiom]
58. (((~rich(john) | strong(john)) & (rich(john) | ~strong(john))) | ! [X0] : ~old(X0)) & (old(sK4) | ((~strong(john) | ~rich(john)) & (rich(john) | strong(john)))) [skolemisation 56,57]
59. ! [X0] : (((~old(X0) & generous(X0)) | (generous(X0) | humble(X0))) & ((~generous(X0) & ~humble(X0)) | (old(X0) | ~generous(X0)))) [nnf transformation 8]
60. ! [X0] : (((~old(X0) & generous(X0)) | generous(X0) | humble(X0)) & ((~generous(X0) & ~humble(X0)) | old(X0) | ~generous(X0))) [flattening 59]
90. ~humble(X0) | patient(X0) | old(X0) | rich(X0) [cnf transformation 41]
114. ~strong(sK2) | ~old(X1) [cnf transformation 54]
116. old(sK4) | ~strong(john) | ~rich(john) [cnf transformation 58]
120. ~generous(X0) | old(X0) | ~generous(X0) [cnf transformation 60]
121. generous(X0) | generous(X0) | humble(X0) [cnf transformation 60]
134. strong(X0) | strong(X0) [cnf transformation 39]
147. ~patient(john) [cnf transformation 24]
148. strong(X0) [duplicate literal removal 134]
149. ~generous(X0) | old(X0) [duplicate literal removal 120]
150. generous(X0) | humble(X0) [duplicate literal removal 121]
184. 9 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (9) [avatar component clause 184]
187. 10 <=> strong(sK2) [avatar definition]
189. ~strong(sK2) <- (~10) [avatar component clause 187]
190. 9 | ~10 [avatar split clause 114,187,184]
196. 12 <=> ! [X3] : strong(X3) [avatar definition]
197. strong(X3) <- (12) [avatar component clause 196]
208. 15 <=> strong(john) [avatar definition]
209. ~strong(john) <- (~15) [avatar component clause 208]
212. 16 <=> rich(john) [avatar definition]
214. ~rich(john) <- (~16) [avatar component clause 212]
218. 17 <=> old(sK4) [avatar definition]
220. old(sK4) <- (17) [avatar component clause 218]
221. ~16 | ~15 | 17 [avatar split clause 116,218,208,212]
283. 12 [avatar split clause 148,196]
326. $false <- (~10, 12) [subsumption resolution 189,197]
327. 10 | ~12 [avatar contradiction clause 326]
335. humble(X0) | old(X0) [resolution 150,149]
339. humble(X0) <- (9) [subsumption resolution 335,185]
382. patient(X0) | old(X0) | rich(X0) <- (9) [resolution 90,339]
393. rich(X0) | patient(X0) <- (9) [subsumption resolution 382,185]
401. patient(john) <- (9, ~16) [resolution 393,214]
403. $false <- (9, ~16) [subsumption resolution 401,147]
404. ~9 | 16 [avatar contradiction clause 403]
410. $false <- (12, ~15) [subsumption resolution 209,197]
411. ~12 | 15 [avatar contradiction clause 410]
412. $false <- (9, 17) [subsumption resolution 220,185]
413. ~9 | ~17 [avatar contradiction clause 412]
414. $false [avatar sat refutation 190,221,283,327,404,411,413]
% SZS output end Proof for 7219711795631759093934253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not rich and not creative then someone is either happy or not happy and vice versa.
If someone is either not quiet or not calm then susan is both not calm and not creative and vice versa.
Everyone who is both not old and quiet is wise or brave and vice versa.
Everyone who is both generous and not brave is brave or not calm and vice versa.
Everyone who is either not humble or not generous is not strong or not generous.
Everyone who is not strong is both calm and not brave.
If susan is both funny and not humble then someone is not old.
Everyone who is not quiet or curious is funny and vice versa.
Everyone who is either old or creative is either creative or patient.
Everyone who is patient or not quiet is not brave and vice versa.
Everyone who is either not kind or not curious is not tall or not generous.
If someone is both funny and not brave then someone is either generous or kind.
If mary is either patient or curious then mary is either patient or not happy.
If someone is both generous and not funny then susan is both not funny and curious and vice versa.
If someone is both not funny and patient then alice is creative or not creative.
If someone is both not patient and calm then someone is calm and vice versa.
Someone is either rich or wise.
Lucy is either not tall or not brave.
Lucy is either rich or creative.
John is both not patient and curious.
Susan is happy.
Someone is both quiet and not old.
Mary is not generous or wise. | Susan is humble. | entailment | (((~rich(mary)&~creative(mary)))<=>(?[X]:((happy(X)<~>~happy(X)))))&
((?[X]:((~quiet(X)<~>~calm(X))))<=>((~calm(susan)&~creative(susan))))&
(![X]:((~old(X)&quiet(X))<=>(wise(X)|brave(X))))&
(![X]:((generous(X)&~brave(X))<=>(brave(X)|~calm(X))))&
(![X]:((~humble(X)<~>~generous(X))=>(~strong(X)|~generous(X))))&
(![X]:(~strong(X)=>(calm(X)&~brave(X))))&
(((funny(susan)&~humble(susan)))=>(?[X]:(~old(X))))&
(![X]:((~quiet(X)|curious(X))<=>funny(X)))&
(![X]:((old(X)<~>creative(X))=>(creative(X)<~>patient(X))))&
(![X]:((patient(X)|~quiet(X))<=>~brave(X)))&
(![X]:((~kind(X)<~>~curious(X))=>(~tall(X)|~generous(X))))&
((?[X]:((funny(X)&~brave(X))))=>(?[X]:((generous(X)<~>kind(X)))))&
(((patient(mary)<~>curious(mary)))=>((patient(mary)<~>~happy(mary))))&
((?[X]:((generous(X)&~funny(X))))<=>((~funny(susan)&curious(susan))))&
((?[X]:((~funny(X)&patient(X))))=>((creative(alice)|~creative(alice))))&
((?[X]:((~patient(X)&calm(X))))<=>(?[X]:(calm(X))))&
(?[X]:((rich(X)<~>wise(X))))&
((~tall(lucy)<~>~brave(lucy)))&
((rich(lucy)<~>creative(lucy)))&
((~patient(john)&curious(john)))&
(happy(susan))&
(?[X]:((quiet(X)&~old(X))))&
((~generous(mary)|wise(mary))) | humble(susan) | [
"p1",
"p3",
"p4",
"p5",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9090258229708257553707296
% SZS output start Proof for 9090258229708257553707296
2. ? [X0] : (~quiet(X0) <~> ~calm(X0)) <=> (~creative(susan) & ~calm(susan)) [input p1]
4. ! [X0] : ((~brave(X0) & generous(X0)) <=> (~calm(X0) | brave(X0))) [input p3]
5. ! [X0] : ((~humble(X0) <~> ~generous(X0)) => (~generous(X0) | ~strong(X0))) [input p4]
6. ! [X0] : (~strong(X0) => (~brave(X0) & calm(X0))) [input p5]
10. ! [X0] : ((~quiet(X0) | patient(X0)) <=> ~brave(X0)) [input p9]
16. ? [X0] : (calm(X0) & ~patient(X0)) <=> ? [X0] : calm(X0) [input p15]
24. ~humble(susan) [input hypothesis]
26. ? [X0] : (calm(X0) & ~patient(X0)) <=> ? [X1] : calm(X1) [rectify 16]
27. ! [X0] : ((~generous(X0) | ~strong(X0)) | (~humble(X0) <=> ~generous(X0))) [ennf transformation 5]
28. ! [X0] : (~generous(X0) | ~strong(X0) | (~humble(X0) <=> ~generous(X0))) [flattening 27]
29. ! [X0] : ((~brave(X0) & calm(X0)) | strong(X0)) [ennf transformation 6]
44. (? [X0] : ((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (creative(susan) | calm(susan))) & ((~creative(susan) & ~calm(susan)) | ! [X0] : ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0)))) [nnf transformation 2]
45. (? [X0] : ((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | creative(susan) | calm(susan)) & ((~creative(susan) & ~calm(susan)) | ! [X0] : ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0)))) [flattening 44]
46. (? [X0] : ((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | creative(susan) | calm(susan)) & ((~creative(susan) & ~calm(susan)) | ! [X1] : ((~quiet(X1) | calm(X1)) & (~calm(X1) | quiet(X1)))) [rectify 45]
47. ? [X0] : ((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) => ((calm(sK1) | quiet(sK1)) & (~calm(sK1) | ~quiet(sK1))) [choice axiom]
48. (((calm(sK1) | quiet(sK1)) & (~calm(sK1) | ~quiet(sK1))) | creative(susan) | calm(susan)) & ((~creative(susan) & ~calm(susan)) | ! [X1] : ((~quiet(X1) | calm(X1)) & (~calm(X1) | quiet(X1)))) [skolemisation 46,47]
51. ! [X0] : (((~brave(X0) & generous(X0)) | (calm(X0) & ~brave(X0))) & ((~calm(X0) | brave(X0)) | (brave(X0) | ~generous(X0)))) [nnf transformation 4]
52. ! [X0] : (((~brave(X0) & generous(X0)) | (calm(X0) & ~brave(X0))) & (~calm(X0) | brave(X0) | brave(X0) | ~generous(X0))) [flattening 51]
53. ! [X0] : (~generous(X0) | ~strong(X0) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) [nnf transformation 28]
59. ! [X0] : (((~quiet(X0) | patient(X0)) | brave(X0)) & (~brave(X0) | (quiet(X0) & ~patient(X0)))) [nnf transformation 10]
60. ! [X0] : ((~quiet(X0) | patient(X0) | brave(X0)) & (~brave(X0) | (quiet(X0) & ~patient(X0)))) [flattening 59]
72. (? [X0] : (calm(X0) & ~patient(X0)) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : (~calm(X0) | patient(X0))) [nnf transformation 26]
73. (? [X0] : (calm(X0) & ~patient(X0)) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : (~calm(X3) | patient(X3))) [rectify 72]
74. ? [X0] : (calm(X0) & ~patient(X0)) => (calm(sK5) & ~patient(sK5)) [choice axiom]
75. ? [X2] : calm(X2) => calm(sK6) [choice axiom]
76. ((calm(sK5) & ~patient(sK5)) | ! [X1] : ~calm(X1)) & (calm(sK6) | ! [X3] : (~calm(X3) | patient(X3))) [skolemisation 73,75,74]
90. ~calm(susan) | ~calm(X1) | quiet(X1) [cnf transformation 48]
101. ~calm(X0) | brave(X0) | brave(X0) | ~generous(X0) [cnf transformation 52]
103. generous(X0) | calm(X0) [cnf transformation 52]
104. ~brave(X0) | ~brave(X0) [cnf transformation 52]
106. ~generous(X0) | ~strong(X0) | ~generous(X0) | humble(X0) [cnf transformation 53]
108. strong(X0) | calm(X0) [cnf transformation 29]
120. ~quiet(X0) | patient(X0) | brave(X0) [cnf transformation 60]
135. ~patient(sK5) | ~calm(X1) [cnf transformation 76]
136. calm(sK5) | ~calm(X1) [cnf transformation 76]
149. ~humble(susan) [cnf transformation 24]
154. ~strong(X0) | ~generous(X0) | humble(X0) [duplicate literal removal 106]
155. ~calm(X0) | brave(X0) | ~generous(X0) [duplicate literal removal 101]
156. ~brave(X0) [duplicate literal removal 104]
180. 5 <=> calm(susan) [avatar definition]
182. calm(susan) <- (5) [avatar component clause 180]
202. 10 <=> ! [X1] : (~calm(X1) | quiet(X1)) [avatar definition]
203. ~calm(X1) | quiet(X1) <- (10) [avatar component clause 202]
206. 10 | ~5 [avatar split clause 90,180,202]
207. ~generous(X0) | ~calm(X0) [subsumption resolution 155,156]
213. 12 <=> humble(susan) [avatar definition]
214. ~humble(susan) <- (~12) [avatar component clause 213]
221. ~quiet(X0) | patient(X0) [subsumption resolution 120,156]
261. 22 <=> ! [X1] : ~calm(X1) [avatar definition]
262. ~calm(X1) <- (22) [avatar component clause 261]
264. 23 <=> calm(sK5) [avatar definition]
266. calm(sK5) <- (23) [avatar component clause 264]
267. 22 | 23 [avatar split clause 136,264,261]
269. 24 <=> patient(sK5) [avatar definition]
271. ~patient(sK5) <- (~24) [avatar component clause 269]
272. 22 | ~24 [avatar split clause 135,269,261]
311. ~12 [avatar split clause 149,213]
357. ~generous(X0) | humble(X0) | calm(X0) [resolution 154,108]
358. ~generous(X0) | humble(X0) [subsumption resolution 357,207]
408. humble(X0) | calm(X0) [resolution 358,103]
410. calm(susan) <- (~12) [resolution 408,214]
413. 5 | 12 [avatar split clause 410,213,180]
421. quiet(sK5) <- (10, 23) [resolution 203,266]
435. patient(sK5) <- (10, 23) [resolution 421,221]
446. $false <- (10, 23, ~24) [subsumption resolution 435,271]
447. ~10 | ~23 | 24 [avatar contradiction clause 446]
448. $false <- (5, 22) [resolution 262,182]
453. ~5 | ~22 [avatar contradiction clause 448]
454. $false [avatar sat refutation 206,267,272,311,413,447,453]
% SZS output end Proof for 9090258229708257553707296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and humble is both not curious and strong and vice versa.
Everyone who is patient or humble is happy.
Everyone who is both not creative and happy is tall and vice versa.
Everyone who is not humble or creative is generous or not happy.
Everyone who is both not wise and strong is either old or quiet.
If alice is either not quiet or funny then mary is either rich or not calm.
Everyone who is both old and quiet is both not calm and rich and vice versa.
If someone is both wise and not rich then paul is not generous or not old.
If someone is not generous then someone is generous or wise and vice versa.
Everyone who is old is either not creative or not funny and vice versa.
Everyone who is humble or not kind is calm or not generous.
If lucy is generous or rich then someone is both not funny and strong and vice versa.
If someone is not quiet or old then alice is not curious and vice versa.
Everyone who is either quiet or not humble is either not calm or quiet.
If susan is not tall or calm then someone is not generous.
If fred is both not patient and generous then lucy is funny.
Someone is both rich and not patient.
Someone is both not funny and quiet.
Someone is not strong.
Someone is both creative and not kind.
Someone is either kind or wise.
Susan is not calm.
Someone is either humble or curious.
Susan is strong or not brave. | Fred is not patient. | neutral | (![X]:((~kind(X)&humble(X))<=>(~curious(X)&strong(X))))&
(![X]:((patient(X)|humble(X))=>happy(X)))&
(![X]:((~creative(X)&happy(X))<=>tall(X)))&
(![X]:((~humble(X)|creative(X))=>(generous(X)|~happy(X))))&
(![X]:((~wise(X)&strong(X))=>(old(X)<~>quiet(X))))&
(((~quiet(alice)<~>funny(alice)))=>((rich(mary)<~>~calm(mary))))&
(![X]:((old(X)&quiet(X))<=>(~calm(X)&rich(X))))&
((?[X]:((wise(X)&~rich(X))))=>((~generous(paul)|~old(paul))))&
((?[X]:(~generous(X)))<=>(?[X]:((generous(X)|wise(X)))))&
(![X]:(old(X)<=>(~creative(X)<~>~funny(X))))&
(![X]:((humble(X)|~kind(X))=>(calm(X)|~generous(X))))&
(((generous(lucy)|rich(lucy)))<=>(?[X]:((~funny(X)&strong(X)))))&
((?[X]:((~quiet(X)|old(X))))<=>(~curious(alice)))&
(![X]:((quiet(X)<~>~humble(X))=>(~calm(X)<~>quiet(X))))&
(((~tall(susan)|calm(susan)))=>(?[X]:(~generous(X))))&
(((~patient(fred)&generous(fred)))=>(funny(lucy)))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:((~funny(X)&quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:((creative(X)&~kind(X))))&
(?[X]:((kind(X)<~>wise(X))))&
(~calm(susan))&
(?[X]:((humble(X)<~>curious(X))))&
((strong(susan)|~brave(susan))) | ~patient(fred) | [] | null | 0 |
If someone is not curious then susan is curious or not humble and vice versa.
If alice is either old or not patient then someone is tall or curious.
Everyone who is both wise and not quiet is curious or strong and vice versa.
If lucy is either not wise or tall then someone is brave and vice versa.
Everyone who is both funny and curious is not wise.
Everyone who is both tall and funny is both old and not patient and vice versa.
If susan is calm then someone is both not strong and rich.
Everyone who is not tall or creative is rich or not old.
If someone is tall or not patient then mary is strong and vice versa.
If someone is not generous then someone is either not curious or generous.
Everyone who is strong is both not humble and kind.
If someone is not quiet or generous then alice is not curious and vice versa.
Everyone who is not patient or patient is both not curious and happy and vice versa.
If someone is both quiet and not rich then susan is strong.
Everyone who is either kind or not brave is both not brave and kind and vice versa.
If someone is not humble or kind then lucy is both not funny and not calm and vice versa.
Someone is either not funny or not calm.
John is either curious or not curious.
Paul is both creative and not curious.
Someone is patient.
Someone is either not funny or strong. | Paul is not humble. | neutral | ((?[X]:(~curious(X)))<=>((curious(susan)|~humble(susan))))&
(((old(alice)<~>~patient(alice)))=>(?[X]:((tall(X)|curious(X)))))&
(![X]:((wise(X)&~quiet(X))<=>(curious(X)|strong(X))))&
(((~wise(lucy)<~>tall(lucy)))<=>(?[X]:(brave(X))))&
(![X]:((funny(X)&curious(X))=>~wise(X)))&
(![X]:((tall(X)&funny(X))<=>(old(X)&~patient(X))))&
((calm(susan))=>(?[X]:((~strong(X)&rich(X)))))&
(![X]:((~tall(X)|creative(X))=>(rich(X)|~old(X))))&
((?[X]:((tall(X)|~patient(X))))<=>(strong(mary)))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:(strong(X)=>(~humble(X)&kind(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>(~curious(alice)))&
(![X]:((~patient(X)|patient(X))<=>(~curious(X)&happy(X))))&
((?[X]:((quiet(X)&~rich(X))))=>(strong(susan)))&
(![X]:((kind(X)<~>~brave(X))<=>(~brave(X)&kind(X))))&
((?[X]:((~humble(X)|kind(X))))<=>((~funny(lucy)&~calm(lucy))))&
(?[X]:((~funny(X)<~>~calm(X))))&
((curious(john)<~>~curious(john)))&
((creative(paul)&~curious(paul)))&
(?[X]:(patient(X)))&
(?[X]:((~funny(X)<~>strong(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is both quiet and not generous is either not tall or brave and vice versa.
If someone is either strong or wise then fred is funny and vice versa.
Everyone who is either not happy or old is either quiet or creative.
Everyone who is both humble and tall is not humble or not calm and vice versa.
If susan is either wise or happy then alice is either humble or old.
Everyone who is both not tall and not wise is not brave and vice versa.
Everyone who is both humble and generous is tall or not tall and vice versa.
Everyone who is both not quiet and not rich is strong or not brave.
Everyone who is either not funny or rich is curious.
Everyone who is either not generous or curious is either creative or not generous.
If someone is not creative or funny then john is rich and vice versa.
If someone is both not old and not rich then someone is both tall and kind and vice versa.
If susan is patient or brave then someone is both not creative and strong and vice versa.
Everyone who is not old is both not creative and generous.
If someone is quiet then someone is not creative.
Lucy is kind or not kind.
Lucy is not rich or wise.
Someone is not happy.
Someone is not strong.
John is either curious or kind.
Someone is not calm or happy. | John is quiet. | neutral | (![X]:((quiet(X)&~generous(X))<=>(~tall(X)<~>brave(X))))&
((?[X]:((strong(X)<~>wise(X))))<=>(funny(fred)))&
(![X]:((~happy(X)<~>old(X))=>(quiet(X)<~>creative(X))))&
(![X]:((humble(X)&tall(X))<=>(~humble(X)|~calm(X))))&
(((wise(susan)<~>happy(susan)))=>((humble(alice)<~>old(alice))))&
(![X]:((~tall(X)&~wise(X))<=>~brave(X)))&
(![X]:((humble(X)&generous(X))<=>(tall(X)|~tall(X))))&
(![X]:((~quiet(X)&~rich(X))=>(strong(X)|~brave(X))))&
(![X]:((~funny(X)<~>rich(X))=>curious(X)))&
(![X]:((~generous(X)<~>curious(X))=>(creative(X)<~>~generous(X))))&
((?[X]:((~creative(X)|funny(X))))<=>(rich(john)))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:((tall(X)&kind(X)))))&
(((patient(susan)|brave(susan)))<=>(?[X]:((~creative(X)&strong(X)))))&
(![X]:(~old(X)=>(~creative(X)&generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:(~creative(X))))&
((kind(lucy)|~kind(lucy)))&
((~rich(lucy)|wise(lucy)))&
(?[X]:(~happy(X)))&
(?[X]:(~strong(X)))&
((curious(john)<~>kind(john)))&
(?[X]:((~calm(X)|happy(X)))) | quiet(john) | [] | null | 0 |
Everyone who is curious is both not quiet and not kind.
If mary is both not old and creative then someone is not patient or not quiet and vice versa.
If someone is generous then paul is both not rich and patient.
Everyone who is humble is rich and vice versa.
If someone is either not kind or not quiet then paul is not rich and vice versa.
Everyone who is either happy or not curious is both not wise and not strong and vice versa.
Everyone who is tall or not generous is not brave or generous and vice versa.
If someone is quiet or calm then someone is patient or not quiet.
Everyone who is kind is not old or not curious.
Everyone who is both quiet and not old is both old and not happy.
If fred is either kind or not happy then mary is both not humble and not calm and vice versa.
Everyone who is both tall and old is both curious and kind and vice versa.
If mary is not funny then fred is both not rich and kind.
If alice is funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy.
Lucy is not kind. | Paul is quiet. | entailment | (![X]:(curious(X)=>(~quiet(X)&~kind(X))))&
(((~old(mary)&creative(mary)))<=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:(generous(X)))=>((~rich(paul)&patient(paul))))&
(![X]:(humble(X)<=>rich(X)))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(~rich(paul)))&
(![X]:((happy(X)<~>~curious(X))<=>(~wise(X)&~strong(X))))&
(![X]:((tall(X)|~generous(X))<=>(~brave(X)|generous(X))))&
((?[X]:((quiet(X)|calm(X))))=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:(kind(X)=>(~old(X)|~curious(X))))&
(![X]:((quiet(X)&~old(X))=>(old(X)&~happy(X))))&
(((kind(fred)<~>~happy(fred)))<=>((~humble(mary)&~calm(mary))))&
(![X]:((tall(X)&old(X))<=>(curious(X)&kind(X))))&
((~funny(mary))=>((~rich(fred)&kind(fred))))&
((funny(alice))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy)))&
(~kind(lucy)) | quiet(paul) | [
"p1",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8457985221817882904213400
% SZS output start Proof for 8457985221817882904213400
2. (creative(mary) & ~old(mary)) <=> ? [X0] : (~quiet(X0) | ~patient(X0)) [input p1]
10. ! [X0] : ((~old(X0) & quiet(X0)) => (~happy(X0) & old(X0))) [input p9]
17. quiet(mary) [input p16]
25. ~quiet(paul) [input hypothesis]
32. ! [X0] : ((~happy(X0) & old(X0)) | (old(X0) | ~quiet(X0))) [ennf transformation 10]
33. ! [X0] : ((~happy(X0) & old(X0)) | old(X0) | ~quiet(X0)) [flattening 32]
37. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X0] : (~quiet(X0) | ~patient(X0)) | (~creative(mary) | old(mary))) [nnf transformation 2]
38. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X0] : (~quiet(X0) | ~patient(X0)) | ~creative(mary) | old(mary)) [flattening 37]
39. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & (? [X1] : (~quiet(X1) | ~patient(X1)) | ~creative(mary) | old(mary)) [rectify 38]
40. ? [X1] : (~quiet(X1) | ~patient(X1)) => (~quiet(sK0) | ~patient(sK0)) [choice axiom]
41. ((creative(mary) & ~old(mary)) | ! [X0] : (quiet(X0) & patient(X0))) & ((~quiet(sK0) | ~patient(sK0)) | ~creative(mary) | old(mary)) [skolemisation 39,40]
77. ~old(mary) | quiet(X0) [cnf transformation 41]
101. old(X0) | old(X0) | ~quiet(X0) [cnf transformation 33]
123. quiet(mary) [cnf transformation 17]
134. ~quiet(paul) [cnf transformation 25]
135. ~quiet(X0) | old(X0) [duplicate literal removal 101]
139. 1 <=> ! [X0] : quiet(X0) [avatar definition]
140. quiet(X0) <- (1) [avatar component clause 139]
151. 4 <=> old(mary) [avatar definition]
154. 1 | ~4 [avatar split clause 77,151,139]
298. old(mary) [resolution 135,123]
302. 4 [avatar split clause 298,151]
305. $false <- (1) [resolution 140,134]
310. ~1 [avatar contradiction clause 305]
311. $false [avatar sat refutation 154,302,310]
% SZS output end Proof for 8457985221817882904213400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not humble is generous or not patient and vice versa. Everyone who is either not wise or kind is both kind and not strong. Everyone who is not calm or not funny is creative or tall and vice versa. Everyone who is patient or humble is either funny or tall. Everyone who is both old and not rich is kind. Everyone who is both kind and quiet is not old or strong. Everyone who is humble is either not patient or funny. If lucy is happy or funny then someone is either not funny or humble. If someone is not humble or not kind then alice is happy or rich and vice versa. Everyone who is both rich and not patient is either kind or rich and vice versa. If alice is both calm and not tall then someone is not humble or rich and vice versa. Everyone who is creative is not strong and vice versa. If someone is both rich and curious then someone is calm or creative and vice versa. If alice is either not strong or not tall then someone is either not rich or not funny and vice versa. If mary is creative or not tall then susan is either calm or not curious. Someone is strong or not tall. Someone is either patient or not patient. Someone is either patient or tall. Someone is either not brave or happy. Someone is funny. Someone is either kind or wise. Someone is not tall. Someone is either not old or wise. | Alice is not creative. | entailment | (![X]:((calm(X)<~>~humble(X))<=>(generous(X)|~patient(X))))&
(![X]:((~wise(X)<~>kind(X))=>(kind(X)&~strong(X))))&
(![X]:((~calm(X)|~funny(X))<=>(creative(X)|tall(X))))&
(![X]:((patient(X)|humble(X))=>(funny(X)<~>tall(X))))&
(![X]:((old(X)&~rich(X))=>kind(X)))&
(![X]:((kind(X)&quiet(X))=>(~old(X)|strong(X))))&
(![X]:(humble(X)=>(~patient(X)<~>funny(X))))&
(((happy(lucy)|funny(lucy)))=>(?[X]:((~funny(X)<~>humble(X)))))&
((?[X]:((~humble(X)|~kind(X))))<=>((happy(alice)|rich(alice))))&
(![X]:((rich(X)&~patient(X))<=>(kind(X)<~>rich(X))))&
(((calm(alice)&~tall(alice)))<=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:(creative(X)<=>~strong(X)))&
((?[X]:((rich(X)&curious(X))))<=>(?[X]:((calm(X)|creative(X)))))&
(((~strong(alice)<~>~tall(alice)))<=>(?[X]:((~rich(X)<~>~funny(X)))))&
(((creative(mary)|~tall(mary)))=>((calm(susan)<~>~curious(susan))))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:((patient(X)<~>tall(X))))&
(?[X]:((~brave(X)<~>happy(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~old(X)<~>wise(X)))) | ~creative(alice) | [
"p0",
"p2",
"p3",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2000136663123490795427391
% SZS output start Proof for 2000136663123490795427391
1. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> (~patient(X0) | generous(X0))) [input p0]
3. ! [X0] : ((~funny(X0) | ~calm(X0)) <=> (tall(X0) | creative(X0))) [input p2]
4. ! [X0] : ((humble(X0) | patient(X0)) => (funny(X0) <~> tall(X0))) [input p3]
11. (~tall(alice) & calm(alice)) <=> ? [X0] : (rich(X0) | ~humble(X0)) [input p10]
13. ? [X0] : (curious(X0) & rich(X0)) <=> ? [X0] : (creative(X0) | calm(X0)) [input p12]
24. creative(alice) [input hypothesis]
25. ? [X0] : (curious(X0) & rich(X0)) <=> ? [X1] : (creative(X1) | calm(X1)) [rectify 13]
28. ! [X0] : ((funny(X0) <~> tall(X0)) | (~humble(X0) & ~patient(X0))) [ennf transformation 4]
34. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (patient(X0) & ~generous(X0))) & ((~patient(X0) | generous(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 1]
35. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (patient(X0) & ~generous(X0))) & (~patient(X0) | generous(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [flattening 34]
37. ! [X0] : (((~funny(X0) | ~calm(X0)) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | (funny(X0) & calm(X0)))) [nnf transformation 3]
38. ! [X0] : ((~funny(X0) | ~calm(X0) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | (funny(X0) & calm(X0)))) [flattening 37]
39. ! [X0] : (((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~humble(X0) & ~patient(X0))) [nnf transformation 28]
51. ((~tall(alice) & calm(alice)) | ! [X0] : (~rich(X0) & humble(X0))) & (? [X0] : (rich(X0) | ~humble(X0)) | (tall(alice) | ~calm(alice))) [nnf transformation 11]
52. ((~tall(alice) & calm(alice)) | ! [X0] : (~rich(X0) & humble(X0))) & (? [X0] : (rich(X0) | ~humble(X0)) | tall(alice) | ~calm(alice)) [flattening 51]
53. ((~tall(alice) & calm(alice)) | ! [X0] : (~rich(X0) & humble(X0))) & (? [X1] : (rich(X1) | ~humble(X1)) | tall(alice) | ~calm(alice)) [rectify 52]
54. ? [X1] : (rich(X1) | ~humble(X1)) => (rich(sK2) | ~humble(sK2)) [choice axiom]
55. ((~tall(alice) & calm(alice)) | ! [X0] : (~rich(X0) & humble(X0))) & ((rich(sK2) | ~humble(sK2)) | tall(alice) | ~calm(alice)) [skolemisation 53,54]
57. (? [X0] : (curious(X0) & rich(X0)) | ! [X1] : (~creative(X1) & ~calm(X1))) & (? [X1] : (creative(X1) | calm(X1)) | ! [X0] : (~curious(X0) | ~rich(X0))) [nnf transformation 25]
58. (? [X0] : (curious(X0) & rich(X0)) | ! [X1] : (~creative(X1) & ~calm(X1))) & (? [X2] : (creative(X2) | calm(X2)) | ! [X3] : (~curious(X3) | ~rich(X3))) [rectify 57]
59. ? [X0] : (curious(X0) & rich(X0)) => (curious(sK3) & rich(sK3)) [choice axiom]
60. ? [X2] : (creative(X2) | calm(X2)) => (creative(sK4) | calm(sK4)) [choice axiom]
61. ((curious(sK3) & rich(sK3)) | ! [X1] : (~creative(X1) & ~calm(X1))) & ((creative(sK4) | calm(sK4)) | ! [X3] : (~curious(X3) | ~rich(X3))) [skolemisation 58,60,59]
93. ~calm(X0) | humble(X0) | patient(X0) [cnf transformation 35]
100. ~creative(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 38]
102. ~patient(X0) | funny(X0) | tall(X0) [cnf transformation 39]
103. ~humble(X0) | funny(X0) | tall(X0) [cnf transformation 39]
125. calm(alice) | ~rich(X0) [cnf transformation 55]
127. ~tall(alice) | ~rich(X0) [cnf transformation 55]
132. rich(sK3) | ~creative(X1) [cnf transformation 61]
160. creative(alice) [cnf transformation 24]
212. 11 <=> ! [X0] : ~rich(X0) [avatar definition]
213. ~rich(X0) <- (11) [avatar component clause 212]
215. 12 <=> tall(alice) [avatar definition]
217. ~tall(alice) <- (~12) [avatar component clause 215]
218. 11 | ~12 [avatar split clause 127,215,212]
221. 13 <=> calm(alice) [avatar definition]
223. calm(alice) <- (13) [avatar component clause 221]
224. 11 | 13 [avatar split clause 125,221,212]
236. 16 <=> ! [X1] : ~creative(X1) [avatar definition]
237. ~creative(X1) <- (16) [avatar component clause 236]
248. 19 <=> rich(sK3) [avatar definition]
250. rich(sK3) <- (19) [avatar component clause 248]
251. 16 | 19 [avatar split clause 132,248,236]
363. $false <- (16) [resolution 237,160]
364. ~16 [avatar contradiction clause 363]
365. $false <- (11, 19) [subsumption resolution 250,213]
366. ~11 | ~19 [avatar contradiction clause 365]
387. humble(alice) | patient(alice) <- (13) [resolution 93,223]
441. ~calm(alice) | ~funny(alice) [resolution 100,160]
444. ~funny(alice) <- (13) [subsumption resolution 441,223]
692. 82 <=> patient(alice) [avatar definition]
694. patient(alice) <- (82) [avatar component clause 692]
696. 83 <=> humble(alice) [avatar definition]
698. humble(alice) <- (83) [avatar component clause 696]
699. 82 | 83 | ~13 [avatar split clause 387,221,696,692]
741. funny(alice) | tall(alice) <- (82) [resolution 694,102]
750. tall(alice) <- (13, 82) [subsumption resolution 741,444]
751. $false <- (~12, 13, 82) [subsumption resolution 750,217]
752. 12 | ~13 | ~82 [avatar contradiction clause 751]
753. funny(alice) | tall(alice) <- (83) [resolution 698,103]
755. tall(alice) <- (13, 83) [subsumption resolution 753,444]
756. $false <- (~12, 13, 83) [subsumption resolution 755,217]
757. 12 | ~13 | ~83 [avatar contradiction clause 756]
758. $false [avatar sat refutation 218,224,251,364,366,699,752,757]
% SZS output end Proof for 2000136663123490795427391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not rich is either humble or not old and vice versa. Everyone who is not quiet or strong is tall and vice versa. If someone is not old then someone is not quiet or not humble and vice versa. If someone is tall then paul is quiet and vice versa. Everyone who is not strong is not kind or old. If someone is either strong or generous then susan is wise or not patient. If mary is both happy and funny then someone is quiet. If someone is either not patient or not strong then alice is happy or not calm. Everyone who is either patient or creative is both not tall and brave and vice versa. Everyone who is either not generous or generous is calm or not brave and vice versa. Everyone who is humble or generous is not old or not tall and vice versa. If someone is both not happy and not brave then someone is either not quiet or tall. Everyone who is not curious is both funny and not happy. If someone is not strong then someone is either tall or not strong. Everyone who is either old or not creative is strong. Everyone who is both patient and brave is either not calm or wise and vice versa. Alice is either patient or not creative. Paul is both old and brave. Someone is quiet. Someone is not brave or not kind. Susan is not humble. Alice is either creative or not strong. Someone is not creative. Someone is both happy and calm. | Paul is calm. | entailment | (![X]:((generous(X)|~rich(X))<=>(humble(X)<~>~old(X))))&
(![X]:((~quiet(X)|strong(X))<=>tall(X)))&
((?[X]:(~old(X)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:(tall(X)))<=>(quiet(paul)))&
(![X]:(~strong(X)=>(~kind(X)|old(X))))&
((?[X]:((strong(X)<~>generous(X))))=>((wise(susan)|~patient(susan))))&
(((happy(mary)&funny(mary)))=>(?[X]:(quiet(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>((happy(alice)|~calm(alice))))&
(![X]:((patient(X)<~>creative(X))<=>(~tall(X)&brave(X))))&
(![X]:((~generous(X)<~>generous(X))<=>(calm(X)|~brave(X))))&
(![X]:((humble(X)|generous(X))<=>(~old(X)|~tall(X))))&
((?[X]:((~happy(X)&~brave(X))))=>(?[X]:((~quiet(X)<~>tall(X)))))&
(![X]:(~curious(X)=>(funny(X)&~happy(X))))&
((?[X]:(~strong(X)))=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:((old(X)<~>~creative(X))=>strong(X)))&
(![X]:((patient(X)&brave(X))<=>(~calm(X)<~>wise(X))))&
((patient(alice)<~>~creative(alice)))&
((old(paul)&brave(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((~brave(X)|~kind(X))))&
(~humble(susan))&
((creative(alice)<~>~strong(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((happy(X)&calm(X)))) | calm(paul) | [
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2757208401517379218726989
% SZS output start Proof for 2757208401517379218726989
10. ! [X0] : ((~generous(X0) <~> generous(X0)) <=> (~brave(X0) | calm(X0))) [input p9]
18. brave(paul) & old(paul) [input p17]
25. ~calm(paul) [input hypothesis]
56. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (brave(X0) & ~calm(X0))) & ((~brave(X0) | calm(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [nnf transformation 10]
57. ! [X0] : ((((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (brave(X0) & ~calm(X0))) & (~brave(X0) | calm(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0))))) [flattening 56]
97. ~brave(X0) | calm(X0) | generous(X0) | generous(X0) [cnf transformation 57]
98. ~brave(X0) | calm(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 57]
120. brave(paul) [cnf transformation 18]
127. ~calm(paul) [cnf transformation 25]
128. ~brave(X0) | calm(X0) | generous(X0) [duplicate literal removal 97]
129. ~brave(X0) | calm(X0) | ~generous(X0) [duplicate literal removal 98]
183. ~brave(X0) | calm(X0) [subsumption resolution 128,129]
215. calm(paul) [resolution 183,120]
216. $false [subsumption resolution 215,127]
% SZS output end Proof for 2757208401517379218726989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not brave is either humble or not brave. Everyone who is patient or calm is funny. Everyone who is either brave or not calm is either not kind or calm. Everyone who is not kind or not old is not funny and vice versa. Everyone who is patient is happy or creative. If someone is creative or not curious then john is either kind or funny and vice versa. If fred is either not tall or not quiet then lucy is curious and vice versa. Everyone who is either calm or not curious is either not quiet or not old. If someone is either generous or not humble then susan is both old and not tall and vice versa. If someone is either quiet or not kind then someone is both happy and not brave. Everyone who is both wise and rich is both not quiet and happy and vice versa. Everyone who is either generous or not brave is both not strong and old and vice versa. If paul is both wise and kind then someone is either calm or brave and vice versa. If someone is strong then fred is either tall or not kind. If lucy is humble then someone is both not brave and not calm and vice versa. Everyone who is brave is both curious and not creative and vice versa. Susan is both not kind and not brave. Someone is not calm or not generous. Someone is both not kind and curious. Alice is either generous or creative. Someone is both happy and funny. Lucy is either not brave or not strong. Alice is both not funny and wise. | John is kind. | entailment | (![X]:((~happy(X)&~brave(X))=>(humble(X)<~>~brave(X))))&
(![X]:((patient(X)|calm(X))=>funny(X)))&
(![X]:((brave(X)<~>~calm(X))=>(~kind(X)<~>calm(X))))&
(![X]:((~kind(X)|~old(X))<=>~funny(X)))&
(![X]:(patient(X)=>(happy(X)|creative(X))))&
((?[X]:((creative(X)|~curious(X))))<=>((kind(john)<~>funny(john))))&
(((~tall(fred)<~>~quiet(fred)))<=>(curious(lucy)))&
(![X]:((calm(X)<~>~curious(X))=>(~quiet(X)<~>~old(X))))&
((?[X]:((generous(X)<~>~humble(X))))<=>((old(susan)&~tall(susan))))&
((?[X]:((quiet(X)<~>~kind(X))))=>(?[X]:((happy(X)&~brave(X)))))&
(![X]:((wise(X)&rich(X))<=>(~quiet(X)&happy(X))))&
(![X]:((generous(X)<~>~brave(X))<=>(~strong(X)&old(X))))&
(((wise(paul)&kind(paul)))<=>(?[X]:((calm(X)<~>brave(X)))))&
((?[X]:(strong(X)))=>((tall(fred)<~>~kind(fred))))&
((humble(lucy))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:(brave(X)<=>(curious(X)&~creative(X))))&
((~kind(susan)&~brave(susan)))&
(?[X]:((~calm(X)|~generous(X))))&
(?[X]:((~kind(X)&curious(X))))&
((generous(alice)<~>creative(alice)))&
(?[X]:((happy(X)&funny(X))))&
((~brave(lucy)<~>~strong(lucy)))&
((~funny(alice)&wise(alice))) | kind(john) | [
"p3",
"p5",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8708140534727277927793978
% SZS output start Proof for 8708140534727277927793978
4. ! [X0] : ((~old(X0) | ~kind(X0)) <=> ~funny(X0)) [input p3]
6. ? [X0] : (~curious(X0) | creative(X0)) <=> (kind(john) <~> funny(john)) [input p5]
16. ! [X0] : (brave(X0) <=> (~creative(X0) & curious(X0))) [input p15]
17. ~brave(susan) & ~kind(susan) [input p16]
24. ~kind(john) [input hypothesis]
37. ! [X0] : (((~old(X0) | ~kind(X0)) | funny(X0)) & (~funny(X0) | (old(X0) & kind(X0)))) [nnf transformation 4]
38. ! [X0] : ((~old(X0) | ~kind(X0) | funny(X0)) & (~funny(X0) | (old(X0) & kind(X0)))) [flattening 37]
39. (? [X0] : (~curious(X0) | creative(X0)) | ((kind(john) | ~funny(john)) & (funny(john) | ~kind(john)))) & (((~funny(john) | ~kind(john)) & (funny(john) | kind(john))) | ! [X0] : (curious(X0) & ~creative(X0))) [nnf transformation 6]
40. (? [X0] : (~curious(X0) | creative(X0)) | ((kind(john) | ~funny(john)) & (funny(john) | ~kind(john)))) & (((~funny(john) | ~kind(john)) & (funny(john) | kind(john))) | ! [X1] : (curious(X1) & ~creative(X1))) [rectify 39]
41. ? [X0] : (~curious(X0) | creative(X0)) => (~curious(sK0) | creative(sK0)) [choice axiom]
42. ((~curious(sK0) | creative(sK0)) | ((kind(john) | ~funny(john)) & (funny(john) | ~kind(john)))) & (((~funny(john) | ~kind(john)) & (funny(john) | kind(john))) | ! [X1] : (curious(X1) & ~creative(X1))) [skolemisation 40,41]
68. ! [X0] : ((brave(X0) | (creative(X0) | ~curious(X0))) & ((~creative(X0) & curious(X0)) | ~brave(X0))) [nnf transformation 16]
69. ! [X0] : ((brave(X0) | creative(X0) | ~curious(X0)) & ((~creative(X0) & curious(X0)) | ~brave(X0))) [flattening 68]
85. ~funny(X0) | kind(X0) [cnf transformation 38]
88. funny(john) | kind(john) | ~creative(X1) [cnf transformation 42]
89. funny(john) | kind(john) | curious(X1) [cnf transformation 42]
135. ~curious(X0) | creative(X0) | brave(X0) [cnf transformation 69]
137. ~brave(susan) [cnf transformation 17]
149. ~kind(john) [cnf transformation 24]
154. 1 <=> kind(john) [avatar definition]
172. 5 <=> ! [X1] : curious(X1) [avatar definition]
173. curious(X1) <- (5) [avatar component clause 172]
177. 6 <=> ! [X1] : ~creative(X1) [avatar definition]
178. ~creative(X1) <- (6) [avatar component clause 177]
180. kind(john) | curious(X1) [subsumption resolution 89,85]
181. 5 | 1 [avatar split clause 180,154,172]
182. kind(john) | ~creative(X1) [subsumption resolution 88,85]
183. 6 | 1 [avatar split clause 182,154,177]
330. ~1 [avatar split clause 149,154]
420. creative(X0) | brave(X0) <- (5) [resolution 135,173]
422. brave(X0) <- (5, 6) [subsumption resolution 420,178]
429. $false <- (5, 6) [resolution 422,137]
440. ~5 | ~6 [avatar contradiction clause 429]
441. $false [avatar sat refutation 181,183,330,440]
% SZS output end Proof for 8708140534727277927793978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or not brave then susan is either not generous or generous.
Everyone who is both not wise and tall is either kind or old and vice versa.
If someone is kind then someone is not rich or strong.
If someone is rich or not patient then lucy is brave and vice versa.
Everyone who is both not brave and not calm is both humble and not funny and vice versa.
Everyone who is not creative is both not happy and quiet and vice versa.
Everyone who is either not quiet or not calm is both not funny and not generous and vice versa.
If susan is not calm or strong then someone is calm.
If someone is both generous and not generous then fred is not strong.
If mary is old or calm then mary is both not creative and patient and vice versa.
Everyone who is both not creative and quiet is happy and vice versa.
Everyone who is brave is either humble or wise and vice versa.
If susan is either not strong or rich then someone is either not humble or creative.
Everyone who is not patient or rich is patient and vice versa.
Everyone who is both not funny and not humble is either creative or not kind and vice versa.
Paul is funny.
Lucy is both not happy and generous.
Alice is not brave or not curious.
Someone is quiet or brave.
Someone is either quiet or curious.
Someone is not old. | Mary is kind. | contradiction | ((?[X]:((happy(X)<~>~brave(X))))=>((~generous(susan)<~>generous(susan))))&
(![X]:((~wise(X)&tall(X))<=>(kind(X)<~>old(X))))&
((?[X]:(kind(X)))=>(?[X]:((~rich(X)|strong(X)))))&
((?[X]:((rich(X)|~patient(X))))<=>(brave(lucy)))&
(![X]:((~brave(X)&~calm(X))<=>(humble(X)&~funny(X))))&
(![X]:(~creative(X)<=>(~happy(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~funny(X)&~generous(X))))&
(((~calm(susan)|strong(susan)))=>(?[X]:(calm(X))))&
((?[X]:((generous(X)&~generous(X))))=>(~strong(fred)))&
(((old(mary)|calm(mary)))<=>((~creative(mary)&patient(mary))))&
(![X]:((~creative(X)&quiet(X))<=>happy(X)))&
(![X]:(brave(X)<=>(humble(X)<~>wise(X))))&
(((~strong(susan)<~>rich(susan)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(![X]:((~patient(X)|rich(X))<=>patient(X)))&
(![X]:((~funny(X)&~humble(X))<=>(creative(X)<~>~kind(X))))&
(funny(paul))&
((~happy(lucy)&generous(lucy)))&
((~brave(alice)|~curious(alice)))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((quiet(X)<~>curious(X))))&
(?[X]:(~old(X))) | kind(mary) | [
"p1",
"p4",
"p5",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3298435693870698154267025
% SZS output start Proof for 3298435693870698154267025
2. ! [X0] : ((tall(X0) & ~wise(X0)) <=> (kind(X0) <~> old(X0))) [input p1]
5. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> (~funny(X0) & humble(X0))) [input p4]
6. ! [X0] : (~creative(X0) <=> (quiet(X0) & ~happy(X0))) [input p5]
10. (calm(mary) | old(mary)) <=> (patient(mary) & ~creative(mary)) [input p9]
11. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> happy(X0)) [input p10]
12. ! [X0] : (brave(X0) <=> (humble(X0) <~> wise(X0))) [input p11]
15. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (creative(X0) <~> ~kind(X0))) [input p14]
22. kind(mary) [input hypothesis]
30. ! [X0] : (((tall(X0) & ~wise(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0)))) & (((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | (~tall(X0) | wise(X0)))) [nnf transformation 2]
31. ! [X0] : (((tall(X0) & ~wise(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0)))) & (((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | ~tall(X0) | wise(X0))) [flattening 30]
39. ! [X0] : (((~calm(X0) & ~brave(X0)) | (funny(X0) | ~humble(X0))) & ((~funny(X0) & humble(X0)) | (calm(X0) | brave(X0)))) [nnf transformation 5]
40. ! [X0] : (((~calm(X0) & ~brave(X0)) | funny(X0) | ~humble(X0)) & ((~funny(X0) & humble(X0)) | calm(X0) | brave(X0))) [flattening 39]
41. ! [X0] : ((~creative(X0) | (~quiet(X0) | happy(X0))) & ((quiet(X0) & ~happy(X0)) | creative(X0))) [nnf transformation 6]
42. ! [X0] : ((~creative(X0) | ~quiet(X0) | happy(X0)) & ((quiet(X0) & ~happy(X0)) | creative(X0))) [flattening 41]
47. ((calm(mary) | old(mary)) | (~patient(mary) | creative(mary))) & ((patient(mary) & ~creative(mary)) | (~calm(mary) & ~old(mary))) [nnf transformation 10]
48. (calm(mary) | old(mary) | ~patient(mary) | creative(mary)) & ((patient(mary) & ~creative(mary)) | (~calm(mary) & ~old(mary))) [flattening 47]
49. ! [X0] : (((quiet(X0) & ~creative(X0)) | ~happy(X0)) & (happy(X0) | (~quiet(X0) | creative(X0)))) [nnf transformation 11]
50. ! [X0] : (((quiet(X0) & ~creative(X0)) | ~happy(X0)) & (happy(X0) | ~quiet(X0) | creative(X0))) [flattening 49]
51. ! [X0] : ((brave(X0) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | ~brave(X0))) [nnf transformation 12]
57. ! [X0] : (((~humble(X0) & ~funny(X0)) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (humble(X0) | funny(X0)))) [nnf transformation 15]
58. ! [X0] : (((~humble(X0) & ~funny(X0)) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | humble(X0) | funny(X0))) [flattening 57]
72. ~kind(X0) | old(X0) | ~wise(X0) [cnf transformation 31]
80. humble(X0) | calm(X0) | brave(X0) [cnf transformation 40]
84. ~happy(X0) | creative(X0) [cnf transformation 42]
85. quiet(X0) | creative(X0) [cnf transformation 42]
96. ~creative(mary) | ~old(mary) [cnf transformation 48]
97. ~creative(mary) | ~calm(mary) [cnf transformation 48]
101. happy(X0) | ~quiet(X0) | creative(X0) [cnf transformation 50]
102. ~creative(X0) | ~happy(X0) [cnf transformation 50]
104. ~brave(X0) | humble(X0) | wise(X0) [cnf transformation 51]
119. ~humble(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 58]
129. kind(mary) [cnf transformation 22]
180. 12 <=> creative(mary) [avatar definition]
181. ~creative(mary) <- (~12) [avatar component clause 180]
188. 14 <=> old(mary) [avatar definition]
189. ~old(mary) <- (~14) [avatar component clause 188]
192. 15 <=> calm(mary) [avatar definition]
193. ~calm(mary) <- (~15) [avatar component clause 192]
198. ~15 | ~12 [avatar split clause 97,180,192]
199. ~14 | ~12 [avatar split clause 96,180,188]
200. ~happy(X0) [subsumption resolution 102,84]
201. ~quiet(X0) | creative(X0) [subsumption resolution 101,200]
202. creative(X0) [subsumption resolution 201,85]
216. ~humble(X0) | ~kind(X0) [subsumption resolution 119,202]
259. old(mary) | ~wise(mary) [resolution 72,129]
260. ~wise(mary) <- (~14) [subsumption resolution 259,189]
263. ~kind(X0) | brave(X0) | calm(X0) [resolution 80,216]
367. brave(mary) | calm(mary) [resolution 263,129]
368. brave(mary) <- (~15) [subsumption resolution 367,193]
369. humble(mary) | wise(mary) <- (~15) [resolution 368,104]
370. humble(mary) <- (~14, ~15) [subsumption resolution 369,260]
378. ~kind(mary) <- (~14, ~15) [resolution 370,216]
380. $false <- (~14, ~15) [subsumption resolution 378,129]
381. 14 | 15 [avatar contradiction clause 380]
397. $false <- (~12) [subsumption resolution 181,202]
398. 12 [avatar contradiction clause 397]
399. $false [avatar sat refutation 198,199,381,398]
% SZS output end Proof for 3298435693870698154267025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not wise. Everyone who is creative or not wise is not happy or strong. If someone is tall or not brave then lucy is wise or funny and vice versa. Everyone who is tall or not patient is either old or not curious and vice versa. Everyone who is quiet or not funny is kind or humble and vice versa. Everyone who is both generous and not brave is humble and vice versa. Everyone who is either generous or kind is not wise or not tall and vice versa. Everyone who is both funny and rich is not strong or humble and vice versa. Everyone who is either not curious or not strong is either rich or calm. Everyone who is not old is not quiet or not patient. Everyone who is not calm is quiet or calm. If john is patient or not generous then paul is both kind and not curious. If lucy is either not humble or not strong then someone is either brave or strong and vice versa. Everyone who is either not tall or patient is both happy and kind and vice versa. Everyone who is both kind and not generous is kind and vice versa. If someone is generous then lucy is patient. John is either not generous or not wise. Someone is either old or strong. Someone is either happy or not humble. Someone is both kind and not funny. Someone is wise or patient. Someone is both tall and not quiet. Someone is not happy. Mary is either tall or not quiet. | Paul is rich. | neutral | (![X]:(rich(X)=>~wise(X)))&
(![X]:((creative(X)|~wise(X))=>(~happy(X)|strong(X))))&
((?[X]:((tall(X)|~brave(X))))<=>((wise(lucy)|funny(lucy))))&
(![X]:((tall(X)|~patient(X))<=>(old(X)<~>~curious(X))))&
(![X]:((quiet(X)|~funny(X))<=>(kind(X)|humble(X))))&
(![X]:((generous(X)&~brave(X))<=>humble(X)))&
(![X]:((generous(X)<~>kind(X))<=>(~wise(X)|~tall(X))))&
(![X]:((funny(X)&rich(X))<=>(~strong(X)|humble(X))))&
(![X]:((~curious(X)<~>~strong(X))=>(rich(X)<~>calm(X))))&
(![X]:(~old(X)=>(~quiet(X)|~patient(X))))&
(![X]:(~calm(X)=>(quiet(X)|calm(X))))&
(((patient(john)|~generous(john)))=>((kind(paul)&~curious(paul))))&
(((~humble(lucy)<~>~strong(lucy)))<=>(?[X]:((brave(X)<~>strong(X)))))&
(![X]:((~tall(X)<~>patient(X))<=>(happy(X)&kind(X))))&
(![X]:((kind(X)&~generous(X))<=>kind(X)))&
((?[X]:(generous(X)))=>(patient(lucy)))&
((~generous(john)<~>~wise(john)))&
(?[X]:((old(X)<~>strong(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((kind(X)&~funny(X))))&
(?[X]:((wise(X)|patient(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:(~happy(X)))&
((tall(mary)<~>~quiet(mary))) | rich(paul) | [] | null | 0 |
Everyone who is not funny is old. If someone is not tall then someone is not calm. If someone is either not strong or calm then john is both old and not happy and vice versa. Everyone who is not kind is either patient or not funny. Everyone who is both not brave and tall is either not brave or quiet and vice versa. Everyone who is not calm is not creative. Everyone who is not calm or happy is both not kind and rich. If susan is either kind or not generous then someone is strong and vice versa. If lucy is both not funny and brave then alice is strong. If someone is not rich or not creative then susan is either not patient or not quiet. If fred is old or generous then someone is not strong or rich. Everyone who is either creative or curious is both strong and creative and vice versa. Everyone who is not creative or calm is not old. If someone is not rich then susan is not brave or tall and vice versa. Everyone who is both not happy and funny is both generous and quiet. Everyone who is both curious and brave is both not patient and not tall. Fred is not generous or creative. Alice is rich. Paul is either patient or not generous. Susan is both not strong and not quiet. Susan is either funny or not humble. Alice is kind. Someone is either creative or not curious. | Alice is not strong. | entailment | (![X]:(~funny(X)=>old(X)))&
((?[X]:(~tall(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~strong(X)<~>calm(X))))<=>((old(john)&~happy(john))))&
(![X]:(~kind(X)=>(patient(X)<~>~funny(X))))&
(![X]:((~brave(X)&tall(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:(~calm(X)=>~creative(X)))&
(![X]:((~calm(X)|happy(X))=>(~kind(X)&rich(X))))&
(((kind(susan)<~>~generous(susan)))<=>(?[X]:(strong(X))))&
(((~funny(lucy)&brave(lucy)))=>(strong(alice)))&
((?[X]:((~rich(X)|~creative(X))))=>((~patient(susan)<~>~quiet(susan))))&
(((old(fred)|generous(fred)))=>(?[X]:((~strong(X)|rich(X)))))&
(![X]:((creative(X)<~>curious(X))<=>(strong(X)&creative(X))))&
(![X]:((~creative(X)|calm(X))=>~old(X)))&
((?[X]:(~rich(X)))<=>((~brave(susan)|tall(susan))))&
(![X]:((~happy(X)&funny(X))=>(generous(X)&quiet(X))))&
(![X]:((curious(X)&brave(X))=>(~patient(X)&~tall(X))))&
((~generous(fred)|creative(fred)))&
(rich(alice))&
((patient(paul)<~>~generous(paul)))&
((~strong(susan)&~quiet(susan)))&
((funny(susan)<~>~humble(susan)))&
(kind(alice))&
(?[X]:((creative(X)<~>~curious(X)))) | ~strong(alice) | [
"p2",
"p5",
"p6",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 127069205478511156294604
% SZS output start Proof for 127069205478511156294604
3. ? [X0] : (~strong(X0) <~> calm(X0)) <=> (~happy(john) & old(john)) [input p2]
6. ! [X0] : (~calm(X0) => ~creative(X0)) [input p5]
7. ! [X0] : ((happy(X0) | ~calm(X0)) => (rich(X0) & ~kind(X0))) [input p6]
13. ! [X0] : ((calm(X0) | ~creative(X0)) => ~old(X0)) [input p12]
22. kind(alice) [input p21]
24. strong(alice) [input hypothesis]
29. ! [X0] : (~creative(X0) | calm(X0)) [ennf transformation 6]
30. ! [X0] : ((rich(X0) & ~kind(X0)) | (~happy(X0) & calm(X0))) [ennf transformation 7]
35. ! [X0] : (~old(X0) | (~calm(X0) & creative(X0))) [ennf transformation 13]
43. (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (happy(john) | ~old(john))) & ((~happy(john) & old(john)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) [nnf transformation 3]
44. (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | happy(john) | ~old(john)) & ((~happy(john) & old(john)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) [flattening 43]
45. (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | happy(john) | ~old(john)) & ((~happy(john) & old(john)) | ! [X1] : ((~strong(X1) | ~calm(X1)) & (calm(X1) | strong(X1)))) [rectify 44]
46. ? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) => ((~calm(sK1) | strong(sK1)) & (calm(sK1) | ~strong(sK1))) [choice axiom]
47. (((~calm(sK1) | strong(sK1)) & (calm(sK1) | ~strong(sK1))) | happy(john) | ~old(john)) & ((~happy(john) & old(john)) | ! [X1] : ((~strong(X1) | ~calm(X1)) & (calm(X1) | strong(X1)))) [skolemisation 45,46]
73. old(john) | ~strong(X1) | ~calm(X1) [cnf transformation 47]
86. ~creative(X0) | calm(X0) [cnf transformation 29]
87. ~kind(X0) | calm(X0) [cnf transformation 30]
108. ~old(X0) | creative(X0) [cnf transformation 35]
109. ~calm(X0) | ~old(X0) [cnf transformation 35]
125. kind(alice) [cnf transformation 22]
128. strong(alice) [cnf transformation 24]
142. 3 <=> old(john) [avatar definition]
143. old(john) <- (3) [avatar component clause 142]
160. 7 <=> ! [X1] : (~strong(X1) | ~calm(X1)) [avatar definition]
161. ~strong(X1) | ~calm(X1) <- (7) [avatar component clause 160]
167. 7 | 3 [avatar split clause 73,142,160]
198. 15 <=> strong(alice) [avatar definition]
200. strong(alice) <- (15) [avatar component clause 198]
288. 15 [avatar split clause 128,198]
292. calm(alice) [resolution 87,125]
295. creative(john) <- (3) [resolution 108,143]
297. calm(john) <- (3) [resolution 295,86]
300. ~old(john) <- (3) [resolution 297,109]
301. $false <- (3) [subsumption resolution 300,143]
302. ~3 [avatar contradiction clause 301]
306. ~calm(alice) <- (7, 15) [resolution 161,200]
308. $false <- (7, 15) [subsumption resolution 306,292]
309. ~7 | ~15 [avatar contradiction clause 308]
310. $false [avatar sat refutation 167,288,302,309]
% SZS output end Proof for 127069205478511156294604
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not brave or old then alice is not funny or happy and vice versa. Everyone who is either rich or not funny is not calm. If mary is either rich or brave then lucy is either not old or not quiet. Everyone who is both not kind and happy is both not tall and curious and vice versa. If alice is both not strong and old then someone is rich or humble and vice versa. Everyone who is kind or rich is both not old and kind. Everyone who is brave or not old is brave or not rich and vice versa. If alice is not kind then lucy is creative or not calm. If someone is either not creative or strong then someone is rich and vice versa. Everyone who is not old or rich is kind or curious and vice versa. Everyone who is either not kind or not old is both rich and not quiet. Everyone who is not wise or happy is rich or funny. If susan is either rich or not patient then fred is both not kind and brave. If paul is both not rich and not kind then paul is patient and vice versa. If someone is either not funny or not humble then susan is both not tall and tall. Everyone who is strong or curious is calm or not generous. Susan is not strong or tall. John is either not strong or curious. Fred is not patient or not brave. | Fred is happy. | contradiction | (((~brave(john)|old(john)))<=>((~funny(alice)|happy(alice))))&
(![X]:((rich(X)<~>~funny(X))=>~calm(X)))&
(((rich(mary)<~>brave(mary)))=>((~old(lucy)<~>~quiet(lucy))))&
(![X]:((~kind(X)&happy(X))<=>(~tall(X)&curious(X))))&
(((~strong(alice)&old(alice)))<=>(?[X]:((rich(X)|humble(X)))))&
(![X]:((kind(X)|rich(X))=>(~old(X)&kind(X))))&
(![X]:((brave(X)|~old(X))<=>(brave(X)|~rich(X))))&
((~kind(alice))=>((creative(lucy)|~calm(lucy))))&
((?[X]:((~creative(X)<~>strong(X))))<=>(?[X]:(rich(X))))&
(![X]:((~old(X)|rich(X))<=>(kind(X)|curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(rich(X)&~quiet(X))))&
(![X]:((~wise(X)|happy(X))=>(rich(X)|funny(X))))&
(((rich(susan)<~>~patient(susan)))=>((~kind(fred)&brave(fred))))&
(((~rich(paul)&~kind(paul)))<=>(patient(paul)))&
((?[X]:((~funny(X)<~>~humble(X))))=>((~tall(susan)&tall(susan))))&
(![X]:((strong(X)|curious(X))=>(calm(X)|~generous(X))))&
((~strong(susan)|tall(susan)))&
((~strong(john)<~>curious(john)))&
((~patient(fred)|~brave(fred))) | happy(fred) | [
"p4",
"p5",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8608458676837450318265034
% SZS output start Proof for 8608458676837450318265034
5. (old(alice) & ~strong(alice)) <=> ? [X0] : (humble(X0) | rich(X0)) [input p4]
6. ! [X0] : ((rich(X0) | kind(X0)) => (kind(X0) & ~old(X0))) [input p5]
11. ! [X0] : ((~kind(X0) <~> ~old(X0)) => (~quiet(X0) & rich(X0))) [input p10]
12. ! [X0] : ((happy(X0) | ~wise(X0)) => (funny(X0) | rich(X0))) [input p11]
15. ? [X0] : (~funny(X0) <~> ~humble(X0)) => (tall(susan) & ~tall(susan)) [input p14]
20. happy(fred) [input hypothesis]
25. ! [X0] : (happy(X0) => (funny(X0) | rich(X0))) [pure predicate removal 12]
27. ! [X0] : ((kind(X0) & ~old(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 6]
28. ! [X0] : ((~quiet(X0) & rich(X0)) | (~kind(X0) <=> ~old(X0))) [ennf transformation 11]
29. ! [X0] : ((funny(X0) | rich(X0)) | ~happy(X0)) [ennf transformation 25]
30. ! [X0] : (funny(X0) | rich(X0) | ~happy(X0)) [flattening 29]
32. (tall(susan) & ~tall(susan)) | ! [X0] : (~funny(X0) <=> ~humble(X0)) [ennf transformation 15]
38. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | (~old(alice) | strong(alice))) [nnf transformation 5]
39. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X0] : (humble(X0) | rich(X0)) | ~old(alice) | strong(alice)) [flattening 38]
40. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & (? [X1] : (humble(X1) | rich(X1)) | ~old(alice) | strong(alice)) [rectify 39]
41. ? [X1] : (humble(X1) | rich(X1)) => (humble(sK0) | rich(sK0)) [choice axiom]
42. ((old(alice) & ~strong(alice)) | ! [X0] : (~humble(X0) & ~rich(X0))) & ((humble(sK0) | rich(sK0)) | ~old(alice) | strong(alice)) [skolemisation 40,41]
52. ! [X0] : ((~quiet(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0)))) [nnf transformation 28]
56. (tall(susan) & ~tall(susan)) | ! [X0] : ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))) [nnf transformation 32]
73. old(alice) | ~rich(X0) [cnf transformation 42]
74. old(alice) | ~humble(X0) [cnf transformation 42]
75. ~kind(X0) | ~old(X0) [cnf transformation 27]
76. ~rich(X0) | ~old(X0) [cnf transformation 27]
91. rich(X0) | ~old(X0) | kind(X0) [cnf transformation 52]
95. ~happy(X0) | rich(X0) | funny(X0) [cnf transformation 30]
104. ~tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 56]
106. tall(susan) | ~funny(X0) | humble(X0) [cnf transformation 56]
111. happy(fred) [cnf transformation 20]
153. 9 <=> ! [X0] : ~humble(X0) [avatar definition]
154. ~humble(X0) <- (9) [avatar component clause 153]
156. 10 <=> old(alice) [avatar definition]
158. old(alice) <- (10) [avatar component clause 156]
159. 9 | 10 [avatar split clause 74,156,153]
161. 11 <=> ! [X0] : ~rich(X0) [avatar definition]
162. ~rich(X0) <- (11) [avatar component clause 161]
163. 11 | 10 [avatar split clause 73,156,161]
207. rich(X0) | ~old(X0) [subsumption resolution 91,75]
208. ~old(X0) [subsumption resolution 207,76]
246. 27 <=> ! [X0] : (~funny(X0) | humble(X0)) [avatar definition]
247. ~funny(X0) | humble(X0) <- (27) [avatar component clause 246]
249. 28 <=> tall(susan) [avatar definition]
252. 27 | 28 [avatar split clause 106,249,246]
257. 27 | ~28 [avatar split clause 104,249,246]
281. $false <- (10) [subsumption resolution 158,208]
282. ~10 [avatar contradiction clause 281]
310. rich(fred) | funny(fred) [resolution 95,111]
311. funny(fred) <- (11) [subsumption resolution 310,162]
334. humble(fred) <- (11, 27) [resolution 311,247]
335. $false <- (9, 11, 27) [subsumption resolution 334,154]
336. ~9 | ~11 | ~27 [avatar contradiction clause 335]
337. $false [avatar sat refutation 159,163,252,257,282,336]
% SZS output end Proof for 8608458676837450318265034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or not funny then lucy is both brave and generous. Everyone who is wise is old. Everyone who is either patient or not wise is both brave and not creative. If someone is not quiet or creative then lucy is tall or wise. Everyone who is both not generous and happy is not happy and vice versa. If someone is not strong or not tall then fred is either not kind or curious. Everyone who is either not rich or funny is strong. If someone is old then fred is happy or not generous. Everyone who is tall is either not generous or not brave and vice versa. If lucy is not quiet then lucy is both not generous and not brave and vice versa. If alice is both not tall and not calm then fred is humble and vice versa. Everyone who is tall or not wise is either patient or not old and vice versa. Everyone who is either not tall or not wise is not calm or not creative and vice versa. Everyone who is not curious or humble is not funny or wise and vice versa. Everyone who is not kind or not rich is both not curious and not tall and vice versa. Everyone who is creative or not wise is both not patient and generous and vice versa. Paul is both old and generous. Someone is not funny or not tall. Susan is not patient or creative. Alice is not creative or not tall. Someone is humble or not creative. | Susan is brave. | entailment | ((?[X]:((funny(X)|~funny(X))))=>((brave(lucy)&generous(lucy))))&
(![X]:(wise(X)=>old(X)))&
(![X]:((patient(X)<~>~wise(X))=>(brave(X)&~creative(X))))&
((?[X]:((~quiet(X)|creative(X))))=>((tall(lucy)|wise(lucy))))&
(![X]:((~generous(X)&happy(X))<=>~happy(X)))&
((?[X]:((~strong(X)|~tall(X))))=>((~kind(fred)<~>curious(fred))))&
(![X]:((~rich(X)<~>funny(X))=>strong(X)))&
((?[X]:(old(X)))=>((happy(fred)|~generous(fred))))&
(![X]:(tall(X)<=>(~generous(X)<~>~brave(X))))&
((~quiet(lucy))<=>((~generous(lucy)&~brave(lucy))))&
(((~tall(alice)&~calm(alice)))<=>(humble(fred)))&
(![X]:((tall(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~calm(X)|~creative(X))))&
(![X]:((~curious(X)|humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((~kind(X)|~rich(X))<=>(~curious(X)&~tall(X))))&
(![X]:((creative(X)|~wise(X))<=>(~patient(X)&generous(X))))&
((old(paul)&generous(paul)))&
(?[X]:((~funny(X)|~tall(X))))&
((~patient(susan)|creative(susan)))&
((~creative(alice)|~tall(alice)))&
(?[X]:((humble(X)|~creative(X)))) | brave(susan) | [
"p1",
"p2",
"p4",
"p8",
"p11",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2931705176968326661728796
% SZS output start Proof for 2931705176968326661728796
2. ! [X0] : (wise(X0) => old(X0)) [input p1]
3. ! [X0] : ((patient(X0) <~> ~wise(X0)) => (~creative(X0) & brave(X0))) [input p2]
5. ! [X0] : ((happy(X0) & ~generous(X0)) <=> ~happy(X0)) [input p4]
9. ! [X0] : (tall(X0) <=> (~generous(X0) <~> ~brave(X0))) [input p8]
12. ! [X0] : ((~wise(X0) | tall(X0)) <=> (patient(X0) <~> ~old(X0))) [input p11]
16. ! [X0] : ((~wise(X0) | creative(X0)) <=> (generous(X0) & ~patient(X0))) [input p15]
19. creative(susan) | ~patient(susan) [input p18]
22. ~brave(susan) [input hypothesis]
26. ! [X0] : (old(X0) | ~wise(X0)) [ennf transformation 2]
27. ! [X0] : ((~creative(X0) & brave(X0)) | (patient(X0) <=> ~wise(X0))) [ennf transformation 3]
33. ! [X0] : ((~creative(X0) & brave(X0)) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) [nnf transformation 27]
34. ! [X0] : (((happy(X0) & ~generous(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) | generous(X0)))) [nnf transformation 5]
35. ! [X0] : (((happy(X0) & ~generous(X0)) | happy(X0)) & (~happy(X0) | ~happy(X0) | generous(X0))) [flattening 34]
37. ! [X0] : ((tall(X0) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0)))) & (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ~tall(X0))) [nnf transformation 9]
42. ! [X0] : (((~wise(X0) | tall(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~tall(X0)))) [nnf transformation 12]
43. ! [X0] : ((~wise(X0) | tall(X0) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~tall(X0)))) [flattening 42]
50. ! [X0] : (((~wise(X0) | creative(X0)) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 16]
51. ! [X0] : ((~wise(X0) | creative(X0) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | (wise(X0) & ~creative(X0)))) [flattening 50]
60. ~wise(X0) | old(X0) [cnf transformation 26]
62. patient(X0) | brave(X0) | wise(X0) [cnf transformation 33]
67. ~happy(X0) | ~happy(X0) | generous(X0) [cnf transformation 35]
69. happy(X0) | happy(X0) [cnf transformation 35]
76. tall(X0) | ~generous(X0) | brave(X0) [cnf transformation 37]
83. ~tall(X0) | patient(X0) | ~old(X0) [cnf transformation 43]
86. old(X0) | ~patient(X0) | wise(X0) [cnf transformation 43]
104. ~creative(X0) | ~patient(X0) [cnf transformation 51]
112. creative(susan) | ~patient(susan) [cnf transformation 19]
115. ~brave(susan) [cnf transformation 22]
116. ~happy(X0) | generous(X0) [duplicate literal removal 67]
117. happy(X0) [duplicate literal removal 69]
152. generous(X0) [subsumption resolution 116,117]
166. tall(X0) | brave(X0) [subsumption resolution 76,152]
191. ~patient(X0) | old(X0) [subsumption resolution 86,60]
202. ~patient(susan) [subsumption resolution 112,104]
230. brave(X1) | wise(X1) | old(X1) [resolution 62,191]
235. old(X1) | brave(X1) [subsumption resolution 230,60]
238. patient(X0) | ~old(X0) | brave(X0) [resolution 83,166]
239. patient(X0) | brave(X0) [subsumption resolution 238,235]
265. brave(susan) [resolution 239,202]
270. $false [subsumption resolution 265,115]
% SZS output end Proof for 2931705176968326661728796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or creative is either generous or old and vice versa. Everyone who is strong or wise is either not brave or quiet and vice versa. Everyone who is kind or happy is not strong. Everyone who is not strong is both wise and not kind and vice versa. Everyone who is both brave and patient is not curious and vice versa. If someone is both kind and rich then mary is both not patient and happy. Everyone who is funny is either not happy or patient and vice versa. If someone is either patient or wise then fred is both not funny and not curious. Everyone who is both not brave and quiet is generous or funny. Everyone who is both rich and happy is patient or quiet and vice versa. Everyone who is not old is both not generous and not calm and vice versa. Everyone who is both wise and curious is not patient. If mary is both not curious and not humble then someone is both not tall and kind and vice versa. If someone is both patient and humble then someone is creative. If lucy is both not humble and quiet then alice is not old or rich. If john is either curious or not strong then lucy is either not generous or calm and vice versa. Someone is not humble. Susan is creative. Someone is either not happy or generous. Fred is both tall and humble. Someone is both brave and not humble. Alice is both old and creative. Mary is humble. | Lucy is happy. | entailment | (![X]:((~wise(X)|creative(X))<=>(generous(X)<~>old(X))))&
(![X]:((strong(X)|wise(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:((kind(X)|happy(X))=>~strong(X)))&
(![X]:(~strong(X)<=>(wise(X)&~kind(X))))&
(![X]:((brave(X)&patient(X))<=>~curious(X)))&
((?[X]:((kind(X)&rich(X))))=>((~patient(mary)&happy(mary))))&
(![X]:(funny(X)<=>(~happy(X)<~>patient(X))))&
((?[X]:((patient(X)<~>wise(X))))=>((~funny(fred)&~curious(fred))))&
(![X]:((~brave(X)&quiet(X))=>(generous(X)|funny(X))))&
(![X]:((rich(X)&happy(X))<=>(patient(X)|quiet(X))))&
(![X]:(~old(X)<=>(~generous(X)&~calm(X))))&
(![X]:((wise(X)&curious(X))=>~patient(X)))&
(((~curious(mary)&~humble(mary)))<=>(?[X]:((~tall(X)&kind(X)))))&
((?[X]:((patient(X)&humble(X))))=>(?[X]:(creative(X))))&
(((~humble(lucy)&quiet(lucy)))=>((~old(alice)|rich(alice))))&
(((curious(john)<~>~strong(john)))<=>((~generous(lucy)<~>calm(lucy))))&
(?[X]:(~humble(X)))&
(creative(susan))&
(?[X]:((~happy(X)<~>generous(X))))&
((tall(fred)&humble(fred)))&
(?[X]:((brave(X)&~humble(X))))&
((old(alice)&creative(alice)))&
(humble(mary)) | happy(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p7",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5523762981117670444229700
% SZS output start Proof for 5523762981117670444229700
1. ! [X0] : ((creative(X0) | ~wise(X0)) <=> (generous(X0) <~> old(X0))) [input p0]
3. ! [X0] : ((happy(X0) | kind(X0)) => ~strong(X0)) [input p2]
4. ! [X0] : (~strong(X0) <=> (~kind(X0) & wise(X0))) [input p3]
5. ! [X0] : ((patient(X0) & brave(X0)) <=> ~curious(X0)) [input p4]
7. ! [X0] : (funny(X0) <=> (~happy(X0) <~> patient(X0))) [input p6]
8. ? [X0] : (patient(X0) <~> wise(X0)) => (~curious(fred) & ~funny(fred)) [input p7]
10. ! [X0] : ((happy(X0) & rich(X0)) <=> (quiet(X0) | patient(X0))) [input p9]
11. ! [X0] : (~old(X0) <=> (~calm(X0) & ~generous(X0))) [input p10]
12. ! [X0] : ((curious(X0) & wise(X0)) => ~patient(X0)) [input p11]
16. (curious(john) <~> ~strong(john)) <=> (~generous(lucy) <~> calm(lucy)) [input p15]
24. ~happy(lucy) [input hypothesis]
26. ! [X0] : (~strong(X0) | (~happy(X0) & ~kind(X0))) [ennf transformation 3]
28. (~curious(fred) & ~funny(fred)) | ! [X0] : (patient(X0) <=> wise(X0)) [ennf transformation 8]
31. ! [X0] : (~patient(X0) | (~curious(X0) | ~wise(X0))) [ennf transformation 12]
32. ! [X0] : (~patient(X0) | ~curious(X0) | ~wise(X0)) [flattening 31]
36. ! [X0] : (((creative(X0) | ~wise(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0)))) & (((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (~creative(X0) & wise(X0)))) [nnf transformation 1]
37. ! [X0] : ((creative(X0) | ~wise(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0)))) & (((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (~creative(X0) & wise(X0)))) [flattening 36]
40. ! [X0] : ((~strong(X0) | (kind(X0) | ~wise(X0))) & ((~kind(X0) & wise(X0)) | strong(X0))) [nnf transformation 4]
41. ! [X0] : ((~strong(X0) | kind(X0) | ~wise(X0)) & ((~kind(X0) & wise(X0)) | strong(X0))) [flattening 40]
42. ! [X0] : (((patient(X0) & brave(X0)) | curious(X0)) & (~curious(X0) | (~patient(X0) | ~brave(X0)))) [nnf transformation 5]
43. ! [X0] : (((patient(X0) & brave(X0)) | curious(X0)) & (~curious(X0) | ~patient(X0) | ~brave(X0))) [flattening 42]
44. ! [X0] : ((funny(X0) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~funny(X0))) [nnf transformation 7]
45. (~curious(fred) & ~funny(fred)) | ! [X0] : ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0))) [nnf transformation 28]
46. ! [X0] : (((happy(X0) & rich(X0)) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | (~happy(X0) | ~rich(X0)))) [nnf transformation 10]
47. ! [X0] : (((happy(X0) & rich(X0)) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ~happy(X0) | ~rich(X0))) [flattening 46]
48. ! [X0] : ((~old(X0) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | old(X0))) [nnf transformation 11]
49. ! [X0] : ((~old(X0) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | old(X0))) [flattening 48]
58. (((strong(john) | ~curious(john)) & (~strong(john) | curious(john))) | ((~generous(lucy) | ~calm(lucy)) & (calm(lucy) | generous(lucy)))) & (((~calm(lucy) | generous(lucy)) & (calm(lucy) | ~generous(lucy))) | ((curious(john) | strong(john)) & (~strong(john) | ~curious(john)))) [nnf transformation 16]
66. old(X0) | generous(X0) | wise(X0) [cnf transformation 37]
68. ~old(X0) | ~generous(X0) | wise(X0) [cnf transformation 37]
78. ~kind(X0) | ~strong(X0) [cnf transformation 26]
80. strong(X0) | wise(X0) [cnf transformation 41]
82. ~strong(X0) | kind(X0) | ~wise(X0) [cnf transformation 41]
85. curious(X0) | patient(X0) [cnf transformation 43]
91. ~patient(X0) | ~happy(X0) | funny(X0) [cnf transformation 44]
92. ~funny(fred) | wise(X0) | ~patient(X0) [cnf transformation 45]
93. ~funny(fred) | patient(X0) | ~wise(X0) [cnf transformation 45]
94. ~curious(fred) | wise(X0) | ~patient(X0) [cnf transformation 45]
95. ~curious(fred) | patient(X0) | ~wise(X0) [cnf transformation 45]
100. ~patient(X0) | happy(X0) [cnf transformation 47]
102. ~generous(X0) | old(X0) [cnf transformation 49]
104. ~old(X0) | calm(X0) | generous(X0) [cnf transformation 49]
105. ~curious(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 32]
114. ~calm(lucy) | generous(lucy) | ~strong(john) | ~curious(john) [cnf transformation 58]
115. ~calm(lucy) | generous(lucy) | curious(john) | strong(john) [cnf transformation 58]
131. ~happy(lucy) [cnf transformation 24]
132. ~strong(X0) | ~wise(X0) [subsumption resolution 82,78]
135. 1 <=> ! [X0] : (patient(X0) | ~wise(X0)) [avatar definition]
136. ~wise(X0) | patient(X0) <- (1) [avatar component clause 135]
138. 2 <=> curious(fred) [avatar definition]
140. ~curious(fred) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 95,138,135]
143. 3 <=> ! [X0] : (wise(X0) | ~patient(X0)) [avatar definition]
144. ~patient(X0) | wise(X0) <- (3) [avatar component clause 143]
145. 3 | ~2 [avatar split clause 94,138,143]
147. 4 <=> funny(fred) [avatar definition]
149. ~funny(fred) <- (~4) [avatar component clause 147]
150. 1 | ~4 [avatar split clause 93,147,135]
151. 3 | ~4 [avatar split clause 92,147,143]
193. 14 <=> calm(lucy) [avatar definition]
195. ~calm(lucy) <- (~14) [avatar component clause 193]
197. 15 <=> generous(lucy) [avatar definition]
198. generous(lucy) <- (15) [avatar component clause 197]
199. ~generous(lucy) <- (~15) [avatar component clause 197]
201. 16 <=> curious(john) [avatar definition]
202. curious(john) <- (16) [avatar component clause 201]
203. ~curious(john) <- (~16) [avatar component clause 201]
205. 17 <=> strong(john) [avatar definition]
206. ~strong(john) <- (~17) [avatar component clause 205]
207. strong(john) <- (17) [avatar component clause 205]
212. 17 | 16 | 15 | ~14 [avatar split clause 115,193,197,201,205]
213. ~16 | ~17 | 15 | ~14 [avatar split clause 114,193,197,205,201]
228. wise(john) <- (~17) [resolution 80,206]
231. patient(fred) <- (~2) [resolution 85,140]
234. happy(fred) <- (~2) [resolution 100,231]
326. ~happy(fred) | funny(fred) <- (~2) [resolution 91,231]
328. funny(fred) <- (~2) [subsumption resolution 326,234]
329. $false <- (~2, ~4) [subsumption resolution 328,149]
330. 2 | 4 [avatar contradiction clause 329]
343. patient(john) <- (1, ~17) [resolution 136,228]
347. calm(X0) | generous(X0) | generous(X0) | wise(X0) [resolution 104,66]
351. calm(X0) | generous(X0) | wise(X0) [duplicate literal removal 347]
402. generous(lucy) | wise(lucy) <- (~14) [resolution 351,195]
404. wise(lucy) <- (~14, ~15) [subsumption resolution 402,199]
405. patient(lucy) <- (1, ~14, ~15) [resolution 404,136]
409. happy(lucy) <- (1, ~14, ~15) [resolution 405,100]
411. $false <- (1, ~14, ~15) [subsumption resolution 409,131]
412. ~1 | 14 | 15 [avatar contradiction clause 411]
414. 30 <=> wise(lucy) [avatar definition]
416. wise(lucy) <- (30) [avatar component clause 414]
419. old(lucy) <- (15) [resolution 198,102]
425. 32 <=> old(lucy) [avatar definition]
427. old(lucy) <- (32) [avatar component clause 425]
429. 32 | ~15 [avatar split clause 419,197,425]
430. ~patient(john) | ~wise(john) <- (16) [resolution 202,105]
432. ~wise(john) <- (1, 16, ~17) [subsumption resolution 430,343]
433. $false <- (1, 16, ~17) [subsumption resolution 432,228]
434. ~1 | ~16 | 17 [avatar contradiction clause 433]
436. patient(john) <- (~16) [resolution 203,85]
438. ~wise(john) <- (17) [resolution 207,132]
442. ~generous(lucy) | wise(lucy) <- (32) [resolution 427,68]
445. wise(lucy) <- (15, 32) [subsumption resolution 442,198]
446. 30 | ~15 | ~32 [avatar split clause 445,425,197,414]
448. wise(john) <- (3, ~16) [resolution 436,144]
452. $false <- (3, ~16, 17) [subsumption resolution 448,438]
453. ~3 | 16 | ~17 [avatar contradiction clause 452]
469. patient(lucy) <- (1, 30) [resolution 416,136]
484. happy(lucy) <- (1, 30) [resolution 469,100]
486. $false <- (1, 30) [subsumption resolution 484,131]
487. ~1 | ~30 [avatar contradiction clause 486]
488. $false [avatar sat refutation 141,145,150,151,212,213,330,412,429,434,446,453,487]
% SZS output end Proof for 5523762981117670444229700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either funny or patient then paul is either quiet or not funny and vice versa.
If someone is either not rich or not happy then someone is both tall and not brave.
Everyone who is strong or not kind is both not calm and not rich.
Everyone who is happy is both brave and curious.
Everyone who is not old is not funny.
If someone is either not happy or rich then someone is either curious or not happy and vice versa.
If alice is brave or not strong then someone is both generous and kind and vice versa.
If someone is not generous or not happy then someone is both not kind and not generous and vice versa.
If someone is strong then lucy is happy or not wise and vice versa.
Everyone who is both patient and not funny is either wise or calm.
Everyone who is not wise is patient or quiet and vice versa.
If someone is rich or strong then someone is rich.
If susan is not kind then alice is funny and vice versa.
Everyone who is either generous or not kind is both not patient and not brave and vice versa.
Everyone who is brave is kind.
Everyone who is not funny is not rich or not strong.
Paul is both happy and wise.
Someone is not happy.
Someone is not quiet.
Fred is not quiet or not calm.
Paul is not wise or not tall.
Someone is both not wise and not generous.
Someone is both old and not quiet. | Paul is not kind. | contradiction | (((funny(lucy)<~>patient(lucy)))<=>((quiet(paul)<~>~funny(paul))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((strong(X)|~kind(X))=>(~calm(X)&~rich(X))))&
(![X]:(happy(X)=>(brave(X)&curious(X))))&
(![X]:(~old(X)=>~funny(X)))&
((?[X]:((~happy(X)<~>rich(X))))<=>(?[X]:((curious(X)<~>~happy(X)))))&
(((brave(alice)|~strong(alice)))<=>(?[X]:((generous(X)&kind(X)))))&
((?[X]:((~generous(X)|~happy(X))))<=>(?[X]:((~kind(X)&~generous(X)))))&
((?[X]:(strong(X)))<=>((happy(lucy)|~wise(lucy))))&
(![X]:((patient(X)&~funny(X))=>(wise(X)<~>calm(X))))&
(![X]:(~wise(X)<=>(patient(X)|quiet(X))))&
((?[X]:((rich(X)|strong(X))))=>(?[X]:(rich(X))))&
((~kind(susan))<=>(funny(alice)))&
(![X]:((generous(X)<~>~kind(X))<=>(~patient(X)&~brave(X))))&
(![X]:(brave(X)=>kind(X)))&
(![X]:(~funny(X)=>(~rich(X)|~strong(X))))&
((happy(paul)&wise(paul)))&
(?[X]:(~happy(X)))&
(?[X]:(~quiet(X)))&
((~quiet(fred)|~calm(fred)))&
((~wise(paul)|~tall(paul)))&
(?[X]:((~wise(X)&~generous(X))))&
(?[X]:((old(X)&~quiet(X)))) | ~kind(paul) | [
"p3",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 445709015739700463267223
% SZS output start Proof for 445709015739700463267223
4. ! [X0] : (happy(X0) => (curious(X0) & brave(X0))) [input p3]
15. ! [X0] : (brave(X0) => kind(X0)) [input p14]
17. wise(paul) & happy(paul) [input p16]
24. ~kind(paul) [input hypothesis]
33. ! [X0] : ((curious(X0) & brave(X0)) | ~happy(X0)) [ennf transformation 4]
37. ! [X0] : (kind(X0) | ~brave(X0)) [ennf transformation 15]
98. ~happy(X0) | brave(X0) [cnf transformation 33]
136. ~brave(X0) | kind(X0) [cnf transformation 37]
138. happy(paul) [cnf transformation 17]
147. ~kind(paul) [cnf transformation 24]
332. brave(paul) [resolution 98,138]
339. kind(paul) [resolution 136,332]
340. $false [subsumption resolution 339,147]
% SZS output end Proof for 445709015739700463267223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or curious is both patient and curious.
If someone is not generous then john is both rich and not funny.
Everyone who is happy is either patient or not tall and vice versa.
If lucy is either tall or happy then lucy is either not curious or not quiet.
Everyone who is tall is not creative or not tall.
Everyone who is either happy or not rich is both not kind and old and vice versa.
If someone is either not old or not funny then someone is both not tall and strong.
Everyone who is both not wise and not old is either strong or curious.
Everyone who is both brave and creative is either curious or not old.
If john is either not patient or not kind then lucy is either tall or creative and vice versa.
Everyone who is curious is either generous or rich and vice versa.
Everyone who is not kind is not old.
If someone is not calm or strong then someone is not rich or not quiet and vice versa.
Everyone who is funny or not rich is both old and tall.
If lucy is not happy then someone is not kind and vice versa.
Everyone who is quiet or happy is either not humble or creative.
Someone is either not tall or humble.
Susan is humble or not generous.
Someone is generous or not patient.
Susan is either not kind or tall.
Someone is not quiet or calm.
Susan is not tall or not happy. | Susan is humble. | neutral | (![X]:((~brave(X)|curious(X))=>(patient(X)&curious(X))))&
((?[X]:(~generous(X)))=>((rich(john)&~funny(john))))&
(![X]:(happy(X)<=>(patient(X)<~>~tall(X))))&
(((tall(lucy)<~>happy(lucy)))=>((~curious(lucy)<~>~quiet(lucy))))&
(![X]:(tall(X)=>(~creative(X)|~tall(X))))&
(![X]:((happy(X)<~>~rich(X))<=>(~kind(X)&old(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~wise(X)&~old(X))=>(strong(X)<~>curious(X))))&
(![X]:((brave(X)&creative(X))=>(curious(X)<~>~old(X))))&
(((~patient(john)<~>~kind(john)))<=>((tall(lucy)<~>creative(lucy))))&
(![X]:(curious(X)<=>(generous(X)<~>rich(X))))&
(![X]:(~kind(X)=>~old(X)))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((funny(X)|~rich(X))=>(old(X)&tall(X))))&
((~happy(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)|happy(X))=>(~humble(X)<~>creative(X))))&
(?[X]:((~tall(X)<~>humble(X))))&
((humble(susan)|~generous(susan)))&
(?[X]:((generous(X)|~patient(X))))&
((~kind(susan)<~>tall(susan)))&
(?[X]:((~quiet(X)|calm(X))))&
((~tall(susan)|~happy(susan))) | humble(susan) | [] | null | 0 |
If someone is creative or not rich then lucy is not calm or old and vice versa.
Everyone who is strong is both rich and kind and vice versa.
Everyone who is not calm or brave is wise.
Everyone who is either funny or not creative is not old or not brave.
Everyone who is generous is either not wise or calm.
Everyone who is not tall or not creative is either old or not tall.
If someone is not humble then john is not happy and vice versa.
If lucy is either humble or not curious then susan is either strong or not kind.
Everyone who is either not tall or not kind is both creative and brave and vice versa.
If someone is not generous then someone is old and vice versa.
If lucy is not tall then someone is either not calm or humble and vice versa.
If someone is either not kind or brave then someone is either calm or not funny.
If john is not funny or brave then john is both not funny and rich and vice versa.
Everyone who is humble or not tall is both tall and wise and vice versa.
If someone is curious then someone is patient.
If someone is both patient and funny then mary is either not patient or tall.
Someone is both not quiet and not old.
Someone is either calm or tall.
Someone is both not creative and not humble.
Someone is not patient.
Susan is not tall or happy.
Someone is not funny or wise.
Fred is not creative or old.
Alice is not strong. | Mary is generous. | contradiction | ((?[X]:((creative(X)|~rich(X))))<=>((~calm(lucy)|old(lucy))))&
(![X]:(strong(X)<=>(rich(X)&kind(X))))&
(![X]:((~calm(X)|brave(X))=>wise(X)))&
(![X]:((funny(X)<~>~creative(X))=>(~old(X)|~brave(X))))&
(![X]:(generous(X)=>(~wise(X)<~>calm(X))))&
(![X]:((~tall(X)|~creative(X))=>(old(X)<~>~tall(X))))&
((?[X]:(~humble(X)))<=>(~happy(john)))&
(((humble(lucy)<~>~curious(lucy)))=>((strong(susan)<~>~kind(susan))))&
(![X]:((~tall(X)<~>~kind(X))<=>(creative(X)&brave(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(old(X))))&
((~tall(lucy))<=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((~kind(X)<~>brave(X))))=>(?[X]:((calm(X)<~>~funny(X)))))&
(((~funny(john)|brave(john)))<=>((~funny(john)&rich(john))))&
(![X]:((humble(X)|~tall(X))<=>(tall(X)&wise(X))))&
((?[X]:(curious(X)))=>(?[X]:(patient(X))))&
((?[X]:((patient(X)&funny(X))))=>((~patient(mary)<~>tall(mary))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:(~patient(X)))&
((~tall(susan)|happy(susan)))&
(?[X]:((~funny(X)|wise(X))))&
((~creative(fred)|old(fred)))&
(~strong(alice)) | generous(mary) | [
"p2",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4848086935140099651283830
% SZS output start Proof for 4848086935140099651283830
3. ! [X0] : ((brave(X0) | ~calm(X0)) => wise(X0)) [input p2]
5. ! [X0] : (generous(X0) => (~wise(X0) <~> calm(X0))) [input p4]
11. ~tall(lucy) <=> ? [X0] : (~calm(X0) <~> humble(X0)) [input p10]
14. ! [X0] : ((~tall(X0) | humble(X0)) <=> (wise(X0) & tall(X0))) [input p13]
25. generous(mary) [input hypothesis]
30. ! [X0] : (wise(X0) | (~brave(X0) & calm(X0))) [ennf transformation 3]
33. ! [X0] : ((~wise(X0) <~> calm(X0)) | ~generous(X0)) [ennf transformation 5]
47. ! [X0] : (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~generous(X0)) [nnf transformation 33]
61. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (? [X0] : ((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | tall(lucy)) [nnf transformation 11]
62. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (? [X1] : ((~humble(X1) | calm(X1)) & (humble(X1) | ~calm(X1))) | tall(lucy)) [rectify 61]
63. ? [X1] : ((~humble(X1) | calm(X1)) & (humble(X1) | ~calm(X1))) => ((~humble(sK4) | calm(sK4)) & (humble(sK4) | ~calm(sK4))) [choice axiom]
64. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(sK4) | calm(sK4)) & (humble(sK4) | ~calm(sK4))) | tall(lucy)) [skolemisation 62,63]
71. ! [X0] : (((~tall(X0) | humble(X0)) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | (tall(X0) & ~humble(X0)))) [nnf transformation 14]
72. ! [X0] : ((~tall(X0) | humble(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | (tall(X0) & ~humble(X0)))) [flattening 71]
95. wise(X0) | calm(X0) [cnf transformation 30]
99. calm(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 47]
100. ~calm(X0) | wise(X0) | ~generous(X0) [cnf transformation 47]
122. ~tall(lucy) | ~calm(X0) | ~humble(X0) [cnf transformation 64]
133. tall(X0) | tall(X0) [cnf transformation 72]
136. ~tall(X0) | humble(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 72]
150. generous(mary) [cnf transformation 25]
151. tall(X0) [duplicate literal removal 133]
152. ~tall(X0) | humble(X0) | ~wise(X0) [duplicate literal removal 136]
180. ~generous(X0) | wise(X0) [subsumption resolution 100,95]
181. ~generous(X0) | calm(X0) [subsumption resolution 99,180]
230. 18 <=> ! [X0] : (~calm(X0) | ~humble(X0)) [avatar definition]
231. ~humble(X0) | ~calm(X0) <- (18) [avatar component clause 230]
233. 19 <=> tall(lucy) [avatar definition]
235. ~tall(lucy) <- (~19) [avatar component clause 233]
236. 18 | ~19 [avatar split clause 122,233,230]
321. $false <- (~19) [subsumption resolution 235,151]
322. 19 [avatar contradiction clause 321]
325. wise(mary) [resolution 180,150]
327. calm(mary) [resolution 181,150]
373. ~wise(X1) | humble(X1) [resolution 152,151]
379. humble(mary) [resolution 373,325]
382. ~calm(mary) <- (18) [resolution 379,231]
384. $false <- (18) [subsumption resolution 382,327]
385. ~18 [avatar contradiction clause 384]
386. $false [avatar sat refutation 236,322,385]
% SZS output end Proof for 4848086935140099651283830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
Everyone who is humble is both happy and not wise.
Everyone who is either not happy or brave is either happy or not wise and vice versa.
If someone is tall then mary is both strong and not calm and vice versa.
Everyone who is old is strong or quiet.
Everyone who is either not curious or not happy is not kind and vice versa.
Everyone who is both not humble and not kind is both funny and not brave.
If mary is rich or brave then paul is quiet or not funny and vice versa.
If someone is quiet or not generous then lucy is either curious or not happy and vice versa.
If someone is creative then paul is either humble or not humble and vice versa.
Susan is creative or not wise.
Someone is brave or happy.
Alice is creative or funny.
Susan is curious or not brave.
Paul is either brave or not rich.
Alice is not funny or kind. | Susan is tall. | entailment | ((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
(![X]:(humble(X)=>(happy(X)&~wise(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~calm(mary))))&
(![X]:(old(X)=>(strong(X)|quiet(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((~humble(X)&~kind(X))=>(funny(X)&~brave(X))))&
(((rich(mary)|brave(mary)))<=>((quiet(paul)|~funny(paul))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
((creative(susan)|~wise(susan)))&
(?[X]:((brave(X)|happy(X))))&
((creative(alice)|funny(alice)))&
((curious(susan)|~brave(susan)))&
((brave(paul)<~>~rich(paul)))&
((~funny(alice)|kind(alice))) | tall(susan) | [
"p0",
"p1",
"p5",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6771143683534931390763936
% SZS output start Proof for 6771143683534931390763936
1. ? [X0] : (rich(X0) | brave(X0)) => (~happy(john) & ~funny(john)) [input p0]
2. ! [X0] : (tall(X0) <=> ~brave(X0)) [input p1]
6. ! [X0] : (~curious(X0) <=> (~kind(X0) & old(X0))) [input p5]
7. ! [X0] : (humble(X0) => (~wise(X0) & happy(X0))) [input p6]
11. ! [X0] : ((~curious(X0) <~> ~happy(X0)) <=> ~kind(X0)) [input p10]
12. ! [X0] : ((~kind(X0) & ~humble(X0)) => (~brave(X0) & funny(X0))) [input p11]
22. ~tall(susan) [input hypothesis]
23. (~happy(john) & ~funny(john)) | ! [X0] : (~rich(X0) & ~brave(X0)) [ennf transformation 1]
24. ! [X0] : ((~wise(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 7]
27. ! [X0] : ((~brave(X0) & funny(X0)) | (kind(X0) | humble(X0))) [ennf transformation 12]
28. ! [X0] : ((~brave(X0) & funny(X0)) | kind(X0) | humble(X0)) [flattening 27]
29. ! [X0] : ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))) [nnf transformation 2]
35. ! [X0] : ((~curious(X0) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | curious(X0))) [nnf transformation 6]
36. ! [X0] : ((~curious(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | curious(X0))) [flattening 35]
43. ! [X0] : ((((happy(X0) | curious(X0)) & (~happy(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))))) [nnf transformation 11]
57. ~funny(john) | ~brave(X0) [cnf transformation 23]
59. ~happy(john) | ~brave(X0) [cnf transformation 23]
62. tall(X0) | brave(X0) [cnf transformation 29]
78. ~kind(X0) | curious(X0) [cnf transformation 36]
80. ~humble(X0) | happy(X0) [cnf transformation 24]
95. ~kind(X0) | ~curious(X0) | happy(X0) [cnf transformation 43]
98. kind(X0) | funny(X0) | humble(X0) [cnf transformation 28]
121. ~tall(susan) [cnf transformation 22]
132. 2 <=> happy(john) [avatar definition]
134. ~happy(john) <- (~2) [avatar component clause 132]
137. 3 <=> ! [X0] : ~brave(X0) [avatar definition]
138. ~brave(X0) <- (3) [avatar component clause 137]
139. 3 | ~2 [avatar split clause 59,132,137]
141. 4 <=> funny(john) [avatar definition]
143. ~funny(john) <- (~4) [avatar component clause 141]
145. 3 | ~4 [avatar split clause 57,141,137]
189. ~kind(X0) | happy(X0) [subsumption resolution 95,78]
283. 32 <=> brave(susan) [avatar definition]
284. brave(susan) <- (32) [avatar component clause 283]
285. ~brave(susan) <- (~32) [avatar component clause 283]
298. brave(susan) [resolution 62,121]
301. $false <- (~32) [subsumption resolution 298,285]
302. 32 [avatar contradiction clause 301]
354. funny(X0) | humble(X0) | happy(X0) [resolution 98,189]
389. happy(X0) | funny(X0) [subsumption resolution 354,80]
450. funny(john) <- (~2) [resolution 389,134]
451. $false <- (~2, ~4) [subsumption resolution 450,143]
452. 2 | 4 [avatar contradiction clause 451]
455. $false <- (3, 32) [resolution 138,284]
456. ~3 | ~32 [avatar contradiction clause 455]
459. $false [avatar sat refutation 139,145,302,452,456]
% SZS output end Proof for 6771143683534931390763936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is curious or not creative.
Everyone who is generous is both not generous and patient and vice versa.
If someone is funny or kind then someone is brave and vice versa.
Everyone who is not patient or not creative is either not humble or creative.
Everyone who is not humble or not funny is either brave or not curious.
Everyone who is either not strong or creative is both strong and brave.
Everyone who is not generous is not humble and vice versa.
Everyone who is both creative and not curious is old and vice versa.
Everyone who is quiet or patient is old or brave.
Everyone who is both quiet and not rich is not tall or old and vice versa.
If paul is both not old and kind then mary is funny or not funny.
If lucy is both creative and not wise then someone is not patient.
Everyone who is not creative or kind is not strong or not funny.
Everyone who is both old and not kind is either wise or brave and vice versa.
If susan is both not wise and not old then someone is funny.
Everyone who is both calm and not humble is either rich or quiet and vice versa.
Someone is calm or not strong.
Someone is either not humble or curious.
Someone is not patient or creative.
Fred is not kind.
Someone is either happy or not humble. | Mary is not brave. | neutral | (![X]:(~creative(X)=>(curious(X)|~creative(X))))&
(![X]:(generous(X)<=>(~generous(X)&patient(X))))&
((?[X]:((funny(X)|kind(X))))<=>(?[X]:(brave(X))))&
(![X]:((~patient(X)|~creative(X))=>(~humble(X)<~>creative(X))))&
(![X]:((~humble(X)|~funny(X))=>(brave(X)<~>~curious(X))))&
(![X]:((~strong(X)<~>creative(X))=>(strong(X)&brave(X))))&
(![X]:(~generous(X)<=>~humble(X)))&
(![X]:((creative(X)&~curious(X))<=>old(X)))&
(![X]:((quiet(X)|patient(X))=>(old(X)|brave(X))))&
(![X]:((quiet(X)&~rich(X))<=>(~tall(X)|old(X))))&
(((~old(paul)&kind(paul)))=>((funny(mary)|~funny(mary))))&
(((creative(lucy)&~wise(lucy)))=>(?[X]:(~patient(X))))&
(![X]:((~creative(X)|kind(X))=>(~strong(X)|~funny(X))))&
(![X]:((old(X)&~kind(X))<=>(wise(X)<~>brave(X))))&
(((~wise(susan)&~old(susan)))=>(?[X]:(funny(X))))&
(![X]:((calm(X)&~humble(X))<=>(rich(X)<~>quiet(X))))&
(?[X]:((calm(X)|~strong(X))))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~patient(X)|creative(X))))&
(~kind(fred))&
(?[X]:((happy(X)<~>~humble(X)))) | ~brave(mary) | [] | null | 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa.
If someone is not happy or not kind then someone is either tall or kind.
Everyone who is strong is both not kind and old and vice versa.
Everyone who is creative or not strong is not calm or not happy.
If someone is either not kind or patient then susan is both not happy and wise.
Everyone who is old is both not strong and strong.
Everyone who is happy is either not humble or not happy.
If lucy is not funny or not brave then lucy is either funny or not curious and vice versa.
Everyone who is both curious and brave is both not patient and old and vice versa.
If someone is either curious or funny then mary is both not funny and not old.
Everyone who is not funny or not brave is not wise.
Everyone who is both not happy and brave is either not calm or strong and vice versa.
Everyone who is both not generous and not wise is either not kind or not generous.
Everyone who is both not tall and generous is brave or not brave and vice versa.
If paul is not wise or not calm then fred is either not wise or not brave and vice versa.
Everyone who is both kind and quiet is rich and vice versa.
John is both humble and not wise.
Lucy is not funny.
Fred is not patient or not old.
Someone is either quiet or wise.
Lucy is brave.
Someone is happy or not happy. | John is old. | contradiction | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((~happy(X)|~kind(X))))=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(strong(X)<=>(~kind(X)&old(X))))&
(![X]:((creative(X)|~strong(X))=>(~calm(X)|~happy(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~happy(susan)&wise(susan))))&
(![X]:(old(X)=>(~strong(X)&strong(X))))&
(![X]:(happy(X)=>(~humble(X)<~>~happy(X))))&
(((~funny(lucy)|~brave(lucy)))<=>((funny(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~patient(X)&old(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~funny(mary)&~old(mary))))&
(![X]:((~funny(X)|~brave(X))=>~wise(X)))&
(![X]:((~happy(X)&brave(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((~generous(X)&~wise(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~tall(X)&generous(X))<=>(brave(X)|~brave(X))))&
(((~wise(paul)|~calm(paul)))<=>((~wise(fred)<~>~brave(fred))))&
(![X]:((kind(X)&quiet(X))<=>rich(X)))&
((humble(john)&~wise(john)))&
(~funny(lucy))&
((~patient(fred)|~old(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(brave(lucy))&
(?[X]:((happy(X)|~happy(X)))) | old(john) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6120205556492016397884254
% SZS output start Proof for 6120205556492016397884254
6. ! [X0] : (old(X0) => (strong(X0) & ~strong(X0))) [input p5]
23. old(john) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~strong(X0)) | ~old(X0)) [ennf transformation 6]
81. ~strong(X0) | ~old(X0) [cnf transformation 30]
82. strong(X0) | ~old(X0) [cnf transformation 30]
128. old(john) [cnf transformation 23]
169. ~old(X0) [subsumption resolution 81,82]
241. $false [subsumption resolution 128,169]
% SZS output end Proof for 6120205556492016397884254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not brave is creative.
If someone is either rich or not old then alice is not wise.
If someone is both not generous and not strong then mary is both funny and patient.
Everyone who is curious or not old is both creative and not patient.
Everyone who is not happy is both not strong and brave.
Everyone who is not tall is not kind or not old.
If fred is both rich and humble then someone is not humble.
If someone is either kind or funny then mary is not generous and vice versa.
If someone is either not funny or not tall then someone is both tall and rich and vice versa.
Everyone who is both strong and not humble is not kind.
Everyone who is both brave and humble is creative and vice versa.
If someone is not rich then someone is not funny or wise and vice versa.
Everyone who is either humble or generous is both curious and old and vice versa.
Everyone who is not creative is both rich and wise and vice versa.
Everyone who is generous is not brave.
Everyone who is humble or brave is happy or not generous and vice versa.
Susan is either old or not tall.
Someone is both brave and calm.
Someone is not wise or not strong.
Someone is both tall and not generous.
Susan is happy.
Mary is not funny or not happy. | Alice is generous. | contradiction | (![X]:((~old(X)&~brave(X))=>creative(X)))&
((?[X]:((rich(X)<~>~old(X))))=>(~wise(alice)))&
((?[X]:((~generous(X)&~strong(X))))=>((funny(mary)&patient(mary))))&
(![X]:((curious(X)|~old(X))=>(creative(X)&~patient(X))))&
(![X]:(~happy(X)=>(~strong(X)&brave(X))))&
(![X]:(~tall(X)=>(~kind(X)|~old(X))))&
(((rich(fred)&humble(fred)))=>(?[X]:(~humble(X))))&
((?[X]:((kind(X)<~>funny(X))))<=>(~generous(mary)))&
((?[X]:((~funny(X)<~>~tall(X))))<=>(?[X]:((tall(X)&rich(X)))))&
(![X]:((strong(X)&~humble(X))=>~kind(X)))&
(![X]:((brave(X)&humble(X))<=>creative(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:((humble(X)<~>generous(X))<=>(curious(X)&old(X))))&
(![X]:(~creative(X)<=>(rich(X)&wise(X))))&
(![X]:(generous(X)=>~brave(X)))&
(![X]:((humble(X)|brave(X))<=>(happy(X)|~generous(X))))&
((old(susan)<~>~tall(susan)))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((tall(X)&~generous(X))))&
(happy(susan))&
((~funny(mary)|~happy(mary))) | generous(alice) | [
"p1",
"p3",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8856932889854573272666907
% SZS output start Proof for 8856932889854573272666907
2. ? [X0] : (rich(X0) <~> ~old(X0)) => ~wise(alice) [input p1]
4. ! [X0] : ((~old(X0) | curious(X0)) => (~patient(X0) & creative(X0))) [input p3]
11. ! [X0] : ((humble(X0) & brave(X0)) <=> creative(X0)) [input p10]
14. ! [X0] : (~creative(X0) <=> (wise(X0) & rich(X0))) [input p13]
15. ! [X0] : (generous(X0) => ~brave(X0)) [input p14]
23. generous(alice) [input hypothesis]
29. ~wise(alice) | ! [X0] : (rich(X0) <=> ~old(X0)) [ennf transformation 2]
31. ! [X0] : ((~patient(X0) & creative(X0)) | (old(X0) & ~curious(X0))) [ennf transformation 4]
39. ! [X0] : (~brave(X0) | ~generous(X0)) [ennf transformation 15]
40. ~wise(alice) | ! [X0] : ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0))) [nnf transformation 29]
52. ! [X0] : (((humble(X0) & brave(X0)) | ~creative(X0)) & (creative(X0) | (~humble(X0) | ~brave(X0)))) [nnf transformation 11]
53. ! [X0] : (((humble(X0) & brave(X0)) | ~creative(X0)) & (creative(X0) | ~humble(X0) | ~brave(X0))) [flattening 52]
61. ! [X0] : ((~creative(X0) | (~wise(X0) | ~rich(X0))) & ((wise(X0) & rich(X0)) | creative(X0))) [nnf transformation 14]
62. ! [X0] : ((~creative(X0) | ~wise(X0) | ~rich(X0)) & ((wise(X0) & rich(X0)) | creative(X0))) [flattening 61]
73. ~wise(alice) | ~old(X0) | ~rich(X0) [cnf transformation 40]
78. creative(X0) | old(X0) [cnf transformation 31]
97. ~creative(X0) | brave(X0) [cnf transformation 53]
108. rich(X0) | creative(X0) [cnf transformation 62]
109. wise(X0) | creative(X0) [cnf transformation 62]
111. ~generous(X0) | ~brave(X0) [cnf transformation 39]
124. generous(alice) [cnf transformation 23]
129. 2 <=> wise(alice) [avatar definition]
131. ~wise(alice) <- (~2) [avatar component clause 129]
134. 3 <=> ! [X0] : (~old(X0) | ~rich(X0)) [avatar definition]
135. ~rich(X0) | ~old(X0) <- (3) [avatar component clause 134]
136. 3 | ~2 [avatar split clause 73,129,134]
271. creative(alice) <- (~2) [resolution 109,131]
274. brave(alice) <- (~2) [resolution 271,97]
275. ~brave(alice) [resolution 111,124]
276. $false <- (~2) [subsumption resolution 275,274]
277. 2 [avatar contradiction clause 276]
282. ~old(X1) | creative(X1) <- (3) [resolution 135,108]
283. creative(X1) <- (3) [subsumption resolution 282,78]
287. brave(X1) <- (3) [resolution 283,97]
363. $false <- (3) [resolution 287,275]
364. ~3 [avatar contradiction clause 363]
365. $false [avatar sat refutation 136,277,364]
% SZS output end Proof for 8856932889854573272666907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not brave is curious or not rich.
If fred is not brave then alice is either not strong or strong and vice versa.
If someone is kind then alice is both humble and calm.
Everyone who is not funny or not generous is either not patient or creative and vice versa.
If susan is humble then mary is either patient or not generous and vice versa.
If someone is both not rich and not patient then john is either calm or not generous and vice versa.
If someone is both not kind and not strong then susan is both kind and tall.
If someone is brave then susan is both not happy and not humble.
Everyone who is not tall is not funny or kind and vice versa.
Everyone who is both not brave and not wise is both happy and patient and vice versa.
If alice is either patient or calm then someone is old.
Everyone who is both not creative and not humble is both not creative and not patient.
If someone is either not humble or not tall then someone is both old and not humble and vice versa.
If someone is both generous and rich then someone is creative.
Everyone who is not curious is not wise or rich and vice versa.
If someone is both not happy and old then susan is not brave or happy and vice versa.
Someone is either curious or not humble.
John is not calm or tall.
Mary is either old or patient.
Someone is not calm or kind.
Someone is either not generous or not curious.
Alice is both not calm and funny.
Someone is rich.
Fred is both not tall and happy. | Susan is not strong. | contradiction | (![X]:((curious(X)&~brave(X))=>(curious(X)|~rich(X))))&
((~brave(fred))<=>((~strong(alice)<~>strong(alice))))&
((?[X]:(kind(X)))=>((humble(alice)&calm(alice))))&
(![X]:((~funny(X)|~generous(X))<=>(~patient(X)<~>creative(X))))&
((humble(susan))<=>((patient(mary)<~>~generous(mary))))&
((?[X]:((~rich(X)&~patient(X))))<=>((calm(john)<~>~generous(john))))&
((?[X]:((~kind(X)&~strong(X))))=>((kind(susan)&tall(susan))))&
((?[X]:(brave(X)))=>((~happy(susan)&~humble(susan))))&
(![X]:(~tall(X)<=>(~funny(X)|kind(X))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)&patient(X))))&
(((patient(alice)<~>calm(alice)))=>(?[X]:(old(X))))&
(![X]:((~creative(X)&~humble(X))=>(~creative(X)&~patient(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(?[X]:((old(X)&~humble(X)))))&
((?[X]:((generous(X)&rich(X))))=>(?[X]:(creative(X))))&
(![X]:(~curious(X)<=>(~wise(X)|rich(X))))&
((?[X]:((~happy(X)&old(X))))<=>((~brave(susan)|happy(susan))))&
(?[X]:((curious(X)<~>~humble(X))))&
((~calm(john)|tall(john)))&
((old(mary)<~>patient(mary)))&
(?[X]:((~calm(X)|kind(X))))&
(?[X]:((~generous(X)<~>~curious(X))))&
((~calm(alice)&funny(alice)))&
(?[X]:(rich(X)))&
((~tall(fred)&happy(fred))) | ~strong(susan) | [
"p2",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1718294979425009235948710
% SZS output start Proof for 1718294979425009235948710
3. ? [X0] : kind(X0) => (calm(alice) & humble(alice)) [input p2]
7. ? [X0] : (~strong(X0) & ~kind(X0)) => (tall(susan) & kind(susan)) [input p6]
22. funny(alice) & ~calm(alice) [input p21]
25. ~strong(susan) [input hypothesis]
30. (calm(alice) & humble(alice)) | ! [X0] : ~kind(X0) [ennf transformation 3]
31. (tall(susan) & kind(susan)) | ! [X0] : (strong(X0) | kind(X0)) [ennf transformation 7]
84. calm(alice) | ~kind(X0) [cnf transformation 30]
101. kind(susan) | strong(X0) | kind(X0) [cnf transformation 31]
139. ~calm(alice) [cnf transformation 22]
144. ~strong(susan) [cnf transformation 25]
158. 3 <=> ! [X0] : ~kind(X0) [avatar definition]
159. ~kind(X0) <- (3) [avatar component clause 158]
161. 4 <=> calm(alice) [avatar definition]
164. 3 | 4 [avatar split clause 84,161,158]
212. 14 <=> ! [X0] : (strong(X0) | kind(X0)) [avatar definition]
213. kind(X0) | strong(X0) <- (14) [avatar component clause 212]
220. 16 <=> kind(susan) [avatar definition]
222. kind(susan) <- (16) [avatar component clause 220]
223. 14 | 16 [avatar split clause 101,220,212]
342. ~4 [avatar split clause 139,161]
344. strong(X0) <- (3, 14) [resolution 213,159]
345. $false <- (3, 14) [resolution 344,144]
346. ~3 | ~14 [avatar contradiction clause 345]
347. $false <- (3, 16) [subsumption resolution 222,159]
348. ~3 | ~16 [avatar contradiction clause 347]
349. $false [avatar sat refutation 164,223,342,346,348]
% SZS output end Proof for 1718294979425009235948710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If mary is brave then someone is not happy or not calm and vice versa.
Everyone who is not creative or not wise is both not old and happy and vice versa.
Everyone who is either not strong or generous is not patient.
If someone is patient or calm then someone is old.
Everyone who is calm or strong is kind and vice versa.
If someone is either not strong or tall then someone is either not funny or brave and vice versa.
If susan is kind or tall then susan is not strong and vice versa.
If someone is both calm and kind then someone is both not generous and not curious and vice versa.
Everyone who is not humble or strong is both quiet and not calm.
Everyone who is not strong is brave or not old.
Everyone who is not strong or happy is not quiet and vice versa.
If someone is not happy or strong then someone is both creative and not tall and vice versa.
If someone is both not funny and creative then someone is both wise and tall and vice versa.
Everyone who is not patient is both humble and funny and vice versa.
Everyone who is both rich and patient is wise or curious and vice versa.
Everyone who is either not quiet or not humble is either funny or not humble.
Fred is not calm.
Someone is either not wise or curious.
Someone is either calm or not rich.
Alice is both quiet and not brave.
Someone is both not funny and not brave.
Someone is calm.
Someone is either wise or humble.
Susan is both not rich and tall. | Susan is not patient. | entailment | ((brave(mary))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~creative(X)|~wise(X))<=>(~old(X)&happy(X))))&
(![X]:((~strong(X)<~>generous(X))=>~patient(X)))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)|strong(X))<=>kind(X)))&
((?[X]:((~strong(X)<~>tall(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(((kind(susan)|tall(susan)))<=>(~strong(susan)))&
((?[X]:((calm(X)&kind(X))))<=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((~humble(X)|strong(X))=>(quiet(X)&~calm(X))))&
(![X]:(~strong(X)=>(brave(X)|~old(X))))&
(![X]:((~strong(X)|happy(X))<=>~quiet(X)))&
((?[X]:((~happy(X)|strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:(~patient(X)<=>(humble(X)&funny(X))))&
(![X]:((rich(X)&patient(X))<=>(wise(X)|curious(X))))&
(![X]:((~quiet(X)<~>~humble(X))=>(funny(X)<~>~humble(X))))&
(~calm(fred))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
((quiet(alice)&~brave(alice)))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((wise(X)<~>humble(X))))&
((~rich(susan)&tall(susan))) | ~patient(susan) | [
"p4",
"p6",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3969063626337065602225302
% SZS output start Proof for 3969063626337065602225302
5. ! [X0] : ((strong(X0) | calm(X0)) <=> kind(X0)) [input p4]
7. (tall(susan) | kind(susan)) <=> ~strong(susan) [input p6]
9. ! [X0] : ((strong(X0) | ~humble(X0)) => (~calm(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((happy(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p10]
14. ! [X0] : (~patient(X0) <=> (funny(X0) & humble(X0))) [input p13]
16. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) => (funny(X0) <~> ~humble(X0))) [input p15]
25. patient(susan) [input hypothesis]
33. ! [X0] : ((~calm(X0) & quiet(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 9]
36. ! [X0] : ((funny(X0) <~> ~humble(X0)) | (~quiet(X0) <=> ~humble(X0))) [ennf transformation 16]
47. ! [X0] : (((strong(X0) | calm(X0)) | ~kind(X0)) & (kind(X0) | (~strong(X0) & ~calm(X0)))) [nnf transformation 5]
48. ! [X0] : ((strong(X0) | calm(X0) | ~kind(X0)) & (kind(X0) | (~strong(X0) & ~calm(X0)))) [flattening 47]
54. ((tall(susan) | kind(susan)) | strong(susan)) & (~strong(susan) | (~tall(susan) & ~kind(susan))) [nnf transformation 7]
55. (tall(susan) | kind(susan) | strong(susan)) & (~strong(susan) | (~tall(susan) & ~kind(susan))) [flattening 54]
61. ! [X0] : (((happy(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (~happy(X0) & strong(X0)))) [nnf transformation 11]
62. ! [X0] : ((happy(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (~happy(X0) & strong(X0)))) [flattening 61]
73. ! [X0] : ((~patient(X0) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | patient(X0))) [nnf transformation 14]
74. ! [X0] : ((~patient(X0) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | patient(X0))) [flattening 73]
77. ! [X0] : (((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0)))) [nnf transformation 36]
104. ~strong(X0) | kind(X0) [cnf transformation 48]
114. ~strong(susan) | ~kind(susan) [cnf transformation 55]
121. quiet(X0) | humble(X0) [cnf transformation 33]
126. ~quiet(X0) | strong(X0) [cnf transformation 62]
140. ~humble(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 74]
146. ~humble(X0) | funny(X0) | ~humble(X0) | quiet(X0) [cnf transformation 77]
164. patient(susan) [cnf transformation 25]
165. ~humble(X0) | funny(X0) | quiet(X0) [duplicate literal removal 146]
247. 19 <=> strong(susan) [avatar definition]
249. ~strong(susan) <- (~19) [avatar component clause 247]
251. ~strong(susan) [subsumption resolution 114,104]
252. ~19 [avatar split clause 251,247]
332. quiet(X0) | funny(X0) [subsumption resolution 165,121]
372. humble(X0) | strong(X0) [resolution 126,121]
406. funny(X1) | strong(X1) [resolution 332,126]
558. strong(X0) | ~funny(X0) | ~patient(X0) [resolution 372,140]
559. ~patient(X0) | strong(X0) [subsumption resolution 558,406]
622. strong(susan) [resolution 559,164]
629. $false <- (~19) [subsumption resolution 622,249]
630. 19 [avatar contradiction clause 629]
633. $false [avatar sat refutation 252,630]
% SZS output end Proof for 3969063626337065602225302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is curious or not kind and vice versa.
If someone is quiet or not strong then susan is patient or not quiet and vice versa.
Everyone who is both not patient and not quiet is both not old and patient and vice versa.
Everyone who is both creative and strong is humble and vice versa.
If someone is either tall or not strong then alice is patient or not creative and vice versa.
Everyone who is not rich or brave is strong and vice versa.
If john is either not strong or not happy then lucy is not humble or not strong and vice versa.
Everyone who is not tall or generous is patient and vice versa.
If paul is either creative or not wise then mary is calm.
Everyone who is quiet or strong is both not happy and old.
Everyone who is rich or old is not funny.
If someone is either patient or not happy then someone is both strong and not creative.
If someone is either not old or old then paul is not creative or kind.
Everyone who is quiet or creative is humble or curious.
Everyone who is not humble is either rich or strong.
If someone is not patient then someone is not kind or not strong and vice versa.
Mary is both calm and not quiet.
Paul is either kind or not brave.
Alice is kind.
Mary is funny or not generous.
Someone is either not rich or not calm.
John is both happy and not curious.
Someone is not strong or happy. | Paul is not wise. | neutral | (![X]:(~creative(X)<=>(curious(X)|~kind(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((patient(susan)|~quiet(susan))))&
(![X]:((~patient(X)&~quiet(X))<=>(~old(X)&patient(X))))&
(![X]:((creative(X)&strong(X))<=>humble(X)))&
((?[X]:((tall(X)<~>~strong(X))))<=>((patient(alice)|~creative(alice))))&
(![X]:((~rich(X)|brave(X))<=>strong(X)))&
(((~strong(john)<~>~happy(john)))<=>((~humble(lucy)|~strong(lucy))))&
(![X]:((~tall(X)|generous(X))<=>patient(X)))&
(((creative(paul)<~>~wise(paul)))=>(calm(mary)))&
(![X]:((quiet(X)|strong(X))=>(~happy(X)&old(X))))&
(![X]:((rich(X)|old(X))=>~funny(X)))&
((?[X]:((patient(X)<~>~happy(X))))=>(?[X]:((strong(X)&~creative(X)))))&
((?[X]:((~old(X)<~>old(X))))=>((~creative(paul)|kind(paul))))&
(![X]:((quiet(X)|creative(X))=>(humble(X)|curious(X))))&
(![X]:(~humble(X)=>(rich(X)<~>strong(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~kind(X)|~strong(X)))))&
((calm(mary)&~quiet(mary)))&
((kind(paul)<~>~brave(paul)))&
(kind(alice))&
((funny(mary)|~generous(mary)))&
(?[X]:((~rich(X)<~>~calm(X))))&
((happy(john)&~curious(john)))&
(?[X]:((~strong(X)|happy(X)))) | ~wise(paul) | [] | null | 0 |
If someone is not old then someone is either curious or rich.
If lucy is either not brave or wise then lucy is either curious or not curious and vice versa.
If fred is not kind then someone is happy or not creative and vice versa.
If lucy is both funny and strong then fred is both not happy and not generous and vice versa.
Everyone who is not curious or humble is not curious or old and vice versa.
Everyone who is not generous is either generous or not generous and vice versa.
If someone is both happy and generous then susan is calm and vice versa.
Everyone who is either rich or not tall is not happy or rich and vice versa.
Everyone who is not happy is either not happy or tall.
Everyone who is either not wise or not curious is either wise or tall and vice versa.
Everyone who is both generous and not kind is either old or funny.
If fred is funny then fred is quiet and vice versa.
Everyone who is funny or rich is not brave or quiet and vice versa.
If john is humble then someone is both not old and quiet and vice versa.
If alice is humble or not creative then someone is either not old or happy.
Everyone who is both not patient and not humble is happy and vice versa.
Someone is humble.
Susan is either old or not generous.
Mary is patient or rich.
Paul is either not old or curious.
Lucy is either not curious or not patient. | Alice is curious. | neutral | ((?[X]:(~old(X)))=>(?[X]:((curious(X)<~>rich(X)))))&
(((~brave(lucy)<~>wise(lucy)))<=>((curious(lucy)<~>~curious(lucy))))&
((~kind(fred))<=>(?[X]:((happy(X)|~creative(X)))))&
(((funny(lucy)&strong(lucy)))<=>((~happy(fred)&~generous(fred))))&
(![X]:((~curious(X)|humble(X))<=>(~curious(X)|old(X))))&
(![X]:(~generous(X)<=>(generous(X)<~>~generous(X))))&
((?[X]:((happy(X)&generous(X))))<=>(calm(susan)))&
(![X]:((rich(X)<~>~tall(X))<=>(~happy(X)|rich(X))))&
(![X]:(~happy(X)=>(~happy(X)<~>tall(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(wise(X)<~>tall(X))))&
(![X]:((generous(X)&~kind(X))=>(old(X)<~>funny(X))))&
((funny(fred))<=>(quiet(fred)))&
(![X]:((funny(X)|rich(X))<=>(~brave(X)|quiet(X))))&
((humble(john))<=>(?[X]:((~old(X)&quiet(X)))))&
(((humble(alice)|~creative(alice)))=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~patient(X)&~humble(X))<=>happy(X)))&
(?[X]:(humble(X)))&
((old(susan)<~>~generous(susan)))&
((patient(mary)|rich(mary)))&
((~old(paul)<~>curious(paul)))&
((~curious(lucy)<~>~patient(lucy))) | curious(alice) | [] | null | 0 |
Everyone who is generous or not old is both quiet and calm.
If someone is kind then someone is both not kind and not patient and vice versa.
Everyone who is tall or calm is either patient or not tall and vice versa.
If someone is either not calm or happy then paul is generous.
Everyone who is wise or rich is both strong and calm and vice versa.
Everyone who is either not curious or not strong is either patient or calm and vice versa.
If alice is not funny then lucy is kind and vice versa.
Everyone who is either humble or not happy is both not brave and not creative and vice versa.
If mary is either funny or wise then fred is kind.
Everyone who is either brave or not strong is both rich and old and vice versa.
If someone is not kind or curious then someone is both curious and not brave.
Everyone who is either patient or happy is either not tall or old and vice versa.
If paul is not kind then alice is creative.
Everyone who is patient or brave is either not rich or not tall and vice versa.
If someone is patient or not humble then alice is both not strong and not wise and vice versa.
Everyone who is both not wise and wise is rich or not patient.
Someone is not tall.
Susan is both strong and creative.
Someone is happy.
Mary is not calm or not humble.
Lucy is both calm and not strong.
Someone is patient or strong.
Someone is creative or patient.
Someone is either not wise or kind. | Lucy is not curious. | entailment | (![X]:((generous(X)|~old(X))=>(quiet(X)&calm(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((tall(X)|calm(X))<=>(patient(X)<~>~tall(X))))&
((?[X]:((~calm(X)<~>happy(X))))=>(generous(paul)))&
(![X]:((wise(X)|rich(X))<=>(strong(X)&calm(X))))&
(![X]:((~curious(X)<~>~strong(X))<=>(patient(X)<~>calm(X))))&
((~funny(alice))<=>(kind(lucy)))&
(![X]:((humble(X)<~>~happy(X))<=>(~brave(X)&~creative(X))))&
(((funny(mary)<~>wise(mary)))=>(kind(fred)))&
(![X]:((brave(X)<~>~strong(X))<=>(rich(X)&old(X))))&
((?[X]:((~kind(X)|curious(X))))=>(?[X]:((curious(X)&~brave(X)))))&
(![X]:((patient(X)<~>happy(X))<=>(~tall(X)<~>old(X))))&
((~kind(paul))=>(creative(alice)))&
(![X]:((patient(X)|brave(X))<=>(~rich(X)<~>~tall(X))))&
((?[X]:((patient(X)|~humble(X))))<=>((~strong(alice)&~wise(alice))))&
(![X]:((~wise(X)&wise(X))=>(rich(X)|~patient(X))))&
(?[X]:(~tall(X)))&
((strong(susan)&creative(susan)))&
(?[X]:(happy(X)))&
((~calm(mary)|~humble(mary)))&
((calm(lucy)&~strong(lucy)))&
(?[X]:((patient(X)|strong(X))))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((~wise(X)<~>kind(X)))) | ~curious(lucy) | [
"p2",
"p4",
"p5",
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5210471334114240267124782
% SZS output start Proof for 5210471334114240267124782
3. ! [X0] : ((calm(X0) | tall(X0)) <=> (patient(X0) <~> ~tall(X0))) [input p2]
5. ! [X0] : ((rich(X0) | wise(X0)) <=> (calm(X0) & strong(X0))) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~strong(X0)) <=> (patient(X0) <~> calm(X0))) [input p5]
10. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (old(X0) & rich(X0))) [input p9]
14. ! [X0] : ((brave(X0) | patient(X0)) <=> (~rich(X0) <~> ~tall(X0))) [input p13]
21. ~strong(lucy) & calm(lucy) [input p20]
25. curious(lucy) [input hypothesis]
41. ! [X0] : (((calm(X0) | tall(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~calm(X0) & ~tall(X0)))) [nnf transformation 3]
42. ! [X0] : ((calm(X0) | tall(X0) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~calm(X0) & ~tall(X0)))) [flattening 41]
44. ! [X0] : (((rich(X0) | wise(X0)) | (~calm(X0) | ~strong(X0))) & ((calm(X0) & strong(X0)) | (~rich(X0) & ~wise(X0)))) [nnf transformation 5]
45. ! [X0] : ((rich(X0) | wise(X0) | ~calm(X0) | ~strong(X0)) & ((calm(X0) & strong(X0)) | (~rich(X0) & ~wise(X0)))) [flattening 44]
46. ! [X0] : ((((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) & (((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | ((~curious(X0) | strong(X0)) & (~strong(X0) | curious(X0))))) [nnf transformation 6]
51. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 10]
52. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 51]
57. ! [X0] : (((brave(X0) | patient(X0)) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~brave(X0) & ~patient(X0)))) [nnf transformation 14]
58. ! [X0] : ((brave(X0) | patient(X0) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~brave(X0) & ~patient(X0)))) [flattening 57]
81. ~tall(X0) | patient(X0) | ~calm(X0) [cnf transformation 42]
89. ~rich(X0) | strong(X0) [cnf transformation 45]
96. ~curious(X0) | ~patient(X0) | ~calm(X0) | strong(X0) [cnf transformation 46]
112. rich(X0) | brave(X0) | strong(X0) [cnf transformation 52]
133. ~brave(X0) | rich(X0) | tall(X0) [cnf transformation 58]
147. calm(lucy) [cnf transformation 21]
148. ~strong(lucy) [cnf transformation 21]
153. curious(lucy) [cnf transformation 25]
214. brave(X0) | strong(X0) [subsumption resolution 112,89]
395. rich(X1) | tall(X1) | strong(X1) [resolution 133,214]
397. strong(X1) | tall(X1) [subsumption resolution 395,89]
398. tall(lucy) [resolution 397,148]
455. patient(lucy) | ~calm(lucy) [resolution 398,81]
466. patient(lucy) [subsumption resolution 455,147]
545. ~patient(lucy) | ~calm(lucy) | strong(lucy) [resolution 96,153]
589. ~calm(lucy) | strong(lucy) [subsumption resolution 545,466]
590. strong(lucy) [subsumption resolution 589,147]
591. $false [subsumption resolution 590,148]
% SZS output end Proof for 5210471334114240267124782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not rich then susan is generous and vice versa.
Everyone who is generous is funny.
Everyone who is wise is both not kind and brave.
Everyone who is both wise and funny is both strong and wise and vice versa.
Everyone who is not rich is either not curious or quiet.
If someone is calm then alice is both not calm and not quiet.
Everyone who is not happy is not rich and vice versa.
If mary is either strong or old then someone is not happy.
If someone is funny then john is not brave or quiet and vice versa.
Everyone who is not brave or not patient is not patient or calm and vice versa.
If paul is not creative or not wise then john is rich and vice versa.
Everyone who is not old or wise is kind and vice versa.
Everyone who is not calm or curious is not funny.
Everyone who is either not humble or funny is happy and vice versa.
Everyone who is quiet or not brave is not humble or patient.
Everyone who is not quiet or not brave is either brave or humble and vice versa.
Someone is not quiet.
Mary is both generous and kind.
Lucy is either not creative or humble.
Paul is generous.
Someone is old or not tall.
Someone is both not rich and brave. | Alice is not creative. | neutral | ((?[X]:((~brave(X)|~rich(X))))<=>(generous(susan)))&
(![X]:(generous(X)=>funny(X)))&
(![X]:(wise(X)=>(~kind(X)&brave(X))))&
(![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(?[X]:(~quiet(X)))&
((generous(mary)&kind(mary)))&
((~creative(lucy)<~>humble(lucy)))&
(generous(paul))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:((~rich(X)&brave(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is quiet is quiet or kind and vice versa.
If someone is quiet or old then someone is either happy or not funny and vice versa.
Everyone who is not curious or wise is both not quiet and not tall and vice versa.
Everyone who is not old is both not old and strong and vice versa.
If lucy is quiet or not humble then alice is either quiet or not strong and vice versa.
If susan is creative then paul is not tall or not kind.
Everyone who is not happy is either not creative or wise and vice versa.
If john is both funny and brave then fred is creative and vice versa.
If someone is either brave or not rich then someone is brave or not happy.
If someone is both not quiet and old then someone is either funny or not humble and vice versa.
If someone is brave then someone is not rich or not old and vice versa.
Everyone who is either tall or not curious is curious or calm.
If someone is not patient or not brave then fred is either funny or rich and vice versa.
If susan is either not kind or generous then someone is not strong.
Everyone who is both not humble and creative is not rich or kind.
If someone is not brave or not funny then susan is either happy or brave.
Someone is either not quiet or wise.
Susan is both not quiet and not patient.
Mary is both not wise and old.
John is either not curious or wise.
Someone is either not generous or not creative.
Someone is either not brave or brave.
Someone is either not patient or funny.
Someone is generous. | Susan is not kind. | entailment | (![X]:(quiet(X)<=>(quiet(X)|kind(X))))&
((?[X]:((quiet(X)|old(X))))<=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:((~curious(X)|wise(X))<=>(~quiet(X)&~tall(X))))&
(![X]:(~old(X)<=>(~old(X)&strong(X))))&
(((quiet(lucy)|~humble(lucy)))<=>((quiet(alice)<~>~strong(alice))))&
((creative(susan))=>((~tall(paul)|~kind(paul))))&
(![X]:(~happy(X)<=>(~creative(X)<~>wise(X))))&
(((funny(john)&brave(john)))<=>(creative(fred)))&
((?[X]:((brave(X)<~>~rich(X))))=>(?[X]:((brave(X)|~happy(X)))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:((funny(X)<~>~humble(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((~rich(X)|~old(X)))))&
(![X]:((tall(X)<~>~curious(X))=>(curious(X)|calm(X))))&
((?[X]:((~patient(X)|~brave(X))))<=>((funny(fred)<~>rich(fred))))&
(((~kind(susan)<~>generous(susan)))=>(?[X]:(~strong(X))))&
(![X]:((~humble(X)&creative(X))=>(~rich(X)|kind(X))))&
((?[X]:((~brave(X)|~funny(X))))=>((happy(susan)<~>brave(susan))))&
(?[X]:((~quiet(X)<~>wise(X))))&
((~quiet(susan)&~patient(susan)))&
((~wise(mary)&old(mary)))&
((~curious(john)<~>wise(john)))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:(generous(X))) | ~kind(susan) | [
"p0",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2170993086919501295695253
% SZS output start Proof for 2170993086919501295695253
1. ! [X0] : (quiet(X0) <=> (kind(X0) | quiet(X0))) [input p0]
18. ~patient(susan) & ~quiet(susan) [input p17]
25. kind(susan) [input hypothesis]
38. ! [X0] : ((quiet(X0) | (~kind(X0) & ~quiet(X0))) & ((kind(X0) | quiet(X0)) | ~quiet(X0))) [nnf transformation 1]
39. ! [X0] : ((quiet(X0) | (~kind(X0) & ~quiet(X0))) & (kind(X0) | quiet(X0) | ~quiet(X0))) [flattening 38]
93. ~kind(X0) | quiet(X0) [cnf transformation 39]
148. ~quiet(susan) [cnf transformation 18]
161. kind(susan) [cnf transformation 25]
350. 43 <=> kind(susan) [avatar definition]
351. kind(susan) <- (43) [avatar component clause 350]
406. 43 [avatar split clause 161,350]
423. quiet(susan) <- (43) [resolution 93,351]
424. $false <- (43) [subsumption resolution 423,148]
425. ~43 [avatar contradiction clause 424]
426. $false [avatar sat refutation 406,425]
% SZS output end Proof for 2170993086919501295695253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not kind is not creative and vice versa.
Everyone who is both humble and not calm is both happy and not brave.
Everyone who is both not creative and generous is both old and not creative and vice versa.
If someone is not kind then paul is either quiet or curious.
Everyone who is not strong or calm is both humble and not wise and vice versa.
If alice is not rich or strong then someone is not happy or patient and vice versa.
Everyone who is both not generous and old is either generous or strong and vice versa.
Everyone who is not wise is both kind and not kind.
Everyone who is happy or not curious is humble.
Everyone who is either not happy or brave is both not strong and not rich.
Everyone who is not calm or not quiet is either funny or wise.
Everyone who is not strong is either rich or strong and vice versa.
Everyone who is either rich or strong is either creative or not brave and vice versa.
If alice is either wise or tall then paul is not curious.
If someone is both not creative and not wise then susan is patient.
If someone is calm then someone is curious or not old.
Alice is patient.
John is either not patient or not kind.
Paul is both tall and not quiet.
Alice is either not kind or humble.
John is happy or humble.
Someone is either not patient or generous.
Lucy is not funny. | Alice is happy. | entailment | (![X]:((humble(X)&~kind(X))<=>~creative(X)))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&~brave(X))))&
(![X]:((~creative(X)&generous(X))<=>(old(X)&~creative(X))))&
((?[X]:(~kind(X)))=>((quiet(paul)<~>curious(paul))))&
(![X]:((~strong(X)|calm(X))<=>(humble(X)&~wise(X))))&
(((~rich(alice)|strong(alice)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>strong(X))))&
(![X]:(~wise(X)=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|~curious(X))=>humble(X)))&
(![X]:((~happy(X)<~>brave(X))=>(~strong(X)&~rich(X))))&
(![X]:((~calm(X)|~quiet(X))=>(funny(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>strong(X))))&
(![X]:((rich(X)<~>strong(X))<=>(creative(X)<~>~brave(X))))&
(((wise(alice)<~>tall(alice)))=>(~curious(paul)))&
((?[X]:((~creative(X)&~wise(X))))=>(patient(susan)))&
((?[X]:(calm(X)))=>(?[X]:((curious(X)|~old(X)))))&
(patient(alice))&
((~patient(john)<~>~kind(john)))&
((tall(paul)&~quiet(paul)))&
((~kind(alice)<~>humble(alice)))&
((happy(john)|humble(john)))&
(?[X]:((~patient(X)<~>generous(X))))&
(~funny(lucy)) | happy(alice) | [
"p0",
"p1",
"p4",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4853406307503854072193016
% SZS output start Proof for 4853406307503854072193016
1. ! [X0] : ((~kind(X0) & humble(X0)) <=> ~creative(X0)) [input p0]
2. ! [X0] : ((~calm(X0) & humble(X0)) => (~brave(X0) & happy(X0))) [input p1]
5. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (~wise(X0) & humble(X0))) [input p4]
8. ! [X0] : (~wise(X0) => (~kind(X0) & kind(X0))) [input p7]
10. ! [X0] : ((~happy(X0) <~> brave(X0)) => (~rich(X0) & ~strong(X0))) [input p9]
12. ! [X0] : (~strong(X0) <=> (rich(X0) <~> strong(X0))) [input p11]
13. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (creative(X0) <~> ~brave(X0))) [input p12]
24. ~happy(alice) [input hypothesis]
26. ! [X0] : ((~brave(X0) & happy(X0)) | (calm(X0) | ~humble(X0))) [ennf transformation 2]
27. ! [X0] : ((~brave(X0) & happy(X0)) | calm(X0) | ~humble(X0)) [flattening 26]
29. ! [X0] : ((~kind(X0) & kind(X0)) | wise(X0)) [ennf transformation 8]
31. ! [X0] : ((~rich(X0) & ~strong(X0)) | (~happy(X0) <=> brave(X0))) [ennf transformation 10]
36. ! [X0] : (((~kind(X0) & humble(X0)) | creative(X0)) & (~creative(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 1]
37. ! [X0] : (((~kind(X0) & humble(X0)) | creative(X0)) & (~creative(X0) | kind(X0) | ~humble(X0))) [flattening 36]
41. ! [X0] : (((calm(X0) | ~strong(X0)) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [nnf transformation 5]
42. ! [X0] : ((calm(X0) | ~strong(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [flattening 41]
50. ! [X0] : ((~rich(X0) & ~strong(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) [nnf transformation 31]
52. ! [X0] : ((~strong(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | strong(X0))) [nnf transformation 12]
53. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0)))) & (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 13]
64. creative(X0) | humble(X0) [cnf transformation 37]
67. ~brave(X0) | calm(X0) | ~humble(X0) [cnf transformation 27]
76. ~wise(X0) | strong(X0) [cnf transformation 42]
77. ~wise(X0) | ~calm(X0) [cnf transformation 42]
89. kind(X0) | wise(X0) [cnf transformation 29]
90. ~kind(X0) | wise(X0) [cnf transformation 29]
93. ~strong(X0) | brave(X0) | happy(X0) [cnf transformation 50]
101. strong(X0) | rich(X0) | strong(X0) [cnf transformation 52]
104. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 52]
111. ~strong(X0) | ~rich(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 53]
128. ~happy(alice) [cnf transformation 24]
129. strong(X0) | rich(X0) [duplicate literal removal 101]
130. ~strong(X0) | rich(X0) [duplicate literal removal 104]
154. 6 <=> strong(alice) [avatar definition]
155. ~strong(alice) <- (~6) [avatar component clause 154]
156. strong(alice) <- (6) [avatar component clause 154]
173. wise(X0) [subsumption resolution 89,90]
176. rich(X0) [subsumption resolution 129,130]
178. ~strong(X0) | ~brave(X0) | ~creative(X0) [subsumption resolution 111,176]
188. 11 <=> ! [X1] : ~calm(X1) [avatar definition]
189. ~calm(X1) <- (11) [avatar component clause 188]
215. 17 <=> humble(alice) [avatar definition]
233. strong(X0) [resolution 76,173]
234. ~calm(X0) [resolution 77,173]
235. 11 [avatar split clause 234,188]
255. brave(alice) | happy(alice) <- (6) [resolution 93,156]
258. brave(alice) <- (6) [subsumption resolution 255,128]
262. 22 <=> creative(alice) [avatar definition]
263. ~creative(alice) <- (~22) [avatar component clause 262]
273. calm(alice) | ~humble(alice) <- (6) [resolution 258,67]
286. ~brave(alice) | ~creative(alice) <- (6) [resolution 178,156]
289. ~creative(alice) <- (6) [subsumption resolution 286,258]
290. ~22 | ~6 [avatar split clause 289,154,262]
291. humble(alice) <- (~22) [resolution 263,64]
294. 17 | 22 [avatar split clause 291,262,215]
295. ~humble(alice) <- (6, 11) [subsumption resolution 273,189]
296. ~17 | ~6 | ~11 [avatar split clause 295,188,154,215]
297. $false <- (~6) [subsumption resolution 155,233]
298. 6 [avatar contradiction clause 297]
299. $false [avatar sat refutation 235,290,294,296,298]
% SZS output end Proof for 4853406307503854072193016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not funny is creative or not humble and vice versa.
Everyone who is not calm or strong is calm or not calm.
If someone is both not quiet and not rich then someone is not brave or not creative.
If lucy is wise or not brave then someone is either rich or tall.
Everyone who is either quiet or not kind is both not wise and funny.
Everyone who is generous is either not quiet or generous and vice versa.
If someone is either not kind or creative then someone is both not strong and strong and vice versa.
Everyone who is both patient and not rich is either not calm or not brave and vice versa.
If lucy is strong then someone is either strong or patient.
Everyone who is both not happy and wise is both creative and not patient and vice versa.
Everyone who is humble or not strong is both old and not brave and vice versa.
If mary is not funny then someone is either wise or not patient.
If lucy is both not brave and rich then someone is both quiet and not quiet and vice versa.
If someone is both not funny and old then susan is happy.
If someone is either wise or not strong then someone is not kind and vice versa.
If someone is either not rich or kind then john is creative and vice versa.
Someone is either strong or not brave.
Someone is both happy and curious.
Someone is both not funny and not curious.
Mary is either not old or old.
Someone is either not patient or not curious.
Someone is both curious and generous.
Someone is both brave and not funny.
Mary is either not brave or not curious. | John is not kind. | entailment | (![X]:((humble(X)<~>~funny(X))<=>(creative(X)|~humble(X))))&
(![X]:((~calm(X)|strong(X))=>(calm(X)|~calm(X))))&
((?[X]:((~quiet(X)&~rich(X))))=>(?[X]:((~brave(X)|~creative(X)))))&
(((wise(lucy)|~brave(lucy)))=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:((quiet(X)<~>~kind(X))=>(~wise(X)&funny(X))))&
(![X]:(generous(X)<=>(~quiet(X)<~>generous(X))))&
((?[X]:((~kind(X)<~>creative(X))))<=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:((patient(X)&~rich(X))<=>(~calm(X)<~>~brave(X))))&
((strong(lucy))=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((~happy(X)&wise(X))<=>(creative(X)&~patient(X))))&
(![X]:((humble(X)|~strong(X))<=>(old(X)&~brave(X))))&
((~funny(mary))=>(?[X]:((wise(X)<~>~patient(X)))))&
(((~brave(lucy)&rich(lucy)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
((?[X]:((~funny(X)&old(X))))=>(happy(susan)))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((~rich(X)<~>kind(X))))<=>(creative(john)))&
(?[X]:((strong(X)<~>~brave(X))))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((~funny(X)&~curious(X))))&
((~old(mary)<~>old(mary)))&
(?[X]:((~patient(X)<~>~curious(X))))&
(?[X]:((curious(X)&generous(X))))&
(?[X]:((brave(X)&~funny(X))))&
((~brave(mary)<~>~curious(mary))) | ~kind(john) | [
"p0",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6338245871116180069644109
% SZS output start Proof for 6338245871116180069644109
1. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~humble(X0) | creative(X0))) [input p0]
5. ! [X0] : ((quiet(X0) <~> ~kind(X0)) => (funny(X0) & ~wise(X0))) [input p4]
6. ! [X0] : (generous(X0) <=> (~quiet(X0) <~> generous(X0))) [input p5]
7. ? [X0] : (~kind(X0) <~> creative(X0)) <=> ? [X0] : (strong(X0) & ~strong(X0)) [input p6]
25. kind(john) [input hypothesis]
27. ? [X0] : (~kind(X0) <~> creative(X0)) <=> ? [X1] : (strong(X1) & ~strong(X1)) [rectify 7]
33. ! [X0] : ((funny(X0) & ~wise(X0)) | (quiet(X0) <=> ~kind(X0))) [ennf transformation 5]
37. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (humble(X0) & ~creative(X0))) & ((~humble(X0) | creative(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 1]
38. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (humble(X0) & ~creative(X0))) & (~humble(X0) | creative(X0) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [flattening 37]
45. ! [X0] : ((funny(X0) & ~wise(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) [nnf transformation 33]
46. ! [X0] : ((generous(X0) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0)))) & (((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | ~generous(X0))) [nnf transformation 6]
47. (? [X0] : ((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ! [X1] : (~strong(X1) | strong(X1))) & (? [X1] : (strong(X1) & ~strong(X1)) | ! [X0] : ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) [nnf transformation 27]
48. (? [X0] : ((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ! [X1] : (~strong(X1) | strong(X1))) & (? [X2] : (strong(X2) & ~strong(X2)) | ! [X3] : ((~kind(X3) | ~creative(X3)) & (creative(X3) | kind(X3)))) [rectify 47]
49. ? [X0] : ((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) => ((~creative(sK2) | kind(sK2)) & (creative(sK2) | ~kind(sK2))) [choice axiom]
50. ? [X2] : (strong(X2) & ~strong(X2)) => (strong(sK3) & ~strong(sK3)) [choice axiom]
51. (((~creative(sK2) | kind(sK2)) & (creative(sK2) | ~kind(sK2))) | ! [X1] : (~strong(X1) | strong(X1))) & ((strong(sK3) & ~strong(sK3)) | ! [X3] : ((~kind(X3) | ~creative(X3)) & (creative(X3) | kind(X3)))) [skolemisation 48,50,49]
94. ~humble(X0) | creative(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 38]
97. ~funny(X0) | humble(X0) | humble(X0) [cnf transformation 38]
109. ~kind(X0) | funny(X0) | ~quiet(X0) [cnf transformation 45]
112. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 46]
113. generous(X0) | generous(X0) | quiet(X0) [cnf transformation 46]
115. ~strong(sK3) | creative(X3) | kind(X3) [cnf transformation 51]
116. ~strong(sK3) | ~kind(X3) | ~creative(X3) [cnf transformation 51]
117. strong(sK3) | creative(X3) | kind(X3) [cnf transformation 51]
118. strong(sK3) | ~kind(X3) | ~creative(X3) [cnf transformation 51]
169. kind(john) [cnf transformation 25]
170. ~generous(X0) | quiet(X0) [duplicate literal removal 112]
171. generous(X0) | quiet(X0) [duplicate literal removal 113]
173. ~humble(X0) | creative(X0) | ~funny(X0) [duplicate literal removal 94]
174. ~funny(X0) | humble(X0) [duplicate literal removal 97]
175. ~funny(X0) | creative(X0) [subsumption resolution 173,174]
208. quiet(X0) [subsumption resolution 170,171]
210. 8 <=> ! [X3] : (~kind(X3) | ~creative(X3)) [avatar definition]
211. ~kind(X3) | ~creative(X3) <- (8) [avatar component clause 210]
213. 9 <=> strong(sK3) [avatar definition]
216. 8 | 9 [avatar split clause 118,213,210]
218. 10 <=> ! [X3] : (creative(X3) | kind(X3)) [avatar definition]
219. kind(X3) | creative(X3) <- (10) [avatar component clause 218]
220. 10 | 9 [avatar split clause 117,213,218]
221. 8 | ~9 [avatar split clause 116,213,210]
222. 10 | ~9 [avatar split clause 115,213,218]
291. 26 <=> creative(john) [avatar definition]
293. ~creative(john) <- (~26) [avatar component clause 291]
345. ~creative(john) <- (8) [resolution 211,169]
348. ~26 | ~8 [avatar split clause 345,210,291]
390. funny(X1) | ~quiet(X1) | creative(X1) <- (10) [resolution 109,219]
393. funny(X1) | creative(X1) <- (10) [subsumption resolution 390,208]
394. creative(X1) <- (10) [subsumption resolution 393,175]
404. $false <- (10, ~26) [resolution 394,293]
406. ~10 | 26 [avatar contradiction clause 404]
407. $false [avatar sat refutation 216,220,221,222,348,406]
% SZS output end Proof for 6338245871116180069644109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both humble and brave. If someone is both not strong and old then susan is not creative. Everyone who is not strong or quiet is either curious or old. Everyone who is both old and generous is not kind or not rich and vice versa. If alice is tall then someone is either not generous or not rich and vice versa. If fred is both funny and not quiet then lucy is either not generous or not wise. Everyone who is not quiet or old is either not calm or not creative and vice versa. Everyone who is both not old and curious is not wise or not brave and vice versa. Everyone who is wise or patient is both not generous and patient and vice versa. If someone is both not happy and not old then fred is strong or not curious. Everyone who is tall or not generous is brave. Everyone who is both not brave and kind is quiet or humble. If someone is not curious or curious then someone is not rich or not curious. Everyone who is both generous and patient is not humble and vice versa. If someone is both quiet and not old then someone is not happy or not kind. Everyone who is not funny or not patient is both not rich and kind and vice versa. Someone is either not wise or not generous. Someone is either not creative or not curious. Someone is either not quiet or calm. Someone is either quiet or not rich. | Lucy is not happy. | neutral | (![X]:(creative(X)=>(humble(X)&brave(X))))&
((?[X]:((~strong(X)&old(X))))=>(~creative(susan)))&
(![X]:((~strong(X)|quiet(X))=>(curious(X)<~>old(X))))&
(![X]:((old(X)&generous(X))<=>(~kind(X)|~rich(X))))&
((tall(alice))<=>(?[X]:((~generous(X)<~>~rich(X)))))&
(((funny(fred)&~quiet(fred)))=>((~generous(lucy)<~>~wise(lucy))))&
(![X]:((~quiet(X)|old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~old(X)&curious(X))<=>(~wise(X)|~brave(X))))&
(![X]:((wise(X)|patient(X))<=>(~generous(X)&patient(X))))&
((?[X]:((~happy(X)&~old(X))))=>((strong(fred)|~curious(fred))))&
(![X]:((tall(X)|~generous(X))=>brave(X)))&
(![X]:((~brave(X)&kind(X))=>(quiet(X)|humble(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((generous(X)&patient(X))<=>~humble(X)))&
((?[X]:((quiet(X)&~old(X))))=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((~funny(X)|~patient(X))<=>(~rich(X)&kind(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
(?[X]:((quiet(X)<~>~rich(X)))) | ~happy(lucy) | [] | null | 0 |
If someone is not funny or quiet then someone is both not rich and not brave and vice versa.
If someone is patient then john is either patient or not curious and vice versa.
Everyone who is both not generous and not funny is strong or not rich.
Everyone who is not kind is not humble.
Everyone who is either tall or not wise is funny and vice versa.
Everyone who is not tall or brave is either not kind or old and vice versa.
Everyone who is not patient is not humble or old and vice versa.
If someone is either not wise or not generous then lucy is both quiet and not humble and vice versa.
If lucy is patient then someone is creative or happy.
If alice is either not wise or generous then someone is both kind and patient.
Everyone who is either not quiet or brave is both generous and not patient and vice versa.
If lucy is either not funny or quiet then someone is not calm and vice versa.
Everyone who is not old is wise or old.
If paul is not creative or strong then someone is either not wise or kind and vice versa.
Everyone who is either not humble or not brave is both not old and not humble and vice versa.
If someone is both not funny and not happy then mary is not strong or not curious.
Someone is both rich and not strong.
Susan is not humble or not generous.
Someone is both not tall and not calm.
Someone is not brave.
Someone is both not kind and happy.
Mary is both not wise and not generous.
Someone is not wise or wise.
Mary is both not funny and not quiet. | Mary is not strong. | neutral | ((?[X]:((~funny(X)|quiet(X))))<=>(?[X]:((~rich(X)&~brave(X)))))&
((?[X]:(patient(X)))<=>((patient(john)<~>~curious(john))))&
(![X]:((~generous(X)&~funny(X))=>(strong(X)|~rich(X))))&
(![X]:(~kind(X)=>~humble(X)))&
(![X]:((tall(X)<~>~wise(X))<=>funny(X)))&
(![X]:((~tall(X)|brave(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~patient(X)<=>(~humble(X)|old(X))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>((quiet(lucy)&~humble(lucy))))&
((patient(lucy))=>(?[X]:((creative(X)|happy(X)))))&
(((~wise(alice)<~>generous(alice)))=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((~quiet(X)<~>brave(X))<=>(generous(X)&~patient(X))))&
(((~funny(lucy)<~>quiet(lucy)))<=>(?[X]:(~calm(X))))&
(![X]:(~old(X)=>(wise(X)|old(X))))&
(((~creative(paul)|strong(paul)))<=>(?[X]:((~wise(X)<~>kind(X)))))&
(![X]:((~humble(X)<~>~brave(X))<=>(~old(X)&~humble(X))))&
((?[X]:((~funny(X)&~happy(X))))=>((~strong(mary)|~curious(mary))))&
(?[X]:((rich(X)&~strong(X))))&
((~humble(susan)|~generous(susan)))&
(?[X]:((~tall(X)&~calm(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)&happy(X))))&
((~wise(mary)&~generous(mary)))&
(?[X]:((~wise(X)|wise(X))))&
((~funny(mary)&~quiet(mary))) | ~strong(mary) | [] | null | 0 |
Everyone who is quiet or generous is both tall and creative.
Everyone who is not old or not curious is not quiet.
If someone is not brave then alice is patient and vice versa.
Everyone who is either not tall or quiet is not kind or kind and vice versa.
Everyone who is not curious is not happy or quiet.
If someone is not tall then alice is rich and vice versa.
If someone is both wise and creative then someone is not brave or not curious and vice versa.
If someone is not creative then lucy is either funny or generous.
Everyone who is either not happy or old is both not rich and creative.
Everyone who is not happy or not strong is both calm and not curious.
Everyone who is both funny and patient is not brave.
Everyone who is not rich is not strong or not rich and vice versa.
Everyone who is both funny and calm is not brave and vice versa.
If someone is brave or kind then someone is not calm or not kind and vice versa.
If lucy is either patient or rich then mary is either not rich or not brave.
Everyone who is both wise and not calm is not generous or rich and vice versa.
Alice is humble.
Lucy is either not kind or happy.
Fred is either happy or not patient.
Lucy is not patient.
John is either humble or not kind.
Someone is not patient or tall.
Someone is both not calm and wise. | Lucy is strong. | entailment | (![X]:((quiet(X)|generous(X))=>(tall(X)&creative(X))))&
(![X]:((~old(X)|~curious(X))=>~quiet(X)))&
((?[X]:(~brave(X)))<=>(patient(alice)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|kind(X))))&
(![X]:(~curious(X)=>(~happy(X)|quiet(X))))&
((?[X]:(~tall(X)))<=>(rich(alice)))&
((?[X]:((wise(X)&creative(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:(~creative(X)))=>((funny(lucy)<~>generous(lucy))))&
(![X]:((~happy(X)<~>old(X))=>(~rich(X)&creative(X))))&
(![X]:((~happy(X)|~strong(X))=>(calm(X)&~curious(X))))&
(![X]:((funny(X)&patient(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~strong(X)|~rich(X))))&
(![X]:((funny(X)&calm(X))<=>~brave(X)))&
((?[X]:((brave(X)|kind(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(((patient(lucy)<~>rich(lucy)))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((wise(X)&~calm(X))<=>(~generous(X)|rich(X))))&
(humble(alice))&
((~kind(lucy)<~>happy(lucy)))&
((happy(fred)<~>~patient(fred)))&
(~patient(lucy))&
((humble(john)<~>~kind(john)))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((~calm(X)&wise(X)))) | strong(lucy) | [
"p0",
"p1",
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3666446823455500244173048
% SZS output start Proof for 3666446823455500244173048
1. ! [X0] : ((generous(X0) | quiet(X0)) => (creative(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | ~old(X0)) => ~quiet(X0)) [input p1]
4. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (kind(X0) | ~kind(X0))) [input p3]
10. ! [X0] : ((~strong(X0) | ~happy(X0)) => (~curious(X0) & calm(X0))) [input p9]
16. ! [X0] : ((~calm(X0) & wise(X0)) <=> (rich(X0) | ~generous(X0))) [input p15]
24. ~strong(lucy) [input hypothesis]
27. ! [X0] : ((creative(X0) & tall(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : (~quiet(X0) | (curious(X0) & old(X0))) [ennf transformation 2]
33. ! [X0] : ((~curious(X0) & calm(X0)) | (strong(X0) & happy(X0))) [ennf transformation 10]
41. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 41]
64. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & ((rich(X0) | ~generous(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 16]
65. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & (rich(X0) | ~generous(X0) | calm(X0) | ~wise(X0))) [flattening 64]
74. ~generous(X0) | tall(X0) [cnf transformation 27]
78. ~quiet(X0) | curious(X0) [cnf transformation 28]
83. quiet(X0) | ~tall(X0) | kind(X0) [cnf transformation 42]
84. ~kind(X0) | ~tall(X0) | quiet(X0) [cnf transformation 42]
102. calm(X0) | strong(X0) [cnf transformation 33]
104. ~curious(X0) | strong(X0) [cnf transformation 33]
123. ~calm(X0) | generous(X0) [cnf transformation 65]
136. ~strong(lucy) [cnf transformation 24]
150. ~tall(X0) | quiet(X0) [subsumption resolution 83,84]
200. 15 <=> generous(lucy) [avatar definition]
201. generous(lucy) <- (15) [avatar component clause 200]
310. strong(X1) | generous(X1) [resolution 123,102]
384. generous(lucy) [resolution 310,136]
385. 15 [avatar split clause 384,200]
387. tall(lucy) <- (15) [resolution 201,74]
388. quiet(lucy) <- (15) [resolution 387,150]
389. curious(lucy) <- (15) [resolution 388,78]
401. strong(lucy) <- (15) [resolution 389,104]
403. $false <- (15) [subsumption resolution 401,136]
404. ~15 [avatar contradiction clause 403]
407. $false [avatar sat refutation 385,404]
% SZS output end Proof for 3666446823455500244173048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not creative or not kind then someone is both happy and not wise.
Everyone who is not patient or not creative is both calm and strong and vice versa.
If someone is brave then lucy is both not tall and not calm and vice versa.
If someone is strong or patient then paul is creative or not patient and vice versa.
If someone is either not calm or creative then alice is either brave or humble and vice versa.
If someone is either generous or not wise then someone is either generous or funny.
If paul is either calm or not old then john is calm and vice versa.
Everyone who is brave is wise or happy.
Everyone who is not quiet is either rich or not humble.
Everyone who is old is not wise or not tall and vice versa.
Everyone who is strong or quiet is tall and vice versa.
Everyone who is either old or not funny is both not humble and not patient and vice versa.
If someone is not calm then someone is both old and strong and vice versa.
Everyone who is both brave and wise is not generous.
Everyone who is either not kind or kind is not quiet or humble and vice versa.
Everyone who is not rich or brave is not patient.
Paul is not happy.
Someone is creative or patient.
Fred is happy.
Someone is either strong or not old.
John is kind.
Lucy is generous.
Alice is strong or funny.
Lucy is not happy or strong. | Fred is not rich. | neutral | ((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(calm(X)&strong(X))))&
((?[X]:(brave(X)))<=>((~tall(lucy)&~calm(lucy))))&
((?[X]:((strong(X)|patient(X))))<=>((creative(paul)|~patient(paul))))&
((?[X]:((~calm(X)<~>creative(X))))<=>((brave(alice)<~>humble(alice))))&
((?[X]:((generous(X)<~>~wise(X))))=>(?[X]:((generous(X)<~>funny(X)))))&
(((calm(paul)<~>~old(paul)))<=>(calm(john)))&
(![X]:(brave(X)=>(wise(X)|happy(X))))&
(![X]:(~quiet(X)=>(rich(X)<~>~humble(X))))&
(![X]:(old(X)<=>(~wise(X)|~tall(X))))&
(![X]:((strong(X)|quiet(X))<=>tall(X)))&
(![X]:((old(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((old(X)&strong(X)))))&
(![X]:((brave(X)&wise(X))=>~generous(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(~quiet(X)|humble(X))))&
(![X]:((~rich(X)|brave(X))=>~patient(X)))&
(~happy(paul))&
(?[X]:((creative(X)|patient(X))))&
(happy(fred))&
(?[X]:((strong(X)<~>~old(X))))&
(kind(john))&
(generous(lucy))&
((strong(alice)|funny(alice)))&
((~happy(lucy)|strong(lucy))) | ~rich(fred) | [] | null | 0 |
If alice is not humble then paul is not curious and vice versa.
Everyone who is both old and not old is not brave and vice versa.
If someone is both not kind and funny then susan is both kind and tall and vice versa.
If someone is not quiet or not brave then fred is patient.
If alice is patient or not tall then someone is both not curious and not rich and vice versa.
Everyone who is both not curious and creative is not calm or not rich and vice versa.
If someone is either humble or not rich then susan is not patient and vice versa.
If someone is not quiet or generous then alice is not happy or wise.
Everyone who is humble is calm.
Everyone who is patient is both strong and old.
If someone is both quiet and not quiet then someone is both wise and not curious and vice versa.
If susan is either strong or patient then john is calm.
If someone is both tall and not happy then alice is either not brave or not curious.
If someone is strong then someone is not funny.
Everyone who is not happy is both not creative and patient and vice versa.
Everyone who is both creative and not funny is both patient and not calm and vice versa.
Someone is not strong or not creative.
Someone is either kind or not strong.
John is not wise.
Fred is either happy or strong.
Someone is both not tall and not quiet.
Mary is creative or not creative.
Lucy is strong or creative.
Fred is either not kind or calm. | John is not brave. | contradiction | ((~humble(alice))<=>(~curious(paul)))&
(![X]:((old(X)&~old(X))<=>~brave(X)))&
((?[X]:((~kind(X)&funny(X))))<=>((kind(susan)&tall(susan))))&
((?[X]:((~quiet(X)|~brave(X))))=>(patient(fred)))&
(((patient(alice)|~tall(alice)))<=>(?[X]:((~curious(X)&~rich(X)))))&
(![X]:((~curious(X)&creative(X))<=>(~calm(X)|~rich(X))))&
((?[X]:((humble(X)<~>~rich(X))))<=>(~patient(susan)))&
((?[X]:((~quiet(X)|generous(X))))=>((~happy(alice)|wise(alice))))&
(![X]:(humble(X)=>calm(X)))&
(![X]:(patient(X)=>(strong(X)&old(X))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(((strong(susan)<~>patient(susan)))=>(calm(john)))&
((?[X]:((tall(X)&~happy(X))))=>((~brave(alice)<~>~curious(alice))))&
((?[X]:(strong(X)))=>(?[X]:(~funny(X))))&
(![X]:(~happy(X)<=>(~creative(X)&patient(X))))&
(![X]:((creative(X)&~funny(X))<=>(patient(X)&~calm(X))))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((kind(X)<~>~strong(X))))&
(~wise(john))&
((happy(fred)<~>strong(fred)))&
(?[X]:((~tall(X)&~quiet(X))))&
((creative(mary)|~creative(mary)))&
((strong(lucy)|creative(lucy)))&
((~kind(fred)<~>calm(fred))) | ~brave(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 125619861394149874979078
% SZS output start Proof for 125619861394149874979078
2. ! [X0] : ((~old(X0) & old(X0)) <=> ~brave(X0)) [input p1]
25. ~brave(john) [input hypothesis]
38. ! [X0] : (((~old(X0) & old(X0)) | brave(X0)) & (~brave(X0) | (old(X0) | ~old(X0)))) [nnf transformation 2]
39. ! [X0] : (((~old(X0) & old(X0)) | brave(X0)) & (~brave(X0) | old(X0) | ~old(X0))) [flattening 38]
82. old(X0) | brave(X0) [cnf transformation 39]
83. ~old(X0) | brave(X0) [cnf transformation 39]
136. ~brave(john) [cnf transformation 25]
147. brave(X0) [subsumption resolution 82,83]
317. $false [subsumption resolution 136,147]
% SZS output end Proof for 125619861394149874979078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then alice is both not quiet and not happy.
If alice is not curious or tall then someone is not rich.
Everyone who is not brave or not wise is both not generous and patient.
Everyone who is both curious and tall is either tall or rich.
If john is humble then someone is not tall or creative.
Everyone who is kind or tall is not rich.
If someone is either not happy or kind then lucy is both tall and not quiet.
Everyone who is both not old and happy is calm or happy and vice versa.
Everyone who is not patient or not funny is either not rich or not tall.
Everyone who is both not old and not brave is tall or not kind and vice versa.
If fred is either creative or not kind then paul is not old or not patient.
Everyone who is either strong or not old is both not kind and patient and vice versa.
If someone is either not brave or tall then someone is either generous or old and vice versa.
Everyone who is either not patient or not funny is strong.
Everyone who is either rich or not generous is either kind or happy and vice versa.
If john is both patient and brave then someone is either not quiet or not calm and vice versa.
Someone is wise.
Alice is quiet.
John is not happy.
Someone is either not humble or not kind.
Someone is not curious or not funny.
Lucy is both not rich and not funny.
Someone is not tall. | Lucy is not calm. | entailment | ((?[X]:(~quiet(X)))=>((~quiet(alice)&~happy(alice))))&
(((~curious(alice)|tall(alice)))=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)|~wise(X))=>(~generous(X)&patient(X))))&
(![X]:((curious(X)&tall(X))=>(tall(X)<~>rich(X))))&
((humble(john))=>(?[X]:((~tall(X)|creative(X)))))&
(![X]:((kind(X)|tall(X))=>~rich(X)))&
((?[X]:((~happy(X)<~>kind(X))))=>((tall(lucy)&~quiet(lucy))))&
(![X]:((~old(X)&happy(X))<=>(calm(X)|happy(X))))&
(![X]:((~patient(X)|~funny(X))=>(~rich(X)<~>~tall(X))))&
(![X]:((~old(X)&~brave(X))<=>(tall(X)|~kind(X))))&
(((creative(fred)<~>~kind(fred)))=>((~old(paul)|~patient(paul))))&
(![X]:((strong(X)<~>~old(X))<=>(~kind(X)&patient(X))))&
((?[X]:((~brave(X)<~>tall(X))))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((~patient(X)<~>~funny(X))=>strong(X)))&
(![X]:((rich(X)<~>~generous(X))<=>(kind(X)<~>happy(X))))&
(((patient(john)&brave(john)))<=>(?[X]:((~quiet(X)<~>~calm(X)))))&
(?[X]:(wise(X)))&
(quiet(alice))&
(~happy(john))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((~curious(X)|~funny(X))))&
((~rich(lucy)&~funny(lucy)))&
(?[X]:(~tall(X))) | ~calm(lucy) | [
"p0",
"p2",
"p6",
"p7",
"p9",
"p11",
"p13",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7626419917774928148353789
% SZS output start Proof for 7626419917774928148353789
1. ? [X0] : ~quiet(X0) => (~happy(alice) & ~quiet(alice)) [input p0]
3. ! [X0] : ((~wise(X0) | ~brave(X0)) => (patient(X0) & ~generous(X0))) [input p2]
7. ? [X0] : (~happy(X0) <~> kind(X0)) => (~quiet(lucy) & tall(lucy)) [input p6]
8. ! [X0] : ((happy(X0) & ~old(X0)) <=> (happy(X0) | calm(X0))) [input p7]
10. ! [X0] : ((~brave(X0) & ~old(X0)) <=> (~kind(X0) | tall(X0))) [input p9]
12. ! [X0] : ((strong(X0) <~> ~old(X0)) <=> (patient(X0) & ~kind(X0))) [input p11]
14. ! [X0] : ((~patient(X0) <~> ~funny(X0)) => strong(X0)) [input p13]
18. quiet(alice) [input p17]
22. ~funny(lucy) & ~rich(lucy) [input p21]
24. calm(lucy) [input hypothesis]
26. ! [X0] : (~brave(X0) => (patient(X0) & ~generous(X0))) [pure predicate removal 3]
28. (~happy(alice) & ~quiet(alice)) | ! [X0] : quiet(X0) [ennf transformation 1]
30. ! [X0] : ((patient(X0) & ~generous(X0)) | brave(X0)) [ennf transformation 26]
35. (~quiet(lucy) & tall(lucy)) | ! [X0] : (~happy(X0) <=> kind(X0)) [ennf transformation 7]
39. ! [X0] : (strong(X0) | (~patient(X0) <=> ~funny(X0))) [ennf transformation 14]
45. (~quiet(lucy) & tall(lucy)) | ! [X0] : ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))) [nnf transformation 35]
46. ! [X0] : (((happy(X0) & ~old(X0)) | (~happy(X0) & ~calm(X0))) & ((happy(X0) | calm(X0)) | (~happy(X0) | old(X0)))) [nnf transformation 8]
47. ! [X0] : (((happy(X0) & ~old(X0)) | (~happy(X0) & ~calm(X0))) & (happy(X0) | calm(X0) | ~happy(X0) | old(X0))) [flattening 46]
49. ! [X0] : (((~brave(X0) & ~old(X0)) | (kind(X0) & ~tall(X0))) & ((~kind(X0) | tall(X0)) | (brave(X0) | old(X0)))) [nnf transformation 10]
50. ! [X0] : (((~brave(X0) & ~old(X0)) | (kind(X0) & ~tall(X0))) & (~kind(X0) | tall(X0) | brave(X0) | old(X0))) [flattening 49]
52. ! [X0] : ((((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0))))) [nnf transformation 12]
53. ! [X0] : ((((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0))))) [flattening 52]
59. ! [X0] : (strong(X0) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) [nnf transformation 39]
73. ~quiet(alice) | quiet(X0) [cnf transformation 28]
78. patient(X0) | brave(X0) [cnf transformation 30]
87. ~quiet(lucy) | ~happy(X0) | ~kind(X0) [cnf transformation 45]
91. ~calm(X0) | happy(X0) [cnf transformation 47]
99. ~old(X0) | kind(X0) [cnf transformation 50]
101. ~brave(X0) | kind(X0) [cnf transformation 50]
109. old(X0) | ~strong(X0) | ~patient(X0) | kind(X0) [cnf transformation 53]
119. ~patient(X0) | strong(X0) | funny(X0) [cnf transformation 59]
134. quiet(alice) [cnf transformation 18]
140. ~funny(lucy) [cnf transformation 22]
142. calm(lucy) [cnf transformation 24]
145. 1 <=> ! [X0] : quiet(X0) [avatar definition]
146. quiet(X0) <- (1) [avatar component clause 145]
153. 3 <=> quiet(alice) [avatar definition]
156. 1 | ~3 [avatar split clause 73,153,145]
185. 10 <=> ! [X0] : (~happy(X0) | ~kind(X0)) [avatar definition]
186. ~kind(X0) | ~happy(X0) <- (10) [avatar component clause 185]
188. 11 <=> quiet(lucy) [avatar definition]
190. ~quiet(lucy) <- (~11) [avatar component clause 188]
191. 10 | ~11 [avatar split clause 87,188,185]
220. ~strong(X0) | ~patient(X0) | kind(X0) [subsumption resolution 109,99]
289. 3 [avatar split clause 134,153]
310. happy(lucy) [resolution 91,142]
358. strong(X1) | funny(X1) | brave(X1) [resolution 119,78]
403. funny(X0) | brave(X0) | ~patient(X0) | kind(X0) [resolution 358,220]
406. ~patient(X0) | funny(X0) | kind(X0) [subsumption resolution 403,101]
411. funny(X1) | kind(X1) | brave(X1) [resolution 406,78]
413. funny(X1) | kind(X1) [subsumption resolution 411,101]
414. kind(lucy) [resolution 413,140]
420. ~happy(lucy) <- (10) [resolution 414,186]
424. $false <- (10) [subsumption resolution 420,310]
425. ~10 [avatar contradiction clause 424]
426. $false <- (1, ~11) [subsumption resolution 190,146]
427. ~1 | 11 [avatar contradiction clause 426]
428. $false [avatar sat refutation 156,191,289,425,427]
% SZS output end Proof for 7626419917774928148353789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or humble then someone is kind.
Everyone who is either calm or not curious is not tall.
Everyone who is either humble or not happy is either quiet or not tall and vice versa.
If fred is not humble or humble then lucy is not curious or curious and vice versa.
If susan is tall or not creative then mary is either not wise or rich.
Everyone who is not creative or quiet is either not happy or not brave.
Everyone who is either not tall or not humble is creative or not humble and vice versa.
If someone is creative or not creative then alice is both not creative and not wise and vice versa.
If susan is curious then paul is strong or not creative and vice versa.
Everyone who is strong or not quiet is funny or wise.
Everyone who is both curious and not kind is patient and vice versa.
Everyone who is both not generous and not brave is not kind.
Everyone who is both rich and not patient is both brave and happy and vice versa.
Everyone who is either not strong or not patient is not quiet and vice versa.
Everyone who is not brave is funny or not funny and vice versa.
If fred is either not curious or quiet then someone is either not old or humble and vice versa.
Susan is both rich and not old.
Paul is both not kind and not creative.
Someone is either not calm or wise.
John is not rich or not curious.
John is not patient.
Someone is old or not generous.
Someone is curious or not happy.
Paul is either rich or not humble. | Mary is not rich. | neutral | ((?[X]:((wise(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((calm(X)<~>~curious(X))=>~tall(X)))&
(![X]:((humble(X)<~>~happy(X))<=>(quiet(X)<~>~tall(X))))&
(((~humble(fred)|humble(fred)))<=>((~curious(lucy)|curious(lucy))))&
(((tall(susan)|~creative(susan)))=>((~wise(mary)<~>rich(mary))))&
(![X]:((~creative(X)|quiet(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
((?[X]:((creative(X)|~creative(X))))<=>((~creative(alice)&~wise(alice))))&
((curious(susan))<=>((strong(paul)|~creative(paul))))&
(![X]:((strong(X)|~quiet(X))=>(funny(X)|wise(X))))&
(![X]:((curious(X)&~kind(X))<=>patient(X)))&
(![X]:((~generous(X)&~brave(X))=>~kind(X)))&
(![X]:((rich(X)&~patient(X))<=>(brave(X)&happy(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>~quiet(X)))&
(![X]:(~brave(X)<=>(funny(X)|~funny(X))))&
(((~curious(fred)<~>quiet(fred)))<=>(?[X]:((~old(X)<~>humble(X)))))&
((rich(susan)&~old(susan)))&
((~kind(paul)&~creative(paul)))&
(?[X]:((~calm(X)<~>wise(X))))&
((~rich(john)|~curious(john)))&
(~patient(john))&
(?[X]:((old(X)|~generous(X))))&
(?[X]:((curious(X)|~happy(X))))&
((rich(paul)<~>~humble(paul))) | ~rich(mary) | [] | null | 0 |
Everyone who is not strong or creative is wise and vice versa.
Everyone who is strong or curious is kind and vice versa.
If john is not happy then someone is both not creative and creative.
Everyone who is either not generous or not calm is either strong or old.
Everyone who is not tall is both not calm and not happy.
If someone is either strong or not patient then someone is either not tall or humble.
Everyone who is not creative or old is curious or not wise and vice versa.
If mary is not kind then john is either not funny or strong.
If john is either not brave or not humble then someone is both not strong and old and vice versa.
Everyone who is not wise or old is either not strong or patient and vice versa.
Everyone who is either curious or not happy is calm and vice versa.
Everyone who is not humble is either patient or not kind and vice versa.
If someone is both not kind and not strong then someone is both not calm and not generous and vice versa.
Everyone who is either wise or not old is both curious and not quiet.
If someone is either quiet or happy then someone is either not patient or not quiet.
Susan is brave or not quiet.
Someone is both wise and not quiet.
Susan is not old or funny.
Someone is both creative and not funny.
Someone is both not curious and calm.
Susan is wise or patient. | John is wise. | neutral | (![X]:((~strong(X)|creative(X))<=>wise(X)))&
(![X]:((strong(X)|curious(X))<=>kind(X)))&
((~happy(john))=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((~generous(X)<~>~calm(X))=>(strong(X)<~>old(X))))&
(![X]:(~tall(X)=>(~calm(X)&~happy(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((~creative(X)|old(X))<=>(curious(X)|~wise(X))))&
((~kind(mary))=>((~funny(john)<~>strong(john))))&
(((~brave(john)<~>~humble(john)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~wise(X)|old(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((curious(X)<~>~happy(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(patient(X)<~>~kind(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((wise(X)<~>~old(X))=>(curious(X)&~quiet(X))))&
((?[X]:((quiet(X)<~>happy(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
((brave(susan)|~quiet(susan)))&
(?[X]:((wise(X)&~quiet(X))))&
((~old(susan)|funny(susan)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((~curious(X)&calm(X))))&
((wise(susan)|patient(susan))) | wise(john) | [] | null | 0 |
Everyone who is not humble or not calm is not calm and vice versa.
Everyone who is not rich is not calm or strong.
If someone is either old or kind then susan is not tall.
If lucy is either not old or humble then someone is not quiet or patient and vice versa.
Everyone who is both patient and calm is either brave or not calm and vice versa.
If fred is strong or humble then susan is not calm.
Everyone who is not brave is either not tall or not old.
Everyone who is either generous or not calm is both brave and curious and vice versa.
If fred is generous then susan is both not old and not generous and vice versa.
If john is either not rich or not creative then lucy is both funny and brave and vice versa.
Everyone who is either not humble or kind is either not funny or not calm.
If alice is not generous then lucy is not strong or strong.
If fred is either not happy or not tall then mary is either strong or not rich.
Everyone who is not generous is not quiet and vice versa.
If someone is both not brave and not wise then paul is either old or not patient and vice versa.
Everyone who is not curious or not kind is either patient or not wise.
Susan is curious or not generous.
Someone is generous.
John is both not strong and not old.
Someone is either happy or not wise.
Lucy is both wise and not quiet.
Lucy is tall.
Someone is both not wise and creative. | Susan is not old. | neutral | (![X]:((~humble(X)|~calm(X))<=>~calm(X)))&
(![X]:(~rich(X)=>(~calm(X)|strong(X))))&
((?[X]:((old(X)<~>kind(X))))=>(~tall(susan)))&
(((~old(lucy)<~>humble(lucy)))<=>(?[X]:((~quiet(X)|patient(X)))))&
(![X]:((patient(X)&calm(X))<=>(brave(X)<~>~calm(X))))&
(((strong(fred)|humble(fred)))=>(~calm(susan)))&
(![X]:(~brave(X)=>(~tall(X)<~>~old(X))))&
(![X]:((generous(X)<~>~calm(X))<=>(brave(X)&curious(X))))&
((generous(fred))<=>((~old(susan)&~generous(susan))))&
(((~rich(john)<~>~creative(john)))<=>((funny(lucy)&brave(lucy))))&
(![X]:((~humble(X)<~>kind(X))=>(~funny(X)<~>~calm(X))))&
((~generous(alice))=>((~strong(lucy)|strong(lucy))))&
(((~happy(fred)<~>~tall(fred)))=>((strong(mary)<~>~rich(mary))))&
(![X]:(~generous(X)<=>~quiet(X)))&
((?[X]:((~brave(X)&~wise(X))))<=>((old(paul)<~>~patient(paul))))&
(![X]:((~curious(X)|~kind(X))=>(patient(X)<~>~wise(X))))&
((curious(susan)|~generous(susan)))&
(?[X]:(generous(X)))&
((~strong(john)&~old(john)))&
(?[X]:((happy(X)<~>~wise(X))))&
((wise(lucy)&~quiet(lucy)))&
(tall(lucy))&
(?[X]:((~wise(X)&creative(X)))) | ~old(susan) | [] | null | 0 |
Everyone who is either not generous or not funny is both not wise and not happy.
If john is not strong then someone is both not funny and not old.
Everyone who is not happy is either funny or humble and vice versa.
Everyone who is generous or patient is calm.
If john is not curious then fred is not calm and vice versa.
If fred is either not humble or rich then paul is both not patient and not strong and vice versa.
If lucy is not calm or wise then john is tall or old and vice versa.
If someone is wise or not curious then lucy is either calm or not strong.
Everyone who is either old or happy is both rich and strong and vice versa.
Everyone who is old is not happy or not kind and vice versa.
Everyone who is tall is curious or not humble and vice versa.
If someone is patient then someone is either brave or wise.
Everyone who is both not happy and kind is quiet or not tall.
Everyone who is both kind and not generous is either not wise or curious.
Everyone who is both brave and not rich is generous or strong and vice versa.
If mary is both not kind and wise then someone is not calm or generous and vice versa.
Someone is either calm or not patient.
Alice is either not funny or tall.
John is both not calm and creative.
Someone is not creative.
Paul is either happy or not brave.
John is not creative or not curious.
John is both quiet and not funny. | Fred is not patient. | entailment | (![X]:((~generous(X)<~>~funny(X))=>(~wise(X)&~happy(X))))&
((~strong(john))=>(?[X]:((~funny(X)&~old(X)))))&
(![X]:(~happy(X)<=>(funny(X)<~>humble(X))))&
(![X]:((generous(X)|patient(X))=>calm(X)))&
((~curious(john))<=>(~calm(fred)))&
(((~humble(fred)<~>rich(fred)))<=>((~patient(paul)&~strong(paul))))&
(((~calm(lucy)|wise(lucy)))<=>((tall(john)|old(john))))&
((?[X]:((wise(X)|~curious(X))))=>((calm(lucy)<~>~strong(lucy))))&
(![X]:((old(X)<~>happy(X))<=>(rich(X)&strong(X))))&
(![X]:(old(X)<=>(~happy(X)|~kind(X))))&
(![X]:(tall(X)<=>(curious(X)|~humble(X))))&
((?[X]:(patient(X)))=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((~happy(X)&kind(X))=>(quiet(X)|~tall(X))))&
(![X]:((kind(X)&~generous(X))=>(~wise(X)<~>curious(X))))&
(![X]:((brave(X)&~rich(X))<=>(generous(X)|strong(X))))&
(((~kind(mary)&wise(mary)))<=>(?[X]:((~calm(X)|generous(X)))))&
(?[X]:((calm(X)<~>~patient(X))))&
((~funny(alice)<~>tall(alice)))&
((~calm(john)&creative(john)))&
(?[X]:(~creative(X)))&
((happy(paul)<~>~brave(paul)))&
((~creative(john)|~curious(john)))&
((quiet(john)&~funny(john))) | ~patient(fred) | [
"p3",
"p4",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7739787589322209442984335
% SZS output start Proof for 7739787589322209442984335
4. ! [X0] : ((patient(X0) | generous(X0)) => calm(X0)) [input p3]
5. ~curious(john) <=> ~calm(fred) [input p4]
19. creative(john) & ~calm(john) [input p18]
22. ~curious(john) | ~creative(john) [input p21]
24. patient(fred) [input hypothesis]
30. ! [X0] : (calm(X0) | (~patient(X0) & ~generous(X0))) [ennf transformation 4]
39. (~curious(john) | calm(fred)) & (~calm(fred) | curious(john)) [nnf transformation 5]
81. ~patient(X0) | calm(X0) [cnf transformation 30]
82. ~calm(fred) | curious(john) [cnf transformation 39]
129. creative(john) [cnf transformation 19]
133. ~curious(john) | ~creative(john) [cnf transformation 22]
135. patient(fred) [cnf transformation 24]
151. 4 <=> calm(fred) [avatar definition]
152. ~calm(fred) <- (~4) [avatar component clause 151]
155. 5 <=> curious(john) [avatar definition]
159. 5 | ~4 [avatar split clause 82,151,155]
285. ~curious(john) [subsumption resolution 133,129]
286. ~5 [avatar split clause 285,155]
289. calm(fred) [resolution 81,135]
290. $false <- (~4) [subsumption resolution 289,152]
291. 4 [avatar contradiction clause 290]
292. $false [avatar sat refutation 159,286,291]
% SZS output end Proof for 7739787589322209442984335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or humble is generous.
Everyone who is not quiet or strong is either wise or not rich.
Everyone who is happy or old is strong and vice versa.
If someone is not rich or not creative then alice is quiet or not strong.
Everyone who is both not strong and not wise is both not tall and patient and vice versa.
If mary is rich or not humble then mary is either calm or wise.
Everyone who is either tall or not rich is both not strong and funny.
If paul is wise or not funny then fred is either not kind or humble.
Everyone who is either not patient or not funny is brave and vice versa.
Everyone who is either not old or not creative is not creative and vice versa.
Everyone who is not wise or humble is both rich and calm.
Everyone who is either not old or funny is old.
If fred is both curious and not creative then fred is not quiet or creative.
If fred is both not brave and calm then mary is not patient or rich and vice versa.
Everyone who is generous or humble is kind or quiet and vice versa.
If someone is happy then lucy is either not patient or generous.
Someone is either creative or not strong.
Paul is either not old or not funny.
Paul is either quiet or not humble.
Lucy is not kind or wise.
Someone is either wise or curious.
Someone is either not humble or tall. | Mary is not funny. | neutral | (![X]:((~patient(X)<~>humble(X))=>generous(X)))&
(![X]:((~quiet(X)|strong(X))=>(wise(X)<~>~rich(X))))&
(![X]:((happy(X)|old(X))<=>strong(X)))&
((?[X]:((~rich(X)|~creative(X))))=>((quiet(alice)|~strong(alice))))&
(![X]:((~strong(X)&~wise(X))<=>(~tall(X)&patient(X))))&
(((rich(mary)|~humble(mary)))=>((calm(mary)<~>wise(mary))))&
(![X]:((tall(X)<~>~rich(X))=>(~strong(X)&funny(X))))&
(((wise(paul)|~funny(paul)))=>((~kind(fred)<~>humble(fred))))&
(![X]:((~patient(X)<~>~funny(X))<=>brave(X)))&
(![X]:((~old(X)<~>~creative(X))<=>~creative(X)))&
(![X]:((~wise(X)|humble(X))=>(rich(X)&calm(X))))&
(![X]:((~old(X)<~>funny(X))=>old(X)))&
(((curious(fred)&~creative(fred)))=>((~quiet(fred)|creative(fred))))&
(((~brave(fred)&calm(fred)))<=>((~patient(mary)|rich(mary))))&
(![X]:((generous(X)|humble(X))<=>(kind(X)|quiet(X))))&
((?[X]:(happy(X)))=>((~patient(lucy)<~>generous(lucy))))&
(?[X]:((creative(X)<~>~strong(X))))&
((~old(paul)<~>~funny(paul)))&
((quiet(paul)<~>~humble(paul)))&
((~kind(lucy)|wise(lucy)))&
(?[X]:((wise(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>tall(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is either not generous or funny is curious and vice versa.
Everyone who is both not quiet and calm is either humble or calm and vice versa.
Everyone who is either not kind or not wise is either not funny or rich and vice versa.
If someone is either funny or rich then someone is not calm or kind and vice versa.
If alice is both quiet and not happy then someone is both not funny and rich and vice versa.
If someone is happy or not wise then john is both wise and not creative.
Everyone who is not rich or not patient is brave or not generous.
Everyone who is not calm or generous is not generous.
If someone is funny then paul is both strong and not creative.
Everyone who is both curious and kind is either kind or tall.
If mary is both patient and not old then john is tall or happy.
Everyone who is either quiet or not rich is funny.
Everyone who is both quiet and not brave is not humble and vice versa.
Everyone who is either old or not tall is both not kind and not brave and vice versa.
Everyone who is either not rich or quiet is both funny and not generous.
If someone is not brave then paul is both patient and funny and vice versa.
Someone is either not wise or happy.
Someone is rich or curious.
Someone is both not happy and not creative.
Someone is both not happy and old.
Someone is either kind or not calm.
Susan is not calm.
Lucy is both happy and wise.
Someone is either not strong or not happy. | Alice is old. | neutral | (![X]:((~generous(X)<~>funny(X))<=>curious(X)))&
(![X]:((~quiet(X)&calm(X))<=>(humble(X)<~>calm(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>(?[X]:((~calm(X)|kind(X)))))&
(((quiet(alice)&~happy(alice)))<=>(?[X]:((~funny(X)&rich(X)))))&
((?[X]:((happy(X)|~wise(X))))=>((wise(john)&~creative(john))))&
(![X]:((~rich(X)|~patient(X))=>(brave(X)|~generous(X))))&
(![X]:((~calm(X)|generous(X))=>~generous(X)))&
((?[X]:(funny(X)))=>((strong(paul)&~creative(paul))))&
(![X]:((curious(X)&kind(X))=>(kind(X)<~>tall(X))))&
(((patient(mary)&~old(mary)))=>((tall(john)|happy(john))))&
(![X]:((quiet(X)<~>~rich(X))=>funny(X)))&
(![X]:((quiet(X)&~brave(X))<=>~humble(X)))&
(![X]:((old(X)<~>~tall(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(funny(X)&~generous(X))))&
((?[X]:(~brave(X)))<=>((patient(paul)&funny(paul))))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((rich(X)|curious(X))))&
(?[X]:((~happy(X)&~creative(X))))&
(?[X]:((~happy(X)&old(X))))&
(?[X]:((kind(X)<~>~calm(X))))&
(~calm(susan))&
((happy(lucy)&wise(lucy)))&
(?[X]:((~strong(X)<~>~happy(X)))) | old(alice) | [] | null | 0 |
If fred is either not strong or brave then mary is both kind and happy.
Everyone who is either not calm or strong is kind or creative.
Everyone who is either strong or not tall is both strong and not kind and vice versa.
Everyone who is both not creative and not generous is calm and vice versa.
Everyone who is either not funny or not strong is either tall or not wise and vice versa.
Everyone who is not humble or not brave is quiet or not old.
If someone is both not calm and not wise then someone is either happy or brave.
Everyone who is both not creative and not kind is both not curious and not kind.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
If paul is not happy or brave then alice is either creative or brave.
Paul is strong or not strong.
John is old.
Alice is strong or wise.
Someone is wise.
Someone is either creative or not humble.
Someone is either happy or not creative. | John is not patient. | entailment | (((~strong(fred)<~>brave(fred)))=>((kind(mary)&happy(mary))))&
(![X]:((~calm(X)<~>strong(X))=>(kind(X)|creative(X))))&
(![X]:((strong(X)<~>~tall(X))<=>(strong(X)&~kind(X))))&
(![X]:((~creative(X)&~generous(X))<=>calm(X)))&
(![X]:((~funny(X)<~>~strong(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~humble(X)|~brave(X))=>(quiet(X)|~old(X))))&
((?[X]:((~calm(X)&~wise(X))))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~creative(X)&~kind(X))=>(~curious(X)&~kind(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
(((~happy(paul)|brave(paul)))=>((creative(alice)<~>brave(alice))))&
((strong(paul)|~strong(paul)))&
(old(john))&
((strong(alice)|wise(alice)))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:((happy(X)<~>~creative(X)))) | ~patient(john) | [
"p2",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7823893297011620358247037
% SZS output start Proof for 7823893297011620358247037
3. ! [X0] : ((strong(X0) <~> ~tall(X0)) <=> (~kind(X0) & strong(X0))) [input p2]
9. ! [X0] : ((~old(X0) & ~wise(X0)) <=> strong(X0)) [input p8]
11. ! [X0] : ((calm(X0) | patient(X0)) <=> (~tall(X0) & creative(X0))) [input p10]
18. old(john) [input p17]
23. patient(john) [input hypothesis]
42. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | (kind(X0) | ~strong(X0))) & ((~kind(X0) & strong(X0)) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [nnf transformation 3]
43. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | kind(X0) | ~strong(X0)) & ((~kind(X0) & strong(X0)) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [flattening 42]
51. ! [X0] : (((~old(X0) & ~wise(X0)) | ~strong(X0)) & (strong(X0) | (old(X0) | wise(X0)))) [nnf transformation 9]
52. ! [X0] : (((~old(X0) & ~wise(X0)) | ~strong(X0)) & (strong(X0) | old(X0) | wise(X0))) [flattening 51]
54. ! [X0] : (((calm(X0) | patient(X0)) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 11]
55. ! [X0] : ((calm(X0) | patient(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [flattening 54]
76. strong(X0) | strong(X0) | tall(X0) [cnf transformation 43]
99. ~old(X0) | ~strong(X0) [cnf transformation 52]
110. ~patient(X0) | ~tall(X0) [cnf transformation 55]
124. old(john) [cnf transformation 18]
131. patient(john) [cnf transformation 23]
136. tall(X0) | strong(X0) [duplicate literal removal 76]
226. ~strong(john) [resolution 99,124]
232. ~tall(john) [resolution 110,131]
237. strong(john) [resolution 136,232]
238. $false [subsumption resolution 237,226]
% SZS output end Proof for 7823893297011620358247037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and generous then someone is wise and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Everyone who is not generous is both humble and curious and vice versa.
If someone is not curious or not generous then fred is both creative and old and vice versa.
If someone is funny then alice is not brave or not wise.
If someone is either not calm or rich then susan is not calm and vice versa.
Everyone who is either not generous or rich is not funny or wise and vice versa.
If paul is either rich or not brave then alice is not generous.
If mary is either not funny or quiet then someone is both brave and creative and vice versa.
Everyone who is both kind and not wise is both not rich and curious.
If fred is both calm and not calm then lucy is rich or strong and vice versa.
If someone is both not generous and not quiet then alice is both not rich and curious and vice versa.
Fred is both curious and not brave.
Someone is brave or humble.
John is humble or not patient.
Fred is not happy.
Mary is tall or not strong.
Mary is both not calm and not kind. | Fred is not humble. | entailment | ((?[X]:((~wise(X)&generous(X))))<=>(?[X]:(wise(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
((?[X]:(funny(X)))=>((~brave(alice)|~wise(alice))))&
((?[X]:((~calm(X)<~>rich(X))))<=>(~calm(susan)))&
(![X]:((~generous(X)<~>rich(X))<=>(~funny(X)|wise(X))))&
(((rich(paul)<~>~brave(paul)))=>(~generous(alice)))&
(((~funny(mary)<~>quiet(mary)))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((kind(X)&~wise(X))=>(~rich(X)&curious(X))))&
(((calm(fred)&~calm(fred)))<=>((rich(lucy)|strong(lucy))))&
((?[X]:((~generous(X)&~quiet(X))))<=>((~rich(alice)&curious(alice))))&
((curious(fred)&~brave(fred)))&
(?[X]:((brave(X)|humble(X))))&
((humble(john)|~patient(john)))&
(~happy(fred))&
((tall(mary)|~strong(mary)))&
((~calm(mary)&~kind(mary))) | ~humble(fred) | [
"p2",
"p5",
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 299885978262344272059903
% SZS output start Proof for 299885978262344272059903
3. (~tall(lucy) & strong(lucy)) <=> old(fred) [input p2]
6. ! [X0] : (~generous(X0) <=> (curious(X0) & humble(X0))) [input p5]
7. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (old(fred) & creative(fred)) [input p6]
14. (~calm(fred) & calm(fred)) <=> (strong(lucy) | rich(lucy)) [input p13]
16. ~brave(fred) & curious(fred) [input p15]
22. humble(fred) [input hypothesis]
38. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | (tall(lucy) | ~strong(lucy))) [nnf transformation 3]
39. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | tall(lucy) | ~strong(lucy)) [flattening 38]
44. ! [X0] : ((~generous(X0) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | generous(X0))) [nnf transformation 6]
45. ! [X0] : ((~generous(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | generous(X0))) [flattening 44]
46. (? [X0] : (~generous(X0) | ~curious(X0)) | (~old(fred) | ~creative(fred))) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 7]
47. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 46]
48. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 47]
49. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK2) | ~curious(sK2)) [choice axiom]
50. ((~generous(sK2) | ~curious(sK2)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 48,49]
62. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & ((strong(lucy) | rich(lucy)) | (calm(fred) | ~calm(fred))) [nnf transformation 14]
63. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & (strong(lucy) | rich(lucy) | calm(fred) | ~calm(fred)) [flattening 62]
77. strong(lucy) | ~old(fred) [cnf transformation 39]
89. ~humble(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 45]
93. old(fred) | generous(X1) [cnf transformation 50]
116. calm(fred) | ~strong(lucy) [cnf transformation 63]
118. ~calm(fred) | ~strong(lucy) [cnf transformation 63]
123. curious(fred) [cnf transformation 16]
128. humble(fred) [cnf transformation 22]
169. 10 <=> old(fred) [avatar definition]
178. 12 <=> strong(lucy) [avatar definition]
181. ~10 | 12 [avatar split clause 77,178,169]
197. 16 <=> ! [X1] : generous(X1) [avatar definition]
198. generous(X1) <- (16) [avatar component clause 197]
199. 16 | 10 [avatar split clause 93,169,197]
276. 33 <=> calm(fred) [avatar definition]
279. ~12 | ~33 [avatar split clause 118,276,178]
285. ~12 | 33 [avatar split clause 116,276,178]
348. ~curious(fred) | ~generous(fred) [resolution 89,128]
350. ~generous(fred) [subsumption resolution 348,123]
351. $false <- (16) [subsumption resolution 350,198]
352. ~16 [avatar contradiction clause 351]
353. $false [avatar sat refutation 181,199,279,285,352]
% SZS output end Proof for 299885978262344272059903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not old is either not strong or not humble and vice versa.
Everyone who is brave or not quiet is either not old or happy.
Everyone who is not generous is either funny or not curious and vice versa.
If someone is old or not patient then paul is kind.
Everyone who is both brave and quiet is not funny and vice versa.
If someone is either not creative or humble then alice is both not kind and not strong and vice versa.
If susan is generous or not humble then fred is either curious or not strong.
Everyone who is both not funny and not curious is both strong and not creative and vice versa.
If paul is not old or creative then lucy is not funny and vice versa.
If susan is not happy or calm then someone is not brave.
If someone is both calm and rich then fred is rich or kind and vice versa.
Everyone who is not tall is both calm and brave.
Everyone who is humble or not humble is both generous and not humble.
Everyone who is either not happy or not rich is either not curious or strong.
If susan is not rich or tall then alice is both brave and not patient and vice versa.
If someone is not kind then fred is not rich.
Someone is either curious or not quiet.
Fred is not calm or not brave.
John is patient or not curious.
Lucy is both not calm and curious.
Someone is either not curious or not old.
Someone is rich.
Someone is not quiet or not rich. | Paul is not old. | neutral | (![X]:((~kind(X)<~>~old(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:((brave(X)|~quiet(X))=>(~old(X)<~>happy(X))))&
(![X]:(~generous(X)<=>(funny(X)<~>~curious(X))))&
((?[X]:((old(X)|~patient(X))))=>(kind(paul)))&
(![X]:((brave(X)&quiet(X))<=>~funny(X)))&
((?[X]:((~creative(X)<~>humble(X))))<=>((~kind(alice)&~strong(alice))))&
(((generous(susan)|~humble(susan)))=>((curious(fred)<~>~strong(fred))))&
(![X]:((~funny(X)&~curious(X))<=>(strong(X)&~creative(X))))&
(((~old(paul)|creative(paul)))<=>(~funny(lucy)))&
(((~happy(susan)|calm(susan)))=>(?[X]:(~brave(X))))&
((?[X]:((calm(X)&rich(X))))<=>((rich(fred)|kind(fred))))&
(![X]:(~tall(X)=>(calm(X)&brave(X))))&
(![X]:((humble(X)|~humble(X))=>(generous(X)&~humble(X))))&
(![X]:((~happy(X)<~>~rich(X))=>(~curious(X)<~>strong(X))))&
(((~rich(susan)|tall(susan)))<=>((brave(alice)&~patient(alice))))&
((?[X]:(~kind(X)))=>(~rich(fred)))&
(?[X]:((curious(X)<~>~quiet(X))))&
((~calm(fred)|~brave(fred)))&
((patient(john)|~curious(john)))&
((~calm(lucy)&curious(lucy)))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)|~rich(X)))) | ~old(paul) | [] | null | 0 |
Everyone who is not rich or generous is both not wise and not strong.
If someone is not generous or not old then mary is both not quiet and not curious and vice versa.
If alice is both brave and creative then lucy is not kind or not curious.
Everyone who is not wise is not old.
If fred is not rich or kind then someone is not tall or not creative.
Everyone who is not curious or generous is both not happy and old.
If someone is either calm or not strong then someone is not humble or not curious and vice versa.
If john is curious or funny then alice is both not quiet and not funny.
Everyone who is tall is humble.
Everyone who is not happy or kind is not brave and vice versa.
If john is not wise then someone is not rich or kind and vice versa.
Everyone who is not quiet is either not funny or funny.
Everyone who is either not quiet or rich is both tall and patient and vice versa.
If lucy is not generous then someone is both humble and not happy.
If someone is both old and curious then someone is both not quiet and humble and vice versa.
Everyone who is funny is either not happy or not tall.
Someone is not quiet or not brave.
Someone is either not brave or not humble.
Someone is kind or wise.
Paul is both not funny and tall.
Mary is not brave.
Fred is either brave or curious. | Mary is not calm. | neutral | (![X]:((~rich(X)|generous(X))=>(~wise(X)&~strong(X))))&
((?[X]:((~generous(X)|~old(X))))<=>((~quiet(mary)&~curious(mary))))&
(((brave(alice)&creative(alice)))=>((~kind(lucy)|~curious(lucy))))&
(![X]:(~wise(X)=>~old(X)))&
(((~rich(fred)|kind(fred)))=>(?[X]:((~tall(X)|~creative(X)))))&
(![X]:((~curious(X)|generous(X))=>(~happy(X)&old(X))))&
((?[X]:((calm(X)<~>~strong(X))))<=>(?[X]:((~humble(X)|~curious(X)))))&
(((curious(john)|funny(john)))=>((~quiet(alice)&~funny(alice))))&
(![X]:(tall(X)=>humble(X)))&
(![X]:((~happy(X)|kind(X))<=>~brave(X)))&
((~wise(john))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:(~quiet(X)=>(~funny(X)<~>funny(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(tall(X)&patient(X))))&
((~generous(lucy))=>(?[X]:((humble(X)&~happy(X)))))&
((?[X]:((old(X)&curious(X))))<=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:(funny(X)=>(~happy(X)<~>~tall(X))))&
(?[X]:((~quiet(X)|~brave(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((kind(X)|wise(X))))&
((~funny(paul)&tall(paul)))&
(~brave(mary))&
((brave(fred)<~>curious(fred))) | ~calm(mary) | [] | null | 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. | Fred is not brave. | neutral | (![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)))) | ~brave(fred) | [] | null | 0 |
Everyone who is both not calm and happy is not strong. If lucy is not calm then someone is not calm. If susan is either not quiet or patient then paul is both not quiet and strong and vice versa. Everyone who is either curious or not rich is both not old and not rich and vice versa. If someone is either not rich or not humble then fred is either humble or kind and vice versa. If mary is not generous or not brave then someone is either not wise or not old and vice versa. If fred is humble then someone is either not humble or not tall. If someone is both not quiet and tall then someone is quiet and vice versa. Everyone who is not creative is not tall or creative and vice versa. Everyone who is not quiet or not old is both not quiet and calm. Everyone who is both calm and not generous is both kind and not rich and vice versa. Everyone who is either generous or patient is both old and not old. Everyone who is curious or not funny is not brave or strong. If lucy is rich or generous then someone is either not old or not humble and vice versa. Everyone who is not humble or kind is either not curious or brave and vice versa. Someone is not curious or humble. Someone is either not curious or kind. Mary is both not tall and not quiet. Someone is both humble and rich. Mary is either kind or not tall. Mary is both not tall and not wise. Someone is curious or kind. Alice is both not happy and not old. | Susan is not patient. | neutral | (![X]:((~calm(X)&happy(X))=>~strong(X)))&
((~calm(lucy))=>(?[X]:(~calm(X))))&
(((~quiet(susan)<~>patient(susan)))<=>((~quiet(paul)&strong(paul))))&
(![X]:((curious(X)<~>~rich(X))<=>(~old(X)&~rich(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((humble(fred)<~>kind(fred))))&
(((~generous(mary)|~brave(mary)))<=>(?[X]:((~wise(X)<~>~old(X)))))&
((humble(fred))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~tall(X)|creative(X))))&
(![X]:((~quiet(X)|~old(X))=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((generous(X)<~>patient(X))=>(old(X)&~old(X))))&
(![X]:((curious(X)|~funny(X))=>(~brave(X)|strong(X))))&
(((rich(lucy)|generous(lucy)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|kind(X))<=>(~curious(X)<~>brave(X))))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:((~curious(X)<~>kind(X))))&
((~tall(mary)&~quiet(mary)))&
(?[X]:((humble(X)&rich(X))))&
((kind(mary)<~>~tall(mary)))&
((~tall(mary)&~wise(mary)))&
(?[X]:((curious(X)|kind(X))))&
((~happy(alice)&~old(alice))) | ~patient(susan) | [] | null | 0 |
If alice is either happy or not funny then mary is either not creative or rich and vice versa.
If someone is both rich and happy then someone is either curious or calm.
If someone is not old or quiet then someone is not wise.
If lucy is generous or quiet then someone is both not wise and not happy and vice versa.
Everyone who is both brave and kind is brave or not funny.
Everyone who is not creative or not curious is either quiet or not creative.
If someone is kind or not brave then alice is not calm.
Everyone who is not humble is both brave and not wise.
Everyone who is not brave is either not strong or curious.
If someone is either not rich or not humble then someone is both not calm and not curious.
Everyone who is both not brave and not quiet is either not generous or quiet and vice versa.
If someone is either not generous or not happy then someone is not calm or not humble.
If john is either calm or brave then alice is not old or not curious.
Everyone who is funny is either wise or not happy.
If john is calm or rich then someone is both brave and not tall.
Everyone who is either not wise or strong is either funny or not brave.
Lucy is either not kind or not wise.
Alice is both calm and not wise.
Someone is both not generous and quiet.
Susan is either tall or wise.
John is either not kind or not tall.
Someone is not wise or not brave. | Mary is calm. | neutral | (((happy(alice)<~>~funny(alice)))<=>((~creative(mary)<~>rich(mary))))&
((?[X]:((rich(X)&happy(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
((?[X]:((~old(X)|quiet(X))))=>(?[X]:(~wise(X))))&
(((generous(lucy)|quiet(lucy)))<=>(?[X]:((~wise(X)&~happy(X)))))&
(![X]:((brave(X)&kind(X))=>(brave(X)|~funny(X))))&
(![X]:((~creative(X)|~curious(X))=>(quiet(X)<~>~creative(X))))&
((?[X]:((kind(X)|~brave(X))))=>(~calm(alice)))&
(![X]:(~humble(X)=>(brave(X)&~wise(X))))&
(![X]:(~brave(X)=>(~strong(X)<~>curious(X))))&
((?[X]:((~rich(X)<~>~humble(X))))=>(?[X]:((~calm(X)&~curious(X)))))&
(![X]:((~brave(X)&~quiet(X))<=>(~generous(X)<~>quiet(X))))&
((?[X]:((~generous(X)<~>~happy(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(((calm(john)<~>brave(john)))=>((~old(alice)|~curious(alice))))&
(![X]:(funny(X)=>(wise(X)<~>~happy(X))))&
(((calm(john)|rich(john)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((~wise(X)<~>strong(X))=>(funny(X)<~>~brave(X))))&
((~kind(lucy)<~>~wise(lucy)))&
((calm(alice)&~wise(alice)))&
(?[X]:((~generous(X)&quiet(X))))&
((tall(susan)<~>wise(susan)))&
((~kind(john)<~>~tall(john)))&
(?[X]:((~wise(X)|~brave(X)))) | calm(mary) | [] | null | 0 |
Everyone who is both funny and not happy is not curious.
If someone is both not brave and happy then fred is not kind and vice versa.
Everyone who is either not tall or not rich is not old.
Everyone who is either rich or not rich is either creative or strong and vice versa.
If someone is both not quiet and rich then lucy is humble or not patient.
Everyone who is generous or not brave is both curious and not tall.
If someone is both not old and not patient then fred is generous or funny.
Everyone who is either strong or quiet is not funny or rich and vice versa.
If paul is curious then someone is creative or not generous.
Everyone who is not calm or not curious is quiet or strong and vice versa.
If lucy is not humble then susan is either strong or happy and vice versa.
Everyone who is quiet or tall is not brave.
Everyone who is not patient or strong is kind and vice versa.
If someone is funny or not creative then john is not patient or funny and vice versa.
If lucy is old or not kind then someone is happy.
If someone is both not humble and not patient then someone is both not kind and not old and vice versa.
Someone is both not happy and brave.
Lucy is either not calm or creative.
Paul is both calm and not quiet.
Someone is both curious and creative.
Someone is creative.
Susan is both humble and not patient.
John is not tall.
Paul is not patient or tall. | Susan is not generous. | neutral | (![X]:((funny(X)&~happy(X))=>~curious(X)))&
((?[X]:((~brave(X)&happy(X))))<=>(~kind(fred)))&
(![X]:((~tall(X)<~>~rich(X))=>~old(X)))&
(![X]:((rich(X)<~>~rich(X))<=>(creative(X)<~>strong(X))))&
((?[X]:((~quiet(X)&rich(X))))=>((humble(lucy)|~patient(lucy))))&
(![X]:((generous(X)|~brave(X))=>(curious(X)&~tall(X))))&
((?[X]:((~old(X)&~patient(X))))=>((generous(fred)|funny(fred))))&
(![X]:((strong(X)<~>quiet(X))<=>(~funny(X)|rich(X))))&
((curious(paul))=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((~calm(X)|~curious(X))<=>(quiet(X)|strong(X))))&
((~humble(lucy))<=>((strong(susan)<~>happy(susan))))&
(![X]:((quiet(X)|tall(X))=>~brave(X)))&
(![X]:((~patient(X)|strong(X))<=>kind(X)))&
((?[X]:((funny(X)|~creative(X))))<=>((~patient(john)|funny(john))))&
(((old(lucy)|~kind(lucy)))=>(?[X]:(happy(X))))&
((?[X]:((~humble(X)&~patient(X))))<=>(?[X]:((~kind(X)&~old(X)))))&
(?[X]:((~happy(X)&brave(X))))&
((~calm(lucy)<~>creative(lucy)))&
((calm(paul)&~quiet(paul)))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:(creative(X)))&
((humble(susan)&~patient(susan)))&
(~tall(john))&
((~patient(paul)|tall(paul))) | ~generous(susan) | [] | null | 0 |
Everyone who is either creative or not kind is either not happy or not calm and vice versa.
If lucy is tall then someone is calm.
If someone is not generous or not wise then someone is both brave and wise.
Everyone who is both not funny and not strong is not old and vice versa.
If someone is either curious or not brave then john is not creative or funny and vice versa.
Everyone who is not brave is wise.
If someone is patient or not quiet then alice is old or wise.
Everyone who is patient or not rich is either old or kind and vice versa.
If someone is rich then someone is either not quiet or calm.
Everyone who is both not old and strong is both wise and happy.
Everyone who is both humble and curious is either brave or humble.
Everyone who is both curious and rich is not kind or curious and vice versa.
If paul is either generous or old then fred is either not happy or wise.
Everyone who is not humble or not funny is either creative or calm and vice versa.
Everyone who is not humble is either rich or not humble.
Everyone who is curious or not funny is not old and vice versa.
Someone is either calm or not quiet.
Someone is either wise or not rich.
Susan is either not patient or funny.
Alice is both not rich and happy.
Fred is either not creative or not kind.
Paul is both kind and not tall.
Mary is not wise or humble.
Fred is brave or not kind. | Alice is strong. | contradiction | (![X]:((creative(X)<~>~kind(X))<=>(~happy(X)<~>~calm(X))))&
((tall(lucy))=>(?[X]:(calm(X))))&
((?[X]:((~generous(X)|~wise(X))))=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((~funny(X)&~strong(X))<=>~old(X)))&
((?[X]:((curious(X)<~>~brave(X))))<=>((~creative(john)|funny(john))))&
(![X]:(~brave(X)=>wise(X)))&
((?[X]:((patient(X)|~quiet(X))))=>((old(alice)|wise(alice))))&
(![X]:((patient(X)|~rich(X))<=>(old(X)<~>kind(X))))&
((?[X]:(rich(X)))=>(?[X]:((~quiet(X)<~>calm(X)))))&
(![X]:((~old(X)&strong(X))=>(wise(X)&happy(X))))&
(![X]:((humble(X)&curious(X))=>(brave(X)<~>humble(X))))&
(![X]:((curious(X)&rich(X))<=>(~kind(X)|curious(X))))&
(((generous(paul)<~>old(paul)))=>((~happy(fred)<~>wise(fred))))&
(![X]:((~humble(X)|~funny(X))<=>(creative(X)<~>calm(X))))&
(![X]:(~humble(X)=>(rich(X)<~>~humble(X))))&
(![X]:((curious(X)|~funny(X))<=>~old(X)))&
(?[X]:((calm(X)<~>~quiet(X))))&
(?[X]:((wise(X)<~>~rich(X))))&
((~patient(susan)<~>funny(susan)))&
((~rich(alice)&happy(alice)))&
((~creative(fred)<~>~kind(fred)))&
((kind(paul)&~tall(paul)))&
((~wise(mary)|humble(mary)))&
((brave(fred)|~kind(fred))) | strong(alice) | [
"p3",
"p7",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9055283121685283172752493
% SZS output start Proof for 9055283121685283172752493
4. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> ~old(X0)) [input p3]
8. ! [X0] : ((~rich(X0) | patient(X0)) <=> (old(X0) <~> kind(X0))) [input p7]
12. ! [X0] : ((rich(X0) & curious(X0)) <=> (curious(X0) | ~kind(X0))) [input p11]
20. happy(alice) & ~rich(alice) [input p19]
25. strong(alice) [input hypothesis]
45. ! [X0] : (((~strong(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (strong(X0) | funny(X0)))) [nnf transformation 4]
46. ! [X0] : (((~strong(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | strong(X0) | funny(X0))) [flattening 45]
52. ! [X0] : (((~rich(X0) | patient(X0)) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0)))) & (((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (rich(X0) & ~patient(X0)))) [nnf transformation 8]
53. ! [X0] : ((~rich(X0) | patient(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0)))) & (((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (rich(X0) & ~patient(X0)))) [flattening 52]
59. ! [X0] : (((rich(X0) & curious(X0)) | (~curious(X0) & kind(X0))) & ((curious(X0) | ~kind(X0)) | (~rich(X0) | ~curious(X0)))) [nnf transformation 12]
60. ! [X0] : (((rich(X0) & curious(X0)) | (~curious(X0) & kind(X0))) & (curious(X0) | ~kind(X0) | ~rich(X0) | ~curious(X0))) [flattening 59]
89. ~strong(X0) | old(X0) [cnf transformation 46]
102. ~old(X0) | ~kind(X0) | rich(X0) [cnf transformation 53]
114. rich(X0) | kind(X0) [cnf transformation 60]
137. ~rich(alice) [cnf transformation 20]
144. strong(alice) [cnf transformation 25]
197. 12 <=> old(alice) [avatar definition]
199. old(alice) <- (12) [avatar component clause 197]
296. old(alice) [resolution 89,144]
299. kind(alice) [resolution 114,137]
311. ~kind(alice) | rich(alice) <- (12) [resolution 102,199]
312. rich(alice) <- (12) [subsumption resolution 311,299]
313. $false <- (12) [subsumption resolution 312,137]
314. ~12 [avatar contradiction clause 313]
315. 12 [avatar split clause 296,197]
316. $false [avatar sat refutation 314,315]
% SZS output end Proof for 9055283121685283172752493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or tall then someone is strong or tall.
Everyone who is either generous or quiet is strong or not generous.
Everyone who is not calm is not curious or not strong.
If alice is both not wise and patient then someone is both not creative and kind.
If susan is both not tall and quiet then mary is both humble and not curious.
Everyone who is happy is either not funny or not wise and vice versa.
Everyone who is either old or not humble is either not quiet or not rich and vice versa.
Everyone who is either funny or creative is quiet or wise and vice versa.
Everyone who is both calm and wise is both brave and not strong and vice versa.
If someone is humble then someone is generous or not old and vice versa.
If john is humble or not happy then mary is not quiet.
Everyone who is both strong and funny is either tall or old and vice versa.
If someone is either brave or patient then alice is either wise or tall and vice versa.
If someone is brave or humble then someone is not tall.
Everyone who is both rich and not rich is not kind or rich and vice versa.
If lucy is not curious or not old then paul is either old or not rich and vice versa.
Mary is either not rich or old.
Alice is humble.
Someone is either generous or not wise.
Someone is generous or not happy.
Someone is not old.
Fred is brave.
Someone is not happy.
Paul is both humble and wise. | John is kind. | entailment | ((?[X]:((~curious(X)<~>tall(X))))=>(?[X]:((strong(X)|tall(X)))))&
(![X]:((generous(X)<~>quiet(X))=>(strong(X)|~generous(X))))&
(![X]:(~calm(X)=>(~curious(X)|~strong(X))))&
(((~wise(alice)&patient(alice)))=>(?[X]:((~creative(X)&kind(X)))))&
(((~tall(susan)&quiet(susan)))=>((humble(mary)&~curious(mary))))&
(![X]:(happy(X)<=>(~funny(X)<~>~wise(X))))&
(![X]:((old(X)<~>~humble(X))<=>(~quiet(X)<~>~rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>(quiet(X)|wise(X))))&
(![X]:((calm(X)&wise(X))<=>(brave(X)&~strong(X))))&
((?[X]:(humble(X)))<=>(?[X]:((generous(X)|~old(X)))))&
(((humble(john)|~happy(john)))=>(~quiet(mary)))&
(![X]:((strong(X)&funny(X))<=>(tall(X)<~>old(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>((wise(alice)<~>tall(alice))))&
((?[X]:((brave(X)|humble(X))))=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~rich(X))<=>(~kind(X)|rich(X))))&
(((~curious(lucy)|~old(lucy)))<=>((old(paul)<~>~rich(paul))))&
((~rich(mary)<~>old(mary)))&
(humble(alice))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:(~old(X)))&
(brave(fred))&
(?[X]:(~happy(X)))&
((humble(paul)&wise(paul))) | kind(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8786804803550897516927444
% SZS output start Proof for 8786804803550897516927444
15. ! [X0] : ((~rich(X0) & rich(X0)) <=> (rich(X0) | ~kind(X0))) [input p14]
25. ~kind(john) [input hypothesis]
67. ! [X0] : (((~rich(X0) & rich(X0)) | (~rich(X0) & kind(X0))) & ((rich(X0) | ~kind(X0)) | (rich(X0) | ~rich(X0)))) [nnf transformation 15]
68. ! [X0] : (((~rich(X0) & rich(X0)) | (~rich(X0) & kind(X0))) & (rich(X0) | ~kind(X0) | rich(X0) | ~rich(X0))) [flattening 67]
134. rich(X0) | kind(X0) [cnf transformation 68]
137. ~rich(X0) | ~rich(X0) [cnf transformation 68]
155. ~kind(john) [cnf transformation 25]
157. ~rich(X0) [duplicate literal removal 137]
284. kind(X0) [subsumption resolution 134,157]
323. $false [subsumption resolution 155,284]
% SZS output end Proof for 8786804803550897516927444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not brave.
Everyone who is either not patient or not quiet is both rich and not wise and vice versa.
Everyone who is either generous or old is not wise and vice versa.
If alice is both not tall and not patient then john is both kind and funny and vice versa.
If someone is both calm and not patient then paul is either tall or generous and vice versa.
Everyone who is curious is both not patient and humble and vice versa.
Everyone who is either wise or brave is either not humble or tall and vice versa.
Everyone who is humble is both not calm and rich and vice versa.
Everyone who is both patient and not rich is either not patient or not humble and vice versa.
Everyone who is either not patient or wise is both not patient and curious and vice versa.
If someone is not creative then someone is old or funny.
Everyone who is not creative is not generous or not quiet.
If someone is both not funny and tall then alice is either strong or not wise and vice versa.
If paul is not creative then susan is not strong and vice versa.
If john is both not kind and funny then someone is funny or generous and vice versa.
Susan is not funny or patient.
Alice is both tall and not rich.
Someone is funny or not old.
John is both happy and not rich.
Fred is either curious or not tall.
Alice is both not funny and not brave.
Someone is rich. | Fred is creative. | neutral | (![X]:(generous(X)=>~brave(X)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(rich(X)&~wise(X))))&
(![X]:((generous(X)<~>old(X))<=>~wise(X)))&
(((~tall(alice)&~patient(alice)))<=>((kind(john)&funny(john))))&
((?[X]:((calm(X)&~patient(X))))<=>((tall(paul)<~>generous(paul))))&
(![X]:(curious(X)<=>(~patient(X)&humble(X))))&
(![X]:((wise(X)<~>brave(X))<=>(~humble(X)<~>tall(X))))&
(![X]:(humble(X)<=>(~calm(X)&rich(X))))&
(![X]:((patient(X)&~rich(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>wise(X))<=>(~patient(X)&curious(X))))&
((?[X]:(~creative(X)))=>(?[X]:((old(X)|funny(X)))))&
(![X]:(~creative(X)=>(~generous(X)|~quiet(X))))&
((?[X]:((~funny(X)&tall(X))))<=>((strong(alice)<~>~wise(alice))))&
((~creative(paul))<=>(~strong(susan)))&
(((~kind(john)&funny(john)))<=>(?[X]:((funny(X)|generous(X)))))&
((~funny(susan)|patient(susan)))&
((tall(alice)&~rich(alice)))&
(?[X]:((funny(X)|~old(X))))&
((happy(john)&~rich(john)))&
((curious(fred)<~>~tall(fred)))&
((~funny(alice)&~brave(alice)))&
(?[X]:(rich(X))) | creative(fred) | [] | null | 0 |
Everyone who is either generous or not strong is both old and not curious and vice versa. Everyone who is both not rich and curious is strong or not curious. If mary is both not tall and not curious then someone is both funny and creative. If john is either quiet or brave then lucy is rich or happy and vice versa. Everyone who is not kind is not quiet or not happy and vice versa. If fred is humble then someone is both not old and not tall. Everyone who is both not calm and funny is both funny and brave and vice versa. Everyone who is generous is both not generous and not calm. Everyone who is either generous or not rich is both rich and strong. Everyone who is either not old or generous is either not humble or not curious and vice versa. If someone is both not quiet and not wise then john is both not happy and not humble. Everyone who is either strong or tall is both not tall and patient and vice versa. If someone is not patient then mary is both not happy and not rich. Everyone who is both tall and brave is not strong or creative. Everyone who is not happy is brave. Everyone who is funny or creative is either not wise or calm and vice versa. Lucy is either strong or not kind. Someone is either not wise or generous. John is both old and not happy. Someone is tall or not curious. Paul is patient. Someone is not kind or not wise. Someone is not kind. Paul is creative or happy. | Fred is not old. | neutral | (![X]:((generous(X)<~>~strong(X))<=>(old(X)&~curious(X))))&
(![X]:((~rich(X)&curious(X))=>(strong(X)|~curious(X))))&
(((~tall(mary)&~curious(mary)))=>(?[X]:((funny(X)&creative(X)))))&
(((quiet(john)<~>brave(john)))<=>((rich(lucy)|happy(lucy))))&
(![X]:(~kind(X)<=>(~quiet(X)|~happy(X))))&
((humble(fred))=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((~calm(X)&funny(X))<=>(funny(X)&brave(X))))&
(![X]:(generous(X)=>(~generous(X)&~calm(X))))&
(![X]:((generous(X)<~>~rich(X))=>(rich(X)&strong(X))))&
(![X]:((~old(X)<~>generous(X))<=>(~humble(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&~wise(X))))=>((~happy(john)&~humble(john))))&
(![X]:((strong(X)<~>tall(X))<=>(~tall(X)&patient(X))))&
((?[X]:(~patient(X)))=>((~happy(mary)&~rich(mary))))&
(![X]:((tall(X)&brave(X))=>(~strong(X)|creative(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:((funny(X)|creative(X))<=>(~wise(X)<~>calm(X))))&
((strong(lucy)<~>~kind(lucy)))&
(?[X]:((~wise(X)<~>generous(X))))&
((old(john)&~happy(john)))&
(?[X]:((tall(X)|~curious(X))))&
(patient(paul))&
(?[X]:((~kind(X)|~wise(X))))&
(?[X]:(~kind(X)))&
((creative(paul)|happy(paul))) | ~old(fred) | [] | null | 0 |
Everyone who is not calm or not quiet is both not patient and patient.
Everyone who is generous or creative is not rich or funny.
Everyone who is not rich is not calm or strong and vice versa.
If someone is not old or strong then someone is either kind or not quiet.
Everyone who is creative is not tall.
Everyone who is both not calm and not kind is creative and vice versa.
Everyone who is either creative or calm is either kind or not humble and vice versa.
If someone is either humble or not generous then someone is not old.
Everyone who is creative is creative or not generous and vice versa.
If someone is both funny and wise then someone is not kind.
Everyone who is either not strong or tall is both not curious and not rich and vice versa.
If paul is either not generous or not happy then someone is either generous or calm and vice versa.
If john is not kind then alice is both creative and generous and vice versa.
If someone is either not tall or happy then someone is not brave.
Everyone who is either old or strong is happy or not humble and vice versa.
Everyone who is both not strong and not patient is both patient and not tall and vice versa.
Susan is wise.
Lucy is both not rich and kind.
Someone is happy.
John is happy.
Someone is wise.
Someone is not wise or happy.
Someone is either rich or not creative. | John is generous. | entailment | (![X]:((~calm(X)|~quiet(X))=>(~patient(X)&patient(X))))&
(![X]:((generous(X)|creative(X))=>(~rich(X)|funny(X))))&
(![X]:(~rich(X)<=>(~calm(X)|strong(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>~tall(X)))&
(![X]:((~calm(X)&~kind(X))<=>creative(X)))&
(![X]:((creative(X)<~>calm(X))<=>(kind(X)<~>~humble(X))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:(~old(X))))&
(![X]:(creative(X)<=>(creative(X)|~generous(X))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~curious(X)&~rich(X))))&
(((~generous(paul)<~>~happy(paul)))<=>(?[X]:((generous(X)<~>calm(X)))))&
((~kind(john))<=>((creative(alice)&generous(alice))))&
((?[X]:((~tall(X)<~>happy(X))))=>(?[X]:(~brave(X))))&
(![X]:((old(X)<~>strong(X))<=>(happy(X)|~humble(X))))&
(![X]:((~strong(X)&~patient(X))<=>(patient(X)&~tall(X))))&
(wise(susan))&
((~rich(lucy)&kind(lucy)))&
(?[X]:(happy(X)))&
(happy(john))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((rich(X)<~>~creative(X)))) | generous(john) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 33166056909999020459566
% SZS output start Proof for 33166056909999020459566
1. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (patient(X0) & ~patient(X0))) [input p0]
6. ! [X0] : ((~kind(X0) & ~calm(X0)) <=> creative(X0)) [input p5]
9. ! [X0] : (creative(X0) <=> (~generous(X0) | creative(X0))) [input p8]
24. ~generous(john) [input hypothesis]
30. ! [X0] : ((patient(X0) & ~patient(X0)) | (quiet(X0) & calm(X0))) [ennf transformation 1]
43. ! [X0] : (((~kind(X0) & ~calm(X0)) | ~creative(X0)) & (creative(X0) | (kind(X0) | calm(X0)))) [nnf transformation 6]
44. ! [X0] : (((~kind(X0) & ~calm(X0)) | ~creative(X0)) & (creative(X0) | kind(X0) | calm(X0))) [flattening 43]
50. ! [X0] : ((creative(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | ~creative(X0))) [nnf transformation 9]
51. ! [X0] : ((creative(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | ~creative(X0))) [flattening 50]
76. ~patient(X0) | calm(X0) [cnf transformation 30]
78. patient(X0) | calm(X0) [cnf transformation 30]
91. ~calm(X0) | ~creative(X0) [cnf transformation 44]
105. creative(X0) | generous(X0) [cnf transformation 51]
143. ~generous(john) [cnf transformation 24]
147. calm(X0) [subsumption resolution 76,78]
163. ~creative(X0) [subsumption resolution 91,147]
180. generous(X0) [subsumption resolution 105,163]
206. $false [subsumption resolution 143,180]
% SZS output end Proof for 33166056909999020459566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either patient or not happy. Everyone who is either calm or brave is kind or curious. Everyone who is strong or not quiet is either curious or funny and vice versa. If paul is either generous or not generous then alice is either humble or wise and vice versa. If someone is both not tall and not generous then alice is both brave and not creative and vice versa. Everyone who is not quiet is not humble or creative and vice versa. Everyone who is not happy or creative is not calm. Everyone who is quiet or old is not happy. Everyone who is either old or not generous is patient or not creative. Everyone who is either not brave or not happy is humble. Everyone who is either not patient or not funny is not patient or wise. Everyone who is either not happy or strong is not generous and vice versa. If susan is generous or not creative then someone is both not patient and calm and vice versa. If someone is not strong or happy then someone is either wise or funny. If someone is either generous or curious then paul is not generous or not patient. Everyone who is either not patient or not brave is not funny or not brave and vice versa. Susan is both kind and funny. Someone is brave or not creative. Someone is tall. Someone is either not brave or rich. Alice is both not kind and not humble. Mary is either not strong or happy. Someone is strong. Fred is both not wise and not happy. | Susan is strong. | entailment | (![X]:(~quiet(X)=>(patient(X)<~>~happy(X))))&
(![X]:((calm(X)<~>brave(X))=>(kind(X)|curious(X))))&
(![X]:((strong(X)|~quiet(X))<=>(curious(X)<~>funny(X))))&
(((generous(paul)<~>~generous(paul)))<=>((humble(alice)<~>wise(alice))))&
((?[X]:((~tall(X)&~generous(X))))<=>((brave(alice)&~creative(alice))))&
(![X]:(~quiet(X)<=>(~humble(X)|creative(X))))&
(![X]:((~happy(X)|creative(X))=>~calm(X)))&
(![X]:((quiet(X)|old(X))=>~happy(X)))&
(![X]:((old(X)<~>~generous(X))=>(patient(X)|~creative(X))))&
(![X]:((~brave(X)<~>~happy(X))=>humble(X)))&
(![X]:((~patient(X)<~>~funny(X))=>(~patient(X)|wise(X))))&
(![X]:((~happy(X)<~>strong(X))<=>~generous(X)))&
(((generous(susan)|~creative(susan)))<=>(?[X]:((~patient(X)&calm(X)))))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((generous(X)<~>curious(X))))=>((~generous(paul)|~patient(paul))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~funny(X)|~brave(X))))&
((kind(susan)&funny(susan)))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:(tall(X)))&
(?[X]:((~brave(X)<~>rich(X))))&
((~kind(alice)&~humble(alice)))&
((~strong(mary)<~>happy(mary)))&
(?[X]:(strong(X)))&
((~wise(fred)&~happy(fred))) | strong(susan) | [
"p0",
"p5",
"p6",
"p7",
"p11",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 13634655454520882297093
% SZS output start Proof for 13634655454520882297093
1. ! [X0] : (~quiet(X0) => (patient(X0) <~> ~happy(X0))) [input p0]
6. ! [X0] : (~quiet(X0) <=> (creative(X0) | ~humble(X0))) [input p5]
7. ! [X0] : ((creative(X0) | ~happy(X0)) => ~calm(X0)) [input p6]
8. ! [X0] : ((old(X0) | quiet(X0)) => ~happy(X0)) [input p7]
12. ! [X0] : ((~happy(X0) <~> strong(X0)) <=> ~generous(X0)) [input p11]
13. (~creative(susan) | generous(susan)) <=> ? [X0] : (calm(X0) & ~patient(X0)) [input p12]
16. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (~brave(X0) | ~funny(X0))) [input p15]
17. funny(susan) & kind(susan) [input p16]
25. ~strong(susan) [input hypothesis]
27. ! [X0] : ((patient(X0) <~> ~happy(X0)) | quiet(X0)) [ennf transformation 1]
30. ! [X0] : (~calm(X0) | (~creative(X0) & happy(X0))) [ennf transformation 7]
31. ! [X0] : (~happy(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 8]
40. ! [X0] : (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | quiet(X0)) [nnf transformation 27]
50. ! [X0] : ((~quiet(X0) | (~creative(X0) & humble(X0))) & ((creative(X0) | ~humble(X0)) | quiet(X0))) [nnf transformation 6]
51. ! [X0] : ((~quiet(X0) | (~creative(X0) & humble(X0))) & (creative(X0) | ~humble(X0) | quiet(X0))) [flattening 50]
55. ! [X0] : ((((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | generous(X0)) & (~generous(X0) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0))))) [nnf transformation 12]
56. ((~creative(susan) | generous(susan)) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X0] : (calm(X0) & ~patient(X0)) | (creative(susan) & ~generous(susan))) [nnf transformation 13]
57. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X0] : (calm(X0) & ~patient(X0)) | (creative(susan) & ~generous(susan))) [flattening 56]
58. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & (? [X1] : (calm(X1) & ~patient(X1)) | (creative(susan) & ~generous(susan))) [rectify 57]
59. ? [X1] : (calm(X1) & ~patient(X1)) => (calm(sK1) & ~patient(sK1)) [choice axiom]
60. (~creative(susan) | generous(susan) | ! [X0] : (~calm(X0) | patient(X0))) & ((calm(sK1) & ~patient(sK1)) | (creative(susan) & ~generous(susan))) [skolemisation 58,59]
66. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 16]
67. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 66]
78. ~happy(X0) | patient(X0) | quiet(X0) [cnf transformation 40]
79. ~patient(X0) | happy(X0) | quiet(X0) [cnf transformation 40]
102. ~creative(X0) | ~quiet(X0) [cnf transformation 51]
103. ~calm(X0) | happy(X0) [cnf transformation 30]
105. ~happy(X0) | ~quiet(X0) [cnf transformation 31]
115. ~happy(X0) | strong(X0) | generous(X0) [cnf transformation 55]
117. ~patient(sK1) | ~generous(susan) [cnf transformation 60]
118. ~patient(sK1) | creative(susan) [cnf transformation 60]
119. calm(sK1) | ~generous(susan) [cnf transformation 60]
120. calm(sK1) | creative(susan) [cnf transformation 60]
128. ~brave(X0) | ~funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 67]
133. brave(X0) | patient(X0) | brave(X0) [cnf transformation 67]
135. funny(susan) [cnf transformation 17]
147. ~strong(susan) [cnf transformation 25]
148. ~brave(X0) | ~funny(X0) | patient(X0) [duplicate literal removal 128]
149. brave(X0) | patient(X0) [duplicate literal removal 133]
198. 10 <=> generous(susan) [avatar definition]
199. ~generous(susan) <- (~10) [avatar component clause 198]
202. 11 <=> creative(susan) [avatar definition]
203. creative(susan) <- (11) [avatar component clause 202]
207. 12 <=> calm(sK1) [avatar definition]
209. calm(sK1) <- (12) [avatar component clause 207]
210. 11 | 12 [avatar split clause 120,207,202]
211. ~10 | 12 [avatar split clause 119,207,198]
213. 13 <=> patient(sK1) [avatar definition]
215. ~patient(sK1) <- (~13) [avatar component clause 213]
216. 11 | ~13 [avatar split clause 118,213,202]
217. ~10 | ~13 [avatar split clause 117,213,198]
248. ~funny(X0) | patient(X0) [subsumption resolution 148,149]
279. ~quiet(susan) <- (11) [resolution 102,203]
282. patient(susan) [resolution 248,135]
284. happy(susan) | quiet(susan) [resolution 79,282]
294. happy(susan) <- (11) [subsumption resolution 284,279]
383. strong(susan) | generous(susan) <- (11) [resolution 115,294]
393. generous(susan) <- (11) [subsumption resolution 383,147]
394. $false <- (~10, 11) [subsumption resolution 393,199]
395. 10 | ~11 [avatar contradiction clause 394]
411. happy(sK1) <- (12) [resolution 209,103]
447. patient(sK1) | quiet(sK1) <- (12) [resolution 411,78]
448. ~quiet(sK1) <- (12) [resolution 411,105]
467. quiet(sK1) <- (12, ~13) [subsumption resolution 447,215]
468. $false <- (12, ~13) [subsumption resolution 448,467]
469. ~12 | 13 [avatar contradiction clause 468]
470. $false [avatar sat refutation 210,211,216,217,395,469]
% SZS output end Proof for 13634655454520882297093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or calm is both not quiet and not kind.
Everyone who is either wise or not tall is not patient or not generous.
Everyone who is kind is either not funny or not curious.
Everyone who is both not wise and not old is either generous or not rich.
Everyone who is either kind or calm is not curious and vice versa.
Everyone who is not humble is either not wise or humble.
If mary is kind then alice is tall or not curious and vice versa.
If john is both strong and not strong then someone is both curious and quiet and vice versa.
Everyone who is either tall or funny is both not calm and not curious and vice versa.
Everyone who is either quiet or strong is calm or not wise.
If someone is not wise or not humble then alice is both funny and quiet.
Everyone who is not rich is either tall or creative and vice versa.
If someone is not kind or generous then alice is brave or not quiet.
If paul is not creative then lucy is brave or quiet and vice versa.
If john is curious or not curious then someone is both happy and curious and vice versa.
Everyone who is quiet or not happy is either strong or happy and vice versa.
Someone is not quiet or not brave.
Paul is not quiet.
Someone is brave or wise.
Paul is rich or patient.
John is not curious or not kind.
Alice is not rich. | John is not rich. | neutral | (![X]:((wise(X)|calm(X))=>(~quiet(X)&~kind(X))))&
(![X]:((wise(X)<~>~tall(X))=>(~patient(X)|~generous(X))))&
(![X]:(kind(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~wise(X)&~old(X))=>(generous(X)<~>~rich(X))))&
(![X]:((kind(X)<~>calm(X))<=>~curious(X)))&
(![X]:(~humble(X)=>(~wise(X)<~>humble(X))))&
((kind(mary))<=>((tall(alice)|~curious(alice))))&
(((strong(john)&~strong(john)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(~calm(X)&~curious(X))))&
(![X]:((quiet(X)<~>strong(X))=>(calm(X)|~wise(X))))&
((?[X]:((~wise(X)|~humble(X))))=>((funny(alice)&quiet(alice))))&
(![X]:(~rich(X)<=>(tall(X)<~>creative(X))))&
((?[X]:((~kind(X)|generous(X))))=>((brave(alice)|~quiet(alice))))&
((~creative(paul))<=>((brave(lucy)|quiet(lucy))))&
(((curious(john)|~curious(john)))<=>(?[X]:((happy(X)&curious(X)))))&
(![X]:((quiet(X)|~happy(X))<=>(strong(X)<~>happy(X))))&
(?[X]:((~quiet(X)|~brave(X))))&
(~quiet(paul))&
(?[X]:((brave(X)|wise(X))))&
((rich(paul)|patient(paul)))&
((~curious(john)|~kind(john)))&
(~rich(alice)) | ~rich(john) | [] | null | 0 |
If john is not patient or not kind then someone is both brave and old and vice versa.
If susan is not tall or not wise then fred is not funny or not creative.
If someone is rich then fred is funny.
If paul is either not creative or tall then someone is not generous and vice versa.
If someone is both not curious and old then alice is both wise and not tall.
If fred is not old then someone is not brave.
If someone is either patient or not old then alice is both generous and funny and vice versa.
Everyone who is rich is funny.
Everyone who is tall is either kind or humble and vice versa.
Everyone who is either tall or funny is either funny or not humble and vice versa.
If mary is either not calm or not generous then someone is kind.
Everyone who is not curious or brave is either not old or not happy and vice versa.
If someone is either brave or creative then someone is not brave and vice versa.
Everyone who is curious is funny.
If lucy is funny then fred is not quiet and vice versa.
Everyone who is calm is either funny or not rich and vice versa.
Fred is tall.
Someone is either quiet or old.
Lucy is not funny.
Fred is not generous.
Mary is both calm and patient.
Fred is both not brave and not creative.
Paul is creative.
Susan is both tall and not rich. | Paul is not tall. | contradiction | (((~patient(john)|~kind(john)))<=>(?[X]:((brave(X)&old(X)))))&
(((~tall(susan)|~wise(susan)))=>((~funny(fred)|~creative(fred))))&
((?[X]:(rich(X)))=>(funny(fred)))&
(((~creative(paul)<~>tall(paul)))<=>(?[X]:(~generous(X))))&
((?[X]:((~curious(X)&old(X))))=>((wise(alice)&~tall(alice))))&
((~old(fred))=>(?[X]:(~brave(X))))&
((?[X]:((patient(X)<~>~old(X))))<=>((generous(alice)&funny(alice))))&
(![X]:(rich(X)=>funny(X)))&
(![X]:(tall(X)<=>(kind(X)<~>humble(X))))&
(![X]:((tall(X)<~>funny(X))<=>(funny(X)<~>~humble(X))))&
(((~calm(mary)<~>~generous(mary)))=>(?[X]:(kind(X))))&
(![X]:((~curious(X)|brave(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((brave(X)<~>creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>funny(X)))&
((funny(lucy))<=>(~quiet(fred)))&
(![X]:(calm(X)<=>(funny(X)<~>~rich(X))))&
(tall(fred))&
(?[X]:((quiet(X)<~>old(X))))&
(~funny(lucy))&
(~generous(fred))&
((calm(mary)&patient(mary)))&
((~brave(fred)&~creative(fred)))&
(creative(paul))&
((tall(susan)&~rich(susan))) | ~tall(paul) | [
"p3",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8138892854614638807559163
% SZS output start Proof for 8138892854614638807559163
4. (~creative(paul) <~> tall(paul)) <=> ? [X0] : ~generous(X0) [input p3]
20. ~generous(fred) [input p19]
23. creative(paul) [input p22]
25. ~tall(paul) [input hypothesis]
42. (((~tall(paul) | creative(paul)) & (tall(paul) | ~creative(paul))) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ((~creative(paul) | ~tall(paul)) & (tall(paul) | creative(paul)))) [nnf transformation 4]
43. (((~tall(paul) | creative(paul)) & (tall(paul) | ~creative(paul))) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ((~creative(paul) | ~tall(paul)) & (tall(paul) | creative(paul)))) [rectify 42]
44. ? [X1] : ~generous(X1) => ~generous(sK1) [choice axiom]
45. (((~tall(paul) | creative(paul)) & (tall(paul) | ~creative(paul))) | ! [X0] : generous(X0)) & (~generous(sK1) | ((~creative(paul) | ~tall(paul)) & (tall(paul) | creative(paul)))) [skolemisation 43,44]
79. tall(paul) | ~creative(paul) | generous(X0) [cnf transformation 45]
125. ~generous(fred) [cnf transformation 20]
130. creative(paul) [cnf transformation 23]
133. ~tall(paul) [cnf transformation 25]
180. 10 <=> ! [X0] : generous(X0) [avatar definition]
181. generous(X0) <- (10) [avatar component clause 180]
183. 11 <=> creative(paul) [avatar definition]
187. 12 <=> tall(paul) [avatar definition]
191. 10 | ~11 | 12 [avatar split clause 79,187,183,180]
309. 11 [avatar split clause 130,183]
311. ~12 [avatar split clause 133,187]
314. $false <- (10) [resolution 181,125]
315. ~10 [avatar contradiction clause 314]
316. $false [avatar sat refutation 191,309,311,315]
% SZS output end Proof for 8138892854614638807559163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or humble then paul is not humble or strong and vice versa.
If someone is not rich then fred is not curious or funny.
Everyone who is funny is both calm and curious.
Everyone who is not generous or tall is either not wise or not funny.
Everyone who is not happy or not curious is kind or happy and vice versa.
If alice is either strong or tall then someone is either wise or old.
Everyone who is either not curious or creative is not funny and vice versa.
Everyone who is both creative and funny is not calm or funny and vice versa.
Everyone who is either patient or humble is not humble.
Everyone who is patient or curious is not brave.
Everyone who is not quiet or not happy is either not brave or not kind and vice versa.
If alice is brave then alice is not generous or not creative and vice versa.
If someone is either not calm or not strong then paul is curious and vice versa.
If someone is both not old and not patient then someone is both not generous and kind and vice versa.
Everyone who is not kind is either not patient or wise.
Everyone who is not tall is not kind or quiet and vice versa.
Someone is not wise or not generous.
Fred is not patient.
Fred is not curious.
Someone is either patient or rich.
Someone is not patient.
Someone is not calm or kind. | Alice is curious. | neutral | ((?[X]:((~rich(X)|humble(X))))<=>((~humble(paul)|strong(paul))))&
((?[X]:(~rich(X)))=>((~curious(fred)|funny(fred))))&
(![X]:(funny(X)=>(calm(X)&curious(X))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((~happy(X)|~curious(X))<=>(kind(X)|happy(X))))&
(((strong(alice)<~>tall(alice)))=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((~curious(X)<~>creative(X))<=>~funny(X)))&
(![X]:((creative(X)&funny(X))<=>(~calm(X)|funny(X))))&
(![X]:((patient(X)<~>humble(X))=>~humble(X)))&
(![X]:((patient(X)|curious(X))=>~brave(X)))&
(![X]:((~quiet(X)|~happy(X))<=>(~brave(X)<~>~kind(X))))&
((brave(alice))<=>((~generous(alice)|~creative(alice))))&
((?[X]:((~calm(X)<~>~strong(X))))<=>(curious(paul)))&
((?[X]:((~old(X)&~patient(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>wise(X))))&
(![X]:(~tall(X)<=>(~kind(X)|quiet(X))))&
(?[X]:((~wise(X)|~generous(X))))&
(~patient(fred))&
(~curious(fred))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)|kind(X)))) | curious(alice) | [] | null | 0 |
Everyone who is either not strong or not happy is not tall and vice versa.
Everyone who is both brave and not strong is not kind.
Everyone who is either brave or not brave is rich or kind.
If alice is funny or strong then mary is both not patient and humble and vice versa.
If someone is quiet or not funny then someone is both not humble and patient and vice versa.
If someone is strong then someone is both not creative and strong.
If someone is not quiet then someone is either strong or brave.
If someone is both quiet and tall then fred is not brave or not happy.
Everyone who is not generous is not happy or strong.
Everyone who is both humble and not patient is not tall and vice versa.
Everyone who is not old is not rich and vice versa.
If someone is both strong and not calm then someone is strong and vice versa.
If susan is both not kind and not calm then someone is kind or funny and vice versa.
Everyone who is either not quiet or quiet is strong.
Everyone who is generous is old or not rich and vice versa.
If lucy is either quiet or kind then fred is not quiet or not brave and vice versa.
Someone is old or not generous.
Someone is either not old or happy.
Someone is either happy or strong.
Someone is both not funny and not creative.
Someone is not strong or not patient.
Paul is either not quiet or not generous.
Susan is either tall or funny.
Someone is both not patient and brave. | Fred is strong. | entailment | (![X]:((~strong(X)<~>~happy(X))<=>~tall(X)))&
(![X]:((brave(X)&~strong(X))=>~kind(X)))&
(![X]:((brave(X)<~>~brave(X))=>(rich(X)|kind(X))))&
(((funny(alice)|strong(alice)))<=>((~patient(mary)&humble(mary))))&
((?[X]:((quiet(X)|~funny(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:(strong(X)))=>(?[X]:((~creative(X)&strong(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((strong(X)<~>brave(X)))))&
((?[X]:((quiet(X)&tall(X))))=>((~brave(fred)|~happy(fred))))&
(![X]:(~generous(X)=>(~happy(X)|strong(X))))&
(![X]:((humble(X)&~patient(X))<=>~tall(X)))&
(![X]:(~old(X)<=>~rich(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:(strong(X))))&
(((~kind(susan)&~calm(susan)))<=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((~quiet(X)<~>quiet(X))=>strong(X)))&
(![X]:(generous(X)<=>(old(X)|~rich(X))))&
(((quiet(lucy)<~>kind(lucy)))<=>((~quiet(fred)|~brave(fred))))&
(?[X]:((old(X)|~generous(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:((happy(X)<~>strong(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((~strong(X)|~patient(X))))&
((~quiet(paul)<~>~generous(paul)))&
((tall(susan)<~>funny(susan)))&
(?[X]:((~patient(X)&brave(X)))) | strong(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1466857112505904880277617
% SZS output start Proof for 1466857112505904880277617
14. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => strong(X0)) [input p13]
25. ~strong(fred) [input hypothesis]
42. ! [X0] : (strong(X0) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 14]
72. ! [X0] : (strong(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 42]
128. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 72]
129. strong(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 72]
152. ~strong(fred) [cnf transformation 25]
153. strong(X0) | quiet(X0) [duplicate literal removal 128]
154. strong(X0) | ~quiet(X0) [duplicate literal removal 129]
287. strong(X0) [subsumption resolution 153,154]
347. $false [subsumption resolution 152,287]
% SZS output end Proof for 1466857112505904880277617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both rich and wise then someone is either funny or not old and vice versa.
Everyone who is both not curious and curious is not brave and vice versa.
Everyone who is rich is both kind and creative.
Everyone who is either tall or not curious is either not calm or brave.
If lucy is tall or quiet then alice is both old and not creative.
Everyone who is not humble is not quiet.
If paul is humble or not old then someone is not strong and vice versa.
Everyone who is not generous or funny is not rich or funny and vice versa.
Everyone who is not rich or generous is both not humble and not generous.
Everyone who is either not curious or not patient is either not patient or not humble.
If someone is brave or not calm then fred is old or not strong and vice versa.
Everyone who is both funny and not patient is old.
Everyone who is both creative and calm is both not tall and not humble and vice versa.
Everyone who is either not patient or not kind is either happy or patient and vice versa.
Everyone who is not generous or brave is not generous and vice versa.
If someone is kind then alice is both not wise and not calm and vice versa.
Someone is either tall or not creative.
Fred is both not humble and not patient.
Fred is both happy and not tall.
Someone is not calm or not quiet.
Someone is both tall and not patient.
Someone is not strong or not humble.
Mary is either calm or funny.
Lucy is both not funny and not calm. | Alice is old. | entailment | (((rich(paul)&wise(paul)))<=>(?[X]:((funny(X)<~>~old(X)))))&
(![X]:((~curious(X)&curious(X))<=>~brave(X)))&
(![X]:(rich(X)=>(kind(X)&creative(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~calm(X)<~>brave(X))))&
(((tall(lucy)|quiet(lucy)))=>((old(alice)&~creative(alice))))&
(![X]:(~humble(X)=>~quiet(X)))&
(((humble(paul)|~old(paul)))<=>(?[X]:(~strong(X))))&
(![X]:((~generous(X)|funny(X))<=>(~rich(X)|funny(X))))&
(![X]:((~rich(X)|generous(X))=>(~humble(X)&~generous(X))))&
(![X]:((~curious(X)<~>~patient(X))=>(~patient(X)<~>~humble(X))))&
((?[X]:((brave(X)|~calm(X))))<=>((old(fred)|~strong(fred))))&
(![X]:((funny(X)&~patient(X))=>old(X)))&
(![X]:((creative(X)&calm(X))<=>(~tall(X)&~humble(X))))&
(![X]:((~patient(X)<~>~kind(X))<=>(happy(X)<~>patient(X))))&
(![X]:((~generous(X)|brave(X))<=>~generous(X)))&
((?[X]:(kind(X)))<=>((~wise(alice)&~calm(alice))))&
(?[X]:((tall(X)<~>~creative(X))))&
((~humble(fred)&~patient(fred)))&
((happy(fred)&~tall(fred)))&
(?[X]:((~calm(X)|~quiet(X))))&
(?[X]:((tall(X)&~patient(X))))&
(?[X]:((~strong(X)|~humble(X))))&
((calm(mary)<~>funny(mary)))&
((~funny(lucy)&~calm(lucy))) | old(alice) | [
"p4",
"p7",
"p8",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 154524920033976771642145
% SZS output start Proof for 154524920033976771642145
5. (quiet(lucy) | tall(lucy)) => (~creative(alice) & old(alice)) [input p4]
8. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (funny(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((generous(X0) | ~rich(X0)) => (~generous(X0) & ~humble(X0))) [input p8]
13. ! [X0] : ((calm(X0) & creative(X0)) <=> (~humble(X0) & ~tall(X0))) [input p12]
24. ~calm(lucy) & ~funny(lucy) [input p23]
25. ~old(alice) [input hypothesis]
27. tall(lucy) => (~creative(alice) & old(alice)) [pure predicate removal 5]
31. (~creative(alice) & old(alice)) | ~tall(lucy) [ennf transformation 27]
32. ! [X0] : ((~generous(X0) & ~humble(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 9]
49. ! [X0] : (((funny(X0) | ~generous(X0)) | (~funny(X0) & rich(X0))) & ((funny(X0) | ~rich(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 8]
50. ! [X0] : ((funny(X0) | ~generous(X0) | (~funny(X0) & rich(X0))) & (funny(X0) | ~rich(X0) | (~funny(X0) & generous(X0)))) [flattening 49]
57. ! [X0] : (((calm(X0) & creative(X0)) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | (~calm(X0) | ~creative(X0)))) [nnf transformation 13]
58. ! [X0] : (((calm(X0) & creative(X0)) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | ~calm(X0) | ~creative(X0))) [flattening 57]
90. old(alice) | ~tall(lucy) [cnf transformation 31]
95. ~rich(X0) | funny(X0) | generous(X0) [cnf transformation 50]
99. ~humble(X0) | rich(X0) [cnf transformation 32]
102. ~generous(X0) | ~generous(X0) [cnf transformation 32]
115. humble(X0) | calm(X0) | tall(X0) [cnf transformation 58]
141. ~funny(lucy) [cnf transformation 24]
142. ~calm(lucy) [cnf transformation 24]
143. ~old(alice) [cnf transformation 25]
150. ~generous(X0) [duplicate literal removal 102]
183. 7 <=> tall(lucy) [avatar definition]
185. ~tall(lucy) <- (~7) [avatar component clause 183]
192. 9 <=> old(alice) [avatar definition]
195. ~7 | 9 [avatar split clause 90,192,183]
277. ~9 [avatar split clause 143,192]
307. calm(X1) | tall(X1) | rich(X1) [resolution 115,99]
414. tall(lucy) | rich(lucy) [resolution 307,142]
416. rich(lucy) <- (~7) [subsumption resolution 414,185]
419. funny(lucy) | generous(lucy) <- (~7) [resolution 416,95]
422. generous(lucy) <- (~7) [subsumption resolution 419,141]
423. $false <- (~7) [subsumption resolution 422,150]
424. 7 [avatar contradiction clause 423]
425. $false [avatar sat refutation 195,277,424]
% SZS output end Proof for 154524920033976771642145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not strong then someone is calm or not brave.
If fred is not curious then susan is either tall or patient.
Everyone who is rich or humble is both not funny and not generous and vice versa.
If mary is brave then john is humble and vice versa.
Everyone who is not happy or generous is both not humble and not quiet.
Everyone who is funny or not brave is not strong.
If lucy is either strong or patient then someone is either happy or old and vice versa.
If someone is humble then john is either not curious or funny and vice versa.
Everyone who is creative is calm or not funny and vice versa.
Everyone who is either humble or strong is both funny and not happy.
If someone is not patient or not generous then someone is quiet or not brave.
Everyone who is not happy or happy is quiet or calm.
Everyone who is not quiet is either not funny or rich.
If someone is not happy or not humble then john is generous and vice versa.
Everyone who is not wise or creative is both happy and creative and vice versa.
Everyone who is either not strong or wise is either happy or not strong.
Susan is not humble or brave.
Fred is strong or brave.
Someone is not tall or not quiet.
Lucy is not funny.
Someone is either wise or not curious.
Lucy is both calm and strong.
Someone is creative or not brave.
Someone is creative or calm. | Lucy is wise. | neutral | ((?[X]:((tall(X)&~strong(X))))=>(?[X]:((calm(X)|~brave(X)))))&
((~curious(fred))=>((tall(susan)<~>patient(susan))))&
(![X]:((rich(X)|humble(X))<=>(~funny(X)&~generous(X))))&
((brave(mary))<=>(humble(john)))&
(![X]:((~happy(X)|generous(X))=>(~humble(X)&~quiet(X))))&
(![X]:((funny(X)|~brave(X))=>~strong(X)))&
(((strong(lucy)<~>patient(lucy)))<=>(?[X]:((happy(X)<~>old(X)))))&
((?[X]:(humble(X)))<=>((~curious(john)<~>funny(john))))&
(![X]:(creative(X)<=>(calm(X)|~funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(funny(X)&~happy(X))))&
((?[X]:((~patient(X)|~generous(X))))=>(?[X]:((quiet(X)|~brave(X)))))&
(![X]:((~happy(X)|happy(X))=>(quiet(X)|calm(X))))&
(![X]:(~quiet(X)=>(~funny(X)<~>rich(X))))&
((?[X]:((~happy(X)|~humble(X))))<=>(generous(john)))&
(![X]:((~wise(X)|creative(X))<=>(happy(X)&creative(X))))&
(![X]:((~strong(X)<~>wise(X))=>(happy(X)<~>~strong(X))))&
((~humble(susan)|brave(susan)))&
((strong(fred)|brave(fred)))&
(?[X]:((~tall(X)|~quiet(X))))&
(~funny(lucy))&
(?[X]:((wise(X)<~>~curious(X))))&
((calm(lucy)&strong(lucy)))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((creative(X)|calm(X)))) | wise(lucy) | [] | null | 0 |
If someone is either not humble or not kind then alice is patient and vice versa.
Everyone who is either not strong or strong is both brave and creative and vice versa.
If lucy is not patient or curious then john is both not generous and generous.
Everyone who is either funny or quiet is not kind.
If someone is either not kind or not rich then someone is both calm and funny.
Everyone who is either quiet or happy is both tall and happy.
Everyone who is either rich or not generous is either not quiet or wise.
Everyone who is patient or creative is tall or old.
Everyone who is not patient or not calm is not wise or humble and vice versa.
Everyone who is both not wise and creative is both not calm and strong and vice versa.
Everyone who is not humble is not patient and vice versa.
If someone is tall or not humble then fred is not calm and vice versa.
Everyone who is not tall or brave is curious or not rich and vice versa.
Everyone who is either creative or not calm is both not happy and not rich and vice versa.
If someone is not generous then someone is either strong or quiet and vice versa.
Everyone who is either old or calm is either old or patient.
Someone is either not wise or not happy.
John is both not strong and patient.
Fred is quiet or not wise.
Mary is either quiet or wise.
Someone is both kind and patient.
Someone is not rich.
Paul is tall. | Alice is tall. | entailment | ((?[X]:((~humble(X)<~>~kind(X))))<=>(patient(alice)))&
(![X]:((~strong(X)<~>strong(X))<=>(brave(X)&creative(X))))&
(((~patient(lucy)|curious(lucy)))=>((~generous(john)&generous(john))))&
(![X]:((funny(X)<~>quiet(X))=>~kind(X)))&
((?[X]:((~kind(X)<~>~rich(X))))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((quiet(X)<~>happy(X))=>(tall(X)&happy(X))))&
(![X]:((rich(X)<~>~generous(X))=>(~quiet(X)<~>wise(X))))&
(![X]:((patient(X)|creative(X))=>(tall(X)|old(X))))&
(![X]:((~patient(X)|~calm(X))<=>(~wise(X)|humble(X))))&
(![X]:((~wise(X)&creative(X))<=>(~calm(X)&strong(X))))&
(![X]:(~humble(X)<=>~patient(X)))&
((?[X]:((tall(X)|~humble(X))))<=>(~calm(fred)))&
(![X]:((~tall(X)|brave(X))<=>(curious(X)|~rich(X))))&
(![X]:((creative(X)<~>~calm(X))<=>(~happy(X)&~rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((old(X)<~>calm(X))=>(old(X)<~>patient(X))))&
(?[X]:((~wise(X)<~>~happy(X))))&
((~strong(john)&patient(john)))&
((quiet(fred)|~wise(fred)))&
((quiet(mary)<~>wise(mary)))&
(?[X]:((kind(X)&patient(X))))&
(?[X]:(~rich(X)))&
(tall(paul)) | tall(alice) | [
"p0",
"p1",
"p2",
"p4",
"p7",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7063552727279018405234758
% SZS output start Proof for 7063552727279018405234758
1. ? [X0] : (~humble(X0) <~> ~kind(X0)) <=> patient(alice) [input p0]
2. ! [X0] : ((~strong(X0) <~> strong(X0)) <=> (creative(X0) & brave(X0))) [input p1]
3. (curious(lucy) | ~patient(lucy)) => (generous(john) & ~generous(john)) [input p2]
5. ? [X0] : (~kind(X0) <~> ~rich(X0)) => ? [X0] : (funny(X0) & calm(X0)) [input p4]
8. ! [X0] : ((creative(X0) | patient(X0)) => (old(X0) | tall(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | ~patient(X0)) <=> (humble(X0) | ~wise(X0))) [input p8]
10. ! [X0] : ((creative(X0) & ~wise(X0)) <=> (strong(X0) & ~calm(X0))) [input p9]
11. ! [X0] : (~humble(X0) <=> ~patient(X0)) [input p10]
13. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (~rich(X0) | curious(X0))) [input p12]
16. ! [X0] : ((old(X0) <~> calm(X0)) => (old(X0) <~> patient(X0))) [input p15]
24. ~tall(alice) [input hypothesis]
25. ? [X0] : (~kind(X0) <~> ~rich(X0)) => ? [X1] : (funny(X1) & calm(X1)) [rectify 5]
27. (generous(john) & ~generous(john)) | (~curious(lucy) & patient(lucy)) [ennf transformation 3]
29. ? [X1] : (funny(X1) & calm(X1)) | ! [X0] : (~kind(X0) <=> ~rich(X0)) [ennf transformation 25]
32. ! [X0] : ((old(X0) | tall(X0)) | (~creative(X0) & ~patient(X0))) [ennf transformation 8]
33. ! [X0] : (old(X0) | tall(X0) | (~creative(X0) & ~patient(X0))) [flattening 32]
34. ! [X0] : ((old(X0) <~> patient(X0)) | (old(X0) <=> calm(X0))) [ennf transformation 16]
35. (? [X0] : ((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | ~patient(alice)) & (patient(alice) | ! [X0] : ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0)))) [nnf transformation 1]
36. (? [X0] : ((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | ~patient(alice)) & (patient(alice) | ! [X1] : ((~humble(X1) | kind(X1)) & (~kind(X1) | humble(X1)))) [rectify 35]
37. ? [X0] : ((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) => ((kind(sK0) | humble(sK0)) & (~kind(sK0) | ~humble(sK0))) [choice axiom]
38. (((kind(sK0) | humble(sK0)) & (~kind(sK0) | ~humble(sK0))) | ~patient(alice)) & (patient(alice) | ! [X1] : ((~humble(X1) | kind(X1)) & (~kind(X1) | humble(X1)))) [skolemisation 36,37]
39. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [flattening 39]
42. ? [X1] : (funny(X1) & calm(X1)) | ! [X0] : ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0))) [nnf transformation 29]
43. ? [X0] : (funny(X0) & calm(X0)) | ! [X1] : ((~kind(X1) | rich(X1)) & (~rich(X1) | kind(X1))) [rectify 42]
44. ? [X0] : (funny(X0) & calm(X0)) => (funny(sK1) & calm(sK1)) [choice axiom]
45. (funny(sK1) & calm(sK1)) | ! [X1] : ((~kind(X1) | rich(X1)) & (~rich(X1) | kind(X1))) [skolemisation 43,44]
48. ! [X0] : (((~calm(X0) | ~patient(X0)) | (~humble(X0) & wise(X0))) & ((humble(X0) | ~wise(X0)) | (calm(X0) & patient(X0)))) [nnf transformation 9]
49. ! [X0] : ((~calm(X0) | ~patient(X0) | (~humble(X0) & wise(X0))) & (humble(X0) | ~wise(X0) | (calm(X0) & patient(X0)))) [flattening 48]
50. ! [X0] : (((creative(X0) & ~wise(X0)) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | (~creative(X0) | wise(X0)))) [nnf transformation 10]
51. ! [X0] : (((creative(X0) & ~wise(X0)) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | ~creative(X0) | wise(X0))) [flattening 50]
52. ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0))) [nnf transformation 11]
57. ! [X0] : (((brave(X0) | ~tall(X0)) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | (~brave(X0) & tall(X0)))) [nnf transformation 13]
58. ! [X0] : ((brave(X0) | ~tall(X0) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | (~brave(X0) & tall(X0)))) [flattening 57]
66. ! [X0] : (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) [nnf transformation 34]
76. patient(alice) | ~humble(X1) | kind(X1) [cnf transformation 38]
79. brave(X0) | strong(X0) | strong(X0) [cnf transformation 40]
80. brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
81. creative(X0) | strong(X0) | strong(X0) [cnf transformation 40]
82. creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
85. ~generous(john) | patient(lucy) [cnf transformation 27]
86. ~generous(john) | ~curious(lucy) [cnf transformation 27]
87. generous(john) | patient(lucy) [cnf transformation 27]
88. generous(john) | ~curious(lucy) [cnf transformation 27]
92. calm(sK1) | ~kind(X1) | rich(X1) [cnf transformation 45]
104. old(X0) | tall(X0) | ~creative(X0) [cnf transformation 33]
105. ~wise(X0) | humble(X0) | patient(X0) [cnf transformation 49]
108. ~calm(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 49]
109. ~calm(X0) | ~creative(X0) | wise(X0) [cnf transformation 51]
113. ~patient(X0) | humble(X0) [cnf transformation 52]
114. ~humble(X0) | patient(X0) [cnf transformation 52]
119. ~rich(X0) | curious(X0) | ~brave(X0) [cnf transformation 58]
134. ~patient(X0) | ~old(X0) | calm(X0) | ~old(X0) [cnf transformation 66]
147. ~tall(alice) [cnf transformation 24]
149. ~old(X0) | ~patient(X0) | calm(X0) [duplicate literal removal 134]
151. brave(X0) | strong(X0) [duplicate literal removal 79]
152. ~strong(X0) | brave(X0) [duplicate literal removal 80]
153. creative(X0) | strong(X0) [duplicate literal removal 81]
154. ~strong(X0) | creative(X0) [duplicate literal removal 82]
156. 1 <=> patient(alice) [avatar definition]
157. patient(alice) <- (1) [avatar component clause 156]
170. 4 <=> ! [X1] : (~humble(X1) | kind(X1)) [avatar definition]
171. ~humble(X1) | kind(X1) <- (4) [avatar component clause 170]
172. 4 | 1 [avatar split clause 76,156,170]
177. creative(X0) [subsumption resolution 153,154]
178. brave(X0) [subsumption resolution 151,152]
180. 6 <=> curious(lucy) [avatar definition]
182. ~curious(lucy) <- (~6) [avatar component clause 180]
184. 7 <=> generous(john) [avatar definition]
187. ~6 | 7 [avatar split clause 88,184,180]
189. 8 <=> patient(lucy) [avatar definition]
191. patient(lucy) <- (8) [avatar component clause 189]
192. 8 | 7 [avatar split clause 87,184,189]
193. ~6 | ~7 [avatar split clause 86,184,180]
194. 8 | ~7 [avatar split clause 85,184,189]
196. 9 <=> ! [X1] : (~kind(X1) | rich(X1)) [avatar definition]
197. ~kind(X1) | rich(X1) <- (9) [avatar component clause 196]
208. 12 <=> calm(sK1) [avatar definition]
210. calm(sK1) <- (12) [avatar component clause 208]
211. 9 | 12 [avatar split clause 92,208,196]
213. old(X0) | tall(X0) [subsumption resolution 104,177]
215. ~calm(X0) | wise(X0) [subsumption resolution 109,177]
237. ~rich(X0) | curious(X0) [subsumption resolution 119,178]
299. humble(lucy) <- (8) [resolution 113,191]
306. kind(lucy) <- (4, 8) [resolution 171,299]
312. rich(lucy) <- (4, 8, 9) [resolution 197,306]
324. curious(lucy) <- (4, 8, 9) [resolution 237,312]
325. $false <- (4, ~6, 8, 9) [subsumption resolution 324,182]
326. ~4 | 6 | ~8 | ~9 [avatar contradiction clause 325]
327. humble(alice) <- (1) [resolution 157,113]
393. ~patient(X0) | calm(X0) | tall(X0) [resolution 149,213]
489. calm(alice) | tall(alice) <- (1) [resolution 393,157]
496. calm(alice) <- (1) [subsumption resolution 489,147]
555. ~patient(alice) | ~humble(alice) <- (1) [resolution 496,108]
559. ~humble(alice) <- (1) [subsumption resolution 555,157]
560. $false <- (1) [subsumption resolution 559,327]
561. ~1 [avatar contradiction clause 560]
574. ~patient(sK1) | ~humble(sK1) <- (12) [resolution 210,108]
577. wise(sK1) <- (12) [resolution 210,215]
579. 57 <=> patient(sK1) [avatar definition]
580. ~patient(sK1) <- (~57) [avatar component clause 579]
587. ~patient(sK1) <- (12) [subsumption resolution 574,113]
588. ~57 | ~12 [avatar split clause 587,208,579]
590. 59 <=> wise(sK1) [avatar definition]
592. wise(sK1) <- (59) [avatar component clause 590]
594. 59 | ~12 [avatar split clause 577,208,590]
624. humble(sK1) | patient(sK1) <- (59) [resolution 592,105]
627. humble(sK1) <- (~57, 59) [subsumption resolution 624,580]
651. patient(sK1) <- (~57, 59) [resolution 627,114]
654. $false <- (~57, 59) [subsumption resolution 651,580]
655. 57 | ~59 [avatar contradiction clause 654]
656. $false [avatar sat refutation 172,187,192,193,194,211,326,561,588,594,655]
% SZS output end Proof for 7063552727279018405234758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not strong is either not kind or kind and vice versa.
If someone is either happy or not patient then someone is tall or funny.
Everyone who is not wise or not curious is generous and vice versa.
Everyone who is both not humble and not creative is both tall and not brave and vice versa.
If lucy is not rich then mary is either not funny or not generous.
If someone is happy then someone is brave or not quiet.
Everyone who is either old or generous is generous or not kind and vice versa.
Everyone who is both not tall and quiet is creative.
If someone is either wise or rich then paul is both not brave and rich and vice versa.
Everyone who is both not curious and not calm is not curious or not creative.
Everyone who is calm or kind is either not funny or not curious.
Everyone who is wise or not curious is both not funny and strong.
Everyone who is humble is not strong.
If john is not brave or rich then someone is both not patient and not tall.
If someone is not kind then someone is not kind or not curious.
If someone is not strong then alice is both not creative and not calm.
Someone is either not rich or kind.
Someone is wise.
Someone is both creative and strong.
Someone is either humble or kind.
Someone is not brave. | Alice is old. | contradiction | (![X]:((generous(X)<~>~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((~wise(X)|~curious(X))<=>generous(X)))&
(![X]:((~humble(X)&~creative(X))<=>(tall(X)&~brave(X))))&
((~rich(lucy))=>((~funny(mary)<~>~generous(mary))))&
((?[X]:(happy(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((old(X)<~>generous(X))<=>(generous(X)|~kind(X))))&
(![X]:((~tall(X)&quiet(X))=>creative(X)))&
((?[X]:((wise(X)<~>rich(X))))<=>((~brave(paul)&rich(paul))))&
(![X]:((~curious(X)&~calm(X))=>(~curious(X)|~creative(X))))&
(![X]:((calm(X)|kind(X))=>(~funny(X)<~>~curious(X))))&
(![X]:((wise(X)|~curious(X))=>(~funny(X)&strong(X))))&
(![X]:(humble(X)=>~strong(X)))&
(((~brave(john)|rich(john)))=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~kind(X)|~curious(X)))))&
((?[X]:(~strong(X)))=>((~creative(alice)&~calm(alice))))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:(~brave(X))) | old(alice) | [
"p0",
"p2",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7610246642857570523262993
% SZS output start Proof for 7610246642857570523262993
1. ! [X0] : ((generous(X0) <~> ~strong(X0)) <=> (~kind(X0) <~> kind(X0))) [input p0]
3. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> generous(X0)) [input p2]
7. ! [X0] : ((old(X0) <~> generous(X0)) <=> (~kind(X0) | generous(X0))) [input p6]
12. ! [X0] : ((~curious(X0) | wise(X0)) => (strong(X0) & ~funny(X0))) [input p11]
22. old(alice) [input hypothesis]
33. ! [X0] : ((strong(X0) & ~funny(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 12]
38. ! [X0] : ((((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0))))) [nnf transformation 1]
43. ! [X0] : (((~curious(X0) | ~wise(X0)) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [nnf transformation 3]
44. ! [X0] : ((~curious(X0) | ~wise(X0) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [flattening 43]
48. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [nnf transformation 7]
49. ! [X0] : ((((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0))))) [flattening 48]
77. ~strong(X0) | generous(X0) | kind(X0) | kind(X0) [cnf transformation 38]
78. ~strong(X0) | generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
83. wise(X0) | generous(X0) [cnf transformation 44]
96. ~generous(X0) | ~old(X0) | ~generous(X0) [cnf transformation 49]
111. ~wise(X0) | strong(X0) [cnf transformation 33]
129. old(alice) [cnf transformation 22]
131. ~old(X0) | ~generous(X0) [duplicate literal removal 96]
132. ~strong(X0) | generous(X0) | kind(X0) [duplicate literal removal 77]
133. ~strong(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 78]
137. ~strong(X0) | generous(X0) [subsumption resolution 132,133]
268. strong(X0) | generous(X0) [resolution 111,83]
269. generous(X0) [subsumption resolution 268,137]
272. ~generous(alice) [resolution 131,129]
273. $false [subsumption resolution 272,269]
% SZS output end Proof for 7610246642857570523262993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or funny then susan is both not kind and tall and vice versa.
If someone is both not wise and rich then paul is either not funny or not calm.
Everyone who is either creative or not kind is rich or not happy.
Everyone who is curious is not old or humble and vice versa.
If alice is creative then susan is both not wise and not tall.
If susan is either curious or not tall then lucy is not generous and vice versa.
If alice is old then john is not rich and vice versa.
Everyone who is either not curious or funny is happy and vice versa.
Everyone who is tall is kind and vice versa.
Everyone who is both calm and not kind is not strong or not funny.
Everyone who is either not generous or strong is either creative or not rich.
If someone is strong then lucy is both not rich and creative.
Everyone who is not humble or not kind is not old.
If john is wise then john is tall or not old and vice versa.
If someone is not kind or rich then someone is kind or old and vice versa.
Everyone who is both not wise and not humble is not funny or not kind.
Someone is not humble or not creative.
John is both rich and quiet.
Someone is both not kind and not tall.
Lucy is not patient or not generous.
John is strong.
John is calm. | Susan is happy. | contradiction | ((?[X]:((old(X)|funny(X))))<=>((~kind(susan)&tall(susan))))&
((?[X]:((~wise(X)&rich(X))))=>((~funny(paul)<~>~calm(paul))))&
(![X]:((creative(X)<~>~kind(X))=>(rich(X)|~happy(X))))&
(![X]:(curious(X)<=>(~old(X)|humble(X))))&
((creative(alice))=>((~wise(susan)&~tall(susan))))&
(((curious(susan)<~>~tall(susan)))<=>(~generous(lucy)))&
((old(alice))<=>(~rich(john)))&
(![X]:((~curious(X)<~>funny(X))<=>happy(X)))&
(![X]:(tall(X)<=>kind(X)))&
(![X]:((calm(X)&~kind(X))=>(~strong(X)|~funny(X))))&
(![X]:((~generous(X)<~>strong(X))=>(creative(X)<~>~rich(X))))&
((?[X]:(strong(X)))=>((~rich(lucy)&creative(lucy))))&
(![X]:((~humble(X)|~kind(X))=>~old(X)))&
((wise(john))<=>((tall(john)|~old(john))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:((kind(X)|old(X)))))&
(![X]:((~wise(X)&~humble(X))=>(~funny(X)|~kind(X))))&
(?[X]:((~humble(X)|~creative(X))))&
((rich(john)&quiet(john)))&
(?[X]:((~kind(X)&~tall(X))))&
((~patient(lucy)|~generous(lucy)))&
(strong(john))&
(calm(john)) | happy(susan) | [
"p0",
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4641201213765542265986231
% SZS output start Proof for 4641201213765542265986231
1. ? [X0] : (funny(X0) | old(X0)) <=> (tall(susan) & ~kind(susan)) [input p0]
4. ! [X0] : (curious(X0) <=> (humble(X0) | ~old(X0))) [input p3]
8. ! [X0] : ((~curious(X0) <~> funny(X0)) <=> happy(X0)) [input p7]
9. ! [X0] : (tall(X0) <=> kind(X0)) [input p8]
23. happy(susan) [input hypothesis]
38. (? [X0] : (funny(X0) | old(X0)) | (~tall(susan) | kind(susan))) & ((tall(susan) & ~kind(susan)) | ! [X0] : (~funny(X0) & ~old(X0))) [nnf transformation 1]
39. (? [X0] : (funny(X0) | old(X0)) | ~tall(susan) | kind(susan)) & ((tall(susan) & ~kind(susan)) | ! [X0] : (~funny(X0) & ~old(X0))) [flattening 38]
40. (? [X0] : (funny(X0) | old(X0)) | ~tall(susan) | kind(susan)) & ((tall(susan) & ~kind(susan)) | ! [X1] : (~funny(X1) & ~old(X1))) [rectify 39]
41. ? [X0] : (funny(X0) | old(X0)) => (funny(sK0) | old(sK0)) [choice axiom]
42. ((funny(sK0) | old(sK0)) | ~tall(susan) | kind(susan)) & ((tall(susan) & ~kind(susan)) | ! [X1] : (~funny(X1) & ~old(X1))) [skolemisation 40,41]
45. ! [X0] : ((curious(X0) | (~humble(X0) & old(X0))) & ((humble(X0) | ~old(X0)) | ~curious(X0))) [nnf transformation 4]
46. ! [X0] : ((curious(X0) | (~humble(X0) & old(X0))) & (humble(X0) | ~old(X0) | ~curious(X0))) [flattening 45]
49. ! [X0] : ((((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | ~happy(X0)) & (happy(X0) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))))) [nnf transformation 8]
50. ! [X0] : ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))) [nnf transformation 9]
63. ~kind(susan) | ~old(X1) [cnf transformation 42]
64. ~kind(susan) | ~funny(X1) [cnf transformation 42]
65. tall(susan) | ~old(X1) [cnf transformation 42]
66. tall(susan) | ~funny(X1) [cnf transformation 42]
73. curious(X0) | old(X0) [cnf transformation 46]
85. ~curious(X0) | funny(X0) | ~happy(X0) [cnf transformation 49]
87. ~tall(X0) | kind(X0) [cnf transformation 50]
112. happy(susan) [cnf transformation 23]
114. 1 <=> kind(susan) [avatar definition]
115. ~kind(susan) <- (~1) [avatar component clause 114]
118. 2 <=> tall(susan) [avatar definition]
119. tall(susan) <- (2) [avatar component clause 118]
131. 5 <=> ! [X1] : ~funny(X1) [avatar definition]
132. ~funny(X1) <- (5) [avatar component clause 131]
133. 5 | 2 [avatar split clause 66,118,131]
135. 6 <=> ! [X1] : ~old(X1) [avatar definition]
136. ~old(X1) <- (6) [avatar component clause 135]
137. 6 | 2 [avatar split clause 65,118,135]
138. 5 | ~1 [avatar split clause 64,114,131]
139. 6 | ~1 [avatar split clause 63,114,135]
257. kind(susan) <- (2) [resolution 87,119]
258. $false <- (~1, 2) [subsumption resolution 257,115]
259. 1 | ~2 [avatar contradiction clause 258]
273. funny(X1) | ~happy(X1) | old(X1) [resolution 85,73]
276. ~happy(X1) | old(X1) <- (5) [subsumption resolution 273,132]
277. ~happy(X1) <- (5, 6) [subsumption resolution 276,136]
278. $false <- (5, 6) [resolution 277,112]
279. ~5 | ~6 [avatar contradiction clause 278]
280. $false [avatar sat refutation 133,137,138,139,259,279]
% SZS output end Proof for 4641201213765542265986231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not creative or old then lucy is tall or patient and vice versa. If alice is wise or not rich then susan is not old or tall. Everyone who is not happy or not kind is both not strong and tall. Everyone who is either not old or not quiet is either not creative or strong and vice versa. If susan is generous then fred is either not old or not brave and vice versa. Everyone who is both not generous and strong is not rich or old and vice versa. If someone is not kind then susan is either rich or not rich and vice versa. If someone is both quiet and rich then someone is creative and vice versa. If lucy is not brave or not creative then someone is tall or not creative and vice versa. If someone is happy or wise then fred is not calm and vice versa. Everyone who is not quiet is either not tall or not calm and vice versa. Everyone who is patient is both not old and generous. Everyone who is both happy and funny is either funny or not kind and vice versa. Everyone who is either calm or not funny is either rich or curious and vice versa. Everyone who is not kind is rich. If someone is creative then someone is old or not calm and vice versa. Someone is either not old or not creative. Someone is not calm. Fred is both not curious and funny. Mary is either quiet or wise. John is calm or patient. Fred is both creative and not rich. Someone is calm. Someone is both wise and happy. | Fred is not happy. | contradiction | (((~creative(alice)|old(alice)))<=>((tall(lucy)|patient(lucy))))&
(((wise(alice)|~rich(alice)))=>((~old(susan)|tall(susan))))&
(![X]:((~happy(X)|~kind(X))=>(~strong(X)&tall(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(~creative(X)<~>strong(X))))&
((generous(susan))<=>((~old(fred)<~>~brave(fred))))&
(![X]:((~generous(X)&strong(X))<=>(~rich(X)|old(X))))&
((?[X]:(~kind(X)))<=>((rich(susan)<~>~rich(susan))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:(creative(X))))&
(((~brave(lucy)|~creative(lucy)))<=>(?[X]:((tall(X)|~creative(X)))))&
((?[X]:((happy(X)|wise(X))))<=>(~calm(fred)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:(patient(X)=>(~old(X)&generous(X))))&
(![X]:((happy(X)&funny(X))<=>(funny(X)<~>~kind(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(rich(X)<~>curious(X))))&
(![X]:(~kind(X)=>rich(X)))&
((?[X]:(creative(X)))<=>(?[X]:((old(X)|~calm(X)))))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:(~calm(X)))&
((~curious(fred)&funny(fred)))&
((quiet(mary)<~>wise(mary)))&
((calm(john)|patient(john)))&
((creative(fred)&~rich(fred)))&
(?[X]:(calm(X)))&
(?[X]:((wise(X)&happy(X)))) | ~happy(fred) | [
"p12",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 27565480310233089374499
% SZS output start Proof for 27565480310233089374499
13. ! [X0] : ((funny(X0) & happy(X0)) <=> (funny(X0) <~> ~kind(X0))) [input p12]
15. ! [X0] : (~kind(X0) => rich(X0)) [input p14]
19. funny(fred) & ~curious(fred) [input p18]
22. ~rich(fred) & creative(fred) [input p21]
25. ~happy(fred) [input hypothesis]
32. ! [X0] : (rich(X0) | kind(X0)) [ennf transformation 15]
58. ! [X0] : (((funny(X0) & happy(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) & (((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (~funny(X0) | ~happy(X0)))) [nnf transformation 13]
59. ! [X0] : (((funny(X0) & happy(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) & (((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ~funny(X0) | ~happy(X0))) [flattening 58]
125. ~funny(X0) | ~kind(X0) | happy(X0) [cnf transformation 59]
137. kind(X0) | rich(X0) [cnf transformation 32]
145. funny(fred) [cnf transformation 19]
150. ~rich(fred) [cnf transformation 22]
154. ~happy(fred) [cnf transformation 25]
437. ~kind(fred) | happy(fred) [resolution 125,145]
439. ~kind(fred) [subsumption resolution 437,154]
581. rich(fred) [resolution 439,137]
583. $false [subsumption resolution 581,150]
% SZS output end Proof for 27565480310233089374499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then alice is not wise and vice versa.
Everyone who is either not happy or strong is both not rich and not humble.
If someone is not rich then fred is quiet and vice versa.
Everyone who is both not creative and not strong is curious and vice versa.
Everyone who is not happy or not quiet is both not quiet and funny.
Everyone who is not curious is either creative or tall.
Everyone who is generous or brave is both old and not funny and vice versa.
Everyone who is wise or not wise is not happy or creative.
If john is not generous then paul is both not wise and wise and vice versa.
If lucy is not curious or not creative then alice is either brave or curious and vice versa.
Everyone who is either not brave or strong is either not humble or old and vice versa.
If someone is not kind or not old then someone is not strong.
If lucy is strong then someone is generous.
If someone is either kind or strong then john is old and vice versa.
Everyone who is either strong or happy is kind.
If someone is not kind then john is both calm and creative and vice versa.
Alice is both kind and not rich.
Someone is both old and calm.
Someone is both rich and not calm.
Someone is either not funny or kind.
Someone is not generous.
Paul is either not wise or calm.
Paul is not brave. | John is not tall. | entailment | ((?[X]:(calm(X)))<=>(~wise(alice)))&
(![X]:((~happy(X)<~>strong(X))=>(~rich(X)&~humble(X))))&
((?[X]:(~rich(X)))<=>(quiet(fred)))&
(![X]:((~creative(X)&~strong(X))<=>curious(X)))&
(![X]:((~happy(X)|~quiet(X))=>(~quiet(X)&funny(X))))&
(![X]:(~curious(X)=>(creative(X)<~>tall(X))))&
(![X]:((generous(X)|brave(X))<=>(old(X)&~funny(X))))&
(![X]:((wise(X)|~wise(X))=>(~happy(X)|creative(X))))&
((~generous(john))<=>((~wise(paul)&wise(paul))))&
(((~curious(lucy)|~creative(lucy)))<=>((brave(alice)<~>curious(alice))))&
(![X]:((~brave(X)<~>strong(X))<=>(~humble(X)<~>old(X))))&
((?[X]:((~kind(X)|~old(X))))=>(?[X]:(~strong(X))))&
((strong(lucy))=>(?[X]:(generous(X))))&
((?[X]:((kind(X)<~>strong(X))))<=>(old(john)))&
(![X]:((strong(X)<~>happy(X))=>kind(X)))&
((?[X]:(~kind(X)))<=>((calm(john)&creative(john))))&
((kind(alice)&~rich(alice)))&
(?[X]:((old(X)&calm(X))))&
(?[X]:((rich(X)&~calm(X))))&
(?[X]:((~funny(X)<~>kind(X))))&
(?[X]:(~generous(X)))&
((~wise(paul)<~>calm(paul)))&
(~brave(paul)) | ~tall(john) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1425420862351947258117311
% SZS output start Proof for 1425420862351947258117311
4. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> curious(X0)) [input p3]
5. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (funny(X0) & ~quiet(X0))) [input p4]
6. ! [X0] : (~curious(X0) => (creative(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((brave(X0) | generous(X0)) <=> (~funny(X0) & old(X0))) [input p6]
8. ! [X0] : ((~wise(X0) | wise(X0)) => (creative(X0) | ~happy(X0))) [input p7]
9. ~generous(john) <=> (wise(paul) & ~wise(paul)) [input p8]
24. tall(john) [input hypothesis]
27. ! [X0] : ((funny(X0) & ~quiet(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 5]
28. ! [X0] : ((creative(X0) <~> tall(X0)) | curious(X0)) [ennf transformation 6]
29. ! [X0] : ((creative(X0) | ~happy(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 8]
30. ! [X0] : (creative(X0) | ~happy(X0) | (wise(X0) & ~wise(X0))) [flattening 29]
43. ! [X0] : (((~strong(X0) & ~creative(X0)) | ~curious(X0)) & (curious(X0) | (strong(X0) | creative(X0)))) [nnf transformation 4]
44. ! [X0] : (((~strong(X0) & ~creative(X0)) | ~curious(X0)) & (curious(X0) | strong(X0) | creative(X0))) [flattening 43]
45. ! [X0] : (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | curious(X0)) [nnf transformation 28]
46. ! [X0] : (((brave(X0) | generous(X0)) | (funny(X0) | ~old(X0))) & ((~funny(X0) & old(X0)) | (~brave(X0) & ~generous(X0)))) [nnf transformation 7]
47. ! [X0] : ((brave(X0) | generous(X0) | funny(X0) | ~old(X0)) & ((~funny(X0) & old(X0)) | (~brave(X0) & ~generous(X0)))) [flattening 46]
48. (~generous(john) | (~wise(paul) | wise(paul))) & ((wise(paul) & ~wise(paul)) | generous(john)) [nnf transformation 9]
49. (~generous(john) | ~wise(paul) | wise(paul)) & ((wise(paul) & ~wise(paul)) | generous(john)) [flattening 48]
87. ~curious(X0) | ~creative(X0) [cnf transformation 44]
91. funny(X0) | happy(X0) [cnf transformation 27]
94. ~tall(X0) | ~creative(X0) | curious(X0) [cnf transformation 45]
97. ~generous(X0) | ~funny(X0) [cnf transformation 47]
100. creative(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 30]
101. creative(X0) | ~happy(X0) | wise(X0) [cnf transformation 30]
102. ~wise(paul) | generous(john) [cnf transformation 49]
103. wise(paul) | generous(john) [cnf transformation 49]
143. tall(john) [cnf transformation 24]
170. ~tall(X0) | ~creative(X0) [subsumption resolution 94,87]
171. ~happy(X0) | creative(X0) [subsumption resolution 100,101]
173. 7 <=> generous(john) [avatar definition]
175. generous(john) <- (7) [avatar component clause 173]
177. 8 <=> wise(paul) [avatar definition]
180. 7 | 8 [avatar split clause 103,177,173]
181. 7 | ~8 [avatar split clause 102,177,173]
254. 24 <=> creative(john) [avatar definition]
256. ~creative(john) <- (~24) [avatar component clause 254]
288. ~funny(john) <- (7) [resolution 97,175]
290. happy(john) <- (7) [resolution 288,91]
294. ~creative(john) [resolution 170,143]
297. ~24 [avatar split clause 294,254]
302. creative(john) <- (7) [resolution 290,171]
303. $false <- (7, ~24) [subsumption resolution 302,256]
304. ~7 | 24 [avatar contradiction clause 303]
305. $false [avatar sat refutation 180,181,297,304]
% SZS output end Proof for 1425420862351947258117311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not brave then john is not kind or happy and vice versa.
Everyone who is kind or not tall is not strong or funny and vice versa.
Everyone who is both humble and not kind is kind and vice versa.
Everyone who is patient is creative or not generous.
Everyone who is brave or old is either not brave or not rich and vice versa.
Everyone who is not kind is both not funny and not old and vice versa.
Everyone who is not quiet is not patient or not kind.
Everyone who is both not calm and not brave is both wise and rich and vice versa.
Everyone who is both wise and happy is not creative.
Everyone who is either strong or not old is either brave or strong.
Everyone who is tall is not creative or wise.
Everyone who is not happy or creative is not curious or wise.
Everyone who is either not creative or calm is either patient or not generous and vice versa.
If fred is not generous or creative then alice is old and vice versa.
Everyone who is either generous or rich is rich or generous.
Someone is either not patient or not kind.
Lucy is either rich or not curious.
Fred is not curious or not creative.
Someone is not funny or brave.
Someone is either not quiet or not calm.
Someone is quiet. | Lucy is not generous. | neutral | ((~brave(john))<=>((~kind(john)|happy(john))))&
(![X]:((kind(X)|~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(((~generous(fred)|creative(fred)))<=>(old(alice)))&
(![X]:((generous(X)<~>rich(X))=>(rich(X)|generous(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
((rich(lucy)<~>~curious(lucy)))&
((~curious(fred)|~creative(fred)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:(quiet(X))) | ~generous(lucy) | [] | null | 0 |
If someone is both patient and quiet then susan is kind and vice versa.
Everyone who is brave or not generous is not tall and vice versa.
If someone is both not happy and not funny then someone is both wise and not quiet.
If someone is both rich and funny then lucy is both not creative and not brave.
If someone is not funny or generous then someone is not curious or not calm.
If susan is not calm or humble then someone is not strong and vice versa.
If someone is both not creative and not strong then someone is not tall and vice versa.
If someone is not tall or rich then john is either old or calm.
Everyone who is not brave is both kind and not kind and vice versa.
If someone is funny or not curious then someone is not rich.
If someone is both not funny and brave then john is both not calm and generous and vice versa.
If lucy is not patient then mary is wise and vice versa.
If mary is generous then someone is generous and vice versa.
Everyone who is humble or patient is not curious.
Everyone who is both wise and not strong is not calm or not rich.
If someone is both not happy and not funny then someone is tall and vice versa.
Someone is both not happy and not strong.
Someone is not generous.
John is both not calm and patient.
John is not calm or not strong.
Susan is old.
Mary is either not generous or not patient.
Paul is either kind or creative.
Paul is both happy and not quiet. | John is not old. | contradiction | ((?[X]:((patient(X)&quiet(X))))<=>(kind(susan)))&
(![X]:((brave(X)|~generous(X))<=>~tall(X)))&
((?[X]:((~happy(X)&~funny(X))))=>(?[X]:((wise(X)&~quiet(X)))))&
((?[X]:((rich(X)&funny(X))))=>((~creative(lucy)&~brave(lucy))))&
((?[X]:((~funny(X)|generous(X))))=>(?[X]:((~curious(X)|~calm(X)))))&
(((~calm(susan)|humble(susan)))<=>(?[X]:(~strong(X))))&
((?[X]:((~creative(X)&~strong(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~tall(X)|rich(X))))=>((old(john)<~>calm(john))))&
(![X]:(~brave(X)<=>(kind(X)&~kind(X))))&
((?[X]:((funny(X)|~curious(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~funny(X)&brave(X))))<=>((~calm(john)&generous(john))))&
((~patient(lucy))<=>(wise(mary)))&
((generous(mary))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|patient(X))=>~curious(X)))&
(![X]:((wise(X)&~strong(X))=>(~calm(X)|~rich(X))))&
((?[X]:((~happy(X)&~funny(X))))<=>(?[X]:(tall(X))))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:(~generous(X)))&
((~calm(john)&patient(john)))&
((~calm(john)|~strong(john)))&
(old(susan))&
((~generous(mary)<~>~patient(mary)))&
((kind(paul)<~>creative(paul)))&
((happy(paul)&~quiet(paul))) | ~old(john) | [
"p1",
"p7",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8894165855207390607818088
% SZS output start Proof for 8894165855207390607818088
2. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~tall(X0)) [input p1]
8. ? [X0] : (rich(X0) | ~tall(X0)) => (old(john) <~> calm(john)) [input p7]
9. ! [X0] : (~brave(X0) <=> (~kind(X0) & kind(X0))) [input p8]
19. patient(john) & ~calm(john) [input p18]
25. ~old(john) [input hypothesis]
32. ? [X0] : ~tall(X0) => (old(john) <~> calm(john)) [pure predicate removal 8]
38. (old(john) <~> calm(john)) | ! [X0] : tall(X0) [ennf transformation 32]
43. ! [X0] : (((~generous(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (generous(X0) & ~brave(X0)))) [nnf transformation 2]
44. ! [X0] : ((~generous(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (generous(X0) & ~brave(X0)))) [flattening 43]
58. ((~calm(john) | ~old(john)) & (calm(john) | old(john))) | ! [X0] : tall(X0) [nnf transformation 38]
59. ! [X0] : ((~brave(X0) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | brave(X0))) [nnf transformation 9]
60. ! [X0] : ((~brave(X0) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | brave(X0))) [flattening 59]
85. ~tall(X0) | ~brave(X0) [cnf transformation 44]
96. calm(john) | old(john) | tall(X0) [cnf transformation 58]
98. kind(X0) | brave(X0) [cnf transformation 60]
99. ~kind(X0) | brave(X0) [cnf transformation 60]
115. ~calm(john) [cnf transformation 19]
125. ~old(john) [cnf transformation 25]
176. 12 <=> ! [X1] : tall(X1) [avatar definition]
177. tall(X1) <- (12) [avatar component clause 176]
197. 17 <=> old(john) [avatar definition]
201. 18 <=> calm(john) [avatar definition]
205. 12 | 17 | 18 [avatar split clause 96,201,197,176]
206. brave(X0) [subsumption resolution 98,99]
264. ~18 [avatar split clause 115,201]
286. ~17 [avatar split clause 125,197]
289. ~brave(X0) <- (12) [resolution 85,177]
290. $false <- (12) [subsumption resolution 289,206]
291. ~12 [avatar contradiction clause 290]
292. $false [avatar sat refutation 205,264,286,291]
% SZS output end Proof for 8894165855207390607818088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is creative.
Everyone who is not patient is both tall and not humble.
If mary is both not generous and tall then alice is both brave and calm.
Everyone who is creative is either not strong or not calm and vice versa.
If someone is either creative or strong then mary is either not generous or not rich and vice versa.
If someone is not creative or strong then someone is patient.
If alice is both tall and wise then someone is either not strong or not calm and vice versa.
Everyone who is both not rich and not humble is both not calm and strong.
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.
Someone is both patient and calm.
Susan is both not strong and creative.
Paul is both funny and not old.
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. | Susan is humble. | entailment | ((?[X]:(~brave(X)))=>(?[X]:(creative(X))))&
(![X]:(~patient(X)=>(tall(X)&~humble(X))))&
(((~generous(mary)&tall(mary)))=>((brave(alice)&calm(alice))))&
(![X]:(creative(X)<=>(~strong(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>strong(X))))<=>((~generous(mary)<~>~rich(mary))))&
((?[X]:((~creative(X)|strong(X))))=>(?[X]:(patient(X))))&
(((tall(alice)&wise(alice)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((~rich(X)&~humble(X))=>(~calm(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]:((patient(X)&calm(X))))&
((~strong(susan)&creative(susan)))&
((funny(paul)&~old(paul)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X)))) | humble(susan) | [
"p8",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7416849919489095501840905
% SZS output start Proof for 7416849919489095501840905
9. ! [X0] : ((creative(X0) | strong(X0)) <=> wise(X0)) [input p8]
14. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p13]
18. creative(susan) & ~strong(susan) [input p17]
24. ~humble(susan) [input hypothesis]
54. ! [X0] : (((creative(X0) | strong(X0)) | ~wise(X0)) & (wise(X0) | (~creative(X0) & ~strong(X0)))) [nnf transformation 9]
55. ! [X0] : ((creative(X0) | strong(X0) | ~wise(X0)) & (wise(X0) | (~creative(X0) & ~strong(X0)))) [flattening 54]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 14]
68. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 67]
104. ~creative(X0) | wise(X0) [cnf transformation 55]
124. ~wise(X0) | humble(X0) [cnf transformation 68]
131. creative(susan) [cnf transformation 18]
138. ~humble(susan) [cnf transformation 24]
314. wise(susan) [resolution 104,131]
322. humble(susan) [resolution 124,314]
325. $false [subsumption resolution 322,138]
% SZS output end Proof for 7416849919489095501840905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not kind is either not calm or strong and vice versa.
If lucy is either brave or not patient then someone is both funny and wise.
If lucy is funny then alice is wise.
Everyone who is generous is not wise or not patient and vice versa.
If someone is strong or calm then paul is either not brave or generous.
Everyone who is old is either quiet or patient.
Everyone who is not patient is tall and vice versa.
If lucy is not calm then someone is both happy and not happy.
If someone is not kind then fred is both creative and not humble and vice versa.
Everyone who is either not brave or humble is both not tall and happy.
If paul is not calm then john is both curious and not strong.
If john is both funny and creative then someone is either not humble or rich.
If someone is calm or creative then alice is either patient or wise.
Everyone who is old is either not creative or curious.
Everyone who is both calm and not tall is either wise or happy.
Everyone who is not brave is either not humble or creative and vice versa.
Someone is either patient or curious.
Fred is funny or wise.
Paul is not wise or quiet.
Someone is kind or not tall.
Alice is not quiet or generous.
Mary is happy or not brave.
Someone is not patient.
John is either not happy or not tall. | Alice is wise. | neutral | (![X]:((~strong(X)&~kind(X))<=>(~calm(X)<~>strong(X))))&
(((brave(lucy)<~>~patient(lucy)))=>(?[X]:((funny(X)&wise(X)))))&
((funny(lucy))=>(wise(alice)))&
(![X]:(generous(X)<=>(~wise(X)|~patient(X))))&
((?[X]:((strong(X)|calm(X))))=>((~brave(paul)<~>generous(paul))))&
(![X]:(old(X)=>(quiet(X)<~>patient(X))))&
(![X]:(~patient(X)<=>tall(X)))&
((~calm(lucy))=>(?[X]:((happy(X)&~happy(X)))))&
((?[X]:(~kind(X)))<=>((creative(fred)&~humble(fred))))&
(![X]:((~brave(X)<~>humble(X))=>(~tall(X)&happy(X))))&
((~calm(paul))=>((curious(john)&~strong(john))))&
(((funny(john)&creative(john)))=>(?[X]:((~humble(X)<~>rich(X)))))&
((?[X]:((calm(X)|creative(X))))=>((patient(alice)<~>wise(alice))))&
(![X]:(old(X)=>(~creative(X)<~>curious(X))))&
(![X]:((calm(X)&~tall(X))=>(wise(X)<~>happy(X))))&
(![X]:(~brave(X)<=>(~humble(X)<~>creative(X))))&
(?[X]:((patient(X)<~>curious(X))))&
((funny(fred)|wise(fred)))&
((~wise(paul)|quiet(paul)))&
(?[X]:((kind(X)|~tall(X))))&
((~quiet(alice)|generous(alice)))&
((happy(mary)|~brave(mary)))&
(?[X]:(~patient(X)))&
((~happy(john)<~>~tall(john))) | wise(alice) | [] | null | 0 |
If someone is either kind or not calm then someone is both humble and not happy and vice versa.
If someone is both not tall and not happy then paul is both funny and not humble and vice versa.
Everyone who is not humble is either creative or not calm.
Everyone who is both patient and happy is both tall and happy.
Everyone who is generous is not generous or quiet and vice versa.
If someone is either strong or not generous then john is either not happy or quiet and vice versa.
If someone is not patient then someone is either wise or not happy and vice versa.
Everyone who is not generous is either not kind or not happy.
If alice is either brave or wise then someone is either not creative or not happy.
If someone is both old and not generous then paul is either not creative or not humble and vice versa.
If someone is humble or not kind then someone is not curious or not quiet and vice versa.
If john is not funny then someone is either not rich or not funny.
If john is rich then someone is either happy or old.
Everyone who is curious is generous and vice versa.
If mary is patient then someone is creative or curious and vice versa.
If someone is not kind or tall then john is not old and vice versa.
Someone is not rich or calm.
Mary is either rich or tall.
Someone is not wise.
Paul is not wise or not happy.
Fred is funny.
Paul is strong or quiet.
John is not wise or tall. | Paul is kind. | entailment | ((?[X]:((kind(X)<~>~calm(X))))<=>(?[X]:((humble(X)&~happy(X)))))&
((?[X]:((~tall(X)&~happy(X))))<=>((funny(paul)&~humble(paul))))&
(![X]:(~humble(X)=>(creative(X)<~>~calm(X))))&
(![X]:((patient(X)&happy(X))=>(tall(X)&happy(X))))&
(![X]:(generous(X)<=>(~generous(X)|quiet(X))))&
((?[X]:((strong(X)<~>~generous(X))))<=>((~happy(john)<~>quiet(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~happy(X))))&
(((brave(alice)<~>wise(alice)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((old(X)&~generous(X))))<=>((~creative(paul)<~>~humble(paul))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~curious(X)|~quiet(X)))))&
((~funny(john))=>(?[X]:((~rich(X)<~>~funny(X)))))&
((rich(john))=>(?[X]:((happy(X)<~>old(X)))))&
(![X]:(curious(X)<=>generous(X)))&
((patient(mary))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:((~kind(X)|tall(X))))<=>(~old(john)))&
(?[X]:((~rich(X)|calm(X))))&
((rich(mary)<~>tall(mary)))&
(?[X]:(~wise(X)))&
((~wise(paul)|~happy(paul)))&
(funny(fred))&
((strong(paul)|quiet(paul)))&
((~wise(john)|tall(john))) | kind(paul) | [
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5870151978340153116208940
% SZS output start Proof for 5870151978340153116208940
5. ! [X0] : (generous(X0) <=> (quiet(X0) | ~generous(X0))) [input p4]
11. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X0] : (~quiet(X0) | ~curious(X0)) [input p10]
14. ! [X0] : (curious(X0) <=> generous(X0)) [input p13]
24. ~kind(paul) [input hypothesis]
27. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X1] : (~quiet(X1) | ~curious(X1)) [rectify 11]
46. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | ~generous(X0))) [nnf transformation 5]
47. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | ~generous(X0))) [flattening 46]
65. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (quiet(X1) & curious(X1))) & (? [X1] : (~quiet(X1) | ~curious(X1)) | ! [X0] : (kind(X0) & ~humble(X0))) [nnf transformation 27]
66. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (quiet(X1) & curious(X1))) & (? [X2] : (~quiet(X2) | ~curious(X2)) | ! [X3] : (kind(X3) & ~humble(X3))) [rectify 65]
67. ? [X0] : (~kind(X0) | humble(X0)) => (~kind(sK8) | humble(sK8)) [choice axiom]
68. ? [X2] : (~quiet(X2) | ~curious(X2)) => (~quiet(sK9) | ~curious(sK9)) [choice axiom]
69. ((~kind(sK8) | humble(sK8)) | ! [X1] : (quiet(X1) & curious(X1))) & ((~quiet(sK9) | ~curious(sK9)) | ! [X3] : (kind(X3) & ~humble(X3))) [skolemisation 66,68,67]
76. ! [X0] : ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0))) [nnf transformation 14]
104. quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 47]
105. generous(X0) | generous(X0) [cnf transformation 47]
132. ~quiet(sK9) | ~curious(sK9) | kind(X3) [cnf transformation 69]
140. curious(X0) | ~generous(X0) [cnf transformation 76]
155. ~kind(paul) [cnf transformation 24]
156. quiet(X0) | ~generous(X0) [duplicate literal removal 104]
157. generous(X0) [duplicate literal removal 105]
212. quiet(X0) [subsumption resolution 156,157]
290. 28 <=> ! [X1] : curious(X1) [avatar definition]
291. curious(X1) <- (28) [avatar component clause 290]
301. ~curious(sK9) | kind(X3) [subsumption resolution 132,212]
303. 31 <=> ! [X3] : kind(X3) [avatar definition]
304. kind(X3) <- (31) [avatar component clause 303]
306. 32 <=> curious(sK9) [avatar definition]
308. ~curious(sK9) <- (~32) [avatar component clause 306]
309. 31 | ~32 [avatar split clause 301,306,303]
343. curious(X0) [subsumption resolution 140,157]
344. 28 [avatar split clause 343,290]
423. $false <- (28, ~32) [subsumption resolution 308,291]
424. ~28 | 32 [avatar contradiction clause 423]
427. $false <- (31) [resolution 304,155]
430. ~31 [avatar contradiction clause 427]
431. $false [avatar sat refutation 309,344,424,430]
% SZS output end Proof for 5870151978340153116208940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or not strong then someone is old or not wise and vice versa.
Everyone who is not happy is either not wise or not curious.
Everyone who is funny is both not old and humble and vice versa.
Everyone who is strong is either patient or not rich and vice versa.
Everyone who is either not old or not funny is not rich or wise and vice versa.
If someone is old or rich then mary is not generous or not kind.
If lucy is creative then alice is not strong.
Everyone who is strong or not patient is not rich or curious and vice versa.
Everyone who is old or not tall is happy or funny and vice versa.
If someone is both not quiet and quiet then mary is both curious and not funny.
Everyone who is both not calm and creative is either not wise or rich.
If someone is both not humble and not generous then someone is not strong or not tall and vice versa.
If someone is not humble then someone is either creative or not patient and vice versa.
If someone is either rich or not rich then john is both not strong and funny.
Everyone who is quiet is either not happy or kind and vice versa.
Alice is either not humble or strong.
John is not curious or generous.
Someone is curious or not humble.
Someone is both not quiet and not kind.
Someone is either funny or not humble.
Someone is both happy and curious.
Someone is both creative and brave.
Paul is either calm or not old. | John is tall. | contradiction | ((?[X]:((quiet(X)<~>~strong(X))))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:(~happy(X)=>(~wise(X)<~>~curious(X))))&
(![X]:(funny(X)<=>(~old(X)&humble(X))))&
(![X]:(strong(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~rich(X)|wise(X))))&
((?[X]:((old(X)|rich(X))))=>((~generous(mary)|~kind(mary))))&
((creative(lucy))=>(~strong(alice)))&
(![X]:((strong(X)|~patient(X))<=>(~rich(X)|curious(X))))&
(![X]:((old(X)|~tall(X))<=>(happy(X)|funny(X))))&
((?[X]:((~quiet(X)&quiet(X))))=>((curious(mary)&~funny(mary))))&
(![X]:((~calm(X)&creative(X))=>(~wise(X)<~>rich(X))))&
((?[X]:((~humble(X)&~generous(X))))<=>(?[X]:((~strong(X)|~tall(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
((?[X]:((rich(X)<~>~rich(X))))=>((~strong(john)&funny(john))))&
(![X]:(quiet(X)<=>(~happy(X)<~>kind(X))))&
((~humble(alice)<~>strong(alice)))&
((~curious(john)|generous(john)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((creative(X)&brave(X))))&
((calm(paul)<~>~old(paul))) | tall(john) | [
"p2",
"p3",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8605152111458037772263852
% SZS output start Proof for 8605152111458037772263852
3. ! [X0] : (funny(X0) <=> (humble(X0) & ~old(X0))) [input p2]
4. ! [X0] : (strong(X0) <=> (patient(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : ((~patient(X0) | strong(X0)) <=> (curious(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | old(X0)) <=> (funny(X0) | happy(X0))) [input p8]
14. ? [X0] : (rich(X0) <~> ~rich(X0)) => (funny(john) & ~strong(john)) [input p13]
24. tall(john) [input hypothesis]
36. (funny(john) & ~strong(john)) | ! [X0] : (rich(X0) <=> ~rich(X0)) [ennf transformation 14]
43. ! [X0] : ((funny(X0) | (~humble(X0) | old(X0))) & ((humble(X0) & ~old(X0)) | ~funny(X0))) [nnf transformation 3]
44. ! [X0] : ((funny(X0) | ~humble(X0) | old(X0)) & ((humble(X0) & ~old(X0)) | ~funny(X0))) [flattening 43]
45. ! [X0] : ((strong(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | ~strong(X0))) [nnf transformation 4]
48. ! [X0] : (((~patient(X0) | strong(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (patient(X0) & ~strong(X0)))) [nnf transformation 8]
49. ! [X0] : ((~patient(X0) | strong(X0) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | (patient(X0) & ~strong(X0)))) [flattening 48]
50. ! [X0] : (((~tall(X0) | old(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (tall(X0) & ~old(X0)))) [nnf transformation 9]
51. ! [X0] : ((~tall(X0) | old(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (tall(X0) & ~old(X0)))) [flattening 50]
63. (funny(john) & ~strong(john)) | ! [X0] : ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))) [nnf transformation 36]
86. ~funny(X0) | ~old(X0) [cnf transformation 44]
92. strong(X0) | patient(X0) | rich(X0) [cnf transformation 45]
104. ~patient(X0) | strong(X0) | rich(X0) [cnf transformation 49]
109. ~tall(X0) | old(X0) | ~funny(X0) [cnf transformation 51]
124. ~strong(john) | rich(X0) | rich(X0) [cnf transformation 63]
125. funny(john) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
144. tall(john) [cnf transformation 24]
146. ~strong(john) | rich(X0) [duplicate literal removal 124]
147. funny(john) | ~rich(X0) [duplicate literal removal 125]
186. 9 <=> ! [X0] : ~rich(X0) [avatar definition]
187. ~rich(X0) <- (9) [avatar component clause 186]
207. rich(X0) | strong(X0) [subsumption resolution 104,92]
208. ~tall(X0) | ~funny(X0) [subsumption resolution 109,86]
219. 16 <=> ! [X1] : strong(X1) [avatar definition]
220. strong(X1) <- (16) [avatar component clause 219]
266. 27 <=> ! [X0] : rich(X0) [avatar definition]
267. rich(X0) <- (27) [avatar component clause 266]
269. 28 <=> funny(john) [avatar definition]
271. funny(john) <- (28) [avatar component clause 269]
273. 9 | 28 [avatar split clause 147,269,186]
275. 29 <=> strong(john) [avatar definition]
277. ~strong(john) <- (~29) [avatar component clause 275]
278. 27 | ~29 [avatar split clause 146,275,266]
323. $false <- (9, 27) [subsumption resolution 187,267]
324. ~9 | ~27 [avatar contradiction clause 323]
327. strong(X0) <- (9) [resolution 207,187]
328. 16 | ~9 [avatar split clause 327,186,219]
330. $false <- (16, ~29) [resolution 220,277]
335. ~16 | 29 [avatar contradiction clause 330]
337. ~funny(john) [resolution 208,144]
338. $false <- (28) [subsumption resolution 337,271]
339. ~28 [avatar contradiction clause 338]
340. $false [avatar sat refutation 273,278,324,328,335,339]
% SZS output end Proof for 8605152111458037772263852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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