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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|---|---|---|---|---|---|---|---|
If paul is both strong and patient then john is both funny and patient.
Everyone who is not creative or not generous is calm and vice versa.
Everyone who is not funny is either not calm or generous.
Everyone who is not quiet or wise is either not quiet or patient.
If susan is old then someone is both not tall and strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Everyone who is both not happy and funny is not funny and vice versa.
Everyone who is both not patient and not curious is funny.
If someone is not tall or not patient then paul is both not generous and not humble.
Everyone who is either funny or not creative is not kind or not old.
If susan is both not tall and not happy then someone is kind or curious.
Everyone who is either old or patient is brave and vice versa.
Fred is kind or not creative.
Someone is not tall or generous.
Someone is not patient.
Alice is funny or happy.
Mary is humble. | Alice is old. | entailment | (((strong(paul)&patient(paul)))=>((funny(john)&patient(john))))&
(![X]:((~creative(X)|~generous(X))<=>calm(X)))&
(![X]:(~funny(X)=>(~calm(X)<~>generous(X))))&
(![X]:((~quiet(X)|wise(X))=>(~quiet(X)<~>patient(X))))&
((old(susan))<=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(![X]:((~happy(X)&funny(X))<=>~funny(X)))&
(![X]:((~patient(X)&~curious(X))=>funny(X)))&
((?[X]:((~tall(X)|~patient(X))))=>((~generous(paul)&~humble(paul))))&
(![X]:((funny(X)<~>~creative(X))=>(~kind(X)|~old(X))))&
(((~tall(susan)&~happy(susan)))=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((old(X)<~>patient(X))<=>brave(X)))&
((kind(fred)|~creative(fred)))&
(?[X]:((~tall(X)|generous(X))))&
(?[X]:(~patient(X)))&
((funny(alice)|happy(alice)))&
(humble(mary)) | old(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5058960588067969997946205
% SZS output start Proof for 5058960588067969997946205
6. ? [X0] : (~old(X0) | quiet(X0)) => ? [X0] : (wise(X0) & ~wise(X0)) [input p5]
22. ~old(alice) [input hypothesis]
23. ? [X0] : (~old(X0) | quiet(X0)) => ? [X1] : (wise(X1) & ~wise(X1)) [rectify 6]
31. ? [X1] : (wise(X1) & ~wise(X1)) | ! [X0] : (old(X0) & ~quiet(X0)) [ennf transformation 23]
45. ? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (old(X1) & ~quiet(X1)) [rectify 31]
46. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
47. (wise(sK1) & ~wise(sK1)) | ! [X1] : (old(X1) & ~quiet(X1)) [skolemisation 45,46]
77. ~wise(sK1) | old(X1) [cnf transformation 47]
79. wise(sK1) | old(X1) [cnf transformation 47]
108. ~old(alice) [cnf transformation 22]
151. 9 <=> ! [X1] : old(X1) [avatar definition]
152. old(X1) <- (9) [avatar component clause 151]
154. 10 <=> wise(sK1) [avatar definition]
157. 9 | 10 [avatar split clause 79,154,151]
162. 9 | ~10 [avatar split clause 77,154,151]
237. $false <- (9) [resolution 152,108]
238. ~9 [avatar contradiction clause 237]
239. $false [avatar sat refutation 157,162,238]
% SZS output end Proof for 5058960588067969997946205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not old or strong then mary is wise. If susan is quiet then john is not creative. Everyone who is patient or not humble is both not wise and not tall. If someone is not wise or strong then lucy is both not humble and not tall and vice versa. If someone is both happy and not strong then someone is either not brave or not curious. If alice is old or not funny then someone is quiet or tall and vice versa. If mary is rich or generous then someone is not creative or not funny. Everyone who is not funny is both strong and brave. Everyone who is either not strong or not calm is not calm and vice versa. If mary is both not happy and not generous then lucy is not calm. Everyone who is patient or not kind is happy and vice versa. If someone is either kind or curious then someone is both curious and calm. Everyone who is not patient is both patient and not curious. Everyone who is both tall and patient is curious and vice versa. Everyone who is both not strong and not generous is not tall. If someone is not wise or wise then fred is not quiet and vice versa. Mary is strong. Someone is not old. Mary is curious or not funny. Fred is both not kind and not brave. John is either tall or not old. Lucy is both not rich and not curious. John is not creative. | Mary is not kind. | entailment | (((~old(lucy)<~>strong(lucy)))=>(wise(mary)))&
((quiet(susan))=>(~creative(john)))&
(![X]:((patient(X)|~humble(X))=>(~wise(X)&~tall(X))))&
((?[X]:((~wise(X)|strong(X))))<=>((~humble(lucy)&~tall(lucy))))&
((?[X]:((happy(X)&~strong(X))))=>(?[X]:((~brave(X)<~>~curious(X)))))&
(((old(alice)|~funny(alice)))<=>(?[X]:((quiet(X)|tall(X)))))&
(((rich(mary)|generous(mary)))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:(~funny(X)=>(strong(X)&brave(X))))&
(![X]:((~strong(X)<~>~calm(X))<=>~calm(X)))&
(((~happy(mary)&~generous(mary)))=>(~calm(lucy)))&
(![X]:((patient(X)|~kind(X))<=>happy(X)))&
((?[X]:((kind(X)<~>curious(X))))=>(?[X]:((curious(X)&calm(X)))))&
(![X]:(~patient(X)=>(patient(X)&~curious(X))))&
(![X]:((tall(X)&patient(X))<=>curious(X)))&
(![X]:((~strong(X)&~generous(X))=>~tall(X)))&
((?[X]:((~wise(X)|wise(X))))<=>(~quiet(fred)))&
(strong(mary))&
(?[X]:(~old(X)))&
((curious(mary)|~funny(mary)))&
((~kind(fred)&~brave(fred)))&
((tall(john)<~>~old(john)))&
((~rich(lucy)&~curious(lucy)))&
(~creative(john)) | ~kind(mary) | [
"p2",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4454257277921376513146329
% SZS output start Proof for 4454257277921376513146329
3. ! [X0] : ((~humble(X0) | patient(X0)) => (~tall(X0) & ~wise(X0))) [input p2]
12. ? [X0] : (kind(X0) <~> curious(X0)) => ? [X0] : (calm(X0) & curious(X0)) [input p11]
13. ! [X0] : (~patient(X0) => (~curious(X0) & patient(X0))) [input p12]
14. ! [X0] : ((patient(X0) & tall(X0)) <=> curious(X0)) [input p13]
24. kind(mary) [input hypothesis]
26. ? [X0] : (kind(X0) <~> curious(X0)) => ? [X1] : (calm(X1) & curious(X1)) [rectify 12]
36. ! [X0] : ((~tall(X0) & ~wise(X0)) | (humble(X0) & ~patient(X0))) [ennf transformation 3]
40. ? [X1] : (calm(X1) & curious(X1)) | ! [X0] : (kind(X0) <=> curious(X0)) [ennf transformation 26]
41. ! [X0] : ((~curious(X0) & patient(X0)) | patient(X0)) [ennf transformation 13]
58. ? [X1] : (calm(X1) & curious(X1)) | ! [X0] : ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))) [nnf transformation 40]
59. ? [X0] : (calm(X0) & curious(X0)) | ! [X1] : ((kind(X1) | ~curious(X1)) & (curious(X1) | ~kind(X1))) [rectify 58]
60. ? [X0] : (calm(X0) & curious(X0)) => (calm(sK3) & curious(sK3)) [choice axiom]
61. (calm(sK3) & curious(sK3)) | ! [X1] : ((kind(X1) | ~curious(X1)) & (curious(X1) | ~kind(X1))) [skolemisation 59,60]
62. ! [X0] : (((patient(X0) & tall(X0)) | ~curious(X0)) & (curious(X0) | (~patient(X0) | ~tall(X0)))) [nnf transformation 14]
63. ! [X0] : (((patient(X0) & tall(X0)) | ~curious(X0)) & (curious(X0) | ~patient(X0) | ~tall(X0))) [flattening 62]
75. ~tall(X0) | ~patient(X0) [cnf transformation 36]
96. curious(sK3) | curious(X1) | ~kind(X1) [cnf transformation 61]
100. patient(X0) | patient(X0) [cnf transformation 41]
103. ~curious(X0) | tall(X0) [cnf transformation 63]
116. kind(mary) [cnf transformation 24]
117. patient(X0) [duplicate literal removal 100]
211. 21 <=> ! [X1] : (curious(X1) | ~kind(X1)) [avatar definition]
212. ~kind(X1) | curious(X1) <- (21) [avatar component clause 211]
215. 22 <=> curious(sK3) [avatar definition]
217. curious(sK3) <- (22) [avatar component clause 215]
219. 21 | 22 [avatar split clause 96,215,211]
230. 25 <=> curious(mary) [avatar definition]
232. curious(mary) <- (25) [avatar component clause 230]
258. curious(mary) <- (21) [resolution 212,116]
260. 25 | ~21 [avatar split clause 258,211,230]
262. tall(sK3) <- (22) [resolution 217,103]
271. ~patient(sK3) <- (22) [resolution 262,75]
272. $false <- (22) [subsumption resolution 271,117]
273. ~22 [avatar contradiction clause 272]
275. tall(mary) <- (25) [resolution 232,103]
280. ~patient(mary) <- (25) [resolution 275,75]
281. $false <- (25) [subsumption resolution 280,117]
282. ~25 [avatar contradiction clause 281]
283. $false [avatar sat refutation 219,260,273,282]
% SZS output end Proof for 4454257277921376513146329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or strong is calm.
Everyone who is both not brave and patient is either not strong or not creative and vice versa.
If susan is both strong and brave then someone is either creative or not calm and vice versa.
If someone is kind then alice is both happy and not funny and vice versa.
Everyone who is not curious is both old and calm and vice versa.
Everyone who is brave is not quiet and vice versa.
Everyone who is wise is either patient or rich.
If someone is funny then lucy is not tall or curious.
Everyone who is either old or happy is not funny or generous and vice versa.
If someone is not kind then lucy is both not strong and not brave.
Everyone who is both calm and curious is both not curious and brave and vice versa.
If someone is both funny and not old then mary is both not funny and not kind.
Everyone who is brave or not tall is either old or brave and vice versa.
If someone is both not creative and not funny then someone is either not strong or not funny.
If alice is either not old or not brave then someone is both tall and old and vice versa.
Everyone who is strong or not funny is not wise or generous.
Lucy is not kind or creative.
Someone is both not generous and funny.
Mary is either not strong or not patient.
John is kind.
Someone is either happy or not brave.
Paul is strong.
Someone is not wise or generous.
Susan is not wise or brave. | Alice is not calm. | entailment | (![X]:((rich(X)|strong(X))=>calm(X)))&
(![X]:((~brave(X)&patient(X))<=>(~strong(X)<~>~creative(X))))&
(((strong(susan)&brave(susan)))<=>(?[X]:((creative(X)<~>~calm(X)))))&
((?[X]:(kind(X)))<=>((happy(alice)&~funny(alice))))&
(![X]:(~curious(X)<=>(old(X)&calm(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
(![X]:(wise(X)=>(patient(X)<~>rich(X))))&
((?[X]:(funny(X)))=>((~tall(lucy)|curious(lucy))))&
(![X]:((old(X)<~>happy(X))<=>(~funny(X)|generous(X))))&
((?[X]:(~kind(X)))=>((~strong(lucy)&~brave(lucy))))&
(![X]:((calm(X)&curious(X))<=>(~curious(X)&brave(X))))&
((?[X]:((funny(X)&~old(X))))=>((~funny(mary)&~kind(mary))))&
(![X]:((brave(X)|~tall(X))<=>(old(X)<~>brave(X))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~old(alice)<~>~brave(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:((strong(X)|~funny(X))=>(~wise(X)|generous(X))))&
((~kind(lucy)|creative(lucy)))&
(?[X]:((~generous(X)&funny(X))))&
((~strong(mary)<~>~patient(mary)))&
(kind(john))&
(?[X]:((happy(X)<~>~brave(X))))&
(strong(paul))&
(?[X]:((~wise(X)|generous(X))))&
((~wise(susan)|brave(susan))) | ~calm(alice) | [
"p3",
"p4",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1069693436396754120789460
% SZS output start Proof for 1069693436396754120789460
4. ? [X0] : kind(X0) <=> (~funny(alice) & happy(alice)) [input p3]
5. ! [X0] : (~curious(X0) <=> (calm(X0) & old(X0))) [input p4]
9. ! [X0] : ((old(X0) <~> happy(X0)) <=> (generous(X0) | ~funny(X0))) [input p8]
11. ! [X0] : ((curious(X0) & calm(X0)) <=> (brave(X0) & ~curious(X0))) [input p10]
20. kind(john) [input p19]
25. calm(alice) [input hypothesis]
45. (? [X0] : kind(X0) | (funny(alice) | ~happy(alice))) & ((~funny(alice) & happy(alice)) | ! [X0] : ~kind(X0)) [nnf transformation 4]
46. (? [X0] : kind(X0) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X0] : ~kind(X0)) [flattening 45]
47. (? [X0] : kind(X0) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X1] : ~kind(X1)) [rectify 46]
48. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
49. (kind(sK1) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X1] : ~kind(X1)) [skolemisation 47,48]
50. ! [X0] : ((~curious(X0) | (~calm(X0) | ~old(X0))) & ((calm(X0) & old(X0)) | curious(X0))) [nnf transformation 5]
51. ! [X0] : ((~curious(X0) | ~calm(X0) | ~old(X0)) & ((calm(X0) & old(X0)) | curious(X0))) [flattening 50]
53. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (~generous(X0) & funny(X0))) & ((generous(X0) | ~funny(X0)) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [nnf transformation 9]
54. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (~generous(X0) & funny(X0))) & (generous(X0) | ~funny(X0) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [flattening 53]
55. ! [X0] : (((curious(X0) & calm(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~curious(X0) | ~calm(X0)))) [nnf transformation 11]
56. ! [X0] : (((curious(X0) & calm(X0)) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | ~curious(X0) | ~calm(X0))) [flattening 55]
86. happy(alice) | ~kind(X1) [cnf transformation 49]
87. ~funny(alice) | ~kind(X1) [cnf transformation 49]
89. old(X0) | curious(X0) [cnf transformation 51]
99. ~old(X0) | ~happy(X0) | funny(X0) [cnf transformation 54]
103. ~curious(X0) | ~curious(X0) | ~calm(X0) [cnf transformation 56]
128. kind(john) [cnf transformation 20]
132. calm(alice) [cnf transformation 25]
135. ~curious(X0) | ~calm(X0) [duplicate literal removal 103]
166. 7 <=> happy(alice) [avatar definition]
167. happy(alice) <- (7) [avatar component clause 166]
170. 8 <=> funny(alice) [avatar definition]
171. ~funny(alice) <- (~8) [avatar component clause 170]
179. 10 <=> ! [X1] : ~kind(X1) [avatar definition]
180. ~kind(X1) <- (10) [avatar component clause 179]
181. 10 | ~8 [avatar split clause 87,170,179]
182. 10 | 7 [avatar split clause 86,166,179]
238. 24 <=> old(alice) [avatar definition]
239. ~old(alice) <- (~24) [avatar component clause 238]
240. old(alice) <- (24) [avatar component clause 238]
294. curious(alice) <- (~24) [resolution 89,239]
298. ~calm(alice) <- (~24) [resolution 135,294]
299. $false <- (~24) [subsumption resolution 298,132]
300. 24 [avatar contradiction clause 299]
317. $false <- (10) [resolution 180,128]
320. ~10 [avatar contradiction clause 317]
380. ~happy(alice) | funny(alice) <- (24) [resolution 99,240]
383. funny(alice) <- (7, 24) [subsumption resolution 380,167]
384. $false <- (7, ~8, 24) [subsumption resolution 383,171]
385. ~7 | 8 | ~24 [avatar contradiction clause 384]
395. $false [avatar sat refutation 181,182,300,320,385]
% SZS output end Proof for 1069693436396754120789460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then lucy is both curious and not patient.
Everyone who is kind is both strong and not humble and vice versa.
If someone is old or calm then someone is both humble and brave and vice versa.
If lucy is not creative or creative then paul is not patient and vice versa.
Everyone who is not creative is either not quiet or funny.
If mary is old then someone is both creative and quiet.
Everyone who is both not happy and calm is generous.
If alice is either not funny or not brave then someone is either brave or happy and vice versa.
Everyone who is both not happy and funny is not calm and vice versa.
Everyone who is both tall and not patient is generous.
Everyone who is either calm or not tall is either not curious or old.
If someone is either kind or not tall then someone is either not rich or tall and vice versa.
If fred is both not wise and not kind then mary is quiet and vice versa.
Everyone who is either not brave or wise is kind.
Everyone who is both not happy and curious is both not rich and not strong and vice versa.
Everyone who is not quiet is happy.
Fred is not creative.
Someone is both kind and brave.
Alice is both not calm and not wise.
Lucy is kind.
Someone is either not happy or kind.
Paul is either tall or patient.
Susan is either not creative or not brave.
Someone is both humble and not strong. | Susan is not tall. | neutral | ((?[X]:(funny(X)))=>((curious(lucy)&~patient(lucy))))&
(![X]:(kind(X)<=>(strong(X)&~humble(X))))&
((?[X]:((old(X)|calm(X))))<=>(?[X]:((humble(X)&brave(X)))))&
(((~creative(lucy)|creative(lucy)))<=>(~patient(paul)))&
(![X]:(~creative(X)=>(~quiet(X)<~>funny(X))))&
((old(mary))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~happy(X)&calm(X))=>generous(X)))&
(((~funny(alice)<~>~brave(alice)))<=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((~happy(X)&funny(X))<=>~calm(X)))&
(![X]:((tall(X)&~patient(X))=>generous(X)))&
(![X]:((calm(X)<~>~tall(X))=>(~curious(X)<~>old(X))))&
((?[X]:((kind(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>tall(X)))))&
(((~wise(fred)&~kind(fred)))<=>(quiet(mary)))&
(![X]:((~brave(X)<~>wise(X))=>kind(X)))&
(![X]:((~happy(X)&curious(X))<=>(~rich(X)&~strong(X))))&
(![X]:(~quiet(X)=>happy(X)))&
(~creative(fred))&
(?[X]:((kind(X)&brave(X))))&
((~calm(alice)&~wise(alice)))&
(kind(lucy))&
(?[X]:((~happy(X)<~>kind(X))))&
((tall(paul)<~>patient(paul)))&
((~creative(susan)<~>~brave(susan)))&
(?[X]:((humble(X)&~strong(X)))) | ~tall(susan) | [] | null | 0 |
Everyone who is either not calm or old is rich and vice versa.
Everyone who is calm is either not tall or not wise.
If someone is creative then someone is either tall or happy.
If lucy is either calm or not humble then paul is generous or not kind.
Everyone who is either not calm or tall is either not rich or not patient.
Everyone who is both kind and not wise is happy and vice versa.
If someone is not rich or not wise then lucy is both not kind and not funny and vice versa.
If susan is either not brave or brave then someone is both not rich and not funny and vice versa.
If someone is not old or not strong then lucy is not funny and vice versa.
If someone is wise then someone is either generous or not happy.
If lucy is humble or curious then susan is either kind or not humble and vice versa.
Everyone who is either not rich or not kind is not old or creative.
If paul is either not quiet or creative then alice is generous or patient.
Everyone who is creative or not calm is either quiet or not happy.
Everyone who is both funny and not strong is generous or happy and vice versa.
Everyone who is both not curious and calm is both creative and not quiet.
Someone is not tall or funny.
Someone is either wise or not rich.
Someone is humble.
Someone is both not tall and not kind.
Someone is either not humble or not curious.
Someone is not creative or not generous.
Susan is either curious or strong. | Lucy is happy. | contradiction | (![X]:((~calm(X)<~>old(X))<=>rich(X)))&
(![X]:(calm(X)=>(~tall(X)<~>~wise(X))))&
((?[X]:(creative(X)))=>(?[X]:((tall(X)<~>happy(X)))))&
(((calm(lucy)<~>~humble(lucy)))=>((generous(paul)|~kind(paul))))&
(![X]:((~calm(X)<~>tall(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((kind(X)&~wise(X))<=>happy(X)))&
((?[X]:((~rich(X)|~wise(X))))<=>((~kind(lucy)&~funny(lucy))))&
(((~brave(susan)<~>brave(susan)))<=>(?[X]:((~rich(X)&~funny(X)))))&
((?[X]:((~old(X)|~strong(X))))<=>(~funny(lucy)))&
((?[X]:(wise(X)))=>(?[X]:((generous(X)<~>~happy(X)))))&
(((humble(lucy)|curious(lucy)))<=>((kind(susan)<~>~humble(susan))))&
(![X]:((~rich(X)<~>~kind(X))=>(~old(X)|creative(X))))&
(((~quiet(paul)<~>creative(paul)))=>((generous(alice)|patient(alice))))&
(![X]:((creative(X)|~calm(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((funny(X)&~strong(X))<=>(generous(X)|happy(X))))&
(![X]:((~curious(X)&calm(X))=>(creative(X)&~quiet(X))))&
(?[X]:((~tall(X)|funny(X))))&
(?[X]:((wise(X)<~>~rich(X))))&
(?[X]:(humble(X)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((~creative(X)|~generous(X))))&
((curious(susan)<~>strong(susan))) | happy(lucy) | [
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4658989554837382777469301
% SZS output start Proof for 4658989554837382777469301
6. ! [X0] : ((~wise(X0) & kind(X0)) <=> happy(X0)) [input p5]
7. ? [X0] : (~wise(X0) | ~rich(X0)) <=> (~funny(lucy) & ~kind(lucy)) [input p6]
8. (~brave(susan) <~> brave(susan)) <=> ? [X0] : (~funny(X0) & ~rich(X0)) [input p7]
24. happy(lucy) [input hypothesis]
48. ! [X0] : (((~wise(X0) & kind(X0)) | ~happy(X0)) & (happy(X0) | (wise(X0) | ~kind(X0)))) [nnf transformation 6]
49. ! [X0] : (((~wise(X0) & kind(X0)) | ~happy(X0)) & (happy(X0) | wise(X0) | ~kind(X0))) [flattening 48]
50. (? [X0] : (~wise(X0) | ~rich(X0)) | (funny(lucy) | kind(lucy))) & ((~funny(lucy) & ~kind(lucy)) | ! [X0] : (wise(X0) & rich(X0))) [nnf transformation 7]
51. (? [X0] : (~wise(X0) | ~rich(X0)) | funny(lucy) | kind(lucy)) & ((~funny(lucy) & ~kind(lucy)) | ! [X0] : (wise(X0) & rich(X0))) [flattening 50]
52. (? [X0] : (~wise(X0) | ~rich(X0)) | funny(lucy) | kind(lucy)) & ((~funny(lucy) & ~kind(lucy)) | ! [X1] : (wise(X1) & rich(X1))) [rectify 51]
53. ? [X0] : (~wise(X0) | ~rich(X0)) => (~wise(sK1) | ~rich(sK1)) [choice axiom]
54. ((~wise(sK1) | ~rich(sK1)) | funny(lucy) | kind(lucy)) & ((~funny(lucy) & ~kind(lucy)) | ! [X1] : (wise(X1) & rich(X1))) [skolemisation 52,53]
55. (((~brave(susan) | brave(susan)) & (brave(susan) | ~brave(susan))) | ! [X0] : (funny(X0) | rich(X0))) & (? [X0] : (~funny(X0) & ~rich(X0)) | ((~brave(susan) | ~brave(susan)) & (brave(susan) | brave(susan)))) [nnf transformation 8]
56. (((~brave(susan) | brave(susan)) & (brave(susan) | ~brave(susan))) | ! [X0] : (funny(X0) | rich(X0))) & (? [X1] : (~funny(X1) & ~rich(X1)) | ((~brave(susan) | ~brave(susan)) & (brave(susan) | brave(susan)))) [rectify 55]
57. ? [X1] : (~funny(X1) & ~rich(X1)) => (~funny(sK2) & ~rich(sK2)) [choice axiom]
58. (((~brave(susan) | brave(susan)) & (brave(susan) | ~brave(susan))) | ! [X0] : (funny(X0) | rich(X0))) & ((~funny(sK2) & ~rich(sK2)) | ((~brave(susan) | ~brave(susan)) & (brave(susan) | brave(susan)))) [skolemisation 56,57]
104. ~happy(X0) | kind(X0) [cnf transformation 49]
106. ~kind(lucy) | rich(X1) [cnf transformation 54]
111. ~rich(sK2) | brave(susan) | brave(susan) [cnf transformation 58]
112. ~rich(sK2) | ~brave(susan) | ~brave(susan) [cnf transformation 58]
154. happy(lucy) [cnf transformation 24]
155. ~rich(sK2) | brave(susan) [duplicate literal removal 111]
156. ~rich(sK2) | ~brave(susan) [duplicate literal removal 112]
191. 8 <=> kind(lucy) [avatar definition]
212. 13 <=> ! [X1] : rich(X1) [avatar definition]
213. rich(X1) <- (13) [avatar component clause 212]
216. 13 | ~8 [avatar split clause 106,191,212]
218. 14 <=> brave(susan) [avatar definition]
228. 16 <=> rich(sK2) [avatar definition]
230. ~rich(sK2) <- (~16) [avatar component clause 228]
231. ~14 | ~16 [avatar split clause 156,228,218]
232. 14 | ~16 [avatar split clause 155,228,218]
347. kind(lucy) [resolution 104,154]
350. 8 [avatar split clause 347,191]
355. $false <- (13, ~16) [resolution 213,230]
356. ~13 | 16 [avatar contradiction clause 355]
357. $false [avatar sat refutation 216,231,232,350,356]
% SZS output end Proof for 4658989554837382777469301
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or brave is not funny or not strong.
Everyone who is not happy or not kind is not calm.
Everyone who is either not funny or wise is both wise and not rich and vice versa.
Everyone who is not creative or not humble is rich and vice versa.
If susan is both generous and not rich then fred is either humble or happy.
If someone is either not kind or not wise then someone is not patient and vice versa.
If someone is not creative then someone is both funny and not quiet.
If alice is both not brave and not wise then someone is both not creative and quiet and vice versa.
If someone is not wise or wise then someone is not rich and vice versa.
Everyone who is not curious is quiet and vice versa.
Everyone who is both not quiet and happy is funny and vice versa.
If mary is brave or rich then someone is both old and curious.
Everyone who is both not kind and not rich is quiet or curious and vice versa.
Everyone who is brave is funny or not generous and vice versa.
Everyone who is either old or not creative is not rich and vice versa.
Everyone who is not creative is not brave and vice versa.
Mary is either tall or not quiet.
Mary is creative or brave.
Alice is happy or tall.
Someone is patient or not brave.
Someone is brave or patient. | Mary is curious. | entailment | (![X]:((calm(X)<~>brave(X))=>(~funny(X)|~strong(X))))&
(![X]:((~happy(X)|~kind(X))=>~calm(X)))&
(![X]:((~funny(X)<~>wise(X))<=>(wise(X)&~rich(X))))&
(![X]:((~creative(X)|~humble(X))<=>rich(X)))&
(((generous(susan)&~rich(susan)))=>((humble(fred)<~>happy(fred))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((funny(X)&~quiet(X)))))&
(((~brave(alice)&~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>quiet(X)))&
(![X]:((~quiet(X)&happy(X))<=>funny(X)))&
(((brave(mary)|rich(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:(brave(X)<=>(funny(X)|~generous(X))))&
(![X]:((old(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~creative(X)<=>~brave(X)))&
((tall(mary)<~>~quiet(mary)))&
((creative(mary)|brave(mary)))&
((happy(alice)|tall(alice)))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((brave(X)|patient(X)))) | curious(mary) | [
"p2",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8867696425558795648923726
% SZS output start Proof for 8867696425558795648923726
3. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> (~rich(X0) & wise(X0))) [input p2]
10. ! [X0] : (~curious(X0) <=> quiet(X0)) [input p9]
11. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> funny(X0)) [input p10]
13. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (curious(X0) | quiet(X0))) [input p12]
22. ~curious(mary) [input hypothesis]
32. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 3]
33. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [flattening 32]
55. ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))) [nnf transformation 10]
56. ! [X0] : (((happy(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | (~happy(X0) | quiet(X0)))) [nnf transformation 11]
57. ! [X0] : (((happy(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | ~happy(X0) | quiet(X0))) [flattening 56]
60. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 13]
61. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | rich(X0) | kind(X0))) [flattening 60]
71. wise(X0) | wise(X0) | funny(X0) [cnf transformation 33]
76. ~wise(X0) | funny(X0) | rich(X0) | ~wise(X0) [cnf transformation 33]
95. curious(X0) | quiet(X0) [cnf transformation 55]
98. ~quiet(X0) | ~funny(X0) [cnf transformation 57]
107. ~quiet(X0) | ~rich(X0) [cnf transformation 61]
108. ~curious(X0) | ~rich(X0) [cnf transformation 61]
124. ~curious(mary) [cnf transformation 22]
125. wise(X0) | funny(X0) [duplicate literal removal 71]
126. ~wise(X0) | funny(X0) | rich(X0) [duplicate literal removal 76]
245. 27 <=> quiet(mary) [avatar definition]
247. quiet(mary) <- (27) [avatar component clause 245]
280. quiet(mary) [resolution 95,124]
283. 27 [avatar split clause 280,245]
285. ~funny(mary) <- (27) [resolution 98,247]
292. ~rich(X0) | quiet(X0) [resolution 108,95]
293. ~rich(X0) [subsumption resolution 292,107]
327. funny(X0) | rich(X0) | funny(X0) [resolution 126,125]
328. funny(X0) | rich(X0) [duplicate literal removal 327]
332. funny(X0) [subsumption resolution 328,293]
336. $false <- (27) [resolution 332,285]
339. ~27 [avatar contradiction clause 336]
340. $false [avatar sat refutation 283,339]
% SZS output end Proof for 8867696425558795648923726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either strong or creative then susan is funny or not calm and vice versa.
Everyone who is either not kind or not happy is not quiet.
Everyone who is not rich is both not strong and strong.
Everyone who is both not calm and creative is either not calm or not wise and vice versa.
If john is either strong or not generous then susan is either generous or patient and vice versa.
If paul is not kind then someone is both brave and not happy.
Everyone who is calm or not curious is generous or not humble.
If someone is happy then fred is not wise.
Everyone who is both not funny and tall is both old and not patient.
Everyone who is both creative and quiet is both not tall and not humble.
If someone is not generous or not quiet then someone is both calm and happy and vice versa.
Everyone who is both not wise and not curious is either not tall or tall and vice versa.
Everyone who is curious or tall is not rich or happy and vice versa.
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.
Susan is rich or tall.
Fred is either happy or strong.
Mary is either calm or kind.
Lucy is both not patient and humble.
Someone is both not curious and strong. | Lucy is not patient. | entailment | (((strong(mary)<~>creative(mary)))<=>((funny(susan)|~calm(susan))))&
(![X]:((~kind(X)<~>~happy(X))=>~quiet(X)))&
(![X]:(~rich(X)=>(~strong(X)&strong(X))))&
(![X]:((~calm(X)&creative(X))<=>(~calm(X)<~>~wise(X))))&
(((strong(john)<~>~generous(john)))<=>((generous(susan)<~>patient(susan))))&
((~kind(paul))=>(?[X]:((brave(X)&~happy(X)))))&
(![X]:((calm(X)|~curious(X))=>(generous(X)|~humble(X))))&
((?[X]:(happy(X)))=>(~wise(fred)))&
(![X]:((~funny(X)&tall(X))=>(old(X)&~patient(X))))&
(![X]:((creative(X)&quiet(X))=>(~tall(X)&~humble(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((calm(X)&happy(X)))))&
(![X]:((~wise(X)&~curious(X))<=>(~tall(X)<~>tall(X))))&
(![X]:((curious(X)|tall(X))<=>(~rich(X)|happy(X))))&
((?[X]:((~rich(X)|humble(X))))<=>((~humble(paul)|strong(paul))))&
((?[X]:(~rich(X)))=>((~curious(fred)|funny(fred))))&
(![X]:(funny(X)=>(calm(X)&curious(X))))&
((rich(susan)|tall(susan)))&
((happy(fred)<~>strong(fred)))&
((calm(mary)<~>kind(mary)))&
((~patient(lucy)&humble(lucy)))&
(?[X]:((~curious(X)&strong(X)))) | ~patient(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3456611646438927140794277
% SZS output start Proof for 3456611646438927140794277
20. humble(lucy) & ~patient(lucy) [input p19]
22. patient(lucy) [input hypothesis]
123. ~patient(lucy) [cnf transformation 20]
127. patient(lucy) [cnf transformation 22]
274. $false [subsumption resolution 127,123]
% SZS output end Proof for 3456611646438927140794277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then susan is not quiet and vice versa. If someone is both not old and patient then lucy is not calm or brave. If someone is not creative or not tall then paul is both kind and not strong and vice versa. Everyone who is patient is quiet or not funny. 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. If susan is either not brave or wise then someone is brave and vice versa. Everyone who is not kind or creative is both not funny and brave. If someone is either curious or not rich then lucy is not rich or not funny. If paul is not quiet or not calm then someone is either not patient or kind. If someone is both not quiet and not humble then fred is patient or calm and vice versa. If someone is both wise and funny then mary is both not tall and not humble and vice versa. Everyone who is patient or quiet is either not creative or quiet and vice versa. Everyone who is not strong is not kind. If susan is curious then someone is either tall or not quiet. If susan is brave or calm then someone is not wise. Someone is patient. Mary is rich. John is wise or brave. Someone is either not humble or old. Alice is tall. John is both not patient and strong. | Susan is brave. | entailment | ((?[X]:(old(X)))<=>(~quiet(susan)))&
((?[X]:((~old(X)&patient(X))))=>((~calm(lucy)|brave(lucy))))&
((?[X]:((~creative(X)|~tall(X))))<=>((kind(paul)&~strong(paul))))&
(![X]:(patient(X)=>(quiet(X)|~funny(X))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
(((~brave(susan)<~>wise(susan)))<=>(?[X]:(brave(X))))&
(![X]:((~kind(X)|creative(X))=>(~funny(X)&brave(X))))&
((?[X]:((curious(X)<~>~rich(X))))=>((~rich(lucy)|~funny(lucy))))&
(((~quiet(paul)|~calm(paul)))=>(?[X]:((~patient(X)<~>kind(X)))))&
((?[X]:((~quiet(X)&~humble(X))))<=>((patient(fred)|calm(fred))))&
((?[X]:((wise(X)&funny(X))))<=>((~tall(mary)&~humble(mary))))&
(![X]:((patient(X)|quiet(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:(~strong(X)=>~kind(X)))&
((curious(susan))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(((brave(susan)|calm(susan)))=>(?[X]:(~wise(X))))&
(?[X]:(patient(X)))&
(rich(mary))&
((wise(john)|brave(john)))&
(?[X]:((~humble(X)<~>old(X))))&
(tall(alice))&
((~patient(john)&strong(john))) | brave(susan) | [
"p2",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 637991220704108816115356
% SZS output start Proof for 637991220704108816115356
3. ? [X0] : (~tall(X0) | ~creative(X0)) <=> (~strong(paul) & kind(paul)) [input p2]
8. ! [X0] : ((creative(X0) | ~kind(X0)) => (brave(X0) & ~funny(X0))) [input p7]
14. ! [X0] : (~strong(X0) => ~kind(X0)) [input p13]
23. ~brave(susan) [input hypothesis]
28. ! [X0] : ((brave(X0) & ~funny(X0)) | (~creative(X0) & kind(X0))) [ennf transformation 8]
32. ! [X0] : (~kind(X0) | strong(X0)) [ennf transformation 14]
39. (? [X0] : (~tall(X0) | ~creative(X0)) | (strong(paul) | ~kind(paul))) & ((~strong(paul) & kind(paul)) | ! [X0] : (tall(X0) & creative(X0))) [nnf transformation 3]
40. (? [X0] : (~tall(X0) | ~creative(X0)) | strong(paul) | ~kind(paul)) & ((~strong(paul) & kind(paul)) | ! [X0] : (tall(X0) & creative(X0))) [flattening 39]
41. (? [X0] : (~tall(X0) | ~creative(X0)) | strong(paul) | ~kind(paul)) & ((~strong(paul) & kind(paul)) | ! [X1] : (tall(X1) & creative(X1))) [rectify 40]
42. ? [X0] : (~tall(X0) | ~creative(X0)) => (~tall(sK1) | ~creative(sK1)) [choice axiom]
43. ((~tall(sK1) | ~creative(sK1)) | strong(paul) | ~kind(paul)) & ((~strong(paul) & kind(paul)) | ! [X1] : (tall(X1) & creative(X1))) [skolemisation 41,42]
85. kind(paul) | creative(X1) [cnf transformation 43]
87. ~strong(paul) | creative(X1) [cnf transformation 43]
108. ~creative(X0) | brave(X0) [cnf transformation 28]
130. ~kind(X0) | strong(X0) [cnf transformation 32]
143. ~brave(susan) [cnf transformation 23]
174. 7 <=> kind(paul) [avatar definition]
175. kind(paul) <- (7) [avatar component clause 174]
178. 8 <=> strong(paul) [avatar definition]
195. 12 <=> ! [X1] : creative(X1) [avatar definition]
196. creative(X1) <- (12) [avatar component clause 195]
197. 12 | ~8 [avatar split clause 87,178,195]
199. 12 | 7 [avatar split clause 85,174,195]
242. 22 <=> brave(susan) [avatar definition]
243. ~brave(susan) <- (~22) [avatar component clause 242]
383. ~22 [avatar split clause 143,242]
390. strong(paul) <- (7) [resolution 130,175]
395. 8 | ~7 [avatar split clause 390,174,178]
400. brave(X0) <- (12) [resolution 196,108]
403. $false <- (12, ~22) [resolution 400,243]
404. ~12 | 22 [avatar contradiction clause 403]
405. $false [avatar sat refutation 197,199,383,395,404]
% SZS output end Proof for 637991220704108816115356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not creative is either not quiet or not curious and vice versa. Everyone who is either wise or patient is not calm or creative. If someone is both tall and not brave then someone is creative. If someone is not calm or not happy then mary is generous. Everyone who is both generous and calm is tall and vice versa. If paul is funny then paul is not creative. Everyone who is either wise or quiet is kind or not brave and vice versa. Everyone who is not kind or kind is either calm or tall. Everyone who is both creative and strong is quiet or patient and vice versa. Everyone who is either quiet or humble is not rich or patient and vice versa. Everyone who is both not tall and funny is not old or curious and vice versa. Everyone who is either patient or not strong is both not calm and brave and vice versa. Everyone who is not strong is kind or not calm and vice versa. If susan is old or not tall then someone is quiet. If someone is both quiet and happy then fred is happy or generous and vice versa. Everyone who is not wise or not rich is both not happy and not brave. Fred is not funny or not brave. Someone is curious or funny. Someone is not quiet or humble. Someone is calm or kind. Someone is either calm or generous. Someone is both not kind and strong. | Mary is not creative. | contradiction | (![X]:((quiet(X)<~>~creative(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((wise(X)<~>patient(X))=>(~calm(X)|creative(X))))&
((?[X]:((tall(X)&~brave(X))))=>(?[X]:(creative(X))))&
((?[X]:((~calm(X)|~happy(X))))=>(generous(mary)))&
(![X]:((generous(X)&calm(X))<=>tall(X)))&
((funny(paul))=>(~creative(paul)))&
(![X]:((wise(X)<~>quiet(X))<=>(kind(X)|~brave(X))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
((~funny(fred)|~brave(fred)))&
(?[X]:((curious(X)|funny(X))))&
(?[X]:((~quiet(X)|humble(X))))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:((calm(X)<~>generous(X))))&
(?[X]:((~kind(X)&strong(X)))) | ~creative(mary) | [
"p1",
"p3",
"p4",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4305174731332904434143716
% SZS output start Proof for 4305174731332904434143716
2. ! [X0] : ((wise(X0) <~> patient(X0)) => (creative(X0) | ~calm(X0))) [input p1]
4. ? [X0] : (~happy(X0) | ~calm(X0)) => generous(mary) [input p3]
5. ! [X0] : ((calm(X0) & generous(X0)) <=> tall(X0)) [input p4]
8. ! [X0] : ((kind(X0) | ~kind(X0)) => (calm(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((strong(X0) & creative(X0)) <=> (patient(X0) | quiet(X0))) [input p8]
12. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p11]
16. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p15]
23. ~creative(mary) [input hypothesis]
25. ! [X0] : ((creative(X0) | ~calm(X0)) | (wise(X0) <=> patient(X0))) [ennf transformation 2]
26. ! [X0] : (creative(X0) | ~calm(X0) | (wise(X0) <=> patient(X0))) [flattening 25]
28. generous(mary) | ! [X0] : (happy(X0) & calm(X0)) [ennf transformation 4]
30. ! [X0] : ((calm(X0) <~> tall(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 8]
32. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 16]
34. ! [X0] : (creative(X0) | ~calm(X0) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0)))) [nnf transformation 26]
38. ! [X0] : (((calm(X0) & generous(X0)) | ~tall(X0)) & (tall(X0) | (~calm(X0) | ~generous(X0)))) [nnf transformation 5]
39. ! [X0] : (((calm(X0) & generous(X0)) | ~tall(X0)) & (tall(X0) | ~calm(X0) | ~generous(X0))) [flattening 38]
42. ! [X0] : (((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (~kind(X0) & kind(X0))) [nnf transformation 30]
43. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 9]
44. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 43]
49. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 12]
50. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 49]
79. ~calm(X0) | creative(X0) | patient(X0) | ~wise(X0) [cnf transformation 34]
83. generous(mary) | happy(X0) [cnf transformation 28]
84. ~generous(X0) | ~calm(X0) | tall(X0) [cnf transformation 39]
86. ~tall(X0) | calm(X0) [cnf transformation 39]
94. tall(X0) | calm(X0) | kind(X0) [cnf transformation 42]
95. tall(X0) | calm(X0) | ~kind(X0) [cnf transformation 42]
96. ~tall(X0) | ~calm(X0) | kind(X0) [cnf transformation 42]
97. ~tall(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 42]
102. ~patient(X0) | strong(X0) [cnf transformation 44]
114. ~calm(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 50]
130. ~happy(X0) | wise(X0) [cnf transformation 32]
142. ~creative(mary) [cnf transformation 23]
158. 3 <=> ! [X0] : happy(X0) [avatar definition]
159. happy(X0) <- (3) [avatar component clause 158]
161. 4 <=> generous(mary) [avatar definition]
163. generous(mary) <- (4) [avatar component clause 161]
164. 3 | 4 [avatar split clause 83,161,158]
166. 5 <=> ! [X0] : calm(X0) [avatar definition]
167. calm(X0) <- (5) [avatar component clause 166]
178. ~kind(X0) | ~tall(X0) [subsumption resolution 97,86]
179. ~tall(X0) | kind(X0) [subsumption resolution 96,86]
180. ~tall(X0) [subsumption resolution 179,178]
181. ~kind(X0) | calm(X0) [subsumption resolution 95,180]
182. calm(X0) | kind(X0) [subsumption resolution 94,180]
183. calm(X0) [subsumption resolution 182,181]
184. 5 [avatar split clause 183,166]
189. ~calm(X0) | ~patient(X0) [subsumption resolution 114,102]
264. ~patient(X0) <- (5) [resolution 189,167]
269. ~calm(mary) | tall(mary) <- (4) [resolution 84,163]
271. tall(mary) <- (4, 5) [subsumption resolution 269,167]
272. $false <- (4, 5) [subsumption resolution 271,180]
273. ~4 | ~5 [avatar contradiction clause 272]
278. wise(X1) <- (3) [resolution 159,130]
298. creative(X0) | patient(X0) | ~wise(X0) <- (5) [resolution 79,167]
301. creative(X0) | ~wise(X0) <- (5) [subsumption resolution 298,264]
302. creative(X0) <- (3, 5) [subsumption resolution 301,278]
306. $false <- (3, 5) [resolution 302,142]
309. ~3 | ~5 [avatar contradiction clause 306]
310. $false [avatar sat refutation 164,184,273,309]
% SZS output end Proof for 4305174731332904434143716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and not brave.
Everyone who is either curious or kind is humble.
If paul is quiet then someone is either rich or not strong.
Everyone who is wise or creative is both not quiet and not patient.
If someone is both happy and not happy then someone is either not tall or strong and vice versa.
Everyone who is either patient or humble is not wise and vice versa.
If someone is funny then someone is wise or generous.
If someone is not curious or old then fred is either not curious or tall.
If lucy is tall then someone is either not rich or not generous.
Everyone who is not humble or not calm is both old and not rich.
If someone is either not generous or not humble then someone is not funny or not rich.
If lucy is either not tall or not calm then paul is humble or not curious and vice versa.
If someone is both not creative and funny then someone is not rich or not curious.
If mary is patient then alice is both patient and not generous and vice versa.
Everyone who is both not rich and not strong is either not happy or kind and vice versa.
If someone is both not strong and quiet then lucy is either not strong or not tall.
Alice is both wise and not quiet.
Someone is either not kind or not calm.
Someone is not wise or kind.
Alice is either not creative or creative.
Someone is both not old and not patient.
John is either wise or not patient.
Fred is both not curious and creative.
Fred is tall or old. | Alice is rich. | contradiction | (![X]:(rich(X)=>(funny(X)&~brave(X))))&
(![X]:((curious(X)<~>kind(X))=>humble(X)))&
((quiet(paul))=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:((wise(X)|creative(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((happy(X)&~happy(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((patient(X)<~>humble(X))<=>~wise(X)))&
((?[X]:(funny(X)))=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:((~curious(X)|old(X))))=>((~curious(fred)<~>tall(fred))))&
((tall(lucy))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((~humble(X)|~calm(X))=>(old(X)&~rich(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(?[X]:((~funny(X)|~rich(X)))))&
(((~tall(lucy)<~>~calm(lucy)))<=>((humble(paul)|~curious(paul))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((patient(mary))<=>((patient(alice)&~generous(alice))))&
(![X]:((~rich(X)&~strong(X))<=>(~happy(X)<~>kind(X))))&
((?[X]:((~strong(X)&quiet(X))))=>((~strong(lucy)<~>~tall(lucy))))&
((wise(alice)&~quiet(alice)))&
(?[X]:((~kind(X)<~>~calm(X))))&
(?[X]:((~wise(X)|kind(X))))&
((~creative(alice)<~>creative(alice)))&
(?[X]:((~old(X)&~patient(X))))&
((wise(john)<~>~patient(john)))&
((~curious(fred)&creative(fred)))&
((tall(fred)|old(fred))) | rich(alice) | [
"p3",
"p5",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 848855315381805476250831
% SZS output start Proof for 848855315381805476250831
4. ! [X0] : ((creative(X0) | wise(X0)) => (~patient(X0) & ~quiet(X0))) [input p3]
6. ! [X0] : ((patient(X0) <~> humble(X0)) <=> ~wise(X0)) [input p5]
10. ! [X0] : ((~calm(X0) | ~humble(X0)) => (~rich(X0) & old(X0))) [input p9]
17. ~quiet(alice) & wise(alice) [input p16]
25. rich(alice) [input hypothesis]
32. ! [X0] : ((creative(X0) | wise(X0)) => ~patient(X0)) [pure predicate removal 4]
33. wise(alice) [pure predicate removal 17]
37. ! [X0] : (~patient(X0) | (~creative(X0) & ~wise(X0))) [ennf transformation 32]
41. ! [X0] : ((~rich(X0) & old(X0)) | (calm(X0) & humble(X0))) [ennf transformation 10]
50. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | wise(X0)) & (~wise(X0) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [nnf transformation 6]
83. ~patient(X0) | ~wise(X0) [cnf transformation 37]
92. ~wise(X0) | patient(X0) | ~humble(X0) [cnf transformation 50]
94. ~humble(X0) | ~patient(X0) | wise(X0) [cnf transformation 50]
104. ~rich(X0) | humble(X0) [cnf transformation 41]
124. wise(alice) [cnf transformation 33]
137. rich(alice) [cnf transformation 25]
152. ~patient(X0) | ~humble(X0) [subsumption resolution 94,83]
153. ~wise(X0) | ~humble(X0) [subsumption resolution 92,152]
293. humble(alice) [resolution 104,137]
300. ~humble(alice) [resolution 153,124]
302. $false [subsumption resolution 300,293]
% SZS output end Proof for 848855315381805476250831
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny then someone is both not patient and not humble. Everyone who is both kind and humble is humble and vice versa. If john is both not quiet and not creative then someone is not happy or not patient and vice versa. If someone is both not rich and not creative then someone is rich. If alice is either kind or funny then someone is not strong or not humble and vice versa. Everyone who is both not strong and not curious is both old and creative and vice versa. Everyone who is either not tall or not generous is both not wise and not calm. If someone is both patient and old then someone is both generous and not strong and vice versa. If someone is both wise and quiet then fred is rich or old and vice versa. Everyone who is either not tall or creative is not kind or not strong and vice versa. If paul is not brave or not quiet then susan is funny and vice versa. If mary is not tall or generous then someone is either calm or strong and vice versa. Everyone who is either wise or tall is both brave and kind. If someone is both not funny and rich then fred is not kind and vice versa. Everyone who is either not old or quiet is not curious or not kind and vice versa. Everyone who is curious is both not brave and old and vice versa. Alice is either not patient or funny. Lucy is patient or not strong. Lucy is kind. Someone is wise. Someone is not patient or not quiet. Someone is either not curious or wise. Fred is both happy and curious. | Susan is wise. | neutral | ((?[X]:(~funny(X)))=>(?[X]:((~patient(X)&~humble(X)))))&
(![X]:((kind(X)&humble(X))<=>humble(X)))&
(((~quiet(john)&~creative(john)))<=>(?[X]:((~happy(X)|~patient(X)))))&
((?[X]:((~rich(X)&~creative(X))))=>(?[X]:(rich(X))))&
(((kind(alice)<~>funny(alice)))<=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((~strong(X)&~curious(X))<=>(old(X)&creative(X))))&
(![X]:((~tall(X)<~>~generous(X))=>(~wise(X)&~calm(X))))&
((?[X]:((patient(X)&old(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:((wise(X)&quiet(X))))<=>((rich(fred)|old(fred))))&
(![X]:((~tall(X)<~>creative(X))<=>(~kind(X)|~strong(X))))&
(((~brave(paul)|~quiet(paul)))<=>(funny(susan)))&
(((~tall(mary)|generous(mary)))<=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((wise(X)<~>tall(X))=>(brave(X)&kind(X))))&
((?[X]:((~funny(X)&rich(X))))<=>(~kind(fred)))&
(![X]:((~old(X)<~>quiet(X))<=>(~curious(X)|~kind(X))))&
(![X]:(curious(X)<=>(~brave(X)&old(X))))&
((~patient(alice)<~>funny(alice)))&
((patient(lucy)|~strong(lucy)))&
(kind(lucy))&
(?[X]:(wise(X)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((happy(fred)&curious(fred))) | wise(susan) | [] | null | 0 |
If someone is both patient and generous then someone is either old or patient and vice versa.
Everyone who is not humble is either not wise or not humble and vice versa.
Everyone who is generous or not funny is strong and vice versa.
Everyone who is either not generous or not rich is not calm or patient and vice versa.
Everyone who is either not tall or creative is either not rich or humble and vice versa.
If someone is both not generous and not creative then someone is funny.
Everyone who is creative is not wise.
Everyone who is not old is both creative and generous.
Everyone who is not curious or generous is both not tall and wise.
Everyone who is patient is either not old or wise and vice versa.
If john is funny or curious then someone is either brave or not tall.
Everyone who is either not happy or tall is both patient and funny and vice versa.
If someone is not quiet or not strong then susan is either not calm or kind and vice versa.
If lucy is funny then someone is both funny and not humble.
Everyone who is happy or not patient is either not rich or not brave.
Paul is brave.
Someone is either kind or happy.
Someone is either not wise or not quiet.
Someone is quiet.
Paul is not tall.
Lucy is humble or not kind. | Paul is curious. | neutral | ((?[X]:((patient(X)&generous(X))))<=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(~humble(X)<=>(~wise(X)<~>~humble(X))))&
(![X]:((generous(X)|~funny(X))<=>strong(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>(~calm(X)|patient(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(~rich(X)<~>humble(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:(funny(X))))&
(![X]:(creative(X)=>~wise(X)))&
(![X]:(~old(X)=>(creative(X)&generous(X))))&
(![X]:((~curious(X)|generous(X))=>(~tall(X)&wise(X))))&
(![X]:(patient(X)<=>(~old(X)<~>wise(X))))&
(((funny(john)|curious(john)))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(patient(X)&funny(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((~calm(susan)<~>kind(susan))))&
((funny(lucy))=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:((happy(X)|~patient(X))=>(~rich(X)<~>~brave(X))))&
(brave(paul))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((~wise(X)<~>~quiet(X))))&
(?[X]:(quiet(X)))&
(~tall(paul))&
((humble(lucy)|~kind(lucy))) | curious(paul) | [] | null | 0 |
If someone is either not funny or not generous then paul is both not patient and not tall and vice versa.
If someone is calm then fred is funny.
Everyone who is either funny or not happy is funny or not old and vice versa.
Everyone who is either not creative or not wise is not patient.
If someone is both calm and not humble then someone is either quiet or creative and vice versa.
If someone is both not creative and not tall then someone is not patient or quiet and vice versa.
Everyone who is either not curious or quiet is either funny or happy and vice versa.
Everyone who is both humble and not old is both not curious and not kind and vice versa.
If someone is either quiet or curious then someone is both quiet and not quiet and vice versa.
If alice is either not quiet or old then someone is either not wise or not strong and vice versa.
If someone is both creative and strong then someone is not brave.
If fred is wise or not funny then someone is not old or rich and vice versa.
If someone is either kind or curious then john is wise or not creative.
Everyone who is not brave is both not patient and not calm.
If someone is either not humble or brave then someone is both not funny and generous and vice versa.
Everyone who is not kind is both not happy and calm and vice versa.
Lucy is patient.
Susan is humble or strong.
John is not creative.
Someone is not funny or not old.
Paul is old or funny. | Susan is not funny. | entailment | ((?[X]:((~funny(X)<~>~generous(X))))<=>((~patient(paul)&~tall(paul))))&
((?[X]:(calm(X)))=>(funny(fred)))&
(![X]:((funny(X)<~>~happy(X))<=>(funny(X)|~old(X))))&
(![X]:((~creative(X)<~>~wise(X))=>~patient(X)))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
((?[X]:((~creative(X)&~tall(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((~curious(X)<~>quiet(X))<=>(funny(X)<~>happy(X))))&
(![X]:((humble(X)&~old(X))<=>(~curious(X)&~kind(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(((~quiet(alice)<~>old(alice)))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
((?[X]:((creative(X)&strong(X))))=>(?[X]:(~brave(X))))&
(((wise(fred)|~funny(fred)))<=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((kind(X)<~>curious(X))))=>((wise(john)|~creative(john))))&
(![X]:(~brave(X)=>(~patient(X)&~calm(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:(~kind(X)<=>(~happy(X)&calm(X))))&
(patient(lucy))&
((humble(susan)|strong(susan)))&
(~creative(john))&
(?[X]:((~funny(X)|~old(X))))&
((old(paul)|funny(paul))) | ~funny(susan) | [
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2154193371611602669226862
% SZS output start Proof for 2154193371611602669226862
3. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (~old(X0) | funny(X0))) [input p2]
7. ! [X0] : ((~curious(X0) <~> quiet(X0)) <=> (funny(X0) <~> happy(X0))) [input p6]
9. ? [X0] : (quiet(X0) <~> curious(X0)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p8]
22. funny(susan) [input hypothesis]
25. ? [X0] : (quiet(X0) <~> curious(X0)) <=> ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 9]
39. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (old(X0) & ~funny(X0))) & ((~old(X0) | funny(X0)) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 3]
40. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (old(X0) & ~funny(X0))) & (~old(X0) | funny(X0) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [flattening 39]
52. ! [X0] : ((((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))))) [nnf transformation 7]
55. (? [X0] : ((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) [nnf transformation 25]
56. (? [X0] : ((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X2] : (~quiet(X2) & quiet(X2)) | ! [X3] : ((quiet(X3) | ~curious(X3)) & (curious(X3) | ~quiet(X3)))) [rectify 55]
57. ? [X0] : ((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) => ((~curious(sK5) | ~quiet(sK5)) & (curious(sK5) | quiet(sK5))) [choice axiom]
58. ? [X2] : (~quiet(X2) & quiet(X2)) => (~quiet(sK6) & quiet(sK6)) [choice axiom]
59. (((~curious(sK5) | ~quiet(sK5)) & (curious(sK5) | quiet(sK5))) | ! [X1] : (quiet(X1) | ~quiet(X1))) & ((~quiet(sK6) & quiet(sK6)) | ! [X3] : ((quiet(X3) | ~curious(X3)) & (curious(X3) | ~quiet(X3)))) [skolemisation 56,58,57]
93. happy(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 40]
110. ~happy(X0) | ~funny(X0) | quiet(X0) | curious(X0) [cnf transformation 52]
111. ~happy(X0) | ~funny(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 52]
120. quiet(sK6) | curious(X3) | ~quiet(X3) [cnf transformation 59]
121. quiet(sK6) | quiet(X3) | ~curious(X3) [cnf transformation 59]
122. ~quiet(sK6) | curious(X3) | ~quiet(X3) [cnf transformation 59]
123. ~quiet(sK6) | quiet(X3) | ~curious(X3) [cnf transformation 59]
157. funny(susan) [cnf transformation 22]
159. ~funny(X0) | happy(X0) [duplicate literal removal 93]
258. ~curious(X0) | ~funny(X0) | ~quiet(X0) [subsumption resolution 111,159]
259. ~funny(X0) | quiet(X0) | curious(X0) [subsumption resolution 110,159]
263. 23 <=> ! [X3] : (quiet(X3) | ~curious(X3)) [avatar definition]
264. ~curious(X3) | quiet(X3) <- (23) [avatar component clause 263]
266. 24 <=> quiet(sK6) [avatar definition]
269. 23 | ~24 [avatar split clause 123,266,263]
271. 25 <=> ! [X3] : (curious(X3) | ~quiet(X3)) [avatar definition]
272. ~quiet(X3) | curious(X3) <- (25) [avatar component clause 271]
273. 25 | ~24 [avatar split clause 122,266,271]
274. 23 | 24 [avatar split clause 121,266,263]
275. 25 | 24 [avatar split clause 120,266,271]
447. quiet(susan) | curious(susan) [resolution 259,157]
448. curious(susan) <- (25) [subsumption resolution 447,272]
449. ~funny(susan) | ~quiet(susan) <- (25) [resolution 448,258]
451. quiet(susan) <- (23, 25) [resolution 448,264]
452. ~quiet(susan) <- (25) [subsumption resolution 449,157]
453. $false <- (23, 25) [subsumption resolution 451,452]
454. ~23 | ~25 [avatar contradiction clause 453]
455. $false [avatar sat refutation 269,273,274,275,454]
% SZS output end Proof for 2154193371611602669226862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is calm.
If someone is not creative then someone is either humble or brave and vice versa.
If mary is both not strong and happy then john is humble.
Everyone who is both not old and creative is not wise and vice versa.
Everyone who is quiet is humble and vice versa.
Everyone who is not tall or curious is both not old and not kind and vice versa.
If paul is not strong then someone is creative and vice versa.
Everyone who is humble or not quiet is both not old and tall and vice versa.
If mary is not creative or curious then paul is tall or wise and vice versa.
Everyone who is either not funny or quiet is either quiet or not wise and vice versa.
Everyone who is not old or not strong is tall.
Everyone who is rich is not kind.
Everyone who is either curious or not creative is old and vice versa.
Everyone who is either not calm or not curious is strong or not kind.
If mary is not curious or not rich then john is not calm and vice versa.
If someone is either not rich or brave then alice is not calm and vice versa.
Someone is either not happy or not creative.
Alice is rich.
John is either not humble or kind.
Someone is both patient and not calm.
Someone is calm.
Someone is either kind or not happy.
Someone is either calm or not happy.
Someone is patient or not old. | Mary is not kind. | entailment | (![X]:(~humble(X)=>calm(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(((~strong(mary)&happy(mary)))=>(humble(john)))&
(![X]:((~old(X)&creative(X))<=>~wise(X)))&
(![X]:(quiet(X)<=>humble(X)))&
(![X]:((~tall(X)|curious(X))<=>(~old(X)&~kind(X))))&
((~strong(paul))<=>(?[X]:(creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~old(X)&tall(X))))&
(((~creative(mary)|curious(mary)))<=>((tall(paul)|wise(paul))))&
(![X]:((~funny(X)<~>quiet(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|~strong(X))=>tall(X)))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:((curious(X)<~>~creative(X))<=>old(X)))&
(![X]:((~calm(X)<~>~curious(X))=>(strong(X)|~kind(X))))&
(((~curious(mary)|~rich(mary)))<=>(~calm(john)))&
((?[X]:((~rich(X)<~>brave(X))))<=>(~calm(alice)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(rich(alice))&
((~humble(john)<~>kind(john)))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:((patient(X)|~old(X)))) | ~kind(mary) | [
"p4",
"p5",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7791383556048285726932056
% SZS output start Proof for 7791383556048285726932056
5. ! [X0] : (quiet(X0) <=> humble(X0)) [input p4]
6. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p5]
8. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (tall(X0) & ~old(X0))) [input p7]
9. (curious(mary) | ~creative(mary)) <=> (wise(paul) | tall(paul)) [input p8]
11. ! [X0] : ((~strong(X0) | ~old(X0)) => tall(X0)) [input p10]
13. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> old(X0)) [input p12]
25. kind(mary) [input hypothesis]
32. ! [X0] : (tall(X0) | (strong(X0) & old(X0))) [ennf transformation 11]
43. ! [X0] : ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))) [nnf transformation 5]
44. ! [X0] : (((curious(X0) | ~tall(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 6]
45. ! [X0] : ((curious(X0) | ~tall(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [flattening 44]
50. ! [X0] : (((~quiet(X0) | humble(X0)) | (~tall(X0) | old(X0))) & ((tall(X0) & ~old(X0)) | (quiet(X0) & ~humble(X0)))) [nnf transformation 8]
51. ! [X0] : ((~quiet(X0) | humble(X0) | ~tall(X0) | old(X0)) & ((tall(X0) & ~old(X0)) | (quiet(X0) & ~humble(X0)))) [flattening 50]
52. ((curious(mary) | ~creative(mary)) | (~wise(paul) & ~tall(paul))) & ((wise(paul) | tall(paul)) | (~curious(mary) & creative(mary))) [nnf transformation 9]
53. (curious(mary) | ~creative(mary) | (~wise(paul) & ~tall(paul))) & (wise(paul) | tall(paul) | (~curious(mary) & creative(mary))) [flattening 52]
55. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~old(X0)) & (old(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 13]
86. ~quiet(X0) | humble(X0) [cnf transformation 43]
88. ~old(X0) | tall(X0) [cnf transformation 45]
91. ~kind(X0) | ~curious(X0) [cnf transformation 45]
95. ~old(X0) | ~humble(X0) [cnf transformation 51]
96. ~old(X0) | quiet(X0) [cnf transformation 51]
102. curious(mary) | ~creative(mary) | ~tall(paul) [cnf transformation 53]
112. tall(X0) | old(X0) [cnf transformation 32]
116. curious(X0) | old(X0) | creative(X0) [cnf transformation 55]
139. kind(mary) [cnf transformation 25]
200. 14 <=> creative(mary) [avatar definition]
202. ~creative(mary) <- (~14) [avatar component clause 200]
204. 15 <=> curious(mary) [avatar definition]
205. ~curious(mary) <- (~15) [avatar component clause 204]
209. 16 <=> tall(paul) [avatar definition]
211. ~tall(paul) <- (~16) [avatar component clause 209]
212. ~16 | ~14 | 15 [avatar split clause 102,204,200,209]
217. tall(X0) [subsumption resolution 112,88]
307. ~curious(mary) [resolution 91,139]
310. ~15 [avatar split clause 307,204]
337. old(mary) | creative(mary) <- (~15) [resolution 116,205]
339. old(mary) <- (~14, ~15) [subsumption resolution 337,202]
342. quiet(mary) <- (~14, ~15) [resolution 339,96]
343. ~humble(mary) <- (~14, ~15) [resolution 339,95]
371. humble(mary) <- (~14, ~15) [resolution 342,86]
372. $false <- (~14, ~15) [subsumption resolution 371,343]
373. 14 | 15 [avatar contradiction clause 372]
379. $false <- (~16) [subsumption resolution 211,217]
380. 16 [avatar contradiction clause 379]
381. $false [avatar sat refutation 212,310,373,380]
% SZS output end Proof for 7791383556048285726932056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and brave then someone is either strong or not strong and vice versa.
If paul is either not happy or not calm then someone is both creative and calm.
If fred is both not wise and brave then john is not old or not wise.
If someone is either tall or not tall then someone is calm or not generous and vice versa.
Everyone who is not calm or not generous is not rich and vice versa.
Everyone who is not patient or strong is either creative or kind and vice versa.
Everyone who is not rich or not calm is funny and vice versa.
If someone is not curious or curious then john is wise and vice versa.
Everyone who is both not kind and not happy is both not generous and not quiet.
If someone is both not curious and old then someone is old or quiet.
If fred is both not strong and calm then someone is calm.
Everyone who is both not rich and generous is not strong or patient and vice versa.
If someone is both not rich and tall then paul is rich.
If someone is brave then someone is funny.
Everyone who is creative is both calm and not kind and vice versa.
Everyone who is not patient or not kind is both not old and quiet and vice versa.
Fred is strong or patient.
Paul is both not generous and funny.
Fred is funny or humble.
Fred is not funny or not rich.
Someone is happy.
Susan is not calm.
Mary is either quiet or strong.
Someone is both calm and brave. | Mary is not funny. | contradiction | ((?[X]:((~strong(X)&brave(X))))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(((~happy(paul)<~>~calm(paul)))=>(?[X]:((creative(X)&calm(X)))))&
(((~wise(fred)&brave(fred)))=>((~old(john)|~wise(john))))&
((?[X]:((tall(X)<~>~tall(X))))<=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((~calm(X)|~generous(X))<=>~rich(X)))&
(![X]:((~patient(X)|strong(X))<=>(creative(X)<~>kind(X))))&
(![X]:((~rich(X)|~calm(X))<=>funny(X)))&
((?[X]:((~curious(X)|curious(X))))<=>(wise(john)))&
(![X]:((~kind(X)&~happy(X))=>(~generous(X)&~quiet(X))))&
((?[X]:((~curious(X)&old(X))))=>(?[X]:((old(X)|quiet(X)))))&
(((~strong(fred)&calm(fred)))=>(?[X]:(calm(X))))&
(![X]:((~rich(X)&generous(X))<=>(~strong(X)|patient(X))))&
((?[X]:((~rich(X)&tall(X))))=>(rich(paul)))&
((?[X]:(brave(X)))=>(?[X]:(funny(X))))&
(![X]:(creative(X)<=>(calm(X)&~kind(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~old(X)&quiet(X))))&
((strong(fred)|patient(fred)))&
((~generous(paul)&funny(paul)))&
((funny(fred)|humble(fred)))&
((~funny(fred)|~rich(fred)))&
(?[X]:(happy(X)))&
(~calm(susan))&
((quiet(mary)<~>strong(mary)))&
(?[X]:((calm(X)&brave(X)))) | ~funny(mary) | [
"p6",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 352147725683244267132567
% SZS output start Proof for 352147725683244267132567
7. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> funny(X0)) [input p6]
12. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (patient(X0) | ~strong(X0))) [input p11]
16. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (quiet(X0) & ~old(X0))) [input p15]
23. quiet(mary) <~> strong(mary) [input p22]
25. ~funny(mary) [input hypothesis]
58. ! [X0] : (((~calm(X0) | ~rich(X0)) | ~funny(X0)) & (funny(X0) | (calm(X0) & rich(X0)))) [nnf transformation 7]
59. ! [X0] : ((~calm(X0) | ~rich(X0) | ~funny(X0)) & (funny(X0) | (calm(X0) & rich(X0)))) [flattening 58]
69. ! [X0] : (((generous(X0) & ~rich(X0)) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | (~generous(X0) | rich(X0)))) [nnf transformation 12]
70. ! [X0] : (((generous(X0) & ~rich(X0)) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ~generous(X0) | rich(X0))) [flattening 69]
76. ! [X0] : (((~kind(X0) | ~patient(X0)) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 16]
77. ! [X0] : ((~kind(X0) | ~patient(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | (kind(X0) & patient(X0)))) [flattening 76]
80. (~strong(mary) | ~quiet(mary)) & (strong(mary) | quiet(mary)) [nnf transformation 23]
109. funny(X0) | rich(X0) [cnf transformation 59]
120. ~rich(X0) | strong(X0) [cnf transformation 70]
121. ~patient(X0) | ~rich(X0) [cnf transformation 70]
131. quiet(X0) | patient(X0) [cnf transformation 77]
141. ~strong(mary) | ~quiet(mary) [cnf transformation 80]
144. ~funny(mary) [cnf transformation 25]
278. 30 <=> quiet(mary) [avatar definition]
280. ~quiet(mary) <- (~30) [avatar component clause 278]
282. 31 <=> strong(mary) [avatar definition]
285. ~30 | ~31 [avatar split clause 141,282,278]
289. rich(mary) [resolution 109,144]
293. strong(mary) [resolution 120,289]
296. 31 [avatar split clause 293,282]
299. patient(mary) <- (~30) [resolution 131,280]
301. ~rich(mary) <- (~30) [resolution 299,121]
302. $false <- (~30) [subsumption resolution 301,289]
303. 30 [avatar contradiction clause 302]
304. $false [avatar sat refutation 285,296,303]
% SZS output end Proof for 352147725683244267132567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not patient is not rich or wise and vice versa.
Everyone who is both not happy and not kind is both kind and not rich.
Everyone who is either happy or not old is not rich and vice versa.
Everyone who is both curious and patient is either brave or not patient and vice versa.
If john is either not funny or not happy then someone is either not happy or brave and vice versa.
If mary is both not humble and not happy then someone is not quiet or not kind.
Everyone who is not humble is generous.
Everyone who is kind is not patient.
If someone is both rich and not quiet then susan is not strong.
Everyone who is not patient is either not old or creative.
Everyone who is old or not calm is both quiet and humble.
If fred is either calm or not kind then alice is tall or brave.
If someone is both rich and patient then someone is not rich or not calm and vice versa.
Everyone who is humble is either not quiet or strong.
Everyone who is both not humble and funny is old or not wise.
Everyone who is both kind and patient is both not kind and not patient and vice versa.
Someone is either not humble or old.
Susan is both not creative and not curious.
Someone is either not calm or not old.
Lucy is either not patient or quiet.
Someone is not patient. | John is not curious. | neutral | (![X]:((rich(X)&~patient(X))<=>(~rich(X)|wise(X))))&
(![X]:((~happy(X)&~kind(X))=>(kind(X)&~rich(X))))&
(![X]:((happy(X)<~>~old(X))<=>~rich(X)))&
(![X]:((curious(X)&patient(X))<=>(brave(X)<~>~patient(X))))&
(((~funny(john)<~>~happy(john)))<=>(?[X]:((~happy(X)<~>brave(X)))))&
(((~humble(mary)&~happy(mary)))=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:(~humble(X)=>generous(X)))&
(![X]:(kind(X)=>~patient(X)))&
((?[X]:((rich(X)&~quiet(X))))=>(~strong(susan)))&
(![X]:(~patient(X)=>(~old(X)<~>creative(X))))&
(![X]:((old(X)|~calm(X))=>(quiet(X)&humble(X))))&
(((calm(fred)<~>~kind(fred)))=>((tall(alice)|brave(alice))))&
((?[X]:((rich(X)&patient(X))))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:(humble(X)=>(~quiet(X)<~>strong(X))))&
(![X]:((~humble(X)&funny(X))=>(old(X)|~wise(X))))&
(![X]:((kind(X)&patient(X))<=>(~kind(X)&~patient(X))))&
(?[X]:((~humble(X)<~>old(X))))&
((~creative(susan)&~curious(susan)))&
(?[X]:((~calm(X)<~>~old(X))))&
((~patient(lucy)<~>quiet(lucy)))&
(?[X]:(~patient(X))) | ~curious(john) | [] | null | 0 |
Everyone who is either not tall or not patient is both old and creative. If someone is happy then someone is both creative and not creative and vice versa. If someone is not creative or not funny then fred is not creative. Everyone who is both not rich and old is not happy. Everyone who is either funny or brave is either not kind or rich and vice versa. Everyone who is either old or happy is not strong or not old and vice versa. If paul is kind or not brave then someone is both not funny and not tall. If alice is either strong or not funny then someone is either curious or not brave. Everyone who is both not happy and not calm is both not kind and not old. Everyone who is not calm or not curious is curious or not brave. Everyone who is both not old and not strong is not tall and vice versa. Everyone who is humble or brave is not funny or old and vice versa. Everyone who is rich or generous is funny and vice versa. Everyone who is not creative is calm or not tall. If susan is generous or not curious then someone is both not strong and generous and vice versa. Someone is not humble. Someone is not creative. Someone is rich. Someone is kind or not brave. Susan is strong or not funny. Someone is either not generous or not brave. | Fred is patient. | entailment | (![X]:((~tall(X)<~>~patient(X))=>(old(X)&creative(X))))&
((?[X]:(happy(X)))<=>(?[X]:((creative(X)&~creative(X)))))&
((?[X]:((~creative(X)|~funny(X))))=>(~creative(fred)))&
(![X]:((~rich(X)&old(X))=>~happy(X)))&
(![X]:((funny(X)<~>brave(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((old(X)<~>happy(X))<=>(~strong(X)|~old(X))))&
(((kind(paul)|~brave(paul)))=>(?[X]:((~funny(X)&~tall(X)))))&
(((strong(alice)<~>~funny(alice)))=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:((~happy(X)&~calm(X))=>(~kind(X)&~old(X))))&
(![X]:((~calm(X)|~curious(X))=>(curious(X)|~brave(X))))&
(![X]:((~old(X)&~strong(X))<=>~tall(X)))&
(![X]:((humble(X)|brave(X))<=>(~funny(X)|old(X))))&
(![X]:((rich(X)|generous(X))<=>funny(X)))&
(![X]:(~creative(X)=>(calm(X)|~tall(X))))&
(((generous(susan)|~curious(susan)))<=>(?[X]:((~strong(X)&generous(X)))))&
(?[X]:(~humble(X)))&
(?[X]:(~creative(X)))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)|~brave(X))))&
((strong(susan)|~funny(susan)))&
(?[X]:((~generous(X)<~>~brave(X)))) | patient(fred) | [
"p0",
"p1",
"p2",
"p5",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8821362501147896213985707
% SZS output start Proof for 8821362501147896213985707
1. ! [X0] : ((~tall(X0) <~> ~patient(X0)) => (creative(X0) & old(X0))) [input p0]
2. ? [X0] : happy(X0) <=> ? [X0] : (~creative(X0) & creative(X0)) [input p1]
3. ? [X0] : (~funny(X0) | ~creative(X0)) => ~creative(fred) [input p2]
6. ! [X0] : ((old(X0) <~> happy(X0)) <=> (~old(X0) | ~strong(X0))) [input p5]
11. ! [X0] : ((~strong(X0) & ~old(X0)) <=> ~tall(X0)) [input p10]
17. ? [X0] : ~creative(X0) [input p16]
22. ~patient(fred) [input hypothesis]
23. ? [X0] : happy(X0) <=> ? [X1] : (~creative(X1) & creative(X1)) [rectify 2]
27. ! [X0] : ((creative(X0) & old(X0)) | (~tall(X0) <=> ~patient(X0))) [ennf transformation 1]
28. ~creative(fred) | ! [X0] : (funny(X0) & creative(X0)) [ennf transformation 3]
35. ! [X0] : ((creative(X0) & old(X0)) | ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0)))) [nnf transformation 27]
36. (? [X0] : happy(X0) | ! [X1] : (creative(X1) | ~creative(X1))) & (? [X1] : (~creative(X1) & creative(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 23]
37. (? [X0] : happy(X0) | ! [X1] : (creative(X1) | ~creative(X1))) & (? [X2] : (~creative(X2) & creative(X2)) | ! [X3] : ~happy(X3)) [rectify 36]
38. ? [X0] : happy(X0) => happy(sK0) [choice axiom]
39. ? [X2] : (~creative(X2) & creative(X2)) => (~creative(sK1) & creative(sK1)) [choice axiom]
40. (happy(sK0) | ! [X1] : (creative(X1) | ~creative(X1))) & ((~creative(sK1) & creative(sK1)) | ! [X3] : ~happy(X3)) [skolemisation 37,39,38]
42. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [nnf transformation 6]
43. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [flattening 42]
49. ! [X0] : (((~strong(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | (strong(X0) | old(X0)))) [nnf transformation 11]
50. ! [X0] : (((~strong(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | strong(X0) | old(X0))) [flattening 49]
62. ? [X0] : ~creative(X0) => ~creative(sK6) [choice axiom]
63. ~creative(sK6) [skolemisation 17,62]
74. ~tall(X0) | creative(X0) | patient(X0) [cnf transformation 35]
75. creative(sK1) | ~happy(X3) [cnf transformation 40]
76. ~creative(sK1) | ~happy(X3) [cnf transformation 40]
78. ~creative(fred) | creative(X0) [cnf transformation 28]
92. happy(X0) | old(X0) | old(X0) [cnf transformation 43]
105. ~old(X0) | tall(X0) [cnf transformation 50]
120. ~creative(sK6) [cnf transformation 63]
126. ~patient(fred) [cnf transformation 22]
129. happy(X0) | old(X0) [duplicate literal removal 92]
131. 1 <=> ! [X3] : ~happy(X3) [avatar definition]
132. ~happy(X3) <- (1) [avatar component clause 131]
134. 2 <=> creative(sK1) [avatar definition]
137. 1 | ~2 [avatar split clause 76,134,131]
138. 1 | 2 [avatar split clause 75,134,131]
143. 4 <=> creative(fred) [avatar definition]
145. ~creative(fred) <- (~4) [avatar component clause 143]
148. 5 <=> ! [X0] : creative(X0) [avatar definition]
149. creative(X0) <- (5) [avatar component clause 148]
150. 5 | ~4 [avatar split clause 78,143,148]
246. old(X0) <- (1) [resolution 129,132]
247. tall(X0) <- (1) [resolution 246,105]
252. creative(X0) | patient(X0) <- (1) [resolution 74,247]
255. patient(fred) <- (1, ~4) [resolution 252,145]
256. $false <- (1, ~4) [subsumption resolution 255,126]
257. ~1 | 4 [avatar contradiction clause 256]
262. $false <- (5) [resolution 149,120]
263. ~5 [avatar contradiction clause 262]
264. $false [avatar sat refutation 137,138,150,257,263]
% SZS output end Proof for 8821362501147896213985707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is humble and vice versa.
If paul is wise then fred is both funny and generous.
Everyone who is not funny or not generous is both strong and not wise and vice versa.
Everyone who is not curious is either not creative or creative.
Everyone who is strong or tall is brave.
Everyone who is both not quiet and kind is both generous and not brave and vice versa.
Everyone who is both strong and calm is not humble or not quiet.
If someone is both patient and not quiet then fred is both happy and not calm.
Everyone who is quiet or not humble is creative or not old and vice versa.
Everyone who is both not old and wise is curious and vice versa.
Everyone who is both quiet and not humble is not humble or not curious.
If fred is either brave or not old then someone is generous and vice versa.
If someone is either not strong or not funny then someone is not humble.
If susan is not curious or not humble then john is both not kind and not curious and vice versa.
Everyone who is generous is both strong and not brave and vice versa.
Everyone who is not strong or rich is both old and curious and vice versa.
Someone is either brave or not brave.
Someone is either quiet or humble.
Someone is calm.
Someone is not calm.
Mary is not calm or funny.
Someone is both humble and not calm. | Susan is patient. | neutral | (![X]:(~calm(X)<=>humble(X)))&
((wise(paul))=>((funny(fred)&generous(fred))))&
(![X]:((~funny(X)|~generous(X))<=>(strong(X)&~wise(X))))&
(![X]:(~curious(X)=>(~creative(X)<~>creative(X))))&
(![X]:((strong(X)|tall(X))=>brave(X)))&
(![X]:((~quiet(X)&kind(X))<=>(generous(X)&~brave(X))))&
(![X]:((strong(X)&calm(X))=>(~humble(X)|~quiet(X))))&
((?[X]:((patient(X)&~quiet(X))))=>((happy(fred)&~calm(fred))))&
(![X]:((quiet(X)|~humble(X))<=>(creative(X)|~old(X))))&
(![X]:((~old(X)&wise(X))<=>curious(X)))&
(![X]:((quiet(X)&~humble(X))=>(~humble(X)|~curious(X))))&
(((brave(fred)<~>~old(fred)))<=>(?[X]:(generous(X))))&
((?[X]:((~strong(X)<~>~funny(X))))=>(?[X]:(~humble(X))))&
(((~curious(susan)|~humble(susan)))<=>((~kind(john)&~curious(john))))&
(![X]:(generous(X)<=>(strong(X)&~brave(X))))&
(![X]:((~strong(X)|rich(X))<=>(old(X)&curious(X))))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:((quiet(X)<~>humble(X))))&
(?[X]:(calm(X)))&
(?[X]:(~calm(X)))&
((~calm(mary)|funny(mary)))&
(?[X]:((humble(X)&~calm(X)))) | patient(susan) | [] | null | 0 |
If someone is not kind or not brave then lucy is both not generous and not strong and vice versa.
If someone is either not funny or curious then paul is not funny or not calm.
If fred is funny or tall then paul is both not generous and strong and vice versa.
Everyone who is both not creative and kind is not kind and vice versa.
Everyone who is not rich is tall or not happy and vice versa.
If someone is both not generous and not humble then someone is both not funny and not old and vice versa.
If alice is not quiet then lucy is generous or funny and vice versa.
Everyone who is kind or old is both not funny and old.
If lucy is not happy then someone is either funny or not rich and vice versa.
If alice is old or not strong then someone is not wise.
If someone is both generous and strong then someone is old and vice versa.
Everyone who is either not quiet or not patient is not tall or not wise and vice versa.
Everyone who is both wise and curious is not strong and vice versa.
Everyone who is generous or not happy is either quiet or humble and vice versa.
Everyone who is either not happy or humble is not curious or not wise.
Someone is not tall or not happy.
Someone is not rich or not creative.
Susan is not brave or not old.
Alice is rich.
John is brave or not curious.
Someone is curious.
Susan is rich or not curious. | Alice is quiet. | entailment | ((?[X]:((~kind(X)|~brave(X))))<=>((~generous(lucy)&~strong(lucy))))&
((?[X]:((~funny(X)<~>curious(X))))=>((~funny(paul)|~calm(paul))))&
(((funny(fred)|tall(fred)))<=>((~generous(paul)&strong(paul))))&
(![X]:((~creative(X)&kind(X))<=>~kind(X)))&
(![X]:(~rich(X)<=>(tall(X)|~happy(X))))&
((?[X]:((~generous(X)&~humble(X))))<=>(?[X]:((~funny(X)&~old(X)))))&
((~quiet(alice))<=>((generous(lucy)|funny(lucy))))&
(![X]:((kind(X)|old(X))=>(~funny(X)&old(X))))&
((~happy(lucy))<=>(?[X]:((funny(X)<~>~rich(X)))))&
(((old(alice)|~strong(alice)))=>(?[X]:(~wise(X))))&
((?[X]:((generous(X)&strong(X))))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)<~>~patient(X))<=>(~tall(X)|~wise(X))))&
(![X]:((wise(X)&curious(X))<=>~strong(X)))&
(![X]:((generous(X)|~happy(X))<=>(quiet(X)<~>humble(X))))&
(![X]:((~happy(X)<~>humble(X))=>(~curious(X)|~wise(X))))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((~rich(X)|~creative(X))))&
((~brave(susan)|~old(susan)))&
(rich(alice))&
((brave(john)|~curious(john)))&
(?[X]:(curious(X)))&
((rich(susan)|~curious(susan))) | quiet(alice) | [
"p0",
"p3",
"p6",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2453335652242713808265982
% SZS output start Proof for 2453335652242713808265982
1. ? [X0] : (~brave(X0) | ~kind(X0)) <=> (~strong(lucy) & ~generous(lucy)) [input p0]
4. ! [X0] : ((kind(X0) & ~creative(X0)) <=> ~kind(X0)) [input p3]
7. ~quiet(alice) <=> (funny(lucy) | generous(lucy)) [input p6]
8. ! [X0] : ((old(X0) | kind(X0)) => (old(X0) & ~funny(X0))) [input p7]
18. ~old(susan) | ~brave(susan) [input p17]
23. ~quiet(alice) [input hypothesis]
27. ! [X0] : ((old(X0) & ~funny(X0)) | (~old(X0) & ~kind(X0))) [ennf transformation 8]
31. (? [X0] : (~brave(X0) | ~kind(X0)) | (strong(lucy) | generous(lucy))) & ((~strong(lucy) & ~generous(lucy)) | ! [X0] : (brave(X0) & kind(X0))) [nnf transformation 1]
32. (? [X0] : (~brave(X0) | ~kind(X0)) | strong(lucy) | generous(lucy)) & ((~strong(lucy) & ~generous(lucy)) | ! [X0] : (brave(X0) & kind(X0))) [flattening 31]
33. (? [X0] : (~brave(X0) | ~kind(X0)) | strong(lucy) | generous(lucy)) & ((~strong(lucy) & ~generous(lucy)) | ! [X1] : (brave(X1) & kind(X1))) [rectify 32]
34. ? [X0] : (~brave(X0) | ~kind(X0)) => (~brave(sK0) | ~kind(sK0)) [choice axiom]
35. ((~brave(sK0) | ~kind(sK0)) | strong(lucy) | generous(lucy)) & ((~strong(lucy) & ~generous(lucy)) | ! [X1] : (brave(X1) & kind(X1))) [skolemisation 33,34]
38. ! [X0] : (((kind(X0) & ~creative(X0)) | kind(X0)) & (~kind(X0) | (~kind(X0) | creative(X0)))) [nnf transformation 4]
39. ! [X0] : (((kind(X0) & ~creative(X0)) | kind(X0)) & (~kind(X0) | ~kind(X0) | creative(X0))) [flattening 38]
47. (~quiet(alice) | (~funny(lucy) & ~generous(lucy))) & ((funny(lucy) | generous(lucy)) | quiet(alice)) [nnf transformation 7]
48. (~quiet(alice) | (~funny(lucy) & ~generous(lucy))) & (funny(lucy) | generous(lucy) | quiet(alice)) [flattening 47]
74. ~generous(lucy) | brave(X1) [cnf transformation 35]
85. kind(X0) | kind(X0) [cnf transformation 39]
93. funny(lucy) | generous(lucy) | quiet(alice) [cnf transformation 48]
96. ~funny(X0) | ~kind(X0) [cnf transformation 27]
98. ~kind(X0) | old(X0) [cnf transformation 27]
128. ~old(susan) | ~brave(susan) [cnf transformation 18]
133. ~quiet(alice) [cnf transformation 23]
135. kind(X0) [duplicate literal removal 85]
137. 1 <=> generous(lucy) [avatar definition]
154. 5 <=> ! [X1] : brave(X1) [avatar definition]
155. brave(X1) <- (5) [avatar component clause 154]
158. 6 <=> ! [X1] : kind(X1) [avatar definition]
159. kind(X1) <- (6) [avatar component clause 158]
161. 5 | ~1 [avatar split clause 74,137,154]
184. 6 [avatar split clause 135,158]
212. 17 <=> funny(lucy) [avatar definition]
213. funny(lucy) <- (17) [avatar component clause 212]
216. 18 <=> quiet(alice) [avatar definition]
221. 18 | 1 | 17 [avatar split clause 93,212,137,216]
298. 36 <=> brave(susan) [avatar definition]
300. ~brave(susan) <- (~36) [avatar component clause 298]
302. 37 <=> old(susan) [avatar definition]
304. ~old(susan) <- (~37) [avatar component clause 302]
305. ~36 | ~37 [avatar split clause 128,302,298]
324. ~18 [avatar split clause 133,216]
327. ~kind(lucy) <- (17) [resolution 96,213]
328. $false <- (6, 17) [subsumption resolution 327,159]
329. ~6 | ~17 [avatar contradiction clause 328]
331. $false <- (5, ~36) [resolution 155,300]
332. ~5 | 36 [avatar contradiction clause 331]
334. old(X0) <- (6) [resolution 98,159]
337. $false <- (6, ~37) [subsumption resolution 304,334]
338. ~6 | 37 [avatar contradiction clause 337]
341. $false [avatar sat refutation 161,184,221,305,324,329,332,338]
% SZS output end Proof for 2453335652242713808265982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is both wise and not kind and vice versa. Everyone who is either not calm or not strong is not funny or not old and vice versa. Everyone who is both strong and brave is either not quiet or curious and vice versa. If someone is not humble or old then someone is either not funny or funny and vice versa. Everyone who is tall or not kind is either generous or humble. Everyone who is either not strong or kind is either not humble or wise and vice versa. Everyone who is not tall is both creative and strong and vice versa. If alice is both not old and patient then alice is either not humble or rich and vice versa. Everyone who is strong is not creative. Everyone who is both not calm and wise is not creative or not funny and vice versa. Everyone who is both not creative and creative is either quiet or not wise and vice versa. If someone is either not curious or not funny then john is either kind or creative and vice versa. Everyone who is either not funny or not humble is humble or not patient. Everyone who is old or not generous is either happy or not rich. If someone is not patient then someone is not generous. If lucy is both not rich and not brave then alice is tall. Someone is not old or not curious. Someone is humble or rich. Paul is generous or not rich. Susan is both not funny and rich. Someone is not funny or patient. Paul is calm or not strong. Susan is not patient. Someone is not tall or not patient. | John is not tall. | contradiction | ((?[X]:(~calm(X)))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~funny(X)|~old(X))))&
(![X]:((strong(X)&brave(X))<=>(~quiet(X)<~>curious(X))))&
((?[X]:((~humble(X)|old(X))))<=>(?[X]:((~funny(X)<~>funny(X)))))&
(![X]:((tall(X)|~kind(X))=>(generous(X)<~>humble(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(~humble(X)<~>wise(X))))&
(![X]:(~tall(X)<=>(creative(X)&strong(X))))&
(((~old(alice)&patient(alice)))<=>((~humble(alice)<~>rich(alice))))&
(![X]:(strong(X)=>~creative(X)))&
(![X]:((~calm(X)&wise(X))<=>(~creative(X)|~funny(X))))&
(![X]:((~creative(X)&creative(X))<=>(quiet(X)<~>~wise(X))))&
((?[X]:((~curious(X)<~>~funny(X))))<=>((kind(john)<~>creative(john))))&
(![X]:((~funny(X)<~>~humble(X))=>(humble(X)|~patient(X))))&
(![X]:((old(X)|~generous(X))=>(happy(X)<~>~rich(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~generous(X))))&
(((~rich(lucy)&~brave(lucy)))=>(tall(alice)))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((humble(X)|rich(X))))&
((generous(paul)|~rich(paul)))&
((~funny(susan)&rich(susan)))&
(?[X]:((~funny(X)|patient(X))))&
((calm(paul)|~strong(paul)))&
(~patient(susan))&
(?[X]:((~tall(X)|~patient(X)))) | ~tall(john) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2904185834173903074759988
% SZS output start Proof for 2904185834173903074759988
7. ! [X0] : (~tall(X0) <=> (strong(X0) & creative(X0))) [input p6]
9. ! [X0] : (strong(X0) => ~creative(X0)) [input p8]
25. ~tall(john) [input hypothesis]
30. ! [X0] : (~creative(X0) | ~strong(X0)) [ennf transformation 9]
53. ! [X0] : ((~tall(X0) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | tall(X0))) [nnf transformation 7]
54. ! [X0] : ((~tall(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | tall(X0))) [flattening 53]
111. creative(X0) | tall(X0) [cnf transformation 54]
112. tall(X0) | strong(X0) [cnf transformation 54]
120. ~creative(X0) | ~strong(X0) [cnf transformation 30]
157. ~tall(john) [cnf transformation 25]
330. ~strong(X0) | tall(X0) [resolution 120,111]
333. tall(X0) [subsumption resolution 330,112]
335. $false [resolution 333,157]
% SZS output end Proof for 2904185834173903074759988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or calm is either old or not strong and vice versa.
Everyone who is not generous or not creative is either rich or creative.
If alice is either not curious or funny then someone is both old and not wise.
Everyone who is not kind is either humble or patient.
If lucy is kind then someone is both humble and not old.
If john is either not rich or generous then someone is rich or kind and vice versa.
Everyone who is old is curious.
If alice is both not creative and happy then someone is not calm or not generous and vice versa.
Everyone who is both not quiet and brave is not humble.
Everyone who is either not tall or not creative is not old.
If someone is either not calm or not patient then someone is both not strong and not calm and vice versa.
Everyone who is either not happy or not patient is not kind or not tall.
If someone is either kind or funny then someone is not funny or not creative.
If susan is not creative or happy then john is either creative or funny and vice versa.
If someone is funny or generous then someone is not rich.
Everyone who is both strong and funny is not happy or not calm.
Someone is not rich or quiet.
Someone is either funny or generous.
Someone is kind or not happy.
Paul is both wise and funny.
Someone is wise.
Fred is either strong or kind.
Fred is kind or wise. | John is creative. | neutral | (![X]:((~calm(X)<~>calm(X))<=>(old(X)<~>~strong(X))))&
(![X]:((~generous(X)|~creative(X))=>(rich(X)<~>creative(X))))&
(((~curious(alice)<~>funny(alice)))=>(?[X]:((old(X)&~wise(X)))))&
(![X]:(~kind(X)=>(humble(X)<~>patient(X))))&
((kind(lucy))=>(?[X]:((humble(X)&~old(X)))))&
(((~rich(john)<~>generous(john)))<=>(?[X]:((rich(X)|kind(X)))))&
(![X]:(old(X)=>curious(X)))&
(((~creative(alice)&happy(alice)))<=>(?[X]:((~calm(X)|~generous(X)))))&
(![X]:((~quiet(X)&brave(X))=>~humble(X)))&
(![X]:((~tall(X)<~>~creative(X))=>~old(X)))&
((?[X]:((~calm(X)<~>~patient(X))))<=>(?[X]:((~strong(X)&~calm(X)))))&
(![X]:((~happy(X)<~>~patient(X))=>(~kind(X)|~tall(X))))&
((?[X]:((kind(X)<~>funny(X))))=>(?[X]:((~funny(X)|~creative(X)))))&
(((~creative(susan)|happy(susan)))<=>((creative(john)<~>funny(john))))&
((?[X]:((funny(X)|generous(X))))=>(?[X]:(~rich(X))))&
(![X]:((strong(X)&funny(X))=>(~happy(X)|~calm(X))))&
(?[X]:((~rich(X)|quiet(X))))&
(?[X]:((funny(X)<~>generous(X))))&
(?[X]:((kind(X)|~happy(X))))&
((wise(paul)&funny(paul)))&
(?[X]:(wise(X)))&
((strong(fred)<~>kind(fred)))&
((kind(fred)|wise(fred))) | creative(john) | [] | null | 0 |
Everyone who is quiet is both strong and not quiet.
Everyone who is both not old and generous is generous and vice versa.
If susan is either strong or calm then someone is old.
If fred is both not quiet and not kind then paul is both humble and not tall.
If john is not humble then someone is not quiet or calm and vice versa.
Everyone who is either not old or not calm is both funny and not generous and vice versa.
If mary is both not patient and not quiet then someone is either not rich or not old and vice versa.
If fred is quiet or old then lucy is not brave or humble and vice versa.
If lucy is both not brave and patient then someone is strong and vice versa.
If someone is curious or not curious then susan is either old or humble.
Everyone who is either creative or wise is both funny and not quiet and vice versa.
Everyone who is not kind is humble and vice versa.
If alice is both not curious and brave then someone is both old and kind and vice versa.
If someone is either not humble or happy then someone is curious and vice versa.
Everyone who is patient or kind is not brave and vice versa.
If someone is both happy and quiet then someone is brave.
Mary is both not happy and patient.
John is both not wise and not creative.
Someone is creative.
Someone is both not quiet and not calm.
Someone is either brave or patient.
John is calm.
Alice is not happy or not kind. | Fred is not rich. | contradiction | (![X]:(quiet(X)=>(strong(X)&~quiet(X))))&
(![X]:((~old(X)&generous(X))<=>generous(X)))&
(((strong(susan)<~>calm(susan)))=>(?[X]:(old(X))))&
(((~quiet(fred)&~kind(fred)))=>((humble(paul)&~tall(paul))))&
((~humble(john))<=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((~old(X)<~>~calm(X))<=>(funny(X)&~generous(X))))&
(((~patient(mary)&~quiet(mary)))<=>(?[X]:((~rich(X)<~>~old(X)))))&
(((quiet(fred)|old(fred)))<=>((~brave(lucy)|humble(lucy))))&
(((~brave(lucy)&patient(lucy)))<=>(?[X]:(strong(X))))&
((?[X]:((curious(X)|~curious(X))))=>((old(susan)<~>humble(susan))))&
(![X]:((creative(X)<~>wise(X))<=>(funny(X)&~quiet(X))))&
(![X]:(~kind(X)<=>humble(X)))&
(((~curious(alice)&brave(alice)))<=>(?[X]:((old(X)&kind(X)))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(?[X]:(curious(X))))&
(![X]:((patient(X)|kind(X))<=>~brave(X)))&
((?[X]:((happy(X)&quiet(X))))=>(?[X]:(brave(X))))&
((~happy(mary)&patient(mary)))&
((~wise(john)&~creative(john)))&
(?[X]:(creative(X)))&
(?[X]:((~quiet(X)&~calm(X))))&
(?[X]:((brave(X)<~>patient(X))))&
(calm(john))&
((~happy(alice)|~kind(alice))) | ~rich(fred) | [
"p0",
"p6",
"p7",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 513630533083809031386208
% SZS output start Proof for 513630533083809031386208
1. ! [X0] : (quiet(X0) => (~quiet(X0) & strong(X0))) [input p0]
7. (~quiet(mary) & ~patient(mary)) <=> ? [X0] : (~rich(X0) <~> ~old(X0)) [input p6]
8. (old(fred) | quiet(fred)) <=> (humble(lucy) | ~brave(lucy)) [input p7]
12. ! [X0] : (~kind(X0) <=> humble(X0)) [input p11]
15. ! [X0] : ((kind(X0) | patient(X0)) <=> ~brave(X0)) [input p14]
17. patient(mary) & ~happy(mary) [input p16]
24. ~rich(fred) [input hypothesis]
28. ! [X0] : ((~quiet(X0) & strong(X0)) | ~quiet(X0)) [ennf transformation 1]
45. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (? [X0] : ((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (quiet(mary) | patient(mary))) [nnf transformation 7]
46. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (? [X0] : ((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | quiet(mary) | patient(mary)) [flattening 45]
47. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (? [X1] : ((old(X1) | rich(X1)) & (~old(X1) | ~rich(X1))) | quiet(mary) | patient(mary)) [rectify 46]
48. ? [X1] : ((old(X1) | rich(X1)) & (~old(X1) | ~rich(X1))) => ((old(sK2) | rich(sK2)) & (~old(sK2) | ~rich(sK2))) [choice axiom]
49. ((~quiet(mary) & ~patient(mary)) | ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(sK2) | rich(sK2)) & (~old(sK2) | ~rich(sK2))) | quiet(mary) | patient(mary)) [skolemisation 47,48]
50. ((old(fred) | quiet(fred)) | (~humble(lucy) & brave(lucy))) & ((humble(lucy) | ~brave(lucy)) | (~old(fred) & ~quiet(fred))) [nnf transformation 8]
51. (old(fred) | quiet(fred) | (~humble(lucy) & brave(lucy))) & (humble(lucy) | ~brave(lucy) | (~old(fred) & ~quiet(fred))) [flattening 50]
60. ! [X0] : ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0))) [nnf transformation 12]
71. ! [X0] : (((kind(X0) | patient(X0)) | brave(X0)) & (~brave(X0) | (~kind(X0) & ~patient(X0)))) [nnf transformation 15]
72. ! [X0] : ((kind(X0) | patient(X0) | brave(X0)) & (~brave(X0) | (~kind(X0) & ~patient(X0)))) [flattening 71]
84. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
102. ~patient(mary) | ~old(X0) | rich(X0) [cnf transformation 49]
108. old(fred) | quiet(fred) | brave(lucy) [cnf transformation 51]
109. old(fred) | quiet(fred) | ~humble(lucy) [cnf transformation 51]
123. humble(X0) | kind(X0) [cnf transformation 60]
134. ~brave(X0) | ~kind(X0) [cnf transformation 72]
138. patient(mary) [cnf transformation 17]
148. ~rich(fred) [cnf transformation 24]
149. ~quiet(X0) [duplicate literal removal 84]
190. 9 <=> patient(mary) [avatar definition]
195. 10 <=> ! [X0] : (~old(X0) | rich(X0)) [avatar definition]
196. ~old(X0) | rich(X0) <- (10) [avatar component clause 195]
197. 10 | ~9 [avatar split clause 102,190,195]
210. old(fred) | ~humble(lucy) [subsumption resolution 109,149]
212. 13 <=> humble(lucy) [avatar definition]
214. ~humble(lucy) <- (~13) [avatar component clause 212]
216. 14 <=> old(fred) [avatar definition]
218. old(fred) <- (14) [avatar component clause 216]
219. ~13 | 14 [avatar split clause 210,216,212]
220. old(fred) | brave(lucy) [subsumption resolution 108,149]
222. 15 <=> brave(lucy) [avatar definition]
224. brave(lucy) <- (15) [avatar component clause 222]
225. 15 | 14 [avatar split clause 220,216,222]
306. 9 [avatar split clause 138,190]
333. rich(fred) <- (10, 14) [resolution 196,218]
335. $false <- (10, 14) [subsumption resolution 333,148]
336. ~10 | ~14 [avatar contradiction clause 335]
337. kind(lucy) <- (~13) [resolution 214,123]
338. ~kind(lucy) <- (15) [resolution 224,134]
340. $false <- (~13, 15) [subsumption resolution 338,337]
341. 13 | ~15 [avatar contradiction clause 340]
342. $false [avatar sat refutation 197,219,225,306,336,341]
% SZS output end Proof for 513630533083809031386208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both not rich and not patient and vice versa.
Everyone who is both humble and generous is brave or tall and vice versa.
Everyone who is patient is generous and vice versa.
Everyone who is either not quiet or not rich is not curious or not strong and vice versa.
Everyone who is both rich and quiet is funny.
Everyone who is both old and not strong is not wise.
Everyone who is kind or not happy is not kind and vice versa.
If paul is wise or curious then paul is either not calm or funny.
If someone is both kind and strong then susan is either not strong or not happy.
If john is either funny or not funny then someone is funny and vice versa.
If alice is either generous or not humble then john is either not calm or quiet and vice versa.
If someone is either not happy or funny then susan is strong and vice versa.
If fred is either tall or quiet then someone is both creative and calm and vice versa.
Everyone who is both not humble and old is kind or wise and vice versa.
If someone is not curious or brave then fred is strong.
Everyone who is happy or not calm is generous or funny.
Lucy is not patient or tall.
John is either creative or curious.
Someone is either quiet or calm.
Susan is both not rich and calm.
Alice is not calm.
Someone is not wise.
Someone is either patient or quiet. | Lucy is calm. | neutral | (![X]:((~happy(X)&~creative(X))<=>(~rich(X)&~patient(X))))&
(![X]:((humble(X)&generous(X))<=>(brave(X)|tall(X))))&
(![X]:(patient(X)<=>generous(X)))&
(![X]:((~quiet(X)<~>~rich(X))<=>(~curious(X)|~strong(X))))&
(![X]:((rich(X)&quiet(X))=>funny(X)))&
(![X]:((old(X)&~strong(X))=>~wise(X)))&
(![X]:((kind(X)|~happy(X))<=>~kind(X)))&
(((wise(paul)|curious(paul)))=>((~calm(paul)<~>funny(paul))))&
((?[X]:((kind(X)&strong(X))))=>((~strong(susan)<~>~happy(susan))))&
(((funny(john)<~>~funny(john)))<=>(?[X]:(funny(X))))&
(((generous(alice)<~>~humble(alice)))<=>((~calm(john)<~>quiet(john))))&
((?[X]:((~happy(X)<~>funny(X))))<=>(strong(susan)))&
(((tall(fred)<~>quiet(fred)))<=>(?[X]:((creative(X)&calm(X)))))&
(![X]:((~humble(X)&old(X))<=>(kind(X)|wise(X))))&
((?[X]:((~curious(X)|brave(X))))=>(strong(fred)))&
(![X]:((happy(X)|~calm(X))=>(generous(X)|funny(X))))&
((~patient(lucy)|tall(lucy)))&
((creative(john)<~>curious(john)))&
(?[X]:((quiet(X)<~>calm(X))))&
((~rich(susan)&calm(susan)))&
(~calm(alice))&
(?[X]:(~wise(X)))&
(?[X]:((patient(X)<~>quiet(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is not creative or strong is not humble and vice versa.
Everyone who is either not old or not curious is patient.
If alice is kind then susan is either wise or not tall and vice versa.
Everyone who is either tall or not patient is either wise or not wise and vice versa.
Everyone who is either not rich or curious is either not strong or not humble and vice versa.
If fred is wise then someone is wise or humble and vice versa.
Everyone who is both not creative and not wise is either quiet or tall and vice versa.
If someone is rich then someone is old and vice versa.
Everyone who is either funny or generous is generous or not wise and vice versa.
Everyone who is either not happy or funny is both quiet and happy and vice versa.
If someone is both not kind and not creative then someone is either not quiet or not humble and vice versa.
Everyone who is both strong and not quiet is either quiet or not calm.
Everyone who is either humble or not calm is tall or not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Someone is strong.
Someone is either not funny or curious.
Susan is strong.
Fred is either not creative or not brave.
Someone is not happy. | Alice is creative. | neutral | (![X]:((~creative(X)|strong(X))<=>~humble(X)))&
(![X]:((~old(X)<~>~curious(X))=>patient(X)))&
((kind(alice))<=>((wise(susan)<~>~tall(susan))))&
(![X]:((tall(X)<~>~patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~strong(X)<~>~humble(X))))&
((wise(fred))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~creative(X)&~wise(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:(rich(X)))<=>(?[X]:(old(X))))&
(![X]:((funny(X)<~>generous(X))<=>(generous(X)|~wise(X))))&
(![X]:((~happy(X)<~>funny(X))<=>(quiet(X)&happy(X))))&
((?[X]:((~kind(X)&~creative(X))))<=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:((strong(X)&~quiet(X))=>(quiet(X)<~>~calm(X))))&
(![X]:((humble(X)<~>~calm(X))=>(tall(X)|~strong(X))))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(?[X]:(strong(X)))&
(?[X]:((~funny(X)<~>curious(X))))&
(strong(susan))&
((~creative(fred)<~>~brave(fred)))&
(?[X]:(~happy(X))) | creative(alice) | [] | null | 0 |
Everyone who is brave or happy is both quiet and not quiet and vice versa.
If mary is either creative or happy then paul is funny or not humble.
If someone is not curious then someone is both not curious and not calm and vice versa.
If someone is not generous or funny then john is not curious.
If alice is either creative or wise then someone is either old or creative.
If someone is not curious or not funny then someone is both not calm and not patient and vice versa.
If alice is not creative or not humble then paul is patient.
Everyone who is generous or quiet is either brave or humble and vice versa.
If someone is quiet or creative then susan is patient or humble.
Everyone who is not funny or not generous is both happy and creative.
If someone is not calm then someone is kind and vice versa.
Everyone who is both not patient and not rich is not humble and vice versa.
If someone is both humble and patient then mary is either not happy or not rich.
If someone is either quiet or not calm then someone is both not old and funny.
Everyone who is creative or patient is either not old or happy and vice versa.
Everyone who is both strong and quiet is either not quiet or funny and vice versa.
John is either tall or not patient.
Paul is not curious or not happy.
Someone is either not humble or curious.
Alice is calm or tall.
John is tall.
Someone is old.
Mary is either creative or not happy.
John is calm. | Mary is not humble. | contradiction | (![X]:((brave(X)|happy(X))<=>(quiet(X)&~quiet(X))))&
(((creative(mary)<~>happy(mary)))=>((funny(paul)|~humble(paul))))&
((?[X]:(~curious(X)))<=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((~generous(X)|funny(X))))=>(~curious(john)))&
(((creative(alice)<~>wise(alice)))=>(?[X]:((old(X)<~>creative(X)))))&
((?[X]:((~curious(X)|~funny(X))))<=>(?[X]:((~calm(X)&~patient(X)))))&
(((~creative(alice)|~humble(alice)))=>(patient(paul)))&
(![X]:((generous(X)|quiet(X))<=>(brave(X)<~>humble(X))))&
((?[X]:((quiet(X)|creative(X))))=>((patient(susan)|humble(susan))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)&creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(kind(X))))&
(![X]:((~patient(X)&~rich(X))<=>~humble(X)))&
((?[X]:((humble(X)&patient(X))))=>((~happy(mary)<~>~rich(mary))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((creative(X)|patient(X))<=>(~old(X)<~>happy(X))))&
(![X]:((strong(X)&quiet(X))<=>(~quiet(X)<~>funny(X))))&
((tall(john)<~>~patient(john)))&
((~curious(paul)|~happy(paul)))&
(?[X]:((~humble(X)<~>curious(X))))&
((calm(alice)|tall(alice)))&
(tall(john))&
(?[X]:(old(X)))&
((creative(mary)<~>~happy(mary)))&
(calm(john)) | ~humble(mary) | [
"p0",
"p11",
"p12",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4764624283641090795838747
% SZS output start Proof for 4764624283641090795838747
1. ! [X0] : ((happy(X0) | brave(X0)) <=> (~quiet(X0) & quiet(X0))) [input p0]
12. ! [X0] : ((~rich(X0) & ~patient(X0)) <=> ~humble(X0)) [input p11]
13. ? [X0] : (patient(X0) & humble(X0)) => (~happy(mary) <~> ~rich(mary)) [input p12]
17. tall(john) <~> ~patient(john) [input p16]
21. tall(john) [input p20]
25. ~humble(mary) [input hypothesis]
38. (~happy(mary) <~> ~rich(mary)) | ! [X0] : (~patient(X0) | ~humble(X0)) [ennf transformation 13]
40. ! [X0] : (((happy(X0) | brave(X0)) | (quiet(X0) | ~quiet(X0))) & ((~quiet(X0) & quiet(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 1]
41. ! [X0] : ((happy(X0) | brave(X0) | quiet(X0) | ~quiet(X0)) & ((~quiet(X0) & quiet(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 40]
63. ! [X0] : (((~rich(X0) & ~patient(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) | patient(X0)))) [nnf transformation 12]
64. ! [X0] : (((~rich(X0) & ~patient(X0)) | humble(X0)) & (~humble(X0) | rich(X0) | patient(X0))) [flattening 63]
65. ((rich(mary) | happy(mary)) & (~rich(mary) | ~happy(mary))) | ! [X0] : (~patient(X0) | ~humble(X0)) [nnf transformation 38]
74. (patient(john) | ~tall(john)) & (~patient(john) | tall(john)) [nnf transformation 17]
82. quiet(X0) | ~happy(X0) [cnf transformation 41]
84. ~quiet(X0) | ~happy(X0) [cnf transformation 41]
119. ~patient(X0) | humble(X0) [cnf transformation 64]
120. ~rich(X0) | humble(X0) [cnf transformation 64]
122. rich(mary) | happy(mary) | ~patient(X0) | ~humble(X0) [cnf transformation 65]
140. patient(john) | ~tall(john) [cnf transformation 74]
145. tall(john) [cnf transformation 21]
150. ~humble(mary) [cnf transformation 25]
153. ~happy(X0) [subsumption resolution 82,84]
298. rich(mary) | ~patient(X0) | ~humble(X0) [subsumption resolution 122,153]
299. rich(mary) | ~patient(X0) [subsumption resolution 298,119]
301. 32 <=> ! [X0] : ~patient(X0) [avatar definition]
302. ~patient(X0) <- (32) [avatar component clause 301]
304. 33 <=> rich(mary) [avatar definition]
306. rich(mary) <- (33) [avatar component clause 304]
307. 32 | 33 [avatar split clause 299,304,301]
331. 38 <=> tall(john) [avatar definition]
335. 39 <=> patient(john) [avatar definition]
337. patient(john) <- (39) [avatar component clause 335]
338. ~38 | 39 [avatar split clause 140,335,331]
359. 38 [avatar split clause 145,331]
374. $false <- (32, 39) [resolution 337,302]
375. ~32 | ~39 [avatar contradiction clause 374]
377. humble(mary) <- (33) [resolution 120,306]
378. $false <- (33) [subsumption resolution 377,150]
379. ~33 [avatar contradiction clause 378]
380. $false [avatar sat refutation 307,338,359,375,379]
% SZS output end Proof for 4764624283641090795838747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Alice is calm. | entailment | (![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)))) | calm(alice) | [
"p0",
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8592297855678113983786593
% SZS output start Proof for 8592297855678113983786593
1. ! [X0] : ((~generous(X0) & quiet(X0)) <=> (~tall(X0) <~> brave(X0))) [input p0]
4. ! [X0] : ((tall(X0) & humble(X0)) <=> (~calm(X0) | ~humble(X0))) [input p3]
6. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> ~brave(X0)) [input p5]
7. ! [X0] : ((generous(X0) & humble(X0)) <=> (~tall(X0) | tall(X0))) [input p6]
22. ~calm(alice) [input hypothesis]
33. ! [X0] : (((~generous(X0) & quiet(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (generous(X0) | ~quiet(X0)))) [nnf transformation 1]
34. ! [X0] : (((~generous(X0) & quiet(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | generous(X0) | ~quiet(X0))) [flattening 33]
40. ! [X0] : (((tall(X0) & humble(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~tall(X0) | ~humble(X0)))) [nnf transformation 4]
41. ! [X0] : (((tall(X0) & humble(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~tall(X0) | ~humble(X0))) [flattening 40]
43. ! [X0] : (((~wise(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | (wise(X0) | tall(X0)))) [nnf transformation 6]
44. ! [X0] : (((~wise(X0) & ~tall(X0)) | brave(X0)) & (~brave(X0) | wise(X0) | tall(X0))) [flattening 43]
45. ! [X0] : (((generous(X0) & humble(X0)) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | (~generous(X0) | ~humble(X0)))) [nnf transformation 7]
46. ! [X0] : (((generous(X0) & humble(X0)) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | ~generous(X0) | ~humble(X0))) [flattening 45]
78. ~brave(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 34]
91. calm(X0) | tall(X0) [cnf transformation 41]
97. ~tall(X0) | brave(X0) [cnf transformation 44]
102. generous(X0) | ~tall(X0) [cnf transformation 46]
103. tall(X0) | generous(X0) [cnf transformation 46]
133. ~calm(alice) [cnf transformation 22]
177. generous(X0) [subsumption resolution 102,103]
288. tall(alice) [resolution 91,133]
290. brave(alice) [resolution 288,97]
330. ~tall(alice) | ~generous(alice) [resolution 78,290]
332. ~generous(alice) [subsumption resolution 330,288]
333. $false [subsumption resolution 332,177]
% SZS output end Proof for 8592297855678113983786593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is either not tall or old and vice versa. If someone is not strong or old then someone is patient. Everyone who is both not rich and not curious is both not creative and not patient and vice versa. Everyone who is rich or not old is both not curious and kind and vice versa. Everyone who is either not generous or curious is not old. If alice is both happy and wise then someone is either old or humble. If someone is quiet or old then someone is both not tall and calm. Everyone who is not wise is either strong or not quiet and vice versa. Everyone who is both curious and generous is funny or not strong and vice versa. Everyone who is either not tall or strong is both not curious and funny. If john is not rich or not old then mary is both quiet and not calm and vice versa. Everyone who is both not creative and old is quiet or not humble and vice versa. If someone is kind or not creative then someone is both not happy and strong and vice versa. Everyone who is not tall is not strong or calm. If someone is both patient and curious then john is patient. Fred is not kind. Susan is not patient or not curious. Someone is either not brave or curious. Someone is not kind or quiet. Someone is not generous. Lucy is both curious and not generous. Someone is happy. | Alice is not calm. | contradiction | (![X]:((creative(X)|brave(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((~strong(X)|old(X))))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&~curious(X))<=>(~creative(X)&~patient(X))))&
(![X]:((rich(X)|~old(X))<=>(~curious(X)&kind(X))))&
(![X]:((~generous(X)<~>curious(X))=>~old(X)))&
(((happy(alice)&wise(alice)))=>(?[X]:((old(X)<~>humble(X)))))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:(~wise(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((curious(X)&generous(X))<=>(funny(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)&funny(X))))&
(((~rich(john)|~old(john)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(~kind(fred))&
((~patient(susan)|~curious(susan)))&
(?[X]:((~brave(X)<~>curious(X))))&
(?[X]:((~kind(X)|quiet(X))))&
(?[X]:(~generous(X)))&
((curious(lucy)&~generous(lucy)))&
(?[X]:(happy(X))) | ~calm(alice) | [
"p3",
"p4",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2503373294022848466187759
% SZS output start Proof for 2503373294022848466187759
4. ! [X0] : ((~old(X0) | rich(X0)) <=> (kind(X0) & ~curious(X0))) [input p3]
5. ! [X0] : ((~generous(X0) <~> curious(X0)) => ~old(X0)) [input p4]
9. ! [X0] : ((generous(X0) & curious(X0)) <=> (~strong(X0) | funny(X0))) [input p8]
10. ! [X0] : ((~tall(X0) <~> strong(X0)) => (funny(X0) & ~curious(X0))) [input p9]
14. ! [X0] : (~tall(X0) => (calm(X0) | ~strong(X0))) [input p13]
23. ~calm(alice) [input hypothesis]
29. ! [X0] : (~old(X0) | (~generous(X0) <=> curious(X0))) [ennf transformation 5]
34. ! [X0] : ((funny(X0) & ~curious(X0)) | (~tall(X0) <=> strong(X0))) [ennf transformation 10]
35. ! [X0] : ((calm(X0) | ~strong(X0)) | tall(X0)) [ennf transformation 14]
36. ! [X0] : (calm(X0) | ~strong(X0) | tall(X0)) [flattening 35]
45. ! [X0] : (((~old(X0) | rich(X0)) | (~kind(X0) | curious(X0))) & ((kind(X0) & ~curious(X0)) | (old(X0) & ~rich(X0)))) [nnf transformation 4]
46. ! [X0] : ((~old(X0) | rich(X0) | ~kind(X0) | curious(X0)) & ((kind(X0) & ~curious(X0)) | (old(X0) & ~rich(X0)))) [flattening 45]
47. ! [X0] : (~old(X0) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [nnf transformation 29]
55. ! [X0] : (((generous(X0) & curious(X0)) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | (~generous(X0) | ~curious(X0)))) [nnf transformation 9]
56. ! [X0] : (((generous(X0) & curious(X0)) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | ~generous(X0) | ~curious(X0))) [flattening 55]
57. ! [X0] : ((funny(X0) & ~curious(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0)))) [nnf transformation 34]
89. ~curious(X0) | old(X0) [cnf transformation 46]
94. ~old(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 47]
104. ~funny(X0) | curious(X0) [cnf transformation 56]
105. curious(X0) | strong(X0) [cnf transformation 56]
106. ~funny(X0) | generous(X0) [cnf transformation 56]
107. generous(X0) | strong(X0) [cnf transformation 56]
108. ~curious(X0) | strong(X0) | tall(X0) [cnf transformation 57]
111. ~strong(X0) | ~tall(X0) | funny(X0) [cnf transformation 57]
127. calm(X0) | ~strong(X0) | tall(X0) [cnf transformation 36]
138. ~calm(alice) [cnf transformation 23]
148. 3 <=> ! [X1] : strong(X1) [avatar definition]
149. strong(X1) <- (3) [avatar component clause 148]
151. ~generous(X0) | ~curious(X0) [subsumption resolution 94,89]
185. strong(X0) | tall(X0) [subsumption resolution 108,105]
237. calm(X0) | tall(X0) [subsumption resolution 127,185]
285. ~curious(X0) | strong(X0) [resolution 151,107]
286. strong(X0) [subsumption resolution 285,105]
287. 3 [avatar split clause 286,148]
288. tall(alice) [resolution 237,138]
500. ~tall(X1) | funny(X1) <- (3) [resolution 111,149]
532. funny(alice) <- (3) [resolution 500,288]
580. generous(alice) <- (3) [resolution 532,106]
581. curious(alice) <- (3) [resolution 532,104]
630. ~curious(alice) <- (3) [resolution 580,151]
631. $false <- (3) [subsumption resolution 630,581]
632. ~3 [avatar contradiction clause 631]
633. $false [avatar sat refutation 287,632]
% SZS output end Proof for 2503373294022848466187759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not quiet. Everyone who is either humble or not calm is not curious. Everyone who is both kind and creative is either wise or not kind. Everyone who is either curious or not rich is either not patient or creative. If alice is both creative and calm then someone is either not calm or not happy. Everyone who is generous or not tall is both not wise and patient and vice versa. Everyone who is either wise or humble is either rich or old. Everyone who is not brave or not old is either not brave or humble. Everyone who is not funny or not patient is happy and vice versa. Everyone who is either not old or not brave is either kind or not calm and vice versa. Everyone who is both strong and rich is not happy. If john is brave or not humble then john is patient or brave and vice versa. Everyone who is both funny and happy is not wise or tall and vice versa. Everyone who is happy or not quiet is not rich. Everyone who is either not brave or creative is either calm or curious and vice versa. If someone is either not brave or calm then lucy is either generous or not calm. Someone is either not humble or not strong. John is brave or humble. Someone is humble or not happy. Alice is both not kind and not humble. Someone is not brave or calm. Someone is either not patient or creative. | Alice is tall. | entailment | ((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((humble(X)<~>~calm(X))=>~curious(X)))&
(![X]:((kind(X)&creative(X))=>(wise(X)<~>~kind(X))))&
(![X]:((curious(X)<~>~rich(X))=>(~patient(X)<~>creative(X))))&
(((creative(alice)&calm(alice)))=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((generous(X)|~tall(X))<=>(~wise(X)&patient(X))))&
(![X]:((wise(X)<~>humble(X))=>(rich(X)<~>old(X))))&
(![X]:((~brave(X)|~old(X))=>(~brave(X)<~>humble(X))))&
(![X]:((~funny(X)|~patient(X))<=>happy(X)))&
(![X]:((~old(X)<~>~brave(X))<=>(kind(X)<~>~calm(X))))&
(![X]:((strong(X)&rich(X))=>~happy(X)))&
(((brave(john)|~humble(john)))<=>((patient(john)|brave(john))))&
(![X]:((funny(X)&happy(X))<=>(~wise(X)|tall(X))))&
(![X]:((happy(X)|~quiet(X))=>~rich(X)))&
(![X]:((~brave(X)<~>creative(X))<=>(calm(X)<~>curious(X))))&
((?[X]:((~brave(X)<~>calm(X))))=>((generous(lucy)<~>~calm(lucy))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((brave(john)|humble(john)))&
(?[X]:((humble(X)|~happy(X))))&
((~kind(alice)&~humble(alice)))&
(?[X]:((~brave(X)|calm(X))))&
(?[X]:((~patient(X)<~>creative(X)))) | tall(alice) | [
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 268045692000950812596270
% SZS output start Proof for 268045692000950812596270
6. ! [X0] : ((~tall(X0) | generous(X0)) <=> (patient(X0) & ~wise(X0))) [input p5]
9. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> happy(X0)) [input p8]
13. ! [X0] : ((happy(X0) & funny(X0)) <=> (tall(X0) | ~wise(X0))) [input p12]
23. ~tall(alice) [input hypothesis]
48. ! [X0] : (((~tall(X0) | generous(X0)) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | (tall(X0) & ~generous(X0)))) [nnf transformation 6]
49. ! [X0] : ((~tall(X0) | generous(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | (tall(X0) & ~generous(X0)))) [flattening 48]
52. ! [X0] : (((~patient(X0) | ~funny(X0)) | ~happy(X0)) & (happy(X0) | (patient(X0) & funny(X0)))) [nnf transformation 9]
53. ! [X0] : ((~patient(X0) | ~funny(X0) | ~happy(X0)) & (happy(X0) | (patient(X0) & funny(X0)))) [flattening 52]
57. ! [X0] : (((happy(X0) & funny(X0)) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | (~happy(X0) | ~funny(X0)))) [nnf transformation 13]
58. ! [X0] : (((happy(X0) & funny(X0)) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | ~happy(X0) | ~funny(X0))) [flattening 57]
84. ~wise(X0) | tall(X0) [cnf transformation 49]
86. tall(X0) | patient(X0) [cnf transformation 49]
98. ~funny(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 53]
113. funny(X0) | wise(X0) [cnf transformation 58]
115. happy(X0) | wise(X0) [cnf transformation 58]
140. ~tall(alice) [cnf transformation 23]
245. patient(alice) [resolution 86,140]
275. ~patient(X1) | ~happy(X1) | wise(X1) [resolution 98,113]
277. ~patient(X1) | wise(X1) [subsumption resolution 275,115]
281. wise(alice) [resolution 277,245]
282. tall(alice) [resolution 281,84]
283. $false [subsumption resolution 282,140]
% SZS output end Proof for 268045692000950812596270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or funny then fred is old or strong.
If someone is both not rich and brave then john is old or not patient.
Everyone who is not wise or not humble is not quiet.
If alice is tall then fred is both rich and not curious and vice versa.
Everyone who is humble or creative is both generous and not brave and vice versa.
Everyone who is not kind is either not creative or rich and vice versa.
If mary is not kind then susan is either generous or not calm.
Everyone who is both not calm and old is not rich.
If fred is both not happy and old then alice is generous or kind and vice versa.
Everyone who is quiet is both old and rich and vice versa.
Everyone who is both not old and not funny is generous and vice versa.
Everyone who is rich or not tall is both kind and patient and vice versa.
Everyone who is both not rich and not strong is both not humble and not old.
If someone is tall then lucy is either not kind or not old and vice versa.
If someone is patient then mary is both patient and tall.
Susan is either not old or tall.
Fred is creative or not creative.
Mary is either not brave or not wise.
Someone is not creative.
Susan is not old.
Someone is kind or not wise. | Lucy is tall. | neutral | ((?[X]:((strong(X)<~>funny(X))))=>((old(fred)|strong(fred))))&
((?[X]:((~rich(X)&brave(X))))=>((old(john)|~patient(john))))&
(![X]:((~wise(X)|~humble(X))=>~quiet(X)))&
((tall(alice))<=>((rich(fred)&~curious(fred))))&
(![X]:((humble(X)|creative(X))<=>(generous(X)&~brave(X))))&
(![X]:(~kind(X)<=>(~creative(X)<~>rich(X))))&
((~kind(mary))=>((generous(susan)<~>~calm(susan))))&
(![X]:((~calm(X)&old(X))=>~rich(X)))&
(((~happy(fred)&old(fred)))<=>((generous(alice)|kind(alice))))&
(![X]:(quiet(X)<=>(old(X)&rich(X))))&
(![X]:((~old(X)&~funny(X))<=>generous(X)))&
(![X]:((rich(X)|~tall(X))<=>(kind(X)&patient(X))))&
(![X]:((~rich(X)&~strong(X))=>(~humble(X)&~old(X))))&
((?[X]:(tall(X)))<=>((~kind(lucy)<~>~old(lucy))))&
((?[X]:(patient(X)))=>((patient(mary)&tall(mary))))&
((~old(susan)<~>tall(susan)))&
((creative(fred)|~creative(fred)))&
((~brave(mary)<~>~wise(mary)))&
(?[X]:(~creative(X)))&
(~old(susan))&
(?[X]:((kind(X)|~wise(X)))) | tall(lucy) | [] | null | 0 |
Everyone who is funny or creative is strong or calm.
Everyone who is either not calm or not rich is patient and vice versa.
Everyone who is funny or not curious is either funny or kind and vice versa.
Everyone who is either patient or not generous is old or brave and vice versa.
Everyone who is both generous and not generous is not generous or quiet.
If someone is not curious or not funny then someone is calm or not wise.
If susan is either rich or humble then someone is both not brave and not humble.
Everyone who is either generous or not calm is humble or creative and vice versa.
Everyone who is both strong and not strong is either creative or not generous.
Everyone who is either not funny or creative is not kind.
Everyone who is wise or not humble is kind and vice versa.
Everyone who is not patient or not old is not tall and vice versa.
Everyone who is not humble is either not old or not creative.
If lucy is either strong or not generous then mary is both not wise and wise.
If john is not patient or not wise then someone is brave or patient and vice versa.
Everyone who is humble is either old or not funny.
Susan is not curious.
Someone is not calm or rich.
Paul is funny.
Someone is wise.
Susan is either not creative or not tall.
John is both patient and funny.
Mary is both not brave and not strong.
Paul is tall. | Susan is not rich. | neutral | (![X]:((funny(X)|creative(X))=>(strong(X)|calm(X))))&
(![X]:((~calm(X)<~>~rich(X))<=>patient(X)))&
(![X]:((funny(X)|~curious(X))<=>(funny(X)<~>kind(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(old(X)|brave(X))))&
(![X]:((generous(X)&~generous(X))=>(~generous(X)|quiet(X))))&
((?[X]:((~curious(X)|~funny(X))))=>(?[X]:((calm(X)|~wise(X)))))&
(((rich(susan)<~>humble(susan)))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((generous(X)<~>~calm(X))<=>(humble(X)|creative(X))))&
(![X]:((strong(X)&~strong(X))=>(creative(X)<~>~generous(X))))&
(![X]:((~funny(X)<~>creative(X))=>~kind(X)))&
(![X]:((wise(X)|~humble(X))<=>kind(X)))&
(![X]:((~patient(X)|~old(X))<=>~tall(X)))&
(![X]:(~humble(X)=>(~old(X)<~>~creative(X))))&
(((strong(lucy)<~>~generous(lucy)))=>((~wise(mary)&wise(mary))))&
(((~patient(john)|~wise(john)))<=>(?[X]:((brave(X)|patient(X)))))&
(![X]:(humble(X)=>(old(X)<~>~funny(X))))&
(~curious(susan))&
(?[X]:((~calm(X)|rich(X))))&
(funny(paul))&
(?[X]:(wise(X)))&
((~creative(susan)<~>~tall(susan)))&
((patient(john)&funny(john)))&
((~brave(mary)&~strong(mary)))&
(tall(paul)) | ~rich(susan) | [] | null | 0 |
Everyone who is both not old and humble is kind or not rich. Everyone who is not wise is not brave and vice versa. Everyone who is both wise and not old is both not quiet and not tall and vice versa. Everyone who is not calm is not patient and vice versa. Everyone who is generous is both not patient and not tall. Everyone who is not old is either not rich or not humble. Everyone who is either not curious or humble is either kind or not curious and vice versa. If someone is either not wise or not patient then susan is either generous or not quiet and vice versa. If someone is quiet then mary is not tall. Everyone who is not patient is both not brave and not quiet and vice versa. If john is tall or creative then someone is happy and vice versa. If someone is either not wise or not creative then someone is not generous. Everyone who is not old is not calm. If someone is either tall or quiet then susan is quiet or generous and vice versa. Everyone who is both not rich and curious is both not calm and wise and vice versa. Everyone who is either not tall or not humble is quiet. Mary is both funny and happy. John is not humble or not quiet. Fred is not brave or not old. Paul is not strong or strong. Susan is either not strong or generous. Lucy is not wise. | Mary is not old. | contradiction | (![X]:((~old(X)&humble(X))=>(kind(X)|~rich(X))))&
(![X]:(~wise(X)<=>~brave(X)))&
(![X]:((wise(X)&~old(X))<=>(~quiet(X)&~tall(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(![X]:(generous(X)=>(~patient(X)&~tall(X))))&
(![X]:(~old(X)=>(~rich(X)<~>~humble(X))))&
(![X]:((~curious(X)<~>humble(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>((generous(susan)<~>~quiet(susan))))&
((?[X]:(quiet(X)))=>(~tall(mary)))&
(![X]:(~patient(X)<=>(~brave(X)&~quiet(X))))&
(((tall(john)|creative(john)))<=>(?[X]:(happy(X))))&
((?[X]:((~wise(X)<~>~creative(X))))=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>~calm(X)))&
((?[X]:((tall(X)<~>quiet(X))))<=>((quiet(susan)|generous(susan))))&
(![X]:((~rich(X)&curious(X))<=>(~calm(X)&wise(X))))&
(![X]:((~tall(X)<~>~humble(X))=>quiet(X)))&
((funny(mary)&happy(mary)))&
((~humble(john)|~quiet(john)))&
((~brave(fred)|~old(fred)))&
((~strong(paul)|strong(paul)))&
((~strong(susan)<~>generous(susan)))&
(~wise(lucy)) | ~old(mary) | [
"p1",
"p2",
"p3",
"p4",
"p7",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2999345235231472847304142
% SZS output start Proof for 2999345235231472847304142
2. ! [X0] : (~wise(X0) <=> ~brave(X0)) [input p1]
3. ! [X0] : ((~old(X0) & wise(X0)) <=> (~tall(X0) & ~quiet(X0))) [input p2]
4. ! [X0] : (~calm(X0) <=> ~patient(X0)) [input p3]
5. ! [X0] : (generous(X0) => (~tall(X0) & ~patient(X0))) [input p4]
8. ? [X0] : (~wise(X0) <~> ~patient(X0)) <=> (generous(susan) <~> ~quiet(susan)) [input p7]
9. ? [X0] : quiet(X0) => ~tall(mary) [input p8]
10. ! [X0] : (~patient(X0) <=> (~quiet(X0) & ~brave(X0))) [input p9]
13. ! [X0] : (~old(X0) => ~calm(X0)) [input p12]
14. ? [X0] : (tall(X0) <~> quiet(X0)) <=> (generous(susan) | quiet(susan)) [input p13]
23. ~old(mary) [input hypothesis]
28. ! [X0] : ((~tall(X0) & ~patient(X0)) | ~generous(X0)) [ennf transformation 5]
30. ~tall(mary) | ! [X0] : ~quiet(X0) [ennf transformation 9]
32. ! [X0] : (~calm(X0) | old(X0)) [ennf transformation 13]
34. ! [X0] : ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))) [nnf transformation 2]
35. ! [X0] : (((~old(X0) & wise(X0)) | (tall(X0) | quiet(X0))) & ((~tall(X0) & ~quiet(X0)) | (old(X0) | ~wise(X0)))) [nnf transformation 3]
36. ! [X0] : (((~old(X0) & wise(X0)) | tall(X0) | quiet(X0)) & ((~tall(X0) & ~quiet(X0)) | old(X0) | ~wise(X0))) [flattening 35]
37. ! [X0] : ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0))) [nnf transformation 4]
40. (? [X0] : ((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((generous(susan) | quiet(susan)) & (~quiet(susan) | ~generous(susan)))) & (((quiet(susan) | ~generous(susan)) & (~quiet(susan) | generous(susan))) | ! [X0] : ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) [nnf transformation 8]
41. (? [X0] : ((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((generous(susan) | quiet(susan)) & (~quiet(susan) | ~generous(susan)))) & (((quiet(susan) | ~generous(susan)) & (~quiet(susan) | generous(susan))) | ! [X1] : ((~wise(X1) | patient(X1)) & (~patient(X1) | wise(X1)))) [rectify 40]
42. ? [X0] : ((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) => ((patient(sK0) | wise(sK0)) & (~patient(sK0) | ~wise(sK0))) [choice axiom]
43. (((patient(sK0) | wise(sK0)) & (~patient(sK0) | ~wise(sK0))) | ((generous(susan) | quiet(susan)) & (~quiet(susan) | ~generous(susan)))) & (((quiet(susan) | ~generous(susan)) & (~quiet(susan) | generous(susan))) | ! [X1] : ((~wise(X1) | patient(X1)) & (~patient(X1) | wise(X1)))) [skolemisation 41,42]
44. ! [X0] : ((~patient(X0) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | patient(X0))) [nnf transformation 10]
45. ! [X0] : ((~patient(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | patient(X0))) [flattening 44]
55. (? [X0] : ((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | (~generous(susan) & ~quiet(susan))) & ((generous(susan) | quiet(susan)) | ! [X0] : ((tall(X0) | ~quiet(X0)) & (quiet(X0) | ~tall(X0)))) [nnf transformation 14]
56. (? [X0] : ((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | (~generous(susan) & ~quiet(susan))) & (generous(susan) | quiet(susan) | ! [X0] : ((tall(X0) | ~quiet(X0)) & (quiet(X0) | ~tall(X0)))) [flattening 55]
57. (? [X0] : ((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | (~generous(susan) & ~quiet(susan))) & (generous(susan) | quiet(susan) | ! [X1] : ((tall(X1) | ~quiet(X1)) & (quiet(X1) | ~tall(X1)))) [rectify 56]
58. ? [X0] : ((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) => ((~quiet(sK3) | ~tall(sK3)) & (quiet(sK3) | tall(sK3))) [choice axiom]
59. (((~quiet(sK3) | ~tall(sK3)) & (quiet(sK3) | tall(sK3))) | (~generous(susan) & ~quiet(susan))) & (generous(susan) | quiet(susan) | ! [X1] : ((tall(X1) | ~quiet(X1)) & (quiet(X1) | ~tall(X1)))) [skolemisation 57,58]
66. ~wise(X0) | brave(X0) [cnf transformation 34]
69. tall(X0) | wise(X0) | quiet(X0) [cnf transformation 36]
71. ~patient(X0) | calm(X0) [cnf transformation 37]
73. ~generous(X0) | ~patient(X0) [cnf transformation 28]
74. ~generous(X0) | ~tall(X0) [cnf transformation 28]
88. quiet(susan) | ~generous(susan) | ~wise(X1) | patient(X1) [cnf transformation 43]
93. ~tall(mary) | ~quiet(X0) [cnf transformation 30]
94. ~brave(X0) | patient(X0) [cnf transformation 45]
95. ~quiet(X0) | patient(X0) [cnf transformation 45]
102. ~calm(X0) | old(X0) [cnf transformation 32]
103. generous(susan) | quiet(susan) | quiet(X1) | ~tall(X1) [cnf transformation 59]
122. ~old(mary) [cnf transformation 23]
130. 1 <=> quiet(susan) [avatar definition]
132. quiet(susan) <- (1) [avatar component clause 130]
134. 2 <=> generous(susan) [avatar definition]
136. generous(susan) <- (2) [avatar component clause 134]
150. 5 <=> ! [X1] : (~wise(X1) | patient(X1)) [avatar definition]
151. ~wise(X1) | patient(X1) <- (5) [avatar component clause 150]
152. 5 | ~2 | 1 [avatar split clause 88,130,134,150]
160. 7 <=> ! [X0] : ~quiet(X0) [avatar definition]
161. ~quiet(X0) <- (7) [avatar component clause 160]
163. 8 <=> tall(mary) [avatar definition]
165. ~tall(mary) <- (~8) [avatar component clause 163]
166. 7 | ~8 [avatar split clause 93,163,160]
214. 19 <=> ! [X1] : (quiet(X1) | ~tall(X1)) [avatar definition]
215. ~tall(X1) | quiet(X1) <- (19) [avatar component clause 214]
216. 19 | 1 | 2 [avatar split clause 103,134,130,214]
251. wise(mary) | quiet(mary) <- (~8) [resolution 69,165]
254. wise(X1) | quiet(X1) | quiet(X1) <- (19) [resolution 69,215]
255. quiet(X1) | wise(X1) <- (19) [duplicate literal removal 254]
257. 25 <=> quiet(mary) [avatar definition]
258. ~quiet(mary) <- (~25) [avatar component clause 257]
259. quiet(mary) <- (25) [avatar component clause 257]
261. 26 <=> wise(mary) [avatar definition]
263. wise(mary) <- (26) [avatar component clause 261]
264. 25 | 26 | 8 [avatar split clause 251,163,261,257]
277. brave(mary) <- (26) [resolution 263,66]
280. patient(mary) <- (26) [resolution 277,94]
287. 27 <=> calm(mary) [avatar definition]
288. ~calm(mary) <- (~27) [avatar component clause 287]
289. calm(mary) <- (27) [avatar component clause 287]
318. old(mary) <- (27) [resolution 289,102]
320. $false <- (27) [subsumption resolution 318,122]
321. ~27 [avatar contradiction clause 320]
349. wise(mary) <- (19, ~25) [resolution 255,258]
380. calm(mary) <- (26) [resolution 280,71]
381. $false <- (26, ~27) [subsumption resolution 380,288]
382. ~26 | 27 [avatar contradiction clause 381]
383. 26 | ~19 | 25 [avatar split clause 349,257,214,261]
391. $false <- (1, 7) [subsumption resolution 132,161]
392. ~1 | ~7 [avatar contradiction clause 391]
410. 40 <=> wise(susan) [avatar definition]
411. wise(susan) <- (40) [avatar component clause 410]
412. ~wise(susan) <- (~40) [avatar component clause 410]
433. patient(mary) <- (25) [resolution 259,95]
451. patient(susan) <- (5, 40) [resolution 411,151]
476. calm(mary) <- (25) [resolution 433,71]
479. $false <- (25, ~27) [subsumption resolution 476,288]
480. ~25 | 27 [avatar contradiction clause 479]
482. 46 <=> tall(susan) [avatar definition]
483. ~tall(susan) <- (~46) [avatar component clause 482]
486. ~tall(susan) <- (2) [resolution 136,74]
487. ~patient(susan) <- (2) [resolution 136,73]
490. $false <- (2, 5, 40) [subsumption resolution 487,451]
491. ~2 | ~5 | ~40 [avatar contradiction clause 490]
492. ~46 | ~2 [avatar split clause 486,134,482]
498. wise(susan) | quiet(susan) <- (~46) [resolution 483,69]
499. quiet(susan) <- (~40, ~46) [subsumption resolution 498,412]
500. $false <- (7, ~40, ~46) [subsumption resolution 499,161]
501. ~7 | 40 | 46 [avatar contradiction clause 500]
502. $false [avatar sat refutation 152,166,216,264,321,382,383,392,480,491,492,501]
% SZS output end Proof for 2999345235231472847304142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not curious is generous and vice versa.
Everyone who is not kind is not quiet or not humble and vice versa.
Everyone who is both generous and happy is both kind and not kind and vice versa.
Everyone who is happy or tall is both wise and curious and vice versa.
Everyone who is not creative or wise is either humble or wise and vice versa.
If mary is either calm or curious then someone is strong.
If mary is either not patient or wise then someone is not kind.
If someone is strong then alice is both not old and strong.
If someone is both quiet and not tall then john is either funny or rich and vice versa.
If alice is not creative or patient then fred is not strong and vice versa.
Everyone who is rich or not calm is rich or curious.
Everyone who is both patient and not creative is either rich or not funny.
Everyone who is either not creative or not quiet is happy and vice versa.
If alice is either not patient or wise then paul is not creative.
If paul is quiet or strong then mary is either not old or not funny.
If paul is either not happy or not rich then someone is rich or not patient and vice versa.
Paul is not rich.
Someone is strong.
Alice is tall or not patient.
Someone is either funny or not happy.
Someone is either not old or calm.
Lucy is either not strong or not calm.
Someone is both not old and not creative.
Mary is quiet. | John is not kind. | entailment | (![X]:((~kind(X)<~>~curious(X))<=>generous(X)))&
(![X]:(~kind(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((generous(X)&happy(X))<=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|tall(X))<=>(wise(X)&curious(X))))&
(![X]:((~creative(X)|wise(X))<=>(humble(X)<~>wise(X))))&
(((calm(mary)<~>curious(mary)))=>(?[X]:(strong(X))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(strong(X)))=>((~old(alice)&strong(alice))))&
((?[X]:((quiet(X)&~tall(X))))<=>((funny(john)<~>rich(john))))&
(((~creative(alice)|patient(alice)))<=>(~strong(fred)))&
(![X]:((rich(X)|~calm(X))=>(rich(X)|curious(X))))&
(![X]:((patient(X)&~creative(X))=>(rich(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>happy(X)))&
(((~patient(alice)<~>wise(alice)))=>(~creative(paul)))&
(((quiet(paul)|strong(paul)))=>((~old(mary)<~>~funny(mary))))&
(((~happy(paul)<~>~rich(paul)))<=>(?[X]:((rich(X)|~patient(X)))))&
(~rich(paul))&
(?[X]:(strong(X)))&
((tall(alice)|~patient(alice)))&
(?[X]:((funny(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((~strong(lucy)<~>~calm(lucy)))&
(?[X]:((~old(X)&~creative(X))))&
(quiet(mary)) | ~kind(john) | [
"p1",
"p3",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4558053124490970477202467
% SZS output start Proof for 4558053124490970477202467
2. ! [X0] : (~kind(X0) <=> (~humble(X0) | ~quiet(X0))) [input p1]
4. ! [X0] : ((tall(X0) | happy(X0)) <=> (curious(X0) & wise(X0))) [input p3]
5. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (humble(X0) <~> wise(X0))) [input p4]
13. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> happy(X0)) [input p12]
25. kind(john) [input hypothesis]
36. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | kind(X0))) [nnf transformation 2]
37. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | kind(X0))) [flattening 36]
40. ! [X0] : (((tall(X0) | happy(X0)) | (~curious(X0) | ~wise(X0))) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 4]
41. ! [X0] : ((tall(X0) | happy(X0) | ~curious(X0) | ~wise(X0)) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 40]
42. ! [X0] : (((wise(X0) | ~creative(X0)) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [nnf transformation 5]
43. ! [X0] : ((wise(X0) | ~creative(X0) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [flattening 42]
57. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~happy(X0)) & (happy(X0) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 13]
80. ~kind(X0) | quiet(X0) [cnf transformation 37]
81. ~kind(X0) | humble(X0) [cnf transformation 37]
86. ~happy(X0) | wise(X0) [cnf transformation 41]
94. ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
95. wise(X0) | ~creative(X0) | wise(X0) | ~humble(X0) [cnf transformation 43]
116. ~quiet(X0) | happy(X0) | creative(X0) [cnf transformation 57]
144. kind(john) [cnf transformation 25]
145. ~wise(X0) | ~humble(X0) [duplicate literal removal 94]
146. ~creative(X0) | wise(X0) | ~humble(X0) [duplicate literal removal 95]
325. quiet(john) [resolution 80,144]
326. humble(john) [resolution 81,144]
411. happy(john) | creative(john) [resolution 116,325]
431. 51 <=> creative(john) [avatar definition]
433. creative(john) <- (51) [avatar component clause 431]
435. 52 <=> happy(john) [avatar definition]
437. happy(john) <- (52) [avatar component clause 435]
438. 51 | 52 [avatar split clause 411,435,431]
528. wise(john) | ~humble(john) <- (51) [resolution 433,146]
531. wise(john) <- (51) [subsumption resolution 528,326]
597. ~humble(john) <- (51) [resolution 531,145]
598. $false <- (51) [subsumption resolution 597,326]
599. ~51 [avatar contradiction clause 598]
626. wise(john) <- (52) [resolution 437,86]
685. ~humble(john) <- (52) [resolution 626,145]
686. $false <- (52) [subsumption resolution 685,326]
687. ~52 [avatar contradiction clause 686]
688. $false [avatar sat refutation 438,599,687]
% SZS output end Proof for 4558053124490970477202467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not funny is not tall or not calm and vice versa. If someone is either brave or not creative then paul is wise and vice versa. If someone is curious then alice is both brave and not happy. If someone is not generous or not old then alice is calm or not calm. Everyone who is both not rich and rich is old and vice versa. Everyone who is both old and kind is either tall or not wise and vice versa. If john is either not wise or not curious then fred is either not happy or not old. Everyone who is funny or not wise is not tall. Everyone who is either not wise or not rich is both not kind and patient. If someone is tall or strong then mary is either not generous or calm and vice versa. If alice is not strong then someone is both not creative and not quiet and vice versa. If john is either not rich or not patient then someone is either not creative or not wise and vice versa. Everyone who is either not happy or curious is not creative or kind. If someone is old or generous then fred is either not rich or not happy and vice versa. Everyone who is either not generous or old is both not brave and not strong. Someone is either not old or not brave. Susan is either old or not old. Someone is tall or brave. Someone is both not old and happy. Susan is either happy or not quiet. Someone is not wise or not quiet. Someone is not strong. Paul is patient or creative. | John is not wise. | contradiction | (![X]:((generous(X)&~funny(X))<=>(~tall(X)|~calm(X))))&
((?[X]:((brave(X)<~>~creative(X))))<=>(wise(paul)))&
((?[X]:(curious(X)))=>((brave(alice)&~happy(alice))))&
((?[X]:((~generous(X)|~old(X))))=>((calm(alice)|~calm(alice))))&
(![X]:((~rich(X)&rich(X))<=>old(X)))&
(![X]:((old(X)&kind(X))<=>(tall(X)<~>~wise(X))))&
(((~wise(john)<~>~curious(john)))=>((~happy(fred)<~>~old(fred))))&
(![X]:((funny(X)|~wise(X))=>~tall(X)))&
(![X]:((~wise(X)<~>~rich(X))=>(~kind(X)&patient(X))))&
((?[X]:((tall(X)|strong(X))))<=>((~generous(mary)<~>calm(mary))))&
((~strong(alice))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(((~rich(john)<~>~patient(john)))<=>(?[X]:((~creative(X)<~>~wise(X)))))&
(![X]:((~happy(X)<~>curious(X))=>(~creative(X)|kind(X))))&
((?[X]:((old(X)|generous(X))))<=>((~rich(fred)<~>~happy(fred))))&
(![X]:((~generous(X)<~>old(X))=>(~brave(X)&~strong(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
((old(susan)<~>~old(susan)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~old(X)&happy(X))))&
((happy(susan)<~>~quiet(susan)))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:(~strong(X)))&
((patient(paul)|creative(paul))) | ~wise(john) | [
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2044899041836898912844316
% SZS output start Proof for 2044899041836898912844316
5. ! [X0] : ((rich(X0) & ~rich(X0)) <=> old(X0)) [input p4]
6. ! [X0] : ((kind(X0) & old(X0)) <=> (tall(X0) <~> ~wise(X0))) [input p5]
8. ! [X0] : ((~wise(X0) | funny(X0)) => ~tall(X0)) [input p7]
24. ~wise(john) [input hypothesis]
29. ! [X0] : (~tall(X0) | (wise(X0) & ~funny(X0))) [ennf transformation 8]
40. ! [X0] : (((rich(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | (~rich(X0) | rich(X0)))) [nnf transformation 5]
41. ! [X0] : (((rich(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | ~rich(X0) | rich(X0))) [flattening 40]
42. ! [X0] : (((kind(X0) & old(X0)) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~kind(X0) | ~old(X0)))) [nnf transformation 6]
43. ! [X0] : (((kind(X0) & old(X0)) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | ~kind(X0) | ~old(X0))) [flattening 42]
91. ~rich(X0) | ~old(X0) [cnf transformation 41]
92. rich(X0) | ~old(X0) [cnf transformation 41]
96. old(X0) | tall(X0) | wise(X0) [cnf transformation 43]
104. ~tall(X0) | wise(X0) [cnf transformation 29]
150. ~wise(john) [cnf transformation 24]
186. ~old(X0) [subsumption resolution 91,92]
187. tall(X0) | wise(X0) [subsumption resolution 96,186]
205. wise(X0) [subsumption resolution 104,187]
330. $false [subsumption resolution 150,205]
% SZS output end Proof for 2044899041836898912844316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or humble is either not old or old and vice versa.
Everyone who is both generous and not wise is both not wise and kind.
If someone is not old then someone is not rich and vice versa.
If susan is both tall and strong then someone is old.
Everyone who is either not strong or not humble is generous or curious and vice versa.
If someone is not old or old then someone is quiet or not creative.
If someone is wise or not quiet then john is either tall or wise.
Everyone who is both strong and not rich is both not creative and not quiet and vice versa.
Everyone who is either funny or not creative is both happy and old and vice versa.
If john is both patient and not happy then lucy is not brave or not humble and vice versa.
Everyone who is not curious is either funny or creative and vice versa.
If someone is funny or not funny then mary is not funny.
If john is not funny or not patient then someone is either not curious or not patient and vice versa.
Everyone who is both not curious and tall is both strong and not funny.
Everyone who is both not happy and old is humble or not quiet and vice versa.
If someone is both not curious and not rich then john is either not old or happy and vice versa.
Paul is both patient and rich.
Mary is both not wise and quiet.
Paul is patient.
Susan is not generous or patient.
Someone is not happy.
Fred is either curious or rich.
Someone is both not generous and not tall.
Someone is both not funny and not curious. | John is funny. | contradiction | (![X]:((old(X)<~>humble(X))<=>(~old(X)<~>old(X))))&
(![X]:((generous(X)&~wise(X))=>(~wise(X)&kind(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~rich(X))))&
(((tall(susan)&strong(susan)))=>(?[X]:(old(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(generous(X)|curious(X))))&
((?[X]:((~old(X)|old(X))))=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:((wise(X)|~quiet(X))))=>((tall(john)<~>wise(john))))&
(![X]:((strong(X)&~rich(X))<=>(~creative(X)&~quiet(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(happy(X)&old(X))))&
(((patient(john)&~happy(john)))<=>((~brave(lucy)|~humble(lucy))))&
(![X]:(~curious(X)<=>(funny(X)<~>creative(X))))&
((?[X]:((funny(X)|~funny(X))))=>(~funny(mary)))&
(((~funny(john)|~patient(john)))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:((~curious(X)&tall(X))=>(strong(X)&~funny(X))))&
(![X]:((~happy(X)&old(X))<=>(humble(X)|~quiet(X))))&
((?[X]:((~curious(X)&~rich(X))))<=>((~old(john)<~>happy(john))))&
((patient(paul)&rich(paul)))&
((~wise(mary)&quiet(mary)))&
(patient(paul))&
((~generous(susan)|patient(susan)))&
(?[X]:(~happy(X)))&
((curious(fred)<~>rich(fred)))&
(?[X]:((~generous(X)&~tall(X))))&
(?[X]:((~funny(X)&~curious(X)))) | funny(john) | [
"p0",
"p8",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3772006817005932334716887
% SZS output start Proof for 3772006817005932334716887
1. ! [X0] : ((old(X0) <~> humble(X0)) <=> (~old(X0) <~> old(X0))) [input p0]
9. ! [X0] : ((funny(X0) <~> ~creative(X0)) <=> (old(X0) & happy(X0))) [input p8]
10. (~happy(john) & patient(john)) <=> (~humble(lucy) | ~brave(lucy)) [input p9]
11. ! [X0] : (~curious(X0) <=> (funny(X0) <~> creative(X0))) [input p10]
13. (~patient(john) | ~funny(john)) <=> ? [X0] : (~curious(X0) <~> ~patient(X0)) [input p12]
15. ! [X0] : ((old(X0) & ~happy(X0)) <=> (~quiet(X0) | humble(X0))) [input p14]
25. funny(john) [input hypothesis]
38. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [nnf transformation 1]
54. ! [X0] : ((((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | (~old(X0) | ~happy(X0))) & ((old(X0) & happy(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))))) [nnf transformation 9]
55. ! [X0] : ((((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | ~old(X0) | ~happy(X0)) & ((old(X0) & happy(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))))) [flattening 54]
56. ((~happy(john) & patient(john)) | (humble(lucy) & brave(lucy))) & ((~humble(lucy) | ~brave(lucy)) | (happy(john) | ~patient(john))) [nnf transformation 10]
57. ((~happy(john) & patient(john)) | (humble(lucy) & brave(lucy))) & (~humble(lucy) | ~brave(lucy) | happy(john) | ~patient(john)) [flattening 56]
58. ! [X0] : ((~curious(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | curious(X0))) [nnf transformation 11]
59. ((~patient(john) | ~funny(john)) | ! [X0] : ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (? [X0] : ((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (patient(john) & funny(john))) [nnf transformation 13]
60. (~patient(john) | ~funny(john) | ! [X0] : ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (? [X0] : ((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (patient(john) & funny(john))) [flattening 59]
61. (~patient(john) | ~funny(john) | ! [X0] : ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (? [X1] : ((patient(X1) | curious(X1)) & (~patient(X1) | ~curious(X1))) | (patient(john) & funny(john))) [rectify 60]
62. ? [X1] : ((patient(X1) | curious(X1)) & (~patient(X1) | ~curious(X1))) => ((patient(sK4) | curious(sK4)) & (~patient(sK4) | ~curious(sK4))) [choice axiom]
63. (~patient(john) | ~funny(john) | ! [X0] : ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(sK4) | curious(sK4)) & (~patient(sK4) | ~curious(sK4))) | (patient(john) & funny(john))) [skolemisation 61,62]
64. ! [X0] : (((old(X0) & ~happy(X0)) | (quiet(X0) & ~humble(X0))) & ((~quiet(X0) | humble(X0)) | (~old(X0) | happy(X0)))) [nnf transformation 15]
65. ! [X0] : (((old(X0) & ~happy(X0)) | (quiet(X0) & ~humble(X0))) & (~quiet(X0) | humble(X0) | ~old(X0) | happy(X0))) [flattening 64]
84. ~humble(X0) | ~old(X0) | ~old(X0) | ~old(X0) [cnf transformation 38]
105. ~funny(X0) | ~creative(X0) | happy(X0) [cnf transformation 55]
113. patient(john) | humble(lucy) [cnf transformation 57]
115. ~happy(john) | humble(lucy) [cnf transformation 57]
118. ~funny(X0) | creative(X0) | ~curious(X0) [cnf transformation 58]
126. ~patient(john) | ~funny(john) | ~patient(X0) | curious(X0) [cnf transformation 63]
133. old(X0) | ~humble(X0) [cnf transformation 65]
154. funny(john) [cnf transformation 25]
162. ~humble(X0) | ~old(X0) [duplicate literal removal 84]
224. 15 <=> humble(lucy) [avatar definition]
226. humble(lucy) <- (15) [avatar component clause 224]
228. 16 <=> happy(john) [avatar definition]
230. ~happy(john) <- (~16) [avatar component clause 228]
231. 15 | ~16 [avatar split clause 115,228,224]
238. 18 <=> patient(john) [avatar definition]
240. patient(john) <- (18) [avatar component clause 238]
241. 15 | 18 [avatar split clause 113,238,224]
260. 23 <=> funny(john) [avatar definition]
261. funny(john) <- (23) [avatar component clause 260]
265. 24 <=> ! [X0] : (~patient(X0) | curious(X0)) [avatar definition]
266. ~patient(X0) | curious(X0) <- (24) [avatar component clause 265]
267. 24 | ~23 | ~18 [avatar split clause 126,238,260,265]
280. ~humble(X0) [subsumption resolution 133,162]
322. 23 [avatar split clause 154,260]
329. $false <- (15) [subsumption resolution 226,280]
330. ~15 [avatar contradiction clause 329]
339. curious(john) <- (18, 24) [resolution 266,240]
372. ~creative(john) | happy(john) <- (23) [resolution 105,261]
373. ~creative(john) <- (~16, 23) [subsumption resolution 372,230]
431. creative(john) | ~curious(john) <- (23) [resolution 118,261]
436. ~curious(john) <- (~16, 23) [subsumption resolution 431,373]
437. $false <- (~16, 18, 23, 24) [subsumption resolution 436,339]
438. 16 | ~18 | ~23 | ~24 [avatar contradiction clause 437]
439. $false [avatar sat refutation 231,241,267,322,330,438]
% SZS output end Proof for 3772006817005932334716887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not patient is calm or tall.
Everyone who is both not rich and not humble is both generous and wise and vice versa.
Everyone who is generous is not quiet and vice versa.
If paul is tall then fred is both kind and not happy and vice versa.
Everyone who is both brave and old is not tall and vice versa.
If john is not rich or not tall then paul is both wise and generous.
Everyone who is funny or calm is both not tall and wise and vice versa.
Everyone who is tall is both funny and not happy.
If lucy is not humble or not calm then lucy is not patient or not calm and vice versa.
Everyone who is either happy or not calm is both not tall and not generous.
Everyone who is either not strong or not tall is either funny or not happy.
Everyone who is brave is not quiet or not patient and vice versa.
Everyone who is both not kind and not creative is either old or patient and vice versa.
Everyone who is both not calm and wise is not old or not calm.
Everyone who is either calm or not wise is either not patient or patient.
If someone is not brave then someone is both tall and not curious and vice versa.
Mary is both not creative and quiet.
Someone is not funny or creative.
Someone is both not patient and not curious.
Fred is not creative.
Fred is both not rich and not humble.
Paul is not happy. | Mary is brave. | entailment | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:(generous(X)<=>~quiet(X)))&
((tall(paul))<=>((kind(fred)&~happy(fred))))&
(![X]:((brave(X)&old(X))<=>~tall(X)))&
(((~rich(john)|~tall(john)))=>((wise(paul)&generous(paul))))&
(![X]:((funny(X)|calm(X))<=>(~tall(X)&wise(X))))&
(![X]:(tall(X)=>(funny(X)&~happy(X))))&
(((~humble(lucy)|~calm(lucy)))<=>((~patient(lucy)|~calm(lucy))))&
(![X]:((happy(X)<~>~calm(X))=>(~tall(X)&~generous(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(funny(X)<~>~happy(X))))&
(![X]:(brave(X)<=>(~quiet(X)|~patient(X))))&
(![X]:((~kind(X)&~creative(X))<=>(old(X)<~>patient(X))))&
(![X]:((~calm(X)&wise(X))=>(~old(X)|~calm(X))))&
(![X]:((calm(X)<~>~wise(X))=>(~patient(X)<~>patient(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((tall(X)&~curious(X)))))&
((~creative(mary)&quiet(mary)))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:((~patient(X)&~curious(X))))&
(~creative(fred))&
((~rich(fred)&~humble(fred)))&
(~happy(paul)) | brave(mary) | [
"p6",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4521097860499740214858665
% SZS output start Proof for 4521097860499740214858665
7. ! [X0] : ((calm(X0) | funny(X0)) <=> (wise(X0) & ~tall(X0))) [input p6]
8. ! [X0] : (tall(X0) => (~happy(X0) & funny(X0))) [input p7]
16. ? [X0] : ~brave(X0) <=> ? [X0] : (~curious(X0) & tall(X0)) [input p15]
23. ~brave(mary) [input hypothesis]
24. ? [X0] : ~brave(X0) <=> ? [X1] : (~curious(X1) & tall(X1)) [rectify 16]
28. ! [X0] : ((~happy(X0) & funny(X0)) | ~tall(X0)) [ennf transformation 8]
41. ! [X0] : (((calm(X0) | funny(X0)) | (~wise(X0) | tall(X0))) & ((wise(X0) & ~tall(X0)) | (~calm(X0) & ~funny(X0)))) [nnf transformation 7]
42. ! [X0] : ((calm(X0) | funny(X0) | ~wise(X0) | tall(X0)) & ((wise(X0) & ~tall(X0)) | (~calm(X0) & ~funny(X0)))) [flattening 41]
52. (? [X0] : ~brave(X0) | ! [X1] : (curious(X1) | ~tall(X1))) & (? [X1] : (~curious(X1) & tall(X1)) | ! [X0] : brave(X0)) [nnf transformation 24]
53. (? [X0] : ~brave(X0) | ! [X1] : (curious(X1) | ~tall(X1))) & (? [X2] : (~curious(X2) & tall(X2)) | ! [X3] : brave(X3)) [rectify 52]
54. ? [X0] : ~brave(X0) => ~brave(sK0) [choice axiom]
55. ? [X2] : (~curious(X2) & tall(X2)) => (~curious(sK1) & tall(sK1)) [choice axiom]
56. (~brave(sK0) | ! [X1] : (curious(X1) | ~tall(X1))) & ((~curious(sK1) & tall(sK1)) | ! [X3] : brave(X3)) [skolemisation 53,55,54]
79. ~tall(X0) | ~funny(X0) [cnf transformation 42]
84. funny(X0) | ~tall(X0) [cnf transformation 28]
112. tall(sK1) | brave(X3) [cnf transformation 56]
124. ~brave(mary) [cnf transformation 23]
161. ~tall(X0) [subsumption resolution 84,79]
179. 11 <=> ! [X3] : brave(X3) [avatar definition]
180. brave(X3) <- (11) [avatar component clause 179]
186. brave(X3) [subsumption resolution 112,161]
187. 11 [avatar split clause 186,179]
199. $false <- (11) [resolution 180,124]
200. ~11 [avatar contradiction clause 199]
201. $false [avatar sat refutation 187,200]
% SZS output end Proof for 4521097860499740214858665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then john is both not kind and tall and vice versa.
Everyone who is either not curious or happy is both strong and not curious.
If someone is not old or wise then someone is both not brave and creative and vice versa.
If someone is calm then fred is both not calm and funny and vice versa.
If someone is either not rich or not generous then alice is either kind or not tall and vice versa.
If someone is quiet then someone is wise or not old and vice versa.
If alice is either not patient or creative then john is either rich or not creative.
Everyone who is not calm or strong is not curious.
If someone is either kind or curious then john is not generous and vice versa.
Everyone who is both generous and not old is not kind or not happy.
If alice is either not generous or tall then lucy is humble or not calm.
If mary is both patient and humble then fred is not strong.
Everyone who is both humble and rich is both creative and not patient.
If susan is both not patient and not funny then someone is not curious or not tall.
Everyone who is both wise and not generous is not generous and vice versa.
If alice is both not creative and wise then someone is quiet or not wise.
Fred is not humble.
Fred is both not funny and not happy.
Someone is not strong or not patient.
Someone is not wise or not curious.
Someone is not old.
Someone is both funny and not patient.
Lucy is not patient.
Someone is creative or not patient. | Susan is not calm. | entailment | ((rich(alice))<=>((~kind(john)&tall(john))))&
(![X]:((~curious(X)<~>happy(X))=>(strong(X)&~curious(X))))&
((?[X]:((~old(X)|wise(X))))<=>(?[X]:((~brave(X)&creative(X)))))&
((?[X]:(calm(X)))<=>((~calm(fred)&funny(fred))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>((kind(alice)<~>~tall(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:((wise(X)|~old(X)))))&
(((~patient(alice)<~>creative(alice)))=>((rich(john)<~>~creative(john))))&
(![X]:((~calm(X)|strong(X))=>~curious(X)))&
((?[X]:((kind(X)<~>curious(X))))<=>(~generous(john)))&
(![X]:((generous(X)&~old(X))=>(~kind(X)|~happy(X))))&
(((~generous(alice)<~>tall(alice)))=>((humble(lucy)|~calm(lucy))))&
(((patient(mary)&humble(mary)))=>(~strong(fred)))&
(![X]:((humble(X)&rich(X))=>(creative(X)&~patient(X))))&
(((~patient(susan)&~funny(susan)))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((wise(X)&~generous(X))<=>~generous(X)))&
(((~creative(alice)&wise(alice)))=>(?[X]:((quiet(X)|~wise(X)))))&
(~humble(fred))&
((~funny(fred)&~happy(fred)))&
(?[X]:((~strong(X)|~patient(X))))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:(~old(X)))&
(?[X]:((funny(X)&~patient(X))))&
(~patient(lucy))&
(?[X]:((creative(X)|~patient(X)))) | ~calm(susan) | [
"p3",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 856371072603721551791247
% SZS output start Proof for 856371072603721551791247
4. ? [X0] : calm(X0) <=> (funny(fred) & ~calm(fred)) [input p3]
18. ~happy(fred) & ~funny(fred) [input p17]
25. calm(susan) [input hypothesis]
51. (? [X0] : calm(X0) | (~funny(fred) | calm(fred))) & ((funny(fred) & ~calm(fred)) | ! [X0] : ~calm(X0)) [nnf transformation 4]
52. (? [X0] : calm(X0) | ~funny(fred) | calm(fred)) & ((funny(fred) & ~calm(fred)) | ! [X0] : ~calm(X0)) [flattening 51]
53. (? [X0] : calm(X0) | ~funny(fred) | calm(fred)) & ((funny(fred) & ~calm(fred)) | ! [X1] : ~calm(X1)) [rectify 52]
54. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
55. (calm(sK2) | ~funny(fred) | calm(fred)) & ((funny(fred) & ~calm(fred)) | ! [X1] : ~calm(X1)) [skolemisation 53,54]
100. funny(fred) | ~calm(X1) [cnf transformation 55]
135. ~funny(fred) [cnf transformation 18]
144. calm(susan) [cnf transformation 25]
196. 12 <=> funny(fred) [avatar definition]
205. 14 <=> ! [X1] : ~calm(X1) [avatar definition]
206. ~calm(X1) <- (14) [avatar component clause 205]
207. 14 | 12 [avatar split clause 100,196,205]
356. ~12 [avatar split clause 135,196]
390. $false <- (14) [resolution 206,144]
391. ~14 [avatar contradiction clause 390]
392. $false [avatar sat refutation 207,356,391]
% SZS output end Proof for 856371072603721551791247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not old is both not patient and funny and vice versa.
Everyone who is both not happy and not generous is either not creative or not funny.
If john is not brave or old then fred is rich and vice versa.
Everyone who is strong is either not patient or not strong and vice versa.
Everyone who is not rich is either not calm or not brave.
Everyone who is humble or rich is curious or not quiet.
If someone is both old and not funny then someone is quiet or not strong and vice versa.
If someone is strong or kind then fred is both old and not patient and vice versa.
If someone is kind or rich then someone is quiet.
Everyone who is curious or creative is wise.
If someone is not strong or brave then someone is generous or strong.
Everyone who is not tall is both not brave and not happy.
Everyone who is both calm and tall is not generous and vice versa.
Everyone who is both not wise and not generous is generous and vice versa.
If someone is both curious and wise then alice is rich and vice versa.
Everyone who is not curious is either rich or humble.
Mary is tall.
Susan is either brave or rich.
Lucy is strong.
Someone is both brave and not happy.
Someone is not creative.
Lucy is not curious or kind.
Someone is either brave or not happy. | Alice is tall. | entailment | (![X]:((patient(X)&~old(X))<=>(~patient(X)&funny(X))))&
(![X]:((~happy(X)&~generous(X))=>(~creative(X)<~>~funny(X))))&
(((~brave(john)|old(john)))<=>(rich(fred)))&
(![X]:(strong(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:(~rich(X)=>(~calm(X)<~>~brave(X))))&
(![X]:((humble(X)|rich(X))=>(curious(X)|~quiet(X))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:((quiet(X)|~strong(X)))))&
((?[X]:((strong(X)|kind(X))))<=>((old(fred)&~patient(fred))))&
((?[X]:((kind(X)|rich(X))))=>(?[X]:(quiet(X))))&
(![X]:((curious(X)|creative(X))=>wise(X)))&
((?[X]:((~strong(X)|brave(X))))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:(~tall(X)=>(~brave(X)&~happy(X))))&
(![X]:((calm(X)&tall(X))<=>~generous(X)))&
(![X]:((~wise(X)&~generous(X))<=>generous(X)))&
((?[X]:((curious(X)&wise(X))))<=>(rich(alice)))&
(![X]:(~curious(X)=>(rich(X)<~>humble(X))))&
(tall(mary))&
((brave(susan)<~>rich(susan)))&
(strong(lucy))&
(?[X]:((brave(X)&~happy(X))))&
(?[X]:(~creative(X)))&
((~curious(lucy)|kind(lucy)))&
(?[X]:((brave(X)<~>~happy(X)))) | tall(alice) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 193060400185157105818073
% SZS output start Proof for 193060400185157105818073
13. ! [X0] : ((tall(X0) & calm(X0)) <=> ~generous(X0)) [input p12]
14. ! [X0] : ((~generous(X0) & ~wise(X0)) <=> generous(X0)) [input p13]
24. ~tall(alice) [input hypothesis]
61. ! [X0] : (((tall(X0) & calm(X0)) | generous(X0)) & (~generous(X0) | (~tall(X0) | ~calm(X0)))) [nnf transformation 13]
62. ! [X0] : (((tall(X0) & calm(X0)) | generous(X0)) & (~generous(X0) | ~tall(X0) | ~calm(X0))) [flattening 61]
63. ! [X0] : (((~generous(X0) & ~wise(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) | wise(X0)))) [nnf transformation 14]
64. ! [X0] : (((~generous(X0) & ~wise(X0)) | ~generous(X0)) & (generous(X0) | generous(X0) | wise(X0))) [flattening 63]
115. tall(X0) | generous(X0) [cnf transformation 62]
118. ~generous(X0) | ~generous(X0) [cnf transformation 64]
134. ~tall(alice) [cnf transformation 24]
136. ~generous(X0) [duplicate literal removal 118]
290. generous(alice) [resolution 115,134]
291. $false [subsumption resolution 290,136]
% SZS output end Proof for 193060400185157105818073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not calm is calm or not brave and vice versa.
If someone is not strong or not creative then paul is either not wise or old.
If susan is not patient or quiet then mary is either not curious or not calm.
If someone is not quiet then someone is patient or not creative and vice versa.
If someone is funny or not rich then someone is not humble or not wise and vice versa.
Everyone who is not curious is both patient and calm.
Everyone who is not old or not rich is not calm.
Everyone who is both not tall and not rich is strong or kind.
Everyone who is patient or not tall is not curious and vice versa.
Everyone who is patient is not brave.
Everyone who is either not brave or not funny is kind.
If fred is humble then john is not humble and vice versa.
Everyone who is not generous or not kind is both not patient and not calm.
If someone is both rich and generous then someone is not funny and vice versa.
Everyone who is either not funny or kind is either not quiet or not kind.
Susan is happy.
Someone is both not brave and generous.
Mary is curious.
Susan is rich.
Paul is not rich or curious.
Someone is not happy or patient.
Someone is rich or funny. | Paul is funny. | neutral | (![X]:((funny(X)&~calm(X))<=>(calm(X)|~brave(X))))&
((?[X]:((~strong(X)|~creative(X))))=>((~wise(paul)<~>old(paul))))&
(((~patient(susan)|quiet(susan)))=>((~curious(mary)<~>~calm(mary))))&
((?[X]:(~quiet(X)))<=>(?[X]:((patient(X)|~creative(X)))))&
((?[X]:((funny(X)|~rich(X))))<=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:(~curious(X)=>(patient(X)&calm(X))))&
(![X]:((~old(X)|~rich(X))=>~calm(X)))&
(![X]:((~tall(X)&~rich(X))=>(strong(X)|kind(X))))&
(![X]:((patient(X)|~tall(X))<=>~curious(X)))&
(![X]:(patient(X)=>~brave(X)))&
(![X]:((~brave(X)<~>~funny(X))=>kind(X)))&
((humble(fred))<=>(~humble(john)))&
(![X]:((~generous(X)|~kind(X))=>(~patient(X)&~calm(X))))&
((?[X]:((rich(X)&generous(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~funny(X)<~>kind(X))=>(~quiet(X)<~>~kind(X))))&
(happy(susan))&
(?[X]:((~brave(X)&generous(X))))&
(curious(mary))&
(rich(susan))&
((~rich(paul)|curious(paul)))&
(?[X]:((~happy(X)|patient(X))))&
(?[X]:((rich(X)|funny(X)))) | funny(paul) | [] | null | 0 |
If someone is curious or strong then someone is not generous and vice versa. If fred is tall then someone is both funny and quiet. Everyone who is not funny or not patient is both not wise and humble. Everyone who is either not calm or generous is both not humble and wise. If susan is kind then someone is not tall or not humble and vice versa. If mary is both tall and curious then someone is both curious and not old and vice versa. Everyone who is both not strong and creative is either calm or happy. Everyone who is calm is either not generous or tall and vice versa. If mary is not rich then susan is either not old or not tall. If lucy is not creative then someone is either not curious or kind. Everyone who is either brave or strong is either not strong or funny and vice versa. If fred is not patient or old then lucy is both not old and curious and vice versa. Everyone who is either not tall or old is funny. Everyone who is patient is either not wise or not creative and vice versa. Everyone who is not tall is kind or not brave. Someone is either not curious or funny. John is either wise or not curious. Lucy is rich or not funny. Someone is not kind. Someone is both not wise and not rich. John is either not brave or not generous. Someone is not brave. Someone is either rich or curious. | Susan is not kind. | contradiction | ((?[X]:((curious(X)|strong(X))))<=>(?[X]:(~generous(X))))&
((tall(fred))=>(?[X]:((funny(X)&quiet(X)))))&
(![X]:((~funny(X)|~patient(X))=>(~wise(X)&humble(X))))&
(![X]:((~calm(X)<~>generous(X))=>(~humble(X)&wise(X))))&
((kind(susan))<=>(?[X]:((~tall(X)|~humble(X)))))&
(((tall(mary)&curious(mary)))<=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((~strong(X)&creative(X))=>(calm(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~generous(X)<~>tall(X))))&
((~rich(mary))=>((~old(susan)<~>~tall(susan))))&
((~creative(lucy))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((brave(X)<~>strong(X))<=>(~strong(X)<~>funny(X))))&
(((~patient(fred)|old(fred)))<=>((~old(lucy)&curious(lucy))))&
(![X]:((~tall(X)<~>old(X))=>funny(X)))&
(![X]:(patient(X)<=>(~wise(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(kind(X)|~brave(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((wise(john)<~>~curious(john)))&
((rich(lucy)|~funny(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~rich(X))))&
((~brave(john)<~>~generous(john)))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>curious(X)))) | ~kind(susan) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7321555962386047524717890
% SZS output start Proof for 7321555962386047524717890
4. ! [X0] : ((~calm(X0) <~> generous(X0)) => (wise(X0) & ~humble(X0))) [input p3]
5. kind(susan) <=> ? [X0] : (~humble(X0) | ~tall(X0)) [input p4]
8. ! [X0] : (calm(X0) <=> (~generous(X0) <~> tall(X0))) [input p7]
24. ~kind(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~humble(X0)) | (~calm(X0) <=> generous(X0))) [ennf transformation 4]
44. ! [X0] : ((wise(X0) & ~humble(X0)) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0)))) [nnf transformation 29]
45. (kind(susan) | ! [X0] : (humble(X0) & tall(X0))) & (? [X0] : (~humble(X0) | ~tall(X0)) | ~kind(susan)) [nnf transformation 5]
46. (kind(susan) | ! [X0] : (humble(X0) & tall(X0))) & (? [X1] : (~humble(X1) | ~tall(X1)) | ~kind(susan)) [rectify 45]
47. ? [X1] : (~humble(X1) | ~tall(X1)) => (~humble(sK3) | ~tall(sK3)) [choice axiom]
48. (kind(susan) | ! [X0] : (humble(X0) & tall(X0))) & ((~humble(sK3) | ~tall(sK3)) | ~kind(susan)) [skolemisation 46,47]
55. ! [X0] : ((calm(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | ~calm(X0))) [nnf transformation 8]
87. ~humble(X0) | generous(X0) | calm(X0) [cnf transformation 44]
88. ~calm(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 44]
92. kind(susan) | tall(X0) [cnf transformation 48]
93. kind(susan) | humble(X0) [cnf transformation 48]
101. ~calm(X0) | generous(X0) | ~tall(X0) [cnf transformation 55]
103. ~tall(X0) | ~generous(X0) | calm(X0) [cnf transformation 55]
141. ~kind(susan) [cnf transformation 24]
147. 1 <=> ! [X1] : generous(X1) [avatar definition]
148. generous(X1) <- (1) [avatar component clause 147]
180. 9 <=> ! [X0] : humble(X0) [avatar definition]
181. humble(X0) <- (9) [avatar component clause 180]
183. 10 <=> kind(susan) [avatar definition]
186. 9 | 10 [avatar split clause 93,183,180]
188. 11 <=> ! [X0] : tall(X0) [avatar definition]
189. tall(X0) <- (11) [avatar component clause 188]
190. 11 | 10 [avatar split clause 92,183,188]
325. ~10 [avatar split clause 141,183]
337. calm(X2) | generous(X2) <- (9) [resolution 87,181]
346. generous(X1) | ~tall(X1) | generous(X1) <- (9) [resolution 101,337]
347. generous(X1) | ~tall(X1) <- (9) [duplicate literal removal 346]
350. generous(X1) <- (9, 11) [subsumption resolution 347,189]
351. 1 | ~9 | ~11 [avatar split clause 350,188,180,147]
371. ~generous(X0) | calm(X0) <- (11) [resolution 103,189]
372. calm(X0) <- (1, 11) [subsumption resolution 371,148]
376. ~humble(X3) | ~generous(X3) <- (1, 11) [resolution 372,88]
378. ~generous(X3) <- (1, 9, 11) [subsumption resolution 376,181]
379. $false <- (1, 9, 11) [subsumption resolution 378,148]
380. ~1 | ~9 | ~11 [avatar contradiction clause 379]
381. $false [avatar sat refutation 186,190,325,351,380]
% SZS output end Proof for 7321555962386047524717890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or humble is not generous. If someone is either patient or quiet then john is calm or not kind. If someone is rich or not generous then lucy is both not tall and calm. If someone is either not happy or not funny then someone is both not curious and not brave. If someone is both not happy and not rich then someone is not strong or not funny. Everyone who is either not wise or calm is both not wise and not old. Everyone who is kind is calm. Everyone who is either tall or old is old and vice versa. If susan is either not kind or funny then fred is not curious or funny. If someone is not brave then someone is either calm or not brave and vice versa. Everyone who is either old or not old is generous and vice versa. Everyone who is wise is not creative or not quiet. If someone is not old then someone is either not tall or happy. Everyone who is either calm or not humble is both generous and not generous and vice versa. If someone is either not kind or not rich then fred is curious or not patient and vice versa. Everyone who is wise or not brave is either rich or tall and vice versa. Someone is both quiet and not rich. Paul is not rich. Someone is wise or curious. Alice is either not quiet or generous. Paul is both not strong and brave. Lucy is either humble or not happy. Mary is either funny or not tall. | Fred is old. | contradiction | (![X]:((generous(X)<~>humble(X))=>~generous(X)))&
((?[X]:((patient(X)<~>quiet(X))))=>((calm(john)|~kind(john))))&
((?[X]:((rich(X)|~generous(X))))=>((~tall(lucy)&calm(lucy))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((~curious(X)&~brave(X)))))&
((?[X]:((~happy(X)&~rich(X))))=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:((~wise(X)<~>calm(X))=>(~wise(X)&~old(X))))&
(![X]:(kind(X)=>calm(X)))&
(![X]:((tall(X)<~>old(X))<=>old(X)))&
(((~kind(susan)<~>funny(susan)))=>((~curious(fred)|funny(fred))))&
((?[X]:(~brave(X)))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((old(X)<~>~old(X))<=>generous(X)))&
(![X]:(wise(X)=>(~creative(X)|~quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((calm(X)<~>~humble(X))<=>(generous(X)&~generous(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>((curious(fred)|~patient(fred))))&
(![X]:((wise(X)|~brave(X))<=>(rich(X)<~>tall(X))))&
(?[X]:((quiet(X)&~rich(X))))&
(~rich(paul))&
(?[X]:((wise(X)|curious(X))))&
((~quiet(alice)<~>generous(alice)))&
((~strong(paul)&brave(paul)))&
((humble(lucy)<~>~happy(lucy)))&
((funny(mary)<~>~tall(mary))) | old(fred) | [
"p0",
"p2",
"p5",
"p7",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 74205991134294448834641
% SZS output start Proof for 74205991134294448834641
1. ! [X0] : ((generous(X0) <~> humble(X0)) => ~generous(X0)) [input p0]
3. ? [X0] : (~generous(X0) | rich(X0)) => (calm(lucy) & ~tall(lucy)) [input p2]
6. ! [X0] : ((~wise(X0) <~> calm(X0)) => (~old(X0) & ~wise(X0))) [input p5]
8. ! [X0] : ((tall(X0) <~> old(X0)) <=> old(X0)) [input p7]
10. ? [X0] : ~brave(X0) <=> ? [X0] : (calm(X0) <~> ~brave(X0)) [input p9]
11. ! [X0] : ((old(X0) <~> ~old(X0)) <=> generous(X0)) [input p10]
14. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> (~generous(X0) & generous(X0))) [input p13]
16. ! [X0] : ((~brave(X0) | wise(X0)) <=> (rich(X0) <~> tall(X0))) [input p15]
24. old(fred) [input hypothesis]
27. ? [X0] : ~brave(X0) <=> ? [X1] : (calm(X1) <~> ~brave(X1)) [rectify 10]
32. ! [X0] : (~generous(X0) | (generous(X0) <=> humble(X0))) [ennf transformation 1]
35. (calm(lucy) & ~tall(lucy)) | ! [X0] : (generous(X0) & ~rich(X0)) [ennf transformation 3]
37. ! [X0] : ((~old(X0) & ~wise(X0)) | (~wise(X0) <=> calm(X0))) [ennf transformation 6]
42. ! [X0] : (~generous(X0) | ((generous(X0) | ~humble(X0)) & (humble(X0) | ~generous(X0)))) [nnf transformation 32]
48. ! [X0] : ((~old(X0) & ~wise(X0)) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) [nnf transformation 37]
49. ! [X0] : ((((~old(X0) | ~tall(X0)) & (old(X0) | tall(X0))) | ~old(X0)) & (old(X0) | ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0))))) [nnf transformation 8]
51. (? [X0] : ~brave(X0) | ! [X1] : ((calm(X1) | brave(X1)) & (~brave(X1) | ~calm(X1)))) & (? [X1] : ((brave(X1) | ~calm(X1)) & (~brave(X1) | calm(X1))) | ! [X0] : brave(X0)) [nnf transformation 27]
52. (? [X0] : ~brave(X0) | ! [X1] : ((calm(X1) | brave(X1)) & (~brave(X1) | ~calm(X1)))) & (? [X2] : ((brave(X2) | ~calm(X2)) & (~brave(X2) | calm(X2))) | ! [X3] : brave(X3)) [rectify 51]
53. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
54. ? [X2] : ((brave(X2) | ~calm(X2)) & (~brave(X2) | calm(X2))) => ((brave(sK2) | ~calm(sK2)) & (~brave(sK2) | calm(sK2))) [choice axiom]
55. (~brave(sK1) | ! [X1] : ((calm(X1) | brave(X1)) & (~brave(X1) | ~calm(X1)))) & (((brave(sK2) | ~calm(sK2)) & (~brave(sK2) | calm(sK2))) | ! [X3] : brave(X3)) [skolemisation 52,54,53]
56. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ~generous(X0)) & (generous(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 11]
61. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 14]
62. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [flattening 61]
68. ! [X0] : (((~brave(X0) | wise(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (brave(X0) & ~wise(X0)))) [nnf transformation 16]
69. ! [X0] : ((~brave(X0) | wise(X0) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (brave(X0) & ~wise(X0)))) [flattening 68]
77. ~generous(X0) | humble(X0) | ~generous(X0) [cnf transformation 42]
83. calm(lucy) | ~rich(X0) [cnf transformation 35]
91. ~old(X0) | calm(X0) | wise(X0) [cnf transformation 48]
94. old(X0) | old(X0) | ~tall(X0) [cnf transformation 49]
97. ~old(X0) | ~tall(X0) | ~old(X0) [cnf transformation 49]
100. ~brave(sK2) | calm(sK2) | brave(X3) [cnf transformation 55]
102. ~brave(sK1) | ~brave(X1) | ~calm(X1) [cnf transformation 55]
104. generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 56]
105. generous(X0) | old(X0) | old(X0) [cnf transformation 56]
112. ~generous(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 62]
122. tall(X0) | rich(X0) | ~wise(X0) [cnf transformation 69]
123. tall(X0) | rich(X0) | brave(X0) [cnf transformation 69]
139. old(fred) [cnf transformation 24]
140. generous(X0) | ~old(X0) [duplicate literal removal 104]
141. old(X0) | generous(X0) [duplicate literal removal 105]
142. old(X0) | ~tall(X0) [duplicate literal removal 94]
143. ~old(X0) | ~tall(X0) [duplicate literal removal 97]
145. ~generous(X0) | humble(X0) [duplicate literal removal 77]
163. 5 <=> ! [X0] : generous(X0) [avatar definition]
164. generous(X0) <- (5) [avatar component clause 163]
166. 6 <=> calm(lucy) [avatar definition]
168. calm(lucy) <- (6) [avatar component clause 166]
171. 7 <=> ! [X0] : ~rich(X0) [avatar definition]
172. ~rich(X0) <- (7) [avatar component clause 171]
173. 7 | 6 [avatar split clause 83,166,171]
198. ~tall(X0) [subsumption resolution 142,143]
221. 18 <=> brave(sK1) [avatar definition]
223. ~brave(sK1) <- (~18) [avatar component clause 221]
226. 19 <=> ! [X1] : (~brave(X1) | ~calm(X1)) [avatar definition]
227. ~brave(X1) | ~calm(X1) <- (19) [avatar component clause 226]
228. 19 | ~18 [avatar split clause 102,221,226]
230. 20 <=> ! [X3] : brave(X3) [avatar definition]
231. brave(X3) <- (20) [avatar component clause 230]
233. 21 <=> calm(sK2) [avatar definition]
234. calm(sK2) <- (21) [avatar component clause 233]
237. 22 <=> brave(sK2) [avatar definition]
238. ~brave(sK2) <- (~22) [avatar component clause 237]
241. 20 | 21 | ~22 [avatar split clause 100,237,233,230]
242. generous(X0) [subsumption resolution 140,141]
243. 5 [avatar split clause 242,163]
253. ~calm(X0) | ~generous(X0) [subsumption resolution 112,145]
281. brave(X0) | rich(X0) [subsumption resolution 123,198]
282. ~wise(X0) | rich(X0) [subsumption resolution 122,198]
320. ~generous(lucy) <- (6) [resolution 253,168]
322. $false <- (5, 6) [subsumption resolution 320,164]
323. ~5 | ~6 [avatar contradiction clause 322]
337. rich(sK1) <- (~18) [resolution 281,223]
338. rich(sK2) <- (~22) [resolution 281,238]
341. $false <- (7, ~18) [subsumption resolution 337,172]
342. ~7 | 18 [avatar contradiction clause 341]
343. $false <- (7, ~22) [subsumption resolution 338,172]
344. ~7 | 22 [avatar contradiction clause 343]
345. ~calm(X1) <- (19, 20) [subsumption resolution 227,231]
352. calm(fred) | wise(fred) [resolution 91,139]
354. wise(fred) <- (19, 20) [subsumption resolution 352,345]
357. rich(fred) <- (19, 20) [resolution 354,282]
359. $false <- (7, 19, 20) [subsumption resolution 357,172]
360. ~7 | ~19 | ~20 [avatar contradiction clause 359]
371. ~generous(sK2) <- (21) [resolution 234,253]
374. $false <- (5, 21) [subsumption resolution 371,164]
375. ~5 | ~21 [avatar contradiction clause 374]
376. $false [avatar sat refutation 173,228,241,243,323,342,344,360,375]
% SZS output end Proof for 74205991134294448834641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or humble then someone is not tall and vice versa.
If someone is generous then alice is both not generous and not wise.
If john is patient or wise then someone is not quiet or not generous and vice versa.
If fred is either not patient or not creative then someone is old.
Everyone who is both not patient and not creative is both not wise and brave and vice versa.
Everyone who is not rich or not wise is either wise or generous and vice versa.
If paul is both rich and not strong then alice is both not strong and quiet.
Everyone who is not old or not brave is happy or rich and vice versa.
Everyone who is old or brave is not happy.
Everyone who is both not patient and not funny is either strong or not quiet.
Everyone who is not tall or wise is not creative.
If mary is either quiet or not humble then someone is both not humble and strong and vice versa.
If susan is not tall then someone is strong or not patient and vice versa.
Everyone who is not rich or not brave is funny and vice versa.
If someone is not generous then mary is both curious and not happy and vice versa.
Mary is either not funny or not tall.
Someone is both not curious and not happy.
Someone is brave.
Someone is either wise or not kind.
John is both not creative and not generous. | Alice is generous. | contradiction | ((?[X]:((quiet(X)|humble(X))))<=>(?[X]:(~tall(X))))&
((?[X]:(generous(X)))=>((~generous(alice)&~wise(alice))))&
(((patient(john)|wise(john)))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(((~patient(fred)<~>~creative(fred)))=>(?[X]:(old(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~wise(X)&brave(X))))&
(![X]:((~rich(X)|~wise(X))<=>(wise(X)<~>generous(X))))&
(((rich(paul)&~strong(paul)))=>((~strong(alice)&quiet(alice))))&
(![X]:((~old(X)|~brave(X))<=>(happy(X)|rich(X))))&
(![X]:((old(X)|brave(X))=>~happy(X)))&
(![X]:((~patient(X)&~funny(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
((~funny(mary)<~>~tall(mary)))&
(?[X]:((~curious(X)&~happy(X))))&
(?[X]:(brave(X)))&
(?[X]:((wise(X)<~>~kind(X))))&
((~creative(john)&~generous(john))) | generous(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 479729729000597202418212
% SZS output start Proof for 479729729000597202418212
2. ? [X0] : generous(X0) => (~wise(alice) & ~generous(alice)) [input p1]
21. generous(alice) [input hypothesis]
23. (~wise(alice) & ~generous(alice)) | ! [X0] : ~generous(X0) [ennf transformation 2]
77. ~generous(alice) | ~generous(X0) [cnf transformation 23]
131. generous(alice) [cnf transformation 21]
159. 7 <=> ! [X0] : ~generous(X0) [avatar definition]
160. ~generous(X0) <- (7) [avatar component clause 159]
167. 9 <=> generous(alice) [avatar definition]
168. generous(alice) <- (9) [avatar component clause 167]
170. 7 | ~9 [avatar split clause 77,167,159]
310. 9 [avatar split clause 131,167]
313. $false <- (7, 9) [subsumption resolution 168,160]
314. ~7 | ~9 [avatar contradiction clause 313]
315. $false [avatar sat refutation 170,310,314]
% SZS output end Proof for 479729729000597202418212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is both not humble and not patient.
If paul is both kind and humble then someone is not funny or quiet and vice versa.
Everyone who is humble is either strong or not rich and vice versa.
Everyone who is not kind is either calm or not old and vice versa.
If someone is either not brave or not creative then paul is old and vice versa.
If someone is both patient and not strong then someone is not wise or not creative.
If someone is either not funny or not curious then someone is not humble.
Everyone who is happy is rich and vice versa.
Everyone who is not quiet or not brave is either tall or not funny.
If someone is not calm or not happy then john is both old and kind and vice versa.
Everyone who is either happy or calm is either not creative or not wise and vice versa.
If lucy is either rich or not kind then alice is both not strong and not quiet.
If alice is both patient and strong then fred is both curious and not wise and vice versa.
Everyone who is not kind or humble is either curious or tall.
If someone is not tall or tall then someone is not creative or not generous and vice versa.
If paul is either brave or creative then someone is both not funny and kind.
Someone is curious.
Someone is both humble and funny.
Mary is not curious or funny.
Alice is both not strong and wise.
Lucy is either quiet or not generous.
Paul is not calm or rich.
Fred is either calm or creative.
Someone is either generous or old. | Alice is wise. | entailment | (![X]:(wise(X)=>(~humble(X)&~patient(X))))&
(((kind(paul)&humble(paul)))<=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:(humble(X)<=>(strong(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(calm(X)<~>~old(X))))&
((?[X]:((~brave(X)<~>~creative(X))))<=>(old(paul)))&
((?[X]:((patient(X)&~strong(X))))=>(?[X]:((~wise(X)|~creative(X)))))&
((?[X]:((~funny(X)<~>~curious(X))))=>(?[X]:(~humble(X))))&
(![X]:(happy(X)<=>rich(X)))&
(![X]:((~quiet(X)|~brave(X))=>(tall(X)<~>~funny(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((old(john)&kind(john))))&
(![X]:((happy(X)<~>calm(X))<=>(~creative(X)<~>~wise(X))))&
(((rich(lucy)<~>~kind(lucy)))=>((~strong(alice)&~quiet(alice))))&
(((patient(alice)&strong(alice)))<=>((curious(fred)&~wise(fred))))&
(![X]:((~kind(X)|humble(X))=>(curious(X)<~>tall(X))))&
((?[X]:((~tall(X)|tall(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
(((brave(paul)<~>creative(paul)))=>(?[X]:((~funny(X)&kind(X)))))&
(?[X]:(curious(X)))&
(?[X]:((humble(X)&funny(X))))&
((~curious(mary)|funny(mary)))&
((~strong(alice)&wise(alice)))&
((quiet(lucy)<~>~generous(lucy)))&
((~calm(paul)|rich(paul)))&
((calm(fred)<~>creative(fred)))&
(?[X]:((generous(X)<~>old(X)))) | wise(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5806259915096017189616598
% SZS output start Proof for 5806259915096017189616598
20. wise(alice) & ~strong(alice) [input p19]
25. ~wise(alice) [input hypothesis]
149. wise(alice) [cnf transformation 20]
157. ~wise(alice) [cnf transformation 25]
379. $false [subsumption resolution 157,149]
% SZS output end Proof for 5806259915096017189616598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not creative is strong and vice versa.
If someone is either not creative or not wise then mary is both not generous and strong and vice versa.
If lucy is either not calm or not tall then alice is not brave or not wise and vice versa.
Everyone who is kind or strong is either not wise or not humble and vice versa.
Everyone who is either not humble or not kind is not funny.
Everyone who is not wise is not calm or not patient and vice versa.
If someone is both rich and kind then someone is not strong.
Everyone who is both funny and quiet is funny or not curious and vice versa.
Everyone who is both not tall and creative is not patient or funny.
Everyone who is both kind and not creative is both not generous and not patient.
Everyone who is not strong or old is not brave and vice versa.
Everyone who is both not happy and curious is rich and vice versa.
Everyone who is both patient and quiet is kind or not strong.
Everyone who is both calm and rich is funny and vice versa.
If fred is curious or patient then lucy is both calm and not strong.
Everyone who is not humble or generous is not old or not curious.
Someone is funny or tall.
Mary is both not humble and calm.
Alice is either creative or not wise.
Fred is quiet or not calm.
Paul is generous or rich.
Paul is not rich or not curious.
Fred is both not funny and not quiet. | Lucy is not funny. | neutral | (![X]:((brave(X)&~creative(X))<=>strong(X)))&
((?[X]:((~creative(X)<~>~wise(X))))<=>((~generous(mary)&strong(mary))))&
(((~calm(lucy)<~>~tall(lucy)))<=>((~brave(alice)|~wise(alice))))&
(![X]:((kind(X)|strong(X))<=>(~wise(X)<~>~humble(X))))&
(![X]:((~humble(X)<~>~kind(X))=>~funny(X)))&
(![X]:(~wise(X)<=>(~calm(X)|~patient(X))))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:(~strong(X))))&
(![X]:((funny(X)&quiet(X))<=>(funny(X)|~curious(X))))&
(![X]:((~tall(X)&creative(X))=>(~patient(X)|funny(X))))&
(![X]:((kind(X)&~creative(X))=>(~generous(X)&~patient(X))))&
(![X]:((~strong(X)|old(X))<=>~brave(X)))&
(![X]:((~happy(X)&curious(X))<=>rich(X)))&
(![X]:((patient(X)&quiet(X))=>(kind(X)|~strong(X))))&
(![X]:((calm(X)&rich(X))<=>funny(X)))&
(((curious(fred)|patient(fred)))=>((calm(lucy)&~strong(lucy))))&
(![X]:((~humble(X)|generous(X))=>(~old(X)|~curious(X))))&
(?[X]:((funny(X)|tall(X))))&
((~humble(mary)&calm(mary)))&
((creative(alice)<~>~wise(alice)))&
((quiet(fred)|~calm(fred)))&
((generous(paul)|rich(paul)))&
((~rich(paul)|~curious(paul)))&
((~funny(fred)&~quiet(fred))) | ~funny(lucy) | [] | null | 0 |
Everyone who is either not rich or generous is not kind or not quiet.
Everyone who is funny or not generous is brave or curious and vice versa.
If alice is both not curious and not brave then someone is either calm or not strong and vice versa.
If someone is both funny and wise then someone is either patient or not old.
Everyone who is either old or not strong is kind and vice versa.
Everyone who is not old is both kind and not creative and vice versa.
If someone is both old and patient then mary is either kind or rich and vice versa.
Everyone who is either strong or quiet is not generous and vice versa.
Everyone who is brave is quiet or not happy.
Everyone who is both not kind and not funny is not creative or not humble and vice versa.
Everyone who is not creative or not brave is strong and vice versa.
Everyone who is either rich or creative is either not curious or not tall and vice versa.
If someone is old or quiet then someone is either not calm or not kind and vice versa.
If mary is both not wise and not generous then someone is both brave and humble.
If paul is either brave or not wise then paul is not funny or curious and vice versa.
If fred is old or calm then paul is curious and vice versa.
Mary is either not happy or funny.
Fred is either kind or not quiet.
Fred is not kind.
Alice is either not patient or not rich.
Someone is creative or not strong.
Someone is not funny.
Someone is both tall and happy.
Someone is either not brave or patient. | Fred is quiet. | contradiction | (![X]:((~rich(X)<~>generous(X))=>(~kind(X)|~quiet(X))))&
(![X]:((funny(X)|~generous(X))<=>(brave(X)|curious(X))))&
(((~curious(alice)&~brave(alice)))<=>(?[X]:((calm(X)<~>~strong(X)))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((old(X)<~>~strong(X))<=>kind(X)))&
(![X]:(~old(X)<=>(kind(X)&~creative(X))))&
((?[X]:((old(X)&patient(X))))<=>((kind(mary)<~>rich(mary))))&
(![X]:((strong(X)<~>quiet(X))<=>~generous(X)))&
(![X]:(brave(X)=>(quiet(X)|~happy(X))))&
(![X]:((~kind(X)&~funny(X))<=>(~creative(X)|~humble(X))))&
(![X]:((~creative(X)|~brave(X))<=>strong(X)))&
(![X]:((rich(X)<~>creative(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(((~wise(mary)&~generous(mary)))=>(?[X]:((brave(X)&humble(X)))))&
(((brave(paul)<~>~wise(paul)))<=>((~funny(paul)|curious(paul))))&
(((old(fred)|calm(fred)))<=>(curious(paul)))&
((~happy(mary)<~>funny(mary)))&
((kind(fred)<~>~quiet(fred)))&
(~kind(fred))&
((~patient(alice)<~>~rich(alice)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((~brave(X)<~>patient(X)))) | quiet(fred) | [
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1377152503245333658855388
% SZS output start Proof for 1377152503245333658855388
18. kind(fred) <~> ~quiet(fred) [input p17]
19. ~kind(fred) [input p18]
25. quiet(fred) [input hypothesis]
72. (quiet(fred) | ~kind(fred)) & (~quiet(fred) | kind(fred)) [nnf transformation 18]
150. ~quiet(fred) | kind(fred) [cnf transformation 72]
152. ~kind(fred) [cnf transformation 19]
161. quiet(fred) [cnf transformation 25]
324. 35 <=> kind(fred) [avatar definition]
328. 36 <=> quiet(fred) [avatar definition]
332. 35 | ~36 [avatar split clause 150,328,324]
333. ~35 [avatar split clause 152,324]
355. 36 [avatar split clause 161,328]
356. $false [avatar sat refutation 332,333,355]
% SZS output end Proof for 1377152503245333658855388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or not generous then john is either calm or not calm and vice versa.
If mary is either not strong or not old then alice is either tall or patient and vice versa.
Everyone who is either not curious or not kind is both not brave and not funny and vice versa.
Everyone who is not wise or not curious is not old and vice versa.
Everyone who is funny or not patient is funny or curious and vice versa.
If someone is either not creative or tall then susan is not brave and vice versa.
Everyone who is both not humble and strong is calm or not generous and vice versa.
Everyone who is old is calm or not old and vice versa.
Everyone who is both not creative and not wise is not generous or tall.
If someone is both kind and wise then lucy is either not creative or not old.
Everyone who is either curious or brave is both not quiet and not kind and vice versa.
If fred is both calm and not happy then someone is not rich and vice versa.
If alice is tall then someone is brave or humble.
Everyone who is either not funny or not calm is either tall or not humble.
Everyone who is either not quiet or not generous is not rich.
Everyone who is both not calm and not funny is both not wise and generous and vice versa.
Someone is rich or not creative.
Fred is either old or not patient.
Fred is either not calm or calm.
Someone is not creative.
Someone is either not funny or not creative.
Someone is both curious and not patient.
Susan is not humble or not old. | Alice is not quiet. | neutral | ((?[X]:((wise(X)<~>~generous(X))))<=>((calm(john)<~>~calm(john))))&
(((~strong(mary)<~>~old(mary)))<=>((tall(alice)<~>patient(alice))))&
(![X]:((~curious(X)<~>~kind(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((funny(X)|~patient(X))<=>(funny(X)|curious(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(~brave(susan)))&
(![X]:((~humble(X)&strong(X))<=>(calm(X)|~generous(X))))&
(![X]:(old(X)<=>(calm(X)|~old(X))))&
(![X]:((~creative(X)&~wise(X))=>(~generous(X)|tall(X))))&
((?[X]:((kind(X)&wise(X))))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((curious(X)<~>brave(X))<=>(~quiet(X)&~kind(X))))&
(((calm(fred)&~happy(fred)))<=>(?[X]:(~rich(X))))&
((tall(alice))=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~funny(X)<~>~calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>~rich(X)))&
(![X]:((~calm(X)&~funny(X))<=>(~wise(X)&generous(X))))&
(?[X]:((rich(X)|~creative(X))))&
((old(fred)<~>~patient(fred)))&
((~calm(fred)<~>calm(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((curious(X)&~patient(X))))&
((~humble(susan)|~old(susan))) | ~quiet(alice) | [] | null | 0 |
Everyone who is wise or funny is kind.
If someone is humble or not generous then mary is wise or kind and vice versa.
If someone is not strong or not calm then someone is not strong and vice versa.
If fred is not calm then john is either kind or strong.
If someone is happy or not happy then alice is either not happy or tall and vice versa.
If mary is old or humble then someone is calm or tall.
If susan is patient then someone is both not humble and generous and vice versa.
Everyone who is happy is either not curious or not brave and vice versa.
Everyone who is both not patient and calm is funny or curious and vice versa.
Everyone who is both not brave and not humble is not brave or brave and vice versa.
Everyone who is either calm or humble is both not generous and wise and vice versa.
Everyone who is both creative and not strong is wise.
If mary is kind or creative then lucy is either patient or generous.
Everyone who is either old or quiet is tall or not strong and vice versa.
If susan is both wise and not kind then mary is both not creative and not brave and vice versa.
Everyone who is both tall and not wise is not brave or not kind.
Lucy is rich or not generous.
Someone is either not curious or wise.
Mary is both tall and rich.
Someone is rich or not tall.
Susan is either not patient or not wise.
Mary is both not calm and not brave.
Someone is not quiet or strong.
Someone is both not funny and happy. | John is brave. | contradiction | (![X]:((wise(X)|funny(X))=>kind(X)))&
((?[X]:((humble(X)|~generous(X))))<=>((wise(mary)|kind(mary))))&
((?[X]:((~strong(X)|~calm(X))))<=>(?[X]:(~strong(X))))&
((~calm(fred))=>((kind(john)<~>strong(john))))&
((?[X]:((happy(X)|~happy(X))))<=>((~happy(alice)<~>tall(alice))))&
(((old(mary)|humble(mary)))=>(?[X]:((calm(X)|tall(X)))))&
((patient(susan))<=>(?[X]:((~humble(X)&generous(X)))))&
(![X]:(happy(X)<=>(~curious(X)<~>~brave(X))))&
(![X]:((~patient(X)&calm(X))<=>(funny(X)|curious(X))))&
(![X]:((~brave(X)&~humble(X))<=>(~brave(X)|brave(X))))&
(![X]:((calm(X)<~>humble(X))<=>(~generous(X)&wise(X))))&
(![X]:((creative(X)&~strong(X))=>wise(X)))&
(((kind(mary)|creative(mary)))=>((patient(lucy)<~>generous(lucy))))&
(![X]:((old(X)<~>quiet(X))<=>(tall(X)|~strong(X))))&
(((wise(susan)&~kind(susan)))<=>((~creative(mary)&~brave(mary))))&
(![X]:((tall(X)&~wise(X))=>(~brave(X)|~kind(X))))&
((rich(lucy)|~generous(lucy)))&
(?[X]:((~curious(X)<~>wise(X))))&
((tall(mary)&rich(mary)))&
(?[X]:((rich(X)|~tall(X))))&
((~patient(susan)<~>~wise(susan)))&
((~calm(mary)&~brave(mary)))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((~funny(X)&happy(X)))) | brave(john) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1354897371137325654966663
% SZS output start Proof for 1354897371137325654966663
10. ! [X0] : ((~humble(X0) & ~brave(X0)) <=> (brave(X0) | ~brave(X0))) [input p9]
25. brave(john) [input hypothesis]
62. ! [X0] : (((~humble(X0) & ~brave(X0)) | (~brave(X0) & brave(X0))) & ((brave(X0) | ~brave(X0)) | (humble(X0) | brave(X0)))) [nnf transformation 10]
63. ! [X0] : (((~humble(X0) & ~brave(X0)) | (~brave(X0) & brave(X0))) & (brave(X0) | ~brave(X0) | humble(X0) | brave(X0))) [flattening 62]
112. ~brave(X0) | ~brave(X0) [cnf transformation 63]
147. brave(john) [cnf transformation 25]
149. ~brave(X0) [duplicate literal removal 112]
318. $false [subsumption resolution 147,149]
% SZS output end Proof for 1354897371137325654966663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and 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.
Everyone who is not happy or not old is not humble or rich.
Everyone who is kind or humble is kind or not creative.
Everyone who is either not humble or not wise is not tall and vice versa.
If someone is wise then fred is both creative and not curious.
Everyone who is either generous or not curious is both not old and old.
If someone is not calm then paul is both not funny and not curious and vice versa.
Everyone who is quiet is both not patient and not calm.
Someone is not brave.
Someone is both strong and not curious.
Someone is creative or generous.
Fred is not brave.
Someone is either not kind or creative.
Someone is either quiet or patient.
Someone is not curious or wise.
Someone is either not creative or funny. | John is not strong. | neutral | (![X]:((generous(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))))&
(![X]:((~happy(X)|~old(X))=>(~humble(X)|rich(X))))&
(![X]:((kind(X)|humble(X))=>(kind(X)|~creative(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>~tall(X)))&
((?[X]:(wise(X)))=>((creative(fred)&~curious(fred))))&
(![X]:((generous(X)<~>~curious(X))=>(~old(X)&old(X))))&
((?[X]:(~calm(X)))<=>((~funny(paul)&~curious(paul))))&
(![X]:(quiet(X)=>(~patient(X)&~calm(X))))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((creative(X)|generous(X))))&
(~brave(fred))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((quiet(X)<~>patient(X))))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:((~creative(X)<~>funny(X)))) | ~strong(john) | [] | null | 0 |
Everyone who is strong is either not calm or not wise. If someone is not calm then susan is both not funny and not humble. Everyone who is both not kind and calm is both rich and not strong. If mary is not happy or not generous then someone is either not tall or patient. Everyone who is wise or calm is generous or not strong and vice versa. If paul is both not patient and funny then someone is either not generous or generous and vice versa. Everyone who is brave is wise and vice versa. Everyone who is either funny or generous is both not calm and kind and vice versa. If someone is calm then lucy is both not wise and not curious. Everyone who is either funny or not wise is both not humble and calm and vice versa. Everyone who is either wise or not humble is rich and vice versa. If someone is tall then someone is calm or happy. Everyone who is rich or not rich is either patient or not wise. Everyone who is either curious or not strong is either not creative or calm and vice versa. If mary is either not calm or patient then someone is not brave or quiet. Fred is generous or not happy. John is not humble. Someone is both not rich and happy. Someone is old. Someone is either not quiet or not curious. Someone is either generous or not rich. Someone is not generous or funny. Alice is both not funny and creative. | Paul is humble. | entailment | (![X]:(strong(X)=>(~calm(X)<~>~wise(X))))&
((?[X]:(~calm(X)))=>((~funny(susan)&~humble(susan))))&
(![X]:((~kind(X)&calm(X))=>(rich(X)&~strong(X))))&
(((~happy(mary)|~generous(mary)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:((wise(X)|calm(X))<=>(generous(X)|~strong(X))))&
(((~patient(paul)&funny(paul)))<=>(?[X]:((~generous(X)<~>generous(X)))))&
(![X]:(brave(X)<=>wise(X)))&
(![X]:((funny(X)<~>generous(X))<=>(~calm(X)&kind(X))))&
((?[X]:(calm(X)))=>((~wise(lucy)&~curious(lucy))))&
(![X]:((funny(X)<~>~wise(X))<=>(~humble(X)&calm(X))))&
(![X]:((wise(X)<~>~humble(X))<=>rich(X)))&
((?[X]:(tall(X)))=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((rich(X)|~rich(X))=>(patient(X)<~>~wise(X))))&
(![X]:((curious(X)<~>~strong(X))<=>(~creative(X)<~>calm(X))))&
(((~calm(mary)<~>patient(mary)))=>(?[X]:((~brave(X)|quiet(X)))))&
((generous(fred)|~happy(fred)))&
(~humble(john))&
(?[X]:((~rich(X)&happy(X))))&
(?[X]:(old(X)))&
(?[X]:((~quiet(X)<~>~curious(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:((~generous(X)|funny(X))))&
((~funny(alice)&creative(alice))) | humble(paul) | [
"p0",
"p4",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2466606780646285675806654
% SZS output start Proof for 2466606780646285675806654
1. ! [X0] : (strong(X0) => (~calm(X0) <~> ~wise(X0))) [input p0]
5. ! [X0] : ((calm(X0) | wise(X0)) <=> (~strong(X0) | generous(X0))) [input p4]
6. (funny(paul) & ~patient(paul)) <=> ? [X0] : (~generous(X0) <~> generous(X0)) [input p5]
10. ! [X0] : ((funny(X0) <~> ~wise(X0)) <=> (calm(X0) & ~humble(X0))) [input p9]
13. ! [X0] : ((~rich(X0) | rich(X0)) => (patient(X0) <~> ~wise(X0))) [input p12]
24. ~humble(paul) [input hypothesis]
28. ! [X0] : ((~calm(X0) <~> ~wise(X0)) | ~strong(X0)) [ennf transformation 1]
36. ! [X0] : ((patient(X0) <~> ~wise(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 13]
38. ! [X0] : (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | ~strong(X0)) [nnf transformation 28]
42. ! [X0] : (((calm(X0) | wise(X0)) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | (~calm(X0) & ~wise(X0)))) [nnf transformation 5]
43. ! [X0] : ((calm(X0) | wise(X0) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | (~calm(X0) & ~wise(X0)))) [flattening 42]
44. ((funny(paul) & ~patient(paul)) | ! [X0] : ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (? [X0] : ((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (~funny(paul) | patient(paul))) [nnf transformation 6]
45. ((funny(paul) & ~patient(paul)) | ! [X0] : ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (? [X0] : ((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | ~funny(paul) | patient(paul)) [flattening 44]
46. ((funny(paul) & ~patient(paul)) | ! [X0] : ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (? [X1] : ((~generous(X1) | generous(X1)) & (generous(X1) | ~generous(X1))) | ~funny(paul) | patient(paul)) [rectify 45]
47. ? [X1] : ((~generous(X1) | generous(X1)) & (generous(X1) | ~generous(X1))) => ((~generous(sK1) | generous(sK1)) & (generous(sK1) | ~generous(sK1))) [choice axiom]
48. ((funny(paul) & ~patient(paul)) | ! [X0] : ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(sK1) | generous(sK1)) & (generous(sK1) | ~generous(sK1))) | ~funny(paul) | patient(paul)) [skolemisation 46,47]
51. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~calm(X0) | humble(X0))) & ((calm(X0) & ~humble(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [nnf transformation 10]
52. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ~calm(X0) | humble(X0)) & ((calm(X0) & ~humble(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [flattening 51]
57. ! [X0] : (((wise(X0) | ~patient(X0)) & (~wise(X0) | patient(X0))) | (rich(X0) & ~rich(X0))) [nnf transformation 36]
73. ~strong(X0) | calm(X0) | wise(X0) [cnf transformation 38]
85. calm(X0) | wise(X0) | strong(X0) [cnf transformation 43]
88. ~patient(paul) | generous(X0) | generous(X0) [cnf transformation 48]
89. ~patient(paul) | ~generous(X0) | ~generous(X0) [cnf transformation 48]
90. funny(paul) | generous(X0) | generous(X0) [cnf transformation 48]
91. funny(paul) | ~generous(X0) | ~generous(X0) [cnf transformation 48]
106. wise(X0) | ~funny(X0) | ~calm(X0) | humble(X0) [cnf transformation 52]
112. ~wise(X0) | patient(X0) | ~rich(X0) [cnf transformation 57]
113. ~wise(X0) | patient(X0) | rich(X0) [cnf transformation 57]
137. ~humble(paul) [cnf transformation 24]
138. ~patient(paul) | generous(X0) [duplicate literal removal 88]
139. ~patient(paul) | ~generous(X0) [duplicate literal removal 89]
140. funny(paul) | generous(X0) [duplicate literal removal 90]
141. funny(paul) | ~generous(X0) [duplicate literal removal 91]
175. wise(X0) | calm(X0) [subsumption resolution 85,73]
177. 8 <=> ! [X0] : ~generous(X0) [avatar definition]
178. ~generous(X0) <- (8) [avatar component clause 177]
180. 9 <=> funny(paul) [avatar definition]
182. funny(paul) <- (9) [avatar component clause 180]
183. 8 | 9 [avatar split clause 141,180,177]
185. 10 <=> ! [X0] : generous(X0) [avatar definition]
186. generous(X0) <- (10) [avatar component clause 185]
187. 10 | 9 [avatar split clause 140,180,185]
189. 11 <=> patient(paul) [avatar definition]
191. ~patient(paul) <- (~11) [avatar component clause 189]
192. 8 | ~11 [avatar split clause 139,189,177]
193. 10 | ~11 [avatar split clause 138,189,185]
207. ~funny(X0) | wise(X0) | humble(X0) [subsumption resolution 106,175]
222. ~wise(X0) | patient(X0) [subsumption resolution 112,113]
318. $false <- (8, 10) [subsumption resolution 178,186]
319. ~8 | ~10 [avatar contradiction clause 318]
489. wise(paul) | humble(paul) <- (9) [resolution 207,182]
490. wise(paul) <- (9) [subsumption resolution 489,137]
524. patient(paul) <- (9) [resolution 490,222]
529. $false <- (9, ~11) [subsumption resolution 524,191]
530. ~9 | 11 [avatar contradiction clause 529]
531. $false [avatar sat refutation 183,187,192,193,319,530]
% SZS output end Proof for 2466606780646285675806654
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not strong then someone is both not strong and calm and vice versa. If someone is either not humble or not brave then someone is either creative or not kind. If someone is happy then fred is either happy or not brave and vice versa. Everyone who is either kind or not strong is either rich or wise. If alice is either quiet or creative then someone is not generous or not curious and vice versa. Everyone who is either funny or not tall is both not curious and tall and vice versa. Everyone who is both not old and not humble is happy and vice versa. If someone is old then someone is either not creative or not tall. If someone is either happy or not strong then someone is quiet. If someone is tall or not curious then paul is either not tall or generous and vice versa. Everyone who is either not kind or not funny is either brave or curious and vice versa. Everyone who is old is both brave and strong and vice versa. Everyone who is either funny or curious is either not creative or not patient. Everyone who is not curious is not humble or patient and vice versa. Everyone who is both patient and brave is either not old or strong and vice versa. If susan is either strong or not rich then susan is patient and vice versa. Susan is kind. Susan is not generous or brave. Paul is patient or strong. Susan is creative or not tall. Susan is not funny. Someone is not old or not patient. John is both not curious and not old. Someone is brave or not tall. | Susan is not patient. | entailment | ((?[X]:((quiet(X)|~strong(X))))<=>(?[X]:((~strong(X)&calm(X)))))&
((?[X]:((~humble(X)<~>~brave(X))))=>(?[X]:((creative(X)<~>~kind(X)))))&
((?[X]:(happy(X)))<=>((happy(fred)<~>~brave(fred))))&
(![X]:((kind(X)<~>~strong(X))=>(rich(X)<~>wise(X))))&
(((quiet(alice)<~>creative(alice)))<=>(?[X]:((~generous(X)|~curious(X)))))&
(![X]:((funny(X)<~>~tall(X))<=>(~curious(X)&tall(X))))&
(![X]:((~old(X)&~humble(X))<=>happy(X)))&
((?[X]:(old(X)))=>(?[X]:((~creative(X)<~>~tall(X)))))&
((?[X]:((happy(X)<~>~strong(X))))=>(?[X]:(quiet(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((~tall(paul)<~>generous(paul))))&
(![X]:((~kind(X)<~>~funny(X))<=>(brave(X)<~>curious(X))))&
(![X]:(old(X)<=>(brave(X)&strong(X))))&
(![X]:((funny(X)<~>curious(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(~curious(X)<=>(~humble(X)|patient(X))))&
(![X]:((patient(X)&brave(X))<=>(~old(X)<~>strong(X))))&
(((strong(susan)<~>~rich(susan)))<=>(patient(susan)))&
(kind(susan))&
((~generous(susan)|brave(susan)))&
((patient(paul)|strong(paul)))&
((creative(susan)|~tall(susan)))&
(~funny(susan))&
(?[X]:((~old(X)|~patient(X))))&
((~curious(john)&~old(john)))&
(?[X]:((brave(X)|~tall(X)))) | ~patient(susan) | [
"p5",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9158132903417860468658967
% SZS output start Proof for 9158132903417860468658967
6. ! [X0] : ((funny(X0) <~> ~tall(X0)) <=> (tall(X0) & ~curious(X0))) [input p5]
14. ! [X0] : (~curious(X0) <=> (patient(X0) | ~humble(X0))) [input p13]
21. ~funny(susan) [input p20]
25. patient(susan) [input hypothesis]
53. ! [X0] : ((((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | (~tall(X0) | curious(X0))) & ((tall(X0) & ~curious(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0))))) [nnf transformation 6]
54. ! [X0] : ((((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | ~tall(X0) | curious(X0)) & ((tall(X0) & ~curious(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0))))) [flattening 53]
73. ! [X0] : ((~curious(X0) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | curious(X0))) [nnf transformation 14]
74. ! [X0] : ((~curious(X0) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | curious(X0))) [flattening 73]
108. tall(X0) | funny(X0) | tall(X0) [cnf transformation 54]
109. ~tall(X0) | funny(X0) | ~tall(X0) | curious(X0) [cnf transformation 54]
141. ~patient(X0) | ~curious(X0) [cnf transformation 74]
156. ~funny(susan) [cnf transformation 21]
161. patient(susan) [cnf transformation 25]
162. tall(X0) | funny(X0) [duplicate literal removal 108]
163. ~tall(X0) | funny(X0) | curious(X0) [duplicate literal removal 109]
313. 33 <=> patient(susan) [avatar definition]
314. patient(susan) <- (33) [avatar component clause 313]
357. 33 [avatar split clause 161,313]
367. ~curious(susan) <- (33) [resolution 141,314]
401. funny(X0) | curious(X0) | funny(X0) [resolution 163,162]
403. funny(X0) | curious(X0) [duplicate literal removal 401]
418. curious(susan) [resolution 403,156]
419. $false <- (33) [subsumption resolution 418,367]
420. ~33 [avatar contradiction clause 419]
421. $false [avatar sat refutation 357,420]
% SZS output end Proof for 9158132903417860468658967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or not strong then someone is both creative and not calm.
If alice is not generous or curious then lucy is not brave.
Everyone who is old or not quiet is either not patient or not tall and vice versa.
If alice is both not curious and creative then mary is either not kind or strong and vice versa.
If someone is curious then mary is both happy and strong.
Everyone who is not happy is both not brave and brave.
Everyone who is both not patient and old is both not happy and not rich and vice versa.
If someone is either happy or brave then fred is either not generous or generous and vice versa.
Everyone who is both not tall and curious is either not generous or not humble and vice versa.
Everyone who is curious or funny is both happy and not funny.
Everyone who is both not happy and tall is kind and vice versa.
If fred is both not curious and strong then someone is either humble or not funny and vice versa.
Everyone who is not old or not curious is either not kind or brave and vice versa.
Everyone who is not kind or rich is quiet or wise.
Everyone who is either old or not old is happy and vice versa.
If alice is both brave and curious then someone is not happy and vice versa.
Someone is not humble or not patient.
Mary is both not kind and wise.
Someone is not tall or creative.
Someone is not strong or not generous.
Alice is both not brave and curious.
Someone is either humble or not kind. | Fred is not strong. | contradiction | ((?[X]:((humble(X)<~>~strong(X))))=>(?[X]:((creative(X)&~calm(X)))))&
(((~generous(alice)|curious(alice)))=>(~brave(lucy)))&
(![X]:((old(X)|~quiet(X))<=>(~patient(X)<~>~tall(X))))&
(((~curious(alice)&creative(alice)))<=>((~kind(mary)<~>strong(mary))))&
((?[X]:(curious(X)))=>((happy(mary)&strong(mary))))&
(![X]:(~happy(X)=>(~brave(X)&brave(X))))&
(![X]:((~patient(X)&old(X))<=>(~happy(X)&~rich(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>((~generous(fred)<~>generous(fred))))&
(![X]:((~tall(X)&curious(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:((curious(X)|funny(X))=>(happy(X)&~funny(X))))&
(![X]:((~happy(X)&tall(X))<=>kind(X)))&
(((~curious(fred)&strong(fred)))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(![X]:((~old(X)|~curious(X))<=>(~kind(X)<~>brave(X))))&
(![X]:((~kind(X)|rich(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)<~>~old(X))<=>happy(X)))&
(((brave(alice)&curious(alice)))<=>(?[X]:(~happy(X))))&
(?[X]:((~humble(X)|~patient(X))))&
((~kind(mary)&wise(mary)))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((~strong(X)|~generous(X))))&
((~brave(alice)&curious(alice)))&
(?[X]:((humble(X)<~>~kind(X)))) | ~strong(fred) | [
"p5",
"p9",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 617738370706641483284306
% SZS output start Proof for 617738370706641483284306
6. ! [X0] : (~happy(X0) => (brave(X0) & ~brave(X0))) [input p5]
10. ! [X0] : ((funny(X0) | curious(X0)) => (~funny(X0) & happy(X0))) [input p9]
11. ! [X0] : ((tall(X0) & ~happy(X0)) <=> kind(X0)) [input p10]
12. (strong(fred) & ~curious(fred)) <=> ? [X0] : (humble(X0) <~> ~funny(X0)) [input p11]
22. ? [X0] : (humble(X0) <~> ~kind(X0)) [input p21]
23. ~strong(fred) [input hypothesis]
31. ! [X0] : ((brave(X0) & ~brave(X0)) | happy(X0)) [ennf transformation 6]
32. ! [X0] : ((~funny(X0) & happy(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 10]
49. ! [X0] : (((tall(X0) & ~happy(X0)) | ~kind(X0)) & (kind(X0) | (~tall(X0) | happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((tall(X0) & ~happy(X0)) | ~kind(X0)) & (kind(X0) | ~tall(X0) | happy(X0))) [flattening 49]
51. ((strong(fred) & ~curious(fred)) | ! [X0] : ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (? [X0] : ((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (~strong(fred) | curious(fred))) [nnf transformation 12]
52. ((strong(fred) & ~curious(fred)) | ! [X0] : ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (? [X0] : ((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ~strong(fred) | curious(fred)) [flattening 51]
53. ((strong(fred) & ~curious(fred)) | ! [X0] : ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (? [X1] : ((funny(X1) | ~humble(X1)) & (~funny(X1) | humble(X1))) | ~strong(fred) | curious(fred)) [rectify 52]
54. ? [X1] : ((funny(X1) | ~humble(X1)) & (~funny(X1) | humble(X1))) => ((funny(sK2) | ~humble(sK2)) & (~funny(sK2) | humble(sK2))) [choice axiom]
55. ((strong(fred) & ~curious(fred)) | ! [X0] : ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(sK2) | ~humble(sK2)) & (~funny(sK2) | humble(sK2))) | ~strong(fred) | curious(fred)) [skolemisation 53,54]
70. ? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) [nnf transformation 22]
71. ? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) => ((kind(sK7) | ~humble(sK7)) & (~kind(sK7) | humble(sK7))) [choice axiom]
72. (kind(sK7) | ~humble(sK7)) & (~kind(sK7) | humble(sK7)) [skolemisation 70,71]
91. ~brave(X0) | happy(X0) [cnf transformation 31]
92. brave(X0) | happy(X0) [cnf transformation 31]
114. ~funny(X0) | ~funny(X0) [cnf transformation 32]
116. ~happy(X0) | ~kind(X0) [cnf transformation 50]
123. strong(fred) | humble(X0) | funny(X0) [cnf transformation 55]
144. kind(sK7) | ~humble(sK7) [cnf transformation 72]
145. ~strong(fred) [cnf transformation 23]
148. ~funny(X0) [duplicate literal removal 114]
206. happy(X0) [subsumption resolution 91,92]
220. ~kind(X0) [subsumption resolution 116,206]
221. strong(fred) | humble(X0) [subsumption resolution 123,148]
223. 14 <=> ! [X0] : humble(X0) [avatar definition]
224. humble(X0) <- (14) [avatar component clause 223]
226. 15 <=> strong(fred) [avatar definition]
229. 14 | 15 [avatar split clause 221,226,223]
275. ~humble(sK7) [subsumption resolution 144,220]
276. ~15 [avatar split clause 145,226]
279. $false <- (14) [resolution 275,224]
280. ~14 [avatar contradiction clause 279]
281. $false [avatar sat refutation 229,276,280]
% SZS output end Proof for 617738370706641483284306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and happy is happy and vice versa.
Everyone who is either not calm or not creative is either not rich or old.
Everyone who is either not rich or not old is not humble and vice versa.
Everyone who is both not old and strong is either not generous or not rich.
Everyone who is both happy and not rich is funny or not patient and vice versa.
If someone is both brave and not wise then someone is both rich and humble.
If someone is not brave then fred is either not rich or not generous and vice versa.
If john is both not curious and tall then mary is both wise and old and vice versa.
If someone is both generous and not tall then someone is not generous or happy and vice versa.
Everyone who is both not creative and old is funny or wise.
Everyone who is either calm or kind is either kind or curious.
Everyone who is funny is not generous.
If someone is humble or quiet then someone is either quiet or strong and vice versa.
Everyone who is happy or not rich is both quiet and not kind.
Everyone who is not rich or not quiet is both not tall and kind and vice versa.
Everyone who is both not wise and not curious is not happy and vice versa.
Fred is not happy or rich.
Susan is not brave.
Alice is both generous and not tall.
Someone is not wise or not old.
Susan is not creative or not funny.
Someone is either generous or wise. | Fred is patient. | entailment | (![X]:((~curious(X)&happy(X))<=>happy(X)))&
(![X]:((~calm(X)<~>~creative(X))=>(~rich(X)<~>old(X))))&
(![X]:((~rich(X)<~>~old(X))<=>~humble(X)))&
(![X]:((~old(X)&strong(X))=>(~generous(X)<~>~rich(X))))&
(![X]:((happy(X)&~rich(X))<=>(funny(X)|~patient(X))))&
((?[X]:((brave(X)&~wise(X))))=>(?[X]:((rich(X)&humble(X)))))&
((?[X]:(~brave(X)))<=>((~rich(fred)<~>~generous(fred))))&
(((~curious(john)&tall(john)))<=>((wise(mary)&old(mary))))&
((?[X]:((generous(X)&~tall(X))))<=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~creative(X)&old(X))=>(funny(X)|wise(X))))&
(![X]:((calm(X)<~>kind(X))=>(kind(X)<~>curious(X))))&
(![X]:(funny(X)=>~generous(X)))&
((?[X]:((humble(X)|quiet(X))))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((happy(X)|~rich(X))=>(quiet(X)&~kind(X))))&
(![X]:((~rich(X)|~quiet(X))<=>(~tall(X)&kind(X))))&
(![X]:((~wise(X)&~curious(X))<=>~happy(X)))&
((~happy(fred)|rich(fred)))&
(~brave(susan))&
((generous(alice)&~tall(alice)))&
(?[X]:((~wise(X)|~old(X))))&
((~creative(susan)|~funny(susan)))&
(?[X]:((generous(X)<~>wise(X)))) | patient(fred) | [
"p4",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 723212302879342926444565
% SZS output start Proof for 723212302879342926444565
5. ! [X0] : ((~rich(X0) & happy(X0)) <=> (~patient(X0) | funny(X0))) [input p4]
14. ! [X0] : ((~rich(X0) | happy(X0)) => (~kind(X0) & quiet(X0))) [input p13]
15. ! [X0] : ((~quiet(X0) | ~rich(X0)) <=> (kind(X0) & ~tall(X0))) [input p14]
23. ~patient(fred) [input hypothesis]
35. ! [X0] : ((~kind(X0) & quiet(X0)) | (rich(X0) & ~happy(X0))) [ennf transformation 14]
41. ! [X0] : (((~rich(X0) & happy(X0)) | (patient(X0) & ~funny(X0))) & ((~patient(X0) | funny(X0)) | (rich(X0) | ~happy(X0)))) [nnf transformation 5]
42. ! [X0] : (((~rich(X0) & happy(X0)) | (patient(X0) & ~funny(X0))) & (~patient(X0) | funny(X0) | rich(X0) | ~happy(X0))) [flattening 41]
63. ! [X0] : (((~quiet(X0) | ~rich(X0)) | (~kind(X0) | tall(X0))) & ((kind(X0) & ~tall(X0)) | (quiet(X0) & rich(X0)))) [nnf transformation 15]
64. ! [X0] : ((~quiet(X0) | ~rich(X0) | ~kind(X0) | tall(X0)) & ((kind(X0) & ~tall(X0)) | (quiet(X0) & rich(X0)))) [flattening 63]
89. ~rich(X0) | patient(X0) [cnf transformation 42]
120. ~kind(X0) | rich(X0) [cnf transformation 35]
123. kind(X0) | rich(X0) [cnf transformation 64]
137. ~patient(fred) [cnf transformation 23]
257. rich(X0) [subsumption resolution 123,120]
300. patient(X0) [resolution 89,257]
301. $false [resolution 300,137]
% SZS output end Proof for 723212302879342926444565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not calm is strong and vice versa.
Everyone who is not humble is kind.
If someone is not generous then mary is not quiet or not rich.
Everyone who is generous or rich is humble.
Everyone who is both not happy and not humble is either not humble or not funny and vice versa.
Everyone who is strong or humble is either creative or not brave.
If susan is either not calm or not patient then mary is calm.
If mary is either curious or rich then fred is either not calm or kind and vice versa.
Everyone who is not quiet is not patient and vice versa.
If someone is wise or not humble then someone is tall.
If someone is not strong then mary is either calm or quiet and vice versa.
If paul is quiet then susan is wise or quiet.
If susan is not generous then mary is both not patient and not brave and vice versa.
Everyone who is not humble or curious is not humble or not quiet and vice versa.
If someone is both patient and generous then someone is creative or generous and vice versa.
Everyone who is either not calm or not strong is both not generous and wise.
Someone is not generous.
Someone is strong or humble.
John is either generous or wise.
John is both kind and tall.
Someone is not curious.
Someone is either kind or not tall.
Alice is not kind or tall.
Lucy is not quiet. | Paul is not curious. | neutral | (![X]:((~rich(X)|~calm(X))<=>strong(X)))&
(![X]:(~humble(X)=>kind(X)))&
((?[X]:(~generous(X)))=>((~quiet(mary)|~rich(mary))))&
(![X]:((generous(X)|rich(X))=>humble(X)))&
(![X]:((~happy(X)&~humble(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((strong(X)|humble(X))=>(creative(X)<~>~brave(X))))&
(((~calm(susan)<~>~patient(susan)))=>(calm(mary)))&
(((curious(mary)<~>rich(mary)))<=>((~calm(fred)<~>kind(fred))))&
(![X]:(~quiet(X)<=>~patient(X)))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:(tall(X))))&
((?[X]:(~strong(X)))<=>((calm(mary)<~>quiet(mary))))&
((quiet(paul))=>((wise(susan)|quiet(susan))))&
((~generous(susan))<=>((~patient(mary)&~brave(mary))))&
(![X]:((~humble(X)|curious(X))<=>(~humble(X)|~quiet(X))))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~calm(X)<~>~strong(X))=>(~generous(X)&wise(X))))&
(?[X]:(~generous(X)))&
(?[X]:((strong(X)|humble(X))))&
((generous(john)<~>wise(john)))&
((kind(john)&tall(john)))&
(?[X]:(~curious(X)))&
(?[X]:((kind(X)<~>~tall(X))))&
((~kind(alice)|tall(alice)))&
(~quiet(lucy)) | ~curious(paul) | [] | null | 0 |
If someone is old then someone is either wise or tall and vice versa.
If fred is either curious or patient then someone is both old and tall.
If alice is either not calm or not strong then someone is humble or rich.
Everyone who is not old or not humble is not strong or not calm and vice versa.
If lucy is either not quiet or not creative then someone is either not funny or kind and vice versa.
Everyone who is either patient or not calm is either strong or not quiet and vice versa.
Everyone who is quiet is either humble or not tall and vice versa.
Everyone who is either not brave or wise is creative or not kind and vice versa.
Everyone who is both not generous and not kind is not kind or not old.
Everyone who is humble or tall is patient and vice versa.
If john is calm then mary is not creative and vice versa.
Everyone who is not funny or wise is both rich and not kind and vice versa.
If lucy is not creative or patient then someone is both funny and quiet and vice versa.
If someone is creative then fred is both wise and humble.
If mary is patient then john is both old and calm and vice versa.
Everyone who is humble or rich is both wise and not curious.
Someone is both generous and old.
John is either not strong or strong.
Susan is not wise or rich.
Someone is both not wise and strong.
Someone is calm.
Mary is both not happy and humble.
Someone is not rich.
Someone is not creative. | John is strong. | neutral | ((?[X]:(old(X)))<=>(?[X]:((wise(X)<~>tall(X)))))&
(((curious(fred)<~>patient(fred)))=>(?[X]:((old(X)&tall(X)))))&
(((~calm(alice)<~>~strong(alice)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:((~old(X)|~humble(X))<=>(~strong(X)|~calm(X))))&
(((~quiet(lucy)<~>~creative(lucy)))<=>(?[X]:((~funny(X)<~>kind(X)))))&
(![X]:((patient(X)<~>~calm(X))<=>(strong(X)<~>~quiet(X))))&
(![X]:(quiet(X)<=>(humble(X)<~>~tall(X))))&
(![X]:((~brave(X)<~>wise(X))<=>(creative(X)|~kind(X))))&
(![X]:((~generous(X)&~kind(X))=>(~kind(X)|~old(X))))&
(![X]:((humble(X)|tall(X))<=>patient(X)))&
((calm(john))<=>(~creative(mary)))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)&~kind(X))))&
(((~creative(lucy)|patient(lucy)))<=>(?[X]:((funny(X)&quiet(X)))))&
((?[X]:(creative(X)))=>((wise(fred)&humble(fred))))&
((patient(mary))<=>((old(john)&calm(john))))&
(![X]:((humble(X)|rich(X))=>(wise(X)&~curious(X))))&
(?[X]:((generous(X)&old(X))))&
((~strong(john)<~>strong(john)))&
((~wise(susan)|rich(susan)))&
(?[X]:((~wise(X)&strong(X))))&
(?[X]:(calm(X)))&
((~happy(mary)&humble(mary)))&
(?[X]:(~rich(X)))&
(?[X]:(~creative(X))) | strong(john) | [] | null | 0 |
If someone is generous or patient then mary is both not wise and not kind. If lucy is both funny and not quiet then fred is kind. Everyone who is either not wise or not tall is either not quiet or not wise and vice versa. If john is generous then lucy is not quiet or rich and vice versa. If someone is calm then someone is not happy. Everyone who is either not happy or not patient is either quiet or patient. If someone is not old or calm then someone is either rich or not funny and vice versa. If alice is both not happy and happy then someone is quiet or not generous and vice versa. If susan is not quiet or not tall then someone is not humble or not tall. Everyone who is both curious and patient is either not brave or calm and vice versa. Everyone who is either not calm or not kind is either kind or not old. Everyone who is both curious and rich is wise and vice versa. Everyone who is either kind or not quiet is either patient or not humble and vice versa. If someone is not creative then lucy is either not tall or not patient and vice versa. Everyone who is both patient and not creative is both tall and brave. If alice is happy or not old then someone is not wise or curious. Someone is funny. Lucy is brave. Someone is either curious or not rich. Susan is either brave or not creative. Susan is both old and not brave. Paul is calm or not brave. | Susan is not creative. | entailment | ((?[X]:((generous(X)|patient(X))))=>((~wise(mary)&~kind(mary))))&
(((funny(lucy)&~quiet(lucy)))=>(kind(fred)))&
(![X]:((~wise(X)<~>~tall(X))<=>(~quiet(X)<~>~wise(X))))&
((generous(john))<=>((~quiet(lucy)|rich(lucy))))&
((?[X]:(calm(X)))=>(?[X]:(~happy(X))))&
(![X]:((~happy(X)<~>~patient(X))=>(quiet(X)<~>patient(X))))&
((?[X]:((~old(X)|calm(X))))<=>(?[X]:((rich(X)<~>~funny(X)))))&
(((~happy(alice)&happy(alice)))<=>(?[X]:((quiet(X)|~generous(X)))))&
(((~quiet(susan)|~tall(susan)))=>(?[X]:((~humble(X)|~tall(X)))))&
(![X]:((curious(X)&patient(X))<=>(~brave(X)<~>calm(X))))&
(![X]:((~calm(X)<~>~kind(X))=>(kind(X)<~>~old(X))))&
(![X]:((curious(X)&rich(X))<=>wise(X)))&
(![X]:((kind(X)<~>~quiet(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(~creative(X)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:((patient(X)&~creative(X))=>(tall(X)&brave(X))))&
(((happy(alice)|~old(alice)))=>(?[X]:((~wise(X)|curious(X)))))&
(?[X]:(funny(X)))&
(brave(lucy))&
(?[X]:((curious(X)<~>~rich(X))))&
((brave(susan)<~>~creative(susan)))&
((old(susan)&~brave(susan)))&
((calm(paul)|~brave(paul))) | ~creative(susan) | [
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6416743185213003144597700
% SZS output start Proof for 6416743185213003144597700
20. brave(susan) <~> ~creative(susan) [input p19]
21. ~brave(susan) & old(susan) [input p20]
23. creative(susan) [input hypothesis]
72. (creative(susan) | ~brave(susan)) & (~creative(susan) | brave(susan)) [nnf transformation 20]
140. ~creative(susan) | brave(susan) [cnf transformation 72]
143. ~brave(susan) [cnf transformation 21]
145. creative(susan) [cnf transformation 23]
299. 32 <=> brave(susan) [avatar definition]
303. 33 <=> creative(susan) [avatar definition]
307. 32 | ~33 [avatar split clause 140,303,299]
308. ~32 [avatar split clause 143,299]
318. 33 [avatar split clause 145,303]
319. $false [avatar sat refutation 307,308,318]
% SZS output end Proof for 6416743185213003144597700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is humble and vice versa. If someone is either not calm or not tall then someone is both not patient and quiet and vice versa. If paul is either quiet or funny then someone is calm or not creative. If someone is both not patient and not curious then someone is quiet. If lucy is either generous or tall then paul is both not quiet and not curious and vice versa. Everyone who is not kind is either not creative or generous. If lucy is both rich and not brave then alice is either not generous or not humble. Everyone who is either funny or not quiet is kind or not rich. If someone is either brave or old then someone is not curious or not happy and vice versa. If john is quiet then someone is both rich and funny. Everyone who is both not funny and not kind is both calm and kind and vice versa. Everyone who is both tall and not funny is not curious or tall and vice versa. If alice is not generous or not kind then someone is quiet or patient and vice versa. Everyone who is either not old or not funny is either calm or old and vice versa. Everyone who is either kind or wise is tall and vice versa. If someone is either not humble or not generous then mary is either creative or not old. Paul is both not patient and wise. Mary is not happy. Someone is either not old or wise. John is either not creative or old. Someone is wise. Someone is both not tall and kind. Alice is both not patient and strong. Fred is either quiet or funny. | Paul is kind. | entailment | (![X]:(funny(X)<=>humble(X)))&
((?[X]:((~calm(X)<~>~tall(X))))<=>(?[X]:((~patient(X)&quiet(X)))))&
(((quiet(paul)<~>funny(paul)))=>(?[X]:((calm(X)|~creative(X)))))&
((?[X]:((~patient(X)&~curious(X))))=>(?[X]:(quiet(X))))&
(((generous(lucy)<~>tall(lucy)))<=>((~quiet(paul)&~curious(paul))))&
(![X]:(~kind(X)=>(~creative(X)<~>generous(X))))&
(((rich(lucy)&~brave(lucy)))=>((~generous(alice)<~>~humble(alice))))&
(![X]:((funny(X)<~>~quiet(X))=>(kind(X)|~rich(X))))&
((?[X]:((brave(X)<~>old(X))))<=>(?[X]:((~curious(X)|~happy(X)))))&
((quiet(john))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(calm(X)&kind(X))))&
(![X]:((tall(X)&~funny(X))<=>(~curious(X)|tall(X))))&
(((~generous(alice)|~kind(alice)))<=>(?[X]:((quiet(X)|patient(X)))))&
(![X]:((~old(X)<~>~funny(X))<=>(calm(X)<~>old(X))))&
(![X]:((kind(X)<~>wise(X))<=>tall(X)))&
((?[X]:((~humble(X)<~>~generous(X))))=>((creative(mary)<~>~old(mary))))&
((~patient(paul)&wise(paul)))&
(~happy(mary))&
(?[X]:((~old(X)<~>wise(X))))&
((~creative(john)<~>old(john)))&
(?[X]:(wise(X)))&
(?[X]:((~tall(X)&kind(X))))&
((~patient(alice)&strong(alice)))&
((quiet(fred)<~>funny(fred))) | kind(paul) | [
"p10",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7101949760200167017826309
% SZS output start Proof for 7101949760200167017826309
11. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (kind(X0) & calm(X0))) [input p10]
12. ! [X0] : ((~funny(X0) & tall(X0)) <=> (tall(X0) | ~curious(X0))) [input p11]
15. ! [X0] : ((kind(X0) <~> wise(X0)) <=> tall(X0)) [input p14]
17. wise(paul) & ~patient(paul) [input p16]
25. ~kind(paul) [input hypothesis]
63. ! [X0] : (((~kind(X0) & ~funny(X0)) | (~kind(X0) | ~calm(X0))) & ((kind(X0) & calm(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 11]
64. ! [X0] : (((~kind(X0) & ~funny(X0)) | ~kind(X0) | ~calm(X0)) & ((kind(X0) & calm(X0)) | kind(X0) | funny(X0))) [flattening 63]
65. ! [X0] : (((~funny(X0) & tall(X0)) | (~tall(X0) & curious(X0))) & ((tall(X0) | ~curious(X0)) | (funny(X0) | ~tall(X0)))) [nnf transformation 12]
66. ! [X0] : (((~funny(X0) & tall(X0)) | (~tall(X0) & curious(X0))) & (tall(X0) | ~curious(X0) | funny(X0) | ~tall(X0))) [flattening 65]
73. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ~tall(X0)) & (tall(X0) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [nnf transformation 15]
116. kind(X0) | kind(X0) | funny(X0) [cnf transformation 64]
123. ~tall(X0) | ~funny(X0) [cnf transformation 66]
137. ~wise(X0) | kind(X0) | tall(X0) [cnf transformation 73]
145. wise(paul) [cnf transformation 17]
157. ~kind(paul) [cnf transformation 25]
162. kind(X0) | funny(X0) [duplicate literal removal 116]
196. 8 <=> funny(paul) [avatar definition]
197. funny(paul) <- (8) [avatar component clause 196]
389. funny(paul) [resolution 162,157]
391. 8 [avatar split clause 389,196]
418. kind(paul) | tall(paul) [resolution 137,145]
421. tall(paul) [subsumption resolution 418,157]
432. ~funny(paul) [resolution 421,123]
433. $false <- (8) [subsumption resolution 432,197]
434. ~8 [avatar contradiction clause 433]
435. $false [avatar sat refutation 391,434]
% SZS output end Proof for 7101949760200167017826309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is not old or not happy and vice versa.
Everyone who is quiet is brave or not happy.
Everyone who is both strong and wise is patient.
Everyone who is strong or not generous is curious and vice versa.
Everyone who is tall is not wise or not calm and vice versa.
Everyone who is both quiet and not rich is both not humble and old and vice versa.
If someone is humble or old then lucy is both not wise and funny.
Everyone who is both humble and old is not funny or not quiet.
If mary is both not brave and not funny then someone is both not strong and humble and vice versa.
Everyone who is either strong or old is not humble or not wise and vice versa.
If someone is funny then paul is not brave and vice versa.
If paul is not tall or not generous then someone is both not patient and funny.
If fred is both not kind and not calm then someone is either funny or brave.
If someone is both funny and creative then mary is both not creative and not strong and vice versa.
Everyone who is either quiet or creative is wise.
Someone is kind or not generous.
Susan is both not old and wise.
Fred is not brave.
Alice is not patient.
Someone is either creative or not generous.
Someone is not strong or not tall.
Someone is both strong and quiet.
Mary is both not strong and not curious. | Paul is brave. | contradiction | (![X]:(~tall(X)<=>(~old(X)|~happy(X))))&
(![X]:(quiet(X)=>(brave(X)|~happy(X))))&
(![X]:((strong(X)&wise(X))=>patient(X)))&
(![X]:((strong(X)|~generous(X))<=>curious(X)))&
(![X]:(tall(X)<=>(~wise(X)|~calm(X))))&
(![X]:((quiet(X)&~rich(X))<=>(~humble(X)&old(X))))&
((?[X]:((humble(X)|old(X))))=>((~wise(lucy)&funny(lucy))))&
(![X]:((humble(X)&old(X))=>(~funny(X)|~quiet(X))))&
(((~brave(mary)&~funny(mary)))<=>(?[X]:((~strong(X)&humble(X)))))&
(![X]:((strong(X)<~>old(X))<=>(~humble(X)|~wise(X))))&
((?[X]:(funny(X)))<=>(~brave(paul)))&
(((~tall(paul)|~generous(paul)))=>(?[X]:((~patient(X)&funny(X)))))&
(((~kind(fred)&~calm(fred)))=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((funny(X)&creative(X))))<=>((~creative(mary)&~strong(mary))))&
(![X]:((quiet(X)<~>creative(X))=>wise(X)))&
(?[X]:((kind(X)|~generous(X))))&
((~old(susan)&wise(susan)))&
(~brave(fred))&
(~patient(alice))&
(?[X]:((creative(X)<~>~generous(X))))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((strong(X)&quiet(X))))&
((~strong(mary)&~curious(mary))) | brave(paul) | [
"p0",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 840944148628975444488426
% SZS output start Proof for 840944148628975444488426
1. ! [X0] : (~tall(X0) <=> (~happy(X0) | ~old(X0))) [input p0]
7. ? [X0] : (old(X0) | humble(X0)) => (funny(lucy) & ~wise(lucy)) [input p6]
11. ? [X0] : funny(X0) <=> ~brave(paul) [input p10]
12. (~generous(paul) | ~tall(paul)) => ? [X0] : (funny(X0) & ~patient(X0)) [input p11]
24. brave(paul) [input hypothesis]
33. (funny(lucy) & ~wise(lucy)) | ! [X0] : (~old(X0) & ~humble(X0)) [ennf transformation 7]
36. ? [X0] : (funny(X0) & ~patient(X0)) | (generous(paul) & tall(paul)) [ennf transformation 12]
38. ! [X0] : ((~tall(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | tall(X0))) [nnf transformation 1]
39. ! [X0] : ((~tall(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | tall(X0))) [flattening 38]
51. (? [X0] : funny(X0) | brave(paul)) & (~brave(paul) | ! [X0] : ~funny(X0)) [nnf transformation 11]
52. (? [X0] : funny(X0) | brave(paul)) & (~brave(paul) | ! [X1] : ~funny(X1)) [rectify 51]
53. ? [X0] : funny(X0) => funny(sK1) [choice axiom]
54. (funny(sK1) | brave(paul)) & (~brave(paul) | ! [X1] : ~funny(X1)) [skolemisation 52,53]
55. ? [X0] : (funny(X0) & ~patient(X0)) => (funny(sK2) & ~patient(sK2)) [choice axiom]
56. (funny(sK2) & ~patient(sK2)) | (generous(paul) & tall(paul)) [skolemisation 36,55]
71. ~tall(X0) | old(X0) [cnf transformation 39]
87. funny(lucy) | ~old(X0) [cnf transformation 33]
99. ~brave(paul) | ~funny(X1) [cnf transformation 54]
103. funny(sK2) | tall(paul) [cnf transformation 56]
122. brave(paul) [cnf transformation 24]
124. 1 <=> ! [X0] : ~old(X0) [avatar definition]
125. ~old(X0) <- (1) [avatar component clause 124]
127. 2 <=> funny(lucy) [avatar definition]
129. funny(lucy) <- (2) [avatar component clause 127]
130. 1 | 2 [avatar split clause 87,127,124]
165. 10 <=> brave(paul) [avatar definition]
174. 12 <=> ! [X1] : ~funny(X1) [avatar definition]
175. ~funny(X1) <- (12) [avatar component clause 174]
176. 12 | ~10 [avatar split clause 99,165,174]
182. 14 <=> funny(sK2) [avatar definition]
184. funny(sK2) <- (14) [avatar component clause 182]
187. 15 <=> tall(paul) [avatar definition]
189. tall(paul) <- (15) [avatar component clause 187]
190. 15 | 14 [avatar split clause 103,182,187]
240. 10 [avatar split clause 122,165]
243. $false <- (2, 12) [subsumption resolution 129,175]
244. ~2 | ~12 [avatar contradiction clause 243]
245. $false <- (12, 14) [resolution 184,175]
246. ~12 | ~14 [avatar contradiction clause 245]
249. old(paul) <- (15) [resolution 71,189]
250. $false <- (1, 15) [subsumption resolution 249,125]
251. ~1 | ~15 [avatar contradiction clause 250]
252. $false [avatar sat refutation 130,176,190,240,244,246,251]
% SZS output end Proof for 840944148628975444488426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not creative is creative or generous and vice versa.
If susan is either quiet or not strong then alice is not kind or not brave.
Everyone who is either not quiet or not creative is both generous and not tall and vice versa.
Everyone who is rich is both curious and not curious and vice versa.
Everyone who is calm or patient is generous or wise.
Everyone who is tall or creative is both generous and rich and vice versa.
If paul is humble then someone is generous or brave.
Everyone who is both not tall and happy is curious and vice versa.
Everyone who is calm is not funny.
If someone is either strong or curious then lucy is generous and vice versa.
If someone is both strong and not generous then paul is both happy and curious and vice versa.
If fred is either strong or curious then someone is not generous or patient.
If alice is either happy or curious then alice is either calm or not rich.
If someone is brave or not generous then paul is not wise.
Everyone who is not curious is quiet or creative and vice versa.
If alice is either rich or not quiet then someone is patient or not tall and vice versa.
Susan is not calm or not generous.
Someone is not patient or not happy.
Someone is not old or old.
Mary is either generous or humble.
Someone is either not humble or generous.
Alice is both not old and not wise.
Alice is wise or funny. | Lucy is not curious. | neutral | (![X]:((wise(X)&~creative(X))<=>(creative(X)|generous(X))))&
(((quiet(susan)<~>~strong(susan)))=>((~kind(alice)|~brave(alice))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(generous(X)&~tall(X))))&
(![X]:(rich(X)<=>(curious(X)&~curious(X))))&
(![X]:((calm(X)|patient(X))=>(generous(X)|wise(X))))&
(![X]:((tall(X)|creative(X))<=>(generous(X)&rich(X))))&
((humble(paul))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~tall(X)&happy(X))<=>curious(X)))&
(![X]:(calm(X)=>~funny(X)))&
((?[X]:((strong(X)<~>curious(X))))<=>(generous(lucy)))&
((?[X]:((strong(X)&~generous(X))))<=>((happy(paul)&curious(paul))))&
(((strong(fred)<~>curious(fred)))=>(?[X]:((~generous(X)|patient(X)))))&
(((happy(alice)<~>curious(alice)))=>((calm(alice)<~>~rich(alice))))&
((?[X]:((brave(X)|~generous(X))))=>(~wise(paul)))&
(![X]:(~curious(X)<=>(quiet(X)|creative(X))))&
(((rich(alice)<~>~quiet(alice)))<=>(?[X]:((patient(X)|~tall(X)))))&
((~calm(susan)|~generous(susan)))&
(?[X]:((~patient(X)|~happy(X))))&
(?[X]:((~old(X)|old(X))))&
((generous(mary)<~>humble(mary)))&
(?[X]:((~humble(X)<~>generous(X))))&
((~old(alice)&~wise(alice)))&
((wise(alice)|funny(alice))) | ~curious(lucy) | [] | null | 0 |
If someone is humble or old then fred is either not quiet or not rich and vice versa.
Everyone who is both old and not tall is both quiet and not happy and vice versa.
If someone is not old then paul is happy.
If someone is not funny then lucy is either patient or humble and vice versa.
Everyone who is not patient or not old is creative or not creative and vice versa.
If john is patient then john is both not calm and brave and vice versa.
If someone is not happy then mary is both not tall and tall and vice versa.
If someone is both tall and curious then someone is not wise or creative and vice versa.
Everyone who is calm or curious is either happy or generous and vice versa.
Everyone who is funny is kind or not generous and vice versa.
If paul is not generous then someone is both generous and brave.
If paul is either not brave or not quiet then lucy is either not old or wise and vice versa.
If paul is generous then someone is not humble or not rich and vice versa.
Everyone who is both curious and patient is either kind or curious and vice versa.
Everyone who is both rich and not quiet is either rich or tall and vice versa.
Everyone who is either not creative or not calm is both not generous and not creative.
Someone is both not rich and patient.
Someone is either not happy or not funny.
Mary is either not brave or generous.
Susan is humble or old.
Someone is either rich or not wise.
Someone is both not rich and generous.
Someone is both not humble and not tall. | Paul is not curious. | entailment | ((?[X]:((humble(X)|old(X))))<=>((~quiet(fred)<~>~rich(fred))))&
(![X]:((old(X)&~tall(X))<=>(quiet(X)&~happy(X))))&
((?[X]:(~old(X)))=>(happy(paul)))&
((?[X]:(~funny(X)))<=>((patient(lucy)<~>humble(lucy))))&
(![X]:((~patient(X)|~old(X))<=>(creative(X)|~creative(X))))&
((patient(john))<=>((~calm(john)&brave(john))))&
((?[X]:(~happy(X)))<=>((~tall(mary)&tall(mary))))&
((?[X]:((tall(X)&curious(X))))<=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:((calm(X)|curious(X))<=>(happy(X)<~>generous(X))))&
(![X]:(funny(X)<=>(kind(X)|~generous(X))))&
((~generous(paul))=>(?[X]:((generous(X)&brave(X)))))&
(((~brave(paul)<~>~quiet(paul)))<=>((~old(lucy)<~>wise(lucy))))&
((generous(paul))<=>(?[X]:((~humble(X)|~rich(X)))))&
(![X]:((curious(X)&patient(X))<=>(kind(X)<~>curious(X))))&
(![X]:((rich(X)&~quiet(X))<=>(rich(X)<~>tall(X))))&
(![X]:((~creative(X)<~>~calm(X))=>(~generous(X)&~creative(X))))&
(?[X]:((~rich(X)&patient(X))))&
(?[X]:((~happy(X)<~>~funny(X))))&
((~brave(mary)<~>generous(mary)))&
((humble(susan)|old(susan)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((~rich(X)&generous(X))))&
(?[X]:((~humble(X)&~tall(X)))) | ~curious(paul) | [
"p6",
"p8",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 75287253592392361878416
% SZS output start Proof for 75287253592392361878416
7. ? [X0] : ~happy(X0) <=> (tall(mary) & ~tall(mary)) [input p6]
9. ! [X0] : ((curious(X0) | calm(X0)) <=> (happy(X0) <~> generous(X0))) [input p8]
13. generous(paul) <=> ? [X0] : (~rich(X0) | ~humble(X0)) [input p12]
17. ? [X0] : (patient(X0) & ~rich(X0)) [input p16]
24. curious(paul) [input hypothesis]
43. (? [X0] : ~happy(X0) | (~tall(mary) | tall(mary))) & ((tall(mary) & ~tall(mary)) | ! [X0] : happy(X0)) [nnf transformation 7]
44. (? [X0] : ~happy(X0) | ~tall(mary) | tall(mary)) & ((tall(mary) & ~tall(mary)) | ! [X0] : happy(X0)) [flattening 43]
45. (? [X0] : ~happy(X0) | ~tall(mary) | tall(mary)) & ((tall(mary) & ~tall(mary)) | ! [X1] : happy(X1)) [rectify 44]
46. ? [X0] : ~happy(X0) => ~happy(sK2) [choice axiom]
47. (~happy(sK2) | ~tall(mary) | tall(mary)) & ((tall(mary) & ~tall(mary)) | ! [X1] : happy(X1)) [skolemisation 45,46]
53. ! [X0] : (((curious(X0) | calm(X0)) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (~curious(X0) & ~calm(X0)))) [nnf transformation 9]
54. ! [X0] : ((curious(X0) | calm(X0) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (~curious(X0) & ~calm(X0)))) [flattening 53]
60. (generous(paul) | ! [X0] : (rich(X0) & humble(X0))) & (? [X0] : (~rich(X0) | ~humble(X0)) | ~generous(paul)) [nnf transformation 13]
61. (generous(paul) | ! [X0] : (rich(X0) & humble(X0))) & (? [X1] : (~rich(X1) | ~humble(X1)) | ~generous(paul)) [rectify 60]
62. ? [X1] : (~rich(X1) | ~humble(X1)) => (~rich(sK6) | ~humble(sK6)) [choice axiom]
63. (generous(paul) | ! [X0] : (rich(X0) & humble(X0))) & ((~rich(sK6) | ~humble(sK6)) | ~generous(paul)) [skolemisation 61,62]
69. ? [X0] : (patient(X0) & ~rich(X0)) => (patient(sK7) & ~rich(sK7)) [choice axiom]
70. patient(sK7) & ~rich(sK7) [skolemisation 17,69]
104. ~tall(mary) | happy(X1) [cnf transformation 47]
105. tall(mary) | happy(X1) [cnf transformation 47]
115. ~generous(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 54]
133. generous(paul) | rich(X0) [cnf transformation 63]
150. ~rich(sK7) [cnf transformation 70]
163. curious(paul) [cnf transformation 24]
241. 16 <=> ! [X1] : happy(X1) [avatar definition]
242. happy(X1) <- (16) [avatar component clause 241]
244. 17 <=> tall(mary) [avatar definition]
247. 16 | 17 [avatar split clause 105,244,241]
248. 16 | ~17 [avatar split clause 104,244,241]
280. 25 <=> generous(paul) [avatar definition]
282. generous(paul) <- (25) [avatar component clause 280]
318. 32 <=> ! [X0] : rich(X0) [avatar definition]
319. rich(X0) <- (32) [avatar component clause 318]
320. 32 | 25 [avatar split clause 133,280,318]
398. ~happy(paul) | ~curious(paul) <- (25) [resolution 115,282]
401. ~curious(paul) <- (16, 25) [subsumption resolution 398,242]
402. $false <- (16, 25) [subsumption resolution 401,163]
403. ~16 | ~25 [avatar contradiction clause 402]
412. $false <- (32) [resolution 319,150]
417. ~32 [avatar contradiction clause 412]
420. $false [avatar sat refutation 247,248,320,403,417]
% SZS output end Proof for 75287253592392361878416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both generous and happy then someone is not funny or not wise and vice versa.
If fred is funny then susan is not strong and vice versa.
Everyone who is either not happy or creative is either not tall or brave and vice versa.
If someone is not tall or curious then someone is not curious and vice versa.
If alice is both brave and not wise then someone is either not old or curious.
Everyone who is tall or not quiet is both quiet and not kind.
Everyone who is both strong and calm is either quiet or not wise.
If lucy is not kind then alice is either not patient or not curious and vice versa.
If someone is tall or funny then mary is either brave or kind.
Everyone who is strong is old.
If someone is both not creative and funny then fred is both not funny and not brave.
If someone is both not patient and not kind then alice is quiet and vice versa.
Everyone who is not curious or not brave is either happy or not funny and vice versa.
If someone is curious or creative then fred is not creative and vice versa.
If someone is either not wise or curious then lucy is rich or wise and vice versa.
If someone is either not brave or brave then alice is either generous or not happy.
Someone is both not happy and not old.
Someone is humble or not patient.
Alice is not kind or quiet.
Someone is funny or strong.
Susan is not humble. | Mary is old. | neutral | (((generous(paul)&happy(paul)))<=>(?[X]:((~funny(X)|~wise(X)))))&
((funny(fred))<=>(~strong(susan)))&
(![X]:((~happy(X)<~>creative(X))<=>(~tall(X)<~>brave(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:(~curious(X))))&
(((brave(alice)&~wise(alice)))=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((tall(X)|~quiet(X))=>(quiet(X)&~kind(X))))&
(![X]:((strong(X)&calm(X))=>(quiet(X)<~>~wise(X))))&
((~kind(lucy))<=>((~patient(alice)<~>~curious(alice))))&
((?[X]:((tall(X)|funny(X))))=>((brave(mary)<~>kind(mary))))&
(![X]:(strong(X)=>old(X)))&
((?[X]:((~creative(X)&funny(X))))=>((~funny(fred)&~brave(fred))))&
((?[X]:((~patient(X)&~kind(X))))<=>(quiet(alice)))&
(![X]:((~curious(X)|~brave(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:((curious(X)|creative(X))))<=>(~creative(fred)))&
((?[X]:((~wise(X)<~>curious(X))))<=>((rich(lucy)|wise(lucy))))&
((?[X]:((~brave(X)<~>brave(X))))=>((generous(alice)<~>~happy(alice))))&
(?[X]:((~happy(X)&~old(X))))&
(?[X]:((humble(X)|~patient(X))))&
((~kind(alice)|quiet(alice)))&
(?[X]:((funny(X)|strong(X))))&
(~humble(susan)) | old(mary) | [] | null | 0 |
If lucy is both tall and patient then alice is either kind or calm. If susan is either not wise or not strong then someone is both curious and calm and vice versa. Everyone who is not strong is both old and calm and vice versa. Everyone who is both not strong and humble is funny and vice versa. If someone is old or not calm then mary is both not strong and patient. Everyone who is creative or not old is either kind or not creative and vice versa. If john is rich or not kind then lucy is generous. If paul is both rich and not rich then alice is quiet or patient. If someone is not quiet then mary is not quiet or tall. If paul is both creative and wise then susan is patient. Everyone who is both kind and wise is both calm and not wise and vice versa. Everyone who is not happy is both not wise and not rich. Everyone who is either humble or tall is either kind or patient and vice versa. If lucy is not calm then lucy is either generous or not wise. Everyone who is old is both not humble and not creative. If fred is either humble or not creative then someone is both not rich and not calm. Someone is tall. Someone is either not rich or happy. Lucy is either curious or quiet. Mary is funny or generous. John is tall. | Paul is humble. | neutral | (((tall(lucy)&patient(lucy)))=>((kind(alice)<~>calm(alice))))&
(((~wise(susan)<~>~strong(susan)))<=>(?[X]:((curious(X)&calm(X)))))&
(![X]:(~strong(X)<=>(old(X)&calm(X))))&
(![X]:((~strong(X)&humble(X))<=>funny(X)))&
((?[X]:((old(X)|~calm(X))))=>((~strong(mary)&patient(mary))))&
(![X]:((creative(X)|~old(X))<=>(kind(X)<~>~creative(X))))&
(((rich(john)|~kind(john)))=>(generous(lucy)))&
(((rich(paul)&~rich(paul)))=>((quiet(alice)|patient(alice))))&
((?[X]:(~quiet(X)))=>((~quiet(mary)|tall(mary))))&
(((creative(paul)&wise(paul)))=>(patient(susan)))&
(![X]:((kind(X)&wise(X))<=>(calm(X)&~wise(X))))&
(![X]:(~happy(X)=>(~wise(X)&~rich(X))))&
(![X]:((humble(X)<~>tall(X))<=>(kind(X)<~>patient(X))))&
((~calm(lucy))=>((generous(lucy)<~>~wise(lucy))))&
(![X]:(old(X)=>(~humble(X)&~creative(X))))&
(((humble(fred)<~>~creative(fred)))=>(?[X]:((~rich(X)&~calm(X)))))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)<~>happy(X))))&
((curious(lucy)<~>quiet(lucy)))&
((funny(mary)|generous(mary)))&
(tall(john)) | humble(paul) | [] | null | 0 |
Everyone who is both patient and not old is not tall or not patient.
If someone is both wise and brave then mary is either happy or generous.
Everyone who is either kind or not kind is happy.
If someone is tall then someone is both tall and not patient and vice versa.
If someone is both not rich and not wise then john is both patient and strong.
If someone is both quiet and not calm then someone is either brave or not quiet and vice versa.
Everyone who is happy or quiet is curious or generous.
If fred is either not wise or not rich then someone is both humble and not patient.
Everyone who is either patient or quiet is happy or wise and vice versa.
Everyone who is not quiet is both wise and not funny.
Everyone who is not patient is not generous.
If susan is creative then lucy is not kind and vice versa.
If someone is not wise then alice is not old and vice versa.
If mary is not old or not generous then someone is both creative and not humble and vice versa.
Everyone who is both kind and rich is not quiet or not calm.
Everyone who is not curious is both not strong and funny and vice versa.
Lucy is brave or not quiet.
Someone is not rich.
Someone is happy.
Someone is either wise or not old.
Someone is not old.
Paul is not curious or humble.
Someone is either wise or not brave. | Alice is not curious. | contradiction | (![X]:((patient(X)&~old(X))=>(~tall(X)|~patient(X))))&
((?[X]:((wise(X)&brave(X))))=>((happy(mary)<~>generous(mary))))&
(![X]:((kind(X)<~>~kind(X))=>happy(X)))&
((?[X]:(tall(X)))<=>(?[X]:((tall(X)&~patient(X)))))&
((?[X]:((~rich(X)&~wise(X))))=>((patient(john)&strong(john))))&
((?[X]:((quiet(X)&~calm(X))))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(![X]:((happy(X)|quiet(X))=>(curious(X)|generous(X))))&
(((~wise(fred)<~>~rich(fred)))=>(?[X]:((humble(X)&~patient(X)))))&
(![X]:((patient(X)<~>quiet(X))<=>(happy(X)|wise(X))))&
(![X]:(~quiet(X)=>(wise(X)&~funny(X))))&
(![X]:(~patient(X)=>~generous(X)))&
((creative(susan))<=>(~kind(lucy)))&
((?[X]:(~wise(X)))<=>(~old(alice)))&
(((~old(mary)|~generous(mary)))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((kind(X)&rich(X))=>(~quiet(X)|~calm(X))))&
(![X]:(~curious(X)<=>(~strong(X)&funny(X))))&
((brave(lucy)|~quiet(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:(happy(X)))&
(?[X]:((wise(X)<~>~old(X))))&
(?[X]:(~old(X)))&
((~curious(paul)|humble(paul)))&
(?[X]:((wise(X)<~>~brave(X)))) | ~curious(alice) | [
"p2",
"p6",
"p8",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2069933649845262839516118
% SZS output start Proof for 2069933649845262839516118
3. ! [X0] : ((kind(X0) <~> ~kind(X0)) => happy(X0)) [input p2]
7. ! [X0] : ((quiet(X0) | happy(X0)) => (generous(X0) | curious(X0))) [input p6]
9. ! [X0] : ((patient(X0) <~> quiet(X0)) <=> (wise(X0) | happy(X0))) [input p8]
10. ! [X0] : (~quiet(X0) => (~funny(X0) & wise(X0))) [input p9]
11. ! [X0] : (~patient(X0) => ~generous(X0)) [input p10]
16. ! [X0] : (~curious(X0) <=> (funny(X0) & ~strong(X0))) [input p15]
24. ~curious(alice) [input hypothesis]
30. ! [X0] : (happy(X0) | (kind(X0) <=> ~kind(X0))) [ennf transformation 3]
32. ! [X0] : ((generous(X0) | curious(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 7]
33. ! [X0] : (generous(X0) | curious(X0) | (~quiet(X0) & ~happy(X0))) [flattening 32]
35. ! [X0] : ((~funny(X0) & wise(X0)) | quiet(X0)) [ennf transformation 10]
36. ! [X0] : (~generous(X0) | patient(X0)) [ennf transformation 11]
40. ! [X0] : (happy(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 30]
54. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~wise(X0) & ~happy(X0))) & ((wise(X0) | happy(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~wise(X0) & ~happy(X0))) & (wise(X0) | happy(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [flattening 54]
66. ! [X0] : ((~curious(X0) | (~funny(X0) | strong(X0))) & ((funny(X0) & ~strong(X0)) | curious(X0))) [nnf transformation 16]
67. ! [X0] : ((~curious(X0) | ~funny(X0) | strong(X0)) & ((funny(X0) & ~strong(X0)) | curious(X0))) [flattening 66]
83. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 40]
84. happy(X0) | kind(X0) | kind(X0) [cnf transformation 40]
96. generous(X0) | curious(X0) | ~happy(X0) [cnf transformation 33]
106. ~quiet(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 55]
109. ~funny(X0) | quiet(X0) [cnf transformation 35]
110. ~generous(X0) | patient(X0) [cnf transformation 36]
122. funny(X0) | curious(X0) [cnf transformation 67]
133. ~curious(alice) [cnf transformation 24]
134. happy(X0) | ~kind(X0) [duplicate literal removal 83]
135. kind(X0) | happy(X0) [duplicate literal removal 84]
150. happy(X0) [subsumption resolution 134,135]
216. curious(X0) | generous(X0) [subsumption resolution 96,150]
237. ~quiet(X0) | ~patient(X0) [subsumption resolution 106,150]
324. curious(X0) | quiet(X0) [resolution 122,109]
337. generous(alice) [resolution 216,133]
341. patient(alice) [resolution 337,110]
359. quiet(alice) [resolution 324,133]
363. ~patient(alice) [resolution 359,237]
366. $false [subsumption resolution 363,341]
% SZS output end Proof for 2069933649845262839516118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is 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. If john is not curious or not brave then 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. John is both wise and happy. Fred is rich or not calm. | John is not generous. | contradiction | (((~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(john)|~brave(john)))=>(?[X]:((brave(X)|humble(X)))))&
((humble(john)|~patient(john)))&
(~happy(fred))&
((tall(mary)|~strong(mary)))&
((~calm(mary)&~kind(mary)))&
((wise(john)&happy(john)))&
((rich(fred)|~calm(fred))) | ~generous(john) | [
"p1",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8962724888508729559781402
% SZS output start Proof for 8962724888508729559781402
2. (~tall(lucy) & strong(lucy)) <=> old(fred) [input p1]
6. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (old(fred) & creative(fred)) [input p5]
13. (~calm(fred) & calm(fred)) <=> (strong(lucy) | rich(lucy)) [input p12]
22. ~generous(john) [input hypothesis]
32. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | (tall(lucy) | ~strong(lucy))) [nnf transformation 2]
33. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | tall(lucy) | ~strong(lucy)) [flattening 32]
40. (? [X0] : (~generous(X0) | ~curious(X0)) | (~old(fred) | ~creative(fred))) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 6]
41. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 40]
42. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 41]
43. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK0) | ~curious(sK0)) [choice axiom]
44. ((~generous(sK0) | ~curious(sK0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 42,43]
56. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & ((strong(lucy) | rich(lucy)) | (calm(fred) | ~calm(fred))) [nnf transformation 13]
57. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & (strong(lucy) | rich(lucy) | calm(fred) | ~calm(fred)) [flattening 56]
68. strong(lucy) | ~old(fred) [cnf transformation 33]
84. old(fred) | generous(X1) [cnf transformation 44]
107. calm(fred) | ~strong(lucy) [cnf transformation 57]
109. ~calm(fred) | ~strong(lucy) [cnf transformation 57]
122. ~generous(john) [cnf transformation 22]
142. 5 <=> old(fred) [avatar definition]
151. 7 <=> strong(lucy) [avatar definition]
154. ~5 | 7 [avatar split clause 68,151,142]
170. 11 <=> ! [X1] : generous(X1) [avatar definition]
171. generous(X1) <- (11) [avatar component clause 170]
172. 11 | 5 [avatar split clause 84,142,170]
249. 28 <=> calm(fred) [avatar definition]
252. ~7 | ~28 [avatar split clause 109,249,151]
258. ~7 | 28 [avatar split clause 107,249,151]
315. $false <- (11) [resolution 171,122]
316. ~11 [avatar contradiction clause 315]
317. $false [avatar sat refutation 154,172,252,258,316]
% SZS output end Proof for 8962724888508729559781402
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not generous is both brave and not patient.
If paul is either not generous or wise then someone is both strong and patient and vice versa.
If fred is either creative or not happy then someone is both rich and not creative and vice versa.
Everyone who is either tall or brave is both not strong and tall and vice versa.
Everyone who is not tall or strong is humble and vice versa.
Everyone who is either not wise or patient is not curious or happy and vice versa.
Everyone who is not quiet is either not strong or not wise and vice versa.
If mary is both not calm and old then susan is both creative and tall and vice versa.
If someone is brave then someone is happy.
Everyone who is not tall or tall is not rich or not brave.
Everyone who is both funny and not patient is not old or not curious.
If mary is not patient or not curious then lucy is either patient or calm and vice versa.
If someone is both not calm and rich then john is both old and tall.
If susan is both rich and not calm then mary is not old and vice versa.
If someone is either happy or not funny then paul is happy and vice versa.
If someone is curious or kind then someone is both not quiet and curious.
Someone is both tall and not wise.
Someone is either kind or not humble.
Mary is either rich or not strong.
Susan is not old or tall.
Lucy is not curious or not funny.
Someone is curious or not tall.
Lucy is both not humble and quiet.
Someone is either not wise or quiet. | Mary is not brave. | entailment | (![X]:((funny(X)<~>~generous(X))=>(brave(X)&~patient(X))))&
(((~generous(paul)<~>wise(paul)))<=>(?[X]:((strong(X)&patient(X)))))&
(((creative(fred)<~>~happy(fred)))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~strong(X)&tall(X))))&
(![X]:((~tall(X)|strong(X))<=>humble(X)))&
(![X]:((~wise(X)<~>patient(X))<=>(~curious(X)|happy(X))))&
(![X]:(~quiet(X)<=>(~strong(X)<~>~wise(X))))&
(((~calm(mary)&old(mary)))<=>((creative(susan)&tall(susan))))&
((?[X]:(brave(X)))=>(?[X]:(happy(X))))&
(![X]:((~tall(X)|tall(X))=>(~rich(X)|~brave(X))))&
(![X]:((funny(X)&~patient(X))=>(~old(X)|~curious(X))))&
(((~patient(mary)|~curious(mary)))<=>((patient(lucy)<~>calm(lucy))))&
((?[X]:((~calm(X)&rich(X))))=>((old(john)&tall(john))))&
(((rich(susan)&~calm(susan)))<=>(~old(mary)))&
((?[X]:((happy(X)<~>~funny(X))))<=>(happy(paul)))&
((?[X]:((curious(X)|kind(X))))=>(?[X]:((~quiet(X)&curious(X)))))&
(?[X]:((tall(X)&~wise(X))))&
(?[X]:((kind(X)<~>~humble(X))))&
((rich(mary)<~>~strong(mary)))&
((~old(susan)|tall(susan)))&
((~curious(lucy)|~funny(lucy)))&
(?[X]:((curious(X)|~tall(X))))&
((~humble(lucy)&quiet(lucy)))&
(?[X]:((~wise(X)<~>quiet(X)))) | ~brave(mary) | [
"p3",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3860751324347210759854571
% SZS output start Proof for 3860751324347210759854571
4. ! [X0] : ((tall(X0) <~> brave(X0)) <=> (tall(X0) & ~strong(X0))) [input p3]
10. ! [X0] : ((tall(X0) | ~tall(X0)) => (~brave(X0) | ~rich(X0))) [input p9]
19. rich(mary) <~> ~strong(mary) [input p18]
25. brave(mary) [input hypothesis]
30. ! [X0] : ((~brave(X0) | ~rich(X0)) | (~tall(X0) & tall(X0))) [ennf transformation 10]
31. ! [X0] : (~brave(X0) | ~rich(X0) | (~tall(X0) & tall(X0))) [flattening 30]
45. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | (~tall(X0) | strong(X0))) & ((tall(X0) & ~strong(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 4]
46. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | ~tall(X0) | strong(X0)) & ((tall(X0) & ~strong(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [flattening 45]
73. (strong(mary) | ~rich(mary)) & (~strong(mary) | rich(mary)) [nnf transformation 19]
98. tall(X0) | tall(X0) | ~brave(X0) [cnf transformation 46]
100. ~brave(X0) | ~tall(X0) | ~tall(X0) | strong(X0) [cnf transformation 46]
120. ~brave(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 31]
145. ~strong(mary) | rich(mary) [cnf transformation 73]
154. brave(mary) [cnf transformation 25]
155. ~brave(X0) | tall(X0) [duplicate literal removal 98]
156. ~tall(X0) | ~brave(X0) | strong(X0) [duplicate literal removal 100]
235. ~rich(X0) | ~brave(X0) [subsumption resolution 120,155]
333. 37 <=> rich(mary) [avatar definition]
334. rich(mary) <- (37) [avatar component clause 333]
337. 38 <=> strong(mary) [avatar definition]
341. 37 | ~38 [avatar split clause 145,337,333]
380. tall(mary) [resolution 155,154]
493. ~brave(mary) | strong(mary) [resolution 156,380]
498. strong(mary) [subsumption resolution 493,154]
509. 38 [avatar split clause 498,337]
511. ~brave(mary) <- (37) [resolution 334,235]
515. $false <- (37) [subsumption resolution 511,154]
516. ~37 [avatar contradiction clause 515]
517. $false [avatar sat refutation 341,509,516]
% SZS output end Proof for 3860751324347210759854571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or quiet is not happy or not calm and vice versa.
If someone is humble then mary is not calm or humble.
Everyone who is humble is either not happy or brave and vice versa.
If someone is either tall or not happy then someone is not happy.
Everyone who is either not funny or not generous is both happy and not generous.
If someone is either creative or funny then alice is either not funny or not strong.
If lucy is curious then lucy is either not rich or humble and vice versa.
Everyone who is both not quiet and not patient is tall or not patient.
Everyone who is not generous or kind is not rich or not old.
If paul is either humble or not curious then paul is creative and vice versa.
Everyone who is both not generous and not happy is kind and vice versa.
Everyone who is both not curious and not creative is either not creative or generous.
Everyone who is strong is both not brave and tall.
Everyone who is both kind and brave is calm and vice versa.
Everyone who is either not brave or not curious is not wise and vice versa.
Everyone who is not calm or strong is not happy and vice versa.
Someone is not kind or generous.
Someone is not creative or wise.
Someone is not curious or not creative.
John is either not humble or humble.
Someone is quiet.
Someone is either not calm or not quiet.
Fred is not quiet or happy. | Mary is not happy. | entailment | (![X]:((~funny(X)<~>quiet(X))<=>(~happy(X)|~calm(X))))&
((?[X]:(humble(X)))=>((~calm(mary)|humble(mary))))&
(![X]:(humble(X)<=>(~happy(X)<~>brave(X))))&
((?[X]:((tall(X)<~>~happy(X))))=>(?[X]:(~happy(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(happy(X)&~generous(X))))&
((?[X]:((creative(X)<~>funny(X))))=>((~funny(alice)<~>~strong(alice))))&
((curious(lucy))<=>((~rich(lucy)<~>humble(lucy))))&
(![X]:((~quiet(X)&~patient(X))=>(tall(X)|~patient(X))))&
(![X]:((~generous(X)|kind(X))=>(~rich(X)|~old(X))))&
(((humble(paul)<~>~curious(paul)))<=>(creative(paul)))&
(![X]:((~generous(X)&~happy(X))<=>kind(X)))&
(![X]:((~curious(X)&~creative(X))=>(~creative(X)<~>generous(X))))&
(![X]:(strong(X)=>(~brave(X)&tall(X))))&
(![X]:((kind(X)&brave(X))<=>calm(X)))&
(![X]:((~brave(X)<~>~curious(X))<=>~wise(X)))&
(![X]:((~calm(X)|strong(X))<=>~happy(X)))&
(?[X]:((~kind(X)|generous(X))))&
(?[X]:((~creative(X)|wise(X))))&
(?[X]:((~curious(X)|~creative(X))))&
((~humble(john)<~>humble(john)))&
(?[X]:(quiet(X)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((~quiet(fred)|happy(fred))) | ~happy(mary) | [
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 327277824292292715094557
% SZS output start Proof for 327277824292292715094557
11. ! [X0] : ((~happy(X0) & ~generous(X0)) <=> kind(X0)) [input p10]
14. ! [X0] : ((brave(X0) & kind(X0)) <=> calm(X0)) [input p13]
16. ! [X0] : ((strong(X0) | ~calm(X0)) <=> ~happy(X0)) [input p15]
24. happy(mary) [input hypothesis]
50. ! [X0] : (((~happy(X0) & ~generous(X0)) | ~kind(X0)) & (kind(X0) | (happy(X0) | generous(X0)))) [nnf transformation 11]
51. ! [X0] : (((~happy(X0) & ~generous(X0)) | ~kind(X0)) & (kind(X0) | happy(X0) | generous(X0))) [flattening 50]
53. ! [X0] : (((brave(X0) & kind(X0)) | ~calm(X0)) & (calm(X0) | (~brave(X0) | ~kind(X0)))) [nnf transformation 14]
54. ! [X0] : (((brave(X0) & kind(X0)) | ~calm(X0)) & (calm(X0) | ~brave(X0) | ~kind(X0))) [flattening 53]
56. ! [X0] : (((strong(X0) | ~calm(X0)) | happy(X0)) & (~happy(X0) | (~strong(X0) & calm(X0)))) [nnf transformation 16]
57. ! [X0] : ((strong(X0) | ~calm(X0) | happy(X0)) & (~happy(X0) | (~strong(X0) & calm(X0)))) [flattening 56]
102. ~kind(X0) | ~happy(X0) [cnf transformation 51]
108. ~calm(X0) | kind(X0) [cnf transformation 54]
112. ~happy(X0) | calm(X0) [cnf transformation 57]
124. happy(mary) [cnf transformation 24]
131. 2 <=> calm(mary) [avatar definition]
132. calm(mary) <- (2) [avatar component clause 131]
243. calm(mary) [resolution 112,124]
246. 2 [avatar split clause 243,131]
248. kind(mary) <- (2) [resolution 132,108]
249. ~happy(mary) <- (2) [resolution 248,102]
251. $false <- (2) [subsumption resolution 249,124]
252. ~2 [avatar contradiction clause 251]
253. $false [avatar sat refutation 246,252]
% SZS output end Proof for 327277824292292715094557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and curious is not curious and vice versa.
Everyone who is not quiet is not kind or not curious.
Everyone who is happy is either curious or humble.
Everyone who is either curious or not happy is curious and vice versa.
If someone is both not kind and not curious then lucy is both not kind and not strong.
Everyone who is either generous or happy is humble or happy and vice versa.
If someone is both old and brave then alice is happy or not calm and vice versa.
Everyone who is not wise is either not funny or not quiet and vice versa.
Everyone who is either not strong or not wise is not kind.
If john is not happy then lucy is not old.
Everyone who is both generous and not creative is not wise and vice versa.
Everyone who is both not wise and not brave is either calm or not generous.
Everyone who is not brave is both humble and kind and vice versa.
If mary is both kind and strong then someone is both quiet and not quiet and vice versa.
Everyone who is both tall and calm is either not happy or not creative and vice versa.
Someone is both curious and not old.
Mary is not old.
Someone is brave.
Someone is old or funny.
Mary is tall.
Someone is not kind.
Fred is not quiet or not kind. | Mary is not kind. | entailment | (![X]:((~funny(X)&curious(X))<=>~curious(X)))&
(![X]:(~quiet(X)=>(~kind(X)|~curious(X))))&
(![X]:(happy(X)=>(curious(X)<~>humble(X))))&
(![X]:((curious(X)<~>~happy(X))<=>curious(X)))&
((?[X]:((~kind(X)&~curious(X))))=>((~kind(lucy)&~strong(lucy))))&
(![X]:((generous(X)<~>happy(X))<=>(humble(X)|happy(X))))&
((?[X]:((old(X)&brave(X))))<=>((happy(alice)|~calm(alice))))&
(![X]:(~wise(X)<=>(~funny(X)<~>~quiet(X))))&
(![X]:((~strong(X)<~>~wise(X))=>~kind(X)))&
((~happy(john))=>(~old(lucy)))&
(![X]:((generous(X)&~creative(X))<=>~wise(X)))&
(![X]:((~wise(X)&~brave(X))=>(calm(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>(humble(X)&kind(X))))&
(((kind(mary)&strong(mary)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((tall(X)&calm(X))<=>(~happy(X)<~>~creative(X))))&
(?[X]:((curious(X)&~old(X))))&
(~old(mary))&
(?[X]:(brave(X)))&
(?[X]:((old(X)|funny(X))))&
(tall(mary))&
(?[X]:(~kind(X)))&
((~quiet(fred)|~kind(fred))) | ~kind(mary) | [
"p0",
"p3",
"p5",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 51165137339712416116516
% SZS output start Proof for 51165137339712416116516
1. ! [X0] : ((curious(X0) & ~funny(X0)) <=> ~curious(X0)) [input p0]
4. ! [X0] : ((curious(X0) <~> ~happy(X0)) <=> curious(X0)) [input p3]
6. ! [X0] : ((generous(X0) <~> happy(X0)) <=> (happy(X0) | humble(X0))) [input p5]
9. ! [X0] : ((~strong(X0) <~> ~wise(X0)) => ~kind(X0)) [input p8]
11. ! [X0] : ((~creative(X0) & generous(X0)) <=> ~wise(X0)) [input p10]
14. (strong(mary) & kind(mary)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p13]
23. kind(mary) [input hypothesis]
28. ! [X0] : (~kind(X0) | (~strong(X0) <=> ~wise(X0))) [ennf transformation 9]
32. ! [X0] : (((curious(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) | funny(X0)))) [nnf transformation 1]
33. ! [X0] : (((curious(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | ~curious(X0) | funny(X0))) [flattening 32]
35. ! [X0] : ((((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | ~curious(X0)) & (curious(X0) | ((curious(X0) | happy(X0)) & (~happy(X0) | ~curious(X0))))) [nnf transformation 4]
36. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (~happy(X0) & ~humble(X0))) & ((happy(X0) | humble(X0)) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [nnf transformation 6]
37. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (~happy(X0) & ~humble(X0))) & (happy(X0) | humble(X0) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [flattening 36]
44. ! [X0] : (~kind(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) [nnf transformation 28]
45. ! [X0] : (((~creative(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | (creative(X0) | ~generous(X0)))) [nnf transformation 11]
46. ! [X0] : (((~creative(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | creative(X0) | ~generous(X0))) [flattening 45]
50. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X0] : (~quiet(X0) & quiet(X0)) | (~strong(mary) | ~kind(mary))) [nnf transformation 14]
51. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X0] : (~quiet(X0) & quiet(X0)) | ~strong(mary) | ~kind(mary)) [flattening 50]
52. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ~strong(mary) | ~kind(mary)) [rectify 51]
53. ? [X1] : (~quiet(X1) & quiet(X1)) => (~quiet(sK1) & quiet(sK1)) [choice axiom]
54. ((strong(mary) & kind(mary)) | ! [X0] : (quiet(X0) | ~quiet(X0))) & ((~quiet(sK1) & quiet(sK1)) | ~strong(mary) | ~kind(mary)) [skolemisation 52,53]
67. curious(X0) | curious(X0) [cnf transformation 33]
74. happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 35]
82. ~happy(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 37]
92. ~wise(X0) | ~kind(X0) | strong(X0) [cnf transformation 44]
96. generous(X0) | wise(X0) [cnf transformation 46]
103. quiet(sK1) | ~strong(mary) | ~kind(mary) [cnf transformation 54]
104. ~quiet(sK1) | ~strong(mary) | ~kind(mary) [cnf transformation 54]
121. kind(mary) [cnf transformation 23]
123. ~happy(X0) | ~generous(X0) [duplicate literal removal 82]
125. happy(X0) | ~curious(X0) [duplicate literal removal 74]
127. curious(X0) [duplicate literal removal 67]
131. happy(X0) [subsumption resolution 125,127]
132. ~generous(X0) [subsumption resolution 123,131]
153. wise(X0) [subsumption resolution 96,132]
155. 4 <=> kind(mary) [avatar definition]
156. kind(mary) <- (4) [avatar component clause 155]
159. 5 <=> strong(mary) [avatar definition]
161. ~strong(mary) <- (~5) [avatar component clause 159]
163. 6 <=> quiet(sK1) [avatar definition]
166. ~4 | ~5 | ~6 [avatar split clause 104,163,159,155]
167. ~4 | ~5 | 6 [avatar split clause 103,163,159,155]
172. 4 [avatar split clause 121,155]
178. ~kind(X0) | strong(X0) [resolution 92,153]
179. strong(mary) <- (4) [resolution 178,156]
180. $false <- (4, ~5) [subsumption resolution 179,161]
181. ~4 | 5 [avatar contradiction clause 180]
182. $false [avatar sat refutation 166,167,172,181]
% SZS output end Proof for 51165137339712416116516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or curious then someone is either old or humble and vice versa.
Everyone who is old is either kind or calm and vice versa.
Everyone who is not old or generous is either not generous or not strong.
If someone is not creative or not quiet then lucy is both not patient and not generous and vice versa.
Everyone who is not calm is not humble or old and vice versa.
Everyone who is both kind and creative is both not tall and not humble and vice versa.
If someone is either not tall or not patient then fred is kind or humble.
Everyone who is not strong or quiet is not calm and vice versa.
If someone is either calm or curious then someone is both generous and curious.
If john is generous or not creative then paul is both not kind and not calm.
If mary is both strong and not brave then alice is either not humble or rich and vice versa.
Everyone who is not generous is either patient or not generous and vice versa.
Everyone who is not quiet is not patient.
If someone is brave then susan is both not strong and not funny and vice versa.
If lucy is rich then someone is either not tall or not old.
Someone is either not calm or not creative.
Someone is not humble.
Someone is both not brave and generous.
Someone is not calm.
Alice is either not strong or funny. | Susan is not humble. | neutral | ((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
(![X]:(old(X)<=>(kind(X)<~>calm(X))))&
(![X]:((~old(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~creative(X)|~quiet(X))))<=>((~patient(lucy)&~generous(lucy))))&
(![X]:(~calm(X)<=>(~humble(X)|old(X))))&
(![X]:((kind(X)&creative(X))<=>(~tall(X)&~humble(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((kind(fred)|humble(fred))))&
(![X]:((~strong(X)|quiet(X))<=>~calm(X)))&
((?[X]:((calm(X)<~>curious(X))))=>(?[X]:((generous(X)&curious(X)))))&
(((generous(john)|~creative(john)))=>((~kind(paul)&~calm(paul))))&
(((strong(mary)&~brave(mary)))<=>((~humble(alice)<~>rich(alice))))&
(![X]:(~generous(X)<=>(patient(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>~patient(X)))&
((?[X]:(brave(X)))<=>((~strong(susan)&~funny(susan))))&
((rich(lucy))=>(?[X]:((~tall(X)<~>~old(X)))))&
(?[X]:((~calm(X)<~>~creative(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:(~calm(X)))&
((~strong(alice)<~>funny(alice))) | ~humble(susan) | [] | null | 0 |
Everyone who is strong is not funny or not rich and vice versa.
If someone is generous or not creative then someone is both happy and not happy.
If someone is not humble or not generous then someone is both curious and kind and vice versa.
If mary is either not curious or strong then paul is either happy or kind and vice versa.
Everyone who is both not strong and not tall is both not curious and quiet and vice versa.
Everyone who is not patient is not calm or not rich and vice versa.
Everyone who is both curious and not funny is both generous and humble and vice versa.
Everyone who is both strong and quiet is both not curious and not calm and vice versa.
If fred is curious then susan is not patient or humble and vice versa.
If lucy is kind or funny then someone is not funny or not wise and vice versa.
Everyone who is both not happy and patient is curious and vice versa.
If someone is not old then lucy is not curious.
If susan is not kind then someone is both not funny and tall and vice versa.
If someone is funny then paul is both not patient and not funny.
If john is not funny or wise then someone is both not strong and not curious.
Everyone who is either not old or not brave is either not humble or quiet and vice versa.
Mary is both curious and funny.
Someone is calm.
Someone is both not tall and calm.
Someone is either not happy or strong.
Someone is curious.
Someone is both happy and old.
Someone is not generous. | Mary is not patient. | contradiction | (![X]:(strong(X)<=>(~funny(X)|~rich(X))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((happy(X)&~happy(X)))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:((curious(X)&kind(X)))))&
(((~curious(mary)<~>strong(mary)))<=>((happy(paul)<~>kind(paul))))&
(![X]:((~strong(X)&~tall(X))<=>(~curious(X)&quiet(X))))&
(![X]:(~patient(X)<=>(~calm(X)|~rich(X))))&
(![X]:((curious(X)&~funny(X))<=>(generous(X)&humble(X))))&
(![X]:((strong(X)&quiet(X))<=>(~curious(X)&~calm(X))))&
((curious(fred))<=>((~patient(susan)|humble(susan))))&
(((kind(lucy)|funny(lucy)))<=>(?[X]:((~funny(X)|~wise(X)))))&
(![X]:((~happy(X)&patient(X))<=>curious(X)))&
((?[X]:(~old(X)))=>(~curious(lucy)))&
((~kind(susan))<=>(?[X]:((~funny(X)&tall(X)))))&
((?[X]:(funny(X)))=>((~patient(paul)&~funny(paul))))&
(((~funny(john)|wise(john)))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~old(X)<~>~brave(X))<=>(~humble(X)<~>quiet(X))))&
((curious(mary)&funny(mary)))&
(?[X]:(calm(X)))&
(?[X]:((~tall(X)&calm(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:(curious(X)))&
(?[X]:((happy(X)&old(X))))&
(?[X]:(~generous(X))) | ~patient(mary) | [
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1890559808437784167360942
% SZS output start Proof for 1890559808437784167360942
11. ! [X0] : ((patient(X0) & ~happy(X0)) <=> curious(X0)) [input p10]
17. funny(mary) & curious(mary) [input p16]
24. ~patient(mary) [input hypothesis]
58. ! [X0] : (((patient(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (~patient(X0) | happy(X0)))) [nnf transformation 11]
59. ! [X0] : (((patient(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | ~patient(X0) | happy(X0))) [flattening 58]
122. ~curious(X0) | patient(X0) [cnf transformation 59]
141. curious(mary) [cnf transformation 17]
152. ~patient(mary) [cnf transformation 24]
201. 12 <=> curious(mary) [avatar definition]
203. curious(mary) <- (12) [avatar component clause 201]
317. 12 [avatar split clause 141,201]
338. patient(mary) <- (12) [resolution 122,203]
342. $false <- (12) [subsumption resolution 338,152]
343. ~12 [avatar contradiction clause 342]
344. $false [avatar sat refutation 317,343]
% SZS output end Proof for 1890559808437784167360942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not tall is either not creative or humble and vice versa.
If someone is not funny or not curious then someone is either not curious or not strong and vice versa.
Everyone who is generous or not curious is not funny or brave.
If paul is not happy then someone is either not tall or not old and vice versa.
Everyone who is both not quiet and not kind is tall and vice versa.
Everyone who is either not curious or not tall is both not quiet and curious and vice versa.
If someone is either happy or not calm then someone is both not brave and tall and vice versa.
If alice is both not wise and brave then someone is not kind.
If paul is either not calm or not rich then someone is not rich or not old.
If mary is either not quiet or not strong then susan is both not happy and funny.
If paul is both not wise and not curious then someone is curious.
Everyone who is both kind and not kind is either not funny or brave.
Everyone who is either happy or not quiet is either wise or happy and vice versa.
If susan is both not humble and not rich then fred is not brave and vice versa.
If mary is not rich or not wise then someone is brave or happy.
Everyone who is either tall or humble is either strong or not creative and vice versa.
Someone is either not tall or tall.
Someone is not generous or not kind.
Fred is both not calm and not kind.
Someone is both not strong and not kind.
Paul is calm or not strong.
Paul is either strong or not happy.
Susan is not happy.
Someone is either not curious or wise. | Paul is curious. | contradiction | (![X]:((quiet(X)<~>~tall(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~funny(X)|~curious(X))))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
(![X]:((generous(X)|~curious(X))=>(~funny(X)|brave(X))))&
((~happy(paul))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(wise(X)<~>happy(X))))&
(((~humble(susan)&~rich(susan)))<=>(~brave(fred)))&
(((~rich(mary)|~wise(mary)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((tall(X)<~>humble(X))<=>(strong(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((~generous(X)|~kind(X))))&
((~calm(fred)&~kind(fred)))&
(?[X]:((~strong(X)&~kind(X))))&
((calm(paul)|~strong(paul)))&
((strong(paul)<~>~happy(paul)))&
(~happy(susan))&
(?[X]:((~curious(X)<~>wise(X)))) | curious(paul) | [
"p0",
"p4",
"p5",
"p6",
"p15",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 612049022052397574341486
% SZS output start Proof for 612049022052397574341486
1. ! [X0] : ((quiet(X0) <~> ~tall(X0)) <=> (~creative(X0) <~> humble(X0))) [input p0]
5. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> tall(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~tall(X0)) <=> (curious(X0) & ~quiet(X0))) [input p5]
7. ? [X0] : (happy(X0) <~> ~calm(X0)) <=> ? [X0] : (tall(X0) & ~brave(X0)) [input p6]
16. ! [X0] : ((tall(X0) <~> humble(X0)) <=> (strong(X0) <~> ~creative(X0))) [input p15]
21. ~strong(paul) | calm(paul) [input p20]
22. strong(paul) <~> ~happy(paul) [input p21]
25. curious(paul) [input hypothesis]
27. ? [X0] : (happy(X0) <~> ~calm(X0)) <=> ? [X1] : (tall(X1) & ~brave(X1)) [rectify 7]
41. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [nnf transformation 1]
51. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | (kind(X0) | quiet(X0)))) [nnf transformation 5]
52. ! [X0] : (((~kind(X0) & ~quiet(X0)) | ~tall(X0)) & (tall(X0) | kind(X0) | quiet(X0))) [flattening 51]
53. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [nnf transformation 6]
54. ! [X0] : ((((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0))))) [flattening 53]
55. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ! [X1] : (~tall(X1) | brave(X1))) & (? [X1] : (tall(X1) & ~brave(X1)) | ! [X0] : ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 27]
56. (? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ! [X1] : (~tall(X1) | brave(X1))) & (? [X2] : (tall(X2) & ~brave(X2)) | ! [X3] : ((happy(X3) | calm(X3)) & (~calm(X3) | ~happy(X3)))) [rectify 55]
57. ? [X0] : ((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) => ((calm(sK3) | ~happy(sK3)) & (~calm(sK3) | happy(sK3))) [choice axiom]
58. ? [X2] : (tall(X2) & ~brave(X2)) => (tall(sK4) & ~brave(sK4)) [choice axiom]
59. (((calm(sK3) | ~happy(sK3)) & (~calm(sK3) | happy(sK3))) | ! [X1] : (~tall(X1) | brave(X1))) & ((tall(sK4) & ~brave(sK4)) | ! [X3] : ((happy(X3) | calm(X3)) & (~calm(X3) | ~happy(X3)))) [skolemisation 56,58,57]
74. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0)))) & (((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 16]
80. (happy(paul) | ~strong(paul)) & (~happy(paul) | strong(paul)) [nnf transformation 22]
85. ~creative(X0) | humble(X0) | quiet(X0) | tall(X0) [cnf transformation 41]
87. ~humble(X0) | creative(X0) | quiet(X0) | tall(X0) [cnf transformation 41]
104. ~tall(X0) | ~quiet(X0) [cnf transformation 52]
107. ~quiet(X0) | ~curious(X0) | tall(X0) [cnf transformation 54]
108. curious(X0) | ~tall(X0) | curious(X0) [cnf transformation 54]
110. ~tall(X0) | ~curious(X0) | ~curious(X0) | quiet(X0) [cnf transformation 54]
114. tall(sK4) | ~calm(X3) | ~happy(X3) [cnf transformation 59]
142. ~creative(X0) | strong(X0) | tall(X0) | ~humble(X0) [cnf transformation 74]
146. humble(X0) | tall(X0) | strong(X0) | creative(X0) [cnf transformation 74]
155. ~strong(paul) | calm(paul) [cnf transformation 21]
157. happy(paul) | ~strong(paul) [cnf transformation 80]
161. curious(paul) [cnf transformation 25]
166. curious(X0) | ~tall(X0) [duplicate literal removal 108]
167. ~tall(X0) | ~curious(X0) | quiet(X0) [duplicate literal removal 110]
206. 10 <=> happy(paul) [avatar definition]
224. ~curious(X0) | ~tall(X0) [subsumption resolution 167,104]
225. ~tall(X0) [subsumption resolution 166,224]
226. ~curious(X0) | ~quiet(X0) [subsumption resolution 107,225]
228. ~calm(X3) | ~happy(X3) [subsumption resolution 114,225]
247. 18 <=> calm(paul) [avatar definition]
248. calm(paul) <- (18) [avatar component clause 247]
285. 26 <=> curious(paul) [avatar definition]
287. curious(paul) <- (26) [avatar component clause 285]
328. strong(X0) | humble(X0) | creative(X0) [subsumption resolution 146,225]
331. ~humble(X0) | strong(X0) | ~creative(X0) [subsumption resolution 142,225]
333. 35 <=> strong(paul) [avatar definition]
335. ~strong(paul) <- (~35) [avatar component clause 333]
336. 18 | ~35 [avatar split clause 155,333,247]
337. ~35 | 10 [avatar split clause 157,206,333]
350. 26 [avatar split clause 161,285]
356. ~quiet(paul) <- (26) [resolution 226,287]
370. humble(paul) | creative(paul) <- (~35) [resolution 328,335]
375. 38 <=> creative(paul) [avatar definition]
376. ~creative(paul) <- (~38) [avatar component clause 375]
377. creative(paul) <- (38) [avatar component clause 375]
379. 39 <=> humble(paul) [avatar definition]
381. humble(paul) <- (39) [avatar component clause 379]
382. 38 | 39 | 35 [avatar split clause 370,333,379,375]
412. ~happy(paul) <- (18) [resolution 248,228]
415. ~10 | ~18 [avatar split clause 412,247,206]
434. humble(paul) | quiet(paul) | tall(paul) <- (38) [resolution 85,377]
435. humble(paul) | tall(paul) <- (26, 38) [subsumption resolution 434,356]
436. humble(paul) <- (26, 38) [subsumption resolution 435,225]
437. 39 | ~26 | ~38 [avatar split clause 436,375,285,379]
438. strong(paul) | ~creative(paul) <- (39) [resolution 381,331]
439. ~creative(paul) <- (~35, 39) [subsumption resolution 438,335]
442. ~38 | 35 | ~39 [avatar split clause 439,379,333,375]
444. creative(paul) | quiet(paul) | tall(paul) <- (39) [resolution 87,381]
445. quiet(paul) | tall(paul) <- (~38, 39) [subsumption resolution 444,376]
446. tall(paul) <- (26, ~38, 39) [subsumption resolution 445,356]
447. $false <- (26, ~38, 39) [subsumption resolution 446,225]
448. ~26 | 38 | ~39 [avatar contradiction clause 447]
449. $false [avatar sat refutation 336,337,350,382,415,437,442,448]
% SZS output end Proof for 612049022052397574341486
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or old then john is either brave or calm and vice versa.
Everyone who is not humble is humble.
If lucy is both curious and tall then someone is strong or not patient and vice versa.
Everyone who is happy is both rich and not kind and vice versa.
Everyone who is not strong or not happy is not funny or calm and vice versa.
If fred is rich or wise then mary is both not tall and not calm and vice versa.
Everyone who is not generous is calm or brave and vice versa.
If fred is not creative then lucy is quiet and vice versa.
Everyone who is either not quiet or not calm is tall or not patient and vice versa.
If someone is both brave and not tall then someone is both curious and strong and vice versa.
If mary is either happy or not kind then lucy is either funny or brave and vice versa.
If someone is kind or not generous then someone is quiet.
If fred is both not funny and tall then lucy is funny.
If lucy is curious then someone is both not quiet and kind.
If someone is creative or kind then someone is not humble and vice versa.
Everyone who is calm or not happy is either not humble or not old.
Someone is either old or not brave.
Someone is not curious or not strong.
Mary is not old.
John is either patient or quiet.
Mary is either rich or not wise.
Mary is not curious.
Someone is either rich or calm.
John is not tall or not strong. | Mary is not strong. | entailment | ((?[X]:((kind(X)<~>old(X))))<=>((brave(john)<~>calm(john))))&
(![X]:(~humble(X)=>humble(X)))&
(((curious(lucy)&tall(lucy)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:(happy(X)<=>(rich(X)&~kind(X))))&
(![X]:((~strong(X)|~happy(X))<=>(~funny(X)|calm(X))))&
(((rich(fred)|wise(fred)))<=>((~tall(mary)&~calm(mary))))&
(![X]:(~generous(X)<=>(calm(X)|brave(X))))&
((~creative(fred))<=>(quiet(lucy)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~patient(X))))&
((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(((happy(mary)<~>~kind(mary)))<=>((funny(lucy)<~>brave(lucy))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(quiet(X))))&
(((~funny(fred)&tall(fred)))=>(funny(lucy)))&
((curious(lucy))=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)|~happy(X))=>(~humble(X)<~>~old(X))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(~old(mary))&
((patient(john)<~>quiet(john)))&
((rich(mary)<~>~wise(mary)))&
(~curious(mary))&
(?[X]:((rich(X)<~>calm(X))))&
((~tall(john)|~strong(john))) | ~strong(mary) | [
"p1",
"p2",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3194860067226446191306370
% SZS output start Proof for 3194860067226446191306370
2. ! [X0] : (~humble(X0) => humble(X0)) [input p1]
3. (tall(lucy) & curious(lucy)) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p2]
14. curious(lucy) => ? [X0] : (kind(X0) & ~quiet(X0)) [input p13]
15. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X0] : ~humble(X0) [input p14]
25. strong(mary) [input hypothesis]
28. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X1] : ~humble(X1) [rectify 15]
30. ! [X0] : (humble(X0) | humble(X0)) [ennf transformation 2]
35. ? [X0] : (kind(X0) & ~quiet(X0)) | ~curious(lucy) [ennf transformation 14]
41. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | (~tall(lucy) | ~curious(lucy))) [nnf transformation 3]
42. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | ~tall(lucy) | ~curious(lucy)) [flattening 41]
43. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | ~tall(lucy) | ~curious(lucy)) [rectify 42]
44. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK1) | strong(sK1)) [choice axiom]
45. ((tall(lucy) & curious(lucy)) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK1) | strong(sK1)) | ~tall(lucy) | ~curious(lucy)) [skolemisation 43,44]
64. ? [X0] : (kind(X0) & ~quiet(X0)) => (kind(sK5) & ~quiet(sK5)) [choice axiom]
65. (kind(sK5) & ~quiet(sK5)) | ~curious(lucy) [skolemisation 35,64]
66. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X1] : ~humble(X1) | ! [X0] : (~kind(X0) & ~creative(X0))) [nnf transformation 28]
67. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X2] : ~humble(X2) | ! [X3] : (~kind(X3) & ~creative(X3))) [rectify 66]
68. ? [X0] : (kind(X0) | creative(X0)) => (kind(sK6) | creative(sK6)) [choice axiom]
69. ? [X2] : ~humble(X2) => ~humble(sK7) [choice axiom]
70. ((kind(sK6) | creative(sK6)) | ! [X1] : humble(X1)) & (~humble(sK7) | ! [X3] : (~kind(X3) & ~creative(X3))) [skolemisation 67,69,68]
90. humble(X0) | humble(X0) [cnf transformation 30]
92. curious(lucy) | ~strong(X0) [cnf transformation 45]
134. kind(sK5) | ~curious(lucy) [cnf transformation 65]
136. ~humble(sK7) | ~kind(X3) [cnf transformation 70]
154. strong(mary) [cnf transformation 25]
155. humble(X0) [duplicate literal removal 90]
195. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
196. ~strong(X0) <- (9) [avatar component clause 195]
199. 10 <=> curious(lucy) [avatar definition]
203. 9 | 10 [avatar split clause 92,199,195]
305. 31 <=> ! [X1] : ~kind(X1) [avatar definition]
306. ~kind(X1) <- (31) [avatar component clause 305]
318. 34 <=> kind(sK5) [avatar definition]
320. kind(sK5) <- (34) [avatar component clause 318]
321. ~10 | 34 [avatar split clause 134,318,199]
327. ~kind(X3) [subsumption resolution 136,155]
328. 31 [avatar split clause 327,305]
392. $false <- (9) [resolution 196,154]
393. ~9 [avatar contradiction clause 392]
394. $false <- (31, 34) [subsumption resolution 320,306]
395. ~31 | ~34 [avatar contradiction clause 394]
398. $false [avatar sat refutation 203,321,328,393,395]
% SZS output end Proof for 3194860067226446191306370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not calm then someone is not rich and vice versa.
Everyone who is not brave or not old is not curious or rich.
Everyone who is tall is both curious and tall and vice versa.
Everyone who is either curious or not rich is either not creative or wise and vice versa.
Everyone who is both funny and not patient is either not tall or not rich.
If john is either not kind or not brave then lucy is either calm or not creative.
Everyone who is not strong or not creative is either not kind or brave.
If john is either strong or not generous then lucy is tall or wise.
Everyone who is not creative or not funny is both calm and creative.
Everyone who is not kind is generous or not rich and vice versa.
Everyone who is patient or brave is not generous.
Everyone who is either funny or brave is both humble and old and vice versa.
Everyone who is either not brave or not tall is calm or tall and vice versa.
Everyone who is either not rich or curious is either not strong or humble and vice versa.
If mary is not tall then someone is patient or not curious and vice versa.
Everyone who is not funny is both creative and not brave and vice versa.
Fred is either not wise or curious.
Someone is not strong.
Lucy is either funny or creative.
Someone is not old or not creative.
Someone is not kind.
John is both humble and not strong.
Paul is quiet.
Someone is rich or not quiet. | Lucy is generous. | neutral | (((~rich(paul)&~calm(paul)))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)|~old(X))=>(~curious(X)|rich(X))))&
(![X]:(tall(X)<=>(curious(X)&tall(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((funny(X)&~patient(X))=>(~tall(X)<~>~rich(X))))&
(((~kind(john)<~>~brave(john)))=>((calm(lucy)<~>~creative(lucy))))&
(![X]:((~strong(X)|~creative(X))=>(~kind(X)<~>brave(X))))&
(((strong(john)<~>~generous(john)))=>((tall(lucy)|wise(lucy))))&
(![X]:((~creative(X)|~funny(X))=>(calm(X)&creative(X))))&
(![X]:(~kind(X)<=>(generous(X)|~rich(X))))&
(![X]:((patient(X)|brave(X))=>~generous(X)))&
(![X]:((funny(X)<~>brave(X))<=>(humble(X)&old(X))))&
(![X]:((~brave(X)<~>~tall(X))<=>(calm(X)|tall(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~strong(X)<~>humble(X))))&
((~tall(mary))<=>(?[X]:((patient(X)|~curious(X)))))&
(![X]:(~funny(X)<=>(creative(X)&~brave(X))))&
((~wise(fred)<~>curious(fred)))&
(?[X]:(~strong(X)))&
((funny(lucy)<~>creative(lucy)))&
(?[X]:((~old(X)|~creative(X))))&
(?[X]:(~kind(X)))&
((humble(john)&~strong(john)))&
(quiet(paul))&
(?[X]:((rich(X)|~quiet(X)))) | generous(lucy) | [] | null | 0 |
If someone is both not patient and rich then mary is both funny and not humble.
Everyone who is either kind or calm is creative.
Everyone who is not old or wise is both calm and not wise.
If paul is strong then someone is not curious and vice versa.
Everyone who is both not happy and not funny is creative or not brave and vice versa.
Everyone who is creative or not tall is either happy or not curious and vice versa.
Everyone who is funny is wise or not generous.
Everyone who is not brave is humble and vice versa.
If someone is curious then someone is not humble or not calm and vice versa.
Everyone who is calm or not old is kind or brave.
Everyone who is both not strong and brave is either not creative or not patient and vice versa.
If someone is creative or curious then alice is both quiet and not strong and vice versa.
Everyone who is both not calm and happy is old or not patient and vice versa.
Everyone who is either humble or not quiet is patient and vice versa.
If someone is tall then someone is not rich or rich and vice versa.
If mary is either old or curious then someone is kind or not old.
Lucy is either not rich or creative.
Mary is not patient or not humble.
Lucy is funny.
Someone is not quiet or not generous.
Someone is not generous.
Paul is calm.
Someone is creative. | Mary is not happy. | neutral | ((?[X]:((~patient(X)&rich(X))))=>((funny(mary)&~humble(mary))))&
(![X]:((kind(X)<~>calm(X))=>creative(X)))&
(![X]:((~old(X)|wise(X))=>(calm(X)&~wise(X))))&
((strong(paul))<=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)&~funny(X))<=>(creative(X)|~brave(X))))&
(![X]:((creative(X)|~tall(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(funny(X)=>(wise(X)|~generous(X))))&
(![X]:(~brave(X)<=>humble(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((calm(X)|~old(X))=>(kind(X)|brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(~creative(X)<~>~patient(X))))&
((?[X]:((creative(X)|curious(X))))<=>((quiet(alice)&~strong(alice))))&
(![X]:((~calm(X)&happy(X))<=>(old(X)|~patient(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|rich(X)))))&
(((old(mary)<~>curious(mary)))=>(?[X]:((kind(X)|~old(X)))))&
((~rich(lucy)<~>creative(lucy)))&
((~patient(mary)|~humble(mary)))&
(funny(lucy))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:(~generous(X)))&
(calm(paul))&
(?[X]:(creative(X))) | ~happy(mary) | [] | null | 0 |
If someone is either quiet or not curious then lucy is not happy or funny. If someone is both not patient and creative then paul is either creative or not quiet. If someone is both not tall and calm then john is either not quiet or not humble and vice versa. If someone is both not tall and humble then someone is either generous or creative. If alice is not calm then john is either humble or not kind. If susan is curious or patient then susan is both not humble and not rich. If mary is both kind and not humble then someone is happy or not generous and vice versa. If lucy is not wise or not brave then someone is either not tall or tall and vice versa. Everyone who is humble is either humble or tall and vice versa. Everyone who is funny or not generous is not strong or not calm. Everyone who is old is both strong and not wise and vice versa. Everyone who is both not wise and quiet is both strong and not funny and vice versa. Everyone who is not funny is both humble and quiet and vice versa. Everyone who is curious or creative is patient or happy. Everyone who is either not brave or tall is either old or not funny and vice versa. If lucy is not brave then someone is both not curious and happy. Mary is curious. Alice is both creative and not strong. Someone is rich. Someone is either happy or creative. Someone is calm or not funny. Susan is both not kind and quiet. Someone is both not kind and not creative. Fred is either wise or not humble. | Lucy is tall. | contradiction | ((?[X]:((quiet(X)<~>~curious(X))))=>((~happy(lucy)|funny(lucy))))&
((?[X]:((~patient(X)&creative(X))))=>((creative(paul)<~>~quiet(paul))))&
((?[X]:((~tall(X)&calm(X))))<=>((~quiet(john)<~>~humble(john))))&
((?[X]:((~tall(X)&humble(X))))=>(?[X]:((generous(X)<~>creative(X)))))&
((~calm(alice))=>((humble(john)<~>~kind(john))))&
(((curious(susan)|patient(susan)))=>((~humble(susan)&~rich(susan))))&
(((kind(mary)&~humble(mary)))<=>(?[X]:((happy(X)|~generous(X)))))&
(((~wise(lucy)|~brave(lucy)))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:(humble(X)<=>(humble(X)<~>tall(X))))&
(![X]:((funny(X)|~generous(X))=>(~strong(X)|~calm(X))))&
(![X]:(old(X)<=>(strong(X)&~wise(X))))&
(![X]:((~wise(X)&quiet(X))<=>(strong(X)&~funny(X))))&
(![X]:(~funny(X)<=>(humble(X)&quiet(X))))&
(![X]:((curious(X)|creative(X))=>(patient(X)|happy(X))))&
(![X]:((~brave(X)<~>tall(X))<=>(old(X)<~>~funny(X))))&
((~brave(lucy))=>(?[X]:((~curious(X)&happy(X)))))&
(curious(mary))&
((creative(alice)&~strong(alice)))&
(?[X]:(rich(X)))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:((calm(X)|~funny(X))))&
((~kind(susan)&quiet(susan)))&
(?[X]:((~kind(X)&~creative(X))))&
((wise(fred)<~>~humble(fred))) | tall(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2494033495867587066518612
% SZS output start Proof for 2494033495867587066518612
9. ! [X0] : (humble(X0) <=> (humble(X0) <~> tall(X0))) [input p8]
25. tall(lucy) [input hypothesis]
59. ! [X0] : ((humble(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 9]
109. ~tall(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 59]
111. humble(X0) | humble(X0) | ~tall(X0) [cnf transformation 59]
149. tall(lucy) [cnf transformation 25]
150. ~tall(X0) | ~humble(X0) [duplicate literal removal 109]
151. humble(X0) | ~tall(X0) [duplicate literal removal 111]
279. 28 <=> ! [X0] : ~tall(X0) [avatar definition]
280. ~tall(X0) <- (28) [avatar component clause 279]
294. ~tall(X0) [subsumption resolution 150,151]
295. 28 [avatar split clause 294,279]
336. $false <- (28) [resolution 280,149]
337. ~28 [avatar contradiction clause 336]
338. $false [avatar sat refutation 295,337]
% SZS output end Proof for 2494033495867587066518612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not quiet is not happy.
Everyone who is either wise or humble is both not rich and tall and vice versa.
Everyone who is either humble or not strong is both not tall and happy.
If someone is not tall then paul is not brave.
Everyone who is not rich is either not tall or strong and vice versa.
If someone is either strong or not old then someone is either not kind or calm.
Everyone who is tall is both not tall and humble.
If lucy is not humble or not rich then paul is not kind or wise.
Everyone who is not happy or creative is either not creative or tall.
If mary is not wise or happy then alice is both not happy and not generous.
If john is wise then lucy is either strong or not strong.
Everyone who is either calm or not old is not tall.
Everyone who is happy is both curious and not quiet.
If someone is both not strong and not curious then alice is both not kind and not curious and vice versa.
Everyone who is either wise or not quiet is either patient or funny.
Everyone who is either quiet or not tall is calm.
Someone is both quiet and generous.
John is both quiet and not old.
Someone is not kind.
Someone is either humble or not creative.
Paul is either not happy or old.
Someone is both not generous and not strong.
Someone is either not brave or curious. | Lucy is curious. | neutral | (![X]:((curious(X)&~quiet(X))=>~happy(X)))&
(![X]:((wise(X)<~>humble(X))<=>(~rich(X)&tall(X))))&
(![X]:((humble(X)<~>~strong(X))=>(~tall(X)&happy(X))))&
((?[X]:(~tall(X)))=>(~brave(paul)))&
(![X]:(~rich(X)<=>(~tall(X)<~>strong(X))))&
((?[X]:((strong(X)<~>~old(X))))=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:(tall(X)=>(~tall(X)&humble(X))))&
(((~humble(lucy)|~rich(lucy)))=>((~kind(paul)|wise(paul))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)<~>tall(X))))&
(((~wise(mary)|happy(mary)))=>((~happy(alice)&~generous(alice))))&
((wise(john))=>((strong(lucy)<~>~strong(lucy))))&
(![X]:((calm(X)<~>~old(X))=>~tall(X)))&
(![X]:(happy(X)=>(curious(X)&~quiet(X))))&
((?[X]:((~strong(X)&~curious(X))))<=>((~kind(alice)&~curious(alice))))&
(![X]:((wise(X)<~>~quiet(X))=>(patient(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~tall(X))=>calm(X)))&
(?[X]:((quiet(X)&generous(X))))&
((quiet(john)&~old(john)))&
(?[X]:(~kind(X)))&
(?[X]:((humble(X)<~>~creative(X))))&
((~happy(paul)<~>old(paul)))&
(?[X]:((~generous(X)&~strong(X))))&
(?[X]:((~brave(X)<~>curious(X)))) | curious(lucy) | [] | null | 0 |
Everyone who is either not brave or calm is both old and curious and vice versa. If someone is both creative and not funny then alice is both quiet and not funny. If fred is not brave or not rich then someone is both not rich and not generous and vice versa. Everyone who is old is tall or not rich and vice versa. If john is happy or rich then fred is either funny or quiet. If lucy is not kind then someone is strong or generous and vice versa. If someone is not generous then fred is both not funny and wise. If john is not quiet or not generous then lucy is either not strong or not brave. If fred is calm or strong then lucy is not old or not calm and vice versa. Everyone who is both not old and tall is not funny. Everyone who is not creative or not rich is either not generous or happy. Everyone who is not funny or not rich is calm or strong and vice versa. Everyone who is either not happy or not patient is either not quiet or strong and vice versa. Everyone who is not wise is either not tall or not kind. Everyone who is not curious is happy or not creative. Everyone who is either rich or not calm is both not calm and not patient and vice versa. Susan is not happy or not tall. Lucy is curious or not strong. Mary is quiet. Someone is wise or old. Someone is either rich or not creative. Mary is both not kind and not humble. Lucy is not patient. Someone is both old and not tall. | John is generous. | neutral | (![X]:((~brave(X)<~>calm(X))<=>(old(X)&curious(X))))&
((?[X]:((creative(X)&~funny(X))))=>((quiet(alice)&~funny(alice))))&
(((~brave(fred)|~rich(fred)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:(old(X)<=>(tall(X)|~rich(X))))&
(((happy(john)|rich(john)))=>((funny(fred)<~>quiet(fred))))&
((~kind(lucy))<=>(?[X]:((strong(X)|generous(X)))))&
((?[X]:(~generous(X)))=>((~funny(fred)&wise(fred))))&
(((~quiet(john)|~generous(john)))=>((~strong(lucy)<~>~brave(lucy))))&
(((calm(fred)|strong(fred)))<=>((~old(lucy)|~calm(lucy))))&
(![X]:((~old(X)&tall(X))=>~funny(X)))&
(![X]:((~creative(X)|~rich(X))=>(~generous(X)<~>happy(X))))&
(![X]:((~funny(X)|~rich(X))<=>(calm(X)|strong(X))))&
(![X]:((~happy(X)<~>~patient(X))<=>(~quiet(X)<~>strong(X))))&
(![X]:(~wise(X)=>(~tall(X)<~>~kind(X))))&
(![X]:(~curious(X)=>(happy(X)|~creative(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~calm(X)&~patient(X))))&
((~happy(susan)|~tall(susan)))&
((curious(lucy)|~strong(lucy)))&
(quiet(mary))&
(?[X]:((wise(X)|old(X))))&
(?[X]:((rich(X)<~>~creative(X))))&
((~kind(mary)&~humble(mary)))&
(~patient(lucy))&
(?[X]:((old(X)&~tall(X)))) | generous(john) | [] | null | 0 |
If someone is not brave or not creative then someone is creative.
Everyone who is not tall or not calm is both rich and not humble and vice versa.
Everyone who is both generous and not wise is calm or not brave and vice versa.
If john is not wise or rich then someone is kind or not strong and vice versa.
If someone is either tall or calm then someone is humble or not rich.
Everyone who is humble is both curious and quiet and vice versa.
Everyone who is either not generous or not old is generous and vice versa.
Everyone who is both humble and not old is not curious.
Everyone who is both patient and generous is both not generous and not curious.
If someone is both rich and old then someone is not calm or patient.
If mary is rich then someone is funny or not calm.
If fred is brave then fred is both not patient and humble.
Everyone who is either not strong or quiet is both generous and not strong and vice versa.
If fred is both not generous and tall then someone is wise and vice versa.
If fred is either wise or not happy then alice is not wise or not patient and vice versa.
If someone is either generous or not quiet then someone is both curious and not curious.
Alice is not tall or generous.
John is either patient or creative.
Someone is both not quiet and generous.
Alice is either humble or quiet.
Someone is both strong and not curious.
Someone is either not kind or generous.
Someone is both not old and not wise.
Someone is not rich. | Alice is not curious. | entailment | ((?[X]:((~brave(X)|~creative(X))))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)|~calm(X))<=>(rich(X)&~humble(X))))&
(![X]:((generous(X)&~wise(X))<=>(calm(X)|~brave(X))))&
(((~wise(john)|rich(john)))<=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((tall(X)<~>calm(X))))=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:(humble(X)<=>(curious(X)&quiet(X))))&
(![X]:((~generous(X)<~>~old(X))<=>generous(X)))&
(![X]:((humble(X)&~old(X))=>~curious(X)))&
(![X]:((patient(X)&generous(X))=>(~generous(X)&~curious(X))))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((~calm(X)|patient(X)))))&
((rich(mary))=>(?[X]:((funny(X)|~calm(X)))))&
((brave(fred))=>((~patient(fred)&humble(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(generous(X)&~strong(X))))&
(((~generous(fred)&tall(fred)))<=>(?[X]:(wise(X))))&
(((wise(fred)<~>~happy(fred)))<=>((~wise(alice)|~patient(alice))))&
((?[X]:((generous(X)<~>~quiet(X))))=>(?[X]:((curious(X)&~curious(X)))))&
((~tall(alice)|generous(alice)))&
((patient(john)<~>creative(john)))&
(?[X]:((~quiet(X)&generous(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((~kind(X)<~>generous(X))))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:(~rich(X))) | ~curious(alice) | [
"p5",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7722075429161404060710799
% SZS output start Proof for 7722075429161404060710799
6. ! [X0] : (humble(X0) <=> (quiet(X0) & curious(X0))) [input p5]
7. ! [X0] : ((~generous(X0) <~> ~old(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : ((~old(X0) & humble(X0)) => ~curious(X0)) [input p7]
20. humble(alice) <~> quiet(alice) [input p19]
25. curious(alice) [input hypothesis]
33. ! [X0] : (~curious(X0) | (old(X0) | ~humble(X0))) [ennf transformation 8]
34. ! [X0] : (~curious(X0) | old(X0) | ~humble(X0)) [flattening 33]
56. ! [X0] : ((humble(X0) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | ~humble(X0))) [nnf transformation 6]
57. ! [X0] : ((humble(X0) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | ~humble(X0))) [flattening 56]
58. ! [X0] : ((((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ~generous(X0)) & (generous(X0) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0))))) [nnf transformation 7]
78. (~quiet(alice) | ~humble(alice)) & (quiet(alice) | humble(alice)) [nnf transformation 20]
106. ~humble(X0) | curious(X0) [cnf transformation 57]
108. ~quiet(X0) | humble(X0) | ~curious(X0) [cnf transformation 57]
109. generous(X0) | ~old(X0) | generous(X0) [cnf transformation 58]
111. ~old(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 58]
113. ~curious(X0) | old(X0) | ~humble(X0) [cnf transformation 34]
143. quiet(alice) | humble(alice) [cnf transformation 78]
152. curious(alice) [cnf transformation 25]
156. generous(X0) | ~old(X0) [duplicate literal removal 109]
157. ~old(X0) | ~generous(X0) [duplicate literal removal 111]
212. ~old(X0) [subsumption resolution 156,157]
213. ~curious(X0) | ~humble(X0) [subsumption resolution 113,212]
214. ~humble(X0) [subsumption resolution 213,106]
289. quiet(alice) [subsumption resolution 143,214]
316. humble(alice) | ~curious(alice) [resolution 108,289]
318. ~curious(alice) [subsumption resolution 316,214]
319. $false [subsumption resolution 318,152]
% SZS output end Proof for 7722075429161404060710799
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not wise is not quiet.
Everyone who is quiet is rich and vice versa.
Everyone who is either not humble or humble is both wise and not quiet and vice versa.
If paul is both kind and patient then someone is curious or not quiet.
Everyone who is not humble is not funny or not brave and vice versa.
If alice is either patient or calm then someone is not funny or old and vice versa.
If paul is either not tall or not patient then someone is either kind or brave.
Everyone who is rich is both not old and not quiet and vice versa.
Everyone who is kind is not calm or not rich.
If paul is old then john is tall and vice versa.
Everyone who is humble is both rich and not happy.
If someone is either calm or kind then someone is not quiet or not happy and vice versa.
If fred is either tall or not kind then someone is both not quiet and not creative.
Everyone who is not tall or kind is not generous and vice versa.
If someone is not creative then someone is wise and vice versa.
Everyone who is both not creative and creative is rich.
Someone is brave.
Lucy is either happy or creative.
Someone is both not strong and curious.
Alice is kind or strong.
Someone is not brave.
Someone is both kind and strong. | John is old. | entailment | (![X]:((kind(X)|~wise(X))=>~quiet(X)))&
(![X]:(quiet(X)<=>rich(X)))&
(![X]:((~humble(X)<~>humble(X))<=>(wise(X)&~quiet(X))))&
(((kind(paul)&patient(paul)))=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:(~humble(X)<=>(~funny(X)|~brave(X))))&
(((patient(alice)<~>calm(alice)))<=>(?[X]:((~funny(X)|old(X)))))&
(((~tall(paul)<~>~patient(paul)))=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:(rich(X)<=>(~old(X)&~quiet(X))))&
(![X]:(kind(X)=>(~calm(X)|~rich(X))))&
((old(paul))<=>(tall(john)))&
(![X]:(humble(X)=>(rich(X)&~happy(X))))&
((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:((~quiet(X)|~happy(X)))))&
(((tall(fred)<~>~kind(fred)))=>(?[X]:((~quiet(X)&~creative(X)))))&
(![X]:((~tall(X)|kind(X))<=>~generous(X)))&
((?[X]:(~creative(X)))<=>(?[X]:(wise(X))))&
(![X]:((~creative(X)&creative(X))=>rich(X)))&
(?[X]:(brave(X)))&
((happy(lucy)<~>creative(lucy)))&
(?[X]:((~strong(X)&curious(X))))&
((kind(alice)|strong(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((kind(X)&strong(X)))) | old(john) | [
"p1",
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6108514742394308326992535
% SZS output start Proof for 6108514742394308326992535
2. ! [X0] : (quiet(X0) <=> rich(X0)) [input p1]
3. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p2]
8. ! [X0] : (rich(X0) <=> (~quiet(X0) & ~old(X0))) [input p7]
23. ~old(john) [input hypothesis]
36. ! [X0] : ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))) [nnf transformation 2]
37. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 37]
48. ! [X0] : ((rich(X0) | (quiet(X0) | old(X0))) & ((~quiet(X0) & ~old(X0)) | ~rich(X0))) [nnf transformation 8]
49. ! [X0] : ((rich(X0) | quiet(X0) | old(X0)) & ((~quiet(X0) & ~old(X0)) | ~rich(X0))) [flattening 48]
76. ~rich(X0) | quiet(X0) [cnf transformation 36]
79. ~quiet(X0) | humble(X0) | humble(X0) [cnf transformation 38]
80. ~quiet(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 38]
98. rich(X0) | quiet(X0) | old(X0) [cnf transformation 49]
125. ~old(john) [cnf transformation 23]
128. ~quiet(X0) | humble(X0) [duplicate literal removal 79]
129. ~humble(X0) | ~quiet(X0) [duplicate literal removal 80]
130. ~quiet(X0) [subsumption resolution 128,129]
180. old(X0) | rich(X0) [subsumption resolution 98,130]
243. rich(john) [resolution 180,125]
256. quiet(john) [resolution 243,76]
257. $false [subsumption resolution 256,130]
% SZS output end Proof for 6108514742394308326992535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then john is not brave or creative. Everyone who is old is both calm and not creative. Everyone who is not curious is not patient and vice versa. Everyone who is not kind is either strong or not strong. If someone is creative then alice is brave. If susan is both not generous and not funny then someone is curious and vice versa. If someone is brave or not generous then someone is not brave or not rich. Everyone who is not kind is both happy and strong. If someone is both not patient and not tall then someone is either kind or not brave and vice versa. Everyone who is both rich and tall is strong or humble and vice versa. Everyone who is rich or not humble is either creative or old. If someone is not old then someone is both not curious and kind and vice versa. Everyone who is both patient and funny is either patient or not humble. Everyone who is both not rich and wise is either not wise or generous. If someone is happy then mary is humble and vice versa. Everyone who is both rich and old is either not humble or humble and vice versa. Mary is either not tall or not strong. Fred is either patient or not curious. Susan is both wise and not funny. John is old. Someone is humble. Mary is funny or humble. Fred is either kind or not funny. | Alice is curious. | neutral | ((?[X]:(old(X)))=>((~brave(john)|creative(john))))&
(![X]:(old(X)=>(calm(X)&~creative(X))))&
(![X]:(~curious(X)<=>~patient(X)))&
(![X]:(~kind(X)=>(strong(X)<~>~strong(X))))&
((?[X]:(creative(X)))=>(brave(alice)))&
(((~generous(susan)&~funny(susan)))<=>(?[X]:(curious(X))))&
((?[X]:((brave(X)|~generous(X))))=>(?[X]:((~brave(X)|~rich(X)))))&
(![X]:(~kind(X)=>(happy(X)&strong(X))))&
((?[X]:((~patient(X)&~tall(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((rich(X)&tall(X))<=>(strong(X)|humble(X))))&
(![X]:((rich(X)|~humble(X))=>(creative(X)<~>old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((patient(X)&funny(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)&wise(X))=>(~wise(X)<~>generous(X))))&
((?[X]:(happy(X)))<=>(humble(mary)))&
(![X]:((rich(X)&old(X))<=>(~humble(X)<~>humble(X))))&
((~tall(mary)<~>~strong(mary)))&
((patient(fred)<~>~curious(fred)))&
((wise(susan)&~funny(susan)))&
(old(john))&
(?[X]:(humble(X)))&
((funny(mary)|humble(mary)))&
((kind(fred)<~>~funny(fred))) | curious(alice) | [] | null | 0 |
Everyone who is both not old and generous is funny or quiet.
Everyone who is not tall is patient or wise.
Everyone who is both not tall and calm is not curious or not generous and vice versa.
Everyone who is both strong and not calm is either humble or brave and vice versa.
Everyone who is not tall or strong is not curious or not brave and vice versa.
If fred is not kind then someone is humble and vice versa.
If someone is wise or happy then fred is funny.
Everyone who is either not happy or not funny is both not generous and curious.
Everyone who is not happy is either not tall or not rich.
Everyone who is creative or kind is both not kind and rich and vice versa.
If someone is both calm and not strong then alice is both not curious and kind.
If someone is not tall then paul is both wise and rich.
If someone is either not quiet or old then someone is creative or quiet and vice versa.
Everyone who is either not brave or not curious is both curious and creative and vice versa.
If someone is both happy and quiet then someone is either quiet or not kind and vice versa.
If john is either old or not old then someone is both not creative and calm and vice versa.
Someone is both not brave and not old.
Someone is not creative or patient.
Fred is either generous or curious.
Someone is either not old or not patient.
Fred is not rich or tall.
Mary is not tall. | Mary is funny. | neutral | (![X]:((~old(X)&generous(X))=>(funny(X)|quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|wise(X))))&
(![X]:((~tall(X)&calm(X))<=>(~curious(X)|~generous(X))))&
(![X]:((strong(X)&~calm(X))<=>(humble(X)<~>brave(X))))&
(![X]:((~tall(X)|strong(X))<=>(~curious(X)|~brave(X))))&
((~kind(fred))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)|happy(X))))=>(funny(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(~generous(X)&curious(X))))&
(![X]:(~happy(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~kind(X)&rich(X))))&
((?[X]:((calm(X)&~strong(X))))=>((~curious(alice)&kind(alice))))&
((?[X]:(~tall(X)))=>((wise(paul)&rich(paul))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>(curious(X)&creative(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((quiet(X)<~>~kind(X)))))&
(((old(john)<~>~old(john)))<=>(?[X]:((~creative(X)&calm(X)))))&
(?[X]:((~brave(X)&~old(X))))&
(?[X]:((~creative(X)|patient(X))))&
((generous(fred)<~>curious(fred)))&
(?[X]:((~old(X)<~>~patient(X))))&
((~rich(fred)|tall(fred)))&
(~tall(mary)) | funny(mary) | [] | null | 0 |
Everyone who is either generous or not strong is both generous and not generous and vice versa.
If john is both quiet and calm then alice is both curious and humble.
Everyone who is either not quiet or not calm is either rich or strong and vice versa.
Everyone who is not strong or not generous is not quiet and vice versa.
Everyone who is not patient or brave is happy or funny.
Everyone who is not rich or brave is either not calm or humble.
If someone is funny or not generous then susan is both brave and not wise.
If lucy is calm or not patient then someone is humble.
If someone is both rich and old then john is either not quiet or curious.
Everyone who is both quiet and not brave is either not rich or not happy and vice versa.
Everyone who is both not rich and strong is not rich or not brave and vice versa.
If someone is happy then paul is either not creative or happy.
Everyone who is creative or happy is not generous.
If someone is not tall then fred is both not funny and quiet and vice versa.
Everyone who is both humble and not curious is either not curious or not brave.
Fred is not quiet or wise.
Someone is both brave and not curious.
Someone is not funny or wise.
Lucy is both calm and not quiet.
Someone is strong or not quiet.
Paul is not kind or humble.
John is either not kind or calm.
Alice is patient or not humble. | Susan is not wise. | entailment | (![X]:((generous(X)<~>~strong(X))<=>(generous(X)&~generous(X))))&
(((quiet(john)&calm(john)))=>((curious(alice)&humble(alice))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))&
(((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))&
(![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((~rich(X)&strong(X))<=>(~rich(X)|~brave(X))))&
((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))&
(![X]:((creative(X)|happy(X))=>~generous(X)))&
((?[X]:(~tall(X)))<=>((~funny(fred)&quiet(fred))))&
(![X]:((humble(X)&~curious(X))=>(~curious(X)<~>~brave(X))))&
((~quiet(fred)|wise(fred)))&
(?[X]:((brave(X)&~curious(X))))&
(?[X]:((~funny(X)|wise(X))))&
((calm(lucy)&~quiet(lucy)))&
(?[X]:((strong(X)|~quiet(X))))&
((~kind(paul)|humble(paul)))&
((~kind(john)<~>calm(john)))&
((patient(alice)|~humble(alice))) | ~wise(susan) | [
"p4",
"p6",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7353846704836426628267628
% SZS output start Proof for 7353846704836426628267628
5. ! [X0] : ((brave(X0) | ~patient(X0)) => (funny(X0) | happy(X0))) [input p4]
7. ? [X0] : (~generous(X0) | funny(X0)) => (~wise(susan) & brave(susan)) [input p6]
13. ! [X0] : ((happy(X0) | creative(X0)) => ~generous(X0)) [input p12]
17. ? [X0] : (~curious(X0) & brave(X0)) [input p16]
24. wise(susan) [input hypothesis]
27. ! [X0] : (brave(X0) => (funny(X0) | happy(X0))) [pure predicate removal 5]
31. ! [X0] : ((funny(X0) | happy(X0)) | ~brave(X0)) [ennf transformation 27]
32. ! [X0] : (funny(X0) | happy(X0) | ~brave(X0)) [flattening 31]
34. (~wise(susan) & brave(susan)) | ! [X0] : (generous(X0) & ~funny(X0)) [ennf transformation 7]
37. ! [X0] : (~generous(X0) | (~happy(X0) & ~creative(X0))) [ennf transformation 13]
59. ? [X0] : (~curious(X0) & brave(X0)) => (~curious(sK2) & brave(sK2)) [choice axiom]
60. ~curious(sK2) & brave(sK2) [skolemisation 17,59]
85. ~brave(X0) | happy(X0) | funny(X0) [cnf transformation 32]
92. ~wise(susan) | ~funny(X0) [cnf transformation 34]
93. ~wise(susan) | generous(X0) [cnf transformation 34]
109. ~happy(X0) | ~generous(X0) [cnf transformation 37]
116. brave(sK2) [cnf transformation 60]
125. wise(susan) [cnf transformation 24]
150. 5 <=> ! [X0] : generous(X0) [avatar definition]
151. generous(X0) <- (5) [avatar component clause 150]
153. 6 <=> wise(susan) [avatar definition]
156. 5 | ~6 [avatar split clause 93,153,150]
158. 7 <=> ! [X0] : ~funny(X0) [avatar definition]
159. ~funny(X0) <- (7) [avatar component clause 158]
160. 7 | ~6 [avatar split clause 92,153,158]
237. 6 [avatar split clause 125,153]
240. happy(sK2) | funny(sK2) [resolution 85,116]
242. happy(sK2) <- (7) [subsumption resolution 240,159]
244. ~generous(sK2) <- (7) [resolution 242,109]
245. $false <- (5, 7) [subsumption resolution 244,151]
246. ~5 | ~7 [avatar contradiction clause 245]
247. $false [avatar sat refutation 156,160,237,246]
% SZS output end Proof for 7353846704836426628267628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or wise then fred is quiet or wise.
Everyone who is either not creative or not strong is both rich and kind and vice versa.
If mary is rich or not humble then someone is either not quiet or humble and vice versa.
If someone is either humble or not curious then someone is generous or not wise and vice versa.
If lucy is either not calm or not funny then john is either not creative or not rich.
If susan is either strong or not strong then lucy is both not old and not quiet and vice versa.
Everyone who is not quiet or strong is either curious or kind.
Everyone who is either not funny or not kind is not quiet and vice versa.
Everyone who is creative or not humble is not happy.
If paul is not tall then paul is not old or not quiet.
If mary is not tall or kind then someone is curious and vice versa.
Everyone who is rich or not brave is not curious and vice versa.
If susan is not tall or happy then someone is funny and vice versa.
If alice is either kind or not calm then paul is either quiet or not calm.
Everyone who is either kind or not curious is calm or tall.
Everyone who is both rich and calm is not wise and vice versa.
Someone is wise or happy.
Fred is not brave or generous.
Someone is either curious or quiet.
Someone is either not happy or kind.
Susan is both humble and brave.
Paul is not curious.
John is either not tall or humble. | Susan is not strong. | neutral | ((?[X]:((~creative(X)|wise(X))))=>((quiet(fred)|wise(fred))))&
(![X]:((~creative(X)<~>~strong(X))<=>(rich(X)&kind(X))))&
(((rich(mary)|~humble(mary)))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:((generous(X)|~wise(X)))))&
(((~calm(lucy)<~>~funny(lucy)))=>((~creative(john)<~>~rich(john))))&
(((strong(susan)<~>~strong(susan)))<=>((~old(lucy)&~quiet(lucy))))&
(![X]:((~quiet(X)|strong(X))=>(curious(X)<~>kind(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>~quiet(X)))&
(![X]:((creative(X)|~humble(X))=>~happy(X)))&
((~tall(paul))=>((~old(paul)|~quiet(paul))))&
(((~tall(mary)|kind(mary)))<=>(?[X]:(curious(X))))&
(![X]:((rich(X)|~brave(X))<=>~curious(X)))&
(((~tall(susan)|happy(susan)))<=>(?[X]:(funny(X))))&
(((kind(alice)<~>~calm(alice)))=>((quiet(paul)<~>~calm(paul))))&
(![X]:((kind(X)<~>~curious(X))=>(calm(X)|tall(X))))&
(![X]:((rich(X)&calm(X))<=>~wise(X)))&
(?[X]:((wise(X)|happy(X))))&
((~brave(fred)|generous(fred)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
((humble(susan)&brave(susan)))&
(~curious(paul))&
((~tall(john)<~>humble(john))) | ~strong(susan) | [] | null | 0 |
Everyone who is not kind is strong. Everyone who is brave or strong is either happy or not strong. Everyone who is not kind is not wise or kind. Everyone who is both not calm and wise is calm. If someone is either curious or not patient then lucy is both not creative and funny and vice versa. If someone is strong or generous then paul is both not old and kind. If someone is both creative and not quiet then someone is not brave. Everyone who is either not calm or not creative is not rich and vice versa. Everyone who is either creative or not generous is both happy and not funny and vice versa. If alice is patient then john is rich or not funny. If someone is either rich or not strong then someone is either humble or old and vice versa. If someone is either generous or not rich then alice is either patient or kind. If alice is either generous or not generous then susan is either patient or brave. Everyone who is brave is not rich and vice versa. If susan is not calm then alice is not calm and vice versa. If john is both generous and old then alice is brave or patient. John is both not curious and not brave. Someone is either not humble or not rich. Someone is either not happy or not rich. John is both not funny and not calm. Someone is both not kind and not quiet. Someone is not funny or brave. Someone is either not kind or funny. Susan is both funny and not brave. | John is calm. | contradiction | (![X]:(~kind(X)=>strong(X)))&
(![X]:((brave(X)|strong(X))=>(happy(X)<~>~strong(X))))&
(![X]:(~kind(X)=>(~wise(X)|kind(X))))&
(![X]:((~calm(X)&wise(X))=>calm(X)))&
((?[X]:((curious(X)<~>~patient(X))))<=>((~creative(lucy)&funny(lucy))))&
((?[X]:((strong(X)|generous(X))))=>((~old(paul)&kind(paul))))&
((?[X]:((creative(X)&~quiet(X))))=>(?[X]:(~brave(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>~rich(X)))&
(![X]:((creative(X)<~>~generous(X))<=>(happy(X)&~funny(X))))&
((patient(alice))=>((rich(john)|~funny(john))))&
((?[X]:((rich(X)<~>~strong(X))))<=>(?[X]:((humble(X)<~>old(X)))))&
((?[X]:((generous(X)<~>~rich(X))))=>((patient(alice)<~>kind(alice))))&
(((generous(alice)<~>~generous(alice)))=>((patient(susan)<~>brave(susan))))&
(![X]:(brave(X)<=>~rich(X)))&
((~calm(susan))<=>(~calm(alice)))&
(((generous(john)&old(john)))=>((brave(alice)|patient(alice))))&
((~curious(john)&~brave(john)))&
(?[X]:((~humble(X)<~>~rich(X))))&
(?[X]:((~happy(X)<~>~rich(X))))&
((~funny(john)&~calm(john)))&
(?[X]:((~kind(X)&~quiet(X))))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~kind(X)<~>funny(X))))&
((funny(susan)&~brave(susan))) | calm(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4719436149431665094987371
% SZS output start Proof for 4719436149431665094987371
20. ~calm(john) & ~funny(john) [input p19]
25. calm(john) [input hypothesis]
129. ~calm(john) [cnf transformation 20]
137. calm(john) [cnf transformation 25]
340. $false [subsumption resolution 137,129]
% SZS output end Proof for 4719436149431665094987371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then fred is both not rich and brave. If alice is either not patient or not old then someone is not tall. Everyone who is not rich or old is both kind and tall and vice versa. Everyone who is not wise or generous is wise. If someone is either patient or not tall then someone is both curious and not happy and vice versa. Everyone who is not old or wise is either wise or curious. If paul is creative or calm then paul is either not quiet or tall and vice versa. If lucy is not brave or wise then fred is quiet. If alice is either not rich or wise then someone is both not old and funny. If someone is both tall and patient then paul is not brave or rich. Everyone who is both happy and not strong is both not creative and not wise and vice versa. If alice is not old or tall then someone is not brave or not quiet. Everyone who is kind or not humble is brave or not curious and vice versa. Everyone who is not funny is tall or rich and vice versa. Everyone who is not kind or not generous is creative or not happy and vice versa. Everyone who is not creative is brave or happy. Someone is both not kind and strong. Someone is strong or calm. Someone is either humble or not rich. Someone is kind or not strong. Someone is either not wise or quiet. Someone is not creative or not humble. Someone is not funny. Susan is brave or not calm. | Alice is not wise. | contradiction | ((?[X]:(~happy(X)))=>((~rich(fred)&brave(fred))))&
(((~patient(alice)<~>~old(alice)))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|old(X))<=>(kind(X)&tall(X))))&
(![X]:((~wise(X)|generous(X))=>wise(X)))&
((?[X]:((patient(X)<~>~tall(X))))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((~old(X)|wise(X))=>(wise(X)<~>curious(X))))&
(((creative(paul)|calm(paul)))<=>((~quiet(paul)<~>tall(paul))))&
(((~brave(lucy)|wise(lucy)))=>(quiet(fred)))&
(((~rich(alice)<~>wise(alice)))=>(?[X]:((~old(X)&funny(X)))))&
((?[X]:((tall(X)&patient(X))))=>((~brave(paul)|rich(paul))))&
(![X]:((happy(X)&~strong(X))<=>(~creative(X)&~wise(X))))&
(((~old(alice)|tall(alice)))=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((kind(X)|~humble(X))<=>(brave(X)|~curious(X))))&
(![X]:(~funny(X)<=>(tall(X)|rich(X))))&
(![X]:((~kind(X)|~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:(~creative(X)=>(brave(X)|happy(X))))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:(~funny(X)))&
((brave(susan)|~calm(susan))) | ~wise(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5534303732396628694618888
% SZS output start Proof for 5534303732396628694618888
4. ! [X0] : ((generous(X0) | ~wise(X0)) => wise(X0)) [input p3]
25. ~wise(alice) [input hypothesis]
29. ! [X0] : (wise(X0) | (~generous(X0) & wise(X0))) [ennf transformation 4]
89. wise(X0) | wise(X0) [cnf transformation 29]
143. ~wise(alice) [cnf transformation 25]
145. wise(X0) [duplicate literal removal 89]
316. $false [subsumption resolution 143,145]
% SZS output end Proof for 5534303732396628694618888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both calm and funny and vice versa.
If someone is either not patient or quiet then susan is curious and vice versa.
If fred is strong then susan is not curious or not humble and vice versa.
Everyone who is either not happy or curious is calm and vice versa.
Everyone who is not strong or not quiet is not brave or not kind.
Everyone who is both not rich and old is either patient or happy.
Everyone who is old or kind is not curious.
Everyone who is either humble or curious is not funny and vice versa.
Everyone who is both patient and not happy is tall or not calm.
Everyone who is not funny or not calm is either kind or generous.
Everyone who is patient is both kind and tall.
If lucy is either not generous or brave then someone is both curious and not curious and vice versa.
Everyone who is not patient is wise or not calm.
If someone is both generous and not brave then john is kind and vice versa.
If someone is tall or rich then someone is both happy and humble and vice versa.
If susan is both not generous and kind then paul is kind or not rich and vice versa.
Someone is not tall.
Paul is not wise.
Someone is not patient or not kind.
Alice is not brave.
Alice is generous.
Paul is either not tall or tall. | Susan is humble. | contradiction | (![X]:(~funny(X)<=>(calm(X)&funny(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(curious(susan)))&
((strong(fred))<=>((~curious(susan)|~humble(susan))))&
(![X]:((~happy(X)<~>curious(X))<=>calm(X)))&
(![X]:((~strong(X)|~quiet(X))=>(~brave(X)|~kind(X))))&
(![X]:((~rich(X)&old(X))=>(patient(X)<~>happy(X))))&
(![X]:((old(X)|kind(X))=>~curious(X)))&
(![X]:((humble(X)<~>curious(X))<=>~funny(X)))&
(![X]:((patient(X)&~happy(X))=>(tall(X)|~calm(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)<~>generous(X))))&
(![X]:(patient(X)=>(kind(X)&tall(X))))&
(((~generous(lucy)<~>brave(lucy)))<=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:(~patient(X)=>(wise(X)|~calm(X))))&
((?[X]:((generous(X)&~brave(X))))<=>(kind(john)))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:((happy(X)&humble(X)))))&
(((~generous(susan)&kind(susan)))<=>((kind(paul)|~rich(paul))))&
(?[X]:(~tall(X)))&
(~wise(paul))&
(?[X]:((~patient(X)|~kind(X))))&
(~brave(alice))&
(generous(alice))&
((~tall(paul)<~>tall(paul))) | humble(susan) | [
"p0",
"p3",
"p6",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3523362604371909352715166
% SZS output start Proof for 3523362604371909352715166
1. ! [X0] : (~funny(X0) <=> (funny(X0) & calm(X0))) [input p0]
4. ! [X0] : ((~happy(X0) <~> curious(X0)) <=> calm(X0)) [input p3]
7. ! [X0] : ((kind(X0) | old(X0)) => ~curious(X0)) [input p6]
8. ! [X0] : ((humble(X0) <~> curious(X0)) <=> ~funny(X0)) [input p7]
15. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X0] : (humble(X0) & happy(X0)) [input p14]
16. (kind(susan) & ~generous(susan)) <=> (~rich(paul) | kind(paul)) [input p15]
23. humble(susan) [input hypothesis]
24. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X1] : (humble(X1) & happy(X1)) [rectify 15]
26. ! [X0] : (kind(X0) => ~curious(X0)) [pure predicate removal 7]
29. ! [X0] : (~curious(X0) | ~kind(X0)) [ennf transformation 26]
36. ! [X0] : ((~funny(X0) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | funny(X0))) [nnf transformation 1]
37. ! [X0] : ((~funny(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | funny(X0))) [flattening 36]
44. ! [X0] : ((((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | ~calm(X0)) & (calm(X0) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))))) [nnf transformation 4]
45. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | funny(X0)) & (~funny(X0) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [nnf transformation 8]
55. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : (~humble(X1) | ~happy(X1))) & (? [X1] : (humble(X1) & happy(X1)) | ! [X0] : (~rich(X0) & ~tall(X0))) [nnf transformation 24]
56. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : (~humble(X1) | ~happy(X1))) & (? [X2] : (humble(X2) & happy(X2)) | ! [X3] : (~rich(X3) & ~tall(X3))) [rectify 55]
57. ? [X0] : (rich(X0) | tall(X0)) => (rich(sK3) | tall(sK3)) [choice axiom]
58. ? [X2] : (humble(X2) & happy(X2)) => (humble(sK4) & happy(sK4)) [choice axiom]
59. ((rich(sK3) | tall(sK3)) | ! [X1] : (~humble(X1) | ~happy(X1))) & ((humble(sK4) & happy(sK4)) | ! [X3] : (~rich(X3) & ~tall(X3))) [skolemisation 56,58,57]
60. ((kind(susan) & ~generous(susan)) | (rich(paul) & ~kind(paul))) & ((~rich(paul) | kind(paul)) | (~kind(susan) | generous(susan))) [nnf transformation 16]
61. ((kind(susan) & ~generous(susan)) | (rich(paul) & ~kind(paul))) & (~rich(paul) | kind(paul) | ~kind(susan) | generous(susan)) [flattening 60]
68. funny(X0) | funny(X0) [cnf transformation 37]
69. ~funny(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 37]
78. ~happy(X0) | calm(X0) | ~curious(X0) [cnf transformation 44]
83. ~kind(X0) | ~curious(X0) [cnf transformation 29]
84. ~funny(X0) | curious(X0) | ~humble(X0) [cnf transformation 45]
106. happy(sK4) | ~rich(X3) [cnf transformation 59]
108. humble(sK4) | ~rich(X3) [cnf transformation 59]
114. kind(susan) | rich(paul) [cnf transformation 61]
122. humble(susan) [cnf transformation 23]
123. funny(X0) [duplicate literal removal 68]
124. ~calm(X0) | ~funny(X0) [duplicate literal removal 69]
126. 1 <=> curious(susan) [avatar definition]
127. curious(susan) <- (1) [avatar component clause 126]
148. 6 <=> humble(susan) [avatar definition]
150. humble(susan) <- (6) [avatar component clause 148]
159. ~humble(X0) | curious(X0) [subsumption resolution 84,123]
207. 18 <=> ! [X3] : ~rich(X3) [avatar definition]
208. ~rich(X3) <- (18) [avatar component clause 207]
210. 19 <=> humble(sK4) [avatar definition]
212. humble(sK4) <- (19) [avatar component clause 210]
213. 18 | 19 [avatar split clause 108,210,207]
219. 21 <=> happy(sK4) [avatar definition]
221. happy(sK4) <- (21) [avatar component clause 219]
222. 18 | 21 [avatar split clause 106,219,207]
225. 22 <=> rich(paul) [avatar definition]
227. rich(paul) <- (22) [avatar component clause 225]
229. 23 <=> kind(susan) [avatar definition]
231. kind(susan) <- (23) [avatar component clause 229]
232. 22 | 23 [avatar split clause 114,229,225]
246. 6 [avatar split clause 122,148]
247. $false <- (18, 22) [resolution 227,208]
248. ~18 | ~22 [avatar contradiction clause 247]
251. curious(susan) <- (6) [resolution 159,150]
252. curious(sK4) <- (19) [resolution 159,212]
255. 1 | ~6 [avatar split clause 251,148,126]
266. calm(sK4) | ~curious(sK4) <- (21) [resolution 78,221]
269. calm(sK4) <- (19, 21) [subsumption resolution 266,252]
270. ~funny(sK4) <- (19, 21) [resolution 269,124]
271. $false <- (19, 21) [subsumption resolution 270,123]
272. ~19 | ~21 [avatar contradiction clause 271]
284. ~curious(susan) <- (23) [resolution 231,83]
285. $false <- (1, 23) [subsumption resolution 284,127]
286. ~1 | ~23 [avatar contradiction clause 285]
287. $false [avatar sat refutation 213,222,232,246,248,255,272,286]
% SZS output end Proof for 3523362604371909352715166
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or old is both rich and brave and vice versa.
If mary is either calm or not quiet then someone is brave or not creative and vice versa.
Everyone who is both not creative and not tall is humble and vice versa.
If lucy is either kind or calm then paul is not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
If lucy is both curious and patient then lucy is not tall.
If someone is either not strong or funny then someone is not generous or humble and vice versa.
Everyone who is not funny or creative is both not humble and wise and vice versa.
Everyone who is both not patient and old is both funny and not humble.
Everyone who is either not strong or not happy is old or not humble.
Everyone who is either not happy or tall is not curious or creative and vice versa.
Everyone who is calm or not old is patient and vice versa.
Everyone who is both not curious and wise is both tall and not strong and vice versa.
Everyone who is brave or old is both not tall and not kind.
If someone is not kind or rich then someone is not old or not creative and vice versa.
Everyone who is either rich or not funny is both not curious and happy and vice versa.
Someone is both strong and not rich.
Paul is patient or not calm.
Alice is not wise.
Fred is both humble and brave.
John is both quiet and old.
Alice is not old or patient.
Paul is either not happy or brave.
Paul is not creative or not kind. | Alice is not happy. | contradiction | (![X]:((curious(X)<~>old(X))<=>(rich(X)&brave(X))))&
(((calm(mary)<~>~quiet(mary)))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((~creative(X)&~tall(X))<=>humble(X)))&
(((kind(lucy)<~>calm(lucy)))=>(~quiet(paul)))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(((curious(lucy)&patient(lucy)))=>(~tall(lucy)))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~funny(X)|creative(X))<=>(~humble(X)&wise(X))))&
(![X]:((~patient(X)&old(X))=>(funny(X)&~humble(X))))&
(![X]:((~strong(X)<~>~happy(X))=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(~curious(X)|creative(X))))&
(![X]:((calm(X)|~old(X))<=>patient(X)))&
(![X]:((~curious(X)&wise(X))<=>(tall(X)&~strong(X))))&
(![X]:((brave(X)|old(X))=>(~tall(X)&~kind(X))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((rich(X)<~>~funny(X))<=>(~curious(X)&happy(X))))&
(?[X]:((strong(X)&~rich(X))))&
((patient(paul)|~calm(paul)))&
(~wise(alice))&
((humble(fred)&brave(fred)))&
((quiet(john)&old(john)))&
((~old(alice)|patient(alice)))&
((~happy(paul)<~>brave(paul)))&
((~creative(paul)|~kind(paul))) | ~happy(alice) | [
"p0",
"p2",
"p4",
"p7",
"p9",
"p10",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 222846719552310911372296
% SZS output start Proof for 222846719552310911372296
1. ! [X0] : ((curious(X0) <~> old(X0)) <=> (brave(X0) & rich(X0))) [input p0]
3. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> humble(X0)) [input p2]
5. ! [X0] : ((funny(X0) | generous(X0)) <=> (patient(X0) & strong(X0))) [input p4]
8. ! [X0] : ((creative(X0) | ~funny(X0)) <=> (wise(X0) & ~humble(X0))) [input p7]
10. ! [X0] : ((~strong(X0) <~> ~happy(X0)) => (~humble(X0) | old(X0))) [input p9]
11. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (creative(X0) | ~curious(X0))) [input p10]
14. ! [X0] : ((old(X0) | brave(X0)) => (~kind(X0) & ~tall(X0))) [input p13]
16. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (happy(X0) & ~curious(X0))) [input p15]
19. ~wise(alice) [input p18]
25. ~happy(alice) [input hypothesis]
33. ! [X0] : ((~humble(X0) | old(X0)) | (~strong(X0) <=> ~happy(X0))) [ennf transformation 10]
34. ! [X0] : (~humble(X0) | old(X0) | (~strong(X0) <=> ~happy(X0))) [flattening 33]
35. ! [X0] : ((~kind(X0) & ~tall(X0)) | (~old(X0) & ~brave(X0))) [ennf transformation 14]
36. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [flattening 36]
42. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~humble(X0)) & (humble(X0) | (tall(X0) | creative(X0)))) [nnf transformation 3]
43. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~humble(X0)) & (humble(X0) | tall(X0) | creative(X0))) [flattening 42]
45. ! [X0] : (((funny(X0) | generous(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 5]
46. ! [X0] : ((funny(X0) | generous(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 45]
52. ! [X0] : (((creative(X0) | ~funny(X0)) | (~wise(X0) | humble(X0))) & ((wise(X0) & ~humble(X0)) | (~creative(X0) & funny(X0)))) [nnf transformation 8]
53. ! [X0] : ((creative(X0) | ~funny(X0) | ~wise(X0) | humble(X0)) & ((wise(X0) & ~humble(X0)) | (~creative(X0) & funny(X0)))) [flattening 52]
54. ! [X0] : (~humble(X0) | old(X0) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) [nnf transformation 34]
55. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 11]
56. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 55]
66. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (~happy(X0) | curious(X0))) & ((happy(X0) & ~curious(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 16]
67. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ~happy(X0) | curious(X0)) & ((happy(X0) & ~curious(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [flattening 66]
72. ~old(X0) | curious(X0) | rich(X0) [cnf transformation 37]
73. ~curious(X0) | old(X0) | brave(X0) [cnf transformation 37]
83. humble(X0) | tall(X0) | creative(X0) [cnf transformation 43]
89. ~funny(X0) | strong(X0) [cnf transformation 46]
102. wise(X0) | funny(X0) [cnf transformation 53]
103. ~creative(X0) | wise(X0) [cnf transformation 53]
108. ~strong(X0) | old(X0) | ~humble(X0) | happy(X0) [cnf transformation 54]
109. ~curious(X0) | creative(X0) | tall(X0) | happy(X0) [cnf transformation 56]
113. ~tall(X0) | happy(X0) | curious(X0) [cnf transformation 56]
122. ~tall(X0) | ~brave(X0) [cnf transformation 35]
123. ~tall(X0) | ~old(X0) [cnf transformation 35]
132. ~funny(X0) | happy(X0) | ~rich(X0) [cnf transformation 67]
139. ~wise(alice) [cnf transformation 19]
148. ~happy(alice) [cnf transformation 25]
296. funny(alice) [resolution 102,139]
298. strong(alice) [resolution 296,89]
338. 37 <=> rich(alice) [avatar definition]
340. ~rich(alice) <- (~37) [avatar component clause 338]
342. 38 <=> curious(alice) [avatar definition]
343. curious(alice) <- (38) [avatar component clause 342]
348. happy(alice) | ~rich(alice) [resolution 132,296]
349. ~rich(alice) [subsumption resolution 348,148]
350. ~37 [avatar split clause 349,338]
400. old(alice) | ~humble(alice) | happy(alice) [resolution 108,298]
413. old(alice) | ~humble(alice) [subsumption resolution 400,148]
415. 45 <=> humble(alice) [avatar definition]
417. ~humble(alice) <- (~45) [avatar component clause 415]
419. 46 <=> old(alice) [avatar definition]
420. ~old(alice) <- (~46) [avatar component clause 419]
421. old(alice) <- (46) [avatar component clause 419]
422. ~45 | 46 [avatar split clause 413,419,415]
701. tall(alice) | creative(alice) <- (~45) [resolution 417,83]
703. 67 <=> creative(alice) [avatar definition]
704. ~creative(alice) <- (~67) [avatar component clause 703]
705. creative(alice) <- (67) [avatar component clause 703]
707. 68 <=> tall(alice) [avatar definition]
708. ~tall(alice) <- (~68) [avatar component clause 707]
709. tall(alice) <- (68) [avatar component clause 707]
710. 67 | 68 | 45 [avatar split clause 701,415,707,703]
752. wise(alice) <- (67) [resolution 705,103]
753. $false <- (67) [subsumption resolution 752,139]
754. ~67 [avatar contradiction clause 753]
758. happy(alice) | curious(alice) <- (68) [resolution 709,113]
759. ~old(alice) <- (68) [resolution 709,123]
760. ~brave(alice) <- (68) [resolution 709,122]
761. curious(alice) <- (68) [subsumption resolution 758,148]
764. ~46 | ~68 [avatar split clause 759,707,419]
765. 38 | ~68 [avatar split clause 761,707,342]
768. old(alice) | brave(alice) <- (38) [resolution 343,73]
770. brave(alice) <- (38, ~46) [subsumption resolution 768,420]
771. $false <- (38, ~46, 68) [subsumption resolution 770,760]
772. ~38 | 46 | ~68 [avatar contradiction clause 771]
782. curious(alice) | rich(alice) <- (46) [resolution 421,72]
790. curious(alice) <- (~37, 46) [subsumption resolution 782,340]
791. 38 | 37 | ~46 [avatar split clause 790,419,338,342]
792. creative(alice) | tall(alice) | happy(alice) <- (38) [resolution 343,109]
796. tall(alice) | happy(alice) <- (38, ~67) [subsumption resolution 792,704]
797. happy(alice) <- (38, ~67, ~68) [subsumption resolution 796,708]
798. $false <- (38, ~67, ~68) [subsumption resolution 797,148]
799. ~38 | 67 | 68 [avatar contradiction clause 798]
800. $false [avatar sat refutation 350,422,710,754,764,765,772,791,799]
% SZS output end Proof for 222846719552310911372296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not patient is rich or not calm and vice versa.
Everyone who is not brave or not humble is both not tall and humble.
If fred is not kind then lucy is both not tall and generous and vice versa.
Everyone who is not generous is curious.
Everyone who is either not funny or kind is either patient or kind.
Everyone who is either not strong or humble is both not wise and not patient.
Everyone who is old is both not generous and strong.
If someone is both humble and rich then paul is not brave and vice versa.
If someone is both not patient and wise then john is kind.
Everyone who is not humble or not curious is either not generous or not funny and vice versa.
Everyone who is either not generous or humble is either generous or kind and vice versa.
Everyone who is both humble and old is either not brave or quiet and vice versa.
If mary is both not calm and not strong then paul is both brave and rich.
Everyone who is either old or kind is quiet or not generous and vice versa.
If someone is both not old and old then someone is not creative or not wise.
Everyone who is either not patient or not brave is either generous or kind.
Mary is funny.
Lucy is brave or strong.
Alice is not kind.
Susan is either strong or generous.
Someone is not quiet.
Lucy is either curious or quiet.
John is brave. | Susan is not old. | entailment | (![X]:((strong(X)|~patient(X))<=>(rich(X)|~calm(X))))&
(![X]:((~brave(X)|~humble(X))=>(~tall(X)&humble(X))))&
((~kind(fred))<=>((~tall(lucy)&generous(lucy))))&
(![X]:(~generous(X)=>curious(X)))&
(![X]:((~funny(X)<~>kind(X))=>(patient(X)<~>kind(X))))&
(![X]:((~strong(X)<~>humble(X))=>(~wise(X)&~patient(X))))&
(![X]:(old(X)=>(~generous(X)&strong(X))))&
((?[X]:((humble(X)&rich(X))))<=>(~brave(paul)))&
((?[X]:((~patient(X)&wise(X))))=>(kind(john)))&
(![X]:((~humble(X)|~curious(X))<=>(~generous(X)<~>~funny(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(generous(X)<~>kind(X))))&
(![X]:((humble(X)&old(X))<=>(~brave(X)<~>quiet(X))))&
(((~calm(mary)&~strong(mary)))=>((brave(paul)&rich(paul))))&
(![X]:((old(X)<~>kind(X))<=>(quiet(X)|~generous(X))))&
((?[X]:((~old(X)&old(X))))=>(?[X]:((~creative(X)|~wise(X)))))&
(![X]:((~patient(X)<~>~brave(X))=>(generous(X)<~>kind(X))))&
(funny(mary))&
((brave(lucy)|strong(lucy)))&
(~kind(alice))&
((strong(susan)<~>generous(susan)))&
(?[X]:(~quiet(X)))&
((curious(lucy)<~>quiet(lucy)))&
(brave(john)) | ~old(susan) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6570517074084411633499005
% SZS output start Proof for 6570517074084411633499005
2. ! [X0] : ((~humble(X0) | ~brave(X0)) => (humble(X0) & ~tall(X0))) [input p1]
4. ! [X0] : (~generous(X0) => curious(X0)) [input p3]
5. ! [X0] : ((~funny(X0) <~> kind(X0)) => (patient(X0) <~> kind(X0))) [input p4]
6. ! [X0] : ((~strong(X0) <~> humble(X0)) => (~patient(X0) & ~wise(X0))) [input p5]
7. ! [X0] : (old(X0) => (strong(X0) & ~generous(X0))) [input p6]
10. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> (~generous(X0) <~> ~funny(X0))) [input p9]
11. ! [X0] : ((~generous(X0) <~> humble(X0)) <=> (generous(X0) <~> kind(X0))) [input p10]
24. old(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) <~> humble(X0)) => ~patient(X0)) [pure predicate removal 6]
29. ! [X0] : ((humble(X0) & ~tall(X0)) | (humble(X0) & brave(X0))) [ennf transformation 2]
30. ! [X0] : (curious(X0) | generous(X0)) [ennf transformation 4]
31. ! [X0] : ((patient(X0) <~> kind(X0)) | (~funny(X0) <=> kind(X0))) [ennf transformation 5]
32. ! [X0] : (~patient(X0) | (~strong(X0) <=> humble(X0))) [ennf transformation 27]
33. ! [X0] : ((strong(X0) & ~generous(X0)) | ~old(X0)) [ennf transformation 7]
41. ! [X0] : (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 31]
42. ! [X0] : (~patient(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) [nnf transformation 32]
47. ! [X0] : (((~curious(X0) | ~humble(X0)) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0)))) & (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (curious(X0) & humble(X0)))) [nnf transformation 10]
48. ! [X0] : ((~curious(X0) | ~humble(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0)))) & (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (curious(X0) & humble(X0)))) [flattening 47]
49. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [nnf transformation 11]
66. humble(X0) | humble(X0) [cnf transformation 29]
70. curious(X0) | generous(X0) [cnf transformation 30]
71. kind(X0) | patient(X0) | kind(X0) | funny(X0) [cnf transformation 41]
76. ~patient(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 42]
77. ~old(X0) | ~generous(X0) [cnf transformation 33]
78. ~old(X0) | strong(X0) [cnf transformation 33]
86. ~curious(X0) | ~humble(X0) | ~funny(X0) | generous(X0) [cnf transformation 48]
91. ~kind(X0) | ~generous(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 49]
95. ~humble(X0) | generous(X0) | generous(X0) | ~kind(X0) [cnf transformation 49]
123. old(susan) [cnf transformation 24]
125. ~kind(X0) | ~generous(X0) | ~humble(X0) [duplicate literal removal 91]
127. ~humble(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 95]
128. funny(X0) | patient(X0) | kind(X0) [duplicate literal removal 71]
130. humble(X0) [duplicate literal removal 66]
146. ~patient(X0) | ~strong(X0) [subsumption resolution 76,130]
162. ~curious(X0) | ~funny(X0) | generous(X0) [subsumption resolution 86,130]
163. ~funny(X0) | generous(X0) [subsumption resolution 162,70]
165. ~kind(X0) | generous(X0) [subsumption resolution 127,130]
166. ~kind(X0) | ~generous(X0) [subsumption resolution 125,130]
167. ~kind(X0) [subsumption resolution 166,165]
198. 12 <=> strong(susan) [avatar definition]
199. strong(susan) <- (12) [avatar component clause 198]
202. 13 <=> generous(susan) [avatar definition]
204. ~generous(susan) <- (~13) [avatar component clause 202]
217. ~generous(susan) [resolution 77,123]
218. strong(susan) [resolution 78,123]
256. patient(X1) | kind(X1) | generous(X1) [resolution 128,163]
258. generous(X1) | patient(X1) [subsumption resolution 256,167]
261. patient(susan) <- (~13) [resolution 258,204]
274. ~strong(susan) <- (~13) [resolution 261,146]
275. $false <- (12, ~13) [subsumption resolution 274,199]
276. ~12 | 13 [avatar contradiction clause 275]
277. 12 [avatar split clause 218,198]
278. ~13 [avatar split clause 217,202]
279. $false [avatar sat refutation 276,277,278]
% SZS output end Proof for 6570517074084411633499005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not curious or not creative then someone is either not brave or not strong. If susan is both humble and not humble then fred is both calm and old and vice versa. Everyone who is not old is both strong and brave. If mary is not brave then someone is either humble or not creative. Everyone who is either not brave or creative is either brave or not kind and vice versa. Everyone who is either not old or calm is either not brave or brave and vice versa. If someone is not calm or generous then someone is kind and vice versa. If someone is not curious or curious then fred is curious or not wise and vice versa. Everyone who is creative or patient is kind or not quiet and vice versa. Everyone who is happy or not brave is both funny and calm. If john is not patient or creative then fred is either strong or rich and vice versa. Everyone who is either not old or not generous is both not calm and calm. Everyone who is both not happy and not creative is both not wise and not calm. Everyone who is not creative or tall is either patient or brave and vice versa. Mary is both happy and funny. Someone is tall or not old. Someone is happy or not creative. Fred is both patient and creative. Someone is both wise and patient. Lucy is both not funny and not creative. | Alice is kind. | neutral | (((~curious(alice)|~creative(alice)))=>(?[X]:((~brave(X)<~>~strong(X)))))&
(((humble(susan)&~humble(susan)))<=>((calm(fred)&old(fred))))&
(![X]:(~old(X)=>(strong(X)&brave(X))))&
((~brave(mary))=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~brave(X)<~>creative(X))<=>(brave(X)<~>~kind(X))))&
(![X]:((~old(X)<~>calm(X))<=>(~brave(X)<~>brave(X))))&
((?[X]:((~calm(X)|generous(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~curious(X)|curious(X))))<=>((curious(fred)|~wise(fred))))&
(![X]:((creative(X)|patient(X))<=>(kind(X)|~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>(funny(X)&calm(X))))&
(((~patient(john)|creative(john)))<=>((strong(fred)<~>rich(fred))))&
(![X]:((~old(X)<~>~generous(X))=>(~calm(X)&calm(X))))&
(![X]:((~happy(X)&~creative(X))=>(~wise(X)&~calm(X))))&
(![X]:((~creative(X)|tall(X))<=>(patient(X)<~>brave(X))))&
((happy(mary)&funny(mary)))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:((happy(X)|~creative(X))))&
((patient(fred)&creative(fred)))&
(?[X]:((wise(X)&patient(X))))&
((~funny(lucy)&~creative(lucy))) | kind(alice) | [] | null | 0 |
If susan is either not tall or not old then someone is not funny or not kind.
If lucy is not funny or patient then someone is not strong and vice versa.
Everyone who is curious or old is both calm and kind and vice versa.
If someone is both not curious and generous then someone is not rich or not generous.
Everyone who is either curious or old is either not strong or not patient and vice versa.
Everyone who is both not calm and strong is either strong or not creative.
Everyone who is either generous or funny is both curious and kind and vice versa.
Everyone who is not strong is either wise or quiet.
If mary is both quiet and patient then someone is either not quiet or curious.
Everyone who is either curious or humble is tall or humble and vice versa.
If someone is kind or not old then someone is not old.
If susan is not funny then mary is happy or quiet.
Everyone who is creative or quiet is both not happy and not quiet.
Everyone who is not wise or not happy is either quiet or kind and vice versa.
Everyone who is either not curious or kind is either not humble or not happy and vice versa.
Everyone who is either wise or curious is not brave or not tall and vice versa.
Someone is humble or not humble.
Someone is not kind.
Someone is quiet or not rich.
Lucy is humble.
Fred is both not humble and not calm.
Someone is both not curious and not strong.
Someone is funny or rich. | Lucy is wise. | contradiction | (((~tall(susan)<~>~old(susan)))=>(?[X]:((~funny(X)|~kind(X)))))&
(((~funny(lucy)|patient(lucy)))<=>(?[X]:(~strong(X))))&
(![X]:((curious(X)|old(X))<=>(calm(X)&kind(X))))&
((?[X]:((~curious(X)&generous(X))))=>(?[X]:((~rich(X)|~generous(X)))))&
(![X]:((curious(X)<~>old(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:((~calm(X)&strong(X))=>(strong(X)<~>~creative(X))))&
(![X]:((generous(X)<~>funny(X))<=>(curious(X)&kind(X))))&
(![X]:(~strong(X)=>(wise(X)<~>quiet(X))))&
(((quiet(mary)&patient(mary)))=>(?[X]:((~quiet(X)<~>curious(X)))))&
(![X]:((curious(X)<~>humble(X))<=>(tall(X)|humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(?[X]:(~old(X))))&
((~funny(susan))=>((happy(mary)|quiet(mary))))&
(![X]:((creative(X)|quiet(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~wise(X)|~happy(X))<=>(quiet(X)<~>kind(X))))&
(![X]:((~curious(X)<~>kind(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:((wise(X)<~>curious(X))<=>(~brave(X)|~tall(X))))&
(?[X]:((humble(X)|~humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:((quiet(X)|~rich(X))))&
(humble(lucy))&
((~humble(fred)&~calm(fred)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((funny(X)|rich(X)))) | wise(lucy) | [
"p9",
"p12",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4467988546113335324227380
% SZS output start Proof for 4467988546113335324227380
10. ! [X0] : ((curious(X0) <~> humble(X0)) <=> (humble(X0) | tall(X0))) [input p9]
13. ! [X0] : ((quiet(X0) | creative(X0)) => (~quiet(X0) & ~happy(X0))) [input p12]
14. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (quiet(X0) <~> kind(X0))) [input p13]
15. ! [X0] : ((~curious(X0) <~> kind(X0)) <=> (~humble(X0) <~> ~happy(X0))) [input p14]
20. humble(lucy) [input p19]
24. wise(lucy) [input hypothesis]
37. ! [X0] : ((~quiet(X0) & ~happy(X0)) | (~quiet(X0) & ~creative(X0))) [ennf transformation 13]
59. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | (~humble(X0) & ~tall(X0))) & ((humble(X0) | tall(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [nnf transformation 10]
60. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | (~humble(X0) & ~tall(X0))) & (humble(X0) | tall(X0) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [flattening 59]
64. ! [X0] : (((~happy(X0) | ~wise(X0)) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (happy(X0) & wise(X0)))) [nnf transformation 14]
65. ! [X0] : ((~happy(X0) | ~wise(X0) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (happy(X0) & wise(X0)))) [flattening 64]
66. ! [X0] : ((((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0)))) & (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | ((~curious(X0) | ~kind(X0)) & (kind(X0) | curious(X0))))) [nnf transformation 15]
115. ~humble(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 60]
122. ~quiet(X0) | ~quiet(X0) [cnf transformation 37]
124. kind(X0) | quiet(X0) | happy(X0) [cnf transformation 65]
128. ~happy(X0) | ~wise(X0) | quiet(X0) | ~kind(X0) [cnf transformation 65]
129. ~happy(X0) | ~humble(X0) | kind(X0) | curious(X0) [cnf transformation 66]
136. ~kind(X0) | curious(X0) | ~humble(X0) | happy(X0) [cnf transformation 66]
146. humble(lucy) [cnf transformation 20]
152. wise(lucy) [cnf transformation 24]
153. ~quiet(X0) [duplicate literal removal 122]
155. ~humble(X0) | ~curious(X0) [duplicate literal removal 115]
247. ~happy(X0) | ~wise(X0) | ~kind(X0) [subsumption resolution 128,153]
248. happy(X0) | kind(X0) [subsumption resolution 124,153]
250. curious(X0) | ~humble(X0) | happy(X0) [subsumption resolution 136,248]
251. ~humble(X0) | happy(X0) [subsumption resolution 250,155]
254. ~happy(X0) | ~humble(X0) | kind(X0) [subsumption resolution 129,155]
255. ~humble(X0) | kind(X0) [subsumption resolution 254,251]
272. happy(lucy) [resolution 251,146]
274. kind(lucy) [resolution 255,146]
304. ~wise(lucy) | ~kind(lucy) [resolution 247,272]
306. ~kind(lucy) [subsumption resolution 304,152]
307. $false [subsumption resolution 306,274]
% SZS output end Proof for 4467988546113335324227380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both quiet and generous then someone is old or happy. Everyone who is both funny and kind is both humble and not rich. Everyone who is not funny or calm is not funny and vice versa. Everyone who is both generous and humble is wise or brave and vice versa. Everyone who is calm is not generous. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Everyone who is either wise or happy is happy. If someone is not rich or kind then lucy is curious and vice versa. Everyone who is either not strong or not quiet is not rich and vice versa. Susan is either patient or not wise. Someone is not calm. Someone is creative or not patient. Someone is not tall or old. John is either not humble or patient. Someone is either funny or not kind. Alice is funny or old. | Alice is curious. | contradiction | (((quiet(fred)&generous(fred)))=>(?[X]:((old(X)|happy(X)))))&
(![X]:((funny(X)&kind(X))=>(humble(X)&~rich(X))))&
(![X]:((~funny(X)|calm(X))<=>~funny(X)))&
(![X]:((generous(X)&humble(X))<=>(wise(X)|brave(X))))&
(![X]:(calm(X)=>~generous(X)))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
((patient(susan)<~>~wise(susan)))&
(?[X]:(~calm(X)))&
(?[X]:((creative(X)|~patient(X))))&
(?[X]:((~tall(X)|old(X))))&
((~humble(john)<~>patient(john)))&
(?[X]:((funny(X)<~>~kind(X))))&
((funny(alice)|old(alice))) | curious(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2185488990281338944442371
% SZS output start Proof for 2185488990281338944442371
10. ! [X0] : ((wise(X0) | curious(X0)) => ~curious(X0)) [input p9]
24. curious(alice) [input hypothesis]
33. ! [X0] : (~curious(X0) | (~wise(X0) & ~curious(X0))) [ennf transformation 10]
87. ~curious(X0) | ~curious(X0) [cnf transformation 33]
119. curious(alice) [cnf transformation 24]
121. ~curious(X0) [duplicate literal removal 87]
213. $false [subsumption resolution 119,121]
% SZS output end Proof for 2185488990281338944442371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or strong is quiet and vice versa. If someone is either not patient or not happy then someone is not wise or not strong and vice versa. Everyone who is either wise or happy is brave or not old and vice versa. If someone is both not quiet and not rich then someone is strong or tall. If someone is calm then someone is kind and vice versa. If fred is not strong or not creative then someone is wise or patient and vice versa. If alice is either strong or kind then someone is either not happy or rich and vice versa. If someone is either not brave or not wise then someone is not generous or strong and vice versa. If paul is either curious or old then someone is not strong or not quiet. Everyone who is brave or kind is funny or not curious. If someone is not tall or not kind then mary is both wise and kind. If someone is either curious or brave then alice is either not generous or not quiet. If susan is both not wise and rich then mary is both calm and rich and vice versa. If someone is old then someone is not funny or not generous. If susan is not calm then someone is not creative and vice versa. Everyone who is not old is either old or not quiet and vice versa. Someone is not quiet. Someone is either not tall or patient. Someone is calm or not old. Someone is generous. Someone is both wise and creative. Someone is not strong. Someone is funny or generous. Someone is happy. | Mary is not brave. | neutral | (![X]:((wise(X)<~>strong(X))<=>quiet(X)))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(brave(X)|~old(X))))&
((?[X]:((~quiet(X)&~rich(X))))=>(?[X]:((strong(X)|tall(X)))))&
((?[X]:(calm(X)))<=>(?[X]:(kind(X))))&
(((~strong(fred)|~creative(fred)))<=>(?[X]:((wise(X)|patient(X)))))&
(((strong(alice)<~>kind(alice)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
((?[X]:((~brave(X)<~>~wise(X))))<=>(?[X]:((~generous(X)|strong(X)))))&
(((curious(paul)<~>old(paul)))=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((brave(X)|kind(X))=>(funny(X)|~curious(X))))&
((?[X]:((~tall(X)|~kind(X))))=>((wise(mary)&kind(mary))))&
((?[X]:((curious(X)<~>brave(X))))=>((~generous(alice)<~>~quiet(alice))))&
(((~wise(susan)&rich(susan)))<=>((calm(mary)&rich(mary))))&
((?[X]:(old(X)))=>(?[X]:((~funny(X)|~generous(X)))))&
((~calm(susan))<=>(?[X]:(~creative(X))))&
(![X]:(~old(X)<=>(old(X)<~>~quiet(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
(?[X]:((calm(X)|~old(X))))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)&creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)|generous(X))))&
(?[X]:(happy(X))) | ~brave(mary) | [] | null | 0 |
Everyone who is funny is either strong or not patient.
If fred is not funny then someone is either not old or tall.
If someone is strong then susan is not curious and vice versa.
If susan is both wise and not brave then someone is wise and vice versa.
If someone is not old or wise then paul is tall.
If someone is not creative then john is not rich or not funny.
If john is either kind or not creative then someone is not tall.
If someone is both not strong and kind then someone is happy and vice versa.
If john is both happy and not old then someone is either brave or not tall.
Everyone who is not humble is generous or kind.
If mary is creative then someone is humble or patient and vice versa.
Everyone who is not patient is both strong and patient and vice versa.
If someone is either strong or not happy then someone is either not curious or not rich.
Everyone who is not quiet or not funny is both not humble and not happy and vice versa.
Everyone who is not creative is either old or kind.
If someone is both strong and kind then someone is both not rich and kind.
Fred is not happy.
Someone is both brave and not strong.
Mary is not happy or kind.
Someone is curious or tall.
John is both curious and not kind.
Someone is patient. | Fred is humble. | contradiction | (![X]:(funny(X)=>(strong(X)<~>~patient(X))))&
((~funny(fred))=>(?[X]:((~old(X)<~>tall(X)))))&
((?[X]:(strong(X)))<=>(~curious(susan)))&
(((wise(susan)&~brave(susan)))<=>(?[X]:(wise(X))))&
((?[X]:((~old(X)|wise(X))))=>(tall(paul)))&
((?[X]:(~creative(X)))=>((~rich(john)|~funny(john))))&
(((kind(john)<~>~creative(john)))=>(?[X]:(~tall(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(happy(X))))&
(((happy(john)&~old(john)))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:(~humble(X)=>(generous(X)|kind(X))))&
((creative(mary))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:(~patient(X)<=>(strong(X)&patient(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:((~quiet(X)|~funny(X))<=>(~humble(X)&~happy(X))))&
(![X]:(~creative(X)=>(old(X)<~>kind(X))))&
((?[X]:((strong(X)&kind(X))))=>(?[X]:((~rich(X)&kind(X)))))&
(~happy(fred))&
(?[X]:((brave(X)&~strong(X))))&
((~happy(mary)|kind(mary)))&
(?[X]:((curious(X)|tall(X))))&
((curious(john)&~kind(john)))&
(?[X]:(patient(X))) | humble(fred) | [
"p0",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7581663304559844603674645
% SZS output start Proof for 7581663304559844603674645
1. ! [X0] : (funny(X0) => (strong(X0) <~> ~patient(X0))) [input p0]
12. ! [X0] : (~patient(X0) <=> (patient(X0) & strong(X0))) [input p11]
14. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p13]
23. humble(fred) [input hypothesis]
28. ! [X0] : ((strong(X0) <~> ~patient(X0)) | ~funny(X0)) [ennf transformation 1]
39. ! [X0] : (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | ~funny(X0)) [nnf transformation 28]
67. ! [X0] : ((~patient(X0) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | patient(X0))) [nnf transformation 12]
68. ! [X0] : ((~patient(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | patient(X0))) [flattening 67]
73. ! [X0] : (((~funny(X0) | ~quiet(X0)) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | (funny(X0) & quiet(X0)))) [nnf transformation 14]
74. ! [X0] : ((~funny(X0) | ~quiet(X0) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | (funny(X0) & quiet(X0)))) [flattening 73]
85. ~patient(X0) | strong(X0) | ~funny(X0) [cnf transformation 39]
108. patient(X0) | patient(X0) [cnf transformation 68]
109. ~patient(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 68]
115. ~humble(X0) | funny(X0) [cnf transformation 74]
131. humble(fred) [cnf transformation 23]
132. patient(X0) [duplicate literal removal 108]
133. ~patient(X0) | ~strong(X0) [duplicate literal removal 109]
135. 1 <=> funny(fred) [avatar definition]
137. funny(fred) <- (1) [avatar component clause 135]
158. 6 <=> ! [X1] : ~strong(X1) [avatar definition]
159. ~strong(X1) <- (6) [avatar component clause 158]
331. funny(fred) [resolution 115,131]
333. 1 [avatar split clause 331,135]
334. ~strong(X0) [resolution 133,132]
335. 6 [avatar split clause 334,158]
338. strong(X0) | ~funny(X0) [resolution 85,132]
339. ~funny(X0) <- (6) [subsumption resolution 338,159]
340. $false <- (1, 6) [resolution 339,137]
343. ~1 | ~6 [avatar contradiction clause 340]
344. $false [avatar sat refutation 333,335,343]
% SZS output end Proof for 7581663304559844603674645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not calm is not humble.
Everyone who is not strong or not creative is both not tall and not happy.
If john is both not quiet and not rich then someone is not quiet or rich.
If fred is both wise and not tall then fred is not strong and vice versa.
Everyone who is both not tall and old is not kind and vice versa.
If mary is not generous or patient then lucy is both not generous and quiet and vice versa.
Everyone who is funny or patient is both not brave and not quiet and vice versa.
If someone is not patient or not brave then someone is either not tall or not creative.
If someone is both not humble and tall then john is not brave or generous and vice versa.
Everyone who is not strong is patient or not brave and vice versa.
If john is happy then john is quiet and vice versa.
If someone is either generous or not curious then susan is both curious and not generous and vice versa.
Everyone who is not funny is generous.
Everyone who is both creative and not humble is either rich or old and vice versa.
If someone is both humble and curious then someone is either generous or quiet.
If john is not creative or generous then mary is both funny and patient.
Paul is either not happy or not creative.
Someone is not patient.
Someone is both kind and not old.
Someone is either not funny or calm.
Someone is generous or brave.
Lucy is both wise and tall.
Fred is either not curious or not rich.
Someone is not happy or not rich. | Paul is creative. | entailment | (![X]:((creative(X)<~>~calm(X))=>~humble(X)))&
(![X]:((~strong(X)|~creative(X))=>(~tall(X)&~happy(X))))&
(((~quiet(john)&~rich(john)))=>(?[X]:((~quiet(X)|rich(X)))))&
(((wise(fred)&~tall(fred)))<=>(~strong(fred)))&
(![X]:((~tall(X)&old(X))<=>~kind(X)))&
(((~generous(mary)|patient(mary)))<=>((~generous(lucy)&quiet(lucy))))&
(![X]:((funny(X)|patient(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~patient(X)|~brave(X))))=>(?[X]:((~tall(X)<~>~creative(X)))))&
((?[X]:((~humble(X)&tall(X))))<=>((~brave(john)|generous(john))))&
(![X]:(~strong(X)<=>(patient(X)|~brave(X))))&
((happy(john))<=>(quiet(john)))&
((?[X]:((generous(X)<~>~curious(X))))<=>((curious(susan)&~generous(susan))))&
(![X]:(~funny(X)=>generous(X)))&
(![X]:((creative(X)&~humble(X))<=>(rich(X)<~>old(X))))&
((?[X]:((humble(X)&curious(X))))=>(?[X]:((generous(X)<~>quiet(X)))))&
(((~creative(john)|generous(john)))=>((funny(mary)&patient(mary))))&
((~happy(paul)<~>~creative(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((kind(X)&~old(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((generous(X)|brave(X))))&
((wise(lucy)&tall(lucy)))&
((~curious(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|~rich(X)))) | creative(paul) | [
"p1",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6949936019144178820104183
% SZS output start Proof for 6949936019144178820104183
2. ! [X0] : ((~creative(X0) | ~strong(X0)) => (~happy(X0) & ~tall(X0))) [input p1]
17. ~happy(paul) <~> ~creative(paul) [input p16]
25. ~creative(paul) [input hypothesis]
30. ! [X0] : ((~happy(X0) & ~tall(X0)) | (creative(X0) & strong(X0))) [ennf transformation 2]
71. (creative(paul) | happy(paul)) & (~creative(paul) | ~happy(paul)) [nnf transformation 17]
89. ~happy(X0) | creative(X0) [cnf transformation 30]
139. creative(paul) | happy(paul) [cnf transformation 71]
151. ~creative(paul) [cnf transformation 25]
310. creative(paul) [subsumption resolution 139,89]
350. $false [subsumption resolution 151,310]
% SZS output end Proof for 6949936019144178820104183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not rich is not kind.
If paul is old or curious then someone is wise or not happy and vice versa.
Everyone who is both patient and wise is quiet or strong and vice versa.
Everyone who is not quiet is strong or not wise.
Everyone who is quiet is either funny or not curious.
Everyone who is both quiet and rich is wise or not humble and vice versa.
Everyone who is quiet is strong and vice versa.
If someone is both not curious and strong then paul is both generous and not calm.
Everyone who is both not curious and happy is either not old or not wise and vice versa.
Everyone who is both not happy and strong is strong or not happy and vice versa.
If mary is either quiet or not quiet then someone is not strong or not curious.
If fred is not brave then someone is both not kind and patient.
Everyone who is both patient and brave is both old and not strong.
If someone is both not creative and quiet then someone is old or not old and vice versa.
If mary is either generous or humble then someone is tall or calm.
If mary is either not creative or creative then paul is either not humble or kind.
Mary is not tall or not happy.
Someone is either not tall or humble.
Paul is calm or not rich.
Mary is not brave.
Someone is not patient.
Someone is both not brave and tall.
Someone is humble.
John is either rich or tall. | Paul is not funny. | contradiction | (![X]:((kind(X)|~rich(X))=>~kind(X)))&
(((old(paul)|curious(paul)))<=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((patient(X)&wise(X))<=>(quiet(X)|strong(X))))&
(![X]:(~quiet(X)=>(strong(X)|~wise(X))))&
(![X]:(quiet(X)=>(funny(X)<~>~curious(X))))&
(![X]:((quiet(X)&rich(X))<=>(wise(X)|~humble(X))))&
(![X]:(quiet(X)<=>strong(X)))&
((?[X]:((~curious(X)&strong(X))))=>((generous(paul)&~calm(paul))))&
(![X]:((~curious(X)&happy(X))<=>(~old(X)<~>~wise(X))))&
(![X]:((~happy(X)&strong(X))<=>(strong(X)|~happy(X))))&
(((quiet(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|~curious(X)))))&
((~brave(fred))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((patient(X)&brave(X))=>(old(X)&~strong(X))))&
((?[X]:((~creative(X)&quiet(X))))<=>(?[X]:((old(X)|~old(X)))))&
(((generous(mary)<~>humble(mary)))=>(?[X]:((tall(X)|calm(X)))))&
(((~creative(mary)<~>creative(mary)))=>((~humble(paul)<~>kind(paul))))&
((~tall(mary)|~happy(mary)))&
(?[X]:((~tall(X)<~>humble(X))))&
((calm(paul)|~rich(paul)))&
(~brave(mary))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)&tall(X))))&
(?[X]:(humble(X)))&
((rich(john)<~>tall(john))) | ~funny(paul) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8742687726029734436496747
% SZS output start Proof for 8742687726029734436496747
1. ! [X0] : ((~rich(X0) | kind(X0)) => ~kind(X0)) [input p0]
5. ! [X0] : (quiet(X0) => (funny(X0) <~> ~curious(X0))) [input p4]
6. ! [X0] : ((rich(X0) & quiet(X0)) <=> (~humble(X0) | wise(X0))) [input p5]
7. ! [X0] : (quiet(X0) <=> strong(X0)) [input p6]
8. ? [X0] : (strong(X0) & ~curious(X0)) => (~calm(paul) & generous(paul)) [input p7]
16. (~creative(mary) <~> creative(mary)) => (~humble(paul) <~> kind(paul)) [input p15]
19. ~rich(paul) | calm(paul) [input p18]
25. ~funny(paul) [input hypothesis]
27. ! [X0] : (~kind(X0) | (rich(X0) & ~kind(X0))) [ennf transformation 1]
30. ! [X0] : ((funny(X0) <~> ~curious(X0)) | ~quiet(X0)) [ennf transformation 5]
31. (~calm(paul) & generous(paul)) | ! [X0] : (~strong(X0) | curious(X0)) [ennf transformation 8]
37. (~humble(paul) <~> kind(paul)) | (~creative(mary) <=> creative(mary)) [ennf transformation 16]
45. ! [X0] : (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ~quiet(X0)) [nnf transformation 30]
46. ! [X0] : (((rich(X0) & quiet(X0)) | (humble(X0) & ~wise(X0))) & ((~humble(X0) | wise(X0)) | (~rich(X0) | ~quiet(X0)))) [nnf transformation 6]
47. ! [X0] : (((rich(X0) & quiet(X0)) | (humble(X0) & ~wise(X0))) & (~humble(X0) | wise(X0) | ~rich(X0) | ~quiet(X0))) [flattening 46]
48. ! [X0] : ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0))) [nnf transformation 7]
66. ((~kind(paul) | humble(paul)) & (kind(paul) | ~humble(paul))) | ((~creative(mary) | ~creative(mary)) & (creative(mary) | creative(mary))) [nnf transformation 37]
77. ~kind(X0) | ~kind(X0) [cnf transformation 27]
89. ~quiet(X0) | funny(X0) | ~curious(X0) [cnf transformation 45]
93. humble(X0) | quiet(X0) [cnf transformation 47]
95. humble(X0) | rich(X0) [cnf transformation 47]
96. ~quiet(X0) | strong(X0) [cnf transformation 48]
99. ~calm(paul) | ~strong(X0) | curious(X0) [cnf transformation 31]
124. kind(paul) | ~humble(paul) | creative(mary) | creative(mary) [cnf transformation 66]
125. kind(paul) | ~humble(paul) | ~creative(mary) | ~creative(mary) [cnf transformation 66]
131. ~rich(paul) | calm(paul) [cnf transformation 19]
139. ~funny(paul) [cnf transformation 25]
140. kind(paul) | ~humble(paul) | creative(mary) [duplicate literal removal 124]
141. kind(paul) | ~humble(paul) | ~creative(mary) [duplicate literal removal 125]
146. ~kind(X0) [duplicate literal removal 77]
155. 3 <=> curious(paul) [avatar definition]
156. ~curious(paul) <- (~3) [avatar component clause 155]
174. 7 <=> ! [X0] : (~strong(X0) | curious(X0)) [avatar definition]
175. ~strong(X0) | curious(X0) <- (7) [avatar component clause 174]
177. 8 <=> calm(paul) [avatar definition]
180. 7 | ~8 [avatar split clause 99,177,174]
246. ~humble(paul) | ~creative(mary) [subsumption resolution 141,146]
248. 23 <=> creative(mary) [avatar definition]
252. 24 <=> humble(paul) [avatar definition]
254. ~humble(paul) <- (~24) [avatar component clause 252]
255. ~23 | ~24 [avatar split clause 246,252,248]
256. ~humble(paul) | creative(mary) [subsumption resolution 140,146]
257. 23 | ~24 [avatar split clause 256,252,248]
278. 29 <=> rich(paul) [avatar definition]
281. 8 | ~29 [avatar split clause 131,278,177]
296. quiet(paul) <- (~24) [resolution 93,254]
307. rich(paul) <- (~24) [resolution 95,254]
311. 29 | 24 [avatar split clause 307,252,278]
314. strong(paul) <- (~24) [resolution 96,296]
341. funny(paul) | ~curious(paul) <- (~24) [resolution 89,296]
345. ~curious(paul) <- (~24) [subsumption resolution 341,139]
346. ~3 | 24 [avatar split clause 345,252,155]
383. curious(paul) <- (7, ~24) [resolution 314,175]
388. $false <- (~3, 7, ~24) [subsumption resolution 383,156]
389. 3 | ~7 | 24 [avatar contradiction clause 388]
390. $false [avatar sat refutation 180,255,257,281,311,346,389]
% SZS output end Proof for 8742687726029734436496747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both strong and not patient then someone is not funny.
If susan is not curious then alice is not funny or not quiet and vice versa.
If paul is not strong then someone is either not creative or not strong and vice versa.
Everyone who is not creative or not funny is brave and vice versa.
If fred is brave then someone is funny and vice versa.
Everyone who is both not calm and patient is either not curious or not calm and vice versa.
Everyone who is both old and not curious is rich.
If susan is both rich and not quiet then alice is either not patient or not happy and vice versa.
If fred is not funny then someone is creative or not old and vice versa.
Everyone who is both tall and not humble is either brave or curious and vice versa.
If john is either rich or not tall then mary is either generous or creative.
If paul is rich then someone is both not tall and wise and vice versa.
Everyone who is either not curious or generous is either funny or not curious.
Everyone who is either old or not generous is old or kind and vice versa.
Everyone who is old is not funny.
Everyone who is either tall or not brave is funny and vice versa.
Mary is either tall or humble.
Someone is both patient and curious.
Paul is not generous or not curious.
Susan is either not old or quiet.
Someone is either humble or brave.
Paul is not creative or not tall.
Susan is not curious.
Fred is humble or strong. | Fred is old. | contradiction | (((strong(alice)&~patient(alice)))=>(?[X]:(~funny(X))))&
((~curious(susan))<=>((~funny(alice)|~quiet(alice))))&
((~strong(paul))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:((~creative(X)|~funny(X))<=>brave(X)))&
((brave(fred))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)&patient(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((old(X)&~curious(X))=>rich(X)))&
(((rich(susan)&~quiet(susan)))<=>((~patient(alice)<~>~happy(alice))))&
((~funny(fred))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((tall(X)&~humble(X))<=>(brave(X)<~>curious(X))))&
(((rich(john)<~>~tall(john)))=>((generous(mary)<~>creative(mary))))&
((rich(paul))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~curious(X)<~>generous(X))=>(funny(X)<~>~curious(X))))&
(![X]:((old(X)<~>~generous(X))<=>(old(X)|kind(X))))&
(![X]:(old(X)=>~funny(X)))&
(![X]:((tall(X)<~>~brave(X))<=>funny(X)))&
((tall(mary)<~>humble(mary)))&
(?[X]:((patient(X)&curious(X))))&
((~generous(paul)|~curious(paul)))&
((~old(susan)<~>quiet(susan)))&
(?[X]:((humble(X)<~>brave(X))))&
((~creative(paul)|~tall(paul)))&
(~curious(susan))&
((humble(fred)|strong(fred))) | old(fred) | [
"p3",
"p9",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4236656006570760849728354
% SZS output start Proof for 4236656006570760849728354
4. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> brave(X0)) [input p3]
10. ! [X0] : ((~humble(X0) & tall(X0)) <=> (brave(X0) <~> curious(X0))) [input p9]
13. ! [X0] : ((~curious(X0) <~> generous(X0)) => (funny(X0) <~> ~curious(X0))) [input p12]
14. ! [X0] : ((old(X0) <~> ~generous(X0)) <=> (kind(X0) | old(X0))) [input p13]
15. ! [X0] : (old(X0) => ~funny(X0)) [input p14]
16. ! [X0] : ((tall(X0) <~> ~brave(X0)) <=> funny(X0)) [input p15]
25. old(fred) [input hypothesis]
31. ! [X0] : ((funny(X0) <~> ~curious(X0)) | (~curious(X0) <=> generous(X0))) [ennf transformation 13]
32. ! [X0] : (~funny(X0) | ~old(X0)) [ennf transformation 15]
41. ! [X0] : (((~funny(X0) | ~creative(X0)) | ~brave(X0)) & (brave(X0) | (funny(X0) & creative(X0)))) [nnf transformation 4]
42. ! [X0] : ((~funny(X0) | ~creative(X0) | ~brave(X0)) & (brave(X0) | (funny(X0) & creative(X0)))) [flattening 41]
55. ! [X0] : (((~humble(X0) & tall(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (humble(X0) | ~tall(X0)))) [nnf transformation 10]
56. ! [X0] : (((~humble(X0) & tall(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | humble(X0) | ~tall(X0))) [flattening 55]
62. ! [X0] : (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 31]
63. ! [X0] : ((((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | (~kind(X0) & ~old(X0))) & ((kind(X0) | old(X0)) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))))) [nnf transformation 14]
64. ! [X0] : ((((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | (~kind(X0) & ~old(X0))) & (kind(X0) | old(X0) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))))) [flattening 63]
65. ! [X0] : ((((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | ~funny(X0)) & (funny(X0) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))))) [nnf transformation 16]
82. brave(X0) | funny(X0) [cnf transformation 42]
104. ~brave(X0) | curious(X0) | tall(X0) [cnf transformation 56]
116. ~curious(X0) | funny(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 62]
123. generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 64]
125. ~old(X0) | ~funny(X0) [cnf transformation 32]
126. funny(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 65]
129. brave(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 65]
142. old(fred) [cnf transformation 25]
144. ~old(X0) | generous(X0) [duplicate literal removal 123]
145. ~generous(X0) | funny(X0) | ~curious(X0) [duplicate literal removal 116]
235. 19 <=> funny(fred) [avatar definition]
237. ~funny(fred) <- (~19) [avatar component clause 235]
291. ~tall(X0) | brave(X0) [subsumption resolution 129,82]
292. ~tall(X0) | funny(X0) [subsumption resolution 126,291]
355. ~funny(fred) [resolution 125,142]
356. generous(fred) [resolution 144,142]
387. 43 <=> curious(fred) [avatar definition]
388. ~curious(fred) <- (~43) [avatar component clause 387]
391. curious(X0) | tall(X0) | funny(X0) [resolution 104,82]
396. curious(X0) | funny(X0) [subsumption resolution 391,292]
446. funny(fred) | ~curious(fred) [resolution 145,356]
447. ~curious(fred) <- (~19) [subsumption resolution 446,237]
450. ~43 | 19 [avatar split clause 447,235,387]
454. funny(fred) <- (~43) [resolution 388,396]
457. 19 | 43 [avatar split clause 454,387,235]
463. ~19 [avatar split clause 355,235]
464. $false [avatar sat refutation 450,457,463]
% SZS output end Proof for 4236656006570760849728354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not calm is both not curious and quiet and vice versa.
If alice is either funny or strong then someone is both not humble and not patient and vice versa.
Everyone who is tall is both patient and not wise and vice versa.
Everyone who is both humble and not strong is both not happy and creative.
Everyone who is not creative is both not kind and quiet and vice versa.
If someone is strong or not tall then mary is quiet and vice versa.
If lucy is not humble then someone is both happy and wise and vice versa.
If alice is either brave or kind then someone is not funny or not tall and vice versa.
Everyone who is either quiet or curious is calm or not curious and vice versa.
Everyone who is creative or not rich is kind.
If paul is not humble or not calm then alice is funny or old and vice versa.
Everyone who is not funny is wise or brave.
If someone is generous then someone is curious or not patient.
Everyone who is both not patient and happy is not brave.
Everyone who is both not patient and calm is quiet or not calm.
If someone is either not tall or not generous then someone is not brave.
Fred is both curious and wise.
Paul is funny.
Someone is both not happy and not strong.
Paul is either not funny or not patient.
Lucy is not rich.
Someone is wise.
Mary is not quiet or not rich. | Alice is funny. | neutral | (![X]:((rich(X)|~calm(X))<=>(~curious(X)&quiet(X))))&
(((funny(alice)<~>strong(alice)))<=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:(tall(X)<=>(patient(X)&~wise(X))))&
(![X]:((humble(X)&~strong(X))=>(~happy(X)&creative(X))))&
(![X]:(~creative(X)<=>(~kind(X)&quiet(X))))&
((?[X]:((strong(X)|~tall(X))))<=>(quiet(mary)))&
((~humble(lucy))<=>(?[X]:((happy(X)&wise(X)))))&
(((brave(alice)<~>kind(alice)))<=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((quiet(X)<~>curious(X))<=>(calm(X)|~curious(X))))&
(![X]:((creative(X)|~rich(X))=>kind(X)))&
(((~humble(paul)|~calm(paul)))<=>((funny(alice)|old(alice))))&
(![X]:(~funny(X)=>(wise(X)|brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((~patient(X)&happy(X))=>~brave(X)))&
(![X]:((~patient(X)&calm(X))=>(quiet(X)|~calm(X))))&
((?[X]:((~tall(X)<~>~generous(X))))=>(?[X]:(~brave(X))))&
((curious(fred)&wise(fred)))&
(funny(paul))&
(?[X]:((~happy(X)&~strong(X))))&
((~funny(paul)<~>~patient(paul)))&
(~rich(lucy))&
(?[X]:(wise(X)))&
((~quiet(mary)|~rich(mary))) | funny(alice) | [] | null | 0 |
Everyone who is both not creative and kind is both not tall and kind and vice versa.
Everyone who is either funny or creative is both not happy and not tall.
If mary is either not funny or generous then john is humble or not calm and vice versa.
Everyone who is humble or old is not patient.
Everyone who is humble is both not calm and not wise and vice versa.
Everyone who is either not strong or not calm is not curious or not creative and vice versa.
Everyone who is both funny and not patient is not old or not rich.
Everyone who is both old and not generous is either rich or not patient and vice versa.
If paul is either funny or patient then john is both not rich and funny and vice versa.
Everyone who is both brave and curious is both not kind and not brave and vice versa.
Everyone who is either not brave or not happy is either not curious or quiet.
Everyone who is either not patient or quiet is both happy and not tall and vice versa.
If someone is not quiet or not patient then susan is not happy or not humble.
Everyone who is either humble or rich is either wise or rich and vice versa.
If someone is not tall or quiet then someone is both kind and not tall.
Everyone who is wise or happy is not tall or not generous.
Someone is not curious or strong.
John is either not wise or not funny.
John is both rich and not creative.
Someone is either funny or not rich.
Someone is either not humble or not patient.
Susan is either patient or old.
Lucy is patient or not brave. | Susan is happy. | neutral | (![X]:((~creative(X)&kind(X))<=>(~tall(X)&kind(X))))&
(![X]:((funny(X)<~>creative(X))=>(~happy(X)&~tall(X))))&
(((~funny(mary)<~>generous(mary)))<=>((humble(john)|~calm(john))))&
(![X]:((humble(X)|old(X))=>~patient(X)))&
(![X]:(humble(X)<=>(~calm(X)&~wise(X))))&
(![X]:((~strong(X)<~>~calm(X))<=>(~curious(X)|~creative(X))))&
(![X]:((funny(X)&~patient(X))=>(~old(X)|~rich(X))))&
(![X]:((old(X)&~generous(X))<=>(rich(X)<~>~patient(X))))&
(((funny(paul)<~>patient(paul)))<=>((~rich(john)&funny(john))))&
(![X]:((brave(X)&curious(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~brave(X)<~>~happy(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(happy(X)&~tall(X))))&
((?[X]:((~quiet(X)|~patient(X))))=>((~happy(susan)|~humble(susan))))&
(![X]:((humble(X)<~>rich(X))<=>(wise(X)<~>rich(X))))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:((kind(X)&~tall(X)))))&
(![X]:((wise(X)|happy(X))=>(~tall(X)|~generous(X))))&
(?[X]:((~curious(X)|strong(X))))&
((~wise(john)<~>~funny(john)))&
((rich(john)&~creative(john)))&
(?[X]:((funny(X)<~>~rich(X))))&
(?[X]:((~humble(X)<~>~patient(X))))&
((patient(susan)<~>old(susan)))&
((patient(lucy)|~brave(lucy))) | happy(susan) | [] | null | 0 |
Everyone who is both not quiet and generous is not happy or creative and vice versa. Everyone who is calm is quiet and vice versa. Everyone who is tall is either not happy or funny. Everyone who is strong is either kind or not generous. Everyone who is not brave is not creative and vice versa. Everyone who is either not calm or happy is brave and vice versa. If mary is not patient or not creative then someone is both not curious and not humble. If alice is not brave or not funny then lucy is either not patient or curious. Everyone who is creative or funny is both humble and strong and vice versa. Everyone who is brave or not curious is both tall and not curious and vice versa. If someone is calm then someone is both not curious and not calm. If someone is both wise and generous then someone is either happy or not strong. Everyone who is humble is either not patient or wise. If someone is not kind then susan is both tall and not funny and vice versa. Everyone who is either strong or not brave is kind. If someone is happy then lucy is humble or not creative. Someone is either generous or not humble. Paul is either generous or not kind. Someone is not generous or not curious. Someone is wise or not old. Alice is either not rich or not quiet. John is kind or not kind. | Mary is quiet. | contradiction | (![X]:((~quiet(X)&generous(X))<=>(~happy(X)|creative(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(tall(X)=>(~happy(X)<~>funny(X))))&
(![X]:(strong(X)=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
((?[X]:(happy(X)))=>((humble(lucy)|~creative(lucy))))&
(?[X]:((generous(X)<~>~humble(X))))&
((generous(paul)<~>~kind(paul)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((wise(X)|~old(X))))&
((~rich(alice)<~>~quiet(alice)))&
((kind(john)|~kind(john))) | quiet(mary) | [
"p0",
"p1",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 229882699211323319280435
% SZS output start Proof for 229882699211323319280435
1. ! [X0] : ((generous(X0) & ~quiet(X0)) <=> (creative(X0) | ~happy(X0))) [input p0]
2. ! [X0] : (calm(X0) <=> quiet(X0)) [input p1]
5. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p4]
6. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> brave(X0)) [input p5]
23. quiet(mary) [input hypothesis]
37. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~generous(X0) | quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~generous(X0) | quiet(X0))) [flattening 37]
39. ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))) [nnf transformation 2]
42. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 5]
43. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 6]
73. ~quiet(X0) | happy(X0) [cnf transformation 38]
74. ~creative(X0) | ~quiet(X0) [cnf transformation 38]
78. ~quiet(X0) | calm(X0) [cnf transformation 39]
84. ~brave(X0) | creative(X0) [cnf transformation 42]
86. ~calm(X0) | brave(X0) | ~happy(X0) [cnf transformation 43]
127. quiet(mary) [cnf transformation 23]
129. 1 <=> creative(mary) [avatar definition]
131. creative(mary) <- (1) [avatar component clause 129]
251. happy(mary) [resolution 73,127]
253. calm(mary) [resolution 78,127]
297. brave(mary) | ~happy(mary) [resolution 86,253]
298. brave(mary) [subsumption resolution 297,251]
303. creative(mary) [resolution 298,84]
304. 1 [avatar split clause 303,129]
309. ~quiet(mary) <- (1) [resolution 131,74]
310. $false <- (1) [subsumption resolution 309,127]
311. ~1 [avatar contradiction clause 310]
312. $false [avatar sat refutation 304,311]
% SZS output end Proof for 229882699211323319280435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and humble is wise or not brave.
If someone is both not funny and not tall then someone is not brave and vice versa.
Everyone who is either brave or tall is not generous or not curious and vice versa.
Everyone who is either not rich or not quiet is both creative and rich and vice versa.
If john is old or not wise then someone is humble or patient.
If paul is not tall or not generous then someone is both not generous and not humble and vice versa.
If john is both old and creative then alice is either not calm or humble.
Everyone who is both not funny and patient is either not patient or not quiet.
If someone is both not strong and strong then alice is quiet or not curious.
If someone is both patient and funny then john is either not patient or brave.
Everyone who is not generous or not tall is not old or old.
Everyone who is either not old or not humble is not humble.
Everyone who is humble is either not strong or not kind.
If someone is either not brave or not calm then alice is happy.
If someone is brave then lucy is creative or not rich.
If someone is generous then lucy is not wise or calm and vice versa.
Someone is calm.
Mary is tall.
Lucy is either strong or not strong.
Someone is either not creative or not wise.
Paul is tall or not rich.
Someone is both tall and not curious.
Someone is either not creative or tall. | John is old. | neutral | (![X]:((~funny(X)&humble(X))=>(wise(X)|~brave(X))))&
((?[X]:((~funny(X)&~tall(X))))<=>(?[X]:(~brave(X))))&
(![X]:((brave(X)<~>tall(X))<=>(~generous(X)|~curious(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(creative(X)&rich(X))))&
(((old(john)|~wise(john)))=>(?[X]:((humble(X)|patient(X)))))&
(((~tall(paul)|~generous(paul)))<=>(?[X]:((~generous(X)&~humble(X)))))&
(((old(john)&creative(john)))=>((~calm(alice)<~>humble(alice))))&
(![X]:((~funny(X)&patient(X))=>(~patient(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&strong(X))))=>((quiet(alice)|~curious(alice))))&
((?[X]:((patient(X)&funny(X))))=>((~patient(john)<~>brave(john))))&
(![X]:((~generous(X)|~tall(X))=>(~old(X)|old(X))))&
(![X]:((~old(X)<~>~humble(X))=>~humble(X)))&
(![X]:(humble(X)=>(~strong(X)<~>~kind(X))))&
((?[X]:((~brave(X)<~>~calm(X))))=>(happy(alice)))&
((?[X]:(brave(X)))=>((creative(lucy)|~rich(lucy))))&
((?[X]:(generous(X)))<=>((~wise(lucy)|calm(lucy))))&
(?[X]:(calm(X)))&
(tall(mary))&
((strong(lucy)<~>~strong(lucy)))&
(?[X]:((~creative(X)<~>~wise(X))))&
((tall(paul)|~rich(paul)))&
(?[X]:((tall(X)&~curious(X))))&
(?[X]:((~creative(X)<~>tall(X)))) | old(john) | [] | null | 0 |
If lucy is either rich or wise then alice is not creative and vice versa.
If alice is not kind then paul is either not calm or funny.
Everyone who is tall is both not generous and not calm and vice versa.
Everyone who is either strong or not curious is both humble and not old and vice versa.
Everyone who is not quiet is not brave.
If paul is both not brave and curious then someone is patient or creative and vice versa.
Everyone who is either patient or not brave is not curious or humble and vice versa.
Everyone who is patient or happy is brave.
Everyone who is both kind and creative is both rich and not creative.
Everyone who is kind or tall is both calm and not creative and vice versa.
If fred is either not strong or not happy then fred is rich.
Everyone who is not old or not happy is tall or wise.
If alice is either generous or not funny then someone is either not generous or tall and vice versa.
Everyone who is either not rich or curious is both not funny and brave.
If paul is quiet or not brave then paul is calm.
Everyone who is either not calm or wise is both not funny and brave and vice versa.
Someone is either not quiet or not brave.
Lucy is both quiet and not creative.
Susan is calm.
Susan is old or humble.
Fred is both wise and not old.
Lucy is happy or humble.
Someone is not funny or rich. | Susan is patient. | contradiction | (((rich(lucy)<~>wise(lucy)))<=>(~creative(alice)))&
((~kind(alice))=>((~calm(paul)<~>funny(paul))))&
(![X]:(tall(X)<=>(~generous(X)&~calm(X))))&
(![X]:((strong(X)<~>~curious(X))<=>(humble(X)&~old(X))))&
(![X]:(~quiet(X)=>~brave(X)))&
(((~brave(paul)&curious(paul)))<=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((patient(X)<~>~brave(X))<=>(~curious(X)|humble(X))))&
(![X]:((patient(X)|happy(X))=>brave(X)))&
(![X]:((kind(X)&creative(X))=>(rich(X)&~creative(X))))&
(![X]:((kind(X)|tall(X))<=>(calm(X)&~creative(X))))&
(((~strong(fred)<~>~happy(fred)))=>(rich(fred)))&
(![X]:((~old(X)|~happy(X))=>(tall(X)|wise(X))))&
(((generous(alice)<~>~funny(alice)))<=>(?[X]:((~generous(X)<~>tall(X)))))&
(![X]:((~rich(X)<~>curious(X))=>(~funny(X)&brave(X))))&
(((quiet(paul)|~brave(paul)))=>(calm(paul)))&
(![X]:((~calm(X)<~>wise(X))<=>(~funny(X)&brave(X))))&
(?[X]:((~quiet(X)<~>~brave(X))))&
((quiet(lucy)&~creative(lucy)))&
(calm(susan))&
((old(susan)|humble(susan)))&
((wise(fred)&~old(fred)))&
((happy(lucy)|humble(lucy)))&
(?[X]:((~funny(X)|rich(X)))) | patient(susan) | [
"p2",
"p5",
"p7",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3593021396470960157936537
% SZS output start Proof for 3593021396470960157936537
3. ! [X0] : (tall(X0) <=> (~calm(X0) & ~generous(X0))) [input p2]
6. (curious(paul) & ~brave(paul)) <=> ? [X0] : (creative(X0) | patient(X0)) [input p5]
8. ! [X0] : ((happy(X0) | patient(X0)) => brave(X0)) [input p7]
10. ! [X0] : ((tall(X0) | kind(X0)) <=> (~creative(X0) & calm(X0))) [input p9]
12. ! [X0] : ((~happy(X0) | ~old(X0)) => (wise(X0) | tall(X0))) [input p11]
15. (~brave(paul) | quiet(paul)) => calm(paul) [input p14]
16. ! [X0] : ((~calm(X0) <~> wise(X0)) <=> (brave(X0) & ~funny(X0))) [input p15]
24. patient(susan) [input hypothesis]
27. ! [X0] : (brave(X0) | (~happy(X0) & ~patient(X0))) [ennf transformation 8]
31. ! [X0] : ((wise(X0) | tall(X0)) | (happy(X0) & old(X0))) [ennf transformation 12]
32. ! [X0] : (wise(X0) | tall(X0) | (happy(X0) & old(X0))) [flattening 31]
34. calm(paul) | (brave(paul) & ~quiet(paul)) [ennf transformation 15]
37. ! [X0] : ((tall(X0) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | ~tall(X0))) [nnf transformation 3]
38. ! [X0] : ((tall(X0) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~tall(X0))) [flattening 37]
41. ((curious(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & ~patient(X0))) & (? [X0] : (creative(X0) | patient(X0)) | (~curious(paul) | brave(paul))) [nnf transformation 6]
42. ((curious(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & ~patient(X0))) & (? [X0] : (creative(X0) | patient(X0)) | ~curious(paul) | brave(paul)) [flattening 41]
43. ((curious(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & ~patient(X0))) & (? [X1] : (creative(X1) | patient(X1)) | ~curious(paul) | brave(paul)) [rectify 42]
44. ? [X1] : (creative(X1) | patient(X1)) => (creative(sK0) | patient(sK0)) [choice axiom]
45. ((curious(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & ~patient(X0))) & ((creative(sK0) | patient(sK0)) | ~curious(paul) | brave(paul)) [skolemisation 43,44]
48. ! [X0] : (((tall(X0) | kind(X0)) | (creative(X0) | ~calm(X0))) & ((~creative(X0) & calm(X0)) | (~tall(X0) & ~kind(X0)))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | kind(X0) | creative(X0) | ~calm(X0)) & ((~creative(X0) & calm(X0)) | (~tall(X0) & ~kind(X0)))) [flattening 48]
56. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (~brave(X0) | funny(X0))) & ((brave(X0) & ~funny(X0)) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [nnf transformation 16]
57. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | ~brave(X0) | funny(X0)) & ((brave(X0) & ~funny(X0)) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [flattening 56]
70. ~tall(X0) | ~calm(X0) [cnf transformation 38]
80. ~brave(paul) | ~patient(X0) [cnf transformation 45]
91. ~happy(X0) | brave(X0) [cnf transformation 27]
95. calm(X0) | ~tall(X0) [cnf transformation 49]
102. wise(X0) | tall(X0) | happy(X0) [cnf transformation 32]
116. calm(paul) | brave(paul) [cnf transformation 34]
120. ~calm(X0) | brave(X0) | ~wise(X0) [cnf transformation 57]
133. patient(susan) [cnf transformation 24]
156. 5 <=> calm(paul) [avatar definition]
158. calm(paul) <- (5) [avatar component clause 156]
174. 9 <=> ! [X0] : ~patient(X0) [avatar definition]
175. ~patient(X0) <- (9) [avatar component clause 174]
178. 10 <=> brave(paul) [avatar definition]
180. ~brave(paul) <- (~10) [avatar component clause 178]
182. 9 | ~10 [avatar split clause 80,178,174]
193. ~tall(X0) [subsumption resolution 95,70]
208. happy(X0) | wise(X0) [subsumption resolution 102,193]
233. 10 | 5 [avatar split clause 116,156,178]
268. $false <- (9) [resolution 175,133]
269. ~9 [avatar contradiction clause 268]
279. brave(X0) | wise(X0) [resolution 208,91]
295. wise(paul) <- (~10) [resolution 279,180]
370. brave(paul) | ~wise(paul) <- (5) [resolution 120,158]
374. ~wise(paul) <- (5, ~10) [subsumption resolution 370,180]
375. $false <- (5, ~10) [subsumption resolution 374,295]
376. ~5 | 10 [avatar contradiction clause 375]
378. $false [avatar sat refutation 182,233,269,376]
% SZS output end Proof for 3593021396470960157936537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not creative or old then lucy is tall or not old 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.
If lucy is either strong or not kind then someone is funny and vice versa.
Everyone who is generous or not tall is either quiet or wise and vice versa.
Everyone who is both not wise and wise is both curious and not quiet.
Someone is not wise.
Someone is not kind or not old.
Someone is either not curious or not happy.
Mary is either not old or old. | Susan is not patient. | neutral | (((~creative(alice)|old(alice)))<=>((tall(lucy)|~old(lucy))))&
(![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)))))&
(((strong(lucy)<~>~kind(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((generous(X)|~tall(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((~wise(X)&wise(X))=>(curious(X)&~quiet(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~kind(X)|~old(X))))&
(?[X]:((~curious(X)<~>~happy(X))))&
((~old(mary)<~>old(mary))) | ~patient(susan) | [] | null | 0 |
If john is either brave or funny then john is tall and vice versa.
Everyone who is happy or patient is either not patient or not kind.
If susan is curious or old then someone is not quiet and vice versa.
Everyone who is not creative or not old is creative or humble and vice versa.
Everyone who is not old or not funny is both not patient and rich and vice versa.
If john is quiet then someone is both strong and humble and vice versa.
Everyone who is either tall or rich is either not creative or creative and vice versa.
If susan is not curious then someone is both not tall and not kind.
Everyone who is strong is both not strong and tall.
Everyone who is not curious is both not humble and not tall.
If susan is patient then alice is both not curious and not patient.
If someone is both brave and not calm then someone is not calm or happy and vice versa.
If lucy is wise or strong then someone is not strong.
Everyone who is strong is not patient or not funny.
If someone is funny then susan is both rich and not brave and vice versa.
Everyone who is kind is not kind.
Someone is curious.
Someone is either not calm or not strong.
Mary is creative or strong.
Someone is not quiet or creative.
Lucy is both not tall and not strong.
Paul is either not generous or humble.
John is not rich or not funny. | John is tall. | neutral | (((brave(john)<~>funny(john)))<=>(tall(john)))&
(![X]:((happy(X)|patient(X))=>(~patient(X)<~>~kind(X))))&
(((curious(susan)|old(susan)))<=>(?[X]:(~quiet(X))))&
(![X]:((~creative(X)|~old(X))<=>(creative(X)|humble(X))))&
(![X]:((~old(X)|~funny(X))<=>(~patient(X)&rich(X))))&
((quiet(john))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((tall(X)<~>rich(X))<=>(~creative(X)<~>creative(X))))&
((~curious(susan))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(strong(X)=>(~strong(X)&tall(X))))&
(![X]:(~curious(X)=>(~humble(X)&~tall(X))))&
((patient(susan))=>((~curious(alice)&~patient(alice))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~calm(X)|happy(X)))))&
(((wise(lucy)|strong(lucy)))=>(?[X]:(~strong(X))))&
(![X]:(strong(X)=>(~patient(X)|~funny(X))))&
((?[X]:(funny(X)))<=>((rich(susan)&~brave(susan))))&
(![X]:(kind(X)=>~kind(X)))&
(?[X]:(curious(X)))&
(?[X]:((~calm(X)<~>~strong(X))))&
((creative(mary)|strong(mary)))&
(?[X]:((~quiet(X)|creative(X))))&
((~tall(lucy)&~strong(lucy)))&
((~generous(paul)<~>humble(paul)))&
((~rich(john)|~funny(john))) | tall(john) | [] | null | 0 |
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