premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is both not strong and strong is tall and vice versa. If someone is both curious and wise then someone is not wise. Everyone who is quiet is strong. Everyone who is humble or not humble is creative. Everyone who is either not curious or not funny is both not quiet and old. Everyone who is either tall or creative is both calm and wise. Everyone who is generous or not quiet is not quiet or kind. Everyone who is both not old and calm is both not curious and not funny and vice versa. Everyone who is tall is strong or old and vice versa. Everyone who is both generous and kind is either not creative or not wise and vice versa. Everyone who is either not funny or quiet is either not tall or old. Everyone who is both not funny and humble is both quiet and not curious and vice versa. Everyone who is either brave or happy is not curious or not happy and vice versa. Everyone who is both not tall and not generous is either not generous or not wise and vice versa. Everyone who is both strong and funny is either creative or not rich and vice versa. If someone is both curious and not curious then someone is either not kind or curious and vice versa. Someone is both kind and creative. John is not brave or not quiet. Someone is both creative and not old. Someone is happy. Someone is not creative or patient. Susan is generous or not brave. | Susan is not humble. | entailment | (![X]:((~strong(X)&strong(X))<=>tall(X)))&
((?[X]:((curious(X)&wise(X))))=>(?[X]:(~wise(X))))&
(![X]:(quiet(X)=>strong(X)))&
(![X]:((humble(X)|~humble(X))=>creative(X)))&
(![X]:((~curious(X)<~>~funny(X))=>(~quiet(X)&old(X))))&
(![X]:((tall(X)<~>creative(X))=>(calm(X)&wise(X))))&
(![X]:((generous(X)|~quiet(X))=>(~quiet(X)|kind(X))))&
(![X]:((~old(X)&calm(X))<=>(~curious(X)&~funny(X))))&
(![X]:(tall(X)<=>(strong(X)|old(X))))&
(![X]:((generous(X)&kind(X))<=>(~creative(X)<~>~wise(X))))&
(![X]:((~funny(X)<~>quiet(X))=>(~tall(X)<~>old(X))))&
(![X]:((~funny(X)&humble(X))<=>(quiet(X)&~curious(X))))&
(![X]:((brave(X)<~>happy(X))<=>(~curious(X)|~happy(X))))&
(![X]:((~tall(X)&~generous(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((strong(X)&funny(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((curious(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>curious(X)))))&
(?[X]:((kind(X)&creative(X))))&
((~brave(john)|~quiet(john)))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:(happy(X)))&
(?[X]:((~creative(X)|patient(X))))&
((generous(susan)|~brave(susan))) | ~humble(susan) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 1520327711186902382492001
% SZS output start Proof for 1520327711186902382492001
1. ! [X0] : ((strong(X0) & ~strong(X0)) <=> tall(X0)) [input p0]
3. ! [X0] : (quiet(X0) => strong(X0)) [input p2]
4. ! [X0] : ((~humble(X0) | humble(X0)) => creative(X0)) [input p3]
6. ! [X0] : ((tall(X0) <~> creative(X0)) => (wise(X0) & calm(X0))) [input p5]
8. ! [X0] : ((calm(X0) & ~old(X0)) <=> (~funny(X0) & ~curious(X0))) [input p7]
9. ! [X0] : (tall(X0) <=> (old(X0) | strong(X0))) [input p8]
12. ! [X0] : ((humble(X0) & ~funny(X0)) <=> (~curious(X0) & quiet(X0))) [input p11]
23. humble(susan) [input hypothesis]
28. ! [X0] : (strong(X0) | ~quiet(X0)) [ennf transformation 3]
29. ! [X0] : (creative(X0) | (humble(X0) & ~humble(X0))) [ennf transformation 4]
31. ! [X0] : ((wise(X0) & calm(X0)) | (tall(X0) <=> creative(X0))) [ennf transformation 6]
35. ! [X0] : (((strong(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | (~strong(X0) | strong(X0)))) [nnf transformation 1]
36. ! [X0] : (((strong(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | ~strong(X0) | strong(X0))) [flattening 35]
41. ! [X0] : ((wise(X0) & calm(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) [nnf transformation 31]
42. ! [X0] : (((calm(X0) & ~old(X0)) | (funny(X0) | curious(X0))) & ((~funny(X0) & ~curious(X0)) | (~calm(X0) | old(X0)))) [nnf transformation 8]
43. ! [X0] : (((calm(X0) & ~old(X0)) | funny(X0) | curious(X0)) & ((~funny(X0) & ~curious(X0)) | ~calm(X0) | old(X0))) [flattening 42]
44. ! [X0] : ((tall(X0) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | ~tall(X0))) [nnf transformation 9]
45. ! [X0] : ((tall(X0) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | ~tall(X0))) [flattening 44]
49. ! [X0] : (((humble(X0) & ~funny(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (~humble(X0) | funny(X0)))) [nnf transformation 12]
50. ! [X0] : (((humble(X0) & ~funny(X0)) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | ~humble(X0) | funny(X0))) [flattening 49]
69. ~strong(X0) | ~tall(X0) [cnf transformation 36]
70. ~tall(X0) | strong(X0) [cnf transformation 36]
72. ~quiet(X0) | strong(X0) [cnf transformation 28]
73. creative(X0) | ~humble(X0) [cnf transformation 29]
74. creative(X0) | humble(X0) [cnf transformation 29]
80. calm(X0) | tall(X0) | ~creative(X0) [cnf transformation 41]
86. ~funny(X0) | ~calm(X0) | old(X0) [cnf transformation 43]
90. tall(X0) | ~strong(X0) [cnf transformation 45]
91. tall(X0) | ~old(X0) [cnf transformation 45]
102. ~humble(X0) | quiet(X0) | funny(X0) [cnf transformation 50]
137. humble(susan) [cnf transformation 23]
142. ~tall(X0) [subsumption resolution 69,70]
151. creative(X0) [subsumption resolution 73,74]
154. calm(X0) | ~creative(X0) [subsumption resolution 80,142]
155. calm(X0) [subsumption resolution 154,151]
156. ~funny(X0) | old(X0) [subsumption resolution 86,155]
158. ~old(X0) [subsumption resolution 91,142]
159. ~strong(X0) [subsumption resolution 90,142]
206. quiet(susan) | funny(susan) [resolution 102,137]
208. 10 <=> funny(susan) [avatar definition]
210. funny(susan) <- (10) [avatar component clause 208]
212. 11 <=> quiet(susan) [avatar definition]
214. quiet(susan) <- (11) [avatar component clause 212]
215. 10 | 11 [avatar split clause 206,212,208]
219. old(susan) <- (10) [resolution 210,156]
225. $false <- (10) [subsumption resolution 219,158]
226. ~10 [avatar contradiction clause 225]
232. strong(susan) <- (11) [resolution 214,72]
233. $false <- (11) [subsumption resolution 232,159]
234. ~11 [avatar contradiction clause 233]
235. $false [avatar sat refutation 215,226,234]
% SZS output end Proof for 1520327711186902382492001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is both not brave and not creative.
Everyone who is not curious or not brave is either tall or not happy.
Everyone who is not patient or not tall is curious.
Everyone who is both not wise and happy is not wise or funny and vice versa.
Everyone who is either not humble or not happy is strong or not patient.
If someone is patient or strong then susan is either generous or not kind and vice versa.
If mary is both not calm and not generous then lucy is not funny.
If someone is kind then lucy is happy and vice versa.
Everyone who is not wise is not humble.
Everyone who is not calm or rich is both wise and quiet and vice versa.
If someone is curious then someone is not generous and vice versa.
If john is brave or not patient then someone is not humble and vice versa.
If paul is brave then alice is both not generous and calm.
If someone is either curious or not funny then someone is both strong and funny.
Everyone who is both kind and not humble is either wise or not curious.
Everyone who is both curious and tall is both humble and not happy.
Someone is either old or not funny.
Someone is both not humble and curious.
Someone is not kind.
Susan is not generous or not tall.
Someone is both humble and strong.
Susan is tall or funny.
Fred is both not happy and not old.
Someone is humble. | Fred is creative. | contradiction | (![X]:(curious(X)=>(~brave(X)&~creative(X))))&
(![X]:((~curious(X)|~brave(X))=>(tall(X)<~>~happy(X))))&
(![X]:((~patient(X)|~tall(X))=>curious(X)))&
(![X]:((~wise(X)&happy(X))<=>(~wise(X)|funny(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(strong(X)|~patient(X))))&
((?[X]:((patient(X)|strong(X))))<=>((generous(susan)<~>~kind(susan))))&
(((~calm(mary)&~generous(mary)))=>(~funny(lucy)))&
((?[X]:(kind(X)))<=>(happy(lucy)))&
(![X]:(~wise(X)=>~humble(X)))&
(![X]:((~calm(X)|rich(X))<=>(wise(X)&quiet(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~generous(X))))&
(((brave(john)|~patient(john)))<=>(?[X]:(~humble(X))))&
((brave(paul))=>((~generous(alice)&calm(alice))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((kind(X)&~humble(X))=>(wise(X)<~>~curious(X))))&
(![X]:((curious(X)&tall(X))=>(humble(X)&~happy(X))))&
(?[X]:((old(X)<~>~funny(X))))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:(~kind(X)))&
((~generous(susan)|~tall(susan)))&
(?[X]:((humble(X)&strong(X))))&
((tall(susan)|funny(susan)))&
((~happy(fred)&~old(fred)))&
(?[X]:(humble(X))) | creative(fred) | [
"p0",
"p1",
"p2",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4797207571967760428308740
% SZS output start Proof for 4797207571967760428308740
1. ! [X0] : (curious(X0) => (~creative(X0) & ~brave(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~curious(X0)) => (tall(X0) <~> ~happy(X0))) [input p1]
3. ! [X0] : ((~tall(X0) | ~patient(X0)) => curious(X0)) [input p2]
23. ~old(fred) & ~happy(fred) [input p22]
25. creative(fred) [input hypothesis]
28. ! [X0] : ((~creative(X0) & ~brave(X0)) | ~curious(X0)) [ennf transformation 1]
29. ! [X0] : ((tall(X0) <~> ~happy(X0)) | (brave(X0) & curious(X0))) [ennf transformation 2]
30. ! [X0] : (curious(X0) | (tall(X0) & patient(X0))) [ennf transformation 3]
42. ! [X0] : (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (brave(X0) & curious(X0))) [nnf transformation 29]
83. ~creative(X0) | ~curious(X0) [cnf transformation 28]
86. ~tall(X0) | happy(X0) | curious(X0) [cnf transformation 42]
89. tall(X0) | curious(X0) [cnf transformation 30]
136. ~happy(fred) [cnf transformation 23]
139. creative(fred) [cnf transformation 25]
283. ~curious(fred) [resolution 83,139]
314. happy(X0) | curious(X0) | curious(X0) [resolution 86,89]
315. happy(X0) | curious(X0) [duplicate literal removal 314]
390. curious(fred) [resolution 315,136]
393. $false [subsumption resolution 390,283]
% SZS output end Proof for 4797207571967760428308740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or old then someone is not calm or not wise.
Everyone who is not creative or not strong is both not tall and kind and vice versa.
Everyone who is both not happy and humble is both curious and not rich and vice versa.
Everyone who is brave is not curious or generous.
Everyone who is not patient is humble or not humble and vice versa.
If john is either not calm or not happy then paul is rich and vice versa.
If someone is both not kind and rich then alice is not strong.
If paul is curious or not rich then someone is either not kind or not funny and vice versa.
If someone is either not creative or strong then mary is both not calm and not tall.
If someone is not happy then alice is either not generous or not brave and vice versa.
Everyone who is either not generous or not funny is not quiet or not creative.
If someone is either not brave or not happy then someone is either kind or not wise.
If someone is either not strong or rich then someone is both not calm and not happy and vice versa.
If someone is both not wise and happy then someone is not humble.
Everyone who is funny or not strong is either tall or patient.
Everyone who is not tall is both calm and not generous.
Someone is happy or not generous.
Someone is either not humble or curious.
Someone is either not generous or not happy.
Fred is either not patient or creative.
Alice is not patient or happy. | Mary is not happy. | neutral | ((?[X]:((~rich(X)|old(X))))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((~creative(X)|~strong(X))<=>(~tall(X)&kind(X))))&
(![X]:((~happy(X)&humble(X))<=>(curious(X)&~rich(X))))&
(![X]:(brave(X)=>(~curious(X)|generous(X))))&
(![X]:(~patient(X)<=>(humble(X)|~humble(X))))&
(((~calm(john)<~>~happy(john)))<=>(rich(paul)))&
((?[X]:((~kind(X)&rich(X))))=>(~strong(alice)))&
(((curious(paul)|~rich(paul)))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:((~creative(X)<~>strong(X))))=>((~calm(mary)&~tall(mary))))&
((?[X]:(~happy(X)))<=>((~generous(alice)<~>~brave(alice))))&
(![X]:((~generous(X)<~>~funny(X))=>(~quiet(X)|~creative(X))))&
((?[X]:((~brave(X)<~>~happy(X))))=>(?[X]:((kind(X)<~>~wise(X)))))&
((?[X]:((~strong(X)<~>rich(X))))<=>(?[X]:((~calm(X)&~happy(X)))))&
((?[X]:((~wise(X)&happy(X))))=>(?[X]:(~humble(X))))&
(![X]:((funny(X)|~strong(X))=>(tall(X)<~>patient(X))))&
(![X]:(~tall(X)=>(calm(X)&~generous(X))))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
((~patient(fred)<~>creative(fred)))&
((~patient(alice)|happy(alice))) | ~happy(mary) | []
| null | 0 |
If mary is both not strong and not curious then fred is not strong or not curious and vice versa.
Everyone who is not funny is rich.
Everyone who is happy is both not creative and wise and vice versa.
Everyone who is either not rich or not old is either strong or patient.
If mary is not strong then someone is wise or quiet.
Everyone who is both not happy and not tall is either tall or happy.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
If paul is either not quiet or strong then someone is calm or not rich and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is not old or not rich is creative and vice versa.
If mary is either not calm or strong then someone is not calm or not brave and vice versa.
If someone is either not wise or not humble then someone is wise.
Everyone who is not humble is not creative or old and vice versa.
Susan is either kind or not funny.
Lucy is generous or not brave.
Alice is both not calm and wise.
Someone is either generous or not old.
Someone is not strong or kind. | Alice is not funny. | contradiction | (((~strong(mary)&~curious(mary)))<=>((~strong(fred)|~curious(fred))))&
(![X]:(~funny(X)=>rich(X)))&
(![X]:(happy(X)<=>(~creative(X)&wise(X))))&
(![X]:((~rich(X)<~>~old(X))=>(strong(X)<~>patient(X))))&
((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~happy(X)&~tall(X))=>(tall(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((~calm(X)|~brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
((kind(susan)<~>~funny(susan)))&
((generous(lucy)|~brave(lucy)))&
((~calm(alice)&wise(alice)))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:((~strong(X)|kind(X)))) | ~funny(alice) | [
"p1",
"p2",
"p8",
"p10",
"p11",
"p14",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7167757883479575875671013
% SZS output start Proof for 7167757883479575875671013
2. ! [X0] : (~funny(X0) => rich(X0)) [input p1]
3. ! [X0] : (happy(X0) <=> (wise(X0) & ~creative(X0))) [input p2]
9. (humble(mary) <~> wise(mary)) <=> ? [X0] : (rich(X0) <~> happy(X0)) [input p8]
11. ! [X0] : (~old(X0) <=> wise(X0)) [input p10]
12. ! [X0] : ((~rich(X0) | ~old(X0)) <=> creative(X0)) [input p11]
15. ! [X0] : (~humble(X0) <=> (old(X0) | ~creative(X0))) [input p14]
18. wise(alice) & ~calm(alice) [input p17]
21. ~funny(alice) [input hypothesis]
23. ! [X0] : (rich(X0) | funny(X0)) [ennf transformation 2]
32. ! [X0] : ((happy(X0) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | ~happy(X0))) [nnf transformation 3]
33. ! [X0] : ((happy(X0) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | ~happy(X0))) [flattening 32]
41. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [nnf transformation 9]
42. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [rectify 41]
43. ? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) => ((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) [choice axiom]
44. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [skolemisation 42,43]
49. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 11]
50. ! [X0] : (((~rich(X0) | ~old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [nnf transformation 12]
51. ! [X0] : ((~rich(X0) | ~old(X0) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [flattening 50]
60. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & ((old(X0) | ~creative(X0)) | humble(X0))) [nnf transformation 15]
61. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & (old(X0) | ~creative(X0) | humble(X0))) [flattening 60]
73. rich(X0) | funny(X0) [cnf transformation 23]
74. ~creative(X0) | ~happy(X0) [cnf transformation 33]
96. wise(mary) | humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 44]
98. ~wise(mary) | ~humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 44]
106. old(X0) | wise(X0) [cnf transformation 49]
107. ~old(X0) | ~wise(X0) [cnf transformation 49]
108. old(X0) | creative(X0) [cnf transformation 51]
119. old(X0) | ~creative(X0) | humble(X0) [cnf transformation 61]
121. ~humble(X0) | ~old(X0) [cnf transformation 61]
126. wise(alice) [cnf transformation 18]
130. ~funny(alice) [cnf transformation 21]
179. 11 <=> humble(mary) [avatar definition]
180. humble(mary) <- (11) [avatar component clause 179]
181. ~humble(mary) <- (~11) [avatar component clause 179]
183. 12 <=> wise(mary) [avatar definition]
185. ~wise(mary) <- (~12) [avatar component clause 183]
188. 13 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
189. ~rich(X0) | happy(X0) <- (13) [avatar component clause 188]
190. 13 | ~11 | ~12 [avatar split clause 98,183,179,188]
192. 13 | 11 | 12 [avatar split clause 96,183,179,188]
269. humble(X0) | old(X0) [subsumption resolution 119,108]
312. ~wise(X0) | creative(X0) [resolution 108,107]
316. happy(X0) | funny(X0) <- (13) [resolution 189,73]
320. old(mary) <- (~11) [resolution 269,181]
323. ~wise(mary) <- (~11) [resolution 320,107]
328. 38 <=> creative(alice) [avatar definition]
330. creative(alice) <- (38) [avatar component clause 328]
332. 39 <=> happy(alice) [avatar definition]
333. ~happy(alice) <- (~39) [avatar component clause 332]
447. creative(alice) [resolution 312,126]
453. 38 [avatar split clause 447,328]
455. ~happy(alice) <- (38) [resolution 330,74]
458. ~39 | ~38 [avatar split clause 455,328,332]
469. funny(alice) <- (13, ~39) [resolution 316,333]
473. $false <- (13, ~39) [subsumption resolution 469,130]
474. ~13 | 39 [avatar contradiction clause 473]
475. ~12 | 11 [avatar split clause 323,179,183]
478. 55 <=> old(mary) [avatar definition]
479. ~old(mary) <- (~55) [avatar component clause 478]
484. ~old(mary) <- (11) [resolution 180,121]
505. ~55 | ~11 [avatar split clause 484,179,478]
635. wise(mary) <- (~55) [resolution 479,106]
636. $false <- (~12, ~55) [subsumption resolution 635,185]
637. 12 | 55 [avatar contradiction clause 636]
638. $false [avatar sat refutation 190,192,453,458,474,475,505,637]
% SZS output end Proof for 7167757883479575875671013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not kind is not funny or not humble and vice versa. Everyone who is both not calm and not patient is both generous and tall. Everyone who is curious is rich. If paul is both kind and not wise then mary is both not strong and generous and vice versa. Everyone who is not happy or brave is either not rich or tall and vice versa. Everyone who is not old or strong is both creative and curious and vice versa. If fred is either quiet or not quiet then someone is kind or not wise and vice versa. Everyone who is generous or tall is brave or calm. If someone is not happy then susan is tall. If fred is rich or brave then susan is either patient or not brave and vice versa. Everyone who is both not creative and not quiet is either generous or not tall. Everyone who is either not rich or not old is either not curious or generous. Everyone who is either not happy or curious is tall or not rich. If susan is generous or not strong then susan is either not creative or curious and vice versa. Everyone who is both not brave and not curious is strong. Everyone who is either not rich or kind is not old or not creative. Someone is kind. Someone is either funny or not curious. John is either tall or not quiet. Someone is not creative or not calm. Someone is either not generous or not kind. Susan is both not rich and not curious. Someone is either happy or not rich. Mary is not calm. | Mary is not brave. | contradiction | (![X]:((patient(X)|~kind(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~calm(X)&~patient(X))=>(generous(X)&tall(X))))&
(![X]:(curious(X)=>rich(X)))&
(((kind(paul)&~wise(paul)))<=>((~strong(mary)&generous(mary))))&
(![X]:((~happy(X)|brave(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~old(X)|strong(X))<=>(creative(X)&curious(X))))&
(((quiet(fred)<~>~quiet(fred)))<=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((generous(X)|tall(X))=>(brave(X)|calm(X))))&
((?[X]:(~happy(X)))=>(tall(susan)))&
(((rich(fred)|brave(fred)))<=>((patient(susan)<~>~brave(susan))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)<~>~tall(X))))&
(![X]:((~rich(X)<~>~old(X))=>(~curious(X)<~>generous(X))))&
(![X]:((~happy(X)<~>curious(X))=>(tall(X)|~rich(X))))&
(((generous(susan)|~strong(susan)))<=>((~creative(susan)<~>curious(susan))))&
(![X]:((~brave(X)&~curious(X))=>strong(X)))&
(![X]:((~rich(X)<~>kind(X))=>(~old(X)|~creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((funny(X)<~>~curious(X))))&
((tall(john)<~>~quiet(john)))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:((~generous(X)<~>~kind(X))))&
((~rich(susan)&~curious(susan)))&
(?[X]:((happy(X)<~>~rich(X))))&
(~calm(mary)) | ~brave(mary) | [
"p2",
"p4",
"p5",
"p7",
"p12",
"p14",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 5942912910551792393407611
% SZS output start Proof for 5942912910551792393407611
3. ! [X0] : (curious(X0) => rich(X0)) [input p2]
5. ! [X0] : ((brave(X0) | ~happy(X0)) <=> (~rich(X0) <~> tall(X0))) [input p4]
6. ! [X0] : ((strong(X0) | ~old(X0)) <=> (curious(X0) & creative(X0))) [input p5]
8. ! [X0] : ((tall(X0) | generous(X0)) => (calm(X0) | brave(X0))) [input p7]
13. ! [X0] : ((~happy(X0) <~> curious(X0)) => (~rich(X0) | tall(X0))) [input p12]
15. ! [X0] : ((~curious(X0) & ~brave(X0)) => strong(X0)) [input p14]
24. ~calm(mary) [input p23]
25. ~brave(mary) [input hypothesis]
28. ! [X0] : (rich(X0) | ~curious(X0)) [ennf transformation 3]
29. ! [X0] : ((calm(X0) | brave(X0)) | (~tall(X0) & ~generous(X0))) [ennf transformation 8]
30. ! [X0] : (calm(X0) | brave(X0) | (~tall(X0) & ~generous(X0))) [flattening 29]
35. ! [X0] : ((~rich(X0) | tall(X0)) | (~happy(X0) <=> curious(X0))) [ennf transformation 13]
36. ! [X0] : (~rich(X0) | tall(X0) | (~happy(X0) <=> curious(X0))) [flattening 35]
37. ! [X0] : (strong(X0) | (curious(X0) | brave(X0))) [ennf transformation 15]
38. ! [X0] : (strong(X0) | curious(X0) | brave(X0)) [flattening 37]
45. ! [X0] : (((brave(X0) | ~happy(X0)) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) & (((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | (~brave(X0) & happy(X0)))) [nnf transformation 5]
46. ! [X0] : ((brave(X0) | ~happy(X0) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) & (((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | (~brave(X0) & happy(X0)))) [flattening 45]
47. ! [X0] : (((strong(X0) | ~old(X0)) | (~curious(X0) | ~creative(X0))) & ((curious(X0) & creative(X0)) | (~strong(X0) & old(X0)))) [nnf transformation 6]
48. ! [X0] : ((strong(X0) | ~old(X0) | ~curious(X0) | ~creative(X0)) & ((curious(X0) & creative(X0)) | (~strong(X0) & old(X0)))) [flattening 47]
57. ! [X0] : (~rich(X0) | tall(X0) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0)))) [nnf transformation 36]
81. ~curious(X0) | rich(X0) [cnf transformation 28]
86. ~rich(X0) | tall(X0) | happy(X0) [cnf transformation 46]
95. ~strong(X0) | curious(X0) [cnf transformation 48]
104. ~tall(X0) | brave(X0) | calm(X0) [cnf transformation 30]
119. ~rich(X0) | tall(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 57]
126. strong(X0) | curious(X0) | brave(X0) [cnf transformation 38]
141. ~calm(mary) [cnf transformation 24]
142. ~brave(mary) [cnf transformation 25]
211. ~happy(X0) | tall(X0) | ~curious(X0) [subsumption resolution 119,81]
237. brave(X0) | curious(X0) [subsumption resolution 126,95]
291. curious(mary) [resolution 237,142]
293. rich(mary) [resolution 291,81]
330. tall(mary) | happy(mary) [resolution 86,293]
341. 35 <=> happy(mary) [avatar definition]
343. happy(mary) <- (35) [avatar component clause 341]
345. 36 <=> tall(mary) [avatar definition]
347. tall(mary) <- (36) [avatar component clause 345]
348. 35 | 36 [avatar split clause 330,345,341]
415. tall(mary) | ~curious(mary) <- (35) [resolution 211,343]
417. tall(mary) <- (35) [subsumption resolution 415,291]
418. 36 | ~35 [avatar split clause 417,341,345]
421. brave(mary) | calm(mary) <- (36) [resolution 347,104]
423. calm(mary) <- (36) [subsumption resolution 421,142]
424. $false <- (36) [subsumption resolution 423,141]
425. ~36 [avatar contradiction clause 424]
426. $false [avatar sat refutation 348,418,425]
% SZS output end Proof for 5942912910551792393407611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not rich and not generous is not rich or wise. Everyone who is either not humble or kind is both wise and humble and vice versa. If susan is not brave or strong then someone is both wise and not strong and vice versa. Everyone who is not calm is not old and vice versa. Everyone who is both not quiet and creative is tall or strong. If mary is curious or tall then lucy is not old. If paul is calm or not funny then paul is wise or kind. Everyone who is either rich or creative is both generous and wise and vice versa. If alice is curious then john is both creative and calm and vice versa. If alice is both brave and humble then paul is not happy or happy and vice versa. If someone is both not strong and funny then someone is either not creative or brave. Everyone who is either not humble or wise is either not generous or wise. If someone is strong or not kind then someone is both strong and wise. Everyone who is both funny and kind is either creative or tall. Everyone who is either not quiet or not happy is happy. Susan is both generous and tall. Mary is either not old or rich. John is not patient or strong. Paul is either tall or not curious. Paul is not humble or creative. | Mary is humble. | neutral | (![X]:((~rich(X)&~generous(X))=>(~rich(X)|wise(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(wise(X)&humble(X))))&
(((~brave(susan)|strong(susan)))<=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:((~quiet(X)&creative(X))=>(tall(X)|strong(X))))&
(((curious(mary)|tall(mary)))=>(~old(lucy)))&
(((calm(paul)|~funny(paul)))=>((wise(paul)|kind(paul))))&
(![X]:((rich(X)<~>creative(X))<=>(generous(X)&wise(X))))&
((curious(alice))<=>((creative(john)&calm(john))))&
(((brave(alice)&humble(alice)))<=>((~happy(paul)|happy(paul))))&
((?[X]:((~strong(X)&funny(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
(![X]:((~humble(X)<~>wise(X))=>(~generous(X)<~>wise(X))))&
((?[X]:((strong(X)|~kind(X))))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((funny(X)&kind(X))=>(creative(X)<~>tall(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>happy(X)))&
((generous(susan)&tall(susan)))&
((~old(mary)<~>rich(mary)))&
((~patient(john)|strong(john)))&
((tall(paul)<~>~curious(paul)))&
((~humble(paul)|creative(paul))) | humble(mary) | []
| null | 0 |
If mary is either not strong or not old then john is either not humble or brave and vice versa.
Everyone who is not kind is both happy and not kind.
If someone is both not kind and not rich then someone is not rich or not humble and vice versa.
Everyone who is either calm or tall is humble or creative and vice versa.
If fred is both not wise and kind then someone is not brave and vice versa.
If alice is rich then alice is either old or not curious.
If mary is either rich or curious then someone is either not kind or not rich and vice versa.
Everyone who is either rich or not strong is both not generous and not kind and vice versa.
Everyone who is calm or not curious is not humble.
Everyone who is funny is both kind and not wise and vice versa.
If susan is either not quiet or happy then alice is not funny.
If john is either not patient or not happy then susan is either humble or old and vice versa.
Everyone who is brave or not strong is either not brave or funny.
If susan is either patient or not humble then someone is curious or wise.
If paul is tall then someone is both not kind and not wise and vice versa.
Everyone who is curious or brave is both brave and not kind and vice versa.
Someone is strong.
Someone is not strong or not calm.
Someone is either tall or not brave.
John is either wise or not rich.
John is both patient and not kind.
Someone is either not patient or strong.
Alice is not creative or generous.
Susan is creative. | Fred is not strong. | contradiction | (((~strong(mary)<~>~old(mary)))<=>((~humble(john)<~>brave(john))))&
(![X]:(~kind(X)=>(happy(X)&~kind(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:((calm(X)<~>tall(X))<=>(humble(X)|creative(X))))&
(((~wise(fred)&kind(fred)))<=>(?[X]:(~brave(X))))&
((rich(alice))=>((old(alice)<~>~curious(alice))))&
(((rich(mary)<~>curious(mary)))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~kind(X))))&
(![X]:((calm(X)|~curious(X))=>~humble(X)))&
(![X]:(funny(X)<=>(kind(X)&~wise(X))))&
(((~quiet(susan)<~>happy(susan)))=>(~funny(alice)))&
(((~patient(john)<~>~happy(john)))<=>((humble(susan)<~>old(susan))))&
(![X]:((brave(X)|~strong(X))=>(~brave(X)<~>funny(X))))&
(((patient(susan)<~>~humble(susan)))=>(?[X]:((curious(X)|wise(X)))))&
((tall(paul))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((curious(X)|brave(X))<=>(brave(X)&~kind(X))))&
(?[X]:(strong(X)))&
(?[X]:((~strong(X)|~calm(X))))&
(?[X]:((tall(X)<~>~brave(X))))&
((wise(john)<~>~rich(john)))&
((patient(john)&~kind(john)))&
(?[X]:((~patient(X)<~>strong(X))))&
((~creative(alice)|generous(alice)))&
(creative(susan)) | ~strong(fred) | [
"p4",
"p9",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 6693541608990798245704548
% SZS output start Proof for 6693541608990798245704548
5. (kind(fred) & ~wise(fred)) <=> ? [X0] : ~brave(X0) [input p4]
10. ! [X0] : (funny(X0) <=> (~wise(X0) & kind(X0))) [input p9]
13. ! [X0] : ((~strong(X0) | brave(X0)) => (~brave(X0) <~> funny(X0))) [input p12]
16. ! [X0] : ((brave(X0) | curious(X0)) <=> (~kind(X0) & brave(X0))) [input p15]
25. ~strong(fred) [input hypothesis]
31. ! [X0] : ((~brave(X0) <~> funny(X0)) | (strong(X0) & ~brave(X0))) [ennf transformation 13]
41. ((kind(fred) & ~wise(fred)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~kind(fred) | wise(fred))) [nnf transformation 5]
42. ((kind(fred) & ~wise(fred)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~kind(fred) | wise(fred)) [flattening 41]
43. ((kind(fred) & ~wise(fred)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~kind(fred) | wise(fred)) [rectify 42]
44. ? [X1] : ~brave(X1) => ~brave(sK2) [choice axiom]
45. ((kind(fred) & ~wise(fred)) | ! [X0] : brave(X0)) & (~brave(sK2) | ~kind(fred) | wise(fred)) [skolemisation 43,44]
53. ! [X0] : ((funny(X0) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | ~funny(X0))) [nnf transformation 10]
54. ! [X0] : ((funny(X0) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ~funny(X0))) [flattening 53]
57. ! [X0] : (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (strong(X0) & ~brave(X0))) [nnf transformation 31]
65. ! [X0] : (((brave(X0) | curious(X0)) | (kind(X0) | ~brave(X0))) & ((~kind(X0) & brave(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 16]
66. ! [X0] : ((brave(X0) | curious(X0) | kind(X0) | ~brave(X0)) & ((~kind(X0) & brave(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 65]
100. ~wise(fred) | brave(X0) [cnf transformation 45]
101. kind(fred) | brave(X0) [cnf transformation 45]
120. ~funny(X0) | kind(X0) [cnf transformation 54]
121. ~funny(X0) | ~wise(X0) [cnf transformation 54]
122. ~kind(X0) | wise(X0) | funny(X0) [cnf transformation 54]
133. funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 57]
136. ~funny(X0) | brave(X0) | strong(X0) [cnf transformation 57]
145. ~kind(X0) | ~brave(X0) [cnf transformation 66]
159. ~strong(fred) [cnf transformation 25]
160. ~brave(X0) | funny(X0) [duplicate literal removal 133]
216. 12 <=> ! [X0] : brave(X0) [avatar definition]
217. brave(X0) <- (12) [avatar component clause 216]
219. 13 <=> kind(fred) [avatar definition]
220. ~kind(fred) <- (~13) [avatar component clause 219]
221. kind(fred) <- (13) [avatar component clause 219]
222. 12 | 13 [avatar split clause 101,219,216]
224. 14 <=> wise(fred) [avatar definition]
225. wise(fred) <- (14) [avatar component clause 224]
226. ~wise(fred) <- (~14) [avatar component clause 224]
227. 12 | ~14 [avatar split clause 100,224,216]
404. ~brave(fred) <- (13) [resolution 145,221]
433. wise(fred) | funny(fred) <- (13) [resolution 122,221]
434. funny(fred) <- (13, ~14) [subsumption resolution 433,226]
437. brave(fred) | strong(fred) <- (13, ~14) [resolution 136,434]
438. strong(fred) <- (13, ~14) [subsumption resolution 437,404]
439. $false <- (13, ~14) [subsumption resolution 438,159]
440. ~13 | 14 [avatar contradiction clause 439]
442. funny(X1) <- (12) [resolution 217,160]
450. ~wise(X1) <- (12) [resolution 442,121]
451. kind(X2) <- (12) [resolution 442,120]
454. $false <- (12, 14) [resolution 450,225]
455. ~12 | ~14 [avatar contradiction clause 454]
456. $false <- (12, ~13) [subsumption resolution 220,451]
457. ~12 | 13 [avatar contradiction clause 456]
458. $false [avatar sat refutation 222,227,440,455,457]
% SZS output end Proof for 6693541608990798245704548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or not brave then alice is not rich or not calm.
Everyone who is not wise or not funny is both not creative and not funny and vice versa.
Everyone who is either rich or tall is either patient or happy.
Everyone who is not quiet is either not happy or not curious and vice versa.
Everyone who is not generous or patient is curious or old.
Everyone who is wise is quiet or rich.
Everyone who is either calm or not happy is not happy and vice versa.
Everyone who is either humble or not old is both not humble and not old and vice versa.
Everyone who is either not patient or not rich is happy or brave.
If someone is either not kind or not calm then paul is not old or not funny and vice versa.
If mary is either kind or not kind then someone is wise or kind and vice versa.
Everyone who is both wise and old is old or not funny.
If susan is tall then paul is either not funny or funny.
Everyone who is either not brave or not creative is either not curious or not calm and vice versa.
Everyone who is not quiet or not humble is not rich or creative and vice versa.
If lucy is either calm or generous then susan is either patient or curious.
Fred is either not patient or not generous.
Paul is quiet.
Paul is not calm.
Susan is tall.
Someone is curious.
Someone is patient or rich.
Lucy is not brave.
Susan is not curious or creative. | Paul is quiet. | entailment | ((?[X]:((~generous(X)<~>~brave(X))))=>((~rich(alice)|~calm(alice))))&
(![X]:((~wise(X)|~funny(X))<=>(~creative(X)&~funny(X))))&
(![X]:((rich(X)<~>tall(X))=>(patient(X)<~>happy(X))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>~curious(X))))&
(![X]:((~generous(X)|patient(X))=>(curious(X)|old(X))))&
(![X]:(wise(X)=>(quiet(X)|rich(X))))&
(![X]:((calm(X)<~>~happy(X))<=>~happy(X)))&
(![X]:((humble(X)<~>~old(X))<=>(~humble(X)&~old(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(happy(X)|brave(X))))&
((?[X]:((~kind(X)<~>~calm(X))))<=>((~old(paul)|~funny(paul))))&
(((kind(mary)<~>~kind(mary)))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((wise(X)&old(X))=>(old(X)|~funny(X))))&
((tall(susan))=>((~funny(paul)<~>funny(paul))))&
(![X]:((~brave(X)<~>~creative(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(~rich(X)|creative(X))))&
(((calm(lucy)<~>generous(lucy)))=>((patient(susan)<~>curious(susan))))&
((~patient(fred)<~>~generous(fred)))&
(quiet(paul))&
(~calm(paul))&
(tall(susan))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)|rich(X))))&
(~brave(lucy))&
((~curious(susan)|creative(susan))) | quiet(paul) | [
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7443529410423524890282028
% SZS output start Proof for 7443529410423524890282028
18. quiet(paul) [input p17]
25. ~quiet(paul) [input hypothesis]
130. quiet(paul) [cnf transformation 18]
137. ~quiet(paul) [cnf transformation 25]
242. $false [subsumption resolution 137,130]
% SZS output end Proof for 7443529410423524890282028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or calm then alice is either not funny or not happy and vice versa. Everyone who is rich or humble is old and vice versa. Everyone who is either not old or calm is both not brave and not tall. If someone is either happy or calm then someone is either not generous or tall and vice versa. If lucy is not happy then someone is either kind or curious. Everyone who is wise or generous is both not happy and creative. Everyone who is rich or not patient is wise. Everyone who is happy or not humble is not patient and vice versa. Everyone who is either not rich or funny is quiet. If mary is not curious then someone is kind or curious and vice versa. If someone is strong then someone is either patient or not kind and vice versa. Everyone who is tall is patient or quiet. If mary is happy then someone is either kind or tall. If someone is both not wise and funny then someone is not wise or not kind. Everyone who is not patient is not happy or rich and vice versa. Everyone who is either not strong or old is curious or not old. Someone is either happy or not humble. Someone is both wise and not funny. Someone is calm or kind. Someone is either brave or not patient. Alice is either not kind or not old. Susan is not quiet. | Alice is not strong. | neutral | ((?[X]:((~patient(X)<~>calm(X))))<=>((~funny(alice)<~>~happy(alice))))&
(![X]:((rich(X)|humble(X))<=>old(X)))&
(![X]:((~old(X)<~>calm(X))=>(~brave(X)&~tall(X))))&
((?[X]:((happy(X)<~>calm(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((~happy(lucy))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((wise(X)|generous(X))=>(~happy(X)&creative(X))))&
(![X]:((rich(X)|~patient(X))=>wise(X)))&
(![X]:((happy(X)|~humble(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>funny(X))=>quiet(X)))&
((~curious(mary))<=>(?[X]:((kind(X)|curious(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)<~>~kind(X)))))&
(![X]:(tall(X)=>(patient(X)|quiet(X))))&
((happy(mary))=>(?[X]:((kind(X)<~>tall(X)))))&
((?[X]:((~wise(X)&funny(X))))=>(?[X]:((~wise(X)|~kind(X)))))&
(![X]:(~patient(X)<=>(~happy(X)|rich(X))))&
(![X]:((~strong(X)<~>old(X))=>(curious(X)|~old(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((wise(X)&~funny(X))))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:((brave(X)<~>~patient(X))))&
((~kind(alice)<~>~old(alice)))&
(~quiet(susan)) | ~strong(alice) | []
| null | 0 |
If paul is quiet then mary is creative and vice versa.
If someone is not happy or tall then susan is both not generous and wise and vice versa.
If paul is not creative or not patient then someone is not creative or strong and vice versa.
Everyone who is not humble or not generous is humble and vice versa.
Everyone who is humble is kind or not strong.
If lucy is humble then someone is both not creative and not curious and vice versa.
If someone is both strong and not creative then someone is brave or generous and vice versa.
If susan is either creative or not strong then lucy is not curious or not kind and vice versa.
If susan is happy then someone is not kind or happy.
Everyone who is calm is not kind and vice versa.
If susan is not generous or not curious then mary is both strong and happy and vice versa.
Everyone who is not calm is both not brave and wise and vice versa.
If someone is calm or curious then someone is both not happy and not kind.
If john is strong or not strong then fred is brave.
Everyone who is not curious is not rich or calm and vice versa.
If someone is both happy and not quiet then alice is brave.
Someone is not wise.
Someone is brave.
Someone is both not kind and not happy.
Alice is happy.
Someone is not wise or calm.
Someone is not quiet.
Someone is either not humble or not tall. | Susan is humble. | entailment | ((quiet(paul))<=>(creative(mary)))&
((?[X]:((~happy(X)|tall(X))))<=>((~generous(susan)&wise(susan))))&
(((~creative(paul)|~patient(paul)))<=>(?[X]:((~creative(X)|strong(X)))))&
(![X]:((~humble(X)|~generous(X))<=>humble(X)))&
(![X]:(humble(X)=>(kind(X)|~strong(X))))&
((humble(lucy))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((strong(X)&~creative(X))))<=>(?[X]:((brave(X)|generous(X)))))&
(((creative(susan)<~>~strong(susan)))<=>((~curious(lucy)|~kind(lucy))))&
((happy(susan))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:(calm(X)<=>~kind(X)))&
(((~generous(susan)|~curious(susan)))<=>((strong(mary)&happy(mary))))&
(![X]:(~calm(X)<=>(~brave(X)&wise(X))))&
((?[X]:((calm(X)|curious(X))))=>(?[X]:((~happy(X)&~kind(X)))))&
(((strong(john)|~strong(john)))=>(brave(fred)))&
(![X]:(~curious(X)<=>(~rich(X)|calm(X))))&
((?[X]:((happy(X)&~quiet(X))))=>(brave(alice)))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X)))&
(?[X]:((~kind(X)&~happy(X))))&
(happy(alice))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~humble(X)<~>~tall(X)))) | humble(susan) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 5692777180319540140666138
% SZS output start Proof for 5692777180319540140666138
4. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> humble(X0)) [input p3]
24. ~humble(susan) [input hypothesis]
44. ! [X0] : (((~generous(X0) | ~humble(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) & humble(X0)))) [nnf transformation 4]
45. ! [X0] : ((~generous(X0) | ~humble(X0) | ~humble(X0)) & (humble(X0) | (generous(X0) & humble(X0)))) [flattening 44]
93. humble(X0) | humble(X0) [cnf transformation 45]
141. ~humble(susan) [cnf transformation 24]
142. humble(X0) [duplicate literal removal 93]
330. $false [subsumption resolution 141,142]
% SZS output end Proof for 5692777180319540140666138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or funny is either funny or creative and vice versa.
If someone is rich or humble then someone is patient and vice versa.
Everyone who is not creative is both brave and not rich and vice versa.
If someone is patient then lucy is not humble and vice versa.
Everyone who is both not calm and old is funny.
Everyone who is not funny is both strong and not creative and vice versa.
If paul is not brave then fred is both not quiet and creative.
If someone is both not quiet and not patient then someone is either calm or happy and vice versa.
If fred is both not wise and not funny then paul is both not calm and not quiet.
Everyone who is old or not quiet is happy and vice versa.
If someone is either calm or not quiet then susan is humble.
If alice is not happy or not funny then alice is either not humble or tall.
Everyone who is both curious and not funny is not happy.
If paul is old or not calm then someone is not brave or not tall and vice versa.
Everyone who is either happy or not curious is either kind or old.
If mary is either strong or rich then fred is strong or brave and vice versa.
Someone is not brave.
Someone is funny.
Paul is either not brave or not kind.
Someone is either not tall or calm.
Paul is both not brave and not patient.
Paul is either not generous or generous.
Someone is not funny or generous.
Someone is brave or tall. | Fred is creative. | entailment | (![X]:((~brave(X)<~>funny(X))<=>(funny(X)<~>creative(X))))&
((?[X]:((rich(X)|humble(X))))<=>(?[X]:(patient(X))))&
(![X]:(~creative(X)<=>(brave(X)&~rich(X))))&
((?[X]:(patient(X)))<=>(~humble(lucy)))&
(![X]:((~calm(X)&old(X))=>funny(X)))&
(![X]:(~funny(X)<=>(strong(X)&~creative(X))))&
((~brave(paul))=>((~quiet(fred)&creative(fred))))&
((?[X]:((~quiet(X)&~patient(X))))<=>(?[X]:((calm(X)<~>happy(X)))))&
(((~wise(fred)&~funny(fred)))=>((~calm(paul)&~quiet(paul))))&
(![X]:((old(X)|~quiet(X))<=>happy(X)))&
((?[X]:((calm(X)<~>~quiet(X))))=>(humble(susan)))&
(((~happy(alice)|~funny(alice)))=>((~humble(alice)<~>tall(alice))))&
(![X]:((curious(X)&~funny(X))=>~happy(X)))&
(((old(paul)|~calm(paul)))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((happy(X)<~>~curious(X))=>(kind(X)<~>old(X))))&
(((strong(mary)<~>rich(mary)))<=>((strong(fred)|brave(fred))))&
(?[X]:(~brave(X)))&
(?[X]:(funny(X)))&
((~brave(paul)<~>~kind(paul)))&
(?[X]:((~tall(X)<~>calm(X))))&
((~brave(paul)&~patient(paul)))&
((~generous(paul)<~>generous(paul)))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:((brave(X)|tall(X)))) | creative(fred) | [
"p6",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 4147914184469704678911770
% SZS output start Proof for 4147914184469704678911770
7. ~brave(paul) => (creative(fred) & ~quiet(fred)) [input p6]
21. ~patient(paul) & ~brave(paul) [input p20]
25. ~creative(fred) [input hypothesis]
31. (creative(fred) & ~quiet(fred)) | brave(paul) [ennf transformation 7]
102. creative(fred) | brave(paul) [cnf transformation 31]
139. ~brave(paul) [cnf transformation 21]
145. ~creative(fred) [cnf transformation 25]
187. 9 <=> brave(paul) [avatar definition]
191. 10 <=> creative(fred) [avatar definition]
194. 9 | 10 [avatar split clause 102,191,187]
329. ~9 [avatar split clause 139,187]
348. ~10 [avatar split clause 145,191]
349. $false [avatar sat refutation 194,329,348]
% SZS output end Proof for 4147914184469704678911770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not rich is either generous or creative.
Everyone who is either happy or curious is not curious and vice versa.
If someone is either generous or not brave then john is not happy.
Everyone who is either not humble or not curious is either not strong or not quiet.
Everyone who is calm is not funny and vice versa.
If susan is both quiet and old then someone is both not quiet and strong.
Everyone who is not brave is curious or not wise and vice versa.
If mary is calm then alice is not wise or not brave and vice versa.
If someone is not generous then someone is either rich or not quiet.
If someone is both not calm and not generous then someone is both not calm and not funny and vice versa.
Everyone who is both not strong and wise is both not humble and patient and vice versa.
Everyone who is either wise or not tall is both rich and funny.
Everyone who is curious is both not kind and wise and vice versa.
Everyone who is humble or not happy is both patient and not funny.
Everyone who is rich or not funny is either not happy or wise.
If someone is either not creative or creative then lucy is either humble or not curious.
Susan is both not patient and not strong.
Lucy is patient.
Mary is either not creative or not brave.
Lucy is not creative or not humble.
Mary is both not patient and not generous.
Paul is either creative or not curious.
Alice is not humble or not generous. | Lucy is funny. | contradiction | (![X]:((generous(X)&~rich(X))=>(generous(X)<~>creative(X))))&
(![X]:((happy(X)<~>curious(X))<=>~curious(X)))&
((?[X]:((generous(X)<~>~brave(X))))=>(~happy(john)))&
(![X]:((~humble(X)<~>~curious(X))=>(~strong(X)<~>~quiet(X))))&
(![X]:(calm(X)<=>~funny(X)))&
(((quiet(susan)&old(susan)))=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:(~brave(X)<=>(curious(X)|~wise(X))))&
((calm(mary))<=>((~wise(alice)|~brave(alice))))&
((?[X]:(~generous(X)))=>(?[X]:((rich(X)<~>~quiet(X)))))&
((?[X]:((~calm(X)&~generous(X))))<=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((~strong(X)&wise(X))<=>(~humble(X)&patient(X))))&
(![X]:((wise(X)<~>~tall(X))=>(rich(X)&funny(X))))&
(![X]:(curious(X)<=>(~kind(X)&wise(X))))&
(![X]:((humble(X)|~happy(X))=>(patient(X)&~funny(X))))&
(![X]:((rich(X)|~funny(X))=>(~happy(X)<~>wise(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>((humble(lucy)<~>~curious(lucy))))&
((~patient(susan)&~strong(susan)))&
(patient(lucy))&
((~creative(mary)<~>~brave(mary)))&
((~creative(lucy)|~humble(lucy)))&
((~patient(mary)&~generous(mary)))&
((creative(paul)<~>~curious(paul)))&
((~humble(alice)|~generous(alice))) | funny(lucy) | [
"p1",
"p2",
"p4",
"p6",
"p9",
"p10",
"p13",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7973725553023419314554062
% SZS output start Proof for 7973725553023419314554062
2. ! [X0] : ((happy(X0) <~> curious(X0)) <=> ~curious(X0)) [input p1]
3. ? [X0] : (generous(X0) <~> ~brave(X0)) => ~happy(john) [input p2]
5. ! [X0] : (calm(X0) <=> ~funny(X0)) [input p4]
7. ! [X0] : (~brave(X0) <=> (~wise(X0) | curious(X0))) [input p6]
10. ? [X0] : (~generous(X0) & ~calm(X0)) <=> ? [X0] : (~funny(X0) & ~calm(X0)) [input p9]
11. ! [X0] : ((wise(X0) & ~strong(X0)) <=> (patient(X0) & ~humble(X0))) [input p10]
14. ! [X0] : ((~happy(X0) | humble(X0)) => (~funny(X0) & patient(X0))) [input p13]
16. ? [X0] : (~creative(X0) <~> creative(X0)) => (humble(lucy) <~> ~curious(lucy)) [input p15]
18. patient(lucy) [input p17]
24. funny(lucy) [input hypothesis]
26. ? [X0] : (~generous(X0) & ~calm(X0)) <=> ? [X1] : (~funny(X1) & ~calm(X1)) [rectify 10]
30. ~happy(john) | ! [X0] : (generous(X0) <=> ~brave(X0)) [ennf transformation 3]
34. ! [X0] : ((~funny(X0) & patient(X0)) | (happy(X0) & ~humble(X0))) [ennf transformation 14]
36. (humble(lucy) <~> ~curious(lucy)) | ! [X0] : (~creative(X0) <=> creative(X0)) [ennf transformation 16]
38. ! [X0] : ((((~curious(X0) | ~happy(X0)) & (curious(X0) | happy(X0))) | curious(X0)) & (~curious(X0) | ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))))) [nnf transformation 2]
39. ~happy(john) | ! [X0] : ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))) [nnf transformation 30]
41. ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0))) [nnf transformation 5]
42. ! [X0] : ((~brave(X0) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | brave(X0))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | brave(X0))) [flattening 42]
50. (? [X0] : (~generous(X0) & ~calm(X0)) | ! [X1] : (funny(X1) | calm(X1))) & (? [X1] : (~funny(X1) & ~calm(X1)) | ! [X0] : (generous(X0) | calm(X0))) [nnf transformation 26]
51. (? [X0] : (~generous(X0) & ~calm(X0)) | ! [X1] : (funny(X1) | calm(X1))) & (? [X2] : (~funny(X2) & ~calm(X2)) | ! [X3] : (generous(X3) | calm(X3))) [rectify 50]
52. ? [X0] : (~generous(X0) & ~calm(X0)) => (~generous(sK1) & ~calm(sK1)) [choice axiom]
53. ? [X2] : (~funny(X2) & ~calm(X2)) => (~funny(sK2) & ~calm(sK2)) [choice axiom]
54. ((~generous(sK1) & ~calm(sK1)) | ! [X1] : (funny(X1) | calm(X1))) & ((~funny(sK2) & ~calm(sK2)) | ! [X3] : (generous(X3) | calm(X3))) [skolemisation 51,53,52]
55. ! [X0] : (((wise(X0) & ~strong(X0)) | (~patient(X0) | humble(X0))) & ((patient(X0) & ~humble(X0)) | (~wise(X0) | strong(X0)))) [nnf transformation 11]
56. ! [X0] : (((wise(X0) & ~strong(X0)) | ~patient(X0) | humble(X0)) & ((patient(X0) & ~humble(X0)) | ~wise(X0) | strong(X0))) [flattening 55]
61. ((curious(lucy) | ~humble(lucy)) & (~curious(lucy) | humble(lucy))) | ! [X0] : ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))) [nnf transformation 36]
67. ~curious(X0) | happy(X0) | ~curious(X0) [cnf transformation 38]
68. curious(X0) | happy(X0) | curious(X0) [cnf transformation 38]
70. ~happy(john) | ~brave(X0) | ~generous(X0) [cnf transformation 39]
76. ~funny(X0) | ~calm(X0) [cnf transformation 41]
77. funny(X0) | calm(X0) [cnf transformation 41]
78. ~wise(X0) | curious(X0) | brave(X0) [cnf transformation 43]
86. ~calm(sK2) | generous(X3) | calm(X3) [cnf transformation 54]
87. ~funny(sK2) | generous(X3) | calm(X3) [cnf transformation 54]
93. ~patient(X0) | wise(X0) | humble(X0) [cnf transformation 56]
103. ~funny(X0) | ~humble(X0) [cnf transformation 34]
109. ~curious(lucy) | humble(lucy) | creative(X0) | creative(X0) [cnf transformation 61]
110. ~curious(lucy) | humble(lucy) | ~creative(X0) | ~creative(X0) [cnf transformation 61]
115. patient(lucy) [cnf transformation 18]
124. funny(lucy) [cnf transformation 24]
125. ~curious(lucy) | humble(lucy) | creative(X0) [duplicate literal removal 109]
126. ~curious(lucy) | humble(lucy) | ~creative(X0) [duplicate literal removal 110]
129. ~curious(X0) | happy(X0) [duplicate literal removal 67]
130. curious(X0) | happy(X0) [duplicate literal removal 68]
132. happy(X0) [subsumption resolution 129,130]
134. ~brave(X0) | ~generous(X0) [subsumption resolution 70,132]
165. 7 <=> ! [X3] : (generous(X3) | calm(X3)) [avatar definition]
166. calm(X3) | generous(X3) <- (7) [avatar component clause 165]
168. 8 <=> funny(sK2) [avatar definition]
170. ~funny(sK2) <- (~8) [avatar component clause 168]
171. 7 | ~8 [avatar split clause 87,168,165]
173. 9 <=> calm(sK2) [avatar definition]
175. ~calm(sK2) <- (~9) [avatar component clause 173]
176. 7 | ~9 [avatar split clause 86,173,165]
180. 10 <=> ! [X0] : ~creative(X0) [avatar definition]
181. ~creative(X0) <- (10) [avatar component clause 180]
183. 11 <=> humble(lucy) [avatar definition]
185. ~humble(lucy) <- (~11) [avatar component clause 183]
187. 12 <=> curious(lucy) [avatar definition]
188. ~curious(lucy) <- (~12) [avatar component clause 187]
192. 13 <=> ! [X0] : creative(X0) [avatar definition]
193. creative(X0) <- (13) [avatar component clause 192]
195. 10 | 11 | ~12 [avatar split clause 126,187,183,180]
196. 13 | 11 | ~12 [avatar split clause 125,187,183,192]
231. ~calm(lucy) [resolution 76,124]
232. calm(sK2) <- (~8) [resolution 77,170]
234. $false <- (~8, ~9) [subsumption resolution 232,175]
235. 8 | 9 [avatar contradiction clause 234]
237. ~humble(lucy) [resolution 103,124]
256. generous(lucy) <- (7) [resolution 166,231]
280. wise(lucy) | humble(lucy) [resolution 93,115]
281. wise(lucy) <- (~11) [subsumption resolution 280,185]
284. curious(lucy) | brave(lucy) <- (~11) [resolution 281,78]
285. brave(lucy) <- (~11, ~12) [subsumption resolution 284,188]
286. ~generous(lucy) <- (~11, ~12) [resolution 285,134]
289. $false <- (7, ~11, ~12) [subsumption resolution 286,256]
290. ~7 | 11 | 12 [avatar contradiction clause 289]
301. ~11 [avatar split clause 237,183]
302. $false <- (10, 13) [subsumption resolution 181,193]
303. ~10 | ~13 [avatar contradiction clause 302]
304. $false [avatar sat refutation 171,176,195,196,235,290,301,303]
% SZS output end Proof for 7973725553023419314554062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is strong.
If someone is funny then someone is either tall or calm.
If someone is not calm or not tall then someone is either not patient or not tall.
If someone is either quiet or not curious then susan is both calm and not generous and vice versa.
Everyone who is kind or quiet is wise or rich and vice versa.
If someone is either brave or not generous then mary is not calm or kind and vice versa.
Everyone who is both not wise and patient is both not creative and not calm.
If lucy is not brave or generous then someone is brave or calm.
Everyone who is either not wise or quiet is not rich.
Everyone who is not calm is happy.
If mary is generous or calm then someone is humble and vice versa.
Everyone who is both not tall and not strong is either strong or rich and vice versa.
If someone is both not quiet and wise then fred is happy or old and vice versa.
If someone is both not rich and calm then someone is old or not quiet and vice versa.
If lucy is patient or not patient then someone is either creative or quiet and vice versa.
If john is not strong or not wise then someone is both not generous and not old and vice versa.
Someone is either not curious or not patient.
Susan is both not old and quiet.
Someone is not calm.
Susan is either not old or not strong.
Someone is both brave and strong.
Lucy is both not happy and curious.
Someone is not wise.
Someone is both not funny and not brave. | John is not strong. | contradiction | (![X]:(~strong(X)=>strong(X)))&
((?[X]:(funny(X)))=>(?[X]:((tall(X)<~>calm(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((~patient(X)<~>~tall(X)))))&
((?[X]:((quiet(X)<~>~curious(X))))<=>((calm(susan)&~generous(susan))))&
(![X]:((kind(X)|quiet(X))<=>(wise(X)|rich(X))))&
((?[X]:((brave(X)<~>~generous(X))))<=>((~calm(mary)|kind(mary))))&
(![X]:((~wise(X)&patient(X))=>(~creative(X)&~calm(X))))&
(((~brave(lucy)|generous(lucy)))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>~rich(X)))&
(![X]:(~calm(X)=>happy(X)))&
(((generous(mary)|calm(mary)))<=>(?[X]:(humble(X))))&
(![X]:((~tall(X)&~strong(X))<=>(strong(X)<~>rich(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((happy(fred)|old(fred))))&
((?[X]:((~rich(X)&calm(X))))<=>(?[X]:((old(X)|~quiet(X)))))&
(((patient(lucy)|~patient(lucy)))<=>(?[X]:((creative(X)<~>quiet(X)))))&
(((~strong(john)|~wise(john)))<=>(?[X]:((~generous(X)&~old(X)))))&
(?[X]:((~curious(X)<~>~patient(X))))&
((~old(susan)&quiet(susan)))&
(?[X]:(~calm(X)))&
((~old(susan)<~>~strong(susan)))&
(?[X]:((brave(X)&strong(X))))&
((~happy(lucy)&curious(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((~funny(X)&~brave(X)))) | ~strong(john) | [
"p0",
"hypothesis"
]
| % SZS status Unsatisfiable for 8978276827951039256994959
% SZS output start Proof for 8978276827951039256994959
1. ! [X0] : (~strong(X0) => strong(X0)) [input p0]
25. ~strong(john) [input hypothesis]
31. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 1]
96. strong(X0) | strong(X0) [cnf transformation 31]
167. ~strong(john) [cnf transformation 25]
170. strong(X0) [duplicate literal removal 96]
363. $false [subsumption resolution 167,170]
% SZS output end Proof for 8978276827951039256994959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not old then someone is tall or not quiet.
If fred is both happy and not rich then someone is generous and vice versa.
Everyone who is rich or not quiet is either happy or not creative and vice versa.
Everyone who is strong is not old.
Everyone who is both generous and not funny is not creative and vice versa.
If someone is funny then susan is either not happy or rich.
If someone is both not happy and brave then someone is happy and vice versa.
Everyone who is funny or humble is not tall.
Everyone who is either wise or happy is either wise or curious and vice versa.
If someone is both not wise and not old then lucy is both not humble and not rich.
Everyone who is either old or not wise is wise.
Everyone who is not generous is either curious or not quiet and vice versa.
Everyone who is either not strong or not generous is either not tall or not calm and vice versa.
If someone is not quiet or happy then someone is either not tall or not patient.
If alice is both not generous and wise then someone is rich or not humble.
If lucy is both happy and not calm then john is both not quiet and not old and vice versa.
Someone is both calm and not curious.
Mary is happy or not generous.
Someone is either old or not rich.
Someone is calm or tall.
Someone is strong or not humble.
Fred is either patient or not patient.
Someone is not brave or not wise.
Lucy is not creative. | Lucy is not rich. | contradiction | ((?[X]:((quiet(X)&~old(X))))=>(?[X]:((tall(X)|~quiet(X)))))&
(((happy(fred)&~rich(fred)))<=>(?[X]:(generous(X))))&
(![X]:((rich(X)|~quiet(X))<=>(happy(X)<~>~creative(X))))&
(![X]:(strong(X)=>~old(X)))&
(![X]:((generous(X)&~funny(X))<=>~creative(X)))&
((?[X]:(funny(X)))=>((~happy(susan)<~>rich(susan))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:(happy(X))))&
(![X]:((funny(X)|humble(X))=>~tall(X)))&
(![X]:((wise(X)<~>happy(X))<=>(wise(X)<~>curious(X))))&
((?[X]:((~wise(X)&~old(X))))=>((~humble(lucy)&~rich(lucy))))&
(![X]:((old(X)<~>~wise(X))=>wise(X)))&
(![X]:(~generous(X)<=>(curious(X)<~>~quiet(X))))&
(![X]:((~strong(X)<~>~generous(X))<=>(~tall(X)<~>~calm(X))))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:((~tall(X)<~>~patient(X)))))&
(((~generous(alice)&wise(alice)))=>(?[X]:((rich(X)|~humble(X)))))&
(((happy(lucy)&~calm(lucy)))<=>((~quiet(john)&~old(john))))&
(?[X]:((calm(X)&~curious(X))))&
((happy(mary)|~generous(mary)))&
(?[X]:((old(X)<~>~rich(X))))&
(?[X]:((calm(X)|tall(X))))&
(?[X]:((strong(X)|~humble(X))))&
((patient(fred)<~>~patient(fred)))&
(?[X]:((~brave(X)|~wise(X))))&
(~creative(lucy)) | ~rich(lucy) | [
"p2",
"p4",
"p8",
"p11",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 2140320717382990083253459
% SZS output start Proof for 2140320717382990083253459
3. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (happy(X0) <~> ~creative(X0))) [input p2]
5. ! [X0] : ((~funny(X0) & generous(X0)) <=> ~creative(X0)) [input p4]
9. ! [X0] : ((wise(X0) <~> happy(X0)) <=> (wise(X0) <~> curious(X0))) [input p8]
12. ! [X0] : (~generous(X0) <=> (curious(X0) <~> ~quiet(X0))) [input p11]
24. ~creative(lucy) [input p23]
25. ~rich(lucy) [input hypothesis]
48. ! [X0] : (((~quiet(X0) | rich(X0)) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) & (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | (quiet(X0) & ~rich(X0)))) [nnf transformation 3]
49. ! [X0] : ((~quiet(X0) | rich(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) & (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | (quiet(X0) & ~rich(X0)))) [flattening 48]
50. ! [X0] : (((~funny(X0) & generous(X0)) | creative(X0)) & (~creative(X0) | (funny(X0) | ~generous(X0)))) [nnf transformation 5]
51. ! [X0] : (((~funny(X0) & generous(X0)) | creative(X0)) & (~creative(X0) | funny(X0) | ~generous(X0))) [flattening 50]
58. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) & (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 9]
60. ! [X0] : ((~generous(X0) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | generous(X0))) [nnf transformation 12]
85. ~happy(X0) | creative(X0) | quiet(X0) [cnf transformation 49]
87. ~quiet(X0) | rich(X0) | happy(X0) | creative(X0) [cnf transformation 49]
90. creative(X0) | generous(X0) [cnf transformation 51]
99. curious(X0) | wise(X0) | wise(X0) | ~happy(X0) [cnf transformation 58]
100. ~curious(X0) | ~wise(X0) | happy(X0) | ~wise(X0) [cnf transformation 58]
103. happy(X0) | wise(X0) | wise(X0) | ~curious(X0) [cnf transformation 58]
104. ~happy(X0) | ~wise(X0) | curious(X0) | ~wise(X0) [cnf transformation 58]
111. ~curious(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 60]
112. ~generous(X0) | curious(X0) | quiet(X0) [cnf transformation 60]
138. ~creative(lucy) [cnf transformation 24]
139. ~rich(lucy) [cnf transformation 25]
141. curious(X0) | wise(X0) | ~happy(X0) [duplicate literal removal 99]
142. ~curious(X0) | ~wise(X0) | happy(X0) [duplicate literal removal 100]
143. ~curious(X0) | wise(X0) | happy(X0) [duplicate literal removal 103]
144. ~wise(X0) | ~happy(X0) | curious(X0) [duplicate literal removal 104]
209. ~curious(X0) | happy(X0) [subsumption resolution 142,143]
210. ~happy(X0) | curious(X0) [subsumption resolution 141,144]
215. 17 <=> rich(lucy) [avatar definition]
217. ~rich(lucy) <- (~17) [avatar component clause 215]
249. 24 <=> happy(lucy) [avatar definition]
251. happy(lucy) <- (24) [avatar component clause 249]
292. ~17 [avatar split clause 139,215]
293. generous(lucy) [resolution 90,138]
348. curious(lucy) | quiet(lucy) [resolution 112,293]
359. 41 <=> quiet(lucy) [avatar definition]
361. quiet(lucy) <- (41) [avatar component clause 359]
363. 42 <=> curious(lucy) [avatar definition]
365. curious(lucy) <- (42) [avatar component clause 363]
366. 41 | 42 [avatar split clause 348,363,359]
374. rich(lucy) | happy(lucy) | creative(lucy) <- (41) [resolution 87,361]
377. happy(lucy) | creative(lucy) <- (~17, 41) [subsumption resolution 374,217]
394. happy(lucy) <- (~17, 41) [subsumption resolution 377,138]
395. 24 | 17 | ~41 [avatar split clause 394,359,215,249]
397. curious(lucy) <- (24) [resolution 251,210]
398. 42 | ~24 [avatar split clause 397,249,363]
625. ~quiet(lucy) | ~generous(lucy) <- (42) [resolution 365,111]
627. happy(lucy) <- (42) [resolution 365,209]
633. 24 | ~42 [avatar split clause 627,363,249]
635. creative(lucy) | quiet(lucy) <- (24) [resolution 251,85]
637. quiet(lucy) <- (24) [subsumption resolution 635,138]
640. 41 | ~24 [avatar split clause 637,249,359]
641. ~quiet(lucy) <- (42) [subsumption resolution 625,293]
642. ~41 | ~42 [avatar split clause 641,363,359]
643. $false [avatar sat refutation 292,366,395,398,633,640,642]
% SZS output end Proof for 2140320717382990083253459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not old and not generous then fred is quiet.
Everyone who is not kind is both not patient and generous.
If fred is not wise then mary is both rich and not rich and vice versa.
Everyone who is not kind is not old.
Everyone who is both rich and old is not happy or not strong and vice versa.
If lucy is both creative and calm then john is rich and vice versa.
If someone is not brave or not strong then john is both not kind and curious and vice versa.
If paul is both not kind and curious then susan is not wise or tall.
Everyone who is not tall or not kind is either not quiet or kind and vice versa.
Everyone who is either calm or not generous is both not rich and quiet.
Everyone who is not generous or happy is creative or brave and vice versa.
Everyone who is not strong is either strong or not generous and vice versa.
If someone is wise or not rich then mary is tall or curious.
If mary is kind then someone is not old or not curious and vice versa.
If someone is either not quiet or old then susan is either not wise or brave.
If paul is generous then someone is generous or not kind and vice versa.
Susan is both wise and not rich.
Someone is funny or not rich.
John is either calm or not strong.
Someone is either not generous or not creative.
Susan is not rich.
Someone is not calm or calm.
Fred is either not calm or funny. | Susan is rich. | contradiction | ((?[X]:((~old(X)&~generous(X))))=>(quiet(fred)))&
(![X]:(~kind(X)=>(~patient(X)&generous(X))))&
((~wise(fred))<=>((rich(mary)&~rich(mary))))&
(![X]:(~kind(X)=>~old(X)))&
(![X]:((rich(X)&old(X))<=>(~happy(X)|~strong(X))))&
(((creative(lucy)&calm(lucy)))<=>(rich(john)))&
((?[X]:((~brave(X)|~strong(X))))<=>((~kind(john)&curious(john))))&
(((~kind(paul)&curious(paul)))=>((~wise(susan)|tall(susan))))&
(![X]:((~tall(X)|~kind(X))<=>(~quiet(X)<~>kind(X))))&
(![X]:((calm(X)<~>~generous(X))=>(~rich(X)&quiet(X))))&
(![X]:((~generous(X)|happy(X))<=>(creative(X)|brave(X))))&
(![X]:(~strong(X)<=>(strong(X)<~>~generous(X))))&
((?[X]:((wise(X)|~rich(X))))=>((tall(mary)|curious(mary))))&
((kind(mary))<=>(?[X]:((~old(X)|~curious(X)))))&
((?[X]:((~quiet(X)<~>old(X))))=>((~wise(susan)<~>brave(susan))))&
((generous(paul))<=>(?[X]:((generous(X)|~kind(X)))))&
((wise(susan)&~rich(susan)))&
(?[X]:((funny(X)|~rich(X))))&
((calm(john)<~>~strong(john)))&
(?[X]:((~generous(X)<~>~creative(X))))&
(~rich(susan))&
(?[X]:((~calm(X)|calm(X))))&
((~calm(fred)<~>funny(fred))) | rich(susan) | [
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 4134760429786716139517757
% SZS output start Proof for 4134760429786716139517757
17. ~rich(susan) & wise(susan) [input p16]
24. rich(susan) [input hypothesis]
121. ~rich(susan) [cnf transformation 17]
131. rich(susan) [cnf transformation 24]
297. $false [subsumption resolution 131,121]
% SZS output end Proof for 4134760429786716139517757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and humble then someone is either old or not curious. Everyone who is either curious or calm is not wise and vice versa. If someone is funny then someone is creative. Everyone who is not brave or brave is both generous and not creative. Everyone who is not funny is either funny or not rich. Everyone who is either funny or creative is tall and vice versa. Everyone who is either not curious or not quiet is strong. If someone is patient or not calm then someone is not tall and vice versa. If someone is both not generous and calm then someone is curious or brave. If someone is calm or brave then someone is curious or not patient. If mary is wise then alice is either generous or tall and vice versa. If someone is not old or humble then susan is both humble and kind. If someone is not happy then mary is both not strong and strong and vice versa. Everyone who is both not humble and curious is both not happy and wise and vice versa. Everyone who is not kind is both not kind and calm and vice versa. Mary is not kind. Alice is both generous and not brave. Lucy is either kind or not curious. Alice is both not wise and not patient. Someone is not humble. Lucy is not calm or not humble. | Mary is wise. | entailment | ((?[X]:((tall(X)&humble(X))))=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:((curious(X)<~>calm(X))<=>~wise(X)))&
((?[X]:(funny(X)))=>(?[X]:(creative(X))))&
(![X]:((~brave(X)|brave(X))=>(generous(X)&~creative(X))))&
(![X]:(~funny(X)=>(funny(X)<~>~rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~quiet(X))=>strong(X)))&
((?[X]:((patient(X)|~calm(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~generous(X)&calm(X))))=>(?[X]:((curious(X)|brave(X)))))&
((?[X]:((calm(X)|brave(X))))=>(?[X]:((curious(X)|~patient(X)))))&
((wise(mary))<=>((generous(alice)<~>tall(alice))))&
((?[X]:((~old(X)|humble(X))))=>((humble(susan)&kind(susan))))&
((?[X]:(~happy(X)))<=>((~strong(mary)&strong(mary))))&
(![X]:((~humble(X)&curious(X))<=>(~happy(X)&wise(X))))&
(![X]:(~kind(X)<=>(~kind(X)&calm(X))))&
(~kind(mary))&
((generous(alice)&~brave(alice)))&
((kind(lucy)<~>~curious(lucy)))&
((~wise(alice)&~patient(alice)))&
(?[X]:(~humble(X)))&
((~calm(lucy)|~humble(lucy))) | wise(mary) | [
"p2",
"p3",
"p5",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 1198593316487332476510163
% SZS output start Proof for 1198593316487332476510163
3. ? [X0] : funny(X0) => ? [X0] : creative(X0) [input p2]
4. ! [X0] : ((brave(X0) | ~brave(X0)) => (~creative(X0) & generous(X0))) [input p3]
6. ! [X0] : ((funny(X0) <~> creative(X0)) <=> tall(X0)) [input p5]
11. wise(mary) <=> (generous(alice) <~> tall(alice)) [input p10]
22. ~wise(mary) [input hypothesis]
24. ? [X0] : funny(X0) => ? [X1] : creative(X1) [rectify 3]
29. ? [X1] : creative(X1) | ! [X0] : ~funny(X0) [ennf transformation 24]
30. ! [X0] : ((~creative(X0) & generous(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 4]
41. ? [X0] : creative(X0) | ! [X1] : ~funny(X1) [rectify 29]
42. ? [X0] : creative(X0) => creative(sK1) [choice axiom]
43. creative(sK1) | ! [X1] : ~funny(X1) [skolemisation 41,42]
45. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~tall(X0)) & (tall(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 6]
58. (wise(mary) | ((generous(alice) | ~tall(alice)) & (tall(alice) | ~generous(alice)))) & (((~tall(alice) | ~generous(alice)) & (tall(alice) | generous(alice))) | ~wise(mary)) [nnf transformation 11]
77. creative(sK1) | ~funny(X1) [cnf transformation 43]
78. generous(X0) | brave(X0) [cnf transformation 30]
79. ~brave(X0) | generous(X0) [cnf transformation 30]
80. ~creative(X0) | brave(X0) [cnf transformation 30]
81. ~brave(X0) | ~creative(X0) [cnf transformation 30]
86. creative(X0) | funny(X0) | ~tall(X0) [cnf transformation 45]
98. wise(mary) | tall(alice) | ~generous(alice) [cnf transformation 58]
123. ~wise(mary) [cnf transformation 22]
139. 4 <=> ! [X1] : ~funny(X1) [avatar definition]
140. ~funny(X1) <- (4) [avatar component clause 139]
142. 5 <=> creative(sK1) [avatar definition]
144. creative(sK1) <- (5) [avatar component clause 142]
145. 4 | 5 [avatar split clause 77,142,139]
146. ~creative(X0) [subsumption resolution 80,81]
147. generous(X0) [subsumption resolution 78,79]
148. ~tall(X0) | funny(X0) [subsumption resolution 86,146]
190. wise(mary) | tall(alice) [subsumption resolution 98,147]
192. 16 <=> tall(alice) [avatar definition]
194. tall(alice) <- (16) [avatar component clause 192]
196. 17 <=> wise(mary) [avatar definition]
199. 16 | 17 [avatar split clause 190,196,192]
248. ~17 [avatar split clause 123,196]
257. funny(alice) <- (16) [resolution 148,194]
258. $false <- (4, 16) [subsumption resolution 257,140]
259. ~4 | ~16 [avatar contradiction clause 258]
260. $false <- (5) [subsumption resolution 144,146]
261. ~5 [avatar contradiction clause 260]
262. $false [avatar sat refutation 145,199,248,259,261]
% SZS output end Proof for 1198593316487332476510163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is creative or not wise then mary is tall or old.
Everyone who is both not strong and rich is both not generous and not old.
Everyone who is both kind and not rich is either not calm or not happy.
Everyone who is not old is either wise or humble and vice versa.
Everyone who is either not tall or not wise is not wise or not creative and vice versa.
If mary is not curious then someone is not patient or tall.
If someone is either not strong or brave then paul is either patient or not funny.
Everyone who is both old and generous is happy or not kind.
Everyone who is either not funny or not generous is both kind and not rich.
If someone is not quiet or not rich then someone is both generous and not generous and vice versa.
If mary is both not humble and humble then susan is funny and vice versa.
If someone is both not strong and wise then someone is not calm and vice versa.
If someone is not rich then alice is old or not wise.
If someone is not brave or generous then someone is either not creative or not tall and vice versa.
Everyone who is humble or not funny is strong.
Everyone who is either not tall or not curious is both not quiet and not wise and vice versa.
Susan is either creative or not creative.
John is old or not tall.
Susan is either curious or happy.
Susan is wise or rich.
Someone is kind or not wise.
Someone is quiet.
Paul is strong or curious. | Alice is not rich. | contradiction | (((creative(mary)|~wise(mary)))=>((tall(mary)|old(mary))))&
(![X]:((~strong(X)&rich(X))=>(~generous(X)&~old(X))))&
(![X]:((kind(X)&~rich(X))=>(~calm(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(wise(X)<~>humble(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~wise(X)|~creative(X))))&
((~curious(mary))=>(?[X]:((~patient(X)|tall(X)))))&
((?[X]:((~strong(X)<~>brave(X))))=>((patient(paul)<~>~funny(paul))))&
(![X]:((old(X)&generous(X))=>(happy(X)|~kind(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(kind(X)&~rich(X))))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((generous(X)&~generous(X)))))&
(((~humble(mary)&humble(mary)))<=>(funny(susan)))&
((?[X]:((~strong(X)&wise(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~rich(X)))=>((old(alice)|~wise(alice))))&
((?[X]:((~brave(X)|generous(X))))<=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((humble(X)|~funny(X))=>strong(X)))&
(![X]:((~tall(X)<~>~curious(X))<=>(~quiet(X)&~wise(X))))&
((creative(susan)<~>~creative(susan)))&
((old(john)|~tall(john)))&
((curious(susan)<~>happy(susan)))&
((wise(susan)|rich(susan)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:(quiet(X)))&
((strong(paul)|curious(paul))) | ~rich(alice) | [
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 681781712122505957405063
% SZS output start Proof for 681781712122505957405063
10. ? [X0] : (~rich(X0) | ~quiet(X0)) <=> ? [X0] : (~generous(X0) & generous(X0)) [input p9]
24. ~rich(alice) [input hypothesis]
25. ? [X0] : (~rich(X0) | ~quiet(X0)) <=> ? [X1] : (~generous(X1) & generous(X1)) [rectify 10]
50. (? [X0] : (~rich(X0) | ~quiet(X0)) | ! [X1] : (generous(X1) | ~generous(X1))) & (? [X1] : (~generous(X1) & generous(X1)) | ! [X0] : (rich(X0) & quiet(X0))) [nnf transformation 25]
51. (? [X0] : (~rich(X0) | ~quiet(X0)) | ! [X1] : (generous(X1) | ~generous(X1))) & (? [X2] : (~generous(X2) & generous(X2)) | ! [X3] : (rich(X3) & quiet(X3))) [rectify 50]
52. ? [X0] : (~rich(X0) | ~quiet(X0)) => (~rich(sK1) | ~quiet(sK1)) [choice axiom]
53. ? [X2] : (~generous(X2) & generous(X2)) => (~generous(sK2) & generous(sK2)) [choice axiom]
54. ((~rich(sK1) | ~quiet(sK1)) | ! [X1] : (generous(X1) | ~generous(X1))) & ((~generous(sK2) & generous(sK2)) | ! [X3] : (rich(X3) & quiet(X3))) [skolemisation 51,53,52]
102. generous(sK2) | rich(X3) [cnf transformation 54]
104. ~generous(sK2) | rich(X3) [cnf transformation 54]
136. ~rich(alice) [cnf transformation 24]
190. 12 <=> ! [X3] : rich(X3) [avatar definition]
191. rich(X3) <- (12) [avatar component clause 190]
193. 13 <=> generous(sK2) [avatar definition]
196. 12 | ~13 [avatar split clause 104,193,190]
201. 12 | 13 [avatar split clause 102,193,190]
325. $false <- (12) [resolution 191,136]
326. ~12 [avatar contradiction clause 325]
327. $false [avatar sat refutation 196,201,326]
% SZS output end Proof for 681781712122505957405063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is both not humble and generous and vice versa. Everyone who is funny is curious or funny. If someone is curious then mary is tall. If john is either brave or not calm then someone is either funny or quiet and vice versa. Everyone who is both not old and tall is either not calm or calm and vice versa. If someone is not humble then someone is either not patient or not quiet and vice versa. Everyone who is both not rich and not humble is not rich. Everyone who is either happy or not calm is both curious and not creative. If someone is both not wise and not strong then paul is either not rich or tall. If someone is not old or not brave then john is calm and vice versa. Everyone who is either calm or not rich is either wise or not strong. If paul is not rich then someone is wise or not tall and vice versa. Everyone who is not creative is rich or not strong and vice versa. Everyone who is both not creative and old is not creative or happy and vice versa. Everyone who is both happy and not calm is not generous or brave. Everyone who is both not patient and calm is either curious or not old and vice versa. Mary is not kind. Someone is happy or not old. Paul is either generous or kind. Someone is either kind or creative. Someone is both generous and not patient. Someone is not rich or not tall. | Paul is not kind. | entailment | (![X]:(tall(X)<=>(~humble(X)&generous(X))))&
(![X]:(funny(X)=>(curious(X)|funny(X))))&
((?[X]:(curious(X)))=>(tall(mary)))&
(((brave(john)<~>~calm(john)))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~old(X)&tall(X))<=>(~calm(X)<~>calm(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&~humble(X))=>~rich(X)))&
(![X]:((happy(X)<~>~calm(X))=>(curious(X)&~creative(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~rich(paul)<~>tall(paul))))&
((?[X]:((~old(X)|~brave(X))))<=>(calm(john)))&
(![X]:((calm(X)<~>~rich(X))=>(wise(X)<~>~strong(X))))&
((~rich(paul))<=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~creative(X)<=>(rich(X)|~strong(X))))&
(![X]:((~creative(X)&old(X))<=>(~creative(X)|happy(X))))&
(![X]:((happy(X)&~calm(X))=>(~generous(X)|brave(X))))&
(![X]:((~patient(X)&calm(X))<=>(curious(X)<~>~old(X))))&
(~kind(mary))&
(?[X]:((happy(X)|~old(X))))&
((generous(paul)<~>kind(paul)))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((~rich(X)|~tall(X)))) | ~kind(paul) | [
"p0",
"p4",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 1249577399971876118388608
% SZS output start Proof for 1249577399971876118388608
1. ! [X0] : (tall(X0) <=> (generous(X0) & ~humble(X0))) [input p0]
5. ! [X0] : ((tall(X0) & ~old(X0)) <=> (~calm(X0) <~> calm(X0))) [input p4]
19. generous(paul) <~> kind(paul) [input p18]
23. kind(paul) [input hypothesis]
35. ! [X0] : ((tall(X0) | (~generous(X0) | humble(X0))) & ((generous(X0) & ~humble(X0)) | ~tall(X0))) [nnf transformation 1]
36. ! [X0] : ((tall(X0) | ~generous(X0) | humble(X0)) & ((generous(X0) & ~humble(X0)) | ~tall(X0))) [flattening 35]
41. ! [X0] : (((tall(X0) & ~old(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~tall(X0) | old(X0)))) [nnf transformation 5]
42. ! [X0] : (((tall(X0) & ~old(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~tall(X0) | old(X0))) [flattening 41]
67. (~kind(paul) | ~generous(paul)) & (kind(paul) | generous(paul)) [nnf transformation 19]
76. ~tall(X0) | generous(X0) [cnf transformation 36]
92. tall(X0) | calm(X0) | calm(X0) [cnf transformation 42]
93. tall(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 42]
133. ~kind(paul) | ~generous(paul) [cnf transformation 67]
139. kind(paul) [cnf transformation 23]
142. tall(X0) | calm(X0) [duplicate literal removal 92]
143. tall(X0) | ~calm(X0) [duplicate literal removal 93]
182. tall(X0) [subsumption resolution 142,143]
240. 20 <=> generous(paul) [avatar definition]
242. ~generous(paul) <- (~20) [avatar component clause 240]
244. 21 <=> kind(paul) [avatar definition]
247. ~20 | ~21 [avatar split clause 133,244,240]
251. 21 [avatar split clause 139,244]
260. generous(X0) [resolution 76,182]
261. $false <- (~20) [resolution 260,242]
262. 20 [avatar contradiction clause 261]
263. $false [avatar sat refutation 247,251,262]
% SZS output end Proof for 1249577399971876118388608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not creative and vice versa. If alice is either not kind or quiet then someone is not strong or not brave and vice versa. Everyone who is either humble or brave is not brave and vice versa. Everyone who is either not patient or not quiet is either not humble or curious and vice versa. Everyone who is both humble and happy is either not tall or funny and vice versa. If someone is not funny then fred is either not tall or not old. If john is curious then john is not curious or calm. If someone is either quiet or kind then lucy is both not generous and not wise. Everyone who is humble is not happy or old. Everyone who is tall or old is not tall or 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. Alice is happy or funny. Mary is not creative. Someone is not calm or strong. Alice is not old or funny. Alice is both not quiet and creative. Someone is not calm. Someone is happy. | John is patient. | neutral | (![X]:(~kind(X)<=>~creative(X)))&
(((~kind(alice)<~>quiet(alice)))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((humble(X)<~>brave(X))<=>~brave(X)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(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)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice)))&
(?[X]:(~calm(X)))&
(?[X]:(happy(X))) | patient(john) | []
| null | 0 |
If someone is either not rich or not generous then someone is either quiet or funny.
Everyone who is both strong and happy is not funny or brave and vice versa.
Everyone who is not strong is not wise and vice versa.
If someone is not tall or tall then mary is either wise or funny.
Everyone who is either not calm or humble is not calm.
If someone is not strong or not wise then someone is wise or not tall.
Everyone who is both happy and curious is funny or brave and vice versa.
Everyone who is both strong and not happy is both not tall and not happy and vice versa.
Everyone who is both humble and wise is happy and vice versa.
If paul is both not tall and not generous then mary is creative or kind.
If susan is either not calm or curious then someone is not humble or wise.
Everyone who is either not creative or not kind is not generous.
If someone is happy then someone is either rich or calm and vice versa.
If susan is not humble then someone is strong or not patient.
Everyone who is either kind or not old is rich.
If lucy is not creative or kind then someone is not wise.
Paul is generous.
Someone is both creative and strong.
Someone is happy.
Someone is kind.
Alice is kind.
John is happy.
Someone is not tall.
Someone is not funny. | Lucy is kind. | contradiction | ((?[X]:((~rich(X)<~>~generous(X))))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((strong(X)&happy(X))<=>(~funny(X)|brave(X))))&
(![X]:(~strong(X)<=>~wise(X)))&
((?[X]:((~tall(X)|tall(X))))=>((wise(mary)<~>funny(mary))))&
(![X]:((~calm(X)<~>humble(X))=>~calm(X)))&
((?[X]:((~strong(X)|~wise(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:((happy(X)&curious(X))<=>(funny(X)|brave(X))))&
(![X]:((strong(X)&~happy(X))<=>(~tall(X)&~happy(X))))&
(![X]:((humble(X)&wise(X))<=>happy(X)))&
(((~tall(paul)&~generous(paul)))=>((creative(mary)|kind(mary))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:((~humble(X)|wise(X)))))&
(![X]:((~creative(X)<~>~kind(X))=>~generous(X)))&
((?[X]:(happy(X)))<=>(?[X]:((rich(X)<~>calm(X)))))&
((~humble(susan))=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((kind(X)<~>~old(X))=>rich(X)))&
(((~creative(lucy)|kind(lucy)))=>(?[X]:(~wise(X))))&
(generous(paul))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:(happy(X)))&
(?[X]:(kind(X)))&
(kind(alice))&
(happy(john))&
(?[X]:(~tall(X)))&
(?[X]:(~funny(X))) | kind(lucy) | [
"p1",
"p6",
"p8",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 9111860770474493643504735
% SZS output start Proof for 9111860770474493643504735
2. ! [X0] : ((happy(X0) & strong(X0)) <=> (brave(X0) | ~funny(X0))) [input p1]
7. ! [X0] : ((curious(X0) & happy(X0)) <=> (brave(X0) | funny(X0))) [input p6]
9. ! [X0] : ((wise(X0) & humble(X0)) <=> happy(X0)) [input p8]
16. (kind(lucy) | ~creative(lucy)) => ? [X0] : ~wise(X0) [input p15]
25. kind(lucy) [input hypothesis]
39. ? [X0] : ~wise(X0) | (~kind(lucy) & creative(lucy)) [ennf transformation 16]
44. ! [X0] : (((happy(X0) & strong(X0)) | (~brave(X0) & funny(X0))) & ((brave(X0) | ~funny(X0)) | (~happy(X0) | ~strong(X0)))) [nnf transformation 2]
45. ! [X0] : (((happy(X0) & strong(X0)) | (~brave(X0) & funny(X0))) & (brave(X0) | ~funny(X0) | ~happy(X0) | ~strong(X0))) [flattening 44]
52. ! [X0] : (((curious(X0) & happy(X0)) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | (~curious(X0) | ~happy(X0)))) [nnf transformation 7]
53. ! [X0] : (((curious(X0) & happy(X0)) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | ~curious(X0) | ~happy(X0))) [flattening 52]
56. ! [X0] : (((wise(X0) & humble(X0)) | ~happy(X0)) & (happy(X0) | (~wise(X0) | ~humble(X0)))) [nnf transformation 9]
57. ! [X0] : (((wise(X0) & humble(X0)) | ~happy(X0)) & (happy(X0) | ~wise(X0) | ~humble(X0))) [flattening 56]
68. ? [X0] : ~wise(X0) => ~wise(sK5) [choice axiom]
69. ~wise(sK5) | (~kind(lucy) & creative(lucy)) [skolemisation 39,68]
87. happy(X0) | funny(X0) [cnf transformation 45]
100. happy(X0) | ~funny(X0) [cnf transformation 53]
110. wise(X0) | ~happy(X0) [cnf transformation 57]
123. ~wise(sK5) | ~kind(lucy) [cnf transformation 69]
133. kind(lucy) [cnf transformation 25]
172. 9 <=> ! [X1] : wise(X1) [avatar definition]
173. wise(X1) <- (9) [avatar component clause 172]
187. happy(X0) [subsumption resolution 100,87]
189. wise(X0) [subsumption resolution 110,187]
190. 9 [avatar split clause 189,172]
238. 22 <=> kind(lucy) [avatar definition]
242. 23 <=> wise(sK5) [avatar definition]
244. ~wise(sK5) <- (~23) [avatar component clause 242]
245. ~22 | ~23 [avatar split clause 123,242,238]
252. 22 [avatar split clause 133,238]
253. $false <- (9, ~23) [resolution 244,173]
254. ~9 | 23 [avatar contradiction clause 253]
255. $false [avatar sat refutation 190,245,252,254]
% SZS output end Proof for 9111860770474493643504735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not kind or not generous then fred is both creative and not rich.
If someone is either happy or creative then someone is not strong or not quiet.
If susan is not funny then someone is either funny or not calm.
If alice is either not kind or rich then someone is either not funny or not generous and vice versa.
If lucy is not strong then someone is calm and vice versa.
Everyone who is not strong or not humble is both not generous and generous.
Everyone who is not calm is not happy or wise.
Everyone who is both brave and not wise is either humble or not creative and vice versa.
Everyone who is either wise or not rich is either not tall or not humble and vice versa.
Everyone who is either not creative or not curious is not patient or old.
If alice is funny then susan is either not strong or not quiet.
If alice is brave then mary is both not humble and not quiet and vice versa.
If lucy is both old and patient then someone is generous or not strong.
Everyone who is not wise or patient is both humble and not old.
If susan is both not patient and not tall then someone is both generous and wise.
If someone is both not rich and happy then someone is not curious or not happy.
Someone is not curious or not kind.
Susan is generous.
Susan is either creative or not quiet.
Fred is curious.
Paul is funny.
John is both generous and patient.
Someone is not old or not kind. | Lucy is calm. | contradiction | (((~kind(alice)|~generous(alice)))=>((creative(fred)&~rich(fred))))&
((?[X]:((happy(X)<~>creative(X))))=>(?[X]:((~strong(X)|~quiet(X)))))&
((~funny(susan))=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~kind(alice)<~>rich(alice)))<=>(?[X]:((~funny(X)<~>~generous(X)))))&
((~strong(lucy))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)|~humble(X))=>(~generous(X)&generous(X))))&
(![X]:(~calm(X)=>(~happy(X)|wise(X))))&
(![X]:((brave(X)&~wise(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>~curious(X))=>(~patient(X)|old(X))))&
((funny(alice))=>((~strong(susan)<~>~quiet(susan))))&
((brave(alice))<=>((~humble(mary)&~quiet(mary))))&
(((old(lucy)&patient(lucy)))=>(?[X]:((generous(X)|~strong(X)))))&
(![X]:((~wise(X)|patient(X))=>(humble(X)&~old(X))))&
(((~patient(susan)&~tall(susan)))=>(?[X]:((generous(X)&wise(X)))))&
((?[X]:((~rich(X)&happy(X))))=>(?[X]:((~curious(X)|~happy(X)))))&
(?[X]:((~curious(X)|~kind(X))))&
(generous(susan))&
((creative(susan)<~>~quiet(susan)))&
(curious(fred))&
(funny(paul))&
((generous(john)&patient(john)))&
(?[X]:((~old(X)|~kind(X)))) | calm(lucy) | [
"p4",
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 626528397890548753793578
% SZS output start Proof for 626528397890548753793578
5. ~strong(lucy) <=> ? [X0] : calm(X0) [input p4]
6. ! [X0] : ((~humble(X0) | ~strong(X0)) => (generous(X0) & ~generous(X0))) [input p5]
24. calm(lucy) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~generous(X0)) | (humble(X0) & strong(X0))) [ennf transformation 6]
53. (~strong(lucy) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | strong(lucy)) [nnf transformation 5]
54. (~strong(lucy) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | strong(lucy)) [rectify 53]
55. ? [X1] : calm(X1) => calm(sK3) [choice axiom]
56. (~strong(lucy) | ! [X0] : ~calm(X0)) & (calm(sK3) | strong(lucy)) [skolemisation 54,55]
93. ~strong(lucy) | ~calm(X0) [cnf transformation 56]
94. ~generous(X0) | strong(X0) [cnf transformation 30]
96. generous(X0) | strong(X0) [cnf transformation 30]
137. calm(lucy) [cnf transformation 24]
215. 17 <=> ! [X0] : ~calm(X0) [avatar definition]
216. ~calm(X0) <- (17) [avatar component clause 215]
218. 18 <=> strong(lucy) [avatar definition]
220. ~strong(lucy) <- (~18) [avatar component clause 218]
221. 17 | ~18 [avatar split clause 93,218,215]
228. strong(X0) [subsumption resolution 94,96]
327. $false <- (17) [resolution 216,137]
328. ~17 [avatar contradiction clause 327]
329. $false <- (~18) [subsumption resolution 220,228]
330. 18 [avatar contradiction clause 329]
331. $false [avatar sat refutation 221,328,330]
% SZS output end Proof for 626528397890548753793578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not old is not wise.
If someone is creative then mary is not funny and vice versa.
Everyone who is either kind or not old is not rich and vice versa.
Everyone who is either not calm or humble is both not tall and not wise and vice versa.
If john is not calm or creative then someone is not tall and vice versa.
If someone is strong then someone is brave or funny and vice versa.
Everyone who is kind is both brave and not generous.
Everyone who is humble or quiet is either not generous or patient and vice versa.
If someone is both tall and patient then someone is both not kind and not wise and vice versa.
If someone is humble then fred is either not happy or calm and vice versa.
Everyone who is old is both not curious and not wise and vice versa.
Everyone who is funny or tall is rich and vice versa.
Everyone who is either not generous or not wise is curious.
If someone is old or not quiet then susan is not happy or not brave and vice versa.
Everyone who is both creative and not kind is both not generous and not strong.
If fred is patient then mary is both not humble and not happy.
Someone is both curious and calm.
Someone is both kind and not rich.
Someone is kind or curious.
Someone is wise.
Alice is either quiet or humble.
John is both rich and wise.
Susan is wise or strong.
Susan is not funny. | John is not generous. | entailment | (![X]:((~tall(X)&~old(X))=>~wise(X)))&
((?[X]:(creative(X)))<=>(~funny(mary)))&
(![X]:((kind(X)<~>~old(X))<=>~rich(X)))&
(![X]:((~calm(X)<~>humble(X))<=>(~tall(X)&~wise(X))))&
(((~calm(john)|creative(john)))<=>(?[X]:(~tall(X))))&
((?[X]:(strong(X)))<=>(?[X]:((brave(X)|funny(X)))))&
(![X]:(kind(X)=>(brave(X)&~generous(X))))&
(![X]:((humble(X)|quiet(X))<=>(~generous(X)<~>patient(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:((~kind(X)&~wise(X)))))&
((?[X]:(humble(X)))<=>((~happy(fred)<~>calm(fred))))&
(![X]:(old(X)<=>(~curious(X)&~wise(X))))&
(![X]:((funny(X)|tall(X))<=>rich(X)))&
(![X]:((~generous(X)<~>~wise(X))=>curious(X)))&
((?[X]:((old(X)|~quiet(X))))<=>((~happy(susan)|~brave(susan))))&
(![X]:((creative(X)&~kind(X))=>(~generous(X)&~strong(X))))&
((patient(fred))=>((~humble(mary)&~happy(mary))))&
(?[X]:((curious(X)&calm(X))))&
(?[X]:((kind(X)&~rich(X))))&
(?[X]:((kind(X)|curious(X))))&
(?[X]:(wise(X)))&
((quiet(alice)<~>humble(alice)))&
((rich(john)&wise(john)))&
((wise(susan)|strong(susan)))&
(~funny(susan)) | ~generous(john) | [
"p2",
"p6",
"p10",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 7038959142094005573588019
% SZS output start Proof for 7038959142094005573588019
3. ! [X0] : ((kind(X0) <~> ~old(X0)) <=> ~rich(X0)) [input p2]
7. ! [X0] : (kind(X0) => (~generous(X0) & brave(X0))) [input p6]
11. ! [X0] : (old(X0) <=> (~wise(X0) & ~curious(X0))) [input p10]
22. wise(john) & rich(john) [input p21]
25. generous(john) [input hypothesis]
30. ! [X0] : ((~generous(X0) & brave(X0)) | ~kind(X0)) [ennf transformation 7]
39. ! [X0] : ((((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | rich(X0)) & (~rich(X0) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0))))) [nnf transformation 3]
63. ! [X0] : ((old(X0) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | ~old(X0))) [nnf transformation 11]
64. ! [X0] : ((old(X0) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | ~old(X0))) [flattening 63]
86. ~rich(X0) | kind(X0) | old(X0) [cnf transformation 39]
102. ~generous(X0) | ~kind(X0) [cnf transformation 30]
118. ~wise(X0) | ~old(X0) [cnf transformation 64]
141. rich(john) [cnf transformation 22]
142. wise(john) [cnf transformation 22]
145. generous(john) [cnf transformation 25]
323. ~kind(john) [resolution 102,145]
326. ~old(john) [resolution 118,142]
354. kind(john) | old(john) [resolution 86,141]
356. old(john) [subsumption resolution 354,323]
357. $false [subsumption resolution 356,326]
% SZS output end Proof for 7038959142094005573588019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or brave is rich or kind. Everyone who is both not generous and happy is both calm and wise. Everyone who is either wise or not curious is either not wise or generous. Everyone who is both kind and creative is both not kind and funny and vice versa. Everyone who is either kind or tall is not old. Everyone who is not funny or creative is both brave and old and vice versa. Everyone who is not curious or brave is brave or not generous. If someone is strong or not humble then someone is curious and vice versa. If alice is either brave or not kind then fred is creative or funny and vice versa. Everyone who is both not strong and tall is not generous. Everyone who is either not rich or strong is either not patient or patient and vice versa. Everyone who is old is both funny and not humble and vice versa. If someone is either rich or not tall then someone is both kind and not creative and vice versa. Everyone who is humble or not rich is not happy or strong and vice versa. Everyone who is patient is both curious and humble and vice versa. If alice is not rich then susan is both not curious and wise and vice versa. Fred is funny or wise. Mary is either humble or not calm. Susan is not curious or happy. John is not curious or not wise. Someone is tall or not creative. Someone is not creative. Someone is rich. Susan is either not patient or calm. | Fred is not tall. | neutral | (![X]:((~patient(X)<~>brave(X))=>(rich(X)|kind(X))))&
(![X]:((~generous(X)&happy(X))=>(calm(X)&wise(X))))&
(![X]:((wise(X)<~>~curious(X))=>(~wise(X)<~>generous(X))))&
(![X]:((kind(X)&creative(X))<=>(~kind(X)&funny(X))))&
(![X]:((kind(X)<~>tall(X))=>~old(X)))&
(![X]:((~funny(X)|creative(X))<=>(brave(X)&old(X))))&
(![X]:((~curious(X)|brave(X))=>(brave(X)|~generous(X))))&
((?[X]:((strong(X)|~humble(X))))<=>(?[X]:(curious(X))))&
(((brave(alice)<~>~kind(alice)))<=>((creative(fred)|funny(fred))))&
(![X]:((~strong(X)&tall(X))=>~generous(X)))&
(![X]:((~rich(X)<~>strong(X))<=>(~patient(X)<~>patient(X))))&
(![X]:(old(X)<=>(funny(X)&~humble(X))))&
((?[X]:((rich(X)<~>~tall(X))))<=>(?[X]:((kind(X)&~creative(X)))))&
(![X]:((humble(X)|~rich(X))<=>(~happy(X)|strong(X))))&
(![X]:(patient(X)<=>(curious(X)&humble(X))))&
((~rich(alice))<=>((~curious(susan)&wise(susan))))&
((funny(fred)|wise(fred)))&
((humble(mary)<~>~calm(mary)))&
((~curious(susan)|happy(susan)))&
((~curious(john)|~wise(john)))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:(~creative(X)))&
(?[X]:(rich(X)))&
((~patient(susan)<~>calm(susan))) | ~tall(fred) | []
| null | 0 |
Everyone who is either not creative or not wise is either not calm or not generous and vice versa. If mary is old or not calm then lucy is not funny. Everyone who is either funny or tall is either not wise or not kind and vice versa. Everyone who is either not kind or not brave is either creative or not old. Everyone who is both calm and not funny is both not quiet and not generous. If someone is not wise then john is not patient and vice versa. Everyone who is not wise is either patient or not rich and vice versa. Everyone who is quiet or happy is creative or not brave. If alice is quiet or old then someone is either curious or not generous. Everyone who is not tall is both creative and not tall and vice versa. Everyone who is generous or not curious is creative or not quiet and vice versa. Everyone who is either not funny or not humble is either not funny or calm and vice versa. If someone is not kind or not humble then paul is rich or not strong and vice versa. Everyone who is either not creative or not calm is not brave or not wise and vice versa. Everyone who is either not generous or strong is creative. If someone is either not patient or not old then mary is not brave or not wise. Someone is both not calm and not quiet. Someone is strong. Someone is not calm. Lucy is kind or not strong. Someone is either generous or tall. Someone is brave or not rich. Mary is kind or not happy. | Lucy is quiet. | neutral | (![X]:((~creative(X)<~>~wise(X))<=>(~calm(X)<~>~generous(X))))&
(((old(mary)|~calm(mary)))=>(~funny(lucy)))&
(![X]:((funny(X)<~>tall(X))<=>(~wise(X)<~>~kind(X))))&
(![X]:((~kind(X)<~>~brave(X))=>(creative(X)<~>~old(X))))&
(![X]:((calm(X)&~funny(X))=>(~quiet(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(~patient(john)))&
(![X]:(~wise(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((quiet(X)|happy(X))=>(creative(X)|~brave(X))))&
(((quiet(alice)|old(alice)))=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~tall(X)<=>(creative(X)&~tall(X))))&
(![X]:((generous(X)|~curious(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~funny(X)<~>~humble(X))<=>(~funny(X)<~>calm(X))))&
((?[X]:((~kind(X)|~humble(X))))<=>((rich(paul)|~strong(paul))))&
(![X]:((~creative(X)<~>~calm(X))<=>(~brave(X)|~wise(X))))&
(![X]:((~generous(X)<~>strong(X))=>creative(X)))&
((?[X]:((~patient(X)<~>~old(X))))=>((~brave(mary)|~wise(mary))))&
(?[X]:((~calm(X)&~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(lucy)|~strong(lucy)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((brave(X)|~rich(X))))&
((kind(mary)|~happy(mary))) | quiet(lucy) | []
| null | 0 |
If alice is not old then someone is creative or not funny and vice versa. If someone is calm then someone is calm or not funny and vice versa. Everyone who is patient is tall or not old and vice versa. Everyone who is generous is both rich and not quiet and vice versa. Everyone who is not funny is either not old or patient and vice versa. If someone is not tall then someone is not brave or not generous and vice versa. Everyone who is either curious or not quiet is both not patient and not rich. If fred is either generous or not patient then fred is not brave. Everyone who is old is both creative and not funny and vice versa. Everyone who is both not quiet and not curious is wise or not funny and vice versa. Everyone who is both calm and not curious is not funny and vice versa. If mary is not strong or strong then someone is creative. If someone is humble then susan is not curious and vice versa. If someone is not happy then someone is not calm or rich and vice versa. Everyone who is creative is not strong or tall. Everyone who is tall or not quiet is both not tall and brave. Mary is both rich and not brave. Someone is not kind. John is both not tall and not calm. Someone is not brave. Someone is calm or tall. Fred is not curious. Paul is either tall or generous. Someone is both strong and not happy. | Fred is quiet. | entailment | ((~old(alice))<=>(?[X]:((creative(X)|~funny(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(patient(X)<=>(tall(X)|~old(X))))&
(![X]:(generous(X)<=>(rich(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))=>(~patient(X)&~rich(X))))&
(((generous(fred)<~>~patient(fred)))=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(wise(X)|~funny(X))))&
(![X]:((calm(X)&~curious(X))<=>~funny(X)))&
(((~strong(mary)|strong(mary)))=>(?[X]:(creative(X))))&
((?[X]:(humble(X)))<=>(~curious(susan)))&
((?[X]:(~happy(X)))<=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:(creative(X)=>(~strong(X)|tall(X))))&
(![X]:((tall(X)|~quiet(X))=>(~tall(X)&brave(X))))&
((rich(mary)&~brave(mary)))&
(?[X]:(~kind(X)))&
((~tall(john)&~calm(john)))&
(?[X]:(~brave(X)))&
(?[X]:((calm(X)|tall(X))))&
(~curious(fred))&
((tall(paul)<~>generous(paul)))&
(?[X]:((strong(X)&~happy(X)))) | quiet(fred) | [
"p2",
"p4",
"p6",
"p8",
"p15",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 4688572934125262470772266
% SZS output start Proof for 4688572934125262470772266
3. ! [X0] : (patient(X0) <=> (~old(X0) | tall(X0))) [input p2]
5. ! [X0] : (~funny(X0) <=> (~old(X0) <~> patient(X0))) [input p4]
7. ! [X0] : ((curious(X0) <~> ~quiet(X0)) => (~rich(X0) & ~patient(X0))) [input p6]
9. ! [X0] : (old(X0) <=> (~funny(X0) & creative(X0))) [input p8]
16. ! [X0] : ((~quiet(X0) | tall(X0)) => (brave(X0) & ~tall(X0))) [input p15]
22. ~curious(fred) [input p21]
25. ~quiet(fred) [input hypothesis]
30. ! [X0] : ((~rich(X0) & ~patient(X0)) | (curious(X0) <=> ~quiet(X0))) [ennf transformation 7]
35. ! [X0] : ((brave(X0) & ~tall(X0)) | (quiet(X0) & ~tall(X0))) [ennf transformation 16]
45. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 3]
46. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~patient(X0))) [flattening 45]
49. ! [X0] : ((~funny(X0) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | funny(X0))) [nnf transformation 5]
55. ! [X0] : ((~rich(X0) & ~patient(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) [nnf transformation 30]
57. ! [X0] : ((old(X0) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | ~old(X0))) [nnf transformation 9]
58. ! [X0] : ((old(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~old(X0))) [flattening 57]
87. ~patient(X0) | tall(X0) | ~old(X0) [cnf transformation 46]
89. patient(X0) | old(X0) [cnf transformation 46]
93. patient(X0) | ~old(X0) | funny(X0) [cnf transformation 49]
94. ~patient(X0) | old(X0) | funny(X0) [cnf transformation 49]
101. ~patient(X0) | curious(X0) | quiet(X0) [cnf transformation 55]
107. ~funny(X0) | ~old(X0) [cnf transformation 58]
125. ~tall(X0) | ~tall(X0) [cnf transformation 35]
135. ~curious(fred) [cnf transformation 22]
140. ~quiet(fred) [cnf transformation 25]
141. ~tall(X0) [duplicate literal removal 125]
181. funny(X0) | old(X0) [subsumption resolution 94,89]
182. patient(X0) | funny(X0) [subsumption resolution 93,181]
291. tall(X0) | ~old(X0) | funny(X0) [resolution 87,182]
294. ~old(X0) | funny(X0) [subsumption resolution 291,141]
295. ~old(X0) [subsumption resolution 294,107]
323. curious(X1) | quiet(X1) | old(X1) [resolution 101,89]
328. curious(X1) | quiet(X1) [subsumption resolution 323,295]
403. quiet(fred) [resolution 328,135]
408. $false [subsumption resolution 403,140]
% SZS output end Proof for 4688572934125262470772266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not kind is not brave or creative.
If someone is either not funny or wise then lucy is both not patient and wise and vice versa.
Everyone who is either brave or not curious is calm or not wise.
Everyone who is creative is calm 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.
Someone is not tall.
John is either not old or curious.
Fred is generous.
Someone is strong.
Someone is not strong.
Someone is both not old and humble. | Fred is not wise. | neutral | (![X]:((generous(X)|~kind(X))=>(~brave(X)|creative(X))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((~patient(lucy)&wise(lucy))))&
(![X]:((brave(X)<~>~curious(X))=>(calm(X)|~wise(X))))&
(![X]:(creative(X)<=>(calm(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)))&
((~old(john)<~>curious(john)))&
(generous(fred))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~old(X)&humble(X)))) | ~wise(fred) | []
| null | 0 |
If alice is not curious or not kind then someone is funny or quiet.
If someone is not tall or rich then someone is both not rich and not wise.
Everyone who is both brave and not brave is funny and vice versa.
Everyone who is either old or brave is creative and vice versa.
Everyone who is humble or not quiet is either not quiet or not rich and vice versa.
If someone is not old then susan is happy or not creative and vice versa.
Everyone who is both rich and not humble is both not humble and not brave and vice versa.
Everyone who is not rich or kind is not strong.
Everyone who is not strong or patient is not wise and vice versa.
If someone is either not funny or curious then lucy is not creative or not humble.
If someone is both not rich and generous then someone is tall or curious.
Everyone who is not rich is both not patient and not old.
If someone is not happy then someone is brave or not funny.
Everyone who is not generous or brave is funny or generous.
Everyone who is not rich is not kind or not generous.
Susan is either not curious or calm.
Alice is both not old and happy.
Alice is both not humble and not funny.
Someone is either calm or not creative.
Susan is calm. | Lucy is not creative. | neutral | (((~curious(alice)|~kind(alice)))=>(?[X]:((funny(X)|quiet(X)))))&
((?[X]:((~tall(X)|rich(X))))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((brave(X)&~brave(X))<=>funny(X)))&
(![X]:((old(X)<~>brave(X))<=>creative(X)))&
(![X]:((humble(X)|~quiet(X))<=>(~quiet(X)<~>~rich(X))))&
((?[X]:(~old(X)))<=>((happy(susan)|~creative(susan))))&
(![X]:((rich(X)&~humble(X))<=>(~humble(X)&~brave(X))))&
(![X]:((~rich(X)|kind(X))=>~strong(X)))&
(![X]:((~strong(X)|patient(X))<=>~wise(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>((~creative(lucy)|~humble(lucy))))&
((?[X]:((~rich(X)&generous(X))))=>(?[X]:((tall(X)|curious(X)))))&
(![X]:(~rich(X)=>(~patient(X)&~old(X))))&
((?[X]:(~happy(X)))=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~generous(X)|brave(X))=>(funny(X)|generous(X))))&
(![X]:(~rich(X)=>(~kind(X)|~generous(X))))&
((~curious(susan)<~>calm(susan)))&
((~old(alice)&happy(alice)))&
((~humble(alice)&~funny(alice)))&
(?[X]:((calm(X)<~>~creative(X))))&
(calm(susan)) | ~creative(lucy) | []
| null | 0 |
Everyone who is generous or not patient is either kind or not happy and vice versa.
Everyone who is not rich is not wise or not strong and vice versa.
If someone is not quiet then someone is both not kind and not tall and vice versa.
Everyone who is calm or wise is not rich or not quiet.
If someone is either not calm or humble then someone is not wise or not creative and vice versa.
Everyone who is both not wise and strong is either tall or happy and vice versa.
Everyone who is either not tall or rich is not brave or not creative.
Everyone who is either not old or not patient is both old and patient and vice versa.
Everyone who is happy is not patient and vice versa.
If paul is either generous or not happy then alice is both not patient and not brave.
If john is either not happy or curious then someone is quiet.
If someone is both calm and not creative then someone is both not patient and brave.
If someone is not patient then someone is quiet and vice versa.
Everyone who is either not tall or not patient is both not calm and tall.
If someone is both old and not creative then paul is not old or generous.
Everyone who is not rich or curious is either patient or not creative.
John is not wise.
Someone is not curious or patient.
Fred is both brave and not humble.
John is funny.
Susan is both tall and quiet.
Alice is either generous or not old.
Alice is either creative or not funny. | Fred is not creative. | entailment | (![X]:((generous(X)|~patient(X))<=>(kind(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~wise(X)|~strong(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~kind(X)&~tall(X)))))&
(![X]:((calm(X)|wise(X))=>(~rich(X)|~quiet(X))))&
((?[X]:((~calm(X)<~>humble(X))))<=>(?[X]:((~wise(X)|~creative(X)))))&
(![X]:((~wise(X)&strong(X))<=>(tall(X)<~>happy(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~brave(X)|~creative(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(old(X)&patient(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(((generous(paul)<~>~happy(paul)))=>((~patient(alice)&~brave(alice))))&
(((~happy(john)<~>curious(john)))=>(?[X]:(quiet(X))))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((~patient(X)&brave(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~calm(X)&tall(X))))&
((?[X]:((old(X)&~creative(X))))=>((~old(paul)|generous(paul))))&
(![X]:((~rich(X)|curious(X))=>(patient(X)<~>~creative(X))))&
(~wise(john))&
(?[X]:((~curious(X)|patient(X))))&
((brave(fred)&~humble(fred)))&
(funny(john))&
((tall(susan)&quiet(susan)))&
((generous(alice)<~>~old(alice)))&
((creative(alice)<~>~funny(alice))) | ~creative(fred) | [
"p0",
"p1",
"p2",
"p3",
"p7",
"p8",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 8882836011152351333710489
% SZS output start Proof for 8882836011152351333710489
1. ! [X0] : ((~patient(X0) | generous(X0)) <=> (kind(X0) <~> ~happy(X0))) [input p0]
2. ! [X0] : (~rich(X0) <=> (~strong(X0) | ~wise(X0))) [input p1]
3. ? [X0] : ~quiet(X0) <=> ? [X0] : (~tall(X0) & ~kind(X0)) [input p2]
4. ! [X0] : ((wise(X0) | calm(X0)) => (~quiet(X0) | ~rich(X0))) [input p3]
8. ! [X0] : ((~old(X0) <~> ~patient(X0)) <=> (patient(X0) & old(X0))) [input p7]
9. ! [X0] : (happy(X0) <=> ~patient(X0)) [input p8]
16. ! [X0] : ((curious(X0) | ~rich(X0)) => (patient(X0) <~> ~creative(X0))) [input p15]
24. creative(fred) [input hypothesis]
25. ? [X0] : ~quiet(X0) <=> ? [X1] : (~tall(X1) & ~kind(X1)) [rectify 3]
29. ! [X0] : ((~quiet(X0) | ~rich(X0)) | (~wise(X0) & ~calm(X0))) [ennf transformation 4]
30. ! [X0] : (~quiet(X0) | ~rich(X0) | (~wise(X0) & ~calm(X0))) [flattening 29]
39. ! [X0] : ((patient(X0) <~> ~creative(X0)) | (~curious(X0) & rich(X0))) [ennf transformation 16]
40. ! [X0] : (((~patient(X0) | generous(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (patient(X0) & ~generous(X0)))) [nnf transformation 1]
41. ! [X0] : ((~patient(X0) | generous(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (patient(X0) & ~generous(X0)))) [flattening 40]
42. ! [X0] : ((~rich(X0) | (strong(X0) & wise(X0))) & ((~strong(X0) | ~wise(X0)) | rich(X0))) [nnf transformation 2]
43. ! [X0] : ((~rich(X0) | (strong(X0) & wise(X0))) & (~strong(X0) | ~wise(X0) | rich(X0))) [flattening 42]
44. (? [X0] : ~quiet(X0) | ! [X1] : (tall(X1) | kind(X1))) & (? [X1] : (~tall(X1) & ~kind(X1)) | ! [X0] : quiet(X0)) [nnf transformation 25]
45. (? [X0] : ~quiet(X0) | ! [X1] : (tall(X1) | kind(X1))) & (? [X2] : (~tall(X2) & ~kind(X2)) | ! [X3] : quiet(X3)) [rectify 44]
46. ? [X0] : ~quiet(X0) => ~quiet(sK0) [choice axiom]
47. ? [X2] : (~tall(X2) & ~kind(X2)) => (~tall(sK1) & ~kind(sK1)) [choice axiom]
48. (~quiet(sK0) | ! [X1] : (tall(X1) | kind(X1))) & ((~tall(sK1) & ~kind(sK1)) | ! [X3] : quiet(X3)) [skolemisation 45,47,46]
57. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [nnf transformation 8]
58. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [flattening 57]
59. ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))) [nnf transformation 9]
73. ! [X0] : (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (~curious(X0) & rich(X0))) [nnf transformation 39]
79. ~happy(X0) | kind(X0) | patient(X0) [cnf transformation 41]
85. ~rich(X0) | wise(X0) [cnf transformation 43]
87. ~kind(sK1) | quiet(X3) [cnf transformation 48]
91. ~quiet(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 30]
106. old(X0) | ~patient(X0) | old(X0) [cnf transformation 58]
109. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 58]
110. ~patient(X0) | ~old(X0) | ~patient(X0) | ~old(X0) [cnf transformation 58]
113. happy(X0) | patient(X0) [cnf transformation 59]
129. ~creative(X0) | patient(X0) | rich(X0) [cnf transformation 73]
144. creative(fred) [cnf transformation 24]
146. old(X0) | ~patient(X0) [duplicate literal removal 106]
147. patient(X0) | ~old(X0) [duplicate literal removal 109]
148. ~old(X0) | ~patient(X0) [duplicate literal removal 110]
158. 3 <=> ! [X3] : quiet(X3) [avatar definition]
159. quiet(X3) <- (3) [avatar component clause 158]
166. 5 <=> kind(sK1) [avatar definition]
168. ~kind(sK1) <- (~5) [avatar component clause 166]
169. 3 | ~5 [avatar split clause 87,166,158]
170. ~quiet(X0) | ~rich(X0) [subsumption resolution 91,85]
205. ~old(X0) [subsumption resolution 147,148]
206. ~patient(X0) [subsumption resolution 146,205]
207. happy(X0) [subsumption resolution 113,206]
239. ~creative(X0) | rich(X0) [subsumption resolution 129,206]
254. rich(fred) [resolution 239,144]
258. kind(X0) | patient(X0) [resolution 79,207]
259. kind(X0) [subsumption resolution 258,206]
260. $false <- (~5) [resolution 259,168]
261. 5 [avatar contradiction clause 260]
263. ~rich(X0) <- (3) [resolution 159,170]
265. $false <- (3) [resolution 263,254]
266. ~3 [avatar contradiction clause 265]
267. $false [avatar sat refutation 169,261,266]
% SZS output end Proof for 8882836011152351333710489
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or humble is quiet. Everyone who is not calm is not humble. If paul is both humble and not strong then someone is either not curious or wise. If someone is either happy or not kind then someone is patient or strong and vice versa. Everyone who is either humble or old is both not funny and humble and vice versa. Everyone who is not quiet is funny and vice versa. Everyone who is not kind is brave and vice versa. Everyone who is either not generous or calm is quiet or rich. Everyone who is not rich or not kind is calm or not rich and vice versa. If someone is either creative or calm then mary is either not funny or generous. If john is not happy or kind then someone is both patient and quiet and vice versa. If someone is either creative or wise then mary is either not humble or not tall. Everyone who is both funny and not strong is both not generous and creative and vice versa. Everyone who is not humble or not old is humble. If someone is not old or brave then someone is not old or patient and vice versa. Everyone who is both rich and not old is generous or creative and vice versa. Lucy is either rich or calm. Someone is both kind and not generous. Mary is not wise. Someone is either not strong or not generous. John is both brave and tall. Someone is both rich and not kind. | John is humble. | entailment | (![X]:((calm(X)|humble(X))=>quiet(X)))&
(![X]:(~calm(X)=>~humble(X)))&
(((humble(paul)&~strong(paul)))=>(?[X]:((~curious(X)<~>wise(X)))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((humble(X)<~>old(X))<=>(~funny(X)&humble(X))))&
(![X]:(~quiet(X)<=>funny(X)))&
(![X]:(~kind(X)<=>brave(X)))&
(![X]:((~generous(X)<~>calm(X))=>(quiet(X)|rich(X))))&
(![X]:((~rich(X)|~kind(X))<=>(calm(X)|~rich(X))))&
((?[X]:((creative(X)<~>calm(X))))=>((~funny(mary)<~>generous(mary))))&
(((~happy(john)|kind(john)))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((creative(X)<~>wise(X))))=>((~humble(mary)<~>~tall(mary))))&
(![X]:((funny(X)&~strong(X))<=>(~generous(X)&creative(X))))&
(![X]:((~humble(X)|~old(X))=>humble(X)))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((rich(X)&~old(X))<=>(generous(X)|creative(X))))&
((rich(lucy)<~>calm(lucy)))&
(?[X]:((kind(X)&~generous(X))))&
(~wise(mary))&
(?[X]:((~strong(X)<~>~generous(X))))&
((brave(john)&tall(john)))&
(?[X]:((rich(X)&~kind(X)))) | humble(john) | [
"p4",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 7490244744236800345179534
% SZS output start Proof for 7490244744236800345179534
5. ! [X0] : ((humble(X0) <~> old(X0)) <=> (humble(X0) & ~funny(X0))) [input p4]
14. ! [X0] : ((~old(X0) | ~humble(X0)) => humble(X0)) [input p13]
23. ~humble(john) [input hypothesis]
34. ! [X0] : (humble(X0) | (old(X0) & humble(X0))) [ennf transformation 14]
43. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~humble(X0) | funny(X0))) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ~humble(X0) | funny(X0)) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 43]
88. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 44]
119. humble(X0) | old(X0) [cnf transformation 34]
140. ~humble(john) [cnf transformation 23]
142. humble(X0) | ~old(X0) [duplicate literal removal 88]
257. humble(X0) [subsumption resolution 119,142]
304. $false [subsumption resolution 140,257]
% SZS output end Proof for 7490244744236800345179534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not funny is kind or tall and vice versa.
Everyone who is not patient or quiet is both not patient and creative.
Everyone who is humble or not wise is not rich or calm.
If lucy is patient then susan is quiet or wise and vice versa.
Everyone who is both funny and brave is both not kind and strong and vice versa.
Everyone who is both not quiet and not curious is not kind or not quiet and vice versa.
Everyone who is patient is not humble or brave and vice versa.
If john is either not quiet or not generous then someone is either not wise or not tall and vice versa.
Everyone who is not brave or not old is not funny.
Everyone who is calm or not old is curious or brave.
If john is patient or rich then john is not creative and vice versa.
If fred is either tall or quiet then lucy is not wise.
Everyone who is not wise is not creative.
If someone is either not humble or strong then someone is not old or strong and vice versa.
If fred is both old and patient then mary is not curious or patient.
Everyone who is either old or quiet is either not funny or not creative.
John is not rich or creative.
Someone is strong.
Someone is not happy or quiet.
Mary is rich or not old.
Someone is both calm and humble.
Lucy is calm or not rich.
Someone is both old and not curious. | Mary is not humble. | neutral | (![X]:((brave(X)&~funny(X))<=>(kind(X)|tall(X))))&
(![X]:((~patient(X)|quiet(X))=>(~patient(X)&creative(X))))&
(![X]:((humble(X)|~wise(X))=>(~rich(X)|calm(X))))&
((patient(lucy))<=>((quiet(susan)|wise(susan))))&
(![X]:((funny(X)&brave(X))<=>(~kind(X)&strong(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(patient(X)<=>(~humble(X)|brave(X))))&
(((~quiet(john)<~>~generous(john)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
(![X]:((~brave(X)|~old(X))=>~funny(X)))&
(![X]:((calm(X)|~old(X))=>(curious(X)|brave(X))))&
(((patient(john)|rich(john)))<=>(~creative(john)))&
(((tall(fred)<~>quiet(fred)))=>(~wise(lucy)))&
(![X]:(~wise(X)=>~creative(X)))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(((old(fred)&patient(fred)))=>((~curious(mary)|patient(mary))))&
(![X]:((old(X)<~>quiet(X))=>(~funny(X)<~>~creative(X))))&
((~rich(john)|creative(john)))&
(?[X]:(strong(X)))&
(?[X]:((~happy(X)|quiet(X))))&
((rich(mary)|~old(mary)))&
(?[X]:((calm(X)&humble(X))))&
((calm(lucy)|~rich(lucy)))&
(?[X]:((old(X)&~curious(X)))) | ~humble(mary) | []
| null | 0 |
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. If john is not rich then someone is curious and vice versa. If paul is either not curious or not rich then someone is old or not tall and vice versa. If someone is either not brave or old then alice is tall. If mary is generous then someone is not happy. Everyone who is creative is both not calm and creative. Everyone who is either not kind or strong is not kind and vice versa. If someone is strong then someone is either rich or not strong and vice versa. Everyone who is funny or not wise is not happy or calm and vice versa. If someone is curious then someone is either humble or not funny and vice versa. Everyone who is curious or not wise is either not tall or generous and vice versa. Everyone who is curious or not strong is old or not brave. Someone is rich or not happy. Fred is both not patient and tall. John is both not patient and funny. Someone is not happy. Mary is both patient and not calm. Someone is either not patient or strong. Paul is both not brave and creative. Someone is tall or not curious. | Fred is curious. | contradiction | ((?[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))))&
((~rich(john))<=>(?[X]:(curious(X))))&
(((~curious(paul)<~>~rich(paul)))<=>(?[X]:((old(X)|~tall(X)))))&
((?[X]:((~brave(X)<~>old(X))))=>(tall(alice)))&
((generous(mary))=>(?[X]:(~happy(X))))&
(![X]:(creative(X)=>(~calm(X)&creative(X))))&
(![X]:((~kind(X)<~>strong(X))<=>~kind(X)))&
((?[X]:(strong(X)))<=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:((funny(X)|~wise(X))<=>(~happy(X)|calm(X))))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(![X]:((curious(X)|~wise(X))<=>(~tall(X)<~>generous(X))))&
(![X]:((curious(X)|~strong(X))=>(old(X)|~brave(X))))&
(?[X]:((rich(X)|~happy(X))))&
((~patient(fred)&tall(fred)))&
((~patient(john)&funny(john)))&
(?[X]:(~happy(X)))&
((patient(mary)&~calm(mary)))&
(?[X]:((~patient(X)<~>strong(X))))&
((~brave(paul)&creative(paul)))&
(?[X]:((tall(X)|~curious(X)))) | curious(fred) | [
"p2",
"p5",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 5468714438344091485523611
% SZS output start Proof for 5468714438344091485523611
3. ! [X0] : (~strong(X0) => ~kind(X0)) [input p2]
6. ~rich(john) <=> ? [X0] : curious(X0) [input p5]
11. ! [X0] : ((~kind(X0) <~> strong(X0)) <=> ~kind(X0)) [input p10]
12. ? [X0] : strong(X0) <=> ? [X0] : (rich(X0) <~> ~strong(X0)) [input p11]
25. curious(fred) [input hypothesis]
26. ? [X0] : strong(X0) <=> ? [X1] : (rich(X1) <~> ~strong(X1)) [rectify 12]
28. ! [X0] : (~kind(X0) | strong(X0)) [ennf transformation 3]
48. (~rich(john) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | rich(john)) [nnf transformation 6]
49. (~rich(john) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | rich(john)) [rectify 48]
50. ? [X1] : curious(X1) => curious(sK3) [choice axiom]
51. (~rich(john) | ! [X0] : ~curious(X0)) & (curious(sK3) | rich(john)) [skolemisation 49,50]
59. ! [X0] : ((((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | kind(X0)) & (~kind(X0) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0))))) [nnf transformation 11]
60. (? [X0] : strong(X0) | ! [X1] : ((rich(X1) | strong(X1)) & (~strong(X1) | ~rich(X1)))) & (? [X1] : ((strong(X1) | ~rich(X1)) & (~strong(X1) | rich(X1))) | ! [X0] : ~strong(X0)) [nnf transformation 26]
61. (? [X0] : strong(X0) | ! [X1] : ((rich(X1) | strong(X1)) & (~strong(X1) | ~rich(X1)))) & (? [X2] : ((strong(X2) | ~rich(X2)) & (~strong(X2) | rich(X2))) | ! [X3] : ~strong(X3)) [rectify 60]
62. ? [X0] : strong(X0) => strong(sK6) [choice axiom]
63. ? [X2] : ((strong(X2) | ~rich(X2)) & (~strong(X2) | rich(X2))) => ((strong(sK7) | ~rich(sK7)) & (~strong(sK7) | rich(sK7))) [choice axiom]
64. (strong(sK6) | ! [X1] : ((rich(X1) | strong(X1)) & (~strong(X1) | ~rich(X1)))) & (((strong(sK7) | ~rich(sK7)) & (~strong(sK7) | rich(sK7))) | ! [X3] : ~strong(X3)) [skolemisation 61,63,62]
93. ~kind(X0) | strong(X0) [cnf transformation 28]
99. ~rich(john) | ~curious(X0) [cnf transformation 51]
112. ~kind(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 59]
114. ~strong(X0) | kind(X0) | kind(X0) [cnf transformation 59]
118. strong(sK6) | rich(X1) | strong(X1) [cnf transformation 64]
148. curious(fred) [cnf transformation 25]
149. ~kind(X0) | ~strong(X0) [duplicate literal removal 112]
150. ~strong(X0) | kind(X0) [duplicate literal removal 114]
205. 12 <=> ! [X0] : ~curious(X0) [avatar definition]
206. ~curious(X0) <- (12) [avatar component clause 205]
208. 13 <=> rich(john) [avatar definition]
210. ~rich(john) <- (~13) [avatar component clause 208]
211. 12 | ~13 [avatar split clause 99,208,205]
266. ~kind(X0) [subsumption resolution 149,93]
268. 26 <=> ! [X1] : (rich(X1) | strong(X1)) [avatar definition]
269. rich(X1) | strong(X1) <- (26) [avatar component clause 268]
271. 27 <=> strong(sK6) [avatar definition]
273. strong(sK6) <- (27) [avatar component clause 271]
274. 26 | 27 [avatar split clause 118,271,268]
342. $false <- (12) [resolution 206,148]
343. ~12 [avatar contradiction clause 342]
344. kind(sK6) <- (27) [resolution 150,273]
345. $false <- (27) [subsumption resolution 344,266]
346. ~27 [avatar contradiction clause 345]
347. strong(john) <- (~13, 26) [resolution 269,210]
355. kind(john) <- (~13, 26) [resolution 347,150]
357. $false <- (~13, 26) [subsumption resolution 355,266]
358. 13 | ~26 [avatar contradiction clause 357]
359. $false [avatar sat refutation 211,274,343,346,358]
% SZS output end Proof for 5468714438344091485523611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not brave or old and vice versa.
Everyone who is both strong and curious is not humble or strong and vice versa.
Everyone who is not humble is both wise and not funny and vice versa.
If susan is both creative and not patient then someone is either not kind or not rich.
Everyone who is both strong and not kind is kind or rich and vice versa.
If someone is not rich then john is both not happy and not funny.
If someone is either brave or not old then someone is either not kind or not calm and vice versa.
Everyone who is either brave or not tall is not kind and vice versa.
If someone is not tall then john is happy or not calm.
If paul is both humble and not generous then paul is both old and not tall.
If alice is either calm or creative then someone is not quiet or not wise and vice versa.
If someone is wise or not kind then lucy is not tall or strong and vice versa.
If someone is creative then lucy is both tall and funny and vice versa.
Everyone who is either not rich or not calm is either quiet or brave and vice versa.
If fred is not patient or kind then someone is either not brave or happy.
If paul is either humble or not strong then someone is wise and vice versa.
Someone is rich or calm.
Someone is not patient.
Susan is rich or not calm.
John is tall.
Fred is not strong.
Susan is funny or strong.
Susan is either not quiet or kind.
John is either rich or not patient. | Paul is not humble. | contradiction | (![X]:(old(X)<=>(~brave(X)|old(X))))&
(![X]:((strong(X)&curious(X))<=>(~humble(X)|strong(X))))&
(![X]:(~humble(X)<=>(wise(X)&~funny(X))))&
(((creative(susan)&~patient(susan)))=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((strong(X)&~kind(X))<=>(kind(X)|rich(X))))&
((?[X]:(~rich(X)))=>((~happy(john)&~funny(john))))&
((?[X]:((brave(X)<~>~old(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:((brave(X)<~>~tall(X))<=>~kind(X)))&
((?[X]:(~tall(X)))=>((happy(john)|~calm(john))))&
(((humble(paul)&~generous(paul)))=>((old(paul)&~tall(paul))))&
(((calm(alice)<~>creative(alice)))<=>(?[X]:((~quiet(X)|~wise(X)))))&
((?[X]:((wise(X)|~kind(X))))<=>((~tall(lucy)|strong(lucy))))&
((?[X]:(creative(X)))<=>((tall(lucy)&funny(lucy))))&
(![X]:((~rich(X)<~>~calm(X))<=>(quiet(X)<~>brave(X))))&
(((~patient(fred)|kind(fred)))=>(?[X]:((~brave(X)<~>happy(X)))))&
(((humble(paul)<~>~strong(paul)))<=>(?[X]:(wise(X))))&
(?[X]:((rich(X)|calm(X))))&
(?[X]:(~patient(X)))&
((rich(susan)|~calm(susan)))&
(tall(john))&
(~strong(fred))&
((funny(susan)|strong(susan)))&
((~quiet(susan)<~>kind(susan)))&
((rich(john)<~>~patient(john))) | ~humble(paul) | [
"p1",
"p2",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 8825457867093630792983616
% SZS output start Proof for 8825457867093630792983616
2. ! [X0] : ((curious(X0) & strong(X0)) <=> (strong(X0) | ~humble(X0))) [input p1]
3. ! [X0] : (~humble(X0) <=> (~funny(X0) & wise(X0))) [input p2]
16. (humble(paul) <~> ~strong(paul)) <=> ? [X0] : wise(X0) [input p15]
25. ~humble(paul) [input hypothesis]
36. ! [X0] : (((curious(X0) & strong(X0)) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | (~curious(X0) | ~strong(X0)))) [nnf transformation 2]
37. ! [X0] : (((curious(X0) & strong(X0)) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | ~curious(X0) | ~strong(X0))) [flattening 36]
38. ! [X0] : ((~humble(X0) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | humble(X0))) [nnf transformation 3]
39. ! [X0] : ((~humble(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | humble(X0))) [flattening 38]
69. (((strong(paul) | ~humble(paul)) & (~strong(paul) | humble(paul))) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | ((humble(paul) | strong(paul)) & (~strong(paul) | ~humble(paul)))) [nnf transformation 16]
70. (((strong(paul) | ~humble(paul)) & (~strong(paul) | humble(paul))) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | ((humble(paul) | strong(paul)) & (~strong(paul) | ~humble(paul)))) [rectify 69]
71. ? [X1] : wise(X1) => wise(sK7) [choice axiom]
72. (((strong(paul) | ~humble(paul)) & (~strong(paul) | humble(paul))) | ! [X0] : ~wise(X0)) & (wise(sK7) | ((humble(paul) | strong(paul)) & (~strong(paul) | ~humble(paul)))) [skolemisation 70,71]
83. humble(X0) | strong(X0) [cnf transformation 37]
87. wise(X0) | humble(X0) [cnf transformation 39]
139. ~strong(paul) | humble(paul) | ~wise(X0) [cnf transformation 72]
151. ~humble(paul) [cnf transformation 25]
261. 23 <=> ! [X1] : ~wise(X1) [avatar definition]
262. ~wise(X1) <- (23) [avatar component clause 261]
298. humble(paul) | ~wise(X0) [subsumption resolution 139,83]
300. 31 <=> humble(paul) [avatar definition]
301. ~humble(paul) <- (~31) [avatar component clause 300]
303. 23 | 31 [avatar split clause 298,300,261]
347. ~31 [avatar split clause 151,300]
356. humble(X0) <- (23) [resolution 87,262]
357. $false <- (23, ~31) [resolution 356,301]
358. ~23 | 31 [avatar contradiction clause 357]
359. $false [avatar sat refutation 303,347,358]
% SZS output end Proof for 8825457867093630792983616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is tall or brave then susan is brave or patient.
Everyone who is both calm and not generous is patient.
Everyone who is not creative is humble or creative and vice versa.
If fred is not creative or rich then someone is either not patient or not creative.
If someone is both not brave and happy then someone is either not brave or not humble and vice versa.
If someone is both funny and humble then john is funny.
Everyone who is either funny or not funny is curious.
If someone is happy or not kind then someone is not humble or tall and vice versa.
If mary is old or brave then paul is not rich and vice versa.
Everyone who is either not curious or not patient is old.
If fred is both wise and not wise then lucy is either brave or generous.
If someone is rich or quiet then someone is either not patient or not quiet.
Everyone who is not curious is kind or creative.
Everyone who is either not creative or not curious is either humble or happy.
Everyone who is both not humble and wise is both not patient and happy.
Everyone who is not old is humble.
Alice is strong.
Susan is creative or tall.
Mary is kind or funny.
Paul is not calm or creative.
Fred is both old and brave.
Someone is either not kind or not curious. | Lucy is not humble. | contradiction | (((tall(john)|brave(john)))=>((brave(susan)|patient(susan))))&
(![X]:((calm(X)&~generous(X))=>patient(X)))&
(![X]:(~creative(X)<=>(humble(X)|creative(X))))&
(((~creative(fred)|rich(fred)))=>(?[X]:((~patient(X)<~>~creative(X)))))&
((?[X]:((~brave(X)&happy(X))))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
((?[X]:((funny(X)&humble(X))))=>(funny(john)))&
(![X]:((funny(X)<~>~funny(X))=>curious(X)))&
((?[X]:((happy(X)|~kind(X))))<=>(?[X]:((~humble(X)|tall(X)))))&
(((old(mary)|brave(mary)))<=>(~rich(paul)))&
(![X]:((~curious(X)<~>~patient(X))=>old(X)))&
(((wise(fred)&~wise(fred)))=>((brave(lucy)<~>generous(lucy))))&
((?[X]:((rich(X)|quiet(X))))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:(~curious(X)=>(kind(X)|creative(X))))&
(![X]:((~creative(X)<~>~curious(X))=>(humble(X)<~>happy(X))))&
(![X]:((~humble(X)&wise(X))=>(~patient(X)&happy(X))))&
(![X]:(~old(X)=>humble(X)))&
(strong(alice))&
((creative(susan)|tall(susan)))&
((kind(mary)|funny(mary)))&
((~calm(paul)|creative(paul)))&
((old(fred)&brave(fred)))&
(?[X]:((~kind(X)<~>~curious(X)))) | ~humble(lucy) | [
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 6179866679673026041274633
% SZS output start Proof for 6179866679673026041274633
3. ! [X0] : (~creative(X0) <=> (creative(X0) | humble(X0))) [input p2]
23. ~humble(lucy) [input hypothesis]
45. ! [X0] : ((~creative(X0) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | creative(X0))) [nnf transformation 3]
46. ! [X0] : ((~creative(X0) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | creative(X0))) [flattening 45]
75. creative(X0) | humble(X0) | creative(X0) [cnf transformation 46]
77. ~creative(X0) | ~creative(X0) [cnf transformation 46]
120. ~humble(lucy) [cnf transformation 23]
123. creative(X0) | humble(X0) [duplicate literal removal 75]
124. ~creative(X0) [duplicate literal removal 77]
143. humble(X0) [subsumption resolution 123,124]
266. $false [subsumption resolution 120,143]
% SZS output end Proof for 6179866679673026041274633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is both not brave and not humble.
Everyone who is not funny or not brave is not brave or not funny.
If someone is calm or brave then fred is either happy or not quiet and vice versa.
If someone is both not funny and creative then someone is either not happy or old.
If someone is wise then paul is either generous or not calm.
Everyone who is both not kind and not brave is rich.
If susan is patient then someone is both not happy and funny.
If someone is both not strong and patient then someone is both generous and not tall and vice versa.
Everyone who is calm or tall is not creative and vice versa.
Everyone who is not patient or not generous is both not brave and not humble and vice versa.
Everyone who is either creative or not wise is either not patient or strong.
Everyone who is calm or not creative is either not creative or wise and vice versa.
Everyone who is both not humble and quiet is not funny or curious.
If susan is not rich or old then someone is not generous and vice versa.
Everyone who is both humble and rich is not patient or not funny and vice versa.
If alice is not creative then someone is not generous or generous.
Someone is brave or tall.
Someone is not generous.
Someone is either calm or funny.
Someone is not happy.
Fred is not tall.
Someone is either not happy or not kind.
Someone is either happy or funny. | Paul is curious. | neutral | (![X]:((creative(X)|humble(X))=>(~brave(X)&~humble(X))))&
(![X]:((~funny(X)|~brave(X))=>(~brave(X)|~funny(X))))&
((?[X]:((calm(X)|brave(X))))<=>((happy(fred)<~>~quiet(fred))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:((~happy(X)<~>old(X)))))&
((?[X]:(wise(X)))=>((generous(paul)<~>~calm(paul))))&
(![X]:((~kind(X)&~brave(X))=>rich(X)))&
((patient(susan))=>(?[X]:((~happy(X)&funny(X)))))&
((?[X]:((~strong(X)&patient(X))))<=>(?[X]:((generous(X)&~tall(X)))))&
(![X]:((calm(X)|tall(X))<=>~creative(X)))&
(![X]:((~patient(X)|~generous(X))<=>(~brave(X)&~humble(X))))&
(![X]:((creative(X)<~>~wise(X))=>(~patient(X)<~>strong(X))))&
(![X]:((calm(X)|~creative(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((~humble(X)&quiet(X))=>(~funny(X)|curious(X))))&
(((~rich(susan)|old(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)&rich(X))<=>(~patient(X)|~funny(X))))&
((~creative(alice))=>(?[X]:((~generous(X)|generous(X)))))&
(?[X]:((brave(X)|tall(X))))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:(~happy(X)))&
(~tall(fred))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((happy(X)<~>funny(X)))) | curious(paul) | []
| null | 0 |
If someone is not strong or not creative then john is both not creative and wise and vice versa. Everyone who is both humble and tall is funny or wise. Everyone who is not patient is funny. Everyone who is kind is both creative and not strong and vice versa. Everyone who is kind or not humble is both not quiet and calm and vice versa. If someone is both brave and calm then mary is patient or not generous and vice versa. Everyone who is not old or not humble is not tall or happy and vice versa. Everyone who is both curious and quiet is not brave. Everyone who is not old is both not tall and not happy. If someone is brave or not creative then susan is both brave and not kind and vice versa. Everyone who is not calm or not humble is not tall and vice versa. Everyone who is not funny or kind is either not patient or humble and vice versa. If someone is either not patient or not creative then someone is humble and vice versa. Everyone who is either not curious or curious is rich and vice versa. Everyone who is either happy or not creative is both not brave and funny and vice versa. If alice is not wise or calm then john is both not kind and old. Someone is either not funny or not kind. Someone is either not old or not wise. Someone is either generous or not brave. Someone is either not humble or happy. Someone is not wise. Mary is generous or rich. | Mary is not rich. | contradiction | ((?[X]:((~strong(X)|~creative(X))))<=>((~creative(john)&wise(john))))&
(![X]:((humble(X)&tall(X))=>(funny(X)|wise(X))))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:(kind(X)<=>(creative(X)&~strong(X))))&
(![X]:((kind(X)|~humble(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((brave(X)&calm(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(?[X]:((~funny(X)<~>~kind(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
(?[X]:(~wise(X)))&
((generous(mary)|rich(mary))) | ~rich(mary) | [
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 6493122885802537639265986
% SZS output start Proof for 6493122885802537639265986
14. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> rich(X0)) [input p13]
23. ~rich(mary) [input hypothesis]
62. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | ~rich(X0)) & (rich(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 14]
124. rich(X0) | curious(X0) | curious(X0) [cnf transformation 62]
125. rich(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 62]
148. ~rich(mary) [cnf transformation 23]
149. rich(X0) | curious(X0) [duplicate literal removal 124]
150. rich(X0) | ~curious(X0) [duplicate literal removal 125]
253. rich(X0) [subsumption resolution 149,150]
314. $false [subsumption resolution 148,253]
% SZS output end Proof for 6493122885802537639265986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and curious is either not generous or curious and vice versa.
Everyone who is not patient is both curious and generous.
If someone is creative or not humble then someone is not wise and vice versa.
Everyone who is both humble and patient is not calm or not tall and vice versa.
Everyone who is happy or not creative is either not wise or creative.
Everyone who is either not humble or not funny is not tall or funny.
Everyone who is kind is wise.
If alice is not curious then alice is both humble and not creative.
If someone is kind then someone is happy or not kind and vice versa.
Everyone who is kind is either curious or old and vice versa.
If fred is both not wise and not strong then someone is either old or generous and vice versa.
Everyone who is patient is not old.
If alice is both tall and not tall then fred is both not curious and not creative and vice versa.
If alice is either not quiet or old then susan is both kind and humble and vice versa.
If someone is not calm or funny then lucy is not patient or not wise and vice versa.
Everyone who is not creative is either wise or rich.
Someone is either happy or old.
Fred is either not humble or not old.
Someone is not brave.
Someone is both funny and not quiet.
Someone is rich or not creative.
Someone is either brave or not funny.
Paul is either humble or kind.
Someone is either kind or old. | Alice is not creative. | neutral | (![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>curious(X))))&
(![X]:(~patient(X)=>(curious(X)&generous(X))))&
((?[X]:((creative(X)|~humble(X))))<=>(?[X]:(~wise(X))))&
(![X]:((humble(X)&patient(X))<=>(~calm(X)|~tall(X))))&
(![X]:((happy(X)|~creative(X))=>(~wise(X)<~>creative(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(~tall(X)|funny(X))))&
(![X]:(kind(X)=>wise(X)))&
((~curious(alice))=>((humble(alice)&~creative(alice))))&
((?[X]:(kind(X)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:(kind(X)<=>(curious(X)<~>old(X))))&
(((~wise(fred)&~strong(fred)))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(patient(X)=>~old(X)))&
(((tall(alice)&~tall(alice)))<=>((~curious(fred)&~creative(fred))))&
(((~quiet(alice)<~>old(alice)))<=>((kind(susan)&humble(susan))))&
((?[X]:((~calm(X)|funny(X))))<=>((~patient(lucy)|~wise(lucy))))&
(![X]:(~creative(X)=>(wise(X)<~>rich(X))))&
(?[X]:((happy(X)<~>old(X))))&
((~humble(fred)<~>~old(fred)))&
(?[X]:(~brave(X)))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:((rich(X)|~creative(X))))&
(?[X]:((brave(X)<~>~funny(X))))&
((humble(paul)<~>kind(paul)))&
(?[X]:((kind(X)<~>old(X)))) | ~creative(alice) | []
| null | 0 |
If susan is both humble and not brave then someone is not calm or curious and vice versa. If someone is happy then fred is not calm. If someone is patient then susan is either humble or rich. Everyone who is both not calm and quiet is quiet. If someone is either old or not rich then someone is not creative or curious and vice versa. Everyone who is not old is not tall or curious. Everyone who is either humble or kind is not happy or patient and vice versa. If someone is either not quiet or creative then someone is not funny or not kind. Everyone who is not humble is both not wise and not old. Everyone who is wise or old is both wise and calm. Everyone who is both patient and humble is either not quiet or generous. Everyone who is kind or funny is not wise. Everyone who is happy is either not patient or not wise and vice versa. Everyone who is curious is either patient or wise and vice versa. Everyone who is either not quiet or creative is both old and not funny. Everyone who is not brave is wise and vice versa. Someone is either not brave or not quiet. John is both strong and not tall. Someone is both kind and quiet. Paul is wise. Someone is not strong or curious. Paul is tall or not wise. John is patient. Paul is happy or not rich. | Paul is rich. | contradiction | (((humble(susan)&~brave(susan)))<=>(?[X]:((~calm(X)|curious(X)))))&
((?[X]:(happy(X)))=>(~calm(fred)))&
((?[X]:(patient(X)))=>((humble(susan)<~>rich(susan))))&
(![X]:((~calm(X)&quiet(X))=>quiet(X)))&
((?[X]:((old(X)<~>~rich(X))))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:(~old(X)=>(~tall(X)|curious(X))))&
(![X]:((humble(X)<~>kind(X))<=>(~happy(X)|patient(X))))&
((?[X]:((~quiet(X)<~>creative(X))))=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:(~humble(X)=>(~wise(X)&~old(X))))&
(![X]:((wise(X)|old(X))=>(wise(X)&calm(X))))&
(![X]:((patient(X)&humble(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((kind(X)|funny(X))=>~wise(X)))&
(![X]:(happy(X)<=>(~patient(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(patient(X)<~>wise(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(old(X)&~funny(X))))&
(![X]:(~brave(X)<=>wise(X)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((strong(john)&~tall(john)))&
(?[X]:((kind(X)&quiet(X))))&
(wise(paul))&
(?[X]:((~strong(X)|curious(X))))&
((tall(paul)|~wise(paul)))&
(patient(john))&
((happy(paul)|~rich(paul))) | rich(paul) | [
"p6",
"p8",
"p11",
"p12",
"p19",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 175396246006963517813022
% SZS output start Proof for 175396246006963517813022
7. ! [X0] : ((humble(X0) <~> kind(X0)) <=> (patient(X0) | ~happy(X0))) [input p6]
9. ! [X0] : (~humble(X0) => (~old(X0) & ~wise(X0))) [input p8]
12. ! [X0] : ((funny(X0) | kind(X0)) => ~wise(X0)) [input p11]
13. ! [X0] : (happy(X0) <=> (~patient(X0) <~> ~wise(X0))) [input p12]
20. wise(paul) [input p19]
24. ~rich(paul) | happy(paul) [input p23]
25. rich(paul) [input hypothesis]
30. ! [X0] : (kind(X0) => ~wise(X0)) [pure predicate removal 12]
37. ! [X0] : ((~old(X0) & ~wise(X0)) | humble(X0)) [ennf transformation 9]
41. ! [X0] : (~wise(X0) | ~kind(X0)) [ennf transformation 30]
54. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~patient(X0) & happy(X0))) & ((patient(X0) | ~happy(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 7]
55. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~patient(X0) & happy(X0))) & (patient(X0) | ~happy(X0) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [flattening 54]
57. ! [X0] : ((happy(X0) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0)))) & (((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~happy(X0))) [nnf transformation 13]
84. ~happy(X0) | patient(X0) | kind(X0) | ~humble(X0) [cnf transformation 55]
90. ~wise(X0) | humble(X0) [cnf transformation 37]
98. ~wise(X0) | ~kind(X0) [cnf transformation 41]
99. ~wise(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 57]
117. wise(paul) [cnf transformation 20]
121. ~rich(paul) | happy(paul) [cnf transformation 24]
122. rich(paul) [cnf transformation 25]
219. 22 <=> happy(paul) [avatar definition]
221. happy(paul) <- (22) [avatar component clause 219]
223. 23 <=> rich(paul) [avatar definition]
226. 22 | ~23 [avatar split clause 121,223,219]
227. 23 [avatar split clause 122,223]
228. humble(paul) [resolution 90,117]
230. ~kind(paul) [resolution 98,117]
281. ~patient(paul) | ~happy(paul) [resolution 99,117]
283. ~patient(paul) <- (22) [subsumption resolution 281,221]
374. patient(paul) | kind(paul) | ~humble(paul) <- (22) [resolution 84,221]
375. kind(paul) | ~humble(paul) <- (22) [subsumption resolution 374,283]
376. ~humble(paul) <- (22) [subsumption resolution 375,230]
377. $false <- (22) [subsumption resolution 376,228]
378. ~22 [avatar contradiction clause 377]
379. $false [avatar sat refutation 226,227,378]
% SZS output end Proof for 175396246006963517813022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or kind is either not humble or not quiet and vice versa. Everyone who is rich or strong is both not curious and not humble and vice versa. If susan is both humble and quiet then mary is creative or kind and vice versa. Everyone who is either brave or not brave is both not strong and generous. Everyone who is both not old and not curious is not happy or curious and vice versa. Everyone who is either happy or generous is either funny or not patient. If someone is either not kind or brave then susan is either humble or creative. Everyone who is both funny and not creative is either rich or not patient and vice versa. Everyone who is both generous and not patient is both not kind and humble. If someone is either strong or tall then alice is humble. Everyone who is both not calm and not curious is old or rich and vice versa. If someone is funny or not brave then someone is not curious or not kind and vice versa. If someone is not wise or not old then lucy is curious or not calm and vice versa. Everyone who is not calm is old. If alice is both not humble and funny then someone is not curious and vice versa. If susan is not strong then someone is not happy or curious and vice versa. Mary is happy or not calm. Lucy is not strong. Someone is either calm or brave. Someone is either happy or funny. Someone is not quiet or strong. Lucy is not calm or brave. Mary is old. Lucy is either not rich or quiet. | Mary is not curious. | entailment | (![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~curious(X)&~humble(X))))&
(((humble(susan)&quiet(susan)))<=>((creative(mary)|kind(mary))))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>(~happy(X)|curious(X))))&
(![X]:((happy(X)<~>generous(X))=>(funny(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>((humble(susan)<~>creative(susan))))&
(![X]:((funny(X)&~creative(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
((happy(mary)|~calm(mary)))&
(~strong(lucy))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy))) | ~curious(mary) | [
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 4542173360306070612195577
% SZS output start Proof for 4542173360306070612195577
5. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (curious(X0) | ~happy(X0))) [input p4]
25. curious(mary) [input hypothesis]
40. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (curious(X0) | old(X0)))) [nnf transformation 5]
41. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | curious(X0) | old(X0))) [flattening 40]
103. ~curious(X0) | ~curious(X0) [cnf transformation 41]
153. curious(mary) [cnf transformation 25]
155. ~curious(X0) [duplicate literal removal 103]
299. $false [subsumption resolution 153,155]
% SZS output end Proof for 4542173360306070612195577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both humble and calm and vice versa.
If paul is tall or not quiet then fred is either not kind or brave and vice versa.
Everyone who is not strong or wise is both not patient and not humble.
If someone is both not wise and not quiet then someone is either happy or not quiet.
Everyone who is not generous is not calm or rich and vice versa.
If susan is not old then someone is kind or not strong.
Everyone who is creative or not rich is not rich.
If someone is not wise then someone is either not funny or old.
If someone is not generous then mary is quiet.
Everyone who is both wise and not tall is not patient or not calm and vice versa.
If someone is patient or not patient then paul is both not strong and kind and vice versa.
Everyone who is patient or not quiet is curious or wise.
Everyone who is either tall or generous is both not quiet and brave.
If someone is rich or calm then paul is both not calm and wise and vice versa.
If someone is humble or generous then susan is either brave or not creative.
Everyone who is both not generous and old is not old.
Mary is old.
Mary is kind or not humble.
Mary is not wise or not humble.
Lucy is not humble.
Lucy is calm or not generous.
Susan is either wise or patient.
Paul is not generous. | Susan is old. | neutral | (![X]:(happy(X)<=>(humble(X)&calm(X))))&
(((tall(paul)|~quiet(paul)))<=>((~kind(fred)<~>brave(fred))))&
(![X]:((~strong(X)|wise(X))=>(~patient(X)&~humble(X))))&
((?[X]:((~wise(X)&~quiet(X))))=>(?[X]:((happy(X)<~>~quiet(X)))))&
(![X]:(~generous(X)<=>(~calm(X)|rich(X))))&
((~old(susan))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((creative(X)|~rich(X))=>~rich(X)))&
((?[X]:(~wise(X)))=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:(~generous(X)))=>(quiet(mary)))&
(![X]:((wise(X)&~tall(X))<=>(~patient(X)|~calm(X))))&
((?[X]:((patient(X)|~patient(X))))<=>((~strong(paul)&kind(paul))))&
(![X]:((patient(X)|~quiet(X))=>(curious(X)|wise(X))))&
(![X]:((tall(X)<~>generous(X))=>(~quiet(X)&brave(X))))&
((?[X]:((rich(X)|calm(X))))<=>((~calm(paul)&wise(paul))))&
((?[X]:((humble(X)|generous(X))))=>((brave(susan)<~>~creative(susan))))&
(![X]:((~generous(X)&old(X))=>~old(X)))&
(old(mary))&
((kind(mary)|~humble(mary)))&
((~wise(mary)|~humble(mary)))&
(~humble(lucy))&
((calm(lucy)|~generous(lucy)))&
((wise(susan)<~>patient(susan)))&
(~generous(paul)) | old(susan) | []
| null | 0 |
If fred is both rich and not wise then someone is rich or creative and vice versa.
Everyone who is rich is either strong or not curious.
Everyone who is not curious or funny is either not generous or tall and vice versa.
If paul is not kind then lucy is rich or not tall.
If someone is quiet then lucy is kind or not brave.
Everyone who is both generous and kind is rich.
If someone is both not wise and not happy then someone is both rich and funny and vice versa.
Everyone who is either happy or not generous is either not strong or not rich and vice versa.
If someone is rich or not humble then lucy is happy.
Everyone who is curious is not kind or not brave and vice versa.
Everyone who is wise is rich and vice versa.
If someone is both not strong and not curious then alice is either not humble or not wise.
Everyone who is either brave or not generous is not strong or not funny and vice versa.
Everyone who is not generous or rich is old or patient.
Everyone who is patient or not rich is funny.
Everyone who is not curious or not happy is not patient or patient.
Someone is generous.
Mary is either creative or calm.
Alice is happy.
Paul is either not creative or not patient.
Susan is either not humble or rich.
Lucy is either happy or brave. | Mary is calm. | entailment | (((rich(fred)&~wise(fred)))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:(rich(X)=>(strong(X)<~>~curious(X))))&
(![X]:((~curious(X)|funny(X))<=>(~generous(X)<~>tall(X))))&
((~kind(paul))=>((rich(lucy)|~tall(lucy))))&
((?[X]:(quiet(X)))=>((kind(lucy)|~brave(lucy))))&
(![X]:((generous(X)&kind(X))=>rich(X)))&
((?[X]:((~wise(X)&~happy(X))))<=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((happy(X)<~>~generous(X))<=>(~strong(X)<~>~rich(X))))&
((?[X]:((rich(X)|~humble(X))))=>(happy(lucy)))&
(![X]:(curious(X)<=>(~kind(X)|~brave(X))))&
(![X]:(wise(X)<=>rich(X)))&
((?[X]:((~strong(X)&~curious(X))))=>((~humble(alice)<~>~wise(alice))))&
(![X]:((brave(X)<~>~generous(X))<=>(~strong(X)|~funny(X))))&
(![X]:((~generous(X)|rich(X))=>(old(X)|patient(X))))&
(![X]:((patient(X)|~rich(X))=>funny(X)))&
(![X]:((~curious(X)|~happy(X))=>(~patient(X)|patient(X))))&
(?[X]:(generous(X)))&
((creative(mary)<~>calm(mary)))&
(happy(alice))&
((~creative(paul)<~>~patient(paul)))&
((~humble(susan)<~>rich(susan)))&
((happy(lucy)<~>brave(lucy))) | calm(mary) | [
"p0",
"p10",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 4311602649973382551676781
% SZS output start Proof for 4311602649973382551676781
1. (~wise(fred) & rich(fred)) <=> ? [X0] : (creative(X0) | rich(X0)) [input p0]
11. ! [X0] : (wise(X0) <=> rich(X0)) [input p10]
18. creative(mary) <~> calm(mary) [input p17]
23. ~calm(mary) [input hypothesis]
37. ((~wise(fred) & rich(fred)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X0] : (creative(X0) | rich(X0)) | (wise(fred) | ~rich(fred))) [nnf transformation 1]
38. ((~wise(fred) & rich(fred)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X0] : (creative(X0) | rich(X0)) | wise(fred) | ~rich(fred)) [flattening 37]
39. ((~wise(fred) & rich(fred)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X1] : (creative(X1) | rich(X1)) | wise(fred) | ~rich(fred)) [rectify 38]
40. ? [X1] : (creative(X1) | rich(X1)) => (creative(sK0) | rich(sK0)) [choice axiom]
41. ((~wise(fred) & rich(fred)) | ! [X0] : (~creative(X0) & ~rich(X0))) & ((creative(sK0) | rich(sK0)) | wise(fred) | ~rich(fred)) [skolemisation 39,40]
53. ! [X0] : ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))) [nnf transformation 11]
59. (~calm(mary) | ~creative(mary)) & (calm(mary) | creative(mary)) [nnf transformation 18]
65. rich(fred) | ~creative(X0) [cnf transformation 41]
67. ~wise(fred) | ~creative(X0) [cnf transformation 41]
96. ~rich(X0) | wise(X0) [cnf transformation 53]
110. calm(mary) | creative(mary) [cnf transformation 59]
119. ~calm(mary) [cnf transformation 23]
121. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
122. ~creative(X0) <- (1) [avatar component clause 121]
124. 2 <=> wise(fred) [avatar definition]
127. 1 | ~2 [avatar split clause 67,124,121]
133. 4 <=> rich(fred) [avatar definition]
135. rich(fred) <- (4) [avatar component clause 133]
136. 1 | 4 [avatar split clause 65,133,121]
209. 21 <=> creative(mary) [avatar definition]
210. creative(mary) <- (21) [avatar component clause 209]
213. 22 <=> calm(mary) [avatar definition]
217. 21 | 22 [avatar split clause 110,213,209]
244. ~22 [avatar split clause 119,213]
246. wise(fred) <- (4) [resolution 96,135]
250. 2 | ~4 [avatar split clause 246,133,124]
251. $false <- (1, 21) [resolution 122,210]
254. ~1 | ~21 [avatar contradiction clause 251]
255. $false [avatar sat refutation 127,136,217,244,250,254]
% SZS output end Proof for 4311602649973382551676781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or tall is not funny. If someone is both rich and not old then fred is both not creative and not patient and vice versa. Everyone who is either curious or tall is not happy and vice versa. If john is not strong or not kind then fred is both not happy and humble. Everyone who is not humble is either wise or rich. If alice is both generous and humble then someone is wise or not humble. If fred is kind or wise then someone is either patient or not humble. If john is calm or not strong then alice is both patient and quiet and vice versa. Everyone who is not creative or not rich is not generous or not brave and vice versa. Everyone who is either humble or not tall is curious and vice versa. Everyone who is either funny or not wise is both not old and humble and vice versa. If fred is creative or not rich then fred is generous and vice versa. If someone is rich or not brave then paul is not old or wise. Everyone who is both not curious and rich is either strong or quiet and vice versa. Everyone who is both brave and not patient is either not rich or funny and vice versa. If someone is both not wise and not strong then alice is either not patient or kind. Paul is both funny and not wise. Alice is both wise and not quiet. Mary is strong. Lucy is both old and not generous. Someone is not creative or funny. Someone is brave or quiet. | John is creative. | neutral | (![X]:((~creative(X)|tall(X))=>~funny(X)))&
((?[X]:((rich(X)&~old(X))))<=>((~creative(fred)&~patient(fred))))&
(![X]:((curious(X)<~>tall(X))<=>~happy(X)))&
(((~strong(john)|~kind(john)))=>((~happy(fred)&humble(fred))))&
(![X]:(~humble(X)=>(wise(X)<~>rich(X))))&
(((generous(alice)&humble(alice)))=>(?[X]:((wise(X)|~humble(X)))))&
(((kind(fred)|wise(fred)))=>(?[X]:((patient(X)<~>~humble(X)))))&
(((calm(john)|~strong(john)))<=>((patient(alice)&quiet(alice))))&
(![X]:((~creative(X)|~rich(X))<=>(~generous(X)|~brave(X))))&
(![X]:((humble(X)<~>~tall(X))<=>curious(X)))&
(![X]:((funny(X)<~>~wise(X))<=>(~old(X)&humble(X))))&
(((creative(fred)|~rich(fred)))<=>(generous(fred)))&
((?[X]:((rich(X)|~brave(X))))=>((~old(paul)|wise(paul))))&
(![X]:((~curious(X)&rich(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((brave(X)&~patient(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~patient(alice)<~>kind(alice))))&
((funny(paul)&~wise(paul)))&
((wise(alice)&~quiet(alice)))&
(strong(mary))&
((old(lucy)&~generous(lucy)))&
(?[X]:((~creative(X)|funny(X))))&
(?[X]:((brave(X)|quiet(X)))) | creative(john) | []
| null | 0 |
If susan is either brave or not quiet then someone is both not humble and not funny.
If alice is either calm or not brave then fred is not brave and vice versa.
Everyone who is either not wise or not tall is strong and vice versa.
If someone is not rich or not patient then someone is not funny.
If john is not calm then someone is not kind.
Everyone who is either wise or old is either not calm or not old and vice versa.
Everyone who is creative is both not generous and not humble and vice versa.
Everyone who is either not humble or not happy is either not generous or not old.
Everyone who is strong or rich is either quiet or not calm and vice versa.
If someone is either not rich or not calm then fred is not creative and vice versa.
Everyone who is both not kind and not funny is either rich or not calm and vice versa.
Everyone who is both rich and creative is rich.
If someone is either funny or humble then someone is creative.
If someone is either not quiet or not kind then someone is either humble or not humble.
If someone is not curious or funny then someone is calm.
If mary is quiet then lucy is both creative and humble and vice versa.
Fred is either brave or quiet.
Mary is strong.
Lucy is either funny or generous.
Someone is tall.
Someone is not funny or not kind.
Someone is either happy or not curious.
Fred is both not brave and quiet.
Someone is both humble and not creative. | Lucy is not rich. | neutral | (((brave(susan)<~>~quiet(susan)))=>(?[X]:((~humble(X)&~funny(X)))))&
(((calm(alice)<~>~brave(alice)))<=>(~brave(fred)))&
(![X]:((~wise(X)<~>~tall(X))<=>strong(X)))&
((?[X]:((~rich(X)|~patient(X))))=>(?[X]:(~funny(X))))&
((~calm(john))=>(?[X]:(~kind(X))))&
(![X]:((wise(X)<~>old(X))<=>(~calm(X)<~>~old(X))))&
(![X]:(creative(X)<=>(~generous(X)&~humble(X))))&
(![X]:((~humble(X)<~>~happy(X))=>(~generous(X)<~>~old(X))))&
(![X]:((strong(X)|rich(X))<=>(quiet(X)<~>~calm(X))))&
((?[X]:((~rich(X)<~>~calm(X))))<=>(~creative(fred)))&
(![X]:((~kind(X)&~funny(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((rich(X)&creative(X))=>rich(X)))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:(calm(X))))&
((quiet(mary))<=>((creative(lucy)&humble(lucy))))&
((brave(fred)<~>quiet(fred)))&
(strong(mary))&
((funny(lucy)<~>generous(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((~funny(X)|~kind(X))))&
(?[X]:((happy(X)<~>~curious(X))))&
((~brave(fred)&quiet(fred)))&
(?[X]:((humble(X)&~creative(X)))) | ~rich(lucy) | []
| null | 0 |
Everyone who is both strong and not wise is either not curious or strong and vice versa.
If someone is quiet then lucy is both not wise and not creative and vice versa.
Everyone who is both not happy and happy is not old or quiet.
Everyone who is not patient is not curious and vice versa.
Everyone who is funny or curious is not humble and vice versa.
Everyone who is either not wise or kind is wise or rich and vice versa.
Everyone who is not strong or not quiet is not strong and vice versa.
Everyone who is either not quiet or not funny is brave.
Everyone who is either wise or not tall is not kind or not creative.
If lucy is wise then someone is funny and vice versa.
If someone is curious or not old then someone is not tall and vice versa.
Everyone who is either not calm or strong is quiet and vice versa.
If paul is either not generous or not calm then someone is either not quiet or not humble.
Everyone who is creative is either curious or not rich.
If lucy is both not calm and not old then fred is either wise or not calm.
If alice is both brave and not old then john is not creative or happy.
Mary is not quiet or old.
Alice is happy or not funny.
Someone is rich or calm.
Susan is not wise or not curious.
Lucy is both wise and not funny.
Paul is kind or not old.
Someone is either not tall or generous.
Paul is not humble or patient. | Paul is calm. | entailment | (![X]:((strong(X)&~wise(X))<=>(~curious(X)<~>strong(X))))&
((?[X]:(quiet(X)))<=>((~wise(lucy)&~creative(lucy))))&
(![X]:((~happy(X)&happy(X))=>(~old(X)|quiet(X))))&
(![X]:(~patient(X)<=>~curious(X)))&
(![X]:((funny(X)|curious(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>kind(X))<=>(wise(X)|rich(X))))&
(![X]:((~strong(X)|~quiet(X))<=>~strong(X)))&
(![X]:((~quiet(X)<~>~funny(X))=>brave(X)))&
(![X]:((wise(X)<~>~tall(X))=>(~kind(X)|~creative(X))))&
((wise(lucy))<=>(?[X]:(funny(X))))&
((?[X]:((curious(X)|~old(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)<~>strong(X))<=>quiet(X)))&
(((~generous(paul)<~>~calm(paul)))=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:(creative(X)=>(curious(X)<~>~rich(X))))&
(((~calm(lucy)&~old(lucy)))=>((wise(fred)<~>~calm(fred))))&
(((brave(alice)&~old(alice)))=>((~creative(john)|happy(john))))&
((~quiet(mary)|old(mary)))&
((happy(alice)|~funny(alice)))&
(?[X]:((rich(X)|calm(X))))&
((~wise(susan)|~curious(susan)))&
((wise(lucy)&~funny(lucy)))&
((kind(paul)|~old(paul)))&
(?[X]:((~tall(X)<~>generous(X))))&
((~humble(paul)|patient(paul))) | calm(paul) | [
"p1",
"p6",
"p11",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3775432839043345002845321
% SZS output start Proof for 3775432839043345002845321
2. ? [X0] : quiet(X0) <=> (~creative(lucy) & ~wise(lucy)) [input p1]
7. ! [X0] : ((~quiet(X0) | ~strong(X0)) <=> ~strong(X0)) [input p6]
12. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> quiet(X0)) [input p11]
21. ~funny(lucy) & wise(lucy) [input p20]
25. ~calm(paul) [input hypothesis]
42. (? [X0] : quiet(X0) | (creative(lucy) | wise(lucy))) & ((~creative(lucy) & ~wise(lucy)) | ! [X0] : ~quiet(X0)) [nnf transformation 2]
43. (? [X0] : quiet(X0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X0] : ~quiet(X0)) [flattening 42]
44. (? [X0] : quiet(X0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X1] : ~quiet(X1)) [rectify 43]
45. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom]
46. (quiet(sK0) | creative(lucy) | wise(lucy)) & ((~creative(lucy) & ~wise(lucy)) | ! [X1] : ~quiet(X1)) [skolemisation 44,45]
51. ! [X0] : (((~quiet(X0) | ~strong(X0)) | strong(X0)) & (~strong(X0) | (quiet(X0) & strong(X0)))) [nnf transformation 7]
52. ! [X0] : ((~quiet(X0) | ~strong(X0) | strong(X0)) & (~strong(X0) | (quiet(X0) & strong(X0)))) [flattening 51]
64. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | ~quiet(X0)) & (quiet(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 12]
81. ~wise(lucy) | ~quiet(X1) [cnf transformation 46]
96. ~strong(X0) | quiet(X0) [cnf transformation 52]
107. quiet(X0) | strong(X0) | calm(X0) [cnf transformation 64]
110. ~strong(X0) | calm(X0) | ~quiet(X0) [cnf transformation 64]
124. wise(lucy) [cnf transformation 21]
130. ~calm(paul) [cnf transformation 25]
137. 1 <=> wise(lucy) [avatar definition]
150. 4 <=> ! [X1] : ~quiet(X1) [avatar definition]
151. ~quiet(X1) <- (4) [avatar component clause 150]
153. 4 | ~1 [avatar split clause 81,137,150]
189. ~strong(X0) | calm(X0) [subsumption resolution 110,96]
190. calm(X0) | quiet(X0) [subsumption resolution 107,189]
192. 13 <=> calm(paul) [avatar definition]
193. ~calm(paul) <- (~13) [avatar component clause 192]
282. 1 [avatar split clause 124,137]
311. ~13 [avatar split clause 130,192]
317. quiet(paul) <- (~13) [resolution 190,193]
319. $false <- (4, ~13) [subsumption resolution 317,151]
320. ~4 | 13 [avatar contradiction clause 319]
323. $false [avatar sat refutation 153,282,311,320]
% SZS output end Proof for 3775432839043345002845321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and patient then someone is either not generous or happy.
Everyone who is not happy or not humble is happy and vice versa.
Everyone who is creative or not quiet is both not brave and brave and vice versa.
If someone is both patient and humble then someone is both quiet and not calm.
If someone is both old and patient then susan is both creative and old.
Everyone who is not old is both creative and not curious and vice versa.
Everyone who is tall is wise and vice versa.
Everyone who is both humble and calm is calm and vice versa.
Everyone who is both strong and not old is either patient or wise and vice versa.
If someone is either rich or curious then someone is patient or tall.
Everyone who is both quiet and strong is either not happy or quiet and vice versa.
Everyone who is rich is both rich and not patient.
Everyone who is either not generous or not strong is curious or quiet.
If someone is tall then someone is humble.
Someone is not calm or not creative.
Someone is not rich or creative.
Lucy is wise or not creative.
Lucy is either tall or not brave.
Someone is not generous or not kind.
Paul is both not generous and not calm.
Someone is both not generous and not rich. | Lucy is not patient. | entailment | (((~old(alice)&patient(alice)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(![X]:((~happy(X)|~humble(X))<=>happy(X)))&
(![X]:((creative(X)|~quiet(X))<=>(~brave(X)&brave(X))))&
((?[X]:((patient(X)&humble(X))))=>(?[X]:((quiet(X)&~calm(X)))))&
((?[X]:((old(X)&patient(X))))=>((creative(susan)&old(susan))))&
(![X]:(~old(X)<=>(creative(X)&~curious(X))))&
(![X]:(tall(X)<=>wise(X)))&
(![X]:((humble(X)&calm(X))<=>calm(X)))&
(![X]:((strong(X)&~old(X))<=>(patient(X)<~>wise(X))))&
((?[X]:((rich(X)<~>curious(X))))=>(?[X]:((patient(X)|tall(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:(rich(X)=>(rich(X)&~patient(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(curious(X)|quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:(humble(X))))&
(?[X]:((~calm(X)|~creative(X))))&
(?[X]:((~rich(X)|creative(X))))&
((wise(lucy)|~creative(lucy)))&
((tall(lucy)<~>~brave(lucy)))&
(?[X]:((~generous(X)|~kind(X))))&
((~generous(paul)&~calm(paul)))&
(?[X]:((~generous(X)&~rich(X)))) | ~patient(lucy) | [
"p2",
"p4",
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 194998187972919486586382
% SZS output start Proof for 194998187972919486586382
3. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (brave(X0) & ~brave(X0))) [input p2]
5. ? [X0] : (patient(X0) & old(X0)) => (old(susan) & creative(susan)) [input p4]
6. ! [X0] : (~old(X0) <=> (~curious(X0) & creative(X0))) [input p5]
22. patient(lucy) [input hypothesis]
30. (old(susan) & creative(susan)) | ! [X0] : (~patient(X0) | ~old(X0)) [ennf transformation 5]
41. ! [X0] : (((~quiet(X0) | creative(X0)) | (~brave(X0) | brave(X0))) & ((brave(X0) & ~brave(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 3]
42. ! [X0] : ((~quiet(X0) | creative(X0) | ~brave(X0) | brave(X0)) & ((brave(X0) & ~brave(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 41]
46. ! [X0] : ((~old(X0) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | old(X0))) [nnf transformation 6]
47. ! [X0] : ((~old(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | old(X0))) [flattening 46]
75. ~brave(X0) | ~creative(X0) [cnf transformation 42]
77. brave(X0) | ~creative(X0) [cnf transformation 42]
82. creative(susan) | ~patient(X0) | ~old(X0) [cnf transformation 30]
84. creative(X0) | old(X0) [cnf transformation 47]
120. patient(lucy) [cnf transformation 22]
144. ~creative(X0) [subsumption resolution 75,77]
154. 7 <=> ! [X0] : (~patient(X0) | ~old(X0)) [avatar definition]
155. ~patient(X0) | ~old(X0) <- (7) [avatar component clause 154]
161. ~patient(X0) | ~old(X0) [subsumption resolution 82,144]
162. 7 [avatar split clause 161,154]
163. old(X0) [subsumption resolution 84,144]
203. ~patient(X0) <- (7) [subsumption resolution 155,163]
204. $false <- (7) [resolution 203,120]
207. ~7 [avatar contradiction clause 204]
208. $false [avatar sat refutation 162,207]
% SZS output end Proof for 194998187972919486586382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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. | Alice is not kind. | contradiction | ((?[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))) | ~kind(alice) | [
"p2",
"p4",
"p7",
"p9",
"p10",
"p11",
"p12",
"p13",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 9076468594923250446330870
% SZS output start Proof for 9076468594923250446330870
3. ! [X0] : ((wise(X0) | ~old(X0)) => (~wise(X0) & calm(X0))) [input p2]
5. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> (~brave(X0) | creative(X0))) [input p4]
8. ! [X0] : (~brave(X0) <=> humble(X0)) [input p7]
10. ! [X0] : ((~old(X0) | calm(X0)) => (brave(X0) | kind(X0))) [input p9]
11. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (~creative(X0) <~> ~patient(X0))) [input p10]
12. ? [X0] : (curious(X0) | creative(X0)) <=> (~strong(alice) & quiet(alice)) [input p11]
13. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (~patient(X0) | old(X0))) [input p12]
14. ! [X0] : ((humble(X0) <~> ~quiet(X0)) <=> patient(X0)) [input p13]
23. ? [X0] : creative(X0) [input p22]
24. ~kind(alice) [input hypothesis]
30. ! [X0] : (~old(X0) => calm(X0)) [pure predicate removal 3]
33. ! [X0] : (calm(X0) | old(X0)) [ennf transformation 30]
34. ! [X0] : ((brave(X0) | kind(X0)) | (old(X0) & ~calm(X0))) [ennf transformation 10]
35. ! [X0] : (brave(X0) | kind(X0) | (old(X0) & ~calm(X0))) [flattening 34]
42. ! [X0] : (((~funny(X0) & ~happy(X0)) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | (funny(X0) | happy(X0)))) [nnf transformation 5]
43. ! [X0] : (((~funny(X0) & ~happy(X0)) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | funny(X0) | happy(X0))) [flattening 42]
46. ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0))) [nnf transformation 8]
52. ! [X0] : (((brave(X0) & ~strong(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (~brave(X0) | strong(X0)))) [nnf transformation 11]
53. ! [X0] : (((brave(X0) & ~strong(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | ~brave(X0) | strong(X0))) [flattening 52]
54. (? [X0] : (curious(X0) | creative(X0)) | (strong(alice) | ~quiet(alice))) & ((~strong(alice) & quiet(alice)) | ! [X0] : (~curious(X0) & ~creative(X0))) [nnf transformation 12]
55. (? [X0] : (curious(X0) | creative(X0)) | strong(alice) | ~quiet(alice)) & ((~strong(alice) & quiet(alice)) | ! [X0] : (~curious(X0) & ~creative(X0))) [flattening 54]
56. (? [X0] : (curious(X0) | creative(X0)) | strong(alice) | ~quiet(alice)) & ((~strong(alice) & quiet(alice)) | ! [X1] : (~curious(X1) & ~creative(X1))) [rectify 55]
57. ? [X0] : (curious(X0) | creative(X0)) => (curious(sK3) | creative(sK3)) [choice axiom]
58. ((curious(sK3) | creative(sK3)) | strong(alice) | ~quiet(alice)) & ((~strong(alice) & quiet(alice)) | ! [X1] : (~curious(X1) & ~creative(X1))) [skolemisation 56,57]
59. ! [X0] : (((happy(X0) & ~calm(X0)) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 13]
60. ! [X0] : (((happy(X0) & ~calm(X0)) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | ~happy(X0) | calm(X0))) [flattening 59]
61. ! [X0] : ((((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | ~patient(X0)) & (patient(X0) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0))))) [nnf transformation 14]
71. ? [X0] : creative(X0) => creative(sK7) [choice axiom]
72. creative(sK7) [skolemisation 23,71]
77. old(X0) | calm(X0) [cnf transformation 33]
81. ~happy(X0) | ~creative(X0) [cnf transformation 43]
82. ~happy(X0) | brave(X0) [cnf transformation 43]
92. ~brave(X0) | ~humble(X0) [cnf transformation 46]
97. brave(X0) | kind(X0) | old(X0) [cnf transformation 35]
99. ~brave(X0) | creative(X0) | patient(X0) | strong(X0) [cnf transformation 53]
102. ~patient(X0) | brave(X0) | creative(X0) [cnf transformation 53]
104. quiet(alice) | ~creative(X1) [cnf transformation 58]
106. ~strong(alice) | ~creative(X1) [cnf transformation 58]
110. ~old(X0) | ~calm(X0) [cnf transformation 60]
112. ~old(X0) | happy(X0) [cnf transformation 60]
113. happy(X0) | patient(X0) [cnf transformation 60]
116. ~quiet(X0) | humble(X0) | ~patient(X0) [cnf transformation 61]
128. creative(sK7) [cnf transformation 72]
129. ~kind(alice) [cnf transformation 24]
183. 13 <=> quiet(alice) [avatar definition]
184. quiet(alice) <- (13) [avatar component clause 183]
187. 14 <=> strong(alice) [avatar definition]
188. ~strong(alice) <- (~14) [avatar component clause 187]
201. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
202. ~creative(X1) <- (17) [avatar component clause 201]
203. 17 | ~14 [avatar split clause 106,187,201]
205. 17 | 13 [avatar split clause 104,183,201]
262. happy(X0) | calm(X0) [resolution 112,77]
263. brave(X0) | patient(X0) [resolution 113,82]
264. ~creative(X1) | patient(X1) [resolution 113,81]
268. $false <- (17) [resolution 202,128]
271. ~17 [avatar contradiction clause 268]
273. ~creative(X1) | calm(X1) [resolution 262,81]
312. ~humble(X0) | old(X0) | kind(X0) [resolution 97,92]
384. humble(alice) | ~patient(alice) <- (13) [resolution 116,184]
388. 39 <=> patient(alice) [avatar definition]
389. patient(alice) <- (39) [avatar component clause 388]
392. 40 <=> humble(alice) [avatar definition]
394. humble(alice) <- (40) [avatar component clause 392]
395. ~39 | 40 | ~13 [avatar split clause 384,183,392,388]
440. creative(X0) | patient(X0) | strong(X0) | patient(X0) [resolution 99,263]
445. creative(X0) | patient(X0) | strong(X0) [duplicate literal removal 440]
446. strong(X0) | patient(X0) [subsumption resolution 445,264]
687. patient(alice) <- (~14) [resolution 446,188]
693. 39 | 14 [avatar split clause 687,187,388]
694. brave(alice) | creative(alice) <- (39) [resolution 389,102]
696. 67 <=> creative(alice) [avatar definition]
698. creative(alice) <- (67) [avatar component clause 696]
700. 68 <=> brave(alice) [avatar definition]
702. brave(alice) <- (68) [avatar component clause 700]
703. 67 | 68 | ~39 [avatar split clause 694,388,700,696]
705. old(alice) | kind(alice) <- (40) [resolution 394,312]
707. old(alice) <- (40) [subsumption resolution 705,129]
708. calm(alice) <- (67) [resolution 698,273]
715. ~calm(alice) <- (40) [resolution 707,110]
716. $false <- (40, 67) [subsumption resolution 715,708]
717. ~40 | ~67 [avatar contradiction clause 716]
721. ~humble(alice) <- (68) [resolution 702,92]
722. $false <- (40, 68) [subsumption resolution 721,394]
723. ~40 | ~68 [avatar contradiction clause 722]
724. $false [avatar sat refutation 203,205,271,395,693,703,717,723]
% SZS output end Proof for 9076468594923250446330870
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not tall or not old then someone is curious or not calm.
Everyone who is not patient or wise is patient or creative and vice versa.
If paul is not old or patient then someone is creative or brave and vice versa.
If alice is not rich or not generous then someone is patient and vice versa.
If someone is tall or not patient then lucy is tall or old.
Everyone who is either kind or wise is not strong or tall and vice versa.
Everyone who is patient or generous is not old or not tall.
If someone is either not tall or not wise then someone is both generous and not wise.
Everyone who is either not strong or not patient is either humble or not old.
Everyone who is both kind and rich is old or not brave and vice versa.
Everyone who is not patient or patient is both not patient and not calm and vice versa.
Everyone who is wise or not old is either not calm or not curious.
If susan is quiet then paul is either not patient or not kind and vice versa.
Everyone who is either strong or humble is calm.
Everyone who is calm is both patient and not wise.
Everyone who is both curious and not tall is tall.
Fred is not kind.
Someone is rich.
Susan is either not brave or happy.
John is either not brave or not patient.
Susan is either not brave or curious.
Someone is either kind or not strong. | Alice is not wise. | neutral | (((~tall(alice)<~>~old(alice)))=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:((~patient(X)|wise(X))<=>(patient(X)|creative(X))))&
(((~old(paul)|patient(paul)))<=>(?[X]:((creative(X)|brave(X)))))&
(((~rich(alice)|~generous(alice)))<=>(?[X]:(patient(X))))&
((?[X]:((tall(X)|~patient(X))))=>((tall(lucy)|old(lucy))))&
(![X]:((kind(X)<~>wise(X))<=>(~strong(X)|tall(X))))&
(![X]:((patient(X)|generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)<~>~old(X))))&
(![X]:((kind(X)&rich(X))<=>(old(X)|~brave(X))))&
(![X]:((~patient(X)|patient(X))<=>(~patient(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))=>(~calm(X)<~>~curious(X))))&
((quiet(susan))<=>((~patient(paul)<~>~kind(paul))))&
(![X]:((strong(X)<~>humble(X))=>calm(X)))&
(![X]:(calm(X)=>(patient(X)&~wise(X))))&
(![X]:((curious(X)&~tall(X))=>tall(X)))&
(~kind(fred))&
(?[X]:(rich(X)))&
((~brave(susan)<~>happy(susan)))&
((~brave(john)<~>~patient(john)))&
((~brave(susan)<~>curious(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | ~wise(alice) | []
| null | 0 |
If alice is either curious or not funny then someone is not brave or wise and vice versa.
If someone is tall or calm then alice is not curious and vice versa.
Everyone who is not wise or not creative is either curious or not tall.
Everyone who is either brave or not generous is not curious or rich.
Everyone who is either not tall or not strong is generous or not generous and vice versa.
Everyone who is both quiet and humble is old.
If mary is calm then someone is not generous and vice versa.
Everyone who is both not calm and strong is strong and vice versa.
If fred is not patient or not curious then someone is both quiet and curious and vice versa.
Everyone who is both kind and humble is both not brave and humble and vice versa.
Everyone who is either not tall or rich is generous and vice versa.
If fred is either not calm or curious then someone is rich or not funny.
Everyone who is either not brave or not kind is not funny or quiet.
If someone is not funny or kind then someone is rich and vice versa.
If someone is funny then mary is either not wise or creative.
Everyone who is either funny or not tall is either strong or patient.
Alice is both patient and not tall.
Someone is both not calm and not humble.
Lucy is either brave or not strong.
Lucy is both wise and quiet.
Someone is either patient or calm.
Mary is strong or not happy. | Fred is kind. | contradiction | (((curious(alice)<~>~funny(alice)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((tall(X)|calm(X))))<=>(~curious(alice)))&
(![X]:((~wise(X)|~creative(X))=>(curious(X)<~>~tall(X))))&
(![X]:((brave(X)<~>~generous(X))=>(~curious(X)|rich(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(generous(X)|~generous(X))))&
(![X]:((quiet(X)&humble(X))=>old(X)))&
((calm(mary))<=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)&strong(X))<=>strong(X)))&
(((~patient(fred)|~curious(fred)))<=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((kind(X)&humble(X))<=>(~brave(X)&humble(X))))&
(![X]:((~tall(X)<~>rich(X))<=>generous(X)))&
(((~calm(fred)<~>curious(fred)))=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~funny(X)|kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:(funny(X)))=>((~wise(mary)<~>creative(mary))))&
(![X]:((funny(X)<~>~tall(X))=>(strong(X)<~>patient(X))))&
((patient(alice)&~tall(alice)))&
(?[X]:((~calm(X)&~humble(X))))&
((brave(lucy)<~>~strong(lucy)))&
((wise(lucy)&quiet(lucy)))&
(?[X]:((patient(X)<~>calm(X))))&
((strong(mary)|~happy(mary))) | kind(fred) | [
"p0",
"p1",
"p4",
"p6",
"p10",
"p13",
"p15",
"p16",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 826777194203120042921524
% SZS output start Proof for 826777194203120042921524
1. (curious(alice) <~> ~funny(alice)) <=> ? [X0] : (wise(X0) | ~brave(X0)) [input p0]
2. ? [X0] : (calm(X0) | tall(X0)) <=> ~curious(alice) [input p1]
5. ! [X0] : ((~tall(X0) <~> ~strong(X0)) <=> (~generous(X0) | generous(X0))) [input p4]
7. calm(mary) <=> ? [X0] : ~generous(X0) [input p6]
11. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> generous(X0)) [input p10]
14. ? [X0] : (kind(X0) | ~funny(X0)) <=> ? [X0] : rich(X0) [input p13]
16. ! [X0] : ((funny(X0) <~> ~tall(X0)) => (strong(X0) <~> patient(X0))) [input p15]
17. ~tall(alice) & patient(alice) [input p16]
20. quiet(lucy) & wise(lucy) [input p19]
23. kind(fred) [input hypothesis]
24. ? [X0] : (kind(X0) | ~funny(X0)) <=> ? [X1] : rich(X1) [rectify 14]
34. ! [X0] : ((strong(X0) <~> patient(X0)) | (funny(X0) <=> ~tall(X0))) [ennf transformation 16]
35. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X0] : (wise(X0) | ~brave(X0)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [nnf transformation 1]
36. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X1] : (wise(X1) | ~brave(X1)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [rectify 35]
37. ? [X1] : (wise(X1) | ~brave(X1)) => (wise(sK0) | ~brave(sK0)) [choice axiom]
38. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & ((wise(sK0) | ~brave(sK0)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [skolemisation 36,37]
39. (? [X0] : (calm(X0) | tall(X0)) | curious(alice)) & (~curious(alice) | ! [X0] : (~calm(X0) & ~tall(X0))) [nnf transformation 2]
40. (? [X0] : (calm(X0) | tall(X0)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~tall(X1))) [rectify 39]
41. ? [X0] : (calm(X0) | tall(X0)) => (calm(sK1) | tall(sK1)) [choice axiom]
42. ((calm(sK1) | tall(sK1)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~tall(X1))) [skolemisation 40,41]
45. ! [X0] : ((((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0))))) [nnf transformation 5]
46. ! [X0] : ((((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0))))) [flattening 45]
47. (calm(mary) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ~calm(mary)) [nnf transformation 7]
48. (calm(mary) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ~calm(mary)) [rectify 47]
49. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
50. (calm(mary) | ! [X0] : generous(X0)) & (~generous(sK2) | ~calm(mary)) [skolemisation 48,49]
60. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | ~generous(X0)) & (generous(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 11]
65. (? [X0] : (kind(X0) | ~funny(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (~kind(X0) & funny(X0))) [nnf transformation 24]
66. (? [X0] : (kind(X0) | ~funny(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (~kind(X3) & funny(X3))) [rectify 65]
67. ? [X0] : (kind(X0) | ~funny(X0)) => (kind(sK5) | ~funny(sK5)) [choice axiom]
68. ? [X2] : rich(X2) => rich(sK6) [choice axiom]
69. ((kind(sK5) | ~funny(sK5)) | ! [X1] : ~rich(X1)) & (rich(sK6) | ! [X3] : (~kind(X3) & funny(X3))) [skolemisation 66,68,67]
71. ! [X0] : (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0)))) [nnf transformation 34]
81. ~funny(alice) | curious(alice) | ~wise(X0) [cnf transformation 38]
84. ~curious(alice) | ~tall(X1) [cnf transformation 42]
85. ~curious(alice) | ~calm(X1) [cnf transformation 42]
95. ~strong(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 46]
96. ~strong(X0) | ~tall(X0) | generous(X0) [cnf transformation 46]
97. strong(X0) | tall(X0) | ~generous(X0) [cnf transformation 46]
98. strong(X0) | tall(X0) | generous(X0) [cnf transformation 46]
100. calm(mary) | generous(X0) [cnf transformation 50]
116. ~rich(X0) | tall(X0) | ~generous(X0) [cnf transformation 60]
122. rich(sK6) | ~kind(X3) [cnf transformation 69]
129. ~patient(X0) | ~strong(X0) | funny(X0) | tall(X0) [cnf transformation 71]
130. patient(alice) [cnf transformation 17]
131. ~tall(alice) [cnf transformation 17]
136. wise(lucy) [cnf transformation 20]
140. kind(fred) [cnf transformation 23]
142. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
143. ~wise(X0) <- (1) [avatar component clause 142]
145. 2 <=> curious(alice) [avatar definition]
149. 3 <=> funny(alice) [avatar definition]
150. ~funny(alice) <- (~3) [avatar component clause 149]
157. 1 | 2 | ~3 [avatar split clause 81,149,145,142]
179. 9 <=> ! [X1] : ~calm(X1) [avatar definition]
180. ~calm(X1) <- (9) [avatar component clause 179]
181. 9 | ~2 [avatar split clause 85,145,179]
183. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
184. ~tall(X1) <- (10) [avatar component clause 183]
185. 10 | ~2 [avatar split clause 84,145,183]
186. strong(X0) | tall(X0) [subsumption resolution 97,98]
187. ~strong(X0) | ~tall(X0) [subsumption resolution 95,96]
189. 11 <=> ! [X0] : generous(X0) [avatar definition]
190. generous(X0) <- (11) [avatar component clause 189]
192. 12 <=> calm(mary) [avatar definition]
194. calm(mary) <- (12) [avatar component clause 192]
195. 11 | 12 [avatar split clause 100,192,189]
252. 25 <=> ! [X3] : ~kind(X3) [avatar definition]
253. ~kind(X3) <- (25) [avatar component clause 252]
255. 26 <=> rich(sK6) [avatar definition]
257. rich(sK6) <- (26) [avatar component clause 255]
258. 25 | 26 [avatar split clause 122,255,252]
276. ~patient(X0) | ~strong(X0) | funny(X0) [subsumption resolution 129,187]
319. $false <- (9, 12) [resolution 180,194]
320. ~9 | ~12 [avatar contradiction clause 319]
375. 43 <=> generous(sK6) [avatar definition]
376. ~generous(sK6) <- (~43) [avatar component clause 375]
379. 44 <=> tall(sK6) [avatar definition]
380. tall(sK6) <- (44) [avatar component clause 379]
381. ~tall(sK6) <- (~44) [avatar component clause 379]
383. tall(sK6) | ~generous(sK6) <- (26) [resolution 116,257]
386. ~generous(sK6) <- (26, ~44) [subsumption resolution 383,381]
387. ~43 | ~26 | 44 [avatar split clause 386,379,255,375]
388. ~strong(alice) | funny(alice) [resolution 276,130]
391. ~strong(alice) <- (~3) [subsumption resolution 388,150]
411. tall(alice) <- (~3) [resolution 391,186]
413. $false <- (~3) [subsumption resolution 411,131]
414. 3 [avatar contradiction clause 413]
420. $false <- (1) [resolution 143,136]
425. ~1 [avatar contradiction clause 420]
440. $false <- (11, ~43) [resolution 190,376]
442. ~11 | 43 [avatar contradiction clause 440]
451. $false <- (25) [resolution 253,140]
452. ~25 [avatar contradiction clause 451]
453. $false <- (10, 44) [subsumption resolution 380,184]
454. ~10 | ~44 [avatar contradiction clause 453]
455. $false [avatar sat refutation 157,181,185,195,258,320,387,414,425,442,452,454]
% SZS output end Proof for 826777194203120042921524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not generous is not brave or humble. Everyone who is both not wise and curious is rich or creative and vice versa. If susan is both not brave and not wise then someone is both strong and funny. Everyone who is either funny or old is either not old or not humble. If someone is not humble or strong then lucy is not patient and vice versa. If someone is rich then fred is kind and vice versa. If someone is kind then someone is either not funny or old and vice versa. If someone is either happy or not brave then someone is either generous or not quiet and vice versa. If lucy is either not rich or old then someone is generous. Everyone who is not brave or not calm is both not humble and curious and vice versa. If someone is both tall and curious then fred is both strong and not happy and vice versa. Everyone who is both calm and not patient is happy or rich and vice versa. If mary is not humble or humble then lucy is either rich or kind. If lucy is both patient and old then mary is tall or not rich and vice versa. Everyone who is both old and generous is kind. Everyone who is either brave or strong is not funny and vice versa. Someone is not kind or not patient. Paul is not tall or calm. Someone is both not creative and not funny. Someone is either kind or happy. Someone is either not brave or humble. Susan is either patient or quiet. Alice is either kind or patient. Alice is tall. | Mary is not tall. | entailment | (![X]:((humble(X)&~generous(X))=>(~brave(X)|humble(X))))&
(![X]:((~wise(X)&curious(X))<=>(rich(X)|creative(X))))&
(((~brave(susan)&~wise(susan)))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((funny(X)<~>old(X))=>(~old(X)<~>~humble(X))))&
((?[X]:((~humble(X)|strong(X))))<=>(~patient(lucy)))&
((?[X]:(rich(X)))<=>(kind(fred)))&
((?[X]:(kind(X)))<=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
(![X]:((old(X)&generous(X))=>kind(X)))&
(![X]:((brave(X)<~>strong(X))<=>~funny(X)))&
(?[X]:((~kind(X)|~patient(X))))&
((~tall(paul)|calm(paul)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((~brave(X)<~>humble(X))))&
((patient(susan)<~>quiet(susan)))&
((kind(alice)<~>patient(alice)))&
(tall(alice)) | ~tall(mary) | [
"p3",
"p4",
"p9",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 175758954763874689011324
% SZS output start Proof for 175758954763874689011324
4. ! [X0] : ((funny(X0) <~> old(X0)) => (~old(X0) <~> ~humble(X0))) [input p3]
5. ? [X0] : (strong(X0) | ~humble(X0)) <=> ~patient(lucy) [input p4]
10. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (curious(X0) & ~humble(X0))) [input p9]
14. (old(lucy) & patient(lucy)) <=> (~rich(mary) | tall(mary)) [input p13]
16. ! [X0] : ((brave(X0) <~> strong(X0)) <=> ~funny(X0)) [input p15]
25. tall(mary) [input hypothesis]
32. ! [X0] : ((~old(X0) <~> ~humble(X0)) | (funny(X0) <=> old(X0))) [ennf transformation 4]
41. ! [X0] : (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) [nnf transformation 32]
42. (? [X0] : (strong(X0) | ~humble(X0)) | patient(lucy)) & (~patient(lucy) | ! [X0] : (~strong(X0) & humble(X0))) [nnf transformation 5]
43. (? [X0] : (strong(X0) | ~humble(X0)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (~strong(X1) & humble(X1))) [rectify 42]
44. ? [X0] : (strong(X0) | ~humble(X0)) => (strong(sK1) | ~humble(sK1)) [choice axiom]
45. ((strong(sK1) | ~humble(sK1)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (~strong(X1) & humble(X1))) [skolemisation 43,44]
63. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 10]
64. ! [X0] : ((~calm(X0) | ~brave(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [flattening 63]
73. ((old(lucy) & patient(lucy)) | (rich(mary) & ~tall(mary))) & ((~rich(mary) | tall(mary)) | (~old(lucy) | ~patient(lucy))) [nnf transformation 14]
74. ((old(lucy) & patient(lucy)) | (rich(mary) & ~tall(mary))) & (~rich(mary) | tall(mary) | ~old(lucy) | ~patient(lucy)) [flattening 73]
75. ! [X0] : ((((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) | funny(X0)) & (~funny(X0) | ((brave(X0) | ~strong(X0)) & (strong(X0) | ~brave(X0))))) [nnf transformation 16]
97. ~humble(X0) | ~old(X0) | funny(X0) | ~old(X0) [cnf transformation 41]
100. ~patient(lucy) | humble(X1) [cnf transformation 45]
101. ~patient(lucy) | ~strong(X1) [cnf transformation 45]
119. ~humble(X0) | brave(X0) [cnf transformation 64]
138. patient(lucy) | ~tall(mary) [cnf transformation 74]
140. old(lucy) | ~tall(mary) [cnf transformation 74]
143. ~funny(X0) | strong(X0) | ~brave(X0) [cnf transformation 75]
160. tall(mary) [cnf transformation 25]
161. ~old(X0) | ~humble(X0) | funny(X0) [duplicate literal removal 97]
182. 5 <=> patient(lucy) [avatar definition]
195. 8 <=> ! [X1] : ~strong(X1) [avatar definition]
196. ~strong(X1) <- (8) [avatar component clause 195]
197. 8 | ~5 [avatar split clause 101,182,195]
199. 9 <=> ! [X1] : humble(X1) [avatar definition]
200. humble(X1) <- (9) [avatar component clause 199]
201. 9 | ~5 [avatar split clause 100,182,199]
277. 27 <=> old(lucy) [avatar definition]
278. old(lucy) <- (27) [avatar component clause 277]
331. 38 <=> tall(mary) [avatar definition]
334. ~38 | 27 [avatar split clause 140,277,331]
336. ~38 | 5 [avatar split clause 138,182,331]
395. 38 [avatar split clause 160,331]
404. brave(X0) <- (9) [resolution 119,200]
435. ~humble(lucy) | funny(lucy) <- (27) [resolution 161,278]
436. funny(lucy) <- (9, 27) [subsumption resolution 435,200]
438. strong(lucy) | ~brave(lucy) <- (9, 27) [resolution 436,143]
439. ~brave(lucy) <- (8, 9, 27) [subsumption resolution 438,196]
440. $false <- (8, 9, 27) [subsumption resolution 439,404]
441. ~8 | ~9 | ~27 [avatar contradiction clause 440]
442. $false [avatar sat refutation 197,201,334,336,395,441]
% SZS output end Proof for 175758954763874689011324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not strong is not curious.
Everyone who is either not strong or not generous is either generous or rich and vice versa.
If someone is either not tall or calm then john is not funny or not kind and vice versa.
If someone is both patient and brave then john is quiet or not rich and vice versa.
Everyone who is not strong or not brave is not wise or not strong.
Everyone who is both calm and not curious is either not generous or not humble and vice versa.
Everyone who is not strong is not funny or not calm.
Everyone who is both calm and kind is not creative and vice versa.
Everyone who is not old or humble is either wise or brave.
Everyone who is either not happy or kind is brave or calm and vice versa.
Everyone who is old is either rich or calm and vice versa.
Everyone who is both not strong and not tall is both quiet and not tall and vice versa.
If someone is both not funny and curious then someone is both quiet and not humble and vice versa.
If fred is either strong or not creative then someone is patient or creative.
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
Someone is both not quiet and happy.
Someone is strong.
John is either creative or not quiet.
Someone is not happy.
Someone is calm.
Susan is rich.
Fred is not quiet or not curious.
Someone is either strong or not funny. | Susan is wise. | neutral | (![X]:((creative(X)|~strong(X))=>~curious(X)))&
(![X]:((~strong(X)<~>~generous(X))<=>(generous(X)<~>rich(X))))&
((?[X]:((~tall(X)<~>calm(X))))<=>((~funny(john)|~kind(john))))&
((?[X]:((patient(X)&brave(X))))<=>((quiet(john)|~rich(john))))&
(![X]:((~strong(X)|~brave(X))=>(~wise(X)|~strong(X))))&
(![X]:((calm(X)&~curious(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:(~strong(X)=>(~funny(X)|~calm(X))))&
(![X]:((calm(X)&kind(X))<=>~creative(X)))&
(![X]:((~old(X)|humble(X))=>(wise(X)<~>brave(X))))&
(![X]:((~happy(X)<~>kind(X))<=>(brave(X)|calm(X))))&
(![X]:(old(X)<=>(rich(X)<~>calm(X))))&
(![X]:((~strong(X)&~tall(X))<=>(quiet(X)&~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:(strong(X)))&
((creative(john)<~>~quiet(john)))&
(?[X]:(~happy(X)))&
(?[X]:(calm(X)))&
(rich(susan))&
((~quiet(fred)|~curious(fred)))&
(?[X]:((strong(X)<~>~funny(X)))) | wise(susan) | []
| null | 0 |
Everyone who is happy or old is both brave and not old.
Everyone who is both not wise and tall is either funny or old and vice versa.
Everyone who is both calm and curious is not calm and vice versa.
If someone is both old and not rich then alice is either not rich or brave.
If john is either strong or not curious then someone is tall.
Everyone who is both not kind and not creative is wise or kind and vice versa.
Everyone who is either not wise or not quiet is not curious.
If someone is not strong then someone is not kind or curious and vice versa.
Everyone who is both not quiet and funny is both strong and not generous and vice versa.
If paul is rich then lucy is either not strong or not quiet.
Everyone who is either wise or not generous is either calm or not curious.
Everyone who is rich or creative is strong.
If paul is either not rich or not kind then someone is either generous or not tall and vice versa.
Everyone who is both calm and patient is either not calm or not kind.
Everyone who is quiet is not humble.
Alice is either kind or happy.
Fred is both strong and brave.
Mary is both not strong and tall.
Someone is either not strong or not tall.
Someone is not rich or not curious.
Someone is either patient or not rich.
Someone is either not happy or not curious. | Alice is not brave. | contradiction | (![X]:((happy(X)|old(X))=>(brave(X)&~old(X))))&
(![X]:((~wise(X)&tall(X))<=>(funny(X)<~>old(X))))&
(![X]:((calm(X)&curious(X))<=>~calm(X)))&
((?[X]:((old(X)&~rich(X))))=>((~rich(alice)<~>brave(alice))))&
(((strong(john)<~>~curious(john)))=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&~creative(X))<=>(wise(X)|kind(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>~curious(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&funny(X))<=>(strong(X)&~generous(X))))&
((rich(paul))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:((wise(X)<~>~generous(X))=>(calm(X)<~>~curious(X))))&
(![X]:((rich(X)|creative(X))=>strong(X)))&
(((~rich(paul)<~>~kind(paul)))<=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>~kind(X))))&
(![X]:(quiet(X)=>~humble(X)))&
((kind(alice)<~>happy(alice)))&
((strong(fred)&brave(fred)))&
((~strong(mary)&tall(mary)))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:((patient(X)<~>~rich(X))))&
(?[X]:((~happy(X)<~>~curious(X)))) | ~brave(alice) | [
"p0",
"p5",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 449080283970570515449646
% SZS output start Proof for 449080283970570515449646
1. ! [X0] : ((old(X0) | happy(X0)) => (~old(X0) & brave(X0))) [input p0]
6. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (kind(X0) | wise(X0))) [input p5]
16. kind(alice) <~> happy(alice) [input p15]
23. ~brave(alice) [input hypothesis]
26. ! [X0] : ((~old(X0) & brave(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 1]
43. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 6]
44. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | creative(X0) | kind(X0))) [flattening 43]
60. (~happy(alice) | ~kind(alice)) & (happy(alice) | kind(alice)) [nnf transformation 16]
72. ~happy(X0) | brave(X0) [cnf transformation 26]
91. ~kind(X0) | ~kind(X0) [cnf transformation 44]
121. happy(alice) | kind(alice) [cnf transformation 60]
134. ~brave(alice) [cnf transformation 23]
137. ~kind(X0) [duplicate literal removal 91]
197. happy(alice) [subsumption resolution 121,137]
219. brave(alice) [resolution 72,197]
221. $false [subsumption resolution 219,134]
% SZS output end Proof for 449080283970570515449646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not curious is not strong or not kind and vice versa.
Everyone who is not generous is not creative or not rich and vice versa.
If paul is kind then fred is not curious or not humble and vice versa.
If someone is both not calm and not funny then paul is not curious or not funny and vice versa.
Everyone who is both not generous and quiet is not wise or not happy and vice versa.
If someone is brave or not kind then someone is both not humble and patient and vice versa.
If lucy is not generous or not rich then paul is both not creative and humble.
Everyone who is not wise is either quiet or not happy and vice versa.
If paul is either creative or tall then alice is either not patient or not kind and vice versa.
If someone is both brave and not generous then mary is either strong or not funny.
If someone is both wise and strong then someone is either not creative or not humble.
Everyone who is not old or not wise is generous and vice versa.
If someone is both not wise and wise then someone is either not wise or happy and vice versa.
If someone is either not quiet or brave then someone is both not kind and happy and vice versa.
If someone is both curious and not generous then alice is brave and vice versa.
If fred is not happy then someone is not tall and vice versa.
John is not wise or not curious.
Someone is both old and not funny.
Mary is tall.
John is rich or not old.
Someone is not funny. | Fred is wise. | entailment | (![X]:((~generous(X)|~curious(X))<=>(~strong(X)|~kind(X))))&
(![X]:(~generous(X)<=>(~creative(X)|~rich(X))))&
((kind(paul))<=>((~curious(fred)|~humble(fred))))&
((?[X]:((~calm(X)&~funny(X))))<=>((~curious(paul)|~funny(paul))))&
(![X]:((~generous(X)&quiet(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~generous(lucy)|~rich(lucy)))=>((~creative(paul)&humble(paul))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~happy(X))))&
(((creative(paul)<~>tall(paul)))<=>((~patient(alice)<~>~kind(alice))))&
((?[X]:((brave(X)&~generous(X))))=>((strong(mary)<~>~funny(mary))))&
((?[X]:((wise(X)&strong(X))))=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((~old(X)|~wise(X))<=>generous(X)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((~quiet(X)<~>brave(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:((curious(X)&~generous(X))))<=>(brave(alice)))&
((~happy(fred))<=>(?[X]:(~tall(X))))&
((~wise(john)|~curious(john)))&
(?[X]:((old(X)&~funny(X))))&
(tall(mary))&
((rich(john)|~old(john)))&
(?[X]:(~funny(X))) | wise(fred) | [
"p4",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 4322103310771965106395869
% SZS output start Proof for 4322103310771965106395869
5. ! [X0] : ((quiet(X0) & ~generous(X0)) <=> (~happy(X0) | ~wise(X0))) [input p4]
12. ! [X0] : ((~wise(X0) | ~old(X0)) <=> generous(X0)) [input p11]
22. ~wise(fred) [input hypothesis]
41. ! [X0] : (((quiet(X0) & ~generous(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~quiet(X0) | generous(X0)))) [nnf transformation 5]
42. ! [X0] : (((quiet(X0) & ~generous(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~quiet(X0) | generous(X0))) [flattening 41]
55. ! [X0] : (((~wise(X0) | ~old(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & old(X0)))) [nnf transformation 12]
56. ! [X0] : ((~wise(X0) | ~old(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & old(X0)))) [flattening 55]
95. ~generous(X0) | wise(X0) [cnf transformation 42]
125. generous(X0) | wise(X0) [cnf transformation 56]
150. ~wise(fred) [cnf transformation 22]
288. wise(X0) [subsumption resolution 125,95]
322. $false [subsumption resolution 150,288]
% SZS output end Proof for 4322103310771965106395869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then paul is humble or not wise and vice versa. Everyone who is not brave or not creative is both funny and not old. If someone is either not generous or funny then john is both not curious and creative. Everyone who is either not happy or calm is both calm and funny and vice versa. Everyone who is both not kind and tall is quiet or patient. If someone is not happy or not rich then lucy is generous. If someone is either not kind or quiet then john is either not patient or kind. Everyone who is funny or not calm is not creative. Everyone who is tall is either calm or not funny and vice versa. Everyone who is humble or not strong is brave and vice versa. If someone is both funny and not rich then someone is both strong and calm and vice versa. If someone is both humble and brave then someone is not strong or not rich. Everyone who is generous or old is strong or funny. If alice is both curious and creative then someone is not tall and vice versa. If someone is both curious and funny then someone is both kind and not old. Everyone who is brave is not kind or not rich. Susan is either quiet or not funny. Lucy is either not tall or not brave. Someone is both not tall and not patient. Someone is not patient. Someone is not strong or rich. Someone is either creative or curious. Someone is both kind and quiet. | Alice is not happy. | entailment | ((~rich(alice))<=>((humble(paul)|~wise(paul))))&
(![X]:((~brave(X)|~creative(X))=>(funny(X)&~old(X))))&
((?[X]:((~generous(X)<~>funny(X))))=>((~curious(john)&creative(john))))&
(![X]:((~happy(X)<~>calm(X))<=>(calm(X)&funny(X))))&
(![X]:((~kind(X)&tall(X))=>(quiet(X)|patient(X))))&
((?[X]:((~happy(X)|~rich(X))))=>(generous(lucy)))&
((?[X]:((~kind(X)<~>quiet(X))))=>((~patient(john)<~>kind(john))))&
(![X]:((funny(X)|~calm(X))=>~creative(X)))&
(![X]:(tall(X)<=>(calm(X)<~>~funny(X))))&
(![X]:((humble(X)|~strong(X))<=>brave(X)))&
((?[X]:((funny(X)&~rich(X))))<=>(?[X]:((strong(X)&calm(X)))))&
((?[X]:((humble(X)&brave(X))))=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:((generous(X)|old(X))=>(strong(X)|funny(X))))&
(((curious(alice)&creative(alice)))<=>(?[X]:(~tall(X))))&
((?[X]:((curious(X)&funny(X))))=>(?[X]:((kind(X)&~old(X)))))&
(![X]:(brave(X)=>(~kind(X)|~rich(X))))&
((quiet(susan)<~>~funny(susan)))&
((~tall(lucy)<~>~brave(lucy)))&
(?[X]:((~tall(X)&~patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~strong(X)|rich(X))))&
(?[X]:((creative(X)<~>curious(X))))&
(?[X]:((kind(X)&quiet(X)))) | ~happy(alice) | [
"p3",
"p7",
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7210967961503614503787767
% SZS output start Proof for 7210967961503614503787767
4. ! [X0] : ((~happy(X0) <~> calm(X0)) <=> (funny(X0) & calm(X0))) [input p3]
8. ! [X0] : ((~calm(X0) | funny(X0)) => ~creative(X0)) [input p7]
14. (creative(alice) & curious(alice)) <=> ? [X0] : ~tall(X0) [input p13]
19. ? [X0] : (~patient(X0) & ~tall(X0)) [input p18]
24. happy(alice) [input hypothesis]
37. ! [X0] : (~creative(X0) | (calm(X0) & ~funny(X0))) [ennf transformation 8]
47. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [nnf transformation 4]
48. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [flattening 47]
61. ((creative(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (~creative(alice) | ~curious(alice))) [nnf transformation 14]
62. ((creative(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ~creative(alice) | ~curious(alice)) [flattening 61]
63. ((creative(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ~creative(alice) | ~curious(alice)) [rectify 62]
64. ? [X1] : ~tall(X1) => ~tall(sK3) [choice axiom]
65. ((creative(alice) & curious(alice)) | ! [X0] : tall(X0)) & (~tall(sK3) | ~creative(alice) | ~curious(alice)) [skolemisation 63,64]
71. ? [X0] : (~patient(X0) & ~tall(X0)) => (~patient(sK5) & ~tall(sK5)) [choice axiom]
72. ~patient(sK5) & ~tall(sK5) [skolemisation 19,71]
94. ~calm(X0) | ~happy(X0) | funny(X0) [cnf transformation 48]
104. ~funny(X0) | ~creative(X0) [cnf transformation 37]
105. ~creative(X0) | calm(X0) [cnf transformation 37]
121. creative(alice) | tall(X0) [cnf transformation 65]
128. ~tall(sK5) [cnf transformation 72]
136. happy(alice) [cnf transformation 24]
242. 24 <=> ! [X0] : tall(X0) [avatar definition]
243. tall(X0) <- (24) [avatar component clause 242]
245. 25 <=> creative(alice) [avatar definition]
247. creative(alice) <- (25) [avatar component clause 245]
248. 24 | 25 [avatar split clause 121,245,242]
306. $false <- (24) [resolution 243,128]
307. ~24 [avatar contradiction clause 306]
312. calm(alice) <- (25) [resolution 105,247]
325. ~happy(alice) | funny(alice) <- (25) [resolution 94,312]
330. funny(alice) <- (25) [subsumption resolution 325,136]
368. ~creative(alice) <- (25) [resolution 330,104]
371. $false <- (25) [subsumption resolution 368,247]
372. ~25 [avatar contradiction clause 371]
373. $false [avatar sat refutation 248,307,372]
% SZS output end Proof for 7210967961503614503787767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not wise is both wise and calm and vice versa.
If lucy is tall or not brave then mary is either funny or not brave and vice versa.
If someone is patient then someone is happy and vice versa.
If someone is both strong and old then susan is calm and vice versa.
Everyone who is both generous and not calm is not brave.
Everyone who is either not kind or tall is either not strong or tall and vice versa.
If someone is either tall or calm then john is either not creative or wise.
If lucy is both not kind and not humble then fred is both not generous and not curious.
Everyone who is either patient or tall is strong or not tall and vice versa.
Everyone who is not quiet is not wise or not calm.
Everyone who is either not wise or tall is both not rich and not quiet.
If mary is calm or not curious then mary is not old.
Everyone who is either calm or wise is both not patient and not strong.
If fred is both not quiet and not patient then someone is both tall and not happy.
Everyone who is not calm or humble is either not curious or not tall and vice versa.
If mary is not patient or not old then someone is not humble and vice versa.
Someone is not patient or tall.
Someone is either brave or calm.
Paul is brave.
Someone is generous or wise.
Someone is either kind or not rich.
Someone is kind or not wise.
Someone is not patient or funny.
Alice is both not rich and not wise. | Fred is not strong. | contradiction | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
(((tall(lucy)|~brave(lucy)))<=>((funny(mary)<~>~brave(mary))))&
((?[X]:(patient(X)))<=>(?[X]:(happy(X))))&
((?[X]:((strong(X)&old(X))))<=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(![X]:((calm(X)<~>wise(X))=>(~patient(X)&~strong(X))))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(((~patient(mary)|~old(mary)))<=>(?[X]:(~humble(X))))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X))))&
((~rich(alice)&~wise(alice))) | ~strong(fred) | [
"p0",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3563698405030062271602623
% SZS output start Proof for 3563698405030062271602623
1. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (calm(X0) & wise(X0))) [input p0]
9. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p8]
13. ! [X0] : ((calm(X0) <~> wise(X0)) => (~strong(X0) & ~patient(X0))) [input p12]
25. ~strong(fred) [input hypothesis]
36. ! [X0] : ((~strong(X0) & ~patient(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 13]
39. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 1]
40. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 39]
54. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 54]
57. ! [X0] : ((~strong(X0) & ~patient(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 36]
82. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 40]
84. ~patient(X0) | calm(X0) | wise(X0) [cnf transformation 40]
85. ~wise(X0) | ~patient(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 40]
114. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 55]
116. tall(X0) | patient(X0) | tall(X0) [cnf transformation 55]
127. ~patient(X0) | calm(X0) | ~wise(X0) [cnf transformation 57]
152. ~strong(fred) [cnf transformation 25]
153. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 114]
154. tall(X0) | patient(X0) [duplicate literal removal 116]
159. ~patient(X0) | wise(X0) [duplicate literal removal 82]
160. ~calm(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 85]
255. strong(X0) | patient(X0) [subsumption resolution 153,154]
270. ~patient(X0) | calm(X0) [subsumption resolution 127,84]
276. 25 <=> patient(fred) [avatar definition]
278. patient(fred) <- (25) [avatar component clause 276]
352. patient(fred) [resolution 255,152]
357. 25 [avatar split clause 352,276]
361. wise(fred) <- (25) [resolution 278,159]
363. calm(fred) <- (25) [resolution 270,278]
446. ~patient(fred) | ~wise(fred) <- (25) [resolution 160,363]
449. ~wise(fred) <- (25) [subsumption resolution 446,278]
450. $false <- (25) [subsumption resolution 449,361]
451. ~25 [avatar contradiction clause 450]
458. $false [avatar sat refutation 357,451]
% SZS output end Proof for 3563698405030062271602623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or kind is wise or rich and vice versa.
Everyone who is not happy is creative or not funny and vice versa.
Everyone who is happy or not generous is tall and vice versa.
If someone is both not old and not wise then fred is happy.
Everyone who is either not generous or not happy is either humble or not brave.
If someone is calm then someone is both not happy and not brave and vice versa.
Everyone who is wise is either not tall or curious and vice versa.
If alice is not patient or generous then fred is not rich.
Everyone who is happy or not tall is not quiet and vice versa.
If lucy is both not humble and kind then susan is both not curious and happy and vice versa.
If john is either not quiet or not humble then someone is strong.
Everyone who is either happy or creative is tall and vice versa.
Everyone who is funny or not rich is either old or not calm and vice versa.
If someone is both not happy and not humble then someone is not tall or not old.
Everyone who is not patient is not tall or not creative and vice versa.
Everyone who is strong is either not rich or not strong and vice versa.
Someone is both not tall and generous.
John is either old or not humble.
Mary is not quiet or not wise.
Alice is not wise or not humble.
Someone is either not wise or strong.
Alice is not patient or patient.
Someone is not strong.
Mary is both humble and happy. | Mary is not tall. | contradiction | (![X]:((~happy(X)|kind(X))<=>(wise(X)|rich(X))))&
(![X]:(~happy(X)<=>(creative(X)|~funny(X))))&
(![X]:((happy(X)|~generous(X))<=>tall(X)))&
((?[X]:((~old(X)&~wise(X))))=>(happy(fred)))&
(![X]:((~generous(X)<~>~happy(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(wise(X)<=>(~tall(X)<~>curious(X))))&
(((~patient(alice)|generous(alice)))=>(~rich(fred)))&
(![X]:((happy(X)|~tall(X))<=>~quiet(X)))&
(((~humble(lucy)&kind(lucy)))<=>((~curious(susan)&happy(susan))))&
(((~quiet(john)<~>~humble(john)))=>(?[X]:(strong(X))))&
(![X]:((happy(X)<~>creative(X))<=>tall(X)))&
(![X]:((funny(X)|~rich(X))<=>(old(X)<~>~calm(X))))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~tall(X)|~old(X)))))&
(![X]:(~patient(X)<=>(~tall(X)|~creative(X))))&
(![X]:(strong(X)<=>(~rich(X)<~>~strong(X))))&
(?[X]:((~tall(X)&generous(X))))&
((old(john)<~>~humble(john)))&
((~quiet(mary)|~wise(mary)))&
((~wise(alice)|~humble(alice)))&
(?[X]:((~wise(X)<~>strong(X))))&
((~patient(alice)|patient(alice)))&
(?[X]:(~strong(X)))&
((humble(mary)&happy(mary))) | ~tall(mary) | [
"p2",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 4942026858708453809967700
% SZS output start Proof for 4942026858708453809967700
3. ! [X0] : ((~generous(X0) | happy(X0)) <=> tall(X0)) [input p2]
24. happy(mary) & humble(mary) [input p23]
25. ~tall(mary) [input hypothesis]
37. ! [X0] : (((~generous(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 3]
38. ! [X0] : ((~generous(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (generous(X0) & ~happy(X0)))) [flattening 37]
77. ~happy(X0) | tall(X0) [cnf transformation 38]
132. happy(mary) [cnf transformation 24]
133. ~tall(mary) [cnf transformation 25]
264. tall(mary) [resolution 77,132]
266. $false [subsumption resolution 264,133]
% SZS output end Proof for 4942026858708453809967700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is both not generous and wise.
Everyone who is both brave and strong is not kind and vice versa.
Everyone who is either not generous or funny is either not creative or not kind and vice versa.
If susan is not strong then someone is old or not humble and vice versa.
If fred is not curious 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.
If lucy is not happy then someone is either not calm or tall.
If lucy is either not funny or not happy then someone is either not rich or kind and vice versa.
Everyone who is calm or not old is patient and vice versa.
Everyone who is either generous or patient is brave or not funny.
If john is calm then john is brave and vice versa.
Lucy is both quiet and kind.
Mary is both not generous and not brave.
Someone is either not kind or not quiet.
Someone is kind or quiet.
Fred is either creative or not old.
Mary is both quiet and not wise.
Alice is either wise or not curious.
Someone is either not strong or calm. | Fred is quiet. | neutral | (![X]:(tall(X)=>(~generous(X)&wise(X))))&
(![X]:((brave(X)&strong(X))<=>~kind(X)))&
(![X]:((~generous(X)<~>funny(X))<=>(~creative(X)<~>~kind(X))))&
((~strong(susan))<=>(?[X]:((old(X)|~humble(X)))))&
((~curious(fred))<=>(?[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))))&
((~happy(lucy))=>(?[X]:((~calm(X)<~>tall(X)))))&
(((~funny(lucy)<~>~happy(lucy)))<=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((calm(X)|~old(X))<=>patient(X)))&
(![X]:((generous(X)<~>patient(X))=>(brave(X)|~funny(X))))&
((calm(john))<=>(brave(john)))&
((quiet(lucy)&kind(lucy)))&
((~generous(mary)&~brave(mary)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
(?[X]:((kind(X)|quiet(X))))&
((creative(fred)<~>~old(fred)))&
((quiet(mary)&~wise(mary)))&
((wise(alice)<~>~curious(alice)))&
(?[X]:((~strong(X)<~>calm(X)))) | quiet(fred) | []
| null | 0 |
Everyone who is not rich is either not old or not rich and vice versa.
Everyone who is either not rich or not kind is either not brave or not funny and vice versa.
Everyone who is not kind or not funny is old or funny and vice versa.
If someone is funny then someone is either curious or not kind.
Everyone who is not strong or not funny is either not creative or tall and vice versa.
Everyone who is not tall or patient is both tall and not calm and vice versa.
Everyone who is either not strong or old is either not tall or kind and vice versa.
If john is both strong and not patient then lucy is either not tall or not kind.
Everyone who is not old is both tall and curious and vice versa.
If someone is not creative then someone is funny or rich and vice versa.
Everyone who is both not strong and not rich is either not wise or not funny.
Everyone who is not strong is both old and not patient and vice versa.
If susan is either not strong or quiet then alice is not tall or wise and vice versa.
Everyone who is either kind or not creative is generous or kind.
Everyone who is either wise or not brave is either calm or not calm.
If susan is calm then someone is either not patient or not kind.
Alice is not happy.
Someone is both not quiet and brave.
John is both creative and not curious.
Someone is either old or generous.
Someone is tall.
John is not rich.
Someone is not brave. | Lucy is rich. | contradiction | (![X]:(~rich(X)<=>(~old(X)<~>~rich(X))))&
(![X]:((~rich(X)<~>~kind(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:((~kind(X)|~funny(X))<=>(old(X)|funny(X))))&
((?[X]:(funny(X)))=>(?[X]:((curious(X)<~>~kind(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((~tall(X)|patient(X))<=>(tall(X)&~calm(X))))&
(![X]:((~strong(X)<~>old(X))<=>(~tall(X)<~>kind(X))))&
(((strong(john)&~patient(john)))=>((~tall(lucy)<~>~kind(lucy))))&
(![X]:(~old(X)<=>(tall(X)&curious(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~strong(X)&~rich(X))=>(~wise(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(old(X)&~patient(X))))&
(((~strong(susan)<~>quiet(susan)))<=>((~tall(alice)|wise(alice))))&
(![X]:((kind(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((wise(X)<~>~brave(X))=>(calm(X)<~>~calm(X))))&
((calm(susan))=>(?[X]:((~patient(X)<~>~kind(X)))))&
(~happy(alice))&
(?[X]:((~quiet(X)&brave(X))))&
((creative(john)&~curious(john)))&
(?[X]:((old(X)<~>generous(X))))&
(?[X]:(tall(X)))&
(~rich(john))&
(?[X]:(~brave(X))) | rich(lucy) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 568457059630086781108547
% SZS output start Proof for 568457059630086781108547
1. ! [X0] : (~rich(X0) <=> (~old(X0) <~> ~rich(X0))) [input p0]
3. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (funny(X0) | old(X0))) [input p2]
5. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> (~creative(X0) <~> tall(X0))) [input p4]
6. ! [X0] : ((patient(X0) | ~tall(X0)) <=> (~calm(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~strong(X0) <~> old(X0)) <=> (~tall(X0) <~> kind(X0))) [input p6]
10. ? [X0] : ~creative(X0) <=> ? [X0] : (rich(X0) | funny(X0)) [input p9]
24. rich(lucy) [input hypothesis]
26. ? [X0] : ~creative(X0) <=> ? [X1] : (rich(X1) | funny(X1)) [rectify 10]
37. ! [X0] : ((~rich(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0)))) & (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | rich(X0))) [nnf transformation 1]
39. ! [X0] : (((~funny(X0) | ~kind(X0)) | (~funny(X0) & ~old(X0))) & ((funny(X0) | old(X0)) | (funny(X0) & kind(X0)))) [nnf transformation 3]
40. ! [X0] : ((~funny(X0) | ~kind(X0) | (~funny(X0) & ~old(X0))) & (funny(X0) | old(X0) | (funny(X0) & kind(X0)))) [flattening 39]
45. ! [X0] : (((~funny(X0) | ~strong(X0)) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) & (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (funny(X0) & strong(X0)))) [nnf transformation 5]
46. ! [X0] : ((~funny(X0) | ~strong(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) & (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (funny(X0) & strong(X0)))) [flattening 45]
47. ! [X0] : (((patient(X0) | ~tall(X0)) | (calm(X0) | ~tall(X0))) & ((~calm(X0) & tall(X0)) | (~patient(X0) & tall(X0)))) [nnf transformation 6]
48. ! [X0] : ((patient(X0) | ~tall(X0) | calm(X0) | ~tall(X0)) & ((~calm(X0) & tall(X0)) | (~patient(X0) & tall(X0)))) [flattening 47]
49. ! [X0] : ((((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0))))) [nnf transformation 7]
53. (? [X0] : ~creative(X0) | ! [X1] : (~rich(X1) & ~funny(X1))) & (? [X1] : (rich(X1) | funny(X1)) | ! [X0] : creative(X0)) [nnf transformation 26]
54. (? [X0] : ~creative(X0) | ! [X1] : (~rich(X1) & ~funny(X1))) & (? [X2] : (rich(X2) | funny(X2)) | ! [X3] : creative(X3)) [rectify 53]
55. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
56. ? [X2] : (rich(X2) | funny(X2)) => (rich(sK2) | funny(sK2)) [choice axiom]
57. (~creative(sK1) | ! [X1] : (~rich(X1) & ~funny(X1))) & ((rich(sK2) | funny(sK2)) | ! [X3] : creative(X3)) [skolemisation 54,56,55]
78. rich(X0) | old(X0) | rich(X0) [cnf transformation 37]
79. ~rich(X0) | ~rich(X0) | old(X0) [cnf transformation 37]
92. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 40]
97. ~tall(X0) | creative(X0) | strong(X0) [cnf transformation 46]
98. ~tall(X0) | creative(X0) | funny(X0) [cnf transformation 46]
101. tall(X0) | tall(X0) [cnf transformation 48]
107. kind(X0) | ~tall(X0) | ~strong(X0) | ~old(X0) [cnf transformation 49]
121. ~creative(sK1) | ~rich(X1) [cnf transformation 57]
150. rich(lucy) [cnf transformation 24]
152. tall(X0) [duplicate literal removal 101]
155. ~funny(X0) | ~kind(X0) [duplicate literal removal 92]
156. rich(X0) | old(X0) [duplicate literal removal 78]
157. ~rich(X0) | old(X0) [duplicate literal removal 79]
158. old(X0) [subsumption resolution 156,157]
174. kind(X0) | ~strong(X0) | ~old(X0) [subsumption resolution 107,152]
175. ~strong(X0) | kind(X0) [subsumption resolution 174,158]
193. 7 <=> ! [X1] : ~rich(X1) [avatar definition]
194. ~rich(X1) <- (7) [avatar component clause 193]
196. 8 <=> creative(sK1) [avatar definition]
198. ~creative(sK1) <- (~8) [avatar component clause 196]
199. 7 | ~8 [avatar split clause 121,196,193]
253. creative(X0) | strong(X0) [resolution 97,152]
254. creative(X0) | funny(X0) [resolution 98,152]
291. 22 <=> funny(sK1) [avatar definition]
293. funny(sK1) <- (22) [avatar component clause 291]
303. strong(sK1) <- (~8) [resolution 198,253]
322. kind(sK1) <- (~8) [resolution 303,175]
376. funny(sK1) <- (~8) [resolution 254,198]
378. 22 | 8 [avatar split clause 376,196,291]
484. ~kind(sK1) <- (22) [resolution 293,155]
488. $false <- (~8, 22) [subsumption resolution 484,322]
489. 8 | ~22 [avatar contradiction clause 488]
514. $false <- (7) [resolution 194,150]
517. ~7 [avatar contradiction clause 514]
518. $false [avatar sat refutation 199,378,489,517]
% SZS output end Proof for 568457059630086781108547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not kind is either not quiet or old.
If mary is both brave and wise then someone is either not happy or creative.
Everyone who is not curious is both patient and not calm and vice versa.
If someone is not calm then someone is both not funny and generous and vice versa.
If someone is either not curious or not calm then someone is not generous.
Everyone who is funny is both old and not curious and vice versa.
If someone is both not tall and not calm then someone is either humble or quiet and vice versa.
If john is either not patient or not curious then someone is not wise and vice versa.
Everyone who is both creative and happy is not creative and vice versa.
If someone is not wise or curious then someone is either strong or creative and vice versa.
Everyone who is not generous or not funny is not calm or brave.
If susan is not curious or not kind then paul is kind.
If someone is not kind then fred is not funny and vice versa.
Everyone who is both quiet and not calm is both quiet and brave.
Everyone who is patient or not quiet is both happy and not strong.
Susan is both rich and not kind.
Paul is creative or not creative.
Lucy is both curious and not strong.
Someone is both rich and not happy.
Someone is not patient or not wise.
Someone is not brave or not calm. | Mary is not curious. | contradiction | (![X]:((happy(X)&~kind(X))=>(~quiet(X)<~>old(X))))&
(((brave(mary)&wise(mary)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:(~curious(X)<=>(patient(X)&~calm(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((~curious(X)<~>~calm(X))))=>(?[X]:(~generous(X))))&
(![X]:(funny(X)<=>(old(X)&~curious(X))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:((humble(X)<~>quiet(X)))))&
(((~patient(john)<~>~curious(john)))<=>(?[X]:(~wise(X))))&
(![X]:((creative(X)&happy(X))<=>~creative(X)))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((~generous(X)|~funny(X))=>(~calm(X)|brave(X))))&
(((~curious(susan)|~kind(susan)))=>(kind(paul)))&
((?[X]:(~kind(X)))<=>(~funny(fred)))&
(![X]:((quiet(X)&~calm(X))=>(quiet(X)&brave(X))))&
(![X]:((patient(X)|~quiet(X))=>(happy(X)&~strong(X))))&
((rich(susan)&~kind(susan)))&
((creative(paul)|~creative(paul)))&
((curious(lucy)&~strong(lucy)))&
(?[X]:((rich(X)&~happy(X))))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:((~brave(X)|~calm(X)))) | ~curious(mary) | [
"p2",
"p8",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 668491530357291967869793
% SZS output start Proof for 668491530357291967869793
3. ! [X0] : (~curious(X0) <=> (~calm(X0) & patient(X0))) [input p2]
9. ! [X0] : ((happy(X0) & creative(X0)) <=> ~creative(X0)) [input p8]
15. ! [X0] : ((~quiet(X0) | patient(X0)) => (~strong(X0) & happy(X0))) [input p14]
22. ~curious(mary) [input hypothesis]
39. ! [X0] : ((~strong(X0) & happy(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 15]
44. ! [X0] : ((~curious(X0) | (calm(X0) | ~patient(X0))) & ((~calm(X0) & patient(X0)) | curious(X0))) [nnf transformation 3]
45. ! [X0] : ((~curious(X0) | calm(X0) | ~patient(X0)) & ((~calm(X0) & patient(X0)) | curious(X0))) [flattening 44]
66. ! [X0] : (((happy(X0) & creative(X0)) | creative(X0)) & (~creative(X0) | (~happy(X0) | ~creative(X0)))) [nnf transformation 9]
67. ! [X0] : (((happy(X0) & creative(X0)) | creative(X0)) & (~creative(X0) | ~happy(X0) | ~creative(X0))) [flattening 66]
87. patient(X0) | curious(X0) [cnf transformation 45]
108. ~creative(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 67]
109. creative(X0) | creative(X0) [cnf transformation 67]
125. happy(X0) | ~patient(X0) [cnf transformation 39]
136. ~curious(mary) [cnf transformation 22]
137. ~creative(X0) | ~happy(X0) [duplicate literal removal 108]
138. creative(X0) [duplicate literal removal 109]
237. ~happy(X0) [subsumption resolution 137,138]
290. ~patient(X0) [subsumption resolution 125,237]
305. curious(X0) [resolution 87,290]
306. $false [resolution 305,136]
% SZS output end Proof for 668491530357291967869793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or old is either funny or not funny.
Everyone who is both curious and happy is not patient.
Everyone who is curious is both patient and kind and vice versa.
Everyone who is not brave or happy is old or not strong and vice versa.
If someone is both not strong and not quiet then someone is either funny or not curious.
Everyone who is not old is happy or not quiet and vice versa.
If fred is not old or not generous then someone is rich or quiet.
Everyone who is both not quiet and not old is both not happy and creative.
Everyone who is either not funny or not rich is curious and vice versa.
If someone is creative then someone is either not tall or patient and vice versa.
Everyone who is both happy and curious is not happy or curious and vice versa.
Everyone who is not curious is both not generous and not humble.
If someone is either patient or funny then someone is either brave or wise and vice versa.
Everyone who is not creative is not patient.
If someone is not old then someone is both not brave and not tall.
Everyone who is both calm and not old is either brave or not tall.
Lucy is brave or not patient.
Someone is either not quiet or rich.
Someone is creative or not generous.
Alice is old or not tall.
Alice is both patient and calm.
Susan is either funny or humble.
Someone is not generous or not rich. | Alice is not kind. | entailment | (![X]:((wise(X)|old(X))=>(funny(X)<~>~funny(X))))&
(![X]:((curious(X)&happy(X))=>~patient(X)))&
(![X]:(curious(X)<=>(patient(X)&kind(X))))&
(![X]:((~brave(X)|happy(X))<=>(old(X)|~strong(X))))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:(~old(X)<=>(happy(X)|~quiet(X))))&
(((~old(fred)|~generous(fred)))=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((~quiet(X)&~old(X))=>(~happy(X)&creative(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>curious(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)<~>patient(X)))))&
(![X]:((happy(X)&curious(X))<=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
((brave(lucy)|~patient(lucy)))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:((creative(X)|~generous(X))))&
((old(alice)|~tall(alice)))&
((patient(alice)&calm(alice)))&
((funny(susan)<~>humble(susan)))&
(?[X]:((~generous(X)|~rich(X)))) | ~kind(alice) | [
"p1",
"p2",
"p10",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 377299614970606504744211
% SZS output start Proof for 377299614970606504744211
2. ! [X0] : ((happy(X0) & curious(X0)) => ~patient(X0)) [input p1]
3. ! [X0] : (curious(X0) <=> (kind(X0) & patient(X0))) [input p2]
11. ! [X0] : ((curious(X0) & happy(X0)) <=> (curious(X0) | ~happy(X0))) [input p10]
21. calm(alice) & patient(alice) [input p20]
24. kind(alice) [input hypothesis]
30. ! [X0] : (~patient(X0) | (~happy(X0) | ~curious(X0))) [ennf transformation 2]
31. ! [X0] : (~patient(X0) | ~happy(X0) | ~curious(X0)) [flattening 30]
42. ! [X0] : ((curious(X0) | (~kind(X0) | ~patient(X0))) & ((kind(X0) & patient(X0)) | ~curious(X0))) [nnf transformation 3]
43. ! [X0] : ((curious(X0) | ~kind(X0) | ~patient(X0)) & ((kind(X0) & patient(X0)) | ~curious(X0))) [flattening 42]
60. ! [X0] : (((curious(X0) & happy(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (~curious(X0) | ~happy(X0)))) [nnf transformation 11]
61. ! [X0] : (((curious(X0) & happy(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | ~curious(X0) | ~happy(X0))) [flattening 60]
83. ~patient(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 31]
86. ~kind(X0) | curious(X0) | ~patient(X0) [cnf transformation 43]
110. happy(X0) | ~curious(X0) [cnf transformation 61]
111. happy(X0) | curious(X0) [cnf transformation 61]
133. patient(alice) [cnf transformation 21]
138. kind(alice) [cnf transformation 24]
199. happy(X0) [subsumption resolution 110,111]
311. ~happy(alice) | ~curious(alice) [resolution 83,133]
313. ~curious(alice) [subsumption resolution 311,199]
317. curious(alice) | ~patient(alice) [resolution 86,138]
318. ~patient(alice) [subsumption resolution 317,313]
319. $false [subsumption resolution 318,133]
% SZS output end Proof for 377299614970606504744211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not funny then someone is not brave and vice versa. Everyone who is either not wise or not old is generous or not strong. Everyone who is not curious or not rich is either not strong or not patient and vice versa. Everyone who is funny is brave or not generous and vice versa. If someone is not rich then lucy is not curious. If paul is happy then alice is calm or curious and vice versa. If someone is either not curious or kind then someone is either curious or calm. Everyone who is both not quiet and rich is both happy and kind. Everyone who is happy or old is both not quiet and not strong and vice versa. Everyone who is either not happy or not kind is funny and vice versa. If paul is either tall or not curious then paul is both brave and not strong and vice versa. Everyone who is both not happy and curious is generous or curious and vice versa. If paul is either not funny or tall then john is not calm and vice versa. If someone is both curious and not curious then paul is both not humble and tall and vice versa. If paul is not funny or not patient then someone is both quiet and funny and vice versa. If someone is both not creative and happy then mary is either curious or creative. Someone is both not old and not humble. Lucy is both not wise and patient. Someone is either kind or calm. John is both not generous and rich. Lucy is not brave. Someone is either rich or not generous. Someone is both not wise and calm. | Lucy is not funny. | neutral | ((?[X]:((tall(X)&~funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~wise(X)<~>~old(X))=>(generous(X)|~strong(X))))&
(![X]:((~curious(X)|~rich(X))<=>(~strong(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(brave(X)|~generous(X))))&
((?[X]:(~rich(X)))=>(~curious(lucy)))&
((happy(paul))<=>((calm(alice)|curious(alice))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((~quiet(X)&rich(X))=>(happy(X)&kind(X))))&
(![X]:((happy(X)|old(X))<=>(~quiet(X)&~strong(X))))&
(![X]:((~happy(X)<~>~kind(X))<=>funny(X)))&
(((tall(paul)<~>~curious(paul)))<=>((brave(paul)&~strong(paul))))&
(![X]:((~happy(X)&curious(X))<=>(generous(X)|curious(X))))&
(((~funny(paul)<~>tall(paul)))<=>(~calm(john)))&
((?[X]:((curious(X)&~curious(X))))<=>((~humble(paul)&tall(paul))))&
(((~funny(paul)|~patient(paul)))<=>(?[X]:((quiet(X)&funny(X)))))&
((?[X]:((~creative(X)&happy(X))))=>((curious(mary)<~>creative(mary))))&
(?[X]:((~old(X)&~humble(X))))&
((~wise(lucy)&patient(lucy)))&
(?[X]:((kind(X)<~>calm(X))))&
((~generous(john)&rich(john)))&
(~brave(lucy))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((~wise(X)&calm(X)))) | ~funny(lucy) | []
| null | 0 |
If someone is either not patient or not strong then john is not tall and vice versa. If paul is either not brave or not happy then someone is both curious and generous and vice versa. If fred is either generous or happy then susan is brave. Everyone who is quiet or creative is either not brave or quiet and vice versa. Everyone who is either not wise or not humble is either wise or not kind. Everyone who is not strong is not old or calm. If someone is either calm or old then someone is either not generous or not old. Everyone who is both not quiet and not happy is not brave. If fred is either happy or not calm then mary is both quiet and not creative and vice versa. Everyone who is either creative or not brave is not patient. If alice is old or not generous then alice is either strong or not brave and vice versa. Everyone who is not strong or patient is patient and vice versa. If someone is wise or brave then alice is both not curious and calm. If someone is both not happy and calm then john is either tall or not patient and vice versa. If john is not humble then mary is not rich or humble and vice versa. Everyone who is either old or tall is not humble. Mary is not tall. Someone is both not calm and funny. Someone is humble. Alice is not calm. Someone is both not generous and happy. Mary is humble or not tall. Mary is patient. Someone is both not humble and creative. | Mary is not quiet. | entailment | ((?[X]:((~patient(X)<~>~strong(X))))<=>(~tall(john)))&
(((~brave(paul)<~>~happy(paul)))<=>(?[X]:((curious(X)&generous(X)))))&
(((generous(fred)<~>happy(fred)))=>(brave(susan)))&
(![X]:((quiet(X)|creative(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:((~wise(X)<~>~humble(X))=>(wise(X)<~>~kind(X))))&
(![X]:(~strong(X)=>(~old(X)|calm(X))))&
((?[X]:((calm(X)<~>old(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
(![X]:((~quiet(X)&~happy(X))=>~brave(X)))&
(((happy(fred)<~>~calm(fred)))<=>((quiet(mary)&~creative(mary))))&
(![X]:((creative(X)<~>~brave(X))=>~patient(X)))&
(((old(alice)|~generous(alice)))<=>((strong(alice)<~>~brave(alice))))&
(![X]:((~strong(X)|patient(X))<=>patient(X)))&
((?[X]:((wise(X)|brave(X))))=>((~curious(alice)&calm(alice))))&
((?[X]:((~happy(X)&calm(X))))<=>((tall(john)<~>~patient(john))))&
((~humble(john))<=>((~rich(mary)|humble(mary))))&
(![X]:((old(X)<~>tall(X))=>~humble(X)))&
(~tall(mary))&
(?[X]:((~calm(X)&funny(X))))&
(?[X]:(humble(X)))&
(~calm(alice))&
(?[X]:((~generous(X)&happy(X))))&
((humble(mary)|~tall(mary)))&
(patient(mary))&
(?[X]:((~humble(X)&creative(X)))) | ~quiet(mary) | [
"p3",
"p12",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7717261848564369684607922
% SZS output start Proof for 7717261848564369684607922
4. ! [X0] : ((creative(X0) | quiet(X0)) <=> (~brave(X0) <~> quiet(X0))) [input p3]
13. ? [X0] : (brave(X0) | wise(X0)) => (calm(alice) & ~curious(alice)) [input p12]
20. ~calm(alice) [input p19]
25. quiet(mary) [input hypothesis]
36. (calm(alice) & ~curious(alice)) | ! [X0] : (~brave(X0) & ~wise(X0)) [ennf transformation 13]
47. ! [X0] : (((creative(X0) | quiet(X0)) | ((~brave(X0) | ~quiet(X0)) & (quiet(X0) | brave(X0)))) & (((~quiet(X0) | brave(X0)) & (quiet(X0) | ~brave(X0))) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 4]
48. ! [X0] : ((creative(X0) | quiet(X0) | ((~brave(X0) | ~quiet(X0)) & (quiet(X0) | brave(X0)))) & (((~quiet(X0) | brave(X0)) & (quiet(X0) | ~brave(X0))) | (~creative(X0) & ~quiet(X0)))) [flattening 47]
90. ~quiet(X0) | brave(X0) | ~quiet(X0) [cnf transformation 48]
124. calm(alice) | ~brave(X0) [cnf transformation 36]
139. ~calm(alice) [cnf transformation 20]
146. quiet(mary) [cnf transformation 25]
149. ~quiet(X0) | brave(X0) [duplicate literal removal 90]
231. 18 <=> quiet(mary) [avatar definition]
232. quiet(mary) <- (18) [avatar component clause 231]
271. 25 <=> ! [X0] : ~brave(X0) [avatar definition]
272. ~brave(X0) <- (25) [avatar component clause 271]
274. 26 <=> calm(alice) [avatar definition]
277. 25 | 26 [avatar split clause 124,274,271]
324. ~26 [avatar split clause 139,274]
325. 18 [avatar split clause 146,231]
328. brave(mary) <- (18) [resolution 149,232]
329. $false <- (18, 25) [subsumption resolution 328,272]
330. ~18 | ~25 [avatar contradiction clause 329]
331. $false [avatar sat refutation 277,324,325,330]
% SZS output end Proof for 7717261848564369684607922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is creative and vice versa.
If someone is both wise and not patient then someone is not quiet or not brave and vice versa.
If john is tall or not funny then alice is wise or not creative and vice versa.
If someone is both funny and wise then alice is either not patient or not wise.
Everyone who is not brave or not old is not calm and vice versa.
Everyone who is either not tall or curious is both strong and not creative and vice versa.
If fred is not funny then paul is not old.
If fred is either rich or humble then someone is strong or rich.
Everyone who is either quiet or calm is kind and vice versa.
Everyone who is both curious and not patient is tall.
Everyone who is both not generous and not rich is both calm and not creative and vice versa.
Everyone who is either wise or humble is both not curious and not wise and vice versa.
If paul is either not happy or not quiet then someone is patient and vice versa.
Everyone who is not calm is either not happy or not wise and vice versa.
Everyone who is not tall or not humble is both strong and generous and vice versa.
If mary is either quiet or not brave then paul is rich.
Someone is not kind or not curious.
Mary is not tall.
Lucy is either not funny or quiet.
Someone is not creative or not funny.
Someone is old or brave.
Susan is not strong or not kind.
Someone is not old or generous. | Paul is not generous. | neutral | (![X]:(~strong(X)<=>creative(X)))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((~quiet(X)|~brave(X)))))&
(((tall(john)|~funny(john)))<=>((wise(alice)|~creative(alice))))&
((?[X]:((funny(X)&wise(X))))=>((~patient(alice)<~>~wise(alice))))&
(![X]:((~brave(X)|~old(X))<=>~calm(X)))&
(![X]:((~tall(X)<~>curious(X))<=>(strong(X)&~creative(X))))&
((~funny(fred))=>(~old(paul)))&
(((rich(fred)<~>humble(fred)))=>(?[X]:((strong(X)|rich(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>kind(X)))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~generous(X)&~rich(X))<=>(calm(X)&~creative(X))))&
(![X]:((wise(X)<~>humble(X))<=>(~curious(X)&~wise(X))))&
(((~happy(paul)<~>~quiet(paul)))<=>(?[X]:(patient(X))))&
(![X]:(~calm(X)<=>(~happy(X)<~>~wise(X))))&
(![X]:((~tall(X)|~humble(X))<=>(strong(X)&generous(X))))&
(((quiet(mary)<~>~brave(mary)))=>(rich(paul)))&
(?[X]:((~kind(X)|~curious(X))))&
(~tall(mary))&
((~funny(lucy)<~>quiet(lucy)))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((old(X)|brave(X))))&
((~strong(susan)|~kind(susan)))&
(?[X]:((~old(X)|generous(X)))) | ~generous(paul) | []
| null | 0 |
If someone is not curious or calm then someone is not humble.
Everyone who is either not curious or generous is not happy and vice versa.
Everyone who is either not funny or not humble is either not kind or kind and vice versa.
Everyone who is not funny is either not humble or not creative and vice versa.
If someone is both not happy and strong then alice is both generous and not strong.
Everyone who is curious or not generous is both not creative and not strong.
Everyone who is wise or strong is creative and vice versa.
Everyone who is both happy and not calm is not curious and vice versa.
Everyone who is both not calm and calm is both wise and not happy and vice versa.
Everyone who is not tall is both not kind and quiet.
If someone is either not happy or funny then someone is patient and vice versa.
Everyone who is not quiet is both brave and not generous and vice versa.
Everyone who is either not rich or strong is either funny or rich and vice versa.
Everyone who is kind or humble is not strong or funny and vice versa.
If paul is not curious or not humble then john is either not creative or not generous and vice versa.
If someone is happy then alice is rich or happy.
Someone is both quiet and rich.
Susan is either humble or not curious.
Someone is quiet.
Alice is either curious or not rich.
Someone is not brave.
Alice is not humble or not kind. | Paul is kind. | entailment | ((?[X]:((~curious(X)|calm(X))))=>(?[X]:(~humble(X))))&
(![X]:((~curious(X)<~>generous(X))<=>~happy(X)))&
(![X]:((~funny(X)<~>~humble(X))<=>(~kind(X)<~>kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~creative(X))))&
((?[X]:((~happy(X)&strong(X))))=>((generous(alice)&~strong(alice))))&
(![X]:((curious(X)|~generous(X))=>(~creative(X)&~strong(X))))&
(![X]:((wise(X)|strong(X))<=>creative(X)))&
(![X]:((happy(X)&~calm(X))<=>~curious(X)))&
(![X]:((~calm(X)&calm(X))<=>(wise(X)&~happy(X))))&
(![X]:(~tall(X)=>(~kind(X)&quiet(X))))&
((?[X]:((~happy(X)<~>funny(X))))<=>(?[X]:(patient(X))))&
(![X]:(~quiet(X)<=>(brave(X)&~generous(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(funny(X)<~>rich(X))))&
(![X]:((kind(X)|humble(X))<=>(~strong(X)|funny(X))))&
(((~curious(paul)|~humble(paul)))<=>((~creative(john)<~>~generous(john))))&
((?[X]:(happy(X)))=>((rich(alice)|happy(alice))))&
(?[X]:((quiet(X)&rich(X))))&
((humble(susan)<~>~curious(susan)))&
(?[X]:(quiet(X)))&
((curious(alice)<~>~rich(alice)))&
(?[X]:(~brave(X)))&
((~humble(alice)|~kind(alice))) | kind(paul) | [
"p2",
"p3",
"p6",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 7714336750242129398547387
% SZS output start Proof for 7714336750242129398547387
3. ! [X0] : ((~funny(X0) <~> ~humble(X0)) <=> (~kind(X0) <~> kind(X0))) [input p2]
4. ! [X0] : (~funny(X0) <=> (~humble(X0) <~> ~creative(X0))) [input p3]
7. ! [X0] : ((strong(X0) | wise(X0)) <=> creative(X0)) [input p6]
13. ! [X0] : ((~rich(X0) <~> strong(X0)) <=> (funny(X0) <~> rich(X0))) [input p12]
14. ! [X0] : ((humble(X0) | kind(X0)) <=> (funny(X0) | ~strong(X0))) [input p13]
23. ~kind(paul) [input hypothesis]
42. ! [X0] : ((((humble(X0) | funny(X0)) & (~humble(X0) | ~funny(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0))))) [nnf transformation 3]
43. ! [X0] : ((~funny(X0) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) & (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | funny(X0))) [nnf transformation 4]
44. ! [X0] : (((strong(X0) | wise(X0)) | ~creative(X0)) & (creative(X0) | (~strong(X0) & ~wise(X0)))) [nnf transformation 7]
45. ! [X0] : ((strong(X0) | wise(X0) | ~creative(X0)) & (creative(X0) | (~strong(X0) & ~wise(X0)))) [flattening 44]
55. ! [X0] : ((((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0)))) & (((~rich(X0) | ~funny(X0)) & (rich(X0) | funny(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))))) [nnf transformation 13]
56. ! [X0] : (((humble(X0) | kind(X0)) | (~funny(X0) & strong(X0))) & ((funny(X0) | ~strong(X0)) | (~humble(X0) & ~kind(X0)))) [nnf transformation 14]
57. ! [X0] : ((humble(X0) | kind(X0) | (~funny(X0) & strong(X0))) & (funny(X0) | ~strong(X0) | (~humble(X0) & ~kind(X0)))) [flattening 56]
74. ~humble(X0) | ~funny(X0) | kind(X0) | kind(X0) [cnf transformation 42]
75. ~humble(X0) | ~funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
76. humble(X0) | funny(X0) | kind(X0) | kind(X0) [cnf transformation 42]
77. humble(X0) | funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
78. ~creative(X0) | ~humble(X0) | funny(X0) [cnf transformation 43]
80. ~funny(X0) | ~creative(X0) | humble(X0) [cnf transformation 43]
89. creative(X0) | ~strong(X0) [cnf transformation 45]
102. rich(X0) | funny(X0) | strong(X0) | rich(X0) [cnf transformation 55]
107. strong(X0) | ~rich(X0) | funny(X0) | ~rich(X0) [cnf transformation 55]
113. humble(X0) | kind(X0) | ~funny(X0) [cnf transformation 57]
127. ~kind(paul) [cnf transformation 23]
128. rich(X0) | funny(X0) | strong(X0) [duplicate literal removal 102]
130. strong(X0) | ~rich(X0) | funny(X0) [duplicate literal removal 107]
132. ~humble(X0) | ~funny(X0) | kind(X0) [duplicate literal removal 74]
133. ~humble(X0) | ~funny(X0) | ~kind(X0) [duplicate literal removal 75]
134. humble(X0) | funny(X0) | kind(X0) [duplicate literal removal 76]
135. humble(X0) | funny(X0) | ~kind(X0) [duplicate literal removal 77]
148. funny(X0) | humble(X0) [subsumption resolution 134,135]
149. ~funny(X0) | ~humble(X0) [subsumption resolution 132,133]
150. ~creative(X0) | ~funny(X0) [subsumption resolution 80,149]
151. ~creative(X0) | funny(X0) [subsumption resolution 78,148]
152. ~creative(X0) [subsumption resolution 151,150]
166. ~strong(X0) [subsumption resolution 89,152]
193. ~rich(X0) | funny(X0) [subsumption resolution 130,166]
194. rich(X0) | funny(X0) [subsumption resolution 128,166]
195. funny(X0) [subsumption resolution 194,193]
196. kind(X0) | humble(X0) [subsumption resolution 113,195]
263. ~humble(X1) [resolution 149,195]
265. humble(paul) [resolution 196,127]
271. $false [subsumption resolution 265,263]
% SZS output end Proof for 7714336750242129398547387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is not quiet. If lucy is either old or happy then mary is both strong and old and vice versa. If someone is generous or happy then fred is generous or not humble. Everyone who is either not calm or brave is not funny or curious and vice versa. Everyone who is either creative or wise is not rich or strong. If someone is quiet then someone is generous or not curious and vice versa. Everyone who is either brave or not old is either not strong or not funny and vice versa. If john is not old or brave then someone is either quiet or not quiet. Everyone who is not kind is not curious or not quiet and vice versa. If someone is tall then someone is both not old and kind. If fred is both not strong and not funny then someone is both not patient and old. Everyone who is either kind or not strong is either tall or strong and vice versa. Everyone who is either not strong or brave is not tall. Everyone who is not generous is both not brave and generous and vice versa. If someone is not calm then susan is either not curious or not creative and vice versa. Everyone who is both not strong and not quiet is both humble and happy and vice versa. Someone is strong. Fred is kind or not funny. Lucy is funny or wise. Someone is not creative or not brave. Someone is either happy or humble. | John is not tall. | neutral | (![X]:((calm(X)<~>~creative(X))=>~quiet(X)))&
(((old(lucy)<~>happy(lucy)))<=>((strong(mary)&old(mary))))&
((?[X]:((generous(X)|happy(X))))=>((generous(fred)|~humble(fred))))&
(![X]:((~calm(X)<~>brave(X))<=>(~funny(X)|curious(X))))&
(![X]:((creative(X)<~>wise(X))=>(~rich(X)|strong(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((brave(X)<~>~old(X))<=>(~strong(X)<~>~funny(X))))&
(((~old(john)|brave(john)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:(~kind(X)<=>(~curious(X)|~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~old(X)&kind(X)))))&
(((~strong(fred)&~funny(fred)))=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~strong(X)<~>brave(X))=>~tall(X)))&
(![X]:(~generous(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~calm(X)))<=>((~curious(susan)<~>~creative(susan))))&
(![X]:((~strong(X)&~quiet(X))<=>(humble(X)&happy(X))))&
(?[X]:(strong(X)))&
((kind(fred)|~funny(fred)))&
((funny(lucy)|wise(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((happy(X)<~>humble(X)))) | ~tall(john) | []
| null | 0 |
Everyone who is quiet is not humble or not curious and vice versa. Everyone who is not creative or not rich is either calm or funny and vice versa. If mary is either not quiet or not funny then someone is both not funny and calm and vice versa. Everyone who is not funny is not wise or not rich and vice versa. If someone is brave then john is tall or not strong. Everyone who is both rich and not calm is generous. Everyone who is quiet is either creative or not tall and vice versa. If someone is both not wise and not patient then someone is generous or creative and vice versa. If john is both not brave and humble then someone is patient. Everyone who is both not rich and not quiet is generous or curious and vice versa. Everyone who is both humble and patient is both not calm and wise and vice versa. If someone is not wise then paul is quiet. Everyone who is both tall and calm is tall and vice versa. Everyone who is either not old or tall is either patient or not kind and vice versa. If someone is not funny then someone is either not curious or not calm. Everyone who is strong or quiet is both patient and not strong. Fred is both old and not creative. Mary is either not brave or patient. Someone is not rich. Someone is not happy or not generous. Someone is creative. Someone is quiet or funny. Someone is either not kind or not humble. | John is not creative. | neutral | (![X]:(quiet(X)<=>(~humble(X)|~curious(X))))&
(![X]:((~creative(X)|~rich(X))<=>(calm(X)<~>funny(X))))&
(((~quiet(mary)<~>~funny(mary)))<=>(?[X]:((~funny(X)&calm(X)))))&
(![X]:(~funny(X)<=>(~wise(X)|~rich(X))))&
((?[X]:(brave(X)))=>((tall(john)|~strong(john))))&
(![X]:((rich(X)&~calm(X))=>generous(X)))&
(![X]:(quiet(X)<=>(creative(X)<~>~tall(X))))&
((?[X]:((~wise(X)&~patient(X))))<=>(?[X]:((generous(X)|creative(X)))))&
(((~brave(john)&humble(john)))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&~quiet(X))<=>(generous(X)|curious(X))))&
(![X]:((humble(X)&patient(X))<=>(~calm(X)&wise(X))))&
((?[X]:(~wise(X)))=>(quiet(paul)))&
(![X]:((tall(X)&calm(X))<=>tall(X)))&
(![X]:((~old(X)<~>tall(X))<=>(patient(X)<~>~kind(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~curious(X)<~>~calm(X)))))&
(![X]:((strong(X)|quiet(X))=>(patient(X)&~strong(X))))&
((old(fred)&~creative(fred)))&
((~brave(mary)<~>patient(mary)))&
(?[X]:(~rich(X)))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:(creative(X)))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((~kind(X)<~>~humble(X)))) | ~creative(john) | []
| null | 0 |
Everyone who is not creative or not wise is both curious and quiet and vice versa. Everyone who is both not brave and not generous is not rich or wise. Everyone who is both patient and brave is not creative or not quiet. If someone is either not wise or humble then alice is both curious and happy and vice versa. If someone is either not generous or generous then someone is tall or not old and vice versa. If fred is both old and wise then someone is wise or not funny. If lucy is kind then someone is either not humble or tall. Everyone who is not happy is either not quiet or funny and vice versa. If alice is funny or creative then someone is not humble and vice versa. Everyone who is either not brave or not humble is both not strong and not creative and vice versa. If someone is generous or not strong then susan is not tall or calm and vice versa. Everyone who is either not wise or not tall is kind. Everyone who is funny or tall is either kind or quiet. Everyone who is both happy and not curious is both not brave and not funny and vice versa. Everyone who is both humble and not funny is both curious and generous and vice versa. If someone is both quiet and humble then paul is creative or generous. Fred is not kind. Alice is not kind. Someone is both not curious and not calm. John is either funny or patient. Mary is either quiet or funny. Someone is patient. Paul is both not calm and kind. | John is not tall. | neutral | (![X]:((~creative(X)|~wise(X))<=>(curious(X)&quiet(X))))&
(![X]:((~brave(X)&~generous(X))=>(~rich(X)|wise(X))))&
(![X]:((patient(X)&brave(X))=>(~creative(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>humble(X))))<=>((curious(alice)&happy(alice))))&
((?[X]:((~generous(X)<~>generous(X))))<=>(?[X]:((tall(X)|~old(X)))))&
(((old(fred)&wise(fred)))=>(?[X]:((wise(X)|~funny(X)))))&
((kind(lucy))=>(?[X]:((~humble(X)<~>tall(X)))))&
(![X]:(~happy(X)<=>(~quiet(X)<~>funny(X))))&
(((funny(alice)|creative(alice)))<=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(~strong(X)&~creative(X))))&
((?[X]:((generous(X)|~strong(X))))<=>((~tall(susan)|calm(susan))))&
(![X]:((~wise(X)<~>~tall(X))=>kind(X)))&
(![X]:((funny(X)|tall(X))=>(kind(X)<~>quiet(X))))&
(![X]:((happy(X)&~curious(X))<=>(~brave(X)&~funny(X))))&
(![X]:((humble(X)&~funny(X))<=>(curious(X)&generous(X))))&
((?[X]:((quiet(X)&humble(X))))=>((creative(paul)|generous(paul))))&
(~kind(fred))&
(~kind(alice))&
(?[X]:((~curious(X)&~calm(X))))&
((funny(john)<~>patient(john)))&
((quiet(mary)<~>funny(mary)))&
(?[X]:(patient(X)))&
((~calm(paul)&kind(paul))) | ~tall(john) | []
| null | 0 |
If lucy is either old or quiet then someone is not funny. Everyone who is both not rich and not tall is not strong or funny and vice versa. Everyone who is both humble and not kind is kind and vice versa. Everyone who is patient is creative or not generous. Everyone who is brave or old is either not brave or not rich and vice versa. Everyone who is not kind is both not funny and not old and vice versa. Everyone who is not quiet is not patient or not kind. Everyone who is both not calm and not brave is both wise and rich and vice versa. Everyone who is both wise and happy is not creative. Everyone who is either strong or not old is either brave or strong. Everyone who is tall is not creative or wise. Everyone who is not strong or calm is not strong. Everyone who is not happy or creative is not curious or wise. Everyone who is either not creative or calm is either patient or not generous and vice versa. If fred is not generous or creative then alice is old and vice versa. Everyone who is either generous or rich is rich or generous. Someone is either not patient or not kind. John is not calm or rich. Lucy is either rich or not curious. Fred is not curious or not creative. Someone is not funny or brave. Someone is either not quiet or not calm. Someone is quiet. | Fred is not tall. | entailment | (((old(lucy)<~>quiet(lucy)))=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)&~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~strong(X)|calm(X))=>~strong(X)))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(((~generous(fred)|creative(fred)))<=>(old(alice)))&
(![X]:((generous(X)<~>rich(X))=>(rich(X)|generous(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
((~calm(john)|rich(john)))&
((rich(lucy)<~>~curious(lucy)))&
((~curious(fred)|~creative(fred)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:(quiet(X))) | ~tall(fred) | [
"p1",
"p2",
"p3",
"p5",
"p11",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5506982204182174481944379
% SZS output start Proof for 5506982204182174481944379
2. ! [X0] : ((~tall(X0) & ~rich(X0)) <=> (funny(X0) | ~strong(X0))) [input p1]
3. ! [X0] : ((~kind(X0) & humble(X0)) <=> kind(X0)) [input p2]
4. ! [X0] : (patient(X0) => (~generous(X0) | creative(X0))) [input p3]
6. ! [X0] : (~kind(X0) <=> (~old(X0) & ~funny(X0))) [input p5]
12. ! [X0] : ((calm(X0) | ~strong(X0)) => ~strong(X0)) [input p11]
14. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> (patient(X0) <~> ~generous(X0))) [input p13]
15. (creative(fred) | ~generous(fred)) <=> old(alice) [input p14]
24. tall(fred) [input hypothesis]
26. ! [X0] : ((~generous(X0) | creative(X0)) | ~patient(X0)) [ennf transformation 4]
27. ! [X0] : (~generous(X0) | creative(X0) | ~patient(X0)) [flattening 26]
35. ! [X0] : (~strong(X0) | (~calm(X0) & strong(X0))) [ennf transformation 12]
43. ! [X0] : (((~tall(X0) & ~rich(X0)) | (~funny(X0) & strong(X0))) & ((funny(X0) | ~strong(X0)) | (tall(X0) | rich(X0)))) [nnf transformation 2]
44. ! [X0] : (((~tall(X0) & ~rich(X0)) | (~funny(X0) & strong(X0))) & (funny(X0) | ~strong(X0) | tall(X0) | rich(X0))) [flattening 43]
45. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 3]
46. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~humble(X0))) [flattening 45]
49. ! [X0] : ((~kind(X0) | (old(X0) | funny(X0))) & ((~old(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 6]
50. ! [X0] : ((~kind(X0) | old(X0) | funny(X0)) & ((~old(X0) & ~funny(X0)) | kind(X0))) [flattening 49]
54. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 14]
55. ((creative(fred) | ~generous(fred)) | ~old(alice)) & (old(alice) | (~creative(fred) & generous(fred))) [nnf transformation 15]
56. (creative(fred) | ~generous(fred) | ~old(alice)) & (old(alice) | (~creative(fred) & generous(fred))) [flattening 55]
74. ~tall(X0) | strong(X0) [cnf transformation 44]
78. ~kind(X0) | ~kind(X0) [cnf transformation 46]
79. ~generous(X0) | creative(X0) | ~patient(X0) [cnf transformation 27]
87. ~old(X0) | kind(X0) [cnf transformation 50]
101. ~calm(X0) | ~strong(X0) [cnf transformation 35]
104. ~generous(X0) | patient(X0) | calm(X0) | creative(X0) [cnf transformation 54]
108. calm(X0) | ~creative(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 54]
112. old(alice) | generous(fred) [cnf transformation 56]
113. old(alice) | ~creative(fred) [cnf transformation 56]
127. tall(fred) [cnf transformation 24]
135. ~kind(X0) [duplicate literal removal 78]
151. ~old(X0) [subsumption resolution 87,135]
154. ~generous(X0) | calm(X0) | ~patient(X0) [subsumption resolution 108,79]
156. ~generous(X0) | calm(X0) | creative(X0) [subsumption resolution 104,154]
157. ~creative(fred) [subsumption resolution 113,151]
158. generous(fred) [subsumption resolution 112,151]
189. strong(fred) [resolution 74,127]
239. calm(fred) | creative(fred) [resolution 156,158]
240. calm(fred) [subsumption resolution 239,157]
241. ~strong(fred) [resolution 240,101]
242. $false [subsumption resolution 241,189]
% SZS output end Proof for 5506982204182174481944379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not rich or not funny and vice versa.
Everyone who is both not rich and quiet is both happy and old and vice versa.
Everyone who is not creative or creative is not old or quiet and vice versa.
Everyone who is quiet is curious or not brave and vice versa.
Everyone who is creative or not kind is not wise or not curious.
If lucy is wise or not brave then someone is not happy or not funny and vice versa.
Everyone who is not creative or strong is both not tall and patient.
If someone is old or not funny then mary is old.
If alice is both generous and old then susan is humble and vice versa.
Everyone who is wise or not old is either rich or not humble.
Everyone who is both not strong and brave is strong or old.
If someone is either patient or not rich then john is both not quiet and not patient.
If alice is either rich or creative then mary is either not generous or humble.
Everyone who is not kind or generous is not kind.
Everyone who is calm is not rich or not happy.
Everyone who is kind or not patient is humble.
Fred is not humble or kind.
Alice is patient or rich.
Someone is brave or not funny.
Someone is tall.
Someone is either not wise or strong.
Someone is either not rich or not happy. | Alice is not kind. | entailment | (![X]:(rich(X)<=>(~rich(X)|~funny(X))))&
(![X]:((~rich(X)&quiet(X))<=>(happy(X)&old(X))))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(((wise(lucy)|~brave(lucy)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~creative(X)|strong(X))=>(~tall(X)&patient(X))))&
((?[X]:((old(X)|~funny(X))))=>(old(mary)))&
(((generous(alice)&old(alice)))<=>(humble(susan)))&
(![X]:((wise(X)|~old(X))=>(rich(X)<~>~humble(X))))&
(![X]:((~strong(X)&brave(X))=>(strong(X)|old(X))))&
((?[X]:((patient(X)<~>~rich(X))))=>((~quiet(john)&~patient(john))))&
(((rich(alice)<~>creative(alice)))=>((~generous(mary)<~>humble(mary))))&
(![X]:((~kind(X)|generous(X))=>~kind(X)))&
(![X]:(calm(X)=>(~rich(X)|~happy(X))))&
(![X]:((kind(X)|~patient(X))=>humble(X)))&
((~humble(fred)|kind(fred)))&
((patient(alice)|rich(alice)))&
(?[X]:((brave(X)|~funny(X))))&
(?[X]:(tall(X)))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~rich(X)<~>~happy(X)))) | ~kind(alice) | [
"p0",
"p2",
"p3",
"p6",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 6563505918555381238924570
% SZS output start Proof for 6563505918555381238924570
1. ! [X0] : (rich(X0) <=> (~funny(X0) | ~rich(X0))) [input p0]
3. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (quiet(X0) | ~old(X0))) [input p2]
4. ! [X0] : (quiet(X0) <=> (~brave(X0) | curious(X0))) [input p3]
7. ! [X0] : ((strong(X0) | ~creative(X0)) => (patient(X0) & ~tall(X0))) [input p6]
9. (old(alice) & generous(alice)) <=> humble(susan) [input p8]
11. ! [X0] : ((brave(X0) & ~strong(X0)) => (old(X0) | strong(X0))) [input p10]
12. ? [X0] : (patient(X0) <~> ~rich(X0)) => (~patient(john) & ~quiet(john)) [input p11]
14. ! [X0] : ((generous(X0) | ~kind(X0)) => ~kind(X0)) [input p13]
16. ! [X0] : ((~patient(X0) | kind(X0)) => humble(X0)) [input p15]
23. kind(alice) [input hypothesis]
27. ! [X0] : ((patient(X0) & ~tall(X0)) | (~strong(X0) & creative(X0))) [ennf transformation 7]
30. ! [X0] : ((old(X0) | strong(X0)) | (~brave(X0) | strong(X0))) [ennf transformation 11]
31. ! [X0] : (old(X0) | strong(X0) | ~brave(X0) | strong(X0)) [flattening 30]
32. (~patient(john) & ~quiet(john)) | ! [X0] : (patient(X0) <=> ~rich(X0)) [ennf transformation 12]
34. ! [X0] : (~kind(X0) | (~generous(X0) & kind(X0))) [ennf transformation 14]
35. ! [X0] : (humble(X0) | (patient(X0) & ~kind(X0))) [ennf transformation 16]
36. ! [X0] : ((rich(X0) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | ~rich(X0))) [nnf transformation 1]
37. ! [X0] : ((rich(X0) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | ~rich(X0))) [flattening 36]
40. ! [X0] : (((creative(X0) | ~creative(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 3]
41. ! [X0] : ((creative(X0) | ~creative(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | (~creative(X0) & creative(X0)))) [flattening 40]
42. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & ((~brave(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 4]
43. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & (~brave(X0) | curious(X0) | ~quiet(X0))) [flattening 42]
49. ((old(alice) & generous(alice)) | ~humble(susan)) & (humble(susan) | (~old(alice) | ~generous(alice))) [nnf transformation 9]
50. ((old(alice) & generous(alice)) | ~humble(susan)) & (humble(susan) | ~old(alice) | ~generous(alice)) [flattening 49]
52. (~patient(john) & ~quiet(john)) | ! [X0] : ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))) [nnf transformation 32]
65. rich(X0) | rich(X0) [cnf transformation 37]
71. quiet(X0) | ~old(X0) | creative(X0) [cnf transformation 41]
72. ~creative(X0) | ~old(X0) | quiet(X0) [cnf transformation 41]
77. brave(X0) | quiet(X0) [cnf transformation 43]
87. ~strong(X0) | patient(X0) [cnf transformation 27]
91. generous(alice) | ~humble(susan) [cnf transformation 50]
97. old(X0) | strong(X0) | ~brave(X0) | strong(X0) [cnf transformation 31]
98. ~quiet(john) | ~rich(X0) | ~patient(X0) [cnf transformation 52]
100. ~patient(john) | ~rich(X0) | ~patient(X0) [cnf transformation 52]
107. ~generous(X0) | ~kind(X0) [cnf transformation 34]
109. humble(X0) | patient(X0) [cnf transformation 35]
118. kind(alice) [cnf transformation 23]
119. ~brave(X0) | strong(X0) | old(X0) [duplicate literal removal 97]
121. rich(X0) [duplicate literal removal 65]
124. ~old(X0) | quiet(X0) [subsumption resolution 71,72]
141. 4 <=> humble(susan) [avatar definition]
143. ~humble(susan) <- (~4) [avatar component clause 141]
150. 6 <=> generous(alice) [avatar definition]
152. generous(alice) <- (6) [avatar component clause 150]
153. ~4 | 6 [avatar split clause 91,150,141]
157. ~patient(john) | ~patient(X0) [subsumption resolution 100,121]
159. 7 <=> ! [X0] : ~patient(X0) [avatar definition]
160. ~patient(X0) <- (7) [avatar component clause 159]
162. 8 <=> patient(john) [avatar definition]
164. ~patient(john) <- (~8) [avatar component clause 162]
165. 7 | ~8 [avatar split clause 157,162,159]
166. ~quiet(john) | ~patient(X0) [subsumption resolution 98,121]
168. 9 <=> quiet(john) [avatar definition]
171. 7 | ~9 [avatar split clause 166,168,159]
254. patient(susan) <- (~4) [resolution 143,109]
255. ~kind(alice) <- (6) [resolution 152,107]
256. $false <- (6) [subsumption resolution 255,118]
257. ~6 [avatar contradiction clause 256]
277. strong(X0) | old(X0) | quiet(X0) [resolution 119,77]
278. strong(X0) | quiet(X0) [subsumption resolution 277,124]
281. patient(X0) | quiet(X0) [resolution 278,87]
282. quiet(john) <- (~8) [resolution 281,164]
285. 9 | 8 [avatar split clause 282,162,168]
289. $false <- (~4, 7) [resolution 160,254]
290. 4 | ~7 [avatar contradiction clause 289]
292. $false [avatar sat refutation 153,165,171,257,285,290]
% SZS output end Proof for 6563505918555381238924570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then fred is either creative or generous. Everyone who is not kind or not old is wise and vice versa. Everyone who is kind is funny or not rich. If paul is not funny or calm then paul is not generous or humble and vice versa. Everyone who is both happy and not curious is not happy or curious. Everyone who is not curious is both not generous and not humble. If someone is either patient or funny then someone is either brave or wise and vice versa. Everyone who is not creative is not patient. If someone is not old then someone is both not brave and not tall. Everyone who is both calm and not old is either brave or not tall. Everyone who is both not generous and not rich is either not creative or rich and vice versa. Everyone who is both not quiet and kind is creative or not generous. If someone is old or not tall then alice is both patient and calm and vice versa. Everyone who is either tall or calm is not tall or not rich and vice versa. Everyone who is humble or not funny is either not tall or not kind and vice versa. If someone is both creative and generous then someone is either calm or rich and vice versa. Fred is either not wise or wise. Someone is both curious and rich. Someone is not funny. Paul is brave. Paul is either kind or not funny. Fred is either happy or creative. John is either funny or tall. Alice is funny. | Alice is curious. | entailment | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((~kind(X)|~old(X))<=>wise(X)))&
(![X]:(kind(X)=>(funny(X)|~rich(X))))&
(((~funny(paul)|calm(paul)))<=>((~generous(paul)|humble(paul))))&
(![X]:((happy(X)&~curious(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:(~funny(X)))&
(brave(paul))&
((kind(paul)<~>~funny(paul)))&
((happy(fred)<~>creative(fred)))&
((funny(john)<~>tall(john)))&
(funny(alice)) | curious(alice) | [
"p5",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 2318174782612802907755385
% SZS output start Proof for 2318174782612802907755385
6. ! [X0] : (~curious(X0) => (~humble(X0) & ~generous(X0))) [input p5]
8. ! [X0] : (~creative(X0) => ~patient(X0)) [input p7]
9. ? [X0] : ~old(X0) => ? [X0] : (~tall(X0) & ~brave(X0)) [input p8]
11. ! [X0] : ((~rich(X0) & ~generous(X0)) <=> (~creative(X0) <~> rich(X0))) [input p10]
13. ? [X0] : (~tall(X0) | old(X0)) <=> (calm(alice) & patient(alice)) [input p12]
25. ~curious(alice) [input hypothesis]
27. ? [X0] : ~old(X0) => ? [X1] : (~tall(X1) & ~brave(X1)) [rectify 9]
34. ! [X0] : ((~humble(X0) & ~generous(X0)) | curious(X0)) [ennf transformation 6]
35. ! [X0] : (~patient(X0) | creative(X0)) [ennf transformation 8]
36. ? [X1] : (~tall(X1) & ~brave(X1)) | ! [X0] : old(X0) [ennf transformation 27]
51. ? [X0] : (~tall(X0) & ~brave(X0)) | ! [X1] : old(X1) [rectify 36]
52. ? [X0] : (~tall(X0) & ~brave(X0)) => (~tall(sK2) & ~brave(sK2)) [choice axiom]
53. (~tall(sK2) & ~brave(sK2)) | ! [X1] : old(X1) [skolemisation 51,52]
55. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | (rich(X0) | generous(X0)))) [nnf transformation 11]
56. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | rich(X0) | generous(X0))) [flattening 55]
57. (? [X0] : (~tall(X0) | old(X0)) | (~calm(alice) | ~patient(alice))) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [nnf transformation 13]
58. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [flattening 57]
59. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [rectify 58]
60. ? [X0] : (~tall(X0) | old(X0)) => (~tall(sK3) | old(sK3)) [choice axiom]
61. ((~tall(sK3) | old(sK3)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [skolemisation 59,60]
90. ~generous(X0) | curious(X0) [cnf transformation 34]
100. ~patient(X0) | creative(X0) [cnf transformation 35]
102. ~tall(sK2) | old(X1) [cnf transformation 53]
105. rich(X0) | ~creative(X0) | rich(X0) | generous(X0) [cnf transformation 56]
110. ~rich(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 56]
112. patient(alice) | ~old(X1) [cnf transformation 61]
113. patient(alice) | tall(X1) [cnf transformation 61]
148. ~curious(alice) [cnf transformation 25]
151. rich(X0) | ~creative(X0) | generous(X0) [duplicate literal removal 105]
152. ~rich(X0) | ~creative(X0) [duplicate literal removal 110]
224. 16 <=> ! [X1] : old(X1) [avatar definition]
225. old(X1) <- (16) [avatar component clause 224]
227. 17 <=> tall(sK2) [avatar definition]
229. ~tall(sK2) <- (~17) [avatar component clause 227]
230. 16 | ~17 [avatar split clause 102,227,224]
236. ~creative(X0) | generous(X0) [subsumption resolution 151,152]
238. 19 <=> patient(alice) [avatar definition]
239. patient(alice) <- (19) [avatar component clause 238]
255. 23 <=> ! [X1] : tall(X1) [avatar definition]
256. tall(X1) <- (23) [avatar component clause 255]
259. 24 <=> ! [X1] : ~old(X1) [avatar definition]
260. ~old(X1) <- (24) [avatar component clause 259]
262. 23 | 19 [avatar split clause 113,238,255]
263. 24 | 19 [avatar split clause 112,238,259]
322. creative(alice) <- (19) [resolution 100,239]
329. generous(alice) <- (19) [resolution 236,322]
386. curious(alice) <- (19) [resolution 329,90]
387. $false <- (19) [subsumption resolution 386,148]
388. ~19 [avatar contradiction clause 387]
393. $false <- (~17, 23) [resolution 256,229]
396. 17 | ~23 [avatar contradiction clause 393]
399. $false <- (16, 24) [subsumption resolution 225,260]
400. ~16 | ~24 [avatar contradiction clause 399]
401. $false [avatar sat refutation 230,262,263,388,396,400]
% SZS output end Proof for 2318174782612802907755385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then fred is both funny and not old and vice versa.
If someone is either not generous or not rich then someone is patient and vice versa.
If paul is not curious or rich then susan is both not quiet and creative and vice versa.
If someone is not kind then lucy is kind.
Everyone who is wise is patient.
Everyone who is both old and not patient is not curious or happy.
Everyone who is not generous or not old is old or not rich.
Everyone who is generous or calm is not generous or happy.
If someone is both not rich and not wise then someone is humble and vice versa.
If someone is either not strong or generous then mary is either calm or humble.
If someone is both humble and not happy then someone is both not old and calm.
Everyone who is either not curious or not quiet is not creative and vice versa.
If john is either creative or not funny then paul is happy or humble and vice versa.
Everyone who is kind is curious.
If mary is happy then someone is either not old or not generous.
Everyone who is happy or not wise is either kind or not generous and vice versa.
Someone is not strong.
Alice is curious.
Mary is strong or generous.
Susan is either not strong or not wise.
Someone is both not rich and brave.
Someone is not happy.
John is generous. | Susan is not strong. | neutral | ((?[X]:(~rich(X)))<=>((funny(fred)&~old(fred))))&
((?[X]:((~generous(X)<~>~rich(X))))<=>(?[X]:(patient(X))))&
(((~curious(paul)|rich(paul)))<=>((~quiet(susan)&creative(susan))))&
((?[X]:(~kind(X)))=>(kind(lucy)))&
(![X]:(wise(X)=>patient(X)))&
(![X]:((old(X)&~patient(X))=>(~curious(X)|happy(X))))&
(![X]:((~generous(X)|~old(X))=>(old(X)|~rich(X))))&
(![X]:((generous(X)|calm(X))=>(~generous(X)|happy(X))))&
((?[X]:((~rich(X)&~wise(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~strong(X)<~>generous(X))))=>((calm(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~happy(X))))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:((~curious(X)<~>~quiet(X))<=>~creative(X)))&
(((creative(john)<~>~funny(john)))<=>((happy(paul)|humble(paul))))&
(![X]:(kind(X)=>curious(X)))&
((happy(mary))=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((happy(X)|~wise(X))<=>(kind(X)<~>~generous(X))))&
(?[X]:(~strong(X)))&
(curious(alice))&
((strong(mary)|generous(mary)))&
((~strong(susan)<~>~wise(susan)))&
(?[X]:((~rich(X)&brave(X))))&
(?[X]:(~happy(X)))&
(generous(john)) | ~strong(susan) | []
| null | 0 |
If someone is strong or creative then someone is both tall and curious.
Everyone who is not patient is both calm and old and vice versa.
If someone is both wise and tall then someone is both wise and not generous and vice versa.
Everyone who is either old or not calm is humble.
Everyone who is either wise or funny is either not kind or kind and vice versa.
If john is both quiet and creative then susan is not rich or brave and vice versa.
If someone is not brave or calm then mary is either tall or not strong.
If lucy is not creative or calm then alice is either kind or creative and vice versa.
Everyone who is either humble or generous is curious or not funny and vice versa.
Everyone who is not calm or creative is both funny and not happy and vice versa.
If lucy is not funny then someone is wise and vice versa.
If someone is curious or wise then susan is both creative and not brave.
If mary is rich then someone is both not kind and not happy and vice versa.
If someone is generous then fred is humble and vice versa.
Everyone who is both not brave and wise is both not happy and not calm.
If someone is not curious or curious then someone is both not patient and not tall and vice versa.
Paul is old or humble.
Susan is either not calm or creative.
Someone is rich.
Fred is not funny or curious.
Someone is patient.
Someone is not wise.
Alice is either wise or not curious.
Lucy is both not generous and not humble. | Susan is not calm. | contradiction | ((?[X]:((strong(X)|creative(X))))=>(?[X]:((tall(X)&curious(X)))))&
(![X]:(~patient(X)<=>(calm(X)&old(X))))&
((?[X]:((wise(X)&tall(X))))<=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:((old(X)<~>~calm(X))=>humble(X)))&
(![X]:((wise(X)<~>funny(X))<=>(~kind(X)<~>kind(X))))&
(((quiet(john)&creative(john)))<=>((~rich(susan)|brave(susan))))&
((?[X]:((~brave(X)|calm(X))))=>((tall(mary)<~>~strong(mary))))&
(((~creative(lucy)|calm(lucy)))<=>((kind(alice)<~>creative(alice))))&
(![X]:((humble(X)<~>generous(X))<=>(curious(X)|~funny(X))))&
(![X]:((~calm(X)|creative(X))<=>(funny(X)&~happy(X))))&
((~funny(lucy))<=>(?[X]:(wise(X))))&
((?[X]:((curious(X)|wise(X))))=>((creative(susan)&~brave(susan))))&
((rich(mary))<=>(?[X]:((~kind(X)&~happy(X)))))&
((?[X]:(generous(X)))<=>(humble(fred)))&
(![X]:((~brave(X)&wise(X))=>(~happy(X)&~calm(X))))&
((?[X]:((~curious(X)|curious(X))))<=>(?[X]:((~patient(X)&~tall(X)))))&
((old(paul)|humble(paul)))&
((~calm(susan)<~>creative(susan)))&
(?[X]:(rich(X)))&
((~funny(fred)|curious(fred)))&
(?[X]:(patient(X)))&
(?[X]:(~wise(X)))&
((wise(alice)<~>~curious(alice)))&
((~generous(lucy)&~humble(lucy))) | ~calm(susan) | [
"p4",
"p11",
"p17",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 6977916979306230402803040
% SZS output start Proof for 6977916979306230402803040
5. ! [X0] : ((wise(X0) <~> funny(X0)) <=> (~kind(X0) <~> kind(X0))) [input p4]
12. ? [X0] : (wise(X0) | curious(X0)) => (~brave(susan) & creative(susan)) [input p11]
18. ~calm(susan) <~> creative(susan) [input p17]
20. curious(fred) | ~funny(fred) [input p19]
25. ~calm(susan) [input hypothesis]
32. (~brave(susan) & creative(susan)) | ! [X0] : (~wise(X0) & ~curious(X0)) [ennf transformation 12]
46. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 5]
73. (~creative(susan) | calm(susan)) & (creative(susan) | ~calm(susan)) [nnf transformation 18]
98. funny(X0) | wise(X0) | kind(X0) | kind(X0) [cnf transformation 46]
99. funny(X0) | wise(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 46]
130. creative(susan) | ~curious(X0) [cnf transformation 32]
131. creative(susan) | ~wise(X0) [cnf transformation 32]
148. ~creative(susan) | calm(susan) [cnf transformation 73]
150. curious(fred) | ~funny(fred) [cnf transformation 20]
157. ~calm(susan) [cnf transformation 25]
158. funny(X0) | wise(X0) | kind(X0) [duplicate literal removal 98]
159. funny(X0) | wise(X0) | ~kind(X0) [duplicate literal removal 99]
207. funny(X0) | wise(X0) [subsumption resolution 158,159]
270. 23 <=> ! [X0] : ~wise(X0) [avatar definition]
271. ~wise(X0) <- (23) [avatar component clause 270]
284. 26 <=> ! [X0] : ~curious(X0) [avatar definition]
285. ~curious(X0) <- (26) [avatar component clause 284]
288. 27 <=> creative(susan) [avatar definition]
291. 23 | 27 [avatar split clause 131,288,270]
292. 26 | 27 [avatar split clause 130,288,284]
349. 40 <=> calm(susan) [avatar definition]
352. 40 | ~27 [avatar split clause 148,288,349]
355. 41 <=> funny(fred) [avatar definition]
357. ~funny(fred) <- (~41) [avatar component clause 355]
359. 42 <=> curious(fred) [avatar definition]
361. curious(fred) <- (42) [avatar component clause 359]
362. ~41 | 42 [avatar split clause 150,359,355]
373. ~40 [avatar split clause 157,349]
382. wise(fred) <- (~41) [resolution 207,357]
384. $false <- (23, ~41) [subsumption resolution 382,271]
385. ~23 | 41 [avatar contradiction clause 384]
386. $false <- (26, 42) [subsumption resolution 361,285]
387. ~26 | ~42 [avatar contradiction clause 386]
388. $false [avatar sat refutation 291,292,352,362,373,385,387]
% SZS output end Proof for 6977916979306230402803040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not happy is not patient and vice versa. If mary is both patient and not quiet then someone is not tall or not generous. Everyone who is both wise and creative is both not funny and calm. If mary is not curious then someone is generous. Everyone who is not generous is not kind or not generous. If someone is rich then alice is not old and vice versa. If someone is either calm or not rich then someone is strong and vice versa. Everyone who is both tall and kind is humble and vice versa. Everyone who is both brave and funny is either not generous or not quiet and vice versa. Everyone who is either strong or humble is either not brave or patient and vice versa. If fred is not rich then paul is creative. If someone is both strong and not funny then paul is curious. If mary is either not creative or old then someone is either strong or not quiet and vice versa. If someone is both not brave and not quiet then john is either patient or kind and vice versa. Everyone who is not curious or patient is strong or curious. Everyone who is wise is both not quiet and creative. Someone is calm or not quiet. Someone is either rich or not happy. Alice is both not kind and patient. Someone is both patient and wise. Someone is old. Someone is not curious or not generous. Someone is not strong or generous. Someone is not happy or humble. | Mary is creative. | neutral | (![X]:((rich(X)|~happy(X))<=>~patient(X)))&
(((patient(mary)&~quiet(mary)))=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:((wise(X)&creative(X))=>(~funny(X)&calm(X))))&
((~curious(mary))=>(?[X]:(generous(X))))&
(![X]:(~generous(X)=>(~kind(X)|~generous(X))))&
((?[X]:(rich(X)))<=>(~old(alice)))&
((?[X]:((calm(X)<~>~rich(X))))<=>(?[X]:(strong(X))))&
(![X]:((tall(X)&kind(X))<=>humble(X)))&
(![X]:((brave(X)&funny(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((strong(X)<~>humble(X))<=>(~brave(X)<~>patient(X))))&
((~rich(fred))=>(creative(paul)))&
((?[X]:((strong(X)&~funny(X))))=>(curious(paul)))&
(((~creative(mary)<~>old(mary)))<=>(?[X]:((strong(X)<~>~quiet(X)))))&
((?[X]:((~brave(X)&~quiet(X))))<=>((patient(john)<~>kind(john))))&
(![X]:((~curious(X)|patient(X))=>(strong(X)|curious(X))))&
(![X]:(wise(X)=>(~quiet(X)&creative(X))))&
(?[X]:((calm(X)|~quiet(X))))&
(?[X]:((rich(X)<~>~happy(X))))&
((~kind(alice)&patient(alice)))&
(?[X]:((patient(X)&wise(X))))&
(?[X]:(old(X)))&
(?[X]:((~curious(X)|~generous(X))))&
(?[X]:((~strong(X)|generous(X))))&
(?[X]:((~happy(X)|humble(X)))) | creative(mary) | []
| null | 0 |
Everyone who is not generous is patient and vice versa.
If paul is either curious or calm then lucy is both humble and tall.
Everyone who is both funny and generous is wise or not creative and vice versa.
Everyone who is both not wise and not creative is either rich or wise.
If someone is not generous then someone is both tall and not rich.
If someone is funny then someone is both not brave and rich and vice versa.
If someone is kind or not rich then someone is old.
If fred is either not quiet or happy then lucy is not funny.
Everyone who is either not quiet or humble is not creative or kind.
If someone is not funny or not old then someone is either not happy or happy and vice versa.
If paul is either quiet or calm then someone is either not tall or calm.
Everyone who is humble is both old and not humble and vice versa.
Everyone who is both not old and kind is either rich or creative and vice versa.
Everyone who is both not funny and funny is patient or wise and vice versa.
If someone is either not generous or not humble then lucy is not happy.
If someone is not brave then someone is both curious and calm and vice versa.
Someone is not curious.
John is rich.
Mary is either not brave or not humble.
Someone is either not strong or old.
Someone is both not curious and tall.
Paul is creative. | Paul is calm. | contradiction | (![X]:(~generous(X)<=>patient(X)))&
(((curious(paul)<~>calm(paul)))=>((humble(lucy)&tall(lucy))))&
(![X]:((funny(X)&generous(X))<=>(wise(X)|~creative(X))))&
(![X]:((~wise(X)&~creative(X))=>(rich(X)<~>wise(X))))&
((?[X]:(~generous(X)))=>(?[X]:((tall(X)&~rich(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((~brave(X)&rich(X)))))&
((?[X]:((kind(X)|~rich(X))))=>(?[X]:(old(X))))&
(((~quiet(fred)<~>happy(fred)))=>(~funny(lucy)))&
(![X]:((~quiet(X)<~>humble(X))=>(~creative(X)|kind(X))))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(((quiet(paul)<~>calm(paul)))=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:(humble(X)<=>(old(X)&~humble(X))))&
(![X]:((~old(X)&kind(X))<=>(rich(X)<~>creative(X))))&
(![X]:((~funny(X)&funny(X))<=>(patient(X)|wise(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(~happy(lucy)))&
((?[X]:(~brave(X)))<=>(?[X]:((curious(X)&calm(X)))))&
(?[X]:(~curious(X)))&
(rich(john))&
((~brave(mary)<~>~humble(mary)))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((~curious(X)&tall(X))))&
(creative(paul)) | calm(paul) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4452050940837088725555924
% SZS output start Proof for 4452050940837088725555924
1. ! [X0] : (~generous(X0) <=> patient(X0)) [input p0]
2. (curious(paul) <~> calm(paul)) => (tall(lucy) & humble(lucy)) [input p1]
3. ! [X0] : ((generous(X0) & funny(X0)) <=> (~creative(X0) | wise(X0))) [input p2]
6. ? [X0] : funny(X0) <=> ? [X0] : (rich(X0) & ~brave(X0)) [input p5]
7. ? [X0] : (~rich(X0) | kind(X0)) => ? [X0] : old(X0) [input p6]
12. ! [X0] : (humble(X0) <=> (~humble(X0) & old(X0))) [input p11]
13. ! [X0] : ((kind(X0) & ~old(X0)) <=> (rich(X0) <~> creative(X0))) [input p12]
14. ! [X0] : ((funny(X0) & ~funny(X0)) <=> (wise(X0) | patient(X0))) [input p13]
16. ? [X0] : ~brave(X0) <=> ? [X0] : (calm(X0) & curious(X0)) [input p15]
23. calm(paul) [input hypothesis]
25. ? [X0] : funny(X0) <=> ? [X1] : (rich(X1) & ~brave(X1)) [rectify 6]
26. ? [X0] : (~rich(X0) | kind(X0)) => ? [X1] : old(X1) [rectify 7]
28. ? [X0] : ~brave(X0) <=> ? [X1] : (calm(X1) & curious(X1)) [rectify 16]
29. (tall(lucy) & humble(lucy)) | (curious(paul) <=> calm(paul)) [ennf transformation 2]
33. ? [X1] : old(X1) | ! [X0] : (rich(X0) & ~kind(X0)) [ennf transformation 26]
39. ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 1]
40. (tall(lucy) & humble(lucy)) | ((curious(paul) | ~calm(paul)) & (calm(paul) | ~curious(paul))) [nnf transformation 29]
41. ! [X0] : (((generous(X0) & funny(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (~generous(X0) | ~funny(X0)))) [nnf transformation 3]
42. ! [X0] : (((generous(X0) & funny(X0)) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | ~generous(X0) | ~funny(X0))) [flattening 41]
47. (? [X0] : funny(X0) | ! [X1] : (~rich(X1) | brave(X1))) & (? [X1] : (rich(X1) & ~brave(X1)) | ! [X0] : ~funny(X0)) [nnf transformation 25]
48. (? [X0] : funny(X0) | ! [X1] : (~rich(X1) | brave(X1))) & (? [X2] : (rich(X2) & ~brave(X2)) | ! [X3] : ~funny(X3)) [rectify 47]
49. ? [X0] : funny(X0) => funny(sK1) [choice axiom]
50. ? [X2] : (rich(X2) & ~brave(X2)) => (rich(sK2) & ~brave(sK2)) [choice axiom]
51. (funny(sK1) | ! [X1] : (~rich(X1) | brave(X1))) & ((rich(sK2) & ~brave(sK2)) | ! [X3] : ~funny(X3)) [skolemisation 48,50,49]
52. ? [X0] : old(X0) | ! [X1] : (rich(X1) & ~kind(X1)) [rectify 33]
53. ? [X0] : old(X0) => old(sK3) [choice axiom]
54. old(sK3) | ! [X1] : (rich(X1) & ~kind(X1)) [skolemisation 52,53]
65. ! [X0] : ((humble(X0) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | ~humble(X0))) [nnf transformation 12]
66. ! [X0] : ((humble(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | ~humble(X0))) [flattening 65]
67. ! [X0] : (((kind(X0) & ~old(X0)) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | (~kind(X0) | old(X0)))) [nnf transformation 13]
68. ! [X0] : (((kind(X0) & ~old(X0)) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | ~kind(X0) | old(X0))) [flattening 67]
69. ! [X0] : (((funny(X0) & ~funny(X0)) | (~wise(X0) & ~patient(X0))) & ((wise(X0) | patient(X0)) | (~funny(X0) | funny(X0)))) [nnf transformation 14]
70. ! [X0] : (((funny(X0) & ~funny(X0)) | (~wise(X0) & ~patient(X0))) & (wise(X0) | patient(X0) | ~funny(X0) | funny(X0))) [flattening 69]
72. (? [X0] : ~brave(X0) | ! [X1] : (~calm(X1) | ~curious(X1))) & (? [X1] : (calm(X1) & curious(X1)) | ! [X0] : brave(X0)) [nnf transformation 28]
73. (? [X0] : ~brave(X0) | ! [X1] : (~calm(X1) | ~curious(X1))) & (? [X2] : (calm(X2) & curious(X2)) | ! [X3] : brave(X3)) [rectify 72]
74. ? [X0] : ~brave(X0) => ~brave(sK7) [choice axiom]
75. ? [X2] : (calm(X2) & curious(X2)) => (calm(sK8) & curious(sK8)) [choice axiom]
76. (~brave(sK7) | ! [X1] : (~calm(X1) | ~curious(X1))) & ((calm(sK8) & curious(sK8)) | ! [X3] : brave(X3)) [skolemisation 73,75,74]
85. patient(X0) | generous(X0) [cnf transformation 39]
88. humble(lucy) | curious(paul) | ~calm(paul) [cnf transformation 40]
91. ~creative(X0) | wise(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 42]
92. ~wise(X0) | funny(X0) [cnf transformation 42]
102. funny(sK1) | ~rich(X1) | brave(X1) [cnf transformation 51]
103. old(sK3) | ~kind(X1) [cnf transformation 54]
104. old(sK3) | rich(X1) [cnf transformation 54]
120. ~humble(X0) | ~humble(X0) [cnf transformation 66]
121. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 66]
126. ~rich(X0) | creative(X0) | kind(X0) [cnf transformation 68]
129. ~funny(X0) | ~patient(X0) [cnf transformation 70]
130. ~funny(X0) | ~wise(X0) [cnf transformation 70]
131. ~patient(X0) | funny(X0) [cnf transformation 70]
137. ~brave(sK7) | ~calm(X1) | ~curious(X1) [cnf transformation 76]
147. calm(paul) [cnf transformation 23]
148. ~humble(X0) [duplicate literal removal 120]
149. ~old(X0) | humble(X0) [duplicate literal removal 121]
154. 1 <=> calm(paul) [avatar definition]
155. calm(paul) <- (1) [avatar component clause 154]
158. 2 <=> curious(paul) [avatar definition]
160. curious(paul) <- (2) [avatar component clause 158]
168. 4 <=> humble(lucy) [avatar definition]
170. humble(lucy) <- (4) [avatar component clause 168]
171. ~1 | 2 | 4 [avatar split clause 88,168,158,154]
174. 5 <=> ! [X1] : generous(X1) [avatar definition]
175. generous(X1) <- (5) [avatar component clause 174]
187. 8 <=> ! [X1] : (~rich(X1) | brave(X1)) [avatar definition]
188. ~rich(X1) | brave(X1) <- (8) [avatar component clause 187]
190. 9 <=> funny(sK1) [avatar definition]
192. funny(sK1) <- (9) [avatar component clause 190]
193. 8 | 9 [avatar split clause 102,190,187]
195. 10 <=> ! [X3] : ~funny(X3) [avatar definition]
196. ~funny(X3) <- (10) [avatar component clause 195]
208. 13 <=> ! [X1] : rich(X1) [avatar definition]
209. rich(X1) <- (13) [avatar component clause 208]
211. 14 <=> old(sK3) [avatar definition]
213. old(sK3) <- (14) [avatar component clause 211]
214. 13 | 14 [avatar split clause 104,211,208]
216. 15 <=> ! [X1] : ~kind(X1) [avatar definition]
217. ~kind(X1) <- (15) [avatar component clause 216]
218. 15 | 14 [avatar split clause 103,211,216]
265. ~wise(X0) [subsumption resolution 130,92]
266. ~patient(X0) [subsumption resolution 129,131]
277. 28 <=> ! [X1] : (~calm(X1) | ~curious(X1)) [avatar definition]
278. ~calm(X1) | ~curious(X1) <- (28) [avatar component clause 277]
280. 29 <=> brave(sK7) [avatar definition]
282. ~brave(sK7) <- (~29) [avatar component clause 280]
283. 28 | ~29 [avatar split clause 137,280,277]
285. 30 <=> ! [X3] : brave(X3) [avatar definition]
286. brave(X3) <- (30) [avatar component clause 285]
308. 1 [avatar split clause 147,154]
309. $false <- (~29, 30) [subsumption resolution 282,286]
310. 29 | ~30 [avatar contradiction clause 309]
311. $false <- (4) [subsumption resolution 170,148]
312. ~4 [avatar contradiction clause 311]
313. generous(X0) [resolution 85,266]
316. humble(sK3) <- (14) [resolution 149,213]
317. $false <- (14) [subsumption resolution 316,148]
318. ~14 [avatar contradiction clause 317]
319. ~curious(paul) <- (1, 28) [resolution 278,155]
320. $false <- (1, 2, 28) [subsumption resolution 319,160]
321. ~1 | ~2 | ~28 [avatar contradiction clause 320]
322. brave(X1) <- (8, 13) [subsumption resolution 188,209]
323. 30 | ~8 | ~13 [avatar split clause 322,208,187,285]
324. $false <- (9, 10) [subsumption resolution 192,196]
325. ~9 | ~10 [avatar contradiction clause 324]
327. creative(X0) | kind(X0) <- (13) [resolution 126,209]
329. creative(X0) <- (13, 15) [subsumption resolution 327,217]
338. wise(X0) | ~generous(X0) | ~funny(X0) <- (13, 15) [resolution 91,329]
344. ~generous(X0) | ~funny(X0) <- (13, 15) [subsumption resolution 338,265]
345. ~funny(X0) <- (5, 13, 15) [subsumption resolution 344,175]
346. 10 | ~5 | ~13 | ~15 [avatar split clause 345,216,208,174,195]
358. 5 [avatar split clause 313,174]
361. $false [avatar sat refutation 171,193,214,218,283,308,310,312,318,321,323,325,346,358]
% SZS output end Proof for 4452050940837088725555924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or funny then alice is both not patient and not humble and vice versa.
If susan is both not rich and not strong then mary is either not happy or quiet and vice versa.
Everyone who is not calm is not creative or not old and vice versa.
If someone is both creative and not quiet then paul is curious or not curious.
Everyone who is both not rich and generous is both happy and generous and vice versa.
Everyone who is either not strong or not old is both funny and not old and vice versa.
Everyone who is funny or not funny is both strong and kind and vice versa.
Everyone who is not quiet or generous is not brave and vice versa.
If alice is both creative and strong then alice is either old or not old.
If mary is calm then someone is calm and vice versa.
Everyone who is happy or not tall is quiet or not calm and vice versa.
Everyone who is patient is either not tall or rich and vice versa.
Everyone who is tall or brave is either not old or rich and vice versa.
If mary is not rich or not strong then mary is not calm or old and vice versa.
Everyone who is not kind is either happy or not old and vice versa.
Everyone who is either not humble or rich is both humble and brave.
Fred is both generous and wise.
Mary is not quiet or not wise.
Paul is not patient or happy.
Someone is not humble or not kind.
Someone is not creative.
Someone is either not humble or curious.
Susan is not calm or not strong. | Fred is not calm. | entailment | (((humble(alice)<~>funny(alice)))<=>((~patient(alice)&~humble(alice))))&
(((~rich(susan)&~strong(susan)))<=>((~happy(mary)<~>quiet(mary))))&
(![X]:(~calm(X)<=>(~creative(X)|~old(X))))&
((?[X]:((creative(X)&~quiet(X))))=>((curious(paul)|~curious(paul))))&
(![X]:((~rich(X)&generous(X))<=>(happy(X)&generous(X))))&
(![X]:((~strong(X)<~>~old(X))<=>(funny(X)&~old(X))))&
(![X]:((funny(X)|~funny(X))<=>(strong(X)&kind(X))))&
(![X]:((~quiet(X)|generous(X))<=>~brave(X)))&
(((creative(alice)&strong(alice)))=>((old(alice)<~>~old(alice))))&
((calm(mary))<=>(?[X]:(calm(X))))&
(![X]:((happy(X)|~tall(X))<=>(quiet(X)|~calm(X))))&
(![X]:(patient(X)<=>(~tall(X)<~>rich(X))))&
(![X]:((tall(X)|brave(X))<=>(~old(X)<~>rich(X))))&
(((~rich(mary)|~strong(mary)))<=>((~calm(mary)|old(mary))))&
(![X]:(~kind(X)<=>(happy(X)<~>~old(X))))&
(![X]:((~humble(X)<~>rich(X))=>(humble(X)&brave(X))))&
((generous(fred)&wise(fred)))&
((~quiet(mary)|~wise(mary)))&
((~patient(paul)|happy(paul)))&
(?[X]:((~humble(X)|~kind(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~humble(X)<~>curious(X))))&
((~calm(susan)|~strong(susan))) | ~calm(fred) | [
"p1",
"p2",
"p4",
"p6",
"p7",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 650071016746111885999104
% SZS output start Proof for 650071016746111885999104
2. (~strong(susan) & ~rich(susan)) <=> (~happy(mary) <~> quiet(mary)) [input p1]
3. ! [X0] : (~calm(X0) <=> (~old(X0) | ~creative(X0))) [input p2]
5. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (generous(X0) & happy(X0))) [input p4]
7. ! [X0] : ((~funny(X0) | funny(X0)) <=> (kind(X0) & strong(X0))) [input p6]
8. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> ~brave(X0)) [input p7]
10. calm(mary) <=> ? [X0] : calm(X0) [input p9]
13. ! [X0] : ((brave(X0) | tall(X0)) <=> (~old(X0) <~> rich(X0))) [input p12]
14. (~strong(mary) | ~rich(mary)) <=> (old(mary) | ~calm(mary)) [input p13]
15. ! [X0] : (~kind(X0) <=> (happy(X0) <~> ~old(X0))) [input p14]
24. calm(fred) [input hypothesis]
32. ((~strong(susan) & ~rich(susan)) | ((~happy(mary) | ~quiet(mary)) & (quiet(mary) | happy(mary)))) & (((~quiet(mary) | happy(mary)) & (quiet(mary) | ~happy(mary))) | (strong(susan) | rich(susan))) [nnf transformation 2]
33. ((~strong(susan) & ~rich(susan)) | ((~happy(mary) | ~quiet(mary)) & (quiet(mary) | happy(mary)))) & (((~quiet(mary) | happy(mary)) & (quiet(mary) | ~happy(mary))) | strong(susan) | rich(susan)) [flattening 32]
34. ! [X0] : ((~calm(X0) | (old(X0) & creative(X0))) & ((~old(X0) | ~creative(X0)) | calm(X0))) [nnf transformation 3]
35. ! [X0] : ((~calm(X0) | (old(X0) & creative(X0))) & (~old(X0) | ~creative(X0) | calm(X0))) [flattening 34]
36. ! [X0] : (((generous(X0) & ~rich(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~generous(X0) | rich(X0)))) [nnf transformation 5]
37. ! [X0] : (((generous(X0) & ~rich(X0)) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | ~generous(X0) | rich(X0))) [flattening 36]
40. ! [X0] : (((~funny(X0) | funny(X0)) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | (funny(X0) & ~funny(X0)))) [nnf transformation 7]
41. ! [X0] : ((~funny(X0) | funny(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | (funny(X0) & ~funny(X0)))) [flattening 40]
42. ! [X0] : (((generous(X0) | ~quiet(X0)) | brave(X0)) & (~brave(X0) | (~generous(X0) & quiet(X0)))) [nnf transformation 8]
43. ! [X0] : ((generous(X0) | ~quiet(X0) | brave(X0)) & (~brave(X0) | (~generous(X0) & quiet(X0)))) [flattening 42]
45. (calm(mary) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~calm(mary)) [nnf transformation 10]
46. (calm(mary) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~calm(mary)) [rectify 45]
47. ? [X1] : calm(X1) => calm(sK0) [choice axiom]
48. (calm(mary) | ! [X0] : ~calm(X0)) & (calm(sK0) | ~calm(mary)) [skolemisation 46,47]
52. ! [X0] : (((brave(X0) | tall(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) & (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (~brave(X0) & ~tall(X0)))) [nnf transformation 13]
53. ! [X0] : ((brave(X0) | tall(X0) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) & (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (~brave(X0) & ~tall(X0)))) [flattening 52]
54. ((~strong(mary) | ~rich(mary)) | (~old(mary) & calm(mary))) & ((old(mary) | ~calm(mary)) | (strong(mary) & rich(mary))) [nnf transformation 14]
55. (~strong(mary) | ~rich(mary) | (~old(mary) & calm(mary))) & (old(mary) | ~calm(mary) | (strong(mary) & rich(mary))) [flattening 54]
56. ! [X0] : ((~kind(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | kind(X0))) [nnf transformation 15]
75. ~strong(susan) | quiet(mary) | happy(mary) [cnf transformation 33]
79. ~calm(X0) | old(X0) [cnf transformation 35]
81. ~generous(X0) | happy(X0) | rich(X0) [cnf transformation 37]
91. strong(X0) | ~funny(X0) [cnf transformation 41]
92. strong(X0) | funny(X0) [cnf transformation 41]
93. kind(X0) | ~funny(X0) [cnf transformation 41]
94. kind(X0) | funny(X0) [cnf transformation 41]
98. ~quiet(X0) | generous(X0) | brave(X0) [cnf transformation 43]
102. calm(mary) | ~calm(X0) [cnf transformation 48]
112. ~brave(X0) | ~old(X0) | rich(X0) [cnf transformation 53]
120. ~strong(mary) | ~rich(mary) | ~old(mary) [cnf transformation 55]
123. ~kind(X0) | ~old(X0) | ~happy(X0) [cnf transformation 56]
138. calm(fred) [cnf transformation 24]
161. 4 <=> quiet(mary) [avatar definition]
162. quiet(mary) <- (4) [avatar component clause 161]
165. 5 <=> happy(mary) [avatar definition]
167. ~happy(mary) <- (~5) [avatar component clause 165]
169. 6 <=> strong(susan) [avatar definition]
171. ~strong(susan) <- (~6) [avatar component clause 169]
173. 5 | 4 | ~6 [avatar split clause 75,169,161,165]
182. kind(X0) [subsumption resolution 93,94]
183. strong(X0) [subsumption resolution 91,92]
185. 8 <=> ! [X0] : ~calm(X0) [avatar definition]
186. ~calm(X0) <- (8) [avatar component clause 185]
188. 9 <=> calm(mary) [avatar definition]
190. calm(mary) <- (9) [avatar component clause 188]
191. 8 | 9 [avatar split clause 102,188,185]
197. ~rich(mary) | ~old(mary) [subsumption resolution 120,183]
199. 11 <=> old(mary) [avatar definition]
200. old(mary) <- (11) [avatar component clause 199]
203. 12 <=> rich(mary) [avatar definition]
205. ~rich(mary) <- (~12) [avatar component clause 203]
206. ~11 | ~12 [avatar split clause 197,203,199]
210. ~old(X0) | ~happy(X0) [subsumption resolution 123,182]
237. $false <- (~6) [subsumption resolution 171,183]
238. 6 [avatar contradiction clause 237]
239. $false <- (8) [resolution 186,138]
240. ~8 [avatar contradiction clause 239]
245. old(mary) <- (9) [resolution 79,190]
247. 11 | ~9 [avatar split clause 245,188,199]
255. ~happy(mary) <- (11) [resolution 210,200]
271. generous(mary) | brave(mary) <- (4) [resolution 98,162]
273. 18 <=> brave(mary) [avatar definition]
275. brave(mary) <- (18) [avatar component clause 273]
277. 19 <=> generous(mary) [avatar definition]
279. generous(mary) <- (19) [avatar component clause 277]
280. 18 | 19 | ~4 [avatar split clause 271,161,277,273]
350. ~old(mary) | rich(mary) <- (18) [resolution 112,275]
351. rich(mary) <- (11, 18) [subsumption resolution 350,200]
352. $false <- (11, ~12, 18) [subsumption resolution 351,205]
353. ~11 | 12 | ~18 [avatar contradiction clause 352]
360. ~5 | ~11 [avatar split clause 255,199,165]
366. happy(mary) | rich(mary) <- (19) [resolution 279,81]
367. rich(mary) <- (~5, 19) [subsumption resolution 366,167]
368. $false <- (~5, ~12, 19) [subsumption resolution 367,205]
369. 5 | 12 | ~19 [avatar contradiction clause 368]
370. $false [avatar sat refutation 173,191,206,238,240,247,280,353,360,369]
% SZS output end Proof for 650071016746111885999104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not humble then mary is either calm or funny.
Everyone who is funny or not happy is not humble and vice versa.
Everyone who is not happy or creative is both funny and happy and vice versa.
If john is creative then paul is not patient and vice versa.
If someone is both not curious and not wise then someone is either not tall or not generous and vice versa.
Everyone who is not brave or not humble is either not strong or old and vice versa.
Everyone who is both not calm and not old is not curious or rich and vice versa.
If john is curious then someone is either patient or happy and vice versa.
Everyone who is either not curious or not kind is not humble or kind and vice versa.
If someone is humble or not old then john is either not rich or happy and vice versa.
Everyone who is quiet or not happy is both not patient and happy and vice versa.
If someone is not humble or tall then someone is not rich or brave and vice versa.
Everyone who is either not kind or generous is not tall and vice versa.
Everyone who is not curious or not generous is either humble or not calm.
Everyone who is both not tall and patient is patient or not rich and vice versa.
Everyone who is calm is either quiet or happy and vice versa.
Someone is not old or calm.
Someone is curious.
Someone is both not curious and quiet.
Someone is both not brave and not curious.
Mary is rich.
Fred is quiet.
Paul is both not curious and wise. | Paul is quiet. | entailment | ((?[X]:((humble(X)&~humble(X))))=>((calm(mary)<~>funny(mary))))&
(![X]:((funny(X)|~happy(X))<=>~humble(X)))&
(![X]:((~happy(X)|creative(X))<=>(funny(X)&happy(X))))&
((creative(john))<=>(~patient(paul)))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(~strong(X)<~>old(X))))&
(![X]:((~calm(X)&~old(X))<=>(~curious(X)|rich(X))))&
((curious(john))<=>(?[X]:((patient(X)<~>happy(X)))))&
(![X]:((~curious(X)<~>~kind(X))<=>(~humble(X)|kind(X))))&
((?[X]:((humble(X)|~old(X))))<=>((~rich(john)<~>happy(john))))&
(![X]:((quiet(X)|~happy(X))<=>(~patient(X)&happy(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~kind(X)<~>generous(X))<=>~tall(X)))&
(![X]:((~curious(X)|~generous(X))=>(humble(X)<~>~calm(X))))&
(![X]:((~tall(X)&patient(X))<=>(patient(X)|~rich(X))))&
(![X]:(calm(X)<=>(quiet(X)<~>happy(X))))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)&quiet(X))))&
(?[X]:((~brave(X)&~curious(X))))&
(rich(mary))&
(quiet(fred))&
((~curious(paul)&wise(paul))) | quiet(paul) | [
"p2",
"p6",
"p15",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 3092965711099901773545816
% SZS output start Proof for 3092965711099901773545816
3. ! [X0] : ((creative(X0) | ~happy(X0)) <=> (happy(X0) & funny(X0))) [input p2]
7. ! [X0] : ((~old(X0) & ~calm(X0)) <=> (rich(X0) | ~curious(X0))) [input p6]
16. ! [X0] : (calm(X0) <=> (quiet(X0) <~> happy(X0))) [input p15]
23. wise(paul) & ~curious(paul) [input p22]
24. ~quiet(paul) [input hypothesis]
32. ! [X0] : (((creative(X0) | ~happy(X0)) | (~happy(X0) | ~funny(X0))) & ((happy(X0) & funny(X0)) | (~creative(X0) & happy(X0)))) [nnf transformation 3]
33. ! [X0] : ((creative(X0) | ~happy(X0) | ~happy(X0) | ~funny(X0)) & ((happy(X0) & funny(X0)) | (~creative(X0) & happy(X0)))) [flattening 32]
42. ! [X0] : (((~old(X0) & ~calm(X0)) | (~rich(X0) & curious(X0))) & ((rich(X0) | ~curious(X0)) | (old(X0) | calm(X0)))) [nnf transformation 7]
43. ! [X0] : (((~old(X0) & ~calm(X0)) | (~rich(X0) & curious(X0))) & (rich(X0) | ~curious(X0) | old(X0) | calm(X0))) [flattening 42]
65. ! [X0] : ((calm(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ~calm(X0))) [nnf transformation 16]
81. happy(X0) | happy(X0) [cnf transformation 33]
99. ~calm(X0) | curious(X0) [cnf transformation 43]
144. calm(X0) | quiet(X0) | ~happy(X0) [cnf transformation 65]
153. ~curious(paul) [cnf transformation 23]
155. ~quiet(paul) [cnf transformation 24]
160. happy(X0) [duplicate literal removal 81]
279. quiet(X0) | calm(X0) [subsumption resolution 144,160]
318. calm(paul) [resolution 279,155]
320. curious(paul) [resolution 318,99]
321. $false [subsumption resolution 320,153]
% SZS output end Proof for 3092965711099901773545816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is old then someone is generous or tall. Everyone who is patient or not quiet is both wise and kind. Everyone who is creative or patient is both not generous and generous. If someone is either creative or quiet then susan is both not happy and curious and vice versa. Everyone who is both generous and not calm is not happy and vice versa. If someone is both not curious and strong then john is either not quiet or rich and vice versa. Everyone who is both curious and not creative is either curious or not calm. Everyone who is either not patient or not rich is both not calm and not curious and vice versa. Everyone who is both not tall and not calm is wise and vice versa. If someone is not kind or not creative then someone is both old and not creative. Everyone who is happy is not happy or old. If someone is both calm and not rich then someone is happy. If lucy is not funny then mary is both kind and not kind. If lucy is either not happy or not generous then susan is not curious. Everyone who is old or brave is not quiet. Someone is not old. Someone is either not rich or not funny. Mary is both generous and not funny. Mary is not quiet or curious. Mary is either tall or brave. | John is not rich. | contradiction | ((old(alice))=>(?[X]:((generous(X)|tall(X)))))&
(![X]:((patient(X)|~quiet(X))=>(wise(X)&kind(X))))&
(![X]:((creative(X)|patient(X))=>(~generous(X)&generous(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>((~happy(susan)&curious(susan))))&
(![X]:((generous(X)&~calm(X))<=>~happy(X)))&
((?[X]:((~curious(X)&strong(X))))<=>((~quiet(john)<~>rich(john))))&
(![X]:((curious(X)&~creative(X))=>(curious(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>~rich(X))<=>(~calm(X)&~curious(X))))&
(![X]:((~tall(X)&~calm(X))<=>wise(X)))&
((?[X]:((~kind(X)|~creative(X))))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:(happy(X)=>(~happy(X)|old(X))))&
((?[X]:((calm(X)&~rich(X))))=>(?[X]:(happy(X))))&
((~funny(lucy))=>((kind(mary)&~kind(mary))))&
(((~happy(lucy)<~>~generous(lucy)))=>(~curious(susan)))&
(![X]:((old(X)|brave(X))=>~quiet(X)))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)<~>~funny(X))))&
((generous(mary)&~funny(mary)))&
((~quiet(mary)|curious(mary)))&
((tall(mary)<~>brave(mary))) | ~rich(john) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 1753360242784169628419984
% SZS output start Proof for 1753360242784169628419984
2. ! [X0] : ((~quiet(X0) | patient(X0)) => (kind(X0) & wise(X0))) [input p1]
3. ! [X0] : ((patient(X0) | creative(X0)) => (generous(X0) & ~generous(X0))) [input p2]
4. ? [X0] : (creative(X0) <~> quiet(X0)) <=> (curious(susan) & ~happy(susan)) [input p3]
5. ! [X0] : ((~calm(X0) & generous(X0)) <=> ~happy(X0)) [input p4]
7. ! [X0] : ((~creative(X0) & curious(X0)) => (curious(X0) <~> ~calm(X0))) [input p6]
8. ! [X0] : ((~patient(X0) <~> ~rich(X0)) <=> (~curious(X0) & ~calm(X0))) [input p7]
9. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> wise(X0)) [input p8]
21. ~rich(john) [input hypothesis]
24. ! [X0] : (wise(X0) => (~calm(X0) & ~tall(X0))) [unused predicate definition removal 9]
26. ! [X0] : ((kind(X0) & wise(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 2]
27. ! [X0] : ((generous(X0) & ~generous(X0)) | (~patient(X0) & ~creative(X0))) [ennf transformation 3]
28. ! [X0] : ((curious(X0) <~> ~calm(X0)) | (creative(X0) | ~curious(X0))) [ennf transformation 7]
29. ! [X0] : ((curious(X0) <~> ~calm(X0)) | creative(X0) | ~curious(X0)) [flattening 28]
30. ! [X0] : ((~calm(X0) & ~tall(X0)) | ~wise(X0)) [ennf transformation 24]
40. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | (~curious(susan) | happy(susan))) & ((curious(susan) & ~happy(susan)) | ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [nnf transformation 4]
41. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~curious(susan) | happy(susan)) & ((curious(susan) & ~happy(susan)) | ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [flattening 40]
42. (? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~curious(susan) | happy(susan)) & ((curious(susan) & ~happy(susan)) | ! [X1] : ((creative(X1) | ~quiet(X1)) & (quiet(X1) | ~creative(X1)))) [rectify 41]
43. ? [X0] : ((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) => ((~quiet(sK1) | ~creative(sK1)) & (quiet(sK1) | creative(sK1))) [choice axiom]
44. (((~quiet(sK1) | ~creative(sK1)) & (quiet(sK1) | creative(sK1))) | ~curious(susan) | happy(susan)) & ((curious(susan) & ~happy(susan)) | ! [X1] : ((creative(X1) | ~quiet(X1)) & (quiet(X1) | ~creative(X1)))) [skolemisation 42,43]
45. ! [X0] : (((~calm(X0) & generous(X0)) | happy(X0)) & (~happy(X0) | (calm(X0) | ~generous(X0)))) [nnf transformation 5]
46. ! [X0] : (((~calm(X0) & generous(X0)) | happy(X0)) & (~happy(X0) | calm(X0) | ~generous(X0))) [flattening 45]
51. ! [X0] : (((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | creative(X0) | ~curious(X0)) [nnf transformation 29]
52. ! [X0] : ((((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0))))) [nnf transformation 8]
53. ! [X0] : ((((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0))))) [flattening 52]
69. wise(X0) | quiet(X0) [cnf transformation 26]
72. ~generous(X0) | ~creative(X0) [cnf transformation 27]
73. ~generous(X0) | ~patient(X0) [cnf transformation 27]
74. ~creative(X0) | generous(X0) [cnf transformation 27]
75. ~patient(X0) | generous(X0) [cnf transformation 27]
77. ~happy(susan) | creative(X1) | ~quiet(X1) [cnf transformation 44]
79. curious(susan) | creative(X1) | ~quiet(X1) [cnf transformation 44]
84. ~calm(X0) | happy(X0) [cnf transformation 46]
92. calm(X0) | ~curious(X0) | creative(X0) | ~curious(X0) [cnf transformation 51]
98. rich(X0) | patient(X0) | curious(X0) | calm(X0) [cnf transformation 53]
100. ~calm(X0) | ~wise(X0) [cnf transformation 30]
121. ~rich(john) [cnf transformation 21]
123. calm(X0) | ~curious(X0) | creative(X0) [duplicate literal removal 92]
137. ~patient(X0) [subsumption resolution 73,75]
138. ~creative(X0) [subsumption resolution 72,74]
141. 4 <=> happy(susan) [avatar definition]
142. ~happy(susan) <- (~4) [avatar component clause 141]
145. 5 <=> curious(susan) [avatar definition]
146. curious(susan) <- (5) [avatar component clause 145]
153. curious(susan) | ~quiet(X1) [subsumption resolution 79,138]
155. 7 <=> ! [X1] : ~quiet(X1) [avatar definition]
156. ~quiet(X1) <- (7) [avatar component clause 155]
157. 7 | 5 [avatar split clause 153,145,155]
158. ~happy(susan) | ~quiet(X1) [subsumption resolution 77,138]
159. 7 | ~4 [avatar split clause 158,141,155]
161. 8 <=> rich(john) [avatar definition]
163. ~rich(john) <- (~8) [avatar component clause 161]
185. ~curious(X0) | calm(X0) [subsumption resolution 123,138]
186. rich(X0) | curious(X0) | calm(X0) [subsumption resolution 98,137]
187. rich(X0) | calm(X0) [subsumption resolution 186,185]
251. ~8 [avatar split clause 121,161]
263. calm(susan) <- (5) [resolution 185,146]
264. calm(john) <- (~8) [resolution 187,163]
268. happy(susan) <- (5) [resolution 263,84]
269. $false <- (~4, 5) [subsumption resolution 268,142]
270. 4 | ~5 [avatar contradiction clause 269]
276. ~wise(john) <- (~8) [resolution 264,100]
293. quiet(john) <- (~8) [resolution 276,69]
296. $false <- (7, ~8) [subsumption resolution 293,156]
297. ~7 | 8 [avatar contradiction clause 296]
300. $false [avatar sat refutation 157,159,251,270,297]
% SZS output end Proof for 1753360242784169628419984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either not funny or creative and vice versa. Everyone who is curious or tall is not brave. Everyone who is old is creative or not humble and vice versa. If someone is brave then lucy is not wise and vice versa. If someone is both happy and wise then susan is both kind and not brave. Everyone who is both wise and not funny is calm or not patient. Everyone who is both not creative and old is not kind. Everyone who is not quiet is quiet. Everyone who is both not wise and old is wise or rich. If someone is not curious or not generous then alice is brave and vice versa. If susan is not old or not kind then someone is both creative and not wise. If someone is both not brave and not happy then someone is not patient. Everyone who is not kind is both not tall and curious. Everyone who is either not old or strong is both not happy and creative and vice versa. Everyone who is both not tall and funny is both kind and not tall and vice versa. Everyone who is humble or kind is both curious and calm. Mary is both not brave and calm. Someone is quiet or curious. Someone is either not brave or not generous. Lucy is funny. Fred is either not old or curious. Alice is either not creative or old. Someone is either not rich or curious. | Fred is not curious. | contradiction | (![X]:(~humble(X)<=>(~funny(X)<~>creative(X))))&
(![X]:((curious(X)|tall(X))=>~brave(X)))&
(![X]:(old(X)<=>(creative(X)|~humble(X))))&
((?[X]:(brave(X)))<=>(~wise(lucy)))&
((?[X]:((happy(X)&wise(X))))=>((kind(susan)&~brave(susan))))&
(![X]:((wise(X)&~funny(X))=>(calm(X)|~patient(X))))&
(![X]:((~creative(X)&old(X))=>~kind(X)))&
(![X]:(~quiet(X)=>quiet(X)))&
(![X]:((~wise(X)&old(X))=>(wise(X)|rich(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>(brave(alice)))&
(((~old(susan)|~kind(susan)))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~brave(X)&~happy(X))))=>(?[X]:(~patient(X))))&
(![X]:(~kind(X)=>(~tall(X)&curious(X))))&
(![X]:((~old(X)<~>strong(X))<=>(~happy(X)&creative(X))))&
(![X]:((~tall(X)&funny(X))<=>(kind(X)&~tall(X))))&
(![X]:((humble(X)|kind(X))=>(curious(X)&calm(X))))&
((~brave(mary)&calm(mary)))&
(?[X]:((quiet(X)|curious(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(funny(lucy))&
((~old(fred)<~>curious(fred)))&
((~creative(alice)<~>old(alice)))&
(?[X]:((~rich(X)<~>curious(X)))) | ~curious(fred) | [
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 869914661389582567077362
% SZS output start Proof for 869914661389582567077362
13. ! [X0] : (~kind(X0) => (curious(X0) & ~tall(X0))) [input p12]
16. ! [X0] : ((kind(X0) | humble(X0)) => (calm(X0) & curious(X0))) [input p15]
24. ~curious(fred) [input hypothesis]
30. ! [X0] : ((kind(X0) | humble(X0)) => curious(X0)) [pure predicate removal 16]
39. ! [X0] : ((curious(X0) & ~tall(X0)) | kind(X0)) [ennf transformation 13]
40. ! [X0] : (curious(X0) | (~kind(X0) & ~humble(X0))) [ennf transformation 30]
89. curious(X0) | kind(X0) [cnf transformation 39]
101. curious(X0) | ~kind(X0) [cnf transformation 40]
112. ~curious(fred) [cnf transformation 24]
158. 11 <=> ! [X1] : curious(X1) [avatar definition]
159. curious(X1) <- (11) [avatar component clause 158]
180. curious(X0) [subsumption resolution 101,89]
181. 11 [avatar split clause 180,158]
197. 18 <=> curious(fred) [avatar definition]
199. ~curious(fred) <- (~18) [avatar component clause 197]
221. ~18 [avatar split clause 112,197]
222. $false <- (11, ~18) [resolution 199,159]
223. ~11 | 18 [avatar contradiction clause 222]
224. $false [avatar sat refutation 181,221,223]
% SZS output end Proof for 869914661389582567077362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not creative then paul is funny or humble.
Everyone who is both calm and not quiet is not calm and vice versa.
Everyone who is either curious or calm is both generous and not humble and vice versa.
If someone is either not calm or happy then someone is brave and vice versa.
Everyone who is either old or strong is not humble or not patient.
If paul is humble or not tall then someone is wise or tall and vice versa.
If someone is either not curious or not patient then someone is both funny and rich.
Everyone who is not wise is not quiet or strong and vice versa.
If someone is either humble or not strong then lucy is not happy and vice versa.
Everyone who is either not rich or creative is both not funny and not kind and vice versa.
Everyone who is not rich is either calm or not humble and vice versa.
If alice is not curious or not funny then someone is calm or funny.
Everyone who is both not strong and generous is both not calm and wise and vice versa.
If paul is both not calm and creative then paul is not patient.
Everyone who is tall or funny is both not creative and not wise.
If fred is either calm or kind then someone is not calm or not tall and vice versa.
Someone is curious or not strong.
Someone is patient or not curious.
Alice is curious.
Someone is either not wise or old.
Someone is both not patient and quiet.
Someone is either tall or calm.
Someone is either not curious or not brave.
Someone is not generous or not brave. | Alice is not rich. | neutral | ((~creative(paul))=>((funny(paul)|humble(paul))))&
(![X]:((calm(X)&~quiet(X))<=>~calm(X)))&
(![X]:((curious(X)<~>calm(X))<=>(generous(X)&~humble(X))))&
((?[X]:((~calm(X)<~>happy(X))))<=>(?[X]:(brave(X))))&
(![X]:((old(X)<~>strong(X))=>(~humble(X)|~patient(X))))&
(((humble(paul)|~tall(paul)))<=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((~curious(X)<~>~patient(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:(~wise(X)<=>(~quiet(X)|strong(X))))&
((?[X]:((humble(X)<~>~strong(X))))<=>(~happy(lucy)))&
(![X]:((~rich(X)<~>creative(X))<=>(~funny(X)&~kind(X))))&
(![X]:(~rich(X)<=>(calm(X)<~>~humble(X))))&
(((~curious(alice)|~funny(alice)))=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((~strong(X)&generous(X))<=>(~calm(X)&wise(X))))&
(((~calm(paul)&creative(paul)))=>(~patient(paul)))&
(![X]:((tall(X)|funny(X))=>(~creative(X)&~wise(X))))&
(((calm(fred)<~>kind(fred)))<=>(?[X]:((~calm(X)|~tall(X)))))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((patient(X)|~curious(X))))&
(curious(alice))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((tall(X)<~>calm(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((~generous(X)|~brave(X)))) | ~rich(alice) | []
| null | 0 |
Everyone who is generous is both funny and not humble and vice versa.
Everyone who is either not quiet or not happy is not curious and vice versa.
Everyone who is both calm and not humble is generous.
If fred is not creative then someone is either curious or not wise and vice versa.
Everyone who is either strong or not brave is both not humble and rich.
Everyone who is both curious and patient is either funny or not wise.
If alice is not creative then mary is not tall.
If someone is either patient or strong then someone is both not old and not curious.
Everyone who is not funny is either not curious or not strong.
If mary is both calm and not wise then someone is either not humble or not tall.
Everyone who is wise or humble is creative.
Everyone who is both generous and wise is not old or not strong and vice versa.
Everyone who is either funny or not old is both not rich and not brave.
Everyone who is both not happy and not strong is either not rich or creative and vice versa.
If someone is not wise or funny then someone is not brave.
Everyone who is not kind or not curious is either not curious or tall and vice versa.
John is brave.
Someone is both not tall and old.
Someone is not funny or not happy.
Lucy is either brave or not rich.
Someone is either tall or curious.
Alice is both not rich and happy.
Mary is not funny. | Mary is not generous. | entailment | (![X]:(generous(X)<=>(funny(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>~curious(X)))&
(![X]:((calm(X)&~humble(X))=>generous(X)))&
((~creative(fred))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(![X]:((strong(X)<~>~brave(X))=>(~humble(X)&rich(X))))&
(![X]:((curious(X)&patient(X))=>(funny(X)<~>~wise(X))))&
((~creative(alice))=>(~tall(mary)))&
((?[X]:((patient(X)<~>strong(X))))=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:(~funny(X)=>(~curious(X)<~>~strong(X))))&
(((calm(mary)&~wise(mary)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:((wise(X)|humble(X))=>creative(X)))&
(![X]:((generous(X)&wise(X))<=>(~old(X)|~strong(X))))&
(![X]:((funny(X)<~>~old(X))=>(~rich(X)&~brave(X))))&
(![X]:((~happy(X)&~strong(X))<=>(~rich(X)<~>creative(X))))&
((?[X]:((~wise(X)|funny(X))))=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)|~curious(X))<=>(~curious(X)<~>tall(X))))&
(brave(john))&
(?[X]:((~tall(X)&old(X))))&
(?[X]:((~funny(X)|~happy(X))))&
((brave(lucy)<~>~rich(lucy)))&
(?[X]:((tall(X)<~>curious(X))))&
((~rich(alice)&happy(alice)))&
(~funny(mary)) | ~generous(mary) | [
"p0",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 7404340540593561570876026
% SZS output start Proof for 7404340540593561570876026
1. ! [X0] : (generous(X0) <=> (~humble(X0) & funny(X0))) [input p0]
23. ~funny(mary) [input p22]
24. generous(mary) [input hypothesis]
38. ! [X0] : ((generous(X0) | (humble(X0) | ~funny(X0))) & ((~humble(X0) & funny(X0)) | ~generous(X0))) [nnf transformation 1]
39. ! [X0] : ((generous(X0) | humble(X0) | ~funny(X0)) & ((~humble(X0) & funny(X0)) | ~generous(X0))) [flattening 38]
70. ~generous(X0) | funny(X0) [cnf transformation 39]
129. ~funny(mary) [cnf transformation 23]
130. generous(mary) [cnf transformation 24]
215. funny(mary) [resolution 70,130]
216. $false [subsumption resolution 215,129]
% SZS output end Proof for 7404340540593561570876026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not rich and not generous then someone is not kind or not quiet.
If someone is curious then mary is both creative and not generous.
If someone is both not humble and not calm then someone is funny.
Everyone who is creative or brave is not quiet.
If mary is not patient or kind then someone is either not wise or kind and vice versa.
Everyone who is either calm or not creative is either curious or not happy.
If someone is not patient or not calm then susan is both humble and not patient and vice versa.
Everyone who is tall or funny is both not curious and wise and vice versa.
If someone is not quiet or calm then someone is old or curious.
If lucy is not tall or brave then someone is generous.
If mary is not wise then someone is both not patient and kind and vice versa.
If someone is both calm and funny then paul is strong or patient.
If john is either not humble or brave then fred is both old and not brave and vice versa.
If someone is both not tall and not generous then someone is both quiet and rich and vice versa.
If paul is not quiet or creative then someone is either not curious or humble and vice versa.
If someone is both not brave and brave then someone is both wise and quiet.
Mary is either not funny or tall.
Someone is both quiet and generous.
Someone is not tall or not rich.
Mary is generous or not wise.
Someone is either not curious or not quiet.
Someone is either not brave or tall.
Paul is not generous or calm.
Someone is not calm. | Paul is generous. | neutral | (((~rich(fred)&~generous(fred)))=>(?[X]:((~kind(X)|~quiet(X)))))&
((?[X]:(curious(X)))=>((creative(mary)&~generous(mary))))&
((?[X]:((~humble(X)&~calm(X))))=>(?[X]:(funny(X))))&
(![X]:((creative(X)|brave(X))=>~quiet(X)))&
(((~patient(mary)|kind(mary)))<=>(?[X]:((~wise(X)<~>kind(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(curious(X)<~>~happy(X))))&
((?[X]:((~patient(X)|~calm(X))))<=>((humble(susan)&~patient(susan))))&
(![X]:((tall(X)|funny(X))<=>(~curious(X)&wise(X))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((old(X)|curious(X)))))&
(((~tall(lucy)|brave(lucy)))=>(?[X]:(generous(X))))&
((~wise(mary))<=>(?[X]:((~patient(X)&kind(X)))))&
((?[X]:((calm(X)&funny(X))))=>((strong(paul)|patient(paul))))&
(((~humble(john)<~>brave(john)))<=>((old(fred)&~brave(fred))))&
((?[X]:((~tall(X)&~generous(X))))<=>(?[X]:((quiet(X)&rich(X)))))&
(((~quiet(paul)|creative(paul)))<=>(?[X]:((~curious(X)<~>humble(X)))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:((wise(X)&quiet(X)))))&
((~funny(mary)<~>tall(mary)))&
(?[X]:((quiet(X)&generous(X))))&
(?[X]:((~tall(X)|~rich(X))))&
((generous(mary)|~wise(mary)))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~brave(X)<~>tall(X))))&
((~generous(paul)|calm(paul)))&
(?[X]:(~calm(X))) | generous(paul) | []
| null | 0 |
Everyone who is either calm or not patient is patient or not happy and vice versa.
Everyone who is both generous and curious is either not curious or funny and vice versa.
If someone is tall or patient then lucy is both funny and not humble and vice versa.
If john is either old or not calm then someone is either old or funny and vice versa.
Everyone who is either happy or not patient is either calm or not humble and vice versa.
If paul is not quiet then someone is curious or not old and vice versa.
If john is not quiet or not generous then paul is both not curious and not calm and vice versa.
Everyone who is not wise or not generous is not old or not tall.
If someone is either not generous or not funny then someone is either not kind or rich and vice versa.
Everyone who is either not generous or wise is not quiet and vice versa.
If susan is calm then someone is generous.
If john is both strong and not calm then someone is rich or funny and vice versa.
Everyone who is either not funny or quiet is either not old or strong and vice versa.
If someone is curious or old then someone is both not kind and not old.
Everyone who is not old or kind is not creative and vice versa.
If paul is not wise then someone is both humble and patient and vice versa.
Paul is both not creative and not kind.
Alice is both funny and not strong.
Someone is old or brave.
Someone is either not generous or not rich.
Susan is quiet.
Paul is not brave or not wise.
Someone is both kind and not calm.
Susan is humble. | John is not calm. | entailment | (![X]:((calm(X)<~>~patient(X))<=>(patient(X)|~happy(X))))&
(![X]:((generous(X)&curious(X))<=>(~curious(X)<~>funny(X))))&
((?[X]:((tall(X)|patient(X))))<=>((funny(lucy)&~humble(lucy))))&
(((old(john)<~>~calm(john)))<=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((happy(X)<~>~patient(X))<=>(calm(X)<~>~humble(X))))&
((~quiet(paul))<=>(?[X]:((curious(X)|~old(X)))))&
(((~quiet(john)|~generous(john)))<=>((~curious(paul)&~calm(paul))))&
(![X]:((~wise(X)|~generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~generous(X)<~>~funny(X))))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(![X]:((~generous(X)<~>wise(X))<=>~quiet(X)))&
((calm(susan))=>(?[X]:(generous(X))))&
(((strong(john)&~calm(john)))<=>(?[X]:((rich(X)|funny(X)))))&
(![X]:((~funny(X)<~>quiet(X))<=>(~old(X)<~>strong(X))))&
((?[X]:((curious(X)|old(X))))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((~old(X)|kind(X))<=>~creative(X)))&
((~wise(paul))<=>(?[X]:((humble(X)&patient(X)))))&
((~creative(paul)&~kind(paul)))&
((funny(alice)&~strong(alice)))&
(?[X]:((old(X)|brave(X))))&
(?[X]:((~generous(X)<~>~rich(X))))&
(quiet(susan))&
((~brave(paul)|~wise(paul)))&
(?[X]:((kind(X)&~calm(X))))&
(humble(susan)) | ~calm(john) | [
"p11",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 4665872516325929186553942
% SZS output start Proof for 4665872516325929186553942
12. (~calm(john) & strong(john)) <=> ? [X0] : (funny(X0) | rich(X0)) [input p11]
18. ~strong(alice) & funny(alice) [input p17]
25. calm(john) [input hypothesis]
63. ((~calm(john) & strong(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & (? [X0] : (funny(X0) | rich(X0)) | (calm(john) | ~strong(john))) [nnf transformation 12]
64. ((~calm(john) & strong(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & (? [X0] : (funny(X0) | rich(X0)) | calm(john) | ~strong(john)) [flattening 63]
65. ((~calm(john) & strong(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & (? [X1] : (funny(X1) | rich(X1)) | calm(john) | ~strong(john)) [rectify 64]
66. ? [X1] : (funny(X1) | rich(X1)) => (funny(sK6) | rich(sK6)) [choice axiom]
67. ((~calm(john) & strong(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & ((funny(sK6) | rich(sK6)) | calm(john) | ~strong(john)) [skolemisation 65,66]
143. ~calm(john) | ~funny(X0) [cnf transformation 67]
162. funny(alice) [cnf transformation 18]
172. calm(john) [cnf transformation 25]
214. 9 <=> calm(john) [avatar definition]
328. 31 <=> ! [X0] : ~funny(X0) [avatar definition]
329. ~funny(X0) <- (31) [avatar component clause 328]
330. 31 | ~9 [avatar split clause 143,214,328]
407. 9 [avatar split clause 172,214]
413. $false <- (31) [resolution 329,162]
414. ~31 [avatar contradiction clause 413]
415. $false [avatar sat refutation 330,407,414]
% SZS output end Proof for 4665872516325929186553942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either generous or not happy then someone is either wise or rich and vice versa.
If someone is both not happy and not kind then someone is calm or curious.
If john is both not old and not quiet then someone is either not quiet or strong and vice versa.
Everyone who is both kind and curious is either patient or not tall and vice versa.
If paul is not humble then susan is either patient or happy and vice versa.
If paul is both not funny and calm then alice is wise or not tall and vice versa.
Everyone who is rich or not strong is both not humble and not creative and vice versa.
Everyone who is tall is both strong and old.
If someone is curious or funny then someone is not humble and vice versa.
Everyone who is generous or not funny is not funny.
Everyone who is not tall is happy and vice versa.
If paul is both not tall and kind then someone is not rich or not humble and vice versa.
Everyone who is tall is not old.
If someone is not quiet then someone is calm or not creative.
Everyone who is calm is not quiet or not wise and vice versa.
Someone is either not curious or generous.
Someone is both not strong and wise.
Fred is both brave and not kind.
John is humble.
Someone is not rich.
Someone is both not generous and funny.
Fred is either not quiet or not wise. | Alice is not creative. | neutral | ((?[X]:((generous(X)<~>~happy(X))))<=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:((~happy(X)&~kind(X))))=>(?[X]:((calm(X)|curious(X)))))&
(((~old(john)&~quiet(john)))<=>(?[X]:((~quiet(X)<~>strong(X)))))&
(![X]:((kind(X)&curious(X))<=>(patient(X)<~>~tall(X))))&
((~humble(paul))<=>((patient(susan)<~>happy(susan))))&
(((~funny(paul)&calm(paul)))<=>((wise(alice)|~tall(alice))))&
(![X]:((rich(X)|~strong(X))<=>(~humble(X)&~creative(X))))&
(![X]:(tall(X)=>(strong(X)&old(X))))&
((?[X]:((curious(X)|funny(X))))<=>(?[X]:(~humble(X))))&
(![X]:((generous(X)|~funny(X))=>~funny(X)))&
(![X]:(~tall(X)<=>happy(X)))&
(((~tall(paul)&kind(paul)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:(tall(X)=>~old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((calm(X)|~creative(X)))))&
(![X]:(calm(X)<=>(~quiet(X)|~wise(X))))&
(?[X]:((~curious(X)<~>generous(X))))&
(?[X]:((~strong(X)&wise(X))))&
((brave(fred)&~kind(fred)))&
(humble(john))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)&funny(X))))&
((~quiet(fred)<~>~wise(fred))) | ~creative(alice) | []
| null | 0 |
Everyone who is not strong is brave.
Everyone who is either old or not rich is generous and vice versa.
If paul is either generous or not old then alice is not calm or old and vice versa.
If someone is curious or kind then someone is not tall or funny.
If someone is rich then fred is kind and vice versa.
Everyone who is not happy is both creative and not tall.
If fred is either patient or quiet then someone is either not strong or funny and vice versa.
Everyone who is both patient and not quiet is calm and vice versa.
Everyone who is not patient is either calm or not quiet.
Everyone who is either not happy or not brave is either not old or quiet and vice versa.
Everyone who is old or not quiet is both strong and patient.
If someone is both not patient and quiet then mary is either creative or old.
Everyone who is either creative or rich is both strong and patient and vice versa.
If john is both wise and quiet then alice is not brave and vice versa.
Everyone who is not tall is not brave.
If alice is not curious or calm then someone is either kind or funny.
Someone is both not happy and kind.
Fred is both not wise and brave.
Fred is either kind or tall.
Someone is either generous or rich.
Fred is either happy or kind.
Someone is either tall or not creative.
Paul is either not brave or not strong. | Alice is not generous. | contradiction | (![X]:(~strong(X)=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>generous(X)))&
(((generous(paul)<~>~old(paul)))<=>((~calm(alice)|old(alice))))&
((?[X]:((curious(X)|kind(X))))=>(?[X]:((~tall(X)|funny(X)))))&
((?[X]:(rich(X)))<=>(kind(fred)))&
(![X]:(~happy(X)=>(creative(X)&~tall(X))))&
(((patient(fred)<~>quiet(fred)))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((patient(X)&~quiet(X))<=>calm(X)))&
(![X]:(~patient(X)=>(calm(X)<~>~quiet(X))))&
(![X]:((~happy(X)<~>~brave(X))<=>(~old(X)<~>quiet(X))))&
(![X]:((old(X)|~quiet(X))=>(strong(X)&patient(X))))&
((?[X]:((~patient(X)&quiet(X))))=>((creative(mary)<~>old(mary))))&
(![X]:((creative(X)<~>rich(X))<=>(strong(X)&patient(X))))&
(((wise(john)&quiet(john)))<=>(~brave(alice)))&
(![X]:(~tall(X)=>~brave(X)))&
(((~curious(alice)|calm(alice)))=>(?[X]:((kind(X)<~>funny(X)))))&
(?[X]:((~happy(X)&kind(X))))&
((~wise(fred)&brave(fred)))&
((kind(fred)<~>tall(fred)))&
(?[X]:((generous(X)<~>rich(X))))&
((happy(fred)<~>kind(fred)))&
(?[X]:((tall(X)<~>~creative(X))))&
((~brave(paul)<~>~strong(paul))) | ~generous(alice) | [
"p1",
"p2",
"p4",
"p14",
"p17",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 2568045573847106819722199
% SZS output start Proof for 2568045573847106819722199
2. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> generous(X0)) [input p1]
3. (generous(paul) <~> ~old(paul)) <=> (old(alice) | ~calm(alice)) [input p2]
5. ? [X0] : rich(X0) <=> kind(fred) [input p4]
15. ! [X0] : (~tall(X0) => ~brave(X0)) [input p14]
18. brave(fred) & ~wise(fred) [input p17]
19. kind(fred) <~> tall(fred) [input p18]
24. ~generous(alice) [input hypothesis]
32. ! [X0] : (~brave(X0) | tall(X0)) [ennf transformation 15]
34. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~generous(X0)) & (generous(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 2]
35. (((old(paul) | ~generous(paul)) & (~old(paul) | generous(paul))) | (~old(alice) & calm(alice))) & ((old(alice) | ~calm(alice)) | ((generous(paul) | old(paul)) & (~old(paul) | ~generous(paul)))) [nnf transformation 3]
36. (((old(paul) | ~generous(paul)) & (~old(paul) | generous(paul))) | (~old(alice) & calm(alice))) & (old(alice) | ~calm(alice) | ((generous(paul) | old(paul)) & (~old(paul) | ~generous(paul)))) [flattening 35]
40. (? [X0] : rich(X0) | ~kind(fred)) & (kind(fred) | ! [X0] : ~rich(X0)) [nnf transformation 5]
41. (? [X0] : rich(X0) | ~kind(fred)) & (kind(fred) | ! [X1] : ~rich(X1)) [rectify 40]
42. ? [X0] : rich(X0) => rich(sK1) [choice axiom]
43. (rich(sK1) | ~kind(fred)) & (kind(fred) | ! [X1] : ~rich(X1)) [skolemisation 41,42]
62. (~tall(fred) | ~kind(fred)) & (tall(fred) | kind(fred)) [nnf transformation 19]
73. generous(X0) | old(X0) | rich(X0) [cnf transformation 34]
75. ~generous(X0) | ~old(X0) | rich(X0) [cnf transformation 34]
79. ~old(paul) | generous(paul) | ~old(alice) [cnf transformation 36]
81. old(paul) | ~generous(paul) | ~old(alice) [cnf transformation 36]
84. kind(fred) | ~rich(X1) [cnf transformation 43]
124. ~brave(X0) | tall(X0) [cnf transformation 32]
132. brave(fred) [cnf transformation 18]
134. ~tall(fred) | ~kind(fred) [cnf transformation 62]
143. ~generous(alice) [cnf transformation 24]
145. 1 <=> old(alice) [avatar definition]
149. 2 <=> generous(paul) [avatar definition]
150. generous(paul) <- (2) [avatar component clause 149]
151. ~generous(paul) <- (~2) [avatar component clause 149]
153. 3 <=> old(paul) [avatar definition]
154. ~old(paul) <- (~3) [avatar component clause 153]
155. old(paul) <- (3) [avatar component clause 153]
156. ~1 | ~2 | 3 [avatar split clause 81,153,149,145]
162. ~1 | 2 | ~3 [avatar split clause 79,153,149,145]
183. 9 <=> kind(fred) [avatar definition]
192. 11 <=> ! [X1] : ~rich(X1) [avatar definition]
193. ~rich(X1) <- (11) [avatar component clause 192]
194. 11 | 9 [avatar split clause 84,183,192]
261. 24 <=> tall(fred) [avatar definition]
264. ~9 | ~24 [avatar split clause 134,261,183]
304. tall(fred) [resolution 124,132]
309. 24 [avatar split clause 304,261]
315. old(alice) | rich(alice) [resolution 73,143]
316. old(paul) | rich(paul) <- (~2) [resolution 73,151]
317. old(alice) <- (11) [subsumption resolution 315,193]
318. 1 | ~11 [avatar split clause 317,192,145]
319. rich(paul) <- (~2, ~3) [subsumption resolution 316,154]
320. $false <- (~2, ~3, 11) [subsumption resolution 319,193]
321. 2 | 3 | ~11 [avatar contradiction clause 320]
334. ~old(paul) | rich(paul) <- (2) [resolution 75,150]
337. rich(paul) <- (2, 3) [subsumption resolution 334,155]
338. $false <- (2, 3, 11) [subsumption resolution 337,193]
339. ~2 | ~3 | ~11 [avatar contradiction clause 338]
340. $false [avatar sat refutation 156,162,194,264,309,318,321,339]
% SZS output end Proof for 2568045573847106819722199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or old then john is both old and not wise and vice versa.
Everyone who is either patient or not brave is funny and vice versa.
Everyone who is patient is not humble and vice versa.
Everyone who is curious or old is rich or curious.
If someone is strong then john is both not generous and not brave.
If someone is both not generous and not kind then someone is either funny or not happy and vice versa.
Everyone who is not generous is both not curious and not happy and vice versa.
Everyone who is either rich or not creative is both not wise and not brave and vice versa.
If paul is not kind or generous then someone is not kind and vice versa.
Everyone who is not creative or tall is not happy or not funny.
Everyone who is both patient and creative is old and vice versa.
If someone is both not funny and not quiet then paul is either happy or not rich and vice versa.
Everyone who is not rich or not happy is either funny or old and vice versa.
Everyone who is calm is either patient or humble.
If someone is rich then john is tall.
If paul is not rich then someone is either not curious or not generous and vice versa.
Someone is not patient.
Someone is either not wise or not brave.
Someone is both curious and quiet.
Fred is either not humble or calm.
John is not tall or old.
Someone is both not humble and funny.
Lucy is not brave.
Someone is generous or not strong. | John is not brave. | entailment | ((?[X]:((~creative(X)<~>old(X))))<=>((old(john)&~wise(john))))&
(![X]:((patient(X)<~>~brave(X))<=>funny(X)))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((curious(X)|old(X))=>(rich(X)|curious(X))))&
((?[X]:(strong(X)))=>((~generous(john)&~brave(john))))&
((?[X]:((~generous(X)&~kind(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(~generous(X)<=>(~curious(X)&~happy(X))))&
(![X]:((rich(X)<~>~creative(X))<=>(~wise(X)&~brave(X))))&
(((~kind(paul)|generous(paul)))<=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)|tall(X))=>(~happy(X)|~funny(X))))&
(![X]:((patient(X)&creative(X))<=>old(X)))&
((?[X]:((~funny(X)&~quiet(X))))<=>((happy(paul)<~>~rich(paul))))&
(![X]:((~rich(X)|~happy(X))<=>(funny(X)<~>old(X))))&
(![X]:(calm(X)=>(patient(X)<~>humble(X))))&
((?[X]:(rich(X)))=>(tall(john)))&
((~rich(paul))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(?[X]:(~patient(X)))&
(?[X]:((~wise(X)<~>~brave(X))))&
(?[X]:((curious(X)&quiet(X))))&
((~humble(fred)<~>calm(fred)))&
((~tall(john)|old(john)))&
(?[X]:((~humble(X)&funny(X))))&
(~brave(lucy))&
(?[X]:((generous(X)|~strong(X)))) | ~brave(john) | [
"p1",
"p2",
"p7",
"p10",
"p12",
"p14",
"p20",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 467931293674947708892247
% SZS output start Proof for 467931293674947708892247
2. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> funny(X0)) [input p1]
3. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p2]
8. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> (~brave(X0) & ~wise(X0))) [input p7]
11. ! [X0] : ((creative(X0) & patient(X0)) <=> old(X0)) [input p10]
13. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> (funny(X0) <~> old(X0))) [input p12]
15. ? [X0] : rich(X0) => tall(john) [input p14]
21. old(john) | ~tall(john) [input p20]
22. ? [X0] : (funny(X0) & ~humble(X0)) [input p21]
25. brave(john) [input hypothesis]
34. tall(john) | ! [X0] : ~rich(X0) [ennf transformation 15]
40. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ~funny(X0)) & (funny(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 2]
41. ! [X0] : ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))) [nnf transformation 3]
49. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 8]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [flattening 49]
56. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0)) & (old(X0) | (~creative(X0) | ~patient(X0)))) [nnf transformation 11]
57. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0)) & (old(X0) | ~creative(X0) | ~patient(X0))) [flattening 56]
62. ! [X0] : (((~happy(X0) | ~rich(X0)) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | (happy(X0) & rich(X0)))) [nnf transformation 13]
63. ! [X0] : ((~happy(X0) | ~rich(X0) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | (happy(X0) & rich(X0)))) [flattening 62]
77. ? [X0] : (funny(X0) & ~humble(X0)) => (funny(sK9) & ~humble(sK9)) [choice axiom]
78. funny(sK9) & ~humble(sK9) [skolemisation 22,77]
85. ~brave(X0) | funny(X0) | ~patient(X0) [cnf transformation 40]
88. ~funny(X0) | ~patient(X0) | brave(X0) [cnf transformation 40]
90. humble(X0) | patient(X0) [cnf transformation 41]
104. ~rich(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 50]
105. ~brave(X0) | rich(X0) | creative(X0) [cnf transformation 50]
113. ~patient(X0) | ~creative(X0) | old(X0) [cnf transformation 57]
114. ~old(X0) | patient(X0) [cnf transformation 57]
115. ~old(X0) | creative(X0) [cnf transformation 57]
124. ~funny(X0) | ~old(X0) | rich(X0) [cnf transformation 63]
130. tall(john) | ~rich(X0) [cnf transformation 34]
142. old(john) | ~tall(john) [cnf transformation 21]
143. ~humble(sK9) [cnf transformation 78]
144. funny(sK9) [cnf transformation 78]
146. brave(john) [cnf transformation 25]
148. 1 <=> old(john) [avatar definition]
149. old(john) <- (1) [avatar component clause 148]
250. 23 <=> ! [X0] : ~rich(X0) [avatar definition]
251. ~rich(X0) <- (23) [avatar component clause 250]
253. 24 <=> tall(john) [avatar definition]
256. 23 | 24 [avatar split clause 130,253,250]
293. ~24 | 1 [avatar split clause 142,148,253]
298. patient(sK9) [resolution 90,143]
306. funny(john) | ~patient(john) [resolution 85,146]
308. 32 <=> patient(john) [avatar definition]
312. 33 <=> funny(john) [avatar definition]
314. funny(john) <- (33) [avatar component clause 312]
315. ~32 | 33 [avatar split clause 306,312,308]
368. ~patient(sK9) | brave(sK9) [resolution 88,144]
374. brave(sK9) [subsumption resolution 368,298]
397. rich(sK9) | creative(sK9) [resolution 105,374]
413. ~creative(sK9) | old(sK9) [resolution 113,298]
431. 46 <=> old(sK9) [avatar definition]
433. old(sK9) <- (46) [avatar component clause 431]
435. 47 <=> creative(sK9) [avatar definition]
438. 46 | ~47 [avatar split clause 413,435,431]
440. creative(sK9) <- (23) [subsumption resolution 397,251]
441. 47 | ~23 [avatar split clause 440,250,435]
448. creative(john) <- (1) [resolution 149,115]
449. patient(john) <- (1) [resolution 149,114]
453. 32 | ~1 [avatar split clause 449,148,308]
465. ~old(john) | rich(john) <- (33) [resolution 124,314]
468. ~old(sK9) | rich(sK9) [resolution 124,144]
469. rich(john) <- (1, 33) [subsumption resolution 465,149]
474. rich(sK9) <- (46) [subsumption resolution 468,433]
475. $false <- (23, 46) [subsumption resolution 474,251]
476. ~23 | ~46 [avatar contradiction clause 475]
650. ~creative(john) | ~brave(john) <- (1, 33) [resolution 469,104]
652. ~brave(john) <- (1, 33) [subsumption resolution 650,448]
653. $false <- (1, 33) [subsumption resolution 652,146]
654. ~1 | ~33 [avatar contradiction clause 653]
655. $false [avatar sat refutation 256,293,315,438,441,453,476,654]
% SZS output end Proof for 467931293674947708892247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or humble is either not brave or not generous. Everyone who is not old or not rich is either not funny or generous. If someone is generous or not funny then someone is not old or not tall and vice versa. If someone is either not humble or not strong then someone is either not happy or calm. If lucy is both not rich and rich then someone is not old or not tall and vice versa. Everyone who is happy or calm is both quiet and happy and vice versa. Everyone who is both not creative and not old is calm and vice versa. Everyone who is both not happy and brave is brave or not quiet. Everyone who is both not generous and old is either not strong or not brave. Everyone who is either curious or not wise is both not generous and not wise and vice versa. If someone is curious or patient then paul is both quiet and not happy. Everyone who is patient is both funny and not wise and vice versa. Everyone who is both brave and not funny is kind. Everyone who is curious or old is either kind or tall. Someone is both humble and not kind. Lucy is patient or quiet. Someone is patient or generous. Lucy is either generous or not kind. Someone is funny. Mary is not wise. | Paul is calm. | contradiction | (![X]:((~generous(X)|humble(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~old(X)|~rich(X))=>(~funny(X)<~>generous(X))))&
((?[X]:((generous(X)|~funny(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))=>(?[X]:((~happy(X)<~>calm(X)))))&
(((~rich(lucy)&rich(lucy)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((happy(X)|calm(X))<=>(quiet(X)&happy(X))))&
(![X]:((~creative(X)&~old(X))<=>calm(X)))&
(![X]:((~happy(X)&brave(X))=>(brave(X)|~quiet(X))))&
(![X]:((~generous(X)&old(X))=>(~strong(X)<~>~brave(X))))&
(![X]:((curious(X)<~>~wise(X))<=>(~generous(X)&~wise(X))))&
((?[X]:((curious(X)|patient(X))))=>((quiet(paul)&~happy(paul))))&
(![X]:(patient(X)<=>(funny(X)&~wise(X))))&
(![X]:((brave(X)&~funny(X))=>kind(X)))&
(![X]:((curious(X)|old(X))=>(kind(X)<~>tall(X))))&
(?[X]:((humble(X)&~kind(X))))&
((patient(lucy)|quiet(lucy)))&
(?[X]:((patient(X)|generous(X))))&
((generous(lucy)<~>~kind(lucy)))&
(?[X]:(funny(X)))&
(~wise(mary)) | calm(paul) | [
"p2",
"p4",
"p5",
"p10",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 1466109802620328783315660
% SZS output start Proof for 1466109802620328783315660
3. ? [X0] : (~funny(X0) | generous(X0)) <=> ? [X0] : (~tall(X0) | ~old(X0)) [input p2]
5. (rich(lucy) & ~rich(lucy)) <=> ? [X0] : (~tall(X0) | ~old(X0)) [input p4]
6. ! [X0] : ((calm(X0) | happy(X0)) <=> (happy(X0) & quiet(X0))) [input p5]
11. ? [X0] : (patient(X0) | curious(X0)) => (~happy(paul) & quiet(paul)) [input p10]
17. ? [X0] : (generous(X0) | patient(X0)) [input p16]
21. calm(paul) [input hypothesis]
22. ? [X0] : (~funny(X0) | generous(X0)) <=> ? [X1] : (~tall(X1) | ~old(X1)) [rectify 3]
31. (~happy(paul) & quiet(paul)) | ! [X0] : (~patient(X0) & ~curious(X0)) [ennf transformation 11]
37. (? [X0] : (~funny(X0) | generous(X0)) | ! [X1] : (tall(X1) & old(X1))) & (? [X1] : (~tall(X1) | ~old(X1)) | ! [X0] : (funny(X0) & ~generous(X0))) [nnf transformation 22]
38. (? [X0] : (~funny(X0) | generous(X0)) | ! [X1] : (tall(X1) & old(X1))) & (? [X2] : (~tall(X2) | ~old(X2)) | ! [X3] : (funny(X3) & ~generous(X3))) [rectify 37]
39. ? [X0] : (~funny(X0) | generous(X0)) => (~funny(sK0) | generous(sK0)) [choice axiom]
40. ? [X2] : (~tall(X2) | ~old(X2)) => (~tall(sK1) | ~old(sK1)) [choice axiom]
41. ((~funny(sK0) | generous(sK0)) | ! [X1] : (tall(X1) & old(X1))) & ((~tall(sK1) | ~old(sK1)) | ! [X3] : (funny(X3) & ~generous(X3))) [skolemisation 38,40,39]
46. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X0] : (~tall(X0) | ~old(X0)) | (~rich(lucy) | rich(lucy))) [nnf transformation 5]
47. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X0] : (~tall(X0) | ~old(X0)) | ~rich(lucy) | rich(lucy)) [flattening 46]
48. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X1] : (~tall(X1) | ~old(X1)) | ~rich(lucy) | rich(lucy)) [rectify 47]
49. ? [X1] : (~tall(X1) | ~old(X1)) => (~tall(sK3) | ~old(sK3)) [choice axiom]
50. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & ((~tall(sK3) | ~old(sK3)) | ~rich(lucy) | rich(lucy)) [skolemisation 48,49]
51. ! [X0] : (((calm(X0) | happy(X0)) | (~happy(X0) | ~quiet(X0))) & ((happy(X0) & quiet(X0)) | (~calm(X0) & ~happy(X0)))) [nnf transformation 6]
52. ! [X0] : ((calm(X0) | happy(X0) | ~happy(X0) | ~quiet(X0)) & ((happy(X0) & quiet(X0)) | (~calm(X0) & ~happy(X0)))) [flattening 51]
63. ? [X0] : (generous(X0) | patient(X0)) => (generous(sK5) | patient(sK5)) [choice axiom]
64. generous(sK5) | patient(sK5) [skolemisation 17,63]
76. ~tall(sK1) | ~old(sK1) | ~generous(X3) [cnf transformation 41]
85. ~rich(lucy) | old(X0) [cnf transformation 50]
86. ~rich(lucy) | tall(X0) [cnf transformation 50]
87. rich(lucy) | old(X0) [cnf transformation 50]
88. rich(lucy) | tall(X0) [cnf transformation 50]
92. ~calm(X0) | happy(X0) [cnf transformation 52]
109. ~happy(paul) | ~patient(X0) [cnf transformation 31]
121. generous(sK5) | patient(sK5) [cnf transformation 64]
126. calm(paul) [cnf transformation 21]
131. 1 <=> ! [X1] : tall(X1) [avatar definition]
132. tall(X1) <- (1) [avatar component clause 131]
143. 4 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (4) [avatar component clause 143]
150. 6 <=> old(sK1) [avatar definition]
152. ~old(sK1) <- (~6) [avatar component clause 150]
154. 7 <=> tall(sK1) [avatar definition]
156. ~tall(sK1) <- (~7) [avatar component clause 154]
159. 8 <=> ! [X3] : ~generous(X3) [avatar definition]
160. ~generous(X3) <- (8) [avatar component clause 159]
161. 8 | ~6 | ~7 [avatar split clause 76,154,150,159]
181. 13 <=> rich(lucy) [avatar definition]
184. 1 | 13 [avatar split clause 88,181,131]
185. 4 | 13 [avatar split clause 87,181,143]
186. 1 | ~13 [avatar split clause 86,181,131]
187. 4 | ~13 [avatar split clause 85,181,143]
190. 14 <=> ! [X0] : ~patient(X0) [avatar definition]
191. ~patient(X0) <- (14) [avatar component clause 190]
193. 15 <=> happy(paul) [avatar definition]
196. 14 | ~15 [avatar split clause 109,193,190]
217. 20 <=> patient(sK5) [avatar definition]
219. patient(sK5) <- (20) [avatar component clause 217]
221. 21 <=> generous(sK5) [avatar definition]
223. generous(sK5) <- (21) [avatar component clause 221]
224. 20 | 21 [avatar split clause 121,221,217]
235. $false <- (1, ~7) [resolution 156,132]
236. ~1 | 7 [avatar contradiction clause 235]
237. $false <- (4, ~6) [subsumption resolution 152,144]
238. ~4 | 6 [avatar contradiction clause 237]
242. happy(paul) [resolution 92,126]
245. 15 [avatar split clause 242,193]
246. $false <- (14, 20) [resolution 191,219]
247. ~14 | ~20 [avatar contradiction clause 246]
248. $false <- (8, 21) [subsumption resolution 223,160]
249. ~8 | ~21 [avatar contradiction clause 248]
250. $false [avatar sat refutation 161,184,185,186,187,196,224,236,238,245,247,249]
% SZS output end Proof for 1466109802620328783315660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not tall then susan is both quiet and curious and vice versa.
If john is not creative or tall then someone is either funny or not calm and vice versa.
If alice is either creative or not wise then someone is both kind and not generous.
If john is either not patient or not creative then someone is both not humble and not brave.
If susan is not kind then someone is either tall or not quiet and vice versa.
If someone is both not creative and not happy then lucy is either not funny or not creative and vice versa.
If someone is not kind then john is happy and vice versa.
Everyone who is either not patient or not happy is not generous or strong and vice versa.
Everyone who is not patient or not creative is not quiet.
Everyone who is either not calm or calm is either not quiet or not creative.
Everyone who is rich is both wise and not brave and vice versa.
Everyone who is either curious or patient is not quiet or wise and vice versa.
If susan is either rich or not curious then someone is patient or not calm.
If someone is either humble or curious then someone is both not strong and quiet and vice versa.
Everyone who is both curious and humble is both not generous and brave.
Someone is both strong and not curious.
John is both not curious and brave.
Someone is either not wise or old.
Someone is both not generous and not calm.
Someone is not curious.
Susan is either not quiet or not patient. | Susan is not curious. | entailment | ((?[X]:((calm(X)|~tall(X))))<=>((quiet(susan)&curious(susan))))&
(((~creative(john)|tall(john)))<=>(?[X]:((funny(X)<~>~calm(X)))))&
(((creative(alice)<~>~wise(alice)))=>(?[X]:((kind(X)&~generous(X)))))&
(((~patient(john)<~>~creative(john)))=>(?[X]:((~humble(X)&~brave(X)))))&
((~kind(susan))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
((?[X]:((~creative(X)&~happy(X))))<=>((~funny(lucy)<~>~creative(lucy))))&
((?[X]:(~kind(X)))<=>(happy(john)))&
(![X]:((~patient(X)<~>~happy(X))<=>(~generous(X)|strong(X))))&
(![X]:((~patient(X)|~creative(X))=>~quiet(X)))&
(![X]:((~calm(X)<~>calm(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:(rich(X)<=>(wise(X)&~brave(X))))&
(![X]:((curious(X)<~>patient(X))<=>(~quiet(X)|wise(X))))&
(((rich(susan)<~>~curious(susan)))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:((humble(X)<~>curious(X))))<=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((curious(X)&humble(X))=>(~generous(X)&brave(X))))&
(?[X]:((strong(X)&~curious(X))))&
((~curious(john)&brave(john)))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~generous(X)&~calm(X))))&
(?[X]:(~curious(X)))&
((~quiet(susan)<~>~patient(susan))) | ~curious(susan) | [
"p8",
"p9",
"p11",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3012671385031898956461033
% SZS output start Proof for 3012671385031898956461033
9. ! [X0] : ((~creative(X0) | ~patient(X0)) => ~quiet(X0)) [input p8]
10. ! [X0] : ((~calm(X0) <~> calm(X0)) => (~quiet(X0) <~> ~creative(X0))) [input p9]
12. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (wise(X0) | ~quiet(X0))) [input p11]
21. ~quiet(susan) <~> ~patient(susan) [input p20]
22. curious(susan) [input hypothesis]
26. ! [X0] : (~quiet(X0) | (creative(X0) & patient(X0))) [ennf transformation 9]
27. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) | (~calm(X0) <=> calm(X0))) [ennf transformation 10]
61. ! [X0] : (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) [nnf transformation 27]
64. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 12]
65. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [flattening 64]
83. (patient(susan) | quiet(susan)) & (~patient(susan) | ~quiet(susan)) [nnf transformation 21]
122. ~quiet(X0) | creative(X0) [cnf transformation 26]
123. ~creative(X0) | ~quiet(X0) | calm(X0) | calm(X0) [cnf transformation 61]
124. ~creative(X0) | ~quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 61]
125. creative(X0) | quiet(X0) | calm(X0) | calm(X0) [cnf transformation 61]
126. creative(X0) | quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 61]
134. ~patient(X0) | ~curious(X0) | quiet(X0) [cnf transformation 65]
156. patient(susan) | quiet(susan) [cnf transformation 83]
157. curious(susan) [cnf transformation 22]
158. ~creative(X0) | ~quiet(X0) | calm(X0) [duplicate literal removal 123]
159. ~creative(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 124]
160. creative(X0) | quiet(X0) | calm(X0) [duplicate literal removal 125]
161. creative(X0) | quiet(X0) | ~calm(X0) [duplicate literal removal 126]
167. 2 <=> curious(susan) [avatar definition]
168. curious(susan) <- (2) [avatar component clause 167]
313. ~calm(X0) | creative(X0) [subsumption resolution 161,122]
314. creative(X0) | calm(X0) [subsumption resolution 160,122]
315. creative(X0) [subsumption resolution 314,313]
316. ~quiet(X0) | ~calm(X0) [subsumption resolution 159,315]
317. ~quiet(X0) | calm(X0) [subsumption resolution 158,315]
318. ~quiet(X0) [subsumption resolution 317,316]
319. ~patient(X0) | ~curious(X0) [subsumption resolution 134,318]
349. patient(susan) [subsumption resolution 156,318]
350. 2 [avatar split clause 157,167]
376. ~curious(susan) [resolution 319,349]
377. $false <- (2) [subsumption resolution 376,168]
378. ~2 [avatar contradiction clause 377]
379. $false [avatar sat refutation 350,378]
% SZS output end Proof for 3012671385031898956461033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and quiet is rich or generous and vice versa.
If fred is both not creative and not happy then mary is either brave or old and vice versa.
Everyone who is curious or happy is not kind and vice versa.
Everyone who is both not strong and quiet is not wise or curious and vice versa.
Everyone who is not old is not old or quiet and vice versa.
If fred is both rich and not strong then someone is not patient and vice versa.
Everyone who is both strong and curious is not brave.
If john is not generous or not happy then someone is not creative and vice versa.
If someone is both strong and rich then susan is not patient.
If lucy is humble or not old then someone is not patient or kind.
Everyone who is either kind or humble is funny or not kind.
Everyone who is both strong and brave is wise.
Everyone who is both not rich and not generous is humble and vice versa.
If someone is wise then someone is both wise and calm.
If mary is not quiet or wise then paul is not strong and vice versa.
Everyone who is curious or not humble is not quiet or humble.
Susan is both calm and happy.
Someone is not creative.
Lucy is either tall or brave.
Someone is not rich or funny.
Someone is happy or not funny.
Someone is both patient and not kind.
Alice is not rich.
Susan is either not curious or creative. | Mary is not curious. | entailment | (![X]:((~old(X)&quiet(X))<=>(rich(X)|generous(X))))&
(((~creative(fred)&~happy(fred)))<=>((brave(mary)<~>old(mary))))&
(![X]:((curious(X)|happy(X))<=>~kind(X)))&
(![X]:((~strong(X)&quiet(X))<=>(~wise(X)|curious(X))))&
(![X]:(~old(X)<=>(~old(X)|quiet(X))))&
(((rich(fred)&~strong(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((strong(X)&curious(X))=>~brave(X)))&
(((~generous(john)|~happy(john)))<=>(?[X]:(~creative(X))))&
((?[X]:((strong(X)&rich(X))))=>(~patient(susan)))&
(((humble(lucy)|~old(lucy)))=>(?[X]:((~patient(X)|kind(X)))))&
(![X]:((kind(X)<~>humble(X))=>(funny(X)|~kind(X))))&
(![X]:((strong(X)&brave(X))=>wise(X)))&
(![X]:((~rich(X)&~generous(X))<=>humble(X)))&
((?[X]:(wise(X)))=>(?[X]:((wise(X)&calm(X)))))&
(((~quiet(mary)|wise(mary)))<=>(~strong(paul)))&
(![X]:((curious(X)|~humble(X))=>(~quiet(X)|humble(X))))&
((calm(susan)&happy(susan)))&
(?[X]:(~creative(X)))&
((tall(lucy)<~>brave(lucy)))&
(?[X]:((~rich(X)|funny(X))))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((patient(X)&~kind(X))))&
(~rich(alice))&
((~curious(susan)<~>creative(susan))) | ~curious(mary) | [
"p0",
"p3",
"p4",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 8926732726817652117750030
% SZS output start Proof for 8926732726817652117750030
1. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (generous(X0) | rich(X0))) [input p0]
4. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> (curious(X0) | ~wise(X0))) [input p3]
5. ! [X0] : (~old(X0) <=> (quiet(X0) | ~old(X0))) [input p4]
13. ! [X0] : ((~generous(X0) & ~rich(X0)) <=> humble(X0)) [input p12]
16. ! [X0] : ((~humble(X0) | curious(X0)) => (humble(X0) | ~quiet(X0))) [input p15]
25. curious(mary) [input hypothesis]
38. ! [X0] : ((humble(X0) | ~quiet(X0)) | (humble(X0) & ~curious(X0))) [ennf transformation 16]
39. ! [X0] : (humble(X0) | ~quiet(X0) | (humble(X0) & ~curious(X0))) [flattening 38]
40. ! [X0] : (((quiet(X0) & ~old(X0)) | (~generous(X0) & ~rich(X0))) & ((generous(X0) | rich(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 1]
41. ! [X0] : (((quiet(X0) & ~old(X0)) | (~generous(X0) & ~rich(X0))) & (generous(X0) | rich(X0) | ~quiet(X0) | old(X0))) [flattening 40]
46. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~curious(X0) & wise(X0))) & ((curious(X0) | ~wise(X0)) | (~quiet(X0) | strong(X0)))) [nnf transformation 4]
47. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~curious(X0) & wise(X0))) & (curious(X0) | ~wise(X0) | ~quiet(X0) | strong(X0))) [flattening 46]
48. ! [X0] : ((~old(X0) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | old(X0))) [nnf transformation 5]
49. ! [X0] : ((~old(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | old(X0))) [flattening 48]
63. ! [X0] : (((~generous(X0) & ~rich(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) | rich(X0)))) [nnf transformation 13]
64. ! [X0] : (((~generous(X0) & ~rich(X0)) | ~humble(X0)) & (humble(X0) | generous(X0) | rich(X0))) [flattening 63]
80. ~quiet(X0) | rich(X0) | generous(X0) | old(X0) [cnf transformation 41]
98. ~curious(X0) | quiet(X0) [cnf transformation 47]
101. ~quiet(X0) | ~old(X0) [cnf transformation 49]
116. ~humble(X0) | ~rich(X0) [cnf transformation 64]
117. ~humble(X0) | ~generous(X0) [cnf transformation 64]
123. humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 39]
135. curious(mary) [cnf transformation 25]
136. ~quiet(X0) | humble(X0) [duplicate literal removal 123]
139. 1 <=> old(mary) [avatar definition]
242. 23 <=> quiet(mary) [avatar definition]
244. quiet(mary) <- (23) [avatar component clause 242]
290. quiet(mary) [resolution 98,135]
291. 23 [avatar split clause 290,242]
293. ~old(mary) <- (23) [resolution 101,244]
295. humble(mary) <- (23) [resolution 136,244]
308. ~generous(mary) <- (23) [resolution 295,117]
309. ~rich(mary) <- (23) [resolution 295,116]
364. rich(mary) | generous(mary) | old(mary) <- (23) [resolution 80,244]
365. generous(mary) | old(mary) <- (23) [subsumption resolution 364,309]
366. old(mary) <- (23) [subsumption resolution 365,308]
369. 1 | ~23 [avatar split clause 366,242,139]
370. ~1 | ~23 [avatar split clause 293,242,139]
371. $false [avatar sat refutation 291,369,370]
% SZS output end Proof for 8926732726817652117750030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is happy or funny then someone is brave and vice versa. Everyone who is curious or strong is not funny. If someone is both tall and humble then someone is not rich or wise. If susan is calm then someone is both not calm and curious and vice versa. Everyone who is generous is kind or not generous and vice versa. Everyone who is either not rich or not tall is not rich. If alice is both not funny and not quiet then someone is kind and vice versa. Everyone who is curious or rich is not curious or not calm. Everyone who is generous or not humble is not brave. Everyone who is curious is either not patient or not funny and vice versa. If someone is humble then someone is not generous or not old and vice versa. Everyone who is either tall or kind is creative or tall. If fred is tall or creative then someone is brave or not patient and vice versa. If someone is either not brave or funny then someone is generous and vice versa. Everyone who is either not generous or tall is either calm or not funny and vice versa. Everyone who is humble or not strong is brave and vice versa. Someone is either curious or not rich. Someone is both strong and calm. Mary is either kind or brave. Someone is not strong or not rich. Alice is not wise. Someone is both not humble and curious. Paul is wise or not patient. | Alice is old. | entailment | (((happy(mary)|funny(mary)))<=>(?[X]:(brave(X))))&
(![X]:((curious(X)|strong(X))=>~funny(X)))&
((?[X]:((tall(X)&humble(X))))=>(?[X]:((~rich(X)|wise(X)))))&
((calm(susan))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:(generous(X)<=>(kind(X)|~generous(X))))&
(![X]:((~rich(X)<~>~tall(X))=>~rich(X)))&
(((~funny(alice)&~quiet(alice)))<=>(?[X]:(kind(X))))&
(![X]:((curious(X)|rich(X))=>(~curious(X)|~calm(X))))&
(![X]:((generous(X)|~humble(X))=>~brave(X)))&
(![X]:(curious(X)<=>(~patient(X)<~>~funny(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:((tall(X)<~>kind(X))=>(creative(X)|tall(X))))&
(((tall(fred)|creative(fred)))<=>(?[X]:((brave(X)|~patient(X)))))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:(generous(X))))&
(![X]:((~generous(X)<~>tall(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((humble(X)|~strong(X))<=>brave(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((strong(X)&calm(X))))&
((kind(mary)<~>brave(mary)))&
(?[X]:((~strong(X)|~rich(X))))&
(~wise(alice))&
(?[X]:((~humble(X)&curious(X))))&
((wise(paul)|~patient(paul))) | old(alice) | [
"p4",
"p8",
"p10",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 6612566424649643763748452
% SZS output start Proof for 6612566424649643763748452
5. ! [X0] : (generous(X0) <=> (~generous(X0) | kind(X0))) [input p4]
9. ! [X0] : ((~humble(X0) | generous(X0)) => ~brave(X0)) [input p8]
11. ? [X0] : humble(X0) <=> ? [X0] : (~old(X0) | ~generous(X0)) [input p10]
16. ! [X0] : ((~strong(X0) | humble(X0)) <=> brave(X0)) [input p15]
24. ~old(alice) [input hypothesis]
26. ? [X0] : humble(X0) <=> ? [X1] : (~old(X1) | ~generous(X1)) [rectify 11]
33. ! [X0] : (~brave(X0) | (humble(X0) & ~generous(X0))) [ennf transformation 9]
48. ! [X0] : ((generous(X0) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | ~generous(X0))) [nnf transformation 5]
49. ! [X0] : ((generous(X0) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | ~generous(X0))) [flattening 48]
57. (? [X0] : humble(X0) | ! [X1] : (old(X1) & generous(X1))) & (? [X1] : (~old(X1) | ~generous(X1)) | ! [X0] : ~humble(X0)) [nnf transformation 26]
58. (? [X0] : humble(X0) | ! [X1] : (old(X1) & generous(X1))) & (? [X2] : (~old(X2) | ~generous(X2)) | ! [X3] : ~humble(X3)) [rectify 57]
59. ? [X0] : humble(X0) => humble(sK4) [choice axiom]
60. ? [X2] : (~old(X2) | ~generous(X2)) => (~old(sK5) | ~generous(sK5)) [choice axiom]
61. (humble(sK4) | ! [X1] : (old(X1) & generous(X1))) & ((~old(sK5) | ~generous(sK5)) | ! [X3] : ~humble(X3)) [skolemisation 58,60,59]
74. ! [X0] : (((~strong(X0) | humble(X0)) | ~brave(X0)) & (brave(X0) | (strong(X0) & ~humble(X0)))) [nnf transformation 16]
75. ! [X0] : ((~strong(X0) | humble(X0) | ~brave(X0)) & (brave(X0) | (strong(X0) & ~humble(X0)))) [flattening 74]
97. generous(X0) | generous(X0) [cnf transformation 49]
105. ~brave(X0) | ~generous(X0) [cnf transformation 33]
113. humble(sK4) | old(X1) [cnf transformation 61]
132. ~humble(X0) | brave(X0) [cnf transformation 75]
146. ~old(alice) [cnf transformation 24]
151. generous(X0) [duplicate literal removal 97]
153. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
154. ~brave(X0) <- (1) [avatar component clause 153]
203. ~brave(X0) [subsumption resolution 105,151]
204. 1 [avatar split clause 203,153]
208. 12 <=> ! [X1] : old(X1) [avatar definition]
209. old(X1) <- (12) [avatar component clause 208]
211. 13 <=> humble(sK4) [avatar definition]
213. humble(sK4) <- (13) [avatar component clause 211]
214. 12 | 13 [avatar split clause 113,211,208]
289. $false <- (12) [resolution 209,146]
290. ~12 [avatar contradiction clause 289]
296. brave(sK4) <- (13) [resolution 132,213]
297. $false <- (1, 13) [subsumption resolution 296,154]
298. ~1 | ~13 [avatar contradiction clause 297]
299. $false [avatar sat refutation 204,214,290,298]
% SZS output end Proof for 6612566424649643763748452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not tall or not brave and vice versa.
If someone is not rich or patient then someone is either funny or strong and vice versa.
If lucy is both not quiet and generous then susan is either rich or calm and vice versa.
If someone is either not brave or patient then someone is both wise and not quiet.
If someone is either not happy or calm then fred is both not quiet and happy.
Everyone who is both not humble and strong is either tall or not happy.
If someone is either not strong or not patient then lucy is not old or brave.
If someone is not humble then someone is both patient and not tall and vice versa.
If alice is both not tall and not wise then lucy is either not rich or generous and vice versa.
Everyone who is tall or creative is both not brave and not kind and vice versa.
Everyone who is both not calm and not wise is either old or happy.
If someone is either strong or quiet then someone is not happy and vice versa.
If lucy is quiet or not happy then lucy is creative or humble and vice versa.
Everyone who is kind or not rich is both not tall and tall and vice versa.
Everyone who is either brave or calm is both funny and not happy and vice versa.
If lucy is not rich or strong then someone is either not generous or not creative and vice versa.
Someone is not wise or strong.
Lucy is both humble and not generous.
Someone is either curious or strong.
Lucy is both curious and strong.
Someone is not kind or not generous.
Someone is either rich or not calm.
Fred is either calm or not humble.
Someone is both not tall and curious. | Lucy is not calm. | neutral | (![X]:(creative(X)<=>(~tall(X)|~brave(X))))&
((?[X]:((~rich(X)|patient(X))))<=>(?[X]:((funny(X)<~>strong(X)))))&
(((~quiet(lucy)&generous(lucy)))<=>((rich(susan)<~>calm(susan))))&
((?[X]:((~brave(X)<~>patient(X))))=>(?[X]:((wise(X)&~quiet(X)))))&
((?[X]:((~happy(X)<~>calm(X))))=>((~quiet(fred)&happy(fred))))&
(![X]:((~humble(X)&strong(X))=>(tall(X)<~>~happy(X))))&
((?[X]:((~strong(X)<~>~patient(X))))=>((~old(lucy)|brave(lucy))))&
((?[X]:(~humble(X)))<=>(?[X]:((patient(X)&~tall(X)))))&
(((~tall(alice)&~wise(alice)))<=>((~rich(lucy)<~>generous(lucy))))&
(![X]:((tall(X)|creative(X))<=>(~brave(X)&~kind(X))))&
(![X]:((~calm(X)&~wise(X))=>(old(X)<~>happy(X))))&
((?[X]:((strong(X)<~>quiet(X))))<=>(?[X]:(~happy(X))))&
(((quiet(lucy)|~happy(lucy)))<=>((creative(lucy)|humble(lucy))))&
(![X]:((kind(X)|~rich(X))<=>(~tall(X)&tall(X))))&
(![X]:((brave(X)<~>calm(X))<=>(funny(X)&~happy(X))))&
(((~rich(lucy)|strong(lucy)))<=>(?[X]:((~generous(X)<~>~creative(X)))))&
(?[X]:((~wise(X)|strong(X))))&
((humble(lucy)&~generous(lucy)))&
(?[X]:((curious(X)<~>strong(X))))&
((curious(lucy)&strong(lucy)))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:((rich(X)<~>~calm(X))))&
((calm(fred)<~>~humble(fred)))&
(?[X]:((~tall(X)&curious(X)))) | ~calm(lucy) | []
| null | 0 |
Everyone who is not rich or patient is not creative or not brave.
If someone is either not happy or not brave then someone is strong or curious.
If someone is creative or patient then alice is generous and vice versa.
Everyone who is strong is patient or brave and vice versa.
Everyone who is not funny is not patient or not brave.
If paul is either humble or not happy then someone is both happy and kind.
Everyone who is curious or not kind is not kind and vice versa.
If someone is both old and humble then paul is either generous or not kind and vice versa.
If susan is not generous or old then someone is not brave or not curious.
Everyone who is calm is both not creative and funny and vice versa.
Everyone who is kind is not humble and vice versa.
If someone is wise or not wise then someone is rich.
Everyone who is rich or old is both patient and not old.
Everyone who is not quiet is curious and vice versa.
If someone is both funny and not calm then someone is both not rich and not creative and vice versa.
Everyone who is humble or not quiet is both not humble and humble and vice versa.
John is quiet.
Susan is both not humble and not happy.
Someone is both not funny and not patient.
Someone is both tall and not rich.
Paul is generous or brave. | Paul is strong. | entailment | (![X]:((~rich(X)|patient(X))=>(~creative(X)|~brave(X))))&
((?[X]:((~happy(X)<~>~brave(X))))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((creative(X)|patient(X))))<=>(generous(alice)))&
(![X]:(strong(X)<=>(patient(X)|brave(X))))&
(![X]:(~funny(X)=>(~patient(X)|~brave(X))))&
(((humble(paul)<~>~happy(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((curious(X)|~kind(X))<=>~kind(X)))&
((?[X]:((old(X)&humble(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~generous(susan)|old(susan)))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:(calm(X)<=>(~creative(X)&funny(X))))&
(![X]:(kind(X)<=>~humble(X)))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|old(X))=>(patient(X)&~old(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
(![X]:((humble(X)|~quiet(X))<=>(~humble(X)&humble(X))))&
(quiet(john))&
((~humble(susan)&~happy(susan)))&
(?[X]:((~funny(X)&~patient(X))))&
(?[X]:((tall(X)&~rich(X))))&
((generous(paul)|brave(paul))) | strong(paul) | [
"p3",
"p7",
"p10",
"p12",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 948563799133691793384593
% SZS output start Proof for 948563799133691793384593
4. ! [X0] : (strong(X0) <=> (brave(X0) | patient(X0))) [input p3]
8. ? [X0] : (humble(X0) & old(X0)) <=> (generous(paul) <~> ~kind(paul)) [input p7]
11. ! [X0] : (kind(X0) <=> ~humble(X0)) [input p10]
13. ! [X0] : ((old(X0) | rich(X0)) => (~old(X0) & patient(X0))) [input p12]
16. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (humble(X0) & ~humble(X0))) [input p15]
21. brave(paul) | generous(paul) [input p20]
22. ~strong(paul) [input hypothesis]
35. ! [X0] : ((~old(X0) & patient(X0)) | (~old(X0) & ~rich(X0))) [ennf transformation 13]
44. ! [X0] : ((strong(X0) | (~brave(X0) & ~patient(X0))) & ((brave(X0) | patient(X0)) | ~strong(X0))) [nnf transformation 4]
45. ! [X0] : ((strong(X0) | (~brave(X0) & ~patient(X0))) & (brave(X0) | patient(X0) | ~strong(X0))) [flattening 44]
51. (? [X0] : (humble(X0) & old(X0)) | ((generous(paul) | kind(paul)) & (~kind(paul) | ~generous(paul)))) & (((kind(paul) | ~generous(paul)) & (~kind(paul) | generous(paul))) | ! [X0] : (~humble(X0) | ~old(X0))) [nnf transformation 8]
52. (? [X0] : (humble(X0) & old(X0)) | ((generous(paul) | kind(paul)) & (~kind(paul) | ~generous(paul)))) & (((kind(paul) | ~generous(paul)) & (~kind(paul) | generous(paul))) | ! [X1] : (~humble(X1) | ~old(X1))) [rectify 51]
53. ? [X0] : (humble(X0) & old(X0)) => (humble(sK3) & old(sK3)) [choice axiom]
54. ((humble(sK3) & old(sK3)) | ((generous(paul) | kind(paul)) & (~kind(paul) | ~generous(paul)))) & (((kind(paul) | ~generous(paul)) & (~kind(paul) | generous(paul))) | ! [X1] : (~humble(X1) | ~old(X1))) [skolemisation 52,53]
59. ! [X0] : ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0))) [nnf transformation 11]
69. ! [X0] : (((~quiet(X0) | humble(X0)) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | (quiet(X0) & ~humble(X0)))) [nnf transformation 16]
70. ! [X0] : ((~quiet(X0) | humble(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | (quiet(X0) & ~humble(X0)))) [flattening 69]
84. ~brave(X0) | strong(X0) [cnf transformation 45]
95. old(sK3) | ~kind(paul) | ~generous(paul) [cnf transformation 54]
105. kind(X0) | humble(X0) [cnf transformation 59]
111. ~old(X0) | ~old(X0) [cnf transformation 35]
118. ~humble(X0) | ~humble(X0) [cnf transformation 70]
129. brave(paul) | generous(paul) [cnf transformation 21]
130. ~strong(paul) [cnf transformation 22]
131. ~humble(X0) [duplicate literal removal 118]
133. ~old(X0) [duplicate literal removal 111]
192. 14 <=> kind(paul) [avatar definition]
193. ~kind(paul) <- (~14) [avatar component clause 192]
196. 15 <=> generous(paul) [avatar definition]
206. 17 <=> old(sK3) [avatar definition]
208. old(sK3) <- (17) [avatar component clause 206]
210. ~15 | ~14 | 17 [avatar split clause 95,206,192,196]
274. 32 <=> brave(paul) [avatar definition]
276. brave(paul) <- (32) [avatar component clause 274]
277. 15 | 32 [avatar split clause 129,274,196]
278. $false <- (17) [subsumption resolution 208,133]
279. ~17 [avatar contradiction clause 278]
282. humble(paul) <- (~14) [resolution 105,193]
285. $false <- (~14) [subsumption resolution 282,131]
286. 14 [avatar contradiction clause 285]
290. strong(paul) <- (32) [resolution 276,84]
291. $false <- (32) [subsumption resolution 290,130]
292. ~32 [avatar contradiction clause 291]
293. $false [avatar sat refutation 210,277,279,286,292]
% SZS output end Proof for 948563799133691793384593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or generous then someone is not happy.
Everyone who is either happy or old is both not quiet and humble and vice versa.
If someone is both not rich and not strong then fred is tall or not patient and vice versa.
If john is creative or old then someone is either strong or not generous.
Everyone who is not curious is patient.
If lucy is rich then someone is patient.
If someone is not humble then lucy is both not happy and tall and vice versa.
Everyone who is not calm is patient and vice versa.
Everyone who is either tall or not happy is not tall or not patient and vice versa.
If john is not wise then someone is not patient.
Everyone who is not creative is either not calm or not wise.
If lucy is curious then alice is not patient and vice versa.
Everyone who is both not patient and not tall is generous or not curious and vice versa.
If someone is either not rich or not wise then paul is either quiet or tall.
If someone is curious or generous then susan is either funny or not generous.
If fred is kind then alice is not generous and vice versa.
Someone is not curious or not strong.
Mary is either quiet or not wise.
Mary is either happy or not funny.
Fred is not tall.
Someone is either tall or rich.
Mary is curious.
Alice is generous or not funny.
Lucy is not generous. | Alice is not generous. | neutral | ((?[X]:((funny(X)|generous(X))))=>(?[X]:(~happy(X))))&
(![X]:((happy(X)<~>old(X))<=>(~quiet(X)&humble(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>((tall(fred)|~patient(fred))))&
(((creative(john)|old(john)))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:(~curious(X)=>patient(X)))&
((rich(lucy))=>(?[X]:(patient(X))))&
((?[X]:(~humble(X)))<=>((~happy(lucy)&tall(lucy))))&
(![X]:(~calm(X)<=>patient(X)))&
(![X]:((tall(X)<~>~happy(X))<=>(~tall(X)|~patient(X))))&
((~wise(john))=>(?[X]:(~patient(X))))&
(![X]:(~creative(X)=>(~calm(X)<~>~wise(X))))&
((curious(lucy))<=>(~patient(alice)))&
(![X]:((~patient(X)&~tall(X))<=>(generous(X)|~curious(X))))&
((?[X]:((~rich(X)<~>~wise(X))))=>((quiet(paul)<~>tall(paul))))&
((?[X]:((curious(X)|generous(X))))=>((funny(susan)<~>~generous(susan))))&
((kind(fred))<=>(~generous(alice)))&
(?[X]:((~curious(X)|~strong(X))))&
((quiet(mary)<~>~wise(mary)))&
((happy(mary)<~>~funny(mary)))&
(~tall(fred))&
(?[X]:((tall(X)<~>rich(X))))&
(curious(mary))&
((generous(alice)|~funny(alice)))&
(~generous(lucy)) | ~generous(alice) | []
| null | 0 |
If fred is either not old or strong then fred is either not funny or not humble and vice versa.
Everyone who is either not patient or not wise is kind or not strong.
If someone is not happy then john is both not happy and funny.
Everyone who is not quiet or not calm is both not creative and not wise.
Everyone who is not brave or old is either not humble or tall and vice versa.
Everyone who is either not brave or not old is both not kind and not old and vice versa.
Everyone who is strong is not creative or not generous and vice versa.
If someone is generous or not quiet then someone is either not old or patient.
Everyone who is either not wise or curious is not old or patient and vice versa.
If lucy is generous or not calm then paul is not rich.
If fred is curious or not kind then lucy is both old and quiet.
Everyone who is strong or not happy is not rich or not quiet.
Everyone who is calm is not strong.
Everyone who is brave is either happy or old and vice versa.
Everyone who is generous is kind and vice versa.
If alice is both not rich and calm then someone is not brave or quiet and vice versa.
Someone is both not creative and not happy.
John is either not generous or kind.
Fred is both old and not kind.
Mary is quiet.
Someone is either not humble or not patient.
Someone is not brave or not creative.
Lucy is both not tall and old.
Susan is not humble. | Susan is not generous. | neutral | (((~old(fred)<~>strong(fred)))<=>((~funny(fred)<~>~humble(fred))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:(~happy(X)))=>((~happy(john)&funny(john))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)&~wise(X))))&
(![X]:((~brave(X)|old(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~kind(X)&~old(X))))&
(![X]:(strong(X)<=>(~creative(X)|~generous(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~old(X)|patient(X))))&
(((generous(lucy)|~calm(lucy)))=>(~rich(paul)))&
(((curious(fred)|~kind(fred)))=>((old(lucy)&quiet(lucy))))&
(![X]:((strong(X)|~happy(X))=>(~rich(X)|~quiet(X))))&
(![X]:(calm(X)=>~strong(X)))&
(![X]:(brave(X)<=>(happy(X)<~>old(X))))&
(![X]:(generous(X)<=>kind(X)))&
(((~rich(alice)&calm(alice)))<=>(?[X]:((~brave(X)|quiet(X)))))&
(?[X]:((~creative(X)&~happy(X))))&
((~generous(john)<~>kind(john)))&
((old(fred)&~kind(fred)))&
(quiet(mary))&
(?[X]:((~humble(X)<~>~patient(X))))&
(?[X]:((~brave(X)|~creative(X))))&
((~tall(lucy)&old(lucy)))&
(~humble(susan)) | ~generous(susan) | []
| null | 0 |
Everyone who is either calm or kind is either tall or not tall and vice versa.
If someone is both wise and curious then someone is not tall or not kind and vice versa.
Everyone who is both happy and not humble is not quiet or funny.
Everyone who is curious is not wise.
Everyone who is strong or not brave is not kind.
If someone is kind or curious then someone is curious.
If someone is both happy and tall then fred is brave or not wise.
If john is either not creative or wise then someone is either brave or not tall and vice versa.
Everyone who is both not creative and tall is both generous and creative.
If someone is brave then someone is not patient or not rich.
Everyone who is both not funny and not strong is either strong or not calm.
Everyone who is not humble is both not strong and not calm and vice versa.
If someone is either rich or not wise then someone is wise.
Everyone who is not creative or not generous is quiet or humble and vice versa.
If paul is old then fred is old.
If someone is both not generous and not funny then mary is either not wise or patient.
Someone is kind.
Someone is brave.
Susan is either not calm or not creative.
Someone is not kind or not calm.
Paul is either patient or happy.
Someone is either not rich or not kind.
Alice is either patient or brave. | John is not wise. | contradiction | (![X]:((calm(X)<~>kind(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((wise(X)&curious(X))))<=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:((happy(X)&~humble(X))=>(~quiet(X)|funny(X))))&
(![X]:(curious(X)=>~wise(X)))&
(![X]:((strong(X)|~brave(X))=>~kind(X)))&
((?[X]:((kind(X)|curious(X))))=>(?[X]:(curious(X))))&
((?[X]:((happy(X)&tall(X))))=>((brave(fred)|~wise(fred))))&
(((~creative(john)<~>wise(john)))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((~creative(X)&tall(X))=>(generous(X)&creative(X))))&
((?[X]:(brave(X)))=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((~funny(X)&~strong(X))=>(strong(X)<~>~calm(X))))&
(![X]:(~humble(X)<=>(~strong(X)&~calm(X))))&
((?[X]:((rich(X)<~>~wise(X))))=>(?[X]:(wise(X))))&
(![X]:((~creative(X)|~generous(X))<=>(quiet(X)|humble(X))))&
((old(paul))=>(old(fred)))&
((?[X]:((~generous(X)&~funny(X))))=>((~wise(mary)<~>patient(mary))))&
(?[X]:(kind(X)))&
(?[X]:(brave(X)))&
((~calm(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)|~calm(X))))&
((patient(paul)<~>happy(paul)))&
(?[X]:((~rich(X)<~>~kind(X))))&
((patient(alice)<~>brave(alice))) | ~wise(john) | [
"p1",
"p3",
"p4",
"p7",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 4558022645221467243957626
% SZS output start Proof for 4558022645221467243957626
2. ? [X0] : (curious(X0) & wise(X0)) <=> ? [X0] : (~kind(X0) | ~tall(X0)) [input p1]
4. ! [X0] : (curious(X0) => ~wise(X0)) [input p3]
5. ! [X0] : ((~brave(X0) | strong(X0)) => ~kind(X0)) [input p4]
8. (~creative(john) <~> wise(john)) <=> ? [X0] : (brave(X0) <~> ~tall(X0)) [input p7]
9. ! [X0] : ((tall(X0) & ~creative(X0)) => (creative(X0) & generous(X0))) [input p8]
24. ~wise(john) [input hypothesis]
25. ? [X0] : (curious(X0) & wise(X0)) <=> ? [X1] : (~kind(X1) | ~tall(X1)) [rectify 2]
32. ! [X0] : (~wise(X0) | ~curious(X0)) [ennf transformation 4]
33. ! [X0] : (~kind(X0) | (brave(X0) & ~strong(X0))) [ennf transformation 5]
37. ! [X0] : ((creative(X0) & generous(X0)) | (~tall(X0) | creative(X0))) [ennf transformation 9]
38. ! [X0] : ((creative(X0) & generous(X0)) | ~tall(X0) | creative(X0)) [flattening 37]
43. (? [X0] : (curious(X0) & wise(X0)) | ! [X1] : (kind(X1) & tall(X1))) & (? [X1] : (~kind(X1) | ~tall(X1)) | ! [X0] : (~curious(X0) | ~wise(X0))) [nnf transformation 25]
44. (? [X0] : (curious(X0) & wise(X0)) | ! [X1] : (kind(X1) & tall(X1))) & (? [X2] : (~kind(X2) | ~tall(X2)) | ! [X3] : (~curious(X3) | ~wise(X3))) [rectify 43]
45. ? [X0] : (curious(X0) & wise(X0)) => (curious(sK0) & wise(sK0)) [choice axiom]
46. ? [X2] : (~kind(X2) | ~tall(X2)) => (~kind(sK1) | ~tall(sK1)) [choice axiom]
47. ((curious(sK0) & wise(sK0)) | ! [X1] : (kind(X1) & tall(X1))) & ((~kind(sK1) | ~tall(sK1)) | ! [X3] : (~curious(X3) | ~wise(X3))) [skolemisation 44,46,45]
51. (((~wise(john) | creative(john)) & (wise(john) | ~creative(john))) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (? [X0] : ((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ((~creative(john) | ~wise(john)) & (wise(john) | creative(john)))) [nnf transformation 8]
52. (((~wise(john) | creative(john)) & (wise(john) | ~creative(john))) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (? [X1] : ((tall(X1) | ~brave(X1)) & (~tall(X1) | brave(X1))) | ((~creative(john) | ~wise(john)) & (wise(john) | creative(john)))) [rectify 51]
53. ? [X1] : ((tall(X1) | ~brave(X1)) & (~tall(X1) | brave(X1))) => ((tall(sK3) | ~brave(sK3)) & (~tall(sK3) | brave(sK3))) [choice axiom]
54. (((~wise(john) | creative(john)) & (wise(john) | ~creative(john))) | ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) & (((tall(sK3) | ~brave(sK3)) & (~tall(sK3) | brave(sK3))) | ((~creative(john) | ~wise(john)) & (wise(john) | creative(john)))) [skolemisation 52,53]
87. wise(sK0) | tall(X1) [cnf transformation 47]
88. wise(sK0) | kind(X1) [cnf transformation 47]
89. curious(sK0) | tall(X1) [cnf transformation 47]
90. curious(sK0) | kind(X1) [cnf transformation 47]
91. ~wise(X0) | ~curious(X0) [cnf transformation 32]
93. ~kind(X0) | brave(X0) [cnf transformation 33]
101. wise(john) | ~creative(john) | ~tall(X0) | ~brave(X0) [cnf transformation 54]
106. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 38]
129. ~wise(john) [cnf transformation 24]
130. ~tall(X0) | creative(X0) [duplicate literal removal 106]
138. 1 <=> ! [X1] : kind(X1) [avatar definition]
139. kind(X1) <- (1) [avatar component clause 138]
141. 2 <=> curious(sK0) [avatar definition]
143. curious(sK0) <- (2) [avatar component clause 141]
144. 1 | 2 [avatar split clause 90,141,138]
146. 3 <=> ! [X1] : tall(X1) [avatar definition]
147. tall(X1) <- (3) [avatar component clause 146]
148. 3 | 2 [avatar split clause 89,141,146]
150. 4 <=> wise(sK0) [avatar definition]
152. wise(sK0) <- (4) [avatar component clause 150]
153. 1 | 4 [avatar split clause 88,150,138]
154. 3 | 4 [avatar split clause 87,150,146]
156. 5 <=> ! [X3] : (~curious(X3) | ~wise(X3)) [avatar definition]
157. ~curious(X3) | ~wise(X3) <- (5) [avatar component clause 156]
167. 5 [avatar split clause 91,156]
196. 15 <=> creative(john) [avatar definition]
197. ~creative(john) <- (~15) [avatar component clause 196]
200. 16 <=> wise(john) [avatar definition]
205. 17 <=> ! [X0] : (~tall(X0) | ~brave(X0)) [avatar definition]
206. ~tall(X0) | ~brave(X0) <- (17) [avatar component clause 205]
209. 17 | ~15 | 16 [avatar split clause 101,200,196,205]
295. ~16 [avatar split clause 129,200]
302. ~wise(sK0) <- (2, 5) [resolution 157,143]
304. $false <- (2, 4, 5) [subsumption resolution 302,152]
305. ~2 | ~4 | ~5 [avatar contradiction clause 304]
308. brave(X1) <- (1) [resolution 139,93]
311. creative(X0) <- (3) [resolution 147,130]
313. ~brave(X0) <- (3, 17) [subsumption resolution 206,147]
314. $false <- (1, 3, 17) [subsumption resolution 313,308]
315. ~1 | ~3 | ~17 [avatar contradiction clause 314]
316. $false <- (3, ~15) [subsumption resolution 197,311]
317. ~3 | 15 [avatar contradiction clause 316]
318. $false [avatar sat refutation 144,148,153,154,167,209,295,305,315,317]
% SZS output end Proof for 4558022645221467243957626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or tall then alice is not kind. Everyone who is both curious and kind is either creative or quiet and vice versa. If someone is both not kind and rich then someone is quiet and vice versa. If someone is patient then someone is kind. Everyone who is rich is patient and vice versa. Everyone who is both humble and not rich is not quiet and vice versa. Everyone who is not patient or funny is not curious or not generous. Everyone who is both funny and not old is not happy or not strong. If someone is old then mary is not creative and vice versa. Everyone who is not old is calm or old and vice versa. Everyone who is both not funny and brave is strong or not strong. Everyone who is not funny or patient is not curious or patient and vice versa. If lucy is not kind or happy then susan is both not calm and creative. If paul is both creative and rich then mary is either not brave or not rich and vice versa. Everyone who is both curious and not humble is wise and vice versa. If john is not quiet then susan is either not humble or funny. Someone is not kind or kind. Lucy is either not calm or not tall. John is patient. Someone is both not brave and not generous. Fred is curious or not tall. Someone is not quiet. Someone is rich. | Alice is not funny. | neutral | (((rich(alice)|tall(alice)))=>(~kind(alice)))&
(![X]:((curious(X)&kind(X))<=>(creative(X)<~>quiet(X))))&
((?[X]:((~kind(X)&rich(X))))<=>(?[X]:(quiet(X))))&
((?[X]:(patient(X)))=>(?[X]:(kind(X))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((humble(X)&~rich(X))<=>~quiet(X)))&
(![X]:((~patient(X)|funny(X))=>(~curious(X)|~generous(X))))&
(![X]:((funny(X)&~old(X))=>(~happy(X)|~strong(X))))&
((?[X]:(old(X)))<=>(~creative(mary)))&
(![X]:(~old(X)<=>(calm(X)|old(X))))&
(![X]:((~funny(X)&brave(X))=>(strong(X)|~strong(X))))&
(![X]:((~funny(X)|patient(X))<=>(~curious(X)|patient(X))))&
(((~kind(lucy)|happy(lucy)))=>((~calm(susan)&creative(susan))))&
(((creative(paul)&rich(paul)))<=>((~brave(mary)<~>~rich(mary))))&
(![X]:((curious(X)&~humble(X))<=>wise(X)))&
((~quiet(john))=>((~humble(susan)<~>funny(susan))))&
(?[X]:((~kind(X)|kind(X))))&
((~calm(lucy)<~>~tall(lucy)))&
(patient(john))&
(?[X]:((~brave(X)&~generous(X))))&
((curious(fred)|~tall(fred)))&
(?[X]:(~quiet(X)))&
(?[X]:(rich(X))) | ~funny(alice) | []
| null | 0 |
If lucy is not creative or kind then someone is kind or brave and vice versa. Everyone who is either generous or curious is creative. Everyone who is curious is funny or not brave. If mary is not strong then someone is not funny and vice versa. Everyone who is not happy or not brave is either calm or not curious. If someone is humble or patient then someone is not funny or not kind and vice versa. Everyone who is generous is either brave or creative. Everyone who is either old or not rich is either not brave or strong and vice versa. Everyone who is both quiet and not generous is not old or patient. Everyone who is either not funny or not calm is either wise or generous and vice versa. If john is either not strong or strong then someone is happy and vice versa. Everyone who is not strong or patient is either patient or not old. If lucy is either not creative or calm then paul is not strong or humble and vice versa. Everyone who is both patient and rich is either wise or not kind and vice versa. Everyone who is not creative or funny is both wise and not rich. Everyone who is not tall or calm is both humble and kind and vice versa. Fred is both happy and not creative. Alice is not calm. Mary is not happy or not brave. Alice is funny or quiet. Someone is not strong. Someone is either brave or funny. Someone is tall or not generous. | Fred is not humble. | neutral | (((~creative(lucy)|kind(lucy)))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((generous(X)<~>curious(X))=>creative(X)))&
(![X]:(curious(X)=>(funny(X)|~brave(X))))&
((~strong(mary))<=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)|~brave(X))=>(calm(X)<~>~curious(X))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:(generous(X)=>(brave(X)<~>creative(X))))&
(![X]:((old(X)<~>~rich(X))<=>(~brave(X)<~>strong(X))))&
(![X]:((quiet(X)&~generous(X))=>(~old(X)|patient(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(wise(X)<~>generous(X))))&
(((~strong(john)<~>strong(john)))<=>(?[X]:(happy(X))))&
(![X]:((~strong(X)|patient(X))=>(patient(X)<~>~old(X))))&
(((~creative(lucy)<~>calm(lucy)))<=>((~strong(paul)|humble(paul))))&
(![X]:((patient(X)&rich(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((~creative(X)|funny(X))=>(wise(X)&~rich(X))))&
(![X]:((~tall(X)|calm(X))<=>(humble(X)&kind(X))))&
((happy(fred)&~creative(fred)))&
(~calm(alice))&
((~happy(mary)|~brave(mary)))&
((funny(alice)|quiet(alice)))&
(?[X]:(~strong(X)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((tall(X)|~generous(X)))) | ~humble(fred) | []
| null | 0 |
If someone is either not curious or not calm then someone is either not funny or not rich and vice versa.
If someone is brave or not quiet then someone is humble and vice versa.
If someone is both brave and not funny then someone is generous and vice versa.
If someone is either not funny or happy then susan is either old or not calm and vice versa.
If john is not tall then someone is strong or not patient and vice versa.
Everyone who is either not tall or not brave is either patient or wise.
Everyone who is not quiet is either not funny or not rich and vice versa.
Everyone who is old or not humble is either not rich or humble and vice versa.
Everyone who is either brave or tall is funny or happy and vice versa.
If someone is either not funny or patient then fred is not curious and vice versa.
If john is either happy or tall then someone is both not humble and not strong and vice versa.
Everyone who is both not tall and not creative is either rich or strong.
Everyone who is both curious and not old is either not old or strong.
If someone is not humble then someone is not creative.
If someone is either not wise or old then lucy is both not kind and not funny.
Everyone who is either not tall or wise is not generous and vice versa.
Fred is both not patient and not tall.
John is both happy and not quiet.
Someone is either old or quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich.
Mary is both funny and brave.
Mary is either not wise or happy. | Paul is old. | entailment | ((?[X]:((~curious(X)<~>~calm(X))))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
((?[X]:((brave(X)|~quiet(X))))<=>(?[X]:(humble(X))))&
((?[X]:((brave(X)&~funny(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~funny(X)<~>happy(X))))<=>((old(susan)<~>~calm(susan))))&
((~tall(john))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~tall(X)<~>~brave(X))=>(patient(X)<~>wise(X))))&
(![X]:(~quiet(X)<=>(~funny(X)<~>~rich(X))))&
(![X]:((old(X)|~humble(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((brave(X)<~>tall(X))<=>(funny(X)|happy(X))))&
((?[X]:((~funny(X)<~>patient(X))))<=>(~curious(fred)))&
(((happy(john)<~>tall(john)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)&~creative(X))=>(rich(X)<~>strong(X))))&
(![X]:((curious(X)&~old(X))=>(~old(X)<~>strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)<~>old(X))))=>((~kind(lucy)&~funny(lucy))))&
(![X]:((~tall(X)<~>wise(X))<=>~generous(X)))&
((~patient(fred)&~tall(fred)))&
((happy(john)&~quiet(john)))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((funny(mary)&brave(mary)))&
((~wise(mary)<~>happy(mary))) | old(paul) | [
"p7",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 2416556394315666840736419
% SZS output start Proof for 2416556394315666840736419
8. ! [X0] : ((~humble(X0) | old(X0)) <=> (~rich(X0) <~> humble(X0))) [input p7]
22. rich(paul) [input p21]
25. ~old(paul) [input hypothesis]
63. ! [X0] : (((~humble(X0) | old(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (humble(X0) & ~old(X0)))) [nnf transformation 8]
64. ! [X0] : ((~humble(X0) | old(X0) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0)))) & (((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (humble(X0) & ~old(X0)))) [flattening 63]
124. humble(X0) | ~rich(X0) | humble(X0) [cnf transformation 64]
128. ~humble(X0) | old(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 64]
164. rich(paul) [cnf transformation 22]
169. ~old(paul) [cnf transformation 25]
171. ~rich(X0) | humble(X0) [duplicate literal removal 124]
172. ~humble(X0) | old(X0) | ~rich(X0) [duplicate literal removal 128]
407. humble(paul) [resolution 171,164]
514. old(paul) | ~rich(paul) [resolution 172,407]
518. ~rich(paul) [subsumption resolution 514,169]
519. $false [subsumption resolution 518,164]
% SZS output end Proof for 2416556394315666840736419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not curious is not quiet and vice versa.
If someone is not calm then someone is either not funny or calm and vice versa.
Everyone who is either quiet or rich is not wise and vice versa.
Everyone who is calm is not humble or not tall and vice versa.
If susan is not rich or not funny then fred is not calm.
Everyone who is brave is kind and vice versa.
If alice is both happy and not quiet then alice is not tall or not brave and vice versa.
Everyone who is not rich is not creative.
Everyone who is not quiet or kind is either not creative or kind and vice versa.
If someone is not funny or not old then susan is either calm or not kind.
Everyone who is either funny or not creative is both not rich and humble.
If someone is rich then someone is not strong and vice versa.
Everyone who is either not humble or creative is either calm or not wise and vice versa.
Everyone who is not creative or strong is not creative and vice versa.
Fred is humble or not humble.
Someone is either not wise or not kind.
Someone is creative.
John is either not old or not happy.
Susan is either curious or not funny. | Susan is quiet. | contradiction | (![X]:((kind(X)&~curious(X))<=>~quiet(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~wise(X)))&
(![X]:(calm(X)<=>(~humble(X)|~tall(X))))&
(((~rich(susan)|~funny(susan)))=>(~calm(fred)))&
(![X]:(brave(X)<=>kind(X)))&
(((happy(alice)&~quiet(alice)))<=>((~tall(alice)|~brave(alice))))&
(![X]:(~rich(X)=>~creative(X)))&
(![X]:((~quiet(X)|kind(X))<=>(~creative(X)<~>kind(X))))&
((?[X]:((~funny(X)|~old(X))))=>((calm(susan)<~>~kind(susan))))&
(![X]:((funny(X)<~>~creative(X))=>(~rich(X)&humble(X))))&
((?[X]:(rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(calm(X)<~>~wise(X))))&
(![X]:((~creative(X)|strong(X))<=>~creative(X)))&
((humble(fred)|~humble(fred)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:(creative(X)))&
((~old(john)<~>~happy(john)))&
((curious(susan)<~>~funny(susan))) | quiet(susan) | [
"p0",
"p2",
"p3",
"p7",
"p8",
"p9",
"p10",
"p12",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 266118948938445520138460
% SZS output start Proof for 266118948938445520138460
1. ! [X0] : ((~curious(X0) & kind(X0)) <=> ~quiet(X0)) [input p0]
3. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> ~wise(X0)) [input p2]
4. ! [X0] : (calm(X0) <=> (~tall(X0) | ~humble(X0))) [input p3]
8. ! [X0] : (~rich(X0) => ~creative(X0)) [input p7]
9. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> (~creative(X0) <~> kind(X0))) [input p8]
10. ? [X0] : (~old(X0) | ~funny(X0)) => (calm(susan) <~> ~kind(susan)) [input p9]
11. ! [X0] : ((funny(X0) <~> ~creative(X0)) => (humble(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((~humble(X0) <~> creative(X0)) <=> (calm(X0) <~> ~wise(X0))) [input p12]
19. curious(susan) <~> ~funny(susan) [input p18]
20. quiet(susan) [input hypothesis]
24. ! [X0] : (~creative(X0) | rich(X0)) [ennf transformation 8]
25. (calm(susan) <~> ~kind(susan)) | ! [X0] : (old(X0) & funny(X0)) [ennf transformation 10]
26. ! [X0] : ((humble(X0) & ~rich(X0)) | (funny(X0) <=> ~creative(X0))) [ennf transformation 11]
27. ! [X0] : (((~curious(X0) & kind(X0)) | quiet(X0)) & (~quiet(X0) | (curious(X0) | ~kind(X0)))) [nnf transformation 1]
28. ! [X0] : (((~curious(X0) & kind(X0)) | quiet(X0)) & (~quiet(X0) | curious(X0) | ~kind(X0))) [flattening 27]
34. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | wise(X0)) & (~wise(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 3]
35. ! [X0] : ((calm(X0) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | ~calm(X0))) [nnf transformation 4]
36. ! [X0] : ((calm(X0) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | ~calm(X0))) [flattening 35]
40. ! [X0] : (((kind(X0) | ~quiet(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~kind(X0) & quiet(X0)))) [nnf transformation 9]
41. ! [X0] : ((kind(X0) | ~quiet(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~kind(X0) & quiet(X0)))) [flattening 40]
42. ((kind(susan) | ~calm(susan)) & (~kind(susan) | calm(susan))) | ! [X0] : (old(X0) & funny(X0)) [nnf transformation 25]
43. ! [X0] : ((humble(X0) & ~rich(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) [nnf transformation 26]
49. ! [X0] : ((((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0))))) [nnf transformation 13]
58. (funny(susan) | ~curious(susan)) & (~funny(susan) | curious(susan)) [nnf transformation 19]
59. ~quiet(X0) | curious(X0) | ~kind(X0) [cnf transformation 28]
60. quiet(X0) | kind(X0) [cnf transformation 28]
69. ~rich(X0) | ~quiet(X0) | wise(X0) [cnf transformation 34]
71. humble(X0) | calm(X0) [cnf transformation 36]
82. ~creative(X0) | rich(X0) [cnf transformation 24]
86. ~kind(X0) | creative(X0) | ~kind(X0) [cnf transformation 41]
87. kind(X0) | ~quiet(X0) | kind(X0) | creative(X0) [cnf transformation 41]
91. kind(susan) | ~calm(susan) | funny(X0) [cnf transformation 42]
93. ~rich(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 43]
100. ~wise(X0) | calm(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 49]
105. ~creative(X0) | humble(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 49]
117. funny(susan) | ~curious(susan) [cnf transformation 58]
118. quiet(susan) [cnf transformation 20]
119. ~kind(X0) | creative(X0) [duplicate literal removal 86]
120. kind(X0) | ~quiet(X0) | creative(X0) [duplicate literal removal 87]
147. 7 <=> funny(susan) [avatar definition]
149. funny(susan) <- (7) [avatar component clause 147]
181. creative(X0) | kind(X0) [subsumption resolution 120,60]
182. creative(X0) [subsumption resolution 119,181]
187. 15 <=> calm(susan) [avatar definition]
191. 16 <=> kind(susan) [avatar definition]
196. 17 <=> ! [X0] : funny(X0) [avatar definition]
197. funny(X0) <- (17) [avatar component clause 196]
198. 17 | ~15 | 16 [avatar split clause 91,191,187,196]
202. ~rich(X0) | ~funny(X0) [subsumption resolution 93,182]
219. humble(X0) | ~wise(X0) | ~calm(X0) [subsumption resolution 105,182]
220. ~wise(X0) | humble(X0) [subsumption resolution 219,71]
222. ~wise(X0) | calm(X0) | ~humble(X0) [subsumption resolution 100,182]
223. ~wise(X0) | calm(X0) [subsumption resolution 222,220]
246. 26 <=> curious(susan) [avatar definition]
249. ~26 | 7 [avatar split clause 117,147,246]
255. rich(X0) [resolution 82,182]
258. ~funny(X0) [resolution 202,255]
261. curious(susan) | ~kind(susan) [resolution 59,118]
274. ~quiet(X0) | wise(X0) [resolution 69,255]
300. wise(susan) [resolution 274,118]
305. calm(susan) [resolution 300,223]
309. 15 [avatar split clause 305,187]
312. $false <- (17) [subsumption resolution 197,258]
313. ~17 [avatar contradiction clause 312]
314. ~16 | 26 [avatar split clause 261,246,191]
315. $false <- (7) [subsumption resolution 149,258]
316. ~7 [avatar contradiction clause 315]
317. $false [avatar sat refutation 198,249,309,313,314,316]
% SZS output end Proof for 266118948938445520138460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is either patient or tall. Everyone who is either creative or not funny is not old or not humble and vice versa. If fred is either old or not quiet then someone is either not strong or generous and vice versa. If someone is either not humble or funny then mary is not strong or tall and vice versa. Everyone who is funny or creative is both not strong and tall. Everyone who is not brave or not patient is not funny. Everyone who is happy or not tall is either not generous or generous and vice versa. Everyone who is happy or brave is rich and vice versa. Everyone who is curious or kind is both not old and not curious. If paul is either strong or humble then lucy is not rich or curious. If paul is generous or not kind then susan is creative and vice versa. If someone is calm or kind then someone is patient or old and vice versa. Everyone who is quiet or not funny is either not calm or curious. If alice is both curious and not old then someone is not strong or happy and vice versa. Everyone who is rich is not quiet or funny. If someone is not rich then someone is either not old or calm and vice versa. Paul is both not creative and not calm. Someone is either curious or quiet. Someone is either patient or rich. Someone is not creative. Lucy is old or rich. Someone is either not curious or wise. Susan is not quiet. Someone is either patient or not strong. | Susan is old. | contradiction | (![X]:(~patient(X)=>(patient(X)<~>tall(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~old(X)|~humble(X))))&
(((old(fred)<~>~quiet(fred)))<=>(?[X]:((~strong(X)<~>generous(X)))))&
((?[X]:((~humble(X)<~>funny(X))))<=>((~strong(mary)|tall(mary))))&
(![X]:((funny(X)|creative(X))=>(~strong(X)&tall(X))))&
(![X]:((~brave(X)|~patient(X))=>~funny(X)))&
(![X]:((happy(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((happy(X)|brave(X))<=>rich(X)))&
(![X]:((curious(X)|kind(X))=>(~old(X)&~curious(X))))&
(((strong(paul)<~>humble(paul)))=>((~rich(lucy)|curious(lucy))))&
(((generous(paul)|~kind(paul)))<=>(creative(susan)))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~calm(X)<~>curious(X))))&
(((curious(alice)&~old(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:(rich(X)=>(~quiet(X)|funny(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
((~creative(paul)&~calm(paul)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:(~creative(X)))&
((old(lucy)|rich(lucy)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~quiet(susan))&
(?[X]:((patient(X)<~>~strong(X)))) | old(susan) | [
"p1",
"p3",
"p4",
"p6",
"p8",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5860771845914141860654264
% SZS output start Proof for 5860771845914141860654264
2. ! [X0] : ((creative(X0) <~> ~funny(X0)) <=> (~humble(X0) | ~old(X0))) [input p1]
4. ? [X0] : (~humble(X0) <~> funny(X0)) <=> (tall(mary) | ~strong(mary)) [input p3]
5. ! [X0] : ((creative(X0) | funny(X0)) => (tall(X0) & ~strong(X0))) [input p4]
7. ! [X0] : ((~tall(X0) | happy(X0)) <=> (~generous(X0) <~> generous(X0))) [input p6]
9. ! [X0] : ((kind(X0) | curious(X0)) => (~curious(X0) & ~old(X0))) [input p8]
14. (~old(alice) & curious(alice)) <=> ? [X0] : (happy(X0) | ~strong(X0)) [input p13]
25. old(susan) [input hypothesis]
29. ! [X0] : ((tall(X0) & ~strong(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 5]
31. ! [X0] : ((~curious(X0) & ~old(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 9]
38. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [nnf transformation 2]
39. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [flattening 38]
44. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & ((tall(mary) | ~strong(mary)) | ! [X0] : ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [nnf transformation 4]
45. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X0] : ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [flattening 44]
46. (? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X1] : ((~humble(X1) | ~funny(X1)) & (funny(X1) | humble(X1)))) [rectify 45]
47. ? [X0] : ((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) => ((~funny(sK1) | humble(sK1)) & (funny(sK1) | ~humble(sK1))) [choice axiom]
48. (((~funny(sK1) | humble(sK1)) & (funny(sK1) | ~humble(sK1))) | (~tall(mary) & strong(mary))) & (tall(mary) | ~strong(mary) | ! [X1] : ((~humble(X1) | ~funny(X1)) & (funny(X1) | humble(X1)))) [skolemisation 46,47]
49. ! [X0] : (((~tall(X0) | happy(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (tall(X0) & ~happy(X0)))) [nnf transformation 7]
50. ! [X0] : ((~tall(X0) | happy(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (tall(X0) & ~happy(X0)))) [flattening 49]
62. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | (old(alice) | ~curious(alice))) [nnf transformation 14]
63. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | old(alice) | ~curious(alice)) [flattening 62]
64. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X1] : (happy(X1) | ~strong(X1)) | old(alice) | ~curious(alice)) [rectify 63]
65. ? [X1] : (happy(X1) | ~strong(X1)) => (happy(sK4) | ~strong(sK4)) [choice axiom]
66. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & ((happy(sK4) | ~strong(sK4)) | old(alice) | ~curious(alice)) [skolemisation 64,65]
89. ~humble(X0) | ~old(X0) | creative(X0) | funny(X0) [cnf transformation 39]
102. tall(mary) | ~strong(mary) | funny(X1) | humble(X1) [cnf transformation 48]
108. ~strong(X0) | ~funny(X0) [cnf transformation 29]
109. ~strong(X0) | ~creative(X0) [cnf transformation 29]
118. ~tall(X0) | happy(X0) | generous(X0) | generous(X0) [cnf transformation 50]
119. ~tall(X0) | happy(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
125. ~curious(X0) | ~curious(X0) [cnf transformation 31]
141. curious(alice) | strong(X0) [cnf transformation 66]
142. curious(alice) | ~happy(X0) [cnf transformation 66]
163. old(susan) [cnf transformation 25]
164. ~curious(X0) [duplicate literal removal 125]
165. ~tall(X0) | happy(X0) | generous(X0) [duplicate literal removal 118]
166. ~generous(X0) | happy(X0) | ~tall(X0) [duplicate literal removal 119]
199. 7 <=> tall(mary) [avatar definition]
200. tall(mary) <- (7) [avatar component clause 199]
212. 10 <=> strong(mary) [avatar definition]
213. ~strong(mary) <- (~10) [avatar component clause 212]
223. 12 <=> ! [X1] : (funny(X1) | humble(X1)) [avatar definition]
224. funny(X1) | humble(X1) <- (12) [avatar component clause 223]
225. 12 | ~10 | 7 [avatar split clause 102,199,212,223]
226. ~tall(X0) | happy(X0) [subsumption resolution 165,166]
259. 19 <=> ! [X1] : ~old(X1) [avatar definition]
260. ~old(X1) <- (19) [avatar component clause 259]
293. 27 <=> ! [X0] : ~happy(X0) [avatar definition]
294. ~happy(X0) <- (27) [avatar component clause 293]
301. 29 <=> ! [X0] : strong(X0) [avatar definition]
302. strong(X0) <- (29) [avatar component clause 301]
304. ~happy(X0) [subsumption resolution 142,164]
305. 27 [avatar split clause 304,293]
306. strong(X0) [subsumption resolution 141,164]
307. 29 [avatar split clause 306,301]
362. $false <- (~10, 29) [subsumption resolution 213,302]
363. 10 | ~29 [avatar contradiction clause 362]
368. ~funny(X0) <- (29) [resolution 108,302]
369. ~creative(X0) <- (29) [resolution 109,302]
374. happy(mary) <- (7) [resolution 226,200]
376. $false <- (7, 27) [subsumption resolution 374,294]
377. ~7 | ~27 [avatar contradiction clause 376]
379. humble(X1) <- (12, 29) [subsumption resolution 224,368]
397. ~old(X0) | creative(X0) | funny(X0) <- (12, 29) [resolution 89,379]
398. ~old(X0) | funny(X0) <- (12, 29) [subsumption resolution 397,369]
399. ~old(X0) <- (12, 29) [subsumption resolution 398,368]
400. 19 | ~12 | ~29 [avatar split clause 399,301,223,259]
401. $false <- (19) [resolution 260,163]
402. ~19 [avatar contradiction clause 401]
403. $false [avatar sat refutation 225,305,307,363,377,400,402]
% SZS output end Proof for 5860771845914141860654264
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is curious or old then someone is quiet or not calm. If someone is either kind or strong then someone is generous and vice versa. If paul is either patient or not creative then someone is both not rich and funny and vice versa. If someone is patient then someone is either not funny or funny. If someone is generous then mary is brave or not rich and vice versa. If someone is both not brave and humble then someone is not strong or not humble. Everyone who is either patient or creative is both old and quiet. Everyone who is both not happy and generous is not calm and vice versa. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. John is not curious or old. Someone is either not quiet or tall. Paul is creative or humble. Fred is both generous and rich. Alice is both not funny and not strong. Mary is either humble or wise. Lucy is both rich and old. Someone is tall or quiet. | Fred is not creative. | contradiction | (((curious(lucy)|old(lucy)))=>(?[X]:((quiet(X)|~calm(X)))))&
((?[X]:((kind(X)<~>strong(X))))<=>(?[X]:(generous(X))))&
(((patient(paul)<~>~creative(paul)))<=>(?[X]:((~rich(X)&funny(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~funny(X)<~>funny(X)))))&
((?[X]:(generous(X)))<=>((brave(mary)|~rich(mary))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((patient(X)<~>creative(X))=>(old(X)&quiet(X))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
((~curious(john)|old(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((creative(paul)|humble(paul)))&
((generous(fred)&rich(fred)))&
((~funny(alice)&~strong(alice)))&
((humble(mary)<~>wise(mary)))&
((rich(lucy)&old(lucy)))&
(?[X]:((tall(X)|quiet(X)))) | ~creative(fred) | [
"p6",
"p11",
"p13",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 3984441487113654623282519
% SZS output start Proof for 3984441487113654623282519
7. ! [X0] : ((patient(X0) <~> creative(X0)) => (quiet(X0) & old(X0))) [input p6]
12. ! [X0] : ((generous(X0) | funny(X0)) => ~quiet(X0)) [input p11]
14. ! [X0] : ((~patient(X0) | wise(X0)) => ~generous(X0)) [input p13]
20. rich(fred) & generous(fred) [input p19]
25. ~creative(fred) [input hypothesis]
34. ! [X0] : ((quiet(X0) & old(X0)) | (patient(X0) <=> creative(X0))) [ennf transformation 7]
35. ! [X0] : (~quiet(X0) | (~generous(X0) & ~funny(X0))) [ennf transformation 12]
37. ! [X0] : (~generous(X0) | (patient(X0) & ~wise(X0))) [ennf transformation 14]
61. ! [X0] : ((quiet(X0) & old(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0)))) [nnf transformation 34]
100. ~patient(X0) | creative(X0) | quiet(X0) [cnf transformation 61]
118. ~generous(X0) | ~quiet(X0) [cnf transformation 35]
122. ~generous(X0) | patient(X0) [cnf transformation 37]
135. generous(fred) [cnf transformation 20]
144. ~creative(fred) [cnf transformation 25]
252. 25 <=> quiet(fred) [avatar definition]
254. ~quiet(fred) <- (~25) [avatar component clause 252]
298. ~quiet(fred) [resolution 118,135]
301. ~25 [avatar split clause 298,252]
303. patient(fred) [resolution 122,135]
338. creative(fred) | quiet(fred) [resolution 100,303]
341. quiet(fred) [subsumption resolution 338,144]
342. $false <- (~25) [subsumption resolution 341,254]
343. 25 [avatar contradiction clause 342]
346. $false [avatar sat refutation 301,343]
% SZS output end Proof for 3984441487113654623282519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is calm then fred is both humble and not kind and vice versa.
Everyone who is curious is not strong.
If someone is old or quiet then lucy is creative or calm.
If someone is creative or not tall then someone is calm or not happy and vice versa.
If someone is not calm or not strong then paul is both not rich and not curious and vice versa.
If susan is old or wise then someone is patient or humble and vice versa.
If paul is not strong or humble then mary is not generous or patient.
Everyone who is either not creative or brave is humble.
Everyone who is either tall or not quiet is happy or creative and vice versa.
Everyone who is either curious or strong is both happy and brave and vice versa.
If john is brave or calm then lucy is either not funny or not patient.
Everyone who is happy is both wise and tall.
If someone is both not calm and not patient then susan is either creative or not old.
Everyone who is both not calm and kind is happy and vice versa.
If someone is both calm and not happy then susan is not funny or generous.
If someone is both not strong and humble then someone is not kind or quiet.
Fred is not wise.
John is both not calm and not happy.
Someone is both tall and funny.
Someone is not generous.
Lucy is not funny or strong.
Someone is both funny and not humble.
Someone is either not old or funny.
Someone is either old or tall. | Mary is patient. | neutral | ((calm(paul))<=>((humble(fred)&~kind(fred))))&
(![X]:(curious(X)=>~strong(X)))&
((?[X]:((old(X)|quiet(X))))=>((creative(lucy)|calm(lucy))))&
((?[X]:((creative(X)|~tall(X))))<=>(?[X]:((calm(X)|~happy(X)))))&
((?[X]:((~calm(X)|~strong(X))))<=>((~rich(paul)&~curious(paul))))&
(((old(susan)|wise(susan)))<=>(?[X]:((patient(X)|humble(X)))))&
(((~strong(paul)|humble(paul)))=>((~generous(mary)|patient(mary))))&
(![X]:((~creative(X)<~>brave(X))=>humble(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(happy(X)|creative(X))))&
(![X]:((curious(X)<~>strong(X))<=>(happy(X)&brave(X))))&
(((brave(john)|calm(john)))=>((~funny(lucy)<~>~patient(lucy))))&
(![X]:(happy(X)=>(wise(X)&tall(X))))&
((?[X]:((~calm(X)&~patient(X))))=>((creative(susan)<~>~old(susan))))&
(![X]:((~calm(X)&kind(X))<=>happy(X)))&
((?[X]:((calm(X)&~happy(X))))=>((~funny(susan)|generous(susan))))&
((?[X]:((~strong(X)&humble(X))))=>(?[X]:((~kind(X)|quiet(X)))))&
(~wise(fred))&
((~calm(john)&~happy(john)))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:(~generous(X)))&
((~funny(lucy)|strong(lucy)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((~old(X)<~>funny(X))))&
(?[X]:((old(X)<~>tall(X)))) | patient(mary) | []
| null | 0 |
If someone is both not generous and brave then someone is not tall. If someone is either not tall or not strong then someone is both happy and not quiet and vice versa. Everyone who is not strong or old is both creative and patient. If mary is either quiet or patient then fred is either not patient or not calm. If john is both not quiet and not patient then fred is both patient and not strong and vice versa. Everyone who is rich or patient is either not kind or not happy and vice versa. If alice is both curious and not kind then alice is not humble or tall and vice versa. If someone is both not calm and not happy then john is either not old or strong. If mary is either not funny or not creative then mary is not humble and vice versa. Everyone who is not old is both not humble and funny and vice versa. If susan is either not creative or not humble then paul is curious and vice versa. Everyone who is either not quiet or wise is wise and vice versa. Everyone who is not wise or not funny is not calm and vice versa. Everyone who is either not happy or wise is both creative and wise and vice versa. If someone is either not quiet or patient then someone is either not quiet or not generous and vice versa. Everyone who is not old or old is quiet or wise and vice versa. Paul is either kind or not curious. Mary is either not funny or rich. Someone is both brave and curious. Paul is either rich or patient. Fred is curious or not rich. Fred is kind. Someone is either not strong or funny. | Susan is quiet. | entailment | ((?[X]:((~generous(X)&brave(X))))=>(?[X]:(~tall(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((~strong(X)|old(X))=>(creative(X)&patient(X))))&
(((quiet(mary)<~>patient(mary)))=>((~patient(fred)<~>~calm(fred))))&
(((~quiet(john)&~patient(john)))<=>((patient(fred)&~strong(fred))))&
(![X]:((rich(X)|patient(X))<=>(~kind(X)<~>~happy(X))))&
(((curious(alice)&~kind(alice)))<=>((~humble(alice)|tall(alice))))&
((?[X]:((~calm(X)&~happy(X))))=>((~old(john)<~>strong(john))))&
(((~funny(mary)<~>~creative(mary)))<=>(~humble(mary)))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(((~creative(susan)<~>~humble(susan)))<=>(curious(paul)))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~old(X)|old(X))<=>(quiet(X)|wise(X))))&
((kind(paul)<~>~curious(paul)))&
((~funny(mary)<~>rich(mary)))&
(?[X]:((brave(X)&curious(X))))&
((rich(paul)<~>patient(paul)))&
((curious(fred)|~rich(fred)))&
(kind(fred))&
(?[X]:((~strong(X)<~>funny(X)))) | quiet(susan) | [
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 3349248194807212965836228
% SZS output start Proof for 3349248194807212965836228
12. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> wise(X0)) [input p11]
24. ~quiet(susan) [input hypothesis]
52. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 12]
115. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 52]
118. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 52]
152. ~quiet(susan) [cnf transformation 24]
155. wise(X0) | quiet(X0) [duplicate literal removal 115]
156. ~wise(X0) | quiet(X0) [duplicate literal removal 118]
300. quiet(X0) [subsumption resolution 155,156]
362. $false [subsumption resolution 152,300]
% SZS output end Proof for 3349248194807212965836228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
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