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 brave and wise is either not kind or not funny and vice versa.
Everyone who is not funny or not happy is both not strong and rich.
Everyone who is both not strong and not humble is old and vice versa.
If someone is either not calm or brave then someone is both rich and not curious.
Everyone who is both strong and not generous is either not strong or not old and vice versa.
Everyone who is calm is not wise and vice versa.
If someone is either not calm or kind then someone is both not generous and not rich.
If mary is both old and not quiet then paul is not funny or not calm.
Everyone who is either not curious or strong is not quiet or not curious and vice versa.
Everyone who is both not tall and patient is old or not calm.
Everyone who is not kind or not quiet is not curious.
Everyone who is curious is both not happy and patient.
Everyone who is either not kind or not happy is either not wise or quiet and vice versa.
Everyone who is either strong or tall is both generous and not happy and vice versa.
If someone is happy or not curious then someone is both not rich and strong.
Everyone who is either not calm or not curious is not old or not calm and vice versa.
Susan is either not funny or not happy.
Someone is either not kind or quiet.
Paul is not old.
Lucy is wise or happy.
Someone is either not kind or not tall.
Someone is not old or funny.
Susan is both quiet and not creative.
Paul is both not calm and tall. | Lucy is not funny. | contradiction | (![X]:((~brave(X)&wise(X))<=>(~kind(X)<~>~funny(X))))&
(![X]:((~funny(X)|~happy(X))=>(~strong(X)&rich(X))))&
(![X]:((~strong(X)&~humble(X))<=>old(X)))&
((?[X]:((~calm(X)<~>brave(X))))=>(?[X]:((rich(X)&~curious(X)))))&
(![X]:((strong(X)&~generous(X))<=>(~strong(X)<~>~old(X))))&
(![X]:(calm(X)<=>~wise(X)))&
((?[X]:((~calm(X)<~>kind(X))))=>(?[X]:((~generous(X)&~rich(X)))))&
(((old(mary)&~quiet(mary)))=>((~funny(paul)|~calm(paul))))&
(![X]:((~curious(X)<~>strong(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((~tall(X)&patient(X))=>(old(X)|~calm(X))))&
(![X]:((~kind(X)|~quiet(X))=>~curious(X)))&
(![X]:(curious(X)=>(~happy(X)&patient(X))))&
(![X]:((~kind(X)<~>~happy(X))<=>(~wise(X)<~>quiet(X))))&
(![X]:((strong(X)<~>tall(X))<=>(generous(X)&~happy(X))))&
((?[X]:((happy(X)|~curious(X))))=>(?[X]:((~rich(X)&strong(X)))))&
(![X]:((~calm(X)<~>~curious(X))<=>(~old(X)|~calm(X))))&
((~funny(susan)<~>~happy(susan)))&
(?[X]:((~kind(X)<~>quiet(X))))&
(~old(paul))&
((wise(lucy)|happy(lucy)))&
(?[X]:((~kind(X)<~>~tall(X))))&
(?[X]:((~old(X)|funny(X))))&
((quiet(susan)&~creative(susan)))&
((~calm(paul)&tall(paul))) | ~funny(lucy) | [
"p0",
"p1",
"p3",
"p6",
"p8",
"p10",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7583515748429806725868742
% SZS output start Proof for 7583515748429806725868742
1. ! [X0] : ((wise(X0) & ~brave(X0)) <=> (~kind(X0) <~> ~funny(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | ~funny(X0)) => (rich(X0) & ~strong(X0))) [input p1]
4. ? [X0] : (~calm(X0) <~> brave(X0)) => ? [X0] : (~curious(X0) & rich(X0)) [input p3]
7. ? [X0] : (~calm(X0) <~> kind(X0)) => ? [X0] : (~rich(X0) & ~generous(X0)) [input p6]
9. ! [X0] : ((~curious(X0) <~> strong(X0)) <=> (~curious(X0) | ~quiet(X0))) [input p8]
11. ! [X0] : ((~quiet(X0) | ~kind(X0)) => ~curious(X0)) [input p10]
12. ! [X0] : (curious(X0) => (patient(X0) & ~happy(X0))) [input p11]
15. ? [X0] : (~curious(X0) | happy(X0)) => ? [X0] : (strong(X0) & ~rich(X0)) [input p14]
25. ~funny(lucy) [input hypothesis]
26. ? [X0] : (~calm(X0) <~> brave(X0)) => ? [X1] : (~curious(X1) & rich(X1)) [rectify 4]
27. ? [X0] : (~calm(X0) <~> kind(X0)) => ? [X1] : (~rich(X1) & ~generous(X1)) [rectify 7]
28. ? [X0] : (~curious(X0) | happy(X0)) => ? [X1] : (strong(X1) & ~rich(X1)) [rectify 15]
30. ! [X0] : ((rich(X0) & ~strong(X0)) | (happy(X0) & funny(X0))) [ennf transformation 2]
31. ? [X1] : (~curious(X1) & rich(X1)) | ! [X0] : (~calm(X0) <=> brave(X0)) [ennf transformation 26]
32. ? [X1] : (~rich(X1) & ~generous(X1)) | ! [X0] : (~calm(X0) <=> kind(X0)) [ennf transformation 27]
37. ! [X0] : (~curious(X0) | (quiet(X0) & kind(X0))) [ennf transformation 11]
38. ! [X0] : ((patient(X0) & ~happy(X0)) | ~curious(X0)) [ennf transformation 12]
39. ? [X1] : (strong(X1) & ~rich(X1)) | ! [X0] : (curious(X0) & ~happy(X0)) [ennf transformation 28]
40. ! [X0] : (((wise(X0) & ~brave(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~wise(X0) | brave(X0)))) [nnf transformation 1]
41. ! [X0] : (((wise(X0) & ~brave(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~wise(X0) | brave(X0))) [flattening 40]
44. ? [X1] : (~curious(X1) & rich(X1)) | ! [X0] : ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))) [nnf transformation 31]
45. ? [X0] : (~curious(X0) & rich(X0)) | ! [X1] : ((~calm(X1) | ~brave(X1)) & (brave(X1) | calm(X1))) [rectify 44]
46. ? [X0] : (~curious(X0) & rich(X0)) => (~curious(sK0) & rich(sK0)) [choice axiom]
47. (~curious(sK0) & rich(sK0)) | ! [X1] : ((~calm(X1) | ~brave(X1)) & (brave(X1) | calm(X1))) [skolemisation 45,46]
51. ? [X1] : (~rich(X1) & ~generous(X1)) | ! [X0] : ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))) [nnf transformation 32]
52. ? [X0] : (~rich(X0) & ~generous(X0)) | ! [X1] : ((~calm(X1) | ~kind(X1)) & (kind(X1) | calm(X1))) [rectify 51]
53. ? [X0] : (~rich(X0) & ~generous(X0)) => (~rich(sK1) & ~generous(sK1)) [choice axiom]
54. (~rich(sK1) & ~generous(sK1)) | ! [X1] : ((~calm(X1) | ~kind(X1)) & (kind(X1) | calm(X1))) [skolemisation 52,53]
55. ! [X0] : ((((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | (curious(X0) & quiet(X0))) & ((~curious(X0) | ~quiet(X0)) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | (curious(X0) & quiet(X0))) & (~curious(X0) | ~quiet(X0) | ((~curious(X0) | ~strong(X0)) & (strong(X0) | curious(X0))))) [flattening 55]
60. ? [X0] : (strong(X0) & ~rich(X0)) | ! [X1] : (curious(X1) & ~happy(X1)) [rectify 39]
61. ? [X0] : (strong(X0) & ~rich(X0)) => (strong(sK2) & ~rich(sK2)) [choice axiom]
62. (strong(sK2) & ~rich(sK2)) | ! [X1] : (curious(X1) & ~happy(X1)) [skolemisation 60,61]
77. ~kind(X0) | ~brave(X0) | funny(X0) [cnf transformation 41]
81. ~strong(X0) | happy(X0) [cnf transformation 30]
83. rich(X0) | happy(X0) [cnf transformation 30]
89. ~curious(sK0) | brave(X1) | calm(X1) [cnf transformation 47]
102. ~rich(sK1) | ~calm(X1) | ~kind(X1) [cnf transformation 54]
109. ~strong(X0) | curious(X0) | curious(X0) [cnf transformation 56]
111. ~curious(X0) | kind(X0) [cnf transformation 37]
113. ~curious(X0) | ~happy(X0) [cnf transformation 38]
130. ~rich(sK2) | curious(X1) [cnf transformation 62]
131. strong(sK2) | ~happy(X1) [cnf transformation 62]
151. ~funny(lucy) [cnf transformation 25]
155. ~strong(X0) | curious(X0) [duplicate literal removal 109]
162. 2 <=> curious(sK0) [avatar definition]
164. ~curious(sK0) <- (~2) [avatar component clause 162]
167. 3 <=> ! [X1] : (brave(X1) | calm(X1)) [avatar definition]
168. calm(X1) | brave(X1) <- (3) [avatar component clause 167]
169. 3 | ~2 [avatar split clause 89,162,167]
180. 5 <=> ! [X1] : (~calm(X1) | ~kind(X1)) [avatar definition]
181. ~calm(X1) | ~kind(X1) <- (5) [avatar component clause 180]
183. 6 <=> rich(sK1) [avatar definition]
185. ~rich(sK1) <- (~6) [avatar component clause 183]
186. 5 | ~6 [avatar split clause 102,183,180]
202. 9 <=> ! [X1] : curious(X1) [avatar definition]
203. curious(X1) <- (9) [avatar component clause 202]
205. 10 <=> strong(sK2) [avatar definition]
207. strong(sK2) <- (10) [avatar component clause 205]
210. 11 <=> ! [X1] : ~happy(X1) [avatar definition]
211. ~happy(X1) <- (11) [avatar component clause 210]
212. 11 | 10 [avatar split clause 131,205,210]
214. 12 <=> rich(sK2) [avatar definition]
216. ~rich(sK2) <- (~12) [avatar component clause 214]
217. 9 | ~12 [avatar split clause 130,214,202]
260. happy(sK2) <- (10) [resolution 81,207]
263. happy(sK1) <- (~6) [resolution 83,185]
264. happy(sK2) <- (~12) [resolution 83,216]
274. curious(sK2) <- (10) [resolution 155,207]
276. ~happy(sK2) <- (10) [resolution 274,113]
279. $false <- (10) [subsumption resolution 276,260]
280. ~10 [avatar contradiction clause 279]
281. $false <- (~2, 9) [resolution 203,164]
285. kind(X3) <- (9) [resolution 203,111]
286. 2 | ~9 [avatar contradiction clause 281]
287. $false <- (~6, 11) [resolution 211,263]
288. 6 | ~11 [avatar contradiction clause 287]
289. ~calm(X1) <- (5, 9) [subsumption resolution 181,285]
292. $false <- (11, ~12) [resolution 264,211]
293. ~11 | 12 [avatar contradiction clause 292]
296. brave(X1) <- (3, 5, 9) [resolution 168,289]
310. ~brave(X0) | funny(X0) <- (9) [resolution 77,285]
312. funny(X0) <- (3, 5, 9) [subsumption resolution 310,296]
316. $false <- (3, 5, 9) [resolution 312,151]
319. ~3 | ~5 | ~9 [avatar contradiction clause 316]
320. $false [avatar sat refutation 169,186,212,217,280,286,288,293,319]
% SZS output end Proof for 7583515748429806725868742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is either not brave or not wise and vice versa. Everyone who is quiet or not calm is either brave or kind and vice versa. Everyone who is not rich or brave is not creative and vice versa. Everyone who is both not patient and not curious is kind or brave. If fred is both wise and not rich then someone is both quiet and old and vice versa. Everyone who is either patient or not happy is both not creative and not kind. Everyone who is creative or not old is either not generous or not quiet and vice versa. Everyone who is generous is both not curious and not creative and vice versa. If someone is not tall or not brave then lucy is not tall or curious and vice versa. If susan is not funny or strong then lucy is either kind or not brave. Everyone who is not kind is either not happy or not strong. Everyone who is funny is happy or tall. If someone is old or not wise then lucy is humble or not funny. If paul is either patient or funny then fred is not tall. Everyone who is either patient or tall is not happy and vice versa. If someone is old or humble then alice is not happy or not funny. Fred is either not strong or not wise. John is not curious. Mary is either wise or not happy. Lucy is not humble. Susan is not creative or humble. Someone is not creative. Someone is not funny or quiet. | John is not old. | neutral | ((?[X]:(~brave(X)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(![X]:((quiet(X)|~calm(X))<=>(brave(X)<~>kind(X))))&
(![X]:((~rich(X)|brave(X))<=>~creative(X)))&
(![X]:((~patient(X)&~curious(X))=>(kind(X)|brave(X))))&
(((wise(fred)&~rich(fred)))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((patient(X)<~>~happy(X))=>(~creative(X)&~kind(X))))&
(![X]:((creative(X)|~old(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(~curious(X)&~creative(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>((~tall(lucy)|curious(lucy))))&
(((~funny(susan)|strong(susan)))=>((kind(lucy)<~>~brave(lucy))))&
(![X]:(~kind(X)=>(~happy(X)<~>~strong(X))))&
(![X]:(funny(X)=>(happy(X)|tall(X))))&
((?[X]:((old(X)|~wise(X))))=>((humble(lucy)|~funny(lucy))))&
(((patient(paul)<~>funny(paul)))=>(~tall(fred)))&
(![X]:((patient(X)<~>tall(X))<=>~happy(X)))&
((?[X]:((old(X)|humble(X))))=>((~happy(alice)|~funny(alice))))&
((~strong(fred)<~>~wise(fred)))&
(~curious(john))&
((wise(mary)<~>~happy(mary)))&
(~humble(lucy))&
((~creative(susan)|humble(susan)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)|quiet(X)))) | ~old(john) | []
| null | 0 |
Everyone who is either not generous or funny is both not quiet and not creative and vice versa.
Everyone who is rich or not funny is either creative or not funny.
Everyone who is curious is tall and vice versa.
If someone is either calm or not strong then fred is not creative or curious and vice versa.
Everyone who is either creative or quiet is not patient or not rich and vice versa.
If someone is both old and quiet then someone is both tall and not kind.
If someone is either generous or not wise then mary is not happy and vice versa.
Everyone who is not wise or not rich is kind and vice versa.
If alice is creative or not generous then paul is not rich.
Everyone who is both not happy and not humble is not happy.
Everyone who is both creative and not funny is not strong.
Everyone who is not calm or not old is both not patient and creative and vice versa.
If fred is not humble then john is old or curious.
If someone is either not patient or rich then someone is humble.
Everyone who is not curious is both not kind and brave.
Everyone who is either strong or kind is both strong and patient.
Someone is not strong or not kind.
Someone is either not humble or happy.
Alice is either not generous or not old.
Someone is wise.
John is not rich or not tall.
Lucy is both not humble and not wise.
Someone is either not curious or happy.
Fred is brave. | Paul is strong. | entailment | (![X]:((~generous(X)<~>funny(X))<=>(~quiet(X)&~creative(X))))&
(![X]:((rich(X)|~funny(X))=>(creative(X)<~>~funny(X))))&
(![X]:(curious(X)<=>tall(X)))&
((?[X]:((calm(X)<~>~strong(X))))<=>((~creative(fred)|curious(fred))))&
(![X]:((creative(X)<~>quiet(X))<=>(~patient(X)|~rich(X))))&
((?[X]:((old(X)&quiet(X))))=>(?[X]:((tall(X)&~kind(X)))))&
((?[X]:((generous(X)<~>~wise(X))))<=>(~happy(mary)))&
(![X]:((~wise(X)|~rich(X))<=>kind(X)))&
(((creative(alice)|~generous(alice)))=>(~rich(paul)))&
(![X]:((~happy(X)&~humble(X))=>~happy(X)))&
(![X]:((creative(X)&~funny(X))=>~strong(X)))&
(![X]:((~calm(X)|~old(X))<=>(~patient(X)&creative(X))))&
((~humble(fred))=>((old(john)|curious(john))))&
((?[X]:((~patient(X)<~>rich(X))))=>(?[X]:(humble(X))))&
(![X]:(~curious(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)<~>kind(X))=>(strong(X)&patient(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
((~generous(alice)<~>~old(alice)))&
(?[X]:(wise(X)))&
((~rich(john)|~tall(john)))&
((~humble(lucy)&~wise(lucy)))&
(?[X]:((~curious(X)<~>happy(X))))&
(brave(fred)) | strong(paul) | [
"p7",
"p8",
"p11",
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 1283670134221748573377279
% SZS output start Proof for 1283670134221748573377279
8. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> kind(X0)) [input p7]
9. (~generous(alice) | creative(alice)) => ~rich(paul) [input p8]
12. ! [X0] : ((~old(X0) | ~calm(X0)) <=> (creative(X0) & ~patient(X0))) [input p11]
16. ! [X0] : ((strong(X0) <~> kind(X0)) => (patient(X0) & strong(X0))) [input p15]
19. ~generous(alice) <~> ~old(alice) [input p18]
25. ~strong(paul) [input hypothesis]
32. ~rich(paul) | (generous(alice) & ~creative(alice)) [ennf transformation 9]
41. ! [X0] : ((patient(X0) & strong(X0)) | (strong(X0) <=> kind(X0))) [ennf transformation 16]
60. ! [X0] : (((~rich(X0) | ~wise(X0)) | ~kind(X0)) & (kind(X0) | (rich(X0) & wise(X0)))) [nnf transformation 8]
61. ! [X0] : ((~rich(X0) | ~wise(X0) | ~kind(X0)) & (kind(X0) | (rich(X0) & wise(X0)))) [flattening 60]
62. ! [X0] : (((~old(X0) | ~calm(X0)) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | (old(X0) & calm(X0)))) [nnf transformation 12]
63. ! [X0] : ((~old(X0) | ~calm(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | (old(X0) & calm(X0)))) [flattening 62]
68. ! [X0] : ((patient(X0) & strong(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) [nnf transformation 41]
74. (old(alice) | generous(alice)) & (~old(alice) | ~generous(alice)) [nnf transformation 19]
111. kind(X0) | rich(X0) [cnf transformation 61]
113. ~rich(paul) | ~creative(alice) [cnf transformation 32]
114. ~rich(paul) | generous(alice) [cnf transformation 32]
120. old(X0) | creative(X0) [cnf transformation 63]
127. strong(X0) | strong(X0) | ~kind(X0) [cnf transformation 68]
133. ~old(alice) | ~generous(alice) [cnf transformation 74]
141. ~strong(paul) [cnf transformation 25]
142. ~kind(X0) | strong(X0) [duplicate literal removal 127]
208. 15 <=> generous(alice) [avatar definition]
212. 16 <=> rich(paul) [avatar definition]
214. ~rich(paul) <- (~16) [avatar component clause 212]
215. 15 | ~16 [avatar split clause 114,212,208]
217. 17 <=> creative(alice) [avatar definition]
220. ~17 | ~16 [avatar split clause 113,212,217]
258. 26 <=> old(alice) [avatar definition]
259. ~old(alice) <- (~26) [avatar component clause 258]
262. ~15 | ~26 [avatar split clause 133,258,208]
286. creative(alice) <- (~26) [resolution 120,259]
287. 17 | 26 [avatar split clause 286,258,217]
292. strong(X0) | rich(X0) [resolution 142,111]
468. rich(paul) [resolution 292,141]
471. $false <- (~16) [subsumption resolution 468,214]
472. 16 [avatar contradiction clause 471]
473. $false [avatar sat refutation 215,220,262,287,472]
% SZS output end Proof for 1283670134221748573377279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or generous is calm or generous and vice versa.
If someone is not patient or patient then paul is brave or old.
Everyone who is either not strong or not old is not calm and vice versa.
Everyone who is both not calm and not patient is patient.
If someone is both generous and not funny then someone is generous and vice versa.
If mary is either strong or not creative then someone is either not calm or generous.
If alice is not generous or not tall then someone is both not curious and calm and vice versa.
If someone is either patient or not strong then someone is either strong or not creative.
Everyone who is old or not quiet is not old and vice versa.
Everyone who is both not strong and calm is humble or old.
Everyone who is curious or generous is tall or not old and vice versa.
Everyone who is both quiet and not rich is both rich and patient and vice versa.
Everyone who is creative is wise and vice versa.
Everyone who is either not wise or not creative is not calm and vice versa.
If someone is either not generous or calm then susan is both not funny and not old.
If mary is calm then mary is humble and vice versa.
Someone is both not curious and not strong.
Someone is either humble or not rich.
Someone is either not old or curious.
Lucy is strong or not tall.
Susan is either quiet or calm.
Someone is not patient or not brave.
Alice is either not humble or not rich. | Susan is not strong. | entailment | (![X]:((~calm(X)|generous(X))<=>(calm(X)|generous(X))))&
((?[X]:((~patient(X)|patient(X))))=>((brave(paul)|old(paul))))&
(![X]:((~strong(X)<~>~old(X))<=>~calm(X)))&
(![X]:((~calm(X)&~patient(X))=>patient(X)))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(generous(X))))&
(((strong(mary)<~>~creative(mary)))=>(?[X]:((~calm(X)<~>generous(X)))))&
(((~generous(alice)|~tall(alice)))<=>(?[X]:((~curious(X)&calm(X)))))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((old(X)|~quiet(X))<=>~old(X)))&
(![X]:((~strong(X)&calm(X))=>(humble(X)|old(X))))&
(![X]:((curious(X)|generous(X))<=>(tall(X)|~old(X))))&
(![X]:((quiet(X)&~rich(X))<=>(rich(X)&patient(X))))&
(![X]:(creative(X)<=>wise(X)))&
(![X]:((~wise(X)<~>~creative(X))<=>~calm(X)))&
((?[X]:((~generous(X)<~>calm(X))))=>((~funny(susan)&~old(susan))))&
((calm(mary))<=>(humble(mary)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((~old(X)<~>curious(X))))&
((strong(lucy)|~tall(lucy)))&
((quiet(susan)<~>calm(susan)))&
(?[X]:((~patient(X)|~brave(X))))&
((~humble(alice)<~>~rich(alice))) | ~strong(susan) | [
"p2",
"p8",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 1685699510616394385828596
% SZS output start Proof for 1685699510616394385828596
3. ! [X0] : ((~strong(X0) <~> ~old(X0)) <=> ~calm(X0)) [input p2]
9. ! [X0] : ((~quiet(X0) | old(X0)) <=> ~old(X0)) [input p8]
13. ! [X0] : (creative(X0) <=> wise(X0)) [input p12]
14. ! [X0] : ((~wise(X0) <~> ~creative(X0)) <=> ~calm(X0)) [input p13]
24. strong(susan) [input hypothesis]
38. ! [X0] : ((((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | calm(X0)) & (~calm(X0) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0))))) [nnf transformation 3]
56. ! [X0] : (((~quiet(X0) | old(X0)) | old(X0)) & (~old(X0) | (quiet(X0) & ~old(X0)))) [nnf transformation 9]
57. ! [X0] : ((~quiet(X0) | old(X0) | old(X0)) & (~old(X0) | (quiet(X0) & ~old(X0)))) [flattening 56]
62. ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))) [nnf transformation 13]
63. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | calm(X0)) & (~calm(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [nnf transformation 14]
85. ~strong(X0) | ~calm(X0) | old(X0) [cnf transformation 38]
105. ~old(X0) | ~old(X0) [cnf transformation 57]
117. ~creative(X0) | wise(X0) [cnf transformation 62]
118. ~wise(X0) | creative(X0) [cnf transformation 62]
121. ~creative(X0) | ~wise(X0) | calm(X0) [cnf transformation 63]
122. creative(X0) | wise(X0) | calm(X0) [cnf transformation 63]
141. strong(susan) [cnf transformation 24]
144. ~old(X0) [duplicate literal removal 105]
221. wise(X0) | calm(X0) [subsumption resolution 122,117]
222. ~wise(X0) | calm(X0) [subsumption resolution 121,118]
223. calm(X0) [subsumption resolution 222,221]
277. ~calm(susan) | old(susan) [resolution 85,141]
278. old(susan) [subsumption resolution 277,223]
279. $false [subsumption resolution 278,144]
% SZS output end Proof for 1685699510616394385828596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If john is not quiet then someone is not brave or tall.
If someone is not creative or humble then paul is both not calm and not patient.
Everyone who is strong or humble is not quiet or curious and vice versa.
If john is not old or patient then someone is both brave and old.
If someone is either strong or not happy then paul is quiet or kind and vice versa.
If paul is both not tall and not patient then fred is not kind.
Everyone who is either not funny or tall is both not humble and not old.
Everyone who is either curious or not funny is either calm or not humble and vice versa.
If someone is not generous or tall then mary is either not tall or calm and vice versa.
Everyone who is either generous or funny is both not curious and calm and vice versa.
Everyone who is both not calm and kind is both not rich and curious and vice versa.
If someone is not funny or quiet then someone is creative or rich.
If someone is both patient and not patient then someone is creative and vice versa.
Everyone who is either not generous or creative is old or not happy and vice versa.
Everyone who is either happy or tall is both not creative and quiet and vice versa.
Everyone who is either curious or strong is not quiet and vice versa.
John is either not tall or creative.
Paul is funny.
Susan is humble or tall.
Mary is not patient.
Someone is either happy or not curious.
Someone is either not calm or creative.
Someone is either patient or not patient. | Mary is old. | neutral | ((~quiet(john))=>(?[X]:((~brave(X)|tall(X)))))&
((?[X]:((~creative(X)|humble(X))))=>((~calm(paul)&~patient(paul))))&
(![X]:((strong(X)|humble(X))<=>(~quiet(X)|curious(X))))&
(((~old(john)|patient(john)))=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((strong(X)<~>~happy(X))))<=>((quiet(paul)|kind(paul))))&
(((~tall(paul)&~patient(paul)))=>(~kind(fred)))&
(![X]:((~funny(X)<~>tall(X))=>(~humble(X)&~old(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(calm(X)<~>~humble(X))))&
((?[X]:((~generous(X)|tall(X))))<=>((~tall(mary)<~>calm(mary))))&
(![X]:((generous(X)<~>funny(X))<=>(~curious(X)&calm(X))))&
(![X]:((~calm(X)&kind(X))<=>(~rich(X)&curious(X))))&
((?[X]:((~funny(X)|quiet(X))))=>(?[X]:((creative(X)|rich(X)))))&
((?[X]:((patient(X)&~patient(X))))<=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>creative(X))<=>(old(X)|~happy(X))))&
(![X]:((happy(X)<~>tall(X))<=>(~creative(X)&quiet(X))))&
(![X]:((curious(X)<~>strong(X))<=>~quiet(X)))&
((~tall(john)<~>creative(john)))&
(funny(paul))&
((humble(susan)|tall(susan)))&
(~patient(mary))&
(?[X]:((happy(X)<~>~curious(X))))&
(?[X]:((~calm(X)<~>creative(X))))&
(?[X]:((patient(X)<~>~patient(X)))) | old(mary) | []
| null | 0 |
If susan is both humble and not rich then someone is both not rich and not funny and vice versa.
Everyone who is either quiet or not happy is either strong or not calm.
Everyone who is strong or not rich is curious.
If someone is either curious or not wise then john is both not calm and not curious.
Everyone who is tall is either not curious or rich.
If someone is brave then someone is both tall and not funny and vice versa.
Everyone who is kind is both happy and kind.
Everyone who is either not old or tall is kind or not humble.
Everyone who is old is not patient or patient and vice versa.
If susan is patient then susan is both not happy and quiet.
If alice is not quiet or strong then alice is kind.
If susan is either curious or not old then someone is not patient or not quiet.
If someone is both brave and curious then alice is both not humble and not wise.
Everyone who is strong or not brave is tall or not tall.
If fred is not curious then someone is both generous and happy and vice versa.
Everyone who is not strong is both rich and kind and vice versa.
Someone is humble.
Someone is calm.
Mary is either humble or brave.
John is either not funny or tall.
John is funny.
Someone is not creative or not curious.
John is not patient.
Someone is not creative or humble. | John is funny. | entailment | (((humble(susan)&~rich(susan)))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))=>(strong(X)<~>~calm(X))))&
(![X]:((strong(X)|~rich(X))=>curious(X)))&
((?[X]:((curious(X)<~>~wise(X))))=>((~calm(john)&~curious(john))))&
(![X]:(tall(X)=>(~curious(X)<~>rich(X))))&
((?[X]:(brave(X)))<=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:(kind(X)=>(happy(X)&kind(X))))&
(![X]:((~old(X)<~>tall(X))=>(kind(X)|~humble(X))))&
(![X]:(old(X)<=>(~patient(X)|patient(X))))&
((patient(susan))=>((~happy(susan)&quiet(susan))))&
(((~quiet(alice)|strong(alice)))=>(kind(alice)))&
(((curious(susan)<~>~old(susan)))=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:((brave(X)&curious(X))))=>((~humble(alice)&~wise(alice))))&
(![X]:((strong(X)|~brave(X))=>(tall(X)|~tall(X))))&
((~curious(fred))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:(~strong(X)<=>(rich(X)&kind(X))))&
(?[X]:(humble(X)))&
(?[X]:(calm(X)))&
((humble(mary)<~>brave(mary)))&
((~funny(john)<~>tall(john)))&
(funny(john))&
(?[X]:((~creative(X)|~curious(X))))&
(~patient(john))&
(?[X]:((~creative(X)|humble(X)))) | funny(john) | [
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3862772415833621762761250
% SZS output start Proof for 3862772415833621762761250
21. funny(john) [input p20]
25. ~funny(john) [input hypothesis]
121. funny(john) [cnf transformation 21]
123. ~funny(john) [cnf transformation 25]
273. 33 <=> funny(john) [avatar definition]
282. 33 [avatar split clause 121,273]
283. ~33 [avatar split clause 123,273]
284. $false [avatar sat refutation 282,283]
% SZS output end Proof for 3862772415833621762761250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not humble or generous then someone is both patient and tall. If alice is either not happy or strong then someone is both not funny and not wise and vice versa. Everyone who is not strong or not funny is either not calm or funny and vice versa. If someone is funny then susan is not generous or strong. Everyone who is not calm is either not generous or not humble and vice versa. If susan is either curious or not rich then someone is either kind or not brave. If someone is not quiet then someone is either tall or strong and vice versa. If fred is either not strong or not patient then someone is not tall or not generous. If susan is not generous then someone is either not rich or generous and vice versa. Everyone who is both not strong and tall is not wise or not calm. If someone is either quiet or not rich then someone is either not humble or not rich and vice versa. If susan is not brave or kind then mary is not brave. Everyone who is both not wise and not creative is tall. Everyone who is old is not happy. Everyone who is generous or strong is either not creative or not brave. Everyone who is not patient or not generous is both not funny and not rich. Mary is either brave or curious. Someone is not kind or not brave. Alice is both not funny and happy. Someone is both rich and curious. Susan is either strong or quiet. John is either not wise or generous. Someone is not creative or patient. | Fred is generous. | neutral | (((~humble(paul)<~>generous(paul)))=>(?[X]:((patient(X)&tall(X)))))&
(((~happy(alice)<~>strong(alice)))<=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~calm(X)<~>funny(X))))&
((?[X]:(funny(X)))=>((~generous(susan)|strong(susan))))&
(![X]:(~calm(X)<=>(~generous(X)<~>~humble(X))))&
(((curious(susan)<~>~rich(susan)))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((tall(X)<~>strong(X)))))&
(((~strong(fred)<~>~patient(fred)))=>(?[X]:((~tall(X)|~generous(X)))))&
((~generous(susan))<=>(?[X]:((~rich(X)<~>generous(X)))))&
(![X]:((~strong(X)&tall(X))=>(~wise(X)|~calm(X))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(((~brave(susan)|kind(susan)))=>(~brave(mary)))&
(![X]:((~wise(X)&~creative(X))=>tall(X)))&
(![X]:(old(X)=>~happy(X)))&
(![X]:((generous(X)|strong(X))=>(~creative(X)<~>~brave(X))))&
(![X]:((~patient(X)|~generous(X))=>(~funny(X)&~rich(X))))&
((brave(mary)<~>curious(mary)))&
(?[X]:((~kind(X)|~brave(X))))&
((~funny(alice)&happy(alice)))&
(?[X]:((rich(X)&curious(X))))&
((strong(susan)<~>quiet(susan)))&
((~wise(john)<~>generous(john)))&
(?[X]:((~creative(X)|patient(X)))) | generous(fred) | []
| null | 0 |
Everyone who is not quiet or not patient is not happy and vice versa. Everyone who is not curious or not calm is not brave. Everyone who is either humble or not patient is both not rich and old. If someone is both not quiet and rich then someone is humble and vice versa. Everyone who is both not kind and not brave is rich. If someone is either brave or patient then someone is not curious. Everyone who is both funny and not kind is both tall and creative and vice versa. Everyone who is patient is brave or wise. Everyone who is kind is either kind or calm. Everyone who is not happy or funny is both not creative and not tall. If mary is both tall and calm then paul is either old or not wise. If john is generous then someone is both not creative and old and vice versa. If someone is both tall and not quiet then someone is brave or calm. Everyone who is both not tall and happy is both brave and rich and vice versa. Everyone who is both not brave and patient is not tall and vice versa. Everyone who is either brave or not humble is quiet or calm. Fred is both not quiet and kind. Someone is either not strong or not generous. Susan is brave or quiet. Alice is not old. Someone is both not calm and not funny. Someone is humble. John is kind or not old. Mary is not happy or happy. | Mary is happy. | neutral | (![X]:((~quiet(X)|~patient(X))<=>~happy(X)))&
(![X]:((~curious(X)|~calm(X))=>~brave(X)))&
(![X]:((humble(X)<~>~patient(X))=>(~rich(X)&old(X))))&
((?[X]:((~quiet(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((~kind(X)&~brave(X))=>rich(X)))&
((?[X]:((brave(X)<~>patient(X))))=>(?[X]:(~curious(X))))&
(![X]:((funny(X)&~kind(X))<=>(tall(X)&creative(X))))&
(![X]:(patient(X)=>(brave(X)|wise(X))))&
(![X]:(kind(X)=>(kind(X)<~>calm(X))))&
(![X]:((~happy(X)|funny(X))=>(~creative(X)&~tall(X))))&
(((tall(mary)&calm(mary)))=>((old(paul)<~>~wise(paul))))&
((generous(john))<=>(?[X]:((~creative(X)&old(X)))))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~tall(X)&happy(X))<=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((~quiet(fred)&kind(fred)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((brave(susan)|quiet(susan)))&
(~old(alice))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:(humble(X)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary))) | happy(mary) | []
| null | 0 |
Everyone who is not tall or not quiet is not old or not rich and vice versa.
If someone is not kind then paul is either old or not curious and vice versa.
Everyone who is both rich and kind is both not creative and calm and vice versa.
If someone is either funny or curious then paul is both not rich and not old and vice versa.
Everyone who is either tall or generous is either not wise or calm and vice versa.
Everyone who is not tall or not creative is either old or not tall.
If someone is not humble then john is not happy and vice versa.
If lucy is either humble or not curious then susan is either strong or not kind.
Everyone who is either not tall or not kind is both creative and brave and vice versa.
If someone is not generous then someone is old and vice versa.
If lucy is not tall then someone is either not calm or humble and vice versa.
If someone is either not kind or brave then someone is either calm or not funny.
If john is not funny or brave then john is both not funny and rich and vice versa.
Everyone who is humble or not tall is both tall and wise and vice versa.
If someone is curious then someone is patient.
If someone is both patient and funny then mary is either not patient or tall.
Someone is both not quiet and not old.
Someone is either calm or tall.
Someone is not patient.
Susan is not tall or happy.
Someone is not funny or wise.
Alice is not strong. | Paul is old. | contradiction | (![X]:((~tall(X)|~quiet(X))<=>(~old(X)|~rich(X))))&
((?[X]:(~kind(X)))<=>((old(paul)<~>~curious(paul))))&
(![X]:((rich(X)&kind(X))<=>(~creative(X)&calm(X))))&
((?[X]:((funny(X)<~>curious(X))))<=>((~rich(paul)&~old(paul))))&
(![X]:((tall(X)<~>generous(X))<=>(~wise(X)<~>calm(X))))&
(![X]:((~tall(X)|~creative(X))=>(old(X)<~>~tall(X))))&
((?[X]:(~humble(X)))<=>(~happy(john)))&
(((humble(lucy)<~>~curious(lucy)))=>((strong(susan)<~>~kind(susan))))&
(![X]:((~tall(X)<~>~kind(X))<=>(creative(X)&brave(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(old(X))))&
((~tall(lucy))<=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((~kind(X)<~>brave(X))))=>(?[X]:((calm(X)<~>~funny(X)))))&
(((~funny(john)|brave(john)))<=>((~funny(john)&rich(john))))&
(![X]:((humble(X)|~tall(X))<=>(tall(X)&wise(X))))&
((?[X]:(curious(X)))=>(?[X]:(patient(X))))&
((?[X]:((patient(X)&funny(X))))=>((~patient(mary)<~>tall(mary))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(?[X]:(~patient(X)))&
((~tall(susan)|happy(susan)))&
(?[X]:((~funny(X)|wise(X))))&
(~strong(alice)) | old(paul) | [
"p4",
"p9",
"p10",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8384305596183360755435308
% SZS output start Proof for 8384305596183360755435308
5. ! [X0] : ((tall(X0) <~> generous(X0)) <=> (~wise(X0) <~> calm(X0))) [input p4]
10. ? [X0] : ~generous(X0) <=> ? [X0] : old(X0) [input p9]
11. ~tall(lucy) <=> ? [X0] : (~calm(X0) <~> humble(X0)) [input p10]
14. ! [X0] : ((~tall(X0) | humble(X0)) <=> (wise(X0) & tall(X0))) [input p13]
23. old(paul) [input hypothesis]
24. ? [X0] : ~generous(X0) <=> ? [X1] : old(X1) [rectify 10]
45. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 5]
54. (? [X0] : ~generous(X0) | ! [X1] : ~old(X1)) & (? [X1] : old(X1) | ! [X0] : generous(X0)) [nnf transformation 24]
55. (? [X0] : ~generous(X0) | ! [X1] : ~old(X1)) & (? [X2] : old(X2) | ! [X3] : generous(X3)) [rectify 54]
56. ? [X0] : ~generous(X0) => ~generous(sK3) [choice axiom]
57. ? [X2] : old(X2) => old(sK4) [choice axiom]
58. (~generous(sK3) | ! [X1] : ~old(X1)) & (old(sK4) | ! [X3] : generous(X3)) [skolemisation 55,57,56]
59. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (? [X0] : ((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | tall(lucy)) [nnf transformation 11]
60. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (? [X1] : ((~humble(X1) | calm(X1)) & (humble(X1) | ~calm(X1))) | tall(lucy)) [rectify 59]
61. ? [X1] : ((~humble(X1) | calm(X1)) & (humble(X1) | ~calm(X1))) => ((~humble(sK5) | calm(sK5)) & (humble(sK5) | ~calm(sK5))) [choice axiom]
62. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(sK5) | calm(sK5)) & (humble(sK5) | ~calm(sK5))) | tall(lucy)) [skolemisation 60,61]
69. ! [X0] : (((~tall(X0) | humble(X0)) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | (tall(X0) & ~humble(X0)))) [nnf transformation 14]
70. ! [X0] : ((~tall(X0) | humble(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | (tall(X0) & ~humble(X0)))) [flattening 69]
102. ~wise(X0) | calm(X0) | generous(X0) | ~tall(X0) [cnf transformation 45]
104. ~calm(X0) | wise(X0) | generous(X0) | ~tall(X0) [cnf transformation 45]
127. ~generous(sK3) | ~old(X1) [cnf transformation 58]
130. ~tall(lucy) | humble(X0) | calm(X0) [cnf transformation 62]
131. ~tall(lucy) | ~calm(X0) | ~humble(X0) [cnf transformation 62]
142. tall(X0) | tall(X0) [cnf transformation 70]
143. ~humble(X0) | wise(X0) [cnf transformation 70]
145. ~tall(X0) | humble(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 70]
157. old(paul) [cnf transformation 23]
158. tall(X0) [duplicate literal removal 142]
159. ~wise(X0) | humble(X0) | ~tall(X0) [duplicate literal removal 145]
166. 2 <=> old(paul) [avatar definition]
168. old(paul) <- (2) [avatar component clause 166]
238. 17 <=> ! [X1] : ~old(X1) [avatar definition]
239. ~old(X1) <- (17) [avatar component clause 238]
241. 18 <=> generous(sK3) [avatar definition]
243. ~generous(sK3) <- (~18) [avatar component clause 241]
244. 17 | ~18 [avatar split clause 127,241,238]
254. 21 <=> ! [X0] : (~calm(X0) | ~humble(X0)) [avatar definition]
255. ~humble(X0) | ~calm(X0) <- (21) [avatar component clause 254]
257. 22 <=> tall(lucy) [avatar definition]
259. ~tall(lucy) <- (~22) [avatar component clause 257]
260. 21 | ~22 [avatar split clause 131,257,254]
262. 23 <=> ! [X0] : (humble(X0) | calm(X0)) [avatar definition]
263. humble(X0) | calm(X0) <- (23) [avatar component clause 262]
264. 23 | ~22 [avatar split clause 130,257,262]
336. 2 [avatar split clause 157,166]
337. $false <- (~22) [subsumption resolution 259,158]
338. 22 [avatar contradiction clause 337]
346. $false <- (2, 17) [resolution 239,168]
347. ~2 | ~17 [avatar contradiction clause 346]
355. wise(X1) | calm(X1) <- (23) [resolution 263,143]
414. calm(X1) | generous(X1) | ~tall(X1) | calm(X1) <- (23) [resolution 102,355]
416. calm(X1) | generous(X1) | ~tall(X1) <- (23) [duplicate literal removal 414]
423. generous(X1) | calm(X1) <- (23) [subsumption resolution 416,158]
463. calm(sK3) <- (~18, 23) [resolution 423,243]
468. wise(sK3) | generous(sK3) | ~tall(sK3) <- (~18, 23) [resolution 463,104]
471. wise(sK3) | ~tall(sK3) <- (~18, 23) [subsumption resolution 468,243]
472. wise(sK3) <- (~18, 23) [subsumption resolution 471,158]
490. humble(sK3) | ~tall(sK3) <- (~18, 23) [resolution 472,159]
491. humble(sK3) <- (~18, 23) [subsumption resolution 490,158]
519. ~calm(sK3) <- (~18, 21, 23) [resolution 491,255]
521. $false <- (~18, 21, 23) [subsumption resolution 519,463]
522. 18 | ~21 | ~23 [avatar contradiction clause 521]
523. $false [avatar sat refutation 244,260,264,336,338,347,522]
% SZS output end Proof for 8384305596183360755435308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not quiet or not rich then someone is not creative or kind and vice versa. Everyone who is both not quiet and strong is both wise and humble. If someone is old or creative then someone is either not brave or not kind and vice versa. Everyone who is either wise or humble is either humble or not old and vice versa. If someone is not funny then someone is both not brave and humble. If mary is patient or not generous then someone is both creative and not rich and vice versa. If john is both happy and not strong then someone is both calm and not old and vice versa. Everyone who is either kind or not calm is both not creative and brave and vice versa. If someone is either happy or quiet then someone is not wise and vice versa. Everyone who is both not wise and humble is either not tall or not calm and vice versa. Everyone who is not wise or not old is either creative or not generous. If someone is not funny then fred is either not curious or not humble. Everyone who is not funny is curious. If john is quiet or not happy then mary is both not funny and tall and vice versa. Everyone who is curious is brave. Everyone who is either curious or not rich is both kind and not wise. Mary is both rich and not calm. Paul is both tall and not generous. Lucy is not calm. Susan is not generous. Someone is either generous or tall. Mary is not creative. Paul is either not quiet or not generous. Susan is wise or brave. | Mary is curious. | contradiction | (((~quiet(alice)<~>~rich(alice)))<=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((~quiet(X)&strong(X))=>(wise(X)&humble(X))))&
((?[X]:((old(X)|creative(X))))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:((wise(X)<~>humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~brave(X)&humble(X)))))&
(((patient(mary)|~generous(mary)))<=>(?[X]:((creative(X)&~rich(X)))))&
(((happy(john)&~strong(john)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((kind(X)<~>~calm(X))<=>(~creative(X)&brave(X))))&
((?[X]:((happy(X)<~>quiet(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~wise(X)&humble(X))<=>(~tall(X)<~>~calm(X))))&
(![X]:((~wise(X)|~old(X))=>(creative(X)<~>~generous(X))))&
((?[X]:(~funny(X)))=>((~curious(fred)<~>~humble(fred))))&
(![X]:(~funny(X)=>curious(X)))&
(((quiet(john)|~happy(john)))<=>((~funny(mary)&tall(mary))))&
(![X]:(curious(X)=>brave(X)))&
(![X]:((curious(X)<~>~rich(X))=>(kind(X)&~wise(X))))&
((rich(mary)&~calm(mary)))&
((tall(paul)&~generous(paul)))&
(~calm(lucy))&
(~generous(susan))&
(?[X]:((generous(X)<~>tall(X))))&
(~creative(mary))&
((~quiet(paul)<~>~generous(paul)))&
((wise(susan)|brave(susan))) | curious(mary) | [
"p7",
"p14",
"p15",
"p16",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 7051808989190311029385356
% SZS output start Proof for 7051808989190311029385356
8. ! [X0] : ((kind(X0) <~> ~calm(X0)) <=> (brave(X0) & ~creative(X0))) [input p7]
15. ! [X0] : (curious(X0) => brave(X0)) [input p14]
16. ! [X0] : ((curious(X0) <~> ~rich(X0)) => (~wise(X0) & kind(X0))) [input p15]
17. ~calm(mary) & rich(mary) [input p16]
22. ~creative(mary) [input p21]
25. curious(mary) [input hypothesis]
35. ! [X0] : (brave(X0) | ~curious(X0)) [ennf transformation 15]
36. ! [X0] : ((~wise(X0) & kind(X0)) | (curious(X0) <=> ~rich(X0))) [ennf transformation 16]
60. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [nnf transformation 8]
61. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [flattening 60]
73. ! [X0] : ((~wise(X0) & kind(X0)) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [nnf transformation 36]
116. ~brave(X0) | ~kind(X0) | calm(X0) | creative(X0) [cnf transformation 61]
139. ~curious(X0) | brave(X0) [cnf transformation 35]
140. ~curious(X0) | ~rich(X0) | kind(X0) [cnf transformation 73]
144. rich(mary) [cnf transformation 17]
145. ~calm(mary) [cnf transformation 17]
152. ~creative(mary) [cnf transformation 22]
156. curious(mary) [cnf transformation 25]
359. brave(mary) [resolution 139,156]
461. ~rich(mary) | kind(mary) [resolution 140,156]
463. kind(mary) [subsumption resolution 461,144]
589. ~kind(mary) | calm(mary) | creative(mary) [resolution 116,359]
591. calm(mary) | creative(mary) [subsumption resolution 589,463]
592. creative(mary) [subsumption resolution 591,145]
593. $false [subsumption resolution 592,152]
% SZS output end Proof for 7051808989190311029385356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or patient is both patient and not brave and vice versa.
If mary is either not creative or not generous then someone is both kind and patient.
Everyone who is funny or not old is both not rich and patient.
Everyone who is funny or not curious is patient or quiet and vice versa.
Everyone who is either not patient or happy is old and vice versa.
If someone is both not kind and not brave then someone is both not strong and not old.
If lucy is either not kind or not calm then someone is old or rich and vice versa.
Everyone who is either happy or generous is both calm and not happy.
If someone is both funny and not calm then someone is not calm and vice versa.
Everyone who is creative or humble is both brave and not old and vice versa.
Everyone who is either not funny or tall is either not tall or not humble and vice versa.
If someone is not kind then mary is either not kind or not generous and vice versa.
If lucy is kind then alice is wise or patient and vice versa.
Everyone who is not old is both not strong and not creative.
If someone is humble then susan is not calm.
If paul is creative then someone is curious.
Someone is either creative or strong.
Someone is not humble.
Lucy is not curious.
Lucy is funny or not happy.
John is not kind or funny.
Someone is not quiet.
Someone is not generous or generous. | Mary is creative. | contradiction | (![X]:((wise(X)|patient(X))<=>(patient(X)&~brave(X))))&
(((~creative(mary)<~>~generous(mary)))=>(?[X]:((kind(X)&patient(X)))))&
(![X]:((funny(X)|~old(X))=>(~rich(X)&patient(X))))&
(![X]:((funny(X)|~curious(X))<=>(patient(X)|quiet(X))))&
(![X]:((~patient(X)<~>happy(X))<=>old(X)))&
((?[X]:((~kind(X)&~brave(X))))=>(?[X]:((~strong(X)&~old(X)))))&
(((~kind(lucy)<~>~calm(lucy)))<=>(?[X]:((old(X)|rich(X)))))&
(![X]:((happy(X)<~>generous(X))=>(calm(X)&~happy(X))))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)|humble(X))<=>(brave(X)&~old(X))))&
(![X]:((~funny(X)<~>tall(X))<=>(~tall(X)<~>~humble(X))))&
((?[X]:(~kind(X)))<=>((~kind(mary)<~>~generous(mary))))&
((kind(lucy))<=>((wise(alice)|patient(alice))))&
(![X]:(~old(X)=>(~strong(X)&~creative(X))))&
((?[X]:(humble(X)))=>(~calm(susan)))&
((creative(paul))=>(?[X]:(curious(X))))&
(?[X]:((creative(X)<~>strong(X))))&
(?[X]:(~humble(X)))&
(~curious(lucy))&
((funny(lucy)|~happy(lucy)))&
((~kind(john)|funny(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)|generous(X)))) | creative(mary) | [
"p9",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 7803712378302510279142809
% SZS output start Proof for 7803712378302510279142809
10. ! [X0] : ((humble(X0) | creative(X0)) <=> (~old(X0) & brave(X0))) [input p9]
14. ! [X0] : (~old(X0) => (~creative(X0) & ~strong(X0))) [input p13]
24. creative(mary) [input hypothesis]
31. ! [X0] : ((~creative(X0) & ~strong(X0)) | old(X0)) [ennf transformation 14]
55. ! [X0] : (((humble(X0) | creative(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (~humble(X0) & ~creative(X0)))) [nnf transformation 10]
56. ! [X0] : ((humble(X0) | creative(X0) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | (~humble(X0) & ~creative(X0)))) [flattening 55]
113. ~old(X0) | ~creative(X0) [cnf transformation 56]
132. ~creative(X0) | old(X0) [cnf transformation 31]
143. creative(mary) [cnf transformation 24]
260. ~creative(X0) [subsumption resolution 132,113]
288. $false [subsumption resolution 143,260]
% SZS output end Proof for 7803712378302510279142809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and humble is either not curious or brave and vice versa.
Everyone who is funny is either funny or not tall and vice versa.
Everyone who is not patient is both quiet and calm and vice versa.
If someone is either not patient or rich then someone is both not patient and calm.
Everyone who is not curious is not rich or not strong and vice versa.
If lucy is either not brave or humble then john is strong and vice versa.
If someone is both not tall and wise then someone is both not patient and not funny.
Everyone who is not wise is not brave and vice versa.
If someone is tall or not strong then someone is both old and quiet and vice versa.
Everyone who is both wise and tall is either old or not quiet.
If someone is both not generous and happy then someone is both not patient and not rich and vice versa.
If john is not generous or not curious then someone is calm or not patient.
If someone is both humble and creative then someone is kind or strong and vice versa.
If someone is rich then fred is both not rich and not wise and vice versa.
Everyone who is brave is both rich and not strong.
Everyone who is kind is wise or not wise.
Someone is generous.
Someone is either happy or brave.
Someone is rich.
Someone is strong or not calm.
Someone is either not funny or generous.
Alice is either not funny or calm.
John is not brave.
Someone is both not curious and not rich. | Fred is not brave. | entailment | (![X]:((patient(X)&humble(X))<=>(~curious(X)<~>brave(X))))&
(![X]:(funny(X)<=>(funny(X)<~>~tall(X))))&
(![X]:(~patient(X)<=>(quiet(X)&calm(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:(~curious(X)<=>(~rich(X)|~strong(X))))&
(((~brave(lucy)<~>humble(lucy)))<=>(strong(john)))&
((?[X]:((~tall(X)&wise(X))))=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:(~wise(X)<=>~brave(X)))&
((?[X]:((tall(X)|~strong(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:((wise(X)&tall(X))=>(old(X)<~>~quiet(X))))&
((?[X]:((~generous(X)&happy(X))))<=>(?[X]:((~patient(X)&~rich(X)))))&
(((~generous(john)|~curious(john)))=>(?[X]:((calm(X)|~patient(X)))))&
((?[X]:((humble(X)&creative(X))))<=>(?[X]:((kind(X)|strong(X)))))&
((?[X]:(rich(X)))<=>((~rich(fred)&~wise(fred))))&
(![X]:(brave(X)=>(rich(X)&~strong(X))))&
(![X]:(kind(X)=>(wise(X)|~wise(X))))&
(?[X]:(generous(X)))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:(rich(X)))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((~funny(X)<~>generous(X))))&
((~funny(alice)<~>calm(alice)))&
(~brave(john))&
(?[X]:((~curious(X)&~rich(X)))) | ~brave(fred) | [
"p7",
"p13",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 4962163407933927521318593
% SZS output start Proof for 4962163407933927521318593
8. ! [X0] : (~wise(X0) <=> ~brave(X0)) [input p7]
14. ? [X0] : rich(X0) <=> (~wise(fred) & ~rich(fred)) [input p13]
19. ? [X0] : rich(X0) [input p18]
25. brave(fred) [input hypothesis]
54. ! [X0] : ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))) [nnf transformation 8]
73. (? [X0] : rich(X0) | (wise(fred) | rich(fred))) & ((~wise(fred) & ~rich(fred)) | ! [X0] : ~rich(X0)) [nnf transformation 14]
74. (? [X0] : rich(X0) | wise(fred) | rich(fred)) & ((~wise(fred) & ~rich(fred)) | ! [X0] : ~rich(X0)) [flattening 73]
75. (? [X0] : rich(X0) | wise(fred) | rich(fred)) & ((~wise(fred) & ~rich(fred)) | ! [X1] : ~rich(X1)) [rectify 74]
76. ? [X0] : rich(X0) => rich(sK9) [choice axiom]
77. (rich(sK9) | wise(fred) | rich(fred)) & ((~wise(fred) & ~rich(fred)) | ! [X1] : ~rich(X1)) [skolemisation 75,76]
83. ? [X0] : rich(X0) => rich(sK12) [choice axiom]
84. rich(sK12) [skolemisation 19,83]
119. ~brave(X0) | wise(X0) [cnf transformation 54]
140. ~wise(fred) | ~rich(X1) [cnf transformation 77]
148. rich(sK12) [cnf transformation 84]
157. brave(fred) [cnf transformation 25]
288. 27 <=> wise(fred) [avatar definition]
297. 29 <=> ! [X1] : ~rich(X1) [avatar definition]
298. ~rich(X1) <- (29) [avatar component clause 297]
299. 29 | ~27 [avatar split clause 140,288,297]
344. wise(fred) [resolution 119,157]
347. 27 [avatar split clause 344,288]
348. $false <- (29) [resolution 298,148]
351. ~29 [avatar contradiction clause 348]
352. $false [avatar sat refutation 299,347,351]
% SZS output end Proof for 4962163407933927521318593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not humble is both not patient and not funny and vice versa.
If someone is not funny then someone is both creative and not brave.
If someone is either funny or humble then someone is not old or tall.
If susan is either strong or not quiet then someone is either not humble or not brave.
If someone is either rich or not creative then someone is both not brave and creative.
If someone is either old or not happy then fred is either rich or curious and vice versa.
If lucy is not wise then mary is old or rich and vice versa.
Everyone who is either wise or generous is both humble and kind and vice versa.
If paul is not wise or curious then someone is either not patient or happy.
If susan is patient or not happy then someone is both old and not happy and vice versa.
If someone is not old then someone is calm or creative and vice versa.
Everyone who is strong or not strong is both wise and curious and vice versa.
If someone is not creative then someone is funny or wise and vice versa.
If mary is funny or patient then fred is either happy or tall and vice versa.
Everyone who is either brave or tall is not funny or happy and vice versa.
Everyone who is either patient or humble is curious.
Alice is both not happy and tall.
Someone is not kind or not old.
Paul is either wise or not kind.
Someone is either not patient or kind.
John is both not old and not strong.
Lucy is both not generous and not rich. | Paul is not tall. | neutral | (![X]:((wise(X)&~humble(X))<=>(~patient(X)&~funny(X))))&
((?[X]:(~funny(X)))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:((~old(X)|tall(X)))))&
(((strong(susan)<~>~quiet(susan)))=>(?[X]:((~humble(X)<~>~brave(X)))))&
((?[X]:((rich(X)<~>~creative(X))))=>(?[X]:((~brave(X)&creative(X)))))&
((?[X]:((old(X)<~>~happy(X))))<=>((rich(fred)<~>curious(fred))))&
((~wise(lucy))<=>((old(mary)|rich(mary))))&
(![X]:((wise(X)<~>generous(X))<=>(humble(X)&kind(X))))&
(((~wise(paul)|curious(paul)))=>(?[X]:((~patient(X)<~>happy(X)))))&
(((patient(susan)|~happy(susan)))<=>(?[X]:((old(X)&~happy(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)|creative(X)))))&
(![X]:((strong(X)|~strong(X))<=>(wise(X)&curious(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)|wise(X)))))&
(((funny(mary)|patient(mary)))<=>((happy(fred)<~>tall(fred))))&
(![X]:((brave(X)<~>tall(X))<=>(~funny(X)|happy(X))))&
(![X]:((patient(X)<~>humble(X))=>curious(X)))&
((~happy(alice)&tall(alice)))&
(?[X]:((~kind(X)|~old(X))))&
((wise(paul)<~>~kind(paul)))&
(?[X]:((~patient(X)<~>kind(X))))&
((~old(john)&~strong(john)))&
((~generous(lucy)&~rich(lucy))) | ~tall(paul) | []
| null | 0 |
Everyone who is funny is either strong or not patient.
If fred is not funny then someone is either not old or tall.
If someone is strong then susan is not curious and vice versa.
If susan is both wise and not brave then someone is wise and vice versa.
If someone is not old or wise then paul is tall.
If someone is not creative then john is not rich or not funny.
If john is either kind or not creative then someone is not tall.
If someone is both not strong and kind then someone is happy and vice versa.
If john is both happy and not old then someone is either brave or not tall.
Everyone who is not humble is generous or kind.
If mary is creative then someone is humble or patient and vice versa.
Everyone who is not patient is both strong and patient and vice versa.
If someone is either strong or not happy then someone is either not curious or not rich.
Everyone who is not quiet or not funny is both not humble and not happy and vice versa.
Everyone who is not creative is either old or kind.
If someone is both strong and kind then someone is both not rich and kind.
Fred is not happy.
Someone is both brave and not strong.
Mary is not happy or kind.
Someone is curious or tall.
John is both curious and not kind.
Someone is patient. | Paul is not strong. | entailment | (![X]:(funny(X)=>(strong(X)<~>~patient(X))))&
((~funny(fred))=>(?[X]:((~old(X)<~>tall(X)))))&
((?[X]:(strong(X)))<=>(~curious(susan)))&
(((wise(susan)&~brave(susan)))<=>(?[X]:(wise(X))))&
((?[X]:((~old(X)|wise(X))))=>(tall(paul)))&
((?[X]:(~creative(X)))=>((~rich(john)|~funny(john))))&
(((kind(john)<~>~creative(john)))=>(?[X]:(~tall(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(happy(X))))&
(((happy(john)&~old(john)))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:(~humble(X)=>(generous(X)|kind(X))))&
((creative(mary))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:(~patient(X)<=>(strong(X)&patient(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:((~quiet(X)|~funny(X))<=>(~humble(X)&~happy(X))))&
(![X]:(~creative(X)=>(old(X)<~>kind(X))))&
((?[X]:((strong(X)&kind(X))))=>(?[X]:((~rich(X)&kind(X)))))&
(~happy(fred))&
(?[X]:((brave(X)&~strong(X))))&
((~happy(mary)|kind(mary)))&
(?[X]:((curious(X)|tall(X))))&
((curious(john)&~kind(john)))&
(?[X]:(patient(X))) | ~strong(paul) | [
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 3147546865071920480821769
% SZS output start Proof for 3147546865071920480821769
12. ! [X0] : (~patient(X0) <=> (patient(X0) & strong(X0))) [input p11]
23. strong(paul) [input hypothesis]
67. ! [X0] : ((~patient(X0) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | patient(X0))) [nnf transformation 12]
68. ! [X0] : ((~patient(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | patient(X0))) [flattening 67]
108. patient(X0) | patient(X0) [cnf transformation 68]
109. ~patient(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 68]
131. strong(paul) [cnf transformation 23]
132. patient(X0) [duplicate literal removal 108]
133. ~patient(X0) | ~strong(X0) [duplicate literal removal 109]
158. 6 <=> ! [X1] : ~strong(X1) [avatar definition]
159. ~strong(X1) <- (6) [avatar component clause 158]
331. ~strong(X0) [resolution 133,132]
332. 6 [avatar split clause 331,158]
333. $false <- (6) [resolution 159,131]
336. ~6 [avatar contradiction clause 333]
337. $false [avatar sat refutation 332,336]
% SZS output end Proof for 3147546865071920480821769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not tall is generous.
Everyone who is wise or quiet is not generous.
If someone is humble or not brave then someone is not patient.
Everyone who is both tall and not generous is not happy.
If mary is not funny or old then someone is both not calm and not wise.
If someone is both calm and strong then someone is not happy and vice versa.
If mary is either humble or not calm then mary is quiet and vice versa.
Everyone who is curious is both strong and not patient.
Everyone who is either not old or not wise is either curious or creative.
Everyone who is tall or brave is not tall and vice versa.
If someone is humble then someone is either creative or quiet.
Everyone who is both funny and patient is both not generous and not tall and vice versa.
If mary is either not tall or brave then someone is both not quiet and funny and vice versa.
Everyone who is either old or not old is either not patient or wise.
Everyone who is either patient or not old is either creative or not calm.
Everyone who is both not funny and not curious is either rich or patient.
Mary is old or patient.
Lucy is either rich or not curious.
Someone is strong or curious.
Someone is brave. | Lucy is not funny. | entailment | (![X]:((creative(X)|~tall(X))=>generous(X)))&
(![X]:((wise(X)|quiet(X))=>~generous(X)))&
((?[X]:((humble(X)|~brave(X))))=>(?[X]:(~patient(X))))&
(![X]:((tall(X)&~generous(X))=>~happy(X)))&
(((~funny(mary)|old(mary)))=>(?[X]:((~calm(X)&~wise(X)))))&
((?[X]:((calm(X)&strong(X))))<=>(?[X]:(~happy(X))))&
(((humble(mary)<~>~calm(mary)))<=>(quiet(mary)))&
(![X]:(curious(X)=>(strong(X)&~patient(X))))&
(![X]:((~old(X)<~>~wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((tall(X)|brave(X))<=>~tall(X)))&
((?[X]:(humble(X)))=>(?[X]:((creative(X)<~>quiet(X)))))&
(![X]:((funny(X)&patient(X))<=>(~generous(X)&~tall(X))))&
(((~tall(mary)<~>brave(mary)))<=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:((old(X)<~>~old(X))=>(~patient(X)<~>wise(X))))&
(![X]:((patient(X)<~>~old(X))=>(creative(X)<~>~calm(X))))&
(![X]:((~funny(X)&~curious(X))=>(rich(X)<~>patient(X))))&
((old(mary)|patient(mary)))&
((rich(lucy)<~>~curious(lucy)))&
(?[X]:((strong(X)|curious(X))))&
(?[X]:(brave(X))) | ~funny(lucy) | [
"p0",
"p1",
"p9",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 7038491125348449979894903
% SZS output start Proof for 7038491125348449979894903
1. ! [X0] : ((~tall(X0) | creative(X0)) => generous(X0)) [input p0]
2. ! [X0] : ((quiet(X0) | wise(X0)) => ~generous(X0)) [input p1]
10. ! [X0] : ((brave(X0) | tall(X0)) <=> ~tall(X0)) [input p9]
13. (~tall(mary) <~> brave(mary)) <=> ? [X0] : (funny(X0) & ~quiet(X0)) [input p12]
21. funny(lucy) [input hypothesis]
25. ! [X0] : (generous(X0) | (tall(X0) & ~creative(X0))) [ennf transformation 1]
26. ! [X0] : (~generous(X0) | (~quiet(X0) & ~wise(X0))) [ennf transformation 2]
50. ! [X0] : (((brave(X0) | tall(X0)) | tall(X0)) & (~tall(X0) | (~brave(X0) & ~tall(X0)))) [nnf transformation 10]
51. ! [X0] : ((brave(X0) | tall(X0) | tall(X0)) & (~tall(X0) | (~brave(X0) & ~tall(X0)))) [flattening 50]
58. (((~brave(mary) | tall(mary)) & (brave(mary) | ~tall(mary))) | ! [X0] : (~funny(X0) | quiet(X0))) & (? [X0] : (funny(X0) & ~quiet(X0)) | ((~tall(mary) | ~brave(mary)) & (brave(mary) | tall(mary)))) [nnf transformation 13]
59. (((~brave(mary) | tall(mary)) & (brave(mary) | ~tall(mary))) | ! [X0] : (~funny(X0) | quiet(X0))) & (? [X1] : (funny(X1) & ~quiet(X1)) | ((~tall(mary) | ~brave(mary)) & (brave(mary) | tall(mary)))) [rectify 58]
60. ? [X1] : (funny(X1) & ~quiet(X1)) => (funny(sK5) & ~quiet(sK5)) [choice axiom]
61. (((~brave(mary) | tall(mary)) & (brave(mary) | ~tall(mary))) | ! [X0] : (~funny(X0) | quiet(X0))) & ((funny(sK5) & ~quiet(sK5)) | ((~tall(mary) | ~brave(mary)) & (brave(mary) | tall(mary)))) [skolemisation 59,60]
71. generous(X0) | tall(X0) [cnf transformation 25]
73. ~quiet(X0) | ~generous(X0) [cnf transformation 26]
94. ~tall(X0) | ~tall(X0) [cnf transformation 51]
96. brave(X0) | tall(X0) | tall(X0) [cnf transformation 51]
108. ~brave(mary) | tall(mary) | ~funny(X0) | quiet(X0) [cnf transformation 61]
124. funny(lucy) [cnf transformation 21]
129. ~tall(X0) [duplicate literal removal 94]
130. brave(X0) | tall(X0) [duplicate literal removal 96]
211. ~brave(mary) | ~funny(X0) | quiet(X0) [subsumption resolution 108,129]
213. 18 <=> ! [X0] : (~funny(X0) | quiet(X0)) [avatar definition]
214. ~funny(X0) | quiet(X0) <- (18) [avatar component clause 213]
216. 19 <=> brave(mary) [avatar definition]
218. ~brave(mary) <- (~19) [avatar component clause 216]
219. 18 | ~19 [avatar split clause 211,216,213]
248. tall(mary) <- (~19) [resolution 130,218]
250. $false <- (~19) [subsumption resolution 248,129]
251. 19 [avatar contradiction clause 250]
253. quiet(lucy) <- (18) [resolution 214,124]
254. ~generous(lucy) <- (18) [resolution 253,73]
255. tall(lucy) <- (18) [resolution 254,71]
256. $false <- (18) [subsumption resolution 255,129]
257. ~18 [avatar contradiction clause 256]
258. $false [avatar sat refutation 219,251,257]
% SZS output end Proof for 7038491125348449979894903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient then someone is either not calm or not quiet and vice versa.
If someone is not creative then someone is either not quiet or curious.
If paul is generous then paul is either not humble or not happy.
Everyone who is both not kind and patient is both kind and tall and vice versa.
If someone is creative or old then mary is not rich and vice versa.
If susan is tall or not curious then alice is rich or old.
Everyone who is not strong is both happy and quiet.
If paul is not generous then mary is patient or kind and vice versa.
Everyone who is both not wise and funny is not funny or generous and vice versa.
If someone is either rich or not generous then someone is not kind.
Everyone who is not calm is both not old and happy and vice versa.
If someone is not patient or not strong then someone is happy and vice versa.
Everyone who is either not old or not creative is either not funny or not happy and vice versa.
Everyone who is humble is both not strong and curious and vice versa.
Everyone who is not old or calm is not old and vice versa.
If fred is either not rich or old then someone is both not patient and funny and vice versa.
Someone is not brave or not calm.
Someone is either not kind or curious.
Alice is creative.
Someone is not curious.
Someone is either kind or not calm.
Lucy is not strong or not creative.
Lucy is not old or not patient. | Lucy is not old. | entailment | ((~patient(alice))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
((?[X]:(~creative(X)))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((generous(paul))=>((~humble(paul)<~>~happy(paul))))&
(![X]:((~kind(X)&patient(X))<=>(kind(X)&tall(X))))&
((?[X]:((creative(X)|old(X))))<=>(~rich(mary)))&
(((tall(susan)|~curious(susan)))=>((rich(alice)|old(alice))))&
(![X]:(~strong(X)=>(happy(X)&quiet(X))))&
((~generous(paul))<=>((patient(mary)|kind(mary))))&
(![X]:((~wise(X)&funny(X))<=>(~funny(X)|generous(X))))&
((?[X]:((rich(X)<~>~generous(X))))=>(?[X]:(~kind(X))))&
(![X]:(~calm(X)<=>(~old(X)&happy(X))))&
((?[X]:((~patient(X)|~strong(X))))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)<~>~creative(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:(humble(X)<=>(~strong(X)&curious(X))))&
(![X]:((~old(X)|calm(X))<=>~old(X)))&
(((~rich(fred)<~>old(fred)))<=>(?[X]:((~patient(X)&funny(X)))))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
(creative(alice))&
(?[X]:(~curious(X)))&
(?[X]:((kind(X)<~>~calm(X))))&
((~strong(lucy)|~creative(lucy)))&
((~old(lucy)|~patient(lucy))) | ~old(lucy) | [
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 6293688215496848919441337
% SZS output start Proof for 6293688215496848919441337
11. ! [X0] : (~calm(X0) <=> (happy(X0) & ~old(X0))) [input p10]
15. ! [X0] : ((calm(X0) | ~old(X0)) <=> ~old(X0)) [input p14]
24. old(lucy) [input hypothesis]
58. ! [X0] : ((~calm(X0) | (~happy(X0) | old(X0))) & ((happy(X0) & ~old(X0)) | calm(X0))) [nnf transformation 11]
59. ! [X0] : ((~calm(X0) | ~happy(X0) | old(X0)) & ((happy(X0) & ~old(X0)) | calm(X0))) [flattening 58]
68. ! [X0] : (((calm(X0) | ~old(X0)) | old(X0)) & (~old(X0) | (~calm(X0) & old(X0)))) [nnf transformation 15]
69. ! [X0] : ((calm(X0) | ~old(X0) | old(X0)) & (~old(X0) | (~calm(X0) & old(X0)))) [flattening 68]
111. ~old(X0) | calm(X0) [cnf transformation 59]
129. ~old(X0) | ~calm(X0) [cnf transformation 69]
145. old(lucy) [cnf transformation 24]
213. 15 <=> ! [X1] : ~old(X1) [avatar definition]
214. ~old(X1) <- (15) [avatar component clause 213]
291. ~old(X0) [subsumption resolution 129,111]
292. 15 [avatar split clause 291,213]
341. 41 <=> old(lucy) [avatar definition]
342. old(lucy) <- (41) [avatar component clause 341]
349. 41 [avatar split clause 145,341]
350. $false <- (15, 41) [resolution 342,214]
351. ~15 | ~41 [avatar contradiction clause 350]
352. $false [avatar sat refutation 292,349,351]
% SZS output end Proof for 6293688215496848919441337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not humble then lucy is both not creative and not calm and vice versa.
If paul is creative or not generous then someone is both old and strong.
If paul is not funny then paul is humble or not quiet.
If john is generous then mary is strong and vice versa.
Everyone who is both not wise and generous is not kind or not brave and vice versa.
If lucy is either tall or not humble then someone is either curious or tall and vice versa.
Everyone who is either not funny or creative is not tall and vice versa.
If fred is both not happy and old then john is both brave and not brave.
If mary is not calm then fred is not creative.
If mary is curious then someone is not generous and vice versa.
If someone is either not happy or not old then john is not creative and vice versa.
Everyone who is tall is either old or quiet.
Everyone who is not creative is both not wise and curious.
Everyone who is both quiet and generous is creative and vice versa.
Everyone who is either not funny or generous is both wise and kind and vice versa.
Everyone who is not kind is wise and vice versa.
Fred is either not creative or not old.
Mary is kind or not generous.
Someone is curious.
Paul is either not generous or creative.
Someone is either funny or generous.
Someone is not generous or wise.
John is happy. | Paul is quiet. | neutral | ((~humble(paul))<=>((~creative(lucy)&~calm(lucy))))&
(((creative(paul)|~generous(paul)))=>(?[X]:((old(X)&strong(X)))))&
((~funny(paul))=>((humble(paul)|~quiet(paul))))&
((generous(john))<=>(strong(mary)))&
(![X]:((~wise(X)&generous(X))<=>(~kind(X)|~brave(X))))&
(((tall(lucy)<~>~humble(lucy)))<=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~funny(X)<~>creative(X))<=>~tall(X)))&
(((~happy(fred)&old(fred)))=>((brave(john)&~brave(john))))&
((~calm(mary))=>(~creative(fred)))&
((curious(mary))<=>(?[X]:(~generous(X))))&
((?[X]:((~happy(X)<~>~old(X))))<=>(~creative(john)))&
(![X]:(tall(X)=>(old(X)<~>quiet(X))))&
(![X]:(~creative(X)=>(~wise(X)&curious(X))))&
(![X]:((quiet(X)&generous(X))<=>creative(X)))&
(![X]:((~funny(X)<~>generous(X))<=>(wise(X)&kind(X))))&
(![X]:(~kind(X)<=>wise(X)))&
((~creative(fred)<~>~old(fred)))&
((kind(mary)|~generous(mary)))&
(?[X]:(curious(X)))&
((~generous(paul)<~>creative(paul)))&
(?[X]:((funny(X)<~>generous(X))))&
(?[X]:((~generous(X)|wise(X))))&
(happy(john)) | quiet(paul) | []
| null | 0 |
Everyone who is humble or not calm is either not humble or curious and vice versa.
If someone is not creative or not curious then someone is either kind or not old and vice versa.
If someone is both not calm and not wise then susan is old or not generous and vice versa.
If mary is both calm and not funny then mary is either creative or not calm.
Everyone who is both wise and curious is not calm or strong.
If someone is wise then paul is not curious and vice versa.
If someone is both not creative and not old then lucy is either humble or not humble.
Everyone who is kind or rich is tall.
If john is either old or patient then lucy is not humble or not strong.
Everyone who is tall or not curious is both not humble and humble and vice versa.
If mary is creative then someone is not tall.
Everyone who is either not tall or not funny is not creative.
Everyone who is either not kind or generous is rich.
Everyone who is curious is either not generous or brave.
If someone is both quiet and curious then someone is both creative and brave and vice versa.
Everyone who is not rich is either humble or not old.
Someone is either happy or generous.
Someone is both not rich and curious.
Alice is not old.
Fred is humble.
Someone is not kind.
John is not tall.
Someone is both not rich and funny. | John is brave. | entailment | (![X]:((humble(X)|~calm(X))<=>(~humble(X)<~>curious(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~calm(X)&~wise(X))))<=>((old(susan)|~generous(susan))))&
(((calm(mary)&~funny(mary)))=>((creative(mary)<~>~calm(mary))))&
(![X]:((wise(X)&curious(X))=>(~calm(X)|strong(X))))&
((?[X]:(wise(X)))<=>(~curious(paul)))&
((?[X]:((~creative(X)&~old(X))))=>((humble(lucy)<~>~humble(lucy))))&
(![X]:((kind(X)|rich(X))=>tall(X)))&
(((old(john)<~>patient(john)))=>((~humble(lucy)|~strong(lucy))))&
(![X]:((tall(X)|~curious(X))<=>(~humble(X)&humble(X))))&
((creative(mary))=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)<~>~funny(X))=>~creative(X)))&
(![X]:((~kind(X)<~>generous(X))=>rich(X)))&
(![X]:(curious(X)=>(~generous(X)<~>brave(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:(~rich(X)=>(humble(X)<~>~old(X))))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((~rich(X)&curious(X))))&
(~old(alice))&
(humble(fred))&
(?[X]:(~kind(X)))&
(~tall(john))&
(?[X]:((~rich(X)&funny(X)))) | brave(john) | [
"p0",
"p7",
"p9",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 9043200607312726554265249
% SZS output start Proof for 9043200607312726554265249
1. ! [X0] : ((~calm(X0) | humble(X0)) <=> (~humble(X0) <~> curious(X0))) [input p0]
8. ! [X0] : ((rich(X0) | kind(X0)) => tall(X0)) [input p7]
10. ! [X0] : ((~curious(X0) | tall(X0)) <=> (humble(X0) & ~humble(X0))) [input p9]
13. ! [X0] : ((~kind(X0) <~> generous(X0)) => rich(X0)) [input p12]
14. ! [X0] : (curious(X0) => (~generous(X0) <~> brave(X0))) [input p13]
24. ~brave(john) [input hypothesis]
32. ! [X0] : (tall(X0) | (~rich(X0) & ~kind(X0))) [ennf transformation 8]
37. ! [X0] : (rich(X0) | (~kind(X0) <=> generous(X0))) [ennf transformation 13]
38. ! [X0] : ((~generous(X0) <~> brave(X0)) | ~curious(X0)) [ennf transformation 14]
40. ! [X0] : (((~calm(X0) | humble(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0)))) & (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | (calm(X0) & ~humble(X0)))) [nnf transformation 1]
41. ! [X0] : ((~calm(X0) | humble(X0) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0)))) & (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | (calm(X0) & ~humble(X0)))) [flattening 40]
59. ! [X0] : (((~curious(X0) | tall(X0)) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | (curious(X0) & ~tall(X0)))) [nnf transformation 10]
60. ! [X0] : ((~curious(X0) | tall(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | (curious(X0) & ~tall(X0)))) [flattening 59]
64. ! [X0] : (rich(X0) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) [nnf transformation 37]
65. ! [X0] : (((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | ~curious(X0)) [nnf transformation 38]
81. curious(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 41]
105. ~kind(X0) | tall(X0) [cnf transformation 32]
106. ~rich(X0) | tall(X0) [cnf transformation 32]
109. ~humble(X0) | ~tall(X0) [cnf transformation 60]
111. ~tall(X0) | humble(X0) [cnf transformation 60]
112. humble(X0) | curious(X0) [cnf transformation 60]
117. rich(X0) | generous(X0) | kind(X0) [cnf transformation 64]
119. ~generous(X0) | brave(X0) | ~curious(X0) [cnf transformation 65]
137. ~brave(john) [cnf transformation 24]
139. ~humble(X0) | curious(X0) [duplicate literal removal 81]
158. 5 <=> ! [X3] : curious(X3) [avatar definition]
159. curious(X3) <- (5) [avatar component clause 158]
243. curious(X0) [subsumption resolution 112,139]
244. 5 [avatar split clause 243,158]
245. ~tall(X0) [subsumption resolution 109,111]
303. generous(X0) | kind(X0) | tall(X0) [resolution 117,106]
322. generous(X0) | kind(X0) [subsumption resolution 303,245]
359. kind(X0) | brave(X0) | ~curious(X0) [resolution 322,119]
361. brave(X0) | kind(X0) <- (5) [subsumption resolution 359,159]
413. kind(john) <- (5) [resolution 361,137]
416. tall(john) <- (5) [resolution 413,105]
417. $false <- (5) [subsumption resolution 416,245]
418. ~5 [avatar contradiction clause 417]
419. $false [avatar sat refutation 244,418]
% SZS output end Proof for 9043200607312726554265249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not funny is humble or not kind and vice versa.
Everyone who is funny or calm is both not rich and strong and vice versa.
Everyone who is either generous or not strong is not wise or old and vice versa.
If someone is humble or not rich then susan is both generous and not tall and vice versa.
If paul is not old then someone is not old or tall and vice versa.
Everyone who is either rich or curious is strong or generous.
Everyone who is quiet is either not wise or not creative.
Everyone who is both generous and old is humble or wise.
If someone is both not wise and not brave then someone is either not humble or not quiet.
Everyone who is happy or not happy is both not humble and kind.
Everyone who is both not funny and quiet is curious or strong and vice versa.
If someone is either generous or not quiet then paul is both not generous and not quiet and vice versa.
If someone is both humble and not creative then someone is not old or not humble.
Everyone who is either not humble or not kind is both not wise and not patient and vice versa.
Everyone who is not kind or curious is either humble or not brave and vice versa.
Lucy is curious or humble.
Susan is either not wise or not rich.
Someone is brave or quiet.
Someone is not tall or generous.
Mary is humble or not patient.
Mary is not humble or not old. | Susan is not calm. | entailment | (![X]:((generous(X)&~funny(X))<=>(humble(X)|~kind(X))))&
(![X]:((funny(X)|calm(X))<=>(~rich(X)&strong(X))))&
(![X]:((generous(X)<~>~strong(X))<=>(~wise(X)|old(X))))&
((?[X]:((humble(X)|~rich(X))))<=>((generous(susan)&~tall(susan))))&
((~old(paul))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((rich(X)<~>curious(X))=>(strong(X)|generous(X))))&
(![X]:(quiet(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((generous(X)&old(X))=>(humble(X)|wise(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((happy(X)|~happy(X))=>(~humble(X)&kind(X))))&
(![X]:((~funny(X)&quiet(X))<=>(curious(X)|strong(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>((~generous(paul)&~quiet(paul))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~wise(X)&~patient(X))))&
(![X]:((~kind(X)|curious(X))<=>(humble(X)<~>~brave(X))))&
((curious(lucy)|humble(lucy)))&
((~wise(susan)<~>~rich(susan)))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:((~tall(X)|generous(X))))&
((humble(mary)|~patient(mary)))&
((~humble(mary)|~old(mary))) | ~calm(susan) | [
"p1",
"p9",
"p13",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 2410353216962522900728399
% SZS output start Proof for 2410353216962522900728399
2. ! [X0] : ((calm(X0) | funny(X0)) <=> (strong(X0) & ~rich(X0))) [input p1]
10. ! [X0] : ((~happy(X0) | happy(X0)) => (kind(X0) & ~humble(X0))) [input p9]
14. ! [X0] : ((~humble(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~wise(X0))) [input p13]
17. ~wise(susan) <~> ~rich(susan) [input p16]
22. calm(susan) [input hypothesis]
31. ! [X0] : ((kind(X0) & ~humble(X0)) | (happy(X0) & ~happy(X0))) [ennf transformation 10]
35. ! [X0] : (((calm(X0) | funny(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (~calm(X0) & ~funny(X0)))) [nnf transformation 2]
36. ! [X0] : ((calm(X0) | funny(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (~calm(X0) & ~funny(X0)))) [flattening 35]
64. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | (patient(X0) | wise(X0))) & ((~patient(X0) & ~wise(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [nnf transformation 14]
65. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | patient(X0) | wise(X0)) & ((~patient(X0) & ~wise(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [flattening 64]
68. (rich(susan) | wise(susan)) & (~rich(susan) | ~wise(susan)) [nnf transformation 17]
79. ~rich(X0) | ~calm(X0) [cnf transformation 36]
104. ~humble(X0) | ~happy(X0) [cnf transformation 31]
105. ~humble(X0) | happy(X0) [cnf transformation 31]
106. kind(X0) | ~happy(X0) [cnf transformation 31]
107. happy(X0) | kind(X0) [cnf transformation 31]
120. ~wise(X0) | ~kind(X0) | humble(X0) [cnf transformation 65]
134. rich(susan) | wise(susan) [cnf transformation 68]
139. calm(susan) [cnf transformation 22]
162. 6 <=> ! [X1] : ~humble(X1) [avatar definition]
163. ~humble(X1) <- (6) [avatar component clause 162]
201. kind(X0) [subsumption resolution 106,107]
202. ~humble(X0) [subsumption resolution 104,105]
203. 6 [avatar split clause 202,162]
248. ~wise(X0) | humble(X0) [subsumption resolution 120,201]
261. 26 <=> wise(susan) [avatar definition]
263. wise(susan) <- (26) [avatar component clause 261]
265. 27 <=> rich(susan) [avatar definition]
267. rich(susan) <- (27) [avatar component clause 265]
268. 26 | 27 [avatar split clause 134,265,261]
303. ~calm(susan) <- (27) [resolution 267,79]
305. $false <- (27) [subsumption resolution 303,139]
306. ~27 [avatar contradiction clause 305]
310. humble(susan) <- (26) [resolution 248,263]
311. $false <- (6, 26) [subsumption resolution 310,163]
312. ~6 | ~26 [avatar contradiction clause 311]
313. $false [avatar sat refutation 203,268,306,312]
% SZS output end Proof for 2410353216962522900728399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or wise is not patient.
If someone is strong then mary is not wise or strong.
If paul is either kind or not humble then someone is humble or old.
If someone is both humble and not calm then fred is strong or not funny.
If someone is not quiet or not happy then someone is both not strong and not quiet.
If someone is happy or not tall then alice is wise or old and vice versa.
Everyone who is not curious or curious is not humble and vice versa.
If someone is either wise or not wise then alice is not humble and vice versa.
Everyone who is creative or not generous is curious and vice versa.
If paul is both humble and not funny then someone is not kind or calm and vice versa.
Everyone who is either not creative or old is either not funny or not humble and vice versa.
If someone is not rich then john is curious or not brave.
If someone is either kind or not calm then someone is either quiet or not funny and vice versa.
If someone is wise or not kind then fred is either not creative or funny.
Everyone who is both generous and not calm is not tall or not kind.
Everyone who is either kind or not tall is generous.
Paul is not curious.
Someone is both not brave and not generous.
Someone is rich.
Alice is both not brave and funny.
Lucy is not rich or not funny.
Mary is curious.
John is creative. | Paul is kind. | entailment | (![X]:((~calm(X)|wise(X))=>~patient(X)))&
((?[X]:(strong(X)))=>((~wise(mary)|strong(mary))))&
(((kind(paul)<~>~humble(paul)))=>(?[X]:((humble(X)|old(X)))))&
((?[X]:((humble(X)&~calm(X))))=>((strong(fred)|~funny(fred))))&
((?[X]:((~quiet(X)|~happy(X))))=>(?[X]:((~strong(X)&~quiet(X)))))&
((?[X]:((happy(X)|~tall(X))))<=>((wise(alice)|old(alice))))&
(![X]:((~curious(X)|curious(X))<=>~humble(X)))&
((?[X]:((wise(X)<~>~wise(X))))<=>(~humble(alice)))&
(![X]:((creative(X)|~generous(X))<=>curious(X)))&
(((humble(paul)&~funny(paul)))<=>(?[X]:((~kind(X)|calm(X)))))&
(![X]:((~creative(X)<~>old(X))<=>(~funny(X)<~>~humble(X))))&
((?[X]:(~rich(X)))=>((curious(john)|~brave(john))))&
((?[X]:((kind(X)<~>~calm(X))))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
((?[X]:((wise(X)|~kind(X))))=>((~creative(fred)<~>funny(fred))))&
(![X]:((generous(X)&~calm(X))=>(~tall(X)|~kind(X))))&
(![X]:((kind(X)<~>~tall(X))=>generous(X)))&
(~curious(paul))&
(?[X]:((~brave(X)&~generous(X))))&
(?[X]:(rich(X)))&
((~brave(alice)&funny(alice)))&
((~rich(lucy)|~funny(lucy)))&
(curious(mary))&
(creative(john)) | kind(paul) | [
"p6",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 7924047047110710511980682
% SZS output start Proof for 7924047047110710511980682
7. ! [X0] : ((curious(X0) | ~curious(X0)) <=> ~humble(X0)) [input p6]
10. (~funny(paul) & humble(paul)) <=> ? [X0] : (calm(X0) | ~kind(X0)) [input p9]
24. ~kind(paul) [input hypothesis]
52. ! [X0] : (((curious(X0) | ~curious(X0)) | humble(X0)) & (~humble(X0) | (~curious(X0) & curious(X0)))) [nnf transformation 7]
53. ! [X0] : ((curious(X0) | ~curious(X0) | humble(X0)) & (~humble(X0) | (~curious(X0) & curious(X0)))) [flattening 52]
60. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & (? [X0] : (calm(X0) | ~kind(X0)) | (funny(paul) | ~humble(paul))) [nnf transformation 10]
61. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & (? [X0] : (calm(X0) | ~kind(X0)) | funny(paul) | ~humble(paul)) [flattening 60]
62. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & (? [X1] : (calm(X1) | ~kind(X1)) | funny(paul) | ~humble(paul)) [rectify 61]
63. ? [X1] : (calm(X1) | ~kind(X1)) => (calm(sK4) | ~kind(sK4)) [choice axiom]
64. ((~funny(paul) & humble(paul)) | ! [X0] : (~calm(X0) & kind(X0))) & ((calm(sK4) | ~kind(sK4)) | funny(paul) | ~humble(paul)) [skolemisation 62,63]
89. ~humble(X0) | curious(X0) [cnf transformation 53]
90. ~humble(X0) | ~curious(X0) [cnf transformation 53]
100. humble(paul) | kind(X0) [cnf transformation 64]
134. ~kind(paul) [cnf transformation 24]
154. 5 <=> kind(paul) [avatar definition]
155. ~kind(paul) <- (~5) [avatar component clause 154]
223. ~humble(X0) [subsumption resolution 89,90]
233. 23 <=> ! [X0] : kind(X0) [avatar definition]
234. kind(X0) <- (23) [avatar component clause 233]
238. kind(X0) [subsumption resolution 100,223]
239. 23 [avatar split clause 238,233]
300. ~5 [avatar split clause 134,154]
301. $false <- (~5, 23) [subsumption resolution 155,234]
302. 5 | ~23 [avatar contradiction clause 301]
305. $false [avatar sat refutation 239,300,302]
% SZS output end Proof for 7924047047110710511980682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not calm is not brave.
If mary is both not kind and creative then lucy is both not quiet and not patient.
If john is not kind or patient then alice is happy and vice versa.
Everyone who is both not humble and funny is wise or not tall.
Everyone who is not patient or not humble is both not creative and not calm.
Everyone who is either not generous or not quiet is both not kind and not brave and vice versa.
Everyone who is not tall or humble is either not generous or not brave and vice versa.
If paul is not calm then lucy is not kind or not generous.
If someone is both not tall and curious then fred is old or humble.
If someone is both tall and not humble then fred is not generous.
If paul is wise or generous then paul is both not old and not funny and vice versa.
Everyone who is either generous or wise is funny or not generous and vice versa.
Everyone who is not strong is either not old or not calm and vice versa.
Everyone who is either not patient or patient is generous.
Everyone who is not calm or not happy is creative or humble.
Everyone who is happy is either calm or not patient and vice versa.
Someone is not funny.
Someone is patient.
Fred is rich or curious.
Someone is not calm.
Someone is both rich and not old.
Fred is old or not brave.
Someone is not brave. | John is not kind. | neutral | (![X]:((~brave(X)<~>~calm(X))=>~brave(X)))&
(((~kind(mary)&creative(mary)))=>((~quiet(lucy)&~patient(lucy))))&
(((~kind(john)|patient(john)))<=>(happy(alice)))&
(![X]:((~humble(X)&funny(X))=>(wise(X)|~tall(X))))&
(![X]:((~patient(X)|~humble(X))=>(~creative(X)&~calm(X))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~tall(X)|humble(X))<=>(~generous(X)<~>~brave(X))))&
((~calm(paul))=>((~kind(lucy)|~generous(lucy))))&
((?[X]:((~tall(X)&curious(X))))=>((old(fred)|humble(fred))))&
((?[X]:((tall(X)&~humble(X))))=>(~generous(fred)))&
(((wise(paul)|generous(paul)))<=>((~old(paul)&~funny(paul))))&
(![X]:((generous(X)<~>wise(X))<=>(funny(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>patient(X))=>generous(X)))&
(![X]:((~calm(X)|~happy(X))=>(creative(X)|humble(X))))&
(![X]:(happy(X)<=>(calm(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:(patient(X)))&
((rich(fred)|curious(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((rich(X)&~old(X))))&
((old(fred)|~brave(fred)))&
(?[X]:(~brave(X))) | ~kind(john) | []
| null | 0 |
If john is not tall then someone is both not tall and brave and vice versa. Everyone who is either kind or not funny is humble. If mary is either funny or creative then susan is humble and vice versa. Everyone who is not curious is curious or creative and vice versa. Everyone who is old is not creative. If lucy is not happy or strong then someone is tall or not curious and vice versa. If someone is not generous or not creative then mary is both patient and not strong and vice versa. If someone is not strong then someone is either calm or not calm. Everyone who is either rich or patient is either curious or not strong. Everyone who is not rich or old is both not quiet and old. Everyone who is brave or not kind is either rich or strong. Everyone who is either brave or funny is creative and vice versa. Everyone who is both not wise and tall is both not kind and kind. If someone is brave or not curious then someone is both strong and not old and vice versa. Everyone who is either not patient or rich is not generous. Everyone who is quiet or calm is either funny or not happy. Lucy is not quiet or not rich. Someone is rich or not kind. Mary is not funny or generous. Someone is both funny and wise. Someone is either old or funny. Someone is not calm or generous. Fred is not calm or not quiet. Fred is both not curious and not funny. | John is not old. | entailment | ((~tall(john))<=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:((kind(X)<~>~funny(X))=>humble(X)))&
(((funny(mary)<~>creative(mary)))<=>(humble(susan)))&
(![X]:(~curious(X)<=>(curious(X)|creative(X))))&
(![X]:(old(X)=>~creative(X)))&
(((~happy(lucy)|strong(lucy)))<=>(?[X]:((tall(X)|~curious(X)))))&
((?[X]:((~generous(X)|~creative(X))))<=>((patient(mary)&~strong(mary))))&
((?[X]:(~strong(X)))=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((rich(X)<~>patient(X))=>(curious(X)<~>~strong(X))))&
(![X]:((~rich(X)|old(X))=>(~quiet(X)&old(X))))&
(![X]:((brave(X)|~kind(X))=>(rich(X)<~>strong(X))))&
(![X]:((brave(X)<~>funny(X))<=>creative(X)))&
(![X]:((~wise(X)&tall(X))=>(~kind(X)&kind(X))))&
((?[X]:((brave(X)|~curious(X))))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:((~patient(X)<~>rich(X))=>~generous(X)))&
(![X]:((quiet(X)|calm(X))=>(funny(X)<~>~happy(X))))&
((~quiet(lucy)|~rich(lucy)))&
(?[X]:((rich(X)|~kind(X))))&
((~funny(mary)|generous(mary)))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((~calm(X)|generous(X))))&
((~calm(fred)|~quiet(fred)))&
((~curious(fred)&~funny(fred))) | ~old(john) | [
"p3",
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 9106121264717551194866909
% SZS output start Proof for 9106121264717551194866909
4. ! [X0] : (~curious(X0) <=> (creative(X0) | curious(X0))) [input p3]
5. ! [X0] : (old(X0) => ~creative(X0)) [input p4]
25. old(john) [input hypothesis]
35. ! [X0] : (~creative(X0) | ~old(X0)) [ennf transformation 5]
48. ! [X0] : ((~curious(X0) | (~creative(X0) & ~curious(X0))) & ((creative(X0) | curious(X0)) | curious(X0))) [nnf transformation 4]
49. ! [X0] : ((~curious(X0) | (~creative(X0) & ~curious(X0))) & (creative(X0) | curious(X0) | curious(X0))) [flattening 48]
92. creative(X0) | curious(X0) | curious(X0) [cnf transformation 49]
93. ~curious(X0) | ~curious(X0) [cnf transformation 49]
95. ~creative(X0) | ~old(X0) [cnf transformation 35]
138. old(john) [cnf transformation 25]
139. creative(X0) | curious(X0) [duplicate literal removal 92]
140. ~curious(X0) [duplicate literal removal 93]
175. creative(X0) [subsumption resolution 139,140]
176. ~old(X0) [subsumption resolution 95,175]
234. $false [subsumption resolution 138,176]
% SZS output end Proof for 9106121264717551194866909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not funny and wise then mary is not curious or funny and vice versa.
If someone is not wise or not curious then someone is either old or calm.
If someone is old or generous then paul is either strong or patient and vice versa.
If susan is both not wise and not brave then alice is quiet or funny.
Everyone who is either not creative or not wise is either strong or rich.
Everyone who is both happy and not tall is both not quiet and not old and vice versa.
Everyone who is generous or old is not funny.
If alice is not curious or not kind then someone is either not tall or curious.
If someone is both not quiet and not creative then someone is not curious or creative.
If someone is both quiet and strong then someone is generous or rich.
Everyone who is not rich is either brave or rich and vice versa.
Everyone who is either not rich or not happy is generous.
If someone is both not humble and strong then someone is rich or not patient.
If fred is both not quiet and wise then john is creative or not wise and vice versa.
Everyone who is either not patient or generous is not old or not wise and vice versa.
Someone is both not patient and strong.
Mary is either not happy or not wise.
Someone is both funny and not humble.
Someone is both patient and not humble.
Lucy is not old.
Lucy is both creative and not rich.
John is either not funny or not wise. | Alice is not wise. | neutral | (((~funny(lucy)&wise(lucy)))<=>((~curious(mary)|funny(mary))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((old(X)|generous(X))))<=>((strong(paul)<~>patient(paul))))&
(((~wise(susan)&~brave(susan)))=>((quiet(alice)|funny(alice))))&
(![X]:((~creative(X)<~>~wise(X))=>(strong(X)<~>rich(X))))&
(![X]:((happy(X)&~tall(X))<=>(~quiet(X)&~old(X))))&
(![X]:((generous(X)|old(X))=>~funny(X)))&
(((~curious(alice)|~kind(alice)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((?[X]:((~quiet(X)&~creative(X))))=>(?[X]:((~curious(X)|creative(X)))))&
((?[X]:((quiet(X)&strong(X))))=>(?[X]:((generous(X)|rich(X)))))&
(![X]:(~rich(X)<=>(brave(X)<~>rich(X))))&
(![X]:((~rich(X)<~>~happy(X))=>generous(X)))&
((?[X]:((~humble(X)&strong(X))))=>(?[X]:((rich(X)|~patient(X)))))&
(((~quiet(fred)&wise(fred)))<=>((creative(john)|~wise(john))))&
(![X]:((~patient(X)<~>generous(X))<=>(~old(X)|~wise(X))))&
(?[X]:((~patient(X)&strong(X))))&
((~happy(mary)<~>~wise(mary)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((patient(X)&~humble(X))))&
(~old(lucy))&
((creative(lucy)&~rich(lucy)))&
((~funny(john)<~>~wise(john))) | ~wise(alice) | []
| null | 0 |
Everyone who is not tall or not kind is not old and vice versa. Everyone who is both brave and patient is wise and vice versa. Everyone who is both not creative and not brave is kind or not humble and vice versa. If susan is either not humble or not quiet then john is both brave and kind and vice versa. Everyone who is either happy or not strong is not happy or patient and vice versa. If alice is not funny then paul is both not happy and not wise and vice versa. Everyone who is both not kind and not strong is not strong and vice versa. If paul is either not patient or wise then someone is generous. Everyone who is generous is both kind and not kind and vice versa. If someone is funny or creative then someone is not strong or not tall. Everyone who is both calm and not tall is both happy and brave. Everyone who is not curious is creative or brave and vice versa. Everyone who is not funny or humble is not brave or not funny and vice versa. If someone is strong then mary is generous and vice versa. Everyone who is either rich or not kind is either not generous or rich. Alice is not tall or not happy. Someone is not humble. Someone is both not wise and creative. Paul is not curious or strong. Susan is not generous. Someone is not tall. Susan is not quiet. Someone is brave. | Alice is creative. | neutral | (![X]:((~tall(X)|~kind(X))<=>~old(X)))&
(![X]:((brave(X)&patient(X))<=>wise(X)))&
(![X]:((~creative(X)&~brave(X))<=>(kind(X)|~humble(X))))&
(((~humble(susan)<~>~quiet(susan)))<=>((brave(john)&kind(john))))&
(![X]:((happy(X)<~>~strong(X))<=>(~happy(X)|patient(X))))&
((~funny(alice))<=>((~happy(paul)&~wise(paul))))&
(![X]:((~kind(X)&~strong(X))<=>~strong(X)))&
(((~patient(paul)<~>wise(paul)))=>(?[X]:(generous(X))))&
(![X]:(generous(X)<=>(kind(X)&~kind(X))))&
((?[X]:((funny(X)|creative(X))))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((calm(X)&~tall(X))=>(happy(X)&brave(X))))&
(![X]:(~curious(X)<=>(creative(X)|brave(X))))&
(![X]:((~funny(X)|humble(X))<=>(~brave(X)|~funny(X))))&
((?[X]:(strong(X)))<=>(generous(mary)))&
(![X]:((rich(X)<~>~kind(X))=>(~generous(X)<~>rich(X))))&
((~tall(alice)|~happy(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~wise(X)&creative(X))))&
((~curious(paul)|strong(paul)))&
(~generous(susan))&
(?[X]:(~tall(X)))&
(~quiet(susan))&
(?[X]:(brave(X))) | creative(alice) | []
| null | 0 |
Everyone who is not calm or patient is generous and vice versa.
Everyone who is wise or not old is both not happy and wise and vice versa.
If fred is not calm or not old then susan is either rich or quiet.
If susan is generous or not generous then someone is either strong or not creative.
Everyone who is not brave or brave is both not strong and not humble.
If someone is either not brave or generous then someone is either generous or not wise.
Everyone who is not tall or happy is either generous or tall and vice versa.
Everyone who is both not brave and not curious is happy.
Everyone who is either not brave or curious is not tall and vice versa.
Everyone who is either not curious or not old is not old and vice versa.
If alice is brave then someone is both not kind and old and vice versa.
Everyone who is calm or not happy is not kind.
If paul is not strong then someone is not old or not kind.
If lucy is generous then alice is either not rich or humble and vice versa.
Everyone who is either not generous or not quiet is creative or not tall.
Everyone who is both quiet and brave is funny or not rich and vice versa.
Someone is not kind or humble.
Paul is either happy or wise.
Someone is not humble.
Someone is kind.
Paul is either tall or generous.
Someone is both tall and old. | Alice is generous. | entailment | (![X]:((~calm(X)|patient(X))<=>generous(X)))&
(![X]:((wise(X)|~old(X))<=>(~happy(X)&wise(X))))&
(((~calm(fred)|~old(fred)))=>((rich(susan)<~>quiet(susan))))&
(((generous(susan)|~generous(susan)))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((~brave(X)|brave(X))=>(~strong(X)&~humble(X))))&
((?[X]:((~brave(X)<~>generous(X))))=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:((~tall(X)|happy(X))<=>(generous(X)<~>tall(X))))&
(![X]:((~brave(X)&~curious(X))=>happy(X)))&
(![X]:((~brave(X)<~>curious(X))<=>~tall(X)))&
(![X]:((~curious(X)<~>~old(X))<=>~old(X)))&
((brave(alice))<=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((calm(X)|~happy(X))=>~kind(X)))&
((~strong(paul))=>(?[X]:((~old(X)|~kind(X)))))&
((generous(lucy))<=>((~rich(alice)<~>humble(alice))))&
(![X]:((~generous(X)<~>~quiet(X))=>(creative(X)|~tall(X))))&
(![X]:((quiet(X)&brave(X))<=>(funny(X)|~rich(X))))&
(?[X]:((~kind(X)|humble(X))))&
((happy(paul)<~>wise(paul)))&
(?[X]:(~humble(X)))&
(?[X]:(kind(X)))&
((tall(paul)<~>generous(paul)))&
(?[X]:((tall(X)&old(X)))) | generous(alice) | [
"p0",
"p6",
"p8",
"p9",
"p10",
"p11",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 2668338357183714504747570
% SZS output start Proof for 2668338357183714504747570
1. ! [X0] : ((patient(X0) | ~calm(X0)) <=> generous(X0)) [input p0]
7. ! [X0] : ((happy(X0) | ~tall(X0)) <=> (generous(X0) <~> tall(X0))) [input p6]
9. ! [X0] : ((~brave(X0) <~> curious(X0)) <=> ~tall(X0)) [input p8]
10. ! [X0] : ((~curious(X0) <~> ~old(X0)) <=> ~old(X0)) [input p9]
11. brave(alice) <=> ? [X0] : (old(X0) & ~kind(X0)) [input p10]
12. ! [X0] : ((~happy(X0) | calm(X0)) => ~kind(X0)) [input p11]
22. ? [X0] : (old(X0) & tall(X0)) [input p21]
23. ~generous(alice) [input hypothesis]
31. ! [X0] : (~kind(X0) | (happy(X0) & ~calm(X0))) [ennf transformation 12]
35. ! [X0] : (((patient(X0) | ~calm(X0)) | ~generous(X0)) & (generous(X0) | (~patient(X0) & calm(X0)))) [nnf transformation 1]
36. ! [X0] : ((patient(X0) | ~calm(X0) | ~generous(X0)) & (generous(X0) | (~patient(X0) & calm(X0)))) [flattening 35]
47. ! [X0] : (((happy(X0) | ~tall(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (~happy(X0) & tall(X0)))) [nnf transformation 7]
48. ! [X0] : ((happy(X0) | ~tall(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (~happy(X0) & tall(X0)))) [flattening 47]
49. ! [X0] : ((((~curious(X0) | brave(X0)) & (curious(X0) | ~brave(X0))) | tall(X0)) & (~tall(X0) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0))))) [nnf transformation 9]
50. ! [X0] : ((((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | old(X0)) & (~old(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))))) [nnf transformation 10]
51. (brave(alice) | ! [X0] : (~old(X0) | kind(X0))) & (? [X0] : (old(X0) & ~kind(X0)) | ~brave(alice)) [nnf transformation 11]
52. (brave(alice) | ! [X0] : (~old(X0) | kind(X0))) & (? [X1] : (old(X1) & ~kind(X1)) | ~brave(alice)) [rectify 51]
53. ? [X1] : (old(X1) & ~kind(X1)) => (old(sK2) & ~kind(sK2)) [choice axiom]
54. (brave(alice) | ! [X0] : (~old(X0) | kind(X0))) & ((old(sK2) & ~kind(sK2)) | ~brave(alice)) [skolemisation 52,53]
69. ? [X0] : (old(X0) & tall(X0)) => (old(sK7) & tall(sK7)) [choice axiom]
70. old(sK7) & tall(sK7) [skolemisation 22,69]
71. generous(X0) | calm(X0) [cnf transformation 36]
95. tall(X0) | generous(X0) | tall(X0) [cnf transformation 48]
98. ~tall(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 48]
103. ~curious(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 49]
106. ~old(X0) | ~old(X0) | curious(X0) [cnf transformation 50]
109. old(X0) | curious(X0) | old(X0) [cnf transformation 50]
112. brave(alice) | ~old(X0) | kind(X0) [cnf transformation 54]
113. ~kind(X0) | ~calm(X0) [cnf transformation 31]
114. ~kind(X0) | happy(X0) [cnf transformation 31]
134. tall(sK7) [cnf transformation 70]
135. old(sK7) [cnf transformation 70]
136. ~generous(alice) [cnf transformation 23]
137. ~old(X0) | curious(X0) [duplicate literal removal 106]
138. curious(X0) | old(X0) [duplicate literal removal 109]
139. tall(X0) | generous(X0) [duplicate literal removal 95]
197. curious(X0) [subsumption resolution 137,138]
199. 12 <=> ! [X0] : (~old(X0) | kind(X0)) [avatar definition]
200. ~old(X0) | kind(X0) <- (12) [avatar component clause 199]
202. 13 <=> brave(alice) [avatar definition]
204. brave(alice) <- (13) [avatar component clause 202]
205. 12 | 13 [avatar split clause 112,202,199]
287. ~generous(sK7) | ~happy(sK7) [resolution 98,134]
290. 24 <=> happy(sK7) [avatar definition]
294. 25 <=> generous(sK7) [avatar definition]
296. ~generous(sK7) <- (~25) [avatar component clause 294]
297. ~24 | ~25 [avatar split clause 287,294,290]
302. ~tall(X2) | ~brave(X2) [resolution 103,197]
304. ~brave(X0) | generous(X0) [resolution 302,139]
321. calm(sK7) <- (~25) [resolution 296,71]
348. generous(alice) <- (13) [resolution 304,204]
349. $false <- (13) [subsumption resolution 348,136]
350. ~13 [avatar contradiction clause 349]
371. kind(sK7) <- (12) [resolution 200,135]
377. happy(sK7) <- (12) [resolution 371,114]
378. ~calm(sK7) <- (12) [resolution 371,113]
379. $false <- (12, ~25) [subsumption resolution 378,321]
380. ~12 | 25 [avatar contradiction clause 379]
381. 24 | ~12 [avatar split clause 377,199,290]
391. $false [avatar sat refutation 205,297,350,380,381]
% SZS output end Proof for 2668338357183714504747570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not patient or not calm then fred is brave or humble. Everyone who is not kind is either not generous or quiet. If fred is tall then paul is strong or not quiet. Everyone who is not funny is not curious and vice versa. Everyone who is either rich or calm is not generous or curious. Everyone who is old or wise is both quiet and not wise and vice versa. If someone is both old and not funny then fred is both not generous and not wise and vice versa. If someone is humble or quiet then someone is creative or funny and vice versa. If alice is both not generous and not tall then someone is both not patient and strong. Everyone who is wise or not wise is both not generous and not humble and vice versa. If john is both not calm and strong then someone is both tall and humble. If alice is either not curious or not humble then someone is either strong or not wise. If mary is both not brave and strong then someone is old or not happy and vice versa. Everyone who is either curious or tall is either funny or not generous and vice versa. Everyone who is both quiet and not creative is wise or tall and vice versa. If paul is both not creative and wise then john is either humble or not kind and vice versa. Lucy is both not creative and calm. Someone is not happy. Paul is tall or not brave. Someone is both strong and not curious. John is wise or not patient. Someone is either not kind or not curious. Someone is not patient or humble. | Paul is quiet. | entailment | (((~patient(alice)|~calm(alice)))=>((brave(fred)|humble(fred))))&
(![X]:(~kind(X)=>(~generous(X)<~>quiet(X))))&
((tall(fred))=>((strong(paul)|~quiet(paul))))&
(![X]:(~funny(X)<=>~curious(X)))&
(![X]:((rich(X)<~>calm(X))=>(~generous(X)|curious(X))))&
(![X]:((old(X)|wise(X))<=>(quiet(X)&~wise(X))))&
((?[X]:((old(X)&~funny(X))))<=>((~generous(fred)&~wise(fred))))&
((?[X]:((humble(X)|quiet(X))))<=>(?[X]:((creative(X)|funny(X)))))&
(((~generous(alice)&~tall(alice)))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((wise(X)|~wise(X))<=>(~generous(X)&~humble(X))))&
(((~calm(john)&strong(john)))=>(?[X]:((tall(X)&humble(X)))))&
(((~curious(alice)<~>~humble(alice)))=>(?[X]:((strong(X)<~>~wise(X)))))&
(((~brave(mary)&strong(mary)))<=>(?[X]:((old(X)|~happy(X)))))&
(![X]:((curious(X)<~>tall(X))<=>(funny(X)<~>~generous(X))))&
(![X]:((quiet(X)&~creative(X))<=>(wise(X)|tall(X))))&
(((~creative(paul)&wise(paul)))<=>((humble(john)<~>~kind(john))))&
((~creative(lucy)&calm(lucy)))&
(?[X]:(~happy(X)))&
((tall(paul)|~brave(paul)))&
(?[X]:((strong(X)&~curious(X))))&
((wise(john)|~patient(john)))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((~patient(X)|humble(X)))) | quiet(paul) | [
"p3",
"p5",
"p9",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 165367936109866498396272
% SZS output start Proof for 165367936109866498396272
4. ! [X0] : (~funny(X0) <=> ~curious(X0)) [input p3]
6. ! [X0] : ((wise(X0) | old(X0)) <=> (~wise(X0) & quiet(X0))) [input p5]
10. ! [X0] : ((~wise(X0) | wise(X0)) <=> (~humble(X0) & ~generous(X0))) [input p9]
14. ! [X0] : ((curious(X0) <~> tall(X0)) <=> (funny(X0) <~> ~generous(X0))) [input p13]
15. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (tall(X0) | wise(X0))) [input p14]
24. ~quiet(paul) [input hypothesis]
39. ! [X0] : ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))) [nnf transformation 4]
41. ! [X0] : (((wise(X0) | old(X0)) | (wise(X0) | ~quiet(X0))) & ((~wise(X0) & quiet(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 6]
42. ! [X0] : ((wise(X0) | old(X0) | wise(X0) | ~quiet(X0)) & ((~wise(X0) & quiet(X0)) | (~wise(X0) & ~old(X0)))) [flattening 41]
55. ! [X0] : (((~wise(X0) | wise(X0)) | (humble(X0) | generous(X0))) & ((~humble(X0) & ~generous(X0)) | (wise(X0) & ~wise(X0)))) [nnf transformation 10]
56. ! [X0] : ((~wise(X0) | wise(X0) | humble(X0) | generous(X0)) & ((~humble(X0) & ~generous(X0)) | (wise(X0) & ~wise(X0)))) [flattening 55]
67. ! [X0] : ((((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0)))) & (((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0))))) [nnf transformation 14]
68. ! [X0] : (((~creative(X0) & quiet(X0)) | (~tall(X0) & ~wise(X0))) & ((tall(X0) | wise(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 15]
69. ! [X0] : (((~creative(X0) & quiet(X0)) | (~tall(X0) & ~wise(X0))) & (tall(X0) | wise(X0) | creative(X0) | ~quiet(X0))) [flattening 68]
86. ~curious(X0) | funny(X0) [cnf transformation 39]
87. ~funny(X0) | curious(X0) [cnf transformation 39]
93. ~wise(X0) | ~wise(X0) [cnf transformation 42]
106. ~generous(X0) | wise(X0) [cnf transformation 56]
123. generous(X0) | ~funny(X0) | tall(X0) | ~curious(X0) [cnf transformation 67]
126. tall(X0) | curious(X0) | funny(X0) | generous(X0) [cnf transformation 67]
131. quiet(X0) | ~tall(X0) [cnf transformation 69]
150. ~quiet(paul) [cnf transformation 24]
151. ~wise(X0) [duplicate literal removal 93]
256. ~generous(X0) [subsumption resolution 106,151]
318. tall(X0) | curious(X0) | funny(X0) [subsumption resolution 126,256]
319. tall(X0) | curious(X0) [subsumption resolution 318,87]
320. ~funny(X0) | tall(X0) | ~curious(X0) [subsumption resolution 123,256]
321. tall(X0) | ~curious(X0) [subsumption resolution 320,86]
322. tall(X0) [subsumption resolution 321,319]
325. quiet(X0) [subsumption resolution 131,322]
364. $false [subsumption resolution 150,325]
% SZS output end Proof for 165367936109866498396272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both not quiet and not wise and vice versa. If someone is brave or kind then john is either not patient or not quiet and vice versa. Everyone who is not creative is both not funny and not old and vice versa. If mary is not old then someone is both not strong and patient. Everyone who is not creative or happy is either tall or not quiet and vice versa. If someone is both not funny and old then someone is not brave or not kind. Everyone who is either creative or not humble is both strong and not creative. Everyone who is both not kind and strong is calm or not kind. Everyone who is not humble is either not quiet or not wise. Everyone who is not old or calm is not humble or patient and vice versa. Everyone who is either not happy or patient is either curious or not brave. Someone is quiet or wise. Susan is not happy or tall. Mary is not quiet or not rich. Someone is either not strong or not old. Alice is not generous. Mary is tall. Susan is not happy or not rich. | Alice is old. | neutral | (![X]:(wise(X)<=>(~quiet(X)&~wise(X))))&
((?[X]:((brave(X)|kind(X))))<=>((~patient(john)<~>~quiet(john))))&
(![X]:(~creative(X)<=>(~funny(X)&~old(X))))&
((~old(mary))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~creative(X)|happy(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((creative(X)<~>~humble(X))=>(strong(X)&~creative(X))))&
(![X]:((~kind(X)&strong(X))=>(calm(X)|~kind(X))))&
(![X]:(~humble(X)=>(~quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|calm(X))<=>(~humble(X)|patient(X))))&
(![X]:((~happy(X)<~>patient(X))=>(curious(X)<~>~brave(X))))&
(?[X]:((quiet(X)|wise(X))))&
((~happy(susan)|tall(susan)))&
((~quiet(mary)|~rich(mary)))&
(?[X]:((~strong(X)<~>~old(X))))&
(~generous(alice))&
(tall(mary))&
((~happy(susan)|~rich(susan))) | old(alice) | []
| null | 0 |
If someone is not kind or humble then someone is both not wise and not quiet and vice versa.
Everyone who is quiet is not wise and vice versa.
Everyone who is quiet or creative is not strong and vice versa.
If someone is not funny then someone is either not patient or calm.
If someone is either not curious or patient then someone is not quiet.
If lucy is not funny then someone is quiet and vice versa.
If someone is not calm or rich then someone is both not patient and funny.
If someone is both humble and patient then alice is either not kind or generous.
If someone is both not old and funny then someone is both not kind and calm.
Everyone who is not humble is both calm and not creative.
Everyone who is either brave or humble is not wise or humble and vice versa.
Everyone who is either calm or not creative is either strong or funny and vice versa.
Everyone who is either calm or wise is both generous and funny and vice versa.
Everyone who is old is both strong and not rich and vice versa.
Everyone who is both not brave and kind is either not rich or creative and vice versa.
Everyone who is both not old and funny is not strong and vice versa.
Mary is not wise or happy.
Someone is both not creative and kind.
Someone is both not humble and not patient.
Someone is both not patient and strong.
Fred is quiet or not brave. | Alice is not brave. | entailment | ((?[X]:((~kind(X)|humble(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:(quiet(X)<=>~wise(X)))&
(![X]:((quiet(X)|creative(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~patient(X)<~>calm(X)))))&
((?[X]:((~curious(X)<~>patient(X))))=>(?[X]:(~quiet(X))))&
((~funny(lucy))<=>(?[X]:(quiet(X))))&
((?[X]:((~calm(X)|rich(X))))=>(?[X]:((~patient(X)&funny(X)))))&
((?[X]:((humble(X)&patient(X))))=>((~kind(alice)<~>generous(alice))))&
((?[X]:((~old(X)&funny(X))))=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:(~humble(X)=>(calm(X)&~creative(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~wise(X)|humble(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)<~>funny(X))))&
(![X]:((calm(X)<~>wise(X))<=>(generous(X)&funny(X))))&
(![X]:(old(X)<=>(strong(X)&~rich(X))))&
(![X]:((~brave(X)&kind(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~old(X)&funny(X))<=>~strong(X)))&
((~wise(mary)|happy(mary)))&
(?[X]:((~creative(X)&kind(X))))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~patient(X)&strong(X))))&
((quiet(fred)|~brave(fred))) | ~brave(alice) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2721299774402757097527059
% SZS output start Proof for 2721299774402757097527059
1. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p0]
2. ! [X0] : (quiet(X0) <=> ~wise(X0)) [input p1]
3. ! [X0] : ((creative(X0) | quiet(X0)) <=> ~strong(X0)) [input p2]
9. ? [X0] : (funny(X0) & ~old(X0)) => ? [X0] : (calm(X0) & ~kind(X0)) [input p8]
11. ! [X0] : ((brave(X0) <~> humble(X0)) <=> (humble(X0) | ~wise(X0))) [input p10]
14. ! [X0] : (old(X0) <=> (~rich(X0) & strong(X0))) [input p13]
16. ! [X0] : ((funny(X0) & ~old(X0)) <=> ~strong(X0)) [input p15]
22. brave(alice) [input hypothesis]
23. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 1]
27. ? [X0] : (funny(X0) & ~old(X0)) => ? [X1] : (calm(X1) & ~kind(X1)) [rectify 9]
33. ? [X1] : (calm(X1) & ~kind(X1)) | ! [X0] : (~funny(X0) | old(X0)) [ennf transformation 27]
35. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : (~humble(X0) & kind(X0))) [nnf transformation 23]
36. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : (~humble(X3) & kind(X3))) [rectify 35]
37. ? [X0] : (humble(X0) | ~kind(X0)) => (humble(sK0) | ~kind(sK0)) [choice axiom]
38. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK1) & ~wise(sK1)) [choice axiom]
39. ((humble(sK0) | ~kind(sK0)) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK1) & ~wise(sK1)) | ! [X3] : (~humble(X3) & kind(X3))) [skolemisation 36,38,37]
40. ! [X0] : ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))) [nnf transformation 2]
41. ! [X0] : (((creative(X0) | quiet(X0)) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 3]
42. ! [X0] : ((creative(X0) | quiet(X0) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [flattening 41]
59. ? [X0] : (calm(X0) & ~kind(X0)) | ! [X1] : (~funny(X1) | old(X1)) [rectify 33]
60. ? [X0] : (calm(X0) & ~kind(X0)) => (calm(sK6) & ~kind(sK6)) [choice axiom]
61. (calm(sK6) & ~kind(sK6)) | ! [X1] : (~funny(X1) | old(X1)) [skolemisation 59,60]
62. ! [X0] : ((((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | (~humble(X0) & wise(X0))) & ((humble(X0) | ~wise(X0)) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0))))) [nnf transformation 11]
63. ! [X0] : ((((~humble(X0) | ~brave(X0)) & (humble(X0) | brave(X0))) | (~humble(X0) & wise(X0))) & (humble(X0) | ~wise(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0))))) [flattening 62]
67. ! [X0] : ((old(X0) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | ~old(X0))) [nnf transformation 14]
68. ! [X0] : ((old(X0) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | ~old(X0))) [flattening 67]
71. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | (~funny(X0) | old(X0)))) [nnf transformation 16]
72. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | ~funny(X0) | old(X0))) [flattening 71]
79. ~wise(sK1) | kind(X3) [cnf transformation 39]
81. ~quiet(sK1) | kind(X3) [cnf transformation 39]
85. quiet(X0) | wise(X0) [cnf transformation 40]
86. ~strong(X0) | ~quiet(X0) [cnf transformation 42]
101. ~kind(sK6) | ~funny(X1) | old(X1) [cnf transformation 61]
105. humble(X0) | ~wise(X0) | humble(X0) | ~brave(X0) [cnf transformation 63]
110. ~humble(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 63]
125. ~old(X0) | strong(X0) [cnf transformation 68]
136. funny(X0) | strong(X0) [cnf transformation 72]
144. brave(alice) [cnf transformation 22]
145. humble(X0) | ~wise(X0) | ~brave(X0) [duplicate literal removal 105]
146. ~brave(X0) | ~humble(X0) [duplicate literal removal 110]
148. 1 <=> ! [X1] : (quiet(X1) | wise(X1)) [avatar definition]
149. quiet(X1) | wise(X1) <- (1) [avatar component clause 148]
163. 5 <=> quiet(sK1) [avatar definition]
165. ~quiet(sK1) <- (~5) [avatar component clause 163]
168. 6 <=> ! [X3] : kind(X3) [avatar definition]
169. kind(X3) <- (6) [avatar component clause 168]
170. 6 | ~5 [avatar split clause 81,163,168]
172. 7 <=> wise(sK1) [avatar definition]
176. 6 | ~7 [avatar split clause 79,172,168]
177. 1 [avatar split clause 85,148]
204. 14 <=> ! [X0] : ~quiet(X0) [avatar definition]
205. ~quiet(X0) <- (14) [avatar component clause 204]
248. 24 <=> ! [X1] : (~funny(X1) | old(X1)) [avatar definition]
249. ~funny(X1) | old(X1) <- (24) [avatar component clause 248]
256. 26 <=> kind(sK6) [avatar definition]
258. ~kind(sK6) <- (~26) [avatar component clause 256]
259. 24 | ~26 [avatar split clause 101,256,248]
260. ~brave(X0) | ~wise(X0) [subsumption resolution 145,146]
290. wise(sK1) <- (1, ~5) [resolution 149,165]
295. 7 | ~1 | 5 [avatar split clause 290,163,148,172]
297. old(X0) | strong(X0) <- (24) [resolution 249,136]
298. strong(X0) <- (24) [subsumption resolution 297,125]
299. ~wise(alice) [resolution 260,144]
305. ~quiet(X1) <- (24) [resolution 298,86]
306. 14 | ~24 [avatar split clause 305,248,204]
308. wise(X0) <- (1, 14) [resolution 205,149]
316. $false <- (1, 14) [resolution 308,299]
317. ~1 | ~14 [avatar contradiction clause 316]
329. $false <- (6, ~26) [subsumption resolution 258,169]
330. ~6 | 26 [avatar contradiction clause 329]
331. $false [avatar sat refutation 170,176,177,259,295,306,317,330]
% SZS output end Proof for 2721299774402757097527059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or happy is both calm and not quiet. Everyone who is not humble is not wise and vice versa. If someone is both curious and not patient then mary is either not rich or happy. Everyone who is either not strong or not curious is humble or not curious and vice versa. If someone is happy or not generous then someone is both not brave and brave. Everyone who is either not patient or not strong is both quiet and happy. Everyone who is either creative or not happy is not generous and vice versa. If someone is both not quiet and not happy then john is either creative or quiet and vice versa. If fred is happy then someone is both not calm and not generous. Everyone who is patient is both not curious and not strong and vice versa. If susan is not wise then someone is not wise or strong and vice versa. Everyone who is either not quiet or not kind is strong or curious and vice versa. Everyone who is either not humble or old is humble. If susan is calm then susan is not patient. If alice is not kind or not brave then someone is happy or not tall and vice versa. Fred is either kind or not tall. Someone is not calm or brave. Mary is either wise or not curious. | Alice is not curious. | contradiction | (![X]:((~patient(X)|happy(X))=>(calm(X)&~quiet(X))))&
(![X]:(~humble(X)<=>~wise(X)))&
((?[X]:((curious(X)&~patient(X))))=>((~rich(mary)<~>happy(mary))))&
(![X]:((~strong(X)<~>~curious(X))<=>(humble(X)|~curious(X))))&
((?[X]:((happy(X)|~generous(X))))=>(?[X]:((~brave(X)&brave(X)))))&
(![X]:((~patient(X)<~>~strong(X))=>(quiet(X)&happy(X))))&
(![X]:((creative(X)<~>~happy(X))<=>~generous(X)))&
((?[X]:((~quiet(X)&~happy(X))))<=>((creative(john)<~>quiet(john))))&
((happy(fred))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:(patient(X)<=>(~curious(X)&~strong(X))))&
((~wise(susan))<=>(?[X]:((~wise(X)|strong(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(strong(X)|curious(X))))&
(![X]:((~humble(X)<~>old(X))=>humble(X)))&
((calm(susan))=>(~patient(susan)))&
(((~kind(alice)|~brave(alice)))<=>(?[X]:((happy(X)|~tall(X)))))&
((kind(fred)<~>~tall(fred)))&
(?[X]:((~calm(X)|brave(X))))&
((wise(mary)<~>~curious(mary))) | ~curious(alice) | [
"p0",
"p3",
"p5",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 7555449761801036579153742
% SZS output start Proof for 7555449761801036579153742
1. ! [X0] : ((happy(X0) | ~patient(X0)) => (~quiet(X0) & calm(X0))) [input p0]
4. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> (~curious(X0) | humble(X0))) [input p3]
6. ! [X0] : ((~patient(X0) <~> ~strong(X0)) => (happy(X0) & quiet(X0))) [input p5]
10. ! [X0] : (patient(X0) <=> (~strong(X0) & ~curious(X0))) [input p9]
19. ~curious(alice) [input hypothesis]
21. ! [X0] : ((~quiet(X0) & calm(X0)) | (~happy(X0) & patient(X0))) [ennf transformation 1]
24. ! [X0] : ((happy(X0) & quiet(X0)) | (~patient(X0) <=> ~strong(X0))) [ennf transformation 6]
30. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 4]
31. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [flattening 30]
35. ! [X0] : ((happy(X0) & quiet(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) [nnf transformation 24]
43. ! [X0] : ((patient(X0) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | ~patient(X0))) [nnf transformation 10]
44. ! [X0] : ((patient(X0) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | ~patient(X0))) [flattening 43]
63. ~quiet(X0) | patient(X0) [cnf transformation 21]
74. curious(X0) | strong(X0) | curious(X0) [cnf transformation 31]
79. quiet(X0) | ~strong(X0) | patient(X0) [cnf transformation 35]
96. ~strong(X0) | ~patient(X0) [cnf transformation 44]
119. ~curious(alice) [cnf transformation 19]
122. strong(X0) | curious(X0) [duplicate literal removal 74]
151. ~strong(X0) | patient(X0) [subsumption resolution 79,63]
191. ~strong(X0) [subsumption resolution 96,151]
270. curious(X0) [resolution 122,191]
272. $false [resolution 270,119]
% SZS output end Proof for 7555449761801036579153742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is not calm.
If alice is both kind and not wise then alice is kind or not brave and vice versa.
Everyone who is not kind or kind is either calm or tall.
Everyone who is both creative and strong is quiet or patient and vice versa.
Everyone who is either quiet or humble is not rich or patient and vice versa.
Everyone who is both not tall and funny is not old or curious and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Someone is humble or not brave.
Someone is not kind.
Susan is not funny or funny.
Someone is both not tall and not wise.
Susan is either not generous or rich.
Someone is either not calm or not quiet. | Fred is kind. | contradiction | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:(~calm(X))))&
(((kind(alice)&~wise(alice)))<=>((kind(alice)|~brave(alice))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:(~kind(X)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X)))) | kind(fred) | [
"p0",
"p4",
"p7",
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 2300672049799273035931114
% SZS output start Proof for 2300672049799273035931114
1. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (calm(X0) & creative(X0))) [input p0]
5. ! [X0] : ((strong(X0) & creative(X0)) <=> (patient(X0) | quiet(X0))) [input p4]
8. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p7]
9. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p8]
12. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p11]
22. kind(fred) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 12]
28. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 1]
29. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [flattening 28]
36. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 5]
37. ! [X0] : (((strong(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 36]
42. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 8]
43. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 9]
45. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 44]
72. ~kind(X0) | ~wise(X0) | calm(X0) [cnf transformation 29]
89. ~patient(X0) | strong(X0) [cnf transformation 37]
102. ~calm(X0) | patient(X0) | strong(X0) [cnf transformation 43]
104. brave(X0) | patient(X0) | strong(X0) [cnf transformation 43]
108. ~strong(X0) | ~kind(X0) [cnf transformation 45]
109. ~strong(X0) | calm(X0) [cnf transformation 45]
119. ~brave(X0) | wise(X0) [cnf transformation 27]
145. kind(fred) [cnf transformation 22]
173. strong(X0) | brave(X0) [subsumption resolution 104,89]
175. ~calm(X0) | strong(X0) [subsumption resolution 102,89]
272. brave(X0) | calm(X0) [resolution 173,109]
315. ~wise(fred) | calm(fred) [resolution 72,145]
518. calm(X2) | wise(X2) [resolution 272,119]
615. calm(fred) [subsumption resolution 315,518]
618. strong(fred) [resolution 615,175]
647. ~kind(fred) [resolution 618,108]
658. $false [subsumption resolution 647,145]
% SZS output end Proof for 2300672049799273035931114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then mary is either not strong or not wise and vice versa.
Everyone who is either calm or not strong is both old and creative.
Everyone who is not strong or quiet is both quiet and old.
If someone is not rich then lucy is both tall and not kind.
Everyone who is not rich or not quiet is both not tall and kind and vice versa.
Everyone who is both not wise and not curious is not happy and vice versa.
Everyone who is either creative or kind is patient or creative.
Everyone who is curious is not humble.
Everyone who is not patient or not strong is old or not patient and vice versa.
Everyone who is either not calm or calm is either not creative or generous.
Everyone who is calm or not calm is calm or brave.
Everyone who is patient is tall.
Everyone who is both not calm and not strong is patient.
Everyone who is not strong or not happy is not wise.
If someone is both old and generous then someone is happy or tall and vice versa.
If someone is both humble and old then paul is funny or tall.
Fred is both not tall and not creative.
Someone is both not creative and not calm.
Someone is not rich or not creative.
Someone is either not curious or not creative.
Lucy is either wise or calm.
Someone is tall or curious.
Someone is either not patient or generous.
Someone is not calm. | Paul is not calm. | neutral | ((?[X]:(~brave(X)))<=>((~strong(mary)<~>~wise(mary))))&
(![X]:((calm(X)<~>~strong(X))=>(old(X)&creative(X))))&
(![X]:((~strong(X)|quiet(X))=>(quiet(X)&old(X))))&
((?[X]:(~rich(X)))=>((tall(lucy)&~kind(lucy))))&
(![X]:((~rich(X)|~quiet(X))<=>(~tall(X)&kind(X))))&
(![X]:((~wise(X)&~curious(X))<=>~happy(X)))&
(![X]:((creative(X)<~>kind(X))=>(patient(X)|creative(X))))&
(![X]:(curious(X)=>~humble(X)))&
(![X]:((~patient(X)|~strong(X))<=>(old(X)|~patient(X))))&
(![X]:((~calm(X)<~>calm(X))=>(~creative(X)<~>generous(X))))&
(![X]:((calm(X)|~calm(X))=>(calm(X)|brave(X))))&
(![X]:(patient(X)=>tall(X)))&
(![X]:((~calm(X)&~strong(X))=>patient(X)))&
(![X]:((~strong(X)|~happy(X))=>~wise(X)))&
((?[X]:((old(X)&generous(X))))<=>(?[X]:((happy(X)|tall(X)))))&
((?[X]:((humble(X)&old(X))))=>((funny(paul)|tall(paul))))&
((~tall(fred)&~creative(fred)))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
((wise(lucy)<~>calm(lucy)))&
(?[X]:((tall(X)|curious(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:(~calm(X))) | ~calm(paul) | []
| null | 0 |
If someone is not old or not calm then mary is both not curious and quiet.
Everyone who is not generous or creative is either not kind or humble.
If paul is calm then someone is either strong or funny.
Everyone who is not calm or rich is either wise or patient.
Everyone who is either funny or not humble is both curious and happy.
Everyone who is not calm is both not generous and rich.
If alice is both not old and calm then someone is not strong and vice versa.
If someone is either generous or not patient then mary is brave or not funny.
Everyone who is either not patient or wise is curious.
If someone is tall then paul is not curious or not kind and vice versa.
If fred is old then john is not brave.
If someone is not humble then someone is not old and vice versa.
If someone is not funny or rich then lucy is both not brave and not calm and vice versa.
Everyone who is either happy or not curious is tall.
Everyone who is both brave and not brave is not generous and vice versa.
Everyone who is both not calm and not curious is both rich and quiet.
Paul is curious.
Someone is not patient or strong.
Someone is either not funny or calm.
Someone is not old or not happy. | Lucy is calm. | entailment | ((?[X]:((~old(X)|~calm(X))))=>((~curious(mary)&quiet(mary))))&
(![X]:((~generous(X)|creative(X))=>(~kind(X)<~>humble(X))))&
((calm(paul))=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((~calm(X)|rich(X))=>(wise(X)<~>patient(X))))&
(![X]:((funny(X)<~>~humble(X))=>(curious(X)&happy(X))))&
(![X]:(~calm(X)=>(~generous(X)&rich(X))))&
(((~old(alice)&calm(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:((generous(X)<~>~patient(X))))=>((brave(mary)|~funny(mary))))&
(![X]:((~patient(X)<~>wise(X))=>curious(X)))&
((?[X]:(tall(X)))<=>((~curious(paul)|~kind(paul))))&
((old(fred))=>(~brave(john)))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
((?[X]:((~funny(X)|rich(X))))<=>((~brave(lucy)&~calm(lucy))))&
(![X]:((happy(X)<~>~curious(X))=>tall(X)))&
(![X]:((brave(X)&~brave(X))<=>~generous(X)))&
(![X]:((~calm(X)&~curious(X))=>(rich(X)&quiet(X))))&
(curious(paul))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((~old(X)|~happy(X)))) | calm(lucy) | [
"p5",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 418091637105971736482796
% SZS output start Proof for 418091637105971736482796
6. ! [X0] : (~calm(X0) => (rich(X0) & ~generous(X0))) [input p5]
15. ! [X0] : ((~brave(X0) & brave(X0)) <=> ~generous(X0)) [input p14]
21. ~calm(lucy) [input hypothesis]
31. ! [X0] : ((rich(X0) & ~generous(X0)) | calm(X0)) [ennf transformation 6]
68. ! [X0] : (((~brave(X0) & brave(X0)) | generous(X0)) & (~generous(X0) | (brave(X0) | ~brave(X0)))) [nnf transformation 15]
69. ! [X0] : (((~brave(X0) & brave(X0)) | generous(X0)) & (~generous(X0) | brave(X0) | ~brave(X0))) [flattening 68]
91. ~generous(X0) | calm(X0) [cnf transformation 31]
114. brave(X0) | generous(X0) [cnf transformation 69]
115. ~brave(X0) | generous(X0) [cnf transformation 69]
122. ~calm(lucy) [cnf transformation 21]
124. 1 <=> ! [X0] : calm(X0) [avatar definition]
125. calm(X0) <- (1) [avatar component clause 124]
228. 25 <=> calm(lucy) [avatar definition]
229. ~calm(lucy) <- (~25) [avatar component clause 228]
250. generous(X0) [subsumption resolution 114,115]
280. ~25 [avatar split clause 122,228]
283. calm(X0) [resolution 91,250]
284. 1 [avatar split clause 283,124]
286. $false <- (1, ~25) [resolution 125,229]
289. ~1 | 25 [avatar contradiction clause 286]
291. $false [avatar sat refutation 280,284,289]
% SZS output end Proof for 418091637105971736482796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either generous or not wise and vice versa.
Everyone who is creative or rich is tall or not funny and vice versa.
If someone is not calm or not tall then lucy is both not strong and not old.
If someone is both patient and not curious then someone is creative or not quiet and vice versa.
Everyone who is calm is either not calm or not patient and vice versa.
Everyone who is either not tall or tall is not creative or creative and vice versa.
Everyone who is either not humble or not quiet is both calm and not quiet and vice versa.
If john is either happy or not rich then susan is tall.
If someone is either old or generous then someone is either kind or not calm.
Everyone who is not funny or wise is rich or not humble and vice versa.
Everyone who is not happy is both not wise and not kind.
If fred is both patient and old then fred is both not curious and wise and vice versa.
Everyone who is either rich or strong is not wise.
If john is not calm then someone is both not strong and funny.
Everyone who is both not tall and not calm is both curious and old and vice versa.
Fred is either tall or not patient.
Someone is either generous or humble.
Fred is either strong or kind.
Mary is not patient or humble.
Someone is not curious or funny.
Lucy is both not tall and not old. | Fred is quiet. | entailment | (![X]:(~generous(X)<=>(generous(X)<~>~wise(X))))&
(![X]:((creative(X)|rich(X))<=>(tall(X)|~funny(X))))&
((?[X]:((~calm(X)|~tall(X))))=>((~strong(lucy)&~old(lucy))))&
((?[X]:((patient(X)&~curious(X))))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(calm(X)<=>(~calm(X)<~>~patient(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~creative(X)|creative(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(calm(X)&~quiet(X))))&
(((happy(john)<~>~rich(john)))=>(tall(susan)))&
((?[X]:((old(X)<~>generous(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)|~humble(X))))&
(![X]:(~happy(X)=>(~wise(X)&~kind(X))))&
(((patient(fred)&old(fred)))<=>((~curious(fred)&wise(fred))))&
(![X]:((rich(X)<~>strong(X))=>~wise(X)))&
((~calm(john))=>(?[X]:((~strong(X)&funny(X)))))&
(![X]:((~tall(X)&~calm(X))<=>(curious(X)&old(X))))&
((tall(fred)<~>~patient(fred)))&
(?[X]:((generous(X)<~>humble(X))))&
((strong(fred)<~>kind(fred)))&
((~patient(mary)|humble(mary)))&
(?[X]:((~curious(X)|funny(X))))&
((~tall(lucy)&~old(lucy))) | quiet(fred) | [
"p3",
"p4",
"hypothesis"
]
| % SZS status Unsatisfiable for 8525430804228592145758408
% SZS output start Proof for 8525430804228592145758408
4. ? [X0] : (~curious(X0) & patient(X0)) <=> ? [X0] : (~quiet(X0) | creative(X0)) [input p3]
5. ! [X0] : (calm(X0) <=> (~calm(X0) <~> ~patient(X0))) [input p4]
22. ~quiet(fred) [input hypothesis]
23. ? [X0] : (~curious(X0) & patient(X0)) <=> ? [X1] : (~quiet(X1) | creative(X1)) [rectify 4]
34. (? [X0] : (~curious(X0) & patient(X0)) | ! [X1] : (quiet(X1) & ~creative(X1))) & (? [X1] : (~quiet(X1) | creative(X1)) | ! [X0] : (curious(X0) | ~patient(X0))) [nnf transformation 23]
35. (? [X0] : (~curious(X0) & patient(X0)) | ! [X1] : (quiet(X1) & ~creative(X1))) & (? [X2] : (~quiet(X2) | creative(X2)) | ! [X3] : (curious(X3) | ~patient(X3))) [rectify 34]
36. ? [X0] : (~curious(X0) & patient(X0)) => (~curious(sK0) & patient(sK0)) [choice axiom]
37. ? [X2] : (~quiet(X2) | creative(X2)) => (~quiet(sK1) | creative(sK1)) [choice axiom]
38. ((~curious(sK0) & patient(sK0)) | ! [X1] : (quiet(X1) & ~creative(X1))) & ((~quiet(sK1) | creative(sK1)) | ! [X3] : (curious(X3) | ~patient(X3))) [skolemisation 35,37,36]
39. ! [X0] : ((calm(X0) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | ~calm(X0))) [nnf transformation 5]
79. patient(sK0) | quiet(X1) [cnf transformation 38]
82. ~patient(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 39]
84. calm(X0) | ~patient(X0) | calm(X0) [cnf transformation 39]
132. ~quiet(fred) [cnf transformation 22]
137. ~patient(X0) | ~calm(X0) [duplicate literal removal 82]
138. calm(X0) | ~patient(X0) [duplicate literal removal 84]
161. 5 <=> ! [X1] : quiet(X1) [avatar definition]
162. quiet(X1) <- (5) [avatar component clause 161]
173. 8 <=> patient(sK0) [avatar definition]
175. patient(sK0) <- (8) [avatar component clause 173]
176. 5 | 8 [avatar split clause 79,173,161]
190. ~patient(X0) [subsumption resolution 137,138]
270. $false <- (5) [resolution 162,132]
271. ~5 [avatar contradiction clause 270]
272. $false <- (8) [subsumption resolution 175,190]
273. ~8 [avatar contradiction clause 272]
274. $false [avatar sat refutation 176,271,273]
% SZS output end Proof for 8525430804228592145758408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not humble is either old or happy.
If someone is generous or kind then someone is calm and vice versa.
If mary is either brave or calm then fred is not humble or not generous and vice versa.
If someone is either not curious or not quiet then john is not strong or not brave.
Everyone who is either not tall or not wise is calm or strong.
Everyone who is either funny or not brave is both generous and not rich.
If someone is not humble then susan is either not generous or not strong and vice versa.
If paul is either calm or patient then someone is not quiet.
If fred is either not creative or not generous then someone is not generous or quiet and vice versa.
Everyone who is either not rich or wise is either quiet or not curious and vice versa.
Everyone who is both creative and patient is either rich or creative and vice versa.
Everyone who is either funny or not calm is not funny and vice versa.
If susan is not wise or not creative then lucy is either tall or not kind and vice versa.
Everyone who is wise or not wise is both wise and humble and vice versa.
Everyone who is creative is both not happy and not kind.
Everyone who is either not humble or not tall is either kind or not humble.
Fred is not wise or not calm.
Someone is strong or not curious.
Someone is wise.
Someone is not curious.
Paul is humble or not tall.
Someone is funny.
Alice is both creative and brave. | Fred is old. | entailment | (![X]:((wise(X)|~humble(X))=>(old(X)<~>happy(X))))&
((?[X]:((generous(X)|kind(X))))<=>(?[X]:(calm(X))))&
(((brave(mary)<~>calm(mary)))<=>((~humble(fred)|~generous(fred))))&
((?[X]:((~curious(X)<~>~quiet(X))))=>((~strong(john)|~brave(john))))&
(![X]:((~tall(X)<~>~wise(X))=>(calm(X)|strong(X))))&
(![X]:((funny(X)<~>~brave(X))=>(generous(X)&~rich(X))))&
((?[X]:(~humble(X)))<=>((~generous(susan)<~>~strong(susan))))&
(((calm(paul)<~>patient(paul)))=>(?[X]:(~quiet(X))))&
(((~creative(fred)<~>~generous(fred)))<=>(?[X]:((~generous(X)|quiet(X)))))&
(![X]:((~rich(X)<~>wise(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((creative(X)&patient(X))<=>(rich(X)<~>creative(X))))&
(![X]:((funny(X)<~>~calm(X))<=>~funny(X)))&
(((~wise(susan)|~creative(susan)))<=>((tall(lucy)<~>~kind(lucy))))&
(![X]:((wise(X)|~wise(X))<=>(wise(X)&humble(X))))&
(![X]:(creative(X)=>(~happy(X)&~kind(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(kind(X)<~>~humble(X))))&
((~wise(fred)|~calm(fred)))&
(?[X]:((strong(X)|~curious(X))))&
(?[X]:(wise(X)))&
(?[X]:(~curious(X)))&
((humble(paul)|~tall(paul)))&
(?[X]:(funny(X)))&
((creative(alice)&brave(alice))) | old(fred) | [
"p0",
"p1",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2158608467234327843856360
% SZS output start Proof for 2158608467234327843856360
1. ! [X0] : ((~humble(X0) | wise(X0)) => (old(X0) <~> happy(X0))) [input p0]
2. ? [X0] : (kind(X0) | generous(X0)) <=> ? [X0] : calm(X0) [input p1]
9. (~creative(fred) <~> ~generous(fred)) <=> ? [X0] : (quiet(X0) | ~generous(X0)) [input p8]
12. ! [X0] : ((funny(X0) <~> ~calm(X0)) <=> ~funny(X0)) [input p11]
14. ! [X0] : ((~wise(X0) | wise(X0)) <=> (humble(X0) & wise(X0))) [input p13]
15. ! [X0] : (creative(X0) => (~kind(X0) & ~happy(X0))) [input p14]
24. ~old(fred) [input hypothesis]
25. ? [X0] : (kind(X0) | generous(X0)) <=> ? [X1] : calm(X1) [rectify 2]
26. ! [X0] : ((old(X0) <~> happy(X0)) | (humble(X0) & ~wise(X0))) [ennf transformation 1]
33. ! [X0] : ((~kind(X0) & ~happy(X0)) | ~creative(X0)) [ennf transformation 15]
35. ! [X0] : (((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (humble(X0) & ~wise(X0))) [nnf transformation 26]
36. (? [X0] : (kind(X0) | generous(X0)) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : (~kind(X0) & ~generous(X0))) [nnf transformation 25]
37. (? [X0] : (kind(X0) | generous(X0)) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : (~kind(X3) & ~generous(X3))) [rectify 36]
38. ? [X0] : (kind(X0) | generous(X0)) => (kind(sK0) | generous(sK0)) [choice axiom]
39. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
40. ((kind(sK0) | generous(sK0)) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : (~kind(X3) & ~generous(X3))) [skolemisation 37,39,38]
53. (((generous(fred) | creative(fred)) & (~generous(fred) | ~creative(fred))) | ! [X0] : (~quiet(X0) & generous(X0))) & (? [X0] : (quiet(X0) | ~generous(X0)) | ((~creative(fred) | generous(fred)) & (~generous(fred) | creative(fred)))) [nnf transformation 9]
54. (((generous(fred) | creative(fred)) & (~generous(fred) | ~creative(fred))) | ! [X0] : (~quiet(X0) & generous(X0))) & (? [X1] : (quiet(X1) | ~generous(X1)) | ((~creative(fred) | generous(fred)) & (~generous(fred) | creative(fred)))) [rectify 53]
55. ? [X1] : (quiet(X1) | ~generous(X1)) => (quiet(sK4) | ~generous(sK4)) [choice axiom]
56. (((generous(fred) | creative(fred)) & (~generous(fred) | ~creative(fred))) | ! [X0] : (~quiet(X0) & generous(X0))) & ((quiet(sK4) | ~generous(sK4)) | ((~creative(fred) | generous(fred)) & (~generous(fred) | creative(fred)))) [skolemisation 54,55]
60. ! [X0] : ((((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | funny(X0)) & (~funny(X0) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0))))) [nnf transformation 12]
63. ! [X0] : (((~wise(X0) | wise(X0)) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | (wise(X0) & ~wise(X0)))) [nnf transformation 14]
64. ! [X0] : ((~wise(X0) | wise(X0) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | (wise(X0) & ~wise(X0)))) [flattening 63]
74. ~wise(X0) | old(X0) | happy(X0) [cnf transformation 35]
78. calm(sK1) | ~generous(X3) [cnf transformation 40]
105. generous(fred) | creative(fred) | generous(X0) [cnf transformation 56]
121. ~funny(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 60]
123. ~calm(X0) | funny(X0) | funny(X0) [cnf transformation 60]
132. wise(X0) | wise(X0) [cnf transformation 64]
136. ~creative(X0) | ~happy(X0) [cnf transformation 33]
150. ~old(fred) [cnf transformation 24]
153. wise(X0) [duplicate literal removal 132]
155. ~funny(X0) | ~calm(X0) [duplicate literal removal 121]
156. ~calm(X0) | funny(X0) [duplicate literal removal 123]
160. 1 <=> ! [X1] : ~calm(X1) [avatar definition]
161. ~calm(X1) <- (1) [avatar component clause 160]
175. 5 <=> calm(sK1) [avatar definition]
177. calm(sK1) <- (5) [avatar component clause 175]
180. 6 <=> ! [X3] : ~generous(X3) [avatar definition]
181. ~generous(X3) <- (6) [avatar component clause 180]
182. 6 | 5 [avatar split clause 78,175,180]
184. 7 <=> generous(fred) [avatar definition]
186. generous(fred) <- (7) [avatar component clause 184]
258. 23 <=> creative(fred) [avatar definition]
260. creative(fred) <- (23) [avatar component clause 258]
263. 24 <=> ! [X0] : generous(X0) [avatar definition]
264. generous(X0) <- (24) [avatar component clause 263]
265. 24 | 23 | 7 [avatar split clause 105,184,258,263]
279. ~calm(X0) [subsumption resolution 155,156]
280. 1 [avatar split clause 279,160]
328. $false <- (1, 5) [resolution 177,161]
329. ~1 | ~5 [avatar contradiction clause 328]
330. $false <- (6, 7) [resolution 186,181]
331. ~6 | ~7 [avatar contradiction clause 330]
333. ~happy(fred) <- (23) [resolution 136,260]
336. happy(X0) | old(X0) [resolution 74,153]
340. old(fred) <- (23) [resolution 336,333]
341. $false <- (23) [subsumption resolution 340,150]
342. ~23 [avatar contradiction clause 341]
343. $false <- (6, 24) [subsumption resolution 264,181]
344. ~6 | ~24 [avatar contradiction clause 343]
345. $false [avatar sat refutation 182,265,280,329,331,342,344]
% SZS output end Proof for 2158608467234327843856360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both rich and curious then someone is both happy and quiet. If susan is both not old and generous then susan is strong or not humble. Everyone who is not patient or not calm is strong or old and vice versa. If someone is either not kind or not strong then someone is not creative. If susan is both not tall and not brave then someone is either not humble or not calm and vice versa. If lucy is either not humble or not brave then john is funny. If alice is quiet then susan is not calm and vice versa. Everyone who is both not funny and creative is humble or not brave and vice versa. Everyone who is calm or creative is both not curious and not brave and vice versa. Everyone who is either creative or quiet is both happy and tall and vice versa. Everyone who is either patient or not curious is either rich or brave. If mary is both not humble and not creative then mary is strong. Everyone who is either brave or not creative is brave or not wise and vice versa. Everyone who is either strong or not kind is either kind or wise. If someone is calm or funny then someone is not humble. If someone is happy then someone is not tall and vice versa. Fred is both not patient and not humble. Susan is both not brave and not strong. Someone is either not curious or humble. Mary is either not curious or quiet. Someone is either calm or tall. | Fred is not strong. | entailment | ((?[X]:((rich(X)&curious(X))))=>(?[X]:((happy(X)&quiet(X)))))&
(((~old(susan)&generous(susan)))=>((strong(susan)|~humble(susan))))&
(![X]:((~patient(X)|~calm(X))<=>(strong(X)|old(X))))&
((?[X]:((~kind(X)<~>~strong(X))))=>(?[X]:(~creative(X))))&
(((~tall(susan)&~brave(susan)))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
(((~humble(lucy)<~>~brave(lucy)))=>(funny(john)))&
((quiet(alice))<=>(~calm(susan)))&
(![X]:((~funny(X)&creative(X))<=>(humble(X)|~brave(X))))&
(![X]:((calm(X)|creative(X))<=>(~curious(X)&~brave(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(happy(X)&tall(X))))&
(![X]:((patient(X)<~>~curious(X))=>(rich(X)<~>brave(X))))&
(((~humble(mary)&~creative(mary)))=>(strong(mary)))&
(![X]:((brave(X)<~>~creative(X))<=>(brave(X)|~wise(X))))&
(![X]:((strong(X)<~>~kind(X))=>(kind(X)<~>wise(X))))&
((?[X]:((calm(X)|funny(X))))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~tall(X))))&
((~patient(fred)&~humble(fred)))&
((~brave(susan)&~strong(susan)))&
(?[X]:((~curious(X)<~>humble(X))))&
((~curious(mary)<~>quiet(mary)))&
(?[X]:((calm(X)<~>tall(X)))) | ~strong(fred) | [
"p3",
"p7",
"p8",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 827520638880367238250092
% SZS output start Proof for 827520638880367238250092
4. ? [X0] : (~kind(X0) <~> ~strong(X0)) => ? [X0] : ~creative(X0) [input p3]
8. ! [X0] : ((creative(X0) & ~funny(X0)) <=> (~brave(X0) | humble(X0))) [input p7]
9. ! [X0] : ((creative(X0) | calm(X0)) <=> (~brave(X0) & ~curious(X0))) [input p8]
13. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> (~wise(X0) | brave(X0))) [input p12]
14. ! [X0] : ((strong(X0) <~> ~kind(X0)) => (kind(X0) <~> wise(X0))) [input p13]
22. strong(fred) [input hypothesis]
24. ? [X0] : (~kind(X0) <~> ~strong(X0)) => ? [X1] : ~creative(X1) [rectify 4]
29. ? [X1] : ~creative(X1) | ! [X0] : (~kind(X0) <=> ~strong(X0)) [ennf transformation 24]
34. ! [X0] : ((kind(X0) <~> wise(X0)) | (strong(X0) <=> ~kind(X0))) [ennf transformation 14]
41. ? [X1] : ~creative(X1) | ! [X0] : ((~kind(X0) | strong(X0)) & (~strong(X0) | kind(X0))) [nnf transformation 29]
42. ? [X0] : ~creative(X0) | ! [X1] : ((~kind(X1) | strong(X1)) & (~strong(X1) | kind(X1))) [rectify 41]
43. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
44. ~creative(sK1) | ! [X1] : ((~kind(X1) | strong(X1)) & (~strong(X1) | kind(X1))) [skolemisation 42,43]
52. ! [X0] : (((creative(X0) & ~funny(X0)) | (brave(X0) & ~humble(X0))) & ((~brave(X0) | humble(X0)) | (~creative(X0) | funny(X0)))) [nnf transformation 8]
53. ! [X0] : (((creative(X0) & ~funny(X0)) | (brave(X0) & ~humble(X0))) & (~brave(X0) | humble(X0) | ~creative(X0) | funny(X0))) [flattening 52]
54. ! [X0] : (((creative(X0) | calm(X0)) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | (~creative(X0) & ~calm(X0)))) [nnf transformation 9]
55. ! [X0] : ((creative(X0) | calm(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | (~creative(X0) & ~calm(X0)))) [flattening 54]
59. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 13]
60. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [flattening 59]
61. ! [X0] : (((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) [nnf transformation 34]
83. ~creative(sK1) | ~strong(X1) | kind(X1) [cnf transformation 44]
99. brave(X0) | creative(X0) [cnf transformation 53]
103. ~brave(X0) | ~creative(X0) [cnf transformation 55]
119. ~creative(X0) | brave(X0) | wise(X0) [cnf transformation 60]
120. creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
124. ~wise(X0) | ~kind(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 61]
140. strong(fred) [cnf transformation 22]
142. ~wise(X0) | ~kind(X0) | ~strong(X0) [duplicate literal removal 124]
144. creative(X0) | ~brave(X0) [duplicate literal removal 120]
162. 5 <=> creative(sK1) [avatar definition]
164. ~creative(sK1) <- (~5) [avatar component clause 162]
167. 6 <=> ! [X1] : (~strong(X1) | kind(X1)) [avatar definition]
168. ~strong(X1) | kind(X1) <- (6) [avatar component clause 167]
169. 6 | ~5 [avatar split clause 83,162,167]
233. ~brave(X0) [subsumption resolution 144,103]
234. ~creative(X0) | wise(X0) [subsumption resolution 119,233]
297. creative(X0) [resolution 99,233]
300. $false <- (~5) [resolution 297,164]
301. 5 [avatar contradiction clause 300]
316. wise(X0) [resolution 234,297]
364. ~kind(X1) | ~strong(X1) [resolution 142,316]
367. ~strong(X1) <- (6) [subsumption resolution 364,168]
370. $false <- (6) [resolution 367,140]
373. ~6 [avatar contradiction clause 370]
374. $false [avatar sat refutation 169,301,373]
% SZS output end Proof for 827520638880367238250092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not calm is both not happy and patient.
Everyone who is creative is not wise or tall and vice versa.
If john is not patient then susan is either not curious or creative and vice versa.
If someone is both not funny and not generous then paul is strong or brave and vice versa.
If someone is humble then someone is both kind and not funny and vice versa.
Everyone who is not happy or strong is either not strong or not patient.
Everyone who is not funny is either not patient or strong.
Everyone who is not humble is calm or wise.
Everyone who is brave is not creative.
Everyone who is not happy is not strong or not calm and vice versa.
Everyone who is both brave and not patient is wise or brave.
If someone is not humble then someone is rich or generous.
Everyone who is generous is not quiet.
If alice is tall then fred is not quiet and vice versa.
Mary is not old or not curious.
Someone is either not funny or generous.
Fred is not kind.
Alice is brave or not funny.
Mary is both not kind and creative. | Mary is humble. | contradiction | (![X]:((~quiet(X)|~calm(X))=>(~happy(X)&patient(X))))&
(![X]:(creative(X)<=>(~wise(X)|tall(X))))&
((~patient(john))<=>((~curious(susan)<~>creative(susan))))&
((?[X]:((~funny(X)&~generous(X))))<=>((strong(paul)|brave(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((~happy(X)|strong(X))=>(~strong(X)<~>~patient(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>strong(X))))&
(![X]:(~humble(X)=>(calm(X)|wise(X))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~calm(X))))&
(![X]:((brave(X)&~patient(X))=>(wise(X)|brave(X))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:(generous(X)=>~quiet(X)))&
((tall(alice))<=>(~quiet(fred)))&
((~old(mary)|~curious(mary)))&
(?[X]:((~funny(X)<~>generous(X))))&
(~kind(fred))&
((brave(alice)|~funny(alice)))&
((~kind(mary)&creative(mary))) | humble(mary) | [
"p4",
"p5",
"p6",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 8768725833466602295963844
% SZS output start Proof for 8768725833466602295963844
5. ? [X0] : humble(X0) <=> ? [X0] : (~funny(X0) & kind(X0)) [input p4]
6. ! [X0] : ((strong(X0) | ~happy(X0)) => (~strong(X0) <~> ~patient(X0))) [input p5]
7. ! [X0] : (~funny(X0) => (~patient(X0) <~> strong(X0))) [input p6]
10. ! [X0] : (~happy(X0) <=> (~calm(X0) | ~strong(X0))) [input p9]
20. humble(mary) [input hypothesis]
21. ? [X0] : humble(X0) <=> ? [X1] : (~funny(X1) & kind(X1)) [rectify 5]
26. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | (~strong(X0) & happy(X0))) [ennf transformation 6]
27. ! [X0] : ((~patient(X0) <~> strong(X0)) | funny(X0)) [ennf transformation 7]
42. (? [X0] : humble(X0) | ! [X1] : (funny(X1) | ~kind(X1))) & (? [X1] : (~funny(X1) & kind(X1)) | ! [X0] : ~humble(X0)) [nnf transformation 21]
43. (? [X0] : humble(X0) | ! [X1] : (funny(X1) | ~kind(X1))) & (? [X2] : (~funny(X2) & kind(X2)) | ! [X3] : ~humble(X3)) [rectify 42]
44. ? [X0] : humble(X0) => humble(sK1) [choice axiom]
45. ? [X2] : (~funny(X2) & kind(X2)) => (~funny(sK2) & kind(sK2)) [choice axiom]
46. (humble(sK1) | ! [X1] : (funny(X1) | ~kind(X1))) & ((~funny(sK2) & kind(sK2)) | ! [X3] : ~humble(X3)) [skolemisation 43,45,44]
47. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~strong(X0) & happy(X0))) [nnf transformation 26]
48. ! [X0] : (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | funny(X0)) [nnf transformation 27]
49. ! [X0] : ((~happy(X0) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | happy(X0))) [nnf transformation 10]
50. ! [X0] : ((~happy(X0) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | happy(X0))) [flattening 49]
72. ~funny(sK2) | ~humble(X3) [cnf transformation 46]
75. ~patient(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 47]
76. strong(X0) | patient(X0) | happy(X0) [cnf transformation 47]
78. strong(X0) | ~patient(X0) | funny(X0) [cnf transformation 48]
79. ~strong(X0) | patient(X0) | funny(X0) [cnf transformation 48]
83. ~happy(X0) | strong(X0) [cnf transformation 50]
95. humble(mary) [cnf transformation 20]
96. ~strong(X0) | ~patient(X0) [duplicate literal removal 75]
146. 11 <=> ! [X3] : ~humble(X3) [avatar definition]
147. ~humble(X3) <- (11) [avatar component clause 146]
149. 12 <=> funny(sK2) [avatar definition]
151. ~funny(sK2) <- (~12) [avatar component clause 149]
152. 11 | ~12 [avatar split clause 72,149,146]
158. ~strong(X0) | funny(X0) [subsumption resolution 79,96]
159. ~patient(X0) | funny(X0) [subsumption resolution 78,96]
189. $false <- (11) [resolution 147,95]
190. ~11 [avatar contradiction clause 189]
204. patient(X0) | happy(X0) | funny(X0) [resolution 76,158]
206. funny(X0) | happy(X0) [subsumption resolution 204,159]
216. happy(sK2) <- (~12) [resolution 206,151]
226. strong(sK2) <- (~12) [resolution 216,83]
248. funny(sK2) <- (~12) [resolution 226,158]
250. $false <- (~12) [subsumption resolution 248,151]
251. 12 [avatar contradiction clause 250]
252. $false [avatar sat refutation 152,190,251]
% SZS output end Proof for 8768725833466602295963844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not tall and not humble then someone is brave or kind.
If mary is strong or calm then lucy is either calm or not kind and vice versa.
If mary is brave or not curious then someone is both not old and not generous and vice versa.
Everyone who is both patient and curious is either old or not old and vice versa.
Everyone who is both not old and not kind is not funny or not creative and vice versa.
Everyone who is not humble or wise is both tall and not kind and vice versa.
Everyone who is either not happy or not tall is curious.
Everyone who is both not generous and generous is both strong and not tall and vice versa.
Everyone who is either patient or not happy is either happy or not funny.
If someone is either kind or generous then someone is both funny and not quiet and vice versa.
If susan is either creative or not brave then susan is either generous or not kind.
If lucy is kind then paul is funny and vice versa.
If someone is both rich and kind then someone is quiet and vice versa.
Everyone who is both kind and tall is patient.
Everyone who is both not old and not calm is tall.
If someone is not kind then someone is not funny or generous and vice versa.
Someone is either not old or not kind.
Lucy is either curious or happy.
Lucy is either creative or not generous.
Paul is either not kind or quiet.
Someone is both not old and quiet.
Someone is not old.
Someone is either old or wise. | Paul is brave. | neutral | (((~tall(susan)&~humble(susan)))=>(?[X]:((brave(X)|kind(X)))))&
(((strong(mary)|calm(mary)))<=>((calm(lucy)<~>~kind(lucy))))&
(((brave(mary)|~curious(mary)))<=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:((patient(X)&curious(X))<=>(old(X)<~>~old(X))))&
(![X]:((~old(X)&~kind(X))<=>(~funny(X)|~creative(X))))&
(![X]:((~humble(X)|wise(X))<=>(tall(X)&~kind(X))))&
(![X]:((~happy(X)<~>~tall(X))=>curious(X)))&
(![X]:((~generous(X)&generous(X))<=>(strong(X)&~tall(X))))&
(![X]:((patient(X)<~>~happy(X))=>(happy(X)<~>~funny(X))))&
((?[X]:((kind(X)<~>generous(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(((creative(susan)<~>~brave(susan)))=>((generous(susan)<~>~kind(susan))))&
((kind(lucy))<=>(funny(paul)))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)&tall(X))=>patient(X)))&
(![X]:((~old(X)&~calm(X))=>tall(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(?[X]:((~old(X)<~>~kind(X))))&
((curious(lucy)<~>happy(lucy)))&
((creative(lucy)<~>~generous(lucy)))&
((~kind(paul)<~>quiet(paul)))&
(?[X]:((~old(X)&quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:((old(X)<~>wise(X)))) | brave(paul) | []
| null | 0 |
Everyone who is curious is either kind or not kind.
Everyone who is either not wise or calm is either curious or not funny and vice versa.
Everyone who is patient is not funny.
Everyone who is not curious or not kind is kind.
If someone is both not kind and funny then someone is not quiet or curious.
If someone is both not quiet and calm then someone is not patient or not generous and vice versa.
If someone is both quiet and not old then paul is both not curious and not wise and vice versa.
Everyone who is not wise or not calm is both happy and kind.
If alice is both brave and not tall then fred is either brave or not humble and vice versa.
Everyone who is old or not calm is either not kind or not patient.
Everyone who is not old is not happy and vice versa.
Everyone who is not humble is either not rich or funny.
If mary is both old and not rich then lucy is calm and vice versa.
If fred is both not kind and curious then fred is calm.
If paul is both not calm and not funny then someone is both humble and happy.
If mary is both funny and brave then someone is either not quiet or generous and vice versa.
Someone is both not generous and not strong.
Someone is not generous.
Someone is either not wise or not strong.
Alice is not happy.
Someone is both not brave and generous.
Someone is not kind or tall.
Lucy is either happy or not brave.
Someone is either not kind or rich. | Alice is not wise. | contradiction | (![X]:(curious(X)=>(kind(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(curious(X)<~>~funny(X))))&
(![X]:(patient(X)=>~funny(X)))&
(![X]:((~curious(X)|~kind(X))=>kind(X)))&
((?[X]:((~kind(X)&funny(X))))=>(?[X]:((~quiet(X)|curious(X)))))&
((?[X]:((~quiet(X)&calm(X))))<=>(?[X]:((~patient(X)|~generous(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>((~curious(paul)&~wise(paul))))&
(![X]:((~wise(X)|~calm(X))=>(happy(X)&kind(X))))&
(((brave(alice)&~tall(alice)))<=>((brave(fred)<~>~humble(fred))))&
(![X]:((old(X)|~calm(X))=>(~kind(X)<~>~patient(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(~humble(X)=>(~rich(X)<~>funny(X))))&
(((old(mary)&~rich(mary)))<=>(calm(lucy)))&
(((~kind(fred)&curious(fred)))=>(calm(fred)))&
(((~calm(paul)&~funny(paul)))=>(?[X]:((humble(X)&happy(X)))))&
(((funny(mary)&brave(mary)))<=>(?[X]:((~quiet(X)<~>generous(X)))))&
(?[X]:((~generous(X)&~strong(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~wise(X)<~>~strong(X))))&
(~happy(alice))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:((~kind(X)|tall(X))))&
((happy(lucy)<~>~brave(lucy)))&
(?[X]:((~kind(X)<~>rich(X)))) | ~wise(alice) | [
"p7",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 1298036072470469798542597
% SZS output start Proof for 1298036072470469798542597
8. ! [X0] : ((~calm(X0) | ~wise(X0)) => (kind(X0) & happy(X0))) [input p7]
20. ~happy(alice) [input p19]
25. ~wise(alice) [input hypothesis]
32. ! [X0] : ((kind(X0) & happy(X0)) | (calm(X0) & wise(X0))) [ennf transformation 8]
106. happy(X0) | wise(X0) [cnf transformation 32]
141. ~happy(alice) [cnf transformation 20]
149. ~wise(alice) [cnf transformation 25]
311. wise(alice) [resolution 106,141]
313. $false [subsumption resolution 311,149]
% SZS output end Proof for 1298036072470469798542597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not creative then fred is rich and vice versa.
If someone is not funny or brave then fred is both funny and creative and vice versa.
If someone is curious or generous then john is not generous or tall and vice versa.
Everyone who is both curious and strong is creative.
Everyone who is not creative or not rich is rich or not humble.
Everyone who is either patient or not generous is kind or not happy and vice versa.
Everyone who is curious is kind and vice versa.
If someone is not calm then alice is tall or old and vice versa.
If mary is wise or rich then susan is either not brave or not patient.
If someone is not creative or not old then someone is not rich.
If alice is not calm then someone is wise.
If paul is funny then someone is wise.
If someone is happy then someone is both not tall and not humble and vice versa.
If lucy is not calm or wise then lucy is either creative or humble.
Everyone who is not brave is not rich.
If mary is both not wise and curious then someone is either calm or not tall and vice versa.
Paul is not creative.
Someone is not kind.
Someone is not rich or not creative.
Someone is happy.
Someone is either not patient or generous.
Someone is not patient or not kind.
Mary is both not tall and not generous.
Fred is both kind and humble. | Fred is brave. | entailment | ((?[X]:((~old(X)|~creative(X))))<=>(rich(fred)))&
((?[X]:((~funny(X)|brave(X))))<=>((funny(fred)&creative(fred))))&
((?[X]:((curious(X)|generous(X))))<=>((~generous(john)|tall(john))))&
(![X]:((curious(X)&strong(X))=>creative(X)))&
(![X]:((~creative(X)|~rich(X))=>(rich(X)|~humble(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(kind(X)|~happy(X))))&
(![X]:(curious(X)<=>kind(X)))&
((?[X]:(~calm(X)))<=>((tall(alice)|old(alice))))&
(((wise(mary)|rich(mary)))=>((~brave(susan)<~>~patient(susan))))&
((?[X]:((~creative(X)|~old(X))))=>(?[X]:(~rich(X))))&
((~calm(alice))=>(?[X]:(wise(X))))&
((funny(paul))=>(?[X]:(wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~tall(X)&~humble(X)))))&
(((~calm(lucy)|wise(lucy)))=>((creative(lucy)<~>humble(lucy))))&
(![X]:(~brave(X)=>~rich(X)))&
(((~wise(mary)&curious(mary)))<=>(?[X]:((calm(X)<~>~tall(X)))))&
(~creative(paul))&
(?[X]:(~kind(X)))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:(happy(X)))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:((~patient(X)|~kind(X))))&
((~tall(mary)&~generous(mary)))&
((kind(fred)&humble(fred))) | brave(fred) | [
"p0",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 3568329448470854135168834
% SZS output start Proof for 3568329448470854135168834
1. ? [X0] : (~creative(X0) | ~old(X0)) <=> rich(fred) [input p0]
15. ! [X0] : (~brave(X0) => ~rich(X0)) [input p14]
17. ~creative(paul) [input p16]
25. ~brave(fred) [input hypothesis]
36. ! [X0] : (~rich(X0) | brave(X0)) [ennf transformation 15]
37. (? [X0] : (~creative(X0) | ~old(X0)) | ~rich(fred)) & (rich(fred) | ! [X0] : (creative(X0) & old(X0))) [nnf transformation 1]
38. (? [X0] : (~creative(X0) | ~old(X0)) | ~rich(fred)) & (rich(fred) | ! [X1] : (creative(X1) & old(X1))) [rectify 37]
39. ? [X0] : (~creative(X0) | ~old(X0)) => (~creative(sK0) | ~old(sK0)) [choice axiom]
40. ((~creative(sK0) | ~old(sK0)) | ~rich(fred)) & (rich(fred) | ! [X1] : (creative(X1) & old(X1))) [skolemisation 38,39]
90. rich(fred) | creative(X1) [cnf transformation 40]
129. ~rich(X0) | brave(X0) [cnf transformation 36]
136. ~creative(paul) [cnf transformation 17]
147. ~brave(fred) [cnf transformation 25]
150. 1 <=> rich(fred) [avatar definition]
151. rich(fred) <- (1) [avatar component clause 150]
163. 4 <=> ! [X1] : creative(X1) [avatar definition]
164. creative(X1) <- (4) [avatar component clause 163]
165. 4 | 1 [avatar split clause 90,150,163]
378. $false <- (4) [resolution 164,136]
379. ~4 [avatar contradiction clause 378]
386. brave(fred) <- (1) [resolution 129,151]
387. $false <- (1) [subsumption resolution 386,147]
388. ~1 [avatar contradiction clause 387]
389. $false [avatar sat refutation 165,379,388]
% SZS output end Proof for 3568329448470854135168834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and wise is either not curious or not old.
If someone is not happy then someone is not patient or not generous and vice versa.
Everyone who is both not calm and strong is not patient and vice versa.
If mary is patient or not humble then mary is both not generous and calm.
Everyone who is generous is both calm and not wise.
If john is either not quiet or wise then paul is not happy and vice versa.
If someone is not creative then lucy is not patient.
If someone is not calm or not wise then fred is generous.
Everyone who is both happy and quiet is calm or rich.
If paul is happy or not funny then someone is not humble or not tall.
If someone is not curious then someone is not creative.
Everyone who is humble or brave is not rich.
If john is both rich and not quiet then someone is creative or not curious.
Everyone who is either not patient or calm is not generous.
Everyone who is both wise and funny is both not wise and not humble and vice versa.
If fred is both kind and not humble then susan is funny and vice versa.
Lucy is kind.
Someone is not happy.
Lucy is curious or not tall.
Someone is either not humble or not rich.
Alice is not happy.
Alice is humble or kind. | Fred is generous. | contradiction | (![X]:((quiet(X)&wise(X))=>(~curious(X)<~>~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(((patient(mary)|~humble(mary)))=>((~generous(mary)&calm(mary))))&
(![X]:(generous(X)=>(calm(X)&~wise(X))))&
(((~quiet(john)<~>wise(john)))<=>(~happy(paul)))&
((?[X]:(~creative(X)))=>(~patient(lucy)))&
((?[X]:((~calm(X)|~wise(X))))=>(generous(fred)))&
(![X]:((happy(X)&quiet(X))=>(calm(X)|rich(X))))&
(((happy(paul)|~funny(paul)))=>(?[X]:((~humble(X)|~tall(X)))))&
((?[X]:(~curious(X)))=>(?[X]:(~creative(X))))&
(![X]:((humble(X)|brave(X))=>~rich(X)))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(((kind(fred)&~humble(fred)))<=>(funny(susan)))&
(kind(lucy))&
(?[X]:(~happy(X)))&
((curious(lucy)|~tall(lucy)))&
(?[X]:((~humble(X)<~>~rich(X))))&
(~happy(alice))&
((humble(alice)|kind(alice))) | generous(fred) | [
"p2",
"p4",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5916480075068958338197200
% SZS output start Proof for 5916480075068958338197200
3. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p2]
5. ! [X0] : (generous(X0) => (~wise(X0) & calm(X0))) [input p4]
14. ! [X0] : ((~patient(X0) <~> calm(X0)) => ~generous(X0)) [input p13]
23. generous(fred) [input hypothesis]
32. ! [X0] : ((~wise(X0) & calm(X0)) | ~generous(X0)) [ennf transformation 5]
41. ! [X0] : (~generous(X0) | (~patient(X0) <=> calm(X0))) [ennf transformation 14]
48. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 3]
49. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 48]
56. ! [X0] : (~generous(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) [nnf transformation 41]
72. ~calm(X0) | patient(X0) [cnf transformation 49]
78. calm(X0) | ~generous(X0) [cnf transformation 32]
92. ~generous(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 56]
106. generous(fred) [cnf transformation 23]
210. ~generous(X0) | ~calm(X0) [subsumption resolution 92,72]
211. ~generous(X0) [subsumption resolution 210,78]
245. $false [subsumption resolution 106,211]
% SZS output end Proof for 5916480075068958338197200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both brave and happy then susan is kind or not humble.
Everyone who is both creative and not generous is generous.
Everyone who is both tall and wise is both not creative and generous.
Everyone who is funny or not generous is both calm and creative.
If paul is either old or quiet then someone is either not strong or not kind.
Everyone who is old or patient is either not old or curious.
Everyone who is either quiet or not brave is either generous or not quiet.
Everyone who is both kind and not kind is not patient or old and vice versa.
If lucy is either not funny or not humble then someone is not brave or humble and vice versa.
Everyone who is brave or strong is not brave and vice versa.
Everyone who is both rich and not tall is either tall or not tall.
If someone is not funny or not strong then someone is humble or not quiet.
Everyone who is either not strong or strong is either creative or not humble.
If someone is funny then alice is either not rich or not happy and vice versa.
If alice is rich then mary is curious and vice versa.
Everyone who is both quiet and curious is not calm or calm.
Lucy is either calm or funny.
Someone is either not creative or humble.
Susan is either happy or patient.
Someone is not funny or humble.
Someone is either not patient or not old.
Fred is either rich or not rich.
Someone is funny. | Fred is not strong. | contradiction | ((?[X]:((brave(X)&happy(X))))=>((kind(susan)|~humble(susan))))&
(![X]:((creative(X)&~generous(X))=>generous(X)))&
(![X]:((tall(X)&wise(X))=>(~creative(X)&generous(X))))&
(![X]:((funny(X)|~generous(X))=>(calm(X)&creative(X))))&
(((old(paul)<~>quiet(paul)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((old(X)|patient(X))=>(~old(X)<~>curious(X))))&
(![X]:((quiet(X)<~>~brave(X))=>(generous(X)<~>~quiet(X))))&
(![X]:((kind(X)&~kind(X))<=>(~patient(X)|old(X))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((brave(X)|strong(X))<=>~brave(X)))&
(![X]:((rich(X)&~tall(X))=>(tall(X)<~>~tall(X))))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>((~rich(alice)<~>~happy(alice))))&
((rich(alice))<=>(curious(mary)))&
(![X]:((quiet(X)&curious(X))=>(~calm(X)|calm(X))))&
((calm(lucy)<~>funny(lucy)))&
(?[X]:((~creative(X)<~>humble(X))))&
((happy(susan)<~>patient(susan)))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
((rich(fred)<~>~rich(fred)))&
(?[X]:(funny(X))) | ~strong(fred) | [
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 6213633117407753459520747
% SZS output start Proof for 6213633117407753459520747
10. ! [X0] : ((strong(X0) | brave(X0)) <=> ~brave(X0)) [input p9]
24. ~strong(fred) [input hypothesis]
52. ! [X0] : (((strong(X0) | brave(X0)) | brave(X0)) & (~brave(X0) | (~strong(X0) & ~brave(X0)))) [nnf transformation 10]
53. ! [X0] : ((strong(X0) | brave(X0) | brave(X0)) & (~brave(X0) | (~strong(X0) & ~brave(X0)))) [flattening 52]
106. ~brave(X0) | ~brave(X0) [cnf transformation 53]
108. strong(X0) | brave(X0) | brave(X0) [cnf transformation 53]
136. ~strong(fred) [cnf transformation 24]
143. ~brave(X0) [duplicate literal removal 106]
144. strong(X0) | brave(X0) [duplicate literal removal 108]
273. brave(fred) [resolution 144,136]
276. $false [subsumption resolution 273,143]
% SZS output end Proof for 6213633117407753459520747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or humble is not humble and vice versa.
If someone is strong then someone is both not old and not wise.
Everyone who is not wise is both kind and not funny and vice versa.
Everyone who is either tall or not strong is not humble and vice versa.
If someone is both patient and not strong then someone is quiet and vice versa.
If lucy is not strong then fred is both humble and not funny.
If lucy is either rich or not patient then someone is kind and vice versa.
Everyone who is either not quiet or not curious is either not tall or not creative.
If someone is not tall then alice is not rich.
If someone is not patient or tall then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not rich is both not curious and rich.
If someone is not brave then someone is both happy and rich.
Everyone who is kind is not strong or rich.
Someone is both not quiet and not creative.
Someone is both not kind and not brave.
Fred is both old and strong.
Mary is rich or old.
Susan is not tall or not calm. | Fred is tall. | entailment | (![X]:((~quiet(X)|humble(X))<=>~humble(X)))&
((?[X]:(strong(X)))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:(~wise(X)<=>(kind(X)&~funny(X))))&
(![X]:((tall(X)<~>~strong(X))<=>~humble(X)))&
((?[X]:((patient(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
((~strong(lucy))=>((humble(fred)&~funny(fred))))&
(((rich(lucy)<~>~patient(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(~rich(alice)))&
((?[X]:((~patient(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~rich(X))=>(~curious(X)&rich(X))))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
(?[X]:((~quiet(X)&~creative(X))))&
(?[X]:((~kind(X)&~brave(X))))&
((old(fred)&strong(fred)))&
((rich(mary)|old(mary)))&
((~tall(susan)|~calm(susan))) | tall(fred) | [
"p8",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 4241934278972634197432735
% SZS output start Proof for 4241934278972634197432735
9. ? [X0] : ~tall(X0) => ~rich(alice) [input p8]
11. ! [X0] : ((~rich(X0) | ~brave(X0)) => (rich(X0) & ~curious(X0))) [input p10]
19. ~tall(fred) [input hypothesis]
29. ~rich(alice) | ! [X0] : tall(X0) [ennf transformation 9]
30. ! [X0] : ((rich(X0) & ~curious(X0)) | (rich(X0) & brave(X0))) [ennf transformation 11]
89. ~rich(alice) | tall(X0) [cnf transformation 29]
98. rich(X0) | rich(X0) [cnf transformation 30]
108. ~tall(fred) [cnf transformation 19]
109. rich(X0) [duplicate literal removal 98]
179. 15 <=> ! [X0] : tall(X0) [avatar definition]
180. tall(X0) <- (15) [avatar component clause 179]
182. 16 <=> rich(alice) [avatar definition]
184. ~rich(alice) <- (~16) [avatar component clause 182]
185. 15 | ~16 [avatar split clause 89,182,179]
216. $false <- (~16) [subsumption resolution 184,109]
217. 16 [avatar contradiction clause 216]
218. $false <- (15) [resolution 180,108]
219. ~15 [avatar contradiction clause 218]
220. $false [avatar sat refutation 185,217,219]
% SZS output end Proof for 4241934278972634197432735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then fred is tall.
If someone is both not tall and patient then someone is both not humble and creative.
If someone is both old and not tall then paul is not old.
Everyone who is both not tall and quiet is wise or humble and vice versa.
Everyone who is not humble or not quiet is both tall and funny.
Everyone who is either not strong or tall is both brave and not brave and vice versa.
If mary is both not patient and not quiet then paul is not creative or not quiet and vice versa.
If someone is either not patient or not happy then someone is not curious and vice versa.
Everyone who is curious is either brave or not rich and vice versa.
Everyone who is quiet is not kind and vice versa.
Everyone who is either not rich or generous is wise or quiet and vice versa.
Everyone who is both not brave and strong is either not curious or not quiet.
Everyone who is both kind and not patient is brave or happy and vice versa.
If alice is not strong or patient then someone is either not quiet or not patient and vice versa.
If fred is not strong or kind then paul is either old or not patient.
Everyone who is not quiet is not tall or old.
Someone is quiet or not calm.
Someone is quiet or generous.
Someone is both not patient and not humble.
Alice is either not strong or happy.
Someone is either not calm or calm.
Fred is not curious or curious.
Someone is both old and brave. | Fred is not creative. | neutral | ((?[X]:(~happy(X)))=>(tall(fred)))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~humble(X)&creative(X)))))&
((?[X]:((old(X)&~tall(X))))=>(~old(paul)))&
(![X]:((~tall(X)&quiet(X))<=>(wise(X)|humble(X))))&
(![X]:((~humble(X)|~quiet(X))=>(tall(X)&funny(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(brave(X)&~brave(X))))&
(((~patient(mary)&~quiet(mary)))<=>((~creative(paul)|~quiet(paul))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:(~curious(X))))&
(![X]:(curious(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>~kind(X)))&
(![X]:((~rich(X)<~>generous(X))<=>(wise(X)|quiet(X))))&
(![X]:((~brave(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:((kind(X)&~patient(X))<=>(brave(X)|happy(X))))&
(((~strong(alice)|patient(alice)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(((~strong(fred)|kind(fred)))=>((old(paul)<~>~patient(paul))))&
(![X]:(~quiet(X)=>(~tall(X)|old(X))))&
(?[X]:((quiet(X)|~calm(X))))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~patient(X)&~humble(X))))&
((~strong(alice)<~>happy(alice)))&
(?[X]:((~calm(X)<~>calm(X))))&
((~curious(fred)|curious(fred)))&
(?[X]:((old(X)&brave(X)))) | ~creative(fred) | []
| null | 0 |
Everyone who is not funny or creative is both curious and happy and vice versa. Everyone who is kind or not old is either not wise or not generous. If someone is creative then paul is either not wise or patient. Everyone who is either humble or not quiet is both happy and not rich. If john is both not patient and not calm then someone is both old and kind. If alice is not calm then someone is both happy and not tall. If someone is strong or calm then paul is both quiet and rich. If someone is either calm or not strong then fred is both not curious and not kind. If someone is happy then paul is either humble or not wise and vice versa. If someone is not wise then alice is both not patient and quiet. If someone is not humble then someone is both generous and not brave. Everyone who is both calm and brave is both not patient and not humble and vice versa. Everyone who is not generous or humble is happy or wise and vice versa. Everyone who is both not wise and not happy is either patient or curious and vice versa. Everyone who is not strong is not humble or humble and vice versa. Everyone who is both not happy and not curious is both calm and brave. Alice is not quiet or not rich. Fred is both old and curious. Lucy is both not old and creative. Someone is not strong. John is happy or generous. Fred is not patient. Someone is not patient or not funny. Someone is not rich or rich. | Alice is quiet. | entailment | (![X]:((~funny(X)|creative(X))<=>(curious(X)&happy(X))))&
(![X]:((kind(X)|~old(X))=>(~wise(X)<~>~generous(X))))&
((?[X]:(creative(X)))=>((~wise(paul)<~>patient(paul))))&
(![X]:((humble(X)<~>~quiet(X))=>(happy(X)&~rich(X))))&
(((~patient(john)&~calm(john)))=>(?[X]:((old(X)&kind(X)))))&
((~calm(alice))=>(?[X]:((happy(X)&~tall(X)))))&
((?[X]:((strong(X)|calm(X))))=>((quiet(paul)&rich(paul))))&
((?[X]:((calm(X)<~>~strong(X))))=>((~curious(fred)&~kind(fred))))&
((?[X]:(happy(X)))<=>((humble(paul)<~>~wise(paul))))&
((?[X]:(~wise(X)))=>((~patient(alice)&quiet(alice))))&
((?[X]:(~humble(X)))=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((calm(X)&brave(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~generous(X)|humble(X))<=>(happy(X)|wise(X))))&
(![X]:((~wise(X)&~happy(X))<=>(patient(X)<~>curious(X))))&
(![X]:(~strong(X)<=>(~humble(X)|humble(X))))&
(![X]:((~happy(X)&~curious(X))=>(calm(X)&brave(X))))&
((~quiet(alice)|~rich(alice)))&
((old(fred)&curious(fred)))&
((~old(lucy)&creative(lucy)))&
(?[X]:(~strong(X)))&
((happy(john)|generous(john)))&
(~patient(fred))&
(?[X]:((~patient(X)|~funny(X))))&
(?[X]:((~rich(X)|rich(X)))) | quiet(alice) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p9",
"p14",
"p17",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 4618758040730322508816386
% SZS output start Proof for 4618758040730322508816386
1. ! [X0] : ((creative(X0) | ~funny(X0)) <=> (happy(X0) & curious(X0))) [input p0]
4. ! [X0] : ((humble(X0) <~> ~quiet(X0)) => (~rich(X0) & happy(X0))) [input p3]
7. ? [X0] : (calm(X0) | strong(X0)) => (rich(paul) & quiet(paul)) [input p6]
8. ? [X0] : (calm(X0) <~> ~strong(X0)) => (~kind(fred) & ~curious(fred)) [input p7]
9. ? [X0] : happy(X0) <=> (humble(paul) <~> ~wise(paul)) [input p8]
10. ? [X0] : ~wise(X0) => (quiet(alice) & ~patient(alice)) [input p9]
15. ! [X0] : (~strong(X0) <=> (humble(X0) | ~humble(X0))) [input p14]
18. curious(fred) & old(fred) [input p17]
19. creative(lucy) & ~old(lucy) [input p18]
25. ~quiet(alice) [input hypothesis]
30. ! [X0] : ((~rich(X0) & happy(X0)) | (humble(X0) <=> ~quiet(X0))) [ennf transformation 4]
34. (rich(paul) & quiet(paul)) | ! [X0] : (~calm(X0) & ~strong(X0)) [ennf transformation 7]
35. (~kind(fred) & ~curious(fred)) | ! [X0] : (calm(X0) <=> ~strong(X0)) [ennf transformation 8]
36. (quiet(alice) & ~patient(alice)) | ! [X0] : wise(X0) [ennf transformation 10]
40. ! [X0] : (((creative(X0) | ~funny(X0)) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | (~creative(X0) & funny(X0)))) [nnf transformation 1]
41. ! [X0] : ((creative(X0) | ~funny(X0) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | (~creative(X0) & funny(X0)))) [flattening 40]
44. ! [X0] : ((~rich(X0) & happy(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) [nnf transformation 30]
49. (~kind(fred) & ~curious(fred)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))) [nnf transformation 35]
50. (? [X0] : happy(X0) | ((humble(paul) | wise(paul)) & (~wise(paul) | ~humble(paul)))) & (((wise(paul) | ~humble(paul)) & (~wise(paul) | humble(paul))) | ! [X0] : ~happy(X0)) [nnf transformation 9]
51. (? [X0] : happy(X0) | ((humble(paul) | wise(paul)) & (~wise(paul) | ~humble(paul)))) & (((wise(paul) | ~humble(paul)) & (~wise(paul) | humble(paul))) | ! [X1] : ~happy(X1)) [rectify 50]
52. ? [X0] : happy(X0) => happy(sK2) [choice axiom]
53. (happy(sK2) | ((humble(paul) | wise(paul)) & (~wise(paul) | ~humble(paul)))) & (((wise(paul) | ~humble(paul)) & (~wise(paul) | humble(paul))) | ! [X1] : ~happy(X1)) [skolemisation 51,52]
63. ! [X0] : ((~strong(X0) | (~humble(X0) & humble(X0))) & ((humble(X0) | ~humble(X0)) | strong(X0))) [nnf transformation 15]
64. ! [X0] : ((~strong(X0) | (~humble(X0) & humble(X0))) & (humble(X0) | ~humble(X0) | strong(X0))) [flattening 63]
74. ~creative(X0) | happy(X0) [cnf transformation 41]
84. ~rich(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 44]
90. quiet(paul) | ~calm(X0) [cnf transformation 34]
92. rich(paul) | ~calm(X0) [cnf transformation 34]
94. ~curious(fred) | calm(X0) | strong(X0) [cnf transformation 49]
97. ~wise(paul) | humble(paul) | ~happy(X1) [cnf transformation 53]
102. quiet(alice) | wise(X0) [cnf transformation 36]
120. ~strong(X0) | humble(X0) [cnf transformation 64]
121. ~strong(X0) | ~humble(X0) [cnf transformation 64]
126. curious(fred) [cnf transformation 18]
128. creative(lucy) [cnf transformation 19]
134. ~quiet(alice) [cnf transformation 25]
139. 2 <=> wise(paul) [avatar definition]
140. ~wise(paul) <- (~2) [avatar component clause 139]
176. 10 <=> ! [X0] : ~calm(X0) [avatar definition]
177. ~calm(X0) <- (10) [avatar component clause 176]
179. 11 <=> rich(paul) [avatar definition]
181. rich(paul) <- (11) [avatar component clause 179]
182. 10 | 11 [avatar split clause 92,179,176]
184. 12 <=> ! [X0] : ~strong(X0) [avatar definition]
185. ~strong(X0) <- (12) [avatar component clause 184]
188. 13 <=> quiet(paul) [avatar definition]
190. quiet(paul) <- (13) [avatar component clause 188]
191. 10 | 13 [avatar split clause 90,188,176]
194. 14 <=> ! [X0] : (calm(X0) | strong(X0)) [avatar definition]
195. strong(X0) | calm(X0) <- (14) [avatar component clause 194]
206. 17 <=> curious(fred) [avatar definition]
209. 14 | ~17 [avatar split clause 94,206,194]
212. 18 <=> humble(paul) [avatar definition]
214. humble(paul) <- (18) [avatar component clause 212]
222. 20 <=> ! [X1] : ~happy(X1) [avatar definition]
223. ~happy(X1) <- (20) [avatar component clause 222]
225. 20 | 18 | ~2 [avatar split clause 97,139,212,222]
227. 21 <=> ! [X0] : wise(X0) [avatar definition]
228. wise(X0) <- (21) [avatar component clause 227]
230. 22 <=> quiet(alice) [avatar definition]
233. 21 | 22 [avatar split clause 102,230,227]
252. ~strong(X0) [subsumption resolution 120,121]
253. 12 [avatar split clause 252,184]
259. 17 [avatar split clause 126,206]
278. ~22 [avatar split clause 134,230]
283. $false <- (~2, 21) [subsumption resolution 140,228]
284. 2 | ~21 [avatar contradiction clause 283]
291. happy(lucy) [resolution 74,128]
292. $false <- (20) [subsumption resolution 291,223]
293. ~20 [avatar contradiction clause 292]
297. calm(X1) <- (12, 14) [resolution 195,185]
324. ~quiet(paul) | ~humble(paul) <- (11) [resolution 84,181]
325. ~humble(paul) <- (11, 13) [subsumption resolution 324,190]
326. $false <- (11, 13, 18) [subsumption resolution 325,214]
327. ~11 | ~13 | ~18 [avatar contradiction clause 326]
328. $false <- (10, 12, 14) [subsumption resolution 177,297]
329. ~10 | ~12 | ~14 [avatar contradiction clause 328]
332. $false [avatar sat refutation 182,191,209,225,233,253,259,278,284,293,327,329]
% SZS output end Proof for 4618758040730322508816386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both wise and brave.
If someone is not wise or not funny then john is either not quiet or funny and vice versa.
Everyone who is not happy is not strong.
Everyone who is creative or not generous is not funny or not curious.
Everyone who is creative is creative or not generous and vice versa.
Everyone who is funny is not tall and vice versa.
Everyone who is not calm or curious is not brave and vice versa.
If someone is generous then fred is either not happy or not creative and vice versa.
If someone is patient then alice is both strong and not generous and vice versa.
Everyone who is either humble or not patient is funny or curious and vice versa.
Everyone who is not quiet is both not old and tall.
Everyone who is kind is generous and vice versa.
Everyone who is both generous and not creative is both strong and generous.
If fred is both funny and quiet then john is both not kind and not curious.
Everyone who is strong is not humble or tall and vice versa.
If mary is not humble or not generous then someone is not calm or not strong.
Paul is both not curious and not strong.
Someone is either not strong or not humble.
Someone is either not brave or funny.
Someone is not brave.
Fred is both strong and not creative.
John is calm or generous. | Paul is creative. | entailment | (![X]:(calm(X)=>(wise(X)&brave(X))))&
((?[X]:((~wise(X)|~funny(X))))<=>((~quiet(john)<~>funny(john))))&
(![X]:(~happy(X)=>~strong(X)))&
(![X]:((creative(X)|~generous(X))=>(~funny(X)|~curious(X))))&
(![X]:(creative(X)<=>(creative(X)|~generous(X))))&
(![X]:(funny(X)<=>~tall(X)))&
(![X]:((~calm(X)|curious(X))<=>~brave(X)))&
((?[X]:(generous(X)))<=>((~happy(fred)<~>~creative(fred))))&
((?[X]:(patient(X)))<=>((strong(alice)&~generous(alice))))&
(![X]:((humble(X)<~>~patient(X))<=>(funny(X)|curious(X))))&
(![X]:(~quiet(X)=>(~old(X)&tall(X))))&
(![X]:(kind(X)<=>generous(X)))&
(![X]:((generous(X)&~creative(X))=>(strong(X)&generous(X))))&
(((funny(fred)&quiet(fred)))=>((~kind(john)&~curious(john))))&
(![X]:(strong(X)<=>(~humble(X)|tall(X))))&
(((~humble(mary)|~generous(mary)))=>(?[X]:((~calm(X)|~strong(X)))))&
((~curious(paul)&~strong(paul)))&
(?[X]:((~strong(X)<~>~humble(X))))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:(~brave(X)))&
((strong(fred)&~creative(fred)))&
((calm(john)|generous(john))) | creative(paul) | [
"p4",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8112619441902738943305033
% SZS output start Proof for 8112619441902738943305033
5. ! [X0] : (creative(X0) <=> (~generous(X0) | creative(X0))) [input p4]
13. ! [X0] : ((~creative(X0) & generous(X0)) => (generous(X0) & strong(X0))) [input p12]
17. ~strong(paul) & ~curious(paul) [input p16]
23. ~creative(paul) [input hypothesis]
32. ! [X0] : ((generous(X0) & strong(X0)) | (creative(X0) | ~generous(X0))) [ennf transformation 13]
33. ! [X0] : ((generous(X0) & strong(X0)) | creative(X0) | ~generous(X0)) [flattening 32]
41. ! [X0] : ((creative(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | ~creative(X0))) [nnf transformation 5]
42. ! [X0] : ((creative(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | ~creative(X0))) [flattening 41]
82. generous(X0) | creative(X0) [cnf transformation 42]
103. strong(X0) | creative(X0) | ~generous(X0) [cnf transformation 33]
113. ~strong(paul) [cnf transformation 17]
122. ~creative(paul) [cnf transformation 23]
188. creative(X0) | strong(X0) [subsumption resolution 103,82]
266. strong(paul) [resolution 188,122]
268. $false [subsumption resolution 266,113]
% SZS output end Proof for 8112619441902738943305033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or old then someone is either not calm or not brave.
Everyone who is both not creative and creative is both wise and not tall and vice versa.
Everyone who is quiet is either happy or not tall.
If someone is both generous and brave then someone is either tall or generous and vice versa.
Everyone who is either tall or not curious is both not tall and patient.
Everyone who is patient is both not rich and curious and vice versa.
Everyone who is not quiet or not kind is either not rich or tall.
If someone is not patient then someone is both funny and not funny.
If lucy is both not old and not quiet then alice is funny or kind.
If john is both not strong and old then susan is either humble or rich.
Everyone who is not kind or kind is both strong and patient and vice versa.
Everyone who is both not brave and patient is either not calm or not patient.
If someone is either old or kind then someone is creative or not generous and vice versa.
Everyone who is either rich or not brave is both quiet and brave and vice versa.
If someone is both not curious and tall then mary is both not old and old and vice versa.
Everyone who is both not calm and not quiet is tall or wise and vice versa.
Someone is not wise.
Someone is either not quiet or not strong.
Someone is not calm or creative.
Mary is both not rich and not happy.
Someone is either not kind or not brave. | Mary is not curious. | contradiction | ((?[X]:((creative(X)<~>old(X))))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((~creative(X)&creative(X))<=>(wise(X)&~tall(X))))&
(![X]:(quiet(X)=>(happy(X)<~>~tall(X))))&
((?[X]:((generous(X)&brave(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
(![X]:((tall(X)<~>~curious(X))=>(~tall(X)&patient(X))))&
(![X]:(patient(X)<=>(~rich(X)&curious(X))))&
(![X]:((~quiet(X)|~kind(X))=>(~rich(X)<~>tall(X))))&
((?[X]:(~patient(X)))=>(?[X]:((funny(X)&~funny(X)))))&
(((~old(lucy)&~quiet(lucy)))=>((funny(alice)|kind(alice))))&
(((~strong(john)&old(john)))=>((humble(susan)<~>rich(susan))))&
(![X]:((~kind(X)|kind(X))<=>(strong(X)&patient(X))))&
(![X]:((~brave(X)&patient(X))=>(~calm(X)<~>~patient(X))))&
((?[X]:((old(X)<~>kind(X))))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(quiet(X)&brave(X))))&
((?[X]:((~curious(X)&tall(X))))<=>((~old(mary)&old(mary))))&
(![X]:((~calm(X)&~quiet(X))<=>(tall(X)|wise(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~calm(X)|creative(X))))&
((~rich(mary)&~happy(mary)))&
(?[X]:((~kind(X)<~>~brave(X)))) | ~curious(mary) | [
"p5",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 2107029726101020780682435
% SZS output start Proof for 2107029726101020780682435
6. ! [X0] : (patient(X0) <=> (curious(X0) & ~rich(X0))) [input p5]
11. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (patient(X0) & strong(X0))) [input p10]
22. ~curious(mary) [input hypothesis]
51. ! [X0] : ((patient(X0) | (~curious(X0) | rich(X0))) & ((curious(X0) & ~rich(X0)) | ~patient(X0))) [nnf transformation 6]
52. ! [X0] : ((patient(X0) | ~curious(X0) | rich(X0)) & ((curious(X0) & ~rich(X0)) | ~patient(X0))) [flattening 51]
58. ! [X0] : (((kind(X0) | ~kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 11]
59. ! [X0] : ((kind(X0) | ~kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~kind(X0) & kind(X0)))) [flattening 58]
106. ~patient(X0) | curious(X0) [cnf transformation 52]
119. patient(X0) | kind(X0) [cnf transformation 59]
120. patient(X0) | ~kind(X0) [cnf transformation 59]
153. ~curious(mary) [cnf transformation 22]
209. 12 <=> ! [X1] : patient(X1) [avatar definition]
210. patient(X1) <- (12) [avatar component clause 209]
252. patient(X0) [subsumption resolution 119,120]
253. 12 [avatar split clause 252,209]
322. curious(X0) <- (12) [resolution 106,210]
324. $false <- (12) [resolution 322,153]
325. ~12 [avatar contradiction clause 324]
326. $false [avatar sat refutation 253,325]
% SZS output end Proof for 2107029726101020780682435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both calm and not kind.
Everyone who is creative or generous is not rich or not happy.
Everyone who is brave is not kind or creative and vice versa.
If susan is patient or calm then susan is both creative and not funny.
Everyone who is calm is both calm and brave.
Everyone who is either not wise or wise is either not generous or not kind and vice versa.
If susan is not patient or brave then someone is patient or not old.
If alice is strong or not patient then someone is not brave and vice versa.
Everyone who is both rich and not curious is not creative and vice versa.
Everyone who is not funny is either strong or not strong.
If someone is both happy and patient then someone is not kind or curious and vice versa.
Everyone who is not quiet is tall or old.
If john is not funny or quiet then someone is both not wise and happy.
If susan is not happy or brave then paul is either happy or old.
Everyone who is either not happy or tall is either not old or creative and vice versa.
John is not strong or not tall.
Someone is tall.
Someone is not patient.
Someone is either not strong or patient.
Alice is either not rich or not funny.
Fred is not creative or not calm. | Fred is quiet. | neutral | (![X]:(kind(X)=>(calm(X)&~kind(X))))&
(![X]:((creative(X)|generous(X))=>(~rich(X)|~happy(X))))&
(![X]:(brave(X)<=>(~kind(X)|creative(X))))&
(((patient(susan)|calm(susan)))=>((creative(susan)&~funny(susan))))&
(![X]:(calm(X)=>(calm(X)&brave(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~generous(X)<~>~kind(X))))&
(((~patient(susan)|brave(susan)))=>(?[X]:((patient(X)|~old(X)))))&
(((strong(alice)|~patient(alice)))<=>(?[X]:(~brave(X))))&
(![X]:((rich(X)&~curious(X))<=>~creative(X)))&
(![X]:(~funny(X)=>(strong(X)<~>~strong(X))))&
((?[X]:((happy(X)&patient(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:(~quiet(X)=>(tall(X)|old(X))))&
(((~funny(john)|quiet(john)))=>(?[X]:((~wise(X)&happy(X)))))&
(((~happy(susan)|brave(susan)))=>((happy(paul)<~>old(paul))))&
(![X]:((~happy(X)<~>tall(X))<=>(~old(X)<~>creative(X))))&
((~strong(john)|~tall(john)))&
(?[X]:(tall(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~strong(X)<~>patient(X))))&
((~rich(alice)<~>~funny(alice)))&
((~creative(fred)|~calm(fred))) | quiet(fred) | []
| null | 0 |
Everyone who is generous or rich is both not wise and not calm.
If someone is not happy or not generous then paul is either happy or not generous and vice versa.
Everyone who is both tall and generous is not happy or not kind and vice versa.
Everyone who is both not funny and brave is creative and vice versa.
If someone is not generous or strong then someone is both quiet and not humble and vice versa.
If lucy is not happy or humble then someone is generous or not strong.
If someone is not brave or not creative then paul is not wise or tall.
Everyone who is both not curious and old is creative or not curious and vice versa.
Everyone who is either not happy or not strong is either wise or not brave.
Everyone who is either not creative or creative is rich or not strong and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Everyone who is not quiet or not tall is either quiet or not strong and vice versa.
If john is either not tall or patient then paul is either not humble or curious and vice versa.
Someone is happy or not quiet.
Mary is rich.
Someone is both curious and not wise.
John is both tall and quiet.
Fred is either not rich or not tall.
Someone is both tall and rich.
Paul is both not rich and not quiet.
Someone is not humble. | Fred is not kind. | contradiction | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
((?[X]:((~happy(X)|~generous(X))))<=>((happy(paul)<~>~generous(paul))))&
(![X]:((tall(X)&generous(X))<=>(~happy(X)|~kind(X))))&
(![X]:((~funny(X)&brave(X))<=>creative(X)))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((~happy(lucy)|humble(lucy)))=>(?[X]:((generous(X)|~strong(X)))))&
((?[X]:((~brave(X)|~creative(X))))=>((~wise(paul)|tall(paul))))&
(![X]:((~curious(X)&old(X))<=>(creative(X)|~curious(X))))&
(![X]:((~happy(X)<~>~strong(X))=>(wise(X)<~>~brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(rich(X)|~strong(X))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
(![X]:((~quiet(X)|~tall(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(john)<~>patient(john)))<=>((~humble(paul)<~>curious(paul))))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john)))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((tall(X)&rich(X))))&
((~rich(paul)&~quiet(paul)))&
(?[X]:(~humble(X))) | ~kind(fred) | [
"p1",
"p2",
"p8",
"p9",
"p11",
"p13",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 1503488199129317253298345
% SZS output start Proof for 1503488199129317253298345
2. ? [X0] : (~generous(X0) | ~happy(X0)) <=> (happy(paul) <~> ~generous(paul)) [input p1]
3. ! [X0] : ((generous(X0) & tall(X0)) <=> (~kind(X0) | ~happy(X0))) [input p2]
9. ! [X0] : ((~happy(X0) <~> ~strong(X0)) => (wise(X0) <~> ~brave(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~strong(X0) | rich(X0))) [input p9]
12. ! [X0] : (funny(X0) <=> ~wise(X0)) [input p11]
14. ? [X0] : (~funny(X0) | ~brave(X0)) <=> ~tall(fred) [input p13]
23. ~quiet(paul) & ~rich(paul) [input p22]
25. ~kind(fred) [input hypothesis]
34. ! [X0] : ((wise(X0) <~> ~brave(X0)) | (~happy(X0) <=> ~strong(X0))) [ennf transformation 9]
36. (? [X0] : (~generous(X0) | ~happy(X0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X0] : (generous(X0) & happy(X0))) [nnf transformation 2]
37. (? [X0] : (~generous(X0) | ~happy(X0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X1] : (generous(X1) & happy(X1))) [rectify 36]
38. ? [X0] : (~generous(X0) | ~happy(X0)) => (~generous(sK0) | ~happy(sK0)) [choice axiom]
39. ((~generous(sK0) | ~happy(sK0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X1] : (generous(X1) & happy(X1))) [skolemisation 37,38]
40. ! [X0] : (((generous(X0) & tall(X0)) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((generous(X0) & tall(X0)) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~generous(X0) | ~tall(X0))) [flattening 40]
53. ! [X0] : (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) [nnf transformation 34]
54. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 10]
55. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 54]
59. ! [X0] : ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))) [nnf transformation 12]
65. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X0] : (funny(X0) & brave(X0))) [nnf transformation 14]
66. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [rectify 65]
67. ? [X0] : (~funny(X0) | ~brave(X0)) => (~funny(sK7) | ~brave(sK7)) [choice axiom]
68. ((~funny(sK7) | ~brave(sK7)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [skolemisation 66,67]
83. ~generous(paul) | happy(paul) | happy(X1) [cnf transformation 39]
91. kind(X0) | tall(X0) [cnf transformation 41]
92. happy(X0) | generous(X0) [cnf transformation 41]
112. ~brave(X0) | wise(X0) | ~happy(X0) | strong(X0) [cnf transformation 53]
115. ~strong(X0) | rich(X0) | creative(X0) | creative(X0) [cnf transformation 55]
116. ~strong(X0) | rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 55]
123. ~funny(X0) | ~wise(X0) [cnf transformation 59]
128. ~tall(fred) | brave(X1) [cnf transformation 68]
129. ~tall(fred) | funny(X1) [cnf transformation 68]
155. ~rich(paul) [cnf transformation 23]
158. ~kind(fred) [cnf transformation 25]
161. ~strong(X0) | rich(X0) | creative(X0) [duplicate literal removal 115]
162. ~strong(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 116]
164. 1 <=> generous(paul) [avatar definition]
165. ~generous(paul) <- (~1) [avatar component clause 164]
168. 2 <=> happy(paul) [avatar definition]
169. ~happy(paul) <- (~2) [avatar component clause 168]
170. happy(paul) <- (2) [avatar component clause 168]
186. 6 <=> ! [X1] : happy(X1) [avatar definition]
187. happy(X1) <- (6) [avatar component clause 186]
190. 6 | 2 | ~1 [avatar split clause 83,164,168,186]
240. 18 <=> wise(paul) [avatar definition]
241. wise(paul) <- (18) [avatar component clause 240]
242. ~wise(paul) <- (~18) [avatar component clause 240]
249. 20 <=> ! [X0] : brave(X0) [avatar definition]
250. brave(X0) <- (20) [avatar component clause 249]
252. ~strong(X0) | rich(X0) [subsumption resolution 161,162]
272. 25 <=> tall(fred) [avatar definition]
285. 28 <=> ! [X1] : funny(X1) [avatar definition]
286. funny(X1) <- (28) [avatar component clause 285]
287. 28 | ~25 [avatar split clause 129,272,285]
288. 20 | ~25 [avatar split clause 128,272,249]
333. tall(fred) [resolution 91,158]
334. generous(paul) <- (~2) [resolution 92,169]
335. $false <- (~1, ~2) [subsumption resolution 334,165]
336. 1 | 2 [avatar contradiction clause 335]
351. ~happy(X0) | wise(X0) | strong(X0) <- (20) [resolution 112,250]
358. 25 [avatar split clause 333,272]
417. ~wise(X0) <- (28) [resolution 286,123]
469. wise(paul) | strong(paul) <- (2, 20) [resolution 351,170]
474. strong(paul) <- (2, ~18, 20) [subsumption resolution 469,242]
480. rich(paul) <- (2, ~18, 20) [resolution 474,252]
485. $false <- (2, ~18, 20) [subsumption resolution 480,155]
486. ~2 | 18 | ~20 [avatar contradiction clause 485]
488. $false <- (18, 28) [subsumption resolution 241,417]
489. ~18 | ~28 [avatar contradiction clause 488]
490. $false <- (~2, 6) [subsumption resolution 169,187]
491. 2 | ~6 [avatar contradiction clause 490]
492. $false [avatar sat refutation 190,287,288,336,358,486,489,491]
% SZS output end Proof for 1503488199129317253298345
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and calm is old. If someone is both not quiet and not calm then fred is not old or calm and vice versa. Everyone who is both not creative and kind is not calm or rich and vice versa. If alice is both old and not calm then someone is quiet or happy and vice versa. Everyone who is kind is both quiet and generous. If someone is both not kind and not calm then someone is both not curious and not tall and vice versa. If someone is not humble or not calm then lucy is strong or not patient. Everyone who is both not rich and happy is curious and vice versa. Everyone who is strong is both funny and strong and vice versa. If fred is either not tall or not creative then fred is not rich or not funny. Everyone who is not brave or funny is not tall and vice versa. If someone is either not kind or curious then paul is both not quiet and not generous. Everyone who is happy or not calm is not brave. Everyone who is either not wise or not curious is not patient and vice versa. Everyone who is both not brave and not old is both not calm and tall. If lucy is both curious and not brave then alice is both rich and patient and vice versa. Lucy is humble. Susan is brave. Someone is either strong or not calm. Alice is quiet or creative. Someone is generous or not old. Susan is both patient and calm. | Alice is rich. | contradiction | (![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:(kind(X)=>(quiet(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
((?[X]:((~humble(X)|~calm(X))))=>((strong(lucy)|~patient(lucy))))&
(![X]:((~rich(X)&happy(X))<=>curious(X)))&
(![X]:(strong(X)<=>(funny(X)&strong(X))))&
(((~tall(fred)<~>~creative(fred)))=>((~rich(fred)|~funny(fred))))&
(![X]:((~brave(X)|funny(X))<=>~tall(X)))&
((?[X]:((~kind(X)<~>curious(X))))=>((~quiet(paul)&~generous(paul))))&
(![X]:((happy(X)|~calm(X))=>~brave(X)))&
(![X]:((~wise(X)<~>~curious(X))<=>~patient(X)))&
(![X]:((~brave(X)&~old(X))=>(~calm(X)&tall(X))))&
(((curious(lucy)&~brave(lucy)))<=>((rich(alice)&patient(alice))))&
(humble(lucy))&
(brave(susan))&
(?[X]:((strong(X)<~>~calm(X))))&
((quiet(alice)|creative(alice)))&
(?[X]:((generous(X)|~old(X))))&
((patient(susan)&calm(susan))) | rich(alice) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p12",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 2619107910846031841708580
% SZS output start Proof for 2619107910846031841708580
3. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p2]
4. (~calm(alice) & old(alice)) <=> ? [X0] : (happy(X0) | quiet(X0)) [input p3]
6. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X0] : (~tall(X0) & ~curious(X0)) [input p5]
8. ! [X0] : ((happy(X0) & ~rich(X0)) <=> curious(X0)) [input p7]
11. ! [X0] : ((funny(X0) | ~brave(X0)) <=> ~tall(X0)) [input p10]
13. ! [X0] : ((~calm(X0) | happy(X0)) => ~brave(X0)) [input p12]
20. creative(alice) | quiet(alice) [input p19]
23. rich(alice) [input hypothesis]
24. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X1] : (~tall(X1) & ~curious(X1)) [rectify 6]
35. ! [X0] : (~brave(X0) | (calm(X0) & ~happy(X0))) [ennf transformation 13]
43. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 3]
44. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 43]
45. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | (calm(alice) | ~old(alice))) [nnf transformation 4]
46. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | calm(alice) | ~old(alice)) [flattening 45]
47. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X1] : (happy(X1) | quiet(X1)) | calm(alice) | ~old(alice)) [rectify 46]
48. ? [X1] : (happy(X1) | quiet(X1)) => (happy(sK1) | quiet(sK1)) [choice axiom]
49. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & ((happy(sK1) | quiet(sK1)) | calm(alice) | ~old(alice)) [skolemisation 47,48]
50. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : (tall(X1) | curious(X1))) & (? [X1] : (~tall(X1) & ~curious(X1)) | ! [X0] : (calm(X0) | kind(X0))) [nnf transformation 24]
51. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : (tall(X1) | curious(X1))) & (? [X2] : (~tall(X2) & ~curious(X2)) | ! [X3] : (calm(X3) | kind(X3))) [rectify 50]
52. ? [X0] : (~calm(X0) & ~kind(X0)) => (~calm(sK2) & ~kind(sK2)) [choice axiom]
53. ? [X2] : (~tall(X2) & ~curious(X2)) => (~tall(sK3) & ~curious(sK3)) [choice axiom]
54. ((~calm(sK2) & ~kind(sK2)) | ! [X1] : (tall(X1) | curious(X1))) & ((~tall(sK3) & ~curious(sK3)) | ! [X3] : (calm(X3) | kind(X3))) [skolemisation 51,53,52]
55. ! [X0] : (((happy(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | (~happy(X0) | rich(X0)))) [nnf transformation 8]
56. ! [X0] : (((happy(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | ~happy(X0) | rich(X0))) [flattening 55]
60. ! [X0] : (((funny(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [nnf transformation 11]
61. ! [X0] : ((funny(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [flattening 60]
79. ~rich(X0) | ~creative(X0) [cnf transformation 44]
80. kind(X0) | calm(X0) [cnf transformation 44]
85. ~calm(alice) | ~quiet(X0) [cnf transformation 49]
91. ~kind(sK2) | tall(X1) | curious(X1) [cnf transformation 54]
92. ~calm(sK2) | tall(X1) | curious(X1) [cnf transformation 54]
95. ~curious(X0) | ~rich(X0) [cnf transformation 56]
102. ~tall(X0) | brave(X0) [cnf transformation 61]
110. ~brave(X0) | calm(X0) [cnf transformation 35]
124. creative(alice) | quiet(alice) [cnf transformation 20]
128. rich(alice) [cnf transformation 23]
157. 7 <=> calm(alice) [avatar definition]
159. ~calm(alice) <- (~7) [avatar component clause 157]
162. 8 <=> ! [X0] : ~quiet(X0) [avatar definition]
163. ~quiet(X0) <- (8) [avatar component clause 162]
164. 8 | ~7 [avatar split clause 85,157,162]
181. 12 <=> ! [X1] : (tall(X1) | curious(X1)) [avatar definition]
182. tall(X1) | curious(X1) <- (12) [avatar component clause 181]
184. 13 <=> calm(sK2) [avatar definition]
187. 12 | ~13 [avatar split clause 92,184,181]
189. 14 <=> kind(sK2) [avatar definition]
191. ~kind(sK2) <- (~14) [avatar component clause 189]
192. 12 | ~14 [avatar split clause 91,189,181]
239. 25 <=> rich(alice) [avatar definition]
240. rich(alice) <- (25) [avatar component clause 239]
269. 31 <=> quiet(alice) [avatar definition]
271. quiet(alice) <- (31) [avatar component clause 269]
273. 32 <=> creative(alice) [avatar definition]
276. 31 | 32 [avatar split clause 124,273,269]
286. 25 [avatar split clause 128,239]
287. $false <- (8, 31) [resolution 271,163]
288. ~8 | ~31 [avatar contradiction clause 287]
289. ~creative(alice) <- (25) [resolution 79,240]
290. ~32 | ~25 [avatar split clause 289,239,273]
291. calm(sK2) <- (~14) [resolution 80,191]
294. 13 | 14 [avatar split clause 291,189,184]
307. brave(X0) | curious(X0) <- (12) [resolution 182,102]
368. curious(X1) | calm(X1) <- (12) [resolution 307,110]
378. ~rich(X1) | calm(X1) <- (12) [resolution 368,95]
405. calm(alice) <- (12, 25) [resolution 378,240]
406. $false <- (~7, 12, 25) [subsumption resolution 405,159]
407. 7 | ~12 | ~25 [avatar contradiction clause 406]
408. $false [avatar sat refutation 164,187,192,276,286,288,290,294,407]
% SZS output end Proof for 2619107910846031841708580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or not quiet then john is both not calm and strong.
Everyone who is both creative and quiet is happy and vice versa.
Everyone who is kind or creative is either not old or not curious.
Everyone who is patient or wise is creative or humble and vice versa.
If alice is creative or not funny then paul is calm or kind and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not old is both calm and not calm.
If someone is either humble or quiet then someone is not humble or not strong and vice versa.
If someone is either not patient or rich then mary is both not quiet and not strong.
Everyone who is both not curious and not old is not quiet and vice versa.
Everyone who is old is kind.
If mary is not patient or old then paul is not happy or strong.
Everyone who is not strong or happy is either not kind or not happy and vice versa.
Everyone who is both calm and not calm is either not happy or not kind.
Everyone who is not rich or creative is either not rich or not quiet.
If susan is not generous then someone is not old or creative and vice versa.
Paul is either not patient or not quiet.
Someone is either generous or not humble.
Susan is humble.
Paul is not calm.
Alice is either not humble or not strong. | Susan is quiet. | entailment | ((?[X]:((~rich(X)<~>~quiet(X))))=>((~calm(john)&strong(john))))&
(![X]:((creative(X)&quiet(X))<=>happy(X)))&
(![X]:((kind(X)|creative(X))=>(~old(X)<~>~curious(X))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|humble(X))))&
(((creative(alice)|~funny(alice)))<=>((calm(paul)|kind(paul))))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:(~old(X)=>(calm(X)&~calm(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((~humble(X)|~strong(X)))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(![X]:((~strong(X)|happy(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((calm(X)&~calm(X))=>(~happy(X)<~>~kind(X))))&
(![X]:((~rich(X)|creative(X))=>(~rich(X)<~>~quiet(X))))&
((~generous(susan))<=>(?[X]:((~old(X)|creative(X)))))&
((~patient(paul)<~>~quiet(paul)))&
(?[X]:((generous(X)<~>~humble(X))))&
(humble(susan))&
(~calm(paul))&
((~humble(alice)<~>~strong(alice))) | quiet(susan) | [
"p6",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 2986469207189781874220886
% SZS output start Proof for 2986469207189781874220886
7. ! [X0] : (~old(X0) => (~calm(X0) & calm(X0))) [input p6]
10. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p9]
22. ~quiet(susan) [input hypothesis]
26. ! [X0] : ((~calm(X0) & calm(X0)) | old(X0)) [ennf transformation 7]
49. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | curious(X0)))) [nnf transformation 10]
50. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | curious(X0))) [flattening 49]
87. calm(X0) | old(X0) [cnf transformation 26]
88. ~calm(X0) | old(X0) [cnf transformation 26]
101. ~old(X0) | quiet(X0) [cnf transformation 50]
128. ~quiet(susan) [cnf transformation 22]
170. old(X0) [subsumption resolution 87,88]
223. quiet(X0) [subsumption resolution 101,170]
279. $false [subsumption resolution 128,223]
% SZS output end Proof for 2986469207189781874220886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not generous is not tall or not generous and vice versa.
Everyone who is quiet or not funny is not tall and vice versa.
If someone is both calm and brave then mary is strong or quiet and vice versa.
If fred is brave then someone is not generous or calm.
Everyone who is not humble is either kind or quiet and vice versa.
Everyone who is not funny is both kind and not old and vice versa.
Everyone who is both not quiet and generous is both not happy and not creative.
Everyone who is not rich is both not old and not kind and vice versa.
Everyone who is either not quiet or funny is not quiet.
If someone is not generous then someone is both not funny and generous and vice versa.
Everyone who is humble or not calm is either calm or not funny and vice versa.
If alice is both curious and creative then alice is both not humble and not happy and vice versa.
Everyone who is old is either not kind or creative and vice versa.
If someone is both not wise and not brave then someone is either rich or kind.
If susan is both not strong and not wise then susan is both funny and not calm and vice versa.
If someone is humble or curious then paul is old or not tall.
Fred is kind.
Someone is wise or humble.
Susan is either not humble or quiet.
Alice is not wise.
Susan is happy or brave.
Someone is brave or not calm.
Someone is not curious or brave.
Susan is both not quiet and not tall. | Mary is not humble. | neutral | (![X]:((brave(X)|~generous(X))<=>(~tall(X)|~generous(X))))&
(![X]:((quiet(X)|~funny(X))<=>~tall(X)))&
((?[X]:((calm(X)&brave(X))))<=>((strong(mary)|quiet(mary))))&
((brave(fred))=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:(~humble(X)<=>(kind(X)<~>quiet(X))))&
(![X]:(~funny(X)<=>(kind(X)&~old(X))))&
(![X]:((~quiet(X)&generous(X))=>(~happy(X)&~creative(X))))&
(![X]:(~rich(X)<=>(~old(X)&~kind(X))))&
(![X]:((~quiet(X)<~>funny(X))=>~quiet(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:((humble(X)|~calm(X))<=>(calm(X)<~>~funny(X))))&
(((curious(alice)&creative(alice)))<=>((~humble(alice)&~happy(alice))))&
(![X]:(old(X)<=>(~kind(X)<~>creative(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((rich(X)<~>kind(X)))))&
(((~strong(susan)&~wise(susan)))<=>((funny(susan)&~calm(susan))))&
((?[X]:((humble(X)|curious(X))))=>((old(paul)|~tall(paul))))&
(kind(fred))&
(?[X]:((wise(X)|humble(X))))&
((~humble(susan)<~>quiet(susan)))&
(~wise(alice))&
((happy(susan)|brave(susan)))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:((~curious(X)|brave(X))))&
((~quiet(susan)&~tall(susan))) | ~humble(mary) | []
| null | 0 |
Everyone who is either humble or not creative is not happy or not rich.
Everyone who is not humble or creative is not strong.
Everyone who is not wise is both generous and strong.
If someone is either not quiet or wise then lucy is creative and vice versa.
Everyone who is strong is either curious or calm and vice versa.
If lucy is both quiet and not kind then susan is either tall or not patient.
If someone is not rich then alice is not rich or brave.
Everyone who is either curious or tall is both tall and not happy.
Everyone who is both old and patient is either not brave or not tall and vice versa.
Everyone who is either quiet or happy is not funny or humble and vice versa.
Everyone who is not generous or not kind is not generous and vice versa.
Everyone who is both strong and tall is either not tall or creative and vice versa.
Everyone who is either not rich or not strong is not curious or calm and vice versa.
If paul is either not generous or not wise then mary is rich.
Everyone who is both curious and creative is not creative or not happy and vice versa.
If alice is either not kind or not creative then john is quiet or not happy and vice versa.
Fred is either not rich or not old.
Someone is not curious or not humble.
Someone is both quiet and not tall.
Someone is either generous or happy.
Mary is strong or generous.
Someone is not wise or old. | Paul is humble. | contradiction | (![X]:((humble(X)<~>~creative(X))=>(~happy(X)|~rich(X))))&
(![X]:((~humble(X)|creative(X))=>~strong(X)))&
(![X]:(~wise(X)=>(generous(X)&strong(X))))&
((?[X]:((~quiet(X)<~>wise(X))))<=>(creative(lucy)))&
(![X]:(strong(X)<=>(curious(X)<~>calm(X))))&
(((quiet(lucy)&~kind(lucy)))=>((tall(susan)<~>~patient(susan))))&
((?[X]:(~rich(X)))=>((~rich(alice)|brave(alice))))&
(![X]:((curious(X)<~>tall(X))=>(tall(X)&~happy(X))))&
(![X]:((old(X)&patient(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>~generous(X)))&
(![X]:((strong(X)&tall(X))<=>(~tall(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(~curious(X)|calm(X))))&
(((~generous(paul)<~>~wise(paul)))=>(rich(mary)))&
(![X]:((curious(X)&creative(X))<=>(~creative(X)|~happy(X))))&
(((~kind(alice)<~>~creative(alice)))<=>((quiet(john)|~happy(john))))&
((~rich(fred)<~>~old(fred)))&
(?[X]:((~curious(X)|~humble(X))))&
(?[X]:((quiet(X)&~tall(X))))&
(?[X]:((generous(X)<~>happy(X))))&
((strong(mary)|generous(mary)))&
(?[X]:((~wise(X)|old(X)))) | humble(paul) | [
"p0",
"p1",
"p4",
"p7",
"p11",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7022639858435518756976648
% SZS output start Proof for 7022639858435518756976648
1. ! [X0] : ((humble(X0) <~> ~creative(X0)) => (~rich(X0) | ~happy(X0))) [input p0]
2. ! [X0] : ((creative(X0) | ~humble(X0)) => ~strong(X0)) [input p1]
5. ! [X0] : (strong(X0) <=> (curious(X0) <~> calm(X0))) [input p4]
8. ! [X0] : ((curious(X0) <~> tall(X0)) => (~happy(X0) & tall(X0))) [input p7]
12. ! [X0] : ((tall(X0) & strong(X0)) <=> (~tall(X0) <~> creative(X0))) [input p11]
13. ! [X0] : ((~rich(X0) <~> ~strong(X0)) <=> (calm(X0) | ~curious(X0))) [input p12]
15. ! [X0] : ((creative(X0) & curious(X0)) <=> (~happy(X0) | ~creative(X0))) [input p14]
23. humble(paul) [input hypothesis]
24. ! [X0] : ((~rich(X0) | ~happy(X0)) | (humble(X0) <=> ~creative(X0))) [ennf transformation 1]
25. ! [X0] : (~rich(X0) | ~happy(X0) | (humble(X0) <=> ~creative(X0))) [flattening 24]
26. ! [X0] : (~strong(X0) | (~creative(X0) & humble(X0))) [ennf transformation 2]
32. ! [X0] : ((~happy(X0) & tall(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 8]
34. ! [X0] : (~rich(X0) | ~happy(X0) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) [nnf transformation 25]
39. ! [X0] : ((strong(X0) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ~strong(X0))) [nnf transformation 5]
41. ! [X0] : ((~happy(X0) & tall(X0)) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 32]
48. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~tall(X0) | ~strong(X0)))) [nnf transformation 12]
49. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ~tall(X0) | ~strong(X0))) [flattening 48]
50. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [nnf transformation 13]
51. ! [X0] : ((((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))))) [flattening 50]
53. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~creative(X0) | ~curious(X0)))) [nnf transformation 15]
54. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~creative(X0) | ~curious(X0))) [flattening 53]
67. ~rich(X0) | ~happy(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 34]
70. ~strong(X0) | ~creative(X0) [cnf transformation 26]
79. ~curious(X0) | calm(X0) | strong(X0) [cnf transformation 39]
84. tall(X0) | tall(X0) | ~curious(X0) [cnf transformation 41]
106. strong(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 49]
113. curious(X0) | rich(X0) | strong(X0) [cnf transformation 51]
114. ~calm(X0) | rich(X0) | strong(X0) [cnf transformation 51]
119. curious(X0) | happy(X0) [cnf transformation 54]
120. creative(X0) | creative(X0) [cnf transformation 54]
137. humble(paul) [cnf transformation 23]
139. creative(X0) [duplicate literal removal 120]
142. ~curious(X0) | tall(X0) [duplicate literal removal 84]
184. 10 <=> ! [X0] : rich(X0) [avatar definition]
185. rich(X0) <- (10) [avatar component clause 184]
195. ~tall(X0) | ~creative(X0) [subsumption resolution 106,70]
302. tall(X0) | happy(X0) [resolution 142,119]
315. happy(X1) | ~creative(X1) [resolution 302,195]
316. happy(X1) [subsumption resolution 315,139]
344. rich(X1) | strong(X1) | calm(X1) | strong(X1) [resolution 113,79]
347. rich(X1) | strong(X1) | calm(X1) [duplicate literal removal 344]
349. strong(X1) | rich(X1) [subsumption resolution 347,114]
358. rich(X3) | ~creative(X3) [resolution 349,70]
362. rich(X3) [subsumption resolution 358,139]
363. 10 [avatar split clause 362,184]
369. ~happy(X1) | ~creative(X1) | ~humble(X1) <- (10) [resolution 67,185]
374. ~creative(X1) | ~humble(X1) <- (10) [subsumption resolution 369,316]
375. ~humble(X1) <- (10) [subsumption resolution 374,139]
395. $false <- (10) [resolution 375,137]
396. ~10 [avatar contradiction clause 395]
397. $false [avatar sat refutation 363,396]
% SZS output end Proof for 7022639858435518756976648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then someone is both creative and wise.
If paul is either not quiet or creative then fred is patient and vice versa.
If someone is not old or not patient then paul is not curious or not strong.
Everyone who is both not funny and wise is both not creative and creative.
Everyone who is generous or not curious is not rich or kind.
Everyone who is either not generous or not happy is both not calm and humble.
If someone is tall then susan is humble and vice versa.
Everyone who is curious or humble is generous or funny and vice versa.
If someone is strong then someone is either humble or curious and vice versa.
If someone is both rich and not old then someone is not kind.
If someone is curious or not calm then paul is both not patient and old and vice versa.
If someone is old or not kind then someone is rich.
If lucy is both not rich and rich then someone is both not rich and humble.
Everyone who is both kind and strong is either humble or funny and vice versa.
Everyone who is strong or not humble is both not kind and not calm and vice versa.
If someone is humble then susan is both old and strong and vice versa.
Someone is both strong and not brave.
Someone is either not humble or not curious.
Someone is either not calm or not quiet.
Someone is not strong.
Someone is not tall.
Someone is either not rich or rich.
Someone is either not brave or patient.
Fred is both not humble and creative. | Paul is not patient. | entailment | ((wise(paul))=>(?[X]:((creative(X)&wise(X)))))&
(((~quiet(paul)<~>creative(paul)))<=>(patient(fred)))&
((?[X]:((~old(X)|~patient(X))))=>((~curious(paul)|~strong(paul))))&
(![X]:((~funny(X)&wise(X))=>(~creative(X)&creative(X))))&
(![X]:((generous(X)|~curious(X))=>(~rich(X)|kind(X))))&
(![X]:((~generous(X)<~>~happy(X))=>(~calm(X)&humble(X))))&
((?[X]:(tall(X)))<=>(humble(susan)))&
(![X]:((curious(X)|humble(X))<=>(generous(X)|funny(X))))&
((?[X]:(strong(X)))<=>(?[X]:((humble(X)<~>curious(X)))))&
((?[X]:((rich(X)&~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~calm(X))))<=>((~patient(paul)&old(paul))))&
((?[X]:((old(X)|~kind(X))))=>(?[X]:(rich(X))))&
(((~rich(lucy)&rich(lucy)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((kind(X)&strong(X))<=>(humble(X)<~>funny(X))))&
(![X]:((strong(X)|~humble(X))<=>(~kind(X)&~calm(X))))&
((?[X]:(humble(X)))<=>((old(susan)&strong(susan))))&
(?[X]:((strong(X)&~brave(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
(?[X]:((~brave(X)<~>patient(X))))&
((~humble(fred)&creative(fred))) | ~patient(paul) | [
"p10",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 6471254426188432798417803
% SZS output start Proof for 6471254426188432798417803
11. ? [X0] : (~calm(X0) | curious(X0)) <=> (old(paul) & ~patient(paul)) [input p10]
15. ! [X0] : ((~humble(X0) | strong(X0)) <=> (~calm(X0) & ~kind(X0))) [input p14]
17. ? [X0] : (~brave(X0) & strong(X0)) [input p16]
25. patient(paul) [input hypothesis]
59. (? [X0] : (~calm(X0) | curious(X0)) | (~old(paul) | patient(paul))) & ((old(paul) & ~patient(paul)) | ! [X0] : (calm(X0) & ~curious(X0))) [nnf transformation 11]
60. (? [X0] : (~calm(X0) | curious(X0)) | ~old(paul) | patient(paul)) & ((old(paul) & ~patient(paul)) | ! [X0] : (calm(X0) & ~curious(X0))) [flattening 59]
61. (? [X0] : (~calm(X0) | curious(X0)) | ~old(paul) | patient(paul)) & ((old(paul) & ~patient(paul)) | ! [X1] : (calm(X1) & ~curious(X1))) [rectify 60]
62. ? [X0] : (~calm(X0) | curious(X0)) => (~calm(sK5) | curious(sK5)) [choice axiom]
63. ((~calm(sK5) | curious(sK5)) | ~old(paul) | patient(paul)) & ((old(paul) & ~patient(paul)) | ! [X1] : (calm(X1) & ~curious(X1))) [skolemisation 61,62]
71. ! [X0] : (((~humble(X0) | strong(X0)) | (calm(X0) | kind(X0))) & ((~calm(X0) & ~kind(X0)) | (humble(X0) & ~strong(X0)))) [nnf transformation 15]
72. ! [X0] : ((~humble(X0) | strong(X0) | calm(X0) | kind(X0)) & ((~calm(X0) & ~kind(X0)) | (humble(X0) & ~strong(X0)))) [flattening 71]
78. ? [X0] : (~brave(X0) & strong(X0)) => (~brave(sK9) & strong(sK9)) [choice axiom]
79. ~brave(sK9) & strong(sK9) [skolemisation 17,78]
124. ~patient(paul) | calm(X1) [cnf transformation 63]
140. ~calm(X0) | ~strong(X0) [cnf transformation 72]
146. strong(sK9) [cnf transformation 79]
160. patient(paul) [cnf transformation 25]
234. 17 <=> ! [X3] : ~strong(X3) [avatar definition]
235. ~strong(X3) <- (17) [avatar component clause 234]
255. 22 <=> patient(paul) [avatar definition]
272. 26 <=> ! [X1] : calm(X1) [avatar definition]
273. calm(X1) <- (26) [avatar component clause 272]
279. 26 | ~22 [avatar split clause 124,255,272]
341. 22 [avatar split clause 160,255]
346. ~strong(X0) <- (26) [resolution 140,273]
348. 17 | ~26 [avatar split clause 346,272,234]
349. $false <- (17) [resolution 235,146]
352. ~17 [avatar contradiction clause 349]
353. $false [avatar sat refutation 279,341,348,352]
% SZS output end Proof for 6471254426188432798417803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not calm is not creative or funny.
If alice is either not quiet or not wise then john is both wise and curious.
If someone is not old or not wise then someone is not kind and vice versa.
Everyone who is either not humble or wise is not brave and vice versa.
Everyone who is both not old and not happy is both not strong and curious and vice versa.
Everyone who is not generous is either not curious or humble.
Everyone who is happy or calm is both humble and not happy and vice versa.
If someone is either quiet or not rich then susan is either wise or brave.
If paul is tall then john is both not tall and not rich and vice versa.
Everyone who is either not calm or strong is wise.
If someone is both tall and not funny then someone is not brave or rich.
Everyone who is patient or strong is rich and vice versa.
Everyone who is creative or not strong is both not calm and strong and vice versa.
If fred is both not rich and not humble then susan is both not funny and quiet and vice versa.
Everyone who is strong is tall or not funny.
If someone is happy or generous then someone is either kind or not tall and vice versa.
Someone is either rich or tall.
Someone is either not patient or not creative.
John is either brave or generous.
Alice is curious or tall.
Someone is not happy.
John is happy or not kind. | Susan is not rich. | contradiction | (![X]:((~funny(X)&~calm(X))=>(~creative(X)|funny(X))))&
(((~quiet(alice)<~>~wise(alice)))=>((wise(john)&curious(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~brave(X)))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&curious(X))))&
(![X]:(~generous(X)=>(~curious(X)<~>humble(X))))&
(![X]:((happy(X)|calm(X))<=>(humble(X)&~happy(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>((wise(susan)<~>brave(susan))))&
((tall(paul))<=>((~tall(john)&~rich(john))))&
(![X]:((~calm(X)<~>strong(X))=>wise(X)))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(![X]:((patient(X)|strong(X))<=>rich(X)))&
(![X]:((creative(X)|~strong(X))<=>(~calm(X)&strong(X))))&
(((~rich(fred)&~humble(fred)))<=>((~funny(susan)&quiet(susan))))&
(![X]:(strong(X)=>(tall(X)|~funny(X))))&
((?[X]:((happy(X)|generous(X))))<=>(?[X]:((kind(X)<~>~tall(X)))))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((~patient(X)<~>~creative(X))))&
((brave(john)<~>generous(john)))&
((curious(alice)|tall(alice)))&
(?[X]:(~happy(X)))&
((happy(john)|~kind(john))) | ~rich(susan) | [
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 5120714182139932912367251
% SZS output start Proof for 5120714182139932912367251
12. ! [X0] : ((strong(X0) | patient(X0)) <=> rich(X0)) [input p11]
13. ! [X0] : ((~strong(X0) | creative(X0)) <=> (strong(X0) & ~calm(X0))) [input p12]
23. ~rich(susan) [input hypothesis]
55. ! [X0] : (((strong(X0) | patient(X0)) | ~rich(X0)) & (rich(X0) | (~strong(X0) & ~patient(X0)))) [nnf transformation 12]
56. ! [X0] : ((strong(X0) | patient(X0) | ~rich(X0)) & (rich(X0) | (~strong(X0) & ~patient(X0)))) [flattening 55]
57. ! [X0] : (((~strong(X0) | creative(X0)) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 13]
58. ! [X0] : ((~strong(X0) | creative(X0) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [flattening 57]
109. ~strong(X0) | rich(X0) [cnf transformation 56]
114. strong(X0) | strong(X0) [cnf transformation 58]
136. ~rich(susan) [cnf transformation 23]
137. strong(X0) [duplicate literal removal 114]
320. rich(X0) [resolution 109,137]
321. $false [resolution 320,136]
% SZS output end Proof for 5120714182139932912367251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not strong then paul is not old or not happy. If john is either not creative or not funny then someone is either generous or wise and vice versa. Everyone who is happy is old. If someone is old or not generous then fred is both tall and not quiet and vice versa. If someone is wise then susan is old and vice versa. Everyone who is either wise or not wise is wise or kind. Everyone who is not generous is both not patient and brave and vice versa. Everyone who is both rich and curious is both not calm and tall and vice versa. If someone is patient or not creative then someone is either old or not happy and vice versa. If someone is calm then paul is both curious and generous and vice versa. Everyone who is creative or not patient is humble. Everyone who is either patient or not brave is not rich and vice versa. Everyone who is not brave or not generous is either humble or not generous. If susan is either happy or not generous then alice is both quiet and not humble. Everyone who is not tall or not funny is either happy or not kind and vice versa. If someone is either not rich or tall then mary is either quiet or not rich. Fred is wise. Someone is not wise. Someone is tall. Someone is not tall. Someone is both not humble and happy. Alice is not wise or happy. John is either funny or tall. Someone is either rich or funny. | John is funny. | neutral | ((?[X]:((calm(X)<~>~strong(X))))=>((~old(paul)|~happy(paul))))&
(((~creative(john)<~>~funny(john)))<=>(?[X]:((generous(X)<~>wise(X)))))&
(![X]:(happy(X)=>old(X)))&
((?[X]:((old(X)|~generous(X))))<=>((tall(fred)&~quiet(fred))))&
((?[X]:(wise(X)))<=>(old(susan)))&
(![X]:((wise(X)<~>~wise(X))=>(wise(X)|kind(X))))&
(![X]:(~generous(X)<=>(~patient(X)&brave(X))))&
(![X]:((rich(X)&curious(X))<=>(~calm(X)&tall(X))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((old(X)<~>~happy(X)))))&
((?[X]:(calm(X)))<=>((curious(paul)&generous(paul))))&
(![X]:((creative(X)|~patient(X))=>humble(X)))&
(![X]:((patient(X)<~>~brave(X))<=>~rich(X)))&
(![X]:((~brave(X)|~generous(X))=>(humble(X)<~>~generous(X))))&
(((happy(susan)<~>~generous(susan)))=>((quiet(alice)&~humble(alice))))&
(![X]:((~tall(X)|~funny(X))<=>(happy(X)<~>~kind(X))))&
((?[X]:((~rich(X)<~>tall(X))))=>((quiet(mary)<~>~rich(mary))))&
(wise(fred))&
(?[X]:(~wise(X)))&
(?[X]:(tall(X)))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)&happy(X))))&
((~wise(alice)|happy(alice)))&
((funny(john)<~>tall(john)))&
(?[X]:((rich(X)<~>funny(X)))) | funny(john) | []
| null | 0 |
If mary is both not wise and not patient then someone is not patient. If someone is creative then paul is both not curious and not funny and vice versa. Everyone who is both rich and happy is generous and vice versa. Everyone who is calm is not happy and vice versa. If mary is not quiet or tall then someone is either generous or not tall and vice versa. If susan is both humble and tall then mary is both rich and not old. Everyone who is patient or not wise is both calm and not strong. If someone is humble or creative then alice is not wise or humble. If someone is either patient or not strong then someone is not strong. Everyone who is either not rich or not happy is creative or not happy and vice versa. If mary is both not rich and not generous then alice is strong. If someone is both funny and not strong then someone is either kind or not brave and vice versa. If someone is rich then mary is both not happy and not patient and vice versa. If paul is both not curious and strong then someone is creative or not tall. Everyone who is either creative or wise is both funny and not funny and vice versa. If alice is not funny or generous then lucy is not curious. Susan is both not kind and not humble. Someone is both calm and not creative. Someone is either not tall or not generous. Someone is both creative and quiet. Someone is not calm or calm. Susan is both brave and not funny. Lucy is either curious or not humble. Lucy is humble. | Susan is humble. | contradiction | (((~wise(mary)&~patient(mary)))=>(?[X]:(~patient(X))))&
((?[X]:(creative(X)))<=>((~curious(paul)&~funny(paul))))&
(![X]:((rich(X)&happy(X))<=>generous(X)))&
(![X]:(calm(X)<=>~happy(X)))&
(((~quiet(mary)|tall(mary)))<=>(?[X]:((generous(X)<~>~tall(X)))))&
(((humble(susan)&tall(susan)))=>((rich(mary)&~old(mary))))&
(![X]:((patient(X)|~wise(X))=>(calm(X)&~strong(X))))&
((?[X]:((humble(X)|creative(X))))=>((~wise(alice)|humble(alice))))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:(~strong(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(creative(X)|~happy(X))))&
(((~rich(mary)&~generous(mary)))=>(strong(alice)))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:(rich(X)))<=>((~happy(mary)&~patient(mary))))&
(((~curious(paul)&strong(paul)))=>(?[X]:((creative(X)|~tall(X)))))&
(![X]:((creative(X)<~>wise(X))<=>(funny(X)&~funny(X))))&
(((~funny(alice)|generous(alice)))=>(~curious(lucy)))&
((~kind(susan)&~humble(susan)))&
(?[X]:((calm(X)&~creative(X))))&
(?[X]:((~tall(X)<~>~generous(X))))&
(?[X]:((creative(X)&quiet(X))))&
(?[X]:((~calm(X)|calm(X))))&
((brave(susan)&~funny(susan)))&
((curious(lucy)<~>~humble(lucy)))&
(humble(lucy)) | humble(susan) | [
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 3357541978463820374531507
% SZS output start Proof for 3357541978463820374531507
17. ~humble(susan) & ~kind(susan) [input p16]
25. humble(susan) [input hypothesis]
137. ~humble(susan) [cnf transformation 17]
150. humble(susan) [cnf transformation 25]
213. 14 <=> humble(susan) [avatar definition]
327. ~14 [avatar split clause 137,213]
345. 14 [avatar split clause 150,213]
346. $false [avatar sat refutation 327,345]
% SZS output end Proof for 3357541978463820374531507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not rich is both generous and humble. Everyone who is either not patient or patient is not funny or generous and vice versa. If john is either generous or calm then fred is both not strong and not calm. Everyone who is either patient or tall is either not strong or old. Everyone who is old or not wise is either quiet or patient and vice versa. Everyone who is humble or rich is both rich and kind. Everyone who is both not quiet and not wise is not funny or not strong and vice versa. If someone is either not old or not humble then paul is tall or happy and vice versa. If someone is wise then fred is wise or not creative. If someone is not calm then lucy is both not tall and not rich and vice versa. Everyone who is both not brave and rich is not quiet and vice versa. Everyone who is both quiet and not brave is either rich or not funny and vice versa. Everyone who is old is calm or not happy and vice versa. Everyone who is both strong and not calm is either kind or happy and vice versa. Everyone who is both curious and not tall is not rich or quiet and vice versa. If paul is funny then someone is both not old and old and vice versa. Alice is either brave or not funny. Someone is either not happy or not generous. Susan is patient. Someone is both brave and not humble. Someone is either not humble or not curious. Someone is generous. | Susan is funny. | contradiction | (![X]:((quiet(X)<~>~rich(X))=>(generous(X)&humble(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(~funny(X)|generous(X))))&
(((generous(john)<~>calm(john)))=>((~strong(fred)&~calm(fred))))&
(![X]:((patient(X)<~>tall(X))=>(~strong(X)<~>old(X))))&
(![X]:((old(X)|~wise(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((humble(X)|rich(X))=>(rich(X)&kind(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(~funny(X)|~strong(X))))&
((?[X]:((~old(X)<~>~humble(X))))<=>((tall(paul)|happy(paul))))&
((?[X]:(wise(X)))=>((wise(fred)|~creative(fred))))&
((?[X]:(~calm(X)))<=>((~tall(lucy)&~rich(lucy))))&
(![X]:((~brave(X)&rich(X))<=>~quiet(X)))&
(![X]:((quiet(X)&~brave(X))<=>(rich(X)<~>~funny(X))))&
(![X]:(old(X)<=>(calm(X)|~happy(X))))&
(![X]:((strong(X)&~calm(X))<=>(kind(X)<~>happy(X))))&
(![X]:((curious(X)&~tall(X))<=>(~rich(X)|quiet(X))))&
((funny(paul))<=>(?[X]:((~old(X)&old(X)))))&
((brave(alice)<~>~funny(alice)))&
(?[X]:((~happy(X)<~>~generous(X))))&
(patient(susan))&
(?[X]:((brave(X)&~humble(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:(generous(X))) | funny(susan) | [
"p3",
"p4",
"p6",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 4530754303611866531596212
% SZS output start Proof for 4530754303611866531596212
4. ! [X0] : ((patient(X0) <~> tall(X0)) => (~strong(X0) <~> old(X0))) [input p3]
5. ! [X0] : ((~wise(X0) | old(X0)) <=> (quiet(X0) <~> patient(X0))) [input p4]
7. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (~strong(X0) | ~funny(X0))) [input p6]
11. ! [X0] : ((rich(X0) & ~brave(X0)) <=> ~quiet(X0)) [input p10]
12. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (rich(X0) <~> ~funny(X0))) [input p11]
15. ! [X0] : ((~tall(X0) & curious(X0)) <=> (quiet(X0) | ~rich(X0))) [input p14]
19. patient(susan) [input p18]
23. funny(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) <~> old(X0)) | (patient(X0) <=> tall(X0))) [ennf transformation 4]
33. ! [X0] : (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) [nnf transformation 27]
34. ! [X0] : (((~wise(X0) | old(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (wise(X0) & ~old(X0)))) [nnf transformation 5]
35. ! [X0] : ((~wise(X0) | old(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (wise(X0) & ~old(X0)))) [flattening 34]
36. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 7]
37. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | wise(X0) | quiet(X0))) [flattening 36]
48. ! [X0] : (((rich(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | (~rich(X0) | brave(X0)))) [nnf transformation 11]
49. ! [X0] : (((rich(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | ~rich(X0) | brave(X0))) [flattening 48]
50. ! [X0] : (((~brave(X0) & quiet(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 12]
51. ! [X0] : (((~brave(X0) & quiet(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | brave(X0) | ~quiet(X0))) [flattening 50]
56. ! [X0] : (((~tall(X0) & curious(X0)) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | (tall(X0) | ~curious(X0)))) [nnf transformation 15]
57. ! [X0] : (((~tall(X0) & curious(X0)) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | tall(X0) | ~curious(X0))) [flattening 56]
87. ~strong(X0) | old(X0) | tall(X0) | ~patient(X0) [cnf transformation 33]
93. ~old(X0) | ~quiet(X0) | ~patient(X0) [cnf transformation 35]
102. ~quiet(X0) | funny(X0) [cnf transformation 37]
103. ~quiet(X0) | strong(X0) [cnf transformation 37]
115. ~rich(X0) | ~quiet(X0) | brave(X0) [cnf transformation 49]
117. rich(X0) | quiet(X0) [cnf transformation 49]
118. ~funny(X0) | rich(X0) | brave(X0) | ~quiet(X0) [cnf transformation 51]
120. quiet(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 51]
122. ~brave(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 51]
136. ~tall(X0) | rich(X0) [cnf transformation 57]
145. patient(susan) [cnf transformation 19]
151. funny(susan) [cnf transformation 23]
221. ~funny(X0) | quiet(X0) [subsumption resolution 120,117]
222. rich(X0) | brave(X0) | ~quiet(X0) [subsumption resolution 118,102]
223. ~quiet(X0) | brave(X0) [subsumption resolution 222,115]
281. quiet(susan) [resolution 221,151]
285. strong(susan) [resolution 281,103]
289. brave(susan) [resolution 223,281]
345. ~funny(susan) | ~rich(susan) [resolution 122,289]
347. ~rich(susan) [subsumption resolution 345,151]
478. old(susan) | tall(susan) | ~patient(susan) [resolution 87,285]
493. old(susan) | tall(susan) [subsumption resolution 478,145]
495. 46 <=> tall(susan) [avatar definition]
497. tall(susan) <- (46) [avatar component clause 495]
499. 47 <=> old(susan) [avatar definition]
501. old(susan) <- (47) [avatar component clause 499]
502. 46 | 47 [avatar split clause 493,499,495]
772. rich(susan) <- (46) [resolution 497,136]
775. $false <- (46) [subsumption resolution 772,347]
776. ~46 [avatar contradiction clause 775]
785. ~quiet(susan) | ~patient(susan) <- (47) [resolution 501,93]
787. ~patient(susan) <- (47) [subsumption resolution 785,281]
788. $false <- (47) [subsumption resolution 787,145]
789. ~47 [avatar contradiction clause 788]
790. $false [avatar sat refutation 502,776,789]
% SZS output end Proof for 4530754303611866531596212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is both not humble and patient then someone is either patient or not wise. If paul is either not kind or not curious then lucy is humble or not curious. Everyone who is both wise and not patient is not generous and vice versa. Everyone who is not old or happy is creative and vice versa. If someone is both not kind and wise then someone is both not happy and generous. Everyone who is not old or not funny is either not funny or not old. If someone is not brave or not curious then mary is calm and vice versa. If someone is not generous or creative then susan is both not humble and creative and vice versa. Everyone who is either quiet or not curious is patient or not funny and vice versa. If someone is curious or not brave then mary is either rich or not patient. If someone is either rich or wise then susan is funny or not old and vice versa. Everyone who is generous is both not happy and curious and vice versa. Everyone who is either patient or strong is not funny or not tall. Everyone who is either not kind or kind is both rich and quiet. If mary is humble then someone is not rich and vice versa. Everyone who is both not kind and funny is either generous or patient. Susan is not creative or tall. Someone is strong. Lucy is not brave or not strong. | Mary is curious. | entailment | (((~humble(paul)&patient(paul)))=>(?[X]:((patient(X)<~>~wise(X)))))&
(((~kind(paul)<~>~curious(paul)))=>((humble(lucy)|~curious(lucy))))&
(![X]:((wise(X)&~patient(X))<=>~generous(X)))&
(![X]:((~old(X)|happy(X))<=>creative(X)))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:((~old(X)|~funny(X))=>(~funny(X)<~>~old(X))))&
((?[X]:((~brave(X)|~curious(X))))<=>(calm(mary)))&
((?[X]:((~generous(X)|creative(X))))<=>((~humble(susan)&creative(susan))))&
(![X]:((quiet(X)<~>~curious(X))<=>(patient(X)|~funny(X))))&
((?[X]:((curious(X)|~brave(X))))=>((rich(mary)<~>~patient(mary))))&
((?[X]:((rich(X)<~>wise(X))))<=>((funny(susan)|~old(susan))))&
(![X]:(generous(X)<=>(~happy(X)&curious(X))))&
(![X]:((patient(X)<~>strong(X))=>(~funny(X)|~tall(X))))&
(![X]:((~kind(X)<~>kind(X))=>(rich(X)&quiet(X))))&
((humble(mary))<=>(?[X]:(~rich(X))))&
(![X]:((~kind(X)&funny(X))=>(generous(X)<~>patient(X))))&
((~creative(susan)|tall(susan)))&
(?[X]:(strong(X)))&
((~brave(lucy)|~strong(lucy))) | curious(mary) | [
"p2",
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 3408693847412333688964497
% SZS output start Proof for 3408693847412333688964497
3. ! [X0] : ((~patient(X0) & wise(X0)) <=> ~generous(X0)) [input p2]
9. ! [X0] : ((quiet(X0) <~> ~curious(X0)) <=> (~funny(X0) | patient(X0))) [input p8]
10. ? [X0] : (~brave(X0) | curious(X0)) => (rich(mary) <~> ~patient(mary)) [input p9]
11. ? [X0] : (rich(X0) <~> wise(X0)) <=> (~old(susan) | funny(susan)) [input p10]
12. ! [X0] : (generous(X0) <=> (curious(X0) & ~happy(X0))) [input p11]
14. ! [X0] : ((~kind(X0) <~> kind(X0)) => (quiet(X0) & rich(X0))) [input p13]
20. ~curious(mary) [input hypothesis]
28. (rich(mary) <~> ~patient(mary)) | ! [X0] : (brave(X0) & ~curious(X0)) [ennf transformation 10]
31. ! [X0] : ((quiet(X0) & rich(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 14]
38. ! [X0] : (((~patient(X0) & wise(X0)) | generous(X0)) & (~generous(X0) | (patient(X0) | ~wise(X0)))) [nnf transformation 3]
39. ! [X0] : (((~patient(X0) & wise(X0)) | generous(X0)) & (~generous(X0) | patient(X0) | ~wise(X0))) [flattening 38]
55. ! [X0] : ((((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | (funny(X0) & ~patient(X0))) & ((~funny(X0) | patient(X0)) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0))))) [nnf transformation 9]
56. ! [X0] : ((((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | (funny(X0) & ~patient(X0))) & (~funny(X0) | patient(X0) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0))))) [flattening 55]
57. ((patient(mary) | ~rich(mary)) & (~patient(mary) | rich(mary))) | ! [X0] : (brave(X0) & ~curious(X0)) [nnf transformation 28]
58. (? [X0] : ((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | (old(susan) & ~funny(susan))) & ((~old(susan) | funny(susan)) | ! [X0] : ((rich(X0) | ~wise(X0)) & (wise(X0) | ~rich(X0)))) [nnf transformation 11]
59. (? [X0] : ((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | (old(susan) & ~funny(susan))) & (~old(susan) | funny(susan) | ! [X0] : ((rich(X0) | ~wise(X0)) & (wise(X0) | ~rich(X0)))) [flattening 58]
60. (? [X0] : ((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | (old(susan) & ~funny(susan))) & (~old(susan) | funny(susan) | ! [X1] : ((rich(X1) | ~wise(X1)) & (wise(X1) | ~rich(X1)))) [rectify 59]
61. ? [X0] : ((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) => ((~wise(sK4) | ~rich(sK4)) & (wise(sK4) | rich(sK4))) [choice axiom]
62. (((~wise(sK4) | ~rich(sK4)) & (wise(sK4) | rich(sK4))) | (old(susan) & ~funny(susan))) & (~old(susan) | funny(susan) | ! [X1] : ((rich(X1) | ~wise(X1)) & (wise(X1) | ~rich(X1)))) [skolemisation 60,61]
63. ! [X0] : ((generous(X0) | (~curious(X0) | happy(X0))) & ((curious(X0) & ~happy(X0)) | ~generous(X0))) [nnf transformation 12]
64. ! [X0] : ((generous(X0) | ~curious(X0) | happy(X0)) & ((curious(X0) & ~happy(X0)) | ~generous(X0))) [flattening 63]
66. ! [X0] : ((quiet(X0) & rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 31]
79. generous(X0) | wise(X0) [cnf transformation 39]
80. ~patient(X0) | generous(X0) [cnf transformation 39]
103. ~quiet(X0) | curious(X0) | funny(X0) [cnf transformation 56]
106. patient(mary) | ~rich(mary) | ~curious(X0) [cnf transformation 57]
112. ~wise(sK4) | ~rich(sK4) | ~funny(susan) [cnf transformation 62]
115. ~generous(X0) | curious(X0) [cnf transformation 64]
119. rich(X0) | kind(X0) | kind(X0) [cnf transformation 66]
120. rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 66]
121. quiet(X0) | kind(X0) | kind(X0) [cnf transformation 66]
122. quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 66]
130. ~curious(mary) [cnf transformation 20]
131. rich(X0) | kind(X0) [duplicate literal removal 119]
132. ~kind(X0) | rich(X0) [duplicate literal removal 120]
133. quiet(X0) | kind(X0) [duplicate literal removal 121]
134. ~kind(X0) | quiet(X0) [duplicate literal removal 122]
235. 23 <=> rich(mary) [avatar definition]
237. ~rich(mary) <- (~23) [avatar component clause 235]
239. 24 <=> patient(mary) [avatar definition]
241. patient(mary) <- (24) [avatar component clause 239]
244. 25 <=> ! [X0] : ~curious(X0) [avatar definition]
245. ~curious(X0) <- (25) [avatar component clause 244]
246. 25 | ~23 | 24 [avatar split clause 106,239,235,244]
254. 27 <=> rich(sK4) [avatar definition]
256. ~rich(sK4) <- (~27) [avatar component clause 254]
258. 28 <=> wise(sK4) [avatar definition]
260. ~wise(sK4) <- (~28) [avatar component clause 258]
263. 29 <=> funny(susan) [avatar definition]
265. ~funny(susan) <- (~29) [avatar component clause 263]
266. ~29 | ~27 | ~28 [avatar split clause 112,258,254,263]
279. quiet(X0) [subsumption resolution 133,134]
280. rich(X0) [subsumption resolution 131,132]
298. $false <- (~23) [subsumption resolution 237,280]
299. 23 [avatar contradiction clause 298]
300. generous(mary) <- (24) [resolution 80,241]
302. curious(X0) | wise(X0) [resolution 115,79]
312. curious(mary) <- (24) [resolution 300,115]
313. $false <- (24) [subsumption resolution 312,130]
314. ~24 [avatar contradiction clause 313]
323. wise(X0) <- (25) [resolution 302,245]
337. curious(X0) | funny(X0) [resolution 103,279]
338. funny(X0) <- (25) [subsumption resolution 337,245]
340. $false <- (25, ~28) [resolution 323,260]
342. ~25 | 28 [avatar contradiction clause 340]
343. $false <- (~27) [subsumption resolution 256,280]
344. 27 [avatar contradiction clause 343]
345. $false <- (25, ~29) [subsumption resolution 265,338]
346. ~25 | 29 [avatar contradiction clause 345]
347. $false [avatar sat refutation 246,266,299,314,342,344,346]
% SZS output end Proof for 3408693847412333688964497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not wise is both not brave and brave. Everyone who is either happy or generous is strong. If someone is kind or tall then john is not kind or not patient. Everyone who is generous or not old is rich or tall. Everyone who is either not funny or curious is not quiet or curious. Everyone who is either tall or not rich is not creative and vice versa. Everyone who is both not patient and not wise is not funny or not happy and vice versa. If someone is not humble or not rich then john is both humble and old. Everyone who is not humble is wise. If someone is funny then someone is both not patient and wise and vice versa. If paul is both not brave and curious then someone is not humble. Everyone who is either not quiet or humble is either patient or not wise. If someone is not quiet or generous then mary is both happy and not calm and vice versa. If someone is quiet then fred is either rich or generous and vice versa. If fred is not calm or tall then mary is either not brave or wise and vice versa. Alice is wise or generous. Someone is either happy or not calm. Paul is both tall and creative. Lucy is old or humble. John is funny. Fred is both funny and not brave. Susan is either rich or generous. Someone is brave. | John is not old. | contradiction | (![X]:((~brave(X)<~>~wise(X))=>(~brave(X)&brave(X))))&
(![X]:((happy(X)<~>generous(X))=>strong(X)))&
((?[X]:((kind(X)|tall(X))))=>((~kind(john)|~patient(john))))&
(![X]:((generous(X)|~old(X))=>(rich(X)|tall(X))))&
(![X]:((~funny(X)<~>curious(X))=>(~quiet(X)|curious(X))))&
(![X]:((tall(X)<~>~rich(X))<=>~creative(X)))&
(![X]:((~patient(X)&~wise(X))<=>(~funny(X)|~happy(X))))&
((?[X]:((~humble(X)|~rich(X))))=>((humble(john)&old(john))))&
(![X]:(~humble(X)=>wise(X)))&
((?[X]:(funny(X)))<=>(?[X]:((~patient(X)&wise(X)))))&
(((~brave(paul)&curious(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~quiet(X)<~>humble(X))=>(patient(X)<~>~wise(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>((happy(mary)&~calm(mary))))&
((?[X]:(quiet(X)))<=>((rich(fred)<~>generous(fred))))&
(((~calm(fred)|tall(fred)))<=>((~brave(mary)<~>wise(mary))))&
((wise(alice)|generous(alice)))&
(?[X]:((happy(X)<~>~calm(X))))&
((tall(paul)&creative(paul)))&
((old(lucy)|humble(lucy)))&
(funny(john))&
((funny(fred)&~brave(fred)))&
((rich(susan)<~>generous(susan)))&
(?[X]:(brave(X))) | ~old(john) | [
"p5",
"p7",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 4227895316503293109567718
% SZS output start Proof for 4227895316503293109567718
6. ! [X0] : ((tall(X0) <~> ~rich(X0)) <=> ~creative(X0)) [input p5]
8. ? [X0] : (~rich(X0) | ~humble(X0)) => (old(john) & humble(john)) [input p7]
18. creative(paul) & tall(paul) [input p17]
24. ~old(john) [input hypothesis]
26. ! [X0] : ((tall(X0) <~> ~rich(X0)) => ~creative(X0)) [unused predicate definition removal 6]
34. ! [X0] : (~creative(X0) | (tall(X0) <=> ~rich(X0))) [ennf transformation 26]
35. (old(john) & humble(john)) | ! [X0] : (rich(X0) & humble(X0)) [ennf transformation 8]
42. ! [X0] : (~creative(X0) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [nnf transformation 34]
78. ~creative(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 42]
88. old(john) | rich(X0) [cnf transformation 35]
116. tall(paul) [cnf transformation 18]
117. creative(paul) [cnf transformation 18]
125. ~old(john) [cnf transformation 24]
130. 1 <=> ! [X0] : rich(X0) [avatar definition]
131. rich(X0) <- (1) [avatar component clause 130]
133. 2 <=> old(john) [avatar definition]
136. 1 | 2 [avatar split clause 88,133,130]
283. ~2 [avatar split clause 125,133]
304. ~rich(paul) | ~tall(paul) [resolution 78,117]
305. ~tall(paul) <- (1) [subsumption resolution 304,131]
306. $false <- (1) [subsumption resolution 305,116]
307. ~1 [avatar contradiction clause 306]
308. $false [avatar sat refutation 136,283,307]
% SZS output end Proof for 4227895316503293109567718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and strong is not creative or creative.
If someone is both not brave and curious then someone is either not happy or creative and vice versa.
Everyone who is both funny and kind is not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Everyone who is happy or not funny is both not strong and not happy and vice versa.
Everyone who is both brave and not generous is both curious and quiet and vice versa.
If someone is both not curious and not wise then paul is wise or patient.
If alice is rich then someone is either funny or brave and vice versa.
If someone is patient or not funny then someone is not humble or not happy.
If mary is brave or generous then mary is not humble.
Everyone who is either kind or quiet is strong and vice versa.
Everyone who is tall or wise is not quiet or happy and vice versa.
Everyone who is not strong or not creative is either curious or not funny and vice versa.
Everyone who is both not happy and not brave is not tall.
If mary is strong then mary is not creative or not brave and vice versa.
Mary is either not happy or wise.
Someone is either humble or tall.
Someone is both old and not funny.
Lucy is either patient or not happy.
Paul is either not happy or old. | Mary is not creative. | contradiction | (![X]:((old(X)&strong(X))=>(~creative(X)|creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((funny(X)&kind(X))=>~strong(X)))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(![X]:((happy(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~generous(X))<=>(curious(X)&quiet(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(paul)|patient(paul))))&
((rich(alice))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
(((brave(mary)|generous(mary)))=>(~humble(mary)))&
(![X]:((kind(X)<~>quiet(X))<=>strong(X)))&
(![X]:((tall(X)|wise(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~strong(X)|~creative(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&~brave(X))=>~tall(X)))&
((strong(mary))<=>((~creative(mary)|~brave(mary))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((old(X)&~funny(X))))&
((patient(lucy)<~>~happy(lucy)))&
((~happy(paul)<~>old(paul))) | ~creative(mary) | [
"p1",
"p2",
"p5",
"p6",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 520805765550676809456247
% SZS output start Proof for 520805765550676809456247
2. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X0] : (~happy(X0) <~> creative(X0)) [input p1]
3. ! [X0] : ((kind(X0) & funny(X0)) => ~strong(X0)) [input p2]
6. ! [X0] : ((~funny(X0) | happy(X0)) <=> (~happy(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((~generous(X0) & brave(X0)) <=> (quiet(X0) & curious(X0))) [input p6]
12. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> strong(X0)) [input p11]
14. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p13]
22. ~creative(mary) [input hypothesis]
23. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X1] : (~happy(X1) <~> creative(X1)) [rectify 2]
27. ! [X0] : (~strong(X0) | (~kind(X0) | ~funny(X0))) [ennf transformation 3]
28. ! [X0] : (~strong(X0) | ~kind(X0) | ~funny(X0)) [flattening 27]
35. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X1] : ((~creative(X1) | happy(X1)) & (creative(X1) | ~happy(X1))) | ! [X0] : (~curious(X0) | brave(X0))) [nnf transformation 23]
36. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) | ! [X3] : (~curious(X3) | brave(X3))) [rectify 35]
37. ? [X0] : (curious(X0) & ~brave(X0)) => (curious(sK0) & ~brave(sK0)) [choice axiom]
38. ? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) => ((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) [choice axiom]
39. ((curious(sK0) & ~brave(sK0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) | ! [X3] : (~curious(X3) | brave(X3))) [skolemisation 36,38,37]
44. ! [X0] : (((~funny(X0) | happy(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~funny(X0) | happy(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [flattening 44]
46. ! [X0] : (((~generous(X0) & brave(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (generous(X0) | ~brave(X0)))) [nnf transformation 7]
47. ! [X0] : (((~generous(X0) & brave(X0)) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | generous(X0) | ~brave(X0))) [flattening 46]
55. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~strong(X0)) & (strong(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 14]
59. ! [X0] : ((~creative(X0) | ~strong(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [flattening 58]
73. ~brave(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
75. curious(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
77. ~kind(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 28]
89. ~strong(X0) | funny(X0) [cnf transformation 45]
90. ~happy(X0) | ~happy(X0) [cnf transformation 45]
92. ~funny(X0) | happy(X0) | happy(X0) | strong(X0) [cnf transformation 45]
95. ~quiet(X0) | brave(X0) | ~curious(X0) [cnf transformation 47]
108. ~strong(X0) | kind(X0) | quiet(X0) [cnf transformation 55]
116. funny(X0) | ~curious(X0) | strong(X0) [cnf transformation 59]
134. ~creative(mary) [cnf transformation 22]
135. ~happy(X0) [duplicate literal removal 90]
136. ~funny(X0) | happy(X0) | strong(X0) [duplicate literal removal 92]
143. 2 <=> curious(sK0) [avatar definition]
145. curious(sK0) <- (2) [avatar component clause 143]
148. 3 <=> ! [X1] : (creative(X1) | happy(X1)) [avatar definition]
149. creative(X1) | happy(X1) <- (3) [avatar component clause 148]
150. 3 | 2 [avatar split clause 75,143,148]
152. 4 <=> brave(sK0) [avatar definition]
154. ~brave(sK0) <- (~4) [avatar component clause 152]
156. 3 | ~4 [avatar split clause 73,152,148]
242. ~curious(X0) | funny(X0) [subsumption resolution 116,89]
250. 24 <=> creative(mary) [avatar definition]
251. ~creative(mary) <- (~24) [avatar component clause 250]
268. ~24 [avatar split clause 134,250]
343. creative(X1) <- (3) [subsumption resolution 149,135]
345. $false <- (3, ~24) [resolution 343,251]
346. ~3 | 24 [avatar contradiction clause 345]
348. funny(sK0) <- (2) [resolution 145,242]
390. 37 <=> strong(sK0) [avatar definition]
391. strong(sK0) <- (37) [avatar component clause 390]
410. happy(sK0) | strong(sK0) <- (2) [resolution 348,136]
413. strong(sK0) <- (2) [subsumption resolution 410,135]
416. 37 | ~2 [avatar split clause 413,143,390]
430. kind(sK0) | quiet(sK0) <- (37) [resolution 391,108]
433. 38 <=> quiet(sK0) [avatar definition]
435. quiet(sK0) <- (38) [avatar component clause 433]
437. 39 <=> kind(sK0) [avatar definition]
439. kind(sK0) <- (39) [avatar component clause 437]
440. 38 | 39 | ~37 [avatar split clause 430,390,437,433]
479. ~strong(sK0) | ~funny(sK0) <- (39) [resolution 439,77]
480. ~funny(sK0) <- (37, 39) [subsumption resolution 479,391]
481. $false <- (2, 37, 39) [subsumption resolution 480,348]
482. ~2 | ~37 | ~39 [avatar contradiction clause 481]
486. brave(sK0) | ~curious(sK0) <- (38) [resolution 435,95]
489. ~curious(sK0) <- (~4, 38) [subsumption resolution 486,154]
490. $false <- (2, ~4, 38) [subsumption resolution 489,145]
491. ~2 | 4 | ~38 [avatar contradiction clause 490]
492. $false [avatar sat refutation 150,156,268,346,416,440,482,491]
% SZS output end Proof for 520805765550676809456247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not quiet then someone is either calm or strong. Everyone who is both not brave and brave is either tall or not generous. Everyone who is brave or not wise is not generous. If alice is not patient or not calm then someone is either creative or not strong. Everyone who is both not generous and not kind is both rich and quiet and vice versa. Everyone who is not brave is old. Everyone who is both strong and not funny is both old and not rich and vice versa. Everyone who is kind is curious and vice versa. If susan is either patient or strong then someone is happy and vice versa. If mary is either happy or old then paul is both rich and not curious and vice versa. If susan is rich or not curious then someone is either quiet or not brave and vice versa. If someone is either not creative or not strong then susan is either wise or not generous. Everyone who is either rich or not quiet is both curious and not calm and vice versa. Everyone who is either funny or not calm is both patient and not old. Everyone who is happy is not funny and vice versa. Everyone who is both not generous and quiet is calm or not wise and vice versa. Alice is both not humble and not generous. Susan is not kind or not calm. Someone is both strong and not wise. Lucy is not curious. Paul is wise. Someone is generous. Lucy is generous or humble. Alice is not wise. | Lucy is not wise. | contradiction | ((?[X]:((creative(X)<~>~quiet(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((~brave(X)&brave(X))=>(tall(X)<~>~generous(X))))&
(![X]:((brave(X)|~wise(X))=>~generous(X)))&
(((~patient(alice)|~calm(alice)))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((~generous(X)&~kind(X))<=>(rich(X)&quiet(X))))&
(![X]:(~brave(X)=>old(X)))&
(![X]:((strong(X)&~funny(X))<=>(old(X)&~rich(X))))&
(![X]:(kind(X)<=>curious(X)))&
(((patient(susan)<~>strong(susan)))<=>(?[X]:(happy(X))))&
(((happy(mary)<~>old(mary)))<=>((rich(paul)&~curious(paul))))&
(((rich(susan)|~curious(susan)))<=>(?[X]:((quiet(X)<~>~brave(X)))))&
((?[X]:((~creative(X)<~>~strong(X))))=>((wise(susan)<~>~generous(susan))))&
(![X]:((rich(X)<~>~quiet(X))<=>(curious(X)&~calm(X))))&
(![X]:((funny(X)<~>~calm(X))=>(patient(X)&~old(X))))&
(![X]:(happy(X)<=>~funny(X)))&
(![X]:((~generous(X)&quiet(X))<=>(calm(X)|~wise(X))))&
((~humble(alice)&~generous(alice)))&
((~kind(susan)|~calm(susan)))&
(?[X]:((strong(X)&~wise(X))))&
(~curious(lucy))&
(wise(paul))&
(?[X]:(generous(X)))&
((generous(lucy)|humble(lucy)))&
(~wise(alice)) | ~wise(lucy) | [
"p2",
"p4",
"p7",
"p12",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 8053929863597717502274109
% SZS output start Proof for 8053929863597717502274109
3. ! [X0] : ((~wise(X0) | brave(X0)) => ~generous(X0)) [input p2]
5. ! [X0] : ((~kind(X0) & ~generous(X0)) <=> (quiet(X0) & rich(X0))) [input p4]
8. ! [X0] : (kind(X0) <=> curious(X0)) [input p7]
13. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (~calm(X0) & curious(X0))) [input p12]
20. ~curious(lucy) [input p19]
25. ~wise(lucy) [input hypothesis]
30. ! [X0] : (~generous(X0) | (wise(X0) & ~brave(X0))) [ennf transformation 3]
43. ! [X0] : (((~kind(X0) & ~generous(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (kind(X0) | generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((~kind(X0) & ~generous(X0)) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | kind(X0) | generous(X0))) [flattening 43]
47. ! [X0] : ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))) [nnf transformation 8]
60. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (calm(X0) | ~curious(X0))) & ((~calm(X0) & curious(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 13]
61. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | calm(X0) | ~curious(X0)) & ((~calm(X0) & curious(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [flattening 60]
77. ~generous(X0) | wise(X0) [cnf transformation 30]
82. rich(X0) | kind(X0) | generous(X0) [cnf transformation 44]
83. kind(X0) | quiet(X0) | generous(X0) [cnf transformation 44]
91. ~kind(X0) | curious(X0) [cnf transformation 47]
113. ~rich(X0) | ~quiet(X0) | curious(X0) [cnf transformation 61]
135. ~curious(lucy) [cnf transformation 20]
140. ~wise(lucy) [cnf transformation 25]
274. 29 <=> generous(lucy) [avatar definition]
275. ~generous(lucy) <- (~29) [avatar component clause 274]
276. generous(lucy) <- (29) [avatar component clause 274]
285. wise(lucy) <- (29) [resolution 77,276]
286. $false <- (29) [subsumption resolution 285,140]
287. ~29 [avatar contradiction clause 286]
350. ~quiet(X0) | curious(X0) | kind(X0) | generous(X0) [resolution 113,82]
352. curious(X0) | kind(X0) | generous(X0) [subsumption resolution 350,83]
353. curious(X0) | generous(X0) [subsumption resolution 352,91]
469. generous(lucy) [resolution 353,135]
472. $false <- (~29) [subsumption resolution 469,275]
473. 29 [avatar contradiction clause 472]
474. $false [avatar sat refutation 287,473]
% SZS output end Proof for 8053929863597717502274109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not old is not wise and vice versa.
Everyone who is either not strong or not kind is wise and vice versa.
Everyone who is not curious is either not curious or wise and vice versa.
If john is brave or not happy then someone is not rich and vice versa.
Everyone who is either happy or wise is both creative and quiet and vice versa.
If someone is both happy and not happy then john is curious or not wise.
Everyone who is both not calm and not quiet is not quiet or not kind.
If someone is either kind or not happy then someone is both not generous and kind.
Everyone who is both calm and tall is both not strong and not kind and vice versa.
If lucy is not rich then paul is not curious and vice versa.
If someone is wise or strong then someone is humble or not funny.
Everyone who is either quiet or generous is either not strong or not rich and vice versa.
Everyone who is funny is not strong and vice versa.
Everyone who is patient or not kind is not strong or not happy and vice versa.
If someone is not humble then someone is not strong.
If someone is either not tall or not humble then someone is not quiet.
John is quiet or not rich.
Paul is either tall or not wise.
Lucy is not old or not patient.
Susan is creative or calm.
Susan is not kind or not creative.
Someone is happy. | Susan is not happy. | neutral | (![X]:((~funny(X)<~>~old(X))<=>~wise(X)))&
(![X]:((~strong(X)<~>~kind(X))<=>wise(X)))&
(![X]:(~curious(X)<=>(~curious(X)<~>wise(X))))&
(((brave(john)|~happy(john)))<=>(?[X]:(~rich(X))))&
(![X]:((happy(X)<~>wise(X))<=>(creative(X)&quiet(X))))&
((?[X]:((happy(X)&~happy(X))))=>((curious(john)|~wise(john))))&
(![X]:((~calm(X)&~quiet(X))=>(~quiet(X)|~kind(X))))&
((?[X]:((kind(X)<~>~happy(X))))=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((calm(X)&tall(X))<=>(~strong(X)&~kind(X))))&
((~rich(lucy))<=>(~curious(paul)))&
((?[X]:((wise(X)|strong(X))))=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~rich(X))))&
(![X]:(funny(X)<=>~strong(X)))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|~happy(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>~humble(X))))=>(?[X]:(~quiet(X))))&
((quiet(john)|~rich(john)))&
((tall(paul)<~>~wise(paul)))&
((~old(lucy)|~patient(lucy)))&
((creative(susan)|calm(susan)))&
((~kind(susan)|~creative(susan)))&
(?[X]:(happy(X))) | ~happy(susan) | []
| null | 0 |
Everyone who is strong is not patient or not brave.
If mary is either brave or not kind then susan is both rich and not rich and vice versa.
Everyone who is not quiet is quiet.
Everyone who is either not happy or tall is both tall and wise.
If john is not calm or wise then someone is patient or not rich.
Everyone who is happy is calm and vice versa.
If paul is either old or kind then susan is either not old or quiet and vice versa.
Everyone who is both not kind and not wise is rich.
If alice is either kind or wise then fred is both not rich and kind and vice versa.
Everyone who is happy is not creative or not happy.
Everyone who is not happy is either tall or creative and vice versa.
If mary is calm then mary is not wise or generous.
Everyone who is happy is both generous and creative and vice versa.
Everyone who is brave or generous is happy or curious.
Everyone who is both humble and quiet is either not tall or patient and vice versa.
If someone is both not patient and tall then someone is not happy or not rich.
Paul is either not creative or brave.
Someone is either quiet or not generous.
Someone is generous or not creative.
Someone is rich or not happy.
Someone is not creative.
Someone is both not funny and not humble. | Mary is quiet. | entailment | (![X]:(strong(X)=>(~patient(X)|~brave(X))))&
(((brave(mary)<~>~kind(mary)))<=>((rich(susan)&~rich(susan))))&
(![X]:(~quiet(X)=>quiet(X)))&
(![X]:((~happy(X)<~>tall(X))=>(tall(X)&wise(X))))&
(((~calm(john)|wise(john)))=>(?[X]:((patient(X)|~rich(X)))))&
(![X]:(happy(X)<=>calm(X)))&
(((old(paul)<~>kind(paul)))<=>((~old(susan)<~>quiet(susan))))&
(![X]:((~kind(X)&~wise(X))=>rich(X)))&
(((kind(alice)<~>wise(alice)))<=>((~rich(fred)&kind(fred))))&
(![X]:(happy(X)=>(~creative(X)|~happy(X))))&
(![X]:(~happy(X)<=>(tall(X)<~>creative(X))))&
((calm(mary))=>((~wise(mary)|generous(mary))))&
(![X]:(happy(X)<=>(generous(X)&creative(X))))&
(![X]:((brave(X)|generous(X))=>(happy(X)|curious(X))))&
(![X]:((humble(X)&quiet(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:((~patient(X)&tall(X))))=>(?[X]:((~happy(X)|~rich(X)))))&
((~creative(paul)<~>brave(paul)))&
(?[X]:((quiet(X)<~>~generous(X))))&
(?[X]:((generous(X)|~creative(X))))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)&~humble(X)))) | quiet(mary) | [
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 153451603824084390889799
% SZS output start Proof for 153451603824084390889799
3. ! [X0] : (~quiet(X0) => quiet(X0)) [input p2]
23. ~quiet(mary) [input hypothesis]
28. ! [X0] : (quiet(X0) | quiet(X0)) [ennf transformation 3]
73. quiet(X0) | quiet(X0) [cnf transformation 28]
121. ~quiet(mary) [cnf transformation 23]
124. quiet(X0) [duplicate literal removal 73]
232. $false [subsumption resolution 121,124]
% SZS output end Proof for 153451603824084390889799
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both humble and calm then someone is wise or not creative. Everyone who is both quiet and not strong is funny or wise and vice versa. Everyone who is tall or not creative is not wise. If lucy is both not happy and not strong then someone is not rich or not quiet. Everyone who is both not tall and tall is both not generous and quiet and vice versa. If susan is either tall or kind then someone is quiet. Everyone who is both rich and not old is either rich or not happy. Everyone who is humble is either not quiet or quiet and vice versa. Everyone who is not strong or rich is not happy. If someone is either not rich or not funny then lucy is both funny and not old. If someone is not curious or rich then someone is happy and vice versa. Everyone who is both strong and happy is not generous or not strong. Everyone who is both not kind and not old is both not old and brave. Everyone who is either not calm or generous is either not creative or kind and vice versa. Everyone who is curious is curious or not brave. Someone is old. Someone is tall or not strong. Paul is funny or not funny. Fred is funny or not calm. Someone is both not tall and kind. Someone is either not kind or not strong. Someone is either tall or not wise. | Lucy is not wise. | neutral | (((humble(fred)&calm(fred)))=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((quiet(X)&~strong(X))<=>(funny(X)|wise(X))))&
(![X]:((tall(X)|~creative(X))=>~wise(X)))&
(((~happy(lucy)&~strong(lucy)))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((~tall(X)&tall(X))<=>(~generous(X)&quiet(X))))&
(((tall(susan)<~>kind(susan)))=>(?[X]:(quiet(X))))&
(![X]:((rich(X)&~old(X))=>(rich(X)<~>~happy(X))))&
(![X]:(humble(X)<=>(~quiet(X)<~>quiet(X))))&
(![X]:((~strong(X)|rich(X))=>~happy(X)))&
((?[X]:((~rich(X)<~>~funny(X))))=>((funny(lucy)&~old(lucy))))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:(happy(X))))&
(![X]:((strong(X)&happy(X))=>(~generous(X)|~strong(X))))&
(![X]:((~kind(X)&~old(X))=>(~old(X)&brave(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(~creative(X)<~>kind(X))))&
(![X]:(curious(X)=>(curious(X)|~brave(X))))&
(?[X]:(old(X)))&
(?[X]:((tall(X)|~strong(X))))&
((funny(paul)|~funny(paul)))&
((funny(fred)|~calm(fred)))&
(?[X]:((~tall(X)&kind(X))))&
(?[X]:((~kind(X)<~>~strong(X))))&
(?[X]:((tall(X)<~>~wise(X)))) | ~wise(lucy) | []
| null | 0 |
If someone is rich then lucy is not generous and vice versa.
If someone is strong or creative then someone is either not wise or humble and vice versa.
If paul is not calm then someone is both creative and not creative.
If someone is brave then someone is strong and vice versa.
If alice is both not funny and not humble then mary is both wise and not tall and vice versa.
Everyone who is either not old or not tall is tall or rich and vice versa.
Everyone who is both not funny and not generous is happy and vice versa.
Everyone who is both not happy and quiet is creative.
If someone is both rich and not tall then mary is calm.
If someone is both not generous and not rich then someone is not patient or not happy.
If someone is not quiet or generous then lucy is generous and vice versa.
If fred is either generous or funny then someone is not happy and vice versa.
If alice is not rich then mary is both not calm and generous.
If someone is either old or rich then alice is not tall.
Everyone who is either not humble or funny is calm or generous and vice versa.
Everyone who is either not calm or happy is not creative.
Someone is both not brave and not tall.
Someone is either wise or not creative.
Lucy is wise or strong.
Someone is both wise and not curious.
Someone is either not patient or calm.
Someone is both funny and not wise.
Susan is either not creative or old.
Someone is either not brave or not wise. | Paul is not calm. | contradiction | ((?[X]:(rich(X)))<=>(~generous(lucy)))&
((?[X]:((strong(X)|creative(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
((~calm(paul))=>(?[X]:((creative(X)&~creative(X)))))&
((?[X]:(brave(X)))<=>(?[X]:(strong(X))))&
(((~funny(alice)&~humble(alice)))<=>((wise(mary)&~tall(mary))))&
(![X]:((~old(X)<~>~tall(X))<=>(tall(X)|rich(X))))&
(![X]:((~funny(X)&~generous(X))<=>happy(X)))&
(![X]:((~happy(X)&quiet(X))=>creative(X)))&
((?[X]:((rich(X)&~tall(X))))=>(calm(mary)))&
((?[X]:((~generous(X)&~rich(X))))=>(?[X]:((~patient(X)|~happy(X)))))&
((?[X]:((~quiet(X)|generous(X))))<=>(generous(lucy)))&
(((generous(fred)<~>funny(fred)))<=>(?[X]:(~happy(X))))&
((~rich(alice))=>((~calm(mary)&generous(mary))))&
((?[X]:((old(X)<~>rich(X))))=>(~tall(alice)))&
(![X]:((~humble(X)<~>funny(X))<=>(calm(X)|generous(X))))&
(![X]:((~calm(X)<~>happy(X))=>~creative(X)))&
(?[X]:((~brave(X)&~tall(X))))&
(?[X]:((wise(X)<~>~creative(X))))&
((wise(lucy)|strong(lucy)))&
(?[X]:((wise(X)&~curious(X))))&
(?[X]:((~patient(X)<~>calm(X))))&
(?[X]:((funny(X)&~wise(X))))&
((~creative(susan)<~>old(susan)))&
(?[X]:((~brave(X)<~>~wise(X)))) | ~calm(paul) | [
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 2680224945652821258803591
% SZS output start Proof for 2680224945652821258803591
3. ~calm(paul) => ? [X0] : (~creative(X0) & creative(X0)) [input p2]
25. ~calm(paul) [input hypothesis]
30. ? [X0] : (~creative(X0) & creative(X0)) | calm(paul) [ennf transformation 3]
47. ? [X0] : (~creative(X0) & creative(X0)) => (~creative(sK3) & creative(sK3)) [choice axiom]
48. (~creative(sK3) & creative(sK3)) | calm(paul) [skolemisation 30,47]
99. creative(sK3) | calm(paul) [cnf transformation 48]
100. ~creative(sK3) | calm(paul) [cnf transformation 48]
152. ~calm(paul) [cnf transformation 25]
203. 12 <=> calm(paul) [avatar definition]
207. 13 <=> creative(sK3) [avatar definition]
210. 12 | ~13 [avatar split clause 100,207,203]
211. 12 | 13 [avatar split clause 99,207,203]
369. ~12 [avatar split clause 152,203]
370. $false [avatar sat refutation 210,211,369]
% SZS output end Proof for 2680224945652821258803591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not rich and vice versa. If someone is either not kind or strong then paul is not generous. If susan is rich or not calm then fred is either calm or wise. Everyone who is not funny or rich is either not rich or not funny. Everyone who is either strong or not funny is both quiet and happy. If susan is both curious and kind then fred is either curious or not patient. Everyone who is both kind and not rich is either kind or not rich. If someone is old or generous then someone is creative or not funny. Everyone who is not wise is not rich and vice versa. If someone is both wise and old then someone is quiet or strong. Everyone who is both curious and not wise is either calm or patient and vice versa. If susan is not calm then someone is curious or rich. If john is happy or not humble then someone is not happy or not tall and vice versa. If someone is quiet or happy then someone is not wise or not quiet and vice versa. Everyone who is both not humble and old is generous. If someone is wise or calm then paul is humble or happy and vice versa. Someone is not humble. Fred is both old and quiet. John is both not happy and curious. Someone is either wise or happy. Someone is both tall and not brave. Fred is not generous or not quiet. Someone is not rich. Paul is curious or kind. | Paul is not happy. | neutral | (![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~kind(X)<~>strong(X))))=>(~generous(paul)))&
(((rich(susan)|~calm(susan)))=>((calm(fred)<~>wise(fred))))&
(![X]:((~funny(X)|rich(X))=>(~rich(X)<~>~funny(X))))&
(![X]:((strong(X)<~>~funny(X))=>(quiet(X)&happy(X))))&
(((curious(susan)&kind(susan)))=>((curious(fred)<~>~patient(fred))))&
(![X]:((kind(X)&~rich(X))=>(kind(X)<~>~rich(X))))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:(~wise(X)<=>~rich(X)))&
((?[X]:((wise(X)&old(X))))=>(?[X]:((quiet(X)|strong(X)))))&
(![X]:((curious(X)&~wise(X))<=>(calm(X)<~>patient(X))))&
((~calm(susan))=>(?[X]:((curious(X)|rich(X)))))&
(((happy(john)|~humble(john)))<=>(?[X]:((~happy(X)|~tall(X)))))&
((?[X]:((quiet(X)|happy(X))))<=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:((~humble(X)&old(X))=>generous(X)))&
((?[X]:((wise(X)|calm(X))))<=>((humble(paul)|happy(paul))))&
(?[X]:(~humble(X)))&
((old(fred)&quiet(fred)))&
((~happy(john)&curious(john)))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((tall(X)&~brave(X))))&
((~generous(fred)|~quiet(fred)))&
(?[X]:(~rich(X)))&
((curious(paul)|kind(paul))) | ~happy(paul) | []
| null | 0 |
If someone is calm or patient then paul is either not humble or not kind and vice versa. If someone is either creative or not generous then someone is not rich. If paul is either not strong or quiet then susan is either quiet or not generous. If paul is either not generous or not humble then someone is creative. If someone is humble or calm then someone is strong and vice versa. Everyone who is not wise is either not happy or calm. If susan is both not humble and not quiet then someone is quiet or not old and vice versa. If lucy is not patient then someone is not tall. Everyone who is quiet is either not old or calm and vice versa. If susan is not quiet or wise then someone is either not old or humble. Everyone who is both not brave and not funny is both not curious and generous and vice versa. If lucy is tall or not tall then paul is both not rich and old. If someone is not brave then someone is either kind or calm. Everyone who is either strong or not brave is tall. If someone is either humble or not brave then someone is not wise or generous. Everyone who is both creative and humble is humble and vice versa. Susan is curious or not tall. Mary is not curious or kind. Lucy is both not wise and humble. Paul is quiet. Alice is humble or not tall. Susan is tall or not calm. Someone is either happy or not tall. | Lucy is creative. | entailment | ((?[X]:((calm(X)|patient(X))))<=>((~humble(paul)<~>~kind(paul))))&
((?[X]:((creative(X)<~>~generous(X))))=>(?[X]:(~rich(X))))&
(((~strong(paul)<~>quiet(paul)))=>((quiet(susan)<~>~generous(susan))))&
(((~generous(paul)<~>~humble(paul)))=>(?[X]:(creative(X))))&
((?[X]:((humble(X)|calm(X))))<=>(?[X]:(strong(X))))&
(![X]:(~wise(X)=>(~happy(X)<~>calm(X))))&
(((~humble(susan)&~quiet(susan)))<=>(?[X]:((quiet(X)|~old(X)))))&
((~patient(lucy))=>(?[X]:(~tall(X))))&
(![X]:(quiet(X)<=>(~old(X)<~>calm(X))))&
(((~quiet(susan)|wise(susan)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~brave(X)&~funny(X))<=>(~curious(X)&generous(X))))&
(((tall(lucy)|~tall(lucy)))=>((~rich(paul)&old(paul))))&
((?[X]:(~brave(X)))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((strong(X)<~>~brave(X))=>tall(X)))&
((?[X]:((humble(X)<~>~brave(X))))=>(?[X]:((~wise(X)|generous(X)))))&
(![X]:((creative(X)&humble(X))<=>humble(X)))&
((curious(susan)|~tall(susan)))&
((~curious(mary)|kind(mary)))&
((~wise(lucy)&humble(lucy)))&
(quiet(paul))&
((humble(alice)|~tall(alice)))&
((tall(susan)|~calm(susan)))&
(?[X]:((happy(X)<~>~tall(X)))) | creative(lucy) | [
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 409262651577728664114296
% SZS output start Proof for 409262651577728664114296
16. ! [X0] : ((humble(X0) & creative(X0)) <=> humble(X0)) [input p15]
19. humble(lucy) & ~wise(lucy) [input p18]
24. ~creative(lucy) [input hypothesis]
76. ! [X0] : (((humble(X0) & creative(X0)) | ~humble(X0)) & (humble(X0) | (~humble(X0) | ~creative(X0)))) [nnf transformation 16]
77. ! [X0] : (((humble(X0) & creative(X0)) | ~humble(X0)) & (humble(X0) | ~humble(X0) | ~creative(X0))) [flattening 76]
125. ~humble(X0) | creative(X0) [cnf transformation 77]
130. humble(lucy) [cnf transformation 19]
136. ~creative(lucy) [cnf transformation 24]
348. creative(lucy) [resolution 125,130]
349. $false [subsumption resolution 348,136]
% SZS output end Proof for 409262651577728664114296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not calm is either not creative or not calm and vice versa.
If paul is both strong and calm then someone is patient.
If john is both not curious and not calm then someone is tall or funny.
Everyone who is funny or not humble is either not strong or not creative and vice versa.
If someone is both not kind and not humble then lucy is both not brave and curious.
Everyone who is both generous and not generous is either not happy or rich and vice versa.
Everyone who is both not creative and patient is old or funny and vice versa.
Everyone who is either not tall or not kind is either not tall or rich.
Everyone who is not kind is happy and vice versa.
Everyone who is not old is both not humble and not tall.
If someone is either not old or creative then paul is both funny and brave.
If someone is calm or humble then someone is not creative and vice versa.
If someone is not brave then someone is both kind and quiet.
Everyone who is not happy is both not calm and humble.
Everyone who is not creative or not calm is both not rich and quiet.
Everyone who is either creative or not old is either not kind or not creative and vice versa.
Susan is curious or strong.
Mary is not kind.
Someone is both strong and not generous.
Susan is both funny and not curious.
Fred is both old and quiet.
Fred is either not humble or not funny. | Lucy is not old. | contradiction | (![X]:((~wise(X)<~>~calm(X))<=>(~creative(X)<~>~calm(X))))&
(((strong(paul)&calm(paul)))=>(?[X]:(patient(X))))&
(((~curious(john)&~calm(john)))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((funny(X)|~humble(X))<=>(~strong(X)<~>~creative(X))))&
((?[X]:((~kind(X)&~humble(X))))=>((~brave(lucy)&curious(lucy))))&
(![X]:((generous(X)&~generous(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((~creative(X)&patient(X))<=>(old(X)|funny(X))))&
(![X]:((~tall(X)<~>~kind(X))=>(~tall(X)<~>rich(X))))&
(![X]:(~kind(X)<=>happy(X)))&
(![X]:(~old(X)=>(~humble(X)&~tall(X))))&
((?[X]:((~old(X)<~>creative(X))))=>((funny(paul)&brave(paul))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:(~creative(X))))&
((?[X]:(~brave(X)))=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:(~happy(X)=>(~calm(X)&humble(X))))&
(![X]:((~creative(X)|~calm(X))=>(~rich(X)&quiet(X))))&
(![X]:((creative(X)<~>~old(X))<=>(~kind(X)<~>~creative(X))))&
((curious(susan)|strong(susan)))&
(~kind(mary))&
(?[X]:((strong(X)&~generous(X))))&
((funny(susan)&~curious(susan)))&
((old(fred)&quiet(fred)))&
((~humble(fred)<~>~funny(fred))) | ~old(lucy) | [
"p5",
"p6",
"p8",
"p13",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 2380965532158441669521718
% SZS output start Proof for 2380965532158441669521718
6. ! [X0] : ((~generous(X0) & generous(X0)) <=> (~happy(X0) <~> rich(X0))) [input p5]
7. ! [X0] : ((patient(X0) & ~creative(X0)) <=> (funny(X0) | old(X0))) [input p6]
9. ! [X0] : (~kind(X0) <=> happy(X0)) [input p8]
14. ! [X0] : (~happy(X0) => (humble(X0) & ~calm(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | ~creative(X0)) => (quiet(X0) & ~rich(X0))) [input p14]
16. ! [X0] : ((creative(X0) <~> ~old(X0)) <=> (~kind(X0) <~> ~creative(X0))) [input p15]
23. ~old(lucy) [input hypothesis]
27. ! [X0] : ((~calm(X0) | ~creative(X0)) => ~rich(X0)) [pure predicate removal 15]
38. ! [X0] : ((humble(X0) & ~calm(X0)) | happy(X0)) [ennf transformation 14]
39. ! [X0] : (~rich(X0) | (calm(X0) & creative(X0))) [ennf transformation 27]
47. ! [X0] : (((~generous(X0) & generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (generous(X0) | ~generous(X0)))) [nnf transformation 6]
48. ! [X0] : (((~generous(X0) & generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | generous(X0) | ~generous(X0))) [flattening 47]
49. ! [X0] : (((patient(X0) & ~creative(X0)) | (~funny(X0) & ~old(X0))) & ((funny(X0) | old(X0)) | (~patient(X0) | creative(X0)))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & ~creative(X0)) | (~funny(X0) & ~old(X0))) & (funny(X0) | old(X0) | ~patient(X0) | creative(X0))) [flattening 49]
52. ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0))) [nnf transformation 9]
62. ! [X0] : ((((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0)))) & (((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0))))) [nnf transformation 16]
86. generous(X0) | rich(X0) | happy(X0) [cnf transformation 48]
88. ~generous(X0) | rich(X0) | happy(X0) [cnf transformation 48]
91. ~old(X0) | ~creative(X0) [cnf transformation 50]
100. ~happy(X0) | ~kind(X0) [cnf transformation 52]
111. ~calm(X0) | happy(X0) [cnf transformation 38]
114. ~rich(X0) | calm(X0) [cnf transformation 39]
118. creative(X0) | kind(X0) | creative(X0) | old(X0) [cnf transformation 62]
121. old(X0) | ~creative(X0) | ~creative(X0) | kind(X0) [cnf transformation 62]
132. ~old(lucy) [cnf transformation 23]
134. creative(X0) | kind(X0) | old(X0) [duplicate literal removal 118]
136. old(X0) | ~creative(X0) | kind(X0) [duplicate literal removal 121]
189. rich(X0) | happy(X0) [subsumption resolution 86,88]
235. ~creative(X0) | kind(X0) [subsumption resolution 136,91]
237. old(X0) | kind(X0) [subsumption resolution 134,235]
278. happy(X1) | calm(X1) [resolution 189,114]
280. happy(X1) [subsumption resolution 278,111]
284. ~kind(X0) [resolution 280,100]
292. kind(lucy) [resolution 237,132]
296. $false [subsumption resolution 292,284]
% SZS output end Proof for 2380965532158441669521718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then someone is strong or patient and vice versa. Everyone who is generous or strong is not curious or kind. If someone is both happy and calm then mary is not brave or not generous. If fred is either quiet or not quiet then someone is rich and vice versa. Everyone who is either not happy or humble is not calm and vice versa. Everyone who is both not quiet and not tall is not patient and vice versa. Everyone who is either strong or not humble is calm or brave. If lucy is either curious or not generous then susan is both brave and not brave. Everyone who is not brave is both not curious and happy. If someone is not patient then someone is strong and vice versa. Everyone who is both not strong and not humble is strong or quiet and vice versa. If mary is both funny and not calm then susan is calm. Everyone who is either not wise or kind is either calm or rich. If lucy is not patient or not wise then alice is not brave. Everyone who is humble or strong is both not wise and not tall. Everyone who is not old is either not quiet or not tall. Someone is quiet or not strong. Someone is not kind or generous. Someone is both creative and not humble. Susan is either not old or funny. Someone is either curious or brave. Fred is either not patient or not kind. Mary is generous or not tall. | Lucy is quiet. | entailment | ((?[X]:(~tall(X)))<=>(?[X]:((strong(X)|patient(X)))))&
(![X]:((generous(X)|strong(X))=>(~curious(X)|kind(X))))&
((?[X]:((happy(X)&calm(X))))=>((~brave(mary)|~generous(mary))))&
(((quiet(fred)<~>~quiet(fred)))<=>(?[X]:(rich(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~quiet(X)&~tall(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~humble(X))=>(calm(X)|brave(X))))&
(((curious(lucy)<~>~generous(lucy)))=>((brave(susan)&~brave(susan))))&
(![X]:(~brave(X)=>(~curious(X)&happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:(strong(X))))&
(![X]:((~strong(X)&~humble(X))<=>(strong(X)|quiet(X))))&
(((funny(mary)&~calm(mary)))=>(calm(susan)))&
(![X]:((~wise(X)<~>kind(X))=>(calm(X)<~>rich(X))))&
(((~patient(lucy)|~wise(lucy)))=>(~brave(alice)))&
(![X]:((humble(X)|strong(X))=>(~wise(X)&~tall(X))))&
(![X]:(~old(X)=>(~quiet(X)<~>~tall(X))))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:((~kind(X)|generous(X))))&
(?[X]:((creative(X)&~humble(X))))&
((~old(susan)<~>funny(susan)))&
(?[X]:((curious(X)<~>brave(X))))&
((~patient(fred)<~>~kind(fred)))&
((generous(mary)|~tall(mary))) | quiet(lucy) | [
"p5",
"p9",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 2014805042030210311481990
% SZS output start Proof for 2014805042030210311481990
6. ! [X0] : ((~tall(X0) & ~quiet(X0)) <=> ~patient(X0)) [input p5]
10. ? [X0] : ~patient(X0) <=> ? [X0] : strong(X0) [input p9]
11. ! [X0] : ((~humble(X0) & ~strong(X0)) <=> (quiet(X0) | strong(X0))) [input p10]
15. ! [X0] : ((strong(X0) | humble(X0)) => (~tall(X0) & ~wise(X0))) [input p14]
24. ~quiet(lucy) [input hypothesis]
26. ? [X0] : ~patient(X0) <=> ? [X1] : strong(X1) [rectify 10]
40. ! [X0] : ((~tall(X0) & ~wise(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 15]
52. ! [X0] : (((~tall(X0) & ~quiet(X0)) | patient(X0)) & (~patient(X0) | (tall(X0) | quiet(X0)))) [nnf transformation 6]
53. ! [X0] : (((~tall(X0) & ~quiet(X0)) | patient(X0)) & (~patient(X0) | tall(X0) | quiet(X0))) [flattening 52]
56. (? [X0] : ~patient(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : patient(X0)) [nnf transformation 26]
57. (? [X0] : ~patient(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : patient(X3)) [rectify 56]
58. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
59. ? [X2] : strong(X2) => strong(sK4) [choice axiom]
60. (~patient(sK3) | ! [X1] : ~strong(X1)) & (strong(sK4) | ! [X3] : patient(X3)) [skolemisation 57,59,58]
61. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (humble(X0) | strong(X0)))) [nnf transformation 11]
62. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | humble(X0) | strong(X0))) [flattening 61]
90. ~patient(X0) | tall(X0) | quiet(X0) [cnf transformation 53]
101. strong(sK4) | patient(X3) [cnf transformation 60]
103. quiet(X0) | strong(X0) | humble(X0) | strong(X0) [cnf transformation 62]
104. ~strong(X0) | ~strong(X0) [cnf transformation 62]
117. ~humble(X0) | ~tall(X0) [cnf transformation 40]
131. ~quiet(lucy) [cnf transformation 24]
132. humble(X0) | strong(X0) | quiet(X0) [duplicate literal removal 103]
133. ~strong(X0) [duplicate literal removal 104]
145. 3 <=> ! [X1] : ~strong(X1) [avatar definition]
146. ~strong(X1) <- (3) [avatar component clause 145]
204. 16 <=> ! [X3] : patient(X3) [avatar definition]
205. patient(X3) <- (16) [avatar component clause 204]
207. 17 <=> strong(sK4) [avatar definition]
209. strong(sK4) <- (17) [avatar component clause 207]
210. 16 | 17 [avatar split clause 101,207,204]
211. 3 [avatar split clause 133,145]
300. quiet(X0) | tall(X0) <- (16) [resolution 90,205]
311. strong(X2) | quiet(X2) | ~tall(X2) [resolution 132,117]
318. quiet(X2) | ~tall(X2) <- (3) [subsumption resolution 311,146]
319. quiet(X2) <- (3, 16) [subsumption resolution 318,300]
333. $false <- (3, 16) [resolution 319,131]
337. ~3 | ~16 [avatar contradiction clause 333]
344. $false <- (3, 17) [subsumption resolution 209,146]
345. ~3 | ~17 [avatar contradiction clause 344]
346. $false [avatar sat refutation 210,211,337,345]
% SZS output end Proof for 2014805042030210311481990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or tall is not patient or not wise and vice versa. Everyone who is funny or not brave is strong and vice versa. Everyone who is humble or funny is either not patient or quiet. If alice is both rich and not humble then someone is either rich or not generous and vice versa. Everyone who is not humble or quiet is either not brave or patient and vice versa. Everyone who is happy or quiet is quiet or tall. Everyone who is either curious or not tall is either happy or funny and vice versa. If susan is either happy or not brave then paul is either tall or kind. If alice is patient then fred is curious or not happy and vice versa. Everyone who is calm or funny is humble or rich and vice versa. Everyone who is not rich or patient is either wise or not brave and vice versa. If john is creative then alice is both not happy and quiet and vice versa. Everyone who is kind is not happy or tall and vice versa. Everyone who is both not humble and not patient is not old and vice versa. If john is happy then susan is not old. Everyone who is both humble and not creative is both strong and not happy. Mary is both not tall and old. Paul is not generous or not strong. Someone is either not creative or generous. Paul is not rich or curious. Someone is not brave or wise. Someone is both happy and not humble. | Fred is not tall. | neutral | (![X]:((brave(X)<~>tall(X))<=>(~patient(X)|~wise(X))))&
(![X]:((funny(X)|~brave(X))<=>strong(X)))&
(![X]:((humble(X)|funny(X))=>(~patient(X)<~>quiet(X))))&
(((rich(alice)&~humble(alice)))<=>(?[X]:((rich(X)<~>~generous(X)))))&
(![X]:((~humble(X)|quiet(X))<=>(~brave(X)<~>patient(X))))&
(![X]:((happy(X)|quiet(X))=>(quiet(X)|tall(X))))&
(![X]:((curious(X)<~>~tall(X))<=>(happy(X)<~>funny(X))))&
(((happy(susan)<~>~brave(susan)))=>((tall(paul)<~>kind(paul))))&
((patient(alice))<=>((curious(fred)|~happy(fred))))&
(![X]:((calm(X)|funny(X))<=>(humble(X)|rich(X))))&
(![X]:((~rich(X)|patient(X))<=>(wise(X)<~>~brave(X))))&
((creative(john))<=>((~happy(alice)&quiet(alice))))&
(![X]:(kind(X)<=>(~happy(X)|tall(X))))&
(![X]:((~humble(X)&~patient(X))<=>~old(X)))&
((happy(john))=>(~old(susan)))&
(![X]:((humble(X)&~creative(X))=>(strong(X)&~happy(X))))&
((~tall(mary)&old(mary)))&
((~generous(paul)|~strong(paul)))&
(?[X]:((~creative(X)<~>generous(X))))&
((~rich(paul)|curious(paul)))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((happy(X)&~humble(X)))) | ~tall(fred) | []
| null | 0 |
If someone is not wise or old then someone is not old or not wise and vice versa.
If someone is kind then lucy is either generous or not humble and vice versa.
Everyone who is either funny or creative is either generous or kind.
If lucy is not curious or not kind then someone is both not patient and not funny.
If susan is not patient then fred is either not curious or brave.
If someone is either creative or calm then lucy is both not strong and not kind and vice versa.
If john is either not calm or not generous then someone is either kind or not funny and vice versa.
If someone is not funny or funny then someone is happy or not kind.
Everyone who is either strong or rich is not quiet and vice versa.
Everyone who is strong is creative or curious and vice versa.
Everyone who is quiet or not quiet is not wise or not rich and vice versa.
Everyone who is either not tall or not funny is either not patient or not funny.
If lucy is both rich and not funny then someone is humble or funny and vice versa.
If lucy is either not calm or quiet then mary is not calm.
Everyone who is either not quiet or not wise is both wise and rich and vice versa.
Everyone who is not tall is either not wise or not humble.
Someone is not wise.
Fred is strong.
Someone is not curious or patient.
Lucy is not old.
Mary is both not brave and not humble.
Alice is not quiet.
Someone is both strong and curious.
John is both curious and not patient. | Lucy is not rich. | contradiction | ((?[X]:((~wise(X)|old(X))))<=>(?[X]:((~old(X)|~wise(X)))))&
((?[X]:(kind(X)))<=>((generous(lucy)<~>~humble(lucy))))&
(![X]:((funny(X)<~>creative(X))=>(generous(X)<~>kind(X))))&
(((~curious(lucy)|~kind(lucy)))=>(?[X]:((~patient(X)&~funny(X)))))&
((~patient(susan))=>((~curious(fred)<~>brave(fred))))&
((?[X]:((creative(X)<~>calm(X))))<=>((~strong(lucy)&~kind(lucy))))&
(((~calm(john)<~>~generous(john)))<=>(?[X]:((kind(X)<~>~funny(X)))))&
((?[X]:((~funny(X)|funny(X))))=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((strong(X)<~>rich(X))<=>~quiet(X)))&
(![X]:(strong(X)<=>(creative(X)|curious(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~wise(X)|~rich(X))))&
(![X]:((~tall(X)<~>~funny(X))=>(~patient(X)<~>~funny(X))))&
(((rich(lucy)&~funny(lucy)))<=>(?[X]:((humble(X)|funny(X)))))&
(((~calm(lucy)<~>quiet(lucy)))=>(~calm(mary)))&
(![X]:((~quiet(X)<~>~wise(X))<=>(wise(X)&rich(X))))&
(![X]:(~tall(X)=>(~wise(X)<~>~humble(X))))&
(?[X]:(~wise(X)))&
(strong(fred))&
(?[X]:((~curious(X)|patient(X))))&
(~old(lucy))&
((~brave(mary)&~humble(mary)))&
(~quiet(alice))&
(?[X]:((strong(X)&curious(X))))&
((curious(john)&~patient(john))) | ~rich(lucy) | [
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 8580682961436360638721053
% SZS output start Proof for 8580682961436360638721053
9. ! [X0] : ((strong(X0) <~> rich(X0)) <=> ~quiet(X0)) [input p8]
10. ! [X0] : (strong(X0) <=> (curious(X0) | creative(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> (~rich(X0) | ~wise(X0))) [input p10]
12. ! [X0] : ((~tall(X0) <~> ~funny(X0)) => (~patient(X0) <~> ~funny(X0))) [input p11]
13. (~funny(lucy) & rich(lucy)) <=> ? [X0] : (funny(X0) | humble(X0)) [input p12]
15. ! [X0] : ((~quiet(X0) <~> ~wise(X0)) <=> (rich(X0) & wise(X0))) [input p14]
16. ! [X0] : (~tall(X0) => (~wise(X0) <~> ~humble(X0))) [input p15]
24. ~patient(john) & curious(john) [input p23]
25. ~rich(lucy) [input hypothesis]
32. ! [X0] : ((~patient(X0) <~> ~funny(X0)) | (~tall(X0) <=> ~funny(X0))) [ennf transformation 12]
34. ! [X0] : ((~wise(X0) <~> ~humble(X0)) | tall(X0)) [ennf transformation 16]
57. ! [X0] : ((((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | quiet(X0)) & (~quiet(X0) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))))) [nnf transformation 9]
58. ! [X0] : ((strong(X0) | (~curious(X0) & ~creative(X0))) & ((curious(X0) | creative(X0)) | ~strong(X0))) [nnf transformation 10]
59. ! [X0] : ((strong(X0) | (~curious(X0) & ~creative(X0))) & (curious(X0) | creative(X0) | ~strong(X0))) [flattening 58]
60. ! [X0] : (((~quiet(X0) | quiet(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 11]
61. ! [X0] : ((~quiet(X0) | quiet(X0) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | (quiet(X0) & ~quiet(X0)))) [flattening 60]
62. ! [X0] : (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0)))) [nnf transformation 32]
63. ((~funny(lucy) & rich(lucy)) | ! [X0] : (~funny(X0) & ~humble(X0))) & (? [X0] : (funny(X0) | humble(X0)) | (funny(lucy) | ~rich(lucy))) [nnf transformation 13]
64. ((~funny(lucy) & rich(lucy)) | ! [X0] : (~funny(X0) & ~humble(X0))) & (? [X0] : (funny(X0) | humble(X0)) | funny(lucy) | ~rich(lucy)) [flattening 63]
65. ((~funny(lucy) & rich(lucy)) | ! [X0] : (~funny(X0) & ~humble(X0))) & (? [X1] : (funny(X1) | humble(X1)) | funny(lucy) | ~rich(lucy)) [rectify 64]
66. ? [X1] : (funny(X1) | humble(X1)) => (funny(sK6) | humble(sK6)) [choice axiom]
67. ((~funny(lucy) & rich(lucy)) | ! [X0] : (~funny(X0) & ~humble(X0))) & ((funny(sK6) | humble(sK6)) | funny(lucy) | ~rich(lucy)) [skolemisation 65,66]
69. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (~rich(X0) | ~wise(X0))) & ((rich(X0) & wise(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [nnf transformation 15]
70. ! [X0] : ((((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | ~rich(X0) | ~wise(X0)) & ((rich(X0) & wise(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0))))) [flattening 69]
71. ! [X0] : (((humble(X0) | wise(X0)) & (~humble(X0) | ~wise(X0))) | tall(X0)) [nnf transformation 34]
110. ~quiet(X0) | rich(X0) | ~strong(X0) [cnf transformation 57]
116. ~curious(X0) | strong(X0) [cnf transformation 59]
117. ~rich(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 61]
118. ~rich(X0) | ~wise(X0) | quiet(X0) [cnf transformation 61]
124. funny(X0) | patient(X0) | ~tall(X0) | funny(X0) [cnf transformation 62]
126. rich(lucy) | ~humble(X0) [cnf transformation 67]
127. rich(lucy) | ~funny(X0) [cnf transformation 67]
134. rich(X0) | ~wise(X0) | quiet(X0) [cnf transformation 70]
139. tall(X0) | wise(X0) | humble(X0) [cnf transformation 71]
149. curious(john) [cnf transformation 24]
150. ~patient(john) [cnf transformation 24]
151. ~rich(lucy) [cnf transformation 25]
155. ~tall(X0) | patient(X0) | funny(X0) [duplicate literal removal 124]
292. ~rich(X0) | ~wise(X0) [subsumption resolution 117,118]
294. 30 <=> ! [X0] : ~funny(X0) [avatar definition]
295. ~funny(X0) <- (30) [avatar component clause 294]
302. 32 <=> ! [X0] : ~humble(X0) [avatar definition]
303. ~humble(X0) <- (32) [avatar component clause 302]
306. 33 <=> rich(lucy) [avatar definition]
309. 30 | 33 [avatar split clause 127,306,294]
310. 32 | 33 [avatar split clause 126,306,302]
334. ~wise(X0) | quiet(X0) [subsumption resolution 134,292]
344. ~33 [avatar split clause 151,306]
347. strong(john) [resolution 116,149]
382. patient(X0) | funny(X0) | wise(X0) | humble(X0) [resolution 155,139]
383. patient(X0) | wise(X0) | humble(X0) <- (30) [subsumption resolution 382,295]
384. patient(X0) | wise(X0) <- (30, 32) [subsumption resolution 383,303]
385. wise(john) <- (30, 32) [resolution 384,150]
388. quiet(john) <- (30, 32) [resolution 385,334]
433. rich(john) | ~strong(john) <- (30, 32) [resolution 388,110]
435. rich(john) <- (30, 32) [subsumption resolution 433,347]
452. ~wise(john) <- (30, 32) [resolution 435,292]
453. $false <- (30, 32) [subsumption resolution 452,385]
454. ~30 | ~32 [avatar contradiction clause 453]
455. $false [avatar sat refutation 309,310,344,454]
% SZS output end Proof for 8580682961436360638721053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not brave is not strong or not happy. Everyone who is not strong or wise is brave or not old and vice versa. If lucy is both not old and not generous then alice is both kind and not brave and vice versa. Everyone who is old is either quiet or not kind and vice versa. Everyone who is either tall or calm is not humble or funny and vice versa. Everyone who is old or not patient is both not quiet and wise. If lucy is brave then john is both not brave and not patient. If alice is either calm or brave then fred is both not brave and calm and vice versa. If someone is either not strong or curious then someone is either not old or not tall. Everyone who is old or strong is not tall and vice versa. Everyone who is both quiet and brave is calm or quiet. Everyone who is not happy or not generous is kind. Everyone who is both not wise and not rich is not generous or happy and vice versa. Everyone who is not humble or not calm is not humble or generous and vice versa. Everyone who is either not funny or not happy is either creative or not funny. If paul is both humble and wise then john is both happy and not calm. Mary is kind or not calm. Alice is either generous or not old. Susan is both rich and not old. Someone is not wise. Someone is both funny and patient. Paul is not rich or not brave. Someone is generous or kind. | Mary is old. | contradiction | (![X]:((~strong(X)&~brave(X))=>(~strong(X)|~happy(X))))&
(![X]:((~strong(X)|wise(X))<=>(brave(X)|~old(X))))&
(((~old(lucy)&~generous(lucy)))<=>((kind(alice)&~brave(alice))))&
(![X]:(old(X)<=>(quiet(X)<~>~kind(X))))&
(![X]:((tall(X)<~>calm(X))<=>(~humble(X)|funny(X))))&
(![X]:((old(X)|~patient(X))=>(~quiet(X)&wise(X))))&
((brave(lucy))=>((~brave(john)&~patient(john))))&
(((calm(alice)<~>brave(alice)))<=>((~brave(fred)&calm(fred))))&
((?[X]:((~strong(X)<~>curious(X))))=>(?[X]:((~old(X)<~>~tall(X)))))&
(![X]:((old(X)|strong(X))<=>~tall(X)))&
(![X]:((quiet(X)&brave(X))=>(calm(X)|quiet(X))))&
(![X]:((~happy(X)|~generous(X))=>kind(X)))&
(![X]:((~wise(X)&~rich(X))<=>(~generous(X)|happy(X))))&
(![X]:((~humble(X)|~calm(X))<=>(~humble(X)|generous(X))))&
(![X]:((~funny(X)<~>~happy(X))=>(creative(X)<~>~funny(X))))&
(((humble(paul)&wise(paul)))=>((happy(john)&~calm(john))))&
((kind(mary)|~calm(mary)))&
((generous(alice)<~>~old(alice)))&
((rich(susan)&~old(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((funny(X)&patient(X))))&
((~rich(paul)|~brave(paul)))&
(?[X]:((generous(X)|kind(X)))) | old(mary) | [
"p3",
"p5",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3817480960516761610324009
% SZS output start Proof for 3817480960516761610324009
4. ! [X0] : (old(X0) <=> (quiet(X0) <~> ~kind(X0))) [input p3]
6. ! [X0] : ((~patient(X0) | old(X0)) => (wise(X0) & ~quiet(X0))) [input p5]
12. ! [X0] : ((~generous(X0) | ~happy(X0)) => kind(X0)) [input p11]
13. ! [X0] : ((~rich(X0) & ~wise(X0)) <=> (happy(X0) | ~generous(X0))) [input p12]
24. old(mary) [input hypothesis]
28. ! [X0] : ((wise(X0) & ~quiet(X0)) | (patient(X0) & ~old(X0))) [ennf transformation 6]
33. ! [X0] : (kind(X0) | (generous(X0) & happy(X0))) [ennf transformation 12]
41. ! [X0] : ((old(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | ~old(X0))) [nnf transformation 4]
52. ! [X0] : (((~rich(X0) & ~wise(X0)) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | (rich(X0) | wise(X0)))) [nnf transformation 13]
53. ! [X0] : (((~rich(X0) & ~wise(X0)) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | rich(X0) | wise(X0))) [flattening 52]
73. ~kind(X0) | quiet(X0) | ~old(X0) [cnf transformation 41]
83. ~quiet(X0) | ~old(X0) [cnf transformation 28]
85. ~old(X0) | wise(X0) [cnf transformation 28]
103. kind(X0) | happy(X0) [cnf transformation 33]
107. ~wise(X0) | ~happy(X0) [cnf transformation 53]
130. old(mary) [cnf transformation 24]
249. wise(mary) [resolution 85,130]
260. ~happy(mary) [resolution 107,249]
298. quiet(X1) | ~old(X1) | happy(X1) [resolution 73,103]
301. ~old(X1) | happy(X1) [subsumption resolution 298,83]
336. happy(mary) [resolution 301,130]
338. $false [subsumption resolution 336,260]
% SZS output end Proof for 3817480960516761610324009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is wise or old.
If paul is humble then someone is either calm or not rich.
If lucy is strong then someone is either creative or generous.
Everyone who is either calm or humble is calm and vice versa.
If someone is both not wise and not strong then susan is not calm and vice versa.
If someone is not humble then susan is not happy and vice versa.
If paul is not funny or brave then someone is not kind and vice versa.
If someone is both wise and not happy then fred is either tall or curious.
Everyone who is either not rich or not patient is not funny.
If fred is not happy then someone is quiet.
If fred is both not wise and not patient then fred is brave and vice versa.
Everyone who is funny is either not old or not quiet and vice versa.
Everyone who is both not humble and old is generous or curious and vice versa.
Everyone who is either not tall or not happy is both old and calm.
Everyone who is not patient or not humble is not creative or not tall and vice versa.
Everyone who is either quiet or funny is rich or kind.
Someone is both not calm and not funny.
Someone is tall or calm.
Someone is either not old or tall.
Lucy is both generous and not calm.
Someone is not happy or calm.
Susan is both not creative and not humble.
John is both curious and not patient.
Someone is either generous or wise. | Susan is not humble. | entailment | ((?[X]:(calm(X)))=>(?[X]:((wise(X)|old(X)))))&
((humble(paul))=>(?[X]:((calm(X)<~>~rich(X)))))&
((strong(lucy))=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((calm(X)<~>humble(X))<=>calm(X)))&
((?[X]:((~wise(X)&~strong(X))))<=>(~calm(susan)))&
((?[X]:(~humble(X)))<=>(~happy(susan)))&
(((~funny(paul)|brave(paul)))<=>(?[X]:(~kind(X))))&
((?[X]:((wise(X)&~happy(X))))=>((tall(fred)<~>curious(fred))))&
(![X]:((~rich(X)<~>~patient(X))=>~funny(X)))&
((~happy(fred))=>(?[X]:(quiet(X))))&
(((~wise(fred)&~patient(fred)))<=>(brave(fred)))&
(![X]:(funny(X)<=>(~old(X)<~>~quiet(X))))&
(![X]:((~humble(X)&old(X))<=>(generous(X)|curious(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(old(X)&calm(X))))&
(![X]:((~patient(X)|~humble(X))<=>(~creative(X)|~tall(X))))&
(![X]:((quiet(X)<~>funny(X))=>(rich(X)|kind(X))))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((~old(X)<~>tall(X))))&
((generous(lucy)&~calm(lucy)))&
(?[X]:((~happy(X)|calm(X))))&
((~creative(susan)&~humble(susan)))&
((curious(john)&~patient(john)))&
(?[X]:((generous(X)<~>wise(X)))) | ~humble(susan) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 6288046138476985875442731
% SZS output start Proof for 6288046138476985875442731
4. ! [X0] : ((calm(X0) <~> humble(X0)) <=> calm(X0)) [input p3]
25. humble(susan) [input hypothesis]
45. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ~calm(X0)) & (calm(X0) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [nnf transformation 4]
90. calm(X0) | calm(X0) | ~humble(X0) [cnf transformation 45]
92. ~humble(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
142. humble(susan) [cnf transformation 25]
143. calm(X0) | ~humble(X0) [duplicate literal removal 90]
144. ~humble(X0) | ~calm(X0) [duplicate literal removal 92]
185. ~humble(X0) [subsumption resolution 143,144]
300. $false [subsumption resolution 142,185]
% SZS output end Proof for 6288046138476985875442731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich is funny.
Everyone who is wise is either not generous or brave.
Everyone who is both not patient and not tall is not old.
If alice is both not kind and not brave then mary is not tall or not humble and vice versa.
Everyone who is both not creative and not calm is either creative or not funny.
If lucy is not funny then someone is either not funny or old and vice versa.
If someone is old or humble then someone is calm.
Everyone who is creative is either not rich or not wise and vice versa.
If someone is either not funny or not kind then someone is both not happy and not creative.
If fred is kind then mary is funny and vice versa.
If someone is both not kind and happy then john is brave.
Everyone who is either not tall or tall is not quiet.
If fred is not wise or kind then fred is strong or humble and vice versa.
Everyone who is patient or tall is not generous or generous.
Everyone who is either wise or kind is not quiet or curious.
If paul is creative or rich then someone is not strong or patient.
Someone is not funny.
Mary is happy.
Alice is not kind or kind.
Someone is either rich or not patient.
John is both not tall and not humble.
Fred is not patient.
Alice is both kind and patient. | Alice is kind. | entailment | (![X]:((quiet(X)&~rich(X))=>funny(X)))&
(![X]:(wise(X)=>(~generous(X)<~>brave(X))))&
(![X]:((~patient(X)&~tall(X))=>~old(X)))&
(((~kind(alice)&~brave(alice)))<=>((~tall(mary)|~humble(mary))))&
(![X]:((~creative(X)&~calm(X))=>(creative(X)<~>~funny(X))))&
((~funny(lucy))<=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:((old(X)|humble(X))))=>(?[X]:(calm(X))))&
(![X]:(creative(X)<=>(~rich(X)<~>~wise(X))))&
((?[X]:((~funny(X)<~>~kind(X))))=>(?[X]:((~happy(X)&~creative(X)))))&
((kind(fred))<=>(funny(mary)))&
((?[X]:((~kind(X)&happy(X))))=>(brave(john)))&
(![X]:((~tall(X)<~>tall(X))=>~quiet(X)))&
(((~wise(fred)|kind(fred)))<=>((strong(fred)|humble(fred))))&
(![X]:((patient(X)|tall(X))=>(~generous(X)|generous(X))))&
(![X]:((wise(X)<~>kind(X))=>(~quiet(X)|curious(X))))&
(((creative(paul)|rich(paul)))=>(?[X]:((~strong(X)|patient(X)))))&
(?[X]:(~funny(X)))&
(happy(mary))&
((~kind(alice)|kind(alice)))&
(?[X]:((rich(X)<~>~patient(X))))&
((~tall(john)&~humble(john)))&
(~patient(fred))&
((kind(alice)&patient(alice))) | kind(alice) | [
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4675977831076133724408373
% SZS output start Proof for 4675977831076133724408373
23. patient(alice) & kind(alice) [input p22]
24. ~kind(alice) [input hypothesis]
101. kind(alice) [cnf transformation 23]
103. ~kind(alice) [cnf transformation 24]
119. 4 <=> kind(alice) [avatar definition]
227. 4 [avatar split clause 101,119]
228. ~4 [avatar split clause 103,119]
229. $false [avatar sat refutation 227,228]
% SZS output end Proof for 4675977831076133724408373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or curious then fred is either curious or not curious and vice versa. Everyone who is old is both rich and not humble and vice versa. Everyone who is wise or creative is both not quiet and not patient. If someone is both happy and not happy then someone is either not tall or strong and vice versa. Everyone who is either patient or humble is not wise and vice versa. If someone is funny then someone is wise or generous. If someone is not curious or old then fred is either not curious or tall. If lucy is tall then someone is either not rich or not generous. Everyone who is not humble or not calm is both old and not rich. If someone is either not generous or not humble then someone is not funny or not rich. If lucy is either not tall or not calm then paul is humble or not curious and vice versa. If someone is both not creative and funny then someone is not rich or not curious. If mary is patient then alice is both patient and not generous and vice versa. Everyone who is both not rich and not strong is either not happy or kind and vice versa. If someone is both not strong and quiet then lucy is either not strong or not tall. If someone is strong then someone is either not quiet or not wise. Someone is either funny or not funny. Someone is either brave or not curious. Susan is either old or funny. Susan is either tall or not happy. Someone is kind. Someone is both not curious and creative. Fred is tall or old. Lucy is not creative or happy. | Fred is not wise. | entailment | ((?[X]:((humble(X)|curious(X))))<=>((curious(fred)<~>~curious(fred))))&
(![X]:(old(X)<=>(rich(X)&~humble(X))))&
(![X]:((wise(X)|creative(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((happy(X)&~happy(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((patient(X)<~>humble(X))<=>~wise(X)))&
((?[X]:(funny(X)))=>(?[X]:((wise(X)|generous(X)))))&
((?[X]:((~curious(X)|old(X))))=>((~curious(fred)<~>tall(fred))))&
((tall(lucy))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((~humble(X)|~calm(X))=>(old(X)&~rich(X))))&
((?[X]:((~generous(X)<~>~humble(X))))=>(?[X]:((~funny(X)|~rich(X)))))&
(((~tall(lucy)<~>~calm(lucy)))<=>((humble(paul)|~curious(paul))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((patient(mary))<=>((patient(alice)&~generous(alice))))&
(![X]:((~rich(X)&~strong(X))<=>(~happy(X)<~>kind(X))))&
((?[X]:((~strong(X)&quiet(X))))=>((~strong(lucy)<~>~tall(lucy))))&
((?[X]:(strong(X)))=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((brave(X)<~>~curious(X))))&
((old(susan)<~>funny(susan)))&
((tall(susan)<~>~happy(susan)))&
(?[X]:(kind(X)))&
(?[X]:((~curious(X)&creative(X))))&
((tall(fred)|old(fred)))&
((~creative(lucy)|happy(lucy))) | ~wise(fred) | [
"p1",
"p2",
"p4",
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 4213727618494496068779288
% SZS output start Proof for 4213727618494496068779288
2. ! [X0] : (old(X0) <=> (~humble(X0) & rich(X0))) [input p1]
3. ! [X0] : ((creative(X0) | wise(X0)) => (~patient(X0) & ~quiet(X0))) [input p2]
5. ! [X0] : ((patient(X0) <~> humble(X0)) <=> ~wise(X0)) [input p4]
9. ! [X0] : ((~calm(X0) | ~humble(X0)) => (~rich(X0) & old(X0))) [input p8]
25. wise(fred) [input hypothesis]
31. ! [X0] : ((~patient(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0))) [ennf transformation 3]
35. ! [X0] : ((~rich(X0) & old(X0)) | (calm(X0) & humble(X0))) [ennf transformation 9]
44. ! [X0] : ((old(X0) | (humble(X0) | ~rich(X0))) & ((~humble(X0) & rich(X0)) | ~old(X0))) [nnf transformation 2]
45. ! [X0] : ((old(X0) | humble(X0) | ~rich(X0)) & ((~humble(X0) & rich(X0)) | ~old(X0))) [flattening 44]
51. ! [X0] : ((((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | wise(X0)) & (~wise(X0) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0))))) [nnf transformation 5]
95. ~old(X0) | rich(X0) [cnf transformation 45]
100. ~patient(X0) | ~wise(X0) [cnf transformation 31]
109. ~wise(X0) | patient(X0) | ~humble(X0) [cnf transformation 51]
119. old(X0) | humble(X0) [cnf transformation 35]
121. ~rich(X0) | humble(X0) [cnf transformation 35]
158. wise(fred) [cnf transformation 25]
190. ~wise(X0) | ~humble(X0) [subsumption resolution 109,100]
366. humble(X1) | rich(X1) [resolution 119,95]
367. humble(X1) [subsumption resolution 366,121]
387. ~humble(fred) [resolution 190,158]
389. $false [subsumption resolution 387,367]
% SZS output end Proof for 4213727618494496068779288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or not generous is either old or generous and vice versa. If someone is both happy and not creative then someone is both not curious and happy. If lucy is strong then paul is both not strong and not humble. Everyone who is calm is both not brave and rich and vice versa. Everyone who is both curious and old is both not old and funny and vice versa. If someone is both rich and kind then someone is both tall and not happy. Everyone who is not tall is both not strong and not tall and vice versa. Everyone who is either creative or strong is either happy or not creative and vice versa. If alice is strong then lucy is quiet or not kind and vice versa. Everyone who is not patient is either creative or not generous and vice versa. Everyone who is either not rich or calm is either not brave or wise and vice versa. Everyone who is creative is rich. Everyone who is calm is rich and vice versa. If fred is quiet then alice is brave or old. Everyone who is both wise and tall is not quiet or humble and vice versa. Everyone who is both generous and happy is either brave or tall and vice versa. John is both not quiet and humble. Someone is both not funny and curious. Paul is both not kind and not curious. Someone is not humble or not curious. Someone is quiet. Someone is generous or not happy. Paul is not curious. | Fred is not quiet. | neutral | (![X]:((tall(X)<~>~generous(X))<=>(old(X)<~>generous(X))))&
((?[X]:((happy(X)&~creative(X))))=>(?[X]:((~curious(X)&happy(X)))))&
((strong(lucy))=>((~strong(paul)&~humble(paul))))&
(![X]:(calm(X)<=>(~brave(X)&rich(X))))&
(![X]:((curious(X)&old(X))<=>(~old(X)&funny(X))))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(~tall(X)<=>(~strong(X)&~tall(X))))&
(![X]:((creative(X)<~>strong(X))<=>(happy(X)<~>~creative(X))))&
((strong(alice))<=>((quiet(lucy)|~kind(lucy))))&
(![X]:(~patient(X)<=>(creative(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>calm(X))<=>(~brave(X)<~>wise(X))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(calm(X)<=>rich(X)))&
((quiet(fred))=>((brave(alice)|old(alice))))&
(![X]:((wise(X)&tall(X))<=>(~quiet(X)|humble(X))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
((~quiet(john)&humble(john)))&
(?[X]:((~funny(X)&curious(X))))&
((~kind(paul)&~curious(paul)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)|~happy(X))))&
(~curious(paul)) | ~quiet(fred) | []
| null | 0 |
Everyone who is either calm or strong is either calm or not creative and vice versa.
If alice is not quiet or not kind then someone is rich and vice versa.
Everyone who is both not old and not creative is not patient.
If alice is either happy or not strong then someone is old or not patient and vice versa.
Everyone who is not wise or not old is patient.
If john is quiet or strong then someone is happy and vice versa.
Everyone who is quiet or funny is either not tall or not humble and vice versa.
If mary is patient or not curious then susan is old and vice versa.
Everyone who is tall or patient is both not creative and funny and vice versa.
Everyone who is both rich and tall is tall or old and vice versa.
If fred is either not happy or curious then susan is not generous or not brave and vice versa.
If someone is not strong then alice is kind.
If susan is not rich or brave then alice is wise or not brave and vice versa.
Everyone who is funny is kind and vice versa.
Everyone who is both not rich and not creative is not brave or calm.
Everyone who is not wise or calm is creative or happy and vice versa.
Mary is kind.
Paul is not calm or humble.
Someone is not rich or wise.
Alice is both funny and happy.
Someone is either funny or not wise.
Paul is not tall or rich. | Mary is not wise. | neutral | (![X]:((calm(X)<~>strong(X))<=>(calm(X)<~>~creative(X))))&
(((~quiet(alice)|~kind(alice)))<=>(?[X]:(rich(X))))&
(![X]:((~old(X)&~creative(X))=>~patient(X)))&
(((happy(alice)<~>~strong(alice)))<=>(?[X]:((old(X)|~patient(X)))))&
(![X]:((~wise(X)|~old(X))=>patient(X)))&
(((quiet(john)|strong(john)))<=>(?[X]:(happy(X))))&
(![X]:((quiet(X)|funny(X))<=>(~tall(X)<~>~humble(X))))&
(((patient(mary)|~curious(mary)))<=>(old(susan)))&
(![X]:((tall(X)|patient(X))<=>(~creative(X)&funny(X))))&
(![X]:((rich(X)&tall(X))<=>(tall(X)|old(X))))&
(((~happy(fred)<~>curious(fred)))<=>((~generous(susan)|~brave(susan))))&
((?[X]:(~strong(X)))=>(kind(alice)))&
(((~rich(susan)|brave(susan)))<=>((wise(alice)|~brave(alice))))&
(![X]:(funny(X)<=>kind(X)))&
(![X]:((~rich(X)&~creative(X))=>(~brave(X)|calm(X))))&
(![X]:((~wise(X)|calm(X))<=>(creative(X)|happy(X))))&
(kind(mary))&
((~calm(paul)|humble(paul)))&
(?[X]:((~rich(X)|wise(X))))&
((funny(alice)&happy(alice)))&
(?[X]:((funny(X)<~>~wise(X))))&
((~tall(paul)|rich(paul))) | ~wise(mary) | []
| null | 0 |
Everyone who is either not patient or not creative is not calm. If alice is both funny and not happy then john is either not tall or not humble. If someone is not rich then someone is strong or not wise. Everyone who is both curious and generous is not generous or not old and vice versa. If someone is not happy or not calm then fred is both not calm and wise and vice versa. Everyone who is generous is not wise. Everyone who is not creative is either not humble or rich. If mary is not wise or curious then mary is not wise. If alice is happy or not patient then mary is either not kind or curious and vice versa. Everyone who is either happy or not humble is strong. Everyone who is not funny is not rich. Everyone who is both not patient and not quiet is both not brave and not wise and vice versa. If someone is either not funny or not humble then paul is not old or not calm and vice versa. If someone is either not curious or rich then someone is generous or not patient. If someone is strong or wise then someone is both not tall and not brave and vice versa. Everyone who is not creative or wise is wise and vice versa. Someone is either not brave or not curious. Someone is both funny and brave. Someone is either not wise or strong. Someone is both not wise and happy. Paul is not quiet or curious. Susan is either not funny or kind. | Paul is generous. | entailment | (![X]:((~patient(X)<~>~creative(X))=>~calm(X)))&
(((funny(alice)&~happy(alice)))=>((~tall(john)<~>~humble(john))))&
((?[X]:(~rich(X)))=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:((curious(X)&generous(X))<=>(~generous(X)|~old(X))))&
((?[X]:((~happy(X)|~calm(X))))<=>((~calm(fred)&wise(fred))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:(~creative(X)=>(~humble(X)<~>rich(X))))&
(((~wise(mary)|curious(mary)))=>(~wise(mary)))&
(((happy(alice)|~patient(alice)))<=>((~kind(mary)<~>curious(mary))))&
(![X]:((happy(X)<~>~humble(X))=>strong(X)))&
(![X]:(~funny(X)=>~rich(X)))&
(![X]:((~patient(X)&~quiet(X))<=>(~brave(X)&~wise(X))))&
((?[X]:((~funny(X)<~>~humble(X))))<=>((~old(paul)|~calm(paul))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~creative(X)|wise(X))<=>wise(X)))&
(?[X]:((~brave(X)<~>~curious(X))))&
(?[X]:((funny(X)&brave(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~wise(X)&happy(X))))&
((~quiet(paul)|curious(paul)))&
((~funny(susan)<~>kind(susan))) | generous(paul) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 349461388196717667247418
% SZS output start Proof for 349461388196717667247418
4. ! [X0] : ((generous(X0) & curious(X0)) <=> (~old(X0) | ~generous(X0))) [input p3]
23. ~generous(paul) [input hypothesis]
42. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | (~generous(X0) | ~curious(X0)))) [nnf transformation 4]
43. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | ~generous(X0) | ~curious(X0))) [flattening 42]
90. generous(X0) | generous(X0) [cnf transformation 43]
142. ~generous(paul) [cnf transformation 23]
144. generous(X0) [duplicate literal removal 90]
305. $false [subsumption resolution 142,144]
% SZS output end Proof for 349461388196717667247418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both curious and humble.
If paul is both not wise and humble then someone is kind.
Everyone who is both humble and brave is not tall and vice versa.
If mary is either not rich or wise then susan is happy and vice versa.
If lucy is both not strong and strong then someone is both not brave and calm and vice versa.
Everyone who is not strong or calm is either not happy or calm.
If someone is not rich or strong then paul is quiet and vice versa.
Everyone who is not wise is both not quiet and not rich and vice versa.
If susan is either not calm or not patient then someone is humble or not quiet.
Everyone who is creative is both not brave and not quiet and vice versa.
Everyone who is either wise or not old is either humble or brave.
If someone is not generous then susan is not calm or rich and vice versa.
Everyone who is not tall or not brave is either creative or funny and vice versa.
If someone is funny then paul is patient.
If lucy is not strong then mary is not rich and vice versa.
Everyone who is either not curious or not humble is not wise and vice versa.
Susan is both not curious and not brave.
Someone is creative.
Someone is not strong.
Fred is not patient.
Someone is funny or curious.
Someone is not quiet or old.
Someone is not tall or tall.
Someone is both not funny and not humble. | Paul is not wise. | contradiction | (![X]:(~kind(X)=>(curious(X)&humble(X))))&
(((~wise(paul)&humble(paul)))=>(?[X]:(kind(X))))&
(![X]:((humble(X)&brave(X))<=>~tall(X)))&
(((~rich(mary)<~>wise(mary)))<=>(happy(susan)))&
(((~strong(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~strong(X)|calm(X))=>(~happy(X)<~>calm(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(quiet(paul)))&
(![X]:(~wise(X)<=>(~quiet(X)&~rich(X))))&
(((~calm(susan)<~>~patient(susan)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:(creative(X)<=>(~brave(X)&~quiet(X))))&
(![X]:((wise(X)<~>~old(X))=>(humble(X)<~>brave(X))))&
((?[X]:(~generous(X)))<=>((~calm(susan)|rich(susan))))&
(![X]:((~tall(X)|~brave(X))<=>(creative(X)<~>funny(X))))&
((?[X]:(funny(X)))=>(patient(paul)))&
((~strong(lucy))<=>(~rich(mary)))&
(![X]:((~curious(X)<~>~humble(X))<=>~wise(X)))&
((~curious(susan)&~brave(susan)))&
(?[X]:(creative(X)))&
(?[X]:(~strong(X)))&
(~patient(fred))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((~tall(X)|tall(X))))&
(?[X]:((~funny(X)&~humble(X)))) | ~wise(paul) | [
"p6",
"p7",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1097491219429236247744041
% SZS output start Proof for 1097491219429236247744041
7. ? [X0] : (strong(X0) | ~rich(X0)) <=> quiet(paul) [input p6]
8. ! [X0] : (~wise(X0) <=> (~rich(X0) & ~quiet(X0))) [input p7]
15. ~strong(lucy) <=> ~rich(mary) [input p14]
25. ~wise(paul) [input hypothesis]
41. (? [X0] : (strong(X0) | ~rich(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X0] : (~strong(X0) & rich(X0))) [nnf transformation 7]
42. (? [X0] : (strong(X0) | ~rich(X0)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (~strong(X1) & rich(X1))) [rectify 41]
43. ? [X0] : (strong(X0) | ~rich(X0)) => (strong(sK1) | ~rich(sK1)) [choice axiom]
44. ((strong(sK1) | ~rich(sK1)) | ~quiet(paul)) & (quiet(paul) | ! [X1] : (~strong(X1) & rich(X1))) [skolemisation 42,43]
45. ! [X0] : ((~wise(X0) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [nnf transformation 8]
46. ! [X0] : ((~wise(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [flattening 45]
60. (~strong(lucy) | rich(mary)) & (~rich(mary) | strong(lucy)) [nnf transformation 15]
89. quiet(paul) | rich(X1) [cnf transformation 44]
90. quiet(paul) | ~strong(X1) [cnf transformation 44]
92. ~quiet(X0) | wise(X0) [cnf transformation 46]
114. ~rich(mary) | strong(lucy) [cnf transformation 60]
130. ~wise(paul) [cnf transformation 25]
137. 2 <=> rich(mary) [avatar definition]
138. ~rich(mary) <- (~2) [avatar component clause 137]
152. 5 <=> strong(lucy) [avatar definition]
154. strong(lucy) <- (5) [avatar component clause 152]
158. 6 <=> quiet(paul) [avatar definition]
159. quiet(paul) <- (6) [avatar component clause 158]
171. 9 <=> ! [X1] : ~strong(X1) [avatar definition]
172. ~strong(X1) <- (9) [avatar component clause 171]
173. 9 | 6 [avatar split clause 90,158,171]
175. 10 <=> ! [X1] : rich(X1) [avatar definition]
176. rich(X1) <- (10) [avatar component clause 175]
177. 10 | 6 [avatar split clause 89,158,175]
221. 5 | ~2 [avatar split clause 114,137,152]
242. wise(paul) <- (6) [resolution 92,159]
243. $false <- (6) [subsumption resolution 242,130]
244. ~6 [avatar contradiction clause 243]
245. $false <- (~2, 10) [resolution 176,138]
248. 2 | ~10 [avatar contradiction clause 245]
249. $false <- (5, 9) [subsumption resolution 154,172]
250. ~5 | ~9 [avatar contradiction clause 249]
251. $false [avatar sat refutation 173,177,221,244,248,250]
% SZS output end Proof for 1097491219429236247744041
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either not brave or not old and vice versa.
If mary is not wise then john is not kind and vice versa.
If john is both quiet and happy then fred is either wise or generous and vice versa.
Everyone who is both not humble and not generous is both not kind and not patient and vice versa.
Everyone who is tall is both not humble and humble.
If someone is both not strong and strong then lucy is either not creative or funny and vice versa.
Everyone who is rich is patient.
Everyone who is either not tall or tall is either not humble or quiet.
If fred is both happy and funny then lucy is both rich and old and vice versa.
Everyone who is either not kind or not calm is both not generous and quiet and vice versa.
Everyone who is kind or not calm is both not patient and quiet and vice versa.
If susan is not calm then fred is not kind or patient.
If someone is either not patient or curious then alice is both not tall and quiet and vice versa.
Everyone who is either curious or kind is either humble or not creative and vice versa.
If someone is not creative then someone is not calm and vice versa.
If fred is either not wise or not humble then susan is brave and vice versa.
Someone is either not calm or not rich.
Someone is not quiet or calm.
Fred is both humble and not generous.
Susan is both creative and wise.
Someone is humble.
Paul is creative or not patient.
Someone is either not calm or kind.
Alice is either not curious or not calm. | Alice is not happy. | neutral | (![X]:(funny(X)<=>(~brave(X)<~>~old(X))))&
((~wise(mary))<=>(~kind(john)))&
(((quiet(john)&happy(john)))<=>((wise(fred)<~>generous(fred))))&
(![X]:((~humble(X)&~generous(X))<=>(~kind(X)&~patient(X))))&
(![X]:(tall(X)=>(~humble(X)&humble(X))))&
((?[X]:((~strong(X)&strong(X))))<=>((~creative(lucy)<~>funny(lucy))))&
(![X]:(rich(X)=>patient(X)))&
(![X]:((~tall(X)<~>tall(X))=>(~humble(X)<~>quiet(X))))&
(((happy(fred)&funny(fred)))<=>((rich(lucy)&old(lucy))))&
(![X]:((~kind(X)<~>~calm(X))<=>(~generous(X)&quiet(X))))&
(![X]:((kind(X)|~calm(X))<=>(~patient(X)&quiet(X))))&
((~calm(susan))=>((~kind(fred)|patient(fred))))&
((?[X]:((~patient(X)<~>curious(X))))<=>((~tall(alice)&quiet(alice))))&
(![X]:((curious(X)<~>kind(X))<=>(humble(X)<~>~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~calm(X))))&
(((~wise(fred)<~>~humble(fred)))<=>(brave(susan)))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((humble(fred)&~generous(fred)))&
((creative(susan)&wise(susan)))&
(?[X]:(humble(X)))&
((creative(paul)|~patient(paul)))&
(?[X]:((~calm(X)<~>kind(X))))&
((~curious(alice)<~>~calm(alice))) | ~happy(alice) | []
| null | 0 |
If someone is not creative then someone is wise or calm. If mary is both patient and creative then someone is old or curious. Everyone who is not funny is both creative and not creative. If someone is kind then someone is not kind or curious. Everyone who is both not wise and quiet is both not quiet and not rich. Everyone who is not rich or not happy is not happy or tall. Everyone who is generous or kind is both not kind and creative. If someone is both not calm and not funny then someone is humble or not funny. If someone is wise or not tall then lucy is humble. If someone is both not rich and not patient then lucy is both rich and funny. Everyone who is either not quiet or not old is either not wise or generous. Everyone who is both not creative and not quiet is both generous and tall. If mary is both not tall and not generous then someone is humble or creative and vice versa. Everyone who is either kind or not generous is not wise or not calm. Everyone who is either not rich or wise is creative. Lucy is strong. Someone is humble or not generous. Susan is not curious. Someone is not creative. Mary is either wise or old. Someone is either not creative or not rich. | Mary is not quiet. | entailment | ((?[X]:(~creative(X)))=>(?[X]:((wise(X)|calm(X)))))&
(((patient(mary)&creative(mary)))=>(?[X]:((old(X)|curious(X)))))&
(![X]:(~funny(X)=>(creative(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~rich(X)|~happy(X))=>(~happy(X)|tall(X))))&
(![X]:((generous(X)|kind(X))=>(~kind(X)&creative(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((humble(X)|~funny(X)))))&
((?[X]:((wise(X)|~tall(X))))=>(humble(lucy)))&
((?[X]:((~rich(X)&~patient(X))))=>((rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)<~>~old(X))=>(~wise(X)<~>generous(X))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)&tall(X))))&
(((~tall(mary)&~generous(mary)))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))=>creative(X)))&
(strong(lucy))&
(?[X]:((humble(X)|~generous(X))))&
(~curious(susan))&
(?[X]:(~creative(X)))&
((wise(mary)<~>old(mary)))&
(?[X]:((~creative(X)<~>~rich(X)))) | ~quiet(mary) | [
"p4",
"p6",
"p8",
"p10",
"p11",
"p12",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 4123673886557521092525799
% SZS output start Proof for 4123673886557521092525799
5. ! [X0] : ((quiet(X0) & ~wise(X0)) => (~rich(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((kind(X0) | generous(X0)) => (creative(X0) & ~kind(X0))) [input p6]
9. ? [X0] : (~tall(X0) | wise(X0)) => humble(lucy) [input p8]
11. ! [X0] : ((~quiet(X0) <~> ~old(X0)) => (~wise(X0) <~> generous(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) & ~creative(X0)) => (tall(X0) & generous(X0))) [input p11]
13. (~generous(mary) & ~tall(mary)) <=> ? [X0] : (creative(X0) | humble(X0)) [input p12]
20. wise(mary) <~> old(mary) [input p19]
22. quiet(mary) [input hypothesis]
32. ! [X0] : ((~rich(X0) & ~quiet(X0)) | (~quiet(X0) | wise(X0))) [ennf transformation 5]
33. ! [X0] : ((~rich(X0) & ~quiet(X0)) | ~quiet(X0) | wise(X0)) [flattening 32]
36. ! [X0] : ((creative(X0) & ~kind(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 7]
38. humble(lucy) | ! [X0] : (tall(X0) & ~wise(X0)) [ennf transformation 9]
40. ! [X0] : ((~wise(X0) <~> generous(X0)) | (~quiet(X0) <=> ~old(X0))) [ennf transformation 11]
41. ! [X0] : ((tall(X0) & generous(X0)) | (quiet(X0) | creative(X0))) [ennf transformation 12]
42. ! [X0] : ((tall(X0) & generous(X0)) | quiet(X0) | creative(X0)) [flattening 41]
57. ! [X0] : (((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) [nnf transformation 40]
58. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X0] : (creative(X0) | humble(X0)) | (generous(mary) | tall(mary))) [nnf transformation 13]
59. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X0] : (creative(X0) | humble(X0)) | generous(mary) | tall(mary)) [flattening 58]
60. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & (? [X1] : (creative(X1) | humble(X1)) | generous(mary) | tall(mary)) [rectify 59]
61. ? [X1] : (creative(X1) | humble(X1)) => (creative(sK4) | humble(sK4)) [choice axiom]
62. ((~generous(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~humble(X0))) & ((creative(sK4) | humble(sK4)) | generous(mary) | tall(mary)) [skolemisation 60,61]
69. (~old(mary) | ~wise(mary)) & (old(mary) | wise(mary)) [nnf transformation 20]
78. ~quiet(X0) | ~quiet(X0) | wise(X0) [cnf transformation 33]
84. ~generous(X0) | creative(X0) [cnf transformation 36]
87. humble(lucy) | ~wise(X0) [cnf transformation 38]
92. generous(X0) | ~wise(X0) | ~quiet(X0) | old(X0) [cnf transformation 57]
95. generous(X0) | quiet(X0) | creative(X0) [cnf transformation 42]
100. ~generous(mary) | ~humble(X0) [cnf transformation 62]
101. ~generous(mary) | ~creative(X0) [cnf transformation 62]
110. ~old(mary) | ~wise(mary) [cnf transformation 69]
113. quiet(mary) [cnf transformation 22]
115. ~quiet(X0) | wise(X0) [duplicate literal removal 78]
163. 12 <=> humble(lucy) [avatar definition]
165. humble(lucy) <- (12) [avatar component clause 163]
168. 13 <=> ! [X0] : ~wise(X0) [avatar definition]
169. ~wise(X0) <- (13) [avatar component clause 168]
170. 13 | 12 [avatar split clause 87,163,168]
180. ~quiet(X0) | generous(X0) | old(X0) [subsumption resolution 92,115]
181. quiet(X0) | creative(X0) [subsumption resolution 95,84]
183. 16 <=> ! [X0] : ~creative(X0) [avatar definition]
184. ~creative(X0) <- (16) [avatar component clause 183]
186. 17 <=> generous(mary) [avatar definition]
189. 16 | ~17 [avatar split clause 101,186,183]
191. 18 <=> ! [X0] : ~humble(X0) [avatar definition]
192. ~humble(X0) <- (18) [avatar component clause 191]
193. 18 | ~17 [avatar split clause 100,186,191]
219. 24 <=> wise(mary) [avatar definition]
223. 25 <=> old(mary) [avatar definition]
226. ~24 | ~25 [avatar split clause 110,223,219]
238. $false <- (12, 18) [subsumption resolution 165,192]
239. ~12 | ~18 [avatar contradiction clause 238]
247. wise(mary) [resolution 115,113]
249. wise(X0) | creative(X0) [resolution 181,115]
265. generous(mary) | old(mary) [resolution 180,113]
271. 24 [avatar split clause 247,219]
273. 25 | 17 [avatar split clause 265,186,223]
274. creative(X0) <- (13) [resolution 169,249]
275. $false <- (13, 16) [subsumption resolution 274,184]
276. ~13 | ~16 [avatar contradiction clause 275]
277. $false [avatar sat refutation 170,189,193,226,239,271,273,276]
% SZS output end Proof for 4123673886557521092525799
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both old and not kind is creative and vice versa.
Everyone who is both kind and not brave is not creative or brave and vice versa.
If fred is either generous or not calm then john is both kind and generous.
Everyone who is both happy and not generous is not rich.
Everyone who is humble is not wise or patient.
Everyone who is not calm is both quiet and not old and vice versa.
If alice is not calm then someone is both generous and not generous.
If paul is not funny then susan is both funny and strong.
If someone is not patient or humble then mary is both not kind and not curious and vice versa.
Everyone who is either curious or rich is both patient and old and vice versa.
If mary is wise or tall then someone is not kind.
Everyone who is both old and brave is both funny and not calm and vice versa.
Everyone who is either not tall or not happy is both not brave and not creative.
If someone is strong or not creative then fred is both not curious and rich and vice versa.
If susan is funny then john is patient or kind.
If john is not calm or tall then mary is brave.
Someone is strong or generous.
Someone is calm or not humble.
Alice is not quiet or not humble.
Paul is either calm or generous.
Someone is either not strong or curious.
John is either generous or not quiet.
Someone is old or not old.
Someone is either not generous or not funny. | Paul is not brave. | entailment | (![X]:((old(X)&~kind(X))<=>creative(X)))&
(![X]:((kind(X)&~brave(X))<=>(~creative(X)|brave(X))))&
(((generous(fred)<~>~calm(fred)))=>((kind(john)&generous(john))))&
(![X]:((happy(X)&~generous(X))=>~rich(X)))&
(![X]:(humble(X)=>(~wise(X)|patient(X))))&
(![X]:(~calm(X)<=>(quiet(X)&~old(X))))&
((~calm(alice))=>(?[X]:((generous(X)&~generous(X)))))&
((~funny(paul))=>((funny(susan)&strong(susan))))&
((?[X]:((~patient(X)|humble(X))))<=>((~kind(mary)&~curious(mary))))&
(![X]:((curious(X)<~>rich(X))<=>(patient(X)&old(X))))&
(((wise(mary)|tall(mary)))=>(?[X]:(~kind(X))))&
(![X]:((old(X)&brave(X))<=>(funny(X)&~calm(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(~brave(X)&~creative(X))))&
((?[X]:((strong(X)|~creative(X))))<=>((~curious(fred)&rich(fred))))&
((funny(susan))=>((patient(john)|kind(john))))&
(((~calm(john)|tall(john)))=>(brave(mary)))&
(?[X]:((strong(X)|generous(X))))&
(?[X]:((calm(X)|~humble(X))))&
((~quiet(alice)|~humble(alice)))&
((calm(paul)<~>generous(paul)))&
(?[X]:((~strong(X)<~>curious(X))))&
((generous(john)<~>~quiet(john)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~generous(X)<~>~funny(X)))) | ~brave(paul) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 1892653714065471516392617
% SZS output start Proof for 1892653714065471516392617
2. ! [X0] : ((~brave(X0) & kind(X0)) <=> (brave(X0) | ~creative(X0))) [input p1]
25. brave(paul) [input hypothesis]
40. ! [X0] : (((~brave(X0) & kind(X0)) | (~brave(X0) & creative(X0))) & ((brave(X0) | ~creative(X0)) | (brave(X0) | ~kind(X0)))) [nnf transformation 2]
41. ! [X0] : (((~brave(X0) & kind(X0)) | (~brave(X0) & creative(X0))) & (brave(X0) | ~creative(X0) | brave(X0) | ~kind(X0))) [flattening 40]
85. ~brave(X0) | ~brave(X0) [cnf transformation 41]
138. brave(paul) [cnf transformation 25]
140. ~brave(X0) [duplicate literal removal 85]
319. $false [subsumption resolution 138,140]
% SZS output end Proof for 1892653714065471516392617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and calm is not generous or not strong and vice versa.
Everyone who is happy is both not tall and old and vice versa.
If someone is both not humble and tall then alice is either tall or not happy.
Everyone who is both not wise and not rich is not calm.
If fred is either not kind or old then someone is both not quiet and creative and vice versa.
Everyone who is tall or old is not patient or brave.
Everyone who is either funny or not happy is either not tall or patient and vice versa.
Everyone who is not curious is either tall or happy.
If alice is both not happy and old then john is both rich and brave and vice versa.
If someone is either not strong or not patient then someone is not strong and vice versa.
If john is either not tall or not creative then john is humble or not calm and vice versa.
Everyone who is not wise or calm is funny.
Everyone who is either quiet or not strong is not patient or not old and vice versa.
Everyone who is both not generous and strong is not humble or not calm and vice versa.
Everyone who is both not brave and calm is either wise or tall.
Lucy is not creative.
Someone is either not quiet or not kind.
Someone is either brave or curious.
Susan is kind.
Someone is either not kind or generous. | Lucy is kind. | neutral | (![X]:((strong(X)&calm(X))<=>(~generous(X)|~strong(X))))&
(![X]:(happy(X)<=>(~tall(X)&old(X))))&
((?[X]:((~humble(X)&tall(X))))=>((tall(alice)<~>~happy(alice))))&
(![X]:((~wise(X)&~rich(X))=>~calm(X)))&
(((~kind(fred)<~>old(fred)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((tall(X)|old(X))=>(~patient(X)|brave(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~tall(X)<~>patient(X))))&
(![X]:(~curious(X)=>(tall(X)<~>happy(X))))&
(((~happy(alice)&old(alice)))<=>((rich(john)&brave(john))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:(~strong(X))))&
(((~tall(john)<~>~creative(john)))<=>((humble(john)|~calm(john))))&
(![X]:((~wise(X)|calm(X))=>funny(X)))&
(![X]:((quiet(X)<~>~strong(X))<=>(~patient(X)|~old(X))))&
(![X]:((~generous(X)&strong(X))<=>(~humble(X)|~calm(X))))&
(![X]:((~brave(X)&calm(X))=>(wise(X)<~>tall(X))))&
(~creative(lucy))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(kind(susan))&
(?[X]:((~kind(X)<~>generous(X)))) | kind(lucy) | []
| null | 0 |
Everyone who is either not wise or not quiet is either humble or not wise and vice versa.
If someone is funny or creative then john is old or wise.
Everyone who is patient or not humble is not generous or curious and vice versa.
If mary is both not rich and funny then alice is not kind or kind and vice versa.
Everyone who is not old is both brave and wise.
Everyone who is either quiet or not old is old or not tall.
Everyone who is both creative and not patient is not tall or not strong and vice versa.
Everyone who is either brave or not old is humble and vice versa.
If someone is either not curious or not old then someone is both tall and wise and vice versa.
If someone is not generous or calm then fred is either not quiet or tall and vice versa.
Everyone who is both humble and happy is not old or strong and vice versa.
If someone is both not patient and brave then paul is tall or wise and vice versa.
Everyone who is either curious or not funny is both not wise and calm and vice versa.
If alice is both humble and patient then someone is both happy and calm.
If someone is not tall then mary is both not quiet and patient and vice versa.
Everyone who is both brave and curious is both quiet and creative and vice versa.
Someone is either not kind or not generous.
Someone is not tall or creative.
Someone is both not happy and not quiet.
Someone is patient.
Someone is either not creative or calm.
Someone is brave or rich.
Fred is not happy or not humble.
Someone is not happy or not rich. | Paul is brave. | entailment | (![X]:((~wise(X)<~>~quiet(X))<=>(humble(X)<~>~wise(X))))&
((?[X]:((funny(X)|creative(X))))=>((old(john)|wise(john))))&
(![X]:((patient(X)|~humble(X))<=>(~generous(X)|curious(X))))&
(((~rich(mary)&funny(mary)))<=>((~kind(alice)|kind(alice))))&
(![X]:(~old(X)=>(brave(X)&wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(old(X)|~tall(X))))&
(![X]:((creative(X)&~patient(X))<=>(~tall(X)|~strong(X))))&
(![X]:((brave(X)<~>~old(X))<=>humble(X)))&
((?[X]:((~curious(X)<~>~old(X))))<=>(?[X]:((tall(X)&wise(X)))))&
((?[X]:((~generous(X)|calm(X))))<=>((~quiet(fred)<~>tall(fred))))&
(![X]:((humble(X)&happy(X))<=>(~old(X)|strong(X))))&
((?[X]:((~patient(X)&brave(X))))<=>((tall(paul)|wise(paul))))&
(![X]:((curious(X)<~>~funny(X))<=>(~wise(X)&calm(X))))&
(((humble(alice)&patient(alice)))=>(?[X]:((happy(X)&calm(X)))))&
((?[X]:(~tall(X)))<=>((~quiet(mary)&patient(mary))))&
(![X]:((brave(X)&curious(X))<=>(quiet(X)&creative(X))))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((~happy(X)&~quiet(X))))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((brave(X)|rich(X))))&
((~happy(fred)|~humble(fred)))&
(?[X]:((~happy(X)|~rich(X)))) | brave(paul) | [
"p0",
"p4",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 548006189930874292227098
% SZS output start Proof for 548006189930874292227098
1. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> (humble(X0) <~> ~wise(X0))) [input p0]
5. ! [X0] : (~old(X0) => (wise(X0) & brave(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~strong(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> humble(X0)) [input p7]
11. ! [X0] : ((happy(X0) & humble(X0)) <=> (strong(X0) | ~old(X0))) [input p10]
16. ! [X0] : ((curious(X0) & brave(X0)) <=> (creative(X0) & quiet(X0))) [input p15]
25. ~brave(paul) [input hypothesis]
29. ! [X0] : ((wise(X0) & brave(X0)) | old(X0)) [ennf transformation 5]
34. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 1]
40. ! [X0] : (((~patient(X0) & creative(X0)) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 7]
41. ! [X0] : (((~patient(X0) & creative(X0)) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | patient(X0) | ~creative(X0))) [flattening 40]
42. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~humble(X0)) & (humble(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 8]
52. ! [X0] : (((happy(X0) & humble(X0)) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | (~happy(X0) | ~humble(X0)))) [nnf transformation 11]
53. ! [X0] : (((happy(X0) & humble(X0)) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | ~happy(X0) | ~humble(X0))) [flattening 52]
68. ! [X0] : (((curious(X0) & brave(X0)) | (~creative(X0) | ~quiet(X0))) & ((creative(X0) & quiet(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 16]
69. ! [X0] : (((curious(X0) & brave(X0)) | ~creative(X0) | ~quiet(X0)) & ((creative(X0) & quiet(X0)) | ~curious(X0) | ~brave(X0))) [flattening 68]
87. ~wise(X0) | humble(X0) | ~wise(X0) | quiet(X0) [cnf transformation 34]
93. quiet(X0) | wise(X0) | humble(X0) | wise(X0) [cnf transformation 34]
105. brave(X0) | old(X0) [cnf transformation 29]
111. strong(X0) | creative(X0) [cnf transformation 41]
116. ~old(X0) | brave(X0) | ~humble(X0) [cnf transformation 42]
132. ~strong(X0) | humble(X0) [cnf transformation 53]
153. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 69]
166. ~brave(paul) [cnf transformation 25]
168. ~wise(X0) | humble(X0) | quiet(X0) [duplicate literal removal 87]
171. quiet(X0) | wise(X0) | humble(X0) [duplicate literal removal 93]
173. humble(X0) | quiet(X0) [subsumption resolution 168,171]
207. ~humble(X0) | brave(X0) [subsumption resolution 116,105]
385. creative(X0) | humble(X0) [resolution 132,111]
514. brave(X0) | ~quiet(X0) | humble(X0) [resolution 153,385]
519. brave(X0) | humble(X0) [subsumption resolution 514,173]
520. brave(X0) [subsumption resolution 519,207]
521. $false [resolution 520,166]
% SZS output end Proof for 548006189930874292227098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not curious is either rich or not kind. Everyone who is both not humble and generous is both humble and wise and vice versa. Everyone who is patient or not calm is either curious or brave and vice versa. If susan is strong then susan is tall and vice versa. Everyone who is both brave and rich is not humble and vice versa. If someone is not patient or not funny then lucy is not tall or calm and vice versa. Everyone who is strong or quiet is old or not tall and vice versa. If someone is either not strong or strong then someone is either not kind or kind and vice versa. If someone is both not creative and not kind then lucy is not curious or not wise and vice versa. If someone is tall or brave then susan is both not calm and brave. Everyone who is either not curious or not creative is either not brave or not curious and vice versa. Everyone who is humble or brave is both tall and generous. If someone is wise then someone is both not humble and not kind. Everyone who is funny or not humble is either not brave or old and vice versa. Everyone who is either not kind or funny is strong or funny and vice versa. If alice is either not curious or not rich then lucy is not rich and vice versa. John is old. Mary is not funny or calm. Lucy is either not wise or not quiet. Someone is wise or humble. Lucy is either quiet or wise. Lucy is humble or kind. Alice is either curious or quiet. | Lucy is not old. | contradiction | (![X]:((generous(X)<~>~curious(X))=>(rich(X)<~>~kind(X))))&
(![X]:((~humble(X)&generous(X))<=>(humble(X)&wise(X))))&
(![X]:((patient(X)|~calm(X))<=>(curious(X)<~>brave(X))))&
((strong(susan))<=>(tall(susan)))&
(![X]:((brave(X)&rich(X))<=>~humble(X)))&
((?[X]:((~patient(X)|~funny(X))))<=>((~tall(lucy)|calm(lucy))))&
(![X]:((strong(X)|quiet(X))<=>(old(X)|~tall(X))))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~kind(X)<~>kind(X)))))&
((?[X]:((~creative(X)&~kind(X))))<=>((~curious(lucy)|~wise(lucy))))&
((?[X]:((tall(X)|brave(X))))=>((~calm(susan)&brave(susan))))&
(![X]:((~curious(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((humble(X)|brave(X))=>(tall(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&~kind(X)))))&
(![X]:((funny(X)|~humble(X))<=>(~brave(X)<~>old(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(strong(X)|funny(X))))&
(((~curious(alice)<~>~rich(alice)))<=>(~rich(lucy)))&
(old(john))&
((~funny(mary)|calm(mary)))&
((~wise(lucy)<~>~quiet(lucy)))&
(?[X]:((wise(X)|humble(X))))&
((quiet(lucy)<~>wise(lucy)))&
((humble(lucy)|kind(lucy)))&
((curious(alice)<~>quiet(alice))) | ~old(lucy) | [
"p1",
"p4",
"p6",
"p11",
"p12",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 1502301314232983145286368
% SZS output start Proof for 1502301314232983145286368
2. ! [X0] : ((generous(X0) & ~humble(X0)) <=> (wise(X0) & humble(X0))) [input p1]
5. ! [X0] : ((rich(X0) & brave(X0)) <=> ~humble(X0)) [input p4]
7. ! [X0] : ((quiet(X0) | strong(X0)) <=> (~tall(X0) | old(X0))) [input p6]
12. ! [X0] : ((brave(X0) | humble(X0)) => (generous(X0) & tall(X0))) [input p11]
13. ? [X0] : wise(X0) => ? [X0] : (~kind(X0) & ~humble(X0)) [input p12]
21. quiet(lucy) <~> wise(lucy) [input p20]
24. ~old(lucy) [input hypothesis]
26. ? [X0] : wise(X0) => ? [X1] : (~kind(X1) & ~humble(X1)) [rectify 13]
29. ! [X0] : ((generous(X0) & tall(X0)) | (~brave(X0) & ~humble(X0))) [ennf transformation 12]
30. ? [X1] : (~kind(X1) & ~humble(X1)) | ! [X0] : ~wise(X0) [ennf transformation 26]
32. ! [X0] : (((generous(X0) & ~humble(X0)) | (~wise(X0) | ~humble(X0))) & ((wise(X0) & humble(X0)) | (~generous(X0) | humble(X0)))) [nnf transformation 2]
33. ! [X0] : (((generous(X0) & ~humble(X0)) | ~wise(X0) | ~humble(X0)) & ((wise(X0) & humble(X0)) | ~generous(X0) | humble(X0))) [flattening 32]
37. ! [X0] : (((rich(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | (~rich(X0) | ~brave(X0)))) [nnf transformation 5]
38. ! [X0] : (((rich(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | ~rich(X0) | ~brave(X0))) [flattening 37]
44. ! [X0] : (((quiet(X0) | strong(X0)) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | (~quiet(X0) & ~strong(X0)))) [nnf transformation 7]
45. ! [X0] : ((quiet(X0) | strong(X0) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | (~quiet(X0) & ~strong(X0)))) [flattening 44]
57. ? [X0] : (~kind(X0) & ~humble(X0)) | ! [X1] : ~wise(X1) [rectify 30]
58. ? [X0] : (~kind(X0) & ~humble(X0)) => (~kind(sK4) & ~humble(sK4)) [choice axiom]
59. (~kind(sK4) & ~humble(sK4)) | ! [X1] : ~wise(X1) [skolemisation 57,58]
68. (~wise(lucy) | ~quiet(lucy)) & (wise(lucy) | quiet(lucy)) [nnf transformation 21]
74. humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 33]
87. brave(X0) | humble(X0) [cnf transformation 38]
94. ~quiet(X0) | old(X0) | ~tall(X0) [cnf transformation 45]
122. ~humble(X0) | tall(X0) [cnf transformation 29]
123. ~brave(X0) | tall(X0) [cnf transformation 29]
125. ~brave(X0) | generous(X0) [cnf transformation 29]
126. ~humble(sK4) | ~wise(X1) [cnf transformation 59]
149. wise(lucy) | quiet(lucy) [cnf transformation 68]
154. ~old(lucy) [cnf transformation 24]
169. ~generous(X0) | humble(X0) [duplicate literal removal 74]
208. 9 <=> wise(lucy) [avatar definition]
210. wise(lucy) <- (9) [avatar component clause 208]
252. 18 <=> ! [X1] : ~wise(X1) [avatar definition]
253. ~wise(X1) <- (18) [avatar component clause 252]
260. 20 <=> humble(sK4) [avatar definition]
262. ~humble(sK4) <- (~20) [avatar component clause 260]
263. 18 | ~20 [avatar split clause 126,260,252]
293. 26 <=> quiet(lucy) [avatar definition]
295. quiet(lucy) <- (26) [avatar component clause 293]
308. 26 | 9 [avatar split clause 149,208,293]
339. tall(X0) | humble(X0) [resolution 123,87]
342. tall(X0) [subsumption resolution 339,122]
351. generous(X0) | humble(X0) [resolution 125,87]
353. humble(X0) [subsumption resolution 351,169]
355. $false <- (~20) [resolution 353,262]
360. 20 [avatar contradiction clause 355]
361. $false <- (9, 18) [resolution 253,210]
364. ~9 | ~18 [avatar contradiction clause 361]
407. old(lucy) | ~tall(lucy) <- (26) [resolution 94,295]
408. ~tall(lucy) <- (26) [subsumption resolution 407,154]
409. $false <- (26) [subsumption resolution 408,342]
410. ~26 [avatar contradiction clause 409]
411. $false [avatar sat refutation 263,308,360,364,410]
% SZS output end Proof for 1502301314232983145286368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not funny is either curious or not quiet and vice versa. Everyone who is either rich or not brave is both creative and not quiet and vice versa. Everyone who is patient or not tall is either happy or funny and vice versa. If alice is quiet or not kind then someone is either calm or funny. If mary is both rich and not kind then someone is not humble or quiet and vice versa. If john is not funny then someone is not brave or strong. Everyone who is creative is happy and vice versa. If fred is curious or not calm then john is either not generous or not funny and vice versa. If someone is either not kind or old then susan is both not patient and not quiet. If alice is not quiet then someone is not curious or not calm and vice versa. If alice is both not wise and not old then someone is creative. If mary is both happy and not funny then paul is not curious and vice versa. Everyone who is either not kind or kind is tall and vice versa. If fred is not patient then mary is both generous and not tall. Everyone who is either not quiet or creative is both not creative and not calm and vice versa. If someone is happy then lucy is strong and vice versa. Someone is both happy and funny. Someone is either not calm or tall. Someone is either rich or generous. Fred is either calm or creative. Someone is both humble and rich. Paul is not creative or not calm. Someone is rich. Lucy is quiet. | Lucy is not happy. | entailment | (![X]:((humble(X)|~funny(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((rich(X)<~>~brave(X))<=>(creative(X)&~quiet(X))))&
(![X]:((patient(X)|~tall(X))<=>(happy(X)<~>funny(X))))&
(((quiet(alice)|~kind(alice)))=>(?[X]:((calm(X)<~>funny(X)))))&
(((rich(mary)&~kind(mary)))<=>(?[X]:((~humble(X)|quiet(X)))))&
((~funny(john))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:(creative(X)<=>happy(X)))&
(((curious(fred)|~calm(fred)))<=>((~generous(john)<~>~funny(john))))&
((?[X]:((~kind(X)<~>old(X))))=>((~patient(susan)&~quiet(susan))))&
((~quiet(alice))<=>(?[X]:((~curious(X)|~calm(X)))))&
(((~wise(alice)&~old(alice)))=>(?[X]:(creative(X))))&
(((happy(mary)&~funny(mary)))<=>(~curious(paul)))&
(![X]:((~kind(X)<~>kind(X))<=>tall(X)))&
((~patient(fred))=>((generous(mary)&~tall(mary))))&
(![X]:((~quiet(X)<~>creative(X))<=>(~creative(X)&~calm(X))))&
((?[X]:(happy(X)))<=>(strong(lucy)))&
(?[X]:((happy(X)&funny(X))))&
(?[X]:((~calm(X)<~>tall(X))))&
(?[X]:((rich(X)<~>generous(X))))&
((calm(fred)<~>creative(fred)))&
(?[X]:((humble(X)&rich(X))))&
((~creative(paul)|~calm(paul)))&
(?[X]:(rich(X)))&
(quiet(lucy)) | ~happy(lucy) | [
"p6",
"p14",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 2845769582634169474446712
% SZS output start Proof for 2845769582634169474446712
7. ! [X0] : (creative(X0) <=> happy(X0)) [input p6]
15. ! [X0] : ((~quiet(X0) <~> creative(X0)) <=> (~calm(X0) & ~creative(X0))) [input p14]
24. quiet(lucy) [input p23]
25. happy(lucy) [input hypothesis]
47. ! [X0] : ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0))) [nnf transformation 7]
58. ! [X0] : ((((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | (calm(X0) | creative(X0))) & ((~calm(X0) & ~creative(X0)) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0))))) [nnf transformation 15]
59. ! [X0] : ((((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | calm(X0) | creative(X0)) & ((~calm(X0) & ~creative(X0)) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0))))) [flattening 58]
106. ~happy(X0) | creative(X0) [cnf transformation 47]
130. ~creative(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 59]
149. quiet(lucy) [cnf transformation 24]
150. happy(lucy) [cnf transformation 25]
151. ~creative(X0) | ~quiet(X0) [duplicate literal removal 130]
329. creative(lucy) [resolution 106,150]
333. ~quiet(lucy) [resolution 329,151]
335. $false [subsumption resolution 333,149]
% SZS output end Proof for 2845769582634169474446712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or brave is calm and vice versa.
Everyone who is rich is both quiet and strong and vice versa.
If someone is not patient or old then lucy is both not quiet and patient and vice versa.
Everyone who is either not wise or not curious is patient and vice versa.
Everyone who is either not quiet or not happy is tall and vice versa.
If fred is both not creative and rich then someone is not humble or not kind and vice versa.
If someone is either happy or curious then someone is both happy and not patient.
Everyone who is either wise or brave is either not old or not rich and vice versa.
Everyone who is not strong or not curious is both calm and not funny and vice versa.
If someone is either humble or kind then susan is both not happy and kind.
Everyone who is either generous or happy is not generous and vice versa.
If lucy is not brave or not quiet then paul is both humble and not generous and vice versa.
If lucy is funny then someone is kind or not happy and vice versa.
Everyone who is either rich or not calm is old.
If john is either not humble or brave then someone is either not calm or not patient and vice versa.
If someone is both quiet and not patient then mary is both not curious and not rich.
Fred is both tall and not quiet.
Susan is both not quiet and not generous.
Someone is not old.
Alice is rich or not curious.
Susan is calm.
Alice is both not generous and calm. | Lucy is kind. | entailment | (![X]:((~happy(X)<~>brave(X))<=>calm(X)))&
(![X]:(rich(X)<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|old(X))))<=>((~quiet(lucy)&patient(lucy))))&
(![X]:((~wise(X)<~>~curious(X))<=>patient(X)))&
(![X]:((~quiet(X)<~>~happy(X))<=>tall(X)))&
(((~creative(fred)&rich(fred)))<=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((happy(X)<~>curious(X))))=>(?[X]:((happy(X)&~patient(X)))))&
(![X]:((wise(X)<~>brave(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((~strong(X)|~curious(X))<=>(calm(X)&~funny(X))))&
((?[X]:((humble(X)<~>kind(X))))=>((~happy(susan)&kind(susan))))&
(![X]:((generous(X)<~>happy(X))<=>~generous(X)))&
(((~brave(lucy)|~quiet(lucy)))<=>((humble(paul)&~generous(paul))))&
((funny(lucy))<=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((rich(X)<~>~calm(X))=>old(X)))&
(((~humble(john)<~>brave(john)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))=>((~curious(mary)&~rich(mary))))&
((tall(fred)&~quiet(fred)))&
((~quiet(susan)&~generous(susan)))&
(?[X]:(~old(X)))&
((rich(alice)|~curious(alice)))&
(calm(susan))&
((~generous(alice)&calm(alice))) | kind(lucy) | [
"p1",
"p5",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 392570341344592016428577
% SZS output start Proof for 392570341344592016428577
2. ! [X0] : (rich(X0) <=> (strong(X0) & quiet(X0))) [input p1]
6. (rich(fred) & ~creative(fred)) <=> ? [X0] : (~kind(X0) | ~humble(X0)) [input p5]
17. ~quiet(fred) & tall(fred) [input p16]
23. ~kind(lucy) [input hypothesis]
32. ! [X0] : ((rich(X0) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | ~rich(X0))) [nnf transformation 2]
33. ! [X0] : ((rich(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | ~rich(X0))) [flattening 32]
41. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X0] : (~kind(X0) | ~humble(X0)) | (~rich(fred) | creative(fred))) [nnf transformation 6]
42. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X0] : (~kind(X0) | ~humble(X0)) | ~rich(fred) | creative(fred)) [flattening 41]
43. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X1] : (~kind(X1) | ~humble(X1)) | ~rich(fred) | creative(fred)) [rectify 42]
44. ? [X1] : (~kind(X1) | ~humble(X1)) => (~kind(sK1) | ~humble(sK1)) [choice axiom]
45. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & ((~kind(sK1) | ~humble(sK1)) | ~rich(fred) | creative(fred)) [skolemisation 43,44]
72. ~rich(X0) | quiet(X0) [cnf transformation 33]
90. rich(fred) | kind(X0) [cnf transformation 45]
137. ~quiet(fred) [cnf transformation 17]
145. ~kind(lucy) [cnf transformation 23]
176. 7 <=> ! [X0] : kind(X0) [avatar definition]
177. kind(X0) <- (7) [avatar component clause 176]
179. 8 <=> rich(fred) [avatar definition]
181. rich(fred) <- (8) [avatar component clause 179]
182. 7 | 8 [avatar split clause 90,179,176]
336. quiet(fred) <- (8) [resolution 72,181]
337. $false <- (8) [subsumption resolution 336,137]
338. ~8 [avatar contradiction clause 337]
339. $false <- (7) [resolution 177,145]
344. ~7 [avatar contradiction clause 339]
345. $false [avatar sat refutation 182,338,344]
% SZS output end Proof for 392570341344592016428577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or happy is either calm or funny and vice versa.
Everyone who is not generous or not old is not funny.
Everyone who is either old or curious is not generous or wise and vice versa.
Everyone who is not generous or quiet is both not rich and not generous and vice versa.
If someone is not calm then someone is not humble and vice versa.
Everyone who is not patient is not happy or not creative and vice versa.
If susan is funny or old then susan is both not patient and creative and vice versa.
If paul is either old or not strong then paul is both humble and kind.
Everyone who is creative or not patient is either not rich or humble.
Everyone who is creative is both not patient and happy and vice versa.
If alice is not strong then someone is creative or not happy and vice versa.
If someone is not old then alice is either happy or not curious and vice versa.
If someone is either funny or strong then someone is either not tall or calm.
If paul is not patient or creative then someone is old or humble and vice versa.
If susan is generous then someone is either not brave or humble.
Alice is not patient.
Someone is both strong and not calm.
Paul is not calm.
John is not rich.
Someone is not tall or not wise.
Someone is both rich and not kind.
Alice is both not tall and humble. | Alice is not kind. | neutral | (![X]:((curious(X)|happy(X))<=>(calm(X)<~>funny(X))))&
(![X]:((~generous(X)|~old(X))=>~funny(X)))&
(![X]:((old(X)<~>curious(X))<=>(~generous(X)|wise(X))))&
(![X]:((~generous(X)|quiet(X))<=>(~rich(X)&~generous(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~humble(X))))&
(![X]:(~patient(X)<=>(~happy(X)|~creative(X))))&
(((funny(susan)|old(susan)))<=>((~patient(susan)&creative(susan))))&
(((old(paul)<~>~strong(paul)))=>((humble(paul)&kind(paul))))&
(![X]:((creative(X)|~patient(X))=>(~rich(X)<~>humble(X))))&
(![X]:(creative(X)<=>(~patient(X)&happy(X))))&
((~strong(alice))<=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:(~old(X)))<=>((happy(alice)<~>~curious(alice))))&
((?[X]:((funny(X)<~>strong(X))))=>(?[X]:((~tall(X)<~>calm(X)))))&
(((~patient(paul)|creative(paul)))<=>(?[X]:((old(X)|humble(X)))))&
((generous(susan))=>(?[X]:((~brave(X)<~>humble(X)))))&
(~patient(alice))&
(?[X]:((strong(X)&~calm(X))))&
(~calm(paul))&
(~rich(john))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:((rich(X)&~kind(X))))&
((~tall(alice)&humble(alice))) | ~kind(alice) | []
| null | 0 |
Everyone who is funny is either not kind or creative and vice versa.
Everyone who is calm or quiet is not funny and vice versa.
If susan is happy then someone is both not creative and tall.
Everyone who is either curious or brave is either tall or not funny and vice versa.
If fred is both creative and quiet then someone is both not strong and not generous and vice versa.
Everyone who is not rich or calm is quiet or not rich and vice versa.
If someone is not wise then susan is not generous or brave and vice versa.
Everyone who is both not curious and creative is either tall or happy and vice versa.
Everyone who is tall or generous is humble and vice versa.
Everyone who is humble or not calm is humble or tall and vice versa.
Everyone who is not rich is either rich or not kind and vice versa.
Everyone who is both not old and strong is not brave or humble and vice versa.
If mary is not creative or wise then john is either rich or not humble.
Everyone who is strong or rich is either generous or creative and vice versa.
Everyone who is curious or not old is not humble or rich.
If fred is not brave then someone is not brave.
Someone is either not brave or not patient.
Paul is both not happy and funny.
Lucy is both not quiet and brave.
Someone is either kind or wise.
John is both not creative and generous.
Fred is either not patient or tall.
John is not humble or happy. | Paul is humble. | entailment | (![X]:(funny(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((calm(X)|quiet(X))<=>~funny(X)))&
((happy(susan))=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((curious(X)<~>brave(X))<=>(tall(X)<~>~funny(X))))&
(((creative(fred)&quiet(fred)))<=>(?[X]:((~strong(X)&~generous(X)))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)|~rich(X))))&
((?[X]:(~wise(X)))<=>((~generous(susan)|brave(susan))))&
(![X]:((~curious(X)&creative(X))<=>(tall(X)<~>happy(X))))&
(![X]:((tall(X)|generous(X))<=>humble(X)))&
(![X]:((humble(X)|~calm(X))<=>(humble(X)|tall(X))))&
(![X]:(~rich(X)<=>(rich(X)<~>~kind(X))))&
(![X]:((~old(X)&strong(X))<=>(~brave(X)|humble(X))))&
(((~creative(mary)|wise(mary)))=>((rich(john)<~>~humble(john))))&
(![X]:((strong(X)|rich(X))<=>(generous(X)<~>creative(X))))&
(![X]:((curious(X)|~old(X))=>(~humble(X)|rich(X))))&
((~brave(fred))=>(?[X]:(~brave(X))))&
(?[X]:((~brave(X)<~>~patient(X))))&
((~happy(paul)&funny(paul)))&
((~quiet(lucy)&brave(lucy)))&
(?[X]:((kind(X)<~>wise(X))))&
((~creative(john)&generous(john)))&
((~patient(fred)<~>tall(fred)))&
((~humble(john)|happy(john))) | humble(paul) | [
"p1",
"p8",
"p9",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 7953333968024844142175966
% SZS output start Proof for 7953333968024844142175966
2. ! [X0] : ((quiet(X0) | calm(X0)) <=> ~funny(X0)) [input p1]
9. ! [X0] : ((generous(X0) | tall(X0)) <=> humble(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | humble(X0)) <=> (tall(X0) | humble(X0))) [input p9]
18. funny(paul) & ~happy(paul) [input p17]
24. ~humble(paul) [input hypothesis]
31. ! [X0] : (((quiet(X0) | calm(X0)) | funny(X0)) & (~funny(X0) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 2]
32. ! [X0] : ((quiet(X0) | calm(X0) | funny(X0)) & (~funny(X0) | (~quiet(X0) & ~calm(X0)))) [flattening 31]
50. ! [X0] : (((generous(X0) | tall(X0)) | ~humble(X0)) & (humble(X0) | (~generous(X0) & ~tall(X0)))) [nnf transformation 9]
51. ! [X0] : ((generous(X0) | tall(X0) | ~humble(X0)) & (humble(X0) | (~generous(X0) & ~tall(X0)))) [flattening 50]
52. ! [X0] : (((~calm(X0) | humble(X0)) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | (calm(X0) & ~humble(X0)))) [nnf transformation 10]
53. ! [X0] : ((~calm(X0) | humble(X0) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | (calm(X0) & ~humble(X0)))) [flattening 52]
73. ~calm(X0) | ~funny(X0) [cnf transformation 32]
103. ~tall(X0) | humble(X0) [cnf transformation 51]
107. tall(X0) | humble(X0) | calm(X0) [cnf transformation 53]
135. funny(paul) [cnf transformation 18]
145. ~humble(paul) [cnf transformation 24]
203. humble(X0) | calm(X0) [subsumption resolution 107,103]
270. calm(paul) [resolution 203,145]
274. ~funny(paul) [resolution 270,73]
275. $false [subsumption resolution 274,135]
% SZS output end Proof for 7953333968024844142175966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not creative is not happy or not rich.
Everyone who is not humble or creative is not strong.
Everyone who is not wise is both generous and strong.
If someone is either not quiet or wise then lucy is creative and vice versa.
Everyone who is strong is either curious or calm and vice versa.
If lucy is both quiet and not kind then susan is either tall or not patient.
If someone is not rich then alice is not rich or brave.
Everyone who is either curious or tall is both tall and not happy.
Everyone who is both old and patient is either not brave or not tall and vice versa.
Everyone who is either quiet or happy is not funny or humble and vice versa.
Everyone who is not generous or not kind is not generous and vice versa.
Everyone who is both strong and tall is either not tall or creative and vice versa.
Everyone who is either not rich or not strong is not curious or calm and vice versa.
If paul is either not generous or not wise then mary is rich.
Everyone who is both curious and creative is not creative or not happy and vice versa.
If alice is either not kind or not creative then john is quiet or not happy and vice versa.
Fred is either not rich or not old.
Someone is not curious or not humble.
Someone is both quiet and not tall.
Someone is either generous or happy.
Mary is strong or generous.
Someone is not wise or old. | Susan is calm. | contradiction | (![X]:((humble(X)<~>~creative(X))=>(~happy(X)|~rich(X))))&
(![X]:((~humble(X)|creative(X))=>~strong(X)))&
(![X]:(~wise(X)=>(generous(X)&strong(X))))&
((?[X]:((~quiet(X)<~>wise(X))))<=>(creative(lucy)))&
(![X]:(strong(X)<=>(curious(X)<~>calm(X))))&
(((quiet(lucy)&~kind(lucy)))=>((tall(susan)<~>~patient(susan))))&
((?[X]:(~rich(X)))=>((~rich(alice)|brave(alice))))&
(![X]:((curious(X)<~>tall(X))=>(tall(X)&~happy(X))))&
(![X]:((old(X)&patient(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>~generous(X)))&
(![X]:((strong(X)&tall(X))<=>(~tall(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(~curious(X)|calm(X))))&
(((~generous(paul)<~>~wise(paul)))=>(rich(mary)))&
(![X]:((curious(X)&creative(X))<=>(~creative(X)|~happy(X))))&
(((~kind(alice)<~>~creative(alice)))<=>((quiet(john)|~happy(john))))&
((~rich(fred)<~>~old(fred)))&
(?[X]:((~curious(X)|~humble(X))))&
(?[X]:((quiet(X)&~tall(X))))&
(?[X]:((generous(X)<~>happy(X))))&
((strong(mary)|generous(mary)))&
(?[X]:((~wise(X)|old(X)))) | calm(susan) | [
"p1",
"p4",
"p7",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 8619628335577897142407181
% SZS output start Proof for 8619628335577897142407181
2. ! [X0] : ((creative(X0) | ~humble(X0)) => ~strong(X0)) [input p1]
5. ! [X0] : (strong(X0) <=> (curious(X0) <~> calm(X0))) [input p4]
8. ! [X0] : ((curious(X0) <~> tall(X0)) => (~happy(X0) & tall(X0))) [input p7]
12. ! [X0] : ((tall(X0) & strong(X0)) <=> (~tall(X0) <~> creative(X0))) [input p11]
15. ! [X0] : ((creative(X0) & curious(X0)) <=> (~happy(X0) | ~creative(X0))) [input p14]
23. calm(susan) [input hypothesis]
26. ! [X0] : (~strong(X0) | (~creative(X0) & humble(X0))) [ennf transformation 2]
32. ! [X0] : ((~happy(X0) & tall(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 8]
39. ! [X0] : ((strong(X0) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ~strong(X0))) [nnf transformation 5]
41. ! [X0] : ((~happy(X0) & tall(X0)) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 32]
48. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~tall(X0) | ~strong(X0)))) [nnf transformation 12]
49. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ~tall(X0) | ~strong(X0))) [flattening 48]
53. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~creative(X0) | ~curious(X0)))) [nnf transformation 15]
54. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~creative(X0) | ~curious(X0))) [flattening 53]
70. ~strong(X0) | ~creative(X0) [cnf transformation 26]
80. ~calm(X0) | curious(X0) | strong(X0) [cnf transformation 39]
84. tall(X0) | tall(X0) | ~curious(X0) [cnf transformation 41]
106. strong(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 49]
120. creative(X0) | creative(X0) [cnf transformation 54]
137. calm(susan) [cnf transformation 23]
139. creative(X0) [duplicate literal removal 120]
142. ~curious(X0) | tall(X0) [duplicate literal removal 84]
174. 8 <=> tall(susan) [avatar definition]
175. tall(susan) <- (8) [avatar component clause 174]
195. ~tall(X0) | ~creative(X0) [subsumption resolution 106,70]
314. 29 <=> strong(susan) [avatar definition]
315. strong(susan) <- (29) [avatar component clause 314]
318. 30 <=> curious(susan) [avatar definition]
319. curious(susan) <- (30) [avatar component clause 318]
323. curious(susan) | strong(susan) [resolution 80,137]
326. 29 | 30 [avatar split clause 323,318,314]
328. ~creative(susan) <- (29) [resolution 315,70]
330. $false <- (29) [subsumption resolution 328,139]
331. ~29 [avatar contradiction clause 330]
337. tall(susan) <- (30) [resolution 319,142]
340. 8 | ~30 [avatar split clause 337,318,174]
343. ~creative(susan) <- (8) [resolution 175,195]
344. $false <- (8) [subsumption resolution 343,139]
345. ~8 [avatar contradiction clause 344]
346. $false [avatar sat refutation 326,331,340,345]
% SZS output end Proof for 8619628335577897142407181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is curious or generous then someone is humble or not wise and vice versa.
Everyone who is strong or not humble is both humble and calm.
If someone is both generous and funny then someone is either funny or quiet and vice versa.
Everyone who is both not funny and not quiet is calm and vice versa.
If lucy is not rich or strong then paul is either not creative or kind and vice versa.
If someone is either not tall or rich then someone is patient or kind and vice versa.
Everyone who is creative or not funny is both patient and not old and vice versa.
Everyone who is curious or funny is either rich or quiet.
If someone is either rich or not happy then john is not patient.
Everyone who is either brave or patient is both quiet and not old.
Everyone who is generous or not strong is either old or strong.
If someone is not curious or not quiet then fred is rich.
Everyone who is not brave or generous is either tall or curious and vice versa.
If fred is not brave or calm then someone is not funny.
Everyone who is funny is either brave or patient.
If susan is either tall or curious then someone is either strong or not funny and vice versa.
Mary is creative or not creative.
Someone is not quiet or wise.
Mary is generous.
Someone is either not humble or kind.
Alice is both tall and not old.
Alice is both not wise and not old. | Mary is not quiet. | entailment | (((curious(alice)|generous(alice)))<=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:((strong(X)|~humble(X))=>(humble(X)&calm(X))))&
((?[X]:((generous(X)&funny(X))))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>calm(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~creative(paul)<~>kind(paul))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((creative(X)|~funny(X))<=>(patient(X)&~old(X))))&
(![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))&
(![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((creative(mary)|~creative(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
(generous(mary))&
(?[X]:((~humble(X)<~>kind(X))))&
((tall(alice)&~old(alice)))&
((~wise(alice)&~old(alice))) | ~quiet(mary) | [
"p1",
"p2",
"p3",
"p6",
"p9",
"p10",
"p14",
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 5846778076535272110511338
% SZS output start Proof for 5846778076535272110511338
2. ! [X0] : ((~humble(X0) | strong(X0)) => (calm(X0) & humble(X0))) [input p1]
3. ? [X0] : (funny(X0) & generous(X0)) <=> ? [X0] : (funny(X0) <~> quiet(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> calm(X0)) [input p3]
7. ! [X0] : ((~funny(X0) | creative(X0)) <=> (~old(X0) & patient(X0))) [input p6]
10. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | generous(X0)) => (old(X0) <~> strong(X0))) [input p10]
15. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p14]
16. (tall(susan) <~> curious(susan)) <=> ? [X0] : (strong(X0) <~> ~funny(X0)) [input p15]
19. generous(mary) [input p18]
23. quiet(mary) [input hypothesis]
24. ? [X0] : (funny(X0) & generous(X0)) <=> ? [X1] : (funny(X1) <~> quiet(X1)) [rectify 3]
26. ! [X0] : ((calm(X0) & humble(X0)) | (humble(X0) & ~strong(X0))) [ennf transformation 2]
29. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 10]
30. ! [X0] : ((old(X0) <~> strong(X0)) | (strong(X0) & ~generous(X0))) [ennf transformation 11]
33. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 15]
39. (? [X0] : (funny(X0) & generous(X0)) | ! [X1] : ((funny(X1) | ~quiet(X1)) & (quiet(X1) | ~funny(X1)))) & (? [X1] : ((~quiet(X1) | ~funny(X1)) & (quiet(X1) | funny(X1))) | ! [X0] : (~funny(X0) | ~generous(X0))) [nnf transformation 24]
40. (? [X0] : (funny(X0) & generous(X0)) | ! [X1] : ((funny(X1) | ~quiet(X1)) & (quiet(X1) | ~funny(X1)))) & (? [X2] : ((~quiet(X2) | ~funny(X2)) & (quiet(X2) | funny(X2))) | ! [X3] : (~funny(X3) | ~generous(X3))) [rectify 39]
41. ? [X0] : (funny(X0) & generous(X0)) => (funny(sK1) & generous(sK1)) [choice axiom]
42. ? [X2] : ((~quiet(X2) | ~funny(X2)) & (quiet(X2) | funny(X2))) => ((~quiet(sK2) | ~funny(sK2)) & (quiet(sK2) | funny(sK2))) [choice axiom]
43. ((funny(sK1) & generous(sK1)) | ! [X1] : ((funny(X1) | ~quiet(X1)) & (quiet(X1) | ~funny(X1)))) & (((~quiet(sK2) | ~funny(sK2)) & (quiet(sK2) | funny(sK2))) | ! [X3] : (~funny(X3) | ~generous(X3))) [skolemisation 40,42,41]
44. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | funny(X0)))) [nnf transformation 4]
45. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | funny(X0))) [flattening 44]
53. ! [X0] : (((~funny(X0) | creative(X0)) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [nnf transformation 7]
54. ! [X0] : ((~funny(X0) | creative(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [flattening 53]
57. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 29]
58. ! [X0] : (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (strong(X0) & ~generous(X0))) [nnf transformation 30]
63. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 33]
64. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X0] : ((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [nnf transformation 16]
65. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [rectify 64]
66. ? [X1] : ((funny(X1) | ~strong(X1)) & (~funny(X1) | strong(X1))) => ((funny(sK6) | ~strong(sK6)) & (~funny(sK6) | strong(sK6))) [choice axiom]
67. (((~curious(susan) | ~tall(susan)) & (curious(susan) | tall(susan))) | ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) & (((funny(sK6) | ~strong(sK6)) & (~funny(sK6) | strong(sK6))) | ((tall(susan) | ~curious(susan)) & (curious(susan) | ~tall(susan)))) [skolemisation 65,66]
79. ~strong(X0) | calm(X0) [cnf transformation 26]
81. quiet(sK2) | funny(sK2) | ~funny(X3) | ~generous(X3) [cnf transformation 43]
82. ~quiet(sK2) | ~funny(sK2) | ~funny(X3) | ~generous(X3) [cnf transformation 43]
83. generous(sK1) | quiet(X1) | ~funny(X1) [cnf transformation 43]
84. generous(sK1) | funny(X1) | ~quiet(X1) [cnf transformation 43]
86. funny(sK1) | funny(X1) | ~quiet(X1) [cnf transformation 43]
88. ~funny(X0) | ~calm(X0) [cnf transformation 45]
103. patient(X0) | funny(X0) [cnf transformation 54]
105. ~old(X0) | funny(X0) [cnf transformation 54]
113. ~brave(X0) | patient(X0) | quiet(X0) [cnf transformation 57]
115. ~brave(X0) | patient(X0) | ~old(X0) [cnf transformation 57]
116. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 57]
118. strong(X0) | old(X0) | strong(X0) [cnf transformation 58]
131. patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 63]
132. ~brave(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 63]
133. ~funny(sK6) | strong(sK6) | curious(susan) | ~tall(susan) [cnf transformation 67]
134. ~funny(sK6) | strong(sK6) | tall(susan) | ~curious(susan) [cnf transformation 67]
135. funny(sK6) | ~strong(sK6) | curious(susan) | ~tall(susan) [cnf transformation 67]
136. funny(sK6) | ~strong(sK6) | tall(susan) | ~curious(susan) [cnf transformation 67]
137. curious(susan) | tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 67]
139. ~curious(susan) | ~tall(susan) | ~funny(X0) | ~strong(X0) [cnf transformation 67]
143. generous(mary) [cnf transformation 19]
150. quiet(mary) [cnf transformation 23]
151. old(X0) | strong(X0) [duplicate literal removal 118]
180. 7 <=> ! [X1] : (funny(X1) | ~quiet(X1)) [avatar definition]
181. ~quiet(X1) | funny(X1) <- (7) [avatar component clause 180]
183. 8 <=> funny(sK1) [avatar definition]
185. funny(sK1) <- (8) [avatar component clause 183]
186. 7 | 8 [avatar split clause 86,183,180]
188. 9 <=> ! [X1] : (quiet(X1) | ~funny(X1)) [avatar definition]
189. ~funny(X1) | quiet(X1) <- (9) [avatar component clause 188]
192. 10 <=> generous(sK1) [avatar definition]
194. generous(sK1) <- (10) [avatar component clause 192]
195. 7 | 10 [avatar split clause 84,192,180]
196. 9 | 10 [avatar split clause 83,192,188]
198. 11 <=> ! [X3] : (~funny(X3) | ~generous(X3)) [avatar definition]
199. ~funny(X3) | ~generous(X3) <- (11) [avatar component clause 198]
201. 12 <=> funny(sK2) [avatar definition]
202. funny(sK2) <- (12) [avatar component clause 201]
203. ~funny(sK2) <- (~12) [avatar component clause 201]
205. 13 <=> quiet(sK2) [avatar definition]
206. quiet(sK2) <- (13) [avatar component clause 205]
207. ~quiet(sK2) <- (~13) [avatar component clause 205]
208. 11 | ~12 | ~13 [avatar split clause 82,205,201,198]
209. 11 | 12 | 13 [avatar split clause 81,205,201,198]
304. brave(X0) | patient(X0) [subsumption resolution 131,103]
306. 35 <=> ! [X0] : (strong(X0) | funny(X0)) [avatar definition]
307. funny(X0) | strong(X0) <- (35) [avatar component clause 306]
309. 36 <=> tall(susan) [avatar definition]
313. 37 <=> curious(susan) [avatar definition]
318. 38 <=> ! [X0] : (~funny(X0) | ~strong(X0)) [avatar definition]
319. ~funny(X0) | ~strong(X0) <- (38) [avatar component clause 318]
320. 38 | ~36 | ~37 [avatar split clause 139,313,309,318]
322. 38 | 36 | 37 [avatar split clause 137,313,309,318]
324. 39 <=> strong(sK6) [avatar definition]
325. strong(sK6) <- (39) [avatar component clause 324]
328. 40 <=> funny(sK6) [avatar definition]
329. ~funny(sK6) <- (~40) [avatar component clause 328]
330. funny(sK6) <- (40) [avatar component clause 328]
331. ~37 | 36 | ~39 | 40 [avatar split clause 136,328,324,309,313]
332. ~36 | 37 | ~39 | 40 [avatar split clause 135,328,324,313,309]
333. ~37 | 36 | 39 | ~40 [avatar split clause 134,328,324,309,313]
334. ~36 | 37 | 39 | ~40 [avatar split clause 133,328,324,313,309]
351. strong(X0) | funny(X0) [resolution 151,105]
353. 35 [avatar split clause 351,306]
354. funny(mary) <- (7) [resolution 181,150]
360. ~generous(mary) <- (7, 11) [resolution 199,354]
361. $false <- (7, 11) [subsumption resolution 360,143]
362. ~7 | ~11 [avatar contradiction clause 361]
363. ~generous(sK1) <- (8, 11) [resolution 185,199]
366. $false <- (8, 10, 11) [subsumption resolution 363,194]
367. ~8 | ~10 | ~11 [avatar contradiction clause 366]
368. quiet(sK2) <- (9, 12) [resolution 202,189]
370. $false <- (9, 12, ~13) [subsumption resolution 368,207]
371. ~9 | ~12 | 13 [avatar contradiction clause 370]
375. strong(sK6) <- (35, ~40) [resolution 307,329]
379. 39 | ~35 | 40 [avatar split clause 375,328,306,324]
380. calm(sK6) <- (39) [resolution 325,79]
384. ~strong(sK1) <- (8, 38) [resolution 319,185]
454. patient(X0) | quiet(X0) | patient(X0) [resolution 113,304]
455. patient(X0) | quiet(X0) [duplicate literal removal 454]
478. patient(X0) | ~old(X0) | patient(X0) [resolution 115,304]
479. ~old(X0) | patient(X0) [duplicate literal removal 478]
481. brave(X0) | ~patient(X0) | strong(X0) [resolution 116,151]
482. brave(X0) | strong(X0) [subsumption resolution 481,304]
576. patient(X0) | strong(X0) [resolution 479,151]
579. strong(X2) | ~patient(X2) | ~funny(X2) [resolution 482,132]
582. ~patient(X2) | ~funny(X2) <- (38) [subsumption resolution 579,319]
714. ~funny(X0) | strong(X0) <- (38) [resolution 582,576]
715. ~funny(X1) | quiet(X1) <- (38) [resolution 582,455]
719. strong(X0) <- (35, 38) [subsumption resolution 714,307]
720. 9 | ~38 [avatar split clause 715,318,188]
732. $false <- (8, 35, 38) [resolution 719,384]
733. ~8 | ~35 | ~38 [avatar contradiction clause 732]
741. funny(sK2) <- (7, 13) [resolution 181,206]
744. $false <- (7, ~12, 13) [subsumption resolution 741,203]
745. ~7 | 12 | ~13 [avatar contradiction clause 744]
781. ~calm(sK6) <- (40) [resolution 330,88]
782. $false <- (39, 40) [subsumption resolution 781,380]
783. ~39 | ~40 [avatar contradiction clause 782]
784. $false [avatar sat refutation 186,195,196,208,209,320,322,331,332,333,334,353,362,367,371,379,720,733,745,783]
% SZS output end Proof for 5846778076535272110511338
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not kind is both not kind and not curious and vice versa. If someone is wise or not creative then fred is either generous or humble and vice versa. Everyone who is brave is both not happy and not old and vice versa. Everyone who is not tall or quiet is not quiet or humble. If someone is not creative then someone is not wise. Everyone who is not brave is kind or not quiet and vice versa. Everyone who is not generous or generous is both not strong and creative and vice versa. If lucy is either not humble or creative then someone is not creative. If someone is wise then someone is not old or not kind. Everyone who is not humble or not brave is not happy or brave. Everyone who is either generous or not calm is either curious or wise. If alice is wise or rich then mary is not creative. If mary is both not happy and quiet then someone is either not brave or not generous. Everyone who is both patient and brave is wise or calm. Everyone who is both brave and not patient is both brave and not humble and vice versa. Everyone who is not curious is generous or tall. Someone is not kind. Someone is not tall. Lucy is either not strong or not calm. Paul is both patient and funny. Lucy is either rich or not quiet. Someone is both not wise and not brave. Lucy is not happy or not humble. Someone is not old. | Alice is creative. | entailment | (![X]:((~creative(X)|~kind(X))<=>(~kind(X)&~curious(X))))&
((?[X]:((wise(X)|~creative(X))))<=>((generous(fred)<~>humble(fred))))&
(![X]:(brave(X)<=>(~happy(X)&~old(X))))&
(![X]:((~tall(X)|quiet(X))=>(~quiet(X)|humble(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)<=>(kind(X)|~quiet(X))))&
(![X]:((~generous(X)|generous(X))<=>(~strong(X)&creative(X))))&
(((~humble(lucy)<~>creative(lucy)))=>(?[X]:(~creative(X))))&
((?[X]:(wise(X)))=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((~humble(X)|~brave(X))=>(~happy(X)|brave(X))))&
(![X]:((generous(X)<~>~calm(X))=>(curious(X)<~>wise(X))))&
(((wise(alice)|rich(alice)))=>(~creative(mary)))&
(((~happy(mary)&quiet(mary)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:((patient(X)&brave(X))=>(wise(X)|calm(X))))&
(![X]:((brave(X)&~patient(X))<=>(brave(X)&~humble(X))))&
(![X]:(~curious(X)=>(generous(X)|tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~tall(X)))&
((~strong(lucy)<~>~calm(lucy)))&
((patient(paul)&funny(paul)))&
((rich(lucy)<~>~quiet(lucy)))&
(?[X]:((~wise(X)&~brave(X))))&
((~happy(lucy)|~humble(lucy)))&
(?[X]:(~old(X))) | creative(alice) | [
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 832012538063061016378487
% SZS output start Proof for 832012538063061016378487
7. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (creative(X0) & ~strong(X0))) [input p6]
25. ~creative(alice) [input hypothesis]
57. ! [X0] : (((generous(X0) | ~generous(X0)) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | (~generous(X0) & generous(X0)))) [nnf transformation 7]
58. ! [X0] : ((generous(X0) | ~generous(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | (~generous(X0) & generous(X0)))) [flattening 57]
103. creative(X0) | generous(X0) [cnf transformation 58]
104. creative(X0) | ~generous(X0) [cnf transformation 58]
136. ~creative(alice) [cnf transformation 25]
158. 5 <=> ! [X1] : creative(X1) [avatar definition]
159. creative(X1) <- (5) [avatar component clause 158]
172. creative(X0) [subsumption resolution 103,104]
173. 5 [avatar split clause 172,158]
242. $false <- (5) [resolution 159,136]
243. ~5 [avatar contradiction clause 242]
244. $false [avatar sat refutation 173,243]
% SZS output end Proof for 832012538063061016378487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not generous is tall and vice versa.
If john is both not brave and not quiet then susan is either old or not kind.
Everyone who is not tall is both not strong and creative.
If someone is happy or not brave then someone is strong or not wise and vice versa.
If someone is wise or not happy then someone is both brave and not happy.
If mary is either kind or not strong then mary is not funny or old.
If fred is both not generous and creative then someone is either not wise or not kind.
Everyone who is not patient or not creative is both not humble and humble and vice versa.
Everyone who is either kind or humble is both not funny and generous.
Everyone who is both creative and not old is either not wise or not patient.
If someone is not tall then alice is both not wise and not happy.
Everyone who is not curious is either not generous or not happy.
Everyone who is not humble is either not creative or strong.
Everyone who is both not brave and strong is either not quiet or not wise and vice versa.
If fred is humble then alice is calm or not tall and vice versa.
If someone is both not curious and old then someone is both not calm and humble.
Lucy is either not humble or not creative.
Someone is both funny and happy.
Alice is creative.
Someone is both not old and not brave.
Someone is either not humble or not kind.
Someone is either wise or not curious.
Someone is funny or rich. | Alice is not wise. | entailment | (![X]:((~happy(X)&~generous(X))<=>tall(X)))&
(((~brave(john)&~quiet(john)))=>((old(susan)<~>~kind(susan))))&
(![X]:(~tall(X)=>(~strong(X)&creative(X))))&
((?[X]:((happy(X)|~brave(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(((kind(mary)<~>~strong(mary)))=>((~funny(mary)|old(mary))))&
(((~generous(fred)&creative(fred)))=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~humble(X)&humble(X))))&
(![X]:((kind(X)<~>humble(X))=>(~funny(X)&generous(X))))&
(![X]:((creative(X)&~old(X))=>(~wise(X)<~>~patient(X))))&
((?[X]:(~tall(X)))=>((~wise(alice)&~happy(alice))))&
(![X]:(~curious(X)=>(~generous(X)<~>~happy(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>strong(X))))&
(![X]:((~brave(X)&strong(X))<=>(~quiet(X)<~>~wise(X))))&
((humble(fred))<=>((calm(alice)|~tall(alice))))&
((?[X]:((~curious(X)&old(X))))=>(?[X]:((~calm(X)&humble(X)))))&
((~humble(lucy)<~>~creative(lucy)))&
(?[X]:((funny(X)&happy(X))))&
(creative(alice))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((funny(X)|rich(X)))) | ~wise(alice) | [
"p0",
"p10",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 8430209688654351938483212
% SZS output start Proof for 8430209688654351938483212
1. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> tall(X0)) [input p0]
11. ? [X0] : ~tall(X0) => (~happy(alice) & ~wise(alice)) [input p10]
18. ? [X0] : (happy(X0) & funny(X0)) [input p17]
24. wise(alice) [input hypothesis]
40. (~happy(alice) & ~wise(alice)) | ! [X0] : tall(X0) [ennf transformation 11]
44. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | (generous(X0) | happy(X0)))) [nnf transformation 1]
45. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~tall(X0)) & (tall(X0) | generous(X0) | happy(X0))) [flattening 44]
73. ? [X0] : (happy(X0) & funny(X0)) => (happy(sK5) & funny(sK5)) [choice axiom]
74. happy(sK5) & funny(sK5) [skolemisation 18,73]
84. ~tall(X0) | ~happy(X0) [cnf transformation 45]
113. ~wise(alice) | tall(X0) [cnf transformation 40]
133. happy(sK5) [cnf transformation 74]
141. wise(alice) [cnf transformation 24]
189. 12 <=> ! [X3] : ~happy(X3) [avatar definition]
190. ~happy(X3) <- (12) [avatar component clause 189]
251. 25 <=> ! [X0] : tall(X0) [avatar definition]
252. tall(X0) <- (25) [avatar component clause 251]
259. 27 <=> wise(alice) [avatar definition]
262. 25 | ~27 [avatar split clause 113,259,251]
313. 27 [avatar split clause 141,259]
320. ~happy(X0) <- (25) [resolution 84,252]
322. 12 | ~25 [avatar split clause 320,251,189]
324. $false <- (12) [resolution 190,133]
325. ~12 [avatar contradiction clause 324]
326. $false [avatar sat refutation 262,313,322,325]
% SZS output end Proof for 8430209688654351938483212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is not old and vice versa. If someone is not patient then john is either creative or not happy and vice versa. Everyone who is not brave is humble or not calm and vice versa. Everyone who is not rich is calm or happy and vice versa. Everyone who is curious or not funny is both not happy and rich. Everyone who is not generous or not wise is happy. If someone is either wise or not tall then someone is either not calm or not quiet and vice versa. Everyone who is both quiet and not calm is rich or not quiet and vice versa. Everyone who is not tall is both not creative and not humble. Everyone who is both patient and wise is generous or creative and vice versa. If lucy is not kind or not funny then someone is either not calm or humble. Everyone who is either old or happy is not old. If someone is not tall or funny then someone is not generous. If someone is either curious or not rich then someone is either old or humble and vice versa. If someone is not kind or funny then paul is both generous and brave. Someone is not wise or brave. Lucy is funny or not generous. Lucy is either not brave or strong. Someone is either not humble or strong. | John is brave. | neutral | (![X]:((generous(X)&~patient(X))<=>~old(X)))&
((?[X]:(~patient(X)))<=>((creative(john)<~>~happy(john))))&
(![X]:(~brave(X)<=>(humble(X)|~calm(X))))&
(![X]:(~rich(X)<=>(calm(X)|happy(X))))&
(![X]:((curious(X)|~funny(X))=>(~happy(X)&rich(X))))&
(![X]:((~generous(X)|~wise(X))=>happy(X)))&
((?[X]:((wise(X)<~>~tall(X))))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~calm(X))<=>(rich(X)|~quiet(X))))&
(![X]:(~tall(X)=>(~creative(X)&~humble(X))))&
(![X]:((patient(X)&wise(X))<=>(generous(X)|creative(X))))&
(((~kind(lucy)|~funny(lucy)))=>(?[X]:((~calm(X)<~>humble(X)))))&
(![X]:((old(X)<~>happy(X))=>~old(X)))&
((?[X]:((~tall(X)|funny(X))))=>(?[X]:(~generous(X))))&
((?[X]:((curious(X)<~>~rich(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
((?[X]:((~kind(X)|funny(X))))=>((generous(paul)&brave(paul))))&
(?[X]:((~wise(X)|brave(X))))&
((funny(lucy)|~generous(lucy)))&
((~brave(lucy)<~>strong(lucy)))&
(?[X]:((~humble(X)<~>strong(X)))) | brave(john) | []
| null | 0 |
If someone is either not patient or not old then someone is either not quiet or tall. If mary is either not kind or not creative then lucy is happy or funny. Everyone who is not old or not creative is not curious and vice versa. Everyone who is not rich is rich or curious. Everyone who is both not old and tall is both not calm and rich. Everyone who is not happy is both calm and tall. If someone is not tall then lucy is either kind or patient and vice versa. If someone is not patient or not strong then mary is not calm. Everyone who is not funny is either not wise or brave and vice versa. Everyone who is both wise and funny is both not calm and kind. If john is either humble or not old then alice is old or tall. If lucy is either not creative or not calm then someone is both kind and wise. Everyone who is brave is both tall and kind. If someone is brave then someone is both not humble and quiet and vice versa. If someone is quiet or kind then mary is not happy. If alice is either not curious or quiet then mary is not patient or not happy. John is not strong. Someone is happy or not funny. Alice is either quiet or old. Paul is both not old and not funny. Lucy is either not happy or not old. Paul is not happy or not quiet. Someone is not curious. | John is not brave. | entailment | ((?[X]:((~patient(X)<~>~old(X))))=>(?[X]:((~quiet(X)<~>tall(X)))))&
(((~kind(mary)<~>~creative(mary)))=>((happy(lucy)|funny(lucy))))&
(![X]:((~old(X)|~creative(X))<=>~curious(X)))&
(![X]:(~rich(X)=>(rich(X)|curious(X))))&
(![X]:((~old(X)&tall(X))=>(~calm(X)&rich(X))))&
(![X]:(~happy(X)=>(calm(X)&tall(X))))&
((?[X]:(~tall(X)))<=>((kind(lucy)<~>patient(lucy))))&
((?[X]:((~patient(X)|~strong(X))))=>(~calm(mary)))&
(![X]:(~funny(X)<=>(~wise(X)<~>brave(X))))&
(![X]:((wise(X)&funny(X))=>(~calm(X)&kind(X))))&
(((humble(john)<~>~old(john)))=>((old(alice)|tall(alice))))&
(((~creative(lucy)<~>~calm(lucy)))=>(?[X]:((kind(X)&wise(X)))))&
(![X]:(brave(X)=>(tall(X)&kind(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((quiet(X)|kind(X))))=>(~happy(mary)))&
(((~curious(alice)<~>quiet(alice)))=>((~patient(mary)|~happy(mary))))&
(~strong(john))&
(?[X]:((happy(X)|~funny(X))))&
((quiet(alice)<~>old(alice)))&
((~old(paul)&~funny(paul)))&
((~happy(lucy)<~>~old(lucy)))&
((~happy(paul)|~quiet(paul)))&
(?[X]:(~curious(X))) | ~brave(john) | [
"p5",
"p7",
"p13",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 4193901646345494126482346
% SZS output start Proof for 4193901646345494126482346
6. ! [X0] : (~happy(X0) => (tall(X0) & calm(X0))) [input p5]
8. ? [X0] : (~strong(X0) | ~patient(X0)) => ~calm(mary) [input p7]
14. ? [X0] : brave(X0) <=> ? [X0] : (quiet(X0) & ~humble(X0)) [input p13]
15. ? [X0] : (kind(X0) | quiet(X0)) => ~happy(mary) [input p14]
17. ~strong(john) [input p16]
24. brave(john) [input hypothesis]
26. ? [X0] : brave(X0) <=> ? [X1] : (quiet(X1) & ~humble(X1)) [rectify 14]
34. ! [X0] : ((tall(X0) & calm(X0)) | happy(X0)) [ennf transformation 6]
35. ~calm(mary) | ! [X0] : (strong(X0) & patient(X0)) [ennf transformation 8]
42. ~happy(mary) | ! [X0] : (~kind(X0) & ~quiet(X0)) [ennf transformation 15]
61. (? [X0] : brave(X0) | ! [X1] : (~quiet(X1) | humble(X1))) & (? [X1] : (quiet(X1) & ~humble(X1)) | ! [X0] : ~brave(X0)) [nnf transformation 26]
62. (? [X0] : brave(X0) | ! [X1] : (~quiet(X1) | humble(X1))) & (? [X2] : (quiet(X2) & ~humble(X2)) | ! [X3] : ~brave(X3)) [rectify 61]
63. ? [X0] : brave(X0) => brave(sK3) [choice axiom]
64. ? [X2] : (quiet(X2) & ~humble(X2)) => (quiet(sK4) & ~humble(sK4)) [choice axiom]
65. (brave(sK3) | ! [X1] : (~quiet(X1) | humble(X1))) & ((quiet(sK4) & ~humble(sK4)) | ! [X3] : ~brave(X3)) [skolemisation 62,64,63]
83. calm(X0) | happy(X0) [cnf transformation 34]
90. ~calm(mary) | strong(X0) [cnf transformation 35]
106. quiet(sK4) | ~brave(X3) [cnf transformation 65]
108. ~happy(mary) | ~quiet(X0) [cnf transformation 42]
112. ~strong(john) [cnf transformation 17]
122. brave(john) [cnf transformation 24]
179. 13 <=> ! [X0] : strong(X0) [avatar definition]
180. strong(X0) <- (13) [avatar component clause 179]
182. 14 <=> calm(mary) [avatar definition]
184. ~calm(mary) <- (~14) [avatar component clause 182]
185. 13 | ~14 [avatar split clause 90,182,179]
237. 26 <=> ! [X3] : ~brave(X3) [avatar definition]
238. ~brave(X3) <- (26) [avatar component clause 237]
240. 27 <=> quiet(sK4) [avatar definition]
242. quiet(sK4) <- (27) [avatar component clause 240]
243. 26 | 27 [avatar split clause 106,240,237]
253. 30 <=> happy(mary) [avatar definition]
255. ~happy(mary) <- (~30) [avatar component clause 253]
258. 31 <=> ! [X0] : ~quiet(X0) [avatar definition]
259. ~quiet(X0) <- (31) [avatar component clause 258]
260. 31 | ~30 [avatar split clause 108,253,258]
301. $false <- (26) [resolution 238,122]
302. ~26 [avatar contradiction clause 301]
303. happy(mary) <- (~14) [resolution 83,184]
305. $false <- (~14, ~30) [subsumption resolution 303,255]
306. 14 | 30 [avatar contradiction clause 305]
307. $false <- (13) [resolution 180,112]
308. ~13 [avatar contradiction clause 307]
312. $false <- (27, 31) [resolution 259,242]
313. ~27 | ~31 [avatar contradiction clause 312]
314. $false [avatar sat refutation 185,243,260,302,306,308,313]
% SZS output end Proof for 4193901646345494126482346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not curious is quiet or not kind.
Everyone who is either not wise or brave is both rich and not creative and vice versa.
If someone is old then mary is not wise and vice versa.
If someone is both not funny and not generous then someone is brave or not brave and vice versa.
Everyone who is both brave and curious is not old or brave and vice versa.
Everyone who is either not kind or not rich is not kind or not creative.
Everyone who is calm or not generous is both not wise and not kind and vice versa.
Everyone who is either humble or brave is either humble or calm and vice versa.
If lucy is not patient then someone is rich or not rich.
Everyone who is either creative or tall is not generous or brave and vice versa.
If fred is not brave then susan is either calm or not tall.
If alice is either not wise or not creative then lucy is not curious and vice versa.
If paul is both not rich and not happy then lucy is both rich and not rich and vice versa.
Everyone who is kind or tall is brave.
If someone is both not old and not creative then paul is not funny and vice versa.
If someone is both not kind and brave then someone is both not humble and not generous.
Someone is rich.
Fred is patient.
Someone is either not calm or not quiet.
Paul is not curious.
Someone is both patient and creative.
Someone is both not tall and quiet.
Susan is either not old or funny.
Lucy is not curious or calm. | Paul is not calm. | entailment | (![X]:((~quiet(X)|~curious(X))=>(quiet(X)|~kind(X))))&
(![X]:((~wise(X)<~>brave(X))<=>(rich(X)&~creative(X))))&
((?[X]:(old(X)))<=>(~wise(mary)))&
((?[X]:((~funny(X)&~generous(X))))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((brave(X)&curious(X))<=>(~old(X)|brave(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~kind(X)|~creative(X))))&
(![X]:((calm(X)|~generous(X))<=>(~wise(X)&~kind(X))))&
(![X]:((humble(X)<~>brave(X))<=>(humble(X)<~>calm(X))))&
((~patient(lucy))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:((creative(X)<~>tall(X))<=>(~generous(X)|brave(X))))&
((~brave(fred))=>((calm(susan)<~>~tall(susan))))&
(((~wise(alice)<~>~creative(alice)))<=>(~curious(lucy)))&
(((~rich(paul)&~happy(paul)))<=>((rich(lucy)&~rich(lucy))))&
(![X]:((kind(X)|tall(X))=>brave(X)))&
((?[X]:((~old(X)&~creative(X))))<=>(~funny(paul)))&
((?[X]:((~kind(X)&brave(X))))=>(?[X]:((~humble(X)&~generous(X)))))&
(?[X]:(rich(X)))&
(patient(fred))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(~curious(paul))&
(?[X]:((patient(X)&creative(X))))&
(?[X]:((~tall(X)&quiet(X))))&
((~old(susan)<~>funny(susan)))&
((~curious(lucy)|calm(lucy))) | ~calm(paul) | [
"p4",
"p7",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 5686898669198816732935966
% SZS output start Proof for 5686898669198816732935966
5. ! [X0] : ((curious(X0) & brave(X0)) <=> (brave(X0) | ~old(X0))) [input p4]
8. ! [X0] : ((humble(X0) <~> brave(X0)) <=> (humble(X0) <~> calm(X0))) [input p7]
20. ~curious(paul) [input p19]
25. calm(paul) [input hypothesis]
49. ! [X0] : (((curious(X0) & brave(X0)) | (~brave(X0) & old(X0))) & ((brave(X0) | ~old(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 5]
50. ! [X0] : (((curious(X0) & brave(X0)) | (~brave(X0) & old(X0))) & (brave(X0) | ~old(X0) | ~curious(X0) | ~brave(X0))) [flattening 49]
54. ! [X0] : ((((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))))) [nnf transformation 8]
97. ~brave(X0) | curious(X0) [cnf transformation 50]
107. ~calm(X0) | ~humble(X0) | brave(X0) | ~humble(X0) [cnf transformation 54]
110. brave(X0) | humble(X0) | humble(X0) | ~calm(X0) [cnf transformation 54]
139. ~curious(paul) [cnf transformation 20]
146. calm(paul) [cnf transformation 25]
148. ~calm(X0) | ~humble(X0) | brave(X0) [duplicate literal removal 107]
149. brave(X0) | humble(X0) | ~calm(X0) [duplicate literal removal 110]
184. ~calm(X0) | brave(X0) [subsumption resolution 148,149]
297. brave(paul) [resolution 184,146]
310. curious(paul) [resolution 297,97]
311. $false [subsumption resolution 310,139]
% SZS output end Proof for 5686898669198816732935966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not wise is quiet. Everyone who is either not happy or not calm is either not creative or not funny and vice versa. Everyone who is not wise or not happy is both curious and tall. If lucy is either patient or not patient then fred is either not curious or creative. If someone is humble then someone is both not tall and strong and vice versa. Everyone who is both not kind and not creative is either not patient or not funny and vice versa. Everyone who is either not happy or generous is both not quiet and brave. If paul is both not creative and quiet then john is strong or rich and vice versa. If susan is quiet then alice is not rich. Everyone who is both rich and not brave is not brave or not strong. Everyone who is kind is either brave or not brave and vice versa. Everyone who is humble is either not patient or kind and vice versa. Everyone who is curious or not generous is both not calm and strong and vice versa. Everyone who is not generous or not wise is both tall and not brave. Everyone who is not wise or humble is not curious and vice versa. If someone is both curious and tall then john is not patient or not tall and vice versa. Someone is either not curious or not happy. Someone is both creative and not patient. Alice is either calm or not patient. Someone is either patient or calm. | Fred is not creative. | neutral | (![X]:((humble(X)|~wise(X))=>quiet(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>(~creative(X)<~>~funny(X))))&
(![X]:((~wise(X)|~happy(X))=>(curious(X)&tall(X))))&
(((patient(lucy)<~>~patient(lucy)))=>((~curious(fred)<~>creative(fred))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((~happy(X)<~>generous(X))=>(~quiet(X)&brave(X))))&
(((~creative(paul)&quiet(paul)))<=>((strong(john)|rich(john))))&
((quiet(susan))=>(~rich(alice)))&
(![X]:((rich(X)&~brave(X))=>(~brave(X)|~strong(X))))&
(![X]:(kind(X)<=>(brave(X)<~>~brave(X))))&
(![X]:(humble(X)<=>(~patient(X)<~>kind(X))))&
(![X]:((curious(X)|~generous(X))<=>(~calm(X)&strong(X))))&
(![X]:((~generous(X)|~wise(X))=>(tall(X)&~brave(X))))&
(![X]:((~wise(X)|humble(X))<=>~curious(X)))&
((?[X]:((curious(X)&tall(X))))<=>((~patient(john)|~tall(john))))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:((creative(X)&~patient(X))))&
((calm(alice)<~>~patient(alice)))&
(?[X]:((patient(X)<~>calm(X)))) | ~creative(fred) | []
| null | 0 |
Everyone who is creative or not happy is both not tall and calm and vice versa.
Everyone who is not funny or not humble is not generous or curious and vice versa.
If someone is humble then mary is either not happy or not brave and vice versa.
Everyone who is curious is not generous or not creative.
Everyone who is either not calm or not brave is both patient and not kind.
Everyone who is not patient is either not wise or humble and vice versa.
If someone is either not happy or not strong then alice is funny.
Everyone who is not funny is either not patient or wise and vice versa.
If someone is either not patient or not funny then someone is either calm or old and vice versa.
If fred is both not funny and not kind then lucy is not brave.
If john is humble then someone is either not strong or not old.
Everyone who is not tall or quiet is not funny or wise.
Everyone who is either happy or not humble is generous or strong and vice versa.
If lucy is either not generous or not happy then someone is funny and vice versa.
Everyone who is generous or not rich is not brave or happy and vice versa.
Everyone who is both funny and not tall is both generous and strong and vice versa.
Fred is either not rich or not humble.
Someone is either funny or rich.
Someone is either humble or not rich.
Someone is not brave.
Someone is not curious.
Alice is either not strong or tall.
Fred is patient or not tall.
Someone is both creative and wise. | Lucy is not calm. | contradiction | (![X]:((creative(X)|~happy(X))<=>(~tall(X)&calm(X))))&
(![X]:((~funny(X)|~humble(X))<=>(~generous(X)|curious(X))))&
((?[X]:(humble(X)))<=>((~happy(mary)<~>~brave(mary))))&
(![X]:(curious(X)=>(~generous(X)|~creative(X))))&
(![X]:((~calm(X)<~>~brave(X))=>(patient(X)&~kind(X))))&
(![X]:(~patient(X)<=>(~wise(X)<~>humble(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>(funny(alice)))&
(![X]:(~funny(X)<=>(~patient(X)<~>wise(X))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((calm(X)<~>old(X)))))&
(((~funny(fred)&~kind(fred)))=>(~brave(lucy)))&
((humble(john))=>(?[X]:((~strong(X)<~>~old(X)))))&
(![X]:((~tall(X)|quiet(X))=>(~funny(X)|wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>(generous(X)|strong(X))))&
(((~generous(lucy)<~>~happy(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((generous(X)|~rich(X))<=>(~brave(X)|happy(X))))&
(![X]:((funny(X)&~tall(X))<=>(generous(X)&strong(X))))&
((~rich(fred)<~>~humble(fred)))&
(?[X]:((funny(X)<~>rich(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~curious(X)))&
((~strong(alice)<~>tall(alice)))&
((patient(fred)|~tall(fred)))&
(?[X]:((creative(X)&wise(X)))) | ~calm(lucy) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p7",
"p12",
"p13",
"p15",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 336775366135543090154590
% SZS output start Proof for 336775366135543090154590
1. ! [X0] : ((~happy(X0) | creative(X0)) <=> (calm(X0) & ~tall(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (curious(X0) | ~generous(X0))) [input p1]
3. ? [X0] : humble(X0) <=> (~happy(mary) <~> ~brave(mary)) [input p2]
6. ! [X0] : (~patient(X0) <=> (~wise(X0) <~> humble(X0))) [input p5]
7. ? [X0] : (~happy(X0) <~> ~strong(X0)) => funny(alice) [input p6]
8. ! [X0] : (~funny(X0) <=> (~patient(X0) <~> wise(X0))) [input p7]
13. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> (strong(X0) | generous(X0))) [input p12]
14. (~generous(lucy) <~> ~happy(lucy)) <=> ? [X0] : funny(X0) [input p13]
16. ! [X0] : ((~tall(X0) & funny(X0)) <=> (strong(X0) & generous(X0))) [input p15]
22. ~strong(alice) <~> tall(alice) [input p21]
25. ~calm(lucy) [input hypothesis]
31. funny(alice) | ! [X0] : (~happy(X0) <=> ~strong(X0)) [ennf transformation 7]
37. ! [X0] : (((~happy(X0) | creative(X0)) | (~calm(X0) | tall(X0))) & ((calm(X0) & ~tall(X0)) | (happy(X0) & ~creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((~happy(X0) | creative(X0) | ~calm(X0) | tall(X0)) & ((calm(X0) & ~tall(X0)) | (happy(X0) & ~creative(X0)))) [flattening 37]
39. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 2]
40. ! [X0] : ((~humble(X0) | ~funny(X0) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | (humble(X0) & funny(X0)))) [flattening 39]
41. (? [X0] : humble(X0) | ((~happy(mary) | brave(mary)) & (~brave(mary) | happy(mary)))) & (((brave(mary) | happy(mary)) & (~brave(mary) | ~happy(mary))) | ! [X0] : ~humble(X0)) [nnf transformation 3]
42. (? [X0] : humble(X0) | ((~happy(mary) | brave(mary)) & (~brave(mary) | happy(mary)))) & (((brave(mary) | happy(mary)) & (~brave(mary) | ~happy(mary))) | ! [X1] : ~humble(X1)) [rectify 41]
43. ? [X0] : humble(X0) => humble(sK0) [choice axiom]
44. (humble(sK0) | ((~happy(mary) | brave(mary)) & (~brave(mary) | happy(mary)))) & (((brave(mary) | happy(mary)) & (~brave(mary) | ~happy(mary))) | ! [X1] : ~humble(X1)) [skolemisation 42,43]
46. ! [X0] : ((~patient(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) & (((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | patient(X0))) [nnf transformation 6]
47. funny(alice) | ! [X0] : ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))) [nnf transformation 31]
48. ! [X0] : ((~funny(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | funny(X0))) [nnf transformation 8]
57. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~strong(X0) & ~generous(X0))) & ((strong(X0) | generous(X0)) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 13]
58. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | (~strong(X0) & ~generous(X0))) & (strong(X0) | generous(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [flattening 57]
59. (((happy(lucy) | generous(lucy)) & (~happy(lucy) | ~generous(lucy))) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | ((~generous(lucy) | happy(lucy)) & (~happy(lucy) | generous(lucy)))) [nnf transformation 14]
60. (((happy(lucy) | generous(lucy)) & (~happy(lucy) | ~generous(lucy))) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | ((~generous(lucy) | happy(lucy)) & (~happy(lucy) | generous(lucy)))) [rectify 59]
61. ? [X1] : funny(X1) => funny(sK4) [choice axiom]
62. (((happy(lucy) | generous(lucy)) & (~happy(lucy) | ~generous(lucy))) | ! [X0] : ~funny(X0)) & (funny(sK4) | ((~generous(lucy) | happy(lucy)) & (~happy(lucy) | generous(lucy)))) [skolemisation 60,61]
65. ! [X0] : (((~tall(X0) & funny(X0)) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | (tall(X0) | ~funny(X0)))) [nnf transformation 16]
66. ! [X0] : (((~tall(X0) & funny(X0)) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | tall(X0) | ~funny(X0))) [flattening 65]
78. (~tall(alice) | strong(alice)) & (tall(alice) | ~strong(alice)) [nnf transformation 22]
82. ~tall(X0) | happy(X0) [cnf transformation 38]
84. calm(X0) | happy(X0) [cnf transformation 38]
88. ~humble(X0) | ~funny(X0) | generous(X0) [cnf transformation 40]
91. brave(mary) | happy(mary) | ~humble(X1) [cnf transformation 44]
92. humble(sK0) | ~brave(mary) | happy(mary) [cnf transformation 44]
100. ~humble(X0) | wise(X0) | patient(X0) [cnf transformation 46]
102. ~wise(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 46]
104. funny(alice) | ~happy(X0) | strong(X0) [cnf transformation 47]
105. ~patient(X0) | wise(X0) | funny(X0) [cnf transformation 48]
106. ~wise(X0) | patient(X0) | funny(X0) [cnf transformation 48]
126. ~strong(X0) | ~happy(X0) | humble(X0) [cnf transformation 58]
129. ~happy(lucy) | ~generous(lucy) | ~funny(X0) [cnf transformation 62]
136. ~funny(X0) | tall(X0) | strong(X0) [cnf transformation 66]
138. ~strong(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 66]
147. tall(alice) | ~strong(alice) [cnf transformation 78]
148. ~tall(alice) | strong(alice) [cnf transformation 78]
152. ~calm(lucy) [cnf transformation 25]
154. 1 <=> brave(mary) [avatar definition]
158. 2 <=> happy(mary) [avatar definition]
159. happy(mary) <- (2) [avatar component clause 158]
162. 3 <=> humble(sK0) [avatar definition]
164. humble(sK0) <- (3) [avatar component clause 162]
166. 2 | ~1 | 3 [avatar split clause 92,162,154,158]
168. 4 <=> ! [X1] : ~humble(X1) [avatar definition]
169. ~humble(X1) <- (4) [avatar component clause 168]
170. 4 | 2 | 1 [avatar split clause 91,154,158,168]
173. 5 <=> ! [X0] : (~happy(X0) | strong(X0)) [avatar definition]
174. ~happy(X0) | strong(X0) <- (5) [avatar component clause 173]
176. 6 <=> funny(alice) [avatar definition]
178. funny(alice) <- (6) [avatar component clause 176]
179. 5 | 6 [avatar split clause 104,176,173]
248. 22 <=> ! [X0] : ~funny(X0) [avatar definition]
249. ~funny(X0) <- (22) [avatar component clause 248]
251. 23 <=> generous(lucy) [avatar definition]
252. ~generous(lucy) <- (~23) [avatar component clause 251]
255. 24 <=> happy(lucy) [avatar definition]
257. happy(lucy) <- (24) [avatar component clause 255]
259. 22 | ~23 | ~24 [avatar split clause 129,255,251,248]
297. 32 <=> strong(alice) [avatar definition]
298. ~strong(alice) <- (~32) [avatar component clause 297]
299. strong(alice) <- (32) [avatar component clause 297]
301. 33 <=> tall(alice) [avatar definition]
302. tall(alice) <- (33) [avatar component clause 301]
303. ~tall(alice) <- (~33) [avatar component clause 301]
304. 32 | ~33 [avatar split clause 148,301,297]
305. ~32 | 33 [avatar split clause 147,301,297]
320. happy(lucy) [resolution 84,152]
323. 24 [avatar split clause 320,255]
324. strong(mary) <- (2, 5) [resolution 174,159]
334. 37 <=> funny(sK0) [avatar definition]
335. funny(sK0) <- (37) [avatar component clause 334]
336. ~funny(sK0) <- (~37) [avatar component clause 334]
379. wise(sK0) | patient(sK0) <- (3) [resolution 100,164]
382. 45 <=> patient(sK0) [avatar definition]
383. ~patient(sK0) <- (~45) [avatar component clause 382]
384. patient(sK0) <- (45) [avatar component clause 382]
386. 46 <=> wise(sK0) [avatar definition]
388. wise(sK0) <- (46) [avatar component clause 386]
389. 45 | 46 | ~3 [avatar split clause 379,162,386,382]
409. wise(sK0) | funny(sK0) <- (45) [resolution 105,384]
410. wise(sK0) <- (~37, 45) [subsumption resolution 409,336]
411. 46 | 37 | ~45 [avatar split clause 410,382,334,386]
412. ~patient(sK0) | ~humble(sK0) <- (46) [resolution 388,102]
414. ~patient(sK0) <- (3, 46) [subsumption resolution 412,164]
415. ~45 | ~3 | ~46 [avatar split clause 414,386,162,382]
418. patient(sK0) | funny(sK0) <- (46) [resolution 106,388]
422. funny(sK0) <- (~45, 46) [subsumption resolution 418,383]
423. $false <- (~37, ~45, 46) [subsumption resolution 422,336]
424. 37 | 45 | ~46 [avatar contradiction clause 423]
493. ~happy(mary) | humble(mary) <- (2, 5) [resolution 126,324]
496. humble(mary) <- (2, 5) [subsumption resolution 493,159]
579. 62 <=> funny(mary) [avatar definition]
580. ~funny(mary) <- (~62) [avatar component clause 579]
581. funny(mary) <- (62) [avatar component clause 579]
613. 65 <=> humble(alice) [avatar definition]
614. ~humble(alice) <- (~65) [avatar component clause 613]
615. humble(alice) <- (65) [avatar component clause 613]
617. 66 <=> happy(alice) [avatar definition]
618. ~happy(alice) <- (~66) [avatar component clause 617]
621. 67 <=> generous(alice) [avatar definition]
630. ~funny(alice) | generous(alice) <- (65) [resolution 615,88]
670. 67 | ~6 | ~65 [avatar split clause 630,613,176,621]
671. tall(alice) | strong(alice) <- (6) [resolution 178,136]
675. strong(alice) <- (6, ~33) [subsumption resolution 671,303]
676. $false <- (6, ~32, ~33) [subsumption resolution 675,298]
677. ~6 | 32 | 33 [avatar contradiction clause 676]
728. wise(mary) | patient(mary) <- (2, 5) [resolution 496,100]
731. 72 <=> patient(mary) [avatar definition]
732. ~patient(mary) <- (~72) [avatar component clause 731]
733. patient(mary) <- (72) [avatar component clause 731]
735. 73 <=> wise(mary) [avatar definition]
737. wise(mary) <- (73) [avatar component clause 735]
738. 72 | 73 | ~2 | ~5 [avatar split clause 728,173,158,735,731]
745. 74 <=> patient(lucy) [avatar definition]
747. patient(lucy) <- (74) [avatar component clause 745]
749. 75 <=> wise(lucy) [avatar definition]
750. ~wise(lucy) <- (~75) [avatar component clause 749]
751. wise(lucy) <- (75) [avatar component clause 749]
866. ~tall(alice) | ~generous(alice) <- (32) [resolution 299,138]
868. ~happy(alice) | humble(alice) <- (32) [resolution 299,126]
872. ~generous(alice) <- (32, 33) [subsumption resolution 866,302]
875. ~happy(alice) <- (32, ~65) [subsumption resolution 868,614]
876. ~66 | ~32 | 65 [avatar split clause 875,613,297,617]
883. ~67 | ~32 | ~33 [avatar split clause 872,301,297,621]
884. happy(alice) <- (33) [resolution 302,82]
886. $false <- (33, ~66) [subsumption resolution 884,618]
887. ~33 | 66 [avatar contradiction clause 886]
900. strong(mary) <- (2, 5) [resolution 174,159]
901. strong(lucy) <- (5, 24) [resolution 174,257]
922. ~happy(mary) | humble(mary) <- (2, 5) [resolution 900,126]
924. humble(mary) <- (2, 5) [subsumption resolution 922,159]
928. ~happy(lucy) | humble(lucy) <- (5, 24) [resolution 901,126]
930. humble(lucy) <- (5, 24) [subsumption resolution 928,257]
971. wise(lucy) | patient(lucy) <- (5, 24) [resolution 930,100]
972. ~funny(lucy) | generous(lucy) <- (5, 24) [resolution 930,88]
973. ~funny(lucy) <- (5, ~23, 24) [subsumption resolution 972,252]
982. wise(mary) | funny(mary) <- (72) [resolution 733,105]
984. wise(mary) <- (~62, 72) [subsumption resolution 982,580]
985. 73 | 62 | ~72 [avatar split clause 984,731,579,735]
987. patient(mary) | funny(mary) <- (73) [resolution 737,106]
988. ~patient(mary) | ~humble(mary) <- (73) [resolution 737,102]
993. ~patient(mary) <- (2, 5, 73) [subsumption resolution 988,924]
994. ~72 | ~2 | ~5 | ~73 [avatar split clause 993,735,173,158,731]
1003. funny(mary) <- (~72, 73) [subsumption resolution 987,732]
1004. 62 | 72 | ~73 [avatar split clause 1003,735,731,579]
1016. patient(lucy) | funny(lucy) <- (75) [resolution 751,106]
1017. ~patient(lucy) | ~humble(lucy) <- (75) [resolution 751,102]
1019. patient(lucy) <- (5, ~23, 24, 75) [subsumption resolution 1016,973]
1020. 74 | ~5 | 23 | ~24 | ~75 [avatar split clause 1019,749,255,251,173,745]
1021. ~patient(lucy) <- (5, 24, 75) [subsumption resolution 1017,930]
1022. ~74 | ~5 | ~24 | ~75 [avatar split clause 1021,749,255,173,745]
1023. 74 | 75 | ~5 | ~24 [avatar split clause 971,255,173,749,745]
1024. wise(lucy) | funny(lucy) <- (74) [resolution 747,105]
1026. funny(lucy) <- (74, ~75) [subsumption resolution 1024,750]
1029. generous(lucy) <- (5, 24, 74, ~75) [subsumption resolution 972,1026]
1030. 23 | ~5 | ~24 | ~74 | 75 [avatar split clause 1029,749,745,255,173,251]
1044. $false <- (22, 62) [resolution 249,581]
1045. $false <- (22, 37) [resolution 249,335]
1050. ~22 | ~37 [avatar contradiction clause 1045]
1051. ~22 | ~62 [avatar contradiction clause 1044]
1122. $false <- (4, 5, 24) [resolution 169,930]
1125. ~4 | ~5 | ~24 [avatar contradiction clause 1122]
1126. $false [avatar sat refutation 166,170,179,259,304,305,323,389,411,415,424,670,677,738,876,883,887,985,994,1004,1020,1022,1023,1030,1050,1051,1125]
% SZS output end Proof for 336775366135543090154590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or brave is creative. Everyone who is not calm or not creative is either strong or not tall. If someone is either kind or humble then paul is funny or not curious. Everyone who is humble is not old or strong and vice versa. Everyone who is both not calm and not creative is not quiet and vice versa. Everyone who is both creative and not generous is either not kind or not wise and vice versa. If someone is either rich or not quiet then alice is either tall or not quiet and vice versa. Everyone who is either not rich or calm is not creative or not generous. If john is either happy or not calm then someone is not curious or not wise. Everyone who is strong is both funny and creative and vice versa. Everyone who is both happy and quiet is funny or not humble and vice versa. If someone is both old and not tall then someone is generous and vice versa. If paul is both patient and not humble then alice is both strong and not tall. If someone is not strong or brave then lucy is not generous and vice versa. If lucy is either generous or not humble then someone is kind or creative and vice versa. Everyone who is both kind and not generous is either generous or not generous and vice versa. Someone is rich or not calm. Alice is not creative or not wise. Someone is not patient or creative. Someone is either not calm or not kind. Someone is humble or not quiet. Mary is not funny or curious. | Lucy is not happy. | contradiction | (![X]:((rich(X)|brave(X))=>creative(X)))&
(![X]:((~calm(X)|~creative(X))=>(strong(X)<~>~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))=>((funny(paul)|~curious(paul))))&
(![X]:(humble(X)<=>(~old(X)|strong(X))))&
(![X]:((~calm(X)&~creative(X))<=>~quiet(X)))&
(![X]:((creative(X)&~generous(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>((tall(alice)<~>~quiet(alice))))&
(![X]:((~rich(X)<~>calm(X))=>(~creative(X)|~generous(X))))&
(((happy(john)<~>~calm(john)))=>(?[X]:((~curious(X)|~wise(X)))))&
(![X]:(strong(X)<=>(funny(X)&creative(X))))&
(![X]:((happy(X)&quiet(X))<=>(funny(X)|~humble(X))))&
((?[X]:((old(X)&~tall(X))))<=>(?[X]:(generous(X))))&
(((patient(paul)&~humble(paul)))=>((strong(alice)&~tall(alice))))&
((?[X]:((~strong(X)|brave(X))))<=>(~generous(lucy)))&
(((generous(lucy)<~>~humble(lucy)))<=>(?[X]:((kind(X)|creative(X)))))&
(![X]:((kind(X)&~generous(X))<=>(generous(X)<~>~generous(X))))&
(?[X]:((rich(X)|~calm(X))))&
((~creative(alice)|~wise(alice)))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((~funny(mary)|curious(mary))) | ~happy(lucy) | [
"p10",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 6240708278143940551857623
% SZS output start Proof for 6240708278143940551857623
11. ! [X0] : ((quiet(X0) & happy(X0)) <=> (~humble(X0) | funny(X0))) [input p10]
15. (generous(lucy) <~> ~humble(lucy)) <=> ? [X0] : (creative(X0) | kind(X0)) [input p14]
16. ! [X0] : ((~generous(X0) & kind(X0)) <=> (generous(X0) <~> ~generous(X0))) [input p15]
23. ~happy(lucy) [input hypothesis]
52. ! [X0] : (((quiet(X0) & happy(X0)) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | (~quiet(X0) | ~happy(X0)))) [nnf transformation 11]
53. ! [X0] : (((quiet(X0) & happy(X0)) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | ~quiet(X0) | ~happy(X0))) [flattening 52]
63. (((humble(lucy) | ~generous(lucy)) & (~humble(lucy) | generous(lucy))) | ! [X0] : (~creative(X0) & ~kind(X0))) & (? [X0] : (creative(X0) | kind(X0)) | ((generous(lucy) | humble(lucy)) & (~humble(lucy) | ~generous(lucy)))) [nnf transformation 15]
64. (((humble(lucy) | ~generous(lucy)) & (~humble(lucy) | generous(lucy))) | ! [X0] : (~creative(X0) & ~kind(X0))) & (? [X1] : (creative(X1) | kind(X1)) | ((generous(lucy) | humble(lucy)) & (~humble(lucy) | ~generous(lucy)))) [rectify 63]
65. ? [X1] : (creative(X1) | kind(X1)) => (creative(sK5) | kind(sK5)) [choice axiom]
66. (((humble(lucy) | ~generous(lucy)) & (~humble(lucy) | generous(lucy))) | ! [X0] : (~creative(X0) & ~kind(X0))) & ((creative(sK5) | kind(sK5)) | ((generous(lucy) | humble(lucy)) & (~humble(lucy) | ~generous(lucy)))) [skolemisation 64,65]
67. ! [X0] : (((~generous(X0) & kind(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (generous(X0) | ~kind(X0)))) [nnf transformation 16]
68. ! [X0] : (((~generous(X0) & kind(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | generous(X0) | ~kind(X0))) [flattening 67]
113. happy(X0) | humble(X0) [cnf transformation 53]
124. ~humble(lucy) | generous(lucy) | ~kind(X0) [cnf transformation 66]
130. kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 68]
131. kind(X0) | generous(X0) | generous(X0) [cnf transformation 68]
132. ~generous(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 68]
140. ~happy(lucy) [cnf transformation 23]
143. kind(X0) | ~generous(X0) [duplicate literal removal 130]
144. kind(X0) | generous(X0) [duplicate literal removal 131]
145. ~generous(X0) [duplicate literal removal 132]
213. 15 <=> ! [X1] : ~generous(X1) [avatar definition]
214. ~generous(X1) <- (15) [avatar component clause 213]
234. 20 <=> generous(lucy) [avatar definition]
236. generous(lucy) <- (20) [avatar component clause 234]
258. 26 <=> humble(lucy) [avatar definition]
263. 27 <=> ! [X0] : ~kind(X0) [avatar definition]
264. ~kind(X0) <- (27) [avatar component clause 263]
267. 27 | 20 | ~26 [avatar split clause 124,258,234,263]
278. 15 [avatar split clause 145,213]
279. kind(X0) [subsumption resolution 143,144]
309. $false <- (27) [subsumption resolution 264,279]
310. ~27 [avatar contradiction clause 309]
327. humble(lucy) [resolution 113,140]
330. 26 [avatar split clause 327,258]
331. $false <- (15, 20) [subsumption resolution 236,214]
332. ~15 | ~20 [avatar contradiction clause 331]
333. $false [avatar sat refutation 267,278,310,330,332]
% SZS output end Proof for 6240708278143940551857623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or calm then mary is either not patient or not quiet.
If someone is not tall then mary is not creative or not rich.
Everyone who is both humble and rich is either old or patient.
Everyone who is not happy or not tall is either strong or quiet and vice versa.
If paul is generous then fred is either not wise or patient and vice versa.
If mary is either not humble or generous then someone is not quiet.
Everyone who is both not patient and generous is not generous or not happy and vice versa.
Everyone who is brave or not creative is not creative.
Everyone who is creative or wise is not curious or not patient and vice versa.
If someone is either rich or generous then someone is both humble and rich and vice versa.
If someone is either rich or kind then someone is both wise and calm.
Everyone who is either tall or not creative is both curious and funny and vice versa.
Everyone who is not humble or kind is creative or not generous.
If someone is either not rich or not wise then someone is both strong and not quiet and vice versa.
Everyone who is not happy is either not humble or curious.
If john is not kind or curious then paul is not calm or not brave and vice versa.
Mary is creative or patient.
John is both quiet and rich.
Someone is strong or not tall.
Someone is both not old and rich.
Alice is either not generous or tall.
Someone is tall.
Someone is not brave. | Paul is not brave. | neutral | ((?[X]:((~old(X)|calm(X))))=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:(~tall(X)))=>((~creative(mary)|~rich(mary))))&
(![X]:((humble(X)&rich(X))=>(old(X)<~>patient(X))))&
(![X]:((~happy(X)|~tall(X))<=>(strong(X)<~>quiet(X))))&
((generous(paul))<=>((~wise(fred)<~>patient(fred))))&
(((~humble(mary)<~>generous(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((~patient(X)&generous(X))<=>(~generous(X)|~happy(X))))&
(![X]:((brave(X)|~creative(X))=>~creative(X)))&
(![X]:((creative(X)|wise(X))<=>(~curious(X)|~patient(X))))&
((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:((humble(X)&rich(X)))))&
((?[X]:((rich(X)<~>kind(X))))=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((tall(X)<~>~creative(X))<=>(curious(X)&funny(X))))&
(![X]:((~humble(X)|kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:(~happy(X)=>(~humble(X)<~>curious(X))))&
(((~kind(john)|curious(john)))<=>((~calm(paul)|~brave(paul))))&
((creative(mary)|patient(mary)))&
((quiet(john)&rich(john)))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((~old(X)&rich(X))))&
((~generous(alice)<~>tall(alice)))&
(?[X]:(tall(X)))&
(?[X]:(~brave(X))) | ~brave(paul) | []
| null | 0 |
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