premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is both not curious and not humble is either strong or curious and vice versa.
Everyone who is both not calm and generous is strong or tall.
If paul is not humble then susan is patient or not brave and vice versa.
If paul is either not rich or patient then fred is both happy and not rich.
If someone is tall then someone is not curious and vice versa.
If someone is wise or not happy then paul is either kind or tall and vice versa.
Everyone who is not generous is tall and vice versa.
If someone is either not brave or strong then someone is either not quiet or tall and vice versa.
If someone is both calm and not wise then alice is funny or calm and vice versa.
If paul is quiet then alice is both not curious and not calm.
If john is brave then john is either not funny or not kind and vice versa.
Everyone who is not quiet is not wise.
Everyone who is both not wise and strong is rich or humble and vice versa.
Everyone who is not generous is both not strong and not patient.
If fred is tall or funny then mary is strong.
Fred is kind or curious.
Lucy is either funny or not humble.
Lucy is either funny or not patient.
Alice is not wise or calm.
Mary is not generous or wise.
Someone is not curious or not patient.
Fred is not kind or strong. | Fred is not generous. | contradiction | (![X]:((~curious(X)&~humble(X))<=>(strong(X)<~>curious(X))))&
(![X]:((~calm(X)&generous(X))=>(strong(X)|tall(X))))&
((~humble(paul))<=>((patient(susan)|~brave(susan))))&
(((~rich(paul)<~>patient(paul)))=>((happy(fred)&~rich(fred))))&
((?[X]:(tall(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((kind(paul)<~>tall(paul))))&
(![X]:(~generous(X)<=>tall(X)))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
((?[X]:((calm(X)&~wise(X))))<=>((funny(alice)|calm(alice))))&
((quiet(paul))=>((~curious(alice)&~calm(alice))))&
((brave(john))<=>((~funny(john)<~>~kind(john))))&
(![X]:(~quiet(X)=>~wise(X)))&
(![X]:((~wise(X)&strong(X))<=>(rich(X)|humble(X))))&
(![X]:(~generous(X)=>(~strong(X)&~patient(X))))&
(((tall(fred)|funny(fred)))=>(strong(mary)))&
((kind(fred)|curious(fred)))&
((funny(lucy)<~>~humble(lucy)))&
((funny(lucy)<~>~patient(lucy)))&
((~wise(alice)|calm(alice)))&
((~generous(mary)|wise(mary)))&
(?[X]:((~curious(X)|~patient(X))))&
((~kind(fred)|strong(fred))) | ~generous(fred) | [
"p0",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5921568127576136376803229
% SZS output start Proof for 5921568127576136376803229
1. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (strong(X0) <~> curious(X0))) [input p0]
13. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (humble(X0) | rich(X0))) [input p12]
14. ! [X0] : (~generous(X0) => (~patient(X0) & ~strong(X0))) [input p13]
23. ~generous(fred) [input hypothesis]
31. ! [X0] : ((~patient(X0) & ~strong(X0)) | generous(X0)) [ennf transformation 14]
33. ! [X0] : (((~humble(X0) & ~curious(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (humble(X0) | curious(X0)))) [nnf transformation 1]
34. ! [X0] : (((~humble(X0) & ~curious(X0)) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | humble(X0) | curious(X0))) [flattening 33]
59. ! [X0] : (((strong(X0) & ~wise(X0)) | (~humble(X0) & ~rich(X0))) & ((humble(X0) | rich(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 13]
60. ! [X0] : (((strong(X0) & ~wise(X0)) | (~humble(X0) & ~rich(X0))) & (humble(X0) | rich(X0) | ~strong(X0) | wise(X0))) [flattening 59]
65. curious(X0) | strong(X0) | humble(X0) | curious(X0) [cnf transformation 34]
68. ~curious(X0) | strong(X0) | ~curious(X0) [cnf transformation 34]
113. strong(X0) | ~humble(X0) [cnf transformation 60]
114. ~strong(X0) | generous(X0) [cnf transformation 31]
127. ~generous(fred) [cnf transformation 23]
128. curious(X0) | strong(X0) | humble(X0) [duplicate literal removal 65]
129. ~curious(X0) | strong(X0) [duplicate literal removal 68]
130. strong(X0) | humble(X0) [subsumption resolution 128,129]
296. strong(X0) [subsumption resolution 113,130]
298. generous(X0) [subsumption resolution 114,296]
339. $false [subsumption resolution 127,298]
% SZS output end Proof for 5921568127576136376803229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not patient or old and vice versa. If someone is quiet or old then alice is both not creative and not funny and vice versa. Everyone who is happy or strong is old and vice versa. Everyone who is tall or rich is strong or creative. Everyone who is quiet is strong or not generous. Everyone who is both old and rich is both brave and patient. If someone is either not rich or not happy then mary is both not patient and wise and vice versa. If john is not brave then someone is either happy or not brave and vice versa. Everyone who is both not tall and not generous is both not tall and rich. If alice is not wise then someone is not kind or quiet. If fred is humble then someone is both not creative and kind and vice versa. If someone is either humble or not creative then someone is quiet and vice versa. Everyone who is either humble or not happy is not rich and vice versa. If paul is rich or not curious then someone is brave and vice versa. Everyone who is not calm is not generous or not happy. If someone is not funny then alice is either tall or humble. John is not rich or strong. Mary is brave. Fred is both not quiet and not happy. Mary is either happy or not rich. John is not brave. Lucy is both not quiet and old. Fred is curious or not humble. Someone is both funny and not old. | Alice is not humble. | contradiction | (![X]:(~tall(X)<=>(~patient(X)|old(X))))&
((?[X]:((quiet(X)|old(X))))<=>((~creative(alice)&~funny(alice))))&
(![X]:((happy(X)|strong(X))<=>old(X)))&
(![X]:((tall(X)|rich(X))=>(strong(X)|creative(X))))&
(![X]:(quiet(X)=>(strong(X)|~generous(X))))&
(![X]:((old(X)&rich(X))=>(brave(X)&patient(X))))&
((?[X]:((~rich(X)<~>~happy(X))))<=>((~patient(mary)&wise(mary))))&
((~brave(john))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~tall(X)&~generous(X))=>(~tall(X)&rich(X))))&
((~wise(alice))=>(?[X]:((~kind(X)|quiet(X)))))&
((humble(fred))<=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:((humble(X)<~>~happy(X))<=>~rich(X)))&
(((rich(paul)|~curious(paul)))<=>(?[X]:(brave(X))))&
(![X]:(~calm(X)=>(~generous(X)|~happy(X))))&
((?[X]:(~funny(X)))=>((tall(alice)<~>humble(alice))))&
((~rich(john)|strong(john)))&
(brave(mary))&
((~quiet(fred)&~happy(fred)))&
((happy(mary)<~>~rich(mary)))&
(~brave(john))&
((~quiet(lucy)&old(lucy)))&
((curious(fred)|~humble(fred)))&
(?[X]:((funny(X)&~old(X)))) | ~humble(alice) | [
"p0",
"p1",
"p2",
"p3",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8223421753916857493542309
% SZS output start Proof for 8223421753916857493542309
1. ! [X0] : (~tall(X0) <=> (old(X0) | ~patient(X0))) [input p0]
2. ? [X0] : (old(X0) | quiet(X0)) <=> (~funny(alice) & ~creative(alice)) [input p1]
3. ! [X0] : ((strong(X0) | happy(X0)) <=> old(X0)) [input p2]
4. ! [X0] : ((rich(X0) | tall(X0)) => (creative(X0) | strong(X0))) [input p3]
16. ? [X0] : ~funny(X0) => (tall(alice) <~> humble(alice)) [input p15]
22. old(lucy) & ~quiet(lucy) [input p21]
25. ~humble(alice) [input hypothesis]
28. ! [X0] : ((creative(X0) | strong(X0)) | (~rich(X0) & ~tall(X0))) [ennf transformation 4]
29. ! [X0] : (creative(X0) | strong(X0) | (~rich(X0) & ~tall(X0))) [flattening 28]
37. (tall(alice) <~> humble(alice)) | ! [X0] : funny(X0) [ennf transformation 16]
38. ! [X0] : ((~tall(X0) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | tall(X0))) [nnf transformation 1]
39. ! [X0] : ((~tall(X0) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | tall(X0))) [flattening 38]
40. (? [X0] : (old(X0) | quiet(X0)) | (funny(alice) | creative(alice))) & ((~funny(alice) & ~creative(alice)) | ! [X0] : (~old(X0) & ~quiet(X0))) [nnf transformation 2]
41. (? [X0] : (old(X0) | quiet(X0)) | funny(alice) | creative(alice)) & ((~funny(alice) & ~creative(alice)) | ! [X0] : (~old(X0) & ~quiet(X0))) [flattening 40]
42. (? [X0] : (old(X0) | quiet(X0)) | funny(alice) | creative(alice)) & ((~funny(alice) & ~creative(alice)) | ! [X1] : (~old(X1) & ~quiet(X1))) [rectify 41]
43. ? [X0] : (old(X0) | quiet(X0)) => (old(sK0) | quiet(sK0)) [choice axiom]
44. ((old(sK0) | quiet(sK0)) | funny(alice) | creative(alice)) & ((~funny(alice) & ~creative(alice)) | ! [X1] : (~old(X1) & ~quiet(X1))) [skolemisation 42,43]
45. ! [X0] : (((strong(X0) | happy(X0)) | ~old(X0)) & (old(X0) | (~strong(X0) & ~happy(X0)))) [nnf transformation 3]
46. ! [X0] : ((strong(X0) | happy(X0) | ~old(X0)) & (old(X0) | (~strong(X0) & ~happy(X0)))) [flattening 45]
73. ((~humble(alice) | ~tall(alice)) & (humble(alice) | tall(alice))) | ! [X0] : funny(X0) [nnf transformation 37]
79. ~old(X0) | ~tall(X0) [cnf transformation 39]
81. ~creative(alice) | ~old(X1) [cnf transformation 44]
83. ~funny(alice) | ~old(X1) [cnf transformation 44]
86. ~strong(X0) | old(X0) [cnf transformation 46]
88. ~tall(X0) | strong(X0) | creative(X0) [cnf transformation 29]
120. humble(alice) | tall(alice) | funny(X0) [cnf transformation 73]
130. old(lucy) [cnf transformation 22]
134. ~humble(alice) [cnf transformation 25]
136. 1 <=> creative(alice) [avatar definition]
137. ~creative(alice) <- (~1) [avatar component clause 136]
140. 2 <=> funny(alice) [avatar definition]
141. ~funny(alice) <- (~2) [avatar component clause 140]
153. 5 <=> ! [X1] : ~old(X1) [avatar definition]
154. ~old(X1) <- (5) [avatar component clause 153]
155. 5 | ~2 [avatar split clause 83,140,153]
160. 5 | ~1 [avatar split clause 81,136,153]
284. 34 <=> ! [X0] : funny(X0) [avatar definition]
285. funny(X0) <- (34) [avatar component clause 284]
287. 35 <=> tall(alice) [avatar definition]
288. tall(alice) <- (35) [avatar component clause 287]
291. 36 <=> humble(alice) [avatar definition]
295. 34 | 35 | 36 [avatar split clause 120,291,287,284]
321. ~36 [avatar split clause 134,291]
322. $false <- (~2, 34) [subsumption resolution 141,285]
323. 2 | ~34 [avatar contradiction clause 322]
324. $false <- (5) [resolution 154,130]
325. ~5 [avatar contradiction clause 324]
344. strong(alice) | creative(alice) <- (35) [resolution 88,288]
345. strong(alice) <- (~1, 35) [subsumption resolution 344,137]
346. old(alice) <- (~1, 35) [resolution 345,86]
359. ~tall(alice) <- (~1, 35) [resolution 346,79]
360. $false <- (~1, 35) [subsumption resolution 359,288]
361. 1 | ~35 [avatar contradiction clause 360]
362. $false [avatar sat refutation 155,160,295,321,323,325,361]
% SZS output end Proof for 8223421753916857493542309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either generous or not humble then someone is both not wise and curious and vice versa. Everyone who is not creative or not rich is not happy or wise and vice versa. If someone is not old or not patient then someone is either tall or not happy and vice versa. Everyone who is both not generous and generous is not creative or not curious. If paul is not rich or quiet then someone is funny or not wise. Everyone who is not curious is not strong. Everyone who is tall or not calm is brave. If john is both not strong and not happy then someone is both kind and tall and vice versa. If someone is generous or old then someone is brave or not brave and vice versa. Everyone who is not creative or curious is either not curious or funny. If lucy is not happy or generous then someone is either not kind or rich. If john is either not funny or calm then paul is either wise or happy and vice versa. Everyone who is rich is both rich and calm and vice versa. If lucy is not kind then lucy is both wise and not calm and vice versa. Everyone who is both not happy and tall is not patient and vice versa. If paul is both strong and rich then john is not old. Lucy is kind or not old. Someone is happy or not curious. Someone is either tall or humble. Someone is not kind or wise. John is either curious or not calm. Someone is either not old or generous. Paul is both kind and not tall. Someone is brave. | Fred is not humble. | neutral | (((generous(fred)<~>~humble(fred)))<=>(?[X]:((~wise(X)&curious(X)))))&
(![X]:((~creative(X)|~rich(X))<=>(~happy(X)|wise(X))))&
((?[X]:((~old(X)|~patient(X))))<=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:((~generous(X)&generous(X))=>(~creative(X)|~curious(X))))&
(((~rich(paul)|quiet(paul)))=>(?[X]:((funny(X)|~wise(X)))))&
(![X]:(~curious(X)=>~strong(X)))&
(![X]:((tall(X)|~calm(X))=>brave(X)))&
(((~strong(john)&~happy(john)))<=>(?[X]:((kind(X)&tall(X)))))&
((?[X]:((generous(X)|old(X))))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~creative(X)|curious(X))=>(~curious(X)<~>funny(X))))&
(((~happy(lucy)|generous(lucy)))=>(?[X]:((~kind(X)<~>rich(X)))))&
(((~funny(john)<~>calm(john)))<=>((wise(paul)<~>happy(paul))))&
(![X]:(rich(X)<=>(rich(X)&calm(X))))&
((~kind(lucy))<=>((wise(lucy)&~calm(lucy))))&
(![X]:((~happy(X)&tall(X))<=>~patient(X)))&
(((strong(paul)&rich(paul)))=>(~old(john)))&
((kind(lucy)|~old(lucy)))&
(?[X]:((happy(X)|~curious(X))))&
(?[X]:((tall(X)<~>humble(X))))&
(?[X]:((~kind(X)|wise(X))))&
((curious(john)<~>~calm(john)))&
(?[X]:((~old(X)<~>generous(X))))&
((kind(paul)&~tall(paul)))&
(?[X]:(brave(X))) | ~humble(fred) | [] | null | 0 |
If susan is not happy or not brave then alice is not generous.
If fred is not rich or generous then fred is both tall and brave and vice versa.
Everyone who is both funny and kind is both curious and not funny and vice versa.
Everyone who is rich or brave is either not old or not tall.
If someone is not old or creative then paul is either not kind or not strong.
Everyone who is not patient or not kind is not patient.
Everyone who is not creative is not wise.
If mary is either not quiet or brave then someone is either generous or not creative and vice versa.
Everyone who is both not brave and calm is both generous and kind and vice versa.
If fred is humble or tall then lucy is not calm or wise.
Everyone who is both tall and kind is tall or not generous.
Everyone who is either happy or not rich is either curious or not curious.
If susan is not old or tall then someone is strong and vice versa.
If someone is not happy then someone is both happy and not funny.
Everyone who is rich is curious and vice versa.
Everyone who is not rich or not curious is both creative and not creative and vice versa.
Someone is not brave.
Someone is not quiet.
Someone is curious or old.
John is either not generous or quiet.
Fred is both not generous and not humble. | Alice is brave. | neutral | (((~happy(susan)|~brave(susan)))=>(~generous(alice)))&
(((~rich(fred)|generous(fred)))<=>((tall(fred)&brave(fred))))&
(![X]:((funny(X)&kind(X))<=>(curious(X)&~funny(X))))&
(![X]:((rich(X)|brave(X))=>(~old(X)<~>~tall(X))))&
((?[X]:((~old(X)|creative(X))))=>((~kind(paul)<~>~strong(paul))))&
(![X]:((~patient(X)|~kind(X))=>~patient(X)))&
(![X]:(~creative(X)=>~wise(X)))&
(((~quiet(mary)<~>brave(mary)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:((~brave(X)&calm(X))<=>(generous(X)&kind(X))))&
(((humble(fred)|tall(fred)))=>((~calm(lucy)|wise(lucy))))&
(![X]:((tall(X)&kind(X))=>(tall(X)|~generous(X))))&
(![X]:((happy(X)<~>~rich(X))=>(curious(X)<~>~curious(X))))&
(((~old(susan)|tall(susan)))<=>(?[X]:(strong(X))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:(rich(X)<=>curious(X)))&
(![X]:((~rich(X)|~curious(X))<=>(creative(X)&~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((curious(X)|old(X))))&
((~generous(john)<~>quiet(john)))&
((~generous(fred)&~humble(fred))) | brave(alice) | [] | null | 0 |
Everyone who is brave is both calm and old and vice versa.
Everyone who is not tall or humble is not generous or wise.
Everyone who is both humble and quiet is not brave.
Everyone who is either not quiet or not happy is both not humble and wise and vice versa.
If lucy is not quiet then susan is either funny or not creative and vice versa.
If someone is both not quiet and patient then susan is not calm or tall.
If fred is not creative or strong then someone is old and vice versa.
If lucy is either funny or not rich then john is not creative and vice versa.
Everyone who is not brave is not humble or happy.
Everyone who is not strong or creative is creative.
If fred is either not patient or not calm then paul is not funny.
Everyone who is strong is both humble and patient.
If paul is happy then susan is happy or old and vice versa.
Everyone who is both kind and not happy is both not curious and not strong.
Everyone who is both old and rich is creative and vice versa.
If someone is rich then alice is wise.
Someone is not kind.
Alice is both not calm and not wise.
Someone is both happy and not kind.
Susan is not brave or old.
Someone is not wise.
Someone is either creative or not happy.
Someone is either curious or happy. | Alice is happy. | entailment | (![X]:(brave(X)<=>(calm(X)&old(X))))&
(![X]:((~tall(X)|humble(X))=>(~generous(X)|wise(X))))&
(![X]:((humble(X)&quiet(X))=>~brave(X)))&
(![X]:((~quiet(X)<~>~happy(X))<=>(~humble(X)&wise(X))))&
((~quiet(lucy))<=>((funny(susan)<~>~creative(susan))))&
((?[X]:((~quiet(X)&patient(X))))=>((~calm(susan)|tall(susan))))&
(((~creative(fred)|strong(fred)))<=>(?[X]:(old(X))))&
(((funny(lucy)<~>~rich(lucy)))<=>(~creative(john)))&
(![X]:(~brave(X)=>(~humble(X)|happy(X))))&
(![X]:((~strong(X)|creative(X))=>creative(X)))&
(((~patient(fred)<~>~calm(fred)))=>(~funny(paul)))&
(![X]:(strong(X)=>(humble(X)&patient(X))))&
((happy(paul))<=>((happy(susan)|old(susan))))&
(![X]:((kind(X)&~happy(X))=>(~curious(X)&~strong(X))))&
(![X]:((old(X)&rich(X))<=>creative(X)))&
((?[X]:(rich(X)))=>(wise(alice)))&
(?[X]:(~kind(X)))&
((~calm(alice)&~wise(alice)))&
(?[X]:((happy(X)&~kind(X))))&
((~brave(susan)|old(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((creative(X)<~>~happy(X))))&
(?[X]:((curious(X)<~>happy(X)))) | happy(alice) | [
"p0",
"p8",
"p9",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 159415695994819190264030
% SZS output start Proof for 159415695994819190264030
1. ! [X0] : (brave(X0) <=> (old(X0) & calm(X0))) [input p0]
9. ! [X0] : (~brave(X0) => (happy(X0) | ~humble(X0))) [input p8]
10. ! [X0] : ((creative(X0) | ~strong(X0)) => creative(X0)) [input p9]
12. ! [X0] : (strong(X0) => (patient(X0) & humble(X0))) [input p11]
15. ! [X0] : ((rich(X0) & old(X0)) <=> creative(X0)) [input p14]
16. ? [X0] : rich(X0) => wise(alice) [input p15]
18. ~wise(alice) & ~calm(alice) [input p17]
24. ~happy(alice) [input hypothesis]
32. ! [X0] : ((happy(X0) | ~humble(X0)) | brave(X0)) [ennf transformation 9]
33. ! [X0] : (happy(X0) | ~humble(X0) | brave(X0)) [flattening 32]
34. ! [X0] : (creative(X0) | (~creative(X0) & strong(X0))) [ennf transformation 10]
36. ! [X0] : ((patient(X0) & humble(X0)) | ~strong(X0)) [ennf transformation 12]
37. wise(alice) | ! [X0] : ~rich(X0) [ennf transformation 16]
38. ! [X0] : ((brave(X0) | (~old(X0) | ~calm(X0))) & ((old(X0) & calm(X0)) | ~brave(X0))) [nnf transformation 1]
39. ! [X0] : ((brave(X0) | ~old(X0) | ~calm(X0)) & ((old(X0) & calm(X0)) | ~brave(X0))) [flattening 38]
52. ! [X0] : (((rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | (~rich(X0) | ~old(X0)))) [nnf transformation 15]
53. ! [X0] : (((rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | ~rich(X0) | ~old(X0))) [flattening 52]
64. ~brave(X0) | calm(X0) [cnf transformation 39]
85. ~humble(X0) | happy(X0) | brave(X0) [cnf transformation 33]
86. strong(X0) | creative(X0) [cnf transformation 34]
90. ~strong(X0) | humble(X0) [cnf transformation 36]
97. ~creative(X0) | rich(X0) [cnf transformation 53]
98. wise(alice) | ~rich(X0) [cnf transformation 37]
99. ~calm(alice) [cnf transformation 18]
100. ~wise(alice) [cnf transformation 18]
108. ~happy(alice) [cnf transformation 24]
189. 17 <=> ! [X0] : ~rich(X0) [avatar definition]
190. ~rich(X0) <- (17) [avatar component clause 189]
192. 18 <=> wise(alice) [avatar definition]
195. 17 | 18 [avatar split clause 98,192,189]
196. ~18 [avatar split clause 100,192]
218. creative(X0) | humble(X0) [resolution 90,86]
229. humble(X0) | rich(X0) [resolution 218,97]
235. humble(X0) <- (17) [subsumption resolution 229,190]
254. happy(X0) | brave(X0) <- (17) [resolution 85,235]
288. brave(alice) <- (17) [resolution 254,108]
333. calm(alice) <- (17) [resolution 288,64]
334. $false <- (17) [subsumption resolution 333,99]
335. ~17 [avatar contradiction clause 334]
336. $false [avatar sat refutation 195,196,335]
% SZS output end Proof for 159415695994819190264030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not patient or not old then susan is both not brave and not kind.
Everyone who is both not funny and not rich is both happy and funny.
Everyone who is not wise is both not tall and not rich.
Everyone who is both calm and creative is brave and vice versa.
Everyone who is both not brave and curious is both curious and not quiet.
Everyone who is quiet is wise or not patient and vice versa.
Everyone who is tall is not generous and vice versa.
Everyone who is both brave and not generous is both not curious and funny.
If john is not old or not funny then mary is both wise and not wise.
If someone is either rich or not calm then susan is not creative or not tall.
Everyone who is not tall is quiet or not patient and vice versa.
If mary is not old then someone is either not strong or calm.
Everyone who is both not strong and brave is both generous and creative and vice versa.
Everyone who is not generous is both not patient and humble and vice versa.
If paul is not rich or old then fred is either strong or wise.
Everyone who is either not strong or quiet is not creative.
Paul is creative or patient.
John is both not kind and not strong.
Someone is either brave or humble.
Someone is either humble or strong.
John is not kind.
John is either not brave or kind.
Susan is either not creative or creative. | Susan is humble. | neutral | (((~patient(lucy)<~>~old(lucy)))=>((~brave(susan)&~kind(susan))))&
(![X]:((~funny(X)&~rich(X))=>(happy(X)&funny(X))))&
(![X]:(~wise(X)=>(~tall(X)&~rich(X))))&
(![X]:((calm(X)&creative(X))<=>brave(X)))&
(![X]:((~brave(X)&curious(X))=>(curious(X)&~quiet(X))))&
(![X]:(quiet(X)<=>(wise(X)|~patient(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:((brave(X)&~generous(X))=>(~curious(X)&funny(X))))&
(((~old(john)|~funny(john)))=>((wise(mary)&~wise(mary))))&
((?[X]:((rich(X)<~>~calm(X))))=>((~creative(susan)|~tall(susan))))&
(![X]:(~tall(X)<=>(quiet(X)|~patient(X))))&
((~old(mary))=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((~strong(X)&brave(X))<=>(generous(X)&creative(X))))&
(![X]:(~generous(X)<=>(~patient(X)&humble(X))))&
(((~rich(paul)|old(paul)))=>((strong(fred)<~>wise(fred))))&
(![X]:((~strong(X)<~>quiet(X))=>~creative(X)))&
((creative(paul)|patient(paul)))&
((~kind(john)&~strong(john)))&
(?[X]:((brave(X)<~>humble(X))))&
(?[X]:((humble(X)<~>strong(X))))&
(~kind(john))&
((~brave(john)<~>kind(john)))&
((~creative(susan)<~>creative(susan))) | humble(susan) | [] | null | 0 |
If someone is both strong and happy then paul is either not funny or kind and vice versa.
If someone is both patient and not happy then lucy is curious or humble and vice versa.
Everyone who is not quiet or happy is either not rich or brave.
Everyone who is both not happy and not generous is generous or not generous and vice versa.
If someone is either not generous or not tall then alice is either creative or not quiet.
Everyone who is not quiet or humble is either not quiet or calm and vice versa.
Everyone who is either wise or not humble is either not generous or wise and vice versa.
Everyone who is not old or generous is either tall or wise and vice versa.
Everyone who is not generous or generous is not old and vice versa.
Everyone who is either patient or not kind is either quiet or not wise and vice versa.
Everyone who is either generous or calm is either not kind or quiet and vice versa.
If paul is either not rich or happy then someone is both not quiet and quiet.
Everyone who is either not patient or patient is both not old and not quiet.
Everyone who is not patient is either not creative or funny and vice versa.
If susan is either not happy or kind then susan is either not tall or not old and vice versa.
Susan is brave or strong.
Susan is both funny and not old.
Someone is not quiet or not calm.
Fred is both not creative and not rich.
Paul is both not tall and not quiet.
Someone is not wise. | Paul is not curious. | neutral | ((?[X]:((strong(X)&happy(X))))<=>((~funny(paul)<~>kind(paul))))&
((?[X]:((patient(X)&~happy(X))))<=>((curious(lucy)|humble(lucy))))&
(![X]:((~quiet(X)|happy(X))=>(~rich(X)<~>brave(X))))&
(![X]:((~happy(X)&~generous(X))<=>(generous(X)|~generous(X))))&
((?[X]:((~generous(X)<~>~tall(X))))=>((creative(alice)<~>~quiet(alice))))&
(![X]:((~quiet(X)|humble(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~old(X)|generous(X))<=>(tall(X)<~>wise(X))))&
(![X]:((~generous(X)|generous(X))<=>~old(X)))&
(![X]:((patient(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~kind(X)<~>quiet(X))))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((~patient(X)<~>patient(X))=>(~old(X)&~quiet(X))))&
(![X]:(~patient(X)<=>(~creative(X)<~>funny(X))))&
(((~happy(susan)<~>kind(susan)))<=>((~tall(susan)<~>~old(susan))))&
((brave(susan)|strong(susan)))&
((funny(susan)&~old(susan)))&
(?[X]:((~quiet(X)|~calm(X))))&
((~creative(fred)&~rich(fred)))&
((~tall(paul)&~quiet(paul)))&
(?[X]:(~wise(X))) | ~curious(paul) | [] | null | 0 |
Everyone who is either generous or not kind is not wise or curious.
Everyone who is happy or strong is either creative or not patient and vice versa.
If john is either not brave or wise then fred is either not creative or not tall and vice versa.
If someone is not strong or not happy then someone is either creative or not happy.
Everyone who is calm or not happy is not generous and vice versa.
If someone is not curious or not strong then someone is either not patient or not brave.
Everyone who is either not kind or not happy is not funny.
If someone is rich then someone is either quiet or old and vice versa.
Everyone who is tall is either not old or not quiet and vice versa.
Everyone who is both wise and not patient is both kind and not funny.
Everyone who is not wise or not brave is not kind or kind and vice versa.
If fred is humble then alice is both not tall and curious.
Everyone who is not kind or kind is either not happy or tall.
If susan is either not generous or funny then someone is both not kind and not creative.
Everyone who is either not patient or not tall is patient.
If alice is not creative or not strong then someone is not tall and vice versa.
Fred is not brave or calm.
John is both calm and curious.
Someone is both not quiet and tall.
Susan is both not curious and not old.
Someone is happy.
Someone is curious.
Fred is not quiet or patient.
John is brave. | Alice is kind. | neutral | (![X]:((generous(X)<~>~kind(X))=>(~wise(X)|curious(X))))&
(![X]:((happy(X)|strong(X))<=>(creative(X)<~>~patient(X))))&
(((~brave(john)<~>wise(john)))<=>((~creative(fred)<~>~tall(fred))))&
((?[X]:((~strong(X)|~happy(X))))=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((calm(X)|~happy(X))<=>~generous(X)))&
((?[X]:((~curious(X)|~strong(X))))=>(?[X]:((~patient(X)<~>~brave(X)))))&
(![X]:((~kind(X)<~>~happy(X))=>~funny(X)))&
((?[X]:(rich(X)))<=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:(tall(X)<=>(~old(X)<~>~quiet(X))))&
(![X]:((wise(X)&~patient(X))=>(kind(X)&~funny(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~kind(X)|kind(X))))&
((humble(fred))=>((~tall(alice)&curious(alice))))&
(![X]:((~kind(X)|kind(X))=>(~happy(X)<~>tall(X))))&
(((~generous(susan)<~>funny(susan)))=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:((~patient(X)<~>~tall(X))=>patient(X)))&
(((~creative(alice)|~strong(alice)))<=>(?[X]:(~tall(X))))&
((~brave(fred)|calm(fred)))&
((calm(john)&curious(john)))&
(?[X]:((~quiet(X)&tall(X))))&
((~curious(susan)&~old(susan)))&
(?[X]:(happy(X)))&
(?[X]:(curious(X)))&
((~quiet(fred)|patient(fred)))&
(brave(john)) | kind(alice) | [] | null | 0 |
If mary is creative or kind then paul is rich.
Everyone who is both happy and kind is not quiet and vice versa.
Everyone who is old is either old or quiet and vice versa.
If fred is both strong and not rich then lucy is both not humble and tall and vice versa.
Everyone who is not humble or strong is both not happy and not curious and vice versa.
If paul is not old or funny then someone is not wise and vice versa.
Everyone who is not funny or curious is patient and vice versa.
If someone is either humble or not curious then someone is not kind and vice versa.
If someone is both funny and not curious then susan is either not strong or not old and vice versa.
If someone is brave or patient then someone is both funny and wise and vice versa.
Everyone who is creative is rich.
Everyone who is not strong is generous.
If alice is not patient then paul is either not rich or not kind and vice versa.
If someone is not wise then paul is patient or not funny and vice versa.
If john is not rich or quiet then lucy is either not brave or not tall and vice versa.
Everyone who is not patient or happy is calm or not quiet and vice versa.
Someone is humble or not generous.
Alice is either rich or wise.
Someone is not brave or creative.
Someone is either not wise or not kind.
Lucy is either calm or not funny.
Fred is either tall or not old. | Mary is not old. | neutral | (((creative(mary)|kind(mary)))=>(rich(paul)))&
(![X]:((happy(X)&kind(X))<=>~quiet(X)))&
(![X]:(old(X)<=>(old(X)<~>quiet(X))))&
(((strong(fred)&~rich(fred)))<=>((~humble(lucy)&tall(lucy))))&
(![X]:((~humble(X)|strong(X))<=>(~happy(X)&~curious(X))))&
(((~old(paul)|funny(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|curious(X))<=>patient(X)))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((funny(X)&~curious(X))))<=>((~strong(susan)<~>~old(susan))))&
((?[X]:((brave(X)|patient(X))))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(~strong(X)=>generous(X)))&
((~patient(alice))<=>((~rich(paul)<~>~kind(paul))))&
((?[X]:(~wise(X)))<=>((patient(paul)|~funny(paul))))&
(((~rich(john)|quiet(john)))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:((~patient(X)|happy(X))<=>(calm(X)|~quiet(X))))&
(?[X]:((humble(X)|~generous(X))))&
((rich(alice)<~>wise(alice)))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((~wise(X)<~>~kind(X))))&
((calm(lucy)<~>~funny(lucy)))&
((tall(fred)<~>~old(fred))) | ~old(mary) | [] | null | 0 |
Everyone who is kind or not happy is either not kind or not old.
If someone is not curious or rich then fred is either humble or not creative.
If someone is humble then someone is not generous and vice versa.
If mary is both not tall and curious then someone is both wise and tall and vice versa.
Everyone who is not happy or curious is either not creative or not funny and vice versa.
Everyone who is both not quiet and not old is both not quiet and not wise and vice versa.
Everyone who is strong is not humble or wise and vice versa.
Everyone who is not brave is both quiet and wise.
If someone is either creative or rich then someone is not brave or generous.
Everyone who is both quiet and humble is either not wise or not strong and vice versa.
If someone is both not brave and not wise then someone is strong or creative.
Everyone who is either not creative or not curious is funny and vice versa.
Everyone who is not happy is brave.
If someone is curious then someone is either not brave or old and vice versa.
Everyone who is both not wise and tall is either curious or not humble.
If someone is not tall then someone is both not happy and not calm and vice versa.
Mary is strong or not rich.
Alice is not calm.
Paul is not wise or rich.
Someone is both rich and generous.
Susan is rich or not rich.
Alice is both creative and tall.
Someone is brave or not curious.
Someone is not quiet. | Paul is not creative. | neutral | (![X]:((kind(X)|~happy(X))=>(~kind(X)<~>~old(X))))&
((?[X]:((~curious(X)|rich(X))))=>((humble(fred)<~>~creative(fred))))&
((?[X]:(humble(X)))<=>(?[X]:(~generous(X))))&
(((~tall(mary)&curious(mary)))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:((~happy(X)|curious(X))<=>(~creative(X)<~>~funny(X))))&
(![X]:((~quiet(X)&~old(X))<=>(~quiet(X)&~wise(X))))&
(![X]:(strong(X)<=>(~humble(X)|wise(X))))&
(![X]:(~brave(X)=>(quiet(X)&wise(X))))&
((?[X]:((creative(X)<~>rich(X))))=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~wise(X)<~>~strong(X))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((~creative(X)<~>~curious(X))<=>funny(X)))&
(![X]:(~happy(X)=>brave(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~wise(X)&tall(X))=>(curious(X)<~>~humble(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~calm(X)))))&
((strong(mary)|~rich(mary)))&
(~calm(alice))&
((~wise(paul)|rich(paul)))&
(?[X]:((rich(X)&generous(X))))&
((rich(susan)|~rich(susan)))&
((creative(alice)&tall(alice)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:(~quiet(X))) | ~creative(paul) | [] | null | 0 |
Everyone who is not old or generous is patient.
If someone is not patient then fred is both not old and not tall and vice versa.
Everyone who is either old or generous is both creative and brave.
Everyone who is both quiet and curious is not patient or not brave.
Everyone who is not quiet or not creative is either curious or not rich.
If susan is both not humble and not old then mary is not happy and vice versa.
Everyone who is both not funny and not old is humble and vice versa.
If mary is either not strong or happy then someone is both not quiet and not humble and vice versa.
Everyone who is both happy and not patient is not generous or not patient and vice versa.
Everyone who is both not creative and not patient is not happy or strong and vice versa.
Everyone who is either not tall or rich is either patient or old and vice versa.
Everyone who is both curious and patient is not happy or funny and vice versa.
Everyone who is happy or not generous is not creative and vice versa.
If mary is creative then someone is either rich or not humble and vice versa.
If mary is both not curious and creative then lucy is either not generous or not kind.
If someone is not funny or not creative then someone is either tall or old.
Someone is not generous or not calm.
Paul is old or funny.
Someone is either wise or not strong.
Fred is both happy and kind.
Someone is not brave or wise.
Fred is either not wise or curious. | Mary is not generous. | contradiction | (![X]:((~old(X)|generous(X))=>patient(X)))&
((?[X]:(~patient(X)))<=>((~old(fred)&~tall(fred))))&
(![X]:((old(X)<~>generous(X))=>(creative(X)&brave(X))))&
(![X]:((quiet(X)&curious(X))=>(~patient(X)|~brave(X))))&
(![X]:((~quiet(X)|~creative(X))=>(curious(X)<~>~rich(X))))&
(((~humble(susan)&~old(susan)))<=>(~happy(mary)))&
(![X]:((~funny(X)&~old(X))<=>humble(X)))&
(((~strong(mary)<~>happy(mary)))<=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:((happy(X)&~patient(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~creative(X)&~patient(X))<=>(~happy(X)|strong(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(patient(X)<~>old(X))))&
(![X]:((curious(X)&patient(X))<=>(~happy(X)|funny(X))))&
(![X]:((happy(X)|~generous(X))<=>~creative(X)))&
((creative(mary))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~curious(mary)&creative(mary)))=>((~generous(lucy)<~>~kind(lucy))))&
((?[X]:((~funny(X)|~creative(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(?[X]:((~generous(X)|~calm(X))))&
((old(paul)|funny(paul)))&
(?[X]:((wise(X)<~>~strong(X))))&
((happy(fred)&kind(fred)))&
(?[X]:((~brave(X)|wise(X))))&
((~wise(fred)<~>curious(fred))) | ~generous(mary) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2605705196863590822870286
% SZS output start Proof for 2605705196863590822870286
1. ! [X0] : ((generous(X0) | ~old(X0)) => patient(X0)) [input p0]
2. ? [X0] : ~patient(X0) <=> (~tall(fred) & ~old(fred)) [input p1]
3. ! [X0] : ((old(X0) <~> generous(X0)) => (brave(X0) & creative(X0))) [input p2]
9. ! [X0] : ((~patient(X0) & happy(X0)) <=> (~patient(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (strong(X0) | ~happy(X0))) [input p9]
13. ! [X0] : ((~generous(X0) | happy(X0)) <=> ~creative(X0)) [input p12]
23. ~generous(mary) [input hypothesis]
26. ! [X0] : (patient(X0) | (~generous(X0) & old(X0))) [ennf transformation 1]
27. ! [X0] : ((brave(X0) & creative(X0)) | (old(X0) <=> generous(X0))) [ennf transformation 3]
34. (? [X0] : ~patient(X0) | (tall(fred) | old(fred))) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [nnf transformation 2]
35. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [flattening 34]
36. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [rectify 35]
37. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
38. (~patient(sK0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [skolemisation 36,37]
39. ! [X0] : ((brave(X0) & creative(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 27]
49. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & ((~patient(X0) | ~generous(X0)) | (patient(X0) | ~happy(X0)))) [nnf transformation 9]
50. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & (~patient(X0) | ~generous(X0) | patient(X0) | ~happy(X0))) [flattening 49]
51. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | (patient(X0) | creative(X0)))) [nnf transformation 10]
52. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | patient(X0) | creative(X0))) [flattening 51]
56. ! [X0] : (((~generous(X0) | happy(X0)) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 13]
57. ! [X0] : ((~generous(X0) | happy(X0) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [flattening 56]
73. patient(X0) | old(X0) [cnf transformation 26]
74. ~generous(X0) | patient(X0) [cnf transformation 26]
75. ~old(fred) | patient(X1) [cnf transformation 38]
76. ~tall(fred) | patient(X1) [cnf transformation 38]
77. ~patient(sK0) | tall(fred) | old(fred) [cnf transformation 38]
78. ~old(X0) | generous(X0) | creative(X0) [cnf transformation 39]
101. happy(X0) | patient(X0) [cnf transformation 50]
102. ~patient(X0) | generous(X0) [cnf transformation 50]
107. ~patient(X0) | happy(X0) [cnf transformation 52]
122. ~creative(X0) | ~happy(X0) [cnf transformation 57]
143. ~generous(mary) [cnf transformation 23]
145. 1 <=> old(fred) [avatar definition]
149. 2 <=> tall(fred) [avatar definition]
153. 3 <=> patient(sK0) [avatar definition]
155. ~patient(sK0) <- (~3) [avatar component clause 153]
156. 1 | 2 | ~3 [avatar split clause 77,153,149,145]
158. 4 <=> ! [X1] : patient(X1) [avatar definition]
159. patient(X1) <- (4) [avatar component clause 158]
160. 4 | ~2 [avatar split clause 76,149,158]
161. 4 | ~1 [avatar split clause 75,145,158]
198. happy(X0) [subsumption resolution 107,101]
205. ~creative(X0) [subsumption resolution 122,198]
265. old(sK0) <- (~3) [resolution 73,155]
280. generous(sK0) | creative(sK0) <- (~3) [resolution 78,265]
282. generous(sK0) <- (~3) [subsumption resolution 280,205]
300. patient(sK0) <- (~3) [resolution 282,74]
301. $false <- (~3) [subsumption resolution 300,155]
302. 3 [avatar contradiction clause 301]
303. generous(X0) <- (4) [resolution 159,102]
304. $false <- (4) [resolution 303,143]
308. ~4 [avatar contradiction clause 304]
310. $false [avatar sat refutation 156,160,161,302,308]
% SZS output end Proof for 2605705196863590822870286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or creative is rich or not humble and vice versa.
Everyone who is not happy is humble.
If mary is either not rich or not humble then john is both rich and tall and vice versa.
If someone is generous then someone is either creative or not brave and vice versa.
Everyone who is not funny is either not strong or funny and vice versa.
If susan is both not creative and wise then someone is not quiet or not funny.
If alice is happy or old then mary is patient and vice versa.
Everyone who is not strong is either not strong or not quiet and vice versa.
Everyone who is both not brave and not tall is generous and vice versa.
If susan is both not old and rich then mary is either not wise or not generous.
Everyone who is either not creative or wise is creative and vice versa.
If someone is not funny or patient then lucy is old or tall.
Everyone who is both quiet and rich is humble or rich.
If someone is happy or not wise then john is both wise and not creative.
Everyone who is not rich or not patient is brave or not generous.
Fred is both tall and funny.
Someone is both not generous and not creative.
Someone is both not strong and not old.
Fred is kind or tall.
Someone is generous.
Susan is not funny. | Lucy is not quiet. | contradiction | (![X]:((generous(X)|creative(X))<=>(rich(X)|~humble(X))))&
(![X]:(~happy(X)=>humble(X)))&
(((~rich(mary)<~>~humble(mary)))<=>((rich(john)&tall(john))))&
((?[X]:(generous(X)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:(~funny(X)<=>(~strong(X)<~>funny(X))))&
(((~creative(susan)&wise(susan)))=>(?[X]:((~quiet(X)|~funny(X)))))&
(((happy(alice)|old(alice)))<=>(patient(mary)))&
(![X]:(~strong(X)<=>(~strong(X)<~>~quiet(X))))&
(![X]:((~brave(X)&~tall(X))<=>generous(X)))&
(((~old(susan)&rich(susan)))=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>wise(X))<=>creative(X)))&
((?[X]:((~funny(X)|patient(X))))=>((old(lucy)|tall(lucy))))&
(![X]:((quiet(X)&rich(X))=>(humble(X)|rich(X))))&
((?[X]:((happy(X)|~wise(X))))=>((wise(john)&~creative(john))))&
(![X]:((~rich(X)|~patient(X))=>(brave(X)|~generous(X))))&
((tall(fred)&funny(fred)))&
(?[X]:((~generous(X)&~creative(X))))&
(?[X]:((~strong(X)&~old(X))))&
((kind(fred)|tall(fred)))&
(?[X]:(generous(X)))&
(~funny(susan)) | ~quiet(lucy) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1333993720317098238625034
% SZS output start Proof for 1333993720317098238625034
5. ! [X0] : (~funny(X0) <=> (~strong(X0) <~> funny(X0))) [input p4]
8. ! [X0] : (~strong(X0) <=> (~strong(X0) <~> ~quiet(X0))) [input p7]
22. ~quiet(lucy) [input hypothesis]
46. ! [X0] : ((~funny(X0) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) & (((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | funny(X0))) [nnf transformation 5]
51. ! [X0] : ((~strong(X0) | ((~strong(X0) | quiet(X0)) & (~quiet(X0) | strong(X0)))) & (((quiet(X0) | strong(X0)) & (~quiet(X0) | ~strong(X0))) | strong(X0))) [nnf transformation 8]
77. funny(X0) | ~strong(X0) | funny(X0) [cnf transformation 46]
80. ~funny(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 46]
86. quiet(X0) | strong(X0) | strong(X0) [cnf transformation 51]
115. ~quiet(lucy) [cnf transformation 22]
118. quiet(X0) | strong(X0) [duplicate literal removal 86]
120. funny(X0) | ~strong(X0) [duplicate literal removal 77]
121. ~funny(X0) | ~strong(X0) [duplicate literal removal 80]
169. ~strong(X0) [subsumption resolution 120,121]
202. quiet(X0) [subsumption resolution 118,169]
248. $false [subsumption resolution 115,202]
% SZS output end Proof for 1333993720317098238625034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is calm or not brave then paul is kind. If john is humble then someone is kind or not rich and vice versa. Everyone who is both not rich and not funny is both calm and patient and vice versa. Everyone who is either not calm or humble is generous or not generous. Everyone who is either not quiet or funny is both not old and not patient and vice versa. If lucy is either not curious or humble then john is both brave and generous and vice versa. Everyone who is not happy is not rich. If someone is happy then someone is both not quiet and strong. Everyone who is both tall and rich is either funny or wise and vice versa. If someone is humble or rich then mary is not brave or curious. Everyone who is not wise is both not brave and happy and vice versa. Everyone who is both brave and not rich is both patient and creative and vice versa. Everyone who is not wise or not rich is both not strong and curious. If fred is both not curious and calm then paul is kind or not quiet and vice versa. If someone is not kind or not tall then paul is either brave or not old and vice versa. Everyone who is both curious and not kind is both not brave and brave and vice versa. Alice is both not patient and not kind. Someone is both not generous and not rich. Someone is not happy. Someone is quiet or calm. Someone is wise or rich. Fred is not old or not creative. Someone is either happy or creative. Lucy is curious or happy. | Fred is not happy. | neutral | (((calm(paul)|~brave(paul)))=>(kind(paul)))&
((humble(john))<=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:((~rich(X)&~funny(X))<=>(calm(X)&patient(X))))&
(![X]:((~calm(X)<~>humble(X))=>(generous(X)|~generous(X))))&
(![X]:((~quiet(X)<~>funny(X))<=>(~old(X)&~patient(X))))&
(((~curious(lucy)<~>humble(lucy)))<=>((brave(john)&generous(john))))&
(![X]:(~happy(X)=>~rich(X)))&
((?[X]:(happy(X)))=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:((tall(X)&rich(X))<=>(funny(X)<~>wise(X))))&
((?[X]:((humble(X)|rich(X))))=>((~brave(mary)|curious(mary))))&
(![X]:(~wise(X)<=>(~brave(X)&happy(X))))&
(![X]:((brave(X)&~rich(X))<=>(patient(X)&creative(X))))&
(![X]:((~wise(X)|~rich(X))=>(~strong(X)&curious(X))))&
(((~curious(fred)&calm(fred)))<=>((kind(paul)|~quiet(paul))))&
((?[X]:((~kind(X)|~tall(X))))<=>((brave(paul)<~>~old(paul))))&
(![X]:((curious(X)&~kind(X))<=>(~brave(X)&brave(X))))&
((~patient(alice)&~kind(alice)))&
(?[X]:((~generous(X)&~rich(X))))&
(?[X]:(~happy(X)))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:((wise(X)|rich(X))))&
((~old(fred)|~creative(fred)))&
(?[X]:((happy(X)<~>creative(X))))&
((curious(lucy)|happy(lucy))) | ~happy(fred) | [] | null | 0 |
If john is happy or old then someone is creative.
If mary is kind then someone is not generous or generous and vice versa.
Everyone who is quiet or not humble is both creative and strong and vice versa.
Everyone who is either not creative or strong is not quiet.
Everyone who is not old or tall is kind or not wise and vice versa.
Everyone who is either creative or kind is generous or not strong and vice versa.
If mary is generous or patient then someone is wise or not calm.
Everyone who is calm or not generous is not quiet.
If paul is not rich or calm then someone is either creative or not curious and vice versa.
If alice is rich or not patient then someone is both curious and quiet and vice versa.
Everyone who is either not calm or not happy is not humble and vice versa.
Everyone who is rich or not funny is either not wise or funny and vice versa.
If mary is quiet then someone is either not brave or creative and vice versa.
If someone is kind then paul is either generous or humble.
If someone is creative or old then someone is both not curious and kind.
If someone is both not quiet and not rich then someone is not humble or not brave and vice versa.
Someone is calm.
Fred is both brave and not curious.
John is not strong or not happy.
Someone is happy.
Someone is rich.
Someone is not old or not quiet.
Someone is both not rich and not funny.
Someone is not happy. | Paul is not strong. | neutral | (((happy(john)|old(john)))=>(?[X]:(creative(X))))&
((kind(mary))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((quiet(X)|~humble(X))<=>(creative(X)&strong(X))))&
(![X]:((~creative(X)<~>strong(X))=>~quiet(X)))&
(![X]:((~old(X)|tall(X))<=>(kind(X)|~wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>(generous(X)|~strong(X))))&
(((generous(mary)|patient(mary)))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:((calm(X)|~generous(X))=>~quiet(X)))&
(((~rich(paul)|calm(paul)))<=>(?[X]:((creative(X)<~>~curious(X)))))&
(((rich(alice)|~patient(alice)))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((~calm(X)<~>~happy(X))<=>~humble(X)))&
(![X]:((rich(X)|~funny(X))<=>(~wise(X)<~>funny(X))))&
((quiet(mary))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((?[X]:(kind(X)))=>((generous(paul)<~>humble(paul))))&
((?[X]:((creative(X)|old(X))))=>(?[X]:((~curious(X)&kind(X)))))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:((~humble(X)|~brave(X)))))&
(?[X]:(calm(X)))&
((brave(fred)&~curious(fred)))&
((~strong(john)|~happy(john)))&
(?[X]:(happy(X)))&
(?[X]:(rich(X)))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((~rich(X)&~funny(X))))&
(?[X]:(~happy(X))) | ~strong(paul) | [] | null | 0 |
Everyone who is quiet is rich or not patient.
If someone is quiet or tall then someone is either not humble or humble.
Everyone who is either not kind or kind is both not funny and happy and vice versa.
Everyone who is not calm or patient is both humble and strong.
Everyone who is quiet is not rich or not calm and vice versa.
Everyone who is not patient or strong is either generous or patient and vice versa.
Everyone who is curious or not rich is both not patient and calm.
Everyone who is not kind or not funny is strong and vice versa.
Everyone who is both not calm and not strong is both not strong and curious and vice versa.
Everyone who is both not wise and patient is both not wise and old.
If someone is both not quiet and not funny then someone is both calm and humble and vice versa.
If someone is strong then someone is tall and vice versa.
If lucy is both strong and old then lucy is either creative or calm and vice versa.
If paul is tall or not curious then alice is either not quiet or not brave and vice versa.
If someone is both creative and not quiet then susan is not wise or old and vice versa.
Everyone who is both not strong and not rich is old or rich and vice versa.
Someone is not humble or not wise.
Lucy is calm or not quiet.
Someone is brave.
Someone is either generous or kind.
Someone is both brave and strong.
Lucy is either rich or not patient.
John is not humble. | Susan is not humble. | entailment | (![X]:(quiet(X)=>(rich(X)|~patient(X))))&
((?[X]:((quiet(X)|tall(X))))=>(?[X]:((~humble(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>kind(X))<=>(~funny(X)&happy(X))))&
(![X]:((~calm(X)|patient(X))=>(humble(X)&strong(X))))&
(![X]:(quiet(X)<=>(~rich(X)|~calm(X))))&
(![X]:((~patient(X)|strong(X))<=>(generous(X)<~>patient(X))))&
(![X]:((curious(X)|~rich(X))=>(~patient(X)&calm(X))))&
(![X]:((~kind(X)|~funny(X))<=>strong(X)))&
(![X]:((~calm(X)&~strong(X))<=>(~strong(X)&curious(X))))&
(![X]:((~wise(X)&patient(X))=>(~wise(X)&old(X))))&
((?[X]:((~quiet(X)&~funny(X))))<=>(?[X]:((calm(X)&humble(X)))))&
((?[X]:(strong(X)))<=>(?[X]:(tall(X))))&
(((strong(lucy)&old(lucy)))<=>((creative(lucy)<~>calm(lucy))))&
(((tall(paul)|~curious(paul)))<=>((~quiet(alice)<~>~brave(alice))))&
((?[X]:((creative(X)&~quiet(X))))<=>((~wise(susan)|old(susan))))&
(![X]:((~strong(X)&~rich(X))<=>(old(X)|rich(X))))&
(?[X]:((~humble(X)|~wise(X))))&
((calm(lucy)|~quiet(lucy)))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)<~>kind(X))))&
(?[X]:((brave(X)&strong(X))))&
((rich(lucy)<~>~patient(lucy)))&
(~humble(john)) | ~humble(susan) | [
"p4",
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7897650466674416945139415
% SZS output start Proof for 7897650466674416945139415
5. ! [X0] : (quiet(X0) <=> (~calm(X0) | ~rich(X0))) [input p4]
7. ! [X0] : ((~rich(X0) | curious(X0)) => (calm(X0) & ~patient(X0))) [input p6]
11. ? [X0] : (~funny(X0) & ~quiet(X0)) <=> ? [X0] : (humble(X0) & calm(X0)) [input p10]
16. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (rich(X0) | old(X0))) [input p15]
24. humble(susan) [input hypothesis]
26. ? [X0] : (~funny(X0) & ~quiet(X0)) <=> ? [X1] : (humble(X1) & calm(X1)) [rectify 11]
32. ! [X0] : ((calm(X0) & ~patient(X0)) | (rich(X0) & ~curious(X0))) [ennf transformation 7]
41. ! [X0] : ((quiet(X0) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | ~quiet(X0))) [nnf transformation 5]
42. ! [X0] : ((quiet(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | ~quiet(X0))) [flattening 41]
49. (? [X0] : (~funny(X0) & ~quiet(X0)) | ! [X1] : (~humble(X1) | ~calm(X1))) & (? [X1] : (humble(X1) & calm(X1)) | ! [X0] : (funny(X0) | quiet(X0))) [nnf transformation 26]
50. (? [X0] : (~funny(X0) & ~quiet(X0)) | ! [X1] : (~humble(X1) | ~calm(X1))) & (? [X2] : (humble(X2) & calm(X2)) | ! [X3] : (funny(X3) | quiet(X3))) [rectify 49]
51. ? [X0] : (~funny(X0) & ~quiet(X0)) => (~funny(sK1) & ~quiet(sK1)) [choice axiom]
52. ? [X2] : (humble(X2) & calm(X2)) => (humble(sK2) & calm(sK2)) [choice axiom]
53. ((~funny(sK1) & ~quiet(sK1)) | ! [X1] : (~humble(X1) | ~calm(X1))) & ((humble(sK2) & calm(sK2)) | ! [X3] : (funny(X3) | quiet(X3))) [skolemisation 50,52,51]
68. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (rich(X0) | strong(X0)))) [nnf transformation 16]
69. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | rich(X0) | strong(X0))) [flattening 68]
96. rich(X0) | quiet(X0) [cnf transformation 42]
107. calm(X0) | rich(X0) [cnf transformation 32]
119. ~quiet(sK1) | ~humble(X1) | ~calm(X1) [cnf transformation 53]
144. ~rich(X0) | ~rich(X0) [cnf transformation 69]
155. humble(susan) [cnf transformation 24]
157. ~rich(X0) [duplicate literal removal 144]
169. 1 <=> ! [X1] : (~humble(X1) | ~calm(X1)) [avatar definition]
170. ~calm(X1) | ~humble(X1) <- (1) [avatar component clause 169]
172. 2 <=> quiet(sK1) [avatar definition]
174. ~quiet(sK1) <- (~2) [avatar component clause 172]
175. 1 | ~2 [avatar split clause 119,172,169]
178. 3 <=> ! [X3] : quiet(X3) [avatar definition]
179. quiet(X3) <- (3) [avatar component clause 178]
282. quiet(X0) [resolution 96,157]
283. 3 [avatar split clause 282,178]
284. $false <- (~2, 3) [resolution 179,174]
289. 2 | ~3 [avatar contradiction clause 284]
294. ~humble(X0) | rich(X0) <- (1) [resolution 170,107]
300. ~humble(X0) <- (1) [subsumption resolution 294,157]
303. $false <- (1) [resolution 300,155]
306. ~1 [avatar contradiction clause 303]
307. $false [avatar sat refutation 175,283,289,306]
% SZS output end Proof for 7897650466674416945139415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not humble is not strong and vice versa. Everyone who is old or generous is either creative or not calm. If someone is either creative or strong then mary is not brave. Everyone who is both humble and happy is either not kind or funny and vice versa. Everyone who is not quiet is not brave or not rich and vice versa. Everyone who is old is generous or not old and vice versa. Everyone who is not rich is both strong and quiet. Everyone who is both not rich and not tall is both patient and happy. Everyone who is quiet or not funny is curious or generous. If someone is humble or not kind then someone is not brave or not old and vice versa. If someone is either tall or not happy then susan is not happy or strong and vice versa. If someone is not quiet then someone is strong and vice versa. If someone is either not brave or curious then someone is both happy and not creative. If john is both tall and not patient then someone is either not funny or not generous. If someone is wise or not wise then someone is happy or not kind. If someone is both not quiet and not funny then someone is not happy or not humble. Someone is kind or not patient. Fred is both patient and not tall. Someone is not tall. Alice is not funny or creative. Someone is not happy or old. Fred is old. Someone is either not happy or old. Alice is kind. | Susan is not kind. | contradiction | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((old(X)|generous(X))=>(creative(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:((humble(X)&happy(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
(![X]:(old(X)<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(strong(X)&quiet(X))))&
(![X]:((~rich(X)&~tall(X))=>(patient(X)&happy(X))))&
(![X]:((quiet(X)|~funny(X))=>(curious(X)|generous(X))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(((tall(john)&~patient(john)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((happy(X)|~kind(X)))))&
((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:((~happy(X)|~humble(X)))))&
(?[X]:((kind(X)|~patient(X))))&
((patient(fred)&~tall(fred)))&
(?[X]:(~tall(X)))&
((~funny(alice)|creative(alice)))&
(?[X]:((~happy(X)|old(X))))&
(old(fred))&
(?[X]:((~happy(X)<~>old(X))))&
(kind(alice)) | ~kind(susan) | [
"p0",
"p4",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2613607648099912663873622
% SZS output start Proof for 2613607648099912663873622
1. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~strong(X0)) [input p0]
5. ! [X0] : (~quiet(X0) <=> (~rich(X0) | ~brave(X0))) [input p4]
6. ! [X0] : (old(X0) <=> (~old(X0) | generous(X0))) [input p5]
10. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X0] : (~old(X0) | ~brave(X0)) [input p9]
12. ? [X0] : ~quiet(X0) <=> ? [X0] : strong(X0) [input p11]
25. ~kind(susan) [input hypothesis]
26. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X1] : (~old(X1) | ~brave(X1)) [rectify 10]
27. ? [X0] : ~quiet(X0) <=> ? [X1] : strong(X1) [rectify 12]
43. ! [X0] : (((~humble(X0) | humble(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 1]
44. ! [X0] : ((~humble(X0) | humble(X0) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [flattening 43]
49. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | quiet(X0))) [nnf transformation 5]
50. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | quiet(X0))) [flattening 49]
51. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | ~old(X0))) [nnf transformation 6]
52. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~old(X0))) [flattening 51]
53. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (old(X1) & brave(X1))) & (? [X1] : (~old(X1) | ~brave(X1)) | ! [X0] : (kind(X0) & ~humble(X0))) [nnf transformation 26]
54. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : (old(X1) & brave(X1))) & (? [X2] : (~old(X2) | ~brave(X2)) | ! [X3] : (kind(X3) & ~humble(X3))) [rectify 53]
55. ? [X0] : (~kind(X0) | humble(X0)) => (~kind(sK0) | humble(sK0)) [choice axiom]
56. ? [X2] : (~old(X2) | ~brave(X2)) => (~old(sK1) | ~brave(sK1)) [choice axiom]
57. ((~kind(sK0) | humble(sK0)) | ! [X1] : (old(X1) & brave(X1))) & ((~old(sK1) | ~brave(sK1)) | ! [X3] : (kind(X3) & ~humble(X3))) [skolemisation 54,56,55]
63. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : quiet(X0)) [nnf transformation 27]
64. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : quiet(X3)) [rectify 63]
65. ? [X0] : ~quiet(X0) => ~quiet(sK3) [choice axiom]
66. ? [X2] : strong(X2) => strong(sK4) [choice axiom]
67. (~quiet(sK3) | ! [X1] : ~strong(X1)) & (strong(sK4) | ! [X3] : quiet(X3)) [skolemisation 64,66,65]
90. ~strong(X0) | ~humble(X0) [cnf transformation 44]
91. ~strong(X0) | humble(X0) [cnf transformation 44]
106. ~quiet(X0) | brave(X0) [cnf transformation 50]
110. old(X0) | old(X0) [cnf transformation 52]
118. ~old(sK1) | ~brave(sK1) | kind(X3) [cnf transformation 57]
127. strong(sK4) | quiet(X3) [cnf transformation 67]
148. ~kind(susan) [cnf transformation 25]
150. old(X0) [duplicate literal removal 110]
151. ~strong(X0) [subsumption resolution 90,91]
164. 3 <=> ! [X1] : brave(X1) [avatar definition]
165. brave(X1) <- (3) [avatar component clause 164]
175. ~brave(sK1) | kind(X3) [subsumption resolution 118,150]
177. 6 <=> ! [X3] : kind(X3) [avatar definition]
178. kind(X3) <- (6) [avatar component clause 177]
180. 7 <=> brave(sK1) [avatar definition]
182. ~brave(sK1) <- (~7) [avatar component clause 180]
183. 6 | ~7 [avatar split clause 175,180,177]
213. quiet(X3) [subsumption resolution 127,151]
281. brave(X0) [resolution 106,213]
282. 3 [avatar split clause 281,164]
284. $false <- (3, ~7) [resolution 165,182]
285. ~3 | 7 [avatar contradiction clause 284]
287. $false <- (6) [resolution 178,148]
292. ~6 [avatar contradiction clause 287]
293. $false [avatar sat refutation 183,282,285,292]
% SZS output end Proof for 2613607648099912663873622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and curious is curious or not creative. If paul is not tall or tall then john is not generous and vice versa. If paul is old then someone is both not rich and not funny and vice versa. Everyone who is both not brave and calm is either not brave or kind. If someone is not tall then someone is both not creative and not curious and vice versa. If mary is not creative or creative then paul is calm. If someone is either creative or not old then someone is not old and vice versa. If someone is either old or not curious then someone is both not happy and not brave. If someone is strong or not kind then someone is both humble and wise. Everyone who is not creative is either happy or brave and vice versa. If someone is funny or humble then susan is not happy and vice versa. If someone is both not rich and not curious then paul is either not patient or not brave and vice versa. Everyone who is both strong and not happy is both quiet and funny and vice versa. Everyone who is not patient or quiet is quiet or happy. Everyone who is not patient is not curious. Everyone who is both not kind and rich is both curious and creative and vice versa. Fred is both not brave and not happy. Someone is both not happy and not generous. Paul is not funny. Mary is both happy and not kind. Someone is either humble or not calm. Someone is quiet or brave. Someone is either curious or strong. | Susan is not brave. | neutral | (![X]:((~rich(X)&curious(X))=>(curious(X)|~creative(X))))&
(((~tall(paul)|tall(paul)))<=>(~generous(john)))&
((old(paul))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((~brave(X)&calm(X))=>(~brave(X)<~>kind(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~creative(X)&~curious(X)))))&
(((~creative(mary)|creative(mary)))=>(calm(paul)))&
((?[X]:((creative(X)<~>~old(X))))<=>(?[X]:(~old(X))))&
((?[X]:((old(X)<~>~curious(X))))=>(?[X]:((~happy(X)&~brave(X)))))&
((?[X]:((strong(X)|~kind(X))))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:(~creative(X)<=>(happy(X)<~>brave(X))))&
((?[X]:((funny(X)|humble(X))))<=>(~happy(susan)))&
((?[X]:((~rich(X)&~curious(X))))<=>((~patient(paul)<~>~brave(paul))))&
(![X]:((strong(X)&~happy(X))<=>(quiet(X)&funny(X))))&
(![X]:((~patient(X)|quiet(X))=>(quiet(X)|happy(X))))&
(![X]:(~patient(X)=>~curious(X)))&
(![X]:((~kind(X)&rich(X))<=>(curious(X)&creative(X))))&
((~brave(fred)&~happy(fred)))&
(?[X]:((~happy(X)&~generous(X))))&
(~funny(paul))&
((happy(mary)&~kind(mary)))&
(?[X]:((humble(X)<~>~calm(X))))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((curious(X)<~>strong(X)))) | ~brave(susan) | [] | null | 0 |
Everyone who is generous is either old or not calm and vice versa.
Everyone who is not old is both quiet and strong.
If someone is either rich or kind then john is either kind or wise.
Everyone who is patient or not happy is calm and vice versa.
If alice is calm then someone is wise.
Everyone who is rich or creative is happy.
If someone is either creative or not generous then mary is either not curious or not creative and vice versa.
Everyone who is brave or rich is not quiet.
Everyone who is rich or not wise is either not strong or tall and vice versa.
Everyone who is strong is not generous or brave and vice versa.
Everyone who is both not old and curious is not quiet or rich and vice versa.
If someone is not old or not calm then alice is not quiet or creative and vice versa.
If someone is either not generous or kind then alice is curious or not kind and vice versa.
If fred is rich then someone is both not strong and strong and vice versa.
Everyone who is both not curious and generous is either not happy or not patient.
If someone is generous then someone is both generous and funny and vice versa.
Fred is either not funny or not quiet.
Someone is either not strong or not wise.
Someone is kind.
Someone is either creative or quiet.
Alice is curious or not rich.
Alice is either not humble or happy. | Alice is quiet. | entailment | (![X]:(generous(X)<=>(old(X)<~>~calm(X))))&
(![X]:(~old(X)=>(quiet(X)&strong(X))))&
((?[X]:((rich(X)<~>kind(X))))=>((kind(john)<~>wise(john))))&
(![X]:((patient(X)|~happy(X))<=>calm(X)))&
((calm(alice))=>(?[X]:(wise(X))))&
(![X]:((rich(X)|creative(X))=>happy(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~curious(mary)<~>~creative(mary))))&
(![X]:((brave(X)|rich(X))=>~quiet(X)))&
(![X]:((rich(X)|~wise(X))<=>(~strong(X)<~>tall(X))))&
(![X]:(strong(X)<=>(~generous(X)|brave(X))))&
(![X]:((~old(X)&curious(X))<=>(~quiet(X)|rich(X))))&
((?[X]:((~old(X)|~calm(X))))<=>((~quiet(alice)|creative(alice))))&
((?[X]:((~generous(X)<~>kind(X))))<=>((curious(alice)|~kind(alice))))&
((rich(fred))<=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:((~curious(X)&generous(X))=>(~happy(X)<~>~patient(X))))&
((?[X]:(generous(X)))<=>(?[X]:((generous(X)&funny(X)))))&
((~funny(fred)<~>~quiet(fred)))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>quiet(X))))&
((curious(alice)|~rich(alice)))&
((~humble(alice)<~>happy(alice))) | quiet(alice) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3679444922534305777677073
% SZS output start Proof for 3679444922534305777677073
2. ! [X0] : (~old(X0) => (strong(X0) & quiet(X0))) [input p1]
11. ! [X0] : ((curious(X0) & ~old(X0)) <=> (rich(X0) | ~quiet(X0))) [input p10]
23. ~quiet(alice) [input hypothesis]
25. ! [X0] : ((strong(X0) & quiet(X0)) | old(X0)) [ennf transformation 2]
46. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | (~curious(X0) | old(X0)))) [nnf transformation 11]
47. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | ~curious(X0) | old(X0))) [flattening 46]
82. quiet(X0) | old(X0) [cnf transformation 25]
114. ~old(X0) | quiet(X0) [cnf transformation 47]
146. ~quiet(alice) [cnf transformation 23]
204. quiet(X0) [subsumption resolution 114,82]
310. $false [subsumption resolution 146,204]
% SZS output end Proof for 3679444922534305777677073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is both not curious and humble.
Everyone who is wise or not kind is brave.
Everyone who is not calm is both generous and not wise and vice versa.
Everyone who is either old or calm is brave and vice versa.
Everyone who is either not quiet or generous is not curious or generous.
Everyone who is not humble or curious is both funny and calm and vice versa.
Everyone who is creative or not strong is both funny and generous.
Everyone who is not curious is not old and vice versa.
If john is not old then fred is either not humble or not happy.
If lucy is either generous or not funny then someone is quiet.
If lucy is rich then someone is both wise and not brave.
Everyone who is happy or not strong is either quiet or curious and vice versa.
If someone is creative then john is strong or generous and vice versa.
If fred is both curious and generous then someone is not quiet and vice versa.
Everyone who is both not wise and happy is either not kind or tall.
Everyone who is not wise or not happy is not curious or not rich and vice versa.
John is either happy or patient.
Someone is either not curious or not happy.
John is either not strong or creative.
Fred is humble or not calm.
Lucy is both happy and generous.
Someone is strong.
Someone is calm.
Lucy is both quiet and not wise. | Lucy is old. | contradiction | (![X]:((~quiet(X)|~humble(X))=>(~curious(X)&humble(X))))&
(![X]:((wise(X)|~kind(X))=>brave(X)))&
(![X]:(~calm(X)<=>(generous(X)&~wise(X))))&
(![X]:((old(X)<~>calm(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>generous(X))=>(~curious(X)|generous(X))))&
(![X]:((~humble(X)|curious(X))<=>(funny(X)&calm(X))))&
(![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((~old(john))=>((~humble(fred)<~>~happy(fred))))&
(((generous(lucy)<~>~funny(lucy)))=>(?[X]:(quiet(X))))&
((rich(lucy))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:(creative(X)))<=>((strong(john)|generous(john))))&
(((curious(fred)&generous(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&happy(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|~rich(X))))&
((happy(john)<~>patient(john)))&
(?[X]:((~curious(X)<~>~happy(X))))&
((~strong(john)<~>creative(john)))&
((humble(fred)|~calm(fred)))&
((happy(lucy)&generous(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(calm(X)))&
((quiet(lucy)&~wise(lucy))) | old(lucy) | [
"p0",
"p7",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1642458961330834729166019
% SZS output start Proof for 1642458961330834729166019
1. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (humble(X0) & ~curious(X0))) [input p0]
8. ! [X0] : (~curious(X0) <=> ~old(X0)) [input p7]
12. ! [X0] : ((~strong(X0) | happy(X0)) <=> (quiet(X0) <~> curious(X0))) [input p11]
21. generous(lucy) & happy(lucy) [input p20]
25. old(lucy) [input hypothesis]
26. ! [X0] : ((humble(X0) & ~curious(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 1]
42. ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))) [nnf transformation 8]
49. ! [X0] : (((~strong(X0) | happy(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [nnf transformation 12]
50. ! [X0] : ((~strong(X0) | happy(X0) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [flattening 49]
73. ~curious(X0) | quiet(X0) [cnf transformation 26]
97. ~old(X0) | curious(X0) [cnf transformation 42]
107. ~curious(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 50]
130. happy(lucy) [cnf transformation 21]
136. old(lucy) [cnf transformation 25]
179. ~happy(X0) | ~curious(X0) [subsumption resolution 107,73]
258. curious(lucy) [resolution 97,136]
272. ~curious(lucy) [resolution 179,130]
274. $false [subsumption resolution 272,258]
% SZS output end Proof for 1642458961330834729166019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not tall is strong or wise and vice versa.
Everyone who is not creative or happy is humble.
If someone is both not curious and not calm then someone is not quiet or generous and vice versa.
If someone is funny or not tall then someone is either calm or brave and vice versa.
Everyone who is both calm and not kind is calm or not patient and vice versa.
If someone is not funny or humble then john is not brave or brave and vice versa.
Everyone who is not strong is both not generous and creative and vice versa.
Everyone who is not tall is not old or calm and vice versa.
If someone is either curious or not creative then paul is happy or curious.
Everyone who is happy or not wise is both not rich and not curious.
Everyone who is both not curious and not quiet is not creative or not quiet and vice versa.
Everyone who is both happy and humble is not wise or strong and vice versa.
Everyone who is not happy or humble is either kind or not brave and vice versa.
Everyone who is both calm and not calm is not curious and vice versa.
If susan is old or not wise then fred is not wise or rich.
Everyone who is calm or curious is either not creative or not rich and vice versa.
Paul is brave.
Fred is not generous.
Someone is either quiet or not curious.
Fred is either creative or not wise.
Lucy is not strong or not creative. | Lucy is not calm. | neutral | (![X]:((~happy(X)|~tall(X))<=>(strong(X)|wise(X))))&
(![X]:((~creative(X)|happy(X))=>humble(X)))&
((?[X]:((~curious(X)&~calm(X))))<=>(?[X]:((~quiet(X)|generous(X)))))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:((calm(X)&~kind(X))<=>(calm(X)|~patient(X))))&
((?[X]:((~funny(X)|humble(X))))<=>((~brave(john)|brave(john))))&
(![X]:(~strong(X)<=>(~generous(X)&creative(X))))&
(![X]:(~tall(X)<=>(~old(X)|calm(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>((happy(paul)|curious(paul))))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&~curious(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~creative(X)|~quiet(X))))&
(![X]:((happy(X)&humble(X))<=>(~wise(X)|strong(X))))&
(![X]:((~happy(X)|humble(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((calm(X)&~calm(X))<=>~curious(X)))&
(((old(susan)|~wise(susan)))=>((~wise(fred)|rich(fred))))&
(![X]:((calm(X)|curious(X))<=>(~creative(X)<~>~rich(X))))&
(brave(paul))&
(~generous(fred))&
(?[X]:((quiet(X)<~>~curious(X))))&
((creative(fred)<~>~wise(fred)))&
((~strong(lucy)|~creative(lucy))) | ~calm(lucy) | [] | null | 0 |
Everyone who is either not wise or not old is either quiet or not calm.
If lucy is not creative or kind then someone is either not rich or not old and vice versa.
If someone is kind then someone is not rich or tall and vice versa.
If someone is either not calm or not happy then john is not brave or not quiet and vice versa.
If john is either not funny or kind then susan is both happy and not humble and vice versa.
Everyone who is not wise or not rich is either humble or tall and vice versa.
Everyone who is both curious and not happy is kind and vice versa.
If paul is both tall and brave then someone is either strong or old and vice versa.
Everyone who is humble is both old and happy and vice versa.
Everyone who is quiet is both not curious and not old and vice versa.
If someone is brave then someone is not humble or not brave and vice versa.
If someone is not happy or not calm then paul is either rich or tall and vice versa.
Everyone who is kind is both calm and happy and vice versa.
If someone is not creative then john is either tall or curious.
If someone is kind then someone is either generous or not wise and vice versa.
Everyone who is humble is both rich and not humble.
Someone is not curious.
Someone is not creative.
Someone is quiet or kind.
Someone is either not brave or not wise.
Mary is not generous. | Paul is not quiet. | neutral | (![X]:((~wise(X)<~>~old(X))=>(quiet(X)<~>~calm(X))))&
(((~creative(lucy)|kind(lucy)))<=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)|tall(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>((~brave(john)|~quiet(john))))&
(((~funny(john)<~>kind(john)))<=>((happy(susan)&~humble(susan))))&
(![X]:((~wise(X)|~rich(X))<=>(humble(X)<~>tall(X))))&
(![X]:((curious(X)&~happy(X))<=>kind(X)))&
(((tall(paul)&brave(paul)))<=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:(humble(X)<=>(old(X)&happy(X))))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)|~brave(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>((rich(paul)<~>tall(paul))))&
(![X]:(kind(X)<=>(calm(X)&happy(X))))&
((?[X]:(~creative(X)))=>((tall(john)<~>curious(john))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:(humble(X)=>(rich(X)&~humble(X))))&
(?[X]:(~curious(X)))&
(?[X]:(~creative(X)))&
(?[X]:((quiet(X)|kind(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
(~generous(mary)) | ~quiet(paul) | [] | null | 0 |
Everyone who is tall or not generous is either not calm or old and vice versa.
If alice is either curious or generous then someone is either calm or not quiet.
If someone is both funny and old then someone is both wise and happy.
If mary is kind or not tall then someone is both funny and not old and vice versa.
Everyone who is not kind is not patient or creative and vice versa.
Everyone who is creative is wise and vice versa.
If someone is not creative then fred is either calm or not generous.
If someone is not calm or tall then mary is not creative or quiet.
Everyone who is either not happy or calm is not creative and vice versa.
If john is generous or brave then someone is either not humble or happy.
Everyone who is both quiet and humble is not patient or curious.
Everyone who is both not strong and not quiet is generous and vice versa.
Everyone who is kind is not happy and vice versa.
If someone is not humble or not wise then paul is either funny or not rich and vice versa.
Everyone who is either wise or generous is both kind and tall.
Everyone who is kind or funny is not brave and vice versa.
Fred is patient or not strong.
Alice is not old.
Fred is not strong or humble.
Fred is rich.
Alice is either generous or rich.
Someone is not rich or happy.
Paul is both brave and patient.
Someone is calm. | Fred is calm. | contradiction | (![X]:((tall(X)|~generous(X))<=>(~calm(X)<~>old(X))))&
(((curious(alice)<~>generous(alice)))=>(?[X]:((calm(X)<~>~quiet(X)))))&
((?[X]:((funny(X)&old(X))))=>(?[X]:((wise(X)&happy(X)))))&
(((kind(mary)|~tall(mary)))<=>(?[X]:((funny(X)&~old(X)))))&
(![X]:(~kind(X)<=>(~patient(X)|creative(X))))&
(![X]:(creative(X)<=>wise(X)))&
((?[X]:(~creative(X)))=>((calm(fred)<~>~generous(fred))))&
((?[X]:((~calm(X)|tall(X))))=>((~creative(mary)|quiet(mary))))&
(![X]:((~happy(X)<~>calm(X))<=>~creative(X)))&
(((generous(john)|brave(john)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:((quiet(X)&humble(X))=>(~patient(X)|curious(X))))&
(![X]:((~strong(X)&~quiet(X))<=>generous(X)))&
(![X]:(kind(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>generous(X))=>(kind(X)&tall(X))))&
(![X]:((kind(X)|funny(X))<=>~brave(X)))&
((patient(fred)|~strong(fred)))&
(~old(alice))&
((~strong(fred)|humble(fred)))&
(rich(fred))&
((generous(alice)<~>rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((brave(paul)&patient(paul)))&
(?[X]:(calm(X))) | calm(fred) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p11",
"p12",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 92381202825304975313542
% SZS output start Proof for 92381202825304975313542
5. ! [X0] : (~kind(X0) <=> (creative(X0) | ~patient(X0))) [input p4]
6. ! [X0] : (creative(X0) <=> wise(X0)) [input p5]
7. ? [X0] : ~creative(X0) => (calm(fred) <~> ~generous(fred)) [input p6]
8. ? [X0] : (tall(X0) | ~calm(X0)) => (quiet(mary) | ~creative(mary)) [input p7]
9. ! [X0] : ((~happy(X0) <~> calm(X0)) <=> ~creative(X0)) [input p8]
12. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> generous(X0)) [input p11]
13. ! [X0] : (kind(X0) <=> ~happy(X0)) [input p12]
15. ! [X0] : ((wise(X0) <~> generous(X0)) => (tall(X0) & kind(X0))) [input p14]
16. ! [X0] : ((funny(X0) | kind(X0)) <=> ~brave(X0)) [input p15]
23. patient(paul) & brave(paul) [input p22]
25. calm(fred) [input hypothesis]
29. (calm(fred) <~> ~generous(fred)) | ! [X0] : creative(X0) [ennf transformation 7]
30. (quiet(mary) | ~creative(mary)) | ! [X0] : (~tall(X0) & calm(X0)) [ennf transformation 8]
31. quiet(mary) | ~creative(mary) | ! [X0] : (~tall(X0) & calm(X0)) [flattening 30]
35. ! [X0] : ((tall(X0) & kind(X0)) | (wise(X0) <=> generous(X0))) [ennf transformation 15]
49. ! [X0] : ((~kind(X0) | (~creative(X0) & patient(X0))) & ((creative(X0) | ~patient(X0)) | kind(X0))) [nnf transformation 5]
50. ! [X0] : ((~kind(X0) | (~creative(X0) & patient(X0))) & (creative(X0) | ~patient(X0) | kind(X0))) [flattening 49]
51. ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))) [nnf transformation 6]
52. ((generous(fred) | ~calm(fred)) & (~generous(fred) | calm(fred))) | ! [X0] : creative(X0) [nnf transformation 29]
53. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | creative(X0)) & (~creative(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [nnf transformation 9]
57. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) | strong(X0)))) [nnf transformation 12]
58. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | quiet(X0) | strong(X0))) [flattening 57]
59. ! [X0] : ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))) [nnf transformation 13]
64. ! [X0] : ((tall(X0) & kind(X0)) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) [nnf transformation 35]
65. ! [X0] : (((funny(X0) | kind(X0)) | brave(X0)) & (~brave(X0) | (~funny(X0) & ~kind(X0)))) [nnf transformation 16]
66. ! [X0] : ((funny(X0) | kind(X0) | brave(X0)) & (~brave(X0) | (~funny(X0) & ~kind(X0)))) [flattening 65]
89. ~patient(X0) | creative(X0) | kind(X0) [cnf transformation 50]
91. ~creative(X0) | ~kind(X0) [cnf transformation 50]
92. ~creative(X0) | wise(X0) [cnf transformation 51]
93. ~wise(X0) | creative(X0) [cnf transformation 51]
95. generous(fred) | ~calm(fred) | creative(X0) [cnf transformation 52]
96. quiet(mary) | ~creative(mary) | calm(X0) [cnf transformation 31]
99. ~creative(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 53]
101. ~calm(X0) | happy(X0) | creative(X0) [cnf transformation 53]
109. ~quiet(X0) | ~generous(X0) [cnf transformation 58]
110. ~kind(X0) | ~happy(X0) [cnf transformation 59]
111. kind(X0) | happy(X0) [cnf transformation 59]
118. ~wise(X0) | generous(X0) | kind(X0) [cnf transformation 64]
119. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 64]
122. ~brave(X0) | ~kind(X0) [cnf transformation 66]
132. brave(paul) [cnf transformation 23]
133. patient(paul) [cnf transformation 23]
135. calm(fred) [cnf transformation 25]
173. 9 <=> kind(mary) [avatar definition]
194. 13 <=> ! [X0] : creative(X0) [avatar definition]
195. creative(X0) <- (13) [avatar component clause 194]
197. 14 <=> calm(fred) [avatar definition]
198. calm(fred) <- (14) [avatar component clause 197]
201. 15 <=> generous(fred) [avatar definition]
203. generous(fred) <- (15) [avatar component clause 201]
204. 13 | ~14 | 15 [avatar split clause 95,201,197,194]
210. 17 <=> creative(mary) [avatar definition]
211. creative(mary) <- (17) [avatar component clause 210]
212. ~creative(mary) <- (~17) [avatar component clause 210]
214. 18 <=> quiet(mary) [avatar definition]
216. quiet(mary) <- (18) [avatar component clause 214]
219. 19 <=> ! [X0] : calm(X0) [avatar definition]
220. calm(X0) <- (19) [avatar component clause 219]
221. 19 | ~17 | 18 [avatar split clause 96,214,210,219]
299. 14 [avatar split clause 135,197]
301. $false <- (13, ~17) [resolution 212,195]
302. ~13 | 17 [avatar contradiction clause 301]
306. ~kind(paul) [resolution 122,132]
307. happy(paul) [resolution 306,111]
338. creative(paul) | kind(paul) [resolution 89,133]
340. creative(paul) [subsumption resolution 338,306]
344. ~happy(paul) | ~calm(paul) [resolution 99,340]
345. ~calm(paul) [subsumption resolution 344,307]
351. happy(fred) | creative(fred) <- (14) [resolution 101,198]
362. 43 <=> creative(fred) [avatar definition]
363. ~creative(fred) <- (~43) [avatar component clause 362]
364. creative(fred) <- (43) [avatar component clause 362]
366. 44 <=> happy(fred) [avatar definition]
367. ~happy(fred) <- (~44) [avatar component clause 366]
368. happy(fred) <- (44) [avatar component clause 366]
369. 43 | 44 | ~14 [avatar split clause 351,197,366,362]
380. ~happy(fred) | ~calm(fred) <- (43) [resolution 364,99]
383. ~kind(fred) <- (43) [resolution 364,91]
384. ~happy(fred) <- (14, 43) [subsumption resolution 380,198]
385. ~44 | ~14 | ~43 [avatar split clause 384,362,197,366]
386. wise(fred) | kind(fred) <- (15) [resolution 119,203]
392. 45 <=> generous(mary) [avatar definition]
407. wise(mary) <- (17) [resolution 211,92]
408. ~kind(mary) <- (17) [resolution 211,91]
410. ~generous(mary) <- (18) [resolution 216,109]
411. ~45 | ~18 [avatar split clause 410,214,392]
419. generous(mary) | kind(mary) <- (17) [resolution 407,118]
434. ~9 | ~17 [avatar split clause 408,210,173]
445. 9 | 45 | ~17 [avatar split clause 419,210,392,173]
460. $false <- (19) [resolution 220,345]
461. ~19 [avatar contradiction clause 460]
540. happy(fred) <- (43) [resolution 383,111]
541. $false <- (43, ~44) [subsumption resolution 540,367]
542. ~43 | 44 [avatar contradiction clause 541]
551. 55 <=> kind(fred) [avatar definition]
553. kind(fred) <- (55) [avatar component clause 551]
555. 56 <=> wise(fred) [avatar definition]
557. wise(fred) <- (56) [avatar component clause 555]
558. 55 | 56 | ~15 [avatar split clause 386,201,555,551]
563. ~happy(fred) <- (55) [resolution 553,110]
565. $false <- (44, 55) [subsumption resolution 563,368]
566. ~44 | ~55 [avatar contradiction clause 565]
571. creative(fred) <- (56) [resolution 557,93]
572. $false <- (~43, 56) [subsumption resolution 571,363]
573. 43 | ~56 [avatar contradiction clause 572]
574. $false [avatar sat refutation 204,221,299,302,369,385,411,434,445,461,542,558,566,573]
% SZS output end Proof for 92381202825304975313542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not rich is not creative or not tall and vice versa.
Everyone who is patient or not quiet is both not kind and not rich and vice versa.
Everyone who is both humble and not strong is either creative or curious and vice versa.
Everyone who is both not creative and not tall is quiet or happy and vice versa.
If fred is not generous or old then someone is happy.
Everyone who is both calm and not generous is calm or old and vice versa.
Everyone who is both funny and curious is not curious or curious.
If susan is both not old and not wise then alice is both not patient and not quiet and vice versa.
If fred is not generous then mary is quiet and vice versa.
Everyone who is either not kind or patient is both not generous and not tall.
If someone is both generous and not humble then someone is not old or not wise.
Everyone who is either tall or not old is not wise and vice versa.
Everyone who is both patient and not rich is both not old and old.
Everyone who is both not rich and not funny is both not calm and not wise and vice versa.
If mary is not creative then someone is both not kind and not quiet and vice versa.
Everyone who is both not kind and old is quiet and vice versa.
John is both not brave and not curious.
Someone is happy or calm.
Lucy is not wise or happy.
Someone is brave.
Mary is curious or rich.
Someone is both not quiet and not happy.
Susan is not creative. | Susan is tall. | contradiction | (![X]:((humble(X)<~>~rich(X))<=>(~creative(X)|~tall(X))))&
(![X]:((patient(X)|~quiet(X))<=>(~kind(X)&~rich(X))))&
(![X]:((humble(X)&~strong(X))<=>(creative(X)<~>curious(X))))&
(![X]:((~creative(X)&~tall(X))<=>(quiet(X)|happy(X))))&
(((~generous(fred)|old(fred)))=>(?[X]:(happy(X))))&
(![X]:((calm(X)&~generous(X))<=>(calm(X)|old(X))))&
(![X]:((funny(X)&curious(X))=>(~curious(X)|curious(X))))&
(((~old(susan)&~wise(susan)))<=>((~patient(alice)&~quiet(alice))))&
((~generous(fred))<=>(quiet(mary)))&
(![X]:((~kind(X)<~>patient(X))=>(~generous(X)&~tall(X))))&
((?[X]:((generous(X)&~humble(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:((tall(X)<~>~old(X))<=>~wise(X)))&
(![X]:((patient(X)&~rich(X))=>(~old(X)&old(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~calm(X)&~wise(X))))&
((~creative(mary))<=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
((~brave(john)&~curious(john)))&
(?[X]:((happy(X)|calm(X))))&
((~wise(lucy)|happy(lucy)))&
(?[X]:(brave(X)))&
((curious(mary)|rich(mary)))&
(?[X]:((~quiet(X)&~happy(X))))&
(~creative(susan)) | tall(susan) | [
"p1",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1337731812805339026199547
% SZS output start Proof for 1337731812805339026199547
2. ! [X0] : ((~quiet(X0) | patient(X0)) <=> (~rich(X0) & ~kind(X0))) [input p1]
10. ! [X0] : ((~kind(X0) <~> patient(X0)) => (~tall(X0) & ~generous(X0))) [input p9]
13. ! [X0] : ((~rich(X0) & patient(X0)) => (old(X0) & ~old(X0))) [input p12]
16. ! [X0] : ((old(X0) & ~kind(X0)) <=> quiet(X0)) [input p15]
24. tall(susan) [input hypothesis]
29. ! [X0] : ((~tall(X0) & ~generous(X0)) | (~kind(X0) <=> patient(X0))) [ennf transformation 10]
31. ! [X0] : ((old(X0) & ~old(X0)) | (rich(X0) | ~patient(X0))) [ennf transformation 13]
32. ! [X0] : ((old(X0) & ~old(X0)) | rich(X0) | ~patient(X0)) [flattening 31]
35. ! [X0] : (((~quiet(X0) | patient(X0)) | (rich(X0) | kind(X0))) & ((~rich(X0) & ~kind(X0)) | (quiet(X0) & ~patient(X0)))) [nnf transformation 2]
36. ! [X0] : ((~quiet(X0) | patient(X0) | rich(X0) | kind(X0)) & ((~rich(X0) & ~kind(X0)) | (quiet(X0) & ~patient(X0)))) [flattening 35]
48. ! [X0] : ((~tall(X0) & ~generous(X0)) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) [nnf transformation 29]
59. ! [X0] : (((old(X0) & ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) | kind(X0)))) [nnf transformation 16]
60. ! [X0] : (((old(X0) & ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | ~old(X0) | kind(X0))) [flattening 59]
74. ~kind(X0) | quiet(X0) [cnf transformation 36]
75. ~patient(X0) | ~rich(X0) [cnf transformation 36]
105. ~tall(X0) | patient(X0) | kind(X0) [cnf transformation 48]
112. ~old(X0) | rich(X0) | ~patient(X0) [cnf transformation 32]
113. old(X0) | rich(X0) | ~patient(X0) [cnf transformation 32]
122. ~kind(X0) | ~quiet(X0) [cnf transformation 60]
133. tall(susan) [cnf transformation 24]
187. ~patient(X0) | old(X0) [subsumption resolution 113,75]
188. ~old(X0) | ~patient(X0) [subsumption resolution 112,75]
189. ~patient(X0) [subsumption resolution 188,187]
209. ~kind(X0) [subsumption resolution 122,74]
284. patient(susan) | kind(susan) [resolution 105,133]
285. kind(susan) [subsumption resolution 284,189]
286. $false [subsumption resolution 285,209]
% SZS output end Proof for 1337731812805339026199547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is calm or generous then someone is not happy.
Everyone who is not tall or creative is either creative or not calm.
If fred is old or not strong then someone is old or kind and vice versa.
Everyone who is both not creative and happy is both patient and not generous.
If alice is both brave and not funny then someone is rich and vice versa.
Everyone who is not happy is either not creative or quiet and vice versa.
Everyone who is either funny or creative is both wise and creative.
Everyone who is either quiet or generous is either not strong or not wise and vice versa.
Everyone who is both not curious and old is either not kind or tall.
If susan is either not brave or tall then someone is tall or curious and vice versa.
Everyone who is quiet is strong or not quiet and vice versa.
Everyone who is wise is not strong or curious and vice versa.
If someone is both not strong and old then mary is not wise or not generous and vice versa.
If someone is generous or quiet then someone is not patient or not old.
Everyone who is not wise is either quiet or not patient.
If alice is creative then lucy is both wise and funny.
Mary is either creative or not kind.
Someone is either humble or generous.
Fred is either patient or not wise.
Lucy is calm or not calm.
Alice is funny or not wise.
Someone is rich or not humble.
Paul is both brave and creative.
Lucy is either not humble or not kind. | Fred is happy. | contradiction | (((calm(john)|generous(john)))=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)|creative(X))=>(creative(X)<~>~calm(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~creative(X)&happy(X))=>(patient(X)&~generous(X))))&
(((brave(alice)&~funny(alice)))<=>(?[X]:(rich(X))))&
(![X]:(~happy(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((funny(X)<~>creative(X))=>(wise(X)&creative(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~wise(X))))&
(![X]:((~curious(X)&old(X))=>(~kind(X)<~>tall(X))))&
(((~brave(susan)<~>tall(susan)))<=>(?[X]:((tall(X)|curious(X)))))&
(![X]:(quiet(X)<=>(strong(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~strong(X)|curious(X))))&
((?[X]:((~strong(X)&old(X))))<=>((~wise(mary)|~generous(mary))))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(~wise(X)=>(quiet(X)<~>~patient(X))))&
((creative(alice))=>((wise(lucy)&funny(lucy))))&
((creative(mary)<~>~kind(mary)))&
(?[X]:((humble(X)<~>generous(X))))&
((patient(fred)<~>~wise(fred)))&
((calm(lucy)|~calm(lucy)))&
((funny(alice)|~wise(alice)))&
(?[X]:((rich(X)|~humble(X))))&
((brave(paul)&creative(paul)))&
((~humble(lucy)<~>~kind(lucy))) | happy(fred) | [
"p3",
"p5",
"p7",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6144138212488533848702480
% SZS output start Proof for 6144138212488533848702480
4. ! [X0] : ((happy(X0) & ~creative(X0)) => (~generous(X0) & patient(X0))) [input p3]
6. ! [X0] : (~happy(X0) <=> (~creative(X0) <~> quiet(X0))) [input p5]
8. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~strong(X0) <~> ~wise(X0))) [input p7]
11. ! [X0] : (quiet(X0) <=> (~quiet(X0) | strong(X0))) [input p10]
15. ! [X0] : (~wise(X0) => (quiet(X0) <~> ~patient(X0))) [input p14]
19. patient(fred) <~> ~wise(fred) [input p18]
25. happy(fred) [input hypothesis]
29. ! [X0] : ((~generous(X0) & patient(X0)) | (~happy(X0) | creative(X0))) [ennf transformation 4]
30. ! [X0] : ((~generous(X0) & patient(X0)) | ~happy(X0) | creative(X0)) [flattening 29]
35. ! [X0] : ((quiet(X0) <~> ~patient(X0)) | wise(X0)) [ennf transformation 15]
50. ! [X0] : ((~happy(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | happy(X0))) [nnf transformation 6]
52. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 8]
58. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 11]
59. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~quiet(X0))) [flattening 58]
70. ! [X0] : (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | wise(X0)) [nnf transformation 35]
75. (wise(fred) | ~patient(fred)) & (~wise(fred) | patient(fred)) [nnf transformation 19]
90. ~happy(X0) | ~generous(X0) | creative(X0) [cnf transformation 30]
97. ~quiet(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 50]
102. ~wise(X0) | ~strong(X0) | generous(X0) | ~quiet(X0) [cnf transformation 52]
118. ~quiet(X0) | strong(X0) | ~quiet(X0) [cnf transformation 59]
120. quiet(X0) | quiet(X0) [cnf transformation 59]
132. patient(X0) | ~quiet(X0) | wise(X0) [cnf transformation 70]
140. wise(fred) | ~patient(fred) [cnf transformation 75]
148. happy(fred) [cnf transformation 25]
149. ~quiet(X0) | strong(X0) [duplicate literal removal 118]
150. quiet(X0) [duplicate literal removal 120]
239. strong(X0) [subsumption resolution 149,150]
273. wise(X0) | patient(X0) [subsumption resolution 132,150]
308. wise(fred) [subsumption resolution 140,273]
355. ~generous(fred) | creative(fred) [resolution 90,148]
357. 38 <=> creative(fred) [avatar definition]
359. creative(fred) <- (38) [avatar component clause 357]
361. 39 <=> generous(fred) [avatar definition]
364. 38 | ~39 [avatar split clause 355,361,357]
378. ~creative(X0) | ~happy(X0) [resolution 97,150]
404. ~strong(fred) | generous(fred) | ~quiet(fred) [resolution 102,308]
409. generous(fred) | ~quiet(fred) [subsumption resolution 404,239]
415. generous(fred) [subsumption resolution 409,150]
416. 39 [avatar split clause 415,361]
440. ~happy(fred) <- (38) [resolution 378,359]
443. $false <- (38) [subsumption resolution 440,148]
444. ~38 [avatar contradiction clause 443]
445. $false [avatar sat refutation 364,416,444]
% SZS output end Proof for 6144138212488533848702480
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm then someone is creative or not happy and vice versa. If someone is not rich or generous then fred is either not humble or not strong and vice versa. Everyone who is calm or not patient is not quiet. If mary is kind then someone is creative and vice versa. If paul is tall then susan is either calm or quiet and vice versa. Everyone who is humble is not strong and vice versa. If john is not kind then susan is either not wise or not calm. If someone is either old or quiet then someone is old or generous and vice versa. Everyone who is either rich or not creative is either not rich or humble. Everyone who is either not quiet or curious is either creative or not old and vice versa. Everyone who is not kind is not generous or generous and vice versa. If alice is not kind then susan is funny. Everyone who is either not curious or rich is both not tall and rich and vice versa. Everyone who is brave or not strong is not humble. Everyone who is not curious is not tall and vice versa. If lucy is either wise or not calm then someone is either not old or not brave. Someone is either calm or not creative. John is not kind. Someone is wise or happy. Someone is old. Someone is both generous and strong. | Alice is not kind. | entailment | ((?[X]:(calm(X)))<=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:((~rich(X)|generous(X))))<=>((~humble(fred)<~>~strong(fred))))&
(![X]:((calm(X)|~patient(X))=>~quiet(X)))&
((kind(mary))<=>(?[X]:(creative(X))))&
((tall(paul))<=>((calm(susan)<~>quiet(susan))))&
(![X]:(humble(X)<=>~strong(X)))&
((~kind(john))=>((~wise(susan)<~>~calm(susan))))&
((?[X]:((old(X)<~>quiet(X))))<=>(?[X]:((old(X)|generous(X)))))&
(![X]:((rich(X)<~>~creative(X))=>(~rich(X)<~>humble(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(creative(X)<~>~old(X))))&
(![X]:(~kind(X)<=>(~generous(X)|generous(X))))&
((~kind(alice))=>(funny(susan)))&
(![X]:((~curious(X)<~>rich(X))<=>(~tall(X)&rich(X))))&
(![X]:((brave(X)|~strong(X))=>~humble(X)))&
(![X]:(~curious(X)<=>~tall(X)))&
(((wise(lucy)<~>~calm(lucy)))=>(?[X]:((~old(X)<~>~brave(X)))))&
(?[X]:((calm(X)<~>~creative(X))))&
(~kind(john))&
(?[X]:((wise(X)|happy(X))))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&strong(X)))) | ~kind(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4608954260022533773221295
% SZS output start Proof for 4608954260022533773221295
11. ! [X0] : (~kind(X0) <=> (generous(X0) | ~generous(X0))) [input p10]
22. kind(alice) [input hypothesis]
55. ! [X0] : ((~kind(X0) | (~generous(X0) & generous(X0))) & ((generous(X0) | ~generous(X0)) | kind(X0))) [nnf transformation 11]
56. ! [X0] : ((~kind(X0) | (~generous(X0) & generous(X0))) & (generous(X0) | ~generous(X0) | kind(X0))) [flattening 55]
111. ~kind(X0) | generous(X0) [cnf transformation 56]
112. ~kind(X0) | ~generous(X0) [cnf transformation 56]
134. kind(alice) [cnf transformation 22]
259. ~kind(X0) [subsumption resolution 111,112]
300. $false [subsumption resolution 134,259]
% SZS output end Proof for 4608954260022533773221295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then fred is funny and vice versa. If someone is either not happy or creative then mary is either quiet or old and vice versa. If john is old or curious then paul is either tall or old. If someone is not kind or not curious then fred is either kind or not funny and vice versa. If someone is not happy then lucy is not rich or not humble and vice versa. If mary is generous then someone is both rich and humble and vice versa. If lucy is rich then someone is both not calm and not kind and vice versa. If someone is not wise then someone is curious or not brave and vice versa. Everyone who is not wise is both kind and quiet. Everyone who is not quiet or not happy is calm or happy and vice versa. Everyone who is both not strong and not tall is both strong and brave and vice versa. If someone is tall or generous then susan is happy. Everyone who is not happy is not patient or happy. Everyone who is either wise or not patient is not quiet. If someone is both not tall and patient then someone is both not old and not funny. If someone is both not funny and kind then fred is both not quiet and not kind and vice versa. Someone is not patient or strong. Someone is generous or not happy. Someone is either humble or not patient. Mary is not happy or not wise. Susan is not creative. Susan is either not humble or not kind. Fred is not old or not kind. Someone is not old or not calm. | Mary is wise. | entailment | ((?[X]:(quiet(X)))<=>(funny(fred)))&
((?[X]:((~happy(X)<~>creative(X))))<=>((quiet(mary)<~>old(mary))))&
(((old(john)|curious(john)))=>((tall(paul)<~>old(paul))))&
((?[X]:((~kind(X)|~curious(X))))<=>((kind(fred)<~>~funny(fred))))&
((?[X]:(~happy(X)))<=>((~rich(lucy)|~humble(lucy))))&
((generous(mary))<=>(?[X]:((rich(X)&humble(X)))))&
((rich(lucy))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:(~wise(X)=>(kind(X)&quiet(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(calm(X)|happy(X))))&
(![X]:((~strong(X)&~tall(X))<=>(strong(X)&brave(X))))&
((?[X]:((tall(X)|generous(X))))=>(happy(susan)))&
(![X]:(~happy(X)=>(~patient(X)|happy(X))))&
(![X]:((wise(X)<~>~patient(X))=>~quiet(X)))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~old(X)&~funny(X)))))&
((?[X]:((~funny(X)&kind(X))))<=>((~quiet(fred)&~kind(fred))))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~happy(mary)|~wise(mary)))&
(~creative(susan))&
((~humble(susan)<~>~kind(susan)))&
((~old(fred)|~kind(fred)))&
(?[X]:((~old(X)|~calm(X)))) | wise(mary) | [
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 23066327692881145917994
% SZS output start Proof for 23066327692881145917994
9. ! [X0] : (~wise(X0) => (quiet(X0) & kind(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (happy(X0) | calm(X0))) [input p9]
13. ! [X0] : (~happy(X0) => (happy(X0) | ~patient(X0))) [input p12]
14. ! [X0] : ((wise(X0) <~> ~patient(X0)) => ~quiet(X0)) [input p13]
25. ~wise(mary) [input hypothesis]
29. ! [X0] : ((quiet(X0) & kind(X0)) | wise(X0)) [ennf transformation 9]
31. ! [X0] : ((happy(X0) | ~patient(X0)) | happy(X0)) [ennf transformation 13]
32. ! [X0] : (happy(X0) | ~patient(X0) | happy(X0)) [flattening 31]
33. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~patient(X0))) [ennf transformation 14]
66. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~happy(X0) & ~calm(X0))) & ((happy(X0) | calm(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 10]
67. ! [X0] : ((~happy(X0) | ~quiet(X0) | (~happy(X0) & ~calm(X0))) & (happy(X0) | calm(X0) | (happy(X0) & quiet(X0)))) [flattening 66]
70. ! [X0] : (~quiet(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) [nnf transformation 33]
122. wise(X0) | quiet(X0) [cnf transformation 29]
126. ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 67]
133. happy(X0) | ~patient(X0) | happy(X0) [cnf transformation 32]
135. ~quiet(X0) | wise(X0) | patient(X0) [cnf transformation 70]
152. ~wise(mary) [cnf transformation 25]
153. ~patient(X0) | happy(X0) [duplicate literal removal 133]
157. ~happy(X0) | ~quiet(X0) [duplicate literal removal 126]
176. 5 <=> quiet(mary) [avatar definition]
177. ~quiet(mary) <- (~5) [avatar component clause 176]
178. quiet(mary) <- (5) [avatar component clause 176]
331. patient(X0) | wise(X0) [subsumption resolution 135,122]
393. 52 <=> happy(mary) [avatar definition]
394. happy(mary) <- (52) [avatar component clause 393]
397. 53 <=> wise(mary) [avatar definition]
399. ~wise(mary) <- (~53) [avatar component clause 397]
425. ~53 [avatar split clause 152,397]
429. quiet(mary) <- (~53) [resolution 122,399]
432. $false <- (~5, ~53) [subsumption resolution 429,177]
433. 5 | 53 [avatar contradiction clause 432]
463. wise(X0) | happy(X0) [resolution 331,153]
475. happy(mary) <- (~53) [resolution 463,399]
477. 52 | 53 [avatar split clause 475,397,393]
478. ~quiet(mary) <- (52) [resolution 394,157]
479. $false <- (5, 52) [subsumption resolution 478,178]
480. ~5 | ~52 [avatar contradiction clause 479]
481. $false [avatar sat refutation 425,433,477,480]
% SZS output end Proof for 23066327692881145917994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not wise or kind then mary is not generous or not happy and vice versa.
Everyone who is curious is both not tall and not kind and vice versa.
If someone is either strong or old then john is not curious and vice versa.
Everyone who is not strong or strong is not rich.
Everyone who is both not wise and not old is not happy.
Everyone who is either not strong or kind is both not strong and strong and vice versa.
If someone is patient or not funny then someone is either happy or not funny.
Everyone who is not brave is both not generous and not rich and vice versa.
If lucy is happy or quiet then alice is not curious and vice versa.
If mary is either not strong or rich then someone is both old and quiet.
If paul is either not curious or not kind then someone is not patient or humble and vice versa.
If john is not rich or patient then someone is not strong or not funny.
Everyone who is rich or not funny is humble or not creative and vice versa.
Everyone who is either not happy or not humble is either not brave or not quiet.
Everyone who is humble or not patient is not generous or not kind and vice versa.
Everyone who is not brave is either not wise or not tall and vice versa.
Fred is either not humble or not calm.
Lucy is not happy.
Someone is either not calm or not curious.
Mary is curious or not wise.
Someone is either creative or tall.
Susan is kind or not brave.
Someone is both not tall and quiet.
Lucy is humble. | Fred is not creative. | neutral | (((~wise(lucy)<~>kind(lucy)))<=>((~generous(mary)|~happy(mary))))&
(![X]:(curious(X)<=>(~tall(X)&~kind(X))))&
((?[X]:((strong(X)<~>old(X))))<=>(~curious(john)))&
(![X]:((~strong(X)|strong(X))=>~rich(X)))&
(![X]:((~wise(X)&~old(X))=>~happy(X)))&
(![X]:((~strong(X)<~>kind(X))<=>(~strong(X)&strong(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:(~brave(X)<=>(~generous(X)&~rich(X))))&
(((happy(lucy)|quiet(lucy)))<=>(~curious(alice)))&
(((~strong(mary)<~>rich(mary)))=>(?[X]:((old(X)&quiet(X)))))&
(((~curious(paul)<~>~kind(paul)))<=>(?[X]:((~patient(X)|humble(X)))))&
(((~rich(john)|patient(john)))=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:((rich(X)|~funny(X))<=>(humble(X)|~creative(X))))&
(![X]:((~happy(X)<~>~humble(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((humble(X)|~patient(X))<=>(~generous(X)|~kind(X))))&
(![X]:(~brave(X)<=>(~wise(X)<~>~tall(X))))&
((~humble(fred)<~>~calm(fred)))&
(~happy(lucy))&
(?[X]:((~calm(X)<~>~curious(X))))&
((curious(mary)|~wise(mary)))&
(?[X]:((creative(X)<~>tall(X))))&
((kind(susan)|~brave(susan)))&
(?[X]:((~tall(X)&quiet(X))))&
(humble(lucy)) | ~creative(fred) | [] | null | 0 |
Everyone who is not tall or not calm is both not humble and not tall. If someone is not creative or wise then someone is both not humble and quiet and vice versa. If someone is both patient and not funny then paul is either not old or happy and vice versa. If someone is not funny then john is happy or funny and vice versa. If someone is either funny or not brave then someone is both strong and not strong. Everyone who is either not strong or quiet is not tall. If someone is not humble then someone is either humble or not humble. Everyone who is both not curious and not funny is both not quiet and not calm. Everyone who is not happy or not calm is both wise and not wise and vice versa. Everyone who is funny or curious is not patient and vice versa. If someone is both not quiet and not kind then someone is rich. Everyone who is either not happy or not calm is not humble or calm. If lucy is either not quiet or creative then susan is both not happy and quiet. Everyone who is either not creative or rich is either not funny or not strong. Everyone who is both not calm and not generous is generous. If susan is wise or old then lucy is not brave and vice versa. Lucy is both kind and creative. Someone is kind. Someone is not patient or not funny. Alice is calm or generous. Someone is both kind and strong. Someone is either tall or strong. Someone is not humble. | Lucy is not brave. | neutral | (![X]:((~tall(X)|~calm(X))=>(~humble(X)&~tall(X))))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((patient(X)&~funny(X))))<=>((~old(paul)<~>happy(paul))))&
((?[X]:(~funny(X)))<=>((happy(john)|funny(john))))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>~tall(X)))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~curious(X)&~funny(X))=>(~quiet(X)&~calm(X))))&
(![X]:((~happy(X)|~calm(X))<=>(wise(X)&~wise(X))))&
(![X]:((funny(X)|curious(X))<=>~patient(X)))&
((?[X]:((~quiet(X)&~kind(X))))=>(?[X]:(rich(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(~humble(X)|calm(X))))&
(((~quiet(lucy)<~>creative(lucy)))=>((~happy(susan)&quiet(susan))))&
(![X]:((~creative(X)<~>rich(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)&~generous(X))=>generous(X)))&
(((wise(susan)|old(susan)))<=>(~brave(lucy)))&
((kind(lucy)&creative(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((~patient(X)|~funny(X))))&
((calm(alice)|generous(alice)))&
(?[X]:((kind(X)&strong(X))))&
(?[X]:((tall(X)<~>strong(X))))&
(?[X]:(~humble(X))) | ~brave(lucy) | [] | null | 0 |
If susan is both strong and patient then alice is not old.
If john is both not tall and brave then someone is not strong and vice versa.
If someone is either generous or not funny then fred is either tall or not curious.
Everyone who is not curious is generous.
Everyone who is either brave or humble is either not strong or calm.
Everyone who is both happy and not patient is either humble or brave and vice versa.
If john is both wise and not brave then fred is either not humble or not calm.
Everyone who is both happy and strong is quiet.
Everyone who is strong or old is not brave or not tall.
Everyone who is not calm is both not brave and not calm and vice versa.
Everyone who is not wise or not happy is strong or not tall and vice versa.
Everyone who is either quiet or funny is both generous and not tall and vice versa.
Everyone who is not patient or tall is tall and vice versa.
If someone is either generous or patient then susan is humble or kind and vice versa.
Everyone who is not humble or not funny is not old.
Everyone who is either curious or not funny is either not tall or not generous.
Susan is both not patient and humble.
Someone is not wise or wise.
Someone is not curious.
Someone is not rich or calm.
Mary is quiet.
Paul is both not quiet and humble.
Someone is either curious or happy.
Someone is not calm or not brave. | Paul is quiet. | contradiction | (((strong(susan)&patient(susan)))=>(~old(alice)))&
(((~tall(john)&brave(john)))<=>(?[X]:(~strong(X))))&
((?[X]:((generous(X)<~>~funny(X))))=>((tall(fred)<~>~curious(fred))))&
(![X]:(~curious(X)=>generous(X)))&
(![X]:((brave(X)<~>humble(X))=>(~strong(X)<~>calm(X))))&
(![X]:((happy(X)&~patient(X))<=>(humble(X)<~>brave(X))))&
(((wise(john)&~brave(john)))=>((~humble(fred)<~>~calm(fred))))&
(![X]:((happy(X)&strong(X))=>quiet(X)))&
(![X]:((strong(X)|old(X))=>(~brave(X)|~tall(X))))&
(![X]:(~calm(X)<=>(~brave(X)&~calm(X))))&
(![X]:((~wise(X)|~happy(X))<=>(strong(X)|~tall(X))))&
(![X]:((quiet(X)<~>funny(X))<=>(generous(X)&~tall(X))))&
(![X]:((~patient(X)|tall(X))<=>tall(X)))&
((?[X]:((generous(X)<~>patient(X))))<=>((humble(susan)|kind(susan))))&
(![X]:((~humble(X)|~funny(X))=>~old(X)))&
(![X]:((curious(X)<~>~funny(X))=>(~tall(X)<~>~generous(X))))&
((~patient(susan)&humble(susan)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)|calm(X))))&
(quiet(mary))&
((~quiet(paul)&humble(paul)))&
(?[X]:((curious(X)<~>happy(X))))&
(?[X]:((~calm(X)|~brave(X)))) | quiet(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5833692009396877901354391
% SZS output start Proof for 5833692009396877901354391
22. humble(paul) & ~quiet(paul) [input p21]
25. quiet(paul) [input hypothesis]
126. ~quiet(paul) [cnf transformation 22]
131. quiet(paul) [cnf transformation 25]
224. $false [subsumption resolution 131,126]
% SZS output end Proof for 5833692009396877901354391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and patient is both not creative and not happy.
Everyone who is tall or not generous is curious and vice versa.
Everyone who is not strong or not wise is old.
If paul is both curious and not patient then fred is strong.
Everyone who is either funny or quiet is old or not tall and vice versa.
Everyone who is both tall and not happy is both not humble and not happy and vice versa.
Everyone who is funny is not calm or old and vice versa.
Everyone who is not calm or kind is strong and vice versa.
Everyone who is not funny is both humble and not wise and vice versa.
Everyone who is not kind or generous is old or not old.
Everyone who is patient or tall is not strong and vice versa.
If fred is both not creative and not quiet then susan is either not kind or wise and vice versa.
If someone is either not humble or not tall then someone is either not creative or funny.
Everyone who is humble is not wise and vice versa.
Everyone who is patient or generous is rich or not creative.
Everyone who is quiet or funny is either quiet or not quiet.
Someone is both not kind and funny.
Alice is not patient.
John is curious or wise.
Mary is either not brave or not happy.
Someone is either not kind or not patient.
Fred is both brave and not calm.
Mary is tall. | Mary is not quiet. | entailment | (![X]:((curious(X)&patient(X))=>(~creative(X)&~happy(X))))&
(![X]:((tall(X)|~generous(X))<=>curious(X)))&
(![X]:((~strong(X)|~wise(X))=>old(X)))&
(((curious(paul)&~patient(paul)))=>(strong(fred)))&
(![X]:((funny(X)<~>quiet(X))<=>(old(X)|~tall(X))))&
(![X]:((tall(X)&~happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:(funny(X)<=>(~calm(X)|old(X))))&
(![X]:((~calm(X)|kind(X))<=>strong(X)))&
(![X]:(~funny(X)<=>(humble(X)&~wise(X))))&
(![X]:((~kind(X)|generous(X))=>(old(X)|~old(X))))&
(![X]:((patient(X)|tall(X))<=>~strong(X)))&
(((~creative(fred)&~quiet(fred)))<=>((~kind(susan)<~>wise(susan))))&
((?[X]:((~humble(X)<~>~tall(X))))=>(?[X]:((~creative(X)<~>funny(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:((patient(X)|generous(X))=>(rich(X)|~creative(X))))&
(![X]:((quiet(X)|funny(X))=>(quiet(X)<~>~quiet(X))))&
(?[X]:((~kind(X)&funny(X))))&
(~patient(alice))&
((curious(john)|wise(john)))&
((~brave(mary)<~>~happy(mary)))&
(?[X]:((~kind(X)<~>~patient(X))))&
((brave(fred)&~calm(fred)))&
(tall(mary)) | ~quiet(mary) | [
"p2",
"p4",
"p6",
"p8",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6703206460614573896138517
% SZS output start Proof for 6703206460614573896138517
3. ! [X0] : ((~wise(X0) | ~strong(X0)) => old(X0)) [input p2]
5. ! [X0] : ((funny(X0) <~> quiet(X0)) <=> (~tall(X0) | old(X0))) [input p4]
7. ! [X0] : (funny(X0) <=> (old(X0) | ~calm(X0))) [input p6]
9. ! [X0] : (~funny(X0) <=> (~wise(X0) & humble(X0))) [input p8]
11. ! [X0] : ((tall(X0) | patient(X0)) <=> ~strong(X0)) [input p10]
23. tall(mary) [input p22]
24. quiet(mary) [input hypothesis]
29. ! [X0] : (old(X0) | (wise(X0) & strong(X0))) [ennf transformation 3]
38. ! [X0] : ((((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0))))) [flattening 38]
42. ! [X0] : ((funny(X0) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | ~funny(X0))) [nnf transformation 7]
43. ! [X0] : ((funny(X0) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ~funny(X0))) [flattening 42]
46. ! [X0] : ((~funny(X0) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | funny(X0))) [nnf transformation 9]
47. ! [X0] : ((~funny(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | funny(X0))) [flattening 46]
48. ! [X0] : (((tall(X0) | patient(X0)) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~patient(X0)))) [nnf transformation 11]
49. ! [X0] : ((tall(X0) | patient(X0) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~patient(X0)))) [flattening 48]
69. old(X0) | strong(X0) [cnf transformation 29]
70. old(X0) | wise(X0) [cnf transformation 29]
76. ~quiet(X0) | ~funny(X0) | ~old(X0) [cnf transformation 39]
84. ~old(X0) | funny(X0) [cnf transformation 43]
89. ~wise(X0) | funny(X0) [cnf transformation 47]
94. ~strong(X0) | ~tall(X0) [cnf transformation 49]
122. tall(mary) [cnf transformation 23]
123. quiet(mary) [cnf transformation 24]
210. funny(X0) | wise(X0) [resolution 84,70]
212. funny(X0) [subsumption resolution 210,89]
238. ~funny(mary) | ~old(mary) [resolution 76,123]
240. ~old(mary) [subsumption resolution 238,212]
245. strong(mary) [resolution 240,69]
252. ~tall(mary) [resolution 245,94]
254. $false [subsumption resolution 252,122]
% SZS output end Proof for 6703206460614573896138517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or happy then someone is either not generous or not patient and vice versa.
If someone is either not funny or wise then alice is either not strong or wise.
Everyone who is either not humble or not quiet is both tall and not wise and vice versa.
If mary is kind then someone is kind.
If lucy is both not calm and brave then fred is both not kind and not wise.
Everyone who is either creative or not tall is both rich and not patient and vice versa.
Everyone who is both not rich and creative is strong and vice versa.
Everyone who is either not wise or funny is both patient and not calm.
Everyone who is both not generous and creative is quiet or brave.
Everyone who is old or tall is happy and vice versa.
Everyone who is curious or calm is rich or not kind.
If someone is both not wise and not strong then fred is curious and vice versa.
If someone is either rich or not calm then someone is not patient.
If fred is both wise and not brave then paul is tall and vice versa.
Everyone who is both not rich and not creative is not calm or happy.
Everyone who is both humble and not humble is humble or not strong and vice versa.
Alice is both not curious and not rich.
Someone is both old and creative.
Someone is strong.
Alice is either not strong or happy.
Someone is happy.
Paul is not rich or not happy. | Paul is not creative. | contradiction | ((?[X]:((~rich(X)|happy(X))))<=>(?[X]:((~generous(X)<~>~patient(X)))))&
((?[X]:((~funny(X)<~>wise(X))))=>((~strong(alice)<~>wise(alice))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(tall(X)&~wise(X))))&
((kind(mary))=>(?[X]:(kind(X))))&
(((~calm(lucy)&brave(lucy)))=>((~kind(fred)&~wise(fred))))&
(![X]:((creative(X)<~>~tall(X))<=>(rich(X)&~patient(X))))&
(![X]:((~rich(X)&creative(X))<=>strong(X)))&
(![X]:((~wise(X)<~>funny(X))=>(patient(X)&~calm(X))))&
(![X]:((~generous(X)&creative(X))=>(quiet(X)|brave(X))))&
(![X]:((old(X)|tall(X))<=>happy(X)))&
(![X]:((curious(X)|calm(X))=>(rich(X)|~kind(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>(curious(fred)))&
((?[X]:((rich(X)<~>~calm(X))))=>(?[X]:(~patient(X))))&
(((wise(fred)&~brave(fred)))<=>(tall(paul)))&
(![X]:((~rich(X)&~creative(X))=>(~calm(X)|happy(X))))&
(![X]:((humble(X)&~humble(X))<=>(humble(X)|~strong(X))))&
((~curious(alice)&~rich(alice)))&
(?[X]:((old(X)&creative(X))))&
(?[X]:(strong(X)))&
((~strong(alice)<~>happy(alice)))&
(?[X]:(happy(X)))&
((~rich(paul)|~happy(paul))) | ~creative(paul) | [
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1911877843632015116941289
% SZS output start Proof for 1911877843632015116941289
7. ! [X0] : ((creative(X0) & ~rich(X0)) <=> strong(X0)) [input p6]
16. ! [X0] : ((~humble(X0) & humble(X0)) <=> (~strong(X0) | humble(X0))) [input p15]
23. ~creative(paul) [input hypothesis]
50. ! [X0] : (((creative(X0) & ~rich(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) | rich(X0)))) [nnf transformation 7]
51. ! [X0] : (((creative(X0) & ~rich(X0)) | ~strong(X0)) & (strong(X0) | ~creative(X0) | rich(X0))) [flattening 50]
65. ! [X0] : (((~humble(X0) & humble(X0)) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | (humble(X0) | ~humble(X0)))) [nnf transformation 16]
66. ! [X0] : (((~humble(X0) & humble(X0)) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | humble(X0) | ~humble(X0))) [flattening 65]
101. ~strong(X0) | creative(X0) [cnf transformation 51]
123. humble(X0) | strong(X0) [cnf transformation 66]
124. ~humble(X0) | ~humble(X0) [cnf transformation 66]
135. ~creative(paul) [cnf transformation 23]
137. ~humble(X0) [duplicate literal removal 124]
258. strong(X0) [subsumption resolution 123,137]
274. creative(X0) [resolution 101,258]
275. $false [resolution 274,135]
% SZS output end Proof for 1911877843632015116941289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not brave is either patient or not humble.
Everyone who is not rich or strong is both calm and quiet.
Everyone who is both old and creative is either not tall or tall and vice versa.
Everyone who is either not kind or not humble is quiet and vice versa.
Everyone who is brave is both curious and not generous.
Everyone who is funny or not brave is either old or not brave.
If someone is not wise or humble then someone is creative.
If someone is both not tall and not creative then someone is either wise or happy.
Everyone who is both curious and not humble is either not wise or rich.
Everyone who is both not wise and old is not old or generous.
Everyone who is either quiet or kind is rich and vice versa.
If someone is not happy or not old then someone is both not generous and kind and vice versa.
If someone is tall then paul is either wise or old and vice versa.
If someone is either kind or quiet then lucy is not funny or wise.
Everyone who is rich is either calm or tall and vice versa.
Someone is not brave or old.
Alice is both not quiet and not generous.
Someone is either not generous or not kind.
Someone is funny.
Someone is either patient or quiet. | Alice is tall. | contradiction | (![X]:((rich(X)|~brave(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~rich(X)|strong(X))=>(calm(X)&quiet(X))))&
(![X]:((old(X)&creative(X))<=>(~tall(X)<~>tall(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>quiet(X)))&
(![X]:(brave(X)=>(curious(X)&~generous(X))))&
(![X]:((funny(X)|~brave(X))=>(old(X)<~>~brave(X))))&
((?[X]:((~wise(X)|humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~tall(X)&~creative(X))))=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((curious(X)&~humble(X))=>(~wise(X)<~>rich(X))))&
(![X]:((~wise(X)&old(X))=>(~old(X)|generous(X))))&
(![X]:((quiet(X)<~>kind(X))<=>rich(X)))&
((?[X]:((~happy(X)|~old(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
((?[X]:(tall(X)))<=>((wise(paul)<~>old(paul))))&
((?[X]:((kind(X)<~>quiet(X))))=>((~funny(lucy)|wise(lucy))))&
(![X]:(rich(X)<=>(calm(X)<~>tall(X))))&
(?[X]:((~brave(X)|old(X))))&
((~quiet(alice)&~generous(alice)))&
(?[X]:((~generous(X)<~>~kind(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)<~>quiet(X)))) | tall(alice) | [
"p2",
"p4",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3446853367653253219622362
% SZS output start Proof for 3446853367653253219622362
3. ! [X0] : ((creative(X0) & old(X0)) <=> (~tall(X0) <~> tall(X0))) [input p2]
5. ! [X0] : (brave(X0) => (~generous(X0) & curious(X0))) [input p4]
6. ! [X0] : ((~brave(X0) | funny(X0)) => (old(X0) <~> ~brave(X0))) [input p5]
10. ! [X0] : ((old(X0) & ~wise(X0)) => (generous(X0) | ~old(X0))) [input p9]
13. ? [X0] : tall(X0) <=> (wise(paul) <~> old(paul)) [input p12]
21. tall(alice) [input hypothesis]
28. ! [X0] : ((~generous(X0) & curious(X0)) | ~brave(X0)) [ennf transformation 5]
29. ! [X0] : ((old(X0) <~> ~brave(X0)) | (brave(X0) & ~funny(X0))) [ennf transformation 6]
34. ! [X0] : ((generous(X0) | ~old(X0)) | (~old(X0) | wise(X0))) [ennf transformation 10]
35. ! [X0] : (generous(X0) | ~old(X0) | ~old(X0) | wise(X0)) [flattening 34]
39. ! [X0] : (((creative(X0) & old(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | (~creative(X0) | ~old(X0)))) [nnf transformation 3]
40. ! [X0] : (((creative(X0) & old(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ~creative(X0) | ~old(X0))) [flattening 39]
42. ! [X0] : (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | (brave(X0) & ~funny(X0))) [nnf transformation 29]
57. (? [X0] : tall(X0) | ((wise(paul) | ~old(paul)) & (old(paul) | ~wise(paul)))) & (((~old(paul) | ~wise(paul)) & (old(paul) | wise(paul))) | ! [X0] : ~tall(X0)) [nnf transformation 13]
58. (? [X0] : tall(X0) | ((wise(paul) | ~old(paul)) & (old(paul) | ~wise(paul)))) & (((~old(paul) | ~wise(paul)) & (old(paul) | wise(paul))) | ! [X1] : ~tall(X1)) [rectify 57]
59. ? [X0] : tall(X0) => tall(sK4) [choice axiom]
60. (tall(sK4) | ((wise(paul) | ~old(paul)) & (old(paul) | ~wise(paul)))) & (((~old(paul) | ~wise(paul)) & (old(paul) | wise(paul))) | ! [X1] : ~tall(X1)) [skolemisation 58,59]
81. old(X0) | tall(X0) | tall(X0) [cnf transformation 40]
82. old(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 40]
90. ~generous(X0) | ~brave(X0) [cnf transformation 28]
94. brave(X0) | ~old(X0) | brave(X0) [cnf transformation 42]
101. generous(X0) | ~old(X0) | ~old(X0) | wise(X0) [cnf transformation 35]
112. ~old(paul) | ~wise(paul) | ~tall(X1) [cnf transformation 60]
129. tall(alice) [cnf transformation 21]
130. generous(X0) | ~old(X0) | wise(X0) [duplicate literal removal 101]
131. brave(X0) | ~old(X0) [duplicate literal removal 94]
132. old(X0) | tall(X0) [duplicate literal removal 81]
133. ~tall(X0) | old(X0) [duplicate literal removal 82]
137. old(X0) [subsumption resolution 132,133]
138. brave(X0) [subsumption resolution 131,137]
139. wise(X0) | generous(X0) [subsumption resolution 130,137]
166. 6 <=> wise(paul) [avatar definition]
167. ~wise(paul) <- (~6) [avatar component clause 166]
174. ~wise(paul) | ~tall(X1) [subsumption resolution 112,137]
176. 8 <=> ! [X1] : ~tall(X1) [avatar definition]
177. ~tall(X1) <- (8) [avatar component clause 176]
178. 8 | ~6 [avatar split clause 174,166,176]
231. generous(paul) <- (~6) [resolution 139,167]
232. ~brave(paul) <- (~6) [resolution 231,90]
233. $false <- (~6) [subsumption resolution 232,138]
234. 6 [avatar contradiction clause 233]
235. $false <- (8) [resolution 177,129]
238. ~8 [avatar contradiction clause 235]
239. $false [avatar sat refutation 178,234,238]
% SZS output end Proof for 3446853367653253219622362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not old is both not calm and not strong.
If someone is both not humble and creative then someone is both not happy and wise and vice versa.
Everyone who is both not strong and humble is both old and not humble and vice versa.
Everyone who is not kind or not creative is not creative or wise.
Everyone who is both not patient and not wise is not creative and vice versa.
Everyone who is both not tall and not happy is strong.
If alice is both not curious and creative then someone is both generous and not funny and vice versa.
Everyone who is not strong or not creative is both funny and not kind.
If susan is not kind or not rich then someone is both old and not old.
Everyone who is either not patient or creative is both not wise and not creative.
If alice is not brave then fred is either not humble or strong and vice versa.
Everyone who is either old or happy is either not calm or calm.
Everyone who is not happy or creative is either calm or not old.
Everyone who is not brave or creative is both old and happy.
If paul is either not calm or not curious then mary is not brave.
If paul is either not happy or not generous then john is calm.
Someone is kind.
Paul is both curious and not quiet.
John is either not calm or not old.
Someone is both tall and not creative.
Someone is not patient.
Alice is both strong and generous. | Fred is wise. | neutral | (![X]:((~creative(X)<~>~old(X))=>(~calm(X)&~strong(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:((~strong(X)&humble(X))<=>(old(X)&~humble(X))))&
(![X]:((~kind(X)|~creative(X))=>(~creative(X)|wise(X))))&
(![X]:((~patient(X)&~wise(X))<=>~creative(X)))&
(![X]:((~tall(X)&~happy(X))=>strong(X)))&
(((~curious(alice)&creative(alice)))<=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((~strong(X)|~creative(X))=>(funny(X)&~kind(X))))&
(((~kind(susan)|~rich(susan)))=>(?[X]:((old(X)&~old(X)))))&
(![X]:((~patient(X)<~>creative(X))=>(~wise(X)&~creative(X))))&
((~brave(alice))<=>((~humble(fred)<~>strong(fred))))&
(![X]:((old(X)<~>happy(X))=>(~calm(X)<~>calm(X))))&
(![X]:((~happy(X)|creative(X))=>(calm(X)<~>~old(X))))&
(![X]:((~brave(X)|creative(X))=>(old(X)&happy(X))))&
(((~calm(paul)<~>~curious(paul)))=>(~brave(mary)))&
(((~happy(paul)<~>~generous(paul)))=>(calm(john)))&
(?[X]:(kind(X)))&
((curious(paul)&~quiet(paul)))&
((~calm(john)<~>~old(john)))&
(?[X]:((tall(X)&~creative(X))))&
(?[X]:(~patient(X)))&
((strong(alice)&generous(alice))) | wise(fred) | [] | null | 0 |
Everyone who is both generous and not strong is either not brave or not tall.
Everyone who is either not patient or calm is either not rich or calm and vice versa.
Everyone who is either not happy or not rich is either not kind or rich.
If someone is either not rich or not humble then alice is not happy.
Everyone who is both wise and humble is both not calm and brave.
If someone is not funny or generous then mary is both rich and not patient and vice versa.
Everyone who is both kind and rich is both kind and happy.
Everyone who is both not curious and not generous is either curious or funny.
If someone is either tall or creative then susan is either not happy or not generous.
If john is either quiet or not funny then someone is creative.
Everyone who is either old or kind is either not strong or tall.
If someone is patient or rich then susan is both rich and not humble.
Everyone who is both tall and not wise is both creative and funny and vice versa.
If someone is curious or not wise then someone is calm and vice versa.
If paul is both not tall and patient then someone is both funny and quiet.
If alice is either quiet or not brave then paul is either kind or not wise and vice versa.
Someone is both not happy and not rich.
Someone is both not brave and not calm.
Mary is not rich.
Someone is not kind or brave.
Someone is quiet or not kind.
Someone is both not calm and not kind.
Fred is either rich or tall. | Mary is not funny. | contradiction | (![X]:((generous(X)&~strong(X))=>(~brave(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>calm(X))<=>(~rich(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~rich(X))=>(~kind(X)<~>rich(X))))&
((?[X]:((~rich(X)<~>~humble(X))))=>(~happy(alice)))&
(![X]:((wise(X)&humble(X))=>(~calm(X)&brave(X))))&
((?[X]:((~funny(X)|generous(X))))<=>((rich(mary)&~patient(mary))))&
(![X]:((kind(X)&rich(X))=>(kind(X)&happy(X))))&
(![X]:((~curious(X)&~generous(X))=>(curious(X)<~>funny(X))))&
((?[X]:((tall(X)<~>creative(X))))=>((~happy(susan)<~>~generous(susan))))&
(((quiet(john)<~>~funny(john)))=>(?[X]:(creative(X))))&
(![X]:((old(X)<~>kind(X))=>(~strong(X)<~>tall(X))))&
((?[X]:((patient(X)|rich(X))))=>((rich(susan)&~humble(susan))))&
(![X]:((tall(X)&~wise(X))<=>(creative(X)&funny(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:(calm(X))))&
(((~tall(paul)&patient(paul)))=>(?[X]:((funny(X)&quiet(X)))))&
(((quiet(alice)<~>~brave(alice)))<=>((kind(paul)<~>~wise(paul))))&
(?[X]:((~happy(X)&~rich(X))))&
(?[X]:((~brave(X)&~calm(X))))&
(~rich(mary))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((quiet(X)|~kind(X))))&
(?[X]:((~calm(X)&~kind(X))))&
((rich(fred)<~>tall(fred))) | ~funny(mary) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3387370121370729802772954
% SZS output start Proof for 3387370121370729802772954
6. ? [X0] : (generous(X0) | ~funny(X0)) <=> (~patient(mary) & rich(mary)) [input p5]
19. ~rich(mary) [input p18]
24. ~funny(mary) [input hypothesis]
46. (? [X0] : (generous(X0) | ~funny(X0)) | (patient(mary) | ~rich(mary))) & ((~patient(mary) & rich(mary)) | ! [X0] : (~generous(X0) & funny(X0))) [nnf transformation 6]
47. (? [X0] : (generous(X0) | ~funny(X0)) | patient(mary) | ~rich(mary)) & ((~patient(mary) & rich(mary)) | ! [X0] : (~generous(X0) & funny(X0))) [flattening 46]
48. (? [X0] : (generous(X0) | ~funny(X0)) | patient(mary) | ~rich(mary)) & ((~patient(mary) & rich(mary)) | ! [X1] : (~generous(X1) & funny(X1))) [rectify 47]
49. ? [X0] : (generous(X0) | ~funny(X0)) => (generous(sK0) | ~funny(sK0)) [choice axiom]
50. ((generous(sK0) | ~funny(sK0)) | patient(mary) | ~rich(mary)) & ((~patient(mary) & rich(mary)) | ! [X1] : (~generous(X1) & funny(X1))) [skolemisation 48,49]
96. rich(mary) | funny(X1) [cnf transformation 50]
140. ~rich(mary) [cnf transformation 19]
147. ~funny(mary) [cnf transformation 24]
178. 6 <=> ! [X1] : funny(X1) [avatar definition]
179. funny(X1) <- (6) [avatar component clause 178]
182. 7 <=> rich(mary) [avatar definition]
186. 6 | 7 [avatar split clause 96,182,178]
304. ~7 [avatar split clause 140,182]
333. $false <- (6) [resolution 179,147]
334. ~6 [avatar contradiction clause 333]
335. $false [avatar sat refutation 186,304,334]
% SZS output end Proof for 3387370121370729802772954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or curious is wise.
If paul is either brave or not brave then someone is not wise or patient.
If someone is not patient or not calm then someone is both generous and kind.
Everyone who is either tall or rich is not happy.
Everyone who is brave or not funny is not wise or creative and vice versa.
Everyone who is patient is either strong or not old.
Everyone who is either creative or calm is both not quiet and not creative and vice versa.
If someone is either quiet or not generous then someone is both not creative and generous and vice versa.
If fred is either humble or tall then paul is not brave and vice versa.
Everyone who is either curious or not generous is not funny or not curious and vice versa.
If someone is either not rich or rich then paul is either quiet or not rich.
Everyone who is not funny is not happy or quiet and vice versa.
Everyone who is either creative or not humble is generous.
Everyone who is wise is not kind.
Everyone who is either not brave or not quiet is kind and vice versa.
Everyone who is either curious or patient is not tall.
Someone is not old.
Someone is either not happy or not curious.
Susan is old.
Paul is either quiet or not old.
Paul is not tall.
Alice is quiet.
Someone is wise or not kind.
Mary is either not funny or not creative. | Mary is calm. | entailment | (![X]:((generous(X)<~>curious(X))=>wise(X)))&
(((brave(paul)<~>~brave(paul)))=>(?[X]:((~wise(X)|patient(X)))))&
((?[X]:((~patient(X)|~calm(X))))=>(?[X]:((generous(X)&kind(X)))))&
(![X]:((tall(X)<~>rich(X))=>~happy(X)))&
(![X]:((brave(X)|~funny(X))<=>(~wise(X)|creative(X))))&
(![X]:(patient(X)=>(strong(X)<~>~old(X))))&
(![X]:((creative(X)<~>calm(X))<=>(~quiet(X)&~creative(X))))&
((?[X]:((quiet(X)<~>~generous(X))))<=>(?[X]:((~creative(X)&generous(X)))))&
(((humble(fred)<~>tall(fred)))<=>(~brave(paul)))&
(![X]:((curious(X)<~>~generous(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~rich(X)<~>rich(X))))=>((quiet(paul)<~>~rich(paul))))&
(![X]:(~funny(X)<=>(~happy(X)|quiet(X))))&
(![X]:((creative(X)<~>~humble(X))=>generous(X)))&
(![X]:(wise(X)=>~kind(X)))&
(![X]:((~brave(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((curious(X)<~>patient(X))=>~tall(X)))&
(?[X]:(~old(X)))&
(?[X]:((~happy(X)<~>~curious(X))))&
(old(susan))&
((quiet(paul)<~>~old(paul)))&
(~tall(paul))&
(quiet(alice))&
(?[X]:((wise(X)|~kind(X))))&
((~funny(mary)<~>~creative(mary))) | calm(mary) | [
"p6",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3875060691108849458740757
% SZS output start Proof for 3875060691108849458740757
7. ! [X0] : ((creative(X0) <~> calm(X0)) <=> (~creative(X0) & ~quiet(X0))) [input p6]
12. ! [X0] : (~funny(X0) <=> (quiet(X0) | ~happy(X0))) [input p11]
24. ~funny(mary) <~> ~creative(mary) [input p23]
25. ~calm(mary) [input hypothesis]
48. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [nnf transformation 7]
49. ! [X0] : ((((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))))) [flattening 48]
59. ! [X0] : ((~funny(X0) | (~quiet(X0) & happy(X0))) & ((quiet(X0) | ~happy(X0)) | funny(X0))) [nnf transformation 12]
60. ! [X0] : ((~funny(X0) | (~quiet(X0) & happy(X0))) & (quiet(X0) | ~happy(X0) | funny(X0))) [flattening 59]
72. (creative(mary) | funny(mary)) & (~creative(mary) | ~funny(mary)) [nnf transformation 24]
91. ~creative(X0) | calm(X0) | ~creative(X0) [cnf transformation 49]
93. calm(X0) | creative(X0) | creative(X0) | quiet(X0) [cnf transformation 49]
117. ~quiet(X0) | ~funny(X0) [cnf transformation 60]
137. creative(mary) | funny(mary) [cnf transformation 72]
138. ~calm(mary) [cnf transformation 25]
145. ~creative(X0) | calm(X0) [duplicate literal removal 91]
146. quiet(X0) | creative(X0) | calm(X0) [duplicate literal removal 93]
261. 24 <=> funny(mary) [avatar definition]
263. funny(mary) <- (24) [avatar component clause 261]
265. 25 <=> creative(mary) [avatar definition]
267. creative(mary) <- (25) [avatar component clause 265]
268. 24 | 25 [avatar split clause 137,265,261]
318. calm(mary) <- (25) [resolution 267,145]
319. $false <- (25) [subsumption resolution 318,138]
320. ~25 [avatar contradiction clause 319]
444. creative(X3) | calm(X3) | ~funny(X3) [resolution 146,117]
451. ~funny(X3) | calm(X3) [subsumption resolution 444,145]
477. calm(mary) <- (24) [resolution 451,263]
478. $false <- (24) [subsumption resolution 477,138]
479. ~24 [avatar contradiction clause 478]
480. $false [avatar sat refutation 268,320,479]
% SZS output end Proof for 3875060691108849458740757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both tall and not humble then someone is either not wise or not generous.
Everyone who is not humble or not happy is both not quiet and not happy and vice versa.
If john is both not calm and old then mary is old or creative.
If someone is either strong or wise then alice is either not quiet or not creative and vice versa.
Everyone who is either strong or not humble is curious and vice versa.
Everyone who is old or not tall is either curious or not humble and vice versa.
If someone is old or not wise then someone is either not humble or tall.
If someone is either not wise or not generous then someone is both not old and not curious.
Everyone who is tall is both creative and generous and vice versa.
Everyone who is both not calm and patient is either quiet or brave and vice versa.
Everyone who is either not calm or patient is either patient or not creative.
If fred is quiet then paul is both not tall and not quiet.
Everyone who is not old or not funny is both not generous and not curious and vice versa.
Everyone who is calm or wise is kind or not creative and vice versa.
Everyone who is not patient is quiet or old.
Everyone who is both not creative and not tall is not happy and vice versa.
Fred is both not kind and not brave.
Paul is not rich or kind.
Alice is creative or not brave.
Susan is either funny or humble.
Someone is not curious.
Paul is calm.
Someone is either not generous or happy.
Someone is both not kind and strong. | Alice is not old. | contradiction | (((tall(mary)&~humble(mary)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:((~humble(X)|~happy(X))<=>(~quiet(X)&~happy(X))))&
(((~calm(john)&old(john)))=>((old(mary)|creative(mary))))&
((?[X]:((strong(X)<~>wise(X))))<=>((~quiet(alice)<~>~creative(alice))))&
(![X]:((strong(X)<~>~humble(X))<=>curious(X)))&
(![X]:((old(X)|~tall(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((old(X)|~wise(X))))=>(?[X]:((~humble(X)<~>tall(X)))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:(tall(X)<=>(creative(X)&generous(X))))&
(![X]:((~calm(X)&patient(X))<=>(quiet(X)<~>brave(X))))&
(![X]:((~calm(X)<~>patient(X))=>(patient(X)<~>~creative(X))))&
((quiet(fred))=>((~tall(paul)&~quiet(paul))))&
(![X]:((~old(X)|~funny(X))<=>(~generous(X)&~curious(X))))&
(![X]:((calm(X)|wise(X))<=>(kind(X)|~creative(X))))&
(![X]:(~patient(X)=>(quiet(X)|old(X))))&
(![X]:((~creative(X)&~tall(X))<=>~happy(X)))&
((~kind(fred)&~brave(fred)))&
((~rich(paul)|kind(paul)))&
((creative(alice)|~brave(alice)))&
((funny(susan)<~>humble(susan)))&
(?[X]:(~curious(X)))&
(calm(paul))&
(?[X]:((~generous(X)<~>happy(X))))&
(?[X]:((~kind(X)&strong(X)))) | ~old(alice) | [
"p1",
"p5",
"p8",
"p9",
"p10",
"p12",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3446718879205043241788381
% SZS output start Proof for 3446718879205043241788381
2. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~happy(X0) & ~quiet(X0))) [input p1]
6. ! [X0] : ((~tall(X0) | old(X0)) <=> (curious(X0) <~> ~humble(X0))) [input p5]
9. ! [X0] : (tall(X0) <=> (generous(X0) & creative(X0))) [input p8]
10. ! [X0] : ((patient(X0) & ~calm(X0)) <=> (quiet(X0) <~> brave(X0))) [input p9]
11. ! [X0] : ((~calm(X0) <~> patient(X0)) => (patient(X0) <~> ~creative(X0))) [input p10]
13. ! [X0] : ((~funny(X0) | ~old(X0)) <=> (~curious(X0) & ~generous(X0))) [input p12]
15. ! [X0] : (~patient(X0) => (old(X0) | quiet(X0))) [input p14]
16. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> ~happy(X0)) [input p15]
19. ~brave(alice) | creative(alice) [input p18]
25. ~old(alice) [input hypothesis]
35. ! [X0] : ((patient(X0) <~> ~creative(X0)) | (~calm(X0) <=> patient(X0))) [ennf transformation 11]
37. ! [X0] : ((old(X0) | quiet(X0)) | patient(X0)) [ennf transformation 15]
38. ! [X0] : (old(X0) | quiet(X0) | patient(X0)) [flattening 37]
42. ! [X0] : (((~happy(X0) | ~humble(X0)) | (happy(X0) | quiet(X0))) & ((~happy(X0) & ~quiet(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 2]
43. ! [X0] : ((~happy(X0) | ~humble(X0) | happy(X0) | quiet(X0)) & ((~happy(X0) & ~quiet(X0)) | (happy(X0) & humble(X0)))) [flattening 42]
49. ! [X0] : (((~tall(X0) | old(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (tall(X0) & ~old(X0)))) [nnf transformation 6]
50. ! [X0] : ((~tall(X0) | old(X0) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (tall(X0) & ~old(X0)))) [flattening 49]
59. ! [X0] : ((tall(X0) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | ~tall(X0))) [nnf transformation 9]
60. ! [X0] : ((tall(X0) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | ~tall(X0))) [flattening 59]
61. ! [X0] : (((patient(X0) & ~calm(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~patient(X0) | calm(X0)))) [nnf transformation 10]
62. ! [X0] : (((patient(X0) & ~calm(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~patient(X0) | calm(X0))) [flattening 61]
63. ! [X0] : (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) [nnf transformation 35]
64. ! [X0] : (((~funny(X0) | ~old(X0)) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | (funny(X0) & old(X0)))) [nnf transformation 13]
65. ! [X0] : ((~funny(X0) | ~old(X0) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | (funny(X0) & old(X0)))) [flattening 64]
68. ! [X0] : (((~tall(X0) & ~creative(X0)) | happy(X0)) & (~happy(X0) | (tall(X0) | creative(X0)))) [nnf transformation 16]
69. ! [X0] : (((~tall(X0) & ~creative(X0)) | happy(X0)) & (~happy(X0) | tall(X0) | creative(X0))) [flattening 68]
81. ~quiet(X0) | happy(X0) [cnf transformation 43]
82. ~happy(X0) | humble(X0) [cnf transformation 43]
99. ~humble(X0) | curious(X0) | tall(X0) [cnf transformation 50]
112. ~tall(X0) | creative(X0) [cnf transformation 60]
113. ~tall(X0) | generous(X0) [cnf transformation 60]
115. ~patient(X0) | quiet(X0) | brave(X0) | calm(X0) [cnf transformation 62]
124. creative(X0) | ~patient(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 63]
127. ~generous(X0) | old(X0) [cnf transformation 65]
129. ~curious(X0) | old(X0) [cnf transformation 65]
136. patient(X0) | quiet(X0) | old(X0) [cnf transformation 38]
137. ~happy(X0) | tall(X0) | creative(X0) [cnf transformation 69]
138. ~creative(X0) | happy(X0) [cnf transformation 69]
142. ~brave(alice) | creative(alice) [cnf transformation 19]
151. ~old(alice) [cnf transformation 25]
153. ~patient(X0) | creative(X0) | ~calm(X0) [duplicate literal removal 124]
190. 9 <=> creative(alice) [avatar definition]
191. ~creative(alice) <- (~9) [avatar component clause 190]
192. creative(alice) <- (9) [avatar component clause 190]
194. 10 <=> quiet(alice) [avatar definition]
195. quiet(alice) <- (10) [avatar component clause 194]
196. ~quiet(alice) <- (~10) [avatar component clause 194]
269. ~happy(X0) | creative(X0) [subsumption resolution 137,112]
271. 26 <=> brave(alice) [avatar definition]
273. ~brave(alice) <- (~26) [avatar component clause 271]
274. 9 | ~26 [avatar split clause 142,271,190]
295. happy(alice) <- (9) [resolution 138,192]
296. humble(alice) <- (9) [resolution 295,82]
347. curious(alice) | tall(alice) <- (9) [resolution 99,296]
349. 39 <=> tall(alice) [avatar definition]
351. tall(alice) <- (39) [avatar component clause 349]
353. 40 <=> curious(alice) [avatar definition]
355. curious(alice) <- (40) [avatar component clause 353]
356. 39 | 40 | ~9 [avatar split clause 347,190,353,349]
368. generous(alice) <- (39) [resolution 351,113]
386. 42 <=> calm(alice) [avatar definition]
387. calm(alice) <- (42) [avatar component clause 386]
401. old(alice) <- (39) [resolution 368,127]
402. $false <- (39) [subsumption resolution 401,151]
403. ~39 [avatar contradiction clause 402]
417. ~calm(X0) | creative(X0) | quiet(X0) | old(X0) [resolution 153,136]
424. old(alice) <- (40) [resolution 355,129]
426. $false <- (40) [subsumption resolution 424,151]
427. ~40 [avatar contradiction clause 426]
447. quiet(X0) | brave(X0) | calm(X0) | quiet(X0) | old(X0) [resolution 115,136]
448. brave(X0) | quiet(X0) | calm(X0) | old(X0) [duplicate literal removal 447]
494. quiet(alice) | calm(alice) | old(alice) <- (~26) [resolution 448,273]
508. calm(alice) | old(alice) <- (~10, ~26) [subsumption resolution 494,196]
513. calm(alice) <- (~10, ~26) [subsumption resolution 508,151]
514. 42 | 10 | 26 [avatar split clause 513,271,194,386]
519. creative(alice) | quiet(alice) | old(alice) <- (42) [resolution 387,417]
521. quiet(alice) | old(alice) <- (~9, 42) [subsumption resolution 519,191]
527. quiet(alice) <- (~9, 42) [subsumption resolution 521,151]
528. 10 | 9 | ~42 [avatar split clause 527,386,190,194]
530. happy(alice) <- (10) [resolution 195,81]
550. creative(alice) <- (10) [resolution 530,269]
552. $false <- (~9, 10) [subsumption resolution 550,191]
553. 9 | ~10 [avatar contradiction clause 552]
554. $false [avatar sat refutation 274,356,403,427,514,528,553]
% SZS output end Proof for 3446718879205043241788381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or creative then someone is either not generous or tall. If someone is quiet then mary is both strong and not patient and vice versa. If someone is both strong and rich then john is both not creative and not calm and vice versa. Everyone who is both quiet and tall is happy or patient and vice versa. Everyone who is patient or not tall is quiet. If someone is kind or not rich then someone is not patient and vice versa. Everyone who is wise or not happy is not kind or not calm and vice versa. If john is both brave and not patient then alice is both funny and curious and vice versa. Everyone who is not brave or old is kind or funny. Everyone who is both not kind and not happy is both curious and not curious and vice versa. If john is not strong then someone is both old and tall. If someone is not calm or not brave then susan is either strong or patient and vice versa. Everyone who is both brave and calm is humble. Everyone who is either not curious or not happy is both rich and brave. If alice is either not funny or kind then alice is both old and quiet and vice versa. Everyone who is either curious or not patient is quiet. Someone is both not quiet and humble. Lucy is not brave. Mary is not rich or calm. Susan is both generous and wise. Mary is not tall. Someone is both patient and funny. Mary is either rich or not calm. Someone is not kind. | Mary is not quiet. | contradiction | ((?[X]:((~generous(X)<~>creative(X))))=>(?[X]:((~generous(X)<~>tall(X)))))&
((?[X]:(quiet(X)))<=>((strong(mary)&~patient(mary))))&
((?[X]:((strong(X)&rich(X))))<=>((~creative(john)&~calm(john))))&
(![X]:((quiet(X)&tall(X))<=>(happy(X)|patient(X))))&
(![X]:((patient(X)|~tall(X))=>quiet(X)))&
((?[X]:((kind(X)|~rich(X))))<=>(?[X]:(~patient(X))))&
(![X]:((wise(X)|~happy(X))<=>(~kind(X)|~calm(X))))&
(((brave(john)&~patient(john)))<=>((funny(alice)&curious(alice))))&
(![X]:((~brave(X)|old(X))=>(kind(X)|funny(X))))&
(![X]:((~kind(X)&~happy(X))<=>(curious(X)&~curious(X))))&
((~strong(john))=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~calm(X)|~brave(X))))<=>((strong(susan)<~>patient(susan))))&
(![X]:((brave(X)&calm(X))=>humble(X)))&
(![X]:((~curious(X)<~>~happy(X))=>(rich(X)&brave(X))))&
(((~funny(alice)<~>kind(alice)))<=>((old(alice)&quiet(alice))))&
(![X]:((curious(X)<~>~patient(X))=>quiet(X)))&
(?[X]:((~quiet(X)&humble(X))))&
(~brave(lucy))&
((~rich(mary)|calm(mary)))&
((generous(susan)&wise(susan)))&
(~tall(mary))&
(?[X]:((patient(X)&funny(X))))&
((rich(mary)<~>~calm(mary)))&
(?[X]:(~kind(X))) | ~quiet(mary) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4747402089670950443488687
% SZS output start Proof for 4747402089670950443488687
5. ! [X0] : ((~tall(X0) | patient(X0)) => quiet(X0)) [input p4]
21. ~tall(mary) [input p20]
25. ~quiet(mary) [input hypothesis]
31. ! [X0] : (quiet(X0) | (tall(X0) & ~patient(X0))) [ennf transformation 5]
98. quiet(X0) | tall(X0) [cnf transformation 31]
141. ~tall(mary) [cnf transformation 21]
147. ~quiet(mary) [cnf transformation 25]
332. tall(mary) [resolution 98,147]
334. $false [subsumption resolution 332,141]
% SZS output end Proof for 4747402089670950443488687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not tall is either happy or not creative.
Everyone who is both not calm and happy is rich.
Everyone who is both rich and kind is generous or not old and vice versa.
If susan is either humble or not curious then someone is both not quiet and quiet and vice versa.
If someone is both not funny and not wise then someone is either not generous or not happy and vice versa.
Everyone who is not curious is either humble or not strong.
If someone is not humble or not quiet then alice is both not brave and not happy and vice versa.
If mary is either not old or wise then mary is creative or calm and vice versa.
If someone is not happy or not strong then someone is not patient or tall.
Everyone who is both old and not calm is either not brave or not quiet and vice versa.
If someone is quiet then alice is both not patient and not happy and vice versa.
Everyone who is either not brave or not happy is humble.
If someone is both old and quiet then paul is funny.
Everyone who is not creative or brave is either not curious or quiet.
Everyone who is both not rich and not happy is creative or rich and vice versa.
If someone is not old or old then paul is both not funny and not generous and vice versa.
Someone is not kind or curious.
Alice is both not generous and not kind.
Someone is either not creative or humble.
Alice is not funny.
Someone is not tall or happy.
Someone is both not funny and strong.
John is either patient or not strong. | Susan is funny. | neutral | (![X]:((quiet(X)&~tall(X))=>(happy(X)<~>~creative(X))))&
(![X]:((~calm(X)&happy(X))=>rich(X)))&
(![X]:((rich(X)&kind(X))<=>(generous(X)|~old(X))))&
(((humble(susan)<~>~curious(susan)))<=>(?[X]:((~quiet(X)&quiet(X)))))&
((?[X]:((~funny(X)&~wise(X))))<=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:(~curious(X)=>(humble(X)<~>~strong(X))))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~brave(alice)&~happy(alice))))&
(((~old(mary)<~>wise(mary)))<=>((creative(mary)|calm(mary))))&
((?[X]:((~happy(X)|~strong(X))))=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((old(X)&~calm(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))<=>((~patient(alice)&~happy(alice))))&
(![X]:((~brave(X)<~>~happy(X))=>humble(X)))&
((?[X]:((old(X)&quiet(X))))=>(funny(paul)))&
(![X]:((~creative(X)|brave(X))=>(~curious(X)<~>quiet(X))))&
(![X]:((~rich(X)&~happy(X))<=>(creative(X)|rich(X))))&
((?[X]:((~old(X)|old(X))))<=>((~funny(paul)&~generous(paul))))&
(?[X]:((~kind(X)|curious(X))))&
((~generous(alice)&~kind(alice)))&
(?[X]:((~creative(X)<~>humble(X))))&
(~funny(alice))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:((~funny(X)&strong(X))))&
((patient(john)<~>~strong(john))) | funny(susan) | [] | null | 0 |
Everyone who is not strong is not brave or wise and vice versa.
Everyone who is either happy or funny is both curious and humble and vice versa.
If someone is patient or not creative then lucy is creative or not rich and vice versa.
Everyone who is not happy is either not curious or kind.
Everyone who is both curious and not tall is either quiet or not brave.
If paul is not old or not calm then lucy is either not tall or funny and vice versa.
Everyone who is not generous or calm is both old and not strong and vice versa.
If someone is funny or not quiet then john is not humble.
If someone is not tall or not humble then lucy is not rich.
If paul is both calm and humble then alice is strong or not happy and vice versa.
If someone is not wise or not curious then someone is not funny.
Everyone who is not brave or tall is tall or not quiet.
Everyone who is calm is either not generous or not patient and vice versa.
Everyone who is either not creative or calm is both not happy and not creative and vice versa.
Everyone who is wise is not funny or not wise and vice versa.
Everyone who is tall or kind is old.
Someone is both humble and not old.
Someone is not happy or funny.
Lucy is not calm or not generous.
Someone is not brave.
Susan is not calm.
Mary is tall or quiet.
Susan is brave. | Alice is kind. | neutral | (![X]:(~strong(X)<=>(~brave(X)|wise(X))))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)&humble(X))))&
((?[X]:((patient(X)|~creative(X))))<=>((creative(lucy)|~rich(lucy))))&
(![X]:(~happy(X)=>(~curious(X)<~>kind(X))))&
(![X]:((curious(X)&~tall(X))=>(quiet(X)<~>~brave(X))))&
(((~old(paul)|~calm(paul)))<=>((~tall(lucy)<~>funny(lucy))))&
(![X]:((~generous(X)|calm(X))<=>(old(X)&~strong(X))))&
((?[X]:((funny(X)|~quiet(X))))=>(~humble(john)))&
((?[X]:((~tall(X)|~humble(X))))=>(~rich(lucy)))&
(((calm(paul)&humble(paul)))<=>((strong(alice)|~happy(alice))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)|tall(X))=>(tall(X)|~quiet(X))))&
(![X]:(calm(X)<=>(~generous(X)<~>~patient(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~happy(X)&~creative(X))))&
(![X]:(wise(X)<=>(~funny(X)|~wise(X))))&
(![X]:((tall(X)|kind(X))=>old(X)))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((~happy(X)|funny(X))))&
((~calm(lucy)|~generous(lucy)))&
(?[X]:(~brave(X)))&
(~calm(susan))&
((tall(mary)|quiet(mary)))&
(brave(susan)) | kind(alice) | [] | null | 0 |
If someone is quiet then john is not rich or not wise.
If someone is either happy or not old then paul is both calm and not humble.
Everyone who is strong or not patient is brave and vice versa.
Everyone who is both rich and creative is old and vice versa.
Everyone who is patient or brave is either kind or not humble.
If paul is not patient or humble then john is either calm or funny and vice versa.
If someone is both quiet and not brave then someone is either not wise or tall and vice versa.
If someone is not creative then paul is either old or kind and vice versa.
Everyone who is not brave or strong is humble or not brave.
If paul is not quiet or not tall then fred is not creative or not brave.
If mary is both kind and brave then john is both kind and wise.
Everyone who is tall or not calm is not curious.
If susan is old or kind then someone is both not kind and not happy and vice versa.
Everyone who is not curious is both not patient and patient.
Everyone who is either not humble or kind is either not calm or not brave and vice versa.
If alice is both not funny and not quiet then fred is either not brave or old.
Someone is not creative.
Alice is both generous and not happy.
Lucy is quiet.
Someone is either patient or not wise.
Someone is either funny or not patient.
Someone is either old or not quiet.
Mary is not generous or not kind. | John is not patient. | contradiction | ((?[X]:(quiet(X)))=>((~rich(john)|~wise(john))))&
((?[X]:((happy(X)<~>~old(X))))=>((calm(paul)&~humble(paul))))&
(![X]:((strong(X)|~patient(X))<=>brave(X)))&
(![X]:((rich(X)&creative(X))<=>old(X)))&
(![X]:((patient(X)|brave(X))=>(kind(X)<~>~humble(X))))&
(((~patient(paul)|humble(paul)))<=>((calm(john)<~>funny(john))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:(~creative(X)))<=>((old(paul)<~>kind(paul))))&
(![X]:((~brave(X)|strong(X))=>(humble(X)|~brave(X))))&
(((~quiet(paul)|~tall(paul)))=>((~creative(fred)|~brave(fred))))&
(((kind(mary)&brave(mary)))=>((kind(john)&wise(john))))&
(![X]:((tall(X)|~calm(X))=>~curious(X)))&
(((old(susan)|kind(susan)))<=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(~curious(X)=>(~patient(X)&patient(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(~calm(X)<~>~brave(X))))&
(((~funny(alice)&~quiet(alice)))=>((~brave(fred)<~>old(fred))))&
(?[X]:(~creative(X)))&
((generous(alice)&~happy(alice)))&
(quiet(lucy))&
(?[X]:((patient(X)<~>~wise(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
((~generous(mary)|~kind(mary))) | ~patient(john) | [
"p2",
"p4",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3399856319483694585555896
% SZS output start Proof for 3399856319483694585555896
3. ! [X0] : ((~patient(X0) | strong(X0)) <=> brave(X0)) [input p2]
5. ! [X0] : ((brave(X0) | patient(X0)) => (kind(X0) <~> ~humble(X0))) [input p4]
12. ! [X0] : ((~calm(X0) | tall(X0)) => ~curious(X0)) [input p11]
14. ! [X0] : (~curious(X0) => (patient(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~calm(X0) <~> ~brave(X0))) [input p14]
24. ~patient(john) [input hypothesis]
29. ! [X0] : ((kind(X0) <~> ~humble(X0)) | (~brave(X0) & ~patient(X0))) [ennf transformation 5]
36. ! [X0] : (~curious(X0) | (calm(X0) & ~tall(X0))) [ennf transformation 12]
37. ! [X0] : ((patient(X0) & ~patient(X0)) | curious(X0)) [ennf transformation 14]
41. ! [X0] : (((~patient(X0) | strong(X0)) | ~brave(X0)) & (brave(X0) | (patient(X0) & ~strong(X0)))) [nnf transformation 3]
42. ! [X0] : ((~patient(X0) | strong(X0) | ~brave(X0)) & (brave(X0) | (patient(X0) & ~strong(X0)))) [flattening 41]
45. ! [X0] : (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~brave(X0) & ~patient(X0))) [nnf transformation 29]
62. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) & (((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 15]
81. brave(X0) | patient(X0) [cnf transformation 42]
87. ~humble(X0) | kind(X0) | ~brave(X0) [cnf transformation 45]
89. humble(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 45]
113. ~curious(X0) | calm(X0) [cnf transformation 36]
119. ~patient(X0) | curious(X0) [cnf transformation 37]
120. curious(X0) | patient(X0) [cnf transformation 37]
121. ~brave(X0) | ~calm(X0) | kind(X0) | humble(X0) [cnf transformation 62]
122. ~brave(X0) | ~calm(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 62]
126. kind(X0) | ~humble(X0) | ~calm(X0) | brave(X0) [cnf transformation 62]
142. ~patient(john) [cnf transformation 24]
298. curious(X0) [subsumption resolution 119,120]
300. kind(X0) | ~humble(X0) | ~calm(X0) [subsumption resolution 126,87]
301. ~brave(X0) | ~calm(X0) | ~kind(X0) [subsumption resolution 122,89]
302. ~brave(X0) | ~calm(X0) | kind(X0) [subsumption resolution 121,300]
303. ~brave(X0) | ~calm(X0) [subsumption resolution 302,301]
355. calm(X0) [resolution 113,298]
375. ~calm(X0) | patient(X0) [resolution 303,81]
376. patient(X0) [subsumption resolution 375,355]
378. $false [resolution 376,142]
% SZS output end Proof for 3399856319483694585555896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or patient is tall or not happy and vice versa.
Everyone who is not humble is wise.
Everyone who is either old or not patient is either kind or not tall and vice versa.
If alice is both not kind and not creative then fred is both not generous and not brave.
If fred is not happy or quiet then someone is not happy and vice versa.
If someone is both humble and not kind then someone is curious or humble and vice versa.
Everyone who is not rich or old is not curious or quiet.
Everyone who is both not kind and humble is wise or not strong and vice versa.
Everyone who is both not happy and wise is not funny or not quiet.
Everyone who is either not kind or tall is not creative or old.
If someone is either not creative or not funny then fred is either not kind or calm.
Everyone who is not funny is not calm or strong.
If someone is both strong and not calm then mary is either happy or not generous and vice versa.
Everyone who is both not happy and creative is either kind or not creative and vice versa.
Everyone who is brave or old is both not creative and patient and vice versa.
If someone is not generous then fred is generous.
Fred is old or patient.
Fred is strong.
Paul is happy.
Susan is not tall or not generous.
Fred is both not calm and kind.
Paul is both humble and wise.
Someone is either rich or generous. | Fred is not brave. | neutral | (![X]:((~creative(X)|patient(X))<=>(tall(X)|~happy(X))))&
(![X]:(~humble(X)=>wise(X)))&
(![X]:((old(X)<~>~patient(X))<=>(kind(X)<~>~tall(X))))&
(((~kind(alice)&~creative(alice)))=>((~generous(fred)&~brave(fred))))&
(((~happy(fred)|quiet(fred)))<=>(?[X]:(~happy(X))))&
((?[X]:((humble(X)&~kind(X))))<=>(?[X]:((curious(X)|humble(X)))))&
(![X]:((~rich(X)|old(X))=>(~curious(X)|quiet(X))))&
(![X]:((~kind(X)&humble(X))<=>(wise(X)|~strong(X))))&
(![X]:((~happy(X)&wise(X))=>(~funny(X)|~quiet(X))))&
(![X]:((~kind(X)<~>tall(X))=>(~creative(X)|old(X))))&
((?[X]:((~creative(X)<~>~funny(X))))=>((~kind(fred)<~>calm(fred))))&
(![X]:(~funny(X)=>(~calm(X)|strong(X))))&
((?[X]:((strong(X)&~calm(X))))<=>((happy(mary)<~>~generous(mary))))&
(![X]:((~happy(X)&creative(X))<=>(kind(X)<~>~creative(X))))&
(![X]:((brave(X)|old(X))<=>(~creative(X)&patient(X))))&
((?[X]:(~generous(X)))=>(generous(fred)))&
((old(fred)|patient(fred)))&
(strong(fred))&
(happy(paul))&
((~tall(susan)|~generous(susan)))&
((~calm(fred)&kind(fred)))&
((humble(paul)&wise(paul)))&
(?[X]:((rich(X)<~>generous(X)))) | ~brave(fred) | [] | null | 0 |
Everyone who is either not strong or not kind is not rich.
Everyone who is humble is brave.
If paul is either patient or funny then someone is both not funny and not happy.
Everyone who is both not creative and calm is both not rich and kind and vice versa.
Everyone who is either creative or not brave is either not happy or not rich and vice versa.
If john is not tall or not quiet then alice is creative or tall.
Everyone who is either curious or not rich is either not creative or not humble.
Everyone who is patient or not humble is both kind and funny.
Everyone who is either quiet or not happy is tall.
If someone is kind or not creative then mary is both funny and happy and vice versa.
If someone is tall or creative then lucy is creative and vice versa.
If someone is either humble or not strong then someone is patient and vice versa.
Everyone who is wise or humble is creative and vice versa.
Everyone who is not creative or kind is both not curious and happy.
If alice is either not brave or not calm then john is strong and vice versa.
If susan is both not calm and not creative then alice is both happy and wise and vice versa.
John is both not quiet and brave.
Mary is not generous or strong.
Someone is funny.
Paul is not patient.
Alice is both not happy and not calm.
Alice is not creative or not generous.
Paul is quiet. | John is not happy. | contradiction | (![X]:((~strong(X)<~>~kind(X))=>~rich(X)))&
(![X]:(humble(X)=>brave(X)))&
(((patient(paul)<~>funny(paul)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((~creative(X)&calm(X))<=>(~rich(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(~happy(X)<~>~rich(X))))&
(((~tall(john)|~quiet(john)))=>((creative(alice)|tall(alice))))&
(![X]:((curious(X)<~>~rich(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((patient(X)|~humble(X))=>(kind(X)&funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
((~quiet(john)&brave(john)))&
((~generous(mary)|strong(mary)))&
(?[X]:(funny(X)))&
(~patient(paul))&
((~happy(alice)&~calm(alice)))&
((~creative(alice)|~generous(alice)))&
(quiet(paul)) | ~happy(john) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p7",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 109774255814028690044019
% SZS output start Proof for 109774255814028690044019
1. ! [X0] : ((~strong(X0) <~> ~kind(X0)) => ~rich(X0)) [input p0]
2. ! [X0] : (humble(X0) => brave(X0)) [input p1]
4. ! [X0] : ((calm(X0) & ~creative(X0)) <=> (kind(X0) & ~rich(X0))) [input p3]
5. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> (~happy(X0) <~> ~rich(X0))) [input p4]
7. ! [X0] : ((curious(X0) <~> ~rich(X0)) => (~creative(X0) <~> ~humble(X0))) [input p6]
8. ! [X0] : ((~humble(X0) | patient(X0)) => (funny(X0) & kind(X0))) [input p7]
13. ! [X0] : ((humble(X0) | wise(X0)) <=> creative(X0)) [input p12]
14. ! [X0] : ((kind(X0) | ~creative(X0)) => (happy(X0) & ~curious(X0))) [input p13]
15. (~brave(alice) <~> ~calm(alice)) <=> strong(john) [input p14]
21. ~calm(alice) & ~happy(alice) [input p20]
24. ~happy(john) [input hypothesis]
28. ! [X0] : (~rich(X0) | (~strong(X0) <=> ~kind(X0))) [ennf transformation 1]
29. ! [X0] : (brave(X0) | ~humble(X0)) [ennf transformation 2]
33. ! [X0] : ((~creative(X0) <~> ~humble(X0)) | (curious(X0) <=> ~rich(X0))) [ennf transformation 7]
34. ! [X0] : ((funny(X0) & kind(X0)) | (humble(X0) & ~patient(X0))) [ennf transformation 8]
36. ! [X0] : ((happy(X0) & ~curious(X0)) | (~kind(X0) & creative(X0))) [ennf transformation 14]
37. ! [X0] : (~rich(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) [nnf transformation 28]
41. ! [X0] : (((calm(X0) & ~creative(X0)) | (~kind(X0) | rich(X0))) & ((kind(X0) & ~rich(X0)) | (~calm(X0) | creative(X0)))) [nnf transformation 4]
42. ! [X0] : (((calm(X0) & ~creative(X0)) | ~kind(X0) | rich(X0)) & ((kind(X0) & ~rich(X0)) | ~calm(X0) | creative(X0))) [flattening 41]
43. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 5]
44. ! [X0] : (((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [nnf transformation 33]
60. ! [X0] : (((humble(X0) | wise(X0)) | ~creative(X0)) & (creative(X0) | (~humble(X0) & ~wise(X0)))) [nnf transformation 13]
61. ! [X0] : ((humble(X0) | wise(X0) | ~creative(X0)) & (creative(X0) | (~humble(X0) & ~wise(X0)))) [flattening 60]
62. (((calm(alice) | brave(alice)) & (~calm(alice) | ~brave(alice))) | ~strong(john)) & (strong(john) | ((~brave(alice) | calm(alice)) & (~calm(alice) | brave(alice)))) [nnf transformation 15]
68. ~rich(X0) | ~strong(X0) | kind(X0) [cnf transformation 37]
69. ~humble(X0) | brave(X0) [cnf transformation 29]
76. ~creative(X0) | ~kind(X0) | rich(X0) [cnf transformation 42]
80. ~creative(X0) | happy(X0) | ~brave(X0) | rich(X0) [cnf transformation 43]
91. curious(X0) | creative(X0) | humble(X0) | rich(X0) [cnf transformation 44]
93. humble(X0) | kind(X0) [cnf transformation 34]
111. ~humble(X0) | creative(X0) [cnf transformation 61]
114. ~curious(X0) | ~kind(X0) [cnf transformation 36]
115. creative(X0) | happy(X0) [cnf transformation 36]
116. ~kind(X0) | happy(X0) [cnf transformation 36]
118. strong(john) | ~brave(alice) | calm(alice) [cnf transformation 62]
129. ~happy(alice) [cnf transformation 21]
130. ~calm(alice) [cnf transformation 21]
132. ~happy(john) [cnf transformation 24]
245. 26 <=> strong(john) [avatar definition]
246. strong(john) <- (26) [avatar component clause 245]
249. 27 <=> brave(alice) [avatar definition]
250. ~brave(alice) <- (~27) [avatar component clause 249]
253. 28 <=> calm(alice) [avatar definition]
258. 28 | ~27 | 26 [avatar split clause 118,245,249,253]
261. 29 <=> happy(alice) [avatar definition]
263. ~happy(alice) <- (~29) [avatar component clause 261]
282. ~28 [avatar split clause 130,253]
283. ~29 [avatar split clause 129,261]
286. brave(X0) | kind(X0) [resolution 93,69]
295. kind(alice) <- (~27) [resolution 286,250]
296. happy(alice) <- (~27) [resolution 295,116]
297. $false <- (~27, ~29) [subsumption resolution 296,263]
298. 27 | 29 [avatar contradiction clause 297]
482. happy(X0) | ~brave(X0) | rich(X0) | happy(X0) [resolution 80,115]
487. ~brave(X0) | happy(X0) | rich(X0) [duplicate literal removal 482]
568. creative(X2) | humble(X2) | rich(X2) | ~kind(X2) [resolution 91,114]
572. creative(X2) | humble(X2) | rich(X2) [subsumption resolution 568,93]
573. creative(X2) | rich(X2) [subsumption resolution 572,111]
641. rich(X0) | ~kind(X0) | rich(X0) [resolution 573,76]
652. ~kind(X0) | rich(X0) [duplicate literal removal 641]
675. happy(X1) | rich(X1) | kind(X1) [resolution 487,286]
680. happy(X1) | rich(X1) [subsumption resolution 675,652]
710. 66 <=> rich(john) [avatar definition]
712. rich(john) <- (66) [avatar component clause 710]
897. rich(john) [resolution 680,132]
903. 66 [avatar split clause 897,710]
931. ~strong(john) | kind(john) <- (66) [resolution 712,68]
933. kind(john) <- (26, 66) [subsumption resolution 931,246]
971. happy(john) <- (26, 66) [resolution 933,116]
972. $false <- (26, 66) [subsumption resolution 971,132]
973. ~26 | ~66 [avatar contradiction clause 972]
974. $false [avatar sat refutation 258,282,283,298,903,973]
% SZS output end Proof for 109774255814028690044019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and old is not humble.
If lucy is both kind and happy then susan is either not kind or quiet and vice versa.
Everyone who is not tall or not quiet is funny or rich and vice versa.
Everyone who is not creative is old or tall and vice versa.
If mary is either wise or not patient then john is either old or not old and vice versa.
Everyone who is not funny or not wise is curious or not wise and vice versa.
If paul is either tall or not kind then someone is wise and vice versa.
If someone is calm or not quiet then someone is both strong and quiet.
If someone is either patient or kind then john is either not funny or happy and vice versa.
Everyone who is old is both not quiet and kind and vice versa.
If someone is not brave or patient then mary is kind or not humble.
If mary is curious or patient then someone is either humble or not humble.
Everyone who is not curious or quiet is not curious or funny and vice versa.
Everyone who is brave is not wise or not quiet.
Everyone who is happy or not calm is generous or not brave.
Everyone who is not creative or not kind is not humble and vice versa.
Someone is either not patient or not generous.
Someone is either not old or not wise.
Lucy is funny or not old.
Someone is patient or curious.
Mary is not calm.
Alice is not quiet.
Someone is either not patient or not brave.
John is tall or not calm. | Mary is not funny. | neutral | (![X]:((~tall(X)&old(X))=>~humble(X)))&
(((kind(lucy)&happy(lucy)))<=>((~kind(susan)<~>quiet(susan))))&
(![X]:((~tall(X)|~quiet(X))<=>(funny(X)|rich(X))))&
(![X]:(~creative(X)<=>(old(X)|tall(X))))&
(((wise(mary)<~>~patient(mary)))<=>((old(john)<~>~old(john))))&
(![X]:((~funny(X)|~wise(X))<=>(curious(X)|~wise(X))))&
(((tall(paul)<~>~kind(paul)))<=>(?[X]:(wise(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((strong(X)&quiet(X)))))&
((?[X]:((patient(X)<~>kind(X))))<=>((~funny(john)<~>happy(john))))&
(![X]:(old(X)<=>(~quiet(X)&kind(X))))&
((?[X]:((~brave(X)|patient(X))))=>((kind(mary)|~humble(mary))))&
(((curious(mary)|patient(mary)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~curious(X)|quiet(X))<=>(~curious(X)|funny(X))))&
(![X]:(brave(X)=>(~wise(X)|~quiet(X))))&
(![X]:((happy(X)|~calm(X))=>(generous(X)|~brave(X))))&
(![X]:((~creative(X)|~kind(X))<=>~humble(X)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
((funny(lucy)|~old(lucy)))&
(?[X]:((patient(X)|curious(X))))&
(~calm(mary))&
(~quiet(alice))&
(?[X]:((~patient(X)<~>~brave(X))))&
((tall(john)|~calm(john))) | ~funny(mary) | [] | null | 0 |
If someone is both not happy and not kind then someone is rich and vice versa.
If someone is happy or old then john is funny or tall.
If someone is happy or strong then john is funny or humble.
If someone is both happy and curious then paul is curious and vice versa.
Everyone who is either brave or not strong is strong or not humble.
Everyone who is either happy or not quiet is either happy or humble.
Everyone who is creative is strong or not happy.
If someone is either funny or not creative then someone is either old or not patient.
Everyone who is either quiet or curious is not brave.
Everyone who is curious is not funny.
If someone is not patient or not generous then someone is tall and vice versa.
Everyone who is happy is not creative or patient and vice versa.
Everyone who is wise or kind is both old and not brave.
Everyone who is not calm is either kind or happy and vice versa.
Everyone who is both strong and not tall is strong or not strong and vice versa.
Everyone who is not kind or not humble is not happy and vice versa.
Paul is old.
Someone is not strong or not funny.
Someone is not curious.
Someone is rich or not funny. | John is not curious. | entailment | ((?[X]:((~happy(X)&~kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:((happy(X)|old(X))))=>((funny(john)|tall(john))))&
((?[X]:((happy(X)|strong(X))))=>((funny(john)|humble(john))))&
((?[X]:((happy(X)&curious(X))))<=>(curious(paul)))&
(![X]:((brave(X)<~>~strong(X))=>(strong(X)|~humble(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(happy(X)<~>humble(X))))&
(![X]:(creative(X)=>(strong(X)|~happy(X))))&
((?[X]:((funny(X)<~>~creative(X))))=>(?[X]:((old(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>curious(X))=>~brave(X)))&
(![X]:(curious(X)=>~funny(X)))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:(tall(X))))&
(![X]:(happy(X)<=>(~creative(X)|patient(X))))&
(![X]:((wise(X)|kind(X))=>(old(X)&~brave(X))))&
(![X]:(~calm(X)<=>(kind(X)<~>happy(X))))&
(![X]:((strong(X)&~tall(X))<=>(strong(X)|~strong(X))))&
(![X]:((~kind(X)|~humble(X))<=>~happy(X)))&
(old(paul))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:((rich(X)|~funny(X)))) | ~curious(john) | [
"p1",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7063459314424189220642558
% SZS output start Proof for 7063459314424189220642558
2. ? [X0] : (old(X0) | happy(X0)) => (tall(john) | funny(john)) [input p1]
10. ! [X0] : (curious(X0) => ~funny(X0)) [input p9]
15. ! [X0] : ((~tall(X0) & strong(X0)) <=> (~strong(X0) | strong(X0))) [input p14]
17. old(paul) [input p16]
21. curious(john) [input hypothesis]
26. (tall(john) | funny(john)) | ! [X0] : (~old(X0) & ~happy(X0)) [ennf transformation 2]
27. tall(john) | funny(john) | ! [X0] : (~old(X0) & ~happy(X0)) [flattening 26]
37. ! [X0] : (~funny(X0) | ~curious(X0)) [ennf transformation 10]
62. ! [X0] : (((~tall(X0) & strong(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (tall(X0) | ~strong(X0)))) [nnf transformation 15]
63. ! [X0] : (((~tall(X0) & strong(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | tall(X0) | ~strong(X0))) [flattening 62]
76. tall(john) | funny(john) | ~old(X0) [cnf transformation 27]
95. ~curious(X0) | ~funny(X0) [cnf transformation 37]
107. ~tall(X0) | ~strong(X0) [cnf transformation 63]
108. ~tall(X0) | strong(X0) [cnf transformation 63]
112. old(paul) [cnf transformation 17]
116. curious(john) [cnf transformation 21]
144. 6 <=> ! [X0] : ~old(X0) [avatar definition]
145. ~old(X0) <- (6) [avatar component clause 144]
147. 7 <=> funny(john) [avatar definition]
151. 8 <=> tall(john) [avatar definition]
153. tall(john) <- (8) [avatar component clause 151]
154. 6 | 7 | 8 [avatar split clause 76,151,147,144]
205. 20 <=> ! [X1] : ~tall(X1) [avatar definition]
206. ~tall(X1) <- (20) [avatar component clause 205]
228. ~tall(X0) [subsumption resolution 107,108]
229. 20 [avatar split clause 228,205]
247. ~funny(john) [resolution 95,116]
252. ~7 [avatar split clause 247,147]
255. $false <- (6) [resolution 145,112]
258. ~6 [avatar contradiction clause 255]
259. $false <- (8, 20) [subsumption resolution 153,206]
260. ~8 | ~20 [avatar contradiction clause 259]
261. $false [avatar sat refutation 154,229,252,258,260]
% SZS output end Proof for 7063459314424189220642558
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If alice is rich then john is both curious and quiet and vice versa. Everyone who is tall is not kind or tall and vice versa. Everyone who is either not curious or happy is both strong and not curious. If someone is not old or wise then someone is both not brave and creative and vice versa. If someone is calm then fred is both not calm and funny and vice versa. If someone is either not rich or not generous then alice is either kind or not tall and vice versa. If someone is quiet then someone is wise or not old and vice versa. If alice is either not patient or creative then john is either rich or not creative. Everyone who is not calm or strong is not curious. If someone is either kind or curious then john is not generous and vice versa. Everyone who is both generous and not old is not kind or not happy. If alice is either not generous or tall then lucy is humble or not calm. If mary is both patient and humble then fred is not strong. Everyone who is both humble and rich is both creative and not patient. If susan is both not patient and not funny then someone is not curious or not tall. Everyone who is both wise and not generous is not generous and vice versa. Alice is both not creative and wise. Someone is quiet or not wise. Fred is not humble. Fred is both not funny and not happy. Someone is not strong or not patient. Someone is not wise or not curious. Someone is not old. Someone is both funny and not patient. | Fred is not curious. | entailment | ((rich(alice))<=>((curious(john)&quiet(john))))&
(![X]:(tall(X)<=>(~kind(X)|tall(X))))&
(![X]:((~curious(X)<~>happy(X))=>(strong(X)&~curious(X))))&
((?[X]:((~old(X)|wise(X))))<=>(?[X]:((~brave(X)&creative(X)))))&
((?[X]:(calm(X)))<=>((~calm(fred)&funny(fred))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>((kind(alice)<~>~tall(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:((wise(X)|~old(X)))))&
(((~patient(alice)<~>creative(alice)))=>((rich(john)<~>~creative(john))))&
(![X]:((~calm(X)|strong(X))=>~curious(X)))&
((?[X]:((kind(X)<~>curious(X))))<=>(~generous(john)))&
(![X]:((generous(X)&~old(X))=>(~kind(X)|~happy(X))))&
(((~generous(alice)<~>tall(alice)))=>((humble(lucy)|~calm(lucy))))&
(((patient(mary)&humble(mary)))=>(~strong(fred)))&
(![X]:((humble(X)&rich(X))=>(creative(X)&~patient(X))))&
(((~patient(susan)&~funny(susan)))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((wise(X)&~generous(X))<=>~generous(X)))&
((~creative(alice)&wise(alice)))&
(?[X]:((quiet(X)|~wise(X))))&
(~humble(fred))&
((~funny(fred)&~happy(fred)))&
(?[X]:((~strong(X)|~patient(X))))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:(~old(X)))&
(?[X]:((funny(X)&~patient(X)))) | ~curious(fred) | [
"p4",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 77050332406451258223664
% SZS output start Proof for 77050332406451258223664
5. ? [X0] : calm(X0) <=> (funny(fred) & ~calm(fred)) [input p4]
9. ! [X0] : ((strong(X0) | ~calm(X0)) => ~curious(X0)) [input p8]
20. ~happy(fred) & ~funny(fred) [input p19]
25. curious(fred) [input hypothesis]
30. ! [X0] : (~curious(X0) | (~strong(X0) & calm(X0))) [ennf transformation 9]
51. (? [X0] : calm(X0) | (~funny(fred) | calm(fred))) & ((funny(fred) & ~calm(fred)) | ! [X0] : ~calm(X0)) [nnf transformation 5]
52. (? [X0] : calm(X0) | ~funny(fred) | calm(fred)) & ((funny(fred) & ~calm(fred)) | ! [X0] : ~calm(X0)) [flattening 51]
53. (? [X0] : calm(X0) | ~funny(fred) | calm(fred)) & ((funny(fred) & ~calm(fred)) | ! [X1] : ~calm(X1)) [rectify 52]
54. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
55. (calm(sK2) | ~funny(fred) | calm(fred)) & ((funny(fred) & ~calm(fred)) | ! [X1] : ~calm(X1)) [skolemisation 53,54]
101. funny(fred) | ~calm(X1) [cnf transformation 55]
118. ~curious(X0) | calm(X0) [cnf transformation 30]
138. ~funny(fred) [cnf transformation 20]
145. curious(fred) [cnf transformation 25]
197. 12 <=> funny(fred) [avatar definition]
206. 14 <=> ! [X1] : ~calm(X1) [avatar definition]
207. ~calm(X1) <- (14) [avatar component clause 206]
208. 14 | 12 [avatar split clause 101,197,206]
356. ~12 [avatar split clause 138,197]
381. calm(fred) [resolution 118,145]
382. $false <- (14) [subsumption resolution 381,207]
383. ~14 [avatar contradiction clause 382]
384. $false [avatar sat refutation 208,356,383]
% SZS output end Proof for 77050332406451258223664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and kind is creative and vice versa. Everyone who is not old is not brave and vice versa. Everyone who is both not old and wise is rich or not old. If someone is not brave or not patient then fred is old and vice versa. If lucy is not creative then fred is not wise and vice versa. Everyone who is brave or not tall is calm or not rich and vice versa. Everyone who is both rich and not patient is tall or curious. Everyone who is not creative is both not quiet and happy. If someone is brave or strong then someone is either not tall or happy and vice versa. Everyone who is not wise or not kind is happy. If fred is either not calm or tall then lucy is not brave or kind. Everyone who is not curious or generous is curious and vice versa. If someone is either creative or wise then john is not tall or tall and vice versa. Everyone who is either not happy or not calm is not tall and vice versa. Everyone who is either tall or not quiet is either wise or not funny and vice versa. Everyone who is both rich and strong is tall or not tall and vice versa. Fred is happy or brave. Someone is not kind or not tall. Mary is both not humble and brave. Someone is not patient. Someone is both humble and not wise. Lucy is either not humble or funny. | Fred is not humble. | neutral | (![X]:((~curious(X)&kind(X))<=>creative(X)))&
(![X]:(~old(X)<=>~brave(X)))&
(![X]:((~old(X)&wise(X))=>(rich(X)|~old(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
((?[X]:((creative(X)<~>wise(X))))<=>((~tall(john)|tall(john))))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((rich(X)&strong(X))<=>(tall(X)|~tall(X))))&
((happy(fred)|brave(fred)))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(mary)&brave(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((humble(X)&~wise(X))))&
((~humble(lucy)<~>funny(lucy))) | ~humble(fred) | [] | null | 0 |
If someone is either not funny or wise then fred is not funny or curious. If someone is not brave then someone is either calm or not curious. Everyone who is humble or not brave is not kind and vice versa. If fred is either not patient or old then john is not rich. Everyone who is both kind and curious is either not funny or patient. If lucy is either old or strong then someone is not humble or not patient. If someone is either not wise or not patient then someone is calm. Everyone who is either curious or rich is both not kind and kind. If susan is not creative then alice is quiet. If paul is either curious or not kind then someone is either not wise or creative. If fred is both generous and curious then mary is either not generous or wise. If someone is funny or brave then fred is either kind or old and vice versa. If lucy is both wise and not calm then someone is either not brave or not calm and vice versa. Everyone who is both not strong and not funny is either old or not creative and vice versa. If fred is both not curious and wise then paul is either not happy or not brave. Everyone who is not creative or not kind is both humble and creative. Someone is funny. Paul is both not happy and creative. Fred is either not happy or funny. Someone is both old and not wise. Someone is not wise or not calm. Someone is either not wise or old. Someone is both creative and strong. Fred is either not happy or quiet. | Susan is creative. | entailment | ((?[X]:((~funny(X)<~>wise(X))))=>((~funny(fred)|curious(fred))))&
((?[X]:(~brave(X)))=>(?[X]:((calm(X)<~>~curious(X)))))&
(![X]:((humble(X)|~brave(X))<=>~kind(X)))&
(((~patient(fred)<~>old(fred)))=>(~rich(john)))&
(![X]:((kind(X)&curious(X))=>(~funny(X)<~>patient(X))))&
(((old(lucy)<~>strong(lucy)))=>(?[X]:((~humble(X)|~patient(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))=>(?[X]:(calm(X))))&
(![X]:((curious(X)<~>rich(X))=>(~kind(X)&kind(X))))&
((~creative(susan))=>(quiet(alice)))&
(((curious(paul)<~>~kind(paul)))=>(?[X]:((~wise(X)<~>creative(X)))))&
(((generous(fred)&curious(fred)))=>((~generous(mary)<~>wise(mary))))&
((?[X]:((funny(X)|brave(X))))<=>((kind(fred)<~>old(fred))))&
(((wise(lucy)&~calm(lucy)))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
(![X]:((~strong(X)&~funny(X))<=>(old(X)<~>~creative(X))))&
(((~curious(fred)&wise(fred)))=>((~happy(paul)<~>~brave(paul))))&
(![X]:((~creative(X)|~kind(X))=>(humble(X)&creative(X))))&
(?[X]:(funny(X)))&
((~happy(paul)&creative(paul)))&
((~happy(fred)<~>funny(fred)))&
(?[X]:((old(X)&~wise(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((creative(X)&strong(X))))&
((~happy(fred)<~>quiet(fred))) | creative(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 263783944416784707454813
% SZS output start Proof for 263783944416784707454813
16. ! [X0] : ((~kind(X0) | ~creative(X0)) => (creative(X0) & humble(X0))) [input p15]
25. ~creative(susan) [input hypothesis]
43. ! [X0] : ((creative(X0) & humble(X0)) | (kind(X0) & creative(X0))) [ennf transformation 16]
138. creative(X0) | creative(X0) [cnf transformation 43]
154. ~creative(susan) [cnf transformation 25]
155. creative(X0) [duplicate literal removal 138]
372. $false [subsumption resolution 154,155]
% SZS output end Proof for 263783944416784707454813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or strong is calm or wise.
If someone is both not rich and old then someone is wise or calm and vice versa.
If susan is both old and not tall then lucy is both not humble and strong.
If paul is both quiet and not humble then someone is not brave or creative and vice versa.
If someone is either happy or funny then lucy is not funny.
If someone is both curious and not tall then someone is either brave or not calm and vice versa.
If someone is happy then susan is tall or curious.
Everyone who is creative is both humble and not creative.
Everyone who is either creative or not generous is not funny.
Everyone who is not calm is either tall or not quiet and vice versa.
Everyone who is both kind and rich is not calm and vice versa.
If someone is either rich or calm then susan is not curious and vice versa.
If alice is not funny then paul is humble and vice versa.
Everyone who is either creative or rich is patient and vice versa.
Everyone who is both wise and not patient is both generous and not tall.
If lucy is either not creative or not rich then fred is not tall.
Fred is not kind or not rich.
Someone is either not brave or not humble.
Someone is both tall and not calm.
Someone is not strong or not humble.
Susan is brave or not strong.
Someone is either not wise or not kind.
Mary is either creative or not funny.
Susan is either kind or calm. | Paul is not creative. | entailment | (![X]:((~strong(X)|strong(X))=>(calm(X)|wise(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((wise(X)|calm(X)))))&
(((old(susan)&~tall(susan)))=>((~humble(lucy)&strong(lucy))))&
(((quiet(paul)&~humble(paul)))<=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:((happy(X)<~>funny(X))))=>(~funny(lucy)))&
((?[X]:((curious(X)&~tall(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
((?[X]:(happy(X)))=>((tall(susan)|curious(susan))))&
(![X]:(creative(X)=>(humble(X)&~creative(X))))&
(![X]:((creative(X)<~>~generous(X))=>~funny(X)))&
(![X]:(~calm(X)<=>(tall(X)<~>~quiet(X))))&
(![X]:((kind(X)&rich(X))<=>~calm(X)))&
((?[X]:((rich(X)<~>calm(X))))<=>(~curious(susan)))&
((~funny(alice))<=>(humble(paul)))&
(![X]:((creative(X)<~>rich(X))<=>patient(X)))&
(![X]:((wise(X)&~patient(X))=>(generous(X)&~tall(X))))&
(((~creative(lucy)<~>~rich(lucy)))=>(~tall(fred)))&
((~kind(fred)|~rich(fred)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((tall(X)&~calm(X))))&
(?[X]:((~strong(X)|~humble(X))))&
((brave(susan)|~strong(susan)))&
(?[X]:((~wise(X)<~>~kind(X))))&
((creative(mary)<~>~funny(mary)))&
((kind(susan)<~>calm(susan))) | ~creative(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4554643875927218523887617
% SZS output start Proof for 4554643875927218523887617
8. ! [X0] : (creative(X0) => (~creative(X0) & humble(X0))) [input p7]
25. creative(paul) [input hypothesis]
36. ! [X0] : ((~creative(X0) & humble(X0)) | ~creative(X0)) [ennf transformation 8]
105. ~creative(X0) | ~creative(X0) [cnf transformation 36]
140. creative(paul) [cnf transformation 25]
141. ~creative(X0) [duplicate literal removal 105]
180. 9 <=> ! [X0] : ~creative(X0) [avatar definition]
181. ~creative(X0) <- (9) [avatar component clause 180]
257. 9 [avatar split clause 141,180]
363. $false <- (9) [resolution 181,140]
364. ~9 [avatar contradiction clause 363]
365. $false [avatar sat refutation 257,364]
% SZS output end Proof for 4554643875927218523887617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is calm then mary is either happy or humble and vice versa. If someone is not creative or tall then someone is either creative or brave and vice versa. Everyone who is not brave or kind is not wise or calm and vice versa. Everyone who is not tall is both not humble and not old and vice versa. Everyone who is not kind is funny. Everyone who is either not strong or wise is not happy and vice versa. Everyone who is both old and not strong is both quiet and not brave. If someone is both not old and not generous then mary is not patient and vice versa. If someone is kind or strong then someone is not tall or happy and vice versa. Everyone who is kind is tall and vice versa. Everyone who is both not happy and not calm is not brave or not wise and vice versa. If someone is both not humble and not happy then someone is both wise and not brave and vice versa. Everyone who is either not humble or funny is calm or wise. Everyone who is either curious or funny is both not humble and not brave and vice versa. Everyone who is tall is both brave and not creative. If someone is both strong and curious then someone is humble. Alice is not calm. Alice is either not generous or not wise. Mary is brave or not strong. Someone is not funny. Lucy is both rich and not wise. Someone is either rich or not creative. Someone is either generous or not rich. Susan is both tall and kind. | Lucy is kind. | entailment | ((calm(susan))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((creative(X)<~>brave(X)))))&
(![X]:((~brave(X)|kind(X))<=>(~wise(X)|calm(X))))&
(![X]:(~tall(X)<=>(~humble(X)&~old(X))))&
(![X]:(~kind(X)=>funny(X)))&
(![X]:((~strong(X)<~>wise(X))<=>~happy(X)))&
(![X]:((old(X)&~strong(X))=>(quiet(X)&~brave(X))))&
((?[X]:((~old(X)&~generous(X))))<=>(~patient(mary)))&
((?[X]:((kind(X)|strong(X))))<=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:(kind(X)<=>tall(X)))&
(![X]:((~happy(X)&~calm(X))<=>(~brave(X)|~wise(X))))&
((?[X]:((~humble(X)&~happy(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((~humble(X)<~>funny(X))=>(calm(X)|wise(X))))&
(![X]:((curious(X)<~>funny(X))<=>(~humble(X)&~brave(X))))&
(![X]:(tall(X)=>(brave(X)&~creative(X))))&
((?[X]:((strong(X)&curious(X))))=>(?[X]:(humble(X))))&
(~calm(alice))&
((~generous(alice)<~>~wise(alice)))&
((brave(mary)|~strong(mary)))&
(?[X]:(~funny(X)))&
((rich(lucy)&~wise(lucy)))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
((tall(susan)&kind(susan))) | kind(lucy) | [
"p2",
"p3",
"p9",
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2349091592436306850860106
% SZS output start Proof for 2349091592436306850860106
3. ! [X0] : ((kind(X0) | ~brave(X0)) <=> (calm(X0) | ~wise(X0))) [input p2]
4. ! [X0] : (~tall(X0) <=> (~old(X0) & ~humble(X0))) [input p3]
10. ! [X0] : (kind(X0) <=> tall(X0)) [input p9]
11. ! [X0] : ((~calm(X0) & ~happy(X0)) <=> (~wise(X0) | ~brave(X0))) [input p10]
12. ? [X0] : (~happy(X0) & ~humble(X0)) <=> ? [X0] : (~brave(X0) & wise(X0)) [input p11]
21. ~wise(lucy) & rich(lucy) [input p20]
25. ~kind(lucy) [input hypothesis]
28. ? [X0] : (~happy(X0) & ~humble(X0)) <=> ? [X1] : (~brave(X1) & wise(X1)) [rectify 12]
44. ! [X0] : (((kind(X0) | ~brave(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~kind(X0) & brave(X0)))) [nnf transformation 3]
45. ! [X0] : ((kind(X0) | ~brave(X0) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | (~kind(X0) & brave(X0)))) [flattening 44]
46. ! [X0] : ((~tall(X0) | (old(X0) | humble(X0))) & ((~old(X0) & ~humble(X0)) | tall(X0))) [nnf transformation 4]
47. ! [X0] : ((~tall(X0) | old(X0) | humble(X0)) & ((~old(X0) & ~humble(X0)) | tall(X0))) [flattening 46]
58. ! [X0] : ((kind(X0) | ~tall(X0)) & (tall(X0) | ~kind(X0))) [nnf transformation 10]
59. ! [X0] : (((~calm(X0) & ~happy(X0)) | (wise(X0) & brave(X0))) & ((~wise(X0) | ~brave(X0)) | (calm(X0) | happy(X0)))) [nnf transformation 11]
60. ! [X0] : (((~calm(X0) & ~happy(X0)) | (wise(X0) & brave(X0))) & (~wise(X0) | ~brave(X0) | calm(X0) | happy(X0))) [flattening 59]
61. (? [X0] : (~happy(X0) & ~humble(X0)) | ! [X1] : (brave(X1) | ~wise(X1))) & (? [X1] : (~brave(X1) & wise(X1)) | ! [X0] : (happy(X0) | humble(X0))) [nnf transformation 28]
62. (? [X0] : (~happy(X0) & ~humble(X0)) | ! [X1] : (brave(X1) | ~wise(X1))) & (? [X2] : (~brave(X2) & wise(X2)) | ! [X3] : (happy(X3) | humble(X3))) [rectify 61]
63. ? [X0] : (~happy(X0) & ~humble(X0)) => (~happy(sK5) & ~humble(sK5)) [choice axiom]
64. ? [X2] : (~brave(X2) & wise(X2)) => (~brave(sK6) & wise(sK6)) [choice axiom]
65. ((~happy(sK5) & ~humble(sK5)) | ! [X1] : (brave(X1) | ~wise(X1))) & ((~brave(sK6) & wise(sK6)) | ! [X3] : (happy(X3) | humble(X3))) [skolemisation 62,64,63]
91. ~wise(X0) | calm(X0) | brave(X0) [cnf transformation 45]
95. ~humble(X0) | tall(X0) [cnf transformation 47]
112. ~tall(X0) | kind(X0) [cnf transformation 58]
115. ~happy(X0) | wise(X0) [cnf transformation 60]
116. ~calm(X0) | brave(X0) [cnf transformation 60]
118. wise(sK6) | happy(X3) | humble(X3) [cnf transformation 65]
119. ~brave(sK6) | happy(X3) | humble(X3) [cnf transformation 65]
139. ~wise(lucy) [cnf transformation 21]
146. ~kind(lucy) [cnf transformation 25]
262. 27 <=> ! [X3] : (happy(X3) | humble(X3)) [avatar definition]
263. humble(X3) | happy(X3) <- (27) [avatar component clause 262]
265. 28 <=> brave(sK6) [avatar definition]
267. ~brave(sK6) <- (~28) [avatar component clause 265]
268. 27 | ~28 [avatar split clause 119,265,262]
270. 29 <=> wise(sK6) [avatar definition]
272. wise(sK6) <- (29) [avatar component clause 270]
273. 27 | 29 [avatar split clause 118,270,262]
343. calm(sK6) | brave(sK6) <- (29) [resolution 91,272]
344. calm(sK6) <- (~28, 29) [subsumption resolution 343,267]
346. brave(sK6) <- (~28, 29) [resolution 344,116]
347. $false <- (~28, 29) [subsumption resolution 346,267]
348. 28 | ~29 [avatar contradiction clause 347]
365. tall(X0) | happy(X0) <- (27) [resolution 263,95]
492. kind(X3) | happy(X3) <- (27) [resolution 365,112]
541. happy(lucy) <- (27) [resolution 492,146]
548. wise(lucy) <- (27) [resolution 541,115]
551. $false <- (27) [subsumption resolution 548,139]
552. ~27 [avatar contradiction clause 551]
553. $false [avatar sat refutation 268,273,348,552]
% SZS output end Proof for 2349091592436306850860106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or old is generous and vice versa. Everyone who is not tall or wise is wise. Everyone who is both not funny and brave is creative. Everyone who is old or quiet is either not quiet or not funny and vice versa. Everyone who is either happy or not quiet is strong. Everyone who is either calm or not strong is either wise or not brave and vice versa. Everyone who is not rich or not strong is both not humble and tall and vice versa. Everyone who is rich is not calm and vice versa. Everyone who is either curious or strong is rich or humble. Everyone who is brave is not humble or not tall. If someone is either funny or tall then alice is either happy or funny. Everyone who is not rich or kind is both not patient and not quiet. If mary is not funny or not kind then someone is not brave and vice versa. Everyone who is both not calm and old is not funny or generous. Everyone who is both not brave and not old is both not curious and not creative and vice versa. Everyone who is both not tall and calm is either not curious or not brave. Someone is humble. Lucy is patient. Someone is brave or tall. Someone is both generous and not patient. Someone is either rich or not quiet. Paul is either happy or funny. Someone is either not humble or strong. Someone is either rich or not funny. | Paul is calm. | neutral | (![X]:((brave(X)|old(X))<=>generous(X)))&
(![X]:((~tall(X)|wise(X))=>wise(X)))&
(![X]:((~funny(X)&brave(X))=>creative(X)))&
(![X]:((old(X)|quiet(X))<=>(~quiet(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~quiet(X))=>strong(X)))&
(![X]:((calm(X)<~>~strong(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((~rich(X)|~strong(X))<=>(~humble(X)&tall(X))))&
(![X]:(rich(X)<=>~calm(X)))&
(![X]:((curious(X)<~>strong(X))=>(rich(X)|humble(X))))&
(![X]:(brave(X)=>(~humble(X)|~tall(X))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(alice)<~>funny(alice))))&
(![X]:((~rich(X)|kind(X))=>(~patient(X)&~quiet(X))))&
(((~funny(mary)|~kind(mary)))<=>(?[X]:(~brave(X))))&
(![X]:((~calm(X)&old(X))=>(~funny(X)|generous(X))))&
(![X]:((~brave(X)&~old(X))<=>(~curious(X)&~creative(X))))&
(![X]:((~tall(X)&calm(X))=>(~curious(X)<~>~brave(X))))&
(?[X]:(humble(X)))&
(patient(lucy))&
(?[X]:((brave(X)|tall(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((rich(X)<~>~quiet(X))))&
((happy(paul)<~>funny(paul)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:((rich(X)<~>~funny(X)))) | calm(paul) | [] | null | 0 |
Everyone who is both not generous and generous is not kind or not patient and vice versa.
Everyone who is quiet or generous is not humble and vice versa.
If susan is not tall or not wise then someone is not calm or creative.
Everyone who is either creative or not kind is not happy.
Everyone who is not tall or not brave is not kind or old.
Everyone who is not quiet is either not humble or not curious and vice versa.
If susan is not tall or brave then someone is both not generous and not funny and vice versa.
If mary is either not rich or calm then fred is either not wise or wise.
If someone is generous then someone is not happy or not wise.
Everyone who is either strong or humble is either old or not old and vice versa.
Everyone who is old is either not funny or not rich and vice versa.
Everyone who is creative or kind is either not generous or not old and vice versa.
Everyone who is either tall or rich is either generous or not kind and vice versa.
Everyone who is both not rich and not strong is kind or not patient.
If john is not old then alice is happy and vice versa.
If lucy is either quiet or not creative then mary is curious and vice versa.
Someone is either not old or quiet.
Someone is not generous or kind.
Lucy is both not funny and curious.
Lucy is either kind or not kind.
Someone is both not wise and happy.
Alice is brave.
Susan is either generous or not funny. | Susan is not quiet. | neutral | (![X]:((~generous(X)&generous(X))<=>(~kind(X)|~patient(X))))&
(![X]:((quiet(X)|generous(X))<=>~humble(X)))&
(((~tall(susan)|~wise(susan)))=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((creative(X)<~>~kind(X))=>~happy(X)))&
(![X]:((~tall(X)|~brave(X))=>(~kind(X)|old(X))))&
(![X]:(~quiet(X)<=>(~humble(X)<~>~curious(X))))&
(((~tall(susan)|brave(susan)))<=>(?[X]:((~generous(X)&~funny(X)))))&
(((~rich(mary)<~>calm(mary)))=>((~wise(fred)<~>wise(fred))))&
((?[X]:(generous(X)))=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:((strong(X)<~>humble(X))<=>(old(X)<~>~old(X))))&
(![X]:(old(X)<=>(~funny(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~generous(X)<~>~old(X))))&
(![X]:((tall(X)<~>rich(X))<=>(generous(X)<~>~kind(X))))&
(![X]:((~rich(X)&~strong(X))=>(kind(X)|~patient(X))))&
((~old(john))<=>(happy(alice)))&
(((quiet(lucy)<~>~creative(lucy)))<=>(curious(mary)))&
(?[X]:((~old(X)<~>quiet(X))))&
(?[X]:((~generous(X)|kind(X))))&
((~funny(lucy)&curious(lucy)))&
((kind(lucy)<~>~kind(lucy)))&
(?[X]:((~wise(X)&happy(X))))&
(brave(alice))&
((generous(susan)<~>~funny(susan))) | ~quiet(susan) | [] | null | 0 |
If fred is both kind and quiet then john is generous. If john is either not tall or tall then susan is both not old and creative and vice versa. If paul is not wise then someone is either not curious or not humble and vice versa. Everyone who is either strong or not brave is tall or not brave. Everyone who is either funny or wise is funny and vice versa. If fred is both not old and not strong then alice is either not patient or not calm. If someone is not happy or curious then fred is both not kind and not calm. If someone is either not generous or brave then susan is not strong or generous and vice versa. If someone is both not strong and rich then mary is both kind and happy and vice versa. Everyone who is either not funny or strong is humble or not tall and vice versa. If john is humble then someone is happy or calm and vice versa. Everyone who is generous is both not kind and funny and vice versa. If lucy is both not patient and humble then someone is both generous and tall. If someone is not kind or generous then mary is not tall and vice versa. Everyone who is not strong or happy is not patient and vice versa. Everyone who is calm is either curious or not tall and vice versa. Susan is either not humble or patient. Susan is not funny or brave. Someone is not strong. Someone is both strong and not curious. Someone is both not brave and happy. Someone is strong. Alice is either humble or old. Fred is calm. | Susan is patient. | contradiction | (((kind(fred)&quiet(fred)))=>(generous(john)))&
(((~tall(john)<~>tall(john)))<=>((~old(susan)&creative(susan))))&
((~wise(paul))<=>(?[X]:((~curious(X)<~>~humble(X)))))&
(![X]:((strong(X)<~>~brave(X))=>(tall(X)|~brave(X))))&
(![X]:((funny(X)<~>wise(X))<=>funny(X)))&
(((~old(fred)&~strong(fred)))=>((~patient(alice)<~>~calm(alice))))&
((?[X]:((~happy(X)|curious(X))))=>((~kind(fred)&~calm(fred))))&
((?[X]:((~generous(X)<~>brave(X))))<=>((~strong(susan)|generous(susan))))&
((?[X]:((~strong(X)&rich(X))))<=>((kind(mary)&happy(mary))))&
(![X]:((~funny(X)<~>strong(X))<=>(humble(X)|~tall(X))))&
((humble(john))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:(generous(X)<=>(~kind(X)&funny(X))))&
(((~patient(lucy)&humble(lucy)))=>(?[X]:((generous(X)&tall(X)))))&
((?[X]:((~kind(X)|generous(X))))<=>(~tall(mary)))&
(![X]:((~strong(X)|happy(X))<=>~patient(X)))&
(![X]:(calm(X)<=>(curious(X)<~>~tall(X))))&
((~humble(susan)<~>patient(susan)))&
((~funny(susan)|brave(susan)))&
(?[X]:(~strong(X)))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:(strong(X)))&
((humble(alice)<~>old(alice)))&
(calm(fred)) | patient(susan) | [
"p6",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 88137609270675905704478
% SZS output start Proof for 88137609270675905704478
7. ? [X0] : (curious(X0) | ~happy(X0)) => (~calm(fred) & ~kind(fred)) [input p6]
15. ! [X0] : ((happy(X0) | ~strong(X0)) <=> ~patient(X0)) [input p14]
24. calm(fred) [input p23]
25. patient(susan) [input hypothesis]
31. (~calm(fred) & ~kind(fred)) | ! [X0] : (~curious(X0) & happy(X0)) [ennf transformation 7]
67. ! [X0] : (((happy(X0) | ~strong(X0)) | patient(X0)) & (~patient(X0) | (~happy(X0) & strong(X0)))) [nnf transformation 15]
68. ! [X0] : ((happy(X0) | ~strong(X0) | patient(X0)) & (~patient(X0) | (~happy(X0) & strong(X0)))) [flattening 67]
100. ~calm(fred) | happy(X0) [cnf transformation 31]
130. ~happy(X0) | ~patient(X0) [cnf transformation 68]
147. calm(fred) [cnf transformation 24]
148. patient(susan) [cnf transformation 25]
217. 14 <=> calm(fred) [avatar definition]
222. 15 <=> ! [X0] : happy(X0) [avatar definition]
223. happy(X0) <- (15) [avatar component clause 222]
224. 15 | ~14 [avatar split clause 100,217,222]
344. 42 <=> patient(susan) [avatar definition]
345. patient(susan) <- (42) [avatar component clause 344]
368. 14 [avatar split clause 147,217]
369. 42 [avatar split clause 148,344]
392. ~patient(X0) <- (15) [resolution 130,223]
393. $false <- (15, 42) [resolution 392,345]
394. ~15 | ~42 [avatar contradiction clause 393]
395. $false [avatar sat refutation 224,368,369,394]
% SZS output end Proof for 88137609270675905704478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not strong and old then someone is not rich or patient.
If someone is either kind or generous then susan is either not generous or creative and vice versa.
Everyone who is both not calm and patient is either not kind or generous and vice versa.
If paul is not kind or not quiet then susan is not calm and vice versa.
Everyone who is not happy is both old and not patient.
Everyone who is rich is not creative.
Everyone who is calm is not old or not patient and vice versa.
If someone is not humble or not old then someone is generous and vice versa.
If someone is either not curious or brave then paul is either quiet or not rich.
If someone is creative then susan is not generous or rich and vice versa.
Everyone who is either not happy or creative is both curious and happy.
If someone is calm or not creative then someone is either not humble or strong and vice versa.
Everyone who is both not patient and creative is both tall and not kind.
If someone is both not old and strong then mary is old or tall.
Everyone who is either kind or quiet is both not patient and rich.
Everyone who is both not rich and not quiet is both generous and not rich and vice versa.
Fred is either not tall or brave.
Susan is curious or generous.
Susan is not quiet.
Someone is tall or not quiet.
Someone is either curious or calm.
Someone is humble or brave.
Someone is not funny or old.
Someone is not rich. | Paul is not quiet. | neutral | (((~strong(mary)&old(mary)))=>(?[X]:((~rich(X)|patient(X)))))&
((?[X]:((kind(X)<~>generous(X))))<=>((~generous(susan)<~>creative(susan))))&
(![X]:((~calm(X)&patient(X))<=>(~kind(X)<~>generous(X))))&
(((~kind(paul)|~quiet(paul)))<=>(~calm(susan)))&
(![X]:(~happy(X)=>(old(X)&~patient(X))))&
(![X]:(rich(X)=>~creative(X)))&
(![X]:(calm(X)<=>(~old(X)|~patient(X))))&
((?[X]:((~humble(X)|~old(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~curious(X)<~>brave(X))))=>((quiet(paul)<~>~rich(paul))))&
((?[X]:(creative(X)))<=>((~generous(susan)|rich(susan))))&
(![X]:((~happy(X)<~>creative(X))=>(curious(X)&happy(X))))&
((?[X]:((calm(X)|~creative(X))))<=>(?[X]:((~humble(X)<~>strong(X)))))&
(![X]:((~patient(X)&creative(X))=>(tall(X)&~kind(X))))&
((?[X]:((~old(X)&strong(X))))=>((old(mary)|tall(mary))))&
(![X]:((kind(X)<~>quiet(X))=>(~patient(X)&rich(X))))&
(![X]:((~rich(X)&~quiet(X))<=>(generous(X)&~rich(X))))&
((~tall(fred)<~>brave(fred)))&
((curious(susan)|generous(susan)))&
(~quiet(susan))&
(?[X]:((tall(X)|~quiet(X))))&
(?[X]:((curious(X)<~>calm(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((~funny(X)|old(X))))&
(?[X]:(~rich(X))) | ~quiet(paul) | [] | null | 0 |
Everyone who is wise is both not calm and old.
If lucy is not rich or not tall then someone is both curious and not patient and vice versa.
Everyone who is not patient or not tall is wise and vice versa.
If someone is brave or not humble then alice is either not old or not happy.
If mary is strong then someone is brave or not old and vice versa.
If paul is not generous or humble then alice is not generous or not happy.
Everyone who is not tall is not curious.
Everyone who is not brave is not patient and vice versa.
If alice is not patient or not rich then someone is not wise and vice versa.
If someone is either not rich or strong then someone is either not kind or not calm and vice versa.
If alice is not calm then susan is calm and vice versa.
Everyone who is either not kind or not creative is tall and vice versa.
Everyone who is happy or curious is not old and vice versa.
Everyone who is not quiet is not generous and vice versa.
If susan is not rich or not strong then paul is quiet or not curious and vice versa.
Everyone who is kind or old is happy or funny and vice versa.
Fred is not patient or funny.
Someone is either happy or curious.
Someone is either creative or not patient.
Lucy is either not old or kind.
John is tall.
Someone is generous or not rich.
Lucy is not funny.
Someone is not strong. | Fred is funny. | entailment | (![X]:(wise(X)=>(~calm(X)&old(X))))&
(((~rich(lucy)|~tall(lucy)))<=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~patient(X)|~tall(X))<=>wise(X)))&
((?[X]:((brave(X)|~humble(X))))=>((~old(alice)<~>~happy(alice))))&
((strong(mary))<=>(?[X]:((brave(X)|~old(X)))))&
(((~generous(paul)|humble(paul)))=>((~generous(alice)|~happy(alice))))&
(![X]:(~tall(X)=>~curious(X)))&
(![X]:(~brave(X)<=>~patient(X)))&
(((~patient(alice)|~rich(alice)))<=>(?[X]:(~wise(X))))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
((~calm(alice))<=>(calm(susan)))&
(![X]:((~kind(X)<~>~creative(X))<=>tall(X)))&
(![X]:((happy(X)|curious(X))<=>~old(X)))&
(![X]:(~quiet(X)<=>~generous(X)))&
(((~rich(susan)|~strong(susan)))<=>((quiet(paul)|~curious(paul))))&
(![X]:((kind(X)|old(X))<=>(happy(X)|funny(X))))&
((~patient(fred)|funny(fred)))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:((creative(X)<~>~patient(X))))&
((~old(lucy)<~>kind(lucy)))&
(tall(john))&
(?[X]:((generous(X)|~rich(X))))&
(~funny(lucy))&
(?[X]:(~strong(X))) | funny(fred) | [
"p0",
"p2",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 817202064603877204215270
% SZS output start Proof for 817202064603877204215270
1. ! [X0] : (wise(X0) => (old(X0) & ~calm(X0))) [input p0]
3. ! [X0] : ((~tall(X0) | ~patient(X0)) <=> wise(X0)) [input p2]
13. ! [X0] : ((curious(X0) | happy(X0)) <=> ~old(X0)) [input p12]
16. ! [X0] : ((old(X0) | kind(X0)) <=> (funny(X0) | happy(X0))) [input p15]
17. funny(fred) | ~patient(fred) [input p16]
25. ~funny(fred) [input hypothesis]
27. ! [X0] : ((old(X0) & ~calm(X0)) | ~wise(X0)) [ennf transformation 1]
37. ! [X0] : (((~tall(X0) | ~patient(X0)) | ~wise(X0)) & (wise(X0) | (tall(X0) & patient(X0)))) [nnf transformation 3]
38. ! [X0] : ((~tall(X0) | ~patient(X0) | ~wise(X0)) & (wise(X0) | (tall(X0) & patient(X0)))) [flattening 37]
57. ! [X0] : (((curious(X0) | happy(X0)) | old(X0)) & (~old(X0) | (~curious(X0) & ~happy(X0)))) [nnf transformation 13]
58. ! [X0] : ((curious(X0) | happy(X0) | old(X0)) & (~old(X0) | (~curious(X0) & ~happy(X0)))) [flattening 57]
62. ! [X0] : (((old(X0) | kind(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 16]
63. ! [X0] : ((old(X0) | kind(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (~old(X0) & ~kind(X0)))) [flattening 62]
76. ~wise(X0) | old(X0) [cnf transformation 27]
82. patient(X0) | wise(X0) [cnf transformation 38]
114. ~happy(X0) | ~old(X0) [cnf transformation 58]
124. funny(X0) | happy(X0) | ~old(X0) [cnf transformation 63]
127. funny(fred) | ~patient(fred) [cnf transformation 17]
138. ~funny(fred) [cnf transformation 25]
298. ~old(X0) | funny(X0) [subsumption resolution 124,114]
300. 35 <=> patient(fred) [avatar definition]
302. ~patient(fred) <- (~35) [avatar component clause 300]
304. 36 <=> funny(fred) [avatar definition]
305. ~funny(fred) <- (~36) [avatar component clause 304]
307. ~35 | 36 [avatar split clause 127,304,300]
347. ~36 [avatar split clause 138,304]
354. wise(fred) <- (~35) [resolution 82,302]
360. old(fred) <- (~35) [resolution 354,76]
413. funny(fred) <- (~35) [resolution 360,298]
414. $false <- (~35, ~36) [subsumption resolution 413,305]
415. 35 | 36 [avatar contradiction clause 414]
416. $false [avatar sat refutation 307,347,415]
% SZS output end Proof for 817202064603877204215270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not creative is either happy or not happy.
If someone is either not kind or not curious then paul is both not patient and not tall and vice versa.
If john is not quiet then alice is either old or not kind.
If susan is both wise and not patient then alice is old.
If someone is both strong and not strong then someone is kind or quiet and vice versa.
Everyone who is both not tall and not strong is not quiet or not curious and vice versa.
Everyone who is both not strong and quiet is both not strong and rich and vice versa.
Everyone who is not happy or calm is kind.
If someone is either generous or not calm then someone is either strong or not rich and vice versa.
If john is not happy or creative then paul is both rich and old and vice versa.
Everyone who is either wise or not rich is either not rich or calm.
Everyone who is either happy or not wise is not kind or not humble.
If someone is funny then mary is not wise or not quiet and vice versa.
Everyone who is either funny or creative is either creative or not brave and vice versa.
Everyone who is both not wise and not strong is generous or strong.
If susan is quiet or generous then someone is both kind and not old and vice versa.
Someone is not calm.
Someone is not old.
Someone is not patient.
Someone is generous.
Fred is not old. | Fred is not calm. | entailment | (![X]:((wise(X)|~creative(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>((~patient(paul)&~tall(paul))))&
((~quiet(john))=>((old(alice)<~>~kind(alice))))&
(((wise(susan)&~patient(susan)))=>(old(alice)))&
((?[X]:((strong(X)&~strong(X))))<=>(?[X]:((kind(X)|quiet(X)))))&
(![X]:((~tall(X)&~strong(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|calm(X))=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(((~happy(john)|creative(john)))<=>((rich(paul)&old(paul))))&
(![X]:((wise(X)<~>~rich(X))=>(~rich(X)<~>calm(X))))&
(![X]:((happy(X)<~>~wise(X))=>(~kind(X)|~humble(X))))&
((?[X]:(funny(X)))<=>((~wise(mary)|~quiet(mary))))&
(![X]:((funny(X)<~>creative(X))<=>(creative(X)<~>~brave(X))))&
(![X]:((~wise(X)&~strong(X))=>(generous(X)|strong(X))))&
(((quiet(susan)|generous(susan)))<=>(?[X]:((kind(X)&~old(X)))))&
(?[X]:(~calm(X)))&
(?[X]:(~old(X)))&
(?[X]:(~patient(X)))&
(?[X]:(generous(X)))&
(~old(fred)) | ~calm(fred) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3745467802075938960360714
% SZS output start Proof for 3745467802075938960360714
5. ? [X0] : (~strong(X0) & strong(X0)) <=> ? [X0] : (quiet(X0) | kind(X0)) [input p4]
8. ! [X0] : ((calm(X0) | ~happy(X0)) => kind(X0)) [input p7]
22. calm(fred) [input hypothesis]
23. ? [X0] : (~strong(X0) & strong(X0)) <=> ? [X1] : (quiet(X1) | kind(X1)) [rectify 5]
30. ! [X0] : (kind(X0) | (~calm(X0) & happy(X0))) [ennf transformation 8]
41. (? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (~quiet(X1) & ~kind(X1))) & (? [X1] : (quiet(X1) | kind(X1)) | ! [X0] : (strong(X0) | ~strong(X0))) [nnf transformation 23]
42. (? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (~quiet(X1) & ~kind(X1))) & (? [X2] : (quiet(X2) | kind(X2)) | ! [X3] : (strong(X3) | ~strong(X3))) [rectify 41]
43. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK1) & strong(sK1)) [choice axiom]
44. ? [X2] : (quiet(X2) | kind(X2)) => (quiet(sK2) | kind(sK2)) [choice axiom]
45. ((~strong(sK1) & strong(sK1)) | ! [X1] : (~quiet(X1) & ~kind(X1))) & ((quiet(sK2) | kind(sK2)) | ! [X3] : (strong(X3) | ~strong(X3))) [skolemisation 42,44,43]
91. strong(sK1) | ~kind(X1) [cnf transformation 45]
93. ~strong(sK1) | ~kind(X1) [cnf transformation 45]
105. ~calm(X0) | kind(X0) [cnf transformation 30]
145. calm(fred) [cnf transformation 22]
208. 13 <=> strong(sK1) [avatar definition]
213. 14 <=> ! [X1] : ~kind(X1) [avatar definition]
214. ~kind(X1) <- (14) [avatar component clause 213]
215. 14 | ~13 [avatar split clause 93,208,213]
217. 14 | 13 [avatar split clause 91,208,213]
323. kind(fred) [resolution 105,145]
324. $false <- (14) [subsumption resolution 323,214]
325. ~14 [avatar contradiction clause 324]
326. $false [avatar sat refutation 215,217,325]
% SZS output end Proof for 3745467802075938960360714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave or not rich then susan is generous and vice versa.
Everyone who is generous is not funny or not strong.
Everyone who is both humble and not quiet is both curious and happy.
If someone is rich or not generous then fred is both not old and creative.
Everyone who is funny or not kind is calm.
Everyone who is not happy is both calm and not creative and vice versa.
Everyone who is humble is either not quiet or humble.
Everyone who is old or kind is not tall or funny and vice versa.
Everyone who is funny is not strong and vice versa.
If alice is rich or brave then alice is creative or not creative and vice versa.
If someone is brave then someone is either not strong or not calm.
Everyone who is both curious and quiet is not humble.
If someone is brave or quiet then someone is both not patient and not kind.
If lucy is both not humble and not curious then fred is either not tall or not curious and vice versa.
If mary is both generous and kind then lucy is either not creative or humble and vice versa.
Everyone who is either quiet or rich is both happy and not happy.
John is not curious.
Someone is both not happy and old.
Paul is brave or not curious.
Someone is either patient or creative.
Someone is either calm or happy.
Someone is either not brave or not generous.
Someone is kind.
John is rich. | Fred is creative. | entailment | ((?[X]:((~brave(X)|~rich(X))))<=>(generous(susan)))&
(![X]:(generous(X)=>(~funny(X)|~strong(X))))&
(![X]:((humble(X)&~quiet(X))=>(curious(X)&happy(X))))&
((?[X]:((rich(X)|~generous(X))))=>((~old(fred)&creative(fred))))&
(![X]:((funny(X)|~kind(X))=>calm(X)))&
(![X]:(~happy(X)<=>(calm(X)&~creative(X))))&
(![X]:(humble(X)=>(~quiet(X)<~>humble(X))))&
(![X]:((old(X)|kind(X))<=>(~tall(X)|funny(X))))&
(![X]:(funny(X)<=>~strong(X)))&
(((rich(alice)|brave(alice)))<=>((creative(alice)|~creative(alice))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((curious(X)&quiet(X))=>~humble(X)))&
((?[X]:((brave(X)|quiet(X))))=>(?[X]:((~patient(X)&~kind(X)))))&
(((~humble(lucy)&~curious(lucy)))<=>((~tall(fred)<~>~curious(fred))))&
(((generous(mary)&kind(mary)))<=>((~creative(lucy)<~>humble(lucy))))&
(![X]:((quiet(X)<~>rich(X))=>(happy(X)&~happy(X))))&
(~curious(john))&
(?[X]:((~happy(X)&old(X))))&
((brave(paul)|~curious(paul)))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
(rich(john)) | creative(fred) | [
"p3",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5104882056952411168119002
% SZS output start Proof for 5104882056952411168119002
4. ? [X0] : (~generous(X0) | rich(X0)) => (creative(fred) & ~old(fred)) [input p3]
24. rich(john) [input p23]
25. ~creative(fred) [input hypothesis]
32. (creative(fred) & ~old(fred)) | ! [X0] : (generous(X0) & ~rich(X0)) [ennf transformation 4]
85. creative(fred) | ~rich(X0) [cnf transformation 32]
138. rich(john) [cnf transformation 24]
139. ~creative(fred) [cnf transformation 25]
166. 7 <=> creative(fred) [avatar definition]
171. 8 <=> ! [X0] : ~rich(X0) [avatar definition]
172. ~rich(X0) <- (8) [avatar component clause 171]
173. 8 | 7 [avatar split clause 85,166,171]
303. ~7 [avatar split clause 139,166]
312. $false <- (8) [resolution 172,138]
313. ~8 [avatar contradiction clause 312]
314. $false [avatar sat refutation 173,303,313]
% SZS output end Proof for 5104882056952411168119002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not humble is not strong and vice versa.
Everyone who is either calm or not tall is tall.
Everyone who is not creative or not old is either not strong or not generous.
If someone is both not brave and wise then someone is not kind or rich.
Everyone who is not funny is either not patient or not happy and vice versa.
If someone is not curious or generous then someone is not rich or happy and vice versa.
If someone is not creative or happy then fred is either happy or funny and vice versa.
If someone is both not curious and not wise then someone is both calm and not generous and vice versa.
Everyone who is both not generous and funny is either not brave or not calm and vice versa.
If someone is old then susan is both kind and not rich and vice versa.
Everyone who is either generous or happy is both funny and not happy.
Everyone who is humble is either not wise or not patient.
If someone is either not happy or old then someone is not tall or not wise and vice versa.
If someone is calm or not tall then mary is not calm or humble and vice versa.
Everyone who is not generous or not curious is either kind or not funny.
Everyone who is either not strong or not quiet is both calm and not humble and vice versa.
Someone is quiet or strong.
Someone is generous.
Someone is calm or wise.
Someone is both kind and wise.
John is not quiet or rich.
Susan is happy.
Fred is both not creative and not generous.
Someone is either not humble or not curious. | Susan is generous. | entailment | (![X]:((~patient(X)&~humble(X))<=>~strong(X)))&
(![X]:((calm(X)<~>~tall(X))=>tall(X)))&
(![X]:((~creative(X)|~old(X))=>(~strong(X)<~>~generous(X))))&
((?[X]:((~brave(X)&wise(X))))=>(?[X]:((~kind(X)|rich(X)))))&
(![X]:(~funny(X)<=>(~patient(X)<~>~happy(X))))&
((?[X]:((~curious(X)|generous(X))))<=>(?[X]:((~rich(X)|happy(X)))))&
((?[X]:((~creative(X)|happy(X))))<=>((happy(fred)<~>funny(fred))))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((~generous(X)&funny(X))<=>(~brave(X)<~>~calm(X))))&
((?[X]:(old(X)))<=>((kind(susan)&~rich(susan))))&
(![X]:((generous(X)<~>happy(X))=>(funny(X)&~happy(X))))&
(![X]:(humble(X)=>(~wise(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>old(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
((?[X]:((calm(X)|~tall(X))))<=>((~calm(mary)|humble(mary))))&
(![X]:((~generous(X)|~curious(X))=>(kind(X)<~>~funny(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(calm(X)&~humble(X))))&
(?[X]:((quiet(X)|strong(X))))&
(?[X]:(generous(X)))&
(?[X]:((calm(X)|wise(X))))&
(?[X]:((kind(X)&wise(X))))&
((~quiet(john)|rich(john)))&
(happy(susan))&
((~creative(fred)&~generous(fred)))&
(?[X]:((~humble(X)<~>~curious(X)))) | generous(susan) | [
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6552954097905073057658855
% SZS output start Proof for 6552954097905073057658855
11. ! [X0] : ((generous(X0) <~> happy(X0)) => (~happy(X0) & funny(X0))) [input p10]
22. happy(susan) [input p21]
25. ~generous(susan) [input hypothesis]
33. ! [X0] : ((~happy(X0) & funny(X0)) | (generous(X0) <=> happy(X0))) [ennf transformation 11]
65. ! [X0] : ((~happy(X0) & funny(X0)) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) [nnf transformation 33]
131. ~happy(X0) | generous(X0) | ~happy(X0) [cnf transformation 65]
160. happy(susan) [cnf transformation 22]
165. ~generous(susan) [cnf transformation 25]
166. ~happy(X0) | generous(X0) [duplicate literal removal 131]
376. generous(susan) [resolution 166,160]
377. $false [subsumption resolution 376,165]
% SZS output end Proof for 6552954097905073057658855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or quiet is both not tall and humble and vice versa.
Everyone who is both quiet and not brave is either not funny or brave and vice versa.
Everyone who is either funny or rich is happy.
If someone is not funny then someone is either not calm or not patient.
If mary is both happy and funny then someone is both not kind and creative and vice versa.
Everyone who is either calm or old is both not patient and patient and vice versa.
Everyone who is not wise is patient.
If alice is either patient or rich then someone is not curious and vice versa.
Everyone who is both curious and not patient is tall.
Everyone who is both not creative and curious is either not tall or not funny and vice versa.
If someone is rich then someone is both not kind and patient.
Everyone who is not old is both quiet and not wise.
Everyone who is both generous and not quiet is not patient and vice versa.
Everyone who is either tall or not creative is funny or not patient and vice versa.
If someone is either generous or tall then fred is not patient.
If someone is either not patient or curious then someone is both not curious and not calm and vice versa.
Mary is both strong and old.
Lucy is both not quiet and rich.
Susan is either humble or not wise.
Lucy is happy.
Someone is patient or wise.
Someone is creative.
Someone is not kind or strong.
John is brave. | Fred is not tall. | entailment | (![X]:((wise(X)|quiet(X))<=>(~tall(X)&humble(X))))&
(![X]:((quiet(X)&~brave(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)<~>rich(X))=>happy(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)<~>~patient(X)))))&
(((happy(mary)&funny(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((calm(X)<~>old(X))<=>(~patient(X)&patient(X))))&
(![X]:(~wise(X)=>patient(X)))&
(((patient(alice)<~>rich(alice)))<=>(?[X]:(~curious(X))))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~creative(X)&curious(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:(rich(X)))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:(~old(X)=>(quiet(X)&~wise(X))))&
(![X]:((generous(X)&~quiet(X))<=>~patient(X)))&
(![X]:((tall(X)<~>~creative(X))<=>(funny(X)|~patient(X))))&
((?[X]:((generous(X)<~>tall(X))))=>(~patient(fred)))&
((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((~curious(X)&~calm(X)))))&
((strong(mary)&old(mary)))&
((~quiet(lucy)&rich(lucy)))&
((humble(susan)<~>~wise(susan)))&
(happy(lucy))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)|strong(X))))&
(brave(john)) | ~tall(fred) | [
"p0",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3383058498828312462642580
% SZS output start Proof for 3383058498828312462642580
1. ! [X0] : ((quiet(X0) | wise(X0)) <=> (humble(X0) & ~tall(X0))) [input p0]
7. ! [X0] : (~wise(X0) => patient(X0)) [input p6]
13. ! [X0] : ((~quiet(X0) & generous(X0)) <=> ~patient(X0)) [input p12]
15. ? [X0] : (generous(X0) <~> tall(X0)) => ~patient(fred) [input p14]
25. tall(fred) [input hypothesis]
33. ! [X0] : (patient(X0) | wise(X0)) [ennf transformation 7]
38. ~patient(fred) | ! [X0] : (generous(X0) <=> tall(X0)) [ennf transformation 15]
39. ! [X0] : (((quiet(X0) | wise(X0)) | (~humble(X0) | tall(X0))) & ((humble(X0) & ~tall(X0)) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 1]
40. ! [X0] : ((quiet(X0) | wise(X0) | ~humble(X0) | tall(X0)) & ((humble(X0) & ~tall(X0)) | (~quiet(X0) & ~wise(X0)))) [flattening 39]
64. ! [X0] : (((~quiet(X0) & generous(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) | ~generous(X0)))) [nnf transformation 13]
65. ! [X0] : (((~quiet(X0) & generous(X0)) | patient(X0)) & (~patient(X0) | quiet(X0) | ~generous(X0))) [flattening 64]
68. ~patient(fred) | ! [X0] : ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))) [nnf transformation 38]
79. ~tall(X0) | ~wise(X0) [cnf transformation 40]
80. ~tall(X0) | ~quiet(X0) [cnf transformation 40]
104. patient(X0) | wise(X0) [cnf transformation 33]
120. ~generous(X0) | quiet(X0) | ~patient(X0) [cnf transformation 65]
130. ~patient(fred) | generous(X0) | ~tall(X0) [cnf transformation 68]
146. tall(fred) [cnf transformation 25]
221. 16 <=> ! [X0] : (generous(X0) | ~tall(X0)) [avatar definition]
222. ~tall(X0) | generous(X0) <- (16) [avatar component clause 221]
224. 17 <=> patient(fred) [avatar definition]
225. patient(fred) <- (17) [avatar component clause 224]
226. ~patient(fred) <- (~17) [avatar component clause 224]
227. 16 | ~17 [avatar split clause 130,224,221]
276. ~wise(fred) [resolution 79,146]
277. ~quiet(fred) [resolution 80,146]
279. wise(fred) <- (~17) [resolution 104,226]
281. $false <- (~17) [subsumption resolution 279,276]
282. 17 [avatar contradiction clause 281]
294. generous(fred) <- (16) [resolution 222,146]
378. quiet(fred) | ~patient(fred) <- (16) [resolution 120,294]
379. ~patient(fred) <- (16) [subsumption resolution 378,277]
380. $false <- (16, 17) [subsumption resolution 379,225]
381. ~16 | ~17 [avatar contradiction clause 380]
382. $false [avatar sat refutation 227,282,381]
% SZS output end Proof for 3383058498828312462642580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not curious is either funny or not brave. Everyone who is not rich is curious or patient and vice versa. Everyone who is rich is either happy or creative. Everyone who is both not strong and not happy is strong. Everyone who is both rich and not creative is both not tall and curious and vice versa. If alice is tall or not kind then paul is wise. Everyone who is kind is both not happy and not old and vice versa. If paul is both happy and wise then someone is not kind or patient. Everyone who is both not humble and old is not kind. Everyone who is not humble is not creative. If someone is not funny then someone is both not humble and patient. Everyone who is old is either wise or calm and vice versa. Everyone who is not funny is both brave and creative and vice versa. If lucy is both strong and not strong then someone is either not happy or not humble. If someone is kind then susan is tall and vice versa. Everyone who is not tall is either not curious or not funny and vice versa. Mary is either not generous or brave. Someone is either strong or tall. Someone is not curious. Someone is either strong or brave. Someone is not rich. | Mary is not funny. | contradiction | (![X]:((~funny(X)|~curious(X))=>(funny(X)<~>~brave(X))))&
(![X]:(~rich(X)<=>(curious(X)|patient(X))))&
(![X]:(rich(X)=>(happy(X)<~>creative(X))))&
(![X]:((~strong(X)&~happy(X))=>strong(X)))&
(![X]:((rich(X)&~creative(X))<=>(~tall(X)&curious(X))))&
(((tall(alice)|~kind(alice)))=>(wise(paul)))&
(![X]:(kind(X)<=>(~happy(X)&~old(X))))&
(((happy(paul)&wise(paul)))=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((~humble(X)&old(X))=>~kind(X)))&
(![X]:(~humble(X)=>~creative(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(old(X)<=>(wise(X)<~>calm(X))))&
(![X]:(~funny(X)<=>(brave(X)&creative(X))))&
(((strong(lucy)&~strong(lucy)))=>(?[X]:((~happy(X)<~>~humble(X)))))&
((?[X]:(kind(X)))<=>(tall(susan)))&
(![X]:(~tall(X)<=>(~curious(X)<~>~funny(X))))&
((~generous(mary)<~>brave(mary)))&
(?[X]:((strong(X)<~>tall(X))))&
(?[X]:(~curious(X)))&
(?[X]:((strong(X)<~>brave(X))))&
(?[X]:(~rich(X))) | ~funny(mary) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2138597608856500996941325
% SZS output start Proof for 2138597608856500996941325
1. ! [X0] : ((~curious(X0) | ~funny(X0)) => (funny(X0) <~> ~brave(X0))) [input p0]
13. ! [X0] : (~funny(X0) <=> (creative(X0) & brave(X0))) [input p12]
22. ~funny(mary) [input hypothesis]
24. ! [X0] : ((funny(X0) <~> ~brave(X0)) | (curious(X0) & funny(X0))) [ennf transformation 1]
37. ! [X0] : (((brave(X0) | ~funny(X0)) & (~brave(X0) | funny(X0))) | (curious(X0) & funny(X0))) [nnf transformation 24]
51. ! [X0] : ((~funny(X0) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | funny(X0))) [nnf transformation 13]
52. ! [X0] : ((~funny(X0) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | funny(X0))) [flattening 51]
72. ~brave(X0) | funny(X0) | funny(X0) [cnf transformation 37]
100. brave(X0) | funny(X0) [cnf transformation 52]
119. ~funny(mary) [cnf transformation 22]
121. ~brave(X0) | funny(X0) [duplicate literal removal 72]
152. 7 <=> ! [X1] : funny(X1) [avatar definition]
153. funny(X1) <- (7) [avatar component clause 152]
165. funny(X0) [subsumption resolution 100,121]
166. 7 [avatar split clause 165,152]
212. $false <- (7) [resolution 153,119]
213. ~7 [avatar contradiction clause 212]
214. $false [avatar sat refutation 166,213]
% SZS output end Proof for 2138597608856500996941325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is calm or patient is both kind and wise and vice versa.
Everyone who is both not kind and kind is either patient or not calm and vice versa.
Everyone who is not happy is not rich or not quiet.
Everyone who is creative or not wise is not strong or humble and vice versa.
Everyone who is not rich or not curious is kind or not happy.
Everyone who is both not happy and not rich is either strong or not curious.
Everyone who is humble is either not rich or not humble and vice versa.
If john is both tall and not humble then fred is either kind or calm and vice versa.
If lucy is either generous or not brave then someone is both humble and not curious.
If someone is not humble or not rich then susan is patient and vice versa.
If fred is brave or funny then mary is either humble or funny and vice versa.
If someone is humble then mary is both rich and kind and vice versa.
If someone is either not happy or not brave then someone is both not quiet and happy and vice versa.
If someone is either kind or tall then alice is not funny.
Everyone who is not strong is generous.
If susan is both not calm and calm then someone is strong and vice versa.
Alice is both calm and not patient.
Someone is patient or tall.
Mary is both funny and not calm.
Someone is not brave.
Someone is creative or generous.
Fred is not brave.
Someone is either not kind or creative. | Mary is humble. | contradiction | (![X]:((calm(X)|patient(X))<=>(kind(X)&wise(X))))&
(![X]:((~kind(X)&kind(X))<=>(patient(X)<~>~calm(X))))&
(![X]:(~happy(X)=>(~rich(X)|~quiet(X))))&
(![X]:((creative(X)|~wise(X))<=>(~strong(X)|humble(X))))&
(![X]:((~rich(X)|~curious(X))=>(kind(X)|~happy(X))))&
(![X]:((~happy(X)&~rich(X))=>(strong(X)<~>~curious(X))))&
(![X]:(humble(X)<=>(~rich(X)<~>~humble(X))))&
(((tall(john)&~humble(john)))<=>((kind(fred)<~>calm(fred))))&
(((generous(lucy)<~>~brave(lucy)))=>(?[X]:((humble(X)&~curious(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(patient(susan)))&
(((brave(fred)|funny(fred)))<=>((humble(mary)<~>funny(mary))))&
((?[X]:(humble(X)))<=>((rich(mary)&kind(mary))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:((kind(X)<~>tall(X))))=>(~funny(alice)))&
(![X]:(~strong(X)=>generous(X)))&
(((~calm(susan)&calm(susan)))<=>(?[X]:(strong(X))))&
((calm(alice)&~patient(alice)))&
(?[X]:((patient(X)|tall(X))))&
((funny(mary)&~calm(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)|generous(X))))&
(~brave(fred))&
(?[X]:((~kind(X)<~>creative(X)))) | humble(mary) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1841191974378080122589389
% SZS output start Proof for 1841191974378080122589389
7. ! [X0] : (humble(X0) <=> (~rich(X0) <~> ~humble(X0))) [input p6]
12. ? [X0] : humble(X0) <=> (kind(mary) & rich(mary)) [input p11]
24. humble(mary) [input hypothesis]
42. ! [X0] : ((humble(X0) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0)))) & (((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | ~humble(X0))) [nnf transformation 7]
54. (? [X0] : humble(X0) | (~kind(mary) | ~rich(mary))) & ((kind(mary) & rich(mary)) | ! [X0] : ~humble(X0)) [nnf transformation 12]
55. (? [X0] : humble(X0) | ~kind(mary) | ~rich(mary)) & ((kind(mary) & rich(mary)) | ! [X0] : ~humble(X0)) [flattening 54]
56. (? [X0] : humble(X0) | ~kind(mary) | ~rich(mary)) & ((kind(mary) & rich(mary)) | ! [X1] : ~humble(X1)) [rectify 55]
57. ? [X0] : humble(X0) => humble(sK2) [choice axiom]
58. (humble(sK2) | ~kind(mary) | ~rich(mary)) & ((kind(mary) & rich(mary)) | ! [X1] : ~humble(X1)) [skolemisation 56,57]
99. ~humble(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 42]
102. humble(X0) | ~rich(X0) | humble(X0) [cnf transformation 42]
122. rich(mary) | ~humble(X1) [cnf transformation 58]
147. humble(mary) [cnf transformation 24]
148. ~humble(X0) | ~rich(X0) [duplicate literal removal 99]
149. humble(X0) | ~rich(X0) [duplicate literal removal 102]
154. ~rich(X0) [subsumption resolution 148,149]
216. ~humble(X1) [subsumption resolution 122,154]
287. $false [subsumption resolution 147,216]
% SZS output end Proof for 1841191974378080122589389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not kind then paul is not wise or strong and vice versa.
If john is rich or not calm then someone is either strong or kind and vice versa.
If fred is not creative then paul is either not tall or not calm and vice versa.
If someone is creative or not humble then fred is both kind and rich and vice versa.
If someone is old or generous then someone is not happy or generous.
Everyone who is both not curious and curious is not quiet or creative.
If someone is both patient and not kind then someone is either not tall or not funny.
If someone is patient or not generous then susan is either not rich or not strong and vice versa.
Everyone who is quiet is both not old and rich.
If lucy is both not calm and generous then someone is both happy and not humble.
Everyone who is not quiet is both tall and not humble.
Everyone who is both not humble and happy is both patient and humble.
If fred is both not old and not patient then someone is not funny and vice versa.
If someone is not calm or not happy then fred is not patient or funny and vice versa.
If alice is both strong and not strong then someone is both calm and not generous.
Everyone who is both humble and creative is rich and vice versa.
Lucy is not humble.
Fred is curious or not old.
Someone is both creative and calm.
Paul is rich or not patient.
Someone is rich or not rich.
Lucy is happy or not calm.
Someone is not curious or quiet. | Lucy is not happy. | entailment | ((?[X]:((~quiet(X)&~kind(X))))<=>((~wise(paul)|strong(paul))))&
(((rich(john)|~calm(john)))<=>(?[X]:((strong(X)<~>kind(X)))))&
((~creative(fred))<=>((~tall(paul)<~>~calm(paul))))&
((?[X]:((creative(X)|~humble(X))))<=>((kind(fred)&rich(fred))))&
((?[X]:((old(X)|generous(X))))=>(?[X]:((~happy(X)|generous(X)))))&
(![X]:((~curious(X)&curious(X))=>(~quiet(X)|creative(X))))&
((?[X]:((patient(X)&~kind(X))))=>(?[X]:((~tall(X)<~>~funny(X)))))&
((?[X]:((patient(X)|~generous(X))))<=>((~rich(susan)<~>~strong(susan))))&
(![X]:(quiet(X)=>(~old(X)&rich(X))))&
(((~calm(lucy)&generous(lucy)))=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:(~quiet(X)=>(tall(X)&~humble(X))))&
(![X]:((~humble(X)&happy(X))=>(patient(X)&humble(X))))&
(((~old(fred)&~patient(fred)))<=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((~patient(fred)|funny(fred))))&
(((strong(alice)&~strong(alice)))=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((humble(X)&creative(X))<=>rich(X)))&
(~humble(lucy))&
((curious(fred)|~old(fred)))&
(?[X]:((creative(X)&calm(X))))&
((rich(paul)|~patient(paul)))&
(?[X]:((rich(X)|~rich(X))))&
((happy(lucy)|~calm(lucy)))&
(?[X]:((~curious(X)|quiet(X)))) | ~happy(lucy) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5651566872959171533213729
% SZS output start Proof for 5651566872959171533213729
12. ! [X0] : ((happy(X0) & ~humble(X0)) => (humble(X0) & patient(X0))) [input p11]
17. ~humble(lucy) [input p16]
24. happy(lucy) [input hypothesis]
35. ! [X0] : ((humble(X0) & patient(X0)) | (~happy(X0) | humble(X0))) [ennf transformation 12]
36. ! [X0] : ((humble(X0) & patient(X0)) | ~happy(X0) | humble(X0)) [flattening 35]
126. humble(X0) | ~happy(X0) | humble(X0) [cnf transformation 36]
139. ~humble(lucy) [cnf transformation 17]
147. happy(lucy) [cnf transformation 24]
148. ~happy(X0) | humble(X0) [duplicate literal removal 126]
374. 50 <=> happy(lucy) [avatar definition]
376. happy(lucy) <- (50) [avatar component clause 374]
387. 50 [avatar split clause 147,374]
397. humble(lucy) <- (50) [resolution 148,376]
398. $false <- (50) [subsumption resolution 397,139]
399. ~50 [avatar contradiction clause 398]
400. $false [avatar sat refutation 387,399]
% SZS output end Proof for 5651566872959171533213729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or calm then someone is both not creative and not calm and vice versa.
Everyone who is either not kind or curious is not old.
Everyone who is either not old or curious is both kind and not tall and vice versa.
If someone is not creative or kind then someone is not calm or wise and vice versa.
Everyone who is generous or patient is not generous.
If someone is both creative and humble then someone is not creative.
Everyone who is either patient or not rich is not funny.
If someone is either not strong or not quiet then john is humble or not funny and vice versa.
If john is both curious and brave then alice is either generous or not generous.
Everyone who is humble or kind is both not tall and brave.
Everyone who is tall or rich is curious.
Everyone who is both not tall and not humble is either generous or brave and vice versa.
Everyone who is either wise or happy is tall and vice versa.
If someone is both generous and not calm then alice is both happy and not happy.
Everyone who is not strong or not kind is both not happy and not tall.
Everyone who is not happy or creative is brave or not quiet.
Fred is either kind or not happy.
Someone is not strong.
Lucy is both not patient and funny.
Someone is not wise.
Mary is both curious and strong.
Susan is not curious or generous. | Lucy is not old. | entailment | ((?[X]:((~funny(X)<~>calm(X))))<=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((~kind(X)<~>curious(X))=>~old(X)))&
(![X]:((~old(X)<~>curious(X))<=>(kind(X)&~tall(X))))&
((?[X]:((~creative(X)|kind(X))))<=>(?[X]:((~calm(X)|wise(X)))))&
(![X]:((generous(X)|patient(X))=>~generous(X)))&
((?[X]:((creative(X)&humble(X))))=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~rich(X))=>~funny(X)))&
((?[X]:((~strong(X)<~>~quiet(X))))<=>((humble(john)|~funny(john))))&
(((curious(john)&brave(john)))=>((generous(alice)<~>~generous(alice))))&
(![X]:((humble(X)|kind(X))=>(~tall(X)&brave(X))))&
(![X]:((tall(X)|rich(X))=>curious(X)))&
(![X]:((~tall(X)&~humble(X))<=>(generous(X)<~>brave(X))))&
(![X]:((wise(X)<~>happy(X))<=>tall(X)))&
((?[X]:((generous(X)&~calm(X))))=>((happy(alice)&~happy(alice))))&
(![X]:((~strong(X)|~kind(X))=>(~happy(X)&~tall(X))))&
(![X]:((~happy(X)|creative(X))=>(brave(X)|~quiet(X))))&
((kind(fred)<~>~happy(fred)))&
(?[X]:(~strong(X)))&
((~patient(lucy)&funny(lucy)))&
(?[X]:(~wise(X)))&
((curious(mary)&strong(mary)))&
((~curious(susan)|generous(susan))) | ~old(lucy) | [
"p1",
"p2",
"p6",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4939361824237411658566101
% SZS output start Proof for 4939361824237411658566101
2. ! [X0] : ((~kind(X0) <~> curious(X0)) => ~old(X0)) [input p1]
3. ! [X0] : ((~old(X0) <~> curious(X0)) <=> (~tall(X0) & kind(X0))) [input p2]
7. ! [X0] : ((patient(X0) <~> ~rich(X0)) => ~funny(X0)) [input p6]
11. ! [X0] : ((rich(X0) | tall(X0)) => curious(X0)) [input p10]
19. funny(lucy) & ~patient(lucy) [input p18]
23. old(lucy) [input hypothesis]
27. ! [X0] : (~old(X0) | (~kind(X0) <=> curious(X0))) [ennf transformation 2]
30. ! [X0] : (~funny(X0) | (patient(X0) <=> ~rich(X0))) [ennf transformation 7]
34. ! [X0] : (curious(X0) | (~rich(X0) & ~tall(X0))) [ennf transformation 11]
44. ! [X0] : (~old(X0) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) [nnf transformation 27]
45. ! [X0] : ((((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0))))) [nnf transformation 3]
46. ! [X0] : ((((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0))))) [flattening 45]
55. ! [X0] : (~funny(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) [nnf transformation 30]
77. ~old(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 44]
79. kind(X0) | ~old(X0) | ~curious(X0) [cnf transformation 46]
92. ~funny(X0) | patient(X0) | rich(X0) [cnf transformation 55]
106. ~rich(X0) | curious(X0) [cnf transformation 34]
128. ~patient(lucy) [cnf transformation 19]
129. funny(lucy) [cnf transformation 19]
134. old(lucy) [cnf transformation 23]
169. ~old(X0) | ~curious(X0) [subsumption resolution 79,77]
255. ~curious(lucy) [resolution 169,134]
265. patient(lucy) | rich(lucy) [resolution 92,129]
266. rich(lucy) [subsumption resolution 265,128]
268. curious(lucy) [resolution 266,106]
269. $false [subsumption resolution 268,255]
% SZS output end Proof for 4939361824237411658566101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not happy is either not curious or not calm and vice versa.
If someone is not curious or strong then someone is either not wise or not patient.
If someone is both old and funny then someone is both rich and kind and vice versa.
If someone is creative then someone is not tall or not brave and vice versa.
Everyone who is either not old or patient is kind and vice versa.
If someone is either not patient or not quiet then someone is both wise and not curious.
If lucy is not happy then someone is both not humble and not wise and vice versa.
Everyone who is not humble or not calm is either tall or brave.
If someone is both not tall and not quiet then someone is patient and vice versa.
If susan is not rich or not calm then someone is not quiet and vice versa.
If someone is not wise then someone is both curious and strong.
Everyone who is not quiet is both not wise and not brave.
Everyone who is both not tall and not brave is not kind or calm and vice versa.
Everyone who is both not humble and not kind is either rich or not funny and vice versa.
If someone is not funny or rich then john is either patient or curious.
Everyone who is creative is both strong and old and vice versa.
Someone is quiet.
Lucy is creative.
Mary is either strong or not strong.
Someone is both creative and tall.
Someone is tall or funny.
Fred is not patient.
Someone is both quiet and not curious.
Paul is both happy and not calm. | Lucy is not strong. | contradiction | (![X]:((humble(X)&~happy(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((~curious(X)|strong(X))))=>(?[X]:((~wise(X)<~>~patient(X)))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:((rich(X)&kind(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:((~old(X)<~>patient(X))<=>kind(X)))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:((wise(X)&~curious(X)))))&
((~happy(lucy))<=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((~humble(X)|~calm(X))=>(tall(X)<~>brave(X))))&
((?[X]:((~tall(X)&~quiet(X))))<=>(?[X]:(patient(X))))&
(((~rich(susan)|~calm(susan)))<=>(?[X]:(~quiet(X))))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)&strong(X)))))&
(![X]:(~quiet(X)=>(~wise(X)&~brave(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~kind(X)|calm(X))))&
(![X]:((~humble(X)&~kind(X))<=>(rich(X)<~>~funny(X))))&
((?[X]:((~funny(X)|rich(X))))=>((patient(john)<~>curious(john))))&
(![X]:(creative(X)<=>(strong(X)&old(X))))&
(?[X]:(quiet(X)))&
(creative(lucy))&
((strong(mary)<~>~strong(mary)))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:((tall(X)|funny(X))))&
(~patient(fred))&
(?[X]:((quiet(X)&~curious(X))))&
((happy(paul)&~calm(paul))) | ~strong(lucy) | [
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7349931574519025941129808
% SZS output start Proof for 7349931574519025941129808
16. ! [X0] : (creative(X0) <=> (old(X0) & strong(X0))) [input p15]
18. creative(lucy) [input p17]
25. ~strong(lucy) [input hypothesis]
82. ! [X0] : ((creative(X0) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | ~creative(X0))) [nnf transformation 16]
83. ! [X0] : ((creative(X0) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | ~creative(X0))) [flattening 82]
150. ~creative(X0) | strong(X0) [cnf transformation 83]
154. creative(lucy) [cnf transformation 18]
165. ~strong(lucy) [cnf transformation 25]
365. strong(lucy) [resolution 150,154]
368. $false [subsumption resolution 365,165]
% SZS output end Proof for 7349931574519025941129808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not creative or patient then lucy is either strong or not brave and vice versa. Everyone who is old is not humble and vice versa. If someone is either not wise or not funny then susan is both not creative and creative. Everyone who is not patient is curious or not curious. Everyone who is rich is old and vice versa. If alice is not curious or old then someone is both calm and not strong. If john is both not quiet and humble then paul is either quiet or not creative. If someone is both humble and not quiet then someone is not creative or creative. Everyone who is not old is both calm and not funny. Everyone who is both old and not patient is either happy or not curious. Everyone who is old or funny is both not happy and not patient. If john is either humble or not rich then someone is both not kind and tall. If susan is not wise then john is generous or funny and vice versa. If someone is either happy or not generous then john is not funny or wise and vice versa. If alice is either rich or not quiet then someone is not strong. Everyone who is calm or not happy is curious and vice versa. John is not happy. John is not patient. Someone is not curious or not brave. Someone is curious or quiet. Lucy is either not curious or kind. | Alice is wise. | contradiction | (((~creative(fred)<~>patient(fred)))<=>((strong(lucy)<~>~brave(lucy))))&
(![X]:(old(X)<=>~humble(X)))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~creative(susan)&creative(susan))))&
(![X]:(~patient(X)=>(curious(X)|~curious(X))))&
(![X]:(rich(X)<=>old(X)))&
(((~curious(alice)|old(alice)))=>(?[X]:((calm(X)&~strong(X)))))&
(((~quiet(john)&humble(john)))=>((quiet(paul)<~>~creative(paul))))&
((?[X]:((humble(X)&~quiet(X))))=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:(~old(X)=>(calm(X)&~funny(X))))&
(![X]:((old(X)&~patient(X))=>(happy(X)<~>~curious(X))))&
(![X]:((old(X)|funny(X))=>(~happy(X)&~patient(X))))&
(((humble(john)<~>~rich(john)))=>(?[X]:((~kind(X)&tall(X)))))&
((~wise(susan))<=>((generous(john)|funny(john))))&
((?[X]:((happy(X)<~>~generous(X))))<=>((~funny(john)|wise(john))))&
(((rich(alice)<~>~quiet(alice)))=>(?[X]:(~strong(X))))&
(![X]:((calm(X)|~happy(X))<=>curious(X)))&
(~happy(john))&
(~patient(john))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((~curious(lucy)<~>kind(lucy))) | wise(alice) | [
"p2",
"p8",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 299921952755057587592144
% SZS output start Proof for 299921952755057587592144
3. ? [X0] : (~wise(X0) <~> ~funny(X0)) => (creative(susan) & ~creative(susan)) [input p2]
9. ! [X0] : (~old(X0) => (~funny(X0) & calm(X0))) [input p8]
10. ! [X0] : ((~patient(X0) & old(X0)) => (happy(X0) <~> ~curious(X0))) [input p9]
11. ! [X0] : ((funny(X0) | old(X0)) => (~patient(X0) & ~happy(X0))) [input p10]
16. ! [X0] : ((~happy(X0) | calm(X0)) <=> curious(X0)) [input p15]
22. wise(alice) [input hypothesis]
25. (creative(susan) & ~creative(susan)) | ! [X0] : (~wise(X0) <=> ~funny(X0)) [ennf transformation 3]
32. ! [X0] : ((~funny(X0) & calm(X0)) | old(X0)) [ennf transformation 9]
33. ! [X0] : ((happy(X0) <~> ~curious(X0)) | (patient(X0) | ~old(X0))) [ennf transformation 10]
34. ! [X0] : ((happy(X0) <~> ~curious(X0)) | patient(X0) | ~old(X0)) [flattening 33]
35. ! [X0] : ((~patient(X0) & ~happy(X0)) | (~funny(X0) & ~old(X0))) [ennf transformation 11]
40. (creative(susan) & ~creative(susan)) | ! [X0] : ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))) [nnf transformation 25]
48. ! [X0] : (((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) | patient(X0) | ~old(X0)) [nnf transformation 34]
62. ! [X0] : (((~happy(X0) | calm(X0)) | ~curious(X0)) & (curious(X0) | (happy(X0) & ~calm(X0)))) [nnf transformation 16]
63. ! [X0] : ((~happy(X0) | calm(X0) | ~curious(X0)) & (curious(X0) | (happy(X0) & ~calm(X0)))) [flattening 62]
80. ~creative(susan) | ~wise(X0) | funny(X0) [cnf transformation 40]
82. creative(susan) | ~wise(X0) | funny(X0) [cnf transformation 40]
93. calm(X0) | old(X0) [cnf transformation 32]
94. ~funny(X0) | old(X0) [cnf transformation 32]
95. ~curious(X0) | happy(X0) | patient(X0) | ~old(X0) [cnf transformation 48]
97. ~happy(X0) | ~old(X0) [cnf transformation 35]
99. ~old(X0) | ~patient(X0) [cnf transformation 35]
114. ~calm(X0) | curious(X0) [cnf transformation 63]
115. happy(X0) | curious(X0) [cnf transformation 63]
123. wise(alice) [cnf transformation 22]
149. 5 <=> ! [X0] : (~wise(X0) | funny(X0)) [avatar definition]
150. ~wise(X0) | funny(X0) <- (5) [avatar component clause 149]
152. 6 <=> creative(susan) [avatar definition]
155. 5 | 6 [avatar split clause 82,152,149]
160. 5 | ~6 [avatar split clause 80,152,149]
163. 8 <=> old(alice) [avatar definition]
164. old(alice) <- (8) [avatar component clause 163]
296. curious(X0) | old(X0) [resolution 114,93]
300. curious(X1) | ~old(X1) [resolution 115,97]
301. curious(X1) [subsumption resolution 300,296]
302. funny(alice) <- (5) [resolution 150,123]
308. old(alice) <- (5) [resolution 302,94]
311. 8 | ~5 [avatar split clause 308,149,163]
321. happy(X0) | patient(X0) | ~old(X0) [resolution 95,301]
326. happy(X0) | ~old(X0) [subsumption resolution 321,99]
327. ~old(X0) [subsumption resolution 326,97]
333. $false <- (8) [resolution 327,164]
336. ~8 [avatar contradiction clause 333]
337. $false [avatar sat refutation 155,160,311,336]
% SZS output end Proof for 299921952755057587592144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not generous is either not old or happy.
Everyone who is both not tall and quiet is funny and vice versa.
If someone is either not happy or not funny then someone is not wise.
If someone is curious then someone is funny and vice versa.
If someone is either not happy or not kind then someone is both rich and kind.
If someone is curious or not happy then mary is both not humble and wise.
If lucy is not quiet or not strong then lucy is old and vice versa.
Everyone who is both old and not patient is generous and vice versa.
Everyone who is strong is both rich and not old and vice versa.
If someone is rich then someone is not calm or wise and vice versa.
If paul is either quiet or not curious then someone is strong and vice versa.
Everyone who is not humble is both patient and strong and vice versa.
Everyone who is not happy is brave or quiet and vice versa.
Everyone who is not rich or not funny is both not old and not calm.
Everyone who is calm is not calm.
If lucy is not happy then lucy is rich.
Someone is not kind.
Someone is not kind or not wise.
John is not quiet.
Susan is not tall.
Someone is either not wise or rich.
Fred is either not happy or not curious. | Lucy is not rich. | contradiction | (![X]:((~quiet(X)<~>~generous(X))=>(~old(X)<~>happy(X))))&
(![X]:((~tall(X)&quiet(X))<=>funny(X)))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:(~wise(X))))&
((?[X]:(curious(X)))<=>(?[X]:(funny(X))))&
((?[X]:((~happy(X)<~>~kind(X))))=>(?[X]:((rich(X)&kind(X)))))&
((?[X]:((curious(X)|~happy(X))))=>((~humble(mary)&wise(mary))))&
(((~quiet(lucy)|~strong(lucy)))<=>(old(lucy)))&
(![X]:((old(X)&~patient(X))<=>generous(X)))&
(![X]:(strong(X)<=>(rich(X)&~old(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)|wise(X)))))&
(((quiet(paul)<~>~curious(paul)))<=>(?[X]:(strong(X))))&
(![X]:(~humble(X)<=>(patient(X)&strong(X))))&
(![X]:(~happy(X)<=>(brave(X)|quiet(X))))&
(![X]:((~rich(X)|~funny(X))=>(~old(X)&~calm(X))))&
(![X]:(calm(X)=>~calm(X)))&
((~happy(lucy))=>(rich(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~kind(X)|~wise(X))))&
(~quiet(john))&
(~tall(susan))&
(?[X]:((~wise(X)<~>rich(X))))&
((~happy(fred)<~>~curious(fred))) | ~rich(lucy) | [
"p6",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5016763748959795725919705
% SZS output start Proof for 5016763748959795725919705
7. (~strong(lucy) | ~quiet(lucy)) <=> old(lucy) [input p6]
13. ! [X0] : (~happy(X0) <=> (quiet(X0) | brave(X0))) [input p12]
14. ! [X0] : ((~funny(X0) | ~rich(X0)) => (~calm(X0) & ~old(X0))) [input p13]
16. ~happy(lucy) => rich(lucy) [input p15]
23. ~rich(lucy) [input hypothesis]
34. ! [X0] : ((~calm(X0) & ~old(X0)) | (funny(X0) & rich(X0))) [ennf transformation 14]
36. rich(lucy) | happy(lucy) [ennf transformation 16]
53. ((~strong(lucy) | ~quiet(lucy)) | ~old(lucy)) & (old(lucy) | (strong(lucy) & quiet(lucy))) [nnf transformation 7]
54. (~strong(lucy) | ~quiet(lucy) | ~old(lucy)) & (old(lucy) | (strong(lucy) & quiet(lucy))) [flattening 53]
68. ! [X0] : ((~happy(X0) | (~quiet(X0) & ~brave(X0))) & ((quiet(X0) | brave(X0)) | happy(X0))) [nnf transformation 13]
69. ! [X0] : ((~happy(X0) | (~quiet(X0) & ~brave(X0))) & (quiet(X0) | brave(X0) | happy(X0))) [flattening 68]
97. old(lucy) | quiet(lucy) [cnf transformation 54]
117. ~happy(X0) | ~quiet(X0) [cnf transformation 69]
118. ~old(X0) | rich(X0) [cnf transformation 34]
123. rich(lucy) | happy(lucy) [cnf transformation 36]
132. ~rich(lucy) [cnf transformation 23]
196. 15 <=> old(lucy) [avatar definition]
197. old(lucy) <- (15) [avatar component clause 196]
200. 16 <=> quiet(lucy) [avatar definition]
209. 16 | 15 [avatar split clause 97,196,200]
254. 28 <=> happy(lucy) [avatar definition]
256. happy(lucy) <- (28) [avatar component clause 254]
258. 29 <=> rich(lucy) [avatar definition]
259. ~rich(lucy) <- (~29) [avatar component clause 258]
261. 28 | 29 [avatar split clause 123,258,254]
291. ~29 [avatar split clause 132,258]
300. ~quiet(lucy) <- (28) [resolution 117,256]
304. ~16 | ~28 [avatar split clause 300,254,200]
318. rich(lucy) <- (15) [resolution 118,197]
319. $false <- (15, ~29) [subsumption resolution 318,259]
320. ~15 | 29 [avatar contradiction clause 319]
321. $false [avatar sat refutation 209,261,291,304,320]
% SZS output end Proof for 5016763748959795725919705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is not funny or strong.
Everyone who is quiet is not funny and vice versa.
Everyone who is not creative is either strong or patient and vice versa.
Everyone who is both not wise and not brave is brave and vice versa.
Everyone who is both kind and not old is both not kind and humble.
If lucy is both not patient and creative then someone is tall or brave and vice versa.
Everyone who is not brave or not kind is curious or not rich and vice versa.
Everyone who is not calm or creative is not wise or brave and vice versa.
If someone is either rich or brave then lucy is both humble and calm and vice versa.
Everyone who is both not quiet and not wise is not old or strong and vice versa.
Everyone who is both not kind and not curious is brave.
If alice is not patient then someone is humble and vice versa.
If someone is either creative or not calm then someone is quiet or not rich.
If someone is not quiet or strong then mary is both not quiet and creative.
Everyone who is quiet or not quiet is calm or not creative and vice versa.
Someone is either wise or brave.
Someone is both not brave and not tall.
Someone is quiet or not old.
John is either calm or rich.
Mary is not creative or kind. | Alice is not creative. | entailment | (![X]:(~wise(X)=>(~funny(X)|strong(X))))&
(![X]:(quiet(X)<=>~funny(X)))&
(![X]:(~creative(X)<=>(strong(X)<~>patient(X))))&
(![X]:((~wise(X)&~brave(X))<=>brave(X)))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&humble(X))))&
(((~patient(lucy)&creative(lucy)))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~brave(X)|~kind(X))<=>(curious(X)|~rich(X))))&
(![X]:((~calm(X)|creative(X))<=>(~wise(X)|brave(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>((humble(lucy)&calm(lucy))))&
(![X]:((~quiet(X)&~wise(X))<=>(~old(X)|strong(X))))&
(![X]:((~kind(X)&~curious(X))=>brave(X)))&
((~patient(alice))<=>(?[X]:(humble(X))))&
((?[X]:((creative(X)<~>~calm(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
((?[X]:((~quiet(X)|strong(X))))=>((~quiet(mary)&creative(mary))))&
(![X]:((quiet(X)|~quiet(X))<=>(calm(X)|~creative(X))))&
(?[X]:((wise(X)<~>brave(X))))&
(?[X]:((~brave(X)&~tall(X))))&
(?[X]:((quiet(X)|~old(X))))&
((calm(john)<~>rich(john)))&
((~creative(mary)|kind(mary))) | ~creative(alice) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 556859680227545227348897
% SZS output start Proof for 556859680227545227348897
4. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> brave(X0)) [input p3]
8. ! [X0] : ((creative(X0) | ~calm(X0)) <=> (brave(X0) | ~wise(X0))) [input p7]
21. creative(alice) [input hypothesis]
33. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | wise(X0)))) [nnf transformation 4]
34. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | wise(X0))) [flattening 33]
42. ! [X0] : (((creative(X0) | ~calm(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (~creative(X0) & calm(X0)))) [nnf transformation 8]
43. ! [X0] : ((creative(X0) | ~calm(X0) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | (~creative(X0) & calm(X0)))) [flattening 42]
76. brave(X0) | brave(X0) | wise(X0) [cnf transformation 34]
78. ~brave(X0) | ~brave(X0) [cnf transformation 34]
91. brave(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 43]
126. creative(alice) [cnf transformation 21]
128. brave(X0) | wise(X0) [duplicate literal removal 76]
129. ~brave(X0) [duplicate literal removal 78]
130. wise(X0) [subsumption resolution 128,129]
151. ~wise(X0) | ~creative(X0) [subsumption resolution 91,129]
152. ~creative(X0) [subsumption resolution 151,130]
189. $false [subsumption resolution 126,152]
% SZS output end Proof for 556859680227545227348897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If fred is curious or tall then fred is not creative or not tall.
Everyone who is both not strong and old is not tall.
Everyone who is both happy and not old is kind or not calm and vice versa.
If someone is both not quiet and not old then alice is both not calm and not humble and vice versa.
If someone is either not wise or kind then john is both not calm and calm and vice versa.
Everyone who is funny is brave or not quiet.
Everyone who is not creative or not brave is calm or brave.
Everyone who is not happy or not old is both curious and not humble and vice versa.
Everyone who is not creative is both creative and not happy.
If someone is either not funny or old then someone is kind or tall.
Everyone who is both not humble and curious is either funny or wise.
If someone is both not funny and not wise then someone is both generous and not calm.
Everyone who is either not rich or not funny is either not creative or not rich and vice versa.
Everyone who is both patient and not rich is not creative or not strong.
Everyone who is both quiet and tall is not kind and vice versa.
If someone is old then paul is patient or not happy.
Fred is not curious or not calm.
Mary is either kind or rich.
Someone is both rich and calm.
John is both not old and not patient.
Lucy is both not calm and not rich.
Susan is both not patient and not quiet.
Mary is either generous or not kind. | Paul is not happy. | contradiction | (((curious(fred)|tall(fred)))=>((~creative(fred)|~tall(fred))))&
(![X]:((~strong(X)&old(X))=>~tall(X)))&
(![X]:((happy(X)&~old(X))<=>(kind(X)|~calm(X))))&
((?[X]:((~quiet(X)&~old(X))))<=>((~calm(alice)&~humble(alice))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((~calm(john)&calm(john))))&
(![X]:(funny(X)=>(brave(X)|~quiet(X))))&
(![X]:((~creative(X)|~brave(X))=>(calm(X)|brave(X))))&
(![X]:((~happy(X)|~old(X))<=>(curious(X)&~humble(X))))&
(![X]:(~creative(X)=>(creative(X)&~happy(X))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((~humble(X)&curious(X))=>(funny(X)<~>wise(X))))&
((?[X]:((~funny(X)&~wise(X))))=>(?[X]:((generous(X)&~calm(X)))))&
(![X]:((~rich(X)<~>~funny(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((patient(X)&~rich(X))=>(~creative(X)|~strong(X))))&
(![X]:((quiet(X)&tall(X))<=>~kind(X)))&
((?[X]:(old(X)))=>((patient(paul)|~happy(paul))))&
((~curious(fred)|~calm(fred)))&
((kind(mary)<~>rich(mary)))&
(?[X]:((rich(X)&calm(X))))&
((~old(john)&~patient(john)))&
((~calm(lucy)&~rich(lucy)))&
((~patient(susan)&~quiet(susan)))&
((generous(mary)<~>~kind(mary))) | ~happy(paul) | [
"p2",
"p4",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7997908328226574055246500
% SZS output start Proof for 7997908328226574055246500
3. ! [X0] : ((~old(X0) & happy(X0)) <=> (~calm(X0) | kind(X0))) [input p2]
5. ? [X0] : (~wise(X0) <~> kind(X0)) <=> (calm(john) & ~calm(john)) [input p4]
8. ! [X0] : ((~old(X0) | ~happy(X0)) <=> (~humble(X0) & curious(X0))) [input p7]
9. ! [X0] : (~creative(X0) => (~happy(X0) & creative(X0))) [input p8]
11. ! [X0] : ((curious(X0) & ~humble(X0)) => (funny(X0) <~> wise(X0))) [input p10]
13. ! [X0] : ((~rich(X0) <~> ~funny(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p12]
24. ~happy(paul) [input hypothesis]
33. ! [X0] : ((~happy(X0) & creative(X0)) | creative(X0)) [ennf transformation 9]
35. ! [X0] : ((funny(X0) <~> wise(X0)) | (~curious(X0) | humble(X0))) [ennf transformation 11]
36. ! [X0] : ((funny(X0) <~> wise(X0)) | ~curious(X0) | humble(X0)) [flattening 35]
42. ! [X0] : (((~old(X0) & happy(X0)) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | (old(X0) | ~happy(X0)))) [nnf transformation 3]
43. ! [X0] : (((~old(X0) & happy(X0)) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | old(X0) | ~happy(X0))) [flattening 42]
49. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (~calm(john) | calm(john))) & ((calm(john) & ~calm(john)) | ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [nnf transformation 5]
50. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(john) | calm(john)) & ((calm(john) & ~calm(john)) | ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [flattening 49]
51. (? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ~calm(john) | calm(john)) & ((calm(john) & ~calm(john)) | ! [X1] : ((~wise(X1) | ~kind(X1)) & (kind(X1) | wise(X1)))) [rectify 50]
52. ? [X0] : ((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) => ((~kind(sK1) | wise(sK1)) & (kind(sK1) | ~wise(sK1))) [choice axiom]
53. (((~kind(sK1) | wise(sK1)) & (kind(sK1) | ~wise(sK1))) | ~calm(john) | calm(john)) & ((calm(john) & ~calm(john)) | ! [X1] : ((~wise(X1) | ~kind(X1)) & (kind(X1) | wise(X1)))) [skolemisation 51,52]
54. ! [X0] : (((~old(X0) | ~happy(X0)) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | (old(X0) & happy(X0)))) [nnf transformation 8]
55. ! [X0] : ((~old(X0) | ~happy(X0) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | (old(X0) & happy(X0)))) [flattening 54]
60. ! [X0] : (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | ~curious(X0) | humble(X0)) [nnf transformation 36]
64. ! [X0] : ((((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0))))) [nnf transformation 13]
75. ~kind(X0) | happy(X0) [cnf transformation 43]
83. ~calm(john) | kind(X1) | wise(X1) [cnf transformation 53]
85. calm(john) | kind(X1) | wise(X1) [cnf transformation 53]
89. happy(X0) | curious(X0) [cnf transformation 55]
91. ~humble(X0) | happy(X0) [cnf transformation 55]
94. creative(X0) | creative(X0) [cnf transformation 33]
99. ~funny(X0) | ~wise(X0) | ~curious(X0) | humble(X0) [cnf transformation 60]
103. ~rich(X0) | ~creative(X0) | ~rich(X0) | funny(X0) [cnf transformation 64]
109. funny(X0) | rich(X0) | ~creative(X0) | rich(X0) [cnf transformation 64]
128. ~happy(paul) [cnf transformation 24]
129. ~rich(X0) | ~creative(X0) | funny(X0) [duplicate literal removal 103]
132. funny(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 109]
133. creative(X0) [duplicate literal removal 94]
176. 10 <=> calm(john) [avatar definition]
181. 11 <=> ! [X1] : (kind(X1) | wise(X1)) [avatar definition]
182. wise(X1) | kind(X1) <- (11) [avatar component clause 181]
183. 11 | 10 [avatar split clause 85,176,181]
185. 11 | ~10 [avatar split clause 83,176,181]
215. rich(X0) | funny(X0) [subsumption resolution 132,133]
216. ~rich(X0) | funny(X0) [subsumption resolution 129,133]
217. funny(X0) [subsumption resolution 216,215]
227. 21 <=> happy(paul) [avatar definition]
229. ~happy(paul) <- (~21) [avatar component clause 227]
252. ~21 [avatar split clause 128,227]
259. curious(paul) <- (~21) [resolution 89,229]
335. ~wise(X0) | ~curious(X0) | humble(X0) [resolution 99,217]
393. ~curious(X0) | humble(X0) | kind(X0) <- (11) [resolution 335,182]
422. humble(paul) | kind(paul) <- (11, ~21) [resolution 393,259]
446. 43 <=> kind(paul) [avatar definition]
448. kind(paul) <- (43) [avatar component clause 446]
450. 44 <=> humble(paul) [avatar definition]
452. humble(paul) <- (44) [avatar component clause 450]
453. 43 | 44 | ~11 | 21 [avatar split clause 422,227,181,450,446]
484. happy(paul) <- (44) [resolution 452,91]
485. $false <- (~21, 44) [subsumption resolution 484,229]
486. 21 | ~44 [avatar contradiction clause 485]
488. happy(paul) <- (43) [resolution 448,75]
489. $false <- (~21, 43) [subsumption resolution 488,229]
490. 21 | ~43 [avatar contradiction clause 489]
491. $false [avatar sat refutation 183,185,252,453,486,490]
% SZS output end Proof for 7997908328226574055246500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then john is not wise.
If someone is not happy or patient then john is both not tall and curious and vice versa.
If john is not funny or humble then john is not wise or wise and vice versa.
Everyone who is both not happy and not curious is either not funny or not patient and vice versa.
Everyone who is not tall or not generous is both tall and not old and vice versa.
Everyone who is tall or generous is both not generous and rich.
Everyone who is strong or not quiet is either generous or not strong and vice versa.
If fred is not humble or not generous then mary is either not wise or patient.
Everyone who is not rich is funny and vice versa.
Everyone who is not creative is old or not happy and vice versa.
If someone is both humble and kind then lucy is not strong or tall and vice versa.
Everyone who is either generous or not humble is both generous and curious and vice versa.
If mary is kind or not curious then mary is either not strong or not rich and vice versa.
Everyone who is both not rich and not happy is not kind and vice versa.
If someone is both humble and not generous then someone is not wise and vice versa.
Fred is either brave or not strong.
Alice is wise. | Mary is wise. | contradiction | ((?[X]:(funny(X)))=>(~wise(john)))&
((?[X]:((~happy(X)|patient(X))))<=>((~tall(john)&curious(john))))&
(((~funny(john)|humble(john)))<=>((~wise(john)|wise(john))))&
(![X]:((~happy(X)&~curious(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)&~old(X))))&
(![X]:((tall(X)|generous(X))=>(~generous(X)&rich(X))))&
(![X]:((strong(X)|~quiet(X))<=>(generous(X)<~>~strong(X))))&
(((~humble(fred)|~generous(fred)))=>((~wise(mary)<~>patient(mary))))&
(![X]:(~rich(X)<=>funny(X)))&
(![X]:(~creative(X)<=>(old(X)|~happy(X))))&
((?[X]:((humble(X)&kind(X))))<=>((~strong(lucy)|tall(lucy))))&
(![X]:((generous(X)<~>~humble(X))<=>(generous(X)&curious(X))))&
(((kind(mary)|~curious(mary)))<=>((~strong(mary)<~>~rich(mary))))&
(![X]:((~rich(X)&~happy(X))<=>~kind(X)))&
((?[X]:((humble(X)&~generous(X))))<=>(?[X]:(~wise(X))))&
((brave(fred)<~>~strong(fred)))&
(wise(alice)) | wise(mary) | [
"p1",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3255982137605667924176052
% SZS output start Proof for 3255982137605667924176052
2. ? [X0] : (patient(X0) | ~happy(X0)) <=> (curious(john) & ~tall(john)) [input p1]
5. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~old(X0) & tall(X0))) [input p4]
6. ! [X0] : ((generous(X0) | tall(X0)) => (rich(X0) & ~generous(X0))) [input p5]
8. (~generous(fred) | ~humble(fred)) => (~wise(mary) <~> patient(mary)) [input p7]
18. wise(mary) [input hypothesis]
21. ! [X0] : ((rich(X0) & ~generous(X0)) | (~generous(X0) & ~tall(X0))) [ennf transformation 6]
22. (~wise(mary) <~> patient(mary)) | (generous(fred) & humble(fred)) [ennf transformation 8]
23. (? [X0] : (patient(X0) | ~happy(X0)) | (~curious(john) | tall(john))) & ((curious(john) & ~tall(john)) | ! [X0] : (~patient(X0) & happy(X0))) [nnf transformation 2]
24. (? [X0] : (patient(X0) | ~happy(X0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X0] : (~patient(X0) & happy(X0))) [flattening 23]
25. (? [X0] : (patient(X0) | ~happy(X0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X1] : (~patient(X1) & happy(X1))) [rectify 24]
26. ? [X0] : (patient(X0) | ~happy(X0)) => (patient(sK0) | ~happy(sK0)) [choice axiom]
27. ((patient(sK0) | ~happy(sK0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X1] : (~patient(X1) & happy(X1))) [skolemisation 25,26]
32. ! [X0] : (((~generous(X0) | ~tall(X0)) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 5]
33. ! [X0] : ((~generous(X0) | ~tall(X0) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [flattening 32]
36. ((~patient(mary) | wise(mary)) & (patient(mary) | ~wise(mary))) | (generous(fred) & humble(fred)) [nnf transformation 22]
57. ~tall(john) | ~patient(X1) [cnf transformation 27]
71. tall(X0) | tall(X0) [cnf transformation 33]
77. ~generous(X0) | ~generous(X0) [cnf transformation 21]
87. patient(mary) | ~wise(mary) | generous(fred) [cnf transformation 36]
118. wise(mary) [cnf transformation 18]
123. ~generous(X0) [duplicate literal removal 77]
124. tall(X0) [duplicate literal removal 71]
135. 3 <=> tall(john) [avatar definition]
136. ~tall(john) <- (~3) [avatar component clause 135]
152. 7 <=> ! [X1] : ~patient(X1) [avatar definition]
153. ~patient(X1) <- (7) [avatar component clause 152]
159. 7 | ~3 [avatar split clause 57,135,152]
177. 11 <=> wise(mary) [avatar definition]
181. 12 <=> patient(mary) [avatar definition]
182. patient(mary) <- (12) [avatar component clause 181]
190. patient(mary) | ~wise(mary) [subsumption resolution 87,123]
191. ~11 | 12 [avatar split clause 190,181,177]
214. 11 [avatar split clause 118,177]
215. $false <- (~3) [subsumption resolution 136,124]
216. 3 [avatar contradiction clause 215]
219. $false <- (7, 12) [resolution 182,153]
220. ~7 | ~12 [avatar contradiction clause 219]
221. $false [avatar sat refutation 159,191,214,216,220]
% SZS output end Proof for 3255982137605667924176052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or calm is both old and not old and vice versa.
If susan is not quiet or strong then someone is either brave or not humble and vice versa.
Everyone who is both rich and not funny is either strong or brave.
Everyone who is either not kind or not creative is both not calm and not patient and vice versa.
If paul is either not funny or quiet then someone is wise.
If mary is happy then john is not kind.
If someone is not generous then susan is strong.
Everyone who is either creative or not old is not generous or not kind.
Everyone who is not strong or not creative is not strong or wise and vice versa.
If someone is both not rich and strong then someone is kind and vice versa.
Everyone who is both not kind and calm is not creative and vice versa.
Everyone who is both not kind and brave is tall or not creative and vice versa.
If someone is quiet then someone is both not strong and funny.
Everyone who is not patient is brave or not rich and vice versa.
If someone is either tall or quiet then someone is not calm or not creative and vice versa.
If someone is either not rich or quiet then john is either old or creative.
Someone is either not curious or kind.
Someone is funny.
Someone is funny or creative.
Paul is wise or not humble.
Someone is not quiet.
Someone is either tall or quiet. | Paul is brave. | neutral | (![X]:((~old(X)|calm(X))<=>(old(X)&~old(X))))&
(((~quiet(susan)|strong(susan)))<=>(?[X]:((brave(X)<~>~humble(X)))))&
(![X]:((rich(X)&~funny(X))=>(strong(X)<~>brave(X))))&
(![X]:((~kind(X)<~>~creative(X))<=>(~calm(X)&~patient(X))))&
(((~funny(paul)<~>quiet(paul)))=>(?[X]:(wise(X))))&
((happy(mary))=>(~kind(john)))&
((?[X]:(~generous(X)))=>(strong(susan)))&
(![X]:((creative(X)<~>~old(X))=>(~generous(X)|~kind(X))))&
(![X]:((~strong(X)|~creative(X))<=>(~strong(X)|wise(X))))&
((?[X]:((~rich(X)&strong(X))))<=>(?[X]:(kind(X))))&
(![X]:((~kind(X)&calm(X))<=>~creative(X)))&
(![X]:((~kind(X)&brave(X))<=>(tall(X)|~creative(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)&funny(X)))))&
(![X]:(~patient(X)<=>(brave(X)|~rich(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>(?[X]:((~calm(X)|~creative(X)))))&
((?[X]:((~rich(X)<~>quiet(X))))=>((old(john)<~>creative(john))))&
(?[X]:((~curious(X)<~>kind(X))))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)|creative(X))))&
((wise(paul)|~humble(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:((tall(X)<~>quiet(X)))) | brave(paul) | [] | null | 0 |
If someone is either patient or old then someone is both kind and not old and vice versa.
Everyone who is brave or funny is both brave and quiet and vice versa.
Everyone who is not patient is both funny and not quiet.
Everyone who is either curious or kind is either not tall or brave.
If susan is either creative or funny then someone is not old and vice versa.
If fred is quiet or patient then fred is either not patient or not happy and vice versa.
If someone is generous or brave then someone is not rich or generous.
If someone is not curious or not funny then alice is both patient and not calm and vice versa.
Everyone who is humble or not generous is either not humble or not happy and vice versa.
If john is brave then someone is generous.
Everyone who is both wise and not humble is generous.
Everyone who is either not rich or not tall is either kind or not happy and vice versa.
Everyone who is strong or not creative is both not wise and not creative and vice versa.
If someone is both not creative and funny then someone is patient.
If someone is either not tall or not patient then alice is either kind or not brave.
Everyone who is creative or not old is strong or patient.
Someone is either not patient or kind.
Paul is not tall.
Someone is creative or wise.
Someone is rich or tall.
Susan is either generous or not wise.
Susan is either kind or humble.
Someone is funny or brave.
Paul is happy. | Fred is not patient. | contradiction | ((?[X]:((patient(X)<~>old(X))))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((brave(X)|funny(X))<=>(brave(X)&quiet(X))))&
(![X]:(~patient(X)=>(funny(X)&~quiet(X))))&
(![X]:((curious(X)<~>kind(X))=>(~tall(X)<~>brave(X))))&
(((creative(susan)<~>funny(susan)))<=>(?[X]:(~old(X))))&
(((quiet(fred)|patient(fred)))<=>((~patient(fred)<~>~happy(fred))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((~rich(X)|generous(X)))))&
((?[X]:((~curious(X)|~funny(X))))<=>((patient(alice)&~calm(alice))))&
(![X]:((humble(X)|~generous(X))<=>(~humble(X)<~>~happy(X))))&
((brave(john))=>(?[X]:(generous(X))))&
(![X]:((wise(X)&~humble(X))=>generous(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(kind(X)<~>~happy(X))))&
(![X]:((strong(X)|~creative(X))<=>(~wise(X)&~creative(X))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:(patient(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((kind(alice)<~>~brave(alice))))&
(![X]:((creative(X)|~old(X))=>(strong(X)|patient(X))))&
(?[X]:((~patient(X)<~>kind(X))))&
(~tall(paul))&
(?[X]:((creative(X)|wise(X))))&
(?[X]:((rich(X)|tall(X))))&
((generous(susan)<~>~wise(susan)))&
((kind(susan)<~>humble(susan)))&
(?[X]:((funny(X)|brave(X))))&
(happy(paul)) | ~patient(fred) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7898718007953671816829885
% SZS output start Proof for 7898718007953671816829885
2. ! [X0] : ((funny(X0) | brave(X0)) <=> (quiet(X0) & brave(X0))) [input p1]
3. ! [X0] : (~patient(X0) => (~quiet(X0) & funny(X0))) [input p2]
25. ~patient(fred) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & funny(X0)) | patient(X0)) [ennf transformation 3]
44. ! [X0] : (((funny(X0) | brave(X0)) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | (~funny(X0) & ~brave(X0)))) [nnf transformation 2]
45. ! [X0] : ((funny(X0) | brave(X0) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | (~funny(X0) & ~brave(X0)))) [flattening 44]
92. ~funny(X0) | quiet(X0) [cnf transformation 45]
94. funny(X0) | patient(X0) [cnf transformation 29]
95. ~quiet(X0) | patient(X0) [cnf transformation 29]
156. ~patient(fred) [cnf transformation 25]
217. 13 <=> patient(fred) [avatar definition]
218. ~patient(fred) <- (~13) [avatar component clause 217]
348. ~13 [avatar split clause 156,217]
357. patient(X0) | quiet(X0) [resolution 94,92]
359. patient(X0) [subsumption resolution 357,95]
361. $false <- (~13) [resolution 359,218]
364. 13 [avatar contradiction clause 361]
365. $false [avatar sat refutation 348,364]
% SZS output end Proof for 7898718007953671816829885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is generous and vice versa. Everyone who is both patient and curious is either not brave or not kind and vice versa. If fred is brave or generous then someone is either funny or not curious. Everyone who is both brave and kind is strong or happy and vice versa. Everyone who is not patient is wise or strong. If mary is not generous or not brave then mary is not quiet. If john is either wise or not generous then alice is either not wise or not calm and vice versa. If someone is not creative or calm then someone is either funny or kind. Everyone who is either old or wise is either not funny or not rich. Everyone who is not creative or not old is both not brave and not funny and vice versa. Everyone who is both not creative and kind is either calm or funny and vice versa. Everyone who is not patient or not strong is kind. Everyone who is creative or not funny is not tall or patient. Everyone who is not strong is quiet. If paul is not happy or brave then someone is both brave and not wise and vice versa. Everyone who is either not curious or not quiet is either brave or not generous. Someone is calm or brave. Alice is either humble or tall. Someone is wise or not calm. Lucy is either rich or not quiet. Susan is not old. Someone is either not funny or tall. | Mary is kind. | entailment | (![X]:(~humble(X)<=>generous(X)))&
(![X]:((patient(X)&curious(X))<=>(~brave(X)<~>~kind(X))))&
(((brave(fred)|generous(fred)))=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:((brave(X)&kind(X))<=>(strong(X)|happy(X))))&
(![X]:(~patient(X)=>(wise(X)|strong(X))))&
(((~generous(mary)|~brave(mary)))=>(~quiet(mary)))&
(((wise(john)<~>~generous(john)))<=>((~wise(alice)<~>~calm(alice))))&
((?[X]:((~creative(X)|calm(X))))=>(?[X]:((funny(X)<~>kind(X)))))&
(![X]:((old(X)<~>wise(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((~creative(X)|~old(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~creative(X)&kind(X))<=>(calm(X)<~>funny(X))))&
(![X]:((~patient(X)|~strong(X))=>kind(X)))&
(![X]:((creative(X)|~funny(X))=>(~tall(X)|patient(X))))&
(![X]:(~strong(X)=>quiet(X)))&
(((~happy(paul)|brave(paul)))<=>(?[X]:((brave(X)&~wise(X)))))&
(![X]:((~curious(X)<~>~quiet(X))=>(brave(X)<~>~generous(X))))&
(?[X]:((calm(X)|brave(X))))&
((humble(alice)<~>tall(alice)))&
(?[X]:((wise(X)|~calm(X))))&
((rich(lucy)<~>~quiet(lucy)))&
(~old(susan))&
(?[X]:((~funny(X)<~>tall(X)))) | kind(mary) | [
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7414272614507830245393004
% SZS output start Proof for 7414272614507830245393004
4. ! [X0] : ((kind(X0) & brave(X0)) <=> (happy(X0) | strong(X0))) [input p3]
12. ! [X0] : ((~strong(X0) | ~patient(X0)) => kind(X0)) [input p11]
23. ~kind(mary) [input hypothesis]
31. ! [X0] : (kind(X0) | (strong(X0) & patient(X0))) [ennf transformation 12]
42. ! [X0] : (((kind(X0) & brave(X0)) | (~happy(X0) & ~strong(X0))) & ((happy(X0) | strong(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 4]
43. ! [X0] : (((kind(X0) & brave(X0)) | (~happy(X0) & ~strong(X0))) & (happy(X0) | strong(X0) | ~kind(X0) | ~brave(X0))) [flattening 42]
84. kind(X0) | ~strong(X0) [cnf transformation 43]
117. kind(X0) | strong(X0) [cnf transformation 31]
139. ~kind(mary) [cnf transformation 23]
218. kind(X0) [subsumption resolution 117,84]
287. $false [subsumption resolution 139,218]
% SZS output end Proof for 7414272614507830245393004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then mary is both not tall and strong.
Everyone who is either wise or humble is both patient and creative and vice versa.
If someone is either humble or brave then mary is not patient or generous.
Everyone who is not generous or not creative is not rich.
If someone is either not rich or curious then someone is either curious or not patient and vice versa.
If someone is both not strong and curious then someone is not tall or brave.
If mary is generous then someone is both not brave and humble.
If someone is creative then someone is both brave and not brave.
Everyone who is not wise or patient is generous or not funny and vice versa.
If someone is not quiet then mary is happy.
If paul is either not happy or not humble then susan is both not generous and not calm.
If someone is old or not patient then someone is either not old or not creative.
If lucy is both calm and curious then someone is either kind or curious and vice versa.
Everyone who is not creative is quiet.
Everyone who is strong is both old and not patient and vice versa.
If susan is not strong or happy then someone is funny or creative.
Someone is either curious or wise.
Someone is happy or not curious.
Someone is not tall or happy.
Someone is not creative.
Someone is not patient.
Someone is both not curious and not creative.
Paul is not calm or brave.
Alice is either calm or humble. | Mary is patient. | contradiction | ((?[X]:(old(X)))=>((~tall(mary)&strong(mary))))&
(![X]:((wise(X)<~>humble(X))<=>(patient(X)&creative(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((~patient(mary)|generous(mary))))&
(![X]:((~generous(X)|~creative(X))=>~rich(X)))&
((?[X]:((~rich(X)<~>curious(X))))<=>(?[X]:((curious(X)<~>~patient(X)))))&
((?[X]:((~strong(X)&curious(X))))=>(?[X]:((~tall(X)|brave(X)))))&
((generous(mary))=>(?[X]:((~brave(X)&humble(X)))))&
((?[X]:(creative(X)))=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((~wise(X)|patient(X))<=>(generous(X)|~funny(X))))&
((?[X]:(~quiet(X)))=>(happy(mary)))&
(((~happy(paul)<~>~humble(paul)))=>((~generous(susan)&~calm(susan))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(((calm(lucy)&curious(lucy)))<=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:(~creative(X)=>quiet(X)))&
(![X]:(strong(X)<=>(old(X)&~patient(X))))&
(((~strong(susan)|happy(susan)))=>(?[X]:((funny(X)|creative(X)))))&
(?[X]:((curious(X)<~>wise(X))))&
(?[X]:((happy(X)|~curious(X))))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~curious(X)&~creative(X))))&
((~calm(paul)|brave(paul)))&
((calm(alice)<~>humble(alice))) | patient(mary) | [
"p0",
"p7",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7797808903049209317283469
% SZS output start Proof for 7797808903049209317283469
1. ? [X0] : old(X0) => (strong(mary) & ~tall(mary)) [input p0]
8. ? [X0] : creative(X0) => ? [X0] : (~brave(X0) & brave(X0)) [input p7]
12. ? [X0] : (~patient(X0) | old(X0)) => ? [X0] : (~old(X0) <~> ~creative(X0)) [input p11]
15. ! [X0] : (strong(X0) <=> (~patient(X0) & old(X0))) [input p14]
21. ? [X0] : ~patient(X0) [input p20]
25. patient(mary) [input hypothesis]
28. ? [X0] : creative(X0) => ? [X1] : (~brave(X1) & brave(X1)) [rectify 8]
29. ? [X0] : (~patient(X0) | old(X0)) => ? [X1] : (~old(X1) <~> ~creative(X1)) [rectify 12]
30. ! [X0] : (strong(X0) => (~patient(X0) & old(X0))) [unused predicate definition removal 15]
33. ? [X0] : old(X0) => strong(mary) [pure predicate removal 1]
36. strong(mary) | ! [X0] : ~old(X0) [ennf transformation 33]
41. ? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : ~creative(X0) [ennf transformation 28]
43. ? [X1] : (~old(X1) <~> ~creative(X1)) | ! [X0] : (patient(X0) & ~old(X0)) [ennf transformation 29]
44. ! [X0] : ((~patient(X0) & old(X0)) | ~strong(X0)) [ennf transformation 30]
56. ? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ~creative(X1) [rectify 41]
57. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK3) & brave(sK3)) [choice axiom]
58. (~brave(sK3) & brave(sK3)) | ! [X1] : ~creative(X1) [skolemisation 56,57]
62. ? [X1] : ((creative(X1) | old(X1)) & (~creative(X1) | ~old(X1))) | ! [X0] : (patient(X0) & ~old(X0)) [nnf transformation 43]
63. ? [X0] : ((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ! [X1] : (patient(X1) & ~old(X1)) [rectify 62]
64. ? [X0] : ((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) => ((creative(sK4) | old(sK4)) & (~creative(sK4) | ~old(sK4))) [choice axiom]
65. ((creative(sK4) | old(sK4)) & (~creative(sK4) | ~old(sK4))) | ! [X1] : (patient(X1) & ~old(X1)) [skolemisation 63,64]
80. ? [X0] : ~patient(X0) => ~patient(sK10) [choice axiom]
81. ~patient(sK10) [skolemisation 21,80]
85. strong(mary) | ~old(X0) [cnf transformation 36]
106. brave(sK3) | ~creative(X1) [cnf transformation 58]
107. ~brave(sK3) | ~creative(X1) [cnf transformation 58]
119. creative(sK4) | old(sK4) | patient(X1) [cnf transformation 65]
127. ~patient(X0) | ~strong(X0) [cnf transformation 44]
134. ~patient(sK10) [cnf transformation 81]
140. patient(mary) [cnf transformation 25]
142. 1 <=> ! [X0] : ~old(X0) [avatar definition]
143. ~old(X0) <- (1) [avatar component clause 142]
145. 2 <=> strong(mary) [avatar definition]
148. 1 | 2 [avatar split clause 85,145,142]
153. 4 <=> patient(mary) [avatar definition]
154. patient(mary) <- (4) [avatar component clause 153]
212. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
213. ~creative(X1) <- (17) [avatar component clause 212]
215. 18 <=> brave(sK3) [avatar definition]
218. 17 | ~18 [avatar split clause 107,215,212]
219. 17 | 18 [avatar split clause 106,215,212]
241. 23 <=> ! [X1] : patient(X1) [avatar definition]
242. patient(X1) <- (23) [avatar component clause 241]
244. 24 <=> old(sK4) [avatar definition]
246. old(sK4) <- (24) [avatar component clause 244]
248. 25 <=> creative(sK4) [avatar definition]
250. creative(sK4) <- (25) [avatar component clause 248]
251. 23 | 24 | 25 [avatar split clause 119,248,244,241]
339. 4 [avatar split clause 140,153]
341. ~strong(mary) <- (4) [resolution 127,154]
344. ~2 | ~4 [avatar split clause 341,153,145]
345. $false <- (1, 24) [resolution 143,246]
346. ~1 | ~24 [avatar contradiction clause 345]
347. $false <- (23) [resolution 242,134]
351. ~23 [avatar contradiction clause 347]
352. $false <- (17, 25) [subsumption resolution 250,213]
353. ~17 | ~25 [avatar contradiction clause 352]
354. $false [avatar sat refutation 148,218,219,251,339,344,346,351,353]
% SZS output end Proof for 7797808903049209317283469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both strong and patient then john is both funny and patient.
Everyone who is not creative or not generous is calm and vice versa.
Everyone who is not funny is either not calm or generous.
Everyone who is not quiet or wise is either not quiet or patient.
If susan is old then someone is both not tall and strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Everyone who is both not happy and funny is not funny and vice versa.
Everyone who is both not patient and not curious is funny.
If someone is not tall or not patient then paul is both not generous and not humble.
Everyone who is either funny or not creative is not kind or not old.
If susan is both not tall and not happy then someone is kind or curious.
Everyone who is either old or patient is brave and vice versa.
Fred is kind or not creative.
Someone is not tall or generous.
Someone is not patient.
Alice is funny or happy.
Mary is humble. | Susan is not old. | contradiction | (((strong(paul)&patient(paul)))=>((funny(john)&patient(john))))&
(![X]:((~creative(X)|~generous(X))<=>calm(X)))&
(![X]:(~funny(X)=>(~calm(X)<~>generous(X))))&
(![X]:((~quiet(X)|wise(X))=>(~quiet(X)<~>patient(X))))&
((old(susan))<=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(![X]:((~happy(X)&funny(X))<=>~funny(X)))&
(![X]:((~patient(X)&~curious(X))=>funny(X)))&
((?[X]:((~tall(X)|~patient(X))))=>((~generous(paul)&~humble(paul))))&
(![X]:((funny(X)<~>~creative(X))=>(~kind(X)|~old(X))))&
(((~tall(susan)&~happy(susan)))=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((old(X)<~>patient(X))<=>brave(X)))&
((kind(fred)|~creative(fred)))&
(?[X]:((~tall(X)|generous(X))))&
(?[X]:(~patient(X)))&
((funny(alice)|happy(alice)))&
(humble(mary)) | ~old(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8766668191752020855973907
% SZS output start Proof for 8766668191752020855973907
6. ? [X0] : (~old(X0) | quiet(X0)) => ? [X0] : (wise(X0) & ~wise(X0)) [input p5]
22. ~old(susan) [input hypothesis]
23. ? [X0] : (~old(X0) | quiet(X0)) => ? [X1] : (wise(X1) & ~wise(X1)) [rectify 6]
31. ? [X1] : (wise(X1) & ~wise(X1)) | ! [X0] : (old(X0) & ~quiet(X0)) [ennf transformation 23]
45. ? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (old(X1) & ~quiet(X1)) [rectify 31]
46. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
47. (wise(sK1) & ~wise(sK1)) | ! [X1] : (old(X1) & ~quiet(X1)) [skolemisation 45,46]
77. ~wise(sK1) | old(X1) [cnf transformation 47]
79. wise(sK1) | old(X1) [cnf transformation 47]
108. ~old(susan) [cnf transformation 22]
136. 6 <=> old(susan) [avatar definition]
137. ~old(susan) <- (~6) [avatar component clause 136]
151. 9 <=> ! [X1] : old(X1) [avatar definition]
152. old(X1) <- (9) [avatar component clause 151]
154. 10 <=> wise(sK1) [avatar definition]
157. 9 | 10 [avatar split clause 79,154,151]
162. 9 | ~10 [avatar split clause 77,154,151]
233. ~6 [avatar split clause 108,136]
234. $false <- (~6, 9) [subsumption resolution 137,152]
235. 6 | ~9 [avatar contradiction clause 234]
238. $false [avatar sat refutation 157,162,233,235]
% SZS output end Proof for 8766668191752020855973907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not happy is either not happy or not curious.
Everyone who is not calm is both not generous and patient and vice versa.
Everyone who is not brave or strong is kind.
If alice is both brave and quiet then john is either happy or not curious and vice versa.
Everyone who is either not strong or tall is generous or not old.
If someone is either not old or curious then someone is not strong or funny and vice versa.
If someone is either quiet or not strong then alice is happy or not old and vice versa.
If paul is not curious then lucy is not tall or generous and vice versa.
Everyone who is both not strong and kind is either not old or tall and vice versa.
Everyone who is creative is either rich or not humble.
Everyone who is calm or kind is both not wise and rich and vice versa.
Everyone who is happy or curious is not kind.
Everyone who is either quiet or humble is both not calm and curious.
If paul is both wise and humble then someone is both not strong and curious.
If someone is happy then paul is not generous or not brave.
Everyone who is either not calm or not brave is patient and vice versa.
Someone is both not brave and tall.
Paul is both tall and kind.
Someone is both not quiet and not creative.
John is either humble or brave.
John is not creative.
Alice is brave. | Lucy is not generous. | contradiction | (![X]:((~generous(X)&~happy(X))=>(~happy(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>(~generous(X)&patient(X))))&
(![X]:((~brave(X)|strong(X))=>kind(X)))&
(((brave(alice)&quiet(alice)))<=>((happy(john)<~>~curious(john))))&
(![X]:((~strong(X)<~>tall(X))=>(generous(X)|~old(X))))&
((?[X]:((~old(X)<~>curious(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
((?[X]:((quiet(X)<~>~strong(X))))<=>((happy(alice)|~old(alice))))&
((~curious(paul))<=>((~tall(lucy)|generous(lucy))))&
(![X]:((~strong(X)&kind(X))<=>(~old(X)<~>tall(X))))&
(![X]:(creative(X)=>(rich(X)<~>~humble(X))))&
(![X]:((calm(X)|kind(X))<=>(~wise(X)&rich(X))))&
(![X]:((happy(X)|curious(X))=>~kind(X)))&
(![X]:((quiet(X)<~>humble(X))=>(~calm(X)&curious(X))))&
(((wise(paul)&humble(paul)))=>(?[X]:((~strong(X)&curious(X)))))&
((?[X]:(happy(X)))=>((~generous(paul)|~brave(paul))))&
(![X]:((~calm(X)<~>~brave(X))<=>patient(X)))&
(?[X]:((~brave(X)&tall(X))))&
((tall(paul)&kind(paul)))&
(?[X]:((~quiet(X)&~creative(X))))&
((humble(john)<~>brave(john)))&
(~creative(john))&
(brave(alice)) | ~generous(lucy) | [
"p0",
"p2",
"p4",
"p7",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8680491738179559278774077
% SZS output start Proof for 8680491738179559278774077
1. ! [X0] : ((~happy(X0) & ~generous(X0)) => (~happy(X0) <~> ~curious(X0))) [input p0]
3. ! [X0] : ((strong(X0) | ~brave(X0)) => kind(X0)) [input p2]
5. ! [X0] : ((~strong(X0) <~> tall(X0)) => (~old(X0) | generous(X0))) [input p4]
8. ~curious(paul) <=> (generous(lucy) | ~tall(lucy)) [input p7]
9. ! [X0] : ((kind(X0) & ~strong(X0)) <=> (~old(X0) <~> tall(X0))) [input p8]
12. ! [X0] : ((curious(X0) | happy(X0)) => ~kind(X0)) [input p11]
18. kind(paul) & tall(paul) [input p17]
23. ~generous(lucy) [input hypothesis]
28. ! [X0] : ((~happy(X0) <~> ~curious(X0)) | (happy(X0) | generous(X0))) [ennf transformation 1]
29. ! [X0] : ((~happy(X0) <~> ~curious(X0)) | happy(X0) | generous(X0)) [flattening 28]
30. ! [X0] : (kind(X0) | (~strong(X0) & brave(X0))) [ennf transformation 3]
31. ! [X0] : ((~old(X0) | generous(X0)) | (~strong(X0) <=> tall(X0))) [ennf transformation 5]
32. ! [X0] : (~old(X0) | generous(X0) | (~strong(X0) <=> tall(X0))) [flattening 31]
33. ! [X0] : (~kind(X0) | (~curious(X0) & ~happy(X0))) [ennf transformation 12]
39. ! [X0] : (((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | happy(X0) | generous(X0)) [nnf transformation 29]
44. ! [X0] : (~old(X0) | generous(X0) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) [nnf transformation 32]
55. (~curious(paul) | (~generous(lucy) & tall(lucy))) & ((generous(lucy) | ~tall(lucy)) | curious(paul)) [nnf transformation 8]
56. (~curious(paul) | (~generous(lucy) & tall(lucy))) & (generous(lucy) | ~tall(lucy) | curious(paul)) [flattening 55]
57. ! [X0] : (((kind(X0) & ~strong(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0)))) & (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | (~kind(X0) | strong(X0)))) [nnf transformation 9]
58. ! [X0] : (((kind(X0) & ~strong(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0)))) & (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | ~kind(X0) | strong(X0))) [flattening 57]
71. curious(X0) | happy(X0) | happy(X0) | generous(X0) [cnf transformation 39]
76. ~strong(X0) | kind(X0) [cnf transformation 30]
83. ~old(X0) | generous(X0) | tall(X0) | strong(X0) [cnf transformation 44]
97. generous(lucy) | ~tall(lucy) | curious(paul) [cnf transformation 56]
104. old(X0) | tall(X0) | kind(X0) [cnf transformation 58]
111. ~kind(X0) | ~happy(X0) [cnf transformation 33]
112. ~kind(X0) | ~curious(X0) [cnf transformation 33]
127. kind(paul) [cnf transformation 18]
132. ~generous(lucy) [cnf transformation 23]
133. curious(X0) | happy(X0) | generous(X0) [duplicate literal removal 71]
219. 19 <=> generous(lucy) [avatar definition]
221. ~generous(lucy) <- (~19) [avatar component clause 219]
223. 20 <=> curious(paul) [avatar definition]
228. 21 <=> tall(lucy) [avatar definition]
229. ~tall(lucy) <- (~21) [avatar component clause 228]
232. 20 | ~21 | 19 [avatar split clause 97,219,228,223]
276. ~19 [avatar split clause 132,219]
281. ~curious(paul) [resolution 112,127]
356. ~20 [avatar split clause 281,223]
362. generous(X0) | tall(X0) | strong(X0) | tall(X0) | kind(X0) [resolution 83,104]
365. generous(X0) | tall(X0) | strong(X0) | kind(X0) [duplicate literal removal 362]
366. tall(X0) | generous(X0) | kind(X0) [subsumption resolution 365,76]
500. generous(lucy) | kind(lucy) <- (~21) [resolution 366,229]
502. kind(lucy) <- (~19, ~21) [subsumption resolution 500,221]
506. ~curious(lucy) <- (~19, ~21) [resolution 502,112]
507. ~happy(lucy) <- (~19, ~21) [resolution 502,111]
514. happy(lucy) | generous(lucy) <- (~19, ~21) [resolution 506,133]
515. generous(lucy) <- (~19, ~21) [subsumption resolution 514,507]
516. $false <- (~19, ~21) [subsumption resolution 515,221]
517. 19 | 21 [avatar contradiction clause 516]
518. $false [avatar sat refutation 232,276,356,517]
% SZS output end Proof for 8680491738179559278774077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is kind or not creative then fred is either not kind or not generous and vice versa.
Everyone who is not old is patient.
Everyone who is both generous and patient is strong or not quiet and vice versa.
If someone is both humble and patient then someone is both not patient and not brave and vice versa.
If john is both tall and rich then someone is creative.
If susan is not humble then someone is both not humble and not wise.
Everyone who is strong or generous is not happy.
Everyone who is not patient or not old is either not rich or not creative and vice versa.
If alice is strong then mary is brave.
If someone is humble then fred is both not old and not generous and vice versa.
Everyone who is either not quiet or tall is either not curious or kind.
Everyone who is either not humble or wise is funny and vice versa.
Everyone who is not wise or not rich is both not quiet and old and vice versa.
If mary is either not happy or not rich then someone is either funny or not happy.
Everyone who is quiet is both old and not humble.
Everyone who is both creative and funny is brave or calm and vice versa.
Someone is old or kind.
Fred is either not creative or not kind.
Someone is not strong.
Fred is not brave.
Someone is either rich or not tall.
Mary is not creative. | Fred is not creative. | neutral | (((kind(paul)|~creative(paul)))<=>((~kind(fred)<~>~generous(fred))))&
(![X]:(~old(X)=>patient(X)))&
(![X]:((generous(X)&patient(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((humble(X)&patient(X))))<=>(?[X]:((~patient(X)&~brave(X)))))&
(((tall(john)&rich(john)))=>(?[X]:(creative(X))))&
((~humble(susan))=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((strong(X)|generous(X))=>~happy(X)))&
(![X]:((~patient(X)|~old(X))<=>(~rich(X)<~>~creative(X))))&
((strong(alice))=>(brave(mary)))&
((?[X]:(humble(X)))<=>((~old(fred)&~generous(fred))))&
(![X]:((~quiet(X)<~>tall(X))=>(~curious(X)<~>kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>funny(X)))&
(![X]:((~wise(X)|~rich(X))<=>(~quiet(X)&old(X))))&
(((~happy(mary)<~>~rich(mary)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(quiet(X)=>(old(X)&~humble(X))))&
(![X]:((creative(X)&funny(X))<=>(brave(X)|calm(X))))&
(?[X]:((old(X)|kind(X))))&
((~creative(fred)<~>~kind(fred)))&
(?[X]:(~strong(X)))&
(~brave(fred))&
(?[X]:((rich(X)<~>~tall(X))))&
(~creative(mary)) | ~creative(fred) | [] | null | 0 |
Everyone who is calm or quiet is both not patient and creative and vice versa.
Everyone who is not calm is not creative or not happy.
Everyone who is not happy or not curious is both calm and not rich.
Everyone who is both not curious and not old is either not calm or not funny and vice versa.
Everyone who is either tall or not tall is either not brave or not quiet and vice versa.
If someone is old or quiet then fred is rich or curious and vice versa.
Everyone who is curious is either rich or humble and vice versa.
Everyone who is both brave and tall is not tall or not curious.
Everyone who is humble is either old or not patient and vice versa.
Everyone who is not wise or not funny is either not humble or not brave and vice versa.
If john is either not humble or not generous then alice is tall.
If paul is both not generous and not funny then john is either creative or not brave.
Everyone who is either not wise or curious is either rich or not generous and vice versa.
Everyone who is either curious or not humble is not rich.
Alice is not quiet or not generous.
Susan is not patient.
Someone is rich or wise.
Alice is curious or not quiet.
John is either not quiet or not brave.
Someone is wise. | Susan is not old. | neutral | (![X]:((calm(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(![X]:(~calm(X)=>(~creative(X)|~happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(calm(X)&~rich(X))))&
(![X]:((~curious(X)&~old(X))<=>(~calm(X)<~>~funny(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(![X]:((~wise(X)<~>curious(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((curious(X)<~>~humble(X))=>~rich(X)))&
((~quiet(alice)|~generous(alice)))&
(~patient(susan))&
(?[X]:((rich(X)|wise(X))))&
((curious(alice)|~quiet(alice)))&
((~quiet(john)<~>~brave(john)))&
(?[X]:(wise(X))) | ~old(susan) | [] | null | 0 |
If someone is both strong and creative then someone is both curious and patient and vice versa.
If someone is not strong then susan is both not generous and quiet and vice versa.
Everyone who is quiet is either not funny or not rich.
If someone is not strong or not curious then someone is either kind or not quiet and vice versa.
Everyone who is calm or quiet is both not patient and patient and vice versa.
If lucy is either curious or not strong then fred is not creative and vice versa.
Everyone who is calm or tall is old or generous.
If alice is both not patient and not brave then someone is either funny or not strong.
If someone is not patient or patient then someone is either strong or not tall.
If someone is not brave or wise then someone is old or not rich and vice versa.
If susan is not curious then someone is not brave or tall.
Everyone who is both not brave and not tall is generous and vice versa.
If susan is both not old and rich then mary is either not wise or not generous.
Everyone who is either not creative or wise is creative and vice versa.
If someone is not funny or patient then lucy is old or tall.
Someone is either rich or not strong.
John is creative.
Someone is either creative or not wise.
Alice is not rich or not patient.
Someone is brave or not generous. | Mary is not creative. | neutral | ((?[X]:((strong(X)&creative(X))))<=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:(~strong(X)))<=>((~generous(susan)&quiet(susan))))&
(![X]:(quiet(X)=>(~funny(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&patient(X))))&
(((curious(lucy)<~>~strong(lucy)))<=>(~creative(fred)))&
(![X]:((calm(X)|tall(X))=>(old(X)|generous(X))))&
(((~patient(alice)&~brave(alice)))=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)|patient(X))))=>(?[X]:((strong(X)<~>~tall(X)))))&
((?[X]:((~brave(X)|wise(X))))<=>(?[X]:((old(X)|~rich(X)))))&
((~curious(susan))=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:((~brave(X)&~tall(X))<=>generous(X)))&
(((~old(susan)&rich(susan)))=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>wise(X))<=>creative(X)))&
((?[X]:((~funny(X)|patient(X))))=>((old(lucy)|tall(lucy))))&
(?[X]:((rich(X)<~>~strong(X))))&
(creative(john))&
(?[X]:((creative(X)<~>~wise(X))))&
((~rich(alice)|~patient(alice)))&
(?[X]:((brave(X)|~generous(X)))) | ~creative(mary) | [] | null | 0 |
Everyone who is happy or strong is either not calm or not brave and vice versa.
Everyone who is not tall or creative is both not happy and not calm.
Everyone who is either not creative or quiet is old or not generous.
If someone is creative or patient then someone is both not humble and wise.
Everyone who is not kind is either tall or rich and vice versa.
If fred is both not funny and not generous then someone is both not wise and not humble and vice versa.
Everyone who is both not brave and rich is not wise or not generous.
If fred is not tall then someone is both not wise and tall and vice versa.
If alice is happy then mary is generous or not generous.
Everyone who is funny or brave is not brave or not humble.
Everyone who is not brave is not calm or not funny.
Everyone who is strong or not curious is both not humble and creative.
If someone is not kind then someone is either curious or not rich and vice versa.
If john is both not patient and brave then someone is both not kind and not old.
Everyone who is either not kind or not patient is not funny or old and vice versa.
Everyone who is patient or not happy is both calm and tall and vice versa.
John is not brave or creative.
Someone is not patient.
Lucy is old.
Someone is both not old and quiet.
Lucy is humble or generous. | Mary is not strong. | entailment | (![X]:((happy(X)|strong(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((~tall(X)|creative(X))=>(~happy(X)&~calm(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(old(X)|~generous(X))))&
((?[X]:((creative(X)|patient(X))))=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:(~kind(X)<=>(tall(X)<~>rich(X))))&
(((~funny(fred)&~generous(fred)))<=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~brave(X)&rich(X))=>(~wise(X)|~generous(X))))&
((~tall(fred))<=>(?[X]:((~wise(X)&tall(X)))))&
((happy(alice))=>((generous(mary)|~generous(mary))))&
(![X]:((funny(X)|brave(X))=>(~brave(X)|~humble(X))))&
(![X]:(~brave(X)=>(~calm(X)|~funny(X))))&
(![X]:((strong(X)|~curious(X))=>(~humble(X)&creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>~rich(X)))))&
(((~patient(john)&brave(john)))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~funny(X)|old(X))))&
(![X]:((patient(X)|~happy(X))<=>(calm(X)&tall(X))))&
((~brave(john)|creative(john)))&
(?[X]:(~patient(X)))&
(old(lucy))&
(?[X]:((~old(X)&quiet(X))))&
((humble(lucy)|generous(lucy))) | ~strong(mary) | [
"p1",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5343897431589009516445556
% SZS output start Proof for 5343897431589009516445556
2. ! [X0] : ((creative(X0) | ~tall(X0)) => (~calm(X0) & ~happy(X0))) [input p1]
12. ! [X0] : ((~curious(X0) | strong(X0)) => (creative(X0) & ~humble(X0))) [input p11]
16. ! [X0] : ((~happy(X0) | patient(X0)) <=> (tall(X0) & calm(X0))) [input p15]
22. strong(mary) [input hypothesis]
25. ! [X0] : ((~calm(X0) & ~happy(X0)) | (~creative(X0) & tall(X0))) [ennf transformation 2]
37. ! [X0] : ((creative(X0) & ~humble(X0)) | (curious(X0) & ~strong(X0))) [ennf transformation 12]
65. ! [X0] : (((~happy(X0) | patient(X0)) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | (happy(X0) & ~patient(X0)))) [nnf transformation 16]
66. ! [X0] : ((~happy(X0) | patient(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | (happy(X0) & ~patient(X0)))) [flattening 65]
78. ~creative(X0) | ~happy(X0) [cnf transformation 25]
80. ~creative(X0) | ~calm(X0) [cnf transformation 25]
105. ~strong(X0) | creative(X0) [cnf transformation 37]
120. calm(X0) | happy(X0) [cnf transformation 66]
130. strong(mary) [cnf transformation 22]
255. creative(mary) [resolution 105,130]
257. ~calm(mary) [resolution 255,80]
258. ~happy(mary) [resolution 255,78]
262. happy(mary) [resolution 257,120]
263. $false [subsumption resolution 262,258]
% SZS output end Proof for 5343897431589009516445556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or strong then someone is not generous and vice versa. If fred is tall then someone is both funny and quiet. Everyone who is not funny or not patient is both not wise and humble. Everyone who is either not calm or generous is both not humble and wise. If susan is kind then someone is not tall or not humble and vice versa. If mary is both tall and curious then someone is both curious and not old and vice versa. Everyone who is both not strong and creative is either calm or happy. Everyone who is calm is either not generous or tall and vice versa. If mary is not rich then susan is either not old or not tall. If lucy is not creative then someone is either not curious or kind. Everyone who is either brave or strong is either not strong or funny and vice versa. If fred is not patient or old then lucy is both not old and curious and vice versa. Everyone who is either not tall or old is funny. Everyone who is patient is either not wise or not creative and vice versa. Everyone who is not tall is kind or not brave. Someone is either not curious or funny. John is either wise or not curious. Lucy is rich or not funny. Someone is not kind. Someone is both not wise and not rich. John is either not brave or not generous. Someone is not brave. Someone is either rich or curious. | Susan is generous. | neutral | ((?[X]:((curious(X)|strong(X))))<=>(?[X]:(~generous(X))))&
((tall(fred))=>(?[X]:((funny(X)&quiet(X)))))&
(![X]:((~funny(X)|~patient(X))=>(~wise(X)&humble(X))))&
(![X]:((~calm(X)<~>generous(X))=>(~humble(X)&wise(X))))&
((kind(susan))<=>(?[X]:((~tall(X)|~humble(X)))))&
(((tall(mary)&curious(mary)))<=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((~strong(X)&creative(X))=>(calm(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~generous(X)<~>tall(X))))&
((~rich(mary))=>((~old(susan)<~>~tall(susan))))&
((~creative(lucy))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((brave(X)<~>strong(X))<=>(~strong(X)<~>funny(X))))&
(((~patient(fred)|old(fred)))<=>((~old(lucy)&curious(lucy))))&
(![X]:((~tall(X)<~>old(X))=>funny(X)))&
(![X]:(patient(X)<=>(~wise(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(kind(X)|~brave(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((wise(john)<~>~curious(john)))&
((rich(lucy)|~funny(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~rich(X))))&
((~brave(john)<~>~generous(john)))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>curious(X)))) | generous(susan) | [] | null | 0 |
Everyone who is either wise or curious is both quiet and not quiet. Everyone who is either happy or not curious is either kind or old and vice versa. If someone is not creative or strong then someone is both patient and tall and vice versa. If paul is both funny and not rich then someone is not curious and vice versa. Everyone who is brave or not curious is both patient and curious and vice versa. If susan is not strong or not rich then someone is not humble and vice versa. Everyone who is not brave or strong is not patient or not strong and vice versa. Everyone who is both not humble and generous is rich and vice versa. If someone is either not happy or tall then someone is not patient or not curious and vice versa. Everyone who is either not calm or calm is curious or creative and vice versa. Everyone who is both not rich and not calm is creative or calm. Everyone who is both not humble and not strong is either not wise or not calm. Everyone who is either creative or quiet is either not rich or humble and vice versa. Everyone who is either curious or not funny is curious or not wise and vice versa. Mary is both not humble and old. Alice is not strong. Mary is funny. Someone is happy or patient. Someone is both kind and tall. Someone is both calm and not strong. Susan is not humble or old. | Paul is not patient. | entailment | (![X]:((wise(X)<~>curious(X))=>(quiet(X)&~quiet(X))))&
(![X]:((happy(X)<~>~curious(X))<=>(kind(X)<~>old(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((patient(X)&tall(X)))))&
(((funny(paul)&~rich(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((brave(X)|~curious(X))<=>(patient(X)&curious(X))))&
(((~strong(susan)|~rich(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)|strong(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~humble(X)&generous(X))<=>rich(X)))&
((?[X]:((~happy(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(curious(X)|creative(X))))&
(![X]:((~rich(X)&~calm(X))=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(curious(X)|~wise(X))))&
((~humble(mary)&old(mary)))&
(~strong(alice))&
(funny(mary))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((kind(X)&tall(X))))&
(?[X]:((calm(X)&~strong(X))))&
((~humble(susan)|old(susan))) | ~patient(paul) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3417866294119012075776994
% SZS output start Proof for 3417866294119012075776994
5. ! [X0] : ((~curious(X0) | brave(X0)) <=> (curious(X0) & patient(X0))) [input p4]
7. ! [X0] : ((strong(X0) | ~brave(X0)) <=> (~strong(X0) | ~patient(X0))) [input p6]
22. patient(paul) [input hypothesis]
42. ! [X0] : (((~curious(X0) | brave(X0)) | (~curious(X0) | ~patient(X0))) & ((curious(X0) & patient(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 5]
43. ! [X0] : ((~curious(X0) | brave(X0) | ~curious(X0) | ~patient(X0)) & ((curious(X0) & patient(X0)) | (curious(X0) & ~brave(X0)))) [flattening 42]
49. ! [X0] : (((strong(X0) | ~brave(X0)) | (strong(X0) & patient(X0))) & ((~strong(X0) | ~patient(X0)) | (~strong(X0) & brave(X0)))) [nnf transformation 7]
50. ! [X0] : ((strong(X0) | ~brave(X0) | (strong(X0) & patient(X0))) & (~strong(X0) | ~patient(X0) | (~strong(X0) & brave(X0)))) [flattening 49]
93. curious(X0) | curious(X0) [cnf transformation 43]
94. ~curious(X0) | brave(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 43]
99. ~strong(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 50]
101. strong(X0) | ~brave(X0) | strong(X0) [cnf transformation 50]
144. patient(paul) [cnf transformation 22]
150. ~patient(X0) | ~strong(X0) [duplicate literal removal 99]
151. ~brave(X0) | strong(X0) [duplicate literal removal 101]
152. curious(X0) [duplicate literal removal 93]
153. ~patient(X0) | brave(X0) | ~curious(X0) [duplicate literal removal 94]
187. 8 <=> ! [X0] : curious(X0) [avatar definition]
188. curious(X0) <- (8) [avatar component clause 187]
204. 8 [avatar split clause 152,187]
284. ~strong(paul) [resolution 150,144]
299. brave(paul) | ~curious(paul) [resolution 153,144]
302. brave(paul) <- (8) [subsumption resolution 299,188]
304. strong(paul) <- (8) [resolution 302,151]
309. $false <- (8) [subsumption resolution 284,304]
310. ~8 [avatar contradiction clause 309]
311. $false [avatar sat refutation 204,310]
% SZS output end Proof for 3417866294119012075776994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not patient is both humble and not wise.
Everyone who is creative or not funny is either old or not strong.
If someone is not rich or not curious then fred is either happy or creative.
Everyone who is not calm is either not old or tall and vice versa.
Everyone who is not rich or not humble is either not rich or not curious and vice versa.
If susan is both not tall and not wise then susan is both not humble and not curious and vice versa.
Everyone who is both not calm and not happy is not rich or not patient and vice versa.
Everyone who is either not wise or not creative is both funny and kind and vice versa.
Everyone who is calm or not kind is both rich and kind and vice versa.
If someone is both not curious and old then someone is both not patient and quiet and vice versa.
If mary is either not wise or not creative then john is either not kind or not curious.
If someone is not creative or not tall then susan is not quiet or not tall and vice versa.
If alice is either brave or not kind then someone is not humble or not old.
If susan is both not patient and not wise then susan is not funny.
Everyone who is not curious or funny is wise.
If someone is both not curious and old then fred is both not kind and humble.
Someone is strong or patient.
John is not quiet.
Alice is either not curious or not quiet.
Fred is both funny and wise.
Someone is not humble.
Alice is creative or not wise.
Someone is humble or happy. | Fred is not rich. | contradiction | (![X]:((strong(X)<~>~patient(X))=>(humble(X)&~wise(X))))&
(![X]:((creative(X)|~funny(X))=>(old(X)<~>~strong(X))))&
((?[X]:((~rich(X)|~curious(X))))=>((happy(fred)<~>creative(fred))))&
(![X]:(~calm(X)<=>(~old(X)<~>tall(X))))&
(![X]:((~rich(X)|~humble(X))<=>(~rich(X)<~>~curious(X))))&
(((~tall(susan)&~wise(susan)))<=>((~humble(susan)&~curious(susan))))&
(![X]:((~calm(X)&~happy(X))<=>(~rich(X)|~patient(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(funny(X)&kind(X))))&
(![X]:((calm(X)|~kind(X))<=>(rich(X)&kind(X))))&
((?[X]:((~curious(X)&old(X))))<=>(?[X]:((~patient(X)&quiet(X)))))&
(((~wise(mary)<~>~creative(mary)))=>((~kind(john)<~>~curious(john))))&
((?[X]:((~creative(X)|~tall(X))))<=>((~quiet(susan)|~tall(susan))))&
(((brave(alice)<~>~kind(alice)))=>(?[X]:((~humble(X)|~old(X)))))&
(((~patient(susan)&~wise(susan)))=>(~funny(susan)))&
(![X]:((~curious(X)|funny(X))=>wise(X)))&
((?[X]:((~curious(X)&old(X))))=>((~kind(fred)&humble(fred))))&
(?[X]:((strong(X)|patient(X))))&
(~quiet(john))&
((~curious(alice)<~>~quiet(alice)))&
((funny(fred)&wise(fred)))&
(?[X]:(~humble(X)))&
((creative(alice)|~wise(alice)))&
(?[X]:((humble(X)|happy(X)))) | ~rich(fred) | [
"p2",
"p6",
"p7",
"p8",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3121867138916644773782303
% SZS output start Proof for 3121867138916644773782303
3. ? [X0] : (~curious(X0) | ~rich(X0)) => (happy(fred) <~> creative(fred)) [input p2]
7. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> (~patient(X0) | ~rich(X0))) [input p6]
8. ! [X0] : ((~wise(X0) <~> ~creative(X0)) <=> (kind(X0) & funny(X0))) [input p7]
9. ! [X0] : ((~kind(X0) | calm(X0)) <=> (kind(X0) & rich(X0))) [input p8]
15. ! [X0] : ((funny(X0) | ~curious(X0)) => wise(X0)) [input p14]
20. wise(fred) & funny(fred) [input p19]
24. ~rich(fred) [input hypothesis]
28. (happy(fred) <~> creative(fred)) | ! [X0] : (curious(X0) & rich(X0)) [ennf transformation 3]
33. ! [X0] : (wise(X0) | (~funny(X0) & curious(X0))) [ennf transformation 15]
37. ((~creative(fred) | ~happy(fred)) & (creative(fred) | happy(fred))) | ! [X0] : (curious(X0) & rich(X0)) [nnf transformation 28]
43. ! [X0] : (((~happy(X0) & ~calm(X0)) | (patient(X0) & rich(X0))) & ((~patient(X0) | ~rich(X0)) | (happy(X0) | calm(X0)))) [nnf transformation 7]
44. ! [X0] : (((~happy(X0) & ~calm(X0)) | (patient(X0) & rich(X0))) & (~patient(X0) | ~rich(X0) | happy(X0) | calm(X0))) [flattening 43]
45. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [nnf transformation 8]
46. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [flattening 45]
47. ! [X0] : (((~kind(X0) | calm(X0)) | (~kind(X0) | ~rich(X0))) & ((kind(X0) & rich(X0)) | (kind(X0) & ~calm(X0)))) [nnf transformation 9]
48. ! [X0] : ((~kind(X0) | calm(X0) | ~kind(X0) | ~rich(X0)) & ((kind(X0) & rich(X0)) | (kind(X0) & ~calm(X0)))) [flattening 47]
78. creative(fred) | happy(fred) | rich(X0) [cnf transformation 37]
99. ~happy(X0) | rich(X0) [cnf transformation 44]
105. ~kind(X0) | ~wise(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 46]
110. kind(X0) | kind(X0) [cnf transformation 48]
128. ~funny(X0) | wise(X0) [cnf transformation 33]
135. funny(fred) [cnf transformation 20]
140. ~rich(fred) [cnf transformation 24]
141. kind(X0) [duplicate literal removal 110]
149. 2 <=> happy(fred) [avatar definition]
150. happy(fred) <- (2) [avatar component clause 149]
153. 3 <=> creative(fred) [avatar definition]
154. creative(fred) <- (3) [avatar component clause 153]
158. 4 <=> ! [X0] : rich(X0) [avatar definition]
159. rich(X0) <- (4) [avatar component clause 158]
162. 4 | 2 | 3 [avatar split clause 78,153,149,158]
314. rich(fred) <- (2) [resolution 99,150]
315. $false <- (2) [subsumption resolution 314,140]
316. ~2 [avatar contradiction clause 315]
473. $false <- (4) [resolution 159,140]
476. ~4 [avatar contradiction clause 473]
496. ~wise(X0) | ~creative(X0) | ~funny(X0) [resolution 105,141]
497. ~funny(X0) | ~creative(X0) [subsumption resolution 496,128]
511. ~creative(fred) [resolution 497,135]
513. $false <- (3) [subsumption resolution 511,154]
514. ~3 [avatar contradiction clause 513]
515. $false [avatar sat refutation 162,316,476,514]
% SZS output end Proof for 3121867138916644773782303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not kind then john is brave and vice versa.
If mary is rich then someone is creative.
Everyone who is either not kind or kind is not tall and vice versa.
If alice is either not curious or not old then alice is happy or not generous and vice versa.
If john is both happy and not calm then someone is not strong and vice versa.
If someone is not patient or humble then someone is rich and vice versa.
If john is both not calm and patient then alice is both brave and not strong.
If someone is both not tall and not funny then someone is not strong or not funny and vice versa.
Everyone who is brave is happy.
Everyone who is calm or strong is both brave and creative and vice versa.
Everyone who is strong is either tall or not brave and vice versa.
Everyone who is not tall is not patient or not humble.
Everyone who is not patient is not old or not generous.
If susan is both calm and not humble then fred is either not strong or not calm and vice versa.
If mary is either wise or not creative then someone is kind and vice versa.
Fred is kind or not strong.
Someone is either not calm or not happy.
Susan is not creative.
John is not old or not creative.
Someone is either not funny or funny.
Susan is either creative or not tall.
Someone is creative. | Fred is not happy. | contradiction | ((?[X]:((quiet(X)|~kind(X))))<=>(brave(john)))&
((rich(mary))=>(?[X]:(creative(X))))&
(![X]:((~kind(X)<~>kind(X))<=>~tall(X)))&
(((~curious(alice)<~>~old(alice)))<=>((happy(alice)|~generous(alice))))&
(((happy(john)&~calm(john)))<=>(?[X]:(~strong(X))))&
((?[X]:((~patient(X)|humble(X))))<=>(?[X]:(rich(X))))&
(((~calm(john)&patient(john)))=>((brave(alice)&~strong(alice))))&
((?[X]:((~tall(X)&~funny(X))))<=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:(brave(X)=>happy(X)))&
(![X]:((calm(X)|strong(X))<=>(brave(X)&creative(X))))&
(![X]:(strong(X)<=>(tall(X)<~>~brave(X))))&
(![X]:(~tall(X)=>(~patient(X)|~humble(X))))&
(![X]:(~patient(X)=>(~old(X)|~generous(X))))&
(((calm(susan)&~humble(susan)))<=>((~strong(fred)<~>~calm(fred))))&
(((wise(mary)<~>~creative(mary)))<=>(?[X]:(kind(X))))&
((kind(fred)|~strong(fred)))&
(?[X]:((~calm(X)<~>~happy(X))))&
(~creative(susan))&
((~old(john)|~creative(john)))&
(?[X]:((~funny(X)<~>funny(X))))&
((creative(susan)<~>~tall(susan)))&
(?[X]:(creative(X))) | ~happy(fred) | [
"p2",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3358341274585760200509892
% SZS output start Proof for 3358341274585760200509892
3. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> ~tall(X0)) [input p2]
9. ! [X0] : (brave(X0) => happy(X0)) [input p8]
10. ! [X0] : ((strong(X0) | calm(X0)) <=> (creative(X0) & brave(X0))) [input p9]
11. ! [X0] : (strong(X0) <=> (tall(X0) <~> ~brave(X0))) [input p10]
23. ~happy(fred) [input hypothesis]
29. ! [X0] : (happy(X0) | ~brave(X0)) [ennf transformation 9]
40. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | tall(X0)) & (~tall(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 3]
58. ! [X0] : (((strong(X0) | calm(X0)) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | (~strong(X0) & ~calm(X0)))) [nnf transformation 10]
59. ! [X0] : ((strong(X0) | calm(X0) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | (~strong(X0) & ~calm(X0)))) [flattening 58]
60. ! [X0] : ((strong(X0) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | ~strong(X0))) [nnf transformation 11]
80. ~tall(X0) | kind(X0) | kind(X0) [cnf transformation 40]
81. ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 40]
103. ~brave(X0) | happy(X0) [cnf transformation 29]
105. brave(X0) | ~strong(X0) [cnf transformation 59]
112. strong(X0) | tall(X0) | brave(X0) [cnf transformation 60]
135. ~happy(fred) [cnf transformation 23]
136. ~tall(X0) | kind(X0) [duplicate literal removal 80]
137. ~tall(X0) | ~kind(X0) [duplicate literal removal 81]
168. ~tall(X0) [subsumption resolution 136,137]
266. strong(X0) | brave(X0) [subsumption resolution 112,168]
267. brave(X0) [subsumption resolution 266,105]
337. happy(X0) [resolution 103,267]
339. $false [resolution 337,135]
% SZS output end Proof for 3358341274585760200509892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or happy is kind and vice versa. If john is both brave and rich then susan is either humble or not curious. Everyone who is tall or not generous is both curious and humble. If susan is both quiet and tall then lucy is not rich. Everyone who is both creative and not tall is not quiet or not generous. If susan is both happy and not tall then alice is rich and vice versa. If someone is not creative or not wise then lucy is both not curious and patient. If paul is either not funny or not kind then paul is rich or not creative. Everyone who is tall or not happy is either curious or wise and vice versa. Everyone who is both not creative and wise is strong and vice versa. Everyone who is not funny or not happy is both not rich and not strong and vice versa. Everyone who is not patient or not quiet is old or calm and vice versa. Everyone who is happy is both funny and not old. Everyone who is humble is either strong or not patient. Everyone who is either not happy or brave is not old or funny and vice versa. Everyone who is either brave or not old is wise or kind and vice versa. John is either not tall or brave. Someone is not calm or calm. Someone is either not patient or not rich. Someone is wise. Someone is not old or not generous. | Lucy is generous. | entailment | (![X]:((~tall(X)|happy(X))<=>kind(X)))&
(((brave(john)&rich(john)))=>((humble(susan)<~>~curious(susan))))&
(![X]:((tall(X)|~generous(X))=>(curious(X)&humble(X))))&
(((quiet(susan)&tall(susan)))=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
((~tall(john)<~>brave(john)))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:(wise(X)))&
(?[X]:((~old(X)|~generous(X)))) | generous(lucy) | [
"p0",
"p2",
"p6",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7903681135931743226470965
% SZS output start Proof for 7903681135931743226470965
1. ! [X0] : ((happy(X0) | ~tall(X0)) <=> kind(X0)) [input p0]
3. ! [X0] : ((~generous(X0) | tall(X0)) => (humble(X0) & curious(X0))) [input p2]
7. ? [X0] : (~wise(X0) | ~creative(X0)) => (patient(lucy) & ~curious(lucy)) [input p6]
9. ! [X0] : ((~happy(X0) | tall(X0)) <=> (curious(X0) <~> wise(X0))) [input p8]
13. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p12]
15. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p14]
16. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p15]
22. ~generous(lucy) [input hypothesis]
25. ! [X0] : ((humble(X0) & curious(X0)) | (generous(X0) & ~tall(X0))) [ennf transformation 3]
30. (patient(lucy) & ~curious(lucy)) | ! [X0] : (wise(X0) & creative(X0)) [ennf transformation 7]
33. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 13]
35. ! [X0] : (((happy(X0) | ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [nnf transformation 1]
36. ! [X0] : ((happy(X0) | ~tall(X0) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [flattening 35]
41. ! [X0] : (((~happy(X0) | tall(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [nnf transformation 9]
42. ! [X0] : ((~happy(X0) | tall(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [flattening 41]
50. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 50]
52. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 16]
53. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 52]
65. ~happy(X0) | kind(X0) [cnf transformation 36]
70. generous(X0) | curious(X0) [cnf transformation 25]
79. ~curious(lucy) | wise(X0) [cnf transformation 30]
87. ~wise(X0) | ~curious(X0) | happy(X0) [cnf transformation 42]
102. ~happy(X0) | funny(X0) [cnf transformation 33]
103. ~old(X0) | ~happy(X0) [cnf transformation 33]
109. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 51]
117. ~brave(X0) | old(X0) | ~kind(X0) [cnf transformation 53]
125. ~generous(lucy) [cnf transformation 22]
169. 10 <=> ! [X0] : wise(X0) [avatar definition]
170. wise(X0) <- (10) [avatar component clause 169]
181. 13 <=> curious(lucy) [avatar definition]
182. curious(lucy) <- (13) [avatar component clause 181]
184. 10 | ~13 [avatar split clause 79,181,169]
206. ~happy(X0) | brave(X0) [subsumption resolution 109,102]
233. curious(lucy) [resolution 70,125]
237. 13 [avatar split clause 233,181]
254. ~curious(X1) | happy(X1) <- (10) [resolution 87,170]
268. happy(lucy) <- (10, 13) [resolution 254,182]
270. brave(lucy) <- (10, 13) [resolution 268,206]
272. kind(lucy) <- (10, 13) [resolution 268,65]
323. old(lucy) | ~kind(lucy) <- (10, 13) [resolution 117,270]
325. old(lucy) <- (10, 13) [subsumption resolution 323,272]
353. ~happy(lucy) <- (10, 13) [resolution 325,103]
354. $false <- (10, 13) [subsumption resolution 353,268]
355. ~10 | ~13 [avatar contradiction clause 354]
356. $false [avatar sat refutation 184,237,355]
% SZS output end Proof for 7903681135931743226470965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or patient is strong and vice versa.
Everyone who is old is either not brave or not tall and vice versa.
If someone is both not happy and brave then john is either happy or patient.
Everyone who is not calm or not rich is both old and not kind and vice versa.
Everyone who is kind or not quiet is both not patient and patient and vice versa.
Everyone who is not old is not quiet and vice versa.
Everyone who is either wise or happy is not patient and vice versa.
Everyone who is kind or old is calm.
Everyone who is wise or brave is not calm and vice versa.
Everyone who is rich or not funny is old and vice versa.
If mary is either calm or not happy then someone is both kind and not patient and vice versa.
Everyone who is not humble is both curious and not patient.
Everyone who is creative is either curious or not tall and vice versa.
Someone is both not brave and not kind.
Someone is either not generous or not wise.
Fred is either curious or rich.
Fred is kind or strong.
Paul is not rich or curious.
Paul is not calm or quiet.
Lucy is not humble. | Paul is brave. | contradiction | (![X]:((old(X)|patient(X))<=>strong(X)))&
(![X]:(old(X)<=>(~brave(X)<~>~tall(X))))&
((?[X]:((~happy(X)&brave(X))))=>((happy(john)<~>patient(john))))&
(![X]:((~calm(X)|~rich(X))<=>(old(X)&~kind(X))))&
(![X]:((kind(X)|~quiet(X))<=>(~patient(X)&patient(X))))&
(![X]:(~old(X)<=>~quiet(X)))&
(![X]:((wise(X)<~>happy(X))<=>~patient(X)))&
(![X]:((kind(X)|old(X))=>calm(X)))&
(![X]:((wise(X)|brave(X))<=>~calm(X)))&
(![X]:((rich(X)|~funny(X))<=>old(X)))&
(((calm(mary)<~>~happy(mary)))<=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:(~humble(X)=>(curious(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)<~>~tall(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((~generous(X)<~>~wise(X))))&
((curious(fred)<~>rich(fred)))&
((kind(fred)|strong(fred)))&
((~rich(paul)|curious(paul)))&
((~calm(paul)|quiet(paul)))&
(~humble(lucy)) | brave(paul) | [
"p4",
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2947544292479405249328537
% SZS output start Proof for 2947544292479405249328537
5. ! [X0] : ((~quiet(X0) | kind(X0)) <=> (patient(X0) & ~patient(X0))) [input p4]
6. ! [X0] : (~old(X0) <=> ~quiet(X0)) [input p5]
8. ! [X0] : ((old(X0) | kind(X0)) => calm(X0)) [input p7]
9. ! [X0] : ((brave(X0) | wise(X0)) <=> ~calm(X0)) [input p8]
21. brave(paul) [input hypothesis]
26. ! [X0] : (calm(X0) | (~old(X0) & ~kind(X0))) [ennf transformation 8]
32. ! [X0] : (((~quiet(X0) | kind(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (quiet(X0) & ~kind(X0)))) [nnf transformation 5]
33. ! [X0] : ((~quiet(X0) | kind(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (quiet(X0) & ~kind(X0)))) [flattening 32]
34. ! [X0] : ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))) [nnf transformation 6]
36. ! [X0] : (((brave(X0) | wise(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) & ~wise(X0)))) [nnf transformation 9]
37. ! [X0] : ((brave(X0) | wise(X0) | calm(X0)) & (~calm(X0) | (~brave(X0) & ~wise(X0)))) [flattening 36]
63. ~patient(X0) | quiet(X0) [cnf transformation 33]
65. patient(X0) | quiet(X0) [cnf transformation 33]
67. ~quiet(X0) | old(X0) [cnf transformation 34]
74. calm(X0) | ~old(X0) [cnf transformation 26]
76. ~calm(X0) | ~brave(X0) [cnf transformation 37]
99. brave(paul) [cnf transformation 21]
113. quiet(X0) [subsumption resolution 63,65]
115. old(X0) [subsumption resolution 67,113]
116. calm(X0) [subsumption resolution 74,115]
117. ~brave(X0) [subsumption resolution 76,116]
154. $false [subsumption resolution 99,117]
% SZS output end Proof for 2947544292479405249328537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is not creative or not strong and vice versa.
Everyone who is rich or not calm is both not humble and not curious.
If susan is wise then someone is not tall.
If john is either not quiet or creative then someone is strong and vice versa.
Everyone who is either not generous or not wise is patient and vice versa.
Everyone who is not happy is either patient or not strong and vice versa.
If someone is not old or tall then alice is not humble and vice versa.
Everyone who is both not humble and brave is either rich or not tall and vice versa.
Everyone who is both not strong and old is calm or quiet and vice versa.
If someone is either not patient or old then someone is not brave.
If someone is tall or rich then someone is calm and vice versa.
Everyone who is both not calm and funny is patient or brave and vice versa.
Everyone who is both rich and not humble is both old and not strong.
If alice is both quiet and rich then alice is not calm and vice versa.
If someone is not calm then someone is wise or calm.
Everyone who is old is not humble.
Someone is both tall and quiet.
Someone is both not patient and not brave.
Someone is calm or not old.
Someone is wise or funny.
Someone is not creative.
Mary is not humble.
Someone is either strong or calm. | Alice is not strong. | entailment | ((?[X]:(~brave(X)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(![X]:((rich(X)|~calm(X))=>(~humble(X)&~curious(X))))&
((wise(susan))=>(?[X]:(~tall(X))))&
(((~quiet(john)<~>creative(john)))<=>(?[X]:(strong(X))))&
(![X]:((~generous(X)<~>~wise(X))<=>patient(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>~strong(X))))&
((?[X]:((~old(X)|tall(X))))<=>(~humble(alice)))&
(![X]:((~humble(X)&brave(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~strong(X)&old(X))<=>(calm(X)|quiet(X))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:(~brave(X))))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:(calm(X))))&
(![X]:((~calm(X)&funny(X))<=>(patient(X)|brave(X))))&
(![X]:((rich(X)&~humble(X))=>(old(X)&~strong(X))))&
(((quiet(alice)&rich(alice)))<=>(~calm(alice)))&
((?[X]:(~calm(X)))=>(?[X]:((wise(X)|calm(X)))))&
(![X]:(old(X)=>~humble(X)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((~patient(X)&~brave(X))))&
(?[X]:((calm(X)|~old(X))))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:(~creative(X)))&
(~humble(mary))&
(?[X]:((strong(X)<~>calm(X)))) | ~strong(alice) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4779321865488675232931029
% SZS output start Proof for 4779321865488675232931029
9. ! [X0] : ((old(X0) & ~strong(X0)) <=> (quiet(X0) | calm(X0))) [input p8]
14. (rich(alice) & quiet(alice)) <=> ~calm(alice) [input p13]
24. strong(alice) [input hypothesis]
55. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (~old(X0) | strong(X0)))) [nnf transformation 9]
56. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | ~old(X0) | strong(X0))) [flattening 55]
68. ((rich(alice) & quiet(alice)) | calm(alice)) & (~calm(alice) | (~rich(alice) | ~quiet(alice))) [nnf transformation 14]
69. ((rich(alice) & quiet(alice)) | calm(alice)) & (~calm(alice) | ~rich(alice) | ~quiet(alice)) [flattening 68]
110. ~calm(X0) | ~strong(X0) [cnf transformation 56]
111. ~quiet(X0) | ~strong(X0) [cnf transformation 56]
127. quiet(alice) | calm(alice) [cnf transformation 69]
141. strong(alice) [cnf transformation 24]
253. 26 <=> calm(alice) [avatar definition]
255. calm(alice) <- (26) [avatar component clause 253]
262. 28 <=> quiet(alice) [avatar definition]
264. quiet(alice) <- (28) [avatar component clause 262]
265. 26 | 28 [avatar split clause 127,262,253]
319. ~strong(alice) <- (26) [resolution 255,110]
320. $false <- (26) [subsumption resolution 319,141]
321. ~26 [avatar contradiction clause 320]
323. ~strong(alice) <- (28) [resolution 111,264]
324. $false <- (28) [subsumption resolution 323,141]
325. ~28 [avatar contradiction clause 324]
326. $false [avatar sat refutation 265,321,325]
% SZS output end Proof for 4779321865488675232931029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is funny then someone is not kind and vice versa.
Everyone who is kind or not quiet is both tall and creative and vice versa.
Everyone who is either calm or not funny is both generous and not wise and vice versa.
Everyone who is quiet or happy is both wise and generous and vice versa.
Everyone who is both generous and not quiet is either not kind or generous.
If someone is not patient or not strong then mary is either happy or not wise.
Everyone who is either strong or rich is both not brave and strong.
If lucy is either funny or not brave then fred is not funny or not creative and vice versa.
Everyone who is strong is both brave and not tall and vice versa.
If someone is curious or not old then someone is either not funny or rich and vice versa.
If someone is either patient or generous then lucy is brave and vice versa.
If susan is creative or not quiet then john is not kind and vice versa.
If mary is not creative then someone is not patient.
Everyone who is either strong or not brave is not patient.
Everyone who is either patient or not brave is rich and vice versa.
Everyone who is both not quiet and not happy is not happy and vice versa.
Fred is generous.
Lucy is not kind or creative.
Lucy is not strong or creative.
Someone is either not happy or old.
John is either not generous or old.
Someone is either kind or not happy.
Someone is calm or rich.
Fred is not patient or not strong. | Mary is not creative. | neutral | ((funny(mary))<=>(?[X]:(~kind(X))))&
(![X]:((kind(X)|~quiet(X))<=>(tall(X)&creative(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(generous(X)&~wise(X))))&
(![X]:((quiet(X)|happy(X))<=>(wise(X)&generous(X))))&
(![X]:((generous(X)&~quiet(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((~patient(X)|~strong(X))))=>((happy(mary)<~>~wise(mary))))&
(![X]:((strong(X)<~>rich(X))=>(~brave(X)&strong(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((~funny(fred)|~creative(fred))))&
(![X]:(strong(X)<=>(brave(X)&~tall(X))))&
((?[X]:((curious(X)|~old(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
((?[X]:((patient(X)<~>generous(X))))<=>(brave(lucy)))&
(((creative(susan)|~quiet(susan)))<=>(~kind(john)))&
((~creative(mary))=>(?[X]:(~patient(X))))&
(![X]:((strong(X)<~>~brave(X))=>~patient(X)))&
(![X]:((patient(X)<~>~brave(X))<=>rich(X)))&
(![X]:((~quiet(X)&~happy(X))<=>~happy(X)))&
(generous(fred))&
((~kind(lucy)|creative(lucy)))&
((~strong(lucy)|creative(lucy)))&
(?[X]:((~happy(X)<~>old(X))))&
((~generous(john)<~>old(john)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((calm(X)|rich(X))))&
((~patient(fred)|~strong(fred))) | ~creative(mary) | [] | null | 0 |
Everyone who is both not rich and strong is both not funny and not creative.
If someone is not funny then fred is either not old or not rich.
Everyone who is brave or not brave is happy or not quiet.
If john is both not brave and strong then alice is calm or brave.
Everyone who is either not rich or calm is humble.
If susan is patient then fred is either not calm or not wise and vice versa.
Everyone who is both strong and calm is both brave and not funny.
Everyone who is both not creative and not rich is both not quiet and quiet.
If someone is either not kind or quiet then lucy is either not wise or curious.
Everyone who is both not curious and curious is both not happy and funny.
If someone is either calm or not generous then alice is not humble and vice versa.
Everyone who is brave is both not rich and not happy and vice versa.
If john is both generous and not strong then someone is not patient or not rich and vice versa.
If someone is both generous and not calm then lucy is not curious or funny and vice versa.
If someone is not kind or generous then someone is both funny and not funny and vice versa.
Everyone who is either not rich or quiet is calm or tall and vice versa.
Someone is either not creative or brave.
Someone is both creative and happy.
Someone is not strong or humble.
Mary is not funny.
Someone is tall.
Fred is both not happy and not generous. | John is not strong. | entailment | (![X]:((~rich(X)&strong(X))=>(~funny(X)&~creative(X))))&
((?[X]:(~funny(X)))=>((~old(fred)<~>~rich(fred))))&
(![X]:((brave(X)|~brave(X))=>(happy(X)|~quiet(X))))&
(((~brave(john)&strong(john)))=>((calm(alice)|brave(alice))))&
(![X]:((~rich(X)<~>calm(X))=>humble(X)))&
((patient(susan))<=>((~calm(fred)<~>~wise(fred))))&
(![X]:((strong(X)&calm(X))=>(brave(X)&~funny(X))))&
(![X]:((~creative(X)&~rich(X))=>(~quiet(X)&quiet(X))))&
((?[X]:((~kind(X)<~>quiet(X))))=>((~wise(lucy)<~>curious(lucy))))&
(![X]:((~curious(X)&curious(X))=>(~happy(X)&funny(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(~humble(alice)))&
(![X]:(brave(X)<=>(~rich(X)&~happy(X))))&
(((generous(john)&~strong(john)))<=>(?[X]:((~patient(X)|~rich(X)))))&
((?[X]:((generous(X)&~calm(X))))<=>((~curious(lucy)|funny(lucy))))&
((?[X]:((~kind(X)|generous(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~rich(X)<~>quiet(X))<=>(calm(X)|tall(X))))&
(?[X]:((~creative(X)<~>brave(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((~strong(X)|humble(X))))&
(~funny(mary))&
(?[X]:(tall(X)))&
((~happy(fred)&~generous(fred))) | ~strong(john) | [
"p3",
"p4",
"p6",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9042879775362127353605140
% SZS output start Proof for 9042879775362127353605140
4. (strong(john) & ~brave(john)) => (brave(alice) | calm(alice)) [input p3]
5. ! [X0] : ((~rich(X0) <~> calm(X0)) => humble(X0)) [input p4]
7. ! [X0] : ((calm(X0) & strong(X0)) => (~funny(X0) & brave(X0))) [input p6]
11. ? [X0] : (calm(X0) <~> ~generous(X0)) <=> ~humble(alice) [input p10]
12. ! [X0] : (brave(X0) <=> (~happy(X0) & ~rich(X0))) [input p11]
13. (~strong(john) & generous(john)) <=> ? [X0] : (~rich(X0) | ~patient(X0)) [input p12]
15. ? [X0] : (generous(X0) | ~kind(X0)) <=> ? [X0] : (~funny(X0) & funny(X0)) [input p14]
23. strong(john) [input hypothesis]
24. ? [X0] : (generous(X0) | ~kind(X0)) <=> ? [X1] : (~funny(X1) & funny(X1)) [rectify 15]
30. (brave(alice) | calm(alice)) | (~strong(john) | brave(john)) [ennf transformation 4]
31. brave(alice) | calm(alice) | ~strong(john) | brave(john) [flattening 30]
32. ! [X0] : (humble(X0) | (~rich(X0) <=> calm(X0))) [ennf transformation 5]
33. ! [X0] : ((~funny(X0) & brave(X0)) | (~calm(X0) | ~strong(X0))) [ennf transformation 7]
34. ! [X0] : ((~funny(X0) & brave(X0)) | ~calm(X0) | ~strong(X0)) [flattening 33]
41. ! [X0] : (humble(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0)))) [nnf transformation 32]
44. (? [X0] : ((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | humble(alice)) & (~humble(alice) | ! [X0] : ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) [nnf transformation 11]
45. (? [X0] : ((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | humble(alice)) & (~humble(alice) | ! [X1] : ((calm(X1) | generous(X1)) & (~generous(X1) | ~calm(X1)))) [rectify 44]
46. ? [X0] : ((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) => ((generous(sK0) | ~calm(sK0)) & (~generous(sK0) | calm(sK0))) [choice axiom]
47. (((generous(sK0) | ~calm(sK0)) & (~generous(sK0) | calm(sK0))) | humble(alice)) & (~humble(alice) | ! [X1] : ((calm(X1) | generous(X1)) & (~generous(X1) | ~calm(X1)))) [skolemisation 45,46]
48. ! [X0] : ((brave(X0) | (happy(X0) | rich(X0))) & ((~happy(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 12]
49. ! [X0] : ((brave(X0) | happy(X0) | rich(X0)) & ((~happy(X0) & ~rich(X0)) | ~brave(X0))) [flattening 48]
50. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X0] : (~rich(X0) | ~patient(X0)) | (strong(john) | ~generous(john))) [nnf transformation 13]
51. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X0] : (~rich(X0) | ~patient(X0)) | strong(john) | ~generous(john)) [flattening 50]
52. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X1] : (~rich(X1) | ~patient(X1)) | strong(john) | ~generous(john)) [rectify 51]
53. ? [X1] : (~rich(X1) | ~patient(X1)) => (~rich(sK1) | ~patient(sK1)) [choice axiom]
54. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & ((~rich(sK1) | ~patient(sK1)) | strong(john) | ~generous(john)) [skolemisation 52,53]
60. (? [X0] : (generous(X0) | ~kind(X0)) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (~generous(X0) & kind(X0))) [nnf transformation 24]
61. (? [X0] : (generous(X0) | ~kind(X0)) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X2] : (~funny(X2) & funny(X2)) | ! [X3] : (~generous(X3) & kind(X3))) [rectify 60]
62. ? [X0] : (generous(X0) | ~kind(X0)) => (generous(sK3) | ~kind(sK3)) [choice axiom]
63. ? [X2] : (~funny(X2) & funny(X2)) => (~funny(sK4) & funny(sK4)) [choice axiom]
64. ((generous(sK3) | ~kind(sK3)) | ! [X1] : (funny(X1) | ~funny(X1))) & ((~funny(sK4) & funny(sK4)) | ! [X3] : (~generous(X3) & kind(X3))) [skolemisation 61,63,62]
82. brave(alice) | calm(alice) | ~strong(john) | brave(john) [cnf transformation 31]
84. ~calm(X0) | ~rich(X0) | humble(X0) [cnf transformation 41]
89. ~calm(X0) | brave(X0) | ~strong(X0) [cnf transformation 34]
100. ~humble(alice) | calm(X1) | generous(X1) [cnf transformation 47]
103. ~brave(X0) | ~rich(X0) [cnf transformation 49]
110. ~strong(john) | rich(X0) [cnf transformation 54]
117. funny(sK4) | ~generous(X3) [cnf transformation 64]
119. ~funny(sK4) | ~generous(X3) [cnf transformation 64]
136. strong(john) [cnf transformation 23]
152. 4 <=> brave(john) [avatar definition]
153. ~brave(john) <- (~4) [avatar component clause 152]
154. brave(john) <- (4) [avatar component clause 152]
156. 5 <=> strong(john) [avatar definition]
157. strong(john) <- (5) [avatar component clause 156]
160. 6 <=> calm(alice) [avatar definition]
162. calm(alice) <- (6) [avatar component clause 160]
164. 7 <=> brave(alice) [avatar definition]
166. brave(alice) <- (7) [avatar component clause 164]
167. 4 | ~5 | 6 | 7 [avatar split clause 82,164,160,156,152]
204. 15 <=> humble(alice) [avatar definition]
205. ~humble(alice) <- (~15) [avatar component clause 204]
218. 18 <=> ! [X1] : (calm(X1) | generous(X1)) [avatar definition]
219. calm(X1) | generous(X1) <- (18) [avatar component clause 218]
220. 18 | ~15 [avatar split clause 100,204,218]
226. 20 <=> ! [X0] : rich(X0) [avatar definition]
227. rich(X0) <- (20) [avatar component clause 226]
228. 20 | ~5 [avatar split clause 110,156,226]
269. 29 <=> ! [X3] : ~generous(X3) [avatar definition]
270. ~generous(X3) <- (29) [avatar component clause 269]
272. 30 <=> funny(sK4) [avatar definition]
275. 29 | ~30 [avatar split clause 119,272,269]
280. 29 | 30 [avatar split clause 117,272,269]
301. 5 [avatar split clause 136,156]
310. ~rich(john) <- (4) [resolution 103,154]
311. $false <- (4, 20) [subsumption resolution 310,227]
312. ~4 | ~20 [avatar contradiction clause 311]
320. ~rich(alice) | humble(alice) <- (6) [resolution 84,162]
322. humble(alice) <- (6, 20) [subsumption resolution 320,227]
323. $false <- (6, ~15, 20) [subsumption resolution 322,205]
324. ~6 | 15 | ~20 [avatar contradiction clause 323]
325. ~rich(alice) <- (7) [resolution 166,103]
326. $false <- (7, 20) [subsumption resolution 325,227]
327. ~7 | ~20 [avatar contradiction clause 326]
328. calm(X1) <- (18, 29) [subsumption resolution 219,270]
336. ~strong(X0) | brave(X0) <- (18, 29) [resolution 89,328]
352. brave(john) <- (5, 18, 29) [resolution 336,157]
353. $false <- (~4, 5, 18, 29) [subsumption resolution 352,153]
354. 4 | ~5 | ~18 | ~29 [avatar contradiction clause 353]
355. $false [avatar sat refutation 167,220,228,275,280,301,312,324,327,354]
% SZS output end Proof for 9042879775362127353605140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise is not quiet or kind and vice versa.
If someone is both quiet and humble then mary is not rich.
Everyone who is both not creative and creative is funny or strong and vice versa.
If someone is both not quiet and not humble then alice is rich and vice versa.
Everyone who is either curious or calm is both not generous and happy and vice versa.
Everyone who is tall is happy or not generous.
If fred is either not tall or funny then alice is old.
Everyone who is not calm or funny is both rich and tall and vice versa.
Everyone who is wise is happy and vice versa.
Everyone who is both patient and generous is happy or not old.
Everyone who is both rich and not tall is kind.
If someone is both patient and brave then someone is both not kind and happy and vice versa.
Everyone who is not patient is not calm or not old and vice versa.
Everyone who is either not happy or funny is rich.
Everyone who is generous or kind is not old or not quiet and vice versa.
Everyone who is quiet or happy is not calm.
Someone is not old or generous.
Someone is either patient or not old.
Someone is not generous or not brave.
Someone is not wise or humble.
Someone is not strong or not creative.
Fred is not old.
Someone is either not wise or not kind.
Mary is both creative and not calm. | Alice is not patient. | neutral | (![X]:(~wise(X)<=>(~quiet(X)|kind(X))))&
((?[X]:((quiet(X)&humble(X))))=>(~rich(mary)))&
(![X]:((~creative(X)&creative(X))<=>(funny(X)|strong(X))))&
((?[X]:((~quiet(X)&~humble(X))))<=>(rich(alice)))&
(![X]:((curious(X)<~>calm(X))<=>(~generous(X)&happy(X))))&
(![X]:(tall(X)=>(happy(X)|~generous(X))))&
(((~tall(fred)<~>funny(fred)))=>(old(alice)))&
(![X]:((~calm(X)|funny(X))<=>(rich(X)&tall(X))))&
(![X]:(wise(X)<=>happy(X)))&
(![X]:((patient(X)&generous(X))=>(happy(X)|~old(X))))&
(![X]:((rich(X)&~tall(X))=>kind(X)))&
((?[X]:((patient(X)&brave(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:(~patient(X)<=>(~calm(X)|~old(X))))&
(![X]:((~happy(X)<~>funny(X))=>rich(X)))&
(![X]:((generous(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(![X]:((quiet(X)|happy(X))=>~calm(X)))&
(?[X]:((~old(X)|generous(X))))&
(?[X]:((patient(X)<~>~old(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((~wise(X)|humble(X))))&
(?[X]:((~strong(X)|~creative(X))))&
(~old(fred))&
(?[X]:((~wise(X)<~>~kind(X))))&
((creative(mary)&~calm(mary))) | ~patient(alice) | [] | null | 0 |
Everyone who is both tall and strong is not wise or not happy and vice versa.
If susan is not curious then someone is either not kind or not wise.
Everyone who is not humble is both not humble and not creative.
If someone is either not happy or not patient then alice is both strong and not creative.
If someone is not rich or rich then paul is either not kind or not calm.
Everyone who is curious or tall is both brave and generous and vice versa.
If lucy is both not quiet and not rich then someone is calm.
Everyone who is either not patient or not kind is not creative or not patient.
If mary is not old then someone is generous.
Everyone who is either creative or generous is either not kind or strong and vice versa.
Everyone who is either not calm or not old is not curious.
Everyone who is either tall or not calm is both not old and not humble.
If someone is generous or patient then lucy is either not patient or funny and vice versa.
Everyone who is kind or patient is both not kind and creative and vice versa.
Everyone who is humble is either not kind or patient.
Someone is rich.
Fred is funny.
Someone is not old or not rich.
Someone is curious.
Mary is either not generous or not funny.
Someone is brave or strong. | Mary is not happy. | contradiction | (![X]:((tall(X)&strong(X))<=>(~wise(X)|~happy(X))))&
((~curious(susan))=>(?[X]:((~kind(X)<~>~wise(X)))))&
(![X]:(~humble(X)=>(~humble(X)&~creative(X))))&
((?[X]:((~happy(X)<~>~patient(X))))=>((strong(alice)&~creative(alice))))&
((?[X]:((~rich(X)|rich(X))))=>((~kind(paul)<~>~calm(paul))))&
(![X]:((curious(X)|tall(X))<=>(brave(X)&generous(X))))&
(((~quiet(lucy)&~rich(lucy)))=>(?[X]:(calm(X))))&
(![X]:((~patient(X)<~>~kind(X))=>(~creative(X)|~patient(X))))&
((~old(mary))=>(?[X]:(generous(X))))&
(![X]:((creative(X)<~>generous(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((~calm(X)<~>~old(X))=>~curious(X)))&
(![X]:((tall(X)<~>~calm(X))=>(~old(X)&~humble(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~patient(lucy)<~>funny(lucy))))&
(![X]:((kind(X)|patient(X))<=>(~kind(X)&creative(X))))&
(![X]:(humble(X)=>(~kind(X)<~>patient(X))))&
(?[X]:(rich(X)))&
(funny(fred))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:(curious(X)))&
((~generous(mary)<~>~funny(mary)))&
(?[X]:((brave(X)|strong(X)))) | ~happy(mary) | [
"p0",
"p5",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7778826621961695816472968
% SZS output start Proof for 7778826621961695816472968
1. ! [X0] : ((strong(X0) & tall(X0)) <=> (~happy(X0) | ~wise(X0))) [input p0]
6. ! [X0] : ((tall(X0) | curious(X0)) <=> (generous(X0) & brave(X0))) [input p5]
8. ! [X0] : ((~patient(X0) <~> ~kind(X0)) => (~patient(X0) | ~creative(X0))) [input p7]
10. ! [X0] : ((creative(X0) <~> generous(X0)) <=> (~kind(X0) <~> strong(X0))) [input p9]
14. ! [X0] : ((patient(X0) | kind(X0)) <=> (creative(X0) & ~kind(X0))) [input p13]
22. ~happy(mary) [input hypothesis]
28. ! [X0] : ((~patient(X0) | ~creative(X0)) | (~patient(X0) <=> ~kind(X0))) [ennf transformation 8]
29. ! [X0] : (~patient(X0) | ~creative(X0) | (~patient(X0) <=> ~kind(X0))) [flattening 28]
34. ! [X0] : (((strong(X0) & tall(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 1]
35. ! [X0] : (((strong(X0) & tall(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~strong(X0) | ~tall(X0))) [flattening 34]
41. ! [X0] : (((tall(X0) | curious(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~tall(X0) & ~curious(X0)))) [nnf transformation 6]
42. ! [X0] : ((tall(X0) | curious(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | (~tall(X0) & ~curious(X0)))) [flattening 41]
43. ! [X0] : (~patient(X0) | ~creative(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) [nnf transformation 29]
46. ! [X0] : ((((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0))))) [nnf transformation 10]
53. ! [X0] : (((patient(X0) | kind(X0)) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | (~patient(X0) & ~kind(X0)))) [nnf transformation 14]
54. ! [X0] : ((patient(X0) | kind(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | (~patient(X0) & ~kind(X0)))) [flattening 53]
67. happy(X0) | tall(X0) [cnf transformation 35]
69. happy(X0) | strong(X0) [cnf transformation 35]
85. ~tall(X0) | generous(X0) [cnf transformation 42]
88. ~patient(X0) | ~creative(X0) | ~patient(X0) | kind(X0) [cnf transformation 43]
93. ~generous(X0) | kind(X0) | creative(X0) | ~strong(X0) [cnf transformation 46]
110. ~kind(X0) | ~kind(X0) [cnf transformation 54]
114. patient(X0) | kind(X0) | ~creative(X0) | kind(X0) [cnf transformation 54]
124. ~happy(mary) [cnf transformation 22]
125. ~kind(X0) [duplicate literal removal 110]
126. patient(X0) | kind(X0) | ~creative(X0) [duplicate literal removal 114]
127. ~patient(X0) | ~creative(X0) | kind(X0) [duplicate literal removal 88]
215. ~creative(X0) | kind(X0) [subsumption resolution 126,127]
227. 22 <=> generous(mary) [avatar definition]
229. generous(mary) <- (22) [avatar component clause 227]
250. tall(mary) [resolution 67,124]
252. strong(mary) [resolution 69,124]
260. generous(mary) [resolution 85,250]
321. kind(mary) | creative(mary) | ~strong(mary) <- (22) [resolution 93,229]
335. creative(mary) | ~strong(mary) <- (22) [subsumption resolution 321,125]
336. creative(mary) <- (22) [subsumption resolution 335,252]
367. kind(mary) <- (22) [resolution 336,215]
369. $false <- (22) [subsumption resolution 367,125]
370. ~22 [avatar contradiction clause 369]
371. 22 [avatar split clause 260,227]
372. $false [avatar sat refutation 370,371]
% SZS output end Proof for 7778826621961695816472968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then mary is both patient and curious.
If someone is both not humble and patient then someone is generous.
Everyone who is generous is rich or funny and vice versa.
If fred is tall then someone is rich or happy.
If someone is not creative then lucy is strong or creative and vice versa.
Everyone who is generous is either wise or tall and vice versa.
Everyone who is both tall and not strong is kind and vice versa.
If susan is creative then someone is not quiet or humble and vice versa.
Everyone who is both not calm and strong is funny or old.
If someone is both not quiet and curious then lucy is either not funny or not kind and vice versa.
Everyone who is kind or patient is either patient or not old and vice versa.
Everyone who is both happy and patient is not humble or not patient.
Everyone who is either not rich or funny is not brave or not humble and vice versa.
Everyone who is patient or not tall is both funny and brave and vice versa.
Everyone who is not strong is kind.
Everyone who is not wise is generous or curious and vice versa.
Someone is strong.
Someone is not creative or not calm.
Mary is either brave or not curious.
Paul is either not creative or not old.
Someone is old or kind.
Susan is either tall or not tall.
Someone is old or funny.
Fred is both patient and not kind. | Fred is not brave. | contradiction | ((?[X]:(humble(X)))=>((patient(mary)&curious(mary))))&
((?[X]:((~humble(X)&patient(X))))=>(?[X]:(generous(X))))&
(![X]:(generous(X)<=>(rich(X)|funny(X))))&
((tall(fred))=>(?[X]:((rich(X)|happy(X)))))&
((?[X]:(~creative(X)))<=>((strong(lucy)|creative(lucy))))&
(![X]:(generous(X)<=>(wise(X)<~>tall(X))))&
(![X]:((tall(X)&~strong(X))<=>kind(X)))&
((creative(susan))<=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((~calm(X)&strong(X))=>(funny(X)|old(X))))&
((?[X]:((~quiet(X)&curious(X))))<=>((~funny(lucy)<~>~kind(lucy))))&
(![X]:((kind(X)|patient(X))<=>(patient(X)<~>~old(X))))&
(![X]:((happy(X)&patient(X))=>(~humble(X)|~patient(X))))&
(![X]:((~rich(X)<~>funny(X))<=>(~brave(X)|~humble(X))))&
(![X]:((patient(X)|~tall(X))<=>(funny(X)&brave(X))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:(~wise(X)<=>(generous(X)|curious(X))))&
(?[X]:(strong(X)))&
(?[X]:((~creative(X)|~calm(X))))&
((brave(mary)<~>~curious(mary)))&
((~creative(paul)<~>~old(paul)))&
(?[X]:((old(X)|kind(X))))&
((tall(susan)<~>~tall(susan)))&
(?[X]:((old(X)|funny(X))))&
((patient(fred)&~kind(fred))) | ~brave(fred) | [
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8838238551097449090842749
% SZS output start Proof for 8838238551097449090842749
14. ! [X0] : ((~tall(X0) | patient(X0)) <=> (brave(X0) & funny(X0))) [input p13]
24. ~kind(fred) & patient(fred) [input p23]
25. ~brave(fred) [input hypothesis]
62. ! [X0] : (((~tall(X0) | patient(X0)) | (~brave(X0) | ~funny(X0))) & ((brave(X0) & funny(X0)) | (tall(X0) & ~patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((~tall(X0) | patient(X0) | ~brave(X0) | ~funny(X0)) & ((brave(X0) & funny(X0)) | (tall(X0) & ~patient(X0)))) [flattening 62]
119. ~patient(X0) | brave(X0) [cnf transformation 63]
136. patient(fred) [cnf transformation 24]
138. ~brave(fred) [cnf transformation 25]
287. brave(fred) [resolution 119,136]
289. $false [subsumption resolution 287,138]
% SZS output end Proof for 8838238551097449090842749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not strong and vice versa. If someone is not humble then mary is not kind and vice versa. Everyone who is funny is not funny or wise and vice versa. Everyone who is not strong or patient is not funny or brave and vice versa. If paul is not happy then someone is either not tall or not old and vice versa. Everyone who is both not quiet and not kind is tall and vice versa. Everyone who is either not curious or not tall is both not quiet and curious and vice versa. If someone is either happy or not calm then someone is both not brave and tall and vice versa. If alice is both not wise and brave then someone is not kind. If paul is either not calm or not rich then someone is not rich or not old. If mary is either not quiet or not strong then susan is both not happy and funny. If paul is both not wise and not curious then someone is curious. Everyone who is both kind and not kind is either not funny or brave. Everyone who is either happy or not quiet is either wise or happy and vice versa. If susan is both not humble and not rich then fred is not brave and vice versa. If mary is not rich or not wise then someone is brave or happy. Someone is curious or not generous. Alice is happy. John is not humble or not happy. Lucy is not calm. Someone is either not brave or humble. | Susan is not quiet. | entailment | (![X]:((quiet(X)<~>~tall(X))<=>~strong(X)))&
((?[X]:(~humble(X)))<=>(~kind(mary)))&
(![X]:(funny(X)<=>(~funny(X)|wise(X))))&
(![X]:((~strong(X)|patient(X))<=>(~funny(X)|brave(X))))&
((~happy(paul))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~quiet(X)&~kind(X))<=>tall(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~brave(X)&tall(X)))))&
(((~wise(alice)&brave(alice)))=>(?[X]:(~kind(X))))&
(((~calm(paul)<~>~rich(paul)))=>(?[X]:((~rich(X)|~old(X)))))&
(((~quiet(mary)<~>~strong(mary)))=>((~happy(susan)&funny(susan))))&
(((~wise(paul)&~curious(paul)))=>(?[X]:(curious(X))))&
(![X]:((kind(X)&~kind(X))=>(~funny(X)<~>brave(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(wise(X)<~>happy(X))))&
(((~humble(susan)&~rich(susan)))<=>(~brave(fred)))&
(((~rich(mary)|~wise(mary)))=>(?[X]:((brave(X)|happy(X)))))&
(?[X]:((curious(X)|~generous(X))))&
(happy(alice))&
((~humble(john)|~happy(john)))&
(~calm(lucy))&
(?[X]:((~brave(X)<~>humble(X)))) | ~quiet(susan) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 911177454159139855520758
% SZS output start Proof for 911177454159139855520758
3. ! [X0] : (funny(X0) <=> (wise(X0) | ~funny(X0))) [input p2]
14. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (wise(X0) <~> happy(X0))) [input p13]
22. quiet(susan) [input hypothesis]
39. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 3]
40. ! [X0] : ((funny(X0) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~funny(X0))) [flattening 39]
65. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0)))) & (((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 14]
79. wise(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 40]
80. funny(X0) | funny(X0) [cnf transformation 40]
117. ~happy(X0) | ~wise(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 65]
119. ~quiet(X0) | happy(X0) | happy(X0) | ~wise(X0) [cnf transformation 65]
133. quiet(susan) [cnf transformation 22]
135. ~happy(X0) | ~wise(X0) | ~quiet(X0) [duplicate literal removal 117]
136. ~quiet(X0) | happy(X0) | ~wise(X0) [duplicate literal removal 119]
140. wise(X0) | ~funny(X0) [duplicate literal removal 79]
141. funny(X0) [duplicate literal removal 80]
155. wise(X0) [subsumption resolution 140,141]
217. ~quiet(X0) | happy(X0) [subsumption resolution 136,155]
218. ~happy(X0) | ~quiet(X0) [subsumption resolution 135,155]
219. ~quiet(X0) [subsumption resolution 218,217]
267. $false [subsumption resolution 133,219]
% SZS output end Proof for 911177454159139855520758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or funny is happy or generous. Everyone who is not old is either tall or creative and vice versa. If someone is either strong or not generous then someone is either kind or not kind. Everyone who is not creative or not happy is generous or not kind. If someone is not kind or not old then lucy is happy and vice versa. If paul is wise then paul is not happy and vice versa. If mary is kind or not quiet then lucy is creative or not happy. Everyone who is not calm is both not creative and not quiet and vice versa. If susan is both not patient and kind then someone is either happy or calm and vice versa. Everyone who is both old and creative is either strong or not kind. If fred is not tall then someone is both calm and not generous and vice versa. Everyone who is either calm or not quiet is rich or kind and vice versa. If someone is humble or not generous then someone is both wise and not curious. If someone is either not old or brave then someone is either rich or calm and vice versa. Everyone who is not humble is either not wise or not quiet. Everyone who is either curious or not creative is not tall. John is not happy. Someone is quiet or brave. Mary is quiet. Susan is not strong. Mary is not creative. John is happy or not strong. Someone is either not generous or patient. Susan is quiet or kind. | Mary is quiet. | entailment | (![X]:((~funny(X)|funny(X))=>(happy(X)|generous(X))))&
(![X]:(~old(X)<=>(tall(X)<~>creative(X))))&
((?[X]:((strong(X)<~>~generous(X))))=>(?[X]:((kind(X)<~>~kind(X)))))&
(![X]:((~creative(X)|~happy(X))=>(generous(X)|~kind(X))))&
((?[X]:((~kind(X)|~old(X))))<=>(happy(lucy)))&
((wise(paul))<=>(~happy(paul)))&
(((kind(mary)|~quiet(mary)))=>((creative(lucy)|~happy(lucy))))&
(![X]:(~calm(X)<=>(~creative(X)&~quiet(X))))&
(((~patient(susan)&kind(susan)))<=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((old(X)&creative(X))=>(strong(X)<~>~kind(X))))&
((~tall(fred))<=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>(rich(X)|kind(X))))&
((?[X]:((humble(X)|~generous(X))))=>(?[X]:((wise(X)&~curious(X)))))&
((?[X]:((~old(X)<~>brave(X))))<=>(?[X]:((rich(X)<~>calm(X)))))&
(![X]:(~humble(X)=>(~wise(X)<~>~quiet(X))))&
(![X]:((curious(X)<~>~creative(X))=>~tall(X)))&
(~happy(john))&
(?[X]:((quiet(X)|brave(X))))&
(quiet(mary))&
(~strong(susan))&
(~creative(mary))&
((happy(john)|~strong(john)))&
(?[X]:((~generous(X)<~>patient(X))))&
((quiet(susan)|kind(susan))) | quiet(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1325790537331300568911337
% SZS output start Proof for 1325790537331300568911337
19. quiet(mary) [input p18]
25. ~quiet(mary) [input hypothesis]
137. quiet(mary) [cnf transformation 19]
144. ~quiet(mary) [cnf transformation 25]
178. 8 <=> quiet(mary) [avatar definition]
302. 8 [avatar split clause 137,178]
319. ~8 [avatar split clause 144,178]
320. $false [avatar sat refutation 302,319]
% SZS output end Proof for 1325790537331300568911337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or humble is either not strong or not old.
If someone is funny then susan is both not happy and not strong.
Everyone who is quiet or not humble is not quiet.
If alice is not brave or not patient then someone is not curious and vice versa.
If someone is not kind then someone is quiet and vice versa.
If paul is both not funny and not wise then mary is both not old and kind and vice versa.
If someone is not curious or not old then fred is either not happy or funny.
If john is both happy and not quiet then someone is either not tall or calm and vice versa.
Everyone who is both humble and quiet is either tall or not quiet.
If lucy is tall then alice is wise or creative and vice versa.
If susan is both patient and strong then someone is either not curious or old and vice versa.
If someone is both not quiet and funny then someone is not humble or humble.
Everyone who is both not happy and not patient is calm.
Everyone who is both happy and not happy is either not wise or not quiet.
Everyone who is both not tall and strong is either creative or funny and vice versa.
If mary is wise then someone is not generous.
Someone is strong or not strong.
Someone is brave.
John is not brave or not calm.
Someone is either rich or humble.
John is not quiet or quiet. | Mary is kind. | entailment | (![X]:((generous(X)|humble(X))=>(~strong(X)<~>~old(X))))&
((?[X]:(funny(X)))=>((~happy(susan)&~strong(susan))))&
(![X]:((quiet(X)|~humble(X))=>~quiet(X)))&
(((~brave(alice)|~patient(alice)))<=>(?[X]:(~curious(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(quiet(X))))&
(((~funny(paul)&~wise(paul)))<=>((~old(mary)&kind(mary))))&
((?[X]:((~curious(X)|~old(X))))=>((~happy(fred)<~>funny(fred))))&
(((happy(john)&~quiet(john)))<=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:((humble(X)&quiet(X))=>(tall(X)<~>~quiet(X))))&
((tall(lucy))<=>((wise(alice)|creative(alice))))&
(((patient(susan)&strong(susan)))<=>(?[X]:((~curious(X)<~>old(X)))))&
((?[X]:((~quiet(X)&funny(X))))=>(?[X]:((~humble(X)|humble(X)))))&
(![X]:((~happy(X)&~patient(X))=>calm(X)))&
(![X]:((happy(X)&~happy(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((~tall(X)&strong(X))<=>(creative(X)<~>funny(X))))&
((wise(mary))=>(?[X]:(~generous(X))))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:(brave(X)))&
((~brave(john)|~calm(john)))&
(?[X]:((rich(X)<~>humble(X))))&
((~quiet(john)|quiet(john))) | kind(mary) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7837478085281151706842726
% SZS output start Proof for 7837478085281151706842726
3. ! [X0] : ((~humble(X0) | quiet(X0)) => ~quiet(X0)) [input p2]
5. ? [X0] : ~kind(X0) <=> ? [X0] : quiet(X0) [input p4]
22. ~kind(mary) [input hypothesis]
23. ? [X0] : ~kind(X0) <=> ? [X1] : quiet(X1) [rectify 5]
29. ! [X0] : (~quiet(X0) | (humble(X0) & ~quiet(X0))) [ennf transformation 3]
44. (? [X0] : ~kind(X0) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : kind(X0)) [nnf transformation 23]
45. (? [X0] : ~kind(X0) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : kind(X3)) [rectify 44]
46. ? [X0] : ~kind(X0) => ~kind(sK1) [choice axiom]
47. ? [X2] : quiet(X2) => quiet(sK2) [choice axiom]
48. (~kind(sK1) | ! [X1] : ~quiet(X1)) & (quiet(sK2) | ! [X3] : kind(X3)) [skolemisation 45,47,46]
82. ~quiet(X0) | ~quiet(X0) [cnf transformation 29]
87. quiet(sK2) | kind(X3) [cnf transformation 48]
130. ~kind(mary) [cnf transformation 22]
132. ~quiet(X0) [duplicate literal removal 82]
164. kind(X3) [subsumption resolution 87,132]
279. $false [subsumption resolution 130,164]
% SZS output end Proof for 7837478085281151706842726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative and calm is both not funny and not happy. Everyone who is not happy is both not curious and not strong and vice versa. Everyone who is funny is patient and vice versa. If someone is not old or not rich then someone is either not strong or not rich. Everyone who is tall or creative is either happy or not rich. If john is calm or not quiet then someone is rich. If someone is either not patient or quiet then someone is both not calm and not kind and vice versa. Everyone who is not curious or curious is not brave. If someone is not generous then lucy is both not funny and generous and vice versa. If paul is funny or not quiet then someone is either not calm or patient and vice versa. Everyone who is not tall or not rich is both not funny and wise and vice versa. If alice is either not calm or happy then paul is not kind and vice versa. Everyone who is not happy or not humble is not tall and vice versa. Everyone who is either patient or not funny is wise. Everyone who is both not patient and tall is patient. Everyone who is not wise or not calm is either not strong or not creative. Someone is either not strong or not rich. Someone is quiet. Someone is either happy or not creative. Alice is old. Someone is not tall or not humble. Someone is strong. Someone is kind or not creative. John is not strong. | Lucy is not patient. | neutral | (![X]:((~creative(X)&calm(X))=>(~funny(X)&~happy(X))))&
(![X]:(~happy(X)<=>(~curious(X)&~strong(X))))&
(![X]:(funny(X)<=>patient(X)))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~strong(X)<~>~rich(X)))))&
(![X]:((tall(X)|creative(X))=>(happy(X)<~>~rich(X))))&
(((calm(john)|~quiet(john)))=>(?[X]:(rich(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((~calm(X)&~kind(X)))))&
(![X]:((~curious(X)|curious(X))=>~brave(X)))&
((?[X]:(~generous(X)))<=>((~funny(lucy)&generous(lucy))))&
(((funny(paul)|~quiet(paul)))<=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:((~tall(X)|~rich(X))<=>(~funny(X)&wise(X))))&
(((~calm(alice)<~>happy(alice)))<=>(~kind(paul)))&
(![X]:((~happy(X)|~humble(X))<=>~tall(X)))&
(![X]:((patient(X)<~>~funny(X))=>wise(X)))&
(![X]:((~patient(X)&tall(X))=>patient(X)))&
(![X]:((~wise(X)|~calm(X))=>(~strong(X)<~>~creative(X))))&
(?[X]:((~strong(X)<~>~rich(X))))&
(?[X]:(quiet(X)))&
(?[X]:((happy(X)<~>~creative(X))))&
(old(alice))&
(?[X]:((~tall(X)|~humble(X))))&
(?[X]:(strong(X)))&
(?[X]:((kind(X)|~creative(X))))&
(~strong(john)) | ~patient(lucy) | [] | null | 0 |
Everyone who is not humble is both not kind and funny and vice versa.
If alice is not humble then mary is strong or wise and vice versa.
Everyone who is both happy and not curious is both not generous and not rich and vice versa.
Everyone who is patient or humble is not funny and vice versa.
Everyone who is humble or curious is both happy and not patient and vice versa.
If alice is both happy and brave then susan is not wise or old and vice versa.
If paul is strong then someone is either not wise or quiet.
Everyone who is both quiet and kind is calm and vice versa.
If mary is either not creative or not calm then lucy is not quiet or not rich.
If someone is not brave or creative then someone is not curious and vice versa.
If paul is both not calm and calm then paul is not generous or patient and vice versa.
If lucy is not funny or wise then someone is either funny or tall.
If someone is not curious or not happy then susan is both not kind and not generous.
If someone is either old or not humble then alice is both not creative and brave and vice versa.
If lucy is both happy and not rich then someone is not happy or not kind and vice versa.
Everyone who is kind or not generous is either creative or not humble and vice versa.
Someone is either kind or not patient.
Someone is not creative or not curious.
Someone is either humble or not quiet.
Someone is not funny or not tall.
Lucy is tall.
Someone is strong.
Lucy is strong or funny.
Someone is either not old or not calm. | Paul is not funny. | neutral | (![X]:(~humble(X)<=>(~kind(X)&funny(X))))&
((~humble(alice))<=>((strong(mary)|wise(mary))))&
(![X]:((happy(X)&~curious(X))<=>(~generous(X)&~rich(X))))&
(![X]:((patient(X)|humble(X))<=>~funny(X)))&
(![X]:((humble(X)|curious(X))<=>(happy(X)&~patient(X))))&
(((happy(alice)&brave(alice)))<=>((~wise(susan)|old(susan))))&
((strong(paul))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((quiet(X)&kind(X))<=>calm(X)))&
(((~creative(mary)<~>~calm(mary)))=>((~quiet(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)|creative(X))))<=>(?[X]:(~curious(X))))&
(((~calm(paul)&calm(paul)))<=>((~generous(paul)|patient(paul))))&
(((~funny(lucy)|wise(lucy)))=>(?[X]:((funny(X)<~>tall(X)))))&
((?[X]:((~curious(X)|~happy(X))))=>((~kind(susan)&~generous(susan))))&
((?[X]:((old(X)<~>~humble(X))))<=>((~creative(alice)&brave(alice))))&
(((happy(lucy)&~rich(lucy)))<=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((kind(X)|~generous(X))<=>(creative(X)<~>~humble(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~creative(X)|~curious(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:((~funny(X)|~tall(X))))&
(tall(lucy))&
(?[X]:(strong(X)))&
((strong(lucy)|funny(lucy)))&
(?[X]:((~old(X)<~>~calm(X)))) | ~funny(paul) | [] | null | 0 |
Everyone who is either creative or not patient is patient and vice versa. Everyone who is strong is tall. If someone is calm then lucy is not patient or not calm. Everyone who is calm is curious and vice versa. If alice is not rich then lucy is not generous. If someone is both not curious and creative then someone is not happy or funny. Everyone who is not creative is funny or not humble and vice versa. If someone is happy or brave then someone is both not generous and funny. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Alice is tall or happy. Someone is either not kind or not rich. Fred is either tall or not generous. Someone is strong. Someone is both not old and tall. Alice is generous or happy. | Susan is not generous. | entailment | (![X]:((creative(X)<~>~patient(X))<=>patient(X)))&
(![X]:(strong(X)=>tall(X)))&
((?[X]:(calm(X)))=>((~patient(lucy)|~calm(lucy))))&
(![X]:(calm(X)<=>curious(X)))&
((~rich(alice))=>(~generous(lucy)))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
((tall(alice)|happy(alice)))&
(?[X]:((~kind(X)<~>~rich(X))))&
((tall(fred)<~>~generous(fred)))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)&tall(X))))&
((generous(alice)|happy(alice))) | ~generous(susan) | [
"p0",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7337427917379719015252814
% SZS output start Proof for 7337427917379719015252814
1. ! [X0] : ((creative(X0) <~> ~patient(X0)) <=> patient(X0)) [input p0]
7. ! [X0] : (~creative(X0) <=> (~humble(X0) | funny(X0))) [input p6]
8. ? [X0] : (brave(X0) | happy(X0)) => ? [X0] : (funny(X0) & ~generous(X0)) [input p7]
11. generous(susan) <=> happy(susan) [input p10]
23. generous(susan) [input hypothesis]
25. ? [X0] : (brave(X0) | happy(X0)) => ? [X1] : (funny(X1) & ~generous(X1)) [rectify 8]
35. ? [X1] : (funny(X1) & ~generous(X1)) | ! [X0] : (~brave(X0) & ~happy(X0)) [ennf transformation 25]
41. ! [X0] : ((((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | ~patient(X0)) & (patient(X0) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0))))) [nnf transformation 1]
45. ! [X0] : ((~creative(X0) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | creative(X0))) [nnf transformation 7]
46. ! [X0] : ((~creative(X0) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | creative(X0))) [flattening 45]
47. ? [X0] : (funny(X0) & ~generous(X0)) | ! [X1] : (~brave(X1) & ~happy(X1)) [rectify 35]
48. ? [X0] : (funny(X0) & ~generous(X0)) => (funny(sK1) & ~generous(sK1)) [choice axiom]
49. (funny(sK1) & ~generous(sK1)) | ! [X1] : (~brave(X1) & ~happy(X1)) [skolemisation 47,48]
52. (generous(susan) | ~happy(susan)) & (happy(susan) | ~generous(susan)) [nnf transformation 11]
66. patient(X0) | creative(X0) | patient(X0) [cnf transformation 41]
67. ~patient(X0) | creative(X0) | ~patient(X0) [cnf transformation 41]
75. ~creative(X0) | ~funny(X0) [cnf transformation 46]
79. funny(sK1) | ~happy(X1) [cnf transformation 49]
89. happy(susan) | ~generous(susan) [cnf transformation 52]
115. generous(susan) [cnf transformation 23]
117. patient(X0) | creative(X0) [duplicate literal removal 66]
118. ~patient(X0) | creative(X0) [duplicate literal removal 67]
119. creative(X0) [subsumption resolution 117,118]
155. ~funny(X0) [subsumption resolution 75,119]
157. ~happy(X1) [subsumption resolution 79,155]
162. ~generous(susan) [subsumption resolution 89,157]
197. $false [subsumption resolution 115,162]
% SZS output end Proof for 7337427917379719015252814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both humble and not rich and vice versa. If alice is not tall or strong then susan is not tall or curious and vice versa. If someone is not humble then paul is both not old and not humble. Everyone who is patient is both not calm and strong and vice versa. If someone is not funny then someone is either curious or not old and vice versa. Everyone who is both quiet and brave is not wise and vice versa. Everyone who is both tall and generous is not kind. If susan is either curious or not funny then fred is both not rich and not brave and vice versa. If alice is either wise or not calm then paul is strong or quiet. If someone is not wise then someone is happy. If someone is both humble and quiet then someone is both happy and not rich and vice versa. If someone is strong or quiet then susan is both not generous and not happy. If someone is either not happy or quiet then fred is both old and not old. Everyone who is either creative or generous is both happy and curious and vice versa. Everyone who is wise is not brave and vice versa. If someone is curious or not kind then paul is funny or brave and vice versa. John is not tall. Someone is not funny or not happy. Someone is not quiet or not happy. Someone is tall. Mary is not strong. Alice is not tall. Susan is generous. Someone is kind. | Fred is not wise. | contradiction | (![X]:(~old(X)<=>(humble(X)&~rich(X))))&
(((~tall(alice)|strong(alice)))<=>((~tall(susan)|curious(susan))))&
((?[X]:(~humble(X)))=>((~old(paul)&~humble(paul))))&
(![X]:(patient(X)<=>(~calm(X)&strong(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((quiet(X)&brave(X))<=>~wise(X)))&
(![X]:((tall(X)&generous(X))=>~kind(X)))&
(((curious(susan)<~>~funny(susan)))<=>((~rich(fred)&~brave(fred))))&
(((wise(alice)<~>~calm(alice)))=>((strong(paul)|quiet(paul))))&
((?[X]:(~wise(X)))=>(?[X]:(happy(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
((?[X]:((strong(X)|quiet(X))))=>((~generous(susan)&~happy(susan))))&
((?[X]:((~happy(X)<~>quiet(X))))=>((old(fred)&~old(fred))))&
(![X]:((creative(X)<~>generous(X))<=>(happy(X)&curious(X))))&
(![X]:(wise(X)<=>~brave(X)))&
((?[X]:((curious(X)|~kind(X))))<=>((funny(paul)|brave(paul))))&
(~tall(john))&
(?[X]:((~funny(X)|~happy(X))))&
(?[X]:((~quiet(X)|~happy(X))))&
(?[X]:(tall(X)))&
(~strong(mary))&
(~tall(alice))&
(generous(susan))&
(?[X]:(kind(X))) | ~wise(fred) | [
"p5",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6873158282293269930482723
% SZS output start Proof for 6873158282293269930482723
6. ! [X0] : ((brave(X0) & quiet(X0)) <=> ~wise(X0)) [input p5]
12. ? [X0] : (quiet(X0) | strong(X0)) => (~happy(susan) & ~generous(susan)) [input p11]
23. generous(susan) [input p22]
25. ~wise(fred) [input hypothesis]
35. (~happy(susan) & ~generous(susan)) | ! [X0] : (~quiet(X0) & ~strong(X0)) [ennf transformation 12]
46. ! [X0] : (((brave(X0) & quiet(X0)) | wise(X0)) & (~wise(X0) | (~brave(X0) | ~quiet(X0)))) [nnf transformation 6]
47. ! [X0] : (((brave(X0) & quiet(X0)) | wise(X0)) & (~wise(X0) | ~brave(X0) | ~quiet(X0))) [flattening 46]
90. wise(X0) | quiet(X0) [cnf transformation 47]
107. ~generous(susan) | ~quiet(X0) [cnf transformation 35]
132. generous(susan) [cnf transformation 23]
134. ~wise(fred) [cnf transformation 25]
264. 29 <=> ! [X0] : ~quiet(X0) [avatar definition]
265. ~quiet(X0) <- (29) [avatar component clause 264]
276. 32 <=> generous(susan) [avatar definition]
279. 29 | ~32 [avatar split clause 107,276,264]
340. 32 [avatar split clause 132,276]
348. quiet(fred) [resolution 90,134]
349. $false <- (29) [subsumption resolution 348,265]
350. ~29 [avatar contradiction clause 349]
351. $false [avatar sat refutation 279,340,350]
% SZS output end Proof for 6873158282293269930482723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not curious is both not patient and calm.
Everyone who is either patient or quiet is both generous and tall and vice versa.
If alice is both not creative and not patient then alice is not curious or funny and vice versa.
Everyone who is either kind or not rich is wise or not brave.
If paul is both wise and strong then fred is generous or not curious and vice versa.
Everyone who is either calm or not wise is funny or not humble and vice versa.
If someone is both not quiet and strong then someone is strong.
If susan is either curious or patient then someone is humble and vice versa.
Everyone who is not rich or patient is both humble and rich and vice versa.
Everyone who is wise or not calm is both happy and calm.
If someone is not creative or not humble then someone is not kind and vice versa.
If someone is not wise then mary is not creative and vice versa.
Everyone who is tall is either not rich or not patient.
Everyone who is rich or humble is not patient and vice versa.
If fred is either funny or not old then john is either creative or patient and vice versa.
Everyone who is wise is both not patient and not kind and vice versa.
Someone is both brave and strong.
Someone is both quiet and generous.
Susan is strong or funny.
Someone is kind or rich.
Paul is quiet.
Fred is not funny or not quiet. | Paul is not patient. | entailment | (![X]:((brave(X)&~curious(X))=>(~patient(X)&calm(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(generous(X)&tall(X))))&
(((~creative(alice)&~patient(alice)))<=>((~curious(alice)|funny(alice))))&
(![X]:((kind(X)<~>~rich(X))=>(wise(X)|~brave(X))))&
(((wise(paul)&strong(paul)))<=>((generous(fred)|~curious(fred))))&
(![X]:((calm(X)<~>~wise(X))<=>(funny(X)|~humble(X))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:(strong(X))))&
(((curious(susan)<~>patient(susan)))<=>(?[X]:(humble(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
(![X]:((wise(X)|~calm(X))=>(happy(X)&calm(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(~wise(X)))<=>(~creative(mary)))&
(![X]:(tall(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)|humble(X))<=>~patient(X)))&
(((funny(fred)<~>~old(fred)))<=>((creative(john)<~>patient(john))))&
(![X]:(wise(X)<=>(~patient(X)&~kind(X))))&
(?[X]:((brave(X)&strong(X))))&
(?[X]:((quiet(X)&generous(X))))&
((strong(susan)|funny(susan)))&
(?[X]:((kind(X)|rich(X))))&
(quiet(paul))&
((~funny(fred)|~quiet(fred))) | ~patient(paul) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1769544610080658674315054
% SZS output start Proof for 1769544610080658674315054
9. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p8]
14. ! [X0] : ((humble(X0) | rich(X0)) <=> ~patient(X0)) [input p13]
23. patient(paul) [input hypothesis]
50. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 9]
51. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 50]
62. ! [X0] : (((humble(X0) | rich(X0)) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 14]
63. ! [X0] : ((humble(X0) | rich(X0) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~rich(X0)))) [flattening 62]
105. humble(X0) | ~patient(X0) [cnf transformation 51]
119. ~patient(X0) | ~humble(X0) [cnf transformation 63]
140. patient(paul) [cnf transformation 23]
251. ~patient(X0) [subsumption resolution 119,105]
287. $false [subsumption resolution 140,251]
% SZS output end Proof for 1769544610080658674315054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not brave then mary is both kind and not humble and vice versa. Everyone who is not happy or rich is both not calm and not rich and vice versa. If lucy is either kind or not quiet then lucy is either generous or not calm. Everyone who is either strong or not quiet is either not calm or not curious. Everyone who is not humble is not happy or curious and vice versa. If someone is not calm then someone is kind or generous. Everyone who is either not curious or not generous is not patient. Everyone who is not generous is calm or generous and vice versa. Everyone who is not kind is brave or not tall and vice versa. If john is both not strong and not tall then alice is not old. Everyone who is both old and generous is both not quiet and not brave and vice versa. Everyone who is not patient is both kind and not funny and vice versa. Everyone who is not brave or not strong is old. Everyone who is both quiet and not wise is not strong or quiet and vice versa. Everyone who is either old or not generous is either patient or generous and vice versa. Susan is both calm and not strong. Someone is not calm or tall. Fred is either not strong or not curious. Susan is quiet or calm. Someone is either not rich or not curious. Mary is either tall or not wise. | Mary is humble. | entailment | ((?[X]:((humble(X)&~brave(X))))<=>((kind(mary)&~humble(mary))))&
(![X]:((~happy(X)|rich(X))<=>(~calm(X)&~rich(X))))&
(((kind(lucy)<~>~quiet(lucy)))=>((generous(lucy)<~>~calm(lucy))))&
(![X]:((strong(X)<~>~quiet(X))=>(~calm(X)<~>~curious(X))))&
(![X]:(~humble(X)<=>(~happy(X)|curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((kind(X)|generous(X)))))&
(![X]:((~curious(X)<~>~generous(X))=>~patient(X)))&
(![X]:(~generous(X)<=>(calm(X)|generous(X))))&
(![X]:(~kind(X)<=>(brave(X)|~tall(X))))&
(((~strong(john)&~tall(john)))=>(~old(alice)))&
(![X]:((old(X)&generous(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(~patient(X)<=>(kind(X)&~funny(X))))&
(![X]:((~brave(X)|~strong(X))=>old(X)))&
(![X]:((quiet(X)&~wise(X))<=>(~strong(X)|quiet(X))))&
(![X]:((old(X)<~>~generous(X))<=>(patient(X)<~>generous(X))))&
((calm(susan)&~strong(susan)))&
(?[X]:((~calm(X)|tall(X))))&
((~strong(fred)<~>~curious(fred)))&
((quiet(susan)|calm(susan)))&
(?[X]:((~rich(X)<~>~curious(X))))&
((tall(mary)<~>~wise(mary))) | humble(mary) | [
"p1",
"p4",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7588312894601125856761270
% SZS output start Proof for 7588312894601125856761270
2. ! [X0] : ((rich(X0) | ~happy(X0)) <=> (~rich(X0) & ~calm(X0))) [input p1]
5. ! [X0] : (~humble(X0) <=> (curious(X0) | ~happy(X0))) [input p4]
7. ! [X0] : ((~curious(X0) <~> ~generous(X0)) => ~patient(X0)) [input p6]
8. ! [X0] : (~generous(X0) <=> (generous(X0) | calm(X0))) [input p7]
9. ! [X0] : (~kind(X0) <=> (~tall(X0) | brave(X0))) [input p8]
11. ! [X0] : ((generous(X0) & old(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p10]
12. ! [X0] : (~patient(X0) <=> (~funny(X0) & kind(X0))) [input p11]
14. ! [X0] : ((~wise(X0) & quiet(X0)) <=> (quiet(X0) | ~strong(X0))) [input p13]
21. tall(mary) <~> ~wise(mary) [input p20]
22. ~humble(mary) [input hypothesis]
27. ! [X0] : (~patient(X0) | (~curious(X0) <=> ~generous(X0))) [ennf transformation 7]
36. ! [X0] : (((rich(X0) | ~happy(X0)) | (rich(X0) | calm(X0))) & ((~rich(X0) & ~calm(X0)) | (~rich(X0) & happy(X0)))) [nnf transformation 2]
37. ! [X0] : ((rich(X0) | ~happy(X0) | rich(X0) | calm(X0)) & ((~rich(X0) & ~calm(X0)) | (~rich(X0) & happy(X0)))) [flattening 36]
40. ! [X0] : ((~humble(X0) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | humble(X0))) [nnf transformation 5]
41. ! [X0] : ((~humble(X0) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | humble(X0))) [flattening 40]
45. ! [X0] : (~patient(X0) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) [nnf transformation 27]
46. ! [X0] : ((~generous(X0) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | generous(X0))) [nnf transformation 8]
47. ! [X0] : ((~generous(X0) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | generous(X0))) [flattening 46]
48. ! [X0] : ((~kind(X0) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | kind(X0))) [nnf transformation 9]
49. ! [X0] : ((~kind(X0) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | kind(X0))) [flattening 48]
50. ! [X0] : (((generous(X0) & old(X0)) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | (~generous(X0) | ~old(X0)))) [nnf transformation 11]
51. ! [X0] : (((generous(X0) & old(X0)) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | ~generous(X0) | ~old(X0))) [flattening 50]
52. ! [X0] : ((~patient(X0) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | patient(X0))) [nnf transformation 12]
53. ! [X0] : ((~patient(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | patient(X0))) [flattening 52]
54. ! [X0] : (((~wise(X0) & quiet(X0)) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | (wise(X0) | ~quiet(X0)))) [nnf transformation 14]
55. ! [X0] : (((~wise(X0) & quiet(X0)) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | wise(X0) | ~quiet(X0))) [flattening 54]
63. (wise(mary) | ~tall(mary)) & (~wise(mary) | tall(mary)) [nnf transformation 21]
68. ~calm(X0) | happy(X0) [cnf transformation 37]
81. ~happy(X0) | curious(X0) | humble(X0) [cnf transformation 41]
86. ~patient(X0) | ~curious(X0) | generous(X0) [cnf transformation 45]
87. generous(X0) | calm(X0) | generous(X0) [cnf transformation 47]
89. ~generous(X0) | ~generous(X0) [cnf transformation 47]
91. ~kind(X0) | ~brave(X0) [cnf transformation 49]
92. ~kind(X0) | tall(X0) [cnf transformation 49]
97. generous(X0) | brave(X0) | quiet(X0) [cnf transformation 51]
98. patient(X0) | kind(X0) [cnf transformation 53]
107. ~wise(X0) | ~quiet(X0) [cnf transformation 55]
125. wise(mary) | ~tall(mary) [cnf transformation 63]
126. ~humble(mary) [cnf transformation 22]
131. generous(X0) | calm(X0) [duplicate literal removal 87]
132. ~generous(X0) [duplicate literal removal 89]
136. 1 <=> kind(mary) [avatar definition]
137. kind(mary) <- (1) [avatar component clause 136]
138. ~kind(mary) <- (~1) [avatar component clause 136]
140. 2 <=> humble(mary) [avatar definition]
141. ~humble(mary) <- (~2) [avatar component clause 140]
179. 10 <=> ! [X1] : calm(X1) [avatar definition]
180. calm(X1) <- (10) [avatar component clause 179]
190. calm(X0) [subsumption resolution 131,132]
191. 10 [avatar split clause 190,179]
205. quiet(X0) | brave(X0) [subsumption resolution 97,132]
229. 20 <=> tall(mary) [avatar definition]
233. 21 <=> wise(mary) [avatar definition]
235. wise(mary) <- (21) [avatar component clause 233]
236. ~20 | 21 [avatar split clause 125,233,229]
238. ~2 [avatar split clause 126,140]
244. happy(X0) <- (10) [resolution 68,180]
254. curious(X0) | humble(X0) <- (10) [resolution 81,244]
268. ~curious(X0) | generous(X0) | kind(X0) [resolution 86,98]
270. ~curious(X0) | kind(X0) [subsumption resolution 268,132]
336. kind(X0) | humble(X0) <- (10) [resolution 254,270]
364. humble(mary) <- (~1, 10) [resolution 336,138]
367. $false <- (~1, ~2, 10) [subsumption resolution 364,141]
368. 1 | 2 | ~10 [avatar contradiction clause 367]
369. tall(mary) <- (1) [resolution 137,92]
370. ~brave(mary) <- (1) [resolution 137,91]
373. 20 | ~1 [avatar split clause 369,136,229]
379. ~quiet(mary) <- (21) [resolution 235,107]
381. brave(mary) <- (21) [resolution 379,205]
382. $false <- (1, 21) [subsumption resolution 381,370]
383. ~1 | ~21 [avatar contradiction clause 382]
384. $false [avatar sat refutation 191,236,238,368,373,383]
% SZS output end Proof for 7588312894601125856761270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not humble then someone is happy or curious.
Everyone who is not happy is not rich.
If mary is either not kind or not old then alice is not brave and vice versa.
Everyone who is not funny is not old.
Everyone who is both not patient and humble is both not tall and not creative.
If john is both not tall and patient then john is both not creative and quiet and vice versa.
If john is both patient and not wise then alice is both not creative and not rich.
If someone is either not creative or creative then john is either not tall or not curious and vice versa.
Everyone who is not funny is either not quiet or not funny.
If someone is not quiet then someone is either patient or not curious and vice versa.
Everyone who is brave or not old is both happy and not generous.
If someone is both not rich and brave then fred is both not calm and strong.
If mary is not happy or not old then someone is either tall or not generous and vice versa.
Everyone who is both brave and curious is either generous or not calm and vice versa.
Everyone who is curious is wise or not curious.
Everyone who is wise is either not rich or not wise.
Mary is not funny.
Someone is either happy or brave.
Susan is tall.
Paul is brave or generous.
Someone is not rich.
Someone is curious or not kind.
Someone is both old and generous.
Someone is not wise or not strong. | Mary is calm. | neutral | ((?[X]:((funny(X)&~humble(X))))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~happy(X)=>~rich(X)))&
(((~kind(mary)<~>~old(mary)))<=>(~brave(alice)))&
(![X]:(~funny(X)=>~old(X)))&
(![X]:((~patient(X)&humble(X))=>(~tall(X)&~creative(X))))&
(((~tall(john)&patient(john)))<=>((~creative(john)&quiet(john))))&
(((patient(john)&~wise(john)))=>((~creative(alice)&~rich(alice))))&
((?[X]:((~creative(X)<~>creative(X))))<=>((~tall(john)<~>~curious(john))))&
(![X]:(~funny(X)=>(~quiet(X)<~>~funny(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:((brave(X)|~old(X))=>(happy(X)&~generous(X))))&
((?[X]:((~rich(X)&brave(X))))=>((~calm(fred)&strong(fred))))&
(((~happy(mary)|~old(mary)))<=>(?[X]:((tall(X)<~>~generous(X)))))&
(![X]:((brave(X)&curious(X))<=>(generous(X)<~>~calm(X))))&
(![X]:(curious(X)=>(wise(X)|~curious(X))))&
(![X]:(wise(X)=>(~rich(X)<~>~wise(X))))&
(~funny(mary))&
(?[X]:((happy(X)<~>brave(X))))&
(tall(susan))&
((brave(paul)|generous(paul)))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~wise(X)|~strong(X)))) | calm(mary) | [] | null | 0 |
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