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
|
|---|---|---|---|---|---|---|---|
Everyone who is not patient or not brave is generous.
If alice is kind then john is not humble or not patient and vice versa.
Everyone who is either calm or happy is brave.
If someone is not old then someone is both not kind and not strong and vice versa.
Everyone who is not funny is funny or not humble and vice versa.
If john is kind or not humble then paul is either funny or not rich and vice versa.
Everyone who is either wise or not calm is brave and vice versa.
Everyone who is happy or funny is strong or tall.
Everyone who is either not creative or generous is either not funny or not calm.
Everyone who is either strong or generous is either kind or not brave and vice versa.
Everyone who is not rich or creative is both not quiet and not generous.
Everyone who is either not creative or not humble is either funny or not rich and vice versa.
If lucy is rich then someone is both not creative and not kind.
Everyone who is happy is either kind or not kind and vice versa.
Everyone who is both not calm and not patient is generous or strong and vice versa.
If mary is generous then susan is not kind or happy and vice versa.
Someone is rich.
John is not patient.
Paul is curious.
Someone is happy.
Someone is not humble or not tall.
Someone is both not kind and not strong. | Alice is not patient. | entailment | (![X]:((~patient(X)|~brave(X))=>generous(X)))&
((kind(alice))<=>((~humble(john)|~patient(john))))&
(![X]:((calm(X)<~>happy(X))=>brave(X)))&
((?[X]:(~old(X)))<=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:(~funny(X)<=>(funny(X)|~humble(X))))&
(((kind(john)|~humble(john)))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)|funny(X))=>(strong(X)|tall(X))))&
(![X]:((~creative(X)<~>generous(X))=>(~funny(X)<~>~calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~rich(X)|creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~creative(X)<~>~humble(X))<=>(funny(X)<~>~rich(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:(happy(X)<=>(kind(X)<~>~kind(X))))&
(![X]:((~calm(X)&~patient(X))<=>(generous(X)|strong(X))))&
((generous(mary))<=>((~kind(susan)|happy(susan))))&
(?[X]:(rich(X)))&
(~patient(john))&
(curious(paul))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:((~kind(X)&~strong(X)))) | ~patient(alice) | [
"p0",
"p1",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 758898259755654642728530
% SZS output start Proof for 758898259755654642728530
1. ! [X0] : ((~brave(X0) | ~patient(X0)) => generous(X0)) [input p0]
2. kind(alice) <=> (~patient(john) | ~humble(john)) [input p1]
10. ! [X0] : ((strong(X0) <~> generous(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p9]
15. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> (strong(X0) | generous(X0))) [input p14]
18. ~patient(john) [input p17]
23. patient(alice) [input hypothesis]
27. ! [X0] : (generous(X0) | (brave(X0) & patient(X0))) [ennf transformation 1]
34. (kind(alice) | (patient(john) & humble(john))) & ((~patient(john) | ~humble(john)) | ~kind(alice)) [nnf transformation 2]
35. (kind(alice) | (patient(john) & humble(john))) & (~patient(john) | ~humble(john) | ~kind(alice)) [flattening 34]
48. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [nnf transformation 10]
53. ! [X0] : (((~patient(X0) & ~calm(X0)) | (~strong(X0) & ~generous(X0))) & ((strong(X0) | generous(X0)) | (patient(X0) | calm(X0)))) [nnf transformation 15]
54. ! [X0] : (((~patient(X0) & ~calm(X0)) | (~strong(X0) & ~generous(X0))) & (strong(X0) | generous(X0) | patient(X0) | calm(X0))) [flattening 53]
66. generous(X0) | brave(X0) [cnf transformation 27]
69. kind(alice) | patient(john) [cnf transformation 35]
98. generous(X0) | strong(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 48]
121. ~generous(X0) | ~patient(X0) [cnf transformation 54]
122. ~strong(X0) | ~patient(X0) [cnf transformation 54]
127. ~patient(john) [cnf transformation 18]
132. patient(alice) [cnf transformation 23]
138. 1 <=> patient(john) [avatar definition]
142. 2 <=> kind(alice) [avatar definition]
144. kind(alice) <- (2) [avatar component clause 142]
145. 1 | 2 [avatar split clause 69,142,138]
179. ~kind(X0) | strong(X0) | generous(X0) [subsumption resolution 98,66]
202. ~1 [avatar split clause 127,138]
236. strong(alice) | generous(alice) <- (2) [resolution 179,144]
238. 12 <=> generous(alice) [avatar definition]
240. generous(alice) <- (12) [avatar component clause 238]
242. 13 <=> strong(alice) [avatar definition]
244. strong(alice) <- (13) [avatar component clause 242]
245. 12 | 13 | ~2 [avatar split clause 236,142,242,238]
246. ~patient(alice) <- (12) [resolution 240,121]
248. $false <- (12) [subsumption resolution 246,132]
249. ~12 [avatar contradiction clause 248]
255. ~patient(alice) <- (13) [resolution 244,122]
257. $false <- (13) [subsumption resolution 255,132]
258. ~13 [avatar contradiction clause 257]
259. $false [avatar sat refutation 145,202,245,249,258]
% SZS output end Proof for 758898259755654642728530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or humble is not tall.
Everyone who is both not strong and not humble is old or rich and vice versa.
Everyone who is not wise is strong and vice versa.
Everyone who is old or calm is not brave and vice versa.
If someone is both rich and kind then someone is both tall and not happy.
Everyone who is not tall is both not strong and not tall and vice versa.
Everyone who is either creative or strong is either happy or not creative and vice versa.
If alice is strong then lucy is quiet or not kind and vice versa.
Everyone who is not patient is either creative or not generous and vice versa.
Everyone who is either not rich or calm is either not brave or wise and vice versa.
Everyone who is creative is rich.
Everyone who is calm is rich and vice versa.
If fred is quiet then alice is brave or old.
Everyone who is both generous and happy is either brave or tall and vice versa.
Everyone who is both not happy and curious is either not calm or happy and vice versa.
Someone is either humble or not wise.
Paul is not kind or patient.
Someone is quiet.
Someone is generous or not happy.
Paul is not curious.
Fred is either generous or strong.
Someone is both curious and not rich. | Alice is not humble. | contradiction | (![X]:((tall(X)|humble(X))=>~tall(X)))&
(![X]:((~strong(X)&~humble(X))<=>(old(X)|rich(X))))&
(![X]:(~wise(X)<=>strong(X)))&
(![X]:((old(X)|calm(X))<=>~brave(X)))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(~tall(X)<=>(~strong(X)&~tall(X))))&
(![X]:((creative(X)<~>strong(X))<=>(happy(X)<~>~creative(X))))&
((strong(alice))<=>((quiet(lucy)|~kind(lucy))))&
(![X]:(~patient(X)<=>(creative(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>calm(X))<=>(~brave(X)<~>wise(X))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(calm(X)<=>rich(X)))&
((quiet(fred))=>((brave(alice)|old(alice))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
(![X]:((~happy(X)&curious(X))<=>(~calm(X)<~>happy(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
((~kind(paul)|patient(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)|~happy(X))))&
(~curious(paul))&
((generous(fred)<~>strong(fred)))&
(?[X]:((curious(X)&~rich(X)))) | ~humble(alice) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p6",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6921305653612704870898830
% SZS output start Proof for 6921305653612704870898830
1. ! [X0] : ((humble(X0) | tall(X0)) => ~tall(X0)) [input p0]
2. ! [X0] : ((~humble(X0) & ~strong(X0)) <=> (rich(X0) | old(X0))) [input p1]
3. ! [X0] : (~wise(X0) <=> strong(X0)) [input p2]
4. ! [X0] : ((calm(X0) | old(X0)) <=> ~brave(X0)) [input p3]
6. ! [X0] : (~tall(X0) <=> (~tall(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((creative(X0) <~> strong(X0)) <=> (happy(X0) <~> ~creative(X0))) [input p6]
10. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> (~brave(X0) <~> wise(X0))) [input p9]
12. ! [X0] : (calm(X0) <=> rich(X0)) [input p11]
15. ! [X0] : ((curious(X0) & ~happy(X0)) <=> (~calm(X0) <~> happy(X0))) [input p14]
23. ~humble(alice) [input hypothesis]
26. ! [X0] : (~tall(X0) | (~humble(X0) & ~tall(X0))) [ennf transformation 1]
32. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (humble(X0) | strong(X0)))) [nnf transformation 2]
33. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | humble(X0) | strong(X0))) [flattening 32]
34. ! [X0] : ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0))) [nnf transformation 3]
35. ! [X0] : (((calm(X0) | old(X0)) | brave(X0)) & (~brave(X0) | (~calm(X0) & ~old(X0)))) [nnf transformation 4]
36. ! [X0] : ((calm(X0) | old(X0) | brave(X0)) & (~brave(X0) | (~calm(X0) & ~old(X0)))) [flattening 35]
40. ! [X0] : ((~tall(X0) | (tall(X0) | strong(X0))) & ((~tall(X0) & ~strong(X0)) | tall(X0))) [nnf transformation 6]
41. ! [X0] : ((~tall(X0) | tall(X0) | strong(X0)) & ((~tall(X0) & ~strong(X0)) | tall(X0))) [flattening 40]
42. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) & (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 10]
47. ! [X0] : ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0))) [nnf transformation 12]
50. ! [X0] : (((curious(X0) & ~happy(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~curious(X0) | happy(X0)))) [nnf transformation 15]
51. ! [X0] : (((curious(X0) & ~happy(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) & (((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | ~curious(X0) | happy(X0))) [flattening 50]
62. ~tall(X0) | ~tall(X0) [cnf transformation 26]
64. rich(X0) | old(X0) | humble(X0) | strong(X0) [cnf transformation 33]
69. wise(X0) | strong(X0) [cnf transformation 34]
71. ~brave(X0) | ~old(X0) [cnf transformation 36]
76. ~strong(X0) | tall(X0) [cnf transformation 41]
79. ~creative(X0) | happy(X0) | strong(X0) | ~creative(X0) [cnf transformation 42]
84. strong(X0) | creative(X0) | happy(X0) | creative(X0) [cnf transformation 42]
94. ~wise(X0) | brave(X0) | calm(X0) | rich(X0) [cnf transformation 46]
102. ~rich(X0) | calm(X0) [cnf transformation 47]
113. ~happy(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 51]
126. ~humble(alice) [cnf transformation 23]
128. ~happy(X0) | ~calm(X0) [duplicate literal removal 113]
129. ~creative(X0) | happy(X0) | strong(X0) [duplicate literal removal 79]
131. strong(X0) | creative(X0) | happy(X0) [duplicate literal removal 84]
133. ~tall(X0) [duplicate literal removal 62]
144. ~strong(X0) [subsumption resolution 76,133]
145. creative(X0) | happy(X0) [subsumption resolution 131,144]
146. ~creative(X0) | happy(X0) [subsumption resolution 129,144]
147. happy(X0) [subsumption resolution 146,145]
171. ~calm(X0) [subsumption resolution 128,147]
265. old(X0) | humble(X0) | strong(X0) | calm(X0) [resolution 64,102]
271. old(X0) | humble(X0) | calm(X0) [subsumption resolution 265,144]
272. old(X0) | humble(X0) [subsumption resolution 271,171]
274. brave(X0) | calm(X0) | rich(X0) | strong(X0) [resolution 94,69]
278. brave(X0) | rich(X0) | strong(X0) [subsumption resolution 274,171]
279. brave(X0) | rich(X0) [subsumption resolution 278,144]
293. ~old(X4) | rich(X4) [resolution 279,71]
306. rich(X0) | humble(X0) [resolution 293,272]
311. humble(X1) | calm(X1) [resolution 306,102]
319. humble(X1) [subsumption resolution 311,171]
320. $false [resolution 319,126]
% SZS output end Proof for 6921305653612704870898830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not happy and curious then paul is either calm or happy.
Everyone who is patient is not tall and vice versa.
Everyone who is both not brave and not happy is not patient and vice versa.
Everyone who is tall is both not strong and not curious and vice versa.
If fred is tall or happy then someone is both not creative and not quiet and vice versa.
Everyone who is not happy or not calm is generous or not calm and vice versa.
If someone is both not rich and rich then someone is both patient and tall.
Everyone who is either not rich or old is either wise or not quiet.
Everyone who is not humble or not curious is wise.
Everyone who is either not brave or not patient is tall and vice versa.
If someone is not generous then paul is not brave and vice versa.
If someone is either patient or strong then alice is both not old and not quiet.
If someone is not patient or generous then someone is rich.
If lucy is curious or creative then someone is not quiet.
Everyone who is kind is not tall or tall and vice versa.
If someone is both not creative and generous then someone is both not funny and quiet.
Paul is strong.
Someone is either quiet or kind.
Lucy is either not rich or not generous.
Someone is either not humble or strong.
Someone is either old or not strong.
Someone is either calm or not patient. | Alice is not generous. | contradiction | (((~happy(susan)&curious(susan)))=>((calm(paul)<~>happy(paul))))&
(![X]:(patient(X)<=>~tall(X)))&
(![X]:((~brave(X)&~happy(X))<=>~patient(X)))&
(![X]:(tall(X)<=>(~strong(X)&~curious(X))))&
(((tall(fred)|happy(fred)))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)|~calm(X))))&
((?[X]:((~rich(X)&rich(X))))=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((~rich(X)<~>old(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((~humble(X)|~curious(X))=>wise(X)))&
(![X]:((~brave(X)<~>~patient(X))<=>tall(X)))&
((?[X]:(~generous(X)))<=>(~brave(paul)))&
((?[X]:((patient(X)<~>strong(X))))=>((~old(alice)&~quiet(alice))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:(rich(X))))&
(((curious(lucy)|creative(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:(kind(X)<=>(~tall(X)|tall(X))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:((~funny(X)&quiet(X)))))&
(strong(paul))&
(?[X]:((quiet(X)<~>kind(X))))&
((~rich(lucy)<~>~generous(lucy)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:((old(X)<~>~strong(X))))&
(?[X]:((calm(X)<~>~patient(X)))) | ~generous(alice) | [
"p1",
"p3",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 94062352576844373614203
% SZS output start Proof for 94062352576844373614203
2. ! [X0] : (patient(X0) <=> ~tall(X0)) [input p1]
4. ! [X0] : (tall(X0) <=> (~curious(X0) & ~strong(X0))) [input p3]
10. ! [X0] : ((~brave(X0) <~> ~patient(X0)) <=> tall(X0)) [input p9]
11. ? [X0] : ~generous(X0) <=> ~brave(paul) [input p10]
17. strong(paul) [input p16]
23. ~generous(alice) [input hypothesis]
38. ! [X0] : ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))) [nnf transformation 2]
41. ! [X0] : ((tall(X0) | (curious(X0) | strong(X0))) & ((~curious(X0) & ~strong(X0)) | ~tall(X0))) [nnf transformation 4]
42. ! [X0] : ((tall(X0) | curious(X0) | strong(X0)) & ((~curious(X0) & ~strong(X0)) | ~tall(X0))) [flattening 41]
54. ! [X0] : ((((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | ~tall(X0)) & (tall(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0))))) [nnf transformation 10]
55. (? [X0] : ~generous(X0) | brave(paul)) & (~brave(paul) | ! [X0] : generous(X0)) [nnf transformation 11]
56. (? [X0] : ~generous(X0) | brave(paul)) & (~brave(paul) | ! [X1] : generous(X1)) [rectify 55]
57. ? [X0] : ~generous(X0) => ~generous(sK2) [choice axiom]
58. (~generous(sK2) | brave(paul)) & (~brave(paul) | ! [X1] : generous(X1)) [skolemisation 56,57]
85. ~tall(X0) | ~patient(X0) [cnf transformation 38]
86. tall(X0) | patient(X0) [cnf transformation 38]
90. ~strong(X0) | ~tall(X0) [cnf transformation 42]
110. tall(X0) | ~patient(X0) | brave(X0) [cnf transformation 54]
113. patient(X0) | brave(X0) | ~tall(X0) [cnf transformation 54]
114. ~brave(paul) | generous(X1) [cnf transformation 58]
128. strong(paul) [cnf transformation 17]
139. ~generous(alice) [cnf transformation 23]
182. ~tall(X0) | brave(X0) [subsumption resolution 113,85]
183. ~patient(X0) | brave(X0) [subsumption resolution 110,182]
185. 10 <=> brave(paul) [avatar definition]
186. ~brave(paul) <- (~10) [avatar component clause 185]
194. 12 <=> ! [X1] : generous(X1) [avatar definition]
195. generous(X1) <- (12) [avatar component clause 194]
196. 12 | ~10 [avatar split clause 114,185,194]
292. ~tall(paul) [resolution 90,128]
293. patient(paul) [resolution 292,86]
312. brave(paul) [resolution 183,293]
314. $false <- (~10) [subsumption resolution 312,186]
315. 10 [avatar contradiction clause 314]
316. $false <- (12) [resolution 195,139]
321. ~12 [avatar contradiction clause 316]
322. $false [avatar sat refutation 196,315,321]
% SZS output end Proof for 94062352576844373614203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and funny is not strong or not creative and vice versa.
If fred is not rich or wise then someone is not strong or rich and vice versa.
If paul is both not curious and not strong then susan is both curious and not humble and vice versa.
If fred is rich or tall then someone is either humble or kind.
If someone is happy then alice is both not wise and not funny and vice versa.
If paul is not happy or not patient then john is not wise.
If susan is not kind or not tall then mary is brave and vice versa.
Everyone who is either not old or happy is not kind and vice versa.
If someone is either not wise or generous then someone is not patient.
Everyone who is tall is not rich and vice versa.
Everyone who is humble is not wise or not creative and vice versa.
Everyone who is both not wise and strong is either tall or happy and vice versa.
Everyone who is either not tall or rich is not brave or not creative.
Everyone who is either not old or not patient is both old and patient and vice versa.
Everyone who is happy is not patient and vice versa.
If paul is either generous or not happy then alice is both not patient and not brave.
Someone is either brave or humble.
John is either not brave or not quiet.
Lucy is humble or not quiet.
Someone is quiet.
John is not tall.
Fred is either not curious or kind. | Fred is tall. | entailment | (![X]:((patient(X)&funny(X))<=>(~strong(X)|~creative(X))))&
(((~rich(fred)|wise(fred)))<=>(?[X]:((~strong(X)|rich(X)))))&
(((~curious(paul)&~strong(paul)))<=>((curious(susan)&~humble(susan))))&
(((rich(fred)|tall(fred)))=>(?[X]:((humble(X)<~>kind(X)))))&
((?[X]:(happy(X)))<=>((~wise(alice)&~funny(alice))))&
(((~happy(paul)|~patient(paul)))=>(~wise(john)))&
(((~kind(susan)|~tall(susan)))<=>(brave(mary)))&
(![X]:((~old(X)<~>happy(X))<=>~kind(X)))&
((?[X]:((~wise(X)<~>generous(X))))=>(?[X]:(~patient(X))))&
(![X]:(tall(X)<=>~rich(X)))&
(![X]:(humble(X)<=>(~wise(X)|~creative(X))))&
(![X]:((~wise(X)&strong(X))<=>(tall(X)<~>happy(X))))&
(![X]:((~tall(X)<~>rich(X))=>(~brave(X)|~creative(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(old(X)&patient(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(((generous(paul)<~>~happy(paul)))=>((~patient(alice)&~brave(alice))))&
(?[X]:((brave(X)<~>humble(X))))&
((~brave(john)<~>~quiet(john)))&
((humble(lucy)|~quiet(lucy)))&
(?[X]:(quiet(X)))&
(~tall(john))&
((~curious(fred)<~>kind(fred))) | tall(fred) | [
"p1",
"p9",
"p11",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4899787164814687271224439
% SZS output start Proof for 4899787164814687271224439
2. (wise(fred) | ~rich(fred)) <=> ? [X0] : (rich(X0) | ~strong(X0)) [input p1]
10. ! [X0] : (tall(X0) <=> ~rich(X0)) [input p9]
12. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (tall(X0) <~> happy(X0))) [input p11]
14. ! [X0] : ((~old(X0) <~> ~patient(X0)) <=> (patient(X0) & old(X0))) [input p13]
15. ! [X0] : (happy(X0) <=> ~patient(X0)) [input p14]
21. ~tall(john) [input p20]
23. ~tall(fred) [input hypothesis]
33. ((wise(fred) | ~rich(fred)) | ! [X0] : (~rich(X0) & strong(X0))) & (? [X0] : (rich(X0) | ~strong(X0)) | (~wise(fred) & rich(fred))) [nnf transformation 2]
34. (wise(fred) | ~rich(fred) | ! [X0] : (~rich(X0) & strong(X0))) & (? [X0] : (rich(X0) | ~strong(X0)) | (~wise(fred) & rich(fred))) [flattening 33]
35. (wise(fred) | ~rich(fred) | ! [X0] : (~rich(X0) & strong(X0))) & (? [X1] : (rich(X1) | ~strong(X1)) | (~wise(fred) & rich(fred))) [rectify 34]
36. ? [X1] : (rich(X1) | ~strong(X1)) => (rich(sK0) | ~strong(sK0)) [choice axiom]
37. (wise(fred) | ~rich(fred) | ! [X0] : (~rich(X0) & strong(X0))) & ((rich(sK0) | ~strong(sK0)) | (~wise(fred) & rich(fred))) [skolemisation 35,36]
55. ! [X0] : ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0))) [nnf transformation 10]
58. ! [X0] : (((strong(X0) & ~wise(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) & (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | (~strong(X0) | wise(X0)))) [nnf transformation 12]
59. ! [X0] : (((strong(X0) & ~wise(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0)))) & (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | ~strong(X0) | wise(X0))) [flattening 58]
61. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [nnf transformation 14]
62. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [flattening 61]
63. ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))) [nnf transformation 15]
80. wise(fred) | ~rich(fred) | ~rich(X0) [cnf transformation 37]
104. tall(X0) | rich(X0) [cnf transformation 55]
111. ~happy(X0) | tall(X0) | ~wise(X0) [cnf transformation 59]
116. old(X0) | ~patient(X0) | old(X0) [cnf transformation 62]
119. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 62]
120. ~patient(X0) | ~old(X0) | ~patient(X0) | ~old(X0) [cnf transformation 62]
123. happy(X0) | patient(X0) [cnf transformation 63]
134. ~tall(john) [cnf transformation 21]
137. ~tall(fred) [cnf transformation 23]
138. old(X0) | ~patient(X0) [duplicate literal removal 116]
139. patient(X0) | ~old(X0) [duplicate literal removal 119]
140. ~old(X0) | ~patient(X0) [duplicate literal removal 120]
142. 1 <=> ! [X0] : ~rich(X0) [avatar definition]
143. ~rich(X0) <- (1) [avatar component clause 142]
145. 2 <=> rich(fred) [avatar definition]
149. 3 <=> wise(fred) [avatar definition]
151. wise(fred) <- (3) [avatar component clause 149]
152. 1 | ~2 | 3 [avatar split clause 80,149,145,142]
188. 11 <=> tall(fred) [avatar definition]
190. ~tall(fred) <- (~11) [avatar component clause 188]
262. ~old(X0) [subsumption resolution 139,140]
263. ~patient(X0) [subsumption resolution 138,262]
264. happy(X0) [subsumption resolution 123,263]
314. ~11 [avatar split clause 137,188]
322. rich(fred) <- (~11) [resolution 104,190]
324. rich(john) [resolution 104,134]
327. 2 | 11 [avatar split clause 322,188,145]
344. ~wise(X0) | tall(X0) [resolution 111,264]
345. tall(fred) <- (3) [resolution 344,151]
349. $false <- (3, ~11) [subsumption resolution 345,190]
350. ~3 | 11 [avatar contradiction clause 349]
355. $false <- (1) [resolution 143,324]
358. ~1 [avatar contradiction clause 355]
361. $false [avatar sat refutation 152,314,327,350,358]
% SZS output end Proof for 4899787164814687271224439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and patient is old or brave and vice versa.
If fred is not curious or creative then mary is both brave and not wise and vice versa.
If someone is either creative or calm then someone is both humble and calm.
Everyone who is creative or not tall is not funny or not brave.
If someone is strong or funny then someone is either wise or not funny and vice versa.
Everyone who is both not humble and not curious is not wise.
If someone is not calm then mary is both not happy and not strong.
Everyone who is either not rich or generous is curious.
If mary is patient then susan is not patient and vice versa.
If lucy is either strong or curious then lucy is both not old and happy.
If someone is not wise then someone is not humble or patient and vice versa.
Everyone who is not wise is not quiet or kind.
Everyone who is either not tall or brave is both creative and not calm.
Everyone who is either not calm or not humble is not kind or kind and vice versa.
Everyone who is either rich or brave is not kind or not happy and vice versa.
Everyone who is quiet or not funny is not curious and vice versa.
Someone is either not brave or quiet.
Someone is both not funny and strong.
Lucy is both not generous and curious.
Fred is wise or not rich.
Fred is both rich and not curious.
Paul is humble or not quiet.
Someone is not patient or funny.
John is both quiet and strong. | Susan is tall. | entailment | (![X]:((~old(X)&patient(X))<=>(old(X)|brave(X))))&
(((~curious(fred)|creative(fred)))<=>((brave(mary)&~wise(mary))))&
((?[X]:((creative(X)<~>calm(X))))=>(?[X]:((humble(X)&calm(X)))))&
(![X]:((creative(X)|~tall(X))=>(~funny(X)|~brave(X))))&
((?[X]:((strong(X)|funny(X))))<=>(?[X]:((wise(X)<~>~funny(X)))))&
(![X]:((~humble(X)&~curious(X))=>~wise(X)))&
((?[X]:(~calm(X)))=>((~happy(mary)&~strong(mary))))&
(![X]:((~rich(X)<~>generous(X))=>curious(X)))&
((patient(mary))<=>(~patient(susan)))&
(((strong(lucy)<~>curious(lucy)))=>((~old(lucy)&happy(lucy))))&
((?[X]:(~wise(X)))<=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:(~wise(X)=>(~quiet(X)|kind(X))))&
(![X]:((~tall(X)<~>brave(X))=>(creative(X)&~calm(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>(~kind(X)|kind(X))))&
(![X]:((rich(X)<~>brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((quiet(X)|~funny(X))<=>~curious(X)))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~funny(X)&strong(X))))&
((~generous(lucy)&curious(lucy)))&
((wise(fred)|~rich(fred)))&
((rich(fred)&~curious(fred)))&
((humble(paul)|~quiet(paul)))&
(?[X]:((~patient(X)|funny(X))))&
((quiet(john)&strong(john))) | tall(susan) | [
"p0",
"p1",
"p2",
"p8",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7331466874939533917969087
% SZS output start Proof for 7331466874939533917969087
1. ! [X0] : ((patient(X0) & ~old(X0)) <=> (brave(X0) | old(X0))) [input p0]
2. (creative(fred) | ~curious(fred)) <=> (~wise(mary) & brave(mary)) [input p1]
3. ? [X0] : (creative(X0) <~> calm(X0)) => ? [X0] : (calm(X0) & humble(X0)) [input p2]
9. patient(mary) <=> ~patient(susan) [input p8]
13. ! [X0] : ((~tall(X0) <~> brave(X0)) => (~calm(X0) & creative(X0))) [input p12]
14. ! [X0] : ((~calm(X0) <~> ~humble(X0)) <=> (kind(X0) | ~kind(X0))) [input p13]
21. ~curious(fred) & rich(fred) [input p20]
25. ~tall(susan) [input hypothesis]
26. ? [X0] : (creative(X0) <~> calm(X0)) => ? [X1] : (calm(X1) & humble(X1)) [rectify 3]
29. ? [X1] : (calm(X1) & humble(X1)) | ! [X0] : (creative(X0) <=> calm(X0)) [ennf transformation 26]
39. ! [X0] : ((~calm(X0) & creative(X0)) | (~tall(X0) <=> brave(X0))) [ennf transformation 13]
40. ! [X0] : (((patient(X0) & ~old(X0)) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | (~patient(X0) | old(X0)))) [nnf transformation 1]
41. ! [X0] : (((patient(X0) & ~old(X0)) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | ~patient(X0) | old(X0))) [flattening 40]
42. ((creative(fred) | ~curious(fred)) | (wise(mary) | ~brave(mary))) & ((~wise(mary) & brave(mary)) | (~creative(fred) & curious(fred))) [nnf transformation 2]
43. (creative(fred) | ~curious(fred) | wise(mary) | ~brave(mary)) & ((~wise(mary) & brave(mary)) | (~creative(fred) & curious(fred))) [flattening 42]
44. ? [X1] : (calm(X1) & humble(X1)) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))) [nnf transformation 29]
45. ? [X0] : (calm(X0) & humble(X0)) | ! [X1] : ((creative(X1) | ~calm(X1)) & (calm(X1) | ~creative(X1))) [rectify 44]
46. ? [X0] : (calm(X0) & humble(X0)) => (calm(sK0) & humble(sK0)) [choice axiom]
47. (calm(sK0) & humble(sK0)) | ! [X1] : ((creative(X1) | ~calm(X1)) & (calm(X1) | ~creative(X1))) [skolemisation 45,46]
54. (patient(mary) | patient(susan)) & (~patient(susan) | ~patient(mary)) [nnf transformation 9]
61. ! [X0] : ((~calm(X0) & creative(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) [nnf transformation 39]
62. ! [X0] : ((((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))))) [nnf transformation 14]
63. ! [X0] : ((((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))))) [flattening 62]
79. ~brave(X0) | patient(X0) [cnf transformation 41]
80. brave(mary) | curious(fred) [cnf transformation 43]
85. humble(sK0) | calm(X1) | ~creative(X1) [cnf transformation 47]
87. calm(sK0) | calm(X1) | ~creative(X1) [cnf transformation 47]
102. ~patient(susan) | ~patient(mary) [cnf transformation 54]
112. tall(X0) | brave(X0) | creative(X0) [cnf transformation 61]
114. ~calm(X0) | brave(X0) | tall(X0) [cnf transformation 61]
118. ~humble(X0) | ~calm(X0) | kind(X0) [cnf transformation 63]
119. ~kind(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 63]
139. ~curious(fred) [cnf transformation 21]
144. ~tall(susan) [cnf transformation 25]
149. 1 <=> brave(mary) [avatar definition]
150. brave(mary) <- (1) [avatar component clause 149]
157. 3 <=> curious(fred) [avatar definition]
168. 3 | 1 [avatar split clause 80,149,157]
173. 6 <=> calm(sK0) [avatar definition]
175. calm(sK0) <- (6) [avatar component clause 173]
178. 7 <=> ! [X1] : (calm(X1) | ~creative(X1)) [avatar definition]
179. ~creative(X1) | calm(X1) <- (7) [avatar component clause 178]
180. 7 | 6 [avatar split clause 87,173,178]
182. 8 <=> humble(sK0) [avatar definition]
184. humble(sK0) <- (8) [avatar component clause 182]
186. 7 | 8 [avatar split clause 85,182,178]
235. 20 <=> patient(susan) [avatar definition]
236. ~patient(susan) <- (~20) [avatar component clause 235]
239. 21 <=> patient(mary) [avatar definition]
243. ~21 | ~20 [avatar split clause 102,235,239]
283. ~humble(X0) | ~calm(X0) [subsumption resolution 118,119]
304. ~3 [avatar split clause 139,157]
325. patient(mary) <- (1) [resolution 79,150]
328. 21 | ~1 [avatar split clause 325,149,239]
368. brave(susan) | creative(susan) [resolution 112,144]
370. 44 <=> creative(susan) [avatar definition]
372. creative(susan) <- (44) [avatar component clause 370]
374. 45 <=> brave(susan) [avatar definition]
376. brave(susan) <- (45) [avatar component clause 374]
377. 44 | 45 [avatar split clause 368,374,370]
382. calm(susan) <- (7, 44) [resolution 372,179]
408. brave(susan) | tall(susan) <- (7, 44) [resolution 382,114]
410. brave(susan) <- (7, 44) [subsumption resolution 408,144]
411. 45 | ~7 | ~44 [avatar split clause 410,370,178,374]
414. patient(susan) <- (45) [resolution 376,79]
416. $false <- (~20, 45) [subsumption resolution 414,236]
417. 20 | ~45 [avatar contradiction clause 416]
429. ~calm(sK0) <- (8) [resolution 184,283]
430. $false <- (6, 8) [subsumption resolution 429,175]
431. ~6 | ~8 [avatar contradiction clause 430]
432. $false [avatar sat refutation 168,180,186,243,304,328,377,411,417,431]
% SZS output end Proof for 7331466874939533917969087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not wise. Everyone who is both strong and not creative is not humble. Everyone who is both curious and not funny is curious. Everyone who is either not patient or wise is both not rich and humble. If someone is not rich then someone is both curious and old. Everyone who is both not old and funny is not strong or patient. If lucy is curious or not creative then john is both not calm and not curious and vice versa. If someone is wise then someone is curious or not humble and vice versa. Everyone who is tall or calm is either not humble or funny. Everyone who is either strong or kind is both not generous and not kind. Everyone who is humble or not calm is either not curious or not strong. Everyone who is both not creative and not kind is either tall or happy and vice versa. If fred is both not wise and wise then mary is either wise or not strong and vice versa. Everyone who is wise or old is either rich or tall. Everyone who is patient or old is not patient and vice versa. If someone is both rich and not old then susan is brave and vice versa. Someone is both funny and not creative. Someone is either not wise or not humble. Alice is not generous. Someone is not tall. Fred is not kind. Fred is both not curious and not kind. Someone is not calm. | Mary is not curious. | entailment | (![X]:(~strong(X)=>~wise(X)))&
(![X]:((strong(X)&~creative(X))=>~humble(X)))&
(![X]:((curious(X)&~funny(X))=>curious(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~rich(X)&humble(X))))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~old(X)&funny(X))=>(~strong(X)|patient(X))))&
(((curious(lucy)|~creative(lucy)))<=>((~calm(john)&~curious(john))))&
((?[X]:(wise(X)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((tall(X)|calm(X))=>(~humble(X)<~>funny(X))))&
(![X]:((strong(X)<~>kind(X))=>(~generous(X)&~kind(X))))&
(![X]:((humble(X)|~calm(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((~creative(X)&~kind(X))<=>(tall(X)<~>happy(X))))&
(((~wise(fred)&wise(fred)))<=>((wise(mary)<~>~strong(mary))))&
(![X]:((wise(X)|old(X))=>(rich(X)<~>tall(X))))&
(![X]:((patient(X)|old(X))<=>~patient(X)))&
((?[X]:((rich(X)&~old(X))))<=>(brave(susan)))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
(~generous(alice))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~curious(fred)&~kind(fred)))&
(?[X]:(~calm(X))) | ~curious(mary) | [
"p0",
"p3",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4440317749373806524215671
% SZS output start Proof for 4440317749373806524215671
1. ! [X0] : (~strong(X0) => ~wise(X0)) [input p0]
4. ! [X0] : ((~patient(X0) <~> wise(X0)) => (humble(X0) & ~rich(X0))) [input p3]
11. ! [X0] : ((~calm(X0) | humble(X0)) => (~curious(X0) <~> ~strong(X0))) [input p10]
13. (wise(fred) & ~wise(fred)) <=> (wise(mary) <~> ~strong(mary)) [input p12]
15. ! [X0] : ((old(X0) | patient(X0)) <=> ~patient(X0)) [input p14]
24. curious(mary) [input hypothesis]
29. ! [X0] : (~wise(X0) | strong(X0)) [ennf transformation 1]
34. ! [X0] : ((humble(X0) & ~rich(X0)) | (~patient(X0) <=> wise(X0))) [ennf transformation 4]
40. ! [X0] : ((~curious(X0) <~> ~strong(X0)) | (calm(X0) & ~humble(X0))) [ennf transformation 11]
42. ! [X0] : ((humble(X0) & ~rich(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 34]
55. ! [X0] : (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | (calm(X0) & ~humble(X0))) [nnf transformation 40]
58. ((wise(fred) & ~wise(fred)) | ((wise(mary) | strong(mary)) & (~strong(mary) | ~wise(mary)))) & (((strong(mary) | ~wise(mary)) & (~strong(mary) | wise(mary))) | (~wise(fred) | wise(fred))) [nnf transformation 13]
59. ((wise(fred) & ~wise(fred)) | ((wise(mary) | strong(mary)) & (~strong(mary) | ~wise(mary)))) & (((strong(mary) | ~wise(mary)) & (~strong(mary) | wise(mary))) | ~wise(fred) | wise(fred)) [flattening 58]
61. ! [X0] : (((old(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [nnf transformation 15]
62. ! [X0] : ((old(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [flattening 61]
76. ~wise(X0) | strong(X0) [cnf transformation 29]
81. patient(X0) | wise(X0) | humble(X0) [cnf transformation 42]
100. ~curious(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 55]
112. ~wise(fred) | ~strong(mary) | ~wise(mary) [cnf transformation 59]
113. ~wise(fred) | wise(mary) | strong(mary) [cnf transformation 59]
114. wise(fred) | ~strong(mary) | ~wise(mary) [cnf transformation 59]
115. wise(fred) | wise(mary) | strong(mary) [cnf transformation 59]
120. ~patient(X0) | ~patient(X0) [cnf transformation 62]
135. curious(mary) [cnf transformation 24]
136. ~patient(X0) [duplicate literal removal 120]
197. wise(fred) | strong(mary) [subsumption resolution 115,76]
199. 14 <=> strong(mary) [avatar definition]
201. strong(mary) <- (14) [avatar component clause 199]
203. 15 <=> wise(fred) [avatar definition]
206. 14 | 15 [avatar split clause 197,203,199]
207. wise(fred) | ~wise(mary) [subsumption resolution 114,76]
209. 16 <=> wise(mary) [avatar definition]
211. ~wise(mary) <- (~16) [avatar component clause 209]
212. ~16 | 15 [avatar split clause 207,203,209]
213. ~wise(fred) | strong(mary) [subsumption resolution 113,76]
214. 14 | ~15 [avatar split clause 213,203,199]
215. ~wise(fred) | ~wise(mary) [subsumption resolution 112,76]
216. ~16 | ~15 [avatar split clause 215,203,209]
258. humble(X0) | wise(X0) [resolution 81,136]
265. ~strong(mary) | ~humble(mary) [resolution 100,135]
267. ~humble(mary) <- (14) [subsumption resolution 265,201]
277. wise(mary) <- (14) [resolution 267,258]
278. $false <- (14, ~16) [subsumption resolution 277,211]
279. ~14 | 16 [avatar contradiction clause 278]
280. $false [avatar sat refutation 206,212,214,216,279]
% SZS output end Proof for 4440317749373806524215671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not humble is both not creative and old.
Everyone who is either strong or quiet is tall.
Everyone who is either not humble or not quiet is either tall or not patient.
Everyone who is not rich or tall is both not funny and not creative.
Everyone who is patient or not tall is not humble or rich.
Everyone who is not calm is tall or generous.
Everyone who is both not generous and kind is quiet.
If fred is not creative or funny then paul is humble and vice versa.
Everyone who is either creative or rich is brave or kind and vice versa.
Everyone who is both curious and rich is patient or not tall.
If someone is humble then paul is curious or not brave and vice versa.
If john is strong or generous then someone is both not brave and happy.
Everyone who is wise is both not kind and humble and vice versa.
Everyone who is not humble or happy is either not kind or not happy.
Everyone who is quiet is either patient or not wise and vice versa.
Everyone who is not funny is creative or quiet and vice versa.
Someone is not quiet.
Someone is both not calm and old.
Someone is not humble or kind.
Someone is funny.
Someone is both happy and not creative.
Someone is either happy or creative.
Alice is not calm or brave.
Fred is either not happy or brave. | Alice is strong. | neutral | (![X]:((calm(X)&~humble(X))=>(~creative(X)&old(X))))&
(![X]:((strong(X)<~>quiet(X))=>tall(X)))&
(![X]:((~humble(X)<~>~quiet(X))=>(tall(X)<~>~patient(X))))&
(![X]:((~rich(X)|tall(X))=>(~funny(X)&~creative(X))))&
(![X]:((patient(X)|~tall(X))=>(~humble(X)|rich(X))))&
(![X]:(~calm(X)=>(tall(X)|generous(X))))&
(![X]:((~generous(X)&kind(X))=>quiet(X)))&
(((~creative(fred)|funny(fred)))<=>(humble(paul)))&
(![X]:((creative(X)<~>rich(X))<=>(brave(X)|kind(X))))&
(![X]:((curious(X)&rich(X))=>(patient(X)|~tall(X))))&
((?[X]:(humble(X)))<=>((curious(paul)|~brave(paul))))&
(((strong(john)|generous(john)))=>(?[X]:((~brave(X)&happy(X)))))&
(![X]:(wise(X)<=>(~kind(X)&humble(X))))&
(![X]:((~humble(X)|happy(X))=>(~kind(X)<~>~happy(X))))&
(![X]:(quiet(X)<=>(patient(X)<~>~wise(X))))&
(![X]:(~funny(X)<=>(creative(X)|quiet(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(funny(X)))&
(?[X]:((happy(X)&~creative(X))))&
(?[X]:((happy(X)<~>creative(X))))&
((~calm(alice)|brave(alice)))&
((~happy(fred)<~>brave(fred))) | strong(alice) | [] | null | 0 |
Everyone who is wise is either not strong or tall and vice versa.
If mary is not funny or calm then lucy is humble or wise and vice versa.
Everyone who is quiet is generous or not quiet and vice versa.
If someone is not creative or not curious then fred is either not rich or brave and vice versa.
Everyone who is old is not generous or kind and vice versa.
If someone is either funny or rich then lucy is not humble and vice versa.
If someone is both not tall and not brave then alice is both happy and wise and vice versa.
If someone is not creative then susan is curious and vice versa.
Everyone who is not tall is not happy.
Everyone who is both generous and old is either curious or not quiet and vice versa.
Everyone who is both not wise and not kind is either patient or not curious and vice versa.
Everyone who is either strong or not creative is either funny or old.
If someone is either not wise or creative then someone is not tall or strong and vice versa.
Everyone who is both curious and not calm is not calm or strong and vice versa.
If someone is either brave or not strong then someone is old or happy.
If someone is brave or not calm then mary is both brave and not strong.
Someone is generous.
Someone is either not humble or not happy.
Fred is either not funny or tall.
Someone is either curious or rich.
Lucy is tall.
Alice is either happy or not rich.
Someone is wise or not rich.
Someone is both not happy and curious. | Lucy is patient. | contradiction | (![X]:(wise(X)<=>(~strong(X)<~>tall(X))))&
(((~funny(mary)|calm(mary)))<=>((humble(lucy)|wise(lucy))))&
(![X]:(quiet(X)<=>(generous(X)|~quiet(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>((~rich(fred)<~>brave(fred))))&
(![X]:(old(X)<=>(~generous(X)|kind(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>(~humble(lucy)))&
((?[X]:((~tall(X)&~brave(X))))<=>((happy(alice)&wise(alice))))&
((?[X]:(~creative(X)))<=>(curious(susan)))&
(![X]:(~tall(X)=>~happy(X)))&
(![X]:((generous(X)&old(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((~wise(X)&~kind(X))<=>(patient(X)<~>~curious(X))))&
(![X]:((strong(X)<~>~creative(X))=>(funny(X)<~>old(X))))&
((?[X]:((~wise(X)<~>creative(X))))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((curious(X)&~calm(X))<=>(~calm(X)|strong(X))))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((old(X)|happy(X)))))&
((?[X]:((brave(X)|~calm(X))))=>((brave(mary)&~strong(mary))))&
(?[X]:(generous(X)))&
(?[X]:((~humble(X)<~>~happy(X))))&
((~funny(fred)<~>tall(fred)))&
(?[X]:((curious(X)<~>rich(X))))&
(tall(lucy))&
((happy(alice)<~>~rich(alice)))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((~happy(X)&curious(X)))) | patient(lucy) | [
"p0",
"p2",
"p4",
"p9",
"p10",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1449778181218837327738387
% SZS output start Proof for 1449778181218837327738387
1. ! [X0] : (wise(X0) <=> (~strong(X0) <~> tall(X0))) [input p0]
3. ! [X0] : (quiet(X0) <=> (~quiet(X0) | generous(X0))) [input p2]
5. ! [X0] : (old(X0) <=> (kind(X0) | ~generous(X0))) [input p4]
10. ! [X0] : ((old(X0) & generous(X0)) <=> (curious(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> (patient(X0) <~> ~curious(X0))) [input p10]
14. ! [X0] : ((~calm(X0) & curious(X0)) <=> (strong(X0) | ~calm(X0))) [input p13]
21. tall(lucy) [input p20]
25. patient(lucy) [input hypothesis]
32. ! [X0] : ((wise(X0) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | ~wise(X0))) [nnf transformation 1]
35. ! [X0] : ((quiet(X0) | (quiet(X0) & ~generous(X0))) & ((~quiet(X0) | generous(X0)) | ~quiet(X0))) [nnf transformation 3]
36. ! [X0] : ((quiet(X0) | (quiet(X0) & ~generous(X0))) & (~quiet(X0) | generous(X0) | ~quiet(X0))) [flattening 35]
41. ! [X0] : ((old(X0) | (~kind(X0) & generous(X0))) & ((kind(X0) | ~generous(X0)) | ~old(X0))) [nnf transformation 5]
42. ! [X0] : ((old(X0) | (~kind(X0) & generous(X0))) & (kind(X0) | ~generous(X0) | ~old(X0))) [flattening 41]
56. ! [X0] : (((old(X0) & generous(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (~old(X0) | ~generous(X0)))) [nnf transformation 10]
57. ! [X0] : (((old(X0) & generous(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | ~old(X0) | ~generous(X0))) [flattening 56]
58. ! [X0] : (((~kind(X0) & ~wise(X0)) | ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (((curious(X0) | ~patient(X0)) & (~curious(X0) | patient(X0))) | (kind(X0) | wise(X0)))) [nnf transformation 11]
59. ! [X0] : (((~kind(X0) & ~wise(X0)) | ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (((curious(X0) | ~patient(X0)) & (~curious(X0) | patient(X0))) | kind(X0) | wise(X0))) [flattening 58]
66. ! [X0] : (((~calm(X0) & curious(X0)) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | (calm(X0) | ~curious(X0)))) [nnf transformation 14]
67. ! [X0] : (((~calm(X0) & curious(X0)) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | calm(X0) | ~curious(X0))) [flattening 66]
87. ~tall(X0) | strong(X0) | ~wise(X0) [cnf transformation 32]
94. ~quiet(X0) | generous(X0) | ~quiet(X0) [cnf transformation 36]
96. quiet(X0) | quiet(X0) [cnf transformation 36]
103. kind(X0) | ~generous(X0) | ~old(X0) [cnf transformation 42]
105. ~kind(X0) | old(X0) [cnf transformation 42]
117. ~quiet(X0) | curious(X0) | ~old(X0) | ~generous(X0) [cnf transformation 57]
121. old(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 57]
124. ~patient(X0) | curious(X0) | kind(X0) | wise(X0) [cnf transformation 59]
127. ~patient(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 59]
141. ~strong(X0) | curious(X0) [cnf transformation 67]
157. tall(lucy) [cnf transformation 21]
163. patient(lucy) [cnf transformation 25]
164. ~quiet(X0) | generous(X0) [duplicate literal removal 94]
165. quiet(X0) [duplicate literal removal 96]
167. 1 <=> wise(lucy) [avatar definition]
168. wise(lucy) <- (1) [avatar component clause 167]
186. generous(X0) [subsumption resolution 164,165]
215. ~old(X0) | kind(X0) [subsumption resolution 103,186]
267. ~curious(X0) | old(X0) [subsumption resolution 121,165]
268. curious(X0) | ~old(X0) | ~generous(X0) [subsumption resolution 117,165]
269. ~old(X0) | curious(X0) [subsumption resolution 268,186]
430. strong(lucy) | ~wise(lucy) [resolution 87,157]
474. ~curious(lucy) | ~kind(lucy) [resolution 127,163]
476. 53 <=> kind(lucy) [avatar definition]
477. kind(lucy) <- (53) [avatar component clause 476]
478. ~kind(lucy) <- (~53) [avatar component clause 476]
480. 54 <=> curious(lucy) [avatar definition]
481. curious(lucy) <- (54) [avatar component clause 480]
482. ~curious(lucy) <- (~54) [avatar component clause 480]
483. ~53 | ~54 [avatar split clause 474,480,476]
496. curious(lucy) | kind(lucy) | wise(lucy) [resolution 124,163]
503. old(lucy) <- (53) [resolution 477,105]
619. curious(lucy) <- (53) [resolution 503,269]
624. $false <- (53, ~54) [subsumption resolution 619,482]
625. ~53 | 54 [avatar contradiction clause 624]
628. old(lucy) <- (54) [resolution 481,267]
638. kind(lucy) <- (54) [resolution 628,215]
642. $false <- (~53, 54) [subsumption resolution 638,478]
643. 53 | ~54 [avatar contradiction clause 642]
644. curious(lucy) | wise(lucy) <- (~53) [subsumption resolution 496,478]
645. 1 | 54 | 53 [avatar split clause 644,476,480,167]
649. strong(lucy) <- (1) [subsumption resolution 430,168]
685. curious(lucy) <- (1) [resolution 649,141]
686. $false <- (1, ~54) [subsumption resolution 685,482]
687. ~1 | 54 [avatar contradiction clause 686]
688. $false [avatar sat refutation 483,625,643,645,687]
% SZS output end Proof for 1449778181218837327738387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or kind is either not generous or quiet.
If alice is not happy then someone is either curious or not brave and vice versa.
If someone is both old and not kind then someone is not curious or generous and vice versa.
If someone is either creative or quiet then someone is not old and vice versa.
Everyone who is not wise is quiet or not creative and vice versa.
Everyone who is not patient is either not calm or not quiet.
Everyone who is either not rich or brave is both kind and rich and vice versa.
Everyone who is wise is either wise or not wise and vice versa.
Everyone who is curious is not curious or not happy and vice versa.
Everyone who is both not generous and calm is both strong and not happy and vice versa.
Everyone who is either not kind or generous is either happy or not funny and vice versa.
Everyone who is tall or not old is not funny or not creative and vice versa.
If fred is not patient or quiet then someone is not brave.
Everyone who is either tall or not happy is quiet or not humble and vice versa.
If susan is either funny or not wise then someone is either not funny or not calm.
Everyone who is not happy is humble and vice versa.
Fred is not old or happy.
Susan is not kind.
Alice is patient or old.
Someone is not brave.
Someone is not calm.
Someone is either not creative or not kind.
Fred is either strong or old.
Someone is brave or not wise. | Alice is funny. | contradiction | (![X]:((~patient(X)<~>kind(X))=>(~generous(X)<~>quiet(X))))&
((~happy(alice))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((old(X)&~kind(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&rich(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(~curious(X)|~happy(X))))&
(![X]:((~generous(X)&calm(X))<=>(strong(X)&~happy(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((tall(X)|~old(X))<=>(~funny(X)|~creative(X))))&
(((~patient(fred)|quiet(fred)))=>(?[X]:(~brave(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(quiet(X)|~humble(X))))&
(((funny(susan)<~>~wise(susan)))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(![X]:(~happy(X)<=>humble(X)))&
((~old(fred)|happy(fred)))&
(~kind(susan))&
((patient(alice)|old(alice)))&
(?[X]:(~brave(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~creative(X)<~>~kind(X))))&
((strong(fred)<~>old(fred)))&
(?[X]:((brave(X)|~wise(X)))) | funny(alice) | [
"p4",
"p7",
"p8",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 111667087516487251147261
% SZS output start Proof for 111667087516487251147261
5. ! [X0] : (~wise(X0) <=> (~creative(X0) | quiet(X0))) [input p4]
8. ! [X0] : (wise(X0) <=> (wise(X0) <~> ~wise(X0))) [input p7]
9. ! [X0] : (curious(X0) <=> (~happy(X0) | ~curious(X0))) [input p8]
12. ! [X0] : ((~old(X0) | tall(X0)) <=> (~creative(X0) | ~funny(X0))) [input p11]
14. ! [X0] : ((tall(X0) <~> ~happy(X0)) <=> (~humble(X0) | quiet(X0))) [input p13]
16. ! [X0] : (~happy(X0) <=> humble(X0)) [input p15]
25. funny(alice) [input hypothesis]
47. ! [X0] : ((~wise(X0) | (creative(X0) & ~quiet(X0))) & ((~creative(X0) | quiet(X0)) | wise(X0))) [nnf transformation 5]
48. ! [X0] : ((~wise(X0) | (creative(X0) & ~quiet(X0))) & (~creative(X0) | quiet(X0) | wise(X0))) [flattening 47]
52. ! [X0] : ((wise(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~wise(X0))) [nnf transformation 8]
53. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & ((~happy(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 9]
54. ! [X0] : ((curious(X0) | (happy(X0) & curious(X0))) & (~happy(X0) | ~curious(X0) | ~curious(X0))) [flattening 53]
58. ! [X0] : (((~old(X0) | tall(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (old(X0) & ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : ((~old(X0) | tall(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | (old(X0) & ~tall(X0)))) [flattening 58]
62. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [nnf transformation 14]
63. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [flattening 62]
67. ! [X0] : ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))) [nnf transformation 16]
96. ~wise(X0) | ~quiet(X0) [cnf transformation 48]
97. ~wise(X0) | creative(X0) [cnf transformation 48]
109. wise(X0) | wise(X0) | wise(X0) [cnf transformation 52]
110. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 54]
111. curious(X0) | curious(X0) [cnf transformation 54]
125. ~tall(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 59]
132. ~humble(X0) | quiet(X0) | tall(X0) | happy(X0) [cnf transformation 63]
141. humble(X0) | happy(X0) [cnf transformation 67]
153. funny(alice) [cnf transformation 25]
154. ~curious(X0) | ~happy(X0) [duplicate literal removal 110]
155. curious(X0) [duplicate literal removal 111]
159. wise(X0) [duplicate literal removal 109]
193. 8 <=> ! [X1] : curious(X1) [avatar definition]
194. curious(X1) <- (8) [avatar component clause 193]
239. 8 [avatar split clause 155,193]
312. ~quiet(X0) [resolution 96,159]
313. creative(X0) [resolution 97,159]
316. ~happy(X1) <- (8) [resolution 154,194]
360. quiet(X0) | tall(X0) | happy(X0) | happy(X0) [resolution 132,141]
361. quiet(X0) | tall(X0) | happy(X0) [duplicate literal removal 360]
362. tall(X0) | happy(X0) [subsumption resolution 361,312]
363. tall(X0) <- (8) [subsumption resolution 362,316]
366. ~funny(X2) | ~creative(X2) <- (8) [resolution 363,125]
367. ~funny(X2) <- (8) [subsumption resolution 366,313]
368. $false <- (8) [resolution 367,153]
369. ~8 [avatar contradiction clause 368]
370. $false [avatar sat refutation 239,369]
% SZS output end Proof for 111667087516487251147261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is old and vice versa.
Everyone who is not brave is funny and vice versa.
If susan is both humble and patient then someone is not rich.
Everyone who is humble or not creative is both not brave and tall and vice versa.
If someone is tall then mary is either calm or strong.
Everyone who is curious is happy and vice versa.
Everyone who is both brave and not kind is quiet and vice versa.
Everyone who is kind or old is brave or not quiet and vice versa.
Everyone who is not kind or calm is not brave or not funny.
Everyone who is wise is not humble.
Everyone who is humble or wise is both not generous and not creative.
Everyone who is humble is rich or brave and vice versa.
If someone is brave then lucy is not patient or not generous and vice versa.
If someone is not quiet or calm then someone is not happy and vice versa.
If alice is either wise or not generous then someone is both not brave and old and vice versa.
Someone is either not tall or rich.
Someone is strong or rich.
Someone is not quiet or quiet.
John is either not calm or happy.
Fred is both tall and not patient.
Someone is not humble.
Susan is not rich or creative. | Fred is creative. | contradiction | (![X]:(happy(X)<=>old(X)))&
(![X]:(~brave(X)<=>funny(X)))&
(((humble(susan)&patient(susan)))=>(?[X]:(~rich(X))))&
(![X]:((humble(X)|~creative(X))<=>(~brave(X)&tall(X))))&
((?[X]:(tall(X)))=>((calm(mary)<~>strong(mary))))&
(![X]:(curious(X)<=>happy(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((kind(X)|old(X))<=>(brave(X)|~quiet(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>(~generous(X)&~creative(X))))&
(![X]:(humble(X)<=>(rich(X)|brave(X))))&
((?[X]:(brave(X)))<=>((~patient(lucy)|~generous(lucy))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((~brave(X)&old(X)))))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((~quiet(X)|quiet(X))))&
((~calm(john)<~>happy(john)))&
((tall(fred)&~patient(fred)))&
(?[X]:(~humble(X)))&
((~rich(susan)|creative(susan))) | creative(fred) | [
"p3",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4303848426313535999693777
% SZS output start Proof for 4303848426313535999693777
4. ! [X0] : ((~creative(X0) | humble(X0)) <=> (tall(X0) & ~brave(X0))) [input p3]
11. ! [X0] : ((wise(X0) | humble(X0)) => (~creative(X0) & ~generous(X0))) [input p10]
12. ! [X0] : (humble(X0) <=> (brave(X0) | rich(X0))) [input p11]
20. ~patient(fred) & tall(fred) [input p19]
23. creative(fred) [input hypothesis]
31. ! [X0] : ((~creative(X0) & ~generous(X0)) | (~wise(X0) & ~humble(X0))) [ennf transformation 11]
36. ! [X0] : (((~creative(X0) | humble(X0)) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | (creative(X0) & ~humble(X0)))) [nnf transformation 4]
37. ! [X0] : ((~creative(X0) | humble(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | (creative(X0) & ~humble(X0)))) [flattening 36]
43. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ~humble(X0))) [nnf transformation 12]
44. ! [X0] : ((humble(X0) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ~humble(X0))) [flattening 43]
74. ~humble(X0) | ~brave(X0) [cnf transformation 37]
78. ~tall(X0) | humble(X0) | ~creative(X0) | brave(X0) [cnf transformation 37]
93. ~creative(X0) | ~humble(X0) [cnf transformation 31]
97. humble(X0) | ~brave(X0) [cnf transformation 44]
116. tall(fred) [cnf transformation 20]
120. creative(fred) [cnf transformation 23]
147. ~brave(X0) [subsumption resolution 97,74]
242. ~humble(fred) [resolution 93,120]
251. humble(fred) | ~creative(fred) | brave(fred) [resolution 78,116]
253. ~creative(fred) | brave(fred) [subsumption resolution 251,242]
254. brave(fred) [subsumption resolution 253,120]
255. $false [subsumption resolution 254,147]
% SZS output end Proof for 4303848426313535999693777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not funny then mary is both not patient and not calm. Everyone who is either kind or not generous is both funny and calm and vice versa. Everyone who is either not strong or not brave is not kind. If someone is both not humble and patient then someone is both not patient and not strong. Everyone who is not brave is not calm and vice versa. Everyone who is both not funny and not quiet is not calm. Everyone who is either wise or patient is both funny and not curious. Everyone who is not wise or not calm is not wise and vice versa. Everyone who is either not humble or old is either not curious or not generous and vice versa. If mary is either rich or not wise then paul is either strong or not generous and vice versa. If paul is both not generous and not brave then someone is not patient or not curious and vice versa. Everyone who is both not patient and calm is not calm or not old and vice versa. If paul is patient then john is not wise or not rich. Everyone who is either not kind or not quiet is either old or not tall. Everyone who is not happy is not strong and vice versa. Everyone who is not rich is old or not curious and vice versa. Someone is not strong or calm. Paul is both not generous and creative. Someone is both humble and happy. Someone is creative or not humble. John is either wise or not patient. Someone is not old or patient. | Paul is rich. | contradiction | ((~funny(paul))=>((~patient(mary)&~calm(mary))))&
(![X]:((kind(X)<~>~generous(X))<=>(funny(X)&calm(X))))&
(![X]:((~strong(X)<~>~brave(X))=>~kind(X)))&
((?[X]:((~humble(X)&patient(X))))=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:(~brave(X)<=>~calm(X)))&
(![X]:((~funny(X)&~quiet(X))=>~calm(X)))&
(![X]:((wise(X)<~>patient(X))=>(funny(X)&~curious(X))))&
(![X]:((~wise(X)|~calm(X))<=>~wise(X)))&
(![X]:((~humble(X)<~>old(X))<=>(~curious(X)<~>~generous(X))))&
(((rich(mary)<~>~wise(mary)))<=>((strong(paul)<~>~generous(paul))))&
(((~generous(paul)&~brave(paul)))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~patient(X)&calm(X))<=>(~calm(X)|~old(X))))&
((patient(paul))=>((~wise(john)|~rich(john))))&
(![X]:((~kind(X)<~>~quiet(X))=>(old(X)<~>~tall(X))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(~rich(X)<=>(old(X)|~curious(X))))&
(?[X]:((~strong(X)|calm(X))))&
((~generous(paul)&creative(paul)))&
(?[X]:((humble(X)&happy(X))))&
(?[X]:((creative(X)|~humble(X))))&
((wise(john)<~>~patient(john)))&
(?[X]:((~old(X)|patient(X)))) | rich(paul) | [
"p4",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1908466255772095844858481
% SZS output start Proof for 1908466255772095844858481
5. ! [X0] : (~brave(X0) <=> ~calm(X0)) [input p4]
11. (~brave(paul) & ~generous(paul)) <=> ? [X0] : (~curious(X0) | ~patient(X0)) [input p10]
12. ! [X0] : ((calm(X0) & ~patient(X0)) <=> (~old(X0) | ~calm(X0))) [input p11]
16. ! [X0] : (~rich(X0) <=> (~curious(X0) | old(X0))) [input p15]
23. rich(paul) [input hypothesis]
44. ! [X0] : ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))) [nnf transformation 5]
50. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | (brave(paul) | generous(paul))) [nnf transformation 11]
51. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | brave(paul) | generous(paul)) [flattening 50]
52. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X1] : (~curious(X1) | ~patient(X1)) | brave(paul) | generous(paul)) [rectify 51]
53. ? [X1] : (~curious(X1) | ~patient(X1)) => (~curious(sK1) | ~patient(sK1)) [choice axiom]
54. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & ((~curious(sK1) | ~patient(sK1)) | brave(paul) | generous(paul)) [skolemisation 52,53]
55. ! [X0] : (((calm(X0) & ~patient(X0)) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | (~calm(X0) | patient(X0)))) [nnf transformation 12]
56. ! [X0] : (((calm(X0) & ~patient(X0)) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | ~calm(X0) | patient(X0))) [flattening 55]
58. ! [X0] : ((~rich(X0) | (curious(X0) & ~old(X0))) & ((~curious(X0) | old(X0)) | rich(X0))) [nnf transformation 16]
59. ! [X0] : ((~rich(X0) | (curious(X0) & ~old(X0))) & (~curious(X0) | old(X0) | rich(X0))) [flattening 58]
79. ~calm(X0) | brave(X0) [cnf transformation 44]
108. ~brave(paul) | patient(X0) [cnf transformation 54]
112. ~patient(X0) | old(X0) [cnf transformation 56]
113. calm(X0) | calm(X0) [cnf transformation 56]
122. ~rich(X0) | ~old(X0) [cnf transformation 59]
131. rich(paul) [cnf transformation 23]
133. calm(X0) [duplicate literal removal 113]
189. 12 <=> brave(paul) [avatar definition]
191. ~brave(paul) <- (~12) [avatar component clause 189]
194. 13 <=> ! [X0] : patient(X0) [avatar definition]
195. patient(X0) <- (13) [avatar component clause 194]
196. 13 | ~12 [avatar split clause 108,189,194]
231. brave(X0) [resolution 79,133]
232. $false <- (~12) [resolution 231,191]
234. 12 [avatar contradiction clause 232]
247. old(X0) <- (13) [resolution 112,195]
249. ~old(paul) [resolution 122,131]
250. $false <- (13) [subsumption resolution 249,247]
251. ~13 [avatar contradiction clause 250]
252. $false [avatar sat refutation 196,234,251]
% SZS output end Proof for 1908466255772095844858481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both old and not old then someone is brave and vice versa.
Everyone who is either wise or not old is patient or humble and vice versa.
If john is not humble or patient then paul is not happy and vice versa.
If susan is not strong or not humble then lucy is both strong and not curious.
Everyone who is both quiet and kind is not funny and vice versa.
If someone is either tall or not humble then paul is either quiet or funny and vice versa.
If someone is both not funny and not brave then someone is not creative or not kind and vice versa.
If paul is curious then fred is not funny or old.
Everyone who is rich or wise is either strong or not rich.
Everyone who is old is generous and vice versa.
Everyone who is either not old or rich is not quiet or not strong.
If someone is either not strong or strong then someone is not funny or not happy.
Everyone who is quiet or not creative is not kind.
Everyone who is not quiet or tall is either patient or happy and vice versa.
Everyone who is not patient is tall or not humble.
If someone is either not rich or not old then susan is not curious and vice versa.
Someone is either not kind or tall.
Someone is either not calm or not rich.
John is either not calm or not brave.
Someone is not humble or tall.
Someone is rich.
Lucy is both kind and not tall.
Someone is wise. | Paul is not brave. | entailment | (((old(fred)&~old(fred)))<=>(?[X]:(brave(X))))&
(![X]:((wise(X)<~>~old(X))<=>(patient(X)|humble(X))))&
(((~humble(john)|patient(john)))<=>(~happy(paul)))&
(((~strong(susan)|~humble(susan)))=>((strong(lucy)&~curious(lucy))))&
(![X]:((quiet(X)&kind(X))<=>~funny(X)))&
((?[X]:((tall(X)<~>~humble(X))))<=>((quiet(paul)<~>funny(paul))))&
((?[X]:((~funny(X)&~brave(X))))<=>(?[X]:((~creative(X)|~kind(X)))))&
((curious(paul))=>((~funny(fred)|old(fred))))&
(![X]:((rich(X)|wise(X))=>(strong(X)<~>~rich(X))))&
(![X]:(old(X)<=>generous(X)))&
(![X]:((~old(X)<~>rich(X))=>(~quiet(X)|~strong(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:((quiet(X)|~creative(X))=>~kind(X)))&
(![X]:((~quiet(X)|tall(X))<=>(patient(X)<~>happy(X))))&
(![X]:(~patient(X)=>(tall(X)|~humble(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>(~curious(susan)))&
(?[X]:((~kind(X)<~>tall(X))))&
(?[X]:((~calm(X)<~>~rich(X))))&
((~calm(john)<~>~brave(john)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(rich(X)))&
((kind(lucy)&~tall(lucy)))&
(?[X]:(wise(X))) | ~brave(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7623309378734731922467167
% SZS output start Proof for 7623309378734731922467167
1. (~old(fred) & old(fred)) <=> ? [X0] : brave(X0) [input p0]
24. brave(paul) [input hypothesis]
37. ((~old(fred) & old(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (old(fred) | ~old(fred))) [nnf transformation 1]
38. ((~old(fred) & old(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | old(fred) | ~old(fred)) [flattening 37]
39. ((~old(fred) & old(fred)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | old(fred) | ~old(fred)) [rectify 38]
40. ? [X1] : brave(X1) => brave(sK0) [choice axiom]
41. ((~old(fred) & old(fred)) | ! [X0] : ~brave(X0)) & (brave(sK0) | old(fred) | ~old(fred)) [skolemisation 39,40]
84. old(fred) | ~brave(X0) [cnf transformation 41]
85. ~old(fred) | ~brave(X0) [cnf transformation 41]
150. brave(paul) [cnf transformation 24]
155. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
156. ~brave(X0) <- (1) [avatar component clause 155]
158. 2 <=> old(fred) [avatar definition]
161. 1 | ~2 [avatar split clause 85,158,155]
162. 1 | 2 [avatar split clause 84,158,155]
347. $false <- (1) [resolution 156,150]
348. ~1 [avatar contradiction clause 347]
349. $false [avatar sat refutation 161,162,348]
% SZS output end Proof for 7623309378734731922467167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not rich is either not strong or generous and vice versa.
Everyone who is not curious is patient and vice versa.
If someone is funny then alice is both curious and rich and vice versa.
Everyone who is both generous and brave is patient or kind and vice versa.
If someone is both not quiet and not curious then alice is both not generous and not curious and vice versa.
If someone is either not creative or generous then someone is curious or not wise.
If someone is not humble or old then lucy is both calm and not humble and vice versa.
Everyone who is both not brave and not quiet is not old and vice versa.
If fred is funny then mary is either rich or not funny and vice versa.
Everyone who is both humble and tall is not patient.
If paul is either patient or not humble then someone is both not kind and not generous and vice versa.
Everyone who is wise is not brave and vice versa.
Everyone who is calm is not old.
If someone is not tall or brave then someone is both not old and patient and vice versa.
If mary is either not rich or creative then someone is strong or humble.
If lucy is not calm or wise then someone is creative and vice versa.
John is not old.
Fred is both wise and funny.
Susan is not generous.
Someone is not patient or not generous.
Someone is not kind.
Someone is brave or not rich.
Someone is either not kind or not tall.
Someone is either creative or curious. | Alice is not kind. | entailment | (![X]:((creative(X)|~rich(X))<=>(~strong(X)<~>generous(X))))&
(![X]:(~curious(X)<=>patient(X)))&
((?[X]:(funny(X)))<=>((curious(alice)&rich(alice))))&
(![X]:((generous(X)&brave(X))<=>(patient(X)|kind(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>((~generous(alice)&~curious(alice))))&
((?[X]:((~creative(X)<~>generous(X))))=>(?[X]:((curious(X)|~wise(X)))))&
((?[X]:((~humble(X)|old(X))))<=>((calm(lucy)&~humble(lucy))))&
(![X]:((~brave(X)&~quiet(X))<=>~old(X)))&
((funny(fred))<=>((rich(mary)<~>~funny(mary))))&
(![X]:((humble(X)&tall(X))=>~patient(X)))&
(((patient(paul)<~>~humble(paul)))<=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(wise(X)<=>~brave(X)))&
(![X]:(calm(X)=>~old(X)))&
((?[X]:((~tall(X)|brave(X))))<=>(?[X]:((~old(X)&patient(X)))))&
(((~rich(mary)<~>creative(mary)))=>(?[X]:((strong(X)|humble(X)))))&
(((~calm(lucy)|wise(lucy)))<=>(?[X]:(creative(X))))&
(~old(john))&
((wise(fred)&funny(fred)))&
(~generous(susan))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:(~kind(X)))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((~kind(X)<~>~tall(X))))&
(?[X]:((creative(X)<~>curious(X)))) | ~kind(alice) | [
"p3",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7749478499687727376804424
% SZS output start Proof for 7749478499687727376804424
4. ! [X0] : ((brave(X0) & generous(X0)) <=> (kind(X0) | patient(X0))) [input p3]
8. ! [X0] : ((~quiet(X0) & ~brave(X0)) <=> ~old(X0)) [input p7]
14. ? [X0] : (brave(X0) | ~tall(X0)) <=> ? [X0] : (patient(X0) & ~old(X0)) [input p13]
25. kind(alice) [input hypothesis]
27. ? [X0] : (brave(X0) | ~tall(X0)) <=> ? [X1] : (patient(X1) & ~old(X1)) [rectify 14]
41. ! [X0] : (((brave(X0) & generous(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (~brave(X0) | ~generous(X0)))) [nnf transformation 4]
42. ! [X0] : (((brave(X0) & generous(X0)) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ~brave(X0) | ~generous(X0))) [flattening 41]
57. ! [X0] : (((~quiet(X0) & ~brave(X0)) | old(X0)) & (~old(X0) | (quiet(X0) | brave(X0)))) [nnf transformation 8]
58. ! [X0] : (((~quiet(X0) & ~brave(X0)) | old(X0)) & (~old(X0) | quiet(X0) | brave(X0))) [flattening 57]
65. (? [X0] : (brave(X0) | ~tall(X0)) | ! [X1] : (~patient(X1) | old(X1))) & (? [X1] : (patient(X1) & ~old(X1)) | ! [X0] : (~brave(X0) & tall(X0))) [nnf transformation 27]
66. (? [X0] : (brave(X0) | ~tall(X0)) | ! [X1] : (~patient(X1) | old(X1))) & (? [X2] : (patient(X2) & ~old(X2)) | ! [X3] : (~brave(X3) & tall(X3))) [rectify 65]
67. ? [X0] : (brave(X0) | ~tall(X0)) => (brave(sK5) | ~tall(sK5)) [choice axiom]
68. ? [X2] : (patient(X2) & ~old(X2)) => (patient(sK6) & ~old(sK6)) [choice axiom]
69. ((brave(sK5) | ~tall(sK5)) | ! [X1] : (~patient(X1) | old(X1))) & ((patient(sK6) & ~old(sK6)) | ! [X3] : (~brave(X3) & tall(X3))) [skolemisation 66,68,67]
104. ~patient(X0) | brave(X0) [cnf transformation 42]
105. ~kind(X0) | brave(X0) [cnf transformation 42]
118. ~brave(X0) | old(X0) [cnf transformation 58]
135. ~old(sK6) | ~brave(X3) [cnf transformation 69]
137. patient(sK6) | ~brave(X3) [cnf transformation 69]
155. kind(alice) [cnf transformation 25]
292. 30 <=> ! [X3] : ~brave(X3) [avatar definition]
293. ~brave(X3) <- (30) [avatar component clause 292]
295. 31 <=> patient(sK6) [avatar definition]
297. patient(sK6) <- (31) [avatar component clause 295]
298. 30 | 31 [avatar split clause 137,295,292]
304. 33 <=> old(sK6) [avatar definition]
306. ~old(sK6) <- (~33) [avatar component clause 304]
307. 30 | ~33 [avatar split clause 135,304,292]
387. brave(sK6) <- (31) [resolution 104,297]
389. brave(alice) [resolution 105,155]
391. old(sK6) <- (31) [resolution 387,118]
392. $false <- (31, ~33) [subsumption resolution 391,306]
393. ~31 | 33 [avatar contradiction clause 392]
399. $false <- (30) [resolution 389,293]
401. ~30 [avatar contradiction clause 399]
402. $false [avatar sat refutation 298,307,393,401]
% SZS output end Proof for 7749478499687727376804424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not wise is happy.
Everyone who is not kind or creative is not calm or strong.
Everyone who is not happy is not old and vice versa.
Everyone who is either strong or curious is both creative and not brave and vice versa.
Everyone who is not generous or not kind is both quiet and not rich.
Everyone who is both tall and not old is both calm and generous.
If someone is either not funny or curious then someone is both not wise and tall.
Everyone who is curious or tall is either not funny or not strong and vice versa.
Everyone who is either not funny or humble is creative.
If someone is not humble or brave then someone is either brave or not quiet and vice versa.
If mary is curious or wise then mary is brave and vice versa.
Everyone who is happy is calm or brave and vice versa.
Everyone who is funny or not funny is either not calm or not patient and vice versa.
If fred is either patient or happy then susan is both not old and not quiet and vice versa.
If lucy is both not generous and funny then alice is both wise and not curious and vice versa.
Everyone who is both not happy and wise is both not kind and not quiet.
John is strong.
Susan is not kind.
Mary is not humble or not quiet.
Someone is not rich.
Someone is both brave and funny.
Someone is not kind.
Fred is not brave or humble.
Someone is humble. | Fred is not patient. | contradiction | (![X]:((strong(X)&~wise(X))=>happy(X)))&
(![X]:((~kind(X)|creative(X))=>(~calm(X)|strong(X))))&
(![X]:(~happy(X)<=>~old(X)))&
(![X]:((strong(X)<~>curious(X))<=>(creative(X)&~brave(X))))&
(![X]:((~generous(X)|~kind(X))=>(quiet(X)&~rich(X))))&
(![X]:((tall(X)&~old(X))=>(calm(X)&generous(X))))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((curious(X)|tall(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((~funny(X)<~>humble(X))=>creative(X)))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(((curious(mary)|wise(mary)))<=>(brave(mary)))&
(![X]:(happy(X)<=>(calm(X)|brave(X))))&
(![X]:((funny(X)|~funny(X))<=>(~calm(X)<~>~patient(X))))&
(((patient(fred)<~>happy(fred)))<=>((~old(susan)&~quiet(susan))))&
(((~generous(lucy)&funny(lucy)))<=>((wise(alice)&~curious(alice))))&
(![X]:((~happy(X)&wise(X))=>(~kind(X)&~quiet(X))))&
(strong(john))&
(~kind(susan))&
((~humble(mary)|~quiet(mary)))&
(?[X]:(~rich(X)))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:(~kind(X)))&
((~brave(fred)|humble(fred)))&
(?[X]:(humble(X))) | ~patient(fred) | [
"p4",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5482268050268863815558560
% SZS output start Proof for 5482268050268863815558560
5. ! [X0] : ((~kind(X0) | ~generous(X0)) => (~rich(X0) & quiet(X0))) [input p4]
12. ! [X0] : (happy(X0) <=> (brave(X0) | calm(X0))) [input p11]
13. ! [X0] : ((~funny(X0) | funny(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p12]
14. (patient(fred) <~> happy(fred)) <=> (~quiet(susan) & ~old(susan)) [input p13]
18. ~kind(susan) [input p17]
25. ~patient(fred) [input hypothesis]
28. ! [X0] : ((~kind(X0) | ~generous(X0)) => quiet(X0)) [pure predicate removal 5]
34. ! [X0] : (quiet(X0) | (kind(X0) & generous(X0))) [ennf transformation 28]
58. ! [X0] : ((happy(X0) | (~brave(X0) & ~calm(X0))) & ((brave(X0) | calm(X0)) | ~happy(X0))) [nnf transformation 12]
59. ! [X0] : ((happy(X0) | (~brave(X0) & ~calm(X0))) & (brave(X0) | calm(X0) | ~happy(X0))) [flattening 58]
60. ! [X0] : (((~funny(X0) | funny(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (funny(X0) & ~funny(X0)))) [nnf transformation 13]
61. ! [X0] : ((~funny(X0) | funny(X0) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (funny(X0) & ~funny(X0)))) [flattening 60]
62. (((~happy(fred) | ~patient(fred)) & (happy(fred) | patient(fred))) | (quiet(susan) | old(susan))) & ((~quiet(susan) & ~old(susan)) | ((patient(fred) | ~happy(fred)) & (happy(fred) | ~patient(fred)))) [nnf transformation 14]
63. (((~happy(fred) | ~patient(fred)) & (happy(fred) | patient(fred))) | quiet(susan) | old(susan)) & ((~quiet(susan) & ~old(susan)) | ((patient(fred) | ~happy(fred)) & (happy(fred) | ~patient(fred)))) [flattening 62]
84. quiet(X0) | kind(X0) [cnf transformation 34]
109. ~calm(X0) | happy(X0) [cnf transformation 59]
113. patient(X0) | calm(X0) | ~funny(X0) [cnf transformation 61]
114. patient(X0) | calm(X0) | funny(X0) [cnf transformation 61]
120. ~quiet(susan) | patient(fred) | ~happy(fred) [cnf transformation 63]
130. ~kind(susan) [cnf transformation 18]
137. ~patient(fred) [cnf transformation 25]
205. patient(X0) | calm(X0) [subsumption resolution 113,114]
212. 17 <=> quiet(susan) [avatar definition]
213. ~quiet(susan) <- (~17) [avatar component clause 212]
216. 18 <=> patient(fred) [avatar definition]
218. ~patient(fred) <- (~18) [avatar component clause 216]
220. 19 <=> happy(fred) [avatar definition]
225. ~19 | 18 | ~17 [avatar split clause 120,212,216,220]
267. ~18 [avatar split clause 137,216]
275. calm(fred) <- (~18) [resolution 205,218]
288. happy(fred) <- (~18) [resolution 275,109]
291. 19 | 18 [avatar split clause 288,216,220]
292. kind(susan) <- (~17) [resolution 213,84]
294. $false <- (~17) [subsumption resolution 292,130]
295. 17 [avatar contradiction clause 294]
296. $false [avatar sat refutation 225,267,291,295]
% SZS output end Proof for 5482268050268863815558560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or kind then john is generous.
Everyone who is both generous and not strong is both calm and not kind and vice versa.
If alice is either not happy or not rich then john is not old or patient and vice versa.
If mary is both not brave and not rich then someone is both generous and not patient.
Everyone who is brave is both humble and not curious and vice versa.
If someone is humble or patient then lucy is both curious and strong and vice versa.
If someone is not curious or humble then someone is both kind and not happy and vice versa.
If alice is not curious then john is wise or old.
Everyone who is both old and brave is either not strong or not funny and vice versa.
Everyone who is brave is calm or kind and vice versa.
Everyone who is happy or creative is not quiet and vice versa.
Everyone who is both not humble and not curious is either brave or not humble.
If someone is funny then someone is both creative and not humble and vice versa.
Everyone who is both generous and not curious is not creative or not rich and vice versa.
Everyone who is generous is either patient or rich.
If mary is either not quiet or funny then john is either not quiet or old and vice versa.
Someone is either kind or not happy.
Someone is brave or not brave.
Susan is not old or not generous.
Lucy is not old or humble.
Fred is curious or funny.
Someone is calm.
Someone is old.
John is brave or calm. | John is not generous. | contradiction | ((?[X]:((creative(X)|kind(X))))=>(generous(john)))&
(![X]:((generous(X)&~strong(X))<=>(calm(X)&~kind(X))))&
(((~happy(alice)<~>~rich(alice)))<=>((~old(john)|patient(john))))&
(((~brave(mary)&~rich(mary)))=>(?[X]:((generous(X)&~patient(X)))))&
(![X]:(brave(X)<=>(humble(X)&~curious(X))))&
((?[X]:((humble(X)|patient(X))))<=>((curious(lucy)&strong(lucy))))&
((?[X]:((~curious(X)|humble(X))))<=>(?[X]:((kind(X)&~happy(X)))))&
((~curious(alice))=>((wise(john)|old(john))))&
(![X]:((old(X)&brave(X))<=>(~strong(X)<~>~funny(X))))&
(![X]:(brave(X)<=>(calm(X)|kind(X))))&
(![X]:((happy(X)|creative(X))<=>~quiet(X)))&
(![X]:((~humble(X)&~curious(X))=>(brave(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((generous(X)&~curious(X))<=>(~creative(X)|~rich(X))))&
(![X]:(generous(X)=>(patient(X)<~>rich(X))))&
(((~quiet(mary)<~>funny(mary)))<=>((~quiet(john)<~>old(john))))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((brave(X)|~brave(X))))&
((~old(susan)|~generous(susan)))&
((~old(lucy)|humble(lucy)))&
((curious(fred)|funny(fred)))&
(?[X]:(calm(X)))&
(?[X]:(old(X)))&
((brave(john)|calm(john))) | ~generous(john) | [
"p0",
"p4",
"p6",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 566940975392422132072873
% SZS output start Proof for 566940975392422132072873
1. ? [X0] : (kind(X0) | creative(X0)) => generous(john) [input p0]
5. ! [X0] : (brave(X0) <=> (~curious(X0) & humble(X0))) [input p4]
7. ? [X0] : (humble(X0) | ~curious(X0)) <=> ? [X0] : (~happy(X0) & kind(X0)) [input p6]
10. ! [X0] : (brave(X0) <=> (kind(X0) | calm(X0))) [input p9]
24. calm(john) | brave(john) [input p23]
25. ~generous(john) [input hypothesis]
26. ? [X0] : (humble(X0) | ~curious(X0)) <=> ? [X1] : (~happy(X1) & kind(X1)) [rectify 7]
29. generous(john) | ! [X0] : (~kind(X0) & ~creative(X0)) [ennf transformation 1]
41. ! [X0] : ((brave(X0) | (curious(X0) | ~humble(X0))) & ((~curious(X0) & humble(X0)) | ~brave(X0))) [nnf transformation 5]
42. ! [X0] : ((brave(X0) | curious(X0) | ~humble(X0)) & ((~curious(X0) & humble(X0)) | ~brave(X0))) [flattening 41]
48. (? [X0] : (humble(X0) | ~curious(X0)) | ! [X1] : (happy(X1) | ~kind(X1))) & (? [X1] : (~happy(X1) & kind(X1)) | ! [X0] : (~humble(X0) & curious(X0))) [nnf transformation 26]
49. (? [X0] : (humble(X0) | ~curious(X0)) | ! [X1] : (happy(X1) | ~kind(X1))) & (? [X2] : (~happy(X2) & kind(X2)) | ! [X3] : (~humble(X3) & curious(X3))) [rectify 48]
50. ? [X0] : (humble(X0) | ~curious(X0)) => (humble(sK2) | ~curious(sK2)) [choice axiom]
51. ? [X2] : (~happy(X2) & kind(X2)) => (~happy(sK3) & kind(sK3)) [choice axiom]
52. ((humble(sK2) | ~curious(sK2)) | ! [X1] : (happy(X1) | ~kind(X1))) & ((~happy(sK3) & kind(sK3)) | ! [X3] : (~humble(X3) & curious(X3))) [skolemisation 49,51,50]
55. ! [X0] : ((brave(X0) | (~kind(X0) & ~calm(X0))) & ((kind(X0) | calm(X0)) | ~brave(X0))) [nnf transformation 10]
56. ! [X0] : ((brave(X0) | (~kind(X0) & ~calm(X0))) & (kind(X0) | calm(X0) | ~brave(X0))) [flattening 55]
79. generous(john) | ~kind(X0) [cnf transformation 29]
92. ~brave(X0) | humble(X0) [cnf transformation 42]
101. kind(sK3) | ~humble(X3) [cnf transformation 52]
112. brave(X0) | ~calm(X0) [cnf transformation 56]
145. calm(john) | brave(john) [cnf transformation 24]
146. ~generous(john) [cnf transformation 25]
149. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
150. ~kind(X0) <- (1) [avatar component clause 149]
152. 2 <=> generous(john) [avatar definition]
155. 1 | 2 [avatar split clause 79,152,149]
222. 17 <=> ! [X1] : ~humble(X1) [avatar definition]
223. ~humble(X1) <- (17) [avatar component clause 222]
249. 23 <=> kind(sK3) [avatar definition]
251. kind(sK3) <- (23) [avatar component clause 249]
252. 17 | 23 [avatar split clause 101,249,222]
333. brave(john) [subsumption resolution 145,112]
334. ~2 [avatar split clause 146,152]
340. humble(john) [resolution 92,333]
343. $false <- (17) [subsumption resolution 340,223]
344. ~17 [avatar contradiction clause 343]
345. $false <- (1, 23) [subsumption resolution 251,150]
346. ~1 | ~23 [avatar contradiction clause 345]
347. $false [avatar sat refutation 155,252,334,344,346]
% SZS output end Proof for 566940975392422132072873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not old is not tall or rich.
Everyone who is both kind and not rich is not strong.
Everyone who is not patient or tall is either happy or not curious.
Everyone who is not calm or old is either patient or generous.
Everyone who is either not rich or not quiet is either generous or not quiet and vice versa.
If lucy is not tall or not humble then someone is humble.
If someone is both not brave and not quiet then alice is not calm or not quiet.
Everyone who is either not kind or not happy is not creative or not curious.
If someone is not generous then someone is both not humble and not creative and vice versa.
Everyone who is both humble and not strong is brave.
Everyone who is both not strong and creative is both curious and not strong and vice versa.
If paul is both not kind and not patient then someone is both quiet and not kind and vice versa.
Everyone who is happy is not generous and vice versa.
If mary is not strong then someone is tall.
If someone is calm or kind then john is not happy and vice versa.
Everyone who is not kind or rich is either not rich or not curious.
Someone is either not curious or not brave.
Someone is either not patient or calm.
Someone is not strong or not quiet.
John is patient or not old.
Susan is both not wise and happy.
Paul is both not patient and not curious.
Someone is not humble or curious.
Lucy is both not quiet and wise. | Susan is curious. | contradiction | (![X]:((strong(X)&~old(X))=>(~tall(X)|rich(X))))&
(![X]:((kind(X)&~rich(X))=>~strong(X)))&
(![X]:((~patient(X)|tall(X))=>(happy(X)<~>~curious(X))))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>generous(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(generous(X)<~>~quiet(X))))&
(((~tall(lucy)|~humble(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((~brave(X)&~quiet(X))))=>((~calm(alice)|~quiet(alice))))&
(![X]:((~kind(X)<~>~happy(X))=>(~creative(X)|~curious(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~humble(X)&~creative(X)))))&
(![X]:((humble(X)&~strong(X))=>brave(X)))&
(![X]:((~strong(X)&creative(X))<=>(curious(X)&~strong(X))))&
(((~kind(paul)&~patient(paul)))<=>(?[X]:((quiet(X)&~kind(X)))))&
(![X]:(happy(X)<=>~generous(X)))&
((~strong(mary))=>(?[X]:(tall(X))))&
((?[X]:((calm(X)|kind(X))))<=>(~happy(john)))&
(![X]:((~kind(X)|rich(X))=>(~rich(X)<~>~curious(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((~patient(X)<~>calm(X))))&
(?[X]:((~strong(X)|~quiet(X))))&
((patient(john)|~old(john)))&
((~wise(susan)&happy(susan)))&
((~patient(paul)&~curious(paul)))&
(?[X]:((~humble(X)|curious(X))))&
((~quiet(lucy)&wise(lucy))) | curious(susan) | [
"p4",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2118312272681135154157695
% SZS output start Proof for 2118312272681135154157695
5. ! [X0] : ((~rich(X0) <~> ~quiet(X0)) <=> (generous(X0) <~> ~quiet(X0))) [input p4]
13. ! [X0] : (happy(X0) <=> ~generous(X0)) [input p12]
16. ! [X0] : ((rich(X0) | ~kind(X0)) => (~rich(X0) <~> ~curious(X0))) [input p15]
21. happy(susan) & ~wise(susan) [input p20]
25. curious(susan) [input hypothesis]
41. ! [X0] : ((~rich(X0) <~> ~curious(X0)) | (~rich(X0) & kind(X0))) [ennf transformation 16]
44. ! [X0] : ((((quiet(X0) | rich(X0)) & (~quiet(X0) | ~rich(X0))) | ((generous(X0) | quiet(X0)) & (~quiet(X0) | ~generous(X0)))) & (((quiet(X0) | ~generous(X0)) & (~quiet(X0) | generous(X0))) | ((~rich(X0) | quiet(X0)) & (~quiet(X0) | rich(X0))))) [nnf transformation 5]
60. ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))) [nnf transformation 13]
67. ! [X0] : (((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | (~rich(X0) & kind(X0))) [nnf transformation 41]
88. ~quiet(X0) | generous(X0) | ~quiet(X0) | rich(X0) [cnf transformation 44]
95. quiet(X0) | rich(X0) | generous(X0) | quiet(X0) [cnf transformation 44]
113. ~generous(X0) | ~happy(X0) [cnf transformation 60]
120. ~curious(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 67]
130. happy(susan) [cnf transformation 21]
136. curious(susan) [cnf transformation 25]
137. ~curious(X0) | ~rich(X0) [duplicate literal removal 120]
138. ~quiet(X0) | generous(X0) | rich(X0) [duplicate literal removal 88]
141. quiet(X0) | rich(X0) | generous(X0) [duplicate literal removal 95]
143. generous(X0) | rich(X0) [subsumption resolution 138,141]
294. ~rich(susan) [resolution 137,136]
299. ~happy(X1) | rich(X1) [resolution 143,113]
323. rich(susan) [resolution 299,130]
325. $false [subsumption resolution 323,294]
% SZS output end Proof for 2118312272681135154157695
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not calm then mary is not kind or happy.
Everyone who is not funny or not wise is both funny and not humble.
If someone is humble or not tall then someone is either not tall or not patient.
Everyone who is both not strong and not tall is either not creative or funny and vice versa.
If fred is both tall and humble then someone is either kind or not strong.
If someone is either funny or curious then mary is either generous or wise.
Everyone who is either not happy or calm is either happy or humble.
Everyone who is either strong or not humble is either happy or tall and vice versa.
Everyone who is both calm and funny is both happy and not curious and vice versa.
Everyone who is not funny is either humble or not wise and vice versa.
If fred is not kind then someone is curious or not patient and vice versa.
Everyone who is not strong is not creative or rich and vice versa.
Everyone who is both not creative and rich is both not creative and not strong.
If lucy is either not humble or generous then someone is either kind or generous and vice versa.
If someone is patient or not quiet then someone is wise and vice versa.
Everyone who is kind or not strong is either generous or not kind.
Paul is not quiet or not rich.
Mary is curious or humble.
Someone is either quiet or curious.
Susan is rich or not strong.
Susan is not brave or rich. | Mary is rich. | entailment | ((~calm(john))=>((~kind(mary)|happy(mary))))&
(![X]:((~funny(X)|~wise(X))=>(funny(X)&~humble(X))))&
((?[X]:((humble(X)|~tall(X))))=>(?[X]:((~tall(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(~creative(X)<~>funny(X))))&
(((tall(fred)&humble(fred)))=>(?[X]:((kind(X)<~>~strong(X)))))&
((?[X]:((funny(X)<~>curious(X))))=>((generous(mary)<~>wise(mary))))&
(![X]:((~happy(X)<~>calm(X))=>(happy(X)<~>humble(X))))&
(![X]:((strong(X)<~>~humble(X))<=>(happy(X)<~>tall(X))))&
(![X]:((calm(X)&funny(X))<=>(happy(X)&~curious(X))))&
(![X]:(~funny(X)<=>(humble(X)<~>~wise(X))))&
((~kind(fred))<=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:(~strong(X)<=>(~creative(X)|rich(X))))&
(![X]:((~creative(X)&rich(X))=>(~creative(X)&~strong(X))))&
(((~humble(lucy)<~>generous(lucy)))<=>(?[X]:((kind(X)<~>generous(X)))))&
((?[X]:((patient(X)|~quiet(X))))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~strong(X))=>(generous(X)<~>~kind(X))))&
((~quiet(paul)|~rich(paul)))&
((curious(mary)|humble(mary)))&
(?[X]:((quiet(X)<~>curious(X))))&
((rich(susan)|~strong(susan)))&
((~brave(susan)|rich(susan))) | rich(mary) | [
"p1",
"p3",
"p6",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6408579142645029394927283
% SZS output start Proof for 6408579142645029394927283
2. ! [X0] : ((~wise(X0) | ~funny(X0)) => (~humble(X0) & funny(X0))) [input p1]
4. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (~creative(X0) <~> funny(X0))) [input p3]
7. ! [X0] : ((~happy(X0) <~> calm(X0)) => (happy(X0) <~> humble(X0))) [input p6]
8. ! [X0] : ((strong(X0) <~> ~humble(X0)) <=> (happy(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((funny(X0) & calm(X0)) <=> (~curious(X0) & happy(X0))) [input p8]
10. ! [X0] : (~funny(X0) <=> (humble(X0) <~> ~wise(X0))) [input p9]
12. ! [X0] : (~strong(X0) <=> (rich(X0) | ~creative(X0))) [input p11]
22. ~rich(mary) [input hypothesis]
28. ! [X0] : ((~humble(X0) & funny(X0)) | (wise(X0) & funny(X0))) [ennf transformation 2]
33. ! [X0] : ((happy(X0) <~> humble(X0)) | (~happy(X0) <=> calm(X0))) [ennf transformation 7]
41. ! [X0] : (((~tall(X0) & ~strong(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (tall(X0) | strong(X0)))) [nnf transformation 4]
42. ! [X0] : (((~tall(X0) & ~strong(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | tall(X0) | strong(X0))) [flattening 41]
47. ! [X0] : (((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0)))) [nnf transformation 33]
48. ! [X0] : ((((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0)))) & (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0))))) [nnf transformation 8]
49. ! [X0] : (((funny(X0) & calm(X0)) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 9]
50. ! [X0] : (((funny(X0) & calm(X0)) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | ~funny(X0) | ~calm(X0))) [flattening 49]
51. ! [X0] : ((~funny(X0) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | funny(X0))) [nnf transformation 10]
56. ! [X0] : ((~strong(X0) | (~rich(X0) & creative(X0))) & ((rich(X0) | ~creative(X0)) | strong(X0))) [nnf transformation 12]
57. ! [X0] : ((~strong(X0) | (~rich(X0) & creative(X0))) & (rich(X0) | ~creative(X0) | strong(X0))) [flattening 56]
72. funny(X0) | funny(X0) [cnf transformation 28]
75. ~humble(X0) | wise(X0) [cnf transformation 28]
81. ~funny(X0) | creative(X0) | tall(X0) | strong(X0) [cnf transformation 42]
83. ~strong(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 42]
92. humble(X0) | happy(X0) | calm(X0) | happy(X0) [cnf transformation 47]
99. ~tall(X0) | ~happy(X0) | strong(X0) | humble(X0) [cnf transformation 48]
104. happy(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 50]
110. ~funny(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 51]
111. ~funny(X0) | humble(X0) | wise(X0) [cnf transformation 51]
115. rich(X0) | ~creative(X0) | strong(X0) [cnf transformation 57]
116. ~strong(X0) | creative(X0) [cnf transformation 57]
140. ~rich(mary) [cnf transformation 22]
142. humble(X0) | happy(X0) | calm(X0) [duplicate literal removal 92]
144. funny(X0) [duplicate literal removal 72]
171. 7 <=> ! [X1] : ~humble(X1) [avatar definition]
172. ~humble(X1) <- (7) [avatar component clause 171]
177. ~creative(X0) | ~strong(X0) [subsumption resolution 83,144]
178. creative(X0) | tall(X0) | strong(X0) [subsumption resolution 81,144]
213. ~calm(X0) | happy(X0) [subsumption resolution 104,144]
214. humble(X0) | wise(X0) [subsumption resolution 111,144]
215. wise(X0) [subsumption resolution 214,75]
216. ~wise(X0) | ~humble(X0) [subsumption resolution 110,144]
217. ~humble(X0) [subsumption resolution 216,215]
218. 7 [avatar split clause 217,171]
240. ~strong(X0) [subsumption resolution 116,177]
241. ~creative(X0) | rich(X0) [subsumption resolution 115,240]
328. happy(X2) | calm(X2) <- (7) [resolution 142,172]
329. happy(X2) <- (7) [subsumption resolution 328,213]
332. tall(X0) | strong(X0) | rich(X0) [resolution 178,241]
335. rich(X0) | tall(X0) [subsumption resolution 332,240]
336. tall(mary) [resolution 335,140]
346. ~happy(mary) | strong(mary) | humble(mary) [resolution 99,336]
351. strong(mary) | humble(mary) <- (7) [subsumption resolution 346,329]
352. humble(mary) <- (7) [subsumption resolution 351,240]
353. $false <- (7) [subsumption resolution 352,172]
354. ~7 [avatar contradiction clause 353]
355. $false [avatar sat refutation 218,354]
% SZS output end Proof for 6408579142645029394927283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not happy is not curious or not happy.
If paul is both not strong and not old then someone is both not creative and kind and vice versa.
Everyone who is happy or wise is not happy or rich and vice versa.
Everyone who is old or tall is not happy.
If someone is both not tall and not rich then someone is either patient or not quiet.
If someone is wise then susan is either not kind or old and vice versa.
Everyone who is either not calm or not rich is strong.
Everyone who is not humble or happy is either not curious or generous and vice versa.
If fred is either not strong or not generous then someone is not creative and vice versa.
Everyone who is either not generous or quiet is both not curious and strong.
If mary is wise or not happy then susan is not strong and vice versa.
If lucy is either not humble or not creative then someone is not wise or happy.
If someone is not happy or generous then john is either not funny or brave and vice versa.
If fred is not calm then someone is funny and vice versa.
Everyone who is not quiet is patient.
Everyone who is humble or not kind is not happy.
Mary is funny.
Fred is both not tall and not brave.
Mary is both kind and rich.
Someone is not rich or rich.
Someone is wise or not quiet.
Someone is either humble or not kind.
Lucy is not old or not tall. | Fred is calm. | contradiction | (![X]:((~brave(X)|~happy(X))=>(~curious(X)|~happy(X))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((happy(X)|wise(X))<=>(~happy(X)|rich(X))))&
(![X]:((old(X)|tall(X))=>~happy(X)))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:(wise(X)))<=>((~kind(susan)<~>old(susan))))&
(![X]:((~calm(X)<~>~rich(X))=>strong(X)))&
(![X]:((~humble(X)|happy(X))<=>(~curious(X)<~>generous(X))))&
(((~strong(fred)<~>~generous(fred)))<=>(?[X]:(~creative(X))))&
(![X]:((~generous(X)<~>quiet(X))=>(~curious(X)&strong(X))))&
(((wise(mary)|~happy(mary)))<=>(~strong(susan)))&
(((~humble(lucy)<~>~creative(lucy)))=>(?[X]:((~wise(X)|happy(X)))))&
((?[X]:((~happy(X)|generous(X))))<=>((~funny(john)<~>brave(john))))&
((~calm(fred))<=>(?[X]:(funny(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(![X]:((humble(X)|~kind(X))=>~happy(X)))&
(funny(mary))&
((~tall(fred)&~brave(fred)))&
((kind(mary)&rich(mary)))&
(?[X]:((~rich(X)|rich(X))))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((humble(X)<~>~kind(X))))&
((~old(lucy)|~tall(lucy))) | calm(fred) | [
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 460019873173868459593631
% SZS output start Proof for 460019873173868459593631
14. ~calm(fred) <=> ? [X0] : funny(X0) [input p13]
17. funny(mary) [input p16]
24. calm(fred) [input hypothesis]
67. (~calm(fred) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | calm(fred)) [nnf transformation 14]
68. (~calm(fred) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | calm(fred)) [rectify 67]
69. ? [X1] : funny(X1) => funny(sK6) [choice axiom]
70. (~calm(fred) | ! [X0] : ~funny(X0)) & (funny(sK6) | calm(fred)) [skolemisation 68,69]
124. ~calm(fred) | ~funny(X0) [cnf transformation 70]
128. funny(mary) [cnf transformation 17]
138. calm(fred) [cnf transformation 24]
276. 29 <=> ! [X0] : ~funny(X0) [avatar definition]
277. ~funny(X0) <- (29) [avatar component clause 276]
279. 30 <=> calm(fred) [avatar definition]
282. 29 | ~30 [avatar split clause 124,279,276]
316. 30 [avatar split clause 138,279]
319. $false <- (29) [resolution 277,128]
320. ~29 [avatar contradiction clause 319]
321. $false [avatar sat refutation 282,316,320]
% SZS output end Proof for 460019873173868459593631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either calm or not funny then someone is tall and vice versa. Everyone who is funny is curious or kind. Everyone who is generous is both not quiet and not happy and vice versa. Everyone who is both not wise and not calm is strong and vice versa. If lucy is not rich then someone is both not quiet and not happy and vice versa. Everyone who is patient is either wise or old. If susan is happy or not rich then someone is not curious and vice versa. If lucy is both calm and quiet then fred is generous and vice versa. Everyone who is not old or wise is both not funny and patient and vice versa. If someone is generous then someone is either rich or quiet and vice versa. Everyone who is wise is both not kind and not old. If someone is either not creative or happy then someone is both not generous and not creative and vice versa. If mary is not strong then alice is either not quiet or wise and vice versa. Everyone who is not old is both not tall and not wise and vice versa. Everyone who is either creative or not curious is either not generous or not humble. Everyone who is either generous or old is not funny and vice versa. Someone is both not happy and not strong. Mary is tall or not patient. Fred is either not strong or not calm. Someone is either calm or not brave. Paul is not creative. Someone is both not wise and tall. Lucy is humble or strong. Alice is funny. | Fred is not curious. | neutral | (((calm(lucy)<~>~funny(lucy)))<=>(?[X]:(tall(X))))&
(![X]:(funny(X)=>(curious(X)|kind(X))))&
(![X]:(generous(X)<=>(~quiet(X)&~happy(X))))&
(![X]:((~wise(X)&~calm(X))<=>strong(X)))&
((~rich(lucy))<=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:(patient(X)=>(wise(X)<~>old(X))))&
(((happy(susan)|~rich(susan)))<=>(?[X]:(~curious(X))))&
(((calm(lucy)&quiet(lucy)))<=>(generous(fred)))&
(![X]:((~old(X)|wise(X))<=>(~funny(X)&patient(X))))&
((?[X]:(generous(X)))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(![X]:(wise(X)=>(~kind(X)&~old(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>(?[X]:((~generous(X)&~creative(X)))))&
((~strong(mary))<=>((~quiet(alice)<~>wise(alice))))&
(![X]:(~old(X)<=>(~tall(X)&~wise(X))))&
(![X]:((creative(X)<~>~curious(X))=>(~generous(X)<~>~humble(X))))&
(![X]:((generous(X)<~>old(X))<=>~funny(X)))&
(?[X]:((~happy(X)&~strong(X))))&
((tall(mary)|~patient(mary)))&
((~strong(fred)<~>~calm(fred)))&
(?[X]:((calm(X)<~>~brave(X))))&
(~creative(paul))&
(?[X]:((~wise(X)&tall(X))))&
((humble(lucy)|strong(lucy)))&
(funny(alice)) | ~curious(fred) | [] | null | 0 |
Everyone who is not kind or not rich is both not curious and not quiet. If john is both calm and patient then someone is either not old or not calm and vice versa. If john is either generous or not funny then someone is either not strong or patient and vice versa. Everyone who is rich or tall is both patient and brave and vice versa. Everyone who is strong or curious is funny or not kind. Everyone who is both not curious and not wise is either happy or patient. If someone is not tall or old then someone is both not happy and not rich and vice versa. Everyone who is kind is calm. Everyone who is either not happy or not quiet is either not calm or not tall and vice versa. Everyone who is either not old or kind is both rich and quiet and vice versa. Everyone who is either not curious or not patient is both not wise and not quiet. Everyone who is either old or strong is creative and vice versa. If lucy is either generous or happy then someone is both not quiet and not funny. If someone is strong then someone is either patient or old. If someone is kind or strong then someone is both not happy and happy and vice versa. Everyone who is either old or not kind is either not patient or kind. Lucy is either not calm or quiet. Lucy is creative. Someone is not wise or brave. Someone is not brave. Lucy is quiet or not happy. Someone is funny. Mary is not happy or curious. Someone is either not kind or generous. | John is brave. | entailment | (![X]:((~kind(X)|~rich(X))=>(~curious(X)&~quiet(X))))&
(((calm(john)&patient(john)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(((generous(john)<~>~funny(john)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(![X]:((rich(X)|tall(X))<=>(patient(X)&brave(X))))&
(![X]:((strong(X)|curious(X))=>(funny(X)|~kind(X))))&
(![X]:((~curious(X)&~wise(X))=>(happy(X)<~>patient(X))))&
((?[X]:((~tall(X)|old(X))))<=>(?[X]:((~happy(X)&~rich(X)))))&
(![X]:(kind(X)=>calm(X)))&
(![X]:((~happy(X)<~>~quiet(X))<=>(~calm(X)<~>~tall(X))))&
(![X]:((~old(X)<~>kind(X))<=>(rich(X)&quiet(X))))&
(![X]:((~curious(X)<~>~patient(X))=>(~wise(X)&~quiet(X))))&
(![X]:((old(X)<~>strong(X))<=>creative(X)))&
(((generous(lucy)<~>happy(lucy)))=>(?[X]:((~quiet(X)&~funny(X)))))&
((?[X]:(strong(X)))=>(?[X]:((patient(X)<~>old(X)))))&
((?[X]:((kind(X)|strong(X))))<=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:((old(X)<~>~kind(X))=>(~patient(X)<~>kind(X))))&
((~calm(lucy)<~>quiet(lucy)))&
(creative(lucy))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:(~brave(X)))&
((quiet(lucy)|~happy(lucy)))&
(?[X]:(funny(X)))&
((~happy(mary)|curious(mary)))&
(?[X]:((~kind(X)<~>generous(X)))) | brave(john) | [
"p0",
"p1",
"p3",
"p5",
"p8",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 588555915592099470026110
% SZS output start Proof for 588555915592099470026110
1. ! [X0] : ((~rich(X0) | ~kind(X0)) => (~quiet(X0) & ~curious(X0))) [input p0]
2. (patient(john) & calm(john)) <=> ? [X0] : (~old(X0) <~> ~calm(X0)) [input p1]
4. ! [X0] : ((tall(X0) | rich(X0)) <=> (brave(X0) & patient(X0))) [input p3]
6. ! [X0] : ((~wise(X0) & ~curious(X0)) => (happy(X0) <~> patient(X0))) [input p5]
9. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> (~calm(X0) <~> ~tall(X0))) [input p8]
10. ! [X0] : ((~old(X0) <~> kind(X0)) <=> (quiet(X0) & rich(X0))) [input p9]
11. ! [X0] : ((~curious(X0) <~> ~patient(X0)) => (~quiet(X0) & ~wise(X0))) [input p10]
15. ? [X0] : (strong(X0) | kind(X0)) <=> ? [X0] : (happy(X0) & ~happy(X0)) [input p14]
17. ~calm(lucy) <~> quiet(lucy) [input p16]
25. ~brave(john) [input hypothesis]
28. ? [X0] : (strong(X0) | kind(X0)) <=> ? [X1] : (happy(X1) & ~happy(X1)) [rectify 15]
30. ! [X0] : ((~quiet(X0) & ~curious(X0)) | (rich(X0) & kind(X0))) [ennf transformation 1]
33. ! [X0] : ((happy(X0) <~> patient(X0)) | (wise(X0) | curious(X0))) [ennf transformation 6]
34. ! [X0] : ((happy(X0) <~> patient(X0)) | wise(X0) | curious(X0)) [flattening 33]
36. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (~curious(X0) <=> ~patient(X0))) [ennf transformation 11]
41. ((patient(john) & calm(john)) | ! [X0] : ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) & (? [X0] : ((calm(X0) | old(X0)) & (~calm(X0) | ~old(X0))) | (~patient(john) | ~calm(john))) [nnf transformation 2]
42. ((patient(john) & calm(john)) | ! [X0] : ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) & (? [X0] : ((calm(X0) | old(X0)) & (~calm(X0) | ~old(X0))) | ~patient(john) | ~calm(john)) [flattening 41]
43. ((patient(john) & calm(john)) | ! [X0] : ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) & (? [X1] : ((calm(X1) | old(X1)) & (~calm(X1) | ~old(X1))) | ~patient(john) | ~calm(john)) [rectify 42]
44. ? [X1] : ((calm(X1) | old(X1)) & (~calm(X1) | ~old(X1))) => ((calm(sK0) | old(sK0)) & (~calm(sK0) | ~old(sK0))) [choice axiom]
45. ((patient(john) & calm(john)) | ! [X0] : ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) & (((calm(sK0) | old(sK0)) & (~calm(sK0) | ~old(sK0))) | ~patient(john) | ~calm(john)) [skolemisation 43,44]
50. ! [X0] : (((tall(X0) | rich(X0)) | (~brave(X0) | ~patient(X0))) & ((brave(X0) & patient(X0)) | (~tall(X0) & ~rich(X0)))) [nnf transformation 4]
51. ! [X0] : ((tall(X0) | rich(X0) | ~brave(X0) | ~patient(X0)) & ((brave(X0) & patient(X0)) | (~tall(X0) & ~rich(X0)))) [flattening 50]
52. ! [X0] : (((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | wise(X0) | curious(X0)) [nnf transformation 34]
58. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 9]
59. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [nnf transformation 10]
60. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [flattening 59]
61. ! [X0] : ((~quiet(X0) & ~wise(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) [nnf transformation 36]
70. (? [X0] : (strong(X0) | kind(X0)) | ! [X1] : (~happy(X1) | happy(X1))) & (? [X1] : (happy(X1) & ~happy(X1)) | ! [X0] : (~strong(X0) & ~kind(X0))) [nnf transformation 28]
71. (? [X0] : (strong(X0) | kind(X0)) | ! [X1] : (~happy(X1) | happy(X1))) & (? [X2] : (happy(X2) & ~happy(X2)) | ! [X3] : (~strong(X3) & ~kind(X3))) [rectify 70]
72. ? [X0] : (strong(X0) | kind(X0)) => (strong(sK6) | kind(sK6)) [choice axiom]
73. ? [X2] : (happy(X2) & ~happy(X2)) => (happy(sK7) & ~happy(sK7)) [choice axiom]
74. ((strong(sK6) | kind(sK6)) | ! [X1] : (~happy(X1) | happy(X1))) & ((happy(sK7) & ~happy(sK7)) | ! [X3] : (~strong(X3) & ~kind(X3))) [skolemisation 71,73,72]
76. (~quiet(lucy) | calm(lucy)) & (quiet(lucy) | ~calm(lucy)) [nnf transformation 17]
86. ~curious(X0) | kind(X0) [cnf transformation 30]
88. ~quiet(X0) | kind(X0) [cnf transformation 30]
89. ~quiet(X0) | rich(X0) [cnf transformation 30]
93. calm(john) | ~old(X0) | calm(X0) [cnf transformation 45]
95. patient(john) | ~old(X0) | calm(X0) [cnf transformation 45]
107. ~tall(X0) | brave(X0) [cnf transformation 51]
112. ~happy(X0) | ~patient(X0) | wise(X0) | curious(X0) [cnf transformation 52]
126. ~calm(X0) | happy(X0) | quiet(X0) | tall(X0) [cnf transformation 58]
129. quiet(X0) | kind(X0) | old(X0) [cnf transformation 60]
132. ~kind(X0) | old(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 60]
133. ~wise(X0) | ~patient(X0) | curious(X0) [cnf transformation 61]
135. ~patient(X0) | ~quiet(X0) | curious(X0) [cnf transformation 61]
145. ~happy(sK7) | ~kind(X3) [cnf transformation 74]
147. happy(sK7) | ~kind(X3) [cnf transformation 74]
154. quiet(lucy) | ~calm(lucy) [cnf transformation 76]
164. ~brave(john) [cnf transformation 25]
168. 1 <=> ! [X0] : (~old(X0) | calm(X0)) [avatar definition]
169. ~old(X0) | calm(X0) <- (1) [avatar component clause 168]
171. 2 <=> patient(john) [avatar definition]
173. patient(john) <- (2) [avatar component clause 171]
174. 1 | 2 [avatar split clause 95,171,168]
180. 4 <=> calm(john) [avatar definition]
182. calm(john) <- (4) [avatar component clause 180]
183. 1 | 4 [avatar split clause 93,180,168]
256. ~kind(X0) | old(X0) | ~quiet(X0) [subsumption resolution 132,89]
257. ~quiet(X0) | old(X0) [subsumption resolution 256,88]
258. old(X0) | kind(X0) [subsumption resolution 129,257]
293. 27 <=> happy(sK7) [avatar definition]
298. 28 <=> ! [X3] : ~kind(X3) [avatar definition]
299. ~kind(X3) <- (28) [avatar component clause 298]
300. 28 | 27 [avatar split clause 147,293,298]
302. 28 | ~27 [avatar split clause 145,293,298]
304. 29 <=> calm(lucy) [avatar definition]
305. ~calm(lucy) <- (~29) [avatar component clause 304]
308. 30 <=> quiet(lucy) [avatar definition]
309. quiet(lucy) <- (30) [avatar component clause 308]
312. ~29 | 30 [avatar split clause 154,308,304]
346. ~quiet(john) | curious(john) <- (2) [resolution 135,173]
348. 37 <=> curious(john) [avatar definition]
350. curious(john) <- (37) [avatar component clause 348]
352. 38 <=> quiet(john) [avatar definition]
354. ~quiet(john) <- (~38) [avatar component clause 352]
355. 37 | ~38 | ~2 [avatar split clause 346,171,352,348]
417. kind(lucy) <- (30) [resolution 309,88]
419. $false <- (28, 30) [subsumption resolution 417,299]
420. ~28 | ~30 [avatar contradiction clause 419]
451. happy(john) | quiet(john) | tall(john) <- (4) [resolution 126,182]
452. happy(john) | tall(john) <- (4, ~38) [subsumption resolution 451,354]
454. 47 <=> tall(john) [avatar definition]
456. tall(john) <- (47) [avatar component clause 454]
458. 48 <=> happy(john) [avatar definition]
460. happy(john) <- (48) [avatar component clause 458]
461. 47 | 48 | ~4 | 38 [avatar split clause 452,352,180,458,454]
464. brave(john) <- (47) [resolution 456,107]
466. $false <- (47) [subsumption resolution 464,164]
467. ~47 [avatar contradiction clause 466]
472. ~patient(john) | wise(john) | curious(john) <- (48) [resolution 460,112]
483. ~patient(john) | curious(john) <- (48) [subsumption resolution 472,133]
484. 37 | ~2 | ~48 [avatar split clause 483,458,171,348]
486. calm(X0) | kind(X0) <- (1) [resolution 169,258]
490. calm(X0) <- (1, 28) [subsumption resolution 486,299]
494. $false <- (1, 28, ~29) [resolution 490,305]
495. ~1 | ~28 | 29 [avatar contradiction clause 494]
505. kind(john) <- (37) [resolution 350,86]
508. $false <- (28, 37) [subsumption resolution 505,299]
509. ~28 | ~37 [avatar contradiction clause 508]
510. $false [avatar sat refutation 174,183,300,302,312,355,420,461,467,484,495,509]
% SZS output end Proof for 588555915592099470026110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not patient then someone is not happy or patient.
If alice is not brave then john is both patient and happy.
Everyone who is generous is not funny.
If someone is not rich then someone is either not kind or not calm and vice versa.
Everyone who is both brave and not wise is wise or not wise and vice versa.
Everyone who is curious is either not wise or not creative and vice versa.
If someone is either not wise or not funny then someone is both not strong and generous.
If paul is either not humble or not happy then john is both not tall and not humble and vice versa.
If mary is both not patient and happy then john is kind or not kind.
If paul is old or happy then someone is either strong or brave and vice versa.
If paul is either old or rich then someone is curious or humble and vice versa.
If mary is happy then someone is either tall or not quiet.
If paul is happy then someone is both not calm and funny and vice versa.
Everyone who is kind is not creative or generous.
Everyone who is not patient is wise or quiet and vice versa.
Everyone who is not brave is either not quiet or quiet.
Paul is not curious or humble.
Someone is tall.
Someone is both calm and tall.
Paul is tall.
Susan is either funny or brave.
Someone is not calm or rich. | Paul is generous. | neutral | ((?[X]:((patient(X)|~patient(X))))=>(?[X]:((~happy(X)|patient(X)))))&
((~brave(alice))=>((patient(john)&happy(john))))&
(![X]:(generous(X)=>~funny(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:((brave(X)&~wise(X))<=>(wise(X)|~wise(X))))&
(![X]:(curious(X)<=>(~wise(X)<~>~creative(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>(?[X]:((~strong(X)&generous(X)))))&
(((~humble(paul)<~>~happy(paul)))<=>((~tall(john)&~humble(john))))&
(((~patient(mary)&happy(mary)))=>((kind(john)|~kind(john))))&
(((old(paul)|happy(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((old(paul)<~>rich(paul)))<=>(?[X]:((curious(X)|humble(X)))))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((happy(paul))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:(kind(X)=>(~creative(X)|generous(X))))&
(![X]:(~patient(X)<=>(wise(X)|quiet(X))))&
(![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
((~curious(paul)|humble(paul)))&
(?[X]:(tall(X)))&
(?[X]:((calm(X)&tall(X))))&
(tall(paul))&
((funny(susan)<~>brave(susan)))&
(?[X]:((~calm(X)|rich(X)))) | generous(paul) | [] | null | 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa.
If someone is not generous or not quiet then mary is both creative and brave.
If someone is generous then alice is tall or not tall.
If john is not rich then someone is patient.
Everyone who is either not old or rich is both not strong and not calm and vice versa.
If someone is either not funny or not creative then john is either brave or not tall.
If someone is either patient or happy then someone is humble and vice versa.
If john is not happy or not kind then someone is either tall or kind and vice versa.
Everyone who is strong is both not kind and old and vice versa.
Everyone who is creative or not strong is not calm or not happy.
If someone is either not kind or patient then susan is both not happy and wise.
Everyone who is old is both not strong and strong.
Everyone who is happy is either not humble or not happy.
If lucy is not funny or not brave then lucy is either funny or not curious and vice versa.
Everyone who is both curious and brave is both not patient and old and vice versa.
If someone is either curious or funny then mary is both not funny and not old.
Someone is not strong.
John is both not calm and not wise.
Mary is not happy.
Someone is both wise and not kind.
Mary is both not brave and wise.
Someone is either curious or kind.
Someone is not kind or patient. | John is rich. | contradiction | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>((creative(mary)&brave(mary))))&
((?[X]:(generous(X)))=>((tall(alice)|~tall(alice))))&
((~rich(john))=>(?[X]:(patient(X))))&
(![X]:((~old(X)<~>rich(X))<=>(~strong(X)&~calm(X))))&
((?[X]:((~funny(X)<~>~creative(X))))=>((brave(john)<~>~tall(john))))&
((?[X]:((patient(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(((~happy(john)|~kind(john)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(strong(X)<=>(~kind(X)&old(X))))&
(![X]:((creative(X)|~strong(X))=>(~calm(X)|~happy(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~happy(susan)&wise(susan))))&
(![X]:(old(X)=>(~strong(X)&strong(X))))&
(![X]:(happy(X)=>(~humble(X)<~>~happy(X))))&
(((~funny(lucy)|~brave(lucy)))<=>((funny(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~patient(X)&old(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~funny(mary)&~old(mary))))&
(?[X]:(~strong(X)))&
((~calm(john)&~wise(john)))&
(~happy(mary))&
(?[X]:((wise(X)&~kind(X))))&
((~brave(mary)&wise(mary)))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:((~kind(X)|patient(X)))) | rich(john) | [
"p4",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8197876446966933128709596
% SZS output start Proof for 8197876446966933128709596
5. ! [X0] : ((~old(X0) <~> rich(X0)) <=> (~calm(X0) & ~strong(X0))) [input p4]
9. ! [X0] : (strong(X0) <=> (old(X0) & ~kind(X0))) [input p8]
12. ! [X0] : (old(X0) => (strong(X0) & ~strong(X0))) [input p11]
18. ~wise(john) & ~calm(john) [input p17]
24. rich(john) [input hypothesis]
35. ! [X0] : ((strong(X0) & ~strong(X0)) | ~old(X0)) [ennf transformation 12]
42. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [flattening 42]
55. ! [X0] : ((strong(X0) | (~old(X0) | kind(X0))) & ((old(X0) & ~kind(X0)) | ~strong(X0))) [nnf transformation 9]
56. ! [X0] : ((strong(X0) | ~old(X0) | kind(X0)) & ((old(X0) & ~kind(X0)) | ~strong(X0))) [flattening 55]
88. ~rich(X0) | old(X0) | calm(X0) | strong(X0) [cnf transformation 43]
104. ~strong(X0) | old(X0) [cnf transformation 56]
112. ~strong(X0) | ~old(X0) [cnf transformation 35]
113. ~old(X0) | strong(X0) [cnf transformation 35]
131. ~calm(john) [cnf transformation 18]
141. rich(john) [cnf transformation 24]
159. 4 <=> rich(john) [avatar definition]
161. rich(john) <- (4) [avatar component clause 159]
256. ~strong(X0) [subsumption resolution 112,104]
311. 4 [avatar split clause 141,159]
357. 42 <=> old(john) [avatar definition]
359. old(john) <- (42) [avatar component clause 357]
364. old(john) | calm(john) | strong(john) <- (4) [resolution 88,161]
365. old(john) | strong(john) <- (4) [subsumption resolution 364,131]
366. old(john) <- (4) [subsumption resolution 365,256]
367. 42 | ~4 [avatar split clause 366,159,357]
373. strong(john) <- (42) [resolution 359,113]
375. $false <- (42) [subsumption resolution 373,256]
376. ~42 [avatar contradiction clause 375]
377. $false [avatar sat refutation 311,367,376]
% SZS output end Proof for 8197876446966933128709596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then john is both not funny and wise.
Everyone who is not calm is calm or not generous.
Everyone who is not curious or not patient is wise or funny and vice versa.
Everyone who is not funny is rich and vice versa.
If someone is humble then someone is both funny and not creative.
Everyone who is generous or not strong is brave.
Everyone who is not calm is both not quiet and old and vice versa.
Everyone who is not tall is either not wise or not creative.
If john is funny or not creative then someone is either not creative or brave and vice versa.
Everyone who is either not rich or not humble is not strong or not kind.
Everyone who is both funny and not creative is both rich and not happy.
If someone is calm then someone is either strong or not creative and vice versa.
If susan is humble or tall then someone is both curious and creative and vice versa.
Everyone who is curious or not patient is wise.
If someone is either not patient or not strong then paul is brave or generous.
Everyone who is creative is either generous or tall.
Someone is either not curious or not quiet.
Someone is both not calm and rich.
Lucy is both funny and not humble.
John is both not calm and not tall.
John is either not humble or not rich.
John is not quiet or humble.
Lucy is quiet.
Someone is either humble or not creative. | John is rich. | entailment | ((?[X]:(~rich(X)))=>((~funny(john)&wise(john))))&
(![X]:(~calm(X)=>(calm(X)|~generous(X))))&
(![X]:((~curious(X)|~patient(X))<=>(wise(X)|funny(X))))&
(![X]:(~funny(X)<=>rich(X)))&
((?[X]:(humble(X)))=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:((generous(X)|~strong(X))=>brave(X)))&
(![X]:(~calm(X)<=>(~quiet(X)&old(X))))&
(![X]:(~tall(X)=>(~wise(X)<~>~creative(X))))&
(((funny(john)|~creative(john)))<=>(?[X]:((~creative(X)<~>brave(X)))))&
(![X]:((~rich(X)<~>~humble(X))=>(~strong(X)|~kind(X))))&
(![X]:((funny(X)&~creative(X))=>(rich(X)&~happy(X))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(((humble(susan)|tall(susan)))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:((curious(X)|~patient(X))=>wise(X)))&
((?[X]:((~patient(X)<~>~strong(X))))=>((brave(paul)|generous(paul))))&
(![X]:(creative(X)=>(generous(X)<~>tall(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~calm(X)&rich(X))))&
((funny(lucy)&~humble(lucy)))&
((~calm(john)&~tall(john)))&
((~humble(john)<~>~rich(john)))&
((~quiet(john)|humble(john)))&
(quiet(lucy))&
(?[X]:((humble(X)<~>~creative(X)))) | rich(john) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2507571591534455350929190
% SZS output start Proof for 2507571591534455350929190
1. ? [X0] : ~rich(X0) => (wise(john) & ~funny(john)) [input p0]
4. ! [X0] : (~funny(X0) <=> rich(X0)) [input p3]
25. ~rich(john) [input hypothesis]
30. (wise(john) & ~funny(john)) | ! [X0] : rich(X0) [ennf transformation 1]
44. ! [X0] : ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0))) [nnf transformation 4]
77. ~funny(john) | rich(X0) [cnf transformation 30]
84. funny(X0) | rich(X0) [cnf transformation 44]
131. ~rich(john) [cnf transformation 25]
134. 1 <=> ! [X0] : rich(X0) [avatar definition]
135. rich(X0) <- (1) [avatar component clause 134]
142. 3 <=> funny(john) [avatar definition]
144. ~funny(john) <- (~3) [avatar component clause 142]
145. 1 | ~3 [avatar split clause 77,142,134]
262. 29 <=> rich(john) [avatar definition]
263. ~rich(john) <- (~29) [avatar component clause 262]
282. ~29 [avatar split clause 131,262]
285. rich(john) <- (~3) [resolution 84,144]
286. $false <- (~3, ~29) [subsumption resolution 285,263]
287. 3 | 29 [avatar contradiction clause 286]
288. $false <- (1, ~29) [resolution 135,263]
289. ~1 | 29 [avatar contradiction clause 288]
290. $false [avatar sat refutation 145,282,287,289]
% SZS output end Proof for 2507571591534455350929190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not quiet is both not funny and generous. If fred is quiet or patient then someone is not quiet or not brave. Everyone who is not generous is not wise or kind and vice versa. If someone is not curious then john is either strong or happy and vice versa. Everyone who is both creative and not kind is both not old and not tall. Everyone who is either calm or kind is either wise or not curious. Everyone who is both not quiet and humble is both wise and not happy and vice versa. Everyone who is happy or not rich is not happy and vice versa. If someone is both not patient and not brave then mary is both not patient and not wise and vice versa. Everyone who is wise is either calm or not tall and vice versa. If alice is both kind and not quiet then susan is either not calm or patient. If lucy is both not old and not curious then someone is either calm or not rich. Everyone who is not generous is both not rich and old and vice versa. If someone is both not patient and not humble then someone is both strong and kind. If someone is both strong and creative then someone is both curious and patient and vice versa. If someone is either calm or not funny then susan is patient and vice versa. Someone is happy or not rich. Someone is either not quiet or not generous. Alice is not brave. Someone is not calm. Someone is not patient or calm. John is not generous or curious. John is not brave. | Alice is not curious. | neutral | (![X]:((~rich(X)|~quiet(X))=>(~funny(X)&generous(X))))&
(((quiet(fred)|patient(fred)))=>(?[X]:((~quiet(X)|~brave(X)))))&
(![X]:(~generous(X)<=>(~wise(X)|kind(X))))&
((?[X]:(~curious(X)))<=>((strong(john)<~>happy(john))))&
(![X]:((creative(X)&~kind(X))=>(~old(X)&~tall(X))))&
(![X]:((calm(X)<~>kind(X))=>(wise(X)<~>~curious(X))))&
(![X]:((~quiet(X)&humble(X))<=>(wise(X)&~happy(X))))&
(![X]:((happy(X)|~rich(X))<=>~happy(X)))&
((?[X]:((~patient(X)&~brave(X))))<=>((~patient(mary)&~wise(mary))))&
(![X]:(wise(X)<=>(calm(X)<~>~tall(X))))&
(((kind(alice)&~quiet(alice)))=>((~calm(susan)<~>patient(susan))))&
(((~old(lucy)&~curious(lucy)))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:(~generous(X)<=>(~rich(X)&old(X))))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:((strong(X)&kind(X)))))&
((?[X]:((strong(X)&creative(X))))<=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:((calm(X)<~>~funny(X))))<=>(patient(susan)))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
(~brave(alice))&
(?[X]:(~calm(X)))&
(?[X]:((~patient(X)|calm(X))))&
((~generous(john)|curious(john)))&
(~brave(john)) | ~curious(alice) | [] | null | 0 |
If someone is either not brave or rich then susan is either generous or happy.
If someone is not brave or happy then someone is either not happy or rich.
If someone is not rich or brave then someone is not patient.
Everyone who is not quiet is not rich.
Everyone who is either not rich or rich is both calm and not tall and vice versa.
Everyone who is not patient or kind is not funny.
If someone is not rich then someone is humble and vice versa.
If fred is either funny or not patient then someone is either brave or humble and vice versa.
If someone is both kind and not rich then someone is strong and vice versa.
Everyone who is not tall or not humble is old.
Everyone who is rich is both rich and kind.
If susan is either not brave or funny then john is either not old or not calm.
If someone is not curious then someone is either not creative or humble and vice versa.
If someone is kind or wise then someone is not strong or not kind.
Everyone who is kind or rich is both quiet and patient.
If someone is not kind then fred is not strong.
Someone is either creative or not strong.
Lucy is not curious or not calm.
Alice is not quiet.
Lucy is generous.
Someone is generous.
Susan is not kind or not brave.
Someone is both happy and not kind.
Someone is not brave. | Alice is calm. | entailment | ((?[X]:((~brave(X)<~>rich(X))))=>((generous(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|happy(X))))=>(?[X]:((~happy(X)<~>rich(X)))))&
((?[X]:((~rich(X)|brave(X))))=>(?[X]:(~patient(X))))&
(![X]:(~quiet(X)=>~rich(X)))&
(![X]:((~rich(X)<~>rich(X))<=>(calm(X)&~tall(X))))&
(![X]:((~patient(X)|kind(X))=>~funny(X)))&
((?[X]:(~rich(X)))<=>(?[X]:(humble(X))))&
(((funny(fred)<~>~patient(fred)))<=>(?[X]:((brave(X)<~>humble(X)))))&
((?[X]:((kind(X)&~rich(X))))<=>(?[X]:(strong(X))))&
(![X]:((~tall(X)|~humble(X))=>old(X)))&
(![X]:(rich(X)=>(rich(X)&kind(X))))&
(((~brave(susan)<~>funny(susan)))=>((~old(john)<~>~calm(john))))&
((?[X]:(~curious(X)))<=>(?[X]:((~creative(X)<~>humble(X)))))&
((?[X]:((kind(X)|wise(X))))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((kind(X)|rich(X))=>(quiet(X)&patient(X))))&
((?[X]:(~kind(X)))=>(~strong(fred)))&
(?[X]:((creative(X)<~>~strong(X))))&
((~curious(lucy)|~calm(lucy)))&
(~quiet(alice))&
(generous(lucy))&
(?[X]:(generous(X)))&
((~kind(susan)|~brave(susan)))&
(?[X]:((happy(X)&~kind(X))))&
(?[X]:(~brave(X))) | calm(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4575994509830158548484282
% SZS output start Proof for 4575994509830158548484282
5. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> (~tall(X0) & calm(X0))) [input p4]
25. ~calm(alice) [input hypothesis]
52. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (tall(X0) | ~calm(X0))) & ((~tall(X0) & calm(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 5]
53. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | tall(X0) | ~calm(X0)) & ((~tall(X0) & calm(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [flattening 52]
97. calm(X0) | rich(X0) | rich(X0) [cnf transformation 53]
98. calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 53]
146. ~calm(alice) [cnf transformation 25]
147. calm(X0) | rich(X0) [duplicate literal removal 97]
148. calm(X0) | ~rich(X0) [duplicate literal removal 98]
200. calm(X0) [subsumption resolution 147,148]
343. $false [subsumption resolution 146,200]
% SZS output end Proof for 4575994509830158548484282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not strong or not humble then someone is patient or happy.
Everyone who is both brave and creative is not humble and vice versa.
Everyone who is not funny is funny or calm and vice versa.
Everyone who is not funny is creative or rich and vice versa.
If someone is both curious and wise then mary is either happy or strong and vice versa.
If paul is calm or wise then someone is not funny and vice versa.
Everyone who is either not patient or wise is both not old and kind.
Everyone who is both not funny and not creative is happy and vice versa.
If alice is either happy or not wise then someone is both not creative and quiet and vice versa.
Everyone who is both not patient and happy is either not calm or creative and vice versa.
If someone is not kind then someone is tall and vice versa.
Everyone who is both creative and not happy is either generous or patient and vice versa.
Everyone who is either not curious or funny is either generous or not quiet and vice versa.
If john is either not happy or happy then susan is either not happy or generous and vice versa.
If someone is creative or curious then paul is not strong or not happy.
Everyone who is not kind is both patient and not quiet.
Fred is not strong or not patient.
Fred is either not brave or not kind.
Someone is not wise.
Fred is either not patient or quiet.
Susan is both not strong and humble.
Someone is either not brave or not generous.
Mary is kind. | Alice is not kind. | contradiction | (((~strong(lucy)|~humble(lucy)))=>(?[X]:((patient(X)|happy(X)))))&
(![X]:((brave(X)&creative(X))<=>~humble(X)))&
(![X]:(~funny(X)<=>(funny(X)|calm(X))))&
(![X]:(~funny(X)<=>(creative(X)|rich(X))))&
((?[X]:((curious(X)&wise(X))))<=>((happy(mary)<~>strong(mary))))&
(((calm(paul)|wise(paul)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)<~>wise(X))=>(~old(X)&kind(X))))&
(![X]:((~funny(X)&~creative(X))<=>happy(X)))&
(((happy(alice)<~>~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~patient(X)&happy(X))<=>(~calm(X)<~>creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(tall(X))))&
(![X]:((creative(X)&~happy(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(generous(X)<~>~quiet(X))))&
(((~happy(john)<~>happy(john)))<=>((~happy(susan)<~>generous(susan))))&
((?[X]:((creative(X)|curious(X))))=>((~strong(paul)|~happy(paul))))&
(![X]:(~kind(X)=>(patient(X)&~quiet(X))))&
((~strong(fred)|~patient(fred)))&
((~brave(fred)<~>~kind(fred)))&
(?[X]:(~wise(X)))&
((~patient(fred)<~>quiet(fred)))&
((~strong(susan)&humble(susan)))&
(?[X]:((~brave(X)<~>~generous(X))))&
(kind(mary)) | ~kind(alice) | [
"p2",
"p6",
"p7",
"p8",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9168075760289195697697357
% SZS output start Proof for 9168075760289195697697357
3. ! [X0] : (~funny(X0) <=> (calm(X0) | funny(X0))) [input p2]
7. ! [X0] : ((~patient(X0) <~> wise(X0)) => (kind(X0) & ~old(X0))) [input p6]
8. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> happy(X0)) [input p7]
9. (happy(alice) <~> ~wise(alice)) <=> ? [X0] : (quiet(X0) & ~creative(X0)) [input p8]
10. ! [X0] : ((happy(X0) & ~patient(X0)) <=> (~calm(X0) <~> creative(X0))) [input p9]
16. ! [X0] : (~kind(X0) => (~quiet(X0) & patient(X0))) [input p15]
20. ~patient(fred) <~> quiet(fred) [input p19]
24. ~kind(alice) [input hypothesis]
27. ! [X0] : ((~patient(X0) <~> wise(X0)) => kind(X0)) [pure predicate removal 7]
31. ! [X0] : (kind(X0) | (~patient(X0) <=> wise(X0))) [ennf transformation 27]
34. ! [X0] : ((~quiet(X0) & patient(X0)) | kind(X0)) [ennf transformation 16]
37. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | funny(X0))) [nnf transformation 3]
38. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | funny(X0))) [flattening 37]
50. ! [X0] : (kind(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 31]
51. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | (creative(X0) | funny(X0)))) [nnf transformation 8]
52. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | creative(X0) | funny(X0))) [flattening 51]
53. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X0] : (quiet(X0) & ~creative(X0)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [nnf transformation 9]
54. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X1] : (quiet(X1) & ~creative(X1)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [rectify 53]
55. ? [X1] : (quiet(X1) & ~creative(X1)) => (quiet(sK3) & ~creative(sK3)) [choice axiom]
56. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & ((quiet(sK3) & ~creative(sK3)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [skolemisation 54,55]
57. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (~happy(X0) | patient(X0)))) [nnf transformation 10]
58. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ~happy(X0) | patient(X0))) [flattening 57]
71. (~quiet(fred) | patient(fred)) & (quiet(fred) | ~patient(fred)) [nnf transformation 20]
78. calm(X0) | funny(X0) | funny(X0) [cnf transformation 38]
79. ~funny(X0) | ~funny(X0) [cnf transformation 38]
94. ~wise(X0) | ~patient(X0) | kind(X0) [cnf transformation 50]
95. happy(X0) | creative(X0) | funny(X0) [cnf transformation 52]
97. ~creative(X0) | ~happy(X0) [cnf transformation 52]
103. wise(alice) | ~happy(alice) | ~quiet(X0) | creative(X0) [cnf transformation 56]
104. creative(X0) | ~calm(X0) | ~happy(X0) | patient(X0) [cnf transformation 58]
109. happy(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 58]
136. kind(X0) | patient(X0) [cnf transformation 34]
142. quiet(fred) | ~patient(fred) [cnf transformation 71]
149. ~kind(alice) [cnf transformation 24]
154. calm(X0) | funny(X0) [duplicate literal removal 78]
155. ~funny(X0) [duplicate literal removal 79]
174. calm(X0) [subsumption resolution 154,155]
201. creative(X0) | happy(X0) [subsumption resolution 95,155]
203. 10 <=> ! [X0] : (~quiet(X0) | creative(X0)) [avatar definition]
204. ~quiet(X0) | creative(X0) <- (10) [avatar component clause 203]
206. 11 <=> happy(alice) [avatar definition]
208. ~happy(alice) <- (~11) [avatar component clause 206]
210. 12 <=> wise(alice) [avatar definition]
212. wise(alice) <- (12) [avatar component clause 210]
213. 10 | ~11 | 12 [avatar split clause 103,210,206,203]
227. happy(X0) | ~creative(X0) [subsumption resolution 109,174]
228. ~creative(X0) [subsumption resolution 227,97]
229. ~calm(X0) | ~happy(X0) | patient(X0) [subsumption resolution 104,228]
230. ~happy(X0) | patient(X0) [subsumption resolution 229,174]
285. 26 <=> patient(fred) [avatar definition]
287. ~patient(fred) <- (~26) [avatar component clause 285]
300. 29 <=> quiet(fred) [avatar definition]
301. quiet(fred) <- (29) [avatar component clause 300]
304. ~26 | 29 [avatar split clause 142,300,285]
317. ~quiet(X0) <- (10) [subsumption resolution 204,228]
323. patient(alice) [resolution 136,149]
329. $false <- (10, 29) [subsumption resolution 301,317]
330. ~10 | ~29 [avatar contradiction clause 329]
337. happy(X1) [resolution 201,228]
340. $false <- (~11) [resolution 337,208]
341. 11 [avatar contradiction clause 340]
345. patient(X0) [resolution 230,337]
361. ~patient(alice) | kind(alice) <- (12) [resolution 94,212]
363. kind(alice) <- (12) [subsumption resolution 361,323]
364. $false <- (12) [subsumption resolution 363,149]
365. ~12 [avatar contradiction clause 364]
366. $false <- (~26) [subsumption resolution 287,345]
367. 26 [avatar contradiction clause 366]
369. $false [avatar sat refutation 213,304,330,341,365,367]
% SZS output end Proof for 9168075760289195697697357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both curious and not calm is calm or kind. Everyone who is brave or not patient is rich or not patient and vice versa. If lucy is both tall and rich then someone is either not kind or not calm. If someone is both not kind and happy then someone is both not quiet and not kind and vice versa. Everyone who is either not wise or wise is either rich or tall. If someone is tall or not brave then someone is not brave or not happy and vice versa. If lucy is both not kind and patient then someone is not happy or quiet and vice versa. If someone is either not generous or curious then someone is both not tall and not rich and vice versa. Everyone who is both not rich and not brave is both kind and not curious and vice versa. Everyone who is both not curious and not calm is either not kind or not patient. If john is brave or not kind then john is wise. Everyone who is either brave or kind is both not brave and not creative. Everyone who is quiet or creative is not patient and vice versa. If someone is either generous or curious then mary is both not brave and not patient and vice versa. If someone is kind then john is both wise and not wise and vice versa. Everyone who is both patient and not wise is either not rich or curious and vice versa. Someone is either humble or not tall. Lucy is either not kind or wise. Paul is not humble. Someone is either not kind or patient. Someone is either not happy or wise. | Paul is curious. | contradiction | (![X]:((curious(X)&~calm(X))=>(calm(X)|kind(X))))&
(![X]:((brave(X)|~patient(X))<=>(rich(X)|~patient(X))))&
(((tall(lucy)&rich(lucy)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
((?[X]:((~kind(X)&happy(X))))<=>(?[X]:((~quiet(X)&~kind(X)))))&
(![X]:((~wise(X)<~>wise(X))=>(rich(X)<~>tall(X))))&
((?[X]:((tall(X)|~brave(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
(((~kind(lucy)&patient(lucy)))<=>(?[X]:((~happy(X)|quiet(X)))))&
((?[X]:((~generous(X)<~>curious(X))))<=>(?[X]:((~tall(X)&~rich(X)))))&
(![X]:((~rich(X)&~brave(X))<=>(kind(X)&~curious(X))))&
(![X]:((~curious(X)&~calm(X))=>(~kind(X)<~>~patient(X))))&
(((brave(john)|~kind(john)))=>(wise(john)))&
(![X]:((brave(X)<~>kind(X))=>(~brave(X)&~creative(X))))&
(![X]:((quiet(X)|creative(X))<=>~patient(X)))&
((?[X]:((generous(X)<~>curious(X))))<=>((~brave(mary)&~patient(mary))))&
((?[X]:(kind(X)))<=>((wise(john)&~wise(john))))&
(![X]:((patient(X)&~wise(X))<=>(~rich(X)<~>curious(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
((~kind(lucy)<~>wise(lucy)))&
(~humble(paul))&
(?[X]:((~kind(X)<~>patient(X))))&
(?[X]:((~happy(X)<~>wise(X)))) | curious(paul) | [
"p1",
"p8",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 227648431032215987264984
% SZS output start Proof for 227648431032215987264984
2. ! [X0] : ((~patient(X0) | brave(X0)) <=> (~patient(X0) | rich(X0))) [input p1]
9. ! [X0] : ((~brave(X0) & ~rich(X0)) <=> (~curious(X0) & kind(X0))) [input p8]
12. ! [X0] : ((brave(X0) <~> kind(X0)) => (~creative(X0) & ~brave(X0))) [input p11]
15. ? [X0] : kind(X0) <=> (~wise(john) & wise(john)) [input p14]
16. ! [X0] : ((~wise(X0) & patient(X0)) <=> (~rich(X0) <~> curious(X0))) [input p15]
22. curious(paul) [input hypothesis]
34. ! [X0] : ((~creative(X0) & ~brave(X0)) | (brave(X0) <=> kind(X0))) [ennf transformation 12]
35. ! [X0] : (((~patient(X0) | brave(X0)) | (patient(X0) & ~rich(X0))) & ((~patient(X0) | rich(X0)) | (patient(X0) & ~brave(X0)))) [nnf transformation 2]
36. ! [X0] : ((~patient(X0) | brave(X0) | (patient(X0) & ~rich(X0))) & (~patient(X0) | rich(X0) | (patient(X0) & ~brave(X0)))) [flattening 35]
61. ! [X0] : (((~brave(X0) & ~rich(X0)) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | (brave(X0) | rich(X0)))) [nnf transformation 9]
62. ! [X0] : (((~brave(X0) & ~rich(X0)) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | brave(X0) | rich(X0))) [flattening 61]
64. ! [X0] : ((~creative(X0) & ~brave(X0)) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) [nnf transformation 34]
72. (? [X0] : kind(X0) | (wise(john) | ~wise(john))) & ((~wise(john) & wise(john)) | ! [X0] : ~kind(X0)) [nnf transformation 15]
73. (? [X0] : kind(X0) | wise(john) | ~wise(john)) & ((~wise(john) & wise(john)) | ! [X0] : ~kind(X0)) [flattening 72]
74. (? [X0] : kind(X0) | wise(john) | ~wise(john)) & ((~wise(john) & wise(john)) | ! [X1] : ~kind(X1)) [rectify 73]
75. ? [X0] : kind(X0) => kind(sK9) [choice axiom]
76. (kind(sK9) | wise(john) | ~wise(john)) & ((~wise(john) & wise(john)) | ! [X1] : ~kind(X1)) [skolemisation 74,75]
77. ! [X0] : (((~wise(X0) & patient(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (wise(X0) | ~patient(X0)))) [nnf transformation 16]
78. ! [X0] : (((~wise(X0) & patient(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | wise(X0) | ~patient(X0))) [flattening 77]
92. ~rich(X0) | brave(X0) | ~patient(X0) [cnf transformation 36]
119. rich(X0) | brave(X0) | kind(X0) [cnf transformation 62]
120. ~curious(X0) | brave(X0) | rich(X0) [cnf transformation 62]
127. ~brave(X0) | kind(X0) | ~brave(X0) [cnf transformation 64]
140. wise(john) | ~kind(X1) [cnf transformation 76]
141. ~wise(john) | ~kind(X1) [cnf transformation 76]
146. ~rich(X0) | patient(X0) | ~curious(X0) [cnf transformation 78]
158. curious(paul) [cnf transformation 22]
159. ~brave(X0) | kind(X0) [duplicate literal removal 127]
288. 28 <=> wise(john) [avatar definition]
326. 36 <=> ! [X1] : ~kind(X1) [avatar definition]
327. ~kind(X1) <- (36) [avatar component clause 326]
328. 36 | ~28 [avatar split clause 141,288,326]
329. 36 | 28 [avatar split clause 140,288,326]
407. brave(X0) | kind(X0) | brave(X0) | ~patient(X0) [resolution 119,92]
408. brave(X0) | kind(X0) | ~patient(X0) [duplicate literal removal 407]
412. ~patient(X0) | brave(X0) <- (36) [subsumption resolution 408,327]
424. brave(paul) | rich(paul) [resolution 120,158]
426. 48 <=> rich(paul) [avatar definition]
428. rich(paul) <- (48) [avatar component clause 426]
430. 49 <=> brave(paul) [avatar definition]
432. brave(paul) <- (49) [avatar component clause 430]
433. 48 | 49 [avatar split clause 424,430,426]
449. patient(paul) | ~curious(paul) <- (48) [resolution 146,428]
456. patient(paul) <- (48) [subsumption resolution 449,158]
494. brave(paul) <- (36, 48) [resolution 456,412]
496. 49 | ~36 | ~48 [avatar split clause 494,426,326,430]
500. kind(paul) <- (49) [resolution 432,159]
501. $false <- (36, 49) [subsumption resolution 500,327]
502. ~36 | ~49 [avatar contradiction clause 501]
503. $false [avatar sat refutation 328,329,433,496,502]
% SZS output end Proof for 227648431032215987264984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and not kind then someone is both not generous and not brave and vice versa. If lucy is old then paul is either not happy or not old and vice versa. Everyone who is either brave or not quiet is either kind or not generous and vice versa. If fred is both old and not calm then someone is either not old or not funny and vice versa. If alice is not generous then paul is not curious or brave and vice versa. If alice is both rich and curious then someone is both not calm and brave. If someone is not wise then mary is either not kind or not old and vice versa. If someone is both not wise and strong then susan is funny or creative and vice versa. Everyone who is humble is not rich. Everyone who is both not creative and old is not wise. Everyone who is either not kind or strong is both rich and not rich. Everyone who is not strong or happy is both generous and not creative. Everyone who is patient is happy and vice versa. If alice is both curious and not wise then someone is either not creative or funny. If someone is either not patient or old then someone is either not happy or rich. If someone is either not happy or not calm then someone is either old or not brave. Paul is old or humble. Someone is patient or curious. Someone is old or wise. John is not brave or not old. Fred is both tall and not curious. Someone is both wise and not calm. John is not old. Someone is either quiet or brave. | Fred is curious. | contradiction | ((?[X]:((wise(X)&~kind(X))))<=>(?[X]:((~generous(X)&~brave(X)))))&
((old(lucy))<=>((~happy(paul)<~>~old(paul))))&
(![X]:((brave(X)<~>~quiet(X))<=>(kind(X)<~>~generous(X))))&
(((old(fred)&~calm(fred)))<=>(?[X]:((~old(X)<~>~funny(X)))))&
((~generous(alice))<=>((~curious(paul)|brave(paul))))&
(((rich(alice)&curious(alice)))=>(?[X]:((~calm(X)&brave(X)))))&
((?[X]:(~wise(X)))<=>((~kind(mary)<~>~old(mary))))&
((?[X]:((~wise(X)&strong(X))))<=>((funny(susan)|creative(susan))))&
(![X]:(humble(X)=>~rich(X)))&
(![X]:((~creative(X)&old(X))=>~wise(X)))&
(![X]:((~kind(X)<~>strong(X))=>(rich(X)&~rich(X))))&
(![X]:((~strong(X)|happy(X))=>(generous(X)&~creative(X))))&
(![X]:(patient(X)<=>happy(X)))&
(((curious(alice)&~wise(alice)))=>(?[X]:((~creative(X)<~>funny(X)))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:((~happy(X)<~>rich(X)))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(?[X]:((old(X)<~>~brave(X)))))&
((old(paul)|humble(paul)))&
(?[X]:((patient(X)|curious(X))))&
(?[X]:((old(X)|wise(X))))&
((~brave(john)|~old(john)))&
((tall(fred)&~curious(fred)))&
(?[X]:((wise(X)&~calm(X))))&
(~old(john))&
(?[X]:((quiet(X)<~>brave(X)))) | curious(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4300008178883958064720578
% SZS output start Proof for 4300008178883958064720578
21. ~curious(fred) & tall(fred) [input p20]
25. curious(fred) [input hypothesis]
29. ~curious(fred) [pure predicate removal 21]
150. ~curious(fred) [cnf transformation 29]
156. curious(fred) [cnf transformation 25]
398. $false [subsumption resolution 156,150]
% SZS output end Proof for 4300008178883958064720578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is either wise or creative.
Everyone who is generous is both patient and not generous.
Everyone who is either not brave or funny is both rich and happy.
If alice is not old or calm then someone is both wise and not curious and vice versa.
Everyone who is not strong is brave.
Everyone who is either not brave or kind is curious and vice versa.
Everyone who is funny or not tall is both not calm and not wise.
Everyone who is not brave or curious is either happy or generous and vice versa.
Everyone who is happy or wise is kind and vice versa.
Everyone who is either not calm or not wise is curious or not calm and vice versa.
Everyone who is not kind is not kind or not humble.
If someone is both calm and creative then someone is not tall and vice versa.
If someone is rich then mary is creative and vice versa.
If alice is not strong then paul is either not generous or old and vice versa.
If susan is either not creative or calm then someone is humble and vice versa.
Alice is curious.
Someone is brave.
Someone is either calm or kind.
Lucy is humble.
Someone is creative or not wise.
Alice is not humble or not curious.
Someone is calm or not brave.
Someone is either not strong or not old. | Alice is tall. | entailment | (![X]:(generous(X)=>(wise(X)<~>creative(X))))&
(![X]:(generous(X)=>(patient(X)&~generous(X))))&
(![X]:((~brave(X)<~>funny(X))=>(rich(X)&happy(X))))&
(((~old(alice)|calm(alice)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((~brave(X)<~>kind(X))<=>curious(X)))&
(![X]:((funny(X)|~tall(X))=>(~calm(X)&~wise(X))))&
(![X]:((~brave(X)|curious(X))<=>(happy(X)<~>generous(X))))&
(![X]:((happy(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)<~>~wise(X))<=>(curious(X)|~calm(X))))&
(![X]:(~kind(X)=>(~kind(X)|~humble(X))))&
((?[X]:((calm(X)&creative(X))))<=>(?[X]:(~tall(X))))&
((?[X]:(rich(X)))<=>(creative(mary)))&
((~strong(alice))<=>((~generous(paul)<~>old(paul))))&
(((~creative(susan)<~>calm(susan)))<=>(?[X]:(humble(X))))&
(curious(alice))&
(?[X]:(brave(X)))&
(?[X]:((calm(X)<~>kind(X))))&
(humble(lucy))&
(?[X]:((creative(X)|~wise(X))))&
((~humble(alice)|~curious(alice)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~strong(X)<~>~old(X)))) | tall(alice) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5396296003302517796111285
% SZS output start Proof for 5396296003302517796111285
7. ! [X0] : ((~tall(X0) | funny(X0)) => (~wise(X0) & ~calm(X0))) [input p6]
10. ! [X0] : ((~calm(X0) <~> ~wise(X0)) <=> (~calm(X0) | curious(X0))) [input p9]
24. ~tall(alice) [input hypothesis]
31. ! [X0] : ((~wise(X0) & ~calm(X0)) | (tall(X0) & ~funny(X0))) [ennf transformation 7]
46. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (calm(X0) & ~curious(X0))) & ((~calm(X0) | curious(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [nnf transformation 10]
47. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (calm(X0) & ~curious(X0))) & (~calm(X0) | curious(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [flattening 46]
92. ~calm(X0) | tall(X0) [cnf transformation 31]
94. ~wise(X0) | tall(X0) [cnf transformation 31]
109. wise(X0) | calm(X0) | calm(X0) [cnf transformation 47]
134. ~tall(alice) [cnf transformation 24]
136. calm(X0) | wise(X0) [duplicate literal removal 109]
167. 6 <=> ! [X1] : tall(X1) [avatar definition]
168. tall(X1) <- (6) [avatar component clause 167]
270. $false <- (6) [resolution 168,134]
271. ~6 [avatar contradiction clause 270]
286. wise(X0) | tall(X0) [resolution 136,92]
289. tall(X0) [subsumption resolution 286,94]
290. 6 [avatar split clause 289,167]
292. $false [avatar sat refutation 271,290]
% SZS output end Proof for 5396296003302517796111285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both 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. | Lucy is wise. | 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))) | wise(lucy) | [] | null | 0 |
Everyone who is curious or not brave is both not creative and old. Everyone who is either brave or not strong is both not patient and patient and vice versa. Everyone who is not tall or not wise is both happy and not creative and vice versa. If lucy is patient or not generous then alice is not old or wise. Everyone who is not funny or not creative is either old or not quiet. Everyone who is both not calm and not generous is both creative and tall and vice versa. If someone is both tall and not patient then someone is not curious or not old. If mary is both not happy and generous then someone is both curious and quiet. If susan is both not old and quiet then mary is either generous or not humble. If someone is not old then susan is kind. Everyone who is quiet is either not brave or patient. Everyone who is not happy is strong or rich and vice versa. If someone is rich or funny then someone is both not quiet and strong and vice versa. Everyone who is wise is both not quiet and rich and vice versa. Everyone who is either wise or not brave is both not tall and rich. Everyone who is both not tall and not happy is not quiet. Someone is either quiet or not strong. Paul is generous or wise. John is both calm and not tall. Someone is not curious. Someone is either not rich or not humble. Someone is either tall or not happy. | Mary is not brave. | contradiction | (![X]:((curious(X)|~brave(X))=>(~creative(X)&old(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~patient(X)&patient(X))))&
(![X]:((~tall(X)|~wise(X))<=>(happy(X)&~creative(X))))&
(((patient(lucy)|~generous(lucy)))=>((~old(alice)|wise(alice))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)<~>~quiet(X))))&
(![X]:((~calm(X)&~generous(X))<=>(creative(X)&tall(X))))&
((?[X]:((tall(X)&~patient(X))))=>(?[X]:((~curious(X)|~old(X)))))&
(((~happy(mary)&generous(mary)))=>(?[X]:((curious(X)&quiet(X)))))&
(((~old(susan)&quiet(susan)))=>((generous(mary)<~>~humble(mary))))&
((?[X]:(~old(X)))=>(kind(susan)))&
(![X]:(quiet(X)=>(~brave(X)<~>patient(X))))&
(![X]:(~happy(X)<=>(strong(X)|rich(X))))&
((?[X]:((rich(X)|funny(X))))<=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:(wise(X)<=>(~quiet(X)&rich(X))))&
(![X]:((wise(X)<~>~brave(X))=>(~tall(X)&rich(X))))&
(![X]:((~tall(X)&~happy(X))=>~quiet(X)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((generous(paul)|wise(paul)))&
((calm(john)&~tall(john)))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((tall(X)<~>~happy(X)))) | ~brave(mary) | [
"p0",
"p1",
"p2",
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 825299186217402581698302
% SZS output start Proof for 825299186217402581698302
1. ! [X0] : ((~brave(X0) | curious(X0)) => (old(X0) & ~creative(X0))) [input p0]
2. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (patient(X0) & ~patient(X0))) [input p1]
3. ! [X0] : ((~wise(X0) | ~tall(X0)) <=> (~creative(X0) & happy(X0))) [input p2]
5. ! [X0] : ((~creative(X0) | ~funny(X0)) => (old(X0) <~> ~quiet(X0))) [input p4]
12. ! [X0] : (~happy(X0) <=> (rich(X0) | strong(X0))) [input p11]
14. ! [X0] : (wise(X0) <=> (rich(X0) & ~quiet(X0))) [input p13]
23. ~brave(mary) [input hypothesis]
27. ! [X0] : ((old(X0) & ~creative(X0)) | (brave(X0) & ~curious(X0))) [ennf transformation 1]
30. ! [X0] : ((old(X0) <~> ~quiet(X0)) | (creative(X0) & funny(X0))) [ennf transformation 5]
40. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 2]
41. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 40]
42. ! [X0] : (((~wise(X0) | ~tall(X0)) | (creative(X0) | ~happy(X0))) & ((~creative(X0) & happy(X0)) | (wise(X0) & tall(X0)))) [nnf transformation 3]
43. ! [X0] : ((~wise(X0) | ~tall(X0) | creative(X0) | ~happy(X0)) & ((~creative(X0) & happy(X0)) | (wise(X0) & tall(X0)))) [flattening 42]
44. ! [X0] : (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (creative(X0) & funny(X0))) [nnf transformation 30]
54. ! [X0] : ((~happy(X0) | (~rich(X0) & ~strong(X0))) & ((rich(X0) | strong(X0)) | happy(X0))) [nnf transformation 12]
55. ! [X0] : ((~happy(X0) | (~rich(X0) & ~strong(X0))) & (rich(X0) | strong(X0) | happy(X0))) [flattening 54]
61. ! [X0] : ((wise(X0) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | ~wise(X0))) [flattening 61]
76. ~creative(X0) | brave(X0) [cnf transformation 27]
78. old(X0) | brave(X0) [cnf transformation 27]
80. ~patient(X0) | brave(X0) | strong(X0) [cnf transformation 41]
82. patient(X0) | brave(X0) | strong(X0) [cnf transformation 41]
86. happy(X0) | wise(X0) [cnf transformation 43]
95. ~old(X0) | quiet(X0) | creative(X0) [cnf transformation 44]
108. ~happy(X0) | ~strong(X0) [cnf transformation 55]
115. ~quiet(X0) | ~wise(X0) [cnf transformation 62]
133. ~brave(mary) [cnf transformation 23]
134. strong(X0) | brave(X0) [subsumption resolution 80,82]
261. ~strong(X0) | wise(X0) [resolution 108,86]
286. wise(X0) | brave(X0) [resolution 261,134]
287. quiet(X0) | creative(X0) | brave(X0) [resolution 95,78]
288. quiet(X0) | brave(X0) [subsumption resolution 287,76]
312. brave(X4) | ~wise(X4) [resolution 288,115]
316. brave(X4) [subsumption resolution 312,286]
345. $false [resolution 316,133]
% SZS output end Proof for 825299186217402581698302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is wise then someone is not tall or brave.
Everyone who is either brave or not old is creative and vice versa.
Everyone who is both humble and brave is not calm or quiet and vice versa.
If someone is strong then paul is brave or not curious.
If susan is either not curious or not strong then susan is happy or not strong.
Everyone who is not brave or not rich is both old and rich and vice versa.
Everyone who is not creative is either calm or not kind and vice versa.
If susan is either generous or kind then someone is not quiet or not generous and vice versa.
If paul is both not kind and rich then someone is not patient or old and vice versa.
Everyone who is funny is not brave.
Everyone who is strong or not strong is both generous and curious and vice versa.
If someone is generous or not strong then someone is not strong and vice versa.
If someone is either not strong or not old then alice is either creative or funny and vice versa.
If someone is calm then someone is tall or not brave.
If someone is both calm and not tall then someone is not strong or not funny and vice versa.
If fred is both wise and not calm then john is not brave and vice versa.
Someone is quiet or not happy.
Alice is old.
Someone is funny or humble.
Someone is either calm or curious.
Alice is both old and funny.
Someone is curious or rich.
Someone is both old and wise.
Mary is both happy and not old. | Susan is funny. | contradiction | ((wise(fred))=>(?[X]:((~tall(X)|brave(X)))))&
(![X]:((brave(X)<~>~old(X))<=>creative(X)))&
(![X]:((humble(X)&brave(X))<=>(~calm(X)|quiet(X))))&
((?[X]:(strong(X)))=>((brave(paul)|~curious(paul))))&
(((~curious(susan)<~>~strong(susan)))=>((happy(susan)|~strong(susan))))&
(![X]:((~brave(X)|~rich(X))<=>(old(X)&rich(X))))&
(![X]:(~creative(X)<=>(calm(X)<~>~kind(X))))&
(((generous(susan)<~>kind(susan)))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(((~kind(paul)&rich(paul)))<=>(?[X]:((~patient(X)|old(X)))))&
(![X]:(funny(X)=>~brave(X)))&
(![X]:((strong(X)|~strong(X))<=>(generous(X)&curious(X))))&
((?[X]:((generous(X)|~strong(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~strong(X)<~>~old(X))))<=>((creative(alice)<~>funny(alice))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)|~brave(X)))))&
((?[X]:((calm(X)&~tall(X))))<=>(?[X]:((~strong(X)|~funny(X)))))&
(((wise(fred)&~calm(fred)))<=>(~brave(john)))&
(?[X]:((quiet(X)|~happy(X))))&
(old(alice))&
(?[X]:((funny(X)|humble(X))))&
(?[X]:((calm(X)<~>curious(X))))&
((old(alice)&funny(alice)))&
(?[X]:((curious(X)|rich(X))))&
(?[X]:((old(X)&wise(X))))&
((happy(mary)&~old(mary))) | funny(susan) | [
"p1",
"p2",
"p5",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2951951960780424641335234
% SZS output start Proof for 2951951960780424641335234
2. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> creative(X0)) [input p1]
3. ! [X0] : ((brave(X0) & humble(X0)) <=> (quiet(X0) | ~calm(X0))) [input p2]
6. ! [X0] : ((~rich(X0) | ~brave(X0)) <=> (rich(X0) & old(X0))) [input p5]
7. ! [X0] : (~creative(X0) <=> (calm(X0) <~> ~kind(X0))) [input p6]
8. (generous(susan) <~> kind(susan)) <=> ? [X0] : (~generous(X0) | ~quiet(X0)) [input p7]
10. ! [X0] : (funny(X0) => ~brave(X0)) [input p9]
11. ! [X0] : ((~strong(X0) | strong(X0)) <=> (curious(X0) & generous(X0))) [input p10]
25. funny(susan) [input hypothesis]
34. ! [X0] : (~brave(X0) | ~funny(X0)) [ennf transformation 10]
38. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~creative(X0)) & (creative(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 2]
39. ! [X0] : (((brave(X0) & humble(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~brave(X0) | ~humble(X0)))) [nnf transformation 3]
40. ! [X0] : (((brave(X0) & humble(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~brave(X0) | ~humble(X0))) [flattening 39]
42. ! [X0] : (((~rich(X0) | ~brave(X0)) | (~rich(X0) | ~old(X0))) & ((rich(X0) & old(X0)) | (rich(X0) & brave(X0)))) [nnf transformation 6]
43. ! [X0] : ((~rich(X0) | ~brave(X0) | ~rich(X0) | ~old(X0)) & ((rich(X0) & old(X0)) | (rich(X0) & brave(X0)))) [flattening 42]
44. ! [X0] : ((~creative(X0) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | creative(X0))) [nnf transformation 7]
45. (((~kind(susan) | ~generous(susan)) & (kind(susan) | generous(susan))) | ! [X0] : (generous(X0) & quiet(X0))) & (? [X0] : (~generous(X0) | ~quiet(X0)) | ((generous(susan) | ~kind(susan)) & (kind(susan) | ~generous(susan)))) [nnf transformation 8]
46. (((~kind(susan) | ~generous(susan)) & (kind(susan) | generous(susan))) | ! [X0] : (generous(X0) & quiet(X0))) & (? [X1] : (~generous(X1) | ~quiet(X1)) | ((generous(susan) | ~kind(susan)) & (kind(susan) | ~generous(susan)))) [rectify 45]
47. ? [X1] : (~generous(X1) | ~quiet(X1)) => (~generous(sK1) | ~quiet(sK1)) [choice axiom]
48. (((~kind(susan) | ~generous(susan)) & (kind(susan) | generous(susan))) | ! [X0] : (generous(X0) & quiet(X0))) & ((~generous(sK1) | ~quiet(sK1)) | ((generous(susan) | ~kind(susan)) & (kind(susan) | ~generous(susan)))) [skolemisation 46,47]
54. ! [X0] : (((~strong(X0) | strong(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (strong(X0) & ~strong(X0)))) [nnf transformation 11]
55. ! [X0] : ((~strong(X0) | strong(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (strong(X0) & ~strong(X0)))) [flattening 54]
89. ~creative(X0) | brave(X0) | ~old(X0) [cnf transformation 38]
94. calm(X0) | brave(X0) [cnf transformation 40]
95. ~quiet(X0) | brave(X0) [cnf transformation 40]
99. old(X0) | brave(X0) [cnf transformation 43]
105. ~calm(X0) | kind(X0) | creative(X0) [cnf transformation 44]
112. ~kind(susan) | ~generous(susan) | quiet(X0) [cnf transformation 48]
119. ~funny(X0) | ~brave(X0) [cnf transformation 34]
120. generous(X0) | ~strong(X0) [cnf transformation 55]
121. generous(X0) | strong(X0) [cnf transformation 55]
157. funny(susan) [cnf transformation 25]
200. 10 <=> ! [X0] : generous(X0) [avatar definition]
201. generous(X0) <- (10) [avatar component clause 200]
203. 11 <=> generous(susan) [avatar definition]
205. ~generous(susan) <- (~11) [avatar component clause 203]
207. 12 <=> kind(susan) [avatar definition]
209. ~kind(susan) <- (~12) [avatar component clause 207]
212. 13 <=> ! [X0] : quiet(X0) [avatar definition]
213. quiet(X0) <- (13) [avatar component clause 212]
214. 13 | ~11 | ~12 [avatar split clause 112,207,203,212]
250. generous(X0) [subsumption resolution 120,121]
251. 10 [avatar split clause 250,200]
388. ~brave(susan) [resolution 119,157]
409. kind(X0) | creative(X0) | brave(X0) [resolution 105,94]
453. creative(susan) | brave(susan) <- (~12) [resolution 409,209]
458. creative(susan) <- (~12) [subsumption resolution 453,388]
461. brave(susan) | ~old(susan) <- (~12) [resolution 458,89]
463. ~old(susan) <- (~12) [subsumption resolution 461,388]
489. brave(susan) <- (~12) [resolution 463,99]
490. $false <- (~12) [subsumption resolution 489,388]
491. 12 [avatar contradiction clause 490]
492. $false <- (10, ~11) [subsumption resolution 205,201]
493. ~10 | 11 [avatar contradiction clause 492]
507. brave(X0) <- (13) [resolution 213,95]
513. $false <- (13) [resolution 507,388]
522. ~13 [avatar contradiction clause 513]
523. $false [avatar sat refutation 214,251,491,493,522]
% SZS output end Proof for 2951951960780424641335234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not happy is either tall or creative and vice versa.
If lucy is not tall or not wise then someone is both quiet and brave.
Everyone who is both brave and tall is generous or funny and vice versa.
Everyone who is not wise or creative is both quiet and not old and vice versa.
If someone is not old or not rich then john is either not creative or not curious.
Everyone who is either tall or not kind is wise.
Everyone who is brave is both old and creative.
If someone is either not patient or happy then susan is not tall or old and vice versa.
Everyone who is either not wise or not calm is rich and vice versa.
Everyone who is both not generous and not brave is not quiet.
If paul is not humble then susan is not generous or not wise.
If fred is both not quiet and calm then mary is either not old or rich and vice versa.
Everyone who is creative or old is brave and vice versa.
If lucy is not tall then paul is humble.
Everyone who is brave or not rich is either creative or old.
Someone is not calm.
Alice is not calm.
Fred is not strong or not patient. | Alice is creative. | contradiction | (![X]:((~tall(X)|~happy(X))<=>(tall(X)<~>creative(X))))&
(((~tall(lucy)|~wise(lucy)))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((brave(X)&tall(X))<=>(generous(X)|funny(X))))&
(![X]:((~wise(X)|creative(X))<=>(quiet(X)&~old(X))))&
((?[X]:((~old(X)|~rich(X))))=>((~creative(john)<~>~curious(john))))&
(![X]:((tall(X)<~>~kind(X))=>wise(X)))&
(![X]:(brave(X)=>(old(X)&creative(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>((~tall(susan)|old(susan))))&
(![X]:((~wise(X)<~>~calm(X))<=>rich(X)))&
(![X]:((~generous(X)&~brave(X))=>~quiet(X)))&
((~humble(paul))=>((~generous(susan)|~wise(susan))))&
(((~quiet(fred)&calm(fred)))<=>((~old(mary)<~>rich(mary))))&
(![X]:((creative(X)|old(X))<=>brave(X)))&
((~tall(lucy))=>(humble(paul)))&
(![X]:((brave(X)|~rich(X))=>(creative(X)<~>old(X))))&
(?[X]:(~calm(X)))&
(~calm(alice))&
((~strong(fred)|~patient(fred))) | creative(alice) | [
"p3",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4974570512601970987403562
% SZS output start Proof for 4974570512601970987403562
4. ! [X0] : ((creative(X0) | ~wise(X0)) <=> (~old(X0) & quiet(X0))) [input p3]
7. ! [X0] : (brave(X0) => (creative(X0) & old(X0))) [input p6]
13. ! [X0] : ((old(X0) | creative(X0)) <=> brave(X0)) [input p12]
19. creative(alice) [input hypothesis]
26. ! [X0] : ((creative(X0) & old(X0)) | ~brave(X0)) [ennf transformation 7]
36. ! [X0] : (((creative(X0) | ~wise(X0)) | (old(X0) | ~quiet(X0))) & ((~old(X0) & quiet(X0)) | (~creative(X0) & wise(X0)))) [nnf transformation 4]
37. ! [X0] : ((creative(X0) | ~wise(X0) | old(X0) | ~quiet(X0)) & ((~old(X0) & quiet(X0)) | (~creative(X0) & wise(X0)))) [flattening 36]
48. ! [X0] : (((old(X0) | creative(X0)) | ~brave(X0)) & (brave(X0) | (~old(X0) & ~creative(X0)))) [nnf transformation 13]
49. ! [X0] : ((old(X0) | creative(X0) | ~brave(X0)) & (brave(X0) | (~old(X0) & ~creative(X0)))) [flattening 48]
71. ~old(X0) | ~creative(X0) [cnf transformation 37]
79. ~brave(X0) | old(X0) [cnf transformation 26]
98. ~creative(X0) | brave(X0) [cnf transformation 49]
107. creative(alice) [cnf transformation 19]
207. brave(alice) [resolution 98,107]
210. old(alice) [resolution 207,79]
250. ~creative(alice) [resolution 210,71]
252. $false [subsumption resolution 250,107]
% SZS output end Proof for 4974570512601970987403562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not wise is both not rich and wise.
If susan is not old then someone is curious and vice versa.
Everyone who is not happy is either strong or not brave and vice versa.
Everyone who is both humble and not humble is either happy or curious and vice versa.
If someone is either quiet or not tall then someone is either rich or not strong and vice versa.
If someone is not kind then someone is both creative and generous.
If someone is not funny or not calm then lucy is both not strong and not funny and vice versa.
Everyone who is not quiet or not brave is both not calm and generous and vice versa.
Everyone who is both not creative and strong is kind or wise.
If mary is creative or kind then fred is not strong.
If someone is not quiet or not funny then fred is calm.
If someone is patient or brave then someone is not curious or humble.
Everyone who is strong or not tall is both strong and funny and vice versa.
Everyone who is curious is both not patient and creative.
If someone is not patient then someone is creative and vice versa.
Everyone who is quiet or humble is not strong or not tall.
John is both not wise and not curious.
Paul is not humble or not curious.
Susan is curious.
Someone is both not generous and funny.
Someone is not old.
Someone is either not rich or patient.
Someone is funny.
Someone is not brave or patient. | Fred is not calm. | contradiction | (![X]:((~quiet(X)&~wise(X))=>(~rich(X)&wise(X))))&
((~old(susan))<=>(?[X]:(curious(X))))&
(![X]:(~happy(X)<=>(strong(X)<~>~brave(X))))&
(![X]:((humble(X)&~humble(X))<=>(happy(X)<~>curious(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((rich(X)<~>~strong(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((creative(X)&generous(X)))))&
((?[X]:((~funny(X)|~calm(X))))<=>((~strong(lucy)&~funny(lucy))))&
(![X]:((~quiet(X)|~brave(X))<=>(~calm(X)&generous(X))))&
(![X]:((~creative(X)&strong(X))=>(kind(X)|wise(X))))&
(((creative(mary)|kind(mary)))=>(~strong(fred)))&
((?[X]:((~quiet(X)|~funny(X))))=>(calm(fred)))&
((?[X]:((patient(X)|brave(X))))=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((strong(X)|~tall(X))<=>(strong(X)&funny(X))))&
(![X]:(curious(X)=>(~patient(X)&creative(X))))&
((?[X]:(~patient(X)))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)|humble(X))=>(~strong(X)|~tall(X))))&
((~wise(john)&~curious(john)))&
((~humble(paul)|~curious(paul)))&
(curious(susan))&
(?[X]:((~generous(X)&funny(X))))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)|patient(X)))) | ~calm(fred) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1581629895661559591772326
% SZS output start Proof for 1581629895661559591772326
7. ? [X0] : (~calm(X0) | ~funny(X0)) <=> (~funny(lucy) & ~strong(lucy)) [input p6]
11. ? [X0] : (~funny(X0) | ~quiet(X0)) => calm(fred) [input p10]
25. ~calm(fred) [input hypothesis]
36. calm(fred) | ! [X0] : (funny(X0) & quiet(X0)) [ennf transformation 11]
56. (? [X0] : (~calm(X0) | ~funny(X0)) | (funny(lucy) | strong(lucy))) & ((~funny(lucy) & ~strong(lucy)) | ! [X0] : (calm(X0) & funny(X0))) [nnf transformation 7]
57. (? [X0] : (~calm(X0) | ~funny(X0)) | funny(lucy) | strong(lucy)) & ((~funny(lucy) & ~strong(lucy)) | ! [X0] : (calm(X0) & funny(X0))) [flattening 56]
58. (? [X0] : (~calm(X0) | ~funny(X0)) | funny(lucy) | strong(lucy)) & ((~funny(lucy) & ~strong(lucy)) | ! [X1] : (calm(X1) & funny(X1))) [rectify 57]
59. ? [X0] : (~calm(X0) | ~funny(X0)) => (~calm(sK4) | ~funny(sK4)) [choice axiom]
60. ((~calm(sK4) | ~funny(sK4)) | funny(lucy) | strong(lucy)) & ((~funny(lucy) & ~strong(lucy)) | ! [X1] : (calm(X1) & funny(X1))) [skolemisation 58,59]
111. ~funny(lucy) | calm(X1) [cnf transformation 60]
122. calm(fred) | funny(X0) [cnf transformation 36]
147. ~calm(fred) [cnf transformation 25]
218. 16 <=> funny(lucy) [avatar definition]
219. ~funny(lucy) <- (~16) [avatar component clause 218]
231. 19 <=> ! [X1] : calm(X1) [avatar definition]
232. calm(X1) <- (19) [avatar component clause 231]
233. 19 | ~16 [avatar split clause 111,218,231]
235. 20 <=> ! [X1] : funny(X1) [avatar definition]
236. funny(X1) <- (20) [avatar component clause 235]
255. 24 <=> calm(fred) [avatar definition]
256. ~calm(fred) <- (~24) [avatar component clause 255]
258. 20 | 24 [avatar split clause 122,255,235]
323. ~24 [avatar split clause 147,255]
326. $false <- (~16, 20) [subsumption resolution 219,236]
327. 16 | ~20 [avatar contradiction clause 326]
332. $false <- (19, ~24) [resolution 256,232]
333. ~19 | 24 [avatar contradiction clause 332]
334. $false [avatar sat refutation 233,258,323,327,333]
% SZS output end Proof for 1581629895661559591772326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not generous then paul is both not rich and wise and vice versa. If susan is both not curious and patient then someone is not strong or funny. Everyone who is either not old or not creative is both wise and tall. Everyone who is either not rich or not happy is both curious and generous and vice versa. If someone is not happy or not kind then john is happy or generous and vice versa. If someone is either not curious or old then john is both not patient and wise and vice versa. Everyone who is old or not generous is brave. Everyone who is both not kind and not tall is not tall or rich and vice versa. Everyone who is both not calm and brave is not funny and vice versa. Everyone who is not kind is not old or tall. Everyone who is not rich or wise is either rich or not curious and vice versa. Everyone who is kind is both patient and not funny and vice versa. Everyone who is either not rich or quiet is tall or creative and vice versa. If someone is both curious and strong then susan is either generous or kind. If someone is curious then mary is not happy. If someone is both not humble and brave then someone is quiet or not humble and vice versa. Mary is not patient. Mary is both rich and funny. Someone is both not kind and not curious. Someone is not brave or not patient. Someone is both not curious and calm. Someone is not calm or wise. | Susan is old. | neutral | ((~generous(mary))<=>((~rich(paul)&wise(paul))))&
(((~curious(susan)&patient(susan)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~old(X)<~>~creative(X))=>(wise(X)&tall(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)&generous(X))))&
((?[X]:((~happy(X)|~kind(X))))<=>((happy(john)|generous(john))))&
((?[X]:((~curious(X)<~>old(X))))<=>((~patient(john)&wise(john))))&
(![X]:((old(X)|~generous(X))=>brave(X)))&
(![X]:((~kind(X)&~tall(X))<=>(~tall(X)|rich(X))))&
(![X]:((~calm(X)&brave(X))<=>~funny(X)))&
(![X]:(~kind(X)=>(~old(X)|tall(X))))&
(![X]:((~rich(X)|wise(X))<=>(rich(X)<~>~curious(X))))&
(![X]:(kind(X)<=>(patient(X)&~funny(X))))&
(![X]:((~rich(X)<~>quiet(X))<=>(tall(X)|creative(X))))&
((?[X]:((curious(X)&strong(X))))=>((generous(susan)<~>kind(susan))))&
((?[X]:(curious(X)))=>(~happy(mary)))&
((?[X]:((~humble(X)&brave(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
(~patient(mary))&
((rich(mary)&funny(mary)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:((~brave(X)|~patient(X))))&
(?[X]:((~curious(X)&calm(X))))&
(?[X]:((~calm(X)|wise(X)))) | old(susan) | [] | null | 0 |
Everyone who is creative is not tall and vice versa.
Everyone who is either curious or creative is funny.
Everyone who is creative or tall is both not kind and quiet and vice versa.
Everyone who is not humble or not creative is either not creative or funny and vice versa.
Everyone who is not happy is patient or not creative and vice versa.
Everyone who is not humble is tall or happy.
Everyone who is not humble is both not rich and patient and vice versa.
If someone is both patient and not tall then john is both not quiet and not curious.
Everyone who is both kind and not old is either not generous or not creative.
Everyone who is both not tall and not strong is both generous and brave and vice versa.
If lucy is both not humble and not calm then someone is either curious or humble and vice versa.
Everyone who is both tall and not old is both not tall and not generous.
If paul is either patient or not kind then someone is rich and vice versa.
Everyone who is both not rich and strong is either not calm or not curious and vice versa.
If someone is either not old or not humble then fred is both wise and funny.
Someone is happy or not rich.
Alice is either not curious or curious.
Alice is not patient or not wise.
Susan is either not old or old.
Someone is brave. | Paul is not quiet. | contradiction | (![X]:(creative(X)<=>~tall(X)))&
(![X]:((curious(X)<~>creative(X))=>funny(X)))&
(![X]:((creative(X)|tall(X))<=>(~kind(X)&quiet(X))))&
(![X]:((~humble(X)|~creative(X))<=>(~creative(X)<~>funny(X))))&
(![X]:(~happy(X)<=>(patient(X)|~creative(X))))&
(![X]:(~humble(X)=>(tall(X)|happy(X))))&
(![X]:(~humble(X)<=>(~rich(X)&patient(X))))&
((?[X]:((patient(X)&~tall(X))))=>((~quiet(john)&~curious(john))))&
(![X]:((kind(X)&~old(X))=>(~generous(X)<~>~creative(X))))&
(![X]:((~tall(X)&~strong(X))<=>(generous(X)&brave(X))))&
(((~humble(lucy)&~calm(lucy)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((tall(X)&~old(X))=>(~tall(X)&~generous(X))))&
(((patient(paul)<~>~kind(paul)))<=>(?[X]:(rich(X))))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~curious(X))))&
((?[X]:((~old(X)<~>~humble(X))))=>((wise(fred)&funny(fred))))&
(?[X]:((happy(X)|~rich(X))))&
((~curious(alice)<~>curious(alice)))&
((~patient(alice)|~wise(alice)))&
((~old(susan)<~>old(susan)))&
(?[X]:(brave(X))) | ~quiet(paul) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 9050124957486673556124793
% SZS output start Proof for 9050124957486673556124793
1. ! [X0] : (creative(X0) <=> ~tall(X0)) [input p0]
3. ! [X0] : ((tall(X0) | creative(X0)) <=> (quiet(X0) & ~kind(X0))) [input p2]
21. ~quiet(paul) [input hypothesis]
33. ! [X0] : ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0))) [nnf transformation 1]
35. ! [X0] : (((tall(X0) | creative(X0)) | (~quiet(X0) | kind(X0))) & ((quiet(X0) & ~kind(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 3]
36. ! [X0] : ((tall(X0) | creative(X0) | ~quiet(X0) | kind(X0)) & ((quiet(X0) & ~kind(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 35]
63. tall(X0) | creative(X0) [cnf transformation 33]
68. ~creative(X0) | quiet(X0) [cnf transformation 36]
69. ~tall(X0) | quiet(X0) [cnf transformation 36]
120. ~quiet(paul) [cnf transformation 21]
222. quiet(X0) | creative(X0) [resolution 69,63]
223. quiet(X0) [subsumption resolution 222,68]
224. $false [resolution 223,120]
% SZS output end Proof for 9050124957486673556124793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not quiet then someone is not strong and vice versa. Everyone who is either brave or quiet is creative or brave and vice versa. If susan is either strong or patient then alice is strong and vice versa. If someone is either not humble or brave then someone is humble or not kind. If john is tall or not quiet then fred is not curious or happy and vice versa. If susan is quiet then someone is both humble and not curious. Everyone who is both not wise and rich is both not kind and quiet. Everyone who is not brave is creative and vice versa. If fred is both patient and strong then lucy is humble. If someone is not happy or not curious then susan is not curious. Everyone who is old is both humble and creative and vice versa. Everyone who is curious or not generous is either curious or generous. If someone is both patient and not happy then someone is not kind or humble. If paul is both brave and happy then someone is not quiet and vice versa. If john is not calm then mary is both not quiet and rich and vice versa. Everyone who is not quiet is creative. Someone is humble or wise. Someone is wise or generous. Alice is not brave or not creative. Someone is quiet or generous. Mary is both calm and not curious. Someone is both strong and not tall. | Fred is quiet. | entailment | ((?[X]:((~humble(X)|~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:((brave(X)<~>quiet(X))<=>(creative(X)|brave(X))))&
(((strong(susan)<~>patient(susan)))<=>(strong(alice)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((humble(X)|~kind(X)))))&
(((tall(john)|~quiet(john)))<=>((~curious(fred)|happy(fred))))&
((quiet(susan))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~wise(X)&rich(X))=>(~kind(X)&quiet(X))))&
(![X]:(~brave(X)<=>creative(X)))&
(((patient(fred)&strong(fred)))=>(humble(lucy)))&
((?[X]:((~happy(X)|~curious(X))))=>(~curious(susan)))&
(![X]:(old(X)<=>(humble(X)&creative(X))))&
(![X]:((curious(X)|~generous(X))=>(curious(X)<~>generous(X))))&
((?[X]:((patient(X)&~happy(X))))=>(?[X]:((~kind(X)|humble(X)))))&
(((brave(paul)&happy(paul)))<=>(?[X]:(~quiet(X))))&
((~calm(john))<=>((~quiet(mary)&rich(mary))))&
(![X]:(~quiet(X)=>creative(X)))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((wise(X)|generous(X))))&
((~brave(alice)|~creative(alice)))&
(?[X]:((quiet(X)|generous(X))))&
((calm(mary)&~curious(mary)))&
(?[X]:((strong(X)&~tall(X)))) | quiet(fred) | [
"p1",
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7364904975294320224536349
% SZS output start Proof for 7364904975294320224536349
2. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> (brave(X0) | creative(X0))) [input p1]
8. ! [X0] : (~brave(X0) <=> creative(X0)) [input p7]
14. (happy(paul) & brave(paul)) <=> ? [X0] : ~quiet(X0) [input p13]
16. ! [X0] : (~quiet(X0) => creative(X0)) [input p15]
23. ~quiet(fred) [input hypothesis]
37. ! [X0] : (creative(X0) | quiet(X0)) [ennf transformation 16]
43. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & ~creative(X0))) & ((brave(X0) | creative(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 2]
44. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (~brave(X0) & ~creative(X0))) & (brave(X0) | creative(X0) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [flattening 43]
50. ! [X0] : ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))) [nnf transformation 8]
52. ((happy(paul) & brave(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~happy(paul) | ~brave(paul))) [nnf transformation 14]
53. ((happy(paul) & brave(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~happy(paul) | ~brave(paul)) [flattening 52]
54. ((happy(paul) & brave(paul)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~happy(paul) | ~brave(paul)) [rectify 53]
55. ? [X1] : ~quiet(X1) => ~quiet(sK3) [choice axiom]
56. ((happy(paul) & brave(paul)) | ! [X0] : quiet(X0)) & (~quiet(sK3) | ~happy(paul) | ~brave(paul)) [skolemisation 54,55]
67. brave(X0) | creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 44]
71. ~quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
83. ~creative(X0) | ~brave(X0) [cnf transformation 50]
92. brave(paul) | quiet(X0) [cnf transformation 56]
97. creative(X0) | quiet(X0) [cnf transformation 37]
104. ~quiet(fred) [cnf transformation 23]
107. brave(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 67]
108. ~quiet(X0) | ~brave(X0) [duplicate literal removal 71]
122. 4 <=> ! [X3] : quiet(X3) [avatar definition]
123. quiet(X3) <- (4) [avatar component clause 122]
133. creative(X0) | ~quiet(X0) [subsumption resolution 107,108]
215. 24 <=> brave(paul) [avatar definition]
217. brave(paul) <- (24) [avatar component clause 215]
218. 4 | 24 [avatar split clause 92,215,122]
239. creative(X0) [subsumption resolution 97,133]
251. $false <- (4) [resolution 123,104]
252. ~4 [avatar contradiction clause 251]
254. ~brave(X1) [resolution 83,239]
255. $false <- (24) [resolution 254,217]
256. ~24 [avatar contradiction clause 255]
257. $false [avatar sat refutation 218,252,256]
% SZS output end Proof for 7364904975294320224536349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not curious then someone is both happy and not creative and vice versa.
Everyone who is either not humble or not calm is both happy and not quiet and vice versa.
If alice is both quiet and not curious then someone is both kind and humble.
If paul is both not brave and kind then alice is both not generous and not calm.
Everyone who is calm or not funny is either tall or not old and vice versa.
Everyone who is either rich or not rich is either generous or curious and vice versa.
Everyone who is kind or rich is rich and vice versa.
If someone is both not kind and tall then someone is both patient and not wise.
Everyone who is both strong and rich is either not happy or generous.
If someone is either not quiet or not creative then susan is creative.
If someone is patient or happy then someone is either not curious or not generous and vice versa.
If someone is rich then fred is both not generous and funny and vice versa.
If john is creative or not humble then lucy is not quiet and vice versa.
If someone is not strong then paul is both not patient and wise.
If someone is curious then mary is either happy or not happy and vice versa.
If someone is both funny and not calm then lucy is either not generous or not calm.
John is both patient and humble.
Mary is either not kind or old.
Lucy is either quiet or not kind.
Susan is either wise or not strong.
Someone is rich.
Susan is wise.
Someone is generous.
Mary is both not quiet and not creative. | Alice is not kind. | neutral | ((~curious(lucy))<=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>(happy(X)&~quiet(X))))&
(((quiet(alice)&~curious(alice)))=>(?[X]:((kind(X)&humble(X)))))&
(((~brave(paul)&kind(paul)))=>((~generous(alice)&~calm(alice))))&
(![X]:((calm(X)|~funny(X))<=>(tall(X)<~>~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(generous(X)<~>curious(X))))&
(![X]:((kind(X)|rich(X))<=>rich(X)))&
((?[X]:((~kind(X)&tall(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((strong(X)&rich(X))=>(~happy(X)<~>generous(X))))&
((?[X]:((~quiet(X)<~>~creative(X))))=>(creative(susan)))&
((?[X]:((patient(X)|happy(X))))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((?[X]:(rich(X)))<=>((~generous(fred)&funny(fred))))&
(((creative(john)|~humble(john)))<=>(~quiet(lucy)))&
((?[X]:(~strong(X)))=>((~patient(paul)&wise(paul))))&
((?[X]:(curious(X)))<=>((happy(mary)<~>~happy(mary))))&
((?[X]:((funny(X)&~calm(X))))=>((~generous(lucy)<~>~calm(lucy))))&
((patient(john)&humble(john)))&
((~kind(mary)<~>old(mary)))&
((quiet(lucy)<~>~kind(lucy)))&
((wise(susan)<~>~strong(susan)))&
(?[X]:(rich(X)))&
(wise(susan))&
(?[X]:(generous(X)))&
((~quiet(mary)&~creative(mary))) | ~kind(alice) | [] | null | 0 |
Everyone who is both not humble and happy is not wise.
Everyone who is either creative or patient is not quiet and vice versa.
Everyone who is old is both rich and not wise.
If someone is not generous or happy then someone is both old and not tall and vice versa.
If alice is both not curious and creative then someone is both not curious and rich.
Everyone who is both not old and not kind is either not happy or not kind and vice versa.
Everyone who is both creative and not calm is either not strong or quiet and vice versa.
Everyone who is both generous and kind is not curious and vice versa.
Everyone who is not humble is both not wise and funny and vice versa.
Everyone who is not generous is both calm and not humble.
If someone is both curious and not old then alice is both funny and calm and vice versa.
Everyone who is both patient and not creative is not patient or rich and vice versa.
Everyone who is happy is not humble or patient.
Everyone who is curious or not happy is not funny and vice versa.
If someone is either quiet or brave then paul is both humble and tall.
Everyone who is either creative or not brave is both strong and curious and vice versa.
Paul is either tall or quiet.
Paul is kind or humble.
Paul is either not funny or not happy.
Alice is tall.
Mary is either tall or strong.
Mary is both curious and brave.
Someone is strong or tall.
Someone is wise or creative. | Alice is calm. | entailment | (![X]:((~humble(X)&happy(X))=>~wise(X)))&
(![X]:((creative(X)<~>patient(X))<=>~quiet(X)))&
(![X]:(old(X)=>(rich(X)&~wise(X))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:((old(X)&~tall(X)))))&
(((~curious(alice)&creative(alice)))=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((creative(X)&~calm(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((generous(X)&kind(X))<=>~curious(X)))&
(![X]:(~humble(X)<=>(~wise(X)&funny(X))))&
(![X]:(~generous(X)=>(calm(X)&~humble(X))))&
((?[X]:((curious(X)&~old(X))))<=>((funny(alice)&calm(alice))))&
(![X]:((patient(X)&~creative(X))<=>(~patient(X)|rich(X))))&
(![X]:(happy(X)=>(~humble(X)|patient(X))))&
(![X]:((curious(X)|~happy(X))<=>~funny(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>((humble(paul)&tall(paul))))&
(![X]:((creative(X)<~>~brave(X))<=>(strong(X)&curious(X))))&
((tall(paul)<~>quiet(paul)))&
((kind(paul)|humble(paul)))&
((~funny(paul)<~>~happy(paul)))&
(tall(alice))&
((tall(mary)<~>strong(mary)))&
((curious(mary)&brave(mary)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:((wise(X)|creative(X)))) | calm(alice) | [
"p5",
"p7",
"p8",
"p9",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4228585523014335838301140
% SZS output start Proof for 4228585523014335838301140
6. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~happy(X0) <~> ~kind(X0))) [input p5]
8. ! [X0] : ((kind(X0) & generous(X0)) <=> ~curious(X0)) [input p7]
9. ! [X0] : (~humble(X0) <=> (funny(X0) & ~wise(X0))) [input p8]
10. ! [X0] : (~generous(X0) => (~humble(X0) & calm(X0))) [input p9]
11. ? [X0] : (~old(X0) & curious(X0)) <=> (calm(alice) & funny(alice)) [input p10]
14. ! [X0] : ((~happy(X0) | curious(X0)) <=> ~funny(X0)) [input p13]
19. ~funny(paul) <~> ~happy(paul) [input p18]
25. ~calm(alice) [input hypothesis]
32. ! [X0] : ((~humble(X0) & calm(X0)) | generous(X0)) [ennf transformation 10]
44. ! [X0] : (((~kind(X0) & ~old(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | (kind(X0) | old(X0)))) [nnf transformation 6]
45. ! [X0] : (((~kind(X0) & ~old(X0)) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) & (((kind(X0) | happy(X0)) & (~kind(X0) | ~happy(X0))) | kind(X0) | old(X0))) [flattening 44]
48. ! [X0] : (((kind(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | (~kind(X0) | ~generous(X0)))) [nnf transformation 8]
49. ! [X0] : (((kind(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | ~kind(X0) | ~generous(X0))) [flattening 48]
50. ! [X0] : ((~humble(X0) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | humble(X0))) [nnf transformation 9]
51. ! [X0] : ((~humble(X0) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | humble(X0))) [flattening 50]
52. (? [X0] : (~old(X0) & curious(X0)) | (~calm(alice) | ~funny(alice))) & ((calm(alice) & funny(alice)) | ! [X0] : (old(X0) | ~curious(X0))) [nnf transformation 11]
53. (? [X0] : (~old(X0) & curious(X0)) | ~calm(alice) | ~funny(alice)) & ((calm(alice) & funny(alice)) | ! [X0] : (old(X0) | ~curious(X0))) [flattening 52]
54. (? [X0] : (~old(X0) & curious(X0)) | ~calm(alice) | ~funny(alice)) & ((calm(alice) & funny(alice)) | ! [X1] : (old(X1) | ~curious(X1))) [rectify 53]
55. ? [X0] : (~old(X0) & curious(X0)) => (~old(sK3) & curious(sK3)) [choice axiom]
56. ((~old(sK3) & curious(sK3)) | ~calm(alice) | ~funny(alice)) & ((calm(alice) & funny(alice)) | ! [X1] : (old(X1) | ~curious(X1))) [skolemisation 54,55]
59. ! [X0] : (((~happy(X0) | curious(X0)) | funny(X0)) & (~funny(X0) | (happy(X0) & ~curious(X0)))) [nnf transformation 14]
60. ! [X0] : ((~happy(X0) | curious(X0) | funny(X0)) & (~funny(X0) | (happy(X0) & ~curious(X0)))) [flattening 59]
65. (happy(paul) | funny(paul)) & (~happy(paul) | ~funny(paul)) [nnf transformation 19]
88. ~old(X0) | ~happy(X0) | kind(X0) [cnf transformation 45]
97. ~kind(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 49]
101. funny(X0) | humble(X0) [cnf transformation 51]
104. ~humble(X0) | generous(X0) [cnf transformation 32]
106. calm(alice) | old(X1) | ~curious(X1) [cnf transformation 56]
116. ~funny(X0) | happy(X0) [cnf transformation 60]
117. ~happy(X0) | curious(X0) | funny(X0) [cnf transformation 60]
131. ~happy(paul) | ~funny(paul) [cnf transformation 65]
132. happy(paul) | funny(paul) [cnf transformation 65]
140. ~calm(alice) [cnf transformation 25]
199. 13 <=> calm(alice) [avatar definition]
213. 16 <=> ! [X1] : (old(X1) | ~curious(X1)) [avatar definition]
214. ~curious(X1) | old(X1) <- (16) [avatar component clause 213]
215. 16 | 13 [avatar split clause 106,199,213]
231. 20 <=> humble(paul) [avatar definition]
233. humble(paul) <- (20) [avatar component clause 231]
243. 22 <=> kind(paul) [avatar definition]
245. kind(paul) <- (22) [avatar component clause 243]
247. happy(paul) [subsumption resolution 132,116]
248. ~funny(paul) [subsumption resolution 131,247]
277. ~13 [avatar split clause 140,199]
285. humble(paul) [resolution 101,248]
287. generous(paul) <- (20) [resolution 104,233]
371. curious(paul) | funny(paul) [resolution 117,247]
374. curious(paul) [subsumption resolution 371,248]
395. old(paul) <- (16) [resolution 374,214]
418. ~happy(paul) | kind(paul) <- (16) [resolution 395,88]
421. kind(paul) <- (16) [subsumption resolution 418,247]
422. 22 | ~16 [avatar split clause 421,213,243]
423. ~curious(paul) | ~generous(paul) <- (22) [resolution 245,97]
425. ~generous(paul) <- (22) [subsumption resolution 423,374]
426. $false <- (20, 22) [subsumption resolution 425,287]
427. ~20 | ~22 [avatar contradiction clause 426]
431. 20 [avatar split clause 285,231]
432. $false [avatar sat refutation 215,277,422,427,431]
% SZS output end Proof for 4228585523014335838301140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either not quiet or not old and vice versa.
If someone is patient or happy then john is both not kind and not patient.
If alice is both not funny and not kind then paul is curious.
Everyone who is either not humble or humble is either calm or brave and vice versa.
If john is not calm then someone is generous.
Everyone who is not calm is both not curious and not wise and vice versa.
Everyone who is not creative or not quiet is patient or not brave.
If susan is either not kind or brave then someone is not quiet or not wise and vice versa.
Everyone who is patient is both calm and generous.
If susan is not tall or patient then susan is happy and vice versa.
Everyone who is rich or not quiet is either brave or not strong and vice versa.
If paul is either strong or happy then someone is old or humble.
Everyone who is either not patient or not old is both not generous and not strong and vice versa.
If susan is either patient or humble then someone is creative and vice versa.
If susan is both patient and old then lucy is not brave and vice versa.
If someone is both patient and brave then john is either calm or generous and vice versa.
Fred is funny or quiet.
Someone is not strong.
Mary is either not quiet or not creative.
Fred is either funny or brave.
Mary is not wise.
Fred is both wise and creative.
Someone is either not creative or not quiet. | John is generous. | entailment | (![X]:(~rich(X)<=>(~quiet(X)<~>~old(X))))&
((?[X]:((patient(X)|happy(X))))=>((~kind(john)&~patient(john))))&
(((~funny(alice)&~kind(alice)))=>(curious(paul)))&
(![X]:((~humble(X)<~>humble(X))<=>(calm(X)<~>brave(X))))&
((~calm(john))=>(?[X]:(generous(X))))&
(![X]:(~calm(X)<=>(~curious(X)&~wise(X))))&
(![X]:((~creative(X)|~quiet(X))=>(patient(X)|~brave(X))))&
(((~kind(susan)<~>brave(susan)))<=>(?[X]:((~quiet(X)|~wise(X)))))&
(![X]:(patient(X)=>(calm(X)&generous(X))))&
(((~tall(susan)|patient(susan)))<=>(happy(susan)))&
(![X]:((rich(X)|~quiet(X))<=>(brave(X)<~>~strong(X))))&
(((strong(paul)<~>happy(paul)))=>(?[X]:((old(X)|humble(X)))))&
(![X]:((~patient(X)<~>~old(X))<=>(~generous(X)&~strong(X))))&
(((patient(susan)<~>humble(susan)))<=>(?[X]:(creative(X))))&
(((patient(susan)&old(susan)))<=>(~brave(lucy)))&
((?[X]:((patient(X)&brave(X))))<=>((calm(john)<~>generous(john))))&
((funny(fred)|quiet(fred)))&
(?[X]:(~strong(X)))&
((~quiet(mary)<~>~creative(mary)))&
((funny(fred)<~>brave(fred)))&
(~wise(mary))&
((wise(fred)&creative(fred)))&
(?[X]:((~creative(X)<~>~quiet(X)))) | generous(john) | [
"p0",
"p1",
"p3",
"p6",
"p8",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 679741081824747442282938
% SZS output start Proof for 679741081824747442282938
1. ! [X0] : (~rich(X0) <=> (~quiet(X0) <~> ~old(X0))) [input p0]
2. ? [X0] : (happy(X0) | patient(X0)) => (~patient(john) & ~kind(john)) [input p1]
4. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (calm(X0) <~> brave(X0))) [input p3]
7. ! [X0] : ((~quiet(X0) | ~creative(X0)) => (~brave(X0) | patient(X0))) [input p6]
9. ! [X0] : (patient(X0) => (generous(X0) & calm(X0))) [input p8]
11. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (brave(X0) <~> ~strong(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> ~old(X0)) <=> (~strong(X0) & ~generous(X0))) [input p12]
16. ? [X0] : (brave(X0) & patient(X0)) <=> (calm(john) <~> generous(john)) [input p15]
24. ~generous(john) [input hypothesis]
25. (~patient(john) & ~kind(john)) | ! [X0] : (~happy(X0) & ~patient(X0)) [ennf transformation 2]
29. ! [X0] : ((~brave(X0) | patient(X0)) | (quiet(X0) & creative(X0))) [ennf transformation 7]
30. ! [X0] : (~brave(X0) | patient(X0) | (quiet(X0) & creative(X0))) [flattening 29]
31. ! [X0] : ((generous(X0) & calm(X0)) | ~patient(X0)) [ennf transformation 9]
33. ! [X0] : ((~rich(X0) | ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0)))) & (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | rich(X0))) [nnf transformation 1]
34. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 4]
45. ! [X0] : (((~quiet(X0) | rich(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0)))) & (((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (quiet(X0) & ~rich(X0)))) [nnf transformation 11]
46. ! [X0] : ((~quiet(X0) | rich(X0) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0)))) & (((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (quiet(X0) & ~rich(X0)))) [flattening 45]
50. ! [X0] : ((((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0))))) [nnf transformation 13]
51. ! [X0] : ((((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0))))) [flattening 50]
58. (? [X0] : (brave(X0) & patient(X0)) | ((calm(john) | ~generous(john)) & (generous(john) | ~calm(john)))) & (((~generous(john) | ~calm(john)) & (generous(john) | calm(john))) | ! [X0] : (~brave(X0) | ~patient(X0))) [nnf transformation 16]
59. (? [X0] : (brave(X0) & patient(X0)) | ((calm(john) | ~generous(john)) & (generous(john) | ~calm(john)))) & (((~generous(john) | ~calm(john)) & (generous(john) | calm(john))) | ! [X1] : (~brave(X1) | ~patient(X1))) [rectify 58]
60. ? [X0] : (brave(X0) & patient(X0)) => (brave(sK4) & patient(sK4)) [choice axiom]
61. ((brave(sK4) & patient(sK4)) | ((calm(john) | ~generous(john)) & (generous(john) | ~calm(john)))) & (((~generous(john) | ~calm(john)) & (generous(john) | calm(john))) | ! [X1] : (~brave(X1) | ~patient(X1))) [skolemisation 59,60]
69. ~old(X0) | ~quiet(X0) | rich(X0) [cnf transformation 33]
72. ~quiet(X0) | ~rich(X0) | old(X0) [cnf transformation 33]
75. ~patient(john) | ~patient(X0) [cnf transformation 25]
78. brave(X0) | calm(X0) | humble(X0) | humble(X0) [cnf transformation 34]
79. brave(X0) | calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 34]
80. ~brave(X0) | ~calm(X0) | humble(X0) | humble(X0) [cnf transformation 34]
81. ~brave(X0) | ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 34]
91. ~brave(X0) | patient(X0) | quiet(X0) [cnf transformation 30]
98. ~patient(X0) | calm(X0) [cnf transformation 31]
99. ~patient(X0) | generous(X0) [cnf transformation 31]
105. ~brave(X0) | strong(X0) | ~rich(X0) [cnf transformation 46]
107. ~strong(X0) | rich(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 46]
113. ~strong(X0) | ~old(X0) | patient(X0) [cnf transformation 51]
116. old(X0) | patient(X0) | strong(X0) | generous(X0) [cnf transformation 51]
126. patient(sK4) | generous(john) | ~calm(john) [cnf transformation 61]
128. brave(sK4) | generous(john) | ~calm(john) [cnf transformation 61]
141. ~generous(john) [cnf transformation 24]
142. brave(X0) | calm(X0) | humble(X0) [duplicate literal removal 78]
143. ~humble(X0) | calm(X0) | brave(X0) [duplicate literal removal 79]
144. ~brave(X0) | ~calm(X0) | humble(X0) [duplicate literal removal 80]
145. ~brave(X0) | ~calm(X0) | ~humble(X0) [duplicate literal removal 81]
150. 2 <=> patient(john) [avatar definition]
151. patient(john) <- (2) [avatar component clause 150]
155. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
156. ~patient(X0) <- (3) [avatar component clause 155]
157. 3 | ~2 [avatar split clause 75,150,155]
177. ~brave(X0) | ~calm(X0) [subsumption resolution 144,145]
178. brave(X0) | calm(X0) [subsumption resolution 142,143]
180. 8 <=> calm(john) [avatar definition]
181. ~calm(john) <- (~8) [avatar component clause 180]
249. strong(X0) | old(X0) | generous(X0) [subsumption resolution 116,99]
279. 28 <=> generous(john) [avatar definition]
281. ~generous(john) <- (~28) [avatar component clause 279]
283. 29 <=> brave(sK4) [avatar definition]
285. brave(sK4) <- (29) [avatar component clause 283]
287. ~8 | 28 | 29 [avatar split clause 128,283,279,180]
289. 30 <=> patient(sK4) [avatar definition]
291. patient(sK4) <- (30) [avatar component clause 289]
293. ~8 | 28 | 30 [avatar split clause 126,289,279,180]
334. ~28 [avatar split clause 141,279]
338. calm(sK4) <- (30) [resolution 98,291]
341. ~calm(sK4) <- (29) [resolution 177,285]
342. $false <- (29, 30) [subsumption resolution 341,338]
343. ~29 | ~30 [avatar contradiction clause 342]
384. patient(X0) | quiet(X0) | calm(X0) [resolution 91,178]
387. calm(X0) | quiet(X0) [subsumption resolution 384,98]
475. rich(X0) | ~quiet(X0) | ~brave(X0) | old(X0) | generous(X0) [resolution 107,249]
476. ~brave(X0) | ~quiet(X0) | old(X0) | generous(X0) [subsumption resolution 475,72]
524. quiet(john) <- (~8) [resolution 387,181]
541. ~quiet(X0) | old(X0) | generous(X0) | calm(X0) [resolution 476,178]
554. generous(X0) | old(X0) | calm(X0) [subsumption resolution 541,387]
564. 67 <=> strong(john) [avatar definition]
565. ~strong(john) <- (~67) [avatar component clause 564]
566. strong(john) <- (67) [avatar component clause 564]
568. 68 <=> brave(john) [avatar definition]
569. ~brave(john) <- (~68) [avatar component clause 568]
570. brave(john) <- (68) [avatar component clause 568]
572. 69 <=> rich(john) [avatar definition]
577. 70 <=> old(john) [avatar definition]
579. old(john) <- (70) [avatar component clause 577]
636. ~old(john) | patient(john) <- (67) [resolution 566,113]
655. old(john) | calm(john) <- (~28) [resolution 554,281]
660. 2 | ~70 | ~67 [avatar split clause 636,564,577,150]
661. old(john) <- (~8, ~28) [subsumption resolution 655,181]
662. 70 | 8 | 28 [avatar split clause 661,279,180,577]
663. $false <- (2, 3) [subsumption resolution 151,156]
664. ~2 | ~3 [avatar contradiction clause 663]
670. strong(john) | ~rich(john) <- (68) [resolution 570,105]
678. ~quiet(john) | rich(john) <- (70) [resolution 579,69]
679. rich(john) <- (~8, 70) [subsumption resolution 678,524]
682. 69 | 8 | ~70 [avatar split clause 679,577,180,572]
683. ~rich(john) <- (~67, 68) [subsumption resolution 670,565]
684. ~69 | 67 | ~68 [avatar split clause 683,568,564,572]
685. calm(john) <- (~68) [resolution 569,178]
686. $false <- (~8, ~68) [subsumption resolution 685,181]
687. 8 | 68 [avatar contradiction clause 686]
688. $false [avatar sat refutation 157,287,293,334,343,660,662,664,682,684,687]
% SZS output end Proof for 679741081824747442282938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and patient is tall or kind.
Everyone who is both happy and humble is both humble and not kind.
If lucy is not kind then someone is not tall.
If paul is tall or not old then someone is not happy.
Everyone who is kind is either funny or not happy.
If paul is humble then paul is both quiet and not curious and vice versa.
Everyone who is not brave is both not strong and not calm.
If paul is curious or brave then someone is not curious.
Everyone who is both generous and not old is wise or tall.
If paul is both not calm and kind then lucy is not humble.
Everyone who is strong or curious is both not old and generous and vice versa.
Everyone who is kind is not strong or not funny and vice versa.
Everyone who is both curious and quiet is both quiet and rich and vice versa.
Everyone who is both not old and funny is both rich and tall.
Everyone who is both wise and tall is both kind and not brave.
If someone is wise or brave then susan is either funny or happy and vice versa.
Someone is old.
Susan is humble or not humble.
Someone is not creative.
Lucy is not funny.
Someone is either not humble or not curious.
John is both not generous and not quiet.
Paul is not tall. | Susan is humble. | neutral | (![X]:((~old(X)&patient(X))=>(tall(X)|kind(X))))&
(![X]:((happy(X)&humble(X))=>(humble(X)&~kind(X))))&
((~kind(lucy))=>(?[X]:(~tall(X))))&
(((tall(paul)|~old(paul)))=>(?[X]:(~happy(X))))&
(![X]:(kind(X)=>(funny(X)<~>~happy(X))))&
((humble(paul))<=>((quiet(paul)&~curious(paul))))&
(![X]:(~brave(X)=>(~strong(X)&~calm(X))))&
(((curious(paul)|brave(paul)))=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&~old(X))=>(wise(X)|tall(X))))&
(((~calm(paul)&kind(paul)))=>(~humble(lucy)))&
(![X]:((strong(X)|curious(X))<=>(~old(X)&generous(X))))&
(![X]:(kind(X)<=>(~strong(X)|~funny(X))))&
(![X]:((curious(X)&quiet(X))<=>(quiet(X)&rich(X))))&
(![X]:((~old(X)&funny(X))=>(rich(X)&tall(X))))&
(![X]:((wise(X)&tall(X))=>(kind(X)&~brave(X))))&
((?[X]:((wise(X)|brave(X))))<=>((funny(susan)<~>happy(susan))))&
(?[X]:(old(X)))&
((humble(susan)|~humble(susan)))&
(?[X]:(~creative(X)))&
(~funny(lucy))&
(?[X]:((~humble(X)<~>~curious(X))))&
((~generous(john)&~quiet(john)))&
(~tall(paul)) | humble(susan) | [] | null | 0 |
If someone is not happy then paul is both not generous and not calm.
Everyone who is both not old and happy is happy or wise and vice versa.
Everyone who is not strong is funny and vice versa.
If someone is either not old or kind then someone is creative and vice versa.
If mary is both happy and funny then someone is not funny.
Everyone who is either not quiet or not happy is both not funny and not calm and vice versa.
If john is not happy or calm then mary is rich or not wise and vice versa.
If lucy is both not generous and not funny then someone is both not calm and not wise and vice versa.
Everyone who is both not patient and not kind is not calm and vice versa.
If someone is curious or wise then someone is strong and vice versa.
Everyone who is either tall or not wise is not old or old and vice versa.
Everyone who is both patient and funny is brave and vice versa.
If alice is strong or not curious then lucy is both happy and not kind.
Everyone who is tall is not quiet or kind and vice versa.
Everyone who is quiet or not strong is not humble and vice versa.
Everyone who is both not calm and calm is tall or humble and vice versa.
Mary is not strong.
Fred is not old.
Someone is both curious and not strong.
Someone is either not kind or not creative.
Fred is humble or strong. | Mary is curious. | neutral | ((?[X]:(~happy(X)))=>((~generous(paul)&~calm(paul))))&
(![X]:((~old(X)&happy(X))<=>(happy(X)|wise(X))))&
(![X]:(~strong(X)<=>funny(X)))&
((?[X]:((~old(X)<~>kind(X))))<=>(?[X]:(creative(X))))&
(((happy(mary)&funny(mary)))=>(?[X]:(~funny(X))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(~funny(X)&~calm(X))))&
(((~happy(john)|calm(john)))<=>((rich(mary)|~wise(mary))))&
(((~generous(lucy)&~funny(lucy)))<=>(?[X]:((~calm(X)&~wise(X)))))&
(![X]:((~patient(X)&~kind(X))<=>~calm(X)))&
((?[X]:((curious(X)|wise(X))))<=>(?[X]:(strong(X))))&
(![X]:((tall(X)<~>~wise(X))<=>(~old(X)|old(X))))&
(![X]:((patient(X)&funny(X))<=>brave(X)))&
(((strong(alice)|~curious(alice)))=>((happy(lucy)&~kind(lucy))))&
(![X]:(tall(X)<=>(~quiet(X)|kind(X))))&
(![X]:((quiet(X)|~strong(X))<=>~humble(X)))&
(![X]:((~calm(X)&calm(X))<=>(tall(X)|humble(X))))&
(~strong(mary))&
(~old(fred))&
(?[X]:((curious(X)&~strong(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
((humble(fred)|strong(fred))) | curious(mary) | [] | null | 0 |
Everyone who is not old is old.
Everyone who is both tall and not generous is both calm and not kind and vice versa.
If fred is both humble and brave then susan is both old and not strong.
If someone is either not calm or not creative then susan is wise.
If john is not old then someone is either not happy or not patient and vice versa.
Everyone who is patient or kind is both curious and strong.
Everyone who is funny is both not happy and patient and vice versa.
If someone is patient or not quiet then alice is both not generous and not funny and vice versa.
Everyone who is not creative is both not strong and generous.
If fred is not curious or humble then susan is strong.
If someone is not quiet then someone is not happy or not creative.
If someone is either happy or kind then susan is either not creative or not curious and vice versa.
Everyone who is both not creative and tall is both not brave and not calm and vice versa.
If paul is either wise or curious then john is both strong and old and vice versa.
If susan is not funny then someone is not kind or rich.
Everyone who is not tall or strong is either old or strong and vice versa.
Someone is humble or not humble.
Susan is old or not curious.
Fred is either not patient or happy.
Alice is either not humble or strong.
Someone is either not calm or humble.
Someone is not generous or not rich. | Paul is brave. | entailment | (![X]:(~old(X)=>old(X)))&
(![X]:((tall(X)&~generous(X))<=>(calm(X)&~kind(X))))&
(((humble(fred)&brave(fred)))=>((old(susan)&~strong(susan))))&
((?[X]:((~calm(X)<~>~creative(X))))=>(wise(susan)))&
((~old(john))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((patient(X)|kind(X))=>(curious(X)&strong(X))))&
(![X]:(funny(X)<=>(~happy(X)&patient(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>((~generous(alice)&~funny(alice))))&
(![X]:(~creative(X)=>(~strong(X)&generous(X))))&
(((~curious(fred)|humble(fred)))=>(strong(susan)))&
((?[X]:(~quiet(X)))=>(?[X]:((~happy(X)|~creative(X)))))&
((?[X]:((happy(X)<~>kind(X))))<=>((~creative(susan)<~>~curious(susan))))&
(![X]:((~creative(X)&tall(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))<=>((strong(john)&old(john))))&
((~funny(susan))=>(?[X]:((~kind(X)|rich(X)))))&
(![X]:((~tall(X)|strong(X))<=>(old(X)<~>strong(X))))&
(?[X]:((humble(X)|~humble(X))))&
((old(susan)|~curious(susan)))&
((~patient(fred)<~>happy(fred)))&
((~humble(alice)<~>strong(alice)))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:((~generous(X)|~rich(X)))) | brave(paul) | [
"p0",
"p1",
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3020213961820858040862835
% SZS output start Proof for 3020213961820858040862835
1. ! [X0] : (~old(X0) => old(X0)) [input p0]
2. ! [X0] : ((~generous(X0) & tall(X0)) <=> (~kind(X0) & calm(X0))) [input p1]
6. ! [X0] : ((kind(X0) | patient(X0)) => (strong(X0) & curious(X0))) [input p5]
13. ! [X0] : ((tall(X0) & ~creative(X0)) <=> (~calm(X0) & ~brave(X0))) [input p12]
16. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (old(X0) <~> strong(X0))) [input p15]
23. ~brave(paul) [input hypothesis]
25. ! [X0] : (old(X0) | old(X0)) [ennf transformation 1]
29. ! [X0] : ((strong(X0) & curious(X0)) | (~kind(X0) & ~patient(X0))) [ennf transformation 6]
34. ! [X0] : (((~generous(X0) & tall(X0)) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 2]
35. ! [X0] : (((~generous(X0) & tall(X0)) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | generous(X0) | ~tall(X0))) [flattening 34]
55. ! [X0] : (((tall(X0) & ~creative(X0)) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | (~tall(X0) | creative(X0)))) [nnf transformation 13]
56. ! [X0] : (((tall(X0) & ~creative(X0)) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | ~tall(X0) | creative(X0))) [flattening 55]
61. ! [X0] : (((strong(X0) | ~tall(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~strong(X0) & tall(X0)))) [nnf transformation 16]
62. ! [X0] : ((strong(X0) | ~tall(X0) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~strong(X0) & tall(X0)))) [flattening 61]
72. old(X0) | old(X0) [cnf transformation 25]
75. ~calm(X0) | kind(X0) | tall(X0) [cnf transformation 35]
88. ~kind(X0) | strong(X0) [cnf transformation 29]
113. brave(X0) | calm(X0) | tall(X0) [cnf transformation 56]
124. ~strong(X0) | ~old(X0) | ~strong(X0) [cnf transformation 62]
125. strong(X0) | ~tall(X0) | strong(X0) | ~old(X0) [cnf transformation 62]
136. ~brave(paul) [cnf transformation 23]
137. ~strong(X0) | ~old(X0) [duplicate literal removal 124]
138. strong(X0) | ~tall(X0) | ~old(X0) [duplicate literal removal 125]
139. old(X0) [duplicate literal removal 72]
270. ~tall(X0) | strong(X0) [subsumption resolution 138,139]
271. ~strong(X0) [subsumption resolution 137,139]
334. calm(paul) | tall(paul) [resolution 113,136]
337. 37 <=> tall(paul) [avatar definition]
339. tall(paul) <- (37) [avatar component clause 337]
341. 38 <=> calm(paul) [avatar definition]
343. calm(paul) <- (38) [avatar component clause 341]
344. 37 | 38 [avatar split clause 334,341,337]
347. kind(paul) | tall(paul) <- (38) [resolution 343,75]
358. 41 <=> kind(paul) [avatar definition]
360. kind(paul) <- (41) [avatar component clause 358]
362. 37 | 41 | ~38 [avatar split clause 347,341,358,337]
372. strong(paul) <- (41) [resolution 360,88]
374. $false <- (41) [subsumption resolution 372,271]
375. ~41 [avatar contradiction clause 374]
380. strong(paul) <- (37) [resolution 339,270]
381. $false <- (37) [subsumption resolution 380,271]
382. ~37 [avatar contradiction clause 381]
383. $false [avatar sat refutation 344,362,375,382]
% SZS output end Proof for 3020213961820858040862835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not brave is both rich and happy and vice versa. If someone is either wise or not brave then mary is not brave and vice versa. Everyone who is patient or humble is not curious or brave and vice versa. Everyone who is both not humble and tall is either patient or not generous. Everyone who is creative or curious is quiet. If someone is not wise or not humble then lucy is calm or old. If john is either curious or not funny then someone is both not happy and curious. Everyone who is not old or not calm is quiet. If someone is not brave or creative then someone is kind and vice versa. If lucy is not quiet then someone is either not wise or not old. If fred is both strong and not strong then someone is tall and vice versa. Everyone who is either not old or patient is old. If someone is both strong and tall then mary is old or tall and vice versa. Everyone who is either kind or not patient is not wise or not generous and vice versa. If mary is either funny or creative then someone is both happy and not old and vice versa. If someone is kind then alice is old and vice versa. Someone is both not wise and not humble. John is calm. Someone is both not quiet and not kind. Alice is patient. Someone is not brave. Someone is both old and quiet. Fred is quiet or curious. | Mary is not brave. | neutral | (![X]:((strong(X)<~>~brave(X))<=>(rich(X)&happy(X))))&
((?[X]:((wise(X)<~>~brave(X))))<=>(~brave(mary)))&
(![X]:((patient(X)|humble(X))<=>(~curious(X)|brave(X))))&
(![X]:((~humble(X)&tall(X))=>(patient(X)<~>~generous(X))))&
(![X]:((creative(X)|curious(X))=>quiet(X)))&
((?[X]:((~wise(X)|~humble(X))))=>((calm(lucy)|old(lucy))))&
(((curious(john)<~>~funny(john)))=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((~old(X)|~calm(X))=>quiet(X)))&
((?[X]:((~brave(X)|creative(X))))<=>(?[X]:(kind(X))))&
((~quiet(lucy))=>(?[X]:((~wise(X)<~>~old(X)))))&
(((strong(fred)&~strong(fred)))<=>(?[X]:(tall(X))))&
(![X]:((~old(X)<~>patient(X))=>old(X)))&
((?[X]:((strong(X)&tall(X))))<=>((old(mary)|tall(mary))))&
(![X]:((kind(X)<~>~patient(X))<=>(~wise(X)|~generous(X))))&
(((funny(mary)<~>creative(mary)))<=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:(kind(X)))<=>(old(alice)))&
(?[X]:((~wise(X)&~humble(X))))&
(calm(john))&
(?[X]:((~quiet(X)&~kind(X))))&
(patient(alice))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)&quiet(X))))&
((quiet(fred)|curious(fred))) | ~brave(mary) | [] | null | 0 |
Everyone who is both quiet and calm is not curious or not rich and vice versa. If susan is curious then susan is not creative or not quiet and vice versa. If paul is kind then mary is both not quiet and old. Everyone who is not kind or not strong is either quiet or tall. If someone is not happy then mary is wise and vice versa. Everyone who is not creative is both not happy and not brave and vice versa. Everyone who is either not quiet or rich is either happy or old and vice versa. Everyone who is wise is either generous or rich and vice versa. Everyone who is either not rich or happy is either old or quiet. Everyone who is either not curious or patient is wise and vice versa. Everyone who is either wise or generous is funny and vice versa. If alice is not brave or creative then someone is both strong and not humble. If john is either generous or not humble then someone is not tall and vice versa. Everyone who is either curious or not old is both not old and patient. Everyone who is both wise and not patient is curious or quiet and vice versa. Everyone who is either not curious or not tall is not humble or happy and vice versa. Someone is both not curious and tall. Someone is patient or calm. Alice is patient or happy. Someone is either not brave or patient. Someone is not patient. Someone is both not strong and old. | Paul is old. | entailment | (![X]:((quiet(X)&calm(X))<=>(~curious(X)|~rich(X))))&
((curious(susan))<=>((~creative(susan)|~quiet(susan))))&
((kind(paul))=>((~quiet(mary)&old(mary))))&
(![X]:((~kind(X)|~strong(X))=>(quiet(X)<~>tall(X))))&
((?[X]:(~happy(X)))<=>(wise(mary)))&
(![X]:(~creative(X)<=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(happy(X)<~>old(X))))&
(![X]:(wise(X)<=>(generous(X)<~>rich(X))))&
(![X]:((~rich(X)<~>happy(X))=>(old(X)<~>quiet(X))))&
(![X]:((~curious(X)<~>patient(X))<=>wise(X)))&
(![X]:((wise(X)<~>generous(X))<=>funny(X)))&
(((~brave(alice)|creative(alice)))=>(?[X]:((strong(X)&~humble(X)))))&
(((generous(john)<~>~humble(john)))<=>(?[X]:(~tall(X))))&
(![X]:((curious(X)<~>~old(X))=>(~old(X)&patient(X))))&
(![X]:((wise(X)&~patient(X))<=>(curious(X)|quiet(X))))&
(![X]:((~curious(X)<~>~tall(X))<=>(~humble(X)|happy(X))))&
(?[X]:((~curious(X)&tall(X))))&
(?[X]:((patient(X)|calm(X))))&
((patient(alice)|happy(alice)))&
(?[X]:((~brave(X)<~>patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~strong(X)&old(X)))) | old(paul) | [
"p0",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2077873169253157876129320
% SZS output start Proof for 2077873169253157876129320
1. ! [X0] : ((calm(X0) & quiet(X0)) <=> (~rich(X0) | ~curious(X0))) [input p0]
10. ! [X0] : ((~curious(X0) <~> patient(X0)) <=> wise(X0)) [input p9]
14. ! [X0] : ((curious(X0) <~> ~old(X0)) => (patient(X0) & ~old(X0))) [input p13]
15. ! [X0] : ((~patient(X0) & wise(X0)) <=> (quiet(X0) | curious(X0))) [input p14]
23. ~old(paul) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~old(X0)) | (curious(X0) <=> ~old(X0))) [ennf transformation 14]
29. ! [X0] : (((calm(X0) & quiet(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (~calm(X0) | ~quiet(X0)))) [nnf transformation 1]
30. ! [X0] : (((calm(X0) & quiet(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | ~calm(X0) | ~quiet(X0))) [flattening 29]
43. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | ~wise(X0)) & (wise(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [nnf transformation 10]
50. ! [X0] : ((patient(X0) & ~old(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 28]
51. ! [X0] : (((~patient(X0) & wise(X0)) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 15]
52. ! [X0] : (((~patient(X0) & wise(X0)) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | patient(X0) | ~wise(X0))) [flattening 51]
67. curious(X0) | quiet(X0) [cnf transformation 30]
103. ~wise(X0) | ~curious(X0) | patient(X0) [cnf transformation 43]
104. ~patient(X0) | curious(X0) | ~wise(X0) [cnf transformation 43]
116. patient(X0) | curious(X0) | old(X0) [cnf transformation 50]
118. ~curious(X0) | wise(X0) [cnf transformation 52]
119. ~quiet(X0) | wise(X0) [cnf transformation 52]
120. ~patient(X0) | ~curious(X0) [cnf transformation 52]
137. ~old(paul) [cnf transformation 23]
259. wise(X1) | quiet(X1) [resolution 118,67]
260. wise(X1) [subsumption resolution 259,119]
352. ~curious(X1) | patient(X1) [resolution 103,260]
355. ~curious(X1) [subsumption resolution 352,120]
375. curious(X0) | old(X0) | curious(X0) | ~wise(X0) [resolution 116,104]
383. curious(X0) | old(X0) | ~wise(X0) [duplicate literal removal 375]
384. old(X0) | ~wise(X0) [subsumption resolution 383,355]
385. old(X0) [subsumption resolution 384,260]
386. $false [resolution 385,137]
% SZS output end Proof for 2077873169253157876129320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and humble is not generous or kind. If someone is both wise and not strong then susan is humble or wise and vice versa. Everyone who is not kind is not curious and vice versa. Everyone who is funny is tall and vice versa. Everyone who is not patient is either rich or not generous and vice versa. Everyone who is not curious or not humble is either curious or wise. Everyone who is calm or not patient is old or not curious. If john is either not curious or not generous then someone is happy and vice versa. If someone is not funny then someone is not calm. If someone is either not brave or not generous then someone is both quiet and not wise. Everyone who is both not calm and quiet is old or not tall. Everyone who is both patient and wise is creative. Everyone who is not brave is patient or old and vice versa. Everyone who is not creative is quiet and vice versa. Everyone who is both not tall and not creative is strong or not old and vice versa. Everyone who is both not generous and creative is either not patient or humble and vice versa. Someone is not kind or tall. Someone is not brave. Susan is either not calm or not patient. Someone is either quiet or creative. Fred is rich or creative. Fred is either quiet or tall. Someone is not strong or humble. | Susan is creative. | neutral | (![X]:((~calm(X)&humble(X))=>(~generous(X)|kind(X))))&
((?[X]:((wise(X)&~strong(X))))<=>((humble(susan)|wise(susan))))&
(![X]:(~kind(X)<=>~curious(X)))&
(![X]:(funny(X)<=>tall(X)))&
(![X]:(~patient(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((~curious(X)|~humble(X))=>(curious(X)<~>wise(X))))&
(![X]:((calm(X)|~patient(X))=>(old(X)|~curious(X))))&
(((~curious(john)<~>~generous(john)))<=>(?[X]:(happy(X))))&
((?[X]:(~funny(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~brave(X)<~>~generous(X))))=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:((~calm(X)&quiet(X))=>(old(X)|~tall(X))))&
(![X]:((patient(X)&wise(X))=>creative(X)))&
(![X]:(~brave(X)<=>(patient(X)|old(X))))&
(![X]:(~creative(X)<=>quiet(X)))&
(![X]:((~tall(X)&~creative(X))<=>(strong(X)|~old(X))))&
(![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>humble(X))))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:(~brave(X)))&
((~calm(susan)<~>~patient(susan)))&
(?[X]:((quiet(X)<~>creative(X))))&
((rich(fred)|creative(fred)))&
((quiet(fred)<~>tall(fred)))&
(?[X]:((~strong(X)|humble(X)))) | creative(susan) | [] | null | 0 |
Everyone who is wise or old is both not kind and not creative.
Everyone who is both not kind and not old is either quiet or not funny.
Everyone who is either tall or old is both tall and not creative.
Everyone who is not generous is not creative.
If someone is quiet then someone is generous.
Everyone who is either not rich or humble is tall or not old and vice versa.
If paul is kind or not patient then lucy is both not happy and patient and vice versa.
If john is kind or not curious then mary is either not kind or old.
Everyone who is both quiet and patient is kind.
If someone is old or not generous then john is kind.
Everyone who is brave is patient or not humble and vice versa.
Everyone who is not old is both brave and not generous and vice versa.
If paul is both rich and not tall then someone is curious.
Everyone who is either old or creative is happy or not rich and vice versa.
Everyone who is either not curious or not brave is quiet or rich and vice versa.
Everyone who is both curious and calm is both happy and not curious and vice versa.
Mary is both not quiet and not kind.
Susan is both not old and patient.
Someone is both funny and not rich.
Someone is both not curious and funny.
Alice is either not kind or not humble.
Susan is either brave or not tall. | Paul is humble. | neutral | (![X]:((wise(X)|old(X))=>(~kind(X)&~creative(X))))&
(![X]:((~kind(X)&~old(X))=>(quiet(X)<~>~funny(X))))&
(![X]:((tall(X)<~>old(X))=>(tall(X)&~creative(X))))&
(![X]:(~generous(X)=>~creative(X)))&
((?[X]:(quiet(X)))=>(?[X]:(generous(X))))&
(![X]:((~rich(X)<~>humble(X))<=>(tall(X)|~old(X))))&
(((kind(paul)|~patient(paul)))<=>((~happy(lucy)&patient(lucy))))&
(((kind(john)|~curious(john)))=>((~kind(mary)<~>old(mary))))&
(![X]:((quiet(X)&patient(X))=>kind(X)))&
((?[X]:((old(X)|~generous(X))))=>(kind(john)))&
(![X]:(brave(X)<=>(patient(X)|~humble(X))))&
(![X]:(~old(X)<=>(brave(X)&~generous(X))))&
(((rich(paul)&~tall(paul)))=>(?[X]:(curious(X))))&
(![X]:((old(X)<~>creative(X))<=>(happy(X)|~rich(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(quiet(X)|rich(X))))&
(![X]:((curious(X)&calm(X))<=>(happy(X)&~curious(X))))&
((~quiet(mary)&~kind(mary)))&
((~old(susan)&patient(susan)))&
(?[X]:((funny(X)&~rich(X))))&
(?[X]:((~curious(X)&funny(X))))&
((~kind(alice)<~>~humble(alice)))&
((brave(susan)<~>~tall(susan))) | humble(paul) | [] | null | 0 |
Everyone who is either not wise or not quiet is either creative or rich and vice versa.
Everyone who is rich is kind and vice versa.
Everyone who is both not rich and not strong is quiet and vice versa.
If susan is not curious then paul is not generous or not wise.
Everyone who is not creative is not tall and vice versa.
Everyone who is either not humble or tall is not strong or not happy.
Everyone who is creative or quiet is either calm or brave.
If lucy is either not quiet or not funny then someone is both not quiet and not old and vice versa.
Everyone who is not wise is either not curious or old and vice versa.
Everyone who is patient is either quiet or not strong and vice versa.
Everyone who is either not patient or brave is creative or not generous and vice versa.
Everyone who is either not patient or not tall is creative and vice versa.
Everyone who is either tall or brave is not rich and vice versa.
If someone is rich then someone is either humble or not creative and vice versa.
Everyone who is either not kind or not calm is kind and vice versa.
If fred is patient then someone is either humble or tall.
Susan is either not funny or not happy.
Someone is generous or happy.
Mary is brave or generous.
Someone is both funny and not generous.
Lucy is either not tall or brave.
Fred is either happy or not tall.
Someone is either happy or old. | Susan is not humble. | neutral | (![X]:((~wise(X)<~>~quiet(X))<=>(creative(X)<~>rich(X))))&
(![X]:(rich(X)<=>kind(X)))&
(![X]:((~rich(X)&~strong(X))<=>quiet(X)))&
((~curious(susan))=>((~generous(paul)|~wise(paul))))&
(![X]:(~creative(X)<=>~tall(X)))&
(![X]:((~humble(X)<~>tall(X))=>(~strong(X)|~happy(X))))&
(![X]:((creative(X)|quiet(X))=>(calm(X)<~>brave(X))))&
(((~quiet(lucy)<~>~funny(lucy)))<=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:(~wise(X)<=>(~curious(X)<~>old(X))))&
(![X]:(patient(X)<=>(quiet(X)<~>~strong(X))))&
(![X]:((~patient(X)<~>brave(X))<=>(creative(X)|~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>creative(X)))&
(![X]:((tall(X)<~>brave(X))<=>~rich(X)))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>kind(X)))&
((patient(fred))=>(?[X]:((humble(X)<~>tall(X)))))&
((~funny(susan)<~>~happy(susan)))&
(?[X]:((generous(X)|happy(X))))&
((brave(mary)|generous(mary)))&
(?[X]:((funny(X)&~generous(X))))&
((~tall(lucy)<~>brave(lucy)))&
((happy(fred)<~>~tall(fred)))&
(?[X]:((happy(X)<~>old(X)))) | ~humble(susan) | [] | null | 0 |
Everyone who is both wise and strong is kind and vice versa.
Everyone who is either not creative or not curious is humble or not creative.
If someone is either kind or creative then mary is either not calm or not strong.
If lucy is either creative or old then lucy is either calm or not tall.
If someone is either not quiet or not humble then someone is both wise and not kind and vice versa.
Everyone who is not strong is quiet and vice versa.
If fred is not curious or not calm then mary is not wise or not rich.
Everyone who is either not happy or happy is old and vice versa.
Everyone who is not strong or not patient is either not old or not quiet.
Everyone who is both tall and curious is not strong and vice versa.
If someone is both not patient and not happy then someone is both old and generous and vice versa.
If someone is both not tall and not generous then alice is either calm or generous.
Everyone who is either not patient or not creative is both generous and old.
If fred is both not wise and not quiet then someone is not wise or not generous.
Everyone who is either patient or not curious is both strong and patient.
Everyone who is either not creative or not quiet is both not brave and quiet and vice versa.
Susan is not calm.
John is not calm or wise.
Someone is not tall.
Someone is kind or brave.
Someone is not funny or kind.
Lucy is not generous or funny.
Someone is either tall or not tall. | John is quiet. | contradiction | (![X]:((wise(X)&strong(X))<=>kind(X)))&
(![X]:((~creative(X)<~>~curious(X))=>(humble(X)|~creative(X))))&
((?[X]:((kind(X)<~>creative(X))))=>((~calm(mary)<~>~strong(mary))))&
(((creative(lucy)<~>old(lucy)))=>((calm(lucy)<~>~tall(lucy))))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:(~strong(X)<=>quiet(X)))&
(((~curious(fred)|~calm(fred)))=>((~wise(mary)|~rich(mary))))&
(![X]:((~happy(X)<~>happy(X))<=>old(X)))&
(![X]:((~strong(X)|~patient(X))=>(~old(X)<~>~quiet(X))))&
(![X]:((tall(X)&curious(X))<=>~strong(X)))&
((?[X]:((~patient(X)&~happy(X))))<=>(?[X]:((old(X)&generous(X)))))&
((?[X]:((~tall(X)&~generous(X))))=>((calm(alice)<~>generous(alice))))&
(![X]:((~patient(X)<~>~creative(X))=>(generous(X)&old(X))))&
(((~wise(fred)&~quiet(fred)))=>(?[X]:((~wise(X)|~generous(X)))))&
(![X]:((patient(X)<~>~curious(X))=>(strong(X)&patient(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(~brave(X)&quiet(X))))&
(~calm(susan))&
((~calm(john)|wise(john)))&
(?[X]:(~tall(X)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~funny(X)|kind(X))))&
((~generous(lucy)|funny(lucy)))&
(?[X]:((tall(X)<~>~tall(X)))) | quiet(john) | [
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 220809472206002266523487
% SZS output start Proof for 220809472206002266523487
6. ! [X0] : (~strong(X0) <=> quiet(X0)) [input p5]
8. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> old(X0)) [input p7]
9. ! [X0] : ((~patient(X0) | ~strong(X0)) => (~old(X0) <~> ~quiet(X0))) [input p8]
24. quiet(john) [input hypothesis]
32. ! [X0] : ((~old(X0) <~> ~quiet(X0)) | (patient(X0) & strong(X0))) [ennf transformation 9]
48. ! [X0] : ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))) [nnf transformation 6]
49. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~old(X0)) & (old(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 8]
50. ! [X0] : (((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (patient(X0) & strong(X0))) [nnf transformation 32]
93. quiet(X0) | strong(X0) [cnf transformation 48]
94. ~quiet(X0) | ~strong(X0) [cnf transformation 48]
95. old(X0) | happy(X0) | happy(X0) [cnf transformation 49]
96. old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 49]
99. ~quiet(X0) | ~old(X0) | strong(X0) [cnf transformation 50]
135. quiet(john) [cnf transformation 24]
139. old(X0) | happy(X0) [duplicate literal removal 95]
140. old(X0) | ~happy(X0) [duplicate literal removal 96]
211. old(X0) [subsumption resolution 139,140]
213. ~quiet(X0) | strong(X0) [subsumption resolution 99,211]
214. strong(X0) [subsumption resolution 213,93]
311. ~strong(john) [resolution 94,135]
313. $false [subsumption resolution 311,214]
% SZS output end Proof for 220809472206002266523487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or curious is kind or generous.
If someone is both not brave and not humble then someone is both quiet and happy and vice versa.
Everyone who is calm or not rich is either creative or strong and vice versa.
Everyone who is either curious or not old is either not curious or rich and vice versa.
Everyone who is kind or generous is both quiet and old.
If lucy is not quiet then paul is not humble.
If someone is quiet then mary is not wise or old and vice versa.
Everyone who is funny or not curious is both not strong and not generous.
If someone is calm or tall then someone is patient and vice versa.
If fred is creative or not happy then someone is not brave and vice versa.
If someone is not strong or patient then someone is not curious or humble.
Everyone who is both rich and humble is both not happy and not creative and vice versa.
Everyone who is not wise or happy is either not curious or not old and vice versa.
If someone is not quiet or quiet then someone is both funny and not creative.
Someone is either wise or not generous.
Someone is not happy.
Someone is not strong.
Someone is either not kind or old.
John is not patient.
Someone is both quiet and not generous.
Someone is both not happy and tall.
Paul is not kind or humble. | Mary is rich. | entailment | (![X]:((~humble(X)|curious(X))=>(kind(X)|generous(X))))&
((?[X]:((~brave(X)&~humble(X))))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((calm(X)|~rich(X))<=>(creative(X)<~>strong(X))))&
(![X]:((curious(X)<~>~old(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((kind(X)|generous(X))=>(quiet(X)&old(X))))&
((~quiet(lucy))=>(~humble(paul)))&
((?[X]:(quiet(X)))<=>((~wise(mary)|old(mary))))&
(![X]:((funny(X)|~curious(X))=>(~strong(X)&~generous(X))))&
((?[X]:((calm(X)|tall(X))))<=>(?[X]:(patient(X))))&
(((creative(fred)|~happy(fred)))<=>(?[X]:(~brave(X))))&
((?[X]:((~strong(X)|patient(X))))=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((rich(X)&humble(X))<=>(~happy(X)&~creative(X))))&
(![X]:((~wise(X)|happy(X))<=>(~curious(X)<~>~old(X))))&
((?[X]:((~quiet(X)|quiet(X))))=>(?[X]:((funny(X)&~creative(X)))))&
(?[X]:((wise(X)<~>~generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~patient(john))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~happy(X)&tall(X))))&
((~kind(paul)|humble(paul))) | rich(mary) | [
"p0",
"p3",
"p4",
"p6",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1012869000434224103275178
% SZS output start Proof for 1012869000434224103275178
1. ! [X0] : ((curious(X0) | ~humble(X0)) => (generous(X0) | kind(X0))) [input p0]
4. ! [X0] : ((curious(X0) <~> ~old(X0)) <=> (~curious(X0) <~> rich(X0))) [input p3]
5. ! [X0] : ((generous(X0) | kind(X0)) => (old(X0) & quiet(X0))) [input p4]
7. ? [X0] : quiet(X0) <=> (old(mary) | ~wise(mary)) [input p6]
13. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (~curious(X0) <~> ~old(X0))) [input p12]
20. ? [X0] : (~generous(X0) & quiet(X0)) [input p19]
23. ~rich(mary) [input hypothesis]
28. ! [X0] : ((generous(X0) | kind(X0)) | (~curious(X0) & humble(X0))) [ennf transformation 1]
29. ! [X0] : (generous(X0) | kind(X0) | (~curious(X0) & humble(X0))) [flattening 28]
30. ! [X0] : ((old(X0) & quiet(X0)) | (~generous(X0) & ~kind(X0))) [ennf transformation 5]
42. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) & (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [nnf transformation 4]
43. (? [X0] : quiet(X0) | (~old(mary) & wise(mary))) & ((old(mary) | ~wise(mary)) | ! [X0] : ~quiet(X0)) [nnf transformation 7]
44. (? [X0] : quiet(X0) | (~old(mary) & wise(mary))) & (old(mary) | ~wise(mary) | ! [X0] : ~quiet(X0)) [flattening 43]
45. (? [X0] : quiet(X0) | (~old(mary) & wise(mary))) & (old(mary) | ~wise(mary) | ! [X1] : ~quiet(X1)) [rectify 44]
46. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
47. (quiet(sK2) | (~old(mary) & wise(mary))) & (old(mary) | ~wise(mary) | ! [X1] : ~quiet(X1)) [skolemisation 45,46]
63. ! [X0] : (((happy(X0) | ~wise(X0)) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~happy(X0) & wise(X0)))) [nnf transformation 13]
64. ! [X0] : ((happy(X0) | ~wise(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~happy(X0) & wise(X0)))) [flattening 63]
78. ? [X0] : (~generous(X0) & quiet(X0)) => (~generous(sK12) & quiet(sK12)) [choice axiom]
79. ~generous(sK12) & quiet(sK12) [skolemisation 20,78]
83. ~curious(X0) | kind(X0) | generous(X0) [cnf transformation 29]
94. rich(X0) | ~curious(X0) | ~old(X0) | ~curious(X0) [cnf transformation 42]
98. ~old(X0) | curious(X0) | rich(X0) | curious(X0) [cnf transformation 42]
104. ~kind(X0) | old(X0) [cnf transformation 30]
105. ~generous(X0) | old(X0) [cnf transformation 30]
107. old(mary) | ~wise(mary) | ~quiet(X1) [cnf transformation 47]
128. wise(X0) | curious(X0) | old(X0) [cnf transformation 64]
143. quiet(sK12) [cnf transformation 79]
148. ~rich(mary) [cnf transformation 23]
149. rich(X0) | ~curious(X0) | ~old(X0) [duplicate literal removal 94]
151. ~old(X0) | curious(X0) | rich(X0) [duplicate literal removal 98]
180. ~old(X0) | rich(X0) [subsumption resolution 149,151]
191. 9 <=> old(mary) [avatar definition]
192. old(mary) <- (9) [avatar component clause 191]
193. ~old(mary) <- (~9) [avatar component clause 191]
200. 11 <=> wise(mary) [avatar definition]
201. ~wise(mary) <- (~11) [avatar component clause 200]
205. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
206. ~quiet(X1) <- (12) [avatar component clause 205]
207. 12 | ~11 | 9 [avatar split clause 107,191,200,205]
417. curious(mary) | old(mary) <- (~11) [resolution 128,201]
419. 47 <=> curious(mary) [avatar definition]
421. curious(mary) <- (47) [avatar component clause 419]
422. 9 | 47 | 11 [avatar split clause 417,200,419,191]
423. kind(mary) | generous(mary) <- (47) [resolution 421,83]
425. 48 <=> generous(mary) [avatar definition]
427. generous(mary) <- (48) [avatar component clause 425]
429. 49 <=> kind(mary) [avatar definition]
431. kind(mary) <- (49) [avatar component clause 429]
432. 48 | 49 | ~47 [avatar split clause 423,419,429,425]
433. old(mary) <- (49) [resolution 431,104]
435. 9 | ~49 [avatar split clause 433,429,191]
438. rich(mary) <- (9) [resolution 192,180]
442. $false <- (9) [subsumption resolution 438,148]
443. ~9 [avatar contradiction clause 442]
448. old(mary) <- (48) [resolution 427,105]
450. $false <- (~9, 48) [subsumption resolution 448,193]
451. 9 | ~48 [avatar contradiction clause 450]
460. $false <- (12) [resolution 206,143]
463. ~12 [avatar contradiction clause 460]
464. $false [avatar sat refutation 207,422,432,435,443,451,463]
% SZS output end Proof for 1012869000434224103275178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or rich then lucy is not brave or not kind.
Everyone who is old is strong or not old and vice versa.
Everyone who is either kind or not happy is not strong or patient and vice versa.
If fred is either happy or not kind then someone is both not quiet and not creative and vice versa.
If someone is both humble and funny then fred is not kind or not rich.
Everyone who is not calm or happy is not curious and vice versa.
Everyone who is either not tall or not generous is both not quiet and brave.
Everyone who is not funny is kind or strong and vice versa.
Everyone who is either creative or not curious is both wise and not calm.
Everyone who is both not happy and tall is old or not rich.
Everyone who is tall or not generous is generous and vice versa.
If someone is both not rich and not curious then someone is not tall.
Everyone who is rich or not curious is not strong or not tall and vice versa.
Everyone who is either not funny or kind is calm and vice versa.
Everyone who is either not happy or humble is happy.
If someone is both wise and not curious then someone is tall.
Lucy is either not brave or not tall.
Mary is wise or not quiet.
Someone is not kind or not funny.
Paul is wise or not creative. | Paul is not patient. | contradiction | ((?[X]:((~funny(X)<~>rich(X))))=>((~brave(lucy)|~kind(lucy))))&
(![X]:(old(X)<=>(strong(X)|~old(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(((happy(fred)<~>~kind(fred)))<=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:((humble(X)&funny(X))))=>((~kind(fred)|~rich(fred))))&
(![X]:((~calm(X)|happy(X))<=>~curious(X)))&
(![X]:((~tall(X)<~>~generous(X))=>(~quiet(X)&brave(X))))&
(![X]:(~funny(X)<=>(kind(X)|strong(X))))&
(![X]:((creative(X)<~>~curious(X))=>(wise(X)&~calm(X))))&
(![X]:((~happy(X)&tall(X))=>(old(X)|~rich(X))))&
(![X]:((tall(X)|~generous(X))<=>generous(X)))&
((?[X]:((~rich(X)&~curious(X))))=>(?[X]:(~tall(X))))&
(![X]:((rich(X)|~curious(X))<=>(~strong(X)|~tall(X))))&
(![X]:((~funny(X)<~>kind(X))<=>calm(X)))&
(![X]:((~happy(X)<~>humble(X))=>happy(X)))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:(tall(X))))&
((~brave(lucy)<~>~tall(lucy)))&
((wise(mary)|~quiet(mary)))&
(?[X]:((~kind(X)|~funny(X))))&
((wise(paul)|~creative(paul))) | ~patient(paul) | [
"p1",
"p2",
"p5",
"p7",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4148560313169667975225357
% SZS output start Proof for 4148560313169667975225357
2. ! [X0] : (old(X0) <=> (~old(X0) | strong(X0))) [input p1]
3. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (patient(X0) | ~strong(X0))) [input p2]
6. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~curious(X0)) [input p5]
8. ! [X0] : (~funny(X0) <=> (strong(X0) | kind(X0))) [input p7]
11. ! [X0] : ((~generous(X0) | tall(X0)) <=> generous(X0)) [input p10]
13. ! [X0] : ((~curious(X0) | rich(X0)) <=> (~tall(X0) | ~strong(X0))) [input p12]
14. ! [X0] : ((~funny(X0) <~> kind(X0)) <=> calm(X0)) [input p13]
21. ~patient(paul) [input hypothesis]
36. ! [X0] : ((old(X0) | (old(X0) & ~strong(X0))) & ((~old(X0) | strong(X0)) | ~old(X0))) [nnf transformation 2]
37. ! [X0] : ((old(X0) | (old(X0) & ~strong(X0))) & (~old(X0) | strong(X0) | ~old(X0))) [flattening 36]
38. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 3]
39. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 38]
44. ! [X0] : (((happy(X0) | ~calm(X0)) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 6]
45. ! [X0] : ((happy(X0) | ~calm(X0) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [flattening 44]
47. ! [X0] : ((~funny(X0) | (~strong(X0) & ~kind(X0))) & ((strong(X0) | kind(X0)) | funny(X0))) [nnf transformation 8]
48. ! [X0] : ((~funny(X0) | (~strong(X0) & ~kind(X0))) & (strong(X0) | kind(X0) | funny(X0))) [flattening 47]
50. ! [X0] : (((~generous(X0) | tall(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [nnf transformation 11]
51. ! [X0] : ((~generous(X0) | tall(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [flattening 50]
55. ! [X0] : (((~curious(X0) | rich(X0)) | (tall(X0) & strong(X0))) & ((~tall(X0) | ~strong(X0)) | (curious(X0) & ~rich(X0)))) [nnf transformation 13]
56. ! [X0] : ((~curious(X0) | rich(X0) | (tall(X0) & strong(X0))) & (~tall(X0) | ~strong(X0) | (curious(X0) & ~rich(X0)))) [flattening 55]
57. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | ~calm(X0)) & (calm(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [nnf transformation 14]
67. ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 37]
69. old(X0) | old(X0) [cnf transformation 37]
71. patient(X0) | ~strong(X0) | kind(X0) | happy(X0) [cnf transformation 39]
83. ~curious(X0) | calm(X0) [cnf transformation 45]
84. ~curious(X0) | ~happy(X0) [cnf transformation 45]
92. ~funny(X0) | ~strong(X0) [cnf transformation 48]
99. generous(X0) | generous(X0) [cnf transformation 51]
100. ~generous(X0) | tall(X0) | ~generous(X0) [cnf transformation 51]
103. ~tall(X0) | ~strong(X0) | curious(X0) [cnf transformation 56]
109. ~kind(X0) | funny(X0) | ~calm(X0) [cnf transformation 57]
118. ~patient(paul) [cnf transformation 21]
120. generous(X0) [duplicate literal removal 99]
121. ~generous(X0) | tall(X0) [duplicate literal removal 100]
122. ~old(X0) | strong(X0) [duplicate literal removal 67]
123. old(X0) [duplicate literal removal 69]
140. strong(X0) [subsumption resolution 122,123]
141. patient(X0) | kind(X0) | happy(X0) [subsumption resolution 71,140]
176. ~funny(X0) [subsumption resolution 92,140]
186. ~tall(X0) | curious(X0) [subsumption resolution 103,140]
188. ~calm(X0) | ~kind(X0) [subsumption resolution 109,176]
222. tall(X0) [resolution 121,120]
230. curious(X0) [resolution 186,222]
232. ~happy(X1) [resolution 230,84]
233. calm(X2) [resolution 230,83]
236. ~kind(X0) [resolution 233,188]
253. kind(paul) | happy(paul) [resolution 141,118]
258. happy(paul) [subsumption resolution 253,236]
259. $false [subsumption resolution 258,232]
% SZS output end Proof for 4148560313169667975225357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not rich then paul is both strong and patient and vice versa.
If alice is kind or generous then john is strong or not curious.
Everyone who is funny is both not happy and patient.
Everyone who is not humble or calm is both rich and not curious.
Everyone who is not old is both not tall and not old.
Everyone who is either creative or patient is either not funny or funny and vice versa.
If someone is both brave and generous then alice is either brave or kind.
Everyone who is both not funny and strong is creative or not tall.
If john is not wise then someone is both rich and strong.
If paul is wise or kind then someone is not wise or rich.
Everyone who is not rich is either not brave or not tall and vice versa.
Everyone who is not happy or not brave is not old and vice versa.
If fred is not old then alice is both not happy and not calm and vice versa.
Everyone who is strong is both not funny and not humble.
If someone is both not funny and not kind then someone is either old or not calm and vice versa.
Everyone who is either not old or not rich is either not creative or not old and vice versa.
Mary is brave or not happy.
Alice is generous or not wise.
Alice is not generous or creative.
Someone is wise.
Someone is strong.
Someone is not wise or not rich. | Fred is not humble. | neutral | ((?[X]:((humble(X)&~rich(X))))<=>((strong(paul)&patient(paul))))&
(((kind(alice)|generous(alice)))=>((strong(john)|~curious(john))))&
(![X]:(funny(X)=>(~happy(X)&patient(X))))&
(![X]:((~humble(X)|calm(X))=>(rich(X)&~curious(X))))&
(![X]:(~old(X)=>(~tall(X)&~old(X))))&
(![X]:((creative(X)<~>patient(X))<=>(~funny(X)<~>funny(X))))&
((?[X]:((brave(X)&generous(X))))=>((brave(alice)<~>kind(alice))))&
(![X]:((~funny(X)&strong(X))=>(creative(X)|~tall(X))))&
((~wise(john))=>(?[X]:((rich(X)&strong(X)))))&
(((wise(paul)|kind(paul)))=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~brave(X)<~>~tall(X))))&
(![X]:((~happy(X)|~brave(X))<=>~old(X)))&
((~old(fred))<=>((~happy(alice)&~calm(alice))))&
(![X]:(strong(X)=>(~funny(X)&~humble(X))))&
((?[X]:((~funny(X)&~kind(X))))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)<~>~old(X))))&
((brave(mary)|~happy(mary)))&
((generous(alice)|~wise(alice)))&
((~generous(alice)|creative(alice)))&
(?[X]:(wise(X)))&
(?[X]:(strong(X)))&
(?[X]:((~wise(X)|~rich(X)))) | ~humble(fred) | [] | null | 0 |
Everyone who is both not calm and brave is not creative or generous.
If susan is calm or not patient then paul is both not curious and calm.
Everyone who is either not wise or calm is not calm and vice versa.
If alice is either not wise or calm then susan is curious or not old.
Everyone who is either funny or brave is not generous or not humble and vice versa.
Everyone who is either kind or strong is calm and vice versa.
Everyone who is old is either rich or calm and vice versa.
Everyone who is both not strong and not tall is both quiet and not tall and vice versa.
If someone is both not funny and curious then someone is both quiet and not humble and vice versa.
If fred is either strong or not creative then someone is patient or creative.
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
If fred is not quiet or not kind then someone is both happy and creative and vice versa.
If susan is both strong and not patient then someone is either curious or quiet.
Everyone who is creative is funny.
Everyone who is not brave is either brave or not happy and vice versa.
Alice is both not strong and generous.
Someone is not brave.
Lucy is not wise or patient.
Mary is either not strong or curious.
Someone is brave or not tall.
Someone is either not calm or funny.
Susan is either quiet or not quiet. | Lucy is not curious. | neutral | (![X]:((~calm(X)&brave(X))=>(~creative(X)|generous(X))))&
(((calm(susan)|~patient(susan)))=>((~curious(paul)&calm(paul))))&
(![X]:((~wise(X)<~>calm(X))<=>~calm(X)))&
(((~wise(alice)<~>calm(alice)))=>((curious(susan)|~old(susan))))&
(![X]:((funny(X)<~>brave(X))<=>(~generous(X)|~humble(X))))&
(![X]:((kind(X)<~>strong(X))<=>calm(X)))&
(![X]:(old(X)<=>(rich(X)<~>calm(X))))&
(![X]:((~strong(X)&~tall(X))<=>(quiet(X)&~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
((~strong(alice)&generous(alice)))&
(?[X]:(~brave(X)))&
((~wise(lucy)|patient(lucy)))&
((~strong(mary)<~>curious(mary)))&
(?[X]:((brave(X)|~tall(X))))&
(?[X]:((~calm(X)<~>funny(X))))&
((quiet(susan)<~>~quiet(susan))) | ~curious(lucy) | [] | null | 0 |
If paul is strong or kind then lucy is tall or not strong and vice versa. Everyone who is not tall or not quiet is both calm and patient and vice versa. If someone is either not tall or not funny then someone is not old or funny and vice versa. Everyone who is both not strong and not curious is not funny. Everyone who is both not kind and not wise is either creative or tall. Everyone who is not patient is generous or tall. If someone is both not kind and old then someone is both not quiet and not generous. If alice is tall or not tall then someone is not rich. If susan is either happy or not calm then someone is not kind or not patient and vice versa. Everyone who is not kind or not calm is curious and vice versa. Everyone who is either happy or tall is both quiet and not generous and vice versa. If alice is either calm or not brave then someone is funny and vice versa. Everyone who is wise is not kind and vice versa. Everyone who is patient is both rich and not humble and vice versa. If someone is not calm or not rich then alice is either wise or calm and vice versa. If someone is either kind or funny then susan is not old or not calm and vice versa. Someone is either happy or not wise. Someone is not creative or not happy. Mary is not patient. Lucy is either not calm or not patient. Someone is both kind and curious. Alice is not quiet. Someone is both not happy and old. Someone is calm or not patient. | Alice is curious. | contradiction | (((strong(paul)|kind(paul)))<=>((tall(lucy)|~strong(lucy))))&
(![X]:((~tall(X)|~quiet(X))<=>(calm(X)&patient(X))))&
((?[X]:((~tall(X)<~>~funny(X))))<=>(?[X]:((~old(X)|funny(X)))))&
(![X]:((~strong(X)&~curious(X))=>~funny(X)))&
(![X]:((~kind(X)&~wise(X))=>(creative(X)<~>tall(X))))&
(![X]:(~patient(X)=>(generous(X)|tall(X))))&
((?[X]:((~kind(X)&old(X))))=>(?[X]:((~quiet(X)&~generous(X)))))&
(((tall(alice)|~tall(alice)))=>(?[X]:(~rich(X))))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:((~kind(X)|~patient(X)))))&
(![X]:((~kind(X)|~calm(X))<=>curious(X)))&
(![X]:((happy(X)<~>tall(X))<=>(quiet(X)&~generous(X))))&
(((calm(alice)<~>~brave(alice)))<=>(?[X]:(funny(X))))&
(![X]:(wise(X)<=>~kind(X)))&
(![X]:(patient(X)<=>(rich(X)&~humble(X))))&
((?[X]:((~calm(X)|~rich(X))))<=>((wise(alice)<~>calm(alice))))&
((?[X]:((kind(X)<~>funny(X))))<=>((~old(susan)|~calm(susan))))&
(?[X]:((happy(X)<~>~wise(X))))&
(?[X]:((~creative(X)|~happy(X))))&
(~patient(mary))&
((~calm(lucy)<~>~patient(lucy)))&
(?[X]:((kind(X)&curious(X))))&
(~quiet(alice))&
(?[X]:((~happy(X)&old(X))))&
(?[X]:((calm(X)|~patient(X)))) | curious(alice) | [
"p1",
"p7",
"p9",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 402449054717925046618830
% SZS output start Proof for 402449054717925046618830
2. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> (patient(X0) & calm(X0))) [input p1]
8. (~tall(alice) | tall(alice)) => ? [X0] : ~rich(X0) [input p7]
10. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> curious(X0)) [input p9]
13. ! [X0] : (wise(X0) <=> ~kind(X0)) [input p12]
15. ? [X0] : (~rich(X0) | ~calm(X0)) <=> (wise(alice) <~> calm(alice)) [input p14]
22. ~quiet(alice) [input p21]
25. curious(alice) [input hypothesis]
28. ! [X0] : (curious(X0) => (~calm(X0) | ~kind(X0))) [unused predicate definition removal 10]
36. ? [X0] : ~rich(X0) | (tall(alice) & ~tall(alice)) [ennf transformation 8]
37. ! [X0] : ((~calm(X0) | ~kind(X0)) | ~curious(X0)) [ennf transformation 28]
38. ! [X0] : (~calm(X0) | ~kind(X0) | ~curious(X0)) [flattening 37]
41. ! [X0] : (((~quiet(X0) | ~tall(X0)) | (~patient(X0) | ~calm(X0))) & ((patient(X0) & calm(X0)) | (quiet(X0) & tall(X0)))) [nnf transformation 2]
42. ! [X0] : ((~quiet(X0) | ~tall(X0) | ~patient(X0) | ~calm(X0)) & ((patient(X0) & calm(X0)) | (quiet(X0) & tall(X0)))) [flattening 41]
52. ? [X0] : ~rich(X0) => ~rich(sK3) [choice axiom]
53. ~rich(sK3) | (tall(alice) & ~tall(alice)) [skolemisation 36,52]
64. ! [X0] : ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0))) [nnf transformation 13]
67. (? [X0] : (~rich(X0) | ~calm(X0)) | ((wise(alice) | ~calm(alice)) & (calm(alice) | ~wise(alice)))) & (((~calm(alice) | ~wise(alice)) & (calm(alice) | wise(alice))) | ! [X0] : (rich(X0) & calm(X0))) [nnf transformation 15]
68. (? [X0] : (~rich(X0) | ~calm(X0)) | ((wise(alice) | ~calm(alice)) & (calm(alice) | ~wise(alice)))) & (((~calm(alice) | ~wise(alice)) & (calm(alice) | wise(alice))) | ! [X1] : (rich(X1) & calm(X1))) [rectify 67]
69. ? [X0] : (~rich(X0) | ~calm(X0)) => (~rich(sK6) | ~calm(sK6)) [choice axiom]
70. ((~rich(sK6) | ~calm(sK6)) | ((wise(alice) | ~calm(alice)) & (calm(alice) | ~wise(alice)))) & (((~calm(alice) | ~wise(alice)) & (calm(alice) | wise(alice))) | ! [X1] : (rich(X1) & calm(X1))) [skolemisation 68,69]
93. calm(X0) | quiet(X0) [cnf transformation 42]
109. ~rich(sK3) | ~tall(alice) [cnf transformation 53]
110. ~rich(sK3) | tall(alice) [cnf transformation 53]
117. ~curious(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 38]
129. wise(X0) | kind(X0) [cnf transformation 64]
136. ~calm(alice) | ~wise(alice) | rich(X1) [cnf transformation 70]
153. ~quiet(alice) [cnf transformation 22]
157. curious(alice) [cnf transformation 25]
226. 16 <=> tall(alice) [avatar definition]
230. 17 <=> rich(sK3) [avatar definition]
232. ~rich(sK3) <- (~17) [avatar component clause 230]
233. 16 | ~17 [avatar split clause 110,230,226]
234. ~16 | ~17 [avatar split clause 109,230,226]
264. 24 <=> calm(alice) [avatar definition]
265. calm(alice) <- (24) [avatar component clause 264]
266. ~calm(alice) <- (~24) [avatar component clause 264]
280. 27 <=> wise(alice) [avatar definition]
281. ~wise(alice) <- (~27) [avatar component clause 280]
294. 30 <=> ! [X1] : rich(X1) [avatar definition]
295. rich(X1) <- (30) [avatar component clause 294]
296. 30 | ~27 | ~24 [avatar split clause 136,264,280,294]
376. kind(alice) <- (~27) [resolution 129,281]
382. ~kind(alice) | ~calm(alice) [resolution 117,157]
384. ~calm(alice) <- (~27) [subsumption resolution 382,376]
385. $false <- (24, ~27) [subsumption resolution 384,265]
386. ~24 | 27 [avatar contradiction clause 385]
392. quiet(alice) <- (~24) [resolution 266,93]
394. $false <- (~24) [subsumption resolution 392,153]
395. 24 [avatar contradiction clause 394]
398. $false <- (~17, 30) [resolution 295,232]
401. 17 | ~30 [avatar contradiction clause 398]
402. $false [avatar sat refutation 233,234,296,386,395,401]
% SZS output end Proof for 402449054717925046618830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both quiet and not funny is either curious or not generous and vice versa.
Everyone who is both tall and not generous is creative or not happy and vice versa.
Everyone who is not curious or wise is not generous and vice versa.
Everyone who is not generous or not funny is funny.
Everyone who is old is not creative and vice versa.
If someone is either not creative or creative then alice is either rich or kind and vice versa.
Everyone who is both not rich and not happy is strong.
If fred is kind or patient then susan is both wise and not generous.
Everyone who is tall is both not rich and not humble.
Everyone who is both not humble and strong is not wise or creative.
If lucy is both kind and not tall then john is curious and vice versa.
If fred is quiet then someone is either curious or wise.
Everyone who is both not brave and not happy is creative or quiet.
If someone is both not tall and not wise then someone is not humble or creative and vice versa.
Everyone who is both kind and not curious is not old or rich and vice versa.
Everyone who is both strong and not tall is not calm.
John is either creative or old.
Someone is not old or brave.
Fred is kind or not creative.
Someone is both wise and strong.
Lucy is either not wise or calm.
Someone is either tall or not patient. | John is not happy. | contradiction | (![X]:((quiet(X)&~funny(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((tall(X)&~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:((~curious(X)|wise(X))<=>~generous(X)))&
(![X]:((~generous(X)|~funny(X))=>funny(X)))&
(![X]:(old(X)<=>~creative(X)))&
((?[X]:((~creative(X)<~>creative(X))))<=>((rich(alice)<~>kind(alice))))&
(![X]:((~rich(X)&~happy(X))=>strong(X)))&
(((kind(fred)|patient(fred)))=>((wise(susan)&~generous(susan))))&
(![X]:(tall(X)=>(~rich(X)&~humble(X))))&
(![X]:((~humble(X)&strong(X))=>(~wise(X)|creative(X))))&
(((kind(lucy)&~tall(lucy)))<=>(curious(john)))&
((quiet(fred))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~brave(X)&~happy(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~old(X)|rich(X))))&
(![X]:((strong(X)&~tall(X))=>~calm(X)))&
((creative(john)<~>old(john)))&
(?[X]:((~old(X)|brave(X))))&
((kind(fred)|~creative(fred)))&
(?[X]:((wise(X)&strong(X))))&
((~wise(lucy)<~>calm(lucy)))&
(?[X]:((tall(X)<~>~patient(X)))) | ~happy(john) | [
"p0",
"p1",
"p2",
"p3",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 318361841276453636910381
% SZS output start Proof for 318361841276453636910381
1. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (curious(X0) <~> ~generous(X0))) [input p0]
2. ! [X0] : ((~generous(X0) & tall(X0)) <=> (~happy(X0) | creative(X0))) [input p1]
3. ! [X0] : ((wise(X0) | ~curious(X0)) <=> ~generous(X0)) [input p2]
4. ! [X0] : ((~funny(X0) | ~generous(X0)) => funny(X0)) [input p3]
9. ! [X0] : (tall(X0) => (~humble(X0) & ~rich(X0))) [input p8]
14. ? [X0] : (~wise(X0) & ~tall(X0)) <=> ? [X0] : (creative(X0) | ~humble(X0)) [input p13]
23. ~happy(john) [input hypothesis]
24. ? [X0] : (~wise(X0) & ~tall(X0)) <=> ? [X1] : (creative(X1) | ~humble(X1)) [rectify 14]
27. ! [X0] : (funny(X0) | (funny(X0) & generous(X0))) [ennf transformation 4]
31. ! [X0] : ((~humble(X0) & ~rich(X0)) | ~tall(X0)) [ennf transformation 9]
37. ! [X0] : (((~funny(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (funny(X0) | ~quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((~funny(X0) & quiet(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | funny(X0) | ~quiet(X0))) [flattening 37]
39. ! [X0] : (((~generous(X0) & tall(X0)) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 2]
40. ! [X0] : (((~generous(X0) & tall(X0)) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | generous(X0) | ~tall(X0))) [flattening 39]
41. ! [X0] : (((wise(X0) | ~curious(X0)) | generous(X0)) & (~generous(X0) | (~wise(X0) & curious(X0)))) [nnf transformation 3]
42. ! [X0] : ((wise(X0) | ~curious(X0) | generous(X0)) & (~generous(X0) | (~wise(X0) & curious(X0)))) [flattening 41]
53. (? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : (~creative(X1) & humble(X1))) & (? [X1] : (creative(X1) | ~humble(X1)) | ! [X0] : (wise(X0) | tall(X0))) [nnf transformation 24]
54. (? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : (~creative(X1) & humble(X1))) & (? [X2] : (creative(X2) | ~humble(X2)) | ! [X3] : (wise(X3) | tall(X3))) [rectify 53]
55. ? [X0] : (~wise(X0) & ~tall(X0)) => (~wise(sK2) & ~tall(sK2)) [choice axiom]
56. ? [X2] : (creative(X2) | ~humble(X2)) => (creative(sK3) | ~humble(sK3)) [choice axiom]
57. ((~wise(sK2) & ~tall(sK2)) | ! [X1] : (~creative(X1) & humble(X1))) & ((creative(sK3) | ~humble(sK3)) | ! [X3] : (wise(X3) | tall(X3))) [skolemisation 54,56,55]
71. ~generous(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 38]
72. ~funny(X0) | curious(X0) | generous(X0) [cnf transformation 38]
75. happy(X0) | tall(X0) [cnf transformation 40]
78. ~generous(X0) | curious(X0) [cnf transformation 42]
80. ~curious(X0) | wise(X0) | generous(X0) [cnf transformation 42]
82. funny(X0) | funny(X0) [cnf transformation 27]
99. ~humble(X0) | ~tall(X0) [cnf transformation 31]
109. ~wise(sK2) | humble(X1) [cnf transformation 57]
126. ~happy(john) [cnf transformation 23]
131. funny(X0) [duplicate literal removal 82]
200. 15 <=> wise(sK2) [avatar definition]
202. ~wise(sK2) <- (~15) [avatar component clause 200]
205. 16 <=> ! [X1] : humble(X1) [avatar definition]
206. humble(X1) <- (16) [avatar component clause 205]
207. 16 | ~15 [avatar split clause 109,200,205]
251. tall(john) [resolution 75,126]
285. curious(X0) | generous(X0) [resolution 72,131]
286. curious(X0) [subsumption resolution 285,78]
291. wise(X0) | generous(X0) [resolution 80,286]
314. generous(sK2) <- (~15) [resolution 291,202]
319. ~funny(sK2) | ~curious(sK2) <- (~15) [resolution 314,71]
323. ~curious(sK2) <- (~15) [subsumption resolution 319,131]
324. $false <- (~15) [subsumption resolution 323,286]
325. 15 [avatar contradiction clause 324]
329. ~tall(X0) <- (16) [resolution 206,99]
348. $false <- (16) [resolution 329,251]
349. ~16 [avatar contradiction clause 348]
350. $false [avatar sat refutation 207,325,349]
% SZS output end Proof for 318361841276453636910381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is curious or not tall.
If someone is curious or not calm then mary is not tall and vice versa.
Everyone who is both creative and not rich is patient or brave.
Everyone who is both not creative and strong is either not calm or not happy.
If mary is both happy and strong then someone is either not tall or not creative.
Everyone who is either not wise or not brave is both old and generous and vice versa.
Everyone who is tall is not tall or not kind.
Everyone who is curious or brave is both not tall and not humble and vice versa.
If lucy is not strong or funny then someone is not funny or not creative and vice versa.
If someone is generous then susan is not calm or not curious.
Everyone who is strong is calm or not happy.
Everyone who is either curious or not tall is both humble and old.
Everyone who is both creative and not humble is not wise.
Everyone who is old is both not tall and kind.
If someone is both strong and not happy then lucy is both tall and curious and vice versa.
Everyone who is generous or not strong is brave.
Someone is not creative.
Lucy is both strong and old.
Alice is either not funny or not wise.
Someone is either not funny or not brave.
Alice is either not funny or not strong.
Fred is both not strong and not funny.
Someone is both funny and calm.
Paul is both curious and old. | Lucy is creative. | entailment | ((?[X]:(~funny(X)))=>(?[X]:((curious(X)|~tall(X)))))&
((?[X]:((curious(X)|~calm(X))))<=>(~tall(mary)))&
(![X]:((creative(X)&~rich(X))=>(patient(X)|brave(X))))&
(![X]:((~creative(X)&strong(X))=>(~calm(X)<~>~happy(X))))&
(((happy(mary)&strong(mary)))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(![X]:((~wise(X)<~>~brave(X))<=>(old(X)&generous(X))))&
(![X]:(tall(X)=>(~tall(X)|~kind(X))))&
(![X]:((curious(X)|brave(X))<=>(~tall(X)&~humble(X))))&
(((~strong(lucy)|funny(lucy)))<=>(?[X]:((~funny(X)|~creative(X)))))&
((?[X]:(generous(X)))=>((~calm(susan)|~curious(susan))))&
(![X]:(strong(X)=>(calm(X)|~happy(X))))&
(![X]:((curious(X)<~>~tall(X))=>(humble(X)&old(X))))&
(![X]:((creative(X)&~humble(X))=>~wise(X)))&
(![X]:(old(X)=>(~tall(X)&kind(X))))&
((?[X]:((strong(X)&~happy(X))))<=>((tall(lucy)&curious(lucy))))&
(![X]:((generous(X)|~strong(X))=>brave(X)))&
(?[X]:(~creative(X)))&
((strong(lucy)&old(lucy)))&
((~funny(alice)<~>~wise(alice)))&
(?[X]:((~funny(X)<~>~brave(X))))&
((~funny(alice)<~>~strong(alice)))&
((~strong(fred)&~funny(fred)))&
(?[X]:((funny(X)&calm(X))))&
((curious(paul)&old(paul))) | creative(lucy) | [
"p3",
"p10",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3431280139873138651607383
% SZS output start Proof for 3431280139873138651607383
4. ! [X0] : ((strong(X0) & ~creative(X0)) => (~calm(X0) <~> ~happy(X0))) [input p3]
11. ! [X0] : (strong(X0) => (~happy(X0) | calm(X0))) [input p10]
14. ! [X0] : (old(X0) => (kind(X0) & ~tall(X0))) [input p13]
15. ? [X0] : (~happy(X0) & strong(X0)) <=> (curious(lucy) & tall(lucy)) [input p14]
18. old(lucy) & strong(lucy) [input p17]
25. ~creative(lucy) [input hypothesis]
29. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | (~strong(X0) | creative(X0))) [ennf transformation 4]
30. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | ~strong(X0) | creative(X0)) [flattening 29]
37. ! [X0] : ((~happy(X0) | calm(X0)) | ~strong(X0)) [ennf transformation 11]
38. ! [X0] : (~happy(X0) | calm(X0) | ~strong(X0)) [flattening 37]
42. ! [X0] : ((kind(X0) & ~tall(X0)) | ~old(X0)) [ennf transformation 14]
51. ! [X0] : (((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | ~strong(X0) | creative(X0)) [nnf transformation 30]
65. (? [X0] : (~happy(X0) & strong(X0)) | (~curious(lucy) | ~tall(lucy))) & ((curious(lucy) & tall(lucy)) | ! [X0] : (happy(X0) | ~strong(X0))) [nnf transformation 15]
66. (? [X0] : (~happy(X0) & strong(X0)) | ~curious(lucy) | ~tall(lucy)) & ((curious(lucy) & tall(lucy)) | ! [X0] : (happy(X0) | ~strong(X0))) [flattening 65]
67. (? [X0] : (~happy(X0) & strong(X0)) | ~curious(lucy) | ~tall(lucy)) & ((curious(lucy) & tall(lucy)) | ! [X1] : (happy(X1) | ~strong(X1))) [rectify 66]
68. ? [X0] : (~happy(X0) & strong(X0)) => (~happy(sK4) & strong(sK4)) [choice axiom]
69. ((~happy(sK4) & strong(sK4)) | ~curious(lucy) | ~tall(lucy)) & ((curious(lucy) & tall(lucy)) | ! [X1] : (happy(X1) | ~strong(X1))) [skolemisation 67,68]
83. ~happy(X0) | ~calm(X0) | ~strong(X0) | creative(X0) [cnf transformation 51]
104. ~happy(X0) | calm(X0) | ~strong(X0) [cnf transformation 38]
110. ~old(X0) | ~tall(X0) [cnf transformation 42]
112. tall(lucy) | happy(X1) | ~strong(X1) [cnf transformation 69]
119. strong(lucy) [cnf transformation 18]
120. old(lucy) [cnf transformation 18]
133. ~creative(lucy) [cnf transformation 25]
190. 14 <=> strong(lucy) [avatar definition]
191. strong(lucy) <- (14) [avatar component clause 190]
222. 21 <=> ! [X1] : (happy(X1) | ~strong(X1)) [avatar definition]
223. ~strong(X1) | happy(X1) <- (21) [avatar component clause 222]
230. 23 <=> tall(lucy) [avatar definition]
233. 21 | 23 [avatar split clause 112,230,222]
234. 14 [avatar split clause 119,190]
261. ~tall(lucy) [resolution 110,120]
263. ~23 [avatar split clause 261,230]
272. happy(lucy) <- (14, 21) [resolution 223,191]
293. calm(lucy) | ~strong(lucy) <- (14, 21) [resolution 104,272]
294. calm(lucy) <- (14, 21) [subsumption resolution 293,191]
312. ~calm(lucy) | ~strong(lucy) | creative(lucy) <- (14, 21) [resolution 83,272]
313. ~strong(lucy) | creative(lucy) <- (14, 21) [subsumption resolution 312,294]
314. creative(lucy) <- (14, 21) [subsumption resolution 313,191]
315. $false <- (14, 21) [subsumption resolution 314,133]
316. ~14 | ~21 [avatar contradiction clause 315]
317. $false [avatar sat refutation 233,234,263,316]
% SZS output end Proof for 3431280139873138651607383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not creative then someone is either wise or curious. If susan is not generous then someone is both creative and not patient and vice versa. Everyone who is not strong is both not creative and not calm. Everyone who is either calm or patient is either not tall or not creative. Everyone who is not rich or not tall is old. If someone is not strong then mary is both curious and quiet. Everyone who is patient or not patient is both calm and curious and vice versa. If someone is either wise or not strong then paul is either humble or quiet. If john is not funny or not humble then someone is not brave or not curious and vice versa. Everyone who is not old is strong. Everyone who is not humble or creative is both not wise and generous and vice versa. Everyone who is both not curious and not brave is both not patient and strong. Everyone who is both not kind and not happy is both not strong and not patient and vice versa. Everyone who is both brave and happy is not creative and vice versa. If john is both not strong and kind then someone is either calm or rich and vice versa. Everyone who is both not happy and creative is both not calm and not generous and vice versa. Someone is either curious or kind. Someone is not old. Someone is not humble. Someone is not patient or wise. Someone is calm or not generous. Someone is wise or not curious. Someone is quiet. | Paul is not happy. | contradiction | ((?[X]:((creative(X)<~>~creative(X))))=>(?[X]:((wise(X)<~>curious(X)))))&
((~generous(susan))<=>(?[X]:((creative(X)&~patient(X)))))&
(![X]:(~strong(X)=>(~creative(X)&~calm(X))))&
(![X]:((calm(X)<~>patient(X))=>(~tall(X)<~>~creative(X))))&
(![X]:((~rich(X)|~tall(X))=>old(X)))&
((?[X]:(~strong(X)))=>((curious(mary)&quiet(mary))))&
(![X]:((patient(X)|~patient(X))<=>(calm(X)&curious(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>((humble(paul)<~>quiet(paul))))&
(((~funny(john)|~humble(john)))<=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:(~old(X)=>strong(X)))&
(![X]:((~humble(X)|creative(X))<=>(~wise(X)&generous(X))))&
(![X]:((~curious(X)&~brave(X))=>(~patient(X)&strong(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~strong(X)&~patient(X))))&
(![X]:((brave(X)&happy(X))<=>~creative(X)))&
(((~strong(john)&kind(john)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~happy(X)&creative(X))<=>(~calm(X)&~generous(X))))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:(~old(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:((calm(X)|~generous(X))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:(quiet(X))) | ~happy(paul) | [
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3083114977372902092987176
% SZS output start Proof for 3083114977372902092987176
7. ! [X0] : ((~patient(X0) | patient(X0)) <=> (curious(X0) & calm(X0))) [input p6]
14. ! [X0] : ((happy(X0) & brave(X0)) <=> ~creative(X0)) [input p13]
16. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (~generous(X0) & ~calm(X0))) [input p15]
24. ~happy(paul) [input hypothesis]
44. ! [X0] : (((~patient(X0) | patient(X0)) | (~curious(X0) | ~calm(X0))) & ((curious(X0) & calm(X0)) | (patient(X0) & ~patient(X0)))) [nnf transformation 7]
45. ! [X0] : ((~patient(X0) | patient(X0) | ~curious(X0) | ~calm(X0)) & ((curious(X0) & calm(X0)) | (patient(X0) & ~patient(X0)))) [flattening 44]
56. ! [X0] : (((happy(X0) & brave(X0)) | creative(X0)) & (~creative(X0) | (~happy(X0) | ~brave(X0)))) [nnf transformation 14]
57. ! [X0] : (((happy(X0) & brave(X0)) | creative(X0)) & (~creative(X0) | ~happy(X0) | ~brave(X0))) [flattening 56]
63. ! [X0] : (((creative(X0) & ~happy(X0)) | (generous(X0) | calm(X0))) & ((~generous(X0) & ~calm(X0)) | (~creative(X0) | happy(X0)))) [nnf transformation 16]
64. ! [X0] : (((creative(X0) & ~happy(X0)) | generous(X0) | calm(X0)) & ((~generous(X0) & ~calm(X0)) | ~creative(X0) | happy(X0))) [flattening 63]
97. calm(X0) | ~patient(X0) [cnf transformation 45]
98. calm(X0) | patient(X0) [cnf transformation 45]
124. happy(X0) | creative(X0) [cnf transformation 57]
131. ~calm(X0) | ~creative(X0) | happy(X0) [cnf transformation 64]
143. ~happy(paul) [cnf transformation 24]
198. calm(X0) [subsumption resolution 97,98]
259. ~creative(X0) | happy(X0) [subsumption resolution 131,198]
260. happy(X0) [subsumption resolution 259,124]
272. $false [subsumption resolution 143,260]
% SZS output end Proof for 3083114977372902092987176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not rich is rich or old.
If someone is happy then mary is not calm.
If alice is either not strong or creative then someone is not tall or not curious.
If someone is both calm and not funny then john is not humble.
If lucy is happy then lucy is quiet or humble.
Everyone who is not funny is either not old or generous and vice versa.
If someone is not quiet or calm then john is either not funny or not calm and vice versa.
If someone is happy or not generous then someone is both generous and not brave.
Everyone who is either curious or not brave is not kind.
Everyone who is funny or quiet is both not patient and not creative and vice versa.
If someone is either happy or not old then someone is either not quiet or not brave.
Everyone who is both not wise and wise is either not generous or not patient.
Everyone who is not generous or brave is curious and vice versa.
Everyone who is tall or old is both quiet and not wise and vice versa.
If susan is either humble or wise then lucy is either not old or not generous and vice versa.
Everyone who is both strong and not kind is humble or funny and vice versa.
Paul is tall or quiet.
Alice is not kind or not humble.
Paul is humble.
John is not curious.
John is calm or strong.
Fred is both patient and kind.
Susan is both old and funny.
Someone is not creative. | Fred is not brave. | entailment | (![X]:((~strong(X)<~>~rich(X))=>(rich(X)|old(X))))&
((?[X]:(happy(X)))=>(~calm(mary)))&
(((~strong(alice)<~>creative(alice)))=>(?[X]:((~tall(X)|~curious(X)))))&
((?[X]:((calm(X)&~funny(X))))=>(~humble(john)))&
((happy(lucy))=>((quiet(lucy)|humble(lucy))))&
(![X]:(~funny(X)<=>(~old(X)<~>generous(X))))&
((?[X]:((~quiet(X)|calm(X))))<=>((~funny(john)<~>~calm(john))))&
((?[X]:((happy(X)|~generous(X))))=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((curious(X)<~>~brave(X))=>~kind(X)))&
(![X]:((funny(X)|quiet(X))<=>(~patient(X)&~creative(X))))&
((?[X]:((happy(X)<~>~old(X))))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((~wise(X)&wise(X))=>(~generous(X)<~>~patient(X))))&
(![X]:((~generous(X)|brave(X))<=>curious(X)))&
(![X]:((tall(X)|old(X))<=>(quiet(X)&~wise(X))))&
(((humble(susan)<~>wise(susan)))<=>((~old(lucy)<~>~generous(lucy))))&
(![X]:((strong(X)&~kind(X))<=>(humble(X)|funny(X))))&
((tall(paul)|quiet(paul)))&
((~kind(alice)|~humble(alice)))&
(humble(paul))&
(~curious(john))&
((calm(john)|strong(john)))&
((patient(fred)&kind(fred)))&
((old(susan)&funny(susan)))&
(?[X]:(~creative(X))) | ~brave(fred) | [
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6006655363487195748771284
% SZS output start Proof for 6006655363487195748771284
9. ! [X0] : ((curious(X0) <~> ~brave(X0)) => ~kind(X0)) [input p8]
13. ! [X0] : ((brave(X0) | ~generous(X0)) <=> curious(X0)) [input p12]
22. kind(fred) & patient(fred) [input p21]
25. brave(fred) [input hypothesis]
36. ! [X0] : (~kind(X0) | (curious(X0) <=> ~brave(X0))) [ennf transformation 9]
52. ! [X0] : (~kind(X0) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) [nnf transformation 36]
60. ! [X0] : (((brave(X0) | ~generous(X0)) | ~curious(X0)) & (curious(X0) | (~brave(X0) & generous(X0)))) [nnf transformation 13]
61. ! [X0] : ((brave(X0) | ~generous(X0) | ~curious(X0)) & (curious(X0) | (~brave(X0) & generous(X0)))) [flattening 60]
90. ~kind(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 52]
104. ~brave(X0) | curious(X0) [cnf transformation 61]
130. kind(fred) [cnf transformation 22]
134. brave(fred) [cnf transformation 25]
280. curious(fred) [resolution 104,134]
315. ~brave(fred) | ~curious(fred) [resolution 90,130]
316. ~curious(fred) [subsumption resolution 315,134]
317. $false [subsumption resolution 316,280]
% SZS output end Proof for 6006655363487195748771284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or humble.
Everyone who is both strong and brave is both patient and not tall.
If fred is not tall then lucy is either not brave or humble.
If susan is either happy or not tall then someone is both not wise and not creative and vice versa.
If fred is both calm and not strong then someone is either strong or not patient.
If fred is funny or not strong then alice is both not old and not funny.
Everyone who is either not funny or creative is not creative and vice versa.
If someone is generous or old then paul is either not calm or calm and vice versa.
Everyone who is both brave and not tall is either not curious or funny and vice versa.
Everyone who is both not calm and not happy is quiet or not kind and vice versa.
Everyone who is not brave is either not happy or not tall and vice versa.
Everyone who is funny or not patient is both wise and creative and vice versa.
If someone is either kind or not generous then someone is not quiet and vice versa.
Everyone who is both curious and creative is both strong and curious.
If lucy is both not patient and not old then someone is calm and vice versa.
Everyone who is not kind or wise is not generous or not patient and vice versa.
Fred is either wise or not creative.
Someone is both not strong and not wise.
Someone is not patient.
Someone is not humble or not funny.
Fred is not happy.
Lucy is not tall. | Lucy is brave. | neutral | (![X]:((~rich(X)&curious(X))=>(~calm(X)|humble(X))))&
(![X]:((strong(X)&brave(X))=>(patient(X)&~tall(X))))&
((~tall(fred))=>((~brave(lucy)<~>humble(lucy))))&
(((happy(susan)<~>~tall(susan)))<=>(?[X]:((~wise(X)&~creative(X)))))&
(((calm(fred)&~strong(fred)))=>(?[X]:((strong(X)<~>~patient(X)))))&
(((funny(fred)|~strong(fred)))=>((~old(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
((?[X]:((generous(X)|old(X))))<=>((~calm(paul)<~>calm(paul))))&
(![X]:((brave(X)&~tall(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~calm(X)&~happy(X))<=>(quiet(X)|~kind(X))))&
(![X]:(~brave(X)<=>(~happy(X)<~>~tall(X))))&
(![X]:((funny(X)|~patient(X))<=>(wise(X)&creative(X))))&
((?[X]:((kind(X)<~>~generous(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((curious(X)&creative(X))=>(strong(X)&curious(X))))&
(((~patient(lucy)&~old(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((~kind(X)|wise(X))<=>(~generous(X)|~patient(X))))&
((wise(fred)<~>~creative(fred)))&
(?[X]:((~strong(X)&~wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~humble(X)|~funny(X))))&
(~happy(fred))&
(~tall(lucy)) | brave(lucy) | [] | null | 0 |
Everyone who is wise is both happy and patient. If someone is not tall then someone is kind or generous. If someone is not wise or not brave then susan is not funny or curious. If someone is old then someone is both wise and generous and vice versa. If paul is both funny and tall then someone is not curious and vice versa. Everyone who is both not strong and not tall is not brave or not creative. If alice is not wise or patient then someone is either not happy or not generous and vice versa. Everyone who is either not tall or funny is old and vice versa. If alice is either curious or not tall then paul is not kind or wise and vice versa. If someone is both not wise and old then someone is both tall and not creative and vice versa. Everyone who is both tall and funny is not happy or tall. Everyone who is humble is both not tall and not generous and vice versa. Everyone who is either happy or brave is not tall. If mary is both happy and patient then someone is not curious or tall and vice versa. Everyone who is both humble and not calm is brave or not creative and vice versa. Everyone who is not quiet or generous is both not humble and old. Someone is either not brave or not funny. Mary is either strong or not curious. Someone is calm or not strong. John is creative or strong. Someone is rich. Lucy is both calm and not happy. Lucy is either not rich or brave. Susan is not creative or not calm. | Alice is curious. | entailment | (![X]:(wise(X)=>(happy(X)&patient(X))))&
((?[X]:(~tall(X)))=>(?[X]:((kind(X)|generous(X)))))&
((?[X]:((~wise(X)|~brave(X))))=>((~funny(susan)|curious(susan))))&
((?[X]:(old(X)))<=>(?[X]:((wise(X)&generous(X)))))&
(((funny(paul)&tall(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~strong(X)&~tall(X))=>(~brave(X)|~creative(X))))&
(((~wise(alice)|patient(alice)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(![X]:((~tall(X)<~>funny(X))<=>old(X)))&
(((curious(alice)<~>~tall(alice)))<=>((~kind(paul)|wise(paul))))&
((?[X]:((~wise(X)&old(X))))<=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((tall(X)&funny(X))=>(~happy(X)|tall(X))))&
(![X]:(humble(X)<=>(~tall(X)&~generous(X))))&
(![X]:((happy(X)<~>brave(X))=>~tall(X)))&
(((happy(mary)&patient(mary)))<=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((humble(X)&~calm(X))<=>(brave(X)|~creative(X))))&
(![X]:((~quiet(X)|generous(X))=>(~humble(X)&old(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((strong(mary)<~>~curious(mary)))&
(?[X]:((calm(X)|~strong(X))))&
((creative(john)|strong(john)))&
(?[X]:(rich(X)))&
((calm(lucy)&~happy(lucy)))&
((~rich(lucy)<~>brave(lucy)))&
((~creative(susan)|~calm(susan))) | curious(alice) | [
"p0",
"p4",
"p7",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4054600763103229073395784
% SZS output start Proof for 4054600763103229073395784
1. ! [X0] : (wise(X0) => (patient(X0) & happy(X0))) [input p0]
5. (tall(paul) & funny(paul)) <=> ? [X0] : ~curious(X0) [input p4]
8. ! [X0] : ((~tall(X0) <~> funny(X0)) <=> old(X0)) [input p7]
10. ? [X0] : (old(X0) & ~wise(X0)) <=> ? [X0] : (~creative(X0) & tall(X0)) [input p9]
12. ! [X0] : (humble(X0) <=> (~generous(X0) & ~tall(X0))) [input p11]
13. ! [X0] : ((happy(X0) <~> brave(X0)) => ~tall(X0)) [input p12]
15. ! [X0] : ((~calm(X0) & humble(X0)) <=> (~creative(X0) | brave(X0))) [input p14]
25. ~curious(alice) [input hypothesis]
28. ? [X0] : (old(X0) & ~wise(X0)) <=> ? [X1] : (~creative(X1) & tall(X1)) [rectify 10]
30. ! [X0] : ((patient(X0) & happy(X0)) | ~wise(X0)) [ennf transformation 1]
38. ! [X0] : (~tall(X0) | (happy(X0) <=> brave(X0))) [ennf transformation 13]
48. ((tall(paul) & funny(paul)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~tall(paul) | ~funny(paul))) [nnf transformation 5]
49. ((tall(paul) & funny(paul)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~tall(paul) | ~funny(paul)) [flattening 48]
50. ((tall(paul) & funny(paul)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~tall(paul) | ~funny(paul)) [rectify 49]
51. ? [X1] : ~curious(X1) => ~curious(sK3) [choice axiom]
52. ((tall(paul) & funny(paul)) | ! [X0] : curious(X0)) & (~curious(sK3) | ~tall(paul) | ~funny(paul)) [skolemisation 50,51]
58. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~old(X0)) & (old(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [nnf transformation 8]
61. (? [X0] : (old(X0) & ~wise(X0)) | ! [X1] : (creative(X1) | ~tall(X1))) & (? [X1] : (~creative(X1) & tall(X1)) | ! [X0] : (~old(X0) | wise(X0))) [nnf transformation 28]
62. (? [X0] : (old(X0) & ~wise(X0)) | ! [X1] : (creative(X1) | ~tall(X1))) & (? [X2] : (~creative(X2) & tall(X2)) | ! [X3] : (~old(X3) | wise(X3))) [rectify 61]
63. ? [X0] : (old(X0) & ~wise(X0)) => (old(sK5) & ~wise(sK5)) [choice axiom]
64. ? [X2] : (~creative(X2) & tall(X2)) => (~creative(sK6) & tall(sK6)) [choice axiom]
65. ((old(sK5) & ~wise(sK5)) | ! [X1] : (creative(X1) | ~tall(X1))) & ((~creative(sK6) & tall(sK6)) | ! [X3] : (~old(X3) | wise(X3))) [skolemisation 62,64,63]
66. ! [X0] : ((humble(X0) | (generous(X0) | tall(X0))) & ((~generous(X0) & ~tall(X0)) | ~humble(X0))) [nnf transformation 12]
67. ! [X0] : ((humble(X0) | generous(X0) | tall(X0)) & ((~generous(X0) & ~tall(X0)) | ~humble(X0))) [flattening 66]
68. ! [X0] : (~tall(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) [nnf transformation 38]
74. ! [X0] : (((~calm(X0) & humble(X0)) | (creative(X0) & ~brave(X0))) & ((~creative(X0) | brave(X0)) | (calm(X0) | ~humble(X0)))) [nnf transformation 15]
75. ! [X0] : (((~calm(X0) & humble(X0)) | (creative(X0) & ~brave(X0))) & (~creative(X0) | brave(X0) | calm(X0) | ~humble(X0))) [flattening 74]
85. ~wise(X0) | happy(X0) [cnf transformation 30]
94. funny(paul) | curious(X0) [cnf transformation 52]
95. tall(paul) | curious(X0) [cnf transformation 52]
104. ~funny(X0) | ~tall(X0) | old(X0) [cnf transformation 58]
113. tall(sK6) | ~old(X3) | wise(X3) [cnf transformation 65]
114. ~creative(sK6) | ~old(X3) | wise(X3) [cnf transformation 65]
118. ~humble(X0) | ~tall(X0) [cnf transformation 67]
121. ~tall(X0) | brave(X0) | ~happy(X0) [cnf transformation 68]
129. ~brave(X0) | humble(X0) [cnf transformation 75]
130. humble(X0) | creative(X0) [cnf transformation 75]
147. ~curious(alice) [cnf transformation 25]
198. 13 <=> ! [X0] : curious(X0) [avatar definition]
199. curious(X0) <- (13) [avatar component clause 198]
201. 14 <=> tall(paul) [avatar definition]
203. tall(paul) <- (14) [avatar component clause 201]
204. 13 | 14 [avatar split clause 95,201,198]
206. 15 <=> funny(paul) [avatar definition]
208. funny(paul) <- (15) [avatar component clause 206]
209. 13 | 15 [avatar split clause 94,206,198]
236. 21 <=> wise(paul) [avatar definition]
237. wise(paul) <- (21) [avatar component clause 236]
240. 22 <=> curious(alice) [avatar definition]
242. ~curious(alice) <- (~22) [avatar component clause 240]
258. 25 <=> ! [X1] : (creative(X1) | ~tall(X1)) [avatar definition]
259. ~tall(X1) | creative(X1) <- (25) [avatar component clause 258]
271. 28 <=> ! [X3] : (~old(X3) | wise(X3)) [avatar definition]
272. ~old(X3) | wise(X3) <- (28) [avatar component clause 271]
274. 29 <=> creative(sK6) [avatar definition]
276. ~creative(sK6) <- (~29) [avatar component clause 274]
277. 28 | ~29 [avatar split clause 114,274,271]
279. 30 <=> tall(sK6) [avatar definition]
281. tall(sK6) <- (30) [avatar component clause 279]
282. 28 | 30 [avatar split clause 113,279,271]
356. ~22 [avatar split clause 147,240]
359. $false <- (13, ~22) [resolution 242,199]
360. ~13 | 22 [avatar contradiction clause 359]
367. creative(X1) | ~tall(X1) [resolution 130,118]
386. ~tall(paul) | old(paul) <- (15) [resolution 104,208]
387. old(paul) <- (14, 15) [subsumption resolution 386,203]
424. wise(paul) <- (14, 15, 28) [resolution 387,272]
425. 21 | ~14 | ~15 | ~28 [avatar split clause 424,271,206,201,236]
427. happy(paul) <- (21) [resolution 237,85]
428. brave(paul) | ~happy(paul) <- (14) [resolution 121,203]
429. brave(paul) <- (14, 21) [subsumption resolution 428,427]
447. humble(paul) <- (14, 21) [resolution 429,129]
474. creative(sK6) <- (25, 30) [resolution 281,259]
484. $false <- (25, ~29, 30) [subsumption resolution 474,276]
485. ~25 | 29 | ~30 [avatar contradiction clause 484]
486. 25 [avatar split clause 367,258]
550. ~tall(paul) <- (14, 21) [resolution 447,118]
551. $false <- (14, 21) [subsumption resolution 550,203]
552. ~14 | ~21 [avatar contradiction clause 551]
553. $false [avatar sat refutation 204,209,277,282,356,360,425,485,486,552]
% SZS output end Proof for 4054600763103229073395784
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not old is not wise and vice versa.
Everyone who is either not wise or not patient is tall.
Everyone who is not calm is not generous.
Everyone who is not happy or old is funny or brave and vice versa.
Everyone who is calm is both patient and calm.
Everyone who is either not creative or not generous is not rich or not happy and vice versa.
Everyone who is either curious or creative is either not creative or patient.
Everyone who is both old and funny is happy.
Everyone who is not happy or patient is both not calm and not generous.
If someone is tall then fred is both brave and not patient and vice versa.
Everyone who is curious is funny or patient.
If someone is both calm and wise then john is not strong.
If someone is both curious and not kind then someone is either rich or kind and vice versa.
If someone is both tall and rich then lucy is either not tall or strong and vice versa.
If someone is not happy or humble then someone is either not kind or not funny and vice versa.
Someone is both quiet and wise.
Someone is both not happy and brave.
Someone is not brave.
Paul is not brave.
John is funny or not patient.
Someone is both not patient and wise.
Someone is rich. | Paul is generous. | contradiction | (![X]:((~wise(X)<~>~old(X))<=>~wise(X)))&
(![X]:((~wise(X)<~>~patient(X))=>tall(X)))&
(![X]:(~calm(X)=>~generous(X)))&
(![X]:((~happy(X)|old(X))<=>(funny(X)|brave(X))))&
(![X]:(calm(X)=>(patient(X)&calm(X))))&
(![X]:((~creative(X)<~>~generous(X))<=>(~rich(X)|~happy(X))))&
(![X]:((curious(X)<~>creative(X))=>(~creative(X)<~>patient(X))))&
(![X]:((old(X)&funny(X))=>happy(X)))&
(![X]:((~happy(X)|patient(X))=>(~calm(X)&~generous(X))))&
((?[X]:(tall(X)))<=>((brave(fred)&~patient(fred))))&
(![X]:(curious(X)=>(funny(X)|patient(X))))&
((?[X]:((calm(X)&wise(X))))=>(~strong(john)))&
((?[X]:((curious(X)&~kind(X))))<=>(?[X]:((rich(X)<~>kind(X)))))&
((?[X]:((tall(X)&rich(X))))<=>((~tall(lucy)<~>strong(lucy))))&
((?[X]:((~happy(X)|humble(X))))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
(?[X]:((quiet(X)&wise(X))))&
(?[X]:((~happy(X)&brave(X))))&
(?[X]:(~brave(X)))&
(~brave(paul))&
((funny(john)|~patient(john)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:(rich(X))) | generous(paul) | [
"p2",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 627556161288319247763976
% SZS output start Proof for 627556161288319247763976
3. ! [X0] : (~calm(X0) => ~generous(X0)) [input p2]
5. ! [X0] : (calm(X0) => (calm(X0) & patient(X0))) [input p4]
9. ! [X0] : ((patient(X0) | ~happy(X0)) => (~generous(X0) & ~calm(X0))) [input p8]
23. generous(paul) [input hypothesis]
28. ! [X0] : (~generous(X0) | calm(X0)) [ennf transformation 3]
29. ! [X0] : ((calm(X0) & patient(X0)) | ~calm(X0)) [ennf transformation 5]
33. ! [X0] : ((~generous(X0) & ~calm(X0)) | (~patient(X0) & happy(X0))) [ennf transformation 9]
79. ~generous(X0) | calm(X0) [cnf transformation 28]
84. patient(X0) | ~calm(X0) [cnf transformation 29]
98. ~calm(X0) | ~patient(X0) [cnf transformation 33]
133. generous(paul) [cnf transformation 23]
141. ~calm(X0) [subsumption resolution 98,84]
261. calm(paul) [resolution 79,133]
262. $false [subsumption resolution 261,141]
% SZS output end Proof for 627556161288319247763976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not patient and happy is not tall and vice versa. If someone is tall or rich then susan is not old or not curious. Everyone who is not calm or not brave is both happy and not wise and vice versa. Everyone who is either happy or not creative is either not calm or not curious and vice versa. If fred is not funny or not kind then someone is funny. Everyone who is not kind or not quiet is both not humble and happy and vice versa. Everyone who is both happy and not kind is not old. If someone is either not rich or creative then alice is creative and vice versa. Everyone who is creative or curious is not kind or not creative. Everyone who is not brave is not curious or not humble and vice versa. If someone is either happy or not rich then someone is either not humble or not rich and vice versa. If john is both funny and tall then susan is either not humble or funny. Everyone who is not calm or not curious is kind. If someone is both not quiet and patient then fred is patient and vice versa. If john is both quiet and old then susan is not humble and vice versa. Everyone who is not generous is not brave and vice versa. Lucy is either not kind or not rich. Someone is generous. Someone is not old. Someone is not wise. Someone is both tall and strong. | Lucy is old. | contradiction | (![X]:((~patient(X)&happy(X))<=>~tall(X)))&
((?[X]:((tall(X)|rich(X))))=>((~old(susan)|~curious(susan))))&
(![X]:((~calm(X)|~brave(X))<=>(happy(X)&~wise(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~curious(X))))&
(((~funny(fred)|~kind(fred)))=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(~humble(X)&happy(X))))&
(![X]:((happy(X)&~kind(X))=>~old(X)))&
((?[X]:((~rich(X)<~>creative(X))))<=>(creative(alice)))&
(![X]:((creative(X)|curious(X))=>(~kind(X)|~creative(X))))&
(![X]:(~brave(X)<=>(~curious(X)|~humble(X))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(((funny(john)&tall(john)))=>((~humble(susan)<~>funny(susan))))&
(![X]:((~calm(X)|~curious(X))=>kind(X)))&
((?[X]:((~quiet(X)&patient(X))))<=>(patient(fred)))&
(((quiet(john)&old(john)))<=>(~humble(susan)))&
(![X]:(~generous(X)<=>~brave(X)))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~old(X)))&
(?[X]:(~wise(X)))&
(?[X]:((tall(X)&strong(X)))) | old(lucy) | [
"p2",
"p3",
"p5",
"p6",
"p7",
"p8",
"p9",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2108622842047761147337926
% SZS output start Proof for 2108622842047761147337926
3. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (~wise(X0) & happy(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> (~calm(X0) <~> ~curious(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (happy(X0) & ~humble(X0))) [input p5]
7. ! [X0] : ((~kind(X0) & happy(X0)) => ~old(X0)) [input p6]
8. ? [X0] : (~rich(X0) <~> creative(X0)) <=> creative(alice) [input p7]
9. ! [X0] : ((curious(X0) | creative(X0)) => (~creative(X0) | ~kind(X0))) [input p8]
10. ! [X0] : (~brave(X0) <=> (~humble(X0) | ~curious(X0))) [input p9]
13. ! [X0] : ((~curious(X0) | ~calm(X0)) => kind(X0)) [input p12]
17. ~kind(lucy) <~> ~rich(lucy) [input p16]
22. old(lucy) [input hypothesis]
29. ! [X0] : (~old(X0) | (kind(X0) | ~happy(X0))) [ennf transformation 7]
30. ! [X0] : (~old(X0) | kind(X0) | ~happy(X0)) [flattening 29]
31. ! [X0] : ((~creative(X0) | ~kind(X0)) | (~curious(X0) & ~creative(X0))) [ennf transformation 9]
32. ! [X0] : (~creative(X0) | ~kind(X0) | (~curious(X0) & ~creative(X0))) [flattening 31]
35. ! [X0] : (kind(X0) | (curious(X0) & calm(X0))) [ennf transformation 13]
39. ! [X0] : (((~brave(X0) | ~calm(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 3]
40. ! [X0] : ((~brave(X0) | ~calm(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (brave(X0) & calm(X0)))) [flattening 39]
41. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0)))) & (((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 4]
44. ! [X0] : (((~quiet(X0) | ~kind(X0)) | (~happy(X0) | humble(X0))) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [nnf transformation 6]
45. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~happy(X0) | humble(X0)) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [flattening 44]
46. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~creative(alice)) & (creative(alice) | ! [X0] : ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) [nnf transformation 8]
47. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~creative(alice)) & (creative(alice) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [rectify 46]
48. ? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) => ((~creative(sK1) | rich(sK1)) & (creative(sK1) | ~rich(sK1))) [choice axiom]
49. (((~creative(sK1) | rich(sK1)) & (creative(sK1) | ~rich(sK1))) | ~creative(alice)) & (creative(alice) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [skolemisation 47,48]
50. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & ((~humble(X0) | ~curious(X0)) | brave(X0))) [nnf transformation 10]
51. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & (~humble(X0) | ~curious(X0) | brave(X0))) [flattening 50]
64. (rich(lucy) | kind(lucy)) & (~rich(lucy) | ~kind(lucy)) [nnf transformation 17]
78. calm(X0) | happy(X0) [cnf transformation 40]
79. brave(X0) | happy(X0) [cnf transformation 40]
83. ~creative(X0) | ~calm(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 41]
84. ~curious(X0) | ~calm(X0) | happy(X0) | creative(X0) [cnf transformation 41]
89. creative(X0) | ~happy(X0) | ~curious(X0) | calm(X0) [cnf transformation 41]
95. kind(X0) | happy(X0) [cnf transformation 45]
98. ~old(X0) | kind(X0) | ~happy(X0) [cnf transformation 30]
99. creative(alice) | creative(X1) | rich(X1) [cnf transformation 49]
103. ~creative(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 32]
106. ~brave(X0) | curious(X0) [cnf transformation 51]
118. kind(X0) | calm(X0) [cnf transformation 35]
119. kind(X0) | curious(X0) [cnf transformation 35]
127. ~rich(lucy) | ~kind(lucy) [cnf transformation 64]
133. old(lucy) [cnf transformation 22]
134. ~kind(X0) | ~creative(X0) [duplicate literal removal 103]
151. ~curious(X0) | creative(X0) | calm(X0) [subsumption resolution 89,78]
154. ~curious(X0) | happy(X0) | creative(X0) [subsumption resolution 84,151]
169. ~old(X0) | kind(X0) [subsumption resolution 98,95]
171. 8 <=> creative(alice) [avatar definition]
172. creative(alice) <- (8) [avatar component clause 171]
189. 12 <=> ! [X1] : (creative(X1) | rich(X1)) [avatar definition]
190. creative(X1) | rich(X1) <- (12) [avatar component clause 189]
191. 12 | 8 [avatar split clause 99,171,189]
276. 31 <=> kind(lucy) [avatar definition]
278. kind(lucy) <- (31) [avatar component clause 276]
280. 32 <=> rich(lucy) [avatar definition]
281. ~rich(lucy) <- (~32) [avatar component clause 280]
284. ~31 | ~32 [avatar split clause 127,280,276]
293. curious(X0) | happy(X0) [resolution 106,79]
296. ~creative(X0) | curious(X0) [resolution 134,119]
297. ~creative(X1) | calm(X1) [resolution 134,118]
298. ~creative(X2) | happy(X2) [resolution 134,95]
300. ~creative(lucy) <- (31) [resolution 134,278]
304. kind(lucy) [resolution 169,133]
341. 37 <=> curious(alice) [avatar definition]
343. curious(alice) <- (37) [avatar component clause 341]
345. 38 <=> calm(alice) [avatar definition]
356. rich(lucy) <- (12, 31) [resolution 190,300]
359. $false <- (12, 31, ~32) [subsumption resolution 356,281]
360. ~12 | ~31 | 32 [avatar contradiction clause 359]
366. 31 [avatar split clause 304,276]
395. ~calm(alice) | ~curious(alice) | ~happy(alice) <- (8) [resolution 83,172]
396. ~calm(alice) | ~happy(alice) <- (8, 37) [subsumption resolution 395,343]
408. happy(X0) | happy(X0) | creative(X0) [resolution 293,154]
410. happy(X0) | creative(X0) [duplicate literal removal 408]
411. happy(X0) [subsumption resolution 410,298]
417. curious(alice) <- (8) [resolution 296,172]
418. calm(alice) <- (8) [resolution 297,172]
421. ~calm(alice) <- (8, 37) [subsumption resolution 396,411]
422. ~38 | ~8 | ~37 [avatar split clause 421,341,171,345]
423. 38 | ~8 [avatar split clause 418,171,345]
424. 37 | ~8 [avatar split clause 417,171,341]
428. $false [avatar sat refutation 191,284,360,366,422,423,424]
% SZS output end Proof for 2108622842047761147337926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not patient or not rich then susan is wise and vice versa. If someone is wise then mary is not wise and vice versa. If someone is creative then someone is not tall and vice versa. Everyone who is not kind or not funny is brave or not calm and vice versa. Everyone who is both happy and not tall is not old. Everyone who is not generous or not quiet is patient or not humble and vice versa. Everyone who is both not calm and happy is rich. If mary is either not patient or brave then mary is curious or rich. Everyone who is both not quiet and not happy is either not brave or strong and vice versa. Everyone who is both rich and not old is either rich or not happy and vice versa. Everyone who is old or not rich is patient or not funny and vice versa. If john is calm or not calm then mary is curious and vice versa. If someone is both rich and not calm then someone is both not curious and curious and vice versa. Everyone who is generous or calm is not patient or brave and vice versa. Everyone who is not old or strong is both not humble and not generous and vice versa. Someone is either not funny or not wise. Susan is not wise or not patient. Someone is not generous. Susan is both not happy and tall. Alice is humble. Susan is rich or tall. Susan is generous. | Susan is patient. | contradiction | (((~patient(mary)|~rich(mary)))<=>(wise(susan)))&
((?[X]:(wise(X)))<=>(~wise(mary)))&
((?[X]:(creative(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~kind(X)|~funny(X))<=>(brave(X)|~calm(X))))&
(![X]:((happy(X)&~tall(X))=>~old(X)))&
(![X]:((~generous(X)|~quiet(X))<=>(patient(X)|~humble(X))))&
(![X]:((~calm(X)&happy(X))=>rich(X)))&
(((~patient(mary)<~>brave(mary)))=>((curious(mary)|rich(mary))))&
(![X]:((~quiet(X)&~happy(X))<=>(~brave(X)<~>strong(X))))&
(![X]:((rich(X)&~old(X))<=>(rich(X)<~>~happy(X))))&
(![X]:((old(X)|~rich(X))<=>(patient(X)|~funny(X))))&
(((calm(john)|~calm(john)))<=>(curious(mary)))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~wise(susan)|~patient(susan)))&
(?[X]:(~generous(X)))&
((~happy(susan)&tall(susan)))&
(humble(alice))&
((rich(susan)|tall(susan)))&
(generous(susan)) | patient(susan) | [
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8343739906876509358303152
% SZS output start Proof for 8343739906876509358303152
6. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (~humble(X0) | patient(X0))) [input p5]
7. ! [X0] : ((happy(X0) & ~calm(X0)) => rich(X0)) [input p6]
9. ! [X0] : ((~happy(X0) & ~quiet(X0)) <=> (~brave(X0) <~> strong(X0))) [input p8]
10. ! [X0] : ((~old(X0) & rich(X0)) <=> (rich(X0) <~> ~happy(X0))) [input p9]
13. ? [X0] : (~calm(X0) & rich(X0)) <=> ? [X0] : (curious(X0) & ~curious(X0)) [input p12]
14. ! [X0] : ((calm(X0) | generous(X0)) <=> (brave(X0) | ~patient(X0))) [input p13]
15. ! [X0] : ((strong(X0) | ~old(X0)) <=> (~generous(X0) & ~humble(X0))) [input p14]
19. tall(susan) & ~happy(susan) [input p18]
22. generous(susan) [input p21]
23. patient(susan) [input hypothesis]
25. ? [X0] : (~calm(X0) & rich(X0)) <=> ? [X1] : (curious(X1) & ~curious(X1)) [rectify 13]
28. ! [X0] : (rich(X0) | (~happy(X0) | calm(X0))) [ennf transformation 7]
29. ! [X0] : (rich(X0) | ~happy(X0) | calm(X0)) [flattening 28]
45. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 6]
46. ! [X0] : ((~quiet(X0) | ~generous(X0) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | (quiet(X0) & generous(X0)))) [flattening 45]
48. ! [X0] : (((~happy(X0) & ~quiet(X0)) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0)))) & (((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | (happy(X0) | quiet(X0)))) [nnf transformation 9]
49. ! [X0] : (((~happy(X0) & ~quiet(X0)) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0)))) & (((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | happy(X0) | quiet(X0))) [flattening 48]
50. ! [X0] : (((~old(X0) & rich(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0)))) & (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (old(X0) | ~rich(X0)))) [nnf transformation 10]
51. ! [X0] : (((~old(X0) & rich(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0)))) & (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | old(X0) | ~rich(X0))) [flattening 50]
56. (? [X0] : (~calm(X0) & rich(X0)) | ! [X1] : (~curious(X1) | curious(X1))) & (? [X1] : (curious(X1) & ~curious(X1)) | ! [X0] : (calm(X0) | ~rich(X0))) [nnf transformation 25]
57. (? [X0] : (~calm(X0) & rich(X0)) | ! [X1] : (~curious(X1) | curious(X1))) & (? [X2] : (curious(X2) & ~curious(X2)) | ! [X3] : (calm(X3) | ~rich(X3))) [rectify 56]
58. ? [X0] : (~calm(X0) & rich(X0)) => (~calm(sK3) & rich(sK3)) [choice axiom]
59. ? [X2] : (curious(X2) & ~curious(X2)) => (curious(sK4) & ~curious(sK4)) [choice axiom]
60. ((~calm(sK3) & rich(sK3)) | ! [X1] : (~curious(X1) | curious(X1))) & ((curious(sK4) & ~curious(sK4)) | ! [X3] : (calm(X3) | ~rich(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((calm(X0) | generous(X0)) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | (~calm(X0) & ~generous(X0)))) [nnf transformation 14]
62. ! [X0] : ((calm(X0) | generous(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | (~calm(X0) & ~generous(X0)))) [flattening 61]
63. ! [X0] : (((strong(X0) | ~old(X0)) | (generous(X0) | humble(X0))) & ((~generous(X0) & ~humble(X0)) | (~strong(X0) & old(X0)))) [nnf transformation 15]
64. ! [X0] : ((strong(X0) | ~old(X0) | generous(X0) | humble(X0)) & ((~generous(X0) & ~humble(X0)) | (~strong(X0) & old(X0)))) [flattening 63]
84. ~quiet(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 46]
86. ~happy(X0) | rich(X0) | calm(X0) [cnf transformation 29]
89. ~brave(X0) | strong(X0) | happy(X0) | quiet(X0) [cnf transformation 49]
98. rich(X0) | rich(X0) | happy(X0) [cnf transformation 51]
108. ~curious(sK4) | calm(X3) | ~rich(X3) [cnf transformation 60]
109. curious(sK4) | calm(X3) | ~rich(X3) [cnf transformation 60]
113. ~calm(X0) | ~patient(X0) | brave(X0) [cnf transformation 62]
119. ~strong(X0) | ~generous(X0) [cnf transformation 64]
125. ~happy(susan) [cnf transformation 19]
129. generous(susan) [cnf transformation 22]
130. patient(susan) [cnf transformation 23]
132. happy(X0) | rich(X0) [duplicate literal removal 98]
195. 14 <=> ! [X3] : (calm(X3) | ~rich(X3)) [avatar definition]
196. ~rich(X3) | calm(X3) <- (14) [avatar component clause 195]
198. 15 <=> curious(sK4) [avatar definition]
201. 14 | 15 [avatar split clause 109,198,195]
202. 14 | ~15 [avatar split clause 108,198,195]
214. 18 <=> patient(susan) [avatar definition]
215. patient(susan) <- (18) [avatar component clause 214]
218. 18 [avatar split clause 130,214]
238. 21 <=> brave(susan) [avatar definition]
240. brave(susan) <- (21) [avatar component clause 238]
298. rich(X0) | calm(X0) | rich(X0) [resolution 86,132]
299. rich(X0) | calm(X0) [duplicate literal removal 298]
300. calm(X0) <- (14) [subsumption resolution 299,196]
345. ~patient(X0) | brave(X0) <- (14) [resolution 113,300]
365. brave(susan) <- (14, 18) [resolution 345,215]
384. 37 <=> quiet(susan) [avatar definition]
386. quiet(susan) <- (37) [avatar component clause 384]
388. 38 <=> strong(susan) [avatar definition]
390. strong(susan) <- (38) [avatar component clause 388]
399. 21 | ~14 | ~18 [avatar split clause 365,214,195,238]
449. strong(susan) | happy(susan) | quiet(susan) <- (21) [resolution 240,89]
499. ~generous(susan) | ~patient(susan) <- (37) [resolution 386,84]
502. ~patient(susan) <- (37) [subsumption resolution 499,129]
503. $false <- (18, 37) [subsumption resolution 502,215]
504. ~18 | ~37 [avatar contradiction clause 503]
505. strong(susan) | quiet(susan) <- (21) [subsumption resolution 449,125]
506. 37 | 38 | ~21 [avatar split clause 505,238,388,384]
526. ~generous(susan) <- (38) [resolution 390,119]
528. $false <- (38) [subsumption resolution 526,129]
529. ~38 [avatar contradiction clause 528]
530. $false [avatar sat refutation 201,202,218,399,504,506,529]
% SZS output end Proof for 8343739906876509358303152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both not tall and kind then lucy is old and vice versa. If mary is curious then fred is either patient or humble. Everyone who is happy is either not curious or quiet and vice versa. Everyone who is both creative and not wise is both calm and not brave and vice versa. Everyone who is either not patient or happy is humble and vice versa. Everyone who is either happy or creative is either old or not wise and vice versa. Everyone who is rich is brave or patient and vice versa. If fred is both not wise and old then someone is either not tall or generous. Everyone who is brave or not curious is either curious or not quiet and vice versa. If someone is either not brave or not curious then someone is both curious and not old. Everyone who is calm is not funny or not old. If someone is rich or curious then lucy is patient and vice versa. Everyone who is both kind and not rich is either not happy or tall and vice versa. Everyone who is kind is not wise or happy and vice versa. Everyone who is not creative is strong and vice versa. If john is quiet or funny then susan is both generous and not funny. Someone is not tall. Someone is not humble. Someone is either funny or humble. Fred is either not curious or generous. Susan is not calm or curious. Mary is either not old or wise. Someone is either not creative or not wise. Someone is old. | Lucy is not rich. | contradiction | ((?[X]:((~tall(X)&kind(X))))<=>(old(lucy)))&
((curious(mary))=>((patient(fred)<~>humble(fred))))&
(![X]:(happy(X)<=>(~curious(X)<~>quiet(X))))&
(![X]:((creative(X)&~wise(X))<=>(calm(X)&~brave(X))))&
(![X]:((~patient(X)<~>happy(X))<=>humble(X)))&
(![X]:((happy(X)<~>creative(X))<=>(old(X)<~>~wise(X))))&
(![X]:(rich(X)<=>(brave(X)|patient(X))))&
(((~wise(fred)&old(fred)))=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:((brave(X)|~curious(X))<=>(curious(X)<~>~quiet(X))))&
((?[X]:((~brave(X)<~>~curious(X))))=>(?[X]:((curious(X)&~old(X)))))&
(![X]:(calm(X)=>(~funny(X)|~old(X))))&
((?[X]:((rich(X)|curious(X))))<=>(patient(lucy)))&
(![X]:((kind(X)&~rich(X))<=>(~happy(X)<~>tall(X))))&
(![X]:(kind(X)<=>(~wise(X)|happy(X))))&
(![X]:(~creative(X)<=>strong(X)))&
(((quiet(john)|funny(john)))=>((generous(susan)&~funny(susan))))&
(?[X]:(~tall(X)))&
(?[X]:(~humble(X)))&
(?[X]:((funny(X)<~>humble(X))))&
((~curious(fred)<~>generous(fred)))&
((~calm(susan)|curious(susan)))&
((~old(mary)<~>wise(mary)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:(old(X))) | ~rich(lucy) | [
"p2",
"p6",
"p8",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3730691645328032146395910
% SZS output start Proof for 3730691645328032146395910
3. ! [X0] : (happy(X0) <=> (~curious(X0) <~> quiet(X0))) [input p2]
7. ! [X0] : (rich(X0) <=> (patient(X0) | brave(X0))) [input p6]
9. ! [X0] : ((~curious(X0) | brave(X0)) <=> (curious(X0) <~> ~quiet(X0))) [input p8]
12. ? [X0] : (curious(X0) | rich(X0)) <=> patient(lucy) [input p11]
13. ! [X0] : ((~rich(X0) & kind(X0)) <=> (~happy(X0) <~> tall(X0))) [input p12]
14. ! [X0] : (kind(X0) <=> (happy(X0) | ~wise(X0))) [input p13]
17. ? [X0] : ~tall(X0) [input p16]
25. ~rich(lucy) [input hypothesis]
39. ! [X0] : ((happy(X0) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) & (((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ~happy(X0))) [nnf transformation 3]
44. ! [X0] : ((rich(X0) | (~patient(X0) & ~brave(X0))) & ((patient(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 7]
45. ! [X0] : ((rich(X0) | (~patient(X0) & ~brave(X0))) & (patient(X0) | brave(X0) | ~rich(X0))) [flattening 44]
49. ! [X0] : (((~curious(X0) | brave(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (curious(X0) & ~brave(X0)))) [nnf transformation 9]
50. ! [X0] : ((~curious(X0) | brave(X0) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (curious(X0) & ~brave(X0)))) [flattening 49]
55. (? [X0] : (curious(X0) | rich(X0)) | ~patient(lucy)) & (patient(lucy) | ! [X0] : (~curious(X0) & ~rich(X0))) [nnf transformation 12]
56. (? [X0] : (curious(X0) | rich(X0)) | ~patient(lucy)) & (patient(lucy) | ! [X1] : (~curious(X1) & ~rich(X1))) [rectify 55]
57. ? [X0] : (curious(X0) | rich(X0)) => (curious(sK3) | rich(sK3)) [choice axiom]
58. ((curious(sK3) | rich(sK3)) | ~patient(lucy)) & (patient(lucy) | ! [X1] : (~curious(X1) & ~rich(X1))) [skolemisation 56,57]
59. ! [X0] : (((~rich(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (rich(X0) | ~kind(X0)))) [nnf transformation 13]
60. ! [X0] : (((~rich(X0) & kind(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | rich(X0) | ~kind(X0))) [flattening 59]
61. ! [X0] : ((kind(X0) | (~happy(X0) & wise(X0))) & ((happy(X0) | ~wise(X0)) | ~kind(X0))) [nnf transformation 14]
62. ! [X0] : ((kind(X0) | (~happy(X0) & wise(X0))) & (happy(X0) | ~wise(X0) | ~kind(X0))) [flattening 61]
64. ? [X0] : ~tall(X0) => ~tall(sK4) [choice axiom]
65. ~tall(sK4) [skolemisation 17,64]
85. quiet(X0) | happy(X0) | curious(X0) [cnf transformation 39]
105. ~patient(X0) | rich(X0) [cnf transformation 45]
109. ~quiet(X0) | curious(X0) | curious(X0) [cnf transformation 50]
119. patient(lucy) | ~rich(X1) [cnf transformation 58]
120. patient(lucy) | ~curious(X1) [cnf transformation 58]
122. ~happy(X0) | tall(X0) | rich(X0) | ~kind(X0) [cnf transformation 60]
130. ~happy(X0) | kind(X0) [cnf transformation 62]
137. ~tall(sK4) [cnf transformation 65]
149. ~rich(lucy) [cnf transformation 25]
150. ~quiet(X0) | curious(X0) [duplicate literal removal 109]
221. 16 <=> patient(lucy) [avatar definition]
222. patient(lucy) <- (16) [avatar component clause 221]
234. 19 <=> ! [X1] : ~curious(X1) [avatar definition]
235. ~curious(X1) <- (19) [avatar component clause 234]
236. 19 | 16 [avatar split clause 120,221,234]
238. 20 <=> ! [X1] : ~rich(X1) [avatar definition]
239. ~rich(X1) <- (20) [avatar component clause 238]
240. 20 | 16 [avatar split clause 119,221,238]
310. rich(lucy) <- (16) [resolution 105,222]
311. $false <- (16) [subsumption resolution 310,149]
312. ~16 [avatar contradiction clause 311]
322. happy(X1) | curious(X1) | curious(X1) [resolution 85,150]
323. happy(X1) | curious(X1) [duplicate literal removal 322]
326. happy(X1) <- (19) [subsumption resolution 323,235]
334. kind(X1) <- (19) [resolution 326,130]
461. tall(X2) | rich(X2) | ~kind(X2) <- (19) [resolution 122,326]
468. tall(X2) | ~kind(X2) <- (19, 20) [subsumption resolution 461,239]
469. tall(X2) <- (19, 20) [subsumption resolution 468,334]
474. $false <- (19, 20) [resolution 469,137]
477. ~19 | ~20 [avatar contradiction clause 474]
478. $false [avatar sat refutation 236,240,312,477]
% SZS output end Proof for 3730691645328032146395910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not wise and quiet then someone is both not humble and creative.
Everyone who is either not humble or not wise is quiet or kind and vice versa.
If fred is not funny or curious then john is both not curious and quiet.
Everyone who is calm is brave or happy and vice versa.
Everyone who is not happy or creative is either funny or creative and vice versa.
Everyone who is not happy or not wise is either not quiet or not happy and vice versa.
Everyone who is generous or not happy is not curious or not brave and vice versa.
If lucy is rich then john is not curious or not quiet and vice versa.
If fred is both creative and not patient then john is both not brave and wise and vice versa.
If someone is either not happy or curious then someone is kind or brave and vice versa.
If someone is strong or brave then susan is either brave or not patient.
If someone is both humble and not creative then someone is either happy or strong and vice versa.
Everyone who is not generous is either not rich or not happy and vice versa.
Everyone who is humble is either humble or calm and vice versa.
Everyone who is either quiet or not curious is either creative or not curious and vice versa.
Everyone who is not patient or not strong is not strong or creative and vice versa.
Paul is either kind or not rich.
Someone is not creative or rich.
Someone is either brave or quiet.
John is either not curious or not humble.
Paul is either generous or old. | Lucy is rich. | entailment | (((~wise(susan)&quiet(susan)))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~humble(X)<~>~wise(X))<=>(quiet(X)|kind(X))))&
(((~funny(fred)|curious(fred)))=>((~curious(john)&quiet(john))))&
(![X]:(calm(X)<=>(brave(X)|happy(X))))&
(![X]:((~happy(X)|creative(X))<=>(funny(X)<~>creative(X))))&
(![X]:((~happy(X)|~wise(X))<=>(~quiet(X)<~>~happy(X))))&
(![X]:((generous(X)|~happy(X))<=>(~curious(X)|~brave(X))))&
((rich(lucy))<=>((~curious(john)|~quiet(john))))&
(((creative(fred)&~patient(fred)))<=>((~brave(john)&wise(john))))&
((?[X]:((~happy(X)<~>curious(X))))<=>(?[X]:((kind(X)|brave(X)))))&
((?[X]:((strong(X)|brave(X))))=>((brave(susan)<~>~patient(susan))))&
((?[X]:((humble(X)&~creative(X))))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:(~generous(X)<=>(~rich(X)<~>~happy(X))))&
(![X]:(humble(X)<=>(humble(X)<~>calm(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((~patient(X)|~strong(X))<=>(~strong(X)|creative(X))))&
((kind(paul)<~>~rich(paul)))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:((brave(X)<~>quiet(X))))&
((~curious(john)<~>~humble(john)))&
((generous(paul)<~>old(paul))) | rich(lucy) | [
"p2",
"p3",
"p4",
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1020794518266439806326953
% SZS output start Proof for 1020794518266439806326953
3. (curious(fred) | ~funny(fred)) => (quiet(john) & ~curious(john)) [input p2]
4. ! [X0] : (calm(X0) <=> (happy(X0) | brave(X0))) [input p3]
5. ! [X0] : ((creative(X0) | ~happy(X0)) <=> (funny(X0) <~> creative(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~quiet(X0) <~> ~happy(X0))) [input p5]
8. rich(lucy) <=> (~quiet(john) | ~curious(john)) [input p7]
14. ! [X0] : (humble(X0) <=> (humble(X0) <~> calm(X0))) [input p13]
15. ! [X0] : ((quiet(X0) <~> ~curious(X0)) <=> (creative(X0) <~> ~curious(X0))) [input p14]
22. ~rich(lucy) [input hypothesis]
27. (quiet(john) & ~curious(john)) | (~curious(fred) & funny(fred)) [ennf transformation 3]
33. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ~calm(X0))) [nnf transformation 4]
34. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~calm(X0))) [flattening 33]
35. ! [X0] : (((creative(X0) | ~happy(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~creative(X0) & happy(X0)))) [nnf transformation 5]
36. ! [X0] : ((creative(X0) | ~happy(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~creative(X0) & happy(X0)))) [flattening 35]
37. ! [X0] : (((~wise(X0) | ~happy(X0)) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0)))) & (((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (wise(X0) & happy(X0)))) [nnf transformation 6]
38. ! [X0] : ((~wise(X0) | ~happy(X0) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0)))) & (((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (wise(X0) & happy(X0)))) [flattening 37]
41. (rich(lucy) | (quiet(john) & curious(john))) & ((~quiet(john) | ~curious(john)) | ~rich(lucy)) [nnf transformation 8]
42. (rich(lucy) | (quiet(john) & curious(john))) & (~quiet(john) | ~curious(john) | ~rich(lucy)) [flattening 41]
57. ! [X0] : ((humble(X0) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 14]
58. ! [X0] : ((((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0))))) [nnf transformation 15]
77. ~curious(john) | funny(fred) [cnf transformation 27]
83. ~happy(X0) | calm(X0) [cnf transformation 34]
87. ~creative(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 36]
92. happy(X0) | quiet(X0) | happy(X0) [cnf transformation 38]
101. rich(lucy) | curious(john) [cnf transformation 42]
128. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 57]
130. humble(X0) | humble(X0) | ~calm(X0) [cnf transformation 57]
131. ~curious(X0) | creative(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 58]
138. curious(X0) | ~quiet(X0) | creative(X0) | curious(X0) [cnf transformation 58]
152. ~rich(lucy) [cnf transformation 22]
153. ~curious(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 131]
156. curious(X0) | ~quiet(X0) | creative(X0) [duplicate literal removal 138]
157. ~calm(X0) | ~humble(X0) [duplicate literal removal 128]
158. ~calm(X0) | humble(X0) [duplicate literal removal 130]
159. happy(X0) | quiet(X0) [duplicate literal removal 92]
161. ~funny(X0) | ~creative(X0) [duplicate literal removal 87]
191. 7 <=> funny(fred) [avatar definition]
193. funny(fred) <- (7) [avatar component clause 191]
196. 8 <=> curious(john) [avatar definition]
200. 7 | ~8 [avatar split clause 77,196,191]
202. 9 <=> rich(lucy) [avatar definition]
206. 8 | 9 [avatar split clause 101,202,196]
308. ~calm(X0) [subsumption resolution 157,158]
310. ~quiet(X0) | creative(X0) [subsumption resolution 153,156]
356. ~9 [avatar split clause 152,202]
361. quiet(X0) | calm(X0) [resolution 159,83]
362. quiet(X0) [subsumption resolution 361,308]
363. ~creative(fred) <- (7) [resolution 161,193]
367. creative(X0) [resolution 310,362]
376. $false <- (7) [subsumption resolution 363,367]
377. ~7 [avatar contradiction clause 376]
378. $false [avatar sat refutation 200,206,356,377]
% SZS output end Proof for 1020794518266439806326953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or brave is calm and vice versa.
If someone is both not curious and humble then lucy is not wise or rich.
Everyone who is quiet or not calm is not rich.
If fred is rich then someone is old or not kind and vice versa.
Everyone who is both creative and not kind is funny and vice versa.
If fred is both kind and not humble then someone is not creative or not funny.
Everyone who is not kind or generous is both not strong and not kind and vice versa.
If lucy is not strong or not tall then someone is happy and vice versa.
Everyone who is not wise or not brave is not strong or rich and vice versa.
If someone is patient or rich then someone is not creative or rich and vice versa.
If someone is patient or not strong then john is old and vice versa.
Everyone who is kind or not funny is not strong or not happy.
If someone is tall then someone is not kind or happy and vice versa.
If someone is both not curious and wise then lucy is both not calm and wise.
Everyone who is either curious or not brave is either not rich or not funny.
If mary is both quiet and old then alice is not curious or brave and vice versa.
Someone is old.
Fred is quiet or not funny.
Someone is both creative and not quiet.
Fred is either not kind or not creative.
Someone is happy or not rich.
Someone is humble. | Fred is wise. | contradiction | (![X]:((~calm(X)|brave(X))<=>calm(X)))&
((?[X]:((~curious(X)&humble(X))))=>((~wise(lucy)|rich(lucy))))&
(![X]:((quiet(X)|~calm(X))=>~rich(X)))&
((rich(fred))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((creative(X)&~kind(X))<=>funny(X)))&
(((kind(fred)&~humble(fred)))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((~kind(X)|generous(X))<=>(~strong(X)&~kind(X))))&
(((~strong(lucy)|~tall(lucy)))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~strong(X)|rich(X))))&
((?[X]:((patient(X)|rich(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
((?[X]:((patient(X)|~strong(X))))<=>(old(john)))&
(![X]:((kind(X)|~funny(X))=>(~strong(X)|~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~kind(X)|happy(X)))))&
((?[X]:((~curious(X)&wise(X))))=>((~calm(lucy)&wise(lucy))))&
(![X]:((curious(X)<~>~brave(X))=>(~rich(X)<~>~funny(X))))&
(((quiet(mary)&old(mary)))<=>((~curious(alice)|brave(alice))))&
(?[X]:(old(X)))&
((quiet(fred)|~funny(fred)))&
(?[X]:((creative(X)&~quiet(X))))&
((~kind(fred)<~>~creative(fred)))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:(humble(X))) | wise(fred) | [
"p0",
"p3",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2615448199304449993380251
% SZS output start Proof for 2615448199304449993380251
1. ! [X0] : ((brave(X0) | ~calm(X0)) <=> calm(X0)) [input p0]
4. rich(fred) <=> ? [X0] : (~kind(X0) | old(X0)) [input p3]
9. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> (rich(X0) | ~strong(X0))) [input p8]
17. ? [X0] : old(X0) [input p16]
23. wise(fred) [input hypothesis]
35. ! [X0] : (((brave(X0) | ~calm(X0)) | ~calm(X0)) & (calm(X0) | (~brave(X0) & calm(X0)))) [nnf transformation 1]
36. ! [X0] : ((brave(X0) | ~calm(X0) | ~calm(X0)) & (calm(X0) | (~brave(X0) & calm(X0)))) [flattening 35]
37. (rich(fred) | ! [X0] : (kind(X0) & ~old(X0))) & (? [X0] : (~kind(X0) | old(X0)) | ~rich(fred)) [nnf transformation 4]
38. (rich(fred) | ! [X0] : (kind(X0) & ~old(X0))) & (? [X1] : (~kind(X1) | old(X1)) | ~rich(fred)) [rectify 37]
39. ? [X1] : (~kind(X1) | old(X1)) => (~kind(sK0) | old(sK0)) [choice axiom]
40. (rich(fred) | ! [X0] : (kind(X0) & ~old(X0))) & ((~kind(sK0) | old(sK0)) | ~rich(fred)) [skolemisation 38,39]
52. ! [X0] : (((~brave(X0) | ~wise(X0)) | (~rich(X0) & strong(X0))) & ((rich(X0) | ~strong(X0)) | (brave(X0) & wise(X0)))) [nnf transformation 9]
53. ! [X0] : ((~brave(X0) | ~wise(X0) | (~rich(X0) & strong(X0))) & (rich(X0) | ~strong(X0) | (brave(X0) & wise(X0)))) [flattening 52]
71. ? [X0] : old(X0) => old(sK8) [choice axiom]
72. old(sK8) [skolemisation 17,71]
80. calm(X0) | calm(X0) [cnf transformation 36]
82. brave(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 36]
87. rich(fred) | ~old(X0) [cnf transformation 40]
104. ~rich(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 53]
128. old(sK8) [cnf transformation 72]
136. wise(fred) [cnf transformation 23]
137. calm(X0) [duplicate literal removal 80]
138. ~calm(X0) | brave(X0) [duplicate literal removal 82]
155. 5 <=> rich(fred) [avatar definition]
157. rich(fred) <- (5) [avatar component clause 155]
160. 6 <=> ! [X0] : ~old(X0) [avatar definition]
161. ~old(X0) <- (6) [avatar component clause 160]
162. 6 | 5 [avatar split clause 87,155,160]
323. $false <- (6) [resolution 161,128]
324. ~6 [avatar contradiction clause 323]
329. brave(X0) [resolution 138,137]
360. ~wise(fred) | ~brave(fred) <- (5) [resolution 104,157]
361. ~brave(fred) <- (5) [subsumption resolution 360,136]
362. $false <- (5) [subsumption resolution 361,329]
363. ~5 [avatar contradiction clause 362]
364. $false [avatar sat refutation 162,324,363]
% SZS output end Proof for 2615448199304449993380251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not creative.
Everyone who is both not strong and not humble is both generous and not brave.
Everyone who is both not humble and funny is either wise or strong and vice versa.
Everyone who is both strong and not patient is kind and vice versa.
If someone is wise or not brave then someone is either rich or not quiet.
Everyone who is either not wise or kind is both happy and tall.
Everyone who is either funny or not creative is not quiet.
Everyone who is either not strong or not rich is either happy or not funny and vice versa.
If someone is both wise and happy then susan is both not curious and not brave.
Everyone who is either happy or kind is not tall and vice versa.
If fred is brave then alice is not generous or not brave.
Everyone who is not strong is either strong or brave and vice versa.
If someone is not happy or quiet then someone is old.
If someone is humble or not happy then alice is curious or not funny.
Everyone who is either not quiet or strong is either creative or humble.
Everyone who is wise is both not brave and wise and vice versa.
Susan is not patient.
Paul is creative.
Someone is not generous.
Mary is not rich.
Someone is either brave or old. | Susan is brave. | entailment | (![X]:(happy(X)=>~creative(X)))&
(![X]:((~strong(X)&~humble(X))=>(generous(X)&~brave(X))))&
(![X]:((~humble(X)&funny(X))<=>(wise(X)<~>strong(X))))&
(![X]:((strong(X)&~patient(X))<=>kind(X)))&
((?[X]:((wise(X)|~brave(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>kind(X))=>(happy(X)&tall(X))))&
(![X]:((funny(X)<~>~creative(X))=>~quiet(X)))&
(![X]:((~strong(X)<~>~rich(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:((wise(X)&happy(X))))=>((~curious(susan)&~brave(susan))))&
(![X]:((happy(X)<~>kind(X))<=>~tall(X)))&
((brave(fred))=>((~generous(alice)|~brave(alice))))&
(![X]:(~strong(X)<=>(strong(X)<~>brave(X))))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)|~happy(X))))=>((curious(alice)|~funny(alice))))&
(![X]:((~quiet(X)<~>strong(X))=>(creative(X)<~>humble(X))))&
(![X]:(wise(X)<=>(~brave(X)&wise(X))))&
(~patient(susan))&
(creative(paul))&
(?[X]:(~generous(X)))&
(~rich(mary))&
(?[X]:((brave(X)<~>old(X)))) | brave(susan) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4083091505889982522267222
% SZS output start Proof for 4083091505889982522267222
12. ! [X0] : (~strong(X0) <=> (strong(X0) <~> brave(X0))) [input p11]
22. ~brave(susan) [input hypothesis]
52. ! [X0] : ((~strong(X0) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | strong(X0))) [nnf transformation 12]
99. brave(X0) | strong(X0) | strong(X0) [cnf transformation 52]
101. ~strong(X0) | brave(X0) | ~strong(X0) [cnf transformation 52]
120. ~brave(susan) [cnf transformation 22]
121. brave(X0) | strong(X0) [duplicate literal removal 99]
122. ~strong(X0) | brave(X0) [duplicate literal removal 101]
124. 1 <=> ! [X1] : brave(X1) [avatar definition]
125. brave(X1) <- (1) [avatar component clause 124]
145. 6 <=> brave(susan) [avatar definition]
147. ~brave(susan) <- (~6) [avatar component clause 145]
167. brave(X0) [subsumption resolution 121,122]
168. 1 [avatar split clause 167,124]
204. ~6 [avatar split clause 120,145]
205. $false <- (1, ~6) [resolution 147,125]
206. ~1 | 6 [avatar contradiction clause 205]
207. $false [avatar sat refutation 168,204,206]
% SZS output end Proof for 4083091505889982522267222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not humble is both funny and curious.
Everyone who is not generous or funny is both not creative and not quiet.
Everyone who is brave or curious is not humble or not tall and vice versa.
Everyone who is not patient is old or happy.
If john is strong or not brave then someone is either not happy or not strong.
Everyone who is not quiet is patient.
If someone is curious then alice is both creative and generous.
Everyone who is not funny is both not wise and patient and vice versa.
If someone is either calm or quiet then mary is curious or not creative.
Everyone who is both not patient and not rich is both tall and creative.
If john is not happy then someone is happy and vice versa.
Everyone who is both creative and wise is not funny or strong and vice versa.
Everyone who is either creative or brave is either rich or not happy and vice versa.
If fred is either not funny or patient then mary is not calm or not happy.
Everyone who is either not patient or kind is not creative or not patient and vice versa.
Someone is both not generous and not brave.
Someone is brave.
Susan is happy or brave.
Lucy is not funny or wise.
Mary is wise or not old.
John is not calm.
Lucy is wise.
Paul is either rich or not brave. | John is old. | neutral | (![X]:((~strong(X)&~humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
(((~funny(fred)<~>patient(fred)))=>((~calm(mary)|~happy(mary))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~patient(X))))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:(brave(X)))&
((happy(susan)|brave(susan)))&
((~funny(lucy)|wise(lucy)))&
((wise(mary)|~old(mary)))&
(~calm(john))&
(wise(lucy))&
((rich(paul)<~>~brave(paul))) | old(john) | [] | null | 0 |
If paul is either kind or strong then lucy is both quiet and not happy. If someone is calm then someone is strong or humble and vice versa. If someone is both calm and humble then someone is either rich or not quiet. If someone is both kind and not patient then someone is both tall and not old. If someone is not generous or generous then fred is either rich or not patient and vice versa. Everyone who is both not old and not strong is not rich or strong and vice versa. If someone is wise then john is not tall or not strong and vice versa. Everyone who is not humble is both not old and wise and vice versa. Everyone who is either not rich or creative is both calm and kind and vice versa. If susan is both calm and not humble then fred is either not old or tall and vice versa. Everyone who is not funny or happy is both funny and humble. Everyone who is curious is either not old or old. Everyone who is not brave is both not calm and not brave. Everyone who is calm or not humble is either not brave or not calm. Everyone who is both rich and not rich is either curious or happy and vice versa. If someone is not calm or calm then someone is both brave and not patient. Someone is wise. Alice is either wise or quiet. Lucy is quiet or not kind. Susan is creative or not creative. John is either not curious or generous. Fred is tall. | John is creative. | entailment | (((kind(paul)<~>strong(paul)))=>((quiet(lucy)&~happy(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)|humble(X)))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((~generous(X)|generous(X))))<=>((rich(fred)<~>~patient(fred))))&
(![X]:((~old(X)&~strong(X))<=>(~rich(X)|strong(X))))&
((?[X]:(wise(X)))<=>((~tall(john)|~strong(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(calm(X)&kind(X))))&
(((calm(susan)&~humble(susan)))<=>((~old(fred)<~>tall(fred))))&
(![X]:((~funny(X)|happy(X))=>(funny(X)&humble(X))))&
(![X]:(curious(X)=>(~old(X)<~>old(X))))&
(![X]:(~brave(X)=>(~calm(X)&~brave(X))))&
(![X]:((calm(X)|~humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)&~rich(X))<=>(curious(X)<~>happy(X))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((brave(X)&~patient(X)))))&
(?[X]:(wise(X)))&
((wise(alice)<~>quiet(alice)))&
((quiet(lucy)|~kind(lucy)))&
((creative(susan)|~creative(susan)))&
((~curious(john)<~>generous(john)))&
(tall(fred)) | creative(john) | [
"p1",
"p5",
"p7",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5192330697048709442915999
% SZS output start Proof for 5192330697048709442915999
2. ? [X0] : calm(X0) <=> ? [X0] : (humble(X0) | strong(X0)) [input p1]
6. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (strong(X0) | ~rich(X0))) [input p5]
8. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p7]
9. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (kind(X0) & calm(X0))) [input p8]
13. ! [X0] : (~brave(X0) => (~brave(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((~humble(X0) | calm(X0)) => (~brave(X0) <~> ~calm(X0))) [input p13]
23. ~creative(john) [input hypothesis]
24. ? [X0] : calm(X0) <=> ? [X1] : (humble(X1) | strong(X1)) [rectify 2]
34. ! [X0] : ((~brave(X0) & ~calm(X0)) | brave(X0)) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 14]
38. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X1] : (humble(X1) | strong(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 24]
39. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X2] : (humble(X2) | strong(X2)) | ! [X3] : ~calm(X3)) [rectify 38]
40. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
41. ? [X2] : (humble(X2) | strong(X2)) => (humble(sK1) | strong(sK1)) [choice axiom]
42. (calm(sK0) | ! [X1] : (~humble(X1) & ~strong(X1))) & ((humble(sK1) | strong(sK1)) | ! [X3] : ~calm(X3)) [skolemisation 39,41,40]
54. ! [X0] : (((~strong(X0) & ~old(X0)) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | (strong(X0) | old(X0)))) [nnf transformation 6]
55. ! [X0] : (((~strong(X0) & ~old(X0)) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | strong(X0) | old(X0))) [flattening 54]
61. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 8]
62. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 61]
63. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~kind(X0) | ~calm(X0))) & ((kind(X0) & calm(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 9]
64. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~kind(X0) | ~calm(X0)) & ((kind(X0) & calm(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [flattening 63]
68. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (humble(X0) & ~calm(X0))) [nnf transformation 35]
84. calm(sK0) | ~humble(X1) [cnf transformation 42]
95. strong(X0) | ~rich(X0) | strong(X0) | old(X0) [cnf transformation 55]
99. ~strong(X0) | ~strong(X0) [cnf transformation 55]
103. ~old(X0) | humble(X0) [cnf transformation 62]
106. creative(X0) | calm(X0) | rich(X0) [cnf transformation 64]
121. ~calm(X0) | brave(X0) [cnf transformation 34]
123. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 68]
145. ~creative(john) [cnf transformation 23]
146. ~calm(X0) | ~brave(X0) [duplicate literal removal 123]
147. ~rich(X0) | strong(X0) | old(X0) [duplicate literal removal 95]
148. ~strong(X0) [duplicate literal removal 99]
170. 5 <=> ! [X1] : ~humble(X1) [avatar definition]
171. ~humble(X1) <- (5) [avatar component clause 170]
173. 6 <=> calm(sK0) [avatar definition]
175. calm(sK0) <- (6) [avatar component clause 173]
176. 5 | 6 [avatar split clause 84,173,170]
178. 7 <=> ! [X1] : ~strong(X1) [avatar definition]
179. ~strong(X1) <- (7) [avatar component clause 178]
182. 8 <=> ! [X3] : ~calm(X3) [avatar definition]
183. ~calm(X3) <- (8) [avatar component clause 182]
237. 7 [avatar split clause 148,178]
239. 21 <=> strong(john) [avatar definition]
240. ~strong(john) <- (~21) [avatar component clause 239]
241. strong(john) <- (21) [avatar component clause 239]
280. ~calm(X0) [subsumption resolution 146,121]
281. 8 [avatar split clause 280,182]
333. calm(john) | rich(john) [resolution 106,145]
334. rich(john) <- (8) [subsumption resolution 333,183]
343. strong(john) | old(john) <- (8) [resolution 147,334]
344. old(john) <- (8, ~21) [subsumption resolution 343,240]
345. humble(john) <- (8, ~21) [resolution 344,103]
348. $false <- (5, 8, ~21) [subsumption resolution 345,171]
349. ~5 | ~8 | 21 [avatar contradiction clause 348]
377. $false <- (6, 8) [subsumption resolution 175,183]
378. ~6 | ~8 [avatar contradiction clause 377]
380. $false <- (7, 21) [subsumption resolution 241,179]
381. ~7 | ~21 [avatar contradiction clause 380]
382. $false [avatar sat refutation 176,237,281,349,378,381]
% SZS output end Proof for 5192330697048709442915999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not tall then someone is not strong and vice versa.
Everyone who is either strong or creative is wise and vice versa.
Everyone who is creative is not quiet or generous and vice versa.
Everyone who is not brave or curious is both not rich and not quiet and vice versa.
Everyone who is not quiet is both not creative and kind and vice versa.
If someone is rich then someone is both brave and tall and vice versa.
Everyone who is calm or wise is not creative.
Everyone who is not patient is both generous and not humble.
Everyone who is rich is either creative or not quiet.
Everyone who is either not patient or not funny is both not curious and funny and vice versa.
Everyone who is not curious or patient is not kind or curious.
If lucy is either quiet or humble then paul is not rich and vice versa.
Everyone who is both brave and not humble is funny and vice versa.
If fred is not brave then susan is creative or not wise.
Everyone who is both rich and not quiet is both not creative and not happy.
Everyone who is both not funny and quiet is rich or not old.
John is either tall or kind.
Lucy is patient or not happy.
Someone is not old or strong.
Someone is creative.
Alice is rich or generous. | Alice is kind. | contradiction | ((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
(![X]:((strong(X)<~>creative(X))<=>wise(X)))&
(![X]:(creative(X)<=>(~quiet(X)|generous(X))))&
(![X]:((~brave(X)|curious(X))<=>(~rich(X)&~quiet(X))))&
(![X]:(~quiet(X)<=>(~creative(X)&kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((calm(X)|wise(X))=>~creative(X)))&
(![X]:(~patient(X)=>(generous(X)&~humble(X))))&
(![X]:(rich(X)=>(creative(X)<~>~quiet(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~curious(X)&funny(X))))&
(![X]:((~curious(X)|patient(X))=>(~kind(X)|curious(X))))&
(((quiet(lucy)<~>humble(lucy)))<=>(~rich(paul)))&
(![X]:((brave(X)&~humble(X))<=>funny(X)))&
((~brave(fred))=>((creative(susan)|~wise(susan))))&
(![X]:((rich(X)&~quiet(X))=>(~creative(X)&~happy(X))))&
(![X]:((~funny(X)&quiet(X))=>(rich(X)|~old(X))))&
((tall(john)<~>kind(john)))&
((patient(lucy)|~happy(lucy)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:(creative(X)))&
((rich(alice)|generous(alice))) | kind(alice) | [
"p2",
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1107365183277565140801832
% SZS output start Proof for 1107365183277565140801832
3. ! [X0] : (creative(X0) <=> (generous(X0) | ~quiet(X0))) [input p2]
4. ! [X0] : ((curious(X0) | ~brave(X0)) <=> (~quiet(X0) & ~rich(X0))) [input p3]
5. ! [X0] : (~quiet(X0) <=> (kind(X0) & ~creative(X0))) [input p4]
11. ! [X0] : ((patient(X0) | ~curious(X0)) => (curious(X0) | ~kind(X0))) [input p10]
22. kind(alice) [input hypothesis]
35. ! [X0] : ((curious(X0) | ~kind(X0)) | (~patient(X0) & curious(X0))) [ennf transformation 11]
36. ! [X0] : (curious(X0) | ~kind(X0) | (~patient(X0) & curious(X0))) [flattening 35]
47. ! [X0] : ((creative(X0) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 3]
48. ! [X0] : ((creative(X0) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0))) [flattening 47]
49. ! [X0] : (((curious(X0) | ~brave(X0)) | (quiet(X0) | rich(X0))) & ((~quiet(X0) & ~rich(X0)) | (~curious(X0) & brave(X0)))) [nnf transformation 4]
50. ! [X0] : ((curious(X0) | ~brave(X0) | quiet(X0) | rich(X0)) & ((~quiet(X0) & ~rich(X0)) | (~curious(X0) & brave(X0)))) [flattening 49]
51. ! [X0] : ((~quiet(X0) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | quiet(X0))) [nnf transformation 5]
52. ! [X0] : ((~quiet(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | quiet(X0))) [flattening 51]
73. quiet(X0) | creative(X0) [cnf transformation 48]
78. ~quiet(X0) | ~curious(X0) [cnf transformation 50]
80. ~creative(X0) | quiet(X0) [cnf transformation 52]
97. curious(X0) | ~kind(X0) | curious(X0) [cnf transformation 36]
112. kind(alice) [cnf transformation 22]
113. ~kind(X0) | curious(X0) [duplicate literal removal 97]
138. quiet(X0) [subsumption resolution 80,73]
209. ~curious(X1) [resolution 78,138]
211. curious(alice) [resolution 113,112]
215. $false [subsumption resolution 211,209]
% SZS output end Proof for 1107365183277565140801832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny then someone is not kind and vice versa. Everyone who is not kind is both old and not calm and vice versa. Everyone who is not strong is either not funny or happy. Everyone who is both creative and happy is both kind and brave and vice versa. If someone is either not quiet or old then someone is both not old and curious. If lucy is both tall and not calm then someone is not brave. If susan is both not old and patient then someone is either not generous or patient and vice versa. If susan is either not strong or not kind then someone is not old or not patient. Everyone who is not quiet or strong is both not strong and wise and vice versa. Everyone who is either not humble or calm is either not happy or generous. Everyone who is both brave and not creative is old and vice versa. Everyone who is curious or calm is not rich and vice versa. If mary is either patient or humble then mary is not kind or not rich. If someone is either curious or generous then someone is either strong or not calm. If someone is both old and tall then lucy is generous and vice versa. Everyone who is both not creative and not old is not strong. Someone is not curious or not funny. Susan is not quiet or not humble. Someone is not rich. Someone is both not kind and not quiet. Susan is tall or not happy. Susan is both not creative and not wise. | Lucy is tall. | neutral | ((funny(alice))<=>(?[X]:(~kind(X))))&
(![X]:(~kind(X)<=>(old(X)&~calm(X))))&
(![X]:(~strong(X)=>(~funny(X)<~>happy(X))))&
(![X]:((creative(X)&happy(X))<=>(kind(X)&brave(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>(?[X]:((~old(X)&curious(X)))))&
(((tall(lucy)&~calm(lucy)))=>(?[X]:(~brave(X))))&
(((~old(susan)&patient(susan)))<=>(?[X]:((~generous(X)<~>patient(X)))))&
(((~strong(susan)<~>~kind(susan)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~quiet(X)|strong(X))<=>(~strong(X)&wise(X))))&
(![X]:((~humble(X)<~>calm(X))=>(~happy(X)<~>generous(X))))&
(![X]:((brave(X)&~creative(X))<=>old(X)))&
(![X]:((curious(X)|calm(X))<=>~rich(X)))&
(((patient(mary)<~>humble(mary)))=>((~kind(mary)|~rich(mary))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((strong(X)<~>~calm(X)))))&
((?[X]:((old(X)&tall(X))))<=>(generous(lucy)))&
(![X]:((~creative(X)&~old(X))=>~strong(X)))&
(?[X]:((~curious(X)|~funny(X))))&
((~quiet(susan)|~humble(susan)))&
(?[X]:(~rich(X)))&
(?[X]:((~kind(X)&~quiet(X))))&
((tall(susan)|~happy(susan)))&
((~creative(susan)&~wise(susan))) | tall(lucy) | [] | null | 0 |
Everyone who is tall is either creative or not humble.
Everyone who is not kind or not curious is curious and vice versa.
Everyone who is rich is wise or happy and vice versa.
If lucy is both not strong and funny then mary is humble.
If fred is brave or tall then paul is either not wise or not creative and vice versa.
If someone is either tall or not wise then someone is either quiet or humble and vice versa.
If someone is not tall or not funny then someone is either not wise or old and vice versa.
If someone is happy then mary is not patient or creative.
If someone is curious or not creative then someone is both strong and not funny.
Everyone who is either not brave or brave is brave and vice versa.
Everyone who is brave is both quiet and not old.
Everyone who is not happy or generous is not calm and vice versa.
Everyone who is humble is wise and vice versa.
Everyone who is humble or creative is not calm or not funny and vice versa.
If john is either not rich or not happy then someone is tall and vice versa.
Everyone who is either not rich or tall is tall.
Paul is not old or not quiet.
Paul is not patient or quiet.
Someone is not patient.
Fred is wise or not tall.
Someone is either not happy or not kind. | Mary is funny. | neutral | (![X]:(tall(X)=>(creative(X)<~>~humble(X))))&
(![X]:((~kind(X)|~curious(X))<=>curious(X)))&
(![X]:(rich(X)<=>(wise(X)|happy(X))))&
(((~strong(lucy)&funny(lucy)))=>(humble(mary)))&
(((brave(fred)|tall(fred)))<=>((~wise(paul)<~>~creative(paul))))&
((?[X]:((tall(X)<~>~wise(X))))<=>(?[X]:((quiet(X)<~>humble(X)))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
((?[X]:(happy(X)))=>((~patient(mary)|creative(mary))))&
((?[X]:((curious(X)|~creative(X))))=>(?[X]:((strong(X)&~funny(X)))))&
(![X]:((~brave(X)<~>brave(X))<=>brave(X)))&
(![X]:(brave(X)=>(quiet(X)&~old(X))))&
(![X]:((~happy(X)|generous(X))<=>~calm(X)))&
(![X]:(humble(X)<=>wise(X)))&
(![X]:((humble(X)|creative(X))<=>(~calm(X)|~funny(X))))&
(((~rich(john)<~>~happy(john)))<=>(?[X]:(tall(X))))&
(![X]:((~rich(X)<~>tall(X))=>tall(X)))&
((~old(paul)|~quiet(paul)))&
((~patient(paul)|quiet(paul)))&
(?[X]:(~patient(X)))&
((wise(fred)|~tall(fred)))&
(?[X]:((~happy(X)<~>~kind(X)))) | funny(mary) | [] | null | 0 |
If someone is both curious and wise then alice is either old or not kind. Everyone who is kind is not brave and vice versa. If someone is creative or curious then someone is both strong and rich and vice versa. If alice is either patient or old then someone is humble or not humble. If someone is both funny and not tall then lucy is both generous and curious. Everyone who is either calm or not happy is not kind or happy and vice versa. Everyone who is not patient or patient is both not humble and not funny and vice versa. Everyone who is not old is both not funny and not calm and vice versa. Everyone who is either not kind or happy is either not brave or not generous. Everyone who is either not humble or not rich is either not tall or funny and vice versa. Everyone who is not old or patient is not creative. If someone is both not generous and funny then fred is both funny and not generous and vice versa. If someone is rich then someone is not quiet and vice versa. Everyone who is not old is both wise and strong and vice versa. Everyone who is both not tall and not wise is both not brave and curious and vice versa. Everyone who is not tall is either not generous or not funny and vice versa. Alice is either creative or not creative. Lucy is either not tall or not happy. Someone is not humble or funny. Someone is both curious and not tall. Someone is strong. Someone is either not kind or not funny. Someone is either not tall or calm. Paul is either kind or curious. | Alice is not curious. | neutral | ((?[X]:((curious(X)&wise(X))))=>((old(alice)<~>~kind(alice))))&
(![X]:(kind(X)<=>~brave(X)))&
((?[X]:((creative(X)|curious(X))))<=>(?[X]:((strong(X)&rich(X)))))&
(((patient(alice)<~>old(alice)))=>(?[X]:((humble(X)|~humble(X)))))&
((?[X]:((funny(X)&~tall(X))))=>((generous(lucy)&curious(lucy))))&
(![X]:((calm(X)<~>~happy(X))<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(~humble(X)&~funny(X))))&
(![X]:(~old(X)<=>(~funny(X)&~calm(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~old(X)|patient(X))=>~creative(X)))&
((?[X]:((~generous(X)&funny(X))))<=>((funny(fred)&~generous(fred))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
(![X]:(~old(X)<=>(wise(X)&strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~brave(X)&curious(X))))&
(![X]:(~tall(X)<=>(~generous(X)<~>~funny(X))))&
((creative(alice)<~>~creative(alice)))&
((~tall(lucy)<~>~happy(lucy)))&
(?[X]:((~humble(X)|funny(X))))&
(?[X]:((curious(X)&~tall(X))))&
(?[X]:(strong(X)))&
(?[X]:((~kind(X)<~>~funny(X))))&
(?[X]:((~tall(X)<~>calm(X))))&
((kind(paul)<~>curious(paul))) | ~curious(alice) | [] | null | 0 |
If john is either funny or tall then mary is both generous and tall and vice versa. Everyone who is both not kind and rich is either not calm or tall. If someone is humble then john is both brave and not strong. If someone is humble or not quiet then fred is tall. If someone is happy or not calm then lucy is both rich and not kind. If lucy is quiet then alice is patient or not calm and vice versa. If someone is both not funny and not strong then paul is not strong or strong and vice versa. Everyone who is not wise is both not calm and not strong. If someone is both not old and patient then someone is not rich or not kind and vice versa. Everyone who is not strong is both not quiet and not generous. If someone is not generous or not old then mary is either not kind or kind and vice versa. Everyone who is either not creative or creative is either calm or wise. If someone is both not generous and not curious then someone is both patient and rich. If fred is either kind or not old then someone is kind or wise and vice versa. If someone is not creative then someone is curious or not tall and vice versa. Someone is rich. Someone is wise or not happy. Someone is patient. Someone is both not strong and curious. Susan is either kind or funny. Lucy is not creative or not humble. Lucy is not brave or tall. Susan is brave. | Lucy is rich. | entailment | (((funny(john)<~>tall(john)))<=>((generous(mary)&tall(mary))))&
(![X]:((~kind(X)&rich(X))=>(~calm(X)<~>tall(X))))&
((?[X]:(humble(X)))=>((brave(john)&~strong(john))))&
((?[X]:((humble(X)|~quiet(X))))=>(tall(fred)))&
((?[X]:((happy(X)|~calm(X))))=>((rich(lucy)&~kind(lucy))))&
((quiet(lucy))<=>((patient(alice)|~calm(alice))))&
((?[X]:((~funny(X)&~strong(X))))<=>((~strong(paul)|strong(paul))))&
(![X]:(~wise(X)=>(~calm(X)&~strong(X))))&
((?[X]:((~old(X)&patient(X))))<=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:(~strong(X)=>(~quiet(X)&~generous(X))))&
((?[X]:((~generous(X)|~old(X))))<=>((~kind(mary)<~>kind(mary))))&
(![X]:((~creative(X)<~>creative(X))=>(calm(X)<~>wise(X))))&
((?[X]:((~generous(X)&~curious(X))))=>(?[X]:((patient(X)&rich(X)))))&
(((kind(fred)<~>~old(fred)))<=>(?[X]:((kind(X)|wise(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((curious(X)|~tall(X)))))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)|~happy(X))))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)&curious(X))))&
((kind(susan)<~>funny(susan)))&
((~creative(lucy)|~humble(lucy)))&
((~brave(lucy)|tall(lucy)))&
(brave(susan)) | rich(lucy) | [
"p4",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4573945083164007928368537
% SZS output start Proof for 4573945083164007928368537
5. ? [X0] : (~calm(X0) | happy(X0)) => (~kind(lucy) & rich(lucy)) [input p4]
8. ! [X0] : (~wise(X0) => (~strong(X0) & ~calm(X0))) [input p7]
12. ! [X0] : ((~creative(X0) <~> creative(X0)) => (calm(X0) <~> wise(X0))) [input p11]
24. ~rich(lucy) [input hypothesis]
29. ? [X0] : ~calm(X0) => (~kind(lucy) & rich(lucy)) [pure predicate removal 5]
36. (~kind(lucy) & rich(lucy)) | ! [X0] : calm(X0) [ennf transformation 29]
37. ! [X0] : ((~strong(X0) & ~calm(X0)) | wise(X0)) [ennf transformation 8]
39. ! [X0] : ((calm(X0) <~> wise(X0)) | (~creative(X0) <=> creative(X0))) [ennf transformation 12]
60. ! [X0] : (((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 39]
89. rich(lucy) | calm(X0) [cnf transformation 36]
99. ~calm(X0) | wise(X0) [cnf transformation 37]
116. ~wise(X0) | ~calm(X0) | creative(X0) | creative(X0) [cnf transformation 60]
117. ~wise(X0) | ~calm(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 60]
137. ~rich(lucy) [cnf transformation 24]
140. ~wise(X0) | ~calm(X0) | creative(X0) [duplicate literal removal 116]
141. ~wise(X0) | ~calm(X0) | ~creative(X0) [duplicate literal removal 117]
175. 7 <=> ! [X0] : calm(X0) [avatar definition]
176. calm(X0) <- (7) [avatar component clause 175]
183. 9 <=> rich(lucy) [avatar definition]
186. 7 | 9 [avatar split clause 89,183,175]
262. ~calm(X0) | ~creative(X0) [subsumption resolution 141,99]
263. ~calm(X0) | creative(X0) [subsumption resolution 140,99]
264. ~calm(X0) [subsumption resolution 263,262]
341. ~9 [avatar split clause 137,183]
344. $false <- (7) [subsumption resolution 176,264]
345. ~7 [avatar contradiction clause 344]
346. $false [avatar sat refutation 186,341,345]
% SZS output end Proof for 4573945083164007928368537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not patient or not funny then paul is both not strong and not calm and vice versa.
If someone is either not happy or strong then someone is generous or not quiet and vice versa.
Everyone who is either not patient or not calm is not curious or calm and vice versa.
If alice is happy then alice is both strong and not quiet and vice versa.
Everyone who is both humble and not rich is either not old or not humble.
If someone is both generous and brave then someone is brave or creative and vice versa.
If lucy is not kind then someone is kind or not old.
Everyone who is either generous or not calm is not patient.
Everyone who is patient or funny is not generous and vice versa.
If fred is both not humble and not strong then someone is either quiet or kind.
If john is both generous and not tall then mary is either not rich or humble and vice versa.
Everyone who is old is not humble.
Everyone who is not curious or not creative is not humble.
If someone is both rich and old then alice is brave and vice versa.
Everyone who is both strong and curious is tall.
Everyone who is both not strong and patient is strong.
Someone is not creative.
Paul is either not old or funny.
Someone is both kind and tall.
John is not calm.
Someone is not funny.
Someone is not humble or tall.
Someone is not happy or not humble. | Susan is not patient. | entailment | (((~patient(susan)<~>~funny(susan)))<=>((~strong(paul)&~calm(paul))))&
((?[X]:((~happy(X)<~>strong(X))))<=>(?[X]:((generous(X)|~quiet(X)))))&
(![X]:((~patient(X)<~>~calm(X))<=>(~curious(X)|calm(X))))&
((happy(alice))<=>((strong(alice)&~quiet(alice))))&
(![X]:((humble(X)&~rich(X))=>(~old(X)<~>~humble(X))))&
((?[X]:((generous(X)&brave(X))))<=>(?[X]:((brave(X)|creative(X)))))&
((~kind(lucy))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:((generous(X)<~>~calm(X))=>~patient(X)))&
(![X]:((patient(X)|funny(X))<=>~generous(X)))&
(((~humble(fred)&~strong(fred)))=>(?[X]:((quiet(X)<~>kind(X)))))&
(((generous(john)&~tall(john)))<=>((~rich(mary)<~>humble(mary))))&
(![X]:(old(X)=>~humble(X)))&
(![X]:((~curious(X)|~creative(X))=>~humble(X)))&
((?[X]:((rich(X)&old(X))))<=>(brave(alice)))&
(![X]:((strong(X)&curious(X))=>tall(X)))&
(![X]:((~strong(X)&patient(X))=>strong(X)))&
(?[X]:(~creative(X)))&
((~old(paul)<~>funny(paul)))&
(?[X]:((kind(X)&tall(X))))&
(~calm(john))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((~happy(X)|~humble(X)))) | ~patient(susan) | [
"p2",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2906357971685808786534920
% SZS output start Proof for 2906357971685808786534920
3. ! [X0] : ((~patient(X0) <~> ~calm(X0)) <=> (calm(X0) | ~curious(X0))) [input p2]
8. ! [X0] : ((generous(X0) <~> ~calm(X0)) => ~patient(X0)) [input p7]
9. ! [X0] : ((funny(X0) | patient(X0)) <=> ~generous(X0)) [input p8]
24. patient(susan) [input hypothesis]
30. ! [X0] : (~patient(X0) | (generous(X0) <=> ~calm(X0))) [ennf transformation 8]
46. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [nnf transformation 3]
47. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [flattening 46]
58. ! [X0] : (~patient(X0) | ((generous(X0) | calm(X0)) & (~calm(X0) | ~generous(X0)))) [nnf transformation 30]
59. ! [X0] : (((funny(X0) | patient(X0)) | generous(X0)) & (~generous(X0) | (~funny(X0) & ~patient(X0)))) [nnf transformation 9]
60. ! [X0] : ((funny(X0) | patient(X0) | generous(X0)) & (~generous(X0) | (~funny(X0) & ~patient(X0)))) [flattening 59]
96. ~calm(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 47]
111. ~patient(X0) | generous(X0) | calm(X0) [cnf transformation 58]
112. ~generous(X0) | ~patient(X0) [cnf transformation 60]
140. patient(susan) [cnf transformation 24]
144. ~calm(X0) | ~patient(X0) [duplicate literal removal 96]
260. ~patient(X0) | generous(X0) [subsumption resolution 111,144]
262. ~patient(X0) [subsumption resolution 112,260]
349. $false [subsumption resolution 140,262]
% SZS output end Proof for 2906357971685808786534920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or calm then someone is patient or curious. Everyone who is not calm or not tall is either rich or not patient and vice versa. If someone is not kind then someone is both creative and not creative and vice versa. Everyone who is wise or rich is not strong or not creative. If mary is either kind or not calm then lucy is creative. If someone is not funny or not wise then someone is not creative or kind. Everyone who is happy or not patient is patient or not generous and vice versa. Everyone who is both strong and not kind is not funny or rich. Everyone who is either not patient or creative is either not funny or patient and vice versa. If fred is happy then john is both calm and not humble and vice versa. Everyone who is both rich and not funny is both patient and not creative and vice versa. Everyone who is both not tall and funny is quiet and vice versa. If fred is either not tall or not brave then someone is both strong and not quiet. Everyone who is tall is not wise. Everyone who is both strong and not kind is not happy and vice versa. Everyone who is not strong is not funny. Someone is either not creative or wise. Mary is either patient or not creative. John is either not rich or not generous. Someone is both not humble and patient. Someone is kind. John is not brave. Alice is either not funny or generous. Someone is happy or rich. | Alice is not quiet. | entailment | ((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((~calm(X)|~tall(X))<=>(rich(X)<~>~patient(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((wise(X)|rich(X))=>(~strong(X)|~creative(X))))&
(((kind(mary)<~>~calm(mary)))=>(creative(lucy)))&
((?[X]:((~funny(X)|~wise(X))))=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((happy(X)|~patient(X))<=>(patient(X)|~generous(X))))&
(![X]:((strong(X)&~kind(X))=>(~funny(X)|rich(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~funny(X)<~>patient(X))))&
((happy(fred))<=>((calm(john)&~humble(john))))&
(![X]:((rich(X)&~funny(X))<=>(patient(X)&~creative(X))))&
(![X]:((~tall(X)&funny(X))<=>quiet(X)))&
(((~tall(fred)<~>~brave(fred)))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:(tall(X)=>~wise(X)))&
(![X]:((strong(X)&~kind(X))<=>~happy(X)))&
(![X]:(~strong(X)=>~funny(X)))&
(?[X]:((~creative(X)<~>wise(X))))&
((patient(mary)<~>~creative(mary)))&
((~rich(john)<~>~generous(john)))&
(?[X]:((~humble(X)&patient(X))))&
(?[X]:(kind(X)))&
(~brave(john))&
((~funny(alice)<~>generous(alice)))&
(?[X]:((happy(X)|rich(X)))) | ~quiet(alice) | [
"p1",
"p3",
"p6",
"p8",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5686148026277183794224046
% SZS output start Proof for 5686148026277183794224046
2. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> (rich(X0) <~> ~patient(X0))) [input p1]
4. ! [X0] : ((rich(X0) | wise(X0)) => (~creative(X0) | ~strong(X0))) [input p3]
7. ! [X0] : ((~patient(X0) | happy(X0)) <=> (~generous(X0) | patient(X0))) [input p6]
9. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (~funny(X0) <~> patient(X0))) [input p8]
12. ! [X0] : ((funny(X0) & ~tall(X0)) <=> quiet(X0)) [input p11]
16. ! [X0] : (~strong(X0) => ~funny(X0)) [input p15]
23. ~funny(alice) <~> generous(alice) [input p22]
25. quiet(alice) [input hypothesis]
30. ! [X0] : ((~creative(X0) | ~strong(X0)) | (~rich(X0) & ~wise(X0))) [ennf transformation 4]
31. ! [X0] : (~creative(X0) | ~strong(X0) | (~rich(X0) & ~wise(X0))) [flattening 30]
38. ! [X0] : (~funny(X0) | strong(X0)) [ennf transformation 16]
39. ! [X0] : (((~tall(X0) | ~calm(X0)) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) & (((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (tall(X0) & calm(X0)))) [nnf transformation 2]
40. ! [X0] : ((~tall(X0) | ~calm(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) & (((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (tall(X0) & calm(X0)))) [flattening 39]
50. ! [X0] : (((~patient(X0) | happy(X0)) | (generous(X0) & ~patient(X0))) & ((~generous(X0) | patient(X0)) | (patient(X0) & ~happy(X0)))) [nnf transformation 7]
51. ! [X0] : ((~patient(X0) | happy(X0) | (generous(X0) & ~patient(X0))) & (~generous(X0) | patient(X0) | (patient(X0) & ~happy(X0)))) [flattening 50]
52. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 9]
57. ! [X0] : (((funny(X0) & ~tall(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) | tall(X0)))) [nnf transformation 12]
58. ! [X0] : (((funny(X0) & ~tall(X0)) | ~quiet(X0)) & (quiet(X0) | ~funny(X0) | tall(X0))) [flattening 57]
73. (~generous(alice) | funny(alice)) & (generous(alice) | ~funny(alice)) [nnf transformation 23]
77. ~patient(X0) | rich(X0) | tall(X0) [cnf transformation 40]
86. ~strong(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 31]
92. ~generous(X0) | patient(X0) | patient(X0) [cnf transformation 51]
96. patient(X0) | ~funny(X0) | creative(X0) | patient(X0) [cnf transformation 52]
101. creative(X0) | ~patient(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 52]
112. ~quiet(X0) | ~tall(X0) [cnf transformation 58]
113. ~quiet(X0) | funny(X0) [cnf transformation 58]
122. ~funny(X0) | strong(X0) [cnf transformation 38]
133. generous(alice) | ~funny(alice) [cnf transformation 73]
136. quiet(alice) [cnf transformation 25]
137. patient(X0) | ~funny(X0) | creative(X0) [duplicate literal removal 96]
139. creative(X0) | ~patient(X0) | ~funny(X0) [duplicate literal removal 101]
141. ~generous(X0) | patient(X0) [duplicate literal removal 92]
183. ~funny(X0) | creative(X0) [subsumption resolution 137,139]
250. 23 <=> funny(alice) [avatar definition]
252. funny(alice) <- (23) [avatar component clause 250]
254. 24 <=> generous(alice) [avatar definition]
255. generous(alice) <- (24) [avatar component clause 254]
258. ~23 | 24 [avatar split clause 133,254,250]
268. ~tall(alice) [resolution 112,136]
269. funny(alice) [resolution 113,136]
272. 23 [avatar split clause 269,250]
277. strong(alice) <- (23) [resolution 122,252]
278. patient(alice) <- (24) [resolution 141,255]
283. creative(alice) <- (23) [resolution 183,252]
301. 30 <=> rich(alice) [avatar definition]
303. rich(alice) <- (30) [avatar component clause 301]
306. rich(alice) | tall(alice) <- (24) [resolution 77,278]
312. rich(alice) <- (24) [subsumption resolution 306,268]
313. 30 | ~24 [avatar split clause 312,254,301]
344. ~creative(alice) | ~rich(alice) <- (23) [resolution 86,277]
345. ~rich(alice) <- (23) [subsumption resolution 344,283]
346. $false <- (23, 30) [subsumption resolution 345,303]
347. ~23 | ~30 [avatar contradiction clause 346]
348. $false [avatar sat refutation 258,272,313,347]
% SZS output end Proof for 5686148026277183794224046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not creative is not brave or generous.
If someone is not old then john is calm or strong.
Everyone who is not strong or curious is not generous or not kind and vice versa.
Everyone who is strong is calm.
Everyone who is either funny or generous is both not rich and not generous and vice versa.
If susan is both generous and happy then someone is either not old or patient and vice versa.
Everyone who is not calm or humble is either brave or creative.
Everyone who is both not old and not curious is either not patient or old.
Everyone who is calm is not rich.
If lucy is funny then john is either not curious or brave.
Everyone who is not rich or not humble is wise or not curious and vice versa.
Everyone who is either not generous or brave is strong and vice versa.
If someone is not calm or humble then someone is both strong and old.
If someone is wise then susan is curious and vice versa.
If someone is either tall or old then lucy is either not old or not rich and vice versa.
Everyone who is happy is both curious and creative and vice versa.
Alice is not funny.
Someone is generous or quiet.
Lucy is old.
Susan is not kind or tall.
Someone is either not tall or curious.
Paul is quiet or wise.
Susan is either not humble or rich.
Lucy is not happy. | Alice is wise. | contradiction | (![X]:((humble(X)<~>~creative(X))=>(~brave(X)|generous(X))))&
((?[X]:(~old(X)))=>((calm(john)|strong(john))))&
(![X]:((~strong(X)|curious(X))<=>(~generous(X)|~kind(X))))&
(![X]:(strong(X)=>calm(X)))&
(![X]:((funny(X)<~>generous(X))<=>(~rich(X)&~generous(X))))&
(((generous(susan)&happy(susan)))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~calm(X)|humble(X))=>(brave(X)<~>creative(X))))&
(![X]:((~old(X)&~curious(X))=>(~patient(X)<~>old(X))))&
(![X]:(calm(X)=>~rich(X)))&
((funny(lucy))=>((~curious(john)<~>brave(john))))&
(![X]:((~rich(X)|~humble(X))<=>(wise(X)|~curious(X))))&
(![X]:((~generous(X)<~>brave(X))<=>strong(X)))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((strong(X)&old(X)))))&
((?[X]:(wise(X)))<=>(curious(susan)))&
((?[X]:((tall(X)<~>old(X))))<=>((~old(lucy)<~>~rich(lucy))))&
(![X]:(happy(X)<=>(curious(X)&creative(X))))&
(~funny(alice))&
(?[X]:((generous(X)|quiet(X))))&
(old(lucy))&
((~kind(susan)|tall(susan)))&
(?[X]:((~tall(X)<~>curious(X))))&
((quiet(paul)|wise(paul)))&
((~humble(susan)<~>rich(susan)))&
(~happy(lucy)) | wise(alice) | [
"p0",
"p3",
"p4",
"p6",
"p8",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8137885142135953069615600
% SZS output start Proof for 8137885142135953069615600
1. ! [X0] : ((humble(X0) <~> ~creative(X0)) => (generous(X0) | ~brave(X0))) [input p0]
4. ! [X0] : (strong(X0) => calm(X0)) [input p3]
5. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (~generous(X0) & ~rich(X0))) [input p4]
7. ! [X0] : ((humble(X0) | ~calm(X0)) => (brave(X0) <~> creative(X0))) [input p6]
9. ! [X0] : (calm(X0) => ~rich(X0)) [input p8]
11. ! [X0] : ((~humble(X0) | ~rich(X0)) <=> (~curious(X0) | wise(X0))) [input p10]
12. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> strong(X0)) [input p11]
17. ~funny(alice) [input p16]
25. wise(alice) [input hypothesis]
29. ! [X0] : ((generous(X0) | ~brave(X0)) | (humble(X0) <=> ~creative(X0))) [ennf transformation 1]
30. ! [X0] : (generous(X0) | ~brave(X0) | (humble(X0) <=> ~creative(X0))) [flattening 29]
33. ! [X0] : (calm(X0) | ~strong(X0)) [ennf transformation 4]
34. ! [X0] : ((brave(X0) <~> creative(X0)) | (~humble(X0) & calm(X0))) [ennf transformation 7]
37. ! [X0] : (~rich(X0) | ~calm(X0)) [ennf transformation 9]
40. ! [X0] : (generous(X0) | ~brave(X0) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) [nnf transformation 30]
43. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (generous(X0) | rich(X0))) & ((~generous(X0) & ~rich(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | generous(X0) | rich(X0)) & ((~generous(X0) & ~rich(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [flattening 43]
50. ! [X0] : (((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | (~humble(X0) & calm(X0))) [nnf transformation 34]
53. ! [X0] : (((~humble(X0) | ~rich(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (humble(X0) & rich(X0)))) [nnf transformation 11]
54. ! [X0] : ((~humble(X0) | ~rich(X0) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | (humble(X0) & rich(X0)))) [flattening 53]
55. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | ~strong(X0)) & (strong(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 12]
74. ~brave(X0) | generous(X0) | humble(X0) | creative(X0) [cnf transformation 40]
80. ~strong(X0) | calm(X0) [cnf transformation 33]
84. ~generous(X0) | funny(X0) | ~generous(X0) [cnf transformation 44]
85. generous(X0) | funny(X0) | generous(X0) | rich(X0) [cnf transformation 44]
95. ~brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 50]
99. ~rich(X0) | ~calm(X0) [cnf transformation 37]
104. ~wise(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 54]
106. strong(X0) | brave(X0) | generous(X0) [cnf transformation 55]
127. ~funny(alice) [cnf transformation 17]
135. wise(alice) [cnf transformation 25]
137. ~generous(X0) | funny(X0) [duplicate literal removal 84]
138. rich(X0) | funny(X0) | generous(X0) [duplicate literal removal 85]
288. ~rich(alice) | ~humble(alice) [resolution 104,135]
293. calm(X2) | generous(X2) | brave(X2) [resolution 106,80]
316. funny(X2) | generous(X2) | ~calm(X2) [resolution 138,99]
339. ~calm(X2) | funny(X2) [subsumption resolution 316,137]
382. generous(X0) | brave(X0) | funny(X0) [resolution 293,339]
383. funny(X0) | brave(X0) [subsumption resolution 382,137]
421. brave(alice) [resolution 383,127]
422. generous(alice) | humble(alice) | creative(alice) [resolution 421,74]
425. ~creative(alice) | calm(alice) [resolution 421,95]
428. 43 <=> creative(alice) [avatar definition]
432. 44 <=> generous(alice) [avatar definition]
434. generous(alice) <- (44) [avatar component clause 432]
437. 45 <=> calm(alice) [avatar definition]
439. calm(alice) <- (45) [avatar component clause 437]
440. 45 | ~43 [avatar split clause 425,428,437]
442. 46 <=> humble(alice) [avatar definition]
447. 43 | 46 | 44 [avatar split clause 422,432,442,428]
482. 54 <=> rich(alice) [avatar definition]
483. rich(alice) <- (54) [avatar component clause 482]
484. ~rich(alice) <- (~54) [avatar component clause 482]
485. ~46 | ~54 [avatar split clause 288,482,442]
490. funny(alice) | generous(alice) <- (~54) [resolution 484,138]
510. funny(alice) <- (44) [resolution 434,137]
512. $false <- (44) [subsumption resolution 510,127]
513. ~44 [avatar contradiction clause 512]
514. generous(alice) <- (~54) [subsumption resolution 490,127]
515. 44 | 54 [avatar split clause 514,482,432]
518. ~calm(alice) <- (54) [resolution 483,99]
519. $false <- (45, 54) [subsumption resolution 518,439]
520. ~45 | ~54 [avatar contradiction clause 519]
521. $false [avatar sat refutation 440,447,485,513,515,520]
% SZS output end Proof for 8137885142135953069615600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both strong and kind then alice is either calm or happy.
Everyone who is generous is generous or patient.
Everyone who is both not strong and not creative is quiet or happy and vice versa.
If someone is both tall and humble then susan is either not calm or not strong and vice versa.
If someone is either patient or not humble then someone is patient and vice versa.
If alice is both not calm and not humble then lucy is kind.
Everyone who is both happy and generous is either not curious or not brave and vice versa.
Everyone who is both calm and not strong is both not creative and not curious and vice versa.
Everyone who is either humble or not wise is not creative or kind and vice versa.
If someone is not calm or not rich then paul is not rich or strong.
If alice is tall then lucy is either quiet or not humble and vice versa.
If someone is both not funny and calm then paul is not rich or not calm and vice versa.
Everyone who is not tall or wise is both strong and calm.
Everyone who is either calm or not strong is both not wise and not calm.
If someone is old then someone is not wise or creative.
Everyone who is old is both not creative and patient.
Mary is old.
John is either calm or old.
Alice is either old or not creative.
Lucy is not calm or rich.
Fred is both not happy and not kind. | Susan is wise. | contradiction | (((strong(alice)&kind(alice)))=>((calm(alice)<~>happy(alice))))&
(![X]:(generous(X)=>(generous(X)|patient(X))))&
(![X]:((~strong(X)&~creative(X))<=>(quiet(X)|happy(X))))&
((?[X]:((tall(X)&humble(X))))<=>((~calm(susan)<~>~strong(susan))))&
((?[X]:((patient(X)<~>~humble(X))))<=>(?[X]:(patient(X))))&
(((~calm(alice)&~humble(alice)))=>(kind(lucy)))&
(![X]:((happy(X)&generous(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((calm(X)&~strong(X))<=>(~creative(X)&~curious(X))))&
(![X]:((humble(X)<~>~wise(X))<=>(~creative(X)|kind(X))))&
((?[X]:((~calm(X)|~rich(X))))=>((~rich(paul)|strong(paul))))&
((tall(alice))<=>((quiet(lucy)<~>~humble(lucy))))&
((?[X]:((~funny(X)&calm(X))))<=>((~rich(paul)|~calm(paul))))&
(![X]:((~tall(X)|wise(X))=>(strong(X)&calm(X))))&
(![X]:((calm(X)<~>~strong(X))=>(~wise(X)&~calm(X))))&
((?[X]:(old(X)))=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:(old(X)=>(~creative(X)&patient(X))))&
(old(mary))&
((calm(john)<~>old(john)))&
((old(alice)<~>~creative(alice)))&
((~calm(lucy)|rich(lucy)))&
((~happy(fred)&~kind(fred))) | wise(susan) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 55004374415636875168355
% SZS output start Proof for 55004374415636875168355
13. ! [X0] : ((wise(X0) | ~tall(X0)) => (calm(X0) & strong(X0))) [input p12]
14. ! [X0] : ((calm(X0) <~> ~strong(X0)) => (~calm(X0) & ~wise(X0))) [input p13]
22. wise(susan) [input hypothesis]
33. ! [X0] : ((calm(X0) & strong(X0)) | (~wise(X0) & tall(X0))) [ennf transformation 13]
34. ! [X0] : ((~calm(X0) & ~wise(X0)) | (calm(X0) <=> ~strong(X0))) [ennf transformation 14]
61. ! [X0] : ((~calm(X0) & ~wise(X0)) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) [nnf transformation 34]
114. ~wise(X0) | strong(X0) [cnf transformation 33]
116. ~wise(X0) | calm(X0) [cnf transformation 33]
119. ~calm(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 61]
132. wise(susan) [cnf transformation 22]
133. ~calm(X0) | ~strong(X0) [duplicate literal removal 119]
153. 5 <=> strong(susan) [avatar definition]
155. strong(susan) <- (5) [avatar component clause 153]
157. 6 <=> calm(susan) [avatar definition]
158. calm(susan) <- (6) [avatar component clause 157]
300. strong(susan) [resolution 114,132]
302. calm(susan) [resolution 116,132]
305. 5 [avatar split clause 300,153]
306. 6 [avatar split clause 302,157]
310. ~strong(susan) <- (6) [resolution 133,158]
315. $false <- (5, 6) [subsumption resolution 310,155]
316. ~5 | ~6 [avatar contradiction clause 315]
317. $false [avatar sat refutation 305,306,316]
% SZS output end Proof for 55004374415636875168355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise and not patient then john is patient or generous and vice versa.
If john is not humble or strong then john is quiet or not patient and vice versa.
If fred is both humble and not curious then someone is either not happy or brave.
If fred is both not happy and happy then paul is not tall.
Everyone who is either not happy or not generous is calm.
If susan is both not tall and not kind then susan is either not wise or calm and vice versa.
Everyone who is both not curious and tall is not wise and vice versa.
Everyone who is not patient is not creative and vice versa.
If paul is both kind and patient then susan is either brave or not tall.
Everyone who is curious or not tall is either old or not creative and vice versa.
If someone is happy or not tall then someone is rich or not generous and vice versa.
Everyone who is either rich or creative is either kind or not old.
Everyone who is either curious or kind is both not kind and not calm.
If someone is either kind or generous then someone is not humble and vice versa.
If someone is not humble then someone is both not funny and not tall.
If someone is either not generous or not curious then john is either not tall or humble.
Susan is humble.
Someone is not patient.
Someone is patient.
Someone is either funny or not funny.
Someone is curious.
Lucy is not kind or not wise.
Alice is not funny or generous. | John is humble. | neutral | ((?[X]:((~wise(X)&~patient(X))))<=>((patient(john)|generous(john))))&
(((~humble(john)|strong(john)))<=>((quiet(john)|~patient(john))))&
(((humble(fred)&~curious(fred)))=>(?[X]:((~happy(X)<~>brave(X)))))&
(((~happy(fred)&happy(fred)))=>(~tall(paul)))&
(![X]:((~happy(X)<~>~generous(X))=>calm(X)))&
(((~tall(susan)&~kind(susan)))<=>((~wise(susan)<~>calm(susan))))&
(![X]:((~curious(X)&tall(X))<=>~wise(X)))&
(![X]:(~patient(X)<=>~creative(X)))&
(((kind(paul)&patient(paul)))=>((brave(susan)<~>~tall(susan))))&
(![X]:((curious(X)|~tall(X))<=>(old(X)<~>~creative(X))))&
((?[X]:((happy(X)|~tall(X))))<=>(?[X]:((rich(X)|~generous(X)))))&
(![X]:((rich(X)<~>creative(X))=>(kind(X)<~>~old(X))))&
(![X]:((curious(X)<~>kind(X))=>(~kind(X)&~calm(X))))&
((?[X]:((kind(X)<~>generous(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~funny(X)&~tall(X)))))&
((?[X]:((~generous(X)<~>~curious(X))))=>((~tall(john)<~>humble(john))))&
(humble(susan))&
(?[X]:(~patient(X)))&
(?[X]:(patient(X)))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:(curious(X)))&
((~kind(lucy)|~wise(lucy)))&
((~funny(alice)|generous(alice))) | humble(john) | [] | null | 0 |
If paul is both not creative and kind then susan is both happy and not tall.
Everyone who is not quiet or old is not patient or calm and vice versa.
If someone is not creative then paul is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
Someone is either not humble or not strong.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is generous.
Someone is either not generous or quiet. | Paul is patient. | neutral | (((~creative(paul)&kind(paul)))=>((happy(susan)&~tall(susan))))&
(![X]:((~quiet(X)|old(X))<=>(~patient(X)|calm(X))))&
((?[X]:(~creative(X)))<=>(old(paul)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:(generous(X)))&
(?[X]:((~generous(X)<~>quiet(X)))) | patient(paul) | [] | null | 0 |
Everyone who is not wise is not kind or curious and vice versa.
If someone is either not patient or not strong then fred is brave or calm and vice versa.
Everyone who is not quiet is not patient or funny.
If susan is not kind then someone is not rich.
If someone is both happy and not creative then someone is either not patient or tall.
Everyone who is not patient is brave or not rich.
If someone is humble then mary is either not kind or rich and vice versa.
If someone is both not rich and generous then fred is both quiet and wise and vice versa.
Everyone who is not funny or strong is either not humble or brave.
Everyone who is kind is either not wise or not old.
Everyone who is either not funny or patient is calm and vice versa.
If fred is not tall or patient then someone is quiet and vice versa.
If susan is happy then john is either not tall or not wise.
If alice is both not kind and wise then someone is both not wise and not calm.
If paul is either calm or not strong then john is not patient and vice versa.
Everyone who is patient is quiet or not humble.
Lucy is either not patient or funny.
Mary is either tall or not calm.
Mary is funny.
Susan is either calm or not generous.
Someone is funny or not patient.
Alice is both not funny and not curious.
Someone is kind.
Fred is either kind or not rich. | Alice is funny. | contradiction | (![X]:(~wise(X)<=>(~kind(X)|curious(X))))&
((?[X]:((~patient(X)<~>~strong(X))))<=>((brave(fred)|calm(fred))))&
(![X]:(~quiet(X)=>(~patient(X)|funny(X))))&
((~kind(susan))=>(?[X]:(~rich(X))))&
((?[X]:((happy(X)&~creative(X))))=>(?[X]:((~patient(X)<~>tall(X)))))&
(![X]:(~patient(X)=>(brave(X)|~rich(X))))&
((?[X]:(humble(X)))<=>((~kind(mary)<~>rich(mary))))&
((?[X]:((~rich(X)&generous(X))))<=>((quiet(fred)&wise(fred))))&
(![X]:((~funny(X)|strong(X))=>(~humble(X)<~>brave(X))))&
(![X]:(kind(X)=>(~wise(X)<~>~old(X))))&
(![X]:((~funny(X)<~>patient(X))<=>calm(X)))&
(((~tall(fred)|patient(fred)))<=>(?[X]:(quiet(X))))&
((happy(susan))=>((~tall(john)<~>~wise(john))))&
(((~kind(alice)&wise(alice)))=>(?[X]:((~wise(X)&~calm(X)))))&
(((calm(paul)<~>~strong(paul)))<=>(~patient(john)))&
(![X]:(patient(X)=>(quiet(X)|~humble(X))))&
((~patient(lucy)<~>funny(lucy)))&
((tall(mary)<~>~calm(mary)))&
(funny(mary))&
((calm(susan)<~>~generous(susan)))&
(?[X]:((funny(X)|~patient(X))))&
((~funny(alice)&~curious(alice)))&
(?[X]:(kind(X)))&
((kind(fred)<~>~rich(fred))) | funny(alice) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8091814578097741669338988
% SZS output start Proof for 8091814578097741669338988
22. ~curious(alice) & ~funny(alice) [input p21]
25. funny(alice) [input hypothesis]
125. ~funny(alice) [cnf transformation 22]
130. funny(alice) [cnf transformation 25]
294. $false [subsumption resolution 130,125]
% SZS output end Proof for 8091814578097741669338988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong then someone is not happy or not rich.
If alice is kind or not curious then someone is not quiet or not strong and vice versa.
Everyone who is both tall and funny is not curious or rich and vice versa.
If someone is not generous or strong then mary is both strong and not humble.
If someone is both creative and not calm then fred is patient or not strong.
Everyone who is kind or not strong is not generous or not rich and vice versa.
If mary is tall or rich then john is not humble or kind.
If someone is either quiet or curious then paul is either not old or not quiet and vice versa.
Everyone who is not calm is both curious and not creative and vice versa.
Everyone who is not calm is both tall and kind and vice versa.
Everyone who is quiet is not brave.
Everyone who is either patient or happy is creative.
If susan is not calm or not old then alice is both funny and tall and vice versa.
Everyone who is kind or not kind is both funny and not tall.
If someone is funny then someone is either wise or brave and vice versa.
Everyone who is not funny or not happy is curious.
Fred is old.
Alice is both strong and creative.
Someone is patient.
Someone is quiet or not strong.
Someone is tall or not rich.
Someone is either tall or not patient. | Alice is not curious. | contradiction | ((?[X]:(strong(X)))=>(?[X]:((~happy(X)|~rich(X)))))&
(((kind(alice)|~curious(alice)))<=>(?[X]:((~quiet(X)|~strong(X)))))&
(![X]:((tall(X)&funny(X))<=>(~curious(X)|rich(X))))&
((?[X]:((~generous(X)|strong(X))))=>((strong(mary)&~humble(mary))))&
((?[X]:((creative(X)&~calm(X))))=>((patient(fred)|~strong(fred))))&
(![X]:((kind(X)|~strong(X))<=>(~generous(X)|~rich(X))))&
(((tall(mary)|rich(mary)))=>((~humble(john)|kind(john))))&
((?[X]:((quiet(X)<~>curious(X))))<=>((~old(paul)<~>~quiet(paul))))&
(![X]:(~calm(X)<=>(curious(X)&~creative(X))))&
(![X]:(~calm(X)<=>(tall(X)&kind(X))))&
(![X]:(quiet(X)=>~brave(X)))&
(![X]:((patient(X)<~>happy(X))=>creative(X)))&
(((~calm(susan)|~old(susan)))<=>((funny(alice)&tall(alice))))&
(![X]:((kind(X)|~kind(X))=>(funny(X)&~tall(X))))&
((?[X]:(funny(X)))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~funny(X)|~happy(X))=>curious(X)))&
(old(fred))&
((strong(alice)&creative(alice)))&
(?[X]:(patient(X)))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((tall(X)<~>~patient(X)))) | ~curious(alice) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1649271813740300312576101
% SZS output start Proof for 1649271813740300312576101
3. ! [X0] : ((funny(X0) & tall(X0)) <=> (rich(X0) | ~curious(X0))) [input p2]
14. ! [X0] : ((~kind(X0) | kind(X0)) => (~tall(X0) & funny(X0))) [input p13]
23. ~curious(alice) [input hypothesis]
34. ! [X0] : ((~tall(X0) & funny(X0)) | (kind(X0) & ~kind(X0))) [ennf transformation 14]
44. ! [X0] : (((funny(X0) & tall(X0)) | (~rich(X0) & curious(X0))) & ((rich(X0) | ~curious(X0)) | (~funny(X0) | ~tall(X0)))) [nnf transformation 3]
45. ! [X0] : (((funny(X0) & tall(X0)) | (~rich(X0) & curious(X0))) & (rich(X0) | ~curious(X0) | ~funny(X0) | ~tall(X0))) [flattening 44]
79. tall(X0) | curious(X0) [cnf transformation 45]
114. ~tall(X0) | ~kind(X0) [cnf transformation 34]
115. ~tall(X0) | kind(X0) [cnf transformation 34]
130. ~curious(alice) [cnf transformation 23]
151. 6 <=> curious(alice) [avatar definition]
153. ~curious(alice) <- (~6) [avatar component clause 151]
242. ~tall(X0) [subsumption resolution 114,115]
266. ~6 [avatar split clause 130,151]
269. curious(X0) [resolution 79,242]
270. $false <- (~6) [resolution 269,153]
273. 6 [avatar contradiction clause 270]
274. $false [avatar sat refutation 266,273]
% SZS output end Proof for 1649271813740300312576101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or calm is both not happy and not funny.
If someone is old or not brave then paul is not funny and vice versa.
If paul is not strong or curious then mary is either not kind or creative and vice versa.
Everyone who is either not generous or not rich is either happy or rich.
Everyone who is both not strong and not patient is quiet and vice versa.
If someone is both brave and not rich then someone is either not strong or strong and vice versa.
Everyone who is not tall or generous is old or calm and vice versa.
If someone is not wise then paul is either not wise or not funny and vice versa.
If paul is both quiet and not curious then susan is old or not generous.
Everyone who is not tall is either not creative or not calm and vice versa.
Everyone who is either not creative or not strong is not calm.
Everyone who is not patient or not generous is quiet.
Everyone who is both not rich and not strong is both not calm and calm and vice versa.
Everyone who is not quiet is not humble or tall and vice versa.
Susan is either curious or not humble.
Someone is either not strong or not quiet.
Lucy is not humble or not tall.
Susan is not happy or quiet.
Someone is not rich. | Lucy is generous. | neutral | (![X]:((happy(X)<~>calm(X))=>(~happy(X)&~funny(X))))&
((?[X]:((old(X)|~brave(X))))<=>(~funny(paul)))&
(((~strong(paul)|curious(paul)))<=>((~kind(mary)<~>creative(mary))))&
(![X]:((~generous(X)<~>~rich(X))=>(happy(X)<~>rich(X))))&
(![X]:((~strong(X)&~patient(X))<=>quiet(X)))&
((?[X]:((brave(X)&~rich(X))))<=>(?[X]:((~strong(X)<~>strong(X)))))&
(![X]:((~tall(X)|generous(X))<=>(old(X)|calm(X))))&
((?[X]:(~wise(X)))<=>((~wise(paul)<~>~funny(paul))))&
(((quiet(paul)&~curious(paul)))=>((old(susan)|~generous(susan))))&
(![X]:(~tall(X)<=>(~creative(X)<~>~calm(X))))&
(![X]:((~creative(X)<~>~strong(X))=>~calm(X)))&
(![X]:((~patient(X)|~generous(X))=>quiet(X)))&
(![X]:((~rich(X)&~strong(X))<=>(~calm(X)&calm(X))))&
(![X]:(~quiet(X)<=>(~humble(X)|tall(X))))&
((curious(susan)<~>~humble(susan)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~humble(lucy)|~tall(lucy)))&
((~happy(susan)|quiet(susan)))&
(?[X]:(~rich(X))) | generous(lucy) | [] | null | 0 |
Everyone who is both funny and not patient is creative or not brave and vice versa.
If someone is both kind and happy then susan is not strong or not rich.
If someone is quiet or not old then paul is not kind.
Everyone who is not strong or not curious is not funny.
Everyone who is either curious or not tall is creative and vice versa.
If john is not funny or brave then fred is both tall and not old.
If mary is either not generous or not tall then someone is not quiet or brave and vice versa.
If someone is not brave or happy then paul is humble and vice versa.
If fred is both kind and not strong then susan is both not old and not generous.
If susan is tall then someone is both quiet and kind and vice versa.
If someone is not creative or wise then someone is either not rich or not humble and vice versa.
If someone is old then lucy is both not funny and generous.
Everyone who is not quiet is either calm or not generous.
If alice is calm or not kind then someone is not generous and vice versa.
If someone is patient then john is both not happy and not wise and vice versa.
If someone is not brave then lucy is either curious or not creative and vice versa.
Lucy is creative.
Someone is both not generous and curious.
Someone is either not funny or not curious.
Alice is both not curious and kind.
Lucy is not tall or generous.
Lucy is either not humble or kind.
John is calm.
Someone is either not curious or not rich. | Lucy is tall. | entailment | (![X]:((funny(X)&~patient(X))<=>(creative(X)|~brave(X))))&
((?[X]:((kind(X)&happy(X))))=>((~strong(susan)|~rich(susan))))&
((?[X]:((quiet(X)|~old(X))))=>(~kind(paul)))&
(![X]:((~strong(X)|~curious(X))=>~funny(X)))&
(![X]:((curious(X)<~>~tall(X))<=>creative(X)))&
(((~funny(john)|brave(john)))=>((tall(fred)&~old(fred))))&
(((~generous(mary)<~>~tall(mary)))<=>(?[X]:((~quiet(X)|brave(X)))))&
((?[X]:((~brave(X)|happy(X))))<=>(humble(paul)))&
(((kind(fred)&~strong(fred)))=>((~old(susan)&~generous(susan))))&
((tall(susan))<=>(?[X]:((quiet(X)&kind(X)))))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
((?[X]:(old(X)))=>((~funny(lucy)&generous(lucy))))&
(![X]:(~quiet(X)=>(calm(X)<~>~generous(X))))&
(((calm(alice)|~kind(alice)))<=>(?[X]:(~generous(X))))&
((?[X]:(patient(X)))<=>((~happy(john)&~wise(john))))&
((?[X]:(~brave(X)))<=>((curious(lucy)<~>~creative(lucy))))&
(creative(lucy))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((~funny(X)<~>~curious(X))))&
((~curious(alice)&kind(alice)))&
((~tall(lucy)|generous(lucy)))&
((~humble(lucy)<~>kind(lucy)))&
(calm(john))&
(?[X]:((~curious(X)<~>~rich(X)))) | tall(lucy) | [
"p0",
"p3",
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6766106616899524072103949
% SZS output start Proof for 6766106616899524072103949
1. ! [X0] : ((~patient(X0) & funny(X0)) <=> (~brave(X0) | creative(X0))) [input p0]
4. ! [X0] : ((~curious(X0) | ~strong(X0)) => ~funny(X0)) [input p3]
5. ! [X0] : ((curious(X0) <~> ~tall(X0)) <=> creative(X0)) [input p4]
17. creative(lucy) [input p16]
25. ~tall(lucy) [input hypothesis]
30. ! [X0] : (~funny(X0) | (curious(X0) & strong(X0))) [ennf transformation 4]
36. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | (patient(X0) | ~funny(X0)))) [nnf transformation 1]
37. ! [X0] : (((~patient(X0) & funny(X0)) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | patient(X0) | ~funny(X0))) [flattening 36]
38. ! [X0] : ((((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | ~creative(X0)) & (creative(X0) | ((curious(X0) | tall(X0)) & (~tall(X0) | ~curious(X0))))) [nnf transformation 5]
81. ~creative(X0) | funny(X0) [cnf transformation 37]
89. ~funny(X0) | curious(X0) [cnf transformation 30]
93. ~curious(X0) | tall(X0) | ~creative(X0) [cnf transformation 38]
132. creative(lucy) [cnf transformation 17]
145. ~tall(lucy) [cnf transformation 25]
318. 40 <=> funny(lucy) [avatar definition]
319. funny(lucy) <- (40) [avatar component clause 318]
359. 49 <=> creative(lucy) [avatar definition]
361. creative(lucy) <- (49) [avatar component clause 359]
363. 50 <=> curious(lucy) [avatar definition]
365. curious(lucy) <- (50) [avatar component clause 363]
374. 49 [avatar split clause 132,359]
379. 52 <=> tall(lucy) [avatar definition]
381. ~tall(lucy) <- (~52) [avatar component clause 379]
403. ~52 [avatar split clause 145,379]
412. funny(lucy) <- (49) [resolution 81,361]
413. 40 | ~49 [avatar split clause 412,359,318]
421. curious(lucy) <- (40) [resolution 89,319]
475. tall(lucy) | ~creative(lucy) <- (50) [resolution 93,365]
488. ~creative(lucy) <- (50, ~52) [subsumption resolution 475,381]
489. $false <- (49, 50, ~52) [subsumption resolution 488,361]
490. ~49 | ~50 | 52 [avatar contradiction clause 489]
518. 50 | ~40 [avatar split clause 421,318,363]
519. $false [avatar sat refutation 374,403,413,490,518]
% SZS output end Proof for 6766106616899524072103949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not curious is either humble or funny.
If mary is strong then someone is old or not strong and vice versa.
Everyone who is old or generous is not happy and vice versa.
If someone is not wise or not happy then lucy is old or not creative.
Everyone who is either not happy or not calm is not creative and vice versa.
Everyone who is not old is either not wise or wise.
Everyone who is curious or not rich is either tall or patient and vice versa.
If someone is either wise or not quiet then john is both strong and kind and vice versa.
If mary is funny then someone is not wise or not calm.
Everyone who is wise is curious or not curious and vice versa.
If mary is either curious or not brave then someone is either creative or kind and vice versa.
If someone is not humble then someone is either patient or not tall and vice versa.
Everyone who is wise or humble is not generous.
Everyone who is calm or not quiet is not wise or not quiet and vice versa.
Everyone who is either not rich or not happy is either funny or not wise and vice versa.
If someone is both creative and curious then lucy is tall or not happy.
Someone is kind.
Someone is funny.
Someone is both humble and not strong.
John is humble or not old.
Someone is curious.
Alice is both old and wise.
Someone is happy or funny.
John is both not strong and not kind. | Lucy is quiet. | contradiction | (![X]:((~humble(X)&~curious(X))=>(humble(X)<~>funny(X))))&
((strong(mary))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((old(X)|generous(X))<=>~happy(X)))&
((?[X]:((~wise(X)|~happy(X))))=>((old(lucy)|~creative(lucy))))&
(![X]:((~happy(X)<~>~calm(X))<=>~creative(X)))&
(![X]:(~old(X)=>(~wise(X)<~>wise(X))))&
(![X]:((curious(X)|~rich(X))<=>(tall(X)<~>patient(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((strong(john)&kind(john))))&
((funny(mary))=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:(wise(X)<=>(curious(X)|~curious(X))))&
(((curious(mary)<~>~brave(mary)))<=>(?[X]:((creative(X)<~>kind(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((wise(X)|humble(X))=>~generous(X)))&
(![X]:((calm(X)|~quiet(X))<=>(~wise(X)|~quiet(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(funny(X)<~>~wise(X))))&
((?[X]:((creative(X)&curious(X))))=>((tall(lucy)|~happy(lucy))))&
(?[X]:(kind(X)))&
(?[X]:(funny(X)))&
(?[X]:((humble(X)&~strong(X))))&
((humble(john)|~old(john)))&
(?[X]:(curious(X)))&
((old(alice)&wise(alice)))&
(?[X]:((happy(X)|funny(X))))&
((~strong(john)&~kind(john))) | quiet(lucy) | [
"p7",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2919183063606555506464039
% SZS output start Proof for 2919183063606555506464039
8. ? [X0] : (wise(X0) <~> ~quiet(X0)) <=> (kind(john) & strong(john)) [input p7]
10. ! [X0] : (wise(X0) <=> (~curious(X0) | curious(X0))) [input p9]
24. ~kind(john) & ~strong(john) [input p23]
25. quiet(lucy) [input hypothesis]
47. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~kind(john) | ~strong(john))) & ((kind(john) & strong(john)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 8]
48. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~kind(john) | ~strong(john)) & ((kind(john) & strong(john)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [flattening 47]
49. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~kind(john) | ~strong(john)) & ((kind(john) & strong(john)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [rectify 48]
50. ? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) => ((quiet(sK1) | ~wise(sK1)) & (~quiet(sK1) | wise(sK1))) [choice axiom]
51. (((quiet(sK1) | ~wise(sK1)) & (~quiet(sK1) | wise(sK1))) | ~kind(john) | ~strong(john)) & ((kind(john) & strong(john)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [skolemisation 49,50]
54. ! [X0] : ((wise(X0) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | ~wise(X0))) [nnf transformation 10]
55. ! [X0] : ((wise(X0) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ~wise(X0))) [flattening 54]
100. strong(john) | ~quiet(X1) | ~wise(X1) [cnf transformation 51]
108. wise(X0) | ~curious(X0) [cnf transformation 55]
109. wise(X0) | curious(X0) [cnf transformation 55]
146. ~strong(john) [cnf transformation 24]
148. quiet(lucy) [cnf transformation 25]
184. 9 <=> ! [X0] : wise(X0) [avatar definition]
185. wise(X0) <- (9) [avatar component clause 184]
188. 10 <=> strong(john) [avatar definition]
210. 15 <=> ! [X1] : (~quiet(X1) | ~wise(X1)) [avatar definition]
211. ~quiet(X1) | ~wise(X1) <- (15) [avatar component clause 210]
214. 15 | 10 [avatar split clause 100,188,210]
228. wise(X0) [subsumption resolution 108,109]
229. 9 [avatar split clause 228,184]
316. ~10 [avatar split clause 146,188]
322. ~wise(lucy) <- (15) [resolution 211,148]
324. $false <- (9, 15) [subsumption resolution 322,185]
325. ~9 | ~15 [avatar contradiction clause 324]
326. $false [avatar sat refutation 214,229,316,325]
% SZS output end Proof for 2919183063606555506464039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either creative or strong. Everyone who is calm or not old is either brave or not brave. Everyone who is not patient or not rich is not generous or curious. Everyone who is either not happy or humble is quiet or happy and vice versa. If someone is both creative and not creative then john is old. If someone is both humble and funny then someone is either not rich or not kind and vice versa. Everyone who is either not quiet or quiet is rich and vice versa. Everyone who is creative is tall and vice versa. Everyone who is either not old or brave is both not funny and funny and vice versa. Everyone who is funny or strong is both not happy and not brave. Everyone who is both strong and rich is both strong and brave and vice versa. If susan is either not rich or not brave then someone is both not curious and curious and vice versa. Everyone who is not happy or creative is either not wise or old. Everyone who is kind is both not tall and calm and vice versa. If lucy is creative or not kind then someone is either not funny or not kind and vice versa. Everyone who is either tall or not happy is either not humble or not strong and vice versa. Lucy is not brave. Fred is either not wise or old. John is both not quiet and tall. Someone is either rich or not old. Paul is not curious or curious. Someone is brave. | Paul is not quiet. | neutral | (![X]:((strong(X)<~>~curious(X))=>(creative(X)<~>strong(X))))&
(![X]:((calm(X)|~old(X))=>(brave(X)<~>~brave(X))))&
(![X]:((~patient(X)|~rich(X))=>(~generous(X)|curious(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(quiet(X)|happy(X))))&
((?[X]:((creative(X)&~creative(X))))=>(old(john)))&
((?[X]:((humble(X)&funny(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>rich(X)))&
(![X]:(creative(X)<=>tall(X)))&
(![X]:((~old(X)<~>brave(X))<=>(~funny(X)&funny(X))))&
(![X]:((funny(X)|strong(X))=>(~happy(X)&~brave(X))))&
(![X]:((strong(X)&rich(X))<=>(strong(X)&brave(X))))&
(((~rich(susan)<~>~brave(susan)))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((~happy(X)|creative(X))=>(~wise(X)<~>old(X))))&
(![X]:(kind(X)<=>(~tall(X)&calm(X))))&
(((creative(lucy)|~kind(lucy)))<=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:((tall(X)<~>~happy(X))<=>(~humble(X)<~>~strong(X))))&
(~brave(lucy))&
((~wise(fred)<~>old(fred)))&
((~quiet(john)&tall(john)))&
(?[X]:((rich(X)<~>~old(X))))&
((~curious(paul)|curious(paul)))&
(?[X]:(brave(X))) | ~quiet(paul) | [] | null | 0 |
If fred is both not calm and curious then fred is both not tall and not generous.
Everyone who is tall or not wise is both quiet and not happy.
If paul is both not creative and generous then someone is curious or not rich.
Everyone who is not calm or not wise is not happy or patient.
Everyone who is both happy and not wise is either not curious or not patient and vice versa.
If fred is not funny then paul is both not funny and quiet.
Everyone who is both not patient and wise is either not rich or humble and vice versa.
Everyone who is strong or tall is either not strong or happy and vice versa.
Everyone who is not patient is both generous and strong.
Everyone who is either kind or brave is both not rich and not funny and vice versa.
Everyone who is either not wise or rich is not happy.
If someone is both tall and strong then someone is generous or tall and vice versa.
If someone is both not quiet and humble then alice is not strong or not patient.
Everyone who is both creative and tall is either old or not old.
Everyone who is not rich is either not calm or kind and vice versa.
Everyone who is strong or not funny is quiet or not tall and vice versa.
Someone is not brave or not quiet.
Fred is not quiet or generous.
Someone is both quiet and curious.
Someone is not strong or quiet.
Susan is not rich or patient.
Someone is both strong and not kind.
Someone is either quiet or not quiet. | Paul is not curious. | contradiction | (((~calm(fred)&curious(fred)))=>((~tall(fred)&~generous(fred))))&
(![X]:((tall(X)|~wise(X))=>(quiet(X)&~happy(X))))&
(((~creative(paul)&generous(paul)))=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((~calm(X)|~wise(X))=>(~happy(X)|patient(X))))&
(![X]:((happy(X)&~wise(X))<=>(~curious(X)<~>~patient(X))))&
((~funny(fred))=>((~funny(paul)&quiet(paul))))&
(![X]:((~patient(X)&wise(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((strong(X)|tall(X))<=>(~strong(X)<~>happy(X))))&
(![X]:(~patient(X)=>(generous(X)&strong(X))))&
(![X]:((kind(X)<~>brave(X))<=>(~rich(X)&~funny(X))))&
(![X]:((~wise(X)<~>rich(X))=>~happy(X)))&
((?[X]:((tall(X)&strong(X))))<=>(?[X]:((generous(X)|tall(X)))))&
((?[X]:((~quiet(X)&humble(X))))=>((~strong(alice)|~patient(alice))))&
(![X]:((creative(X)&tall(X))=>(old(X)<~>~old(X))))&
(![X]:(~rich(X)<=>(~calm(X)<~>kind(X))))&
(![X]:((strong(X)|~funny(X))<=>(quiet(X)|~tall(X))))&
(?[X]:((~brave(X)|~quiet(X))))&
((~quiet(fred)|generous(fred)))&
(?[X]:((quiet(X)&curious(X))))&
(?[X]:((~strong(X)|quiet(X))))&
((~rich(susan)|patient(susan)))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:((quiet(X)<~>~quiet(X)))) | ~curious(paul) | [
"p1",
"p4",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6251008488639189198487271
% SZS output start Proof for 6251008488639189198487271
2. ! [X0] : ((~wise(X0) | tall(X0)) => (~happy(X0) & quiet(X0))) [input p1]
5. ! [X0] : ((~wise(X0) & happy(X0)) <=> (~curious(X0) <~> ~patient(X0))) [input p4]
8. ! [X0] : ((tall(X0) | strong(X0)) <=> (~strong(X0) <~> happy(X0))) [input p7]
9. ! [X0] : (~patient(X0) => (strong(X0) & generous(X0))) [input p8]
12. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X0] : (tall(X0) | generous(X0)) [input p11]
24. ~curious(paul) [input hypothesis]
25. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X1] : (tall(X1) | generous(X1)) [rectify 12]
28. ! [X0] : ((~happy(X0) & quiet(X0)) | (wise(X0) & ~tall(X0))) [ennf transformation 2]
34. ! [X0] : ((strong(X0) & generous(X0)) | patient(X0)) [ennf transformation 9]
42. ! [X0] : (((~wise(X0) & happy(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (wise(X0) | ~happy(X0)))) [nnf transformation 5]
43. ! [X0] : (((~wise(X0) & happy(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | wise(X0) | ~happy(X0))) [flattening 42]
46. ! [X0] : (((tall(X0) | strong(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [nnf transformation 8]
47. ! [X0] : ((tall(X0) | strong(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [flattening 46]
51. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X1] : (tall(X1) | generous(X1)) | ! [X0] : (~strong(X0) | ~tall(X0))) [nnf transformation 25]
52. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X2] : (tall(X2) | generous(X2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [rectify 51]
53. ? [X0] : (strong(X0) & tall(X0)) => (strong(sK1) & tall(sK1)) [choice axiom]
54. ? [X2] : (tall(X2) | generous(X2)) => (tall(sK2) | generous(sK2)) [choice axiom]
55. ((strong(sK1) & tall(sK1)) | ! [X1] : (~tall(X1) & ~generous(X1))) & ((tall(sK2) | generous(sK2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [skolemisation 52,54,53]
75. ~happy(X0) | ~tall(X0) [cnf transformation 28]
76. ~happy(X0) | wise(X0) [cnf transformation 28]
82. ~patient(X0) | happy(X0) | curious(X0) [cnf transformation 43]
84. ~patient(X0) | ~wise(X0) | curious(X0) [cnf transformation 43]
95. happy(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 47]
100. patient(X0) | generous(X0) [cnf transformation 34]
111. tall(sK1) | ~generous(X1) [cnf transformation 55]
113. strong(sK1) | ~generous(X1) [cnf transformation 55]
136. ~curious(paul) [cnf transformation 24]
188. ~strong(X0) | ~tall(X0) [subsumption resolution 95,75]
194. 13 <=> strong(sK1) [avatar definition]
196. strong(sK1) <- (13) [avatar component clause 194]
199. 14 <=> ! [X1] : ~generous(X1) [avatar definition]
200. ~generous(X1) <- (14) [avatar component clause 199]
201. 14 | 13 [avatar split clause 113,194,199]
203. 15 <=> tall(sK1) [avatar definition]
207. 14 | 15 [avatar split clause 111,203,199]
265. ~tall(sK1) <- (13) [resolution 188,196]
269. ~15 | ~13 [avatar split clause 265,194,203]
295. happy(X0) | curious(X0) | generous(X0) [resolution 82,100]
298. happy(X0) | curious(X0) <- (14) [subsumption resolution 295,200]
300. ~wise(X0) | curious(X0) | generous(X0) [resolution 84,100]
303. ~wise(X0) | curious(X0) <- (14) [subsumption resolution 300,200]
335. curious(X1) | wise(X1) <- (14) [resolution 298,76]
337. curious(X1) <- (14) [subsumption resolution 335,303]
340. $false <- (14) [resolution 337,136]
343. ~14 [avatar contradiction clause 340]
345. $false [avatar sat refutation 201,207,269,343]
% SZS output end Proof for 6251008488639189198487271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or old is either happy or rich.
Everyone who is both brave and not strong is not calm or curious and vice versa.
If lucy is humble or generous then someone is not generous or creative.
If john is both not rich and kind then someone is both strong and not kind and vice versa.
If someone is not calm then paul is either wise or not rich and vice versa.
Everyone who is not patient or old is either patient or strong and vice versa.
If someone is either not old or generous then alice is curious and vice versa.
Everyone who is not rich or generous is either kind or not kind.
Everyone who is either humble or not brave is not brave or patient and vice versa.
If lucy is old or happy then someone is rich and vice versa.
If mary is not generous then lucy is either not rich or kind and vice versa.
Everyone who is either not quiet or calm is not wise.
Everyone who is either generous or not strong is either not kind or kind and vice versa.
If someone is either happy or not patient then someone is tall or funny.
Everyone who is not wise or not curious is generous and vice versa.
Everyone who is both not humble and not creative is both tall and not brave and vice versa.
Mary is either not wise or not generous.
Someone is strong or not wise.
Mary is either quiet or patient.
Someone is either not creative or old.
Someone is calm.
Someone is either not funny or not old.
Someone is not generous. | Mary is not calm. | contradiction | (![X]:((~old(X)<~>old(X))=>(happy(X)<~>rich(X))))&
(![X]:((brave(X)&~strong(X))<=>(~calm(X)|curious(X))))&
(((humble(lucy)|generous(lucy)))=>(?[X]:((~generous(X)|creative(X)))))&
(((~rich(john)&kind(john)))<=>(?[X]:((strong(X)&~kind(X)))))&
((?[X]:(~calm(X)))<=>((wise(paul)<~>~rich(paul))))&
(![X]:((~patient(X)|old(X))<=>(patient(X)<~>strong(X))))&
((?[X]:((~old(X)<~>generous(X))))<=>(curious(alice)))&
(![X]:((~rich(X)|generous(X))=>(kind(X)<~>~kind(X))))&
(![X]:((humble(X)<~>~brave(X))<=>(~brave(X)|patient(X))))&
(((old(lucy)|happy(lucy)))<=>(?[X]:(rich(X))))&
((~generous(mary))<=>((~rich(lucy)<~>kind(lucy))))&
(![X]:((~quiet(X)<~>calm(X))=>~wise(X)))&
(![X]:((generous(X)<~>~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((~wise(X)|~curious(X))<=>generous(X)))&
(![X]:((~humble(X)&~creative(X))<=>(tall(X)&~brave(X))))&
((~wise(mary)<~>~generous(mary)))&
(?[X]:((strong(X)|~wise(X))))&
((quiet(mary)<~>patient(mary)))&
(?[X]:((~creative(X)<~>old(X))))&
(?[X]:(calm(X)))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:(~generous(X))) | ~calm(mary) | [
"p1",
"p5",
"p11",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3892709342088274552663845
% SZS output start Proof for 3892709342088274552663845
2. ! [X0] : ((~strong(X0) & brave(X0)) <=> (curious(X0) | ~calm(X0))) [input p1]
6. ! [X0] : ((old(X0) | ~patient(X0)) <=> (patient(X0) <~> strong(X0))) [input p5]
12. ! [X0] : ((~quiet(X0) <~> calm(X0)) => ~wise(X0)) [input p11]
13. ! [X0] : ((generous(X0) <~> ~strong(X0)) <=> (~kind(X0) <~> kind(X0))) [input p12]
15. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> generous(X0)) [input p14]
19. quiet(mary) <~> patient(mary) [input p18]
24. ~calm(mary) [input hypothesis]
29. ! [X0] : (~wise(X0) | (~quiet(X0) <=> calm(X0))) [ennf transformation 12]
32. ! [X0] : (((~strong(X0) & brave(X0)) | (~curious(X0) & calm(X0))) & ((curious(X0) | ~calm(X0)) | (strong(X0) | ~brave(X0)))) [nnf transformation 2]
33. ! [X0] : (((~strong(X0) & brave(X0)) | (~curious(X0) & calm(X0))) & (curious(X0) | ~calm(X0) | strong(X0) | ~brave(X0))) [flattening 32]
45. ! [X0] : (((old(X0) | ~patient(X0)) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (~old(X0) & patient(X0)))) [nnf transformation 6]
46. ! [X0] : ((old(X0) | ~patient(X0) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (~old(X0) & patient(X0)))) [flattening 45]
60. ! [X0] : (~wise(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) [nnf transformation 29]
61. ! [X0] : ((((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0))))) [nnf transformation 13]
66. ! [X0] : (((~curious(X0) | ~wise(X0)) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [nnf transformation 15]
67. ! [X0] : ((~curious(X0) | ~wise(X0) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [flattening 66]
73. (~patient(mary) | ~quiet(mary)) & (patient(mary) | quiet(mary)) [nnf transformation 19]
91. ~strong(X0) | calm(X0) [cnf transformation 33]
103. strong(X0) | patient(X0) | patient(X0) [cnf transformation 46]
130. ~wise(X0) | calm(X0) | quiet(X0) [cnf transformation 60]
138. strong(X0) | ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 61]
139. strong(X0) | ~generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 61]
142. wise(X0) | generous(X0) [cnf transformation 67]
153. ~patient(mary) | ~quiet(mary) [cnf transformation 73]
160. ~calm(mary) [cnf transformation 24]
163. strong(X0) | ~generous(X0) | kind(X0) [duplicate literal removal 138]
164. strong(X0) | ~generous(X0) | ~kind(X0) [duplicate literal removal 139]
167. patient(X0) | strong(X0) [duplicate literal removal 103]
285. 25 <=> generous(mary) [avatar definition]
286. generous(mary) <- (25) [avatar component clause 285]
292. ~generous(X0) | strong(X0) [subsumption resolution 163,164]
311. 30 <=> wise(mary) [avatar definition]
312. wise(mary) <- (30) [avatar component clause 311]
313. ~wise(mary) <- (~30) [avatar component clause 311]
325. 33 <=> quiet(mary) [avatar definition]
327. ~quiet(mary) <- (~33) [avatar component clause 325]
329. 34 <=> patient(mary) [avatar definition]
331. ~patient(mary) <- (~34) [avatar component clause 329]
332. ~33 | ~34 [avatar split clause 153,329,325]
364. strong(mary) <- (~34) [resolution 167,331]
369. generous(mary) <- (~30) [resolution 313,142]
380. calm(mary) <- (~34) [resolution 364,91]
381. $false <- (~34) [subsumption resolution 380,160]
382. 34 [avatar contradiction clause 381]
390. strong(mary) <- (25) [resolution 292,286]
398. calm(mary) <- (25) [resolution 390,91]
399. $false <- (25) [subsumption resolution 398,160]
400. ~25 [avatar contradiction clause 399]
401. 25 | 30 [avatar split clause 369,311,285]
423. calm(mary) | quiet(mary) <- (30) [resolution 130,312]
424. quiet(mary) <- (30) [subsumption resolution 423,160]
425. $false <- (30, ~33) [subsumption resolution 424,327]
426. ~30 | 33 [avatar contradiction clause 425]
427. $false [avatar sat refutation 332,382,400,401,426]
% SZS output end Proof for 3892709342088274552663845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and patient is either not strong or rich and vice versa. Everyone who is both not curious and not calm is either creative or not humble and vice versa. If someone is wise or rich then alice is tall or creative and vice versa. If alice is not humble or not creative then someone is either quiet or not strong. Everyone who is happy is not humble or not old and vice versa. Everyone who is either curious or tall is calm or happy. If fred is not generous then alice is brave or not humble and vice versa. Everyone who is not humble is both not creative and not curious. If someone is both tall and brave then someone is generous or wise. Everyone who is either not humble or kind is both kind and not humble and vice versa. If someone is not curious or happy then someone is kind and vice versa. If someone is not calm then someone is not brave or kind and vice versa. Everyone who is rich or wise is either not rich or not tall. If john is not quiet or funny then someone is curious or not old. Everyone who is both not wise and happy is both tall and not rich and vice versa. Someone is either patient or happy. Paul is not quiet or strong. Lucy is both humble and not happy. Fred is both not strong and not creative. Someone is both strong and not happy. Someone is calm or creative. Someone is either quiet or not strong. | Lucy is rich. | contradiction | (![X]:((~creative(X)&patient(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((~curious(X)&~calm(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((wise(X)|rich(X))))<=>((tall(alice)|creative(alice))))&
(((~humble(alice)|~creative(alice)))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:(happy(X)<=>(~humble(X)|~old(X))))&
(![X]:((curious(X)<~>tall(X))=>(calm(X)|happy(X))))&
((~generous(fred))<=>((brave(alice)|~humble(alice))))&
(![X]:(~humble(X)=>(~creative(X)&~curious(X))))&
((?[X]:((tall(X)&brave(X))))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&~humble(X))))&
((?[X]:((~curious(X)|happy(X))))<=>(?[X]:(kind(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((rich(X)|wise(X))=>(~rich(X)<~>~tall(X))))&
(((~quiet(john)|funny(john)))=>(?[X]:((curious(X)|~old(X)))))&
(![X]:((~wise(X)&happy(X))<=>(tall(X)&~rich(X))))&
(?[X]:((patient(X)<~>happy(X))))&
((~quiet(paul)|strong(paul)))&
((humble(lucy)&~happy(lucy)))&
((~strong(fred)&~creative(fred)))&
(?[X]:((strong(X)&~happy(X))))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((quiet(X)<~>~strong(X)))) | rich(lucy) | [
"p1",
"p2",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5692713642044064933398398
% SZS output start Proof for 5692713642044064933398398
2. ! [X0] : ((~calm(X0) & ~curious(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p1]
3. ? [X0] : (rich(X0) | wise(X0)) <=> (creative(alice) | tall(alice)) [input p2]
10. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~humble(X0) & kind(X0))) [input p9]
11. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X0] : kind(X0) [input p10]
13. ! [X0] : ((wise(X0) | rich(X0)) => (~rich(X0) <~> ~tall(X0))) [input p12]
15. ! [X0] : ((happy(X0) & ~wise(X0)) <=> (~rich(X0) & tall(X0))) [input p14]
23. rich(lucy) [input hypothesis]
25. ? [X0] : (happy(X0) | ~curious(X0)) <=> ? [X1] : kind(X1) [rectify 11]
33. ! [X0] : ((~rich(X0) <~> ~tall(X0)) | (~wise(X0) & ~rich(X0))) [ennf transformation 13]
37. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (calm(X0) | curious(X0)))) [nnf transformation 2]
38. ! [X0] : (((~calm(X0) & ~curious(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | calm(X0) | curious(X0))) [flattening 37]
39. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & ((creative(alice) | tall(alice)) | ! [X0] : (~rich(X0) & ~wise(X0))) [nnf transformation 3]
40. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X0] : (~rich(X0) & ~wise(X0))) [flattening 39]
41. (? [X0] : (rich(X0) | wise(X0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X1] : (~rich(X1) & ~wise(X1))) [rectify 40]
42. ? [X0] : (rich(X0) | wise(X0)) => (rich(sK0) | wise(sK0)) [choice axiom]
43. ((rich(sK0) | wise(sK0)) | (~creative(alice) & ~tall(alice))) & (creative(alice) | tall(alice) | ! [X1] : (~rich(X1) & ~wise(X1))) [skolemisation 41,42]
55. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (humble(X0) | ~kind(X0))) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 10]
56. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | humble(X0) | ~kind(X0)) & ((~humble(X0) & kind(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [flattening 55]
57. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (~happy(X0) & curious(X0))) [nnf transformation 25]
58. (? [X0] : (happy(X0) | ~curious(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (~happy(X3) & curious(X3))) [rectify 57]
59. ? [X0] : (happy(X0) | ~curious(X0)) => (happy(sK3) | ~curious(sK3)) [choice axiom]
60. ? [X2] : kind(X2) => kind(sK4) [choice axiom]
61. ((happy(sK3) | ~curious(sK3)) | ! [X1] : ~kind(X1)) & (kind(sK4) | ! [X3] : (~happy(X3) & curious(X3))) [skolemisation 58,60,59]
67. ! [X0] : (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~wise(X0) & ~rich(X0))) [nnf transformation 33]
70. ! [X0] : (((happy(X0) & ~wise(X0)) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | (~happy(X0) | wise(X0)))) [nnf transformation 15]
71. ! [X0] : (((happy(X0) & ~wise(X0)) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | ~happy(X0) | wise(X0))) [flattening 70]
90. ~humble(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 38]
95. creative(alice) | tall(alice) | ~rich(X1) [cnf transformation 43]
113. kind(X0) | kind(X0) | humble(X0) [cnf transformation 56]
116. ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 56]
118. ~kind(X0) | humble(X0) | humble(X0) | ~kind(X0) [cnf transformation 56]
119. kind(sK4) | curious(X3) [cnf transformation 61]
120. kind(sK4) | ~happy(X3) [cnf transformation 61]
125. ~tall(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 67]
133. happy(X0) | rich(X0) | ~tall(X0) [cnf transformation 71]
146. rich(lucy) [cnf transformation 23]
147. ~tall(X0) | ~rich(X0) [duplicate literal removal 125]
148. kind(X0) | humble(X0) [duplicate literal removal 113]
149. ~humble(X0) | ~kind(X0) [duplicate literal removal 116]
150. ~kind(X0) | humble(X0) [duplicate literal removal 118]
152. 1 <=> creative(alice) [avatar definition]
153. creative(alice) <- (1) [avatar component clause 152]
165. 4 <=> tall(alice) [avatar definition]
166. tall(alice) <- (4) [avatar component clause 165]
170. 5 <=> ! [X1] : ~rich(X1) [avatar definition]
171. ~rich(X1) <- (5) [avatar component clause 170]
172. 5 | 4 | 1 [avatar split clause 95,152,165,170]
216. ~kind(X0) [subsumption resolution 149,150]
217. humble(X0) [subsumption resolution 148,216]
218. ~happy(X3) [subsumption resolution 120,216]
219. curious(X3) [subsumption resolution 119,216]
237. rich(X0) | ~tall(X0) [subsumption resolution 133,218]
238. ~tall(X0) [subsumption resolution 237,147]
270. $false <- (4) [subsumption resolution 166,238]
271. ~4 [avatar contradiction clause 270]
272. $false <- (5) [resolution 171,146]
273. ~5 [avatar contradiction clause 272]
308. ~curious(X0) | ~creative(X0) [resolution 90,217]
309. ~creative(X0) [subsumption resolution 308,219]
310. $false <- (1) [resolution 309,153]
311. ~1 [avatar contradiction clause 310]
312. $false [avatar sat refutation 172,271,273,311]
% SZS output end Proof for 5692713642044064933398398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not tall then lucy is not strong and vice versa. If someone is not generous or humble then someone is both happy and not rich and vice versa. Everyone who is not old is either not funny or generous. Everyone who is happy is both not old and not patient and vice versa. Everyone who is both not creative and old is either not patient or not old and vice versa. Everyone who is either tall or not funny is either calm or old. Everyone who is not curious or wise is both generous and not creative. Everyone who is happy is not wise or happy. If mary is both not old and not generous then fred is not strong and vice versa. If someone is generous or humble then john is not patient or calm and vice versa. Everyone who is not rich or creative is not generous and vice versa. Everyone who is both not patient and not curious is not rich. Everyone who is either not curious or generous is curious or brave and vice versa. Everyone who is not creative or not rich is either not rich or not patient. Everyone who is either rich or happy is not calm or brave and vice versa. If someone is both calm and not generous then paul is calm and vice versa. Mary is either not brave or not tall. Someone is either humble or not funny. John is either tall or not creative. Someone is both not wise and kind. Someone is either tall or not patient. Someone is either not wise or happy. Susan is not tall or patient. | Lucy is not curious. | contradiction | ((~tall(paul))<=>(~strong(lucy)))&
((?[X]:((~generous(X)|humble(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:(~old(X)=>(~funny(X)<~>generous(X))))&
(![X]:(happy(X)<=>(~old(X)&~patient(X))))&
(![X]:((~creative(X)&old(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((tall(X)<~>~funny(X))=>(calm(X)<~>old(X))))&
(![X]:((~curious(X)|wise(X))=>(generous(X)&~creative(X))))&
(![X]:(happy(X)=>(~wise(X)|happy(X))))&
(((~old(mary)&~generous(mary)))<=>(~strong(fred)))&
((?[X]:((generous(X)|humble(X))))<=>((~patient(john)|calm(john))))&
(![X]:((~rich(X)|creative(X))<=>~generous(X)))&
(![X]:((~patient(X)&~curious(X))=>~rich(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(curious(X)|brave(X))))&
(![X]:((~creative(X)|~rich(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)<~>happy(X))<=>(~calm(X)|brave(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(calm(paul)))&
((~brave(mary)<~>~tall(mary)))&
(?[X]:((humble(X)<~>~funny(X))))&
((tall(john)<~>~creative(john)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>happy(X))))&
((~tall(susan)|patient(susan))) | ~curious(lucy) | [
"p4",
"p6",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8375094573608920272589119
% SZS output start Proof for 8375094573608920272589119
5. ! [X0] : ((old(X0) & ~creative(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((wise(X0) | ~curious(X0)) => (~creative(X0) & generous(X0))) [input p6]
11. ! [X0] : ((creative(X0) | ~rich(X0)) <=> ~generous(X0)) [input p10]
12. ! [X0] : ((~curious(X0) & ~patient(X0)) => ~rich(X0)) [input p11]
13. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> (brave(X0) | curious(X0))) [input p12]
24. ~curious(lucy) [input hypothesis]
29. ! [X0] : ((~creative(X0) & generous(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 7]
32. ! [X0] : (~rich(X0) | (curious(X0) | patient(X0))) [ennf transformation 12]
33. ! [X0] : (~rich(X0) | curious(X0) | patient(X0)) [flattening 32]
44. ! [X0] : (((old(X0) & ~creative(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~old(X0) | creative(X0)))) [nnf transformation 5]
45. ! [X0] : (((old(X0) & ~creative(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ~old(X0) | creative(X0))) [flattening 44]
54. ! [X0] : (((creative(X0) | ~rich(X0)) | generous(X0)) & (~generous(X0) | (~creative(X0) & rich(X0)))) [nnf transformation 11]
55. ! [X0] : ((creative(X0) | ~rich(X0) | generous(X0)) & (~generous(X0) | (~creative(X0) & rich(X0)))) [flattening 54]
56. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [nnf transformation 13]
57. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [flattening 56]
90. ~old(X0) | ~patient(X0) | ~old(X0) | creative(X0) [cnf transformation 45]
95. old(X0) | ~patient(X0) | old(X0) [cnf transformation 45]
100. curious(X0) | generous(X0) [cnf transformation 29]
102. ~creative(X0) | curious(X0) [cnf transformation 29]
112. ~generous(X0) | rich(X0) [cnf transformation 55]
115. ~rich(X0) | curious(X0) | patient(X0) [cnf transformation 33]
118. generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
147. ~curious(lucy) [cnf transformation 24]
150. generous(X0) | ~curious(X0) [duplicate literal removal 118]
151. ~old(X0) | ~patient(X0) | creative(X0) [duplicate literal removal 90]
152. ~patient(X0) | old(X0) [duplicate literal removal 95]
184. 8 <=> ! [X3] : generous(X3) [avatar definition]
185. generous(X3) <- (8) [avatar component clause 184]
193. ~patient(X0) | creative(X0) [subsumption resolution 151,152]
234. generous(X0) [subsumption resolution 150,100]
235. 8 [avatar split clause 234,184]
322. rich(X0) <- (8) [resolution 112,185]
380. curious(X0) | patient(X0) <- (8) [resolution 115,322]
398. patient(lucy) <- (8) [resolution 380,147]
400. creative(lucy) <- (8) [resolution 398,193]
461. curious(lucy) <- (8) [resolution 400,102]
464. $false <- (8) [subsumption resolution 461,147]
465. ~8 [avatar contradiction clause 464]
466. $false [avatar sat refutation 235,465]
% SZS output end Proof for 8375094573608920272589119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not rich is not funny or not curious. If alice is quiet or generous then someone is not generous or not rich and vice versa. Everyone who is both not brave and curious is kind and vice versa. Everyone who is both not curious and patient is either funny or rich. Everyone who is both happy and not patient is either happy or kind. Everyone who is not patient or not humble is patient and vice versa. Everyone who is wise or not strong is not patient and vice versa. Everyone who is happy or not wise is tall and vice versa. Everyone who is either not brave or not creative is both rich and not calm and vice versa. Everyone who is both quiet and rich is not calm or kind. If someone is either not kind or not rich then someone is either not brave or humble and vice versa. Everyone who is both not curious and strong is old or generous. Everyone who is rich or wise is either not humble or not funny. Everyone who is tall or not tall is either not creative or not patient and vice versa. If fred is happy or not curious then alice is either kind or not old. If susan is both curious and not funny then fred is both generous and wise and vice versa. Fred is both patient and calm. Fred is curious or humble. Fred is not old or not tall. Fred is both not old and funny. Someone is curious or not calm. Alice is not wise. Alice is either patient or not curious. | Fred is not creative. | entailment | (![X]:(~rich(X)=>(~funny(X)|~curious(X))))&
(((quiet(alice)|generous(alice)))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~brave(X)&curious(X))<=>kind(X)))&
(![X]:((~curious(X)&patient(X))=>(funny(X)<~>rich(X))))&
(![X]:((happy(X)&~patient(X))=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)|~humble(X))<=>patient(X)))&
(![X]:((wise(X)|~strong(X))<=>~patient(X)))&
(![X]:((happy(X)|~wise(X))<=>tall(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>(rich(X)&~calm(X))))&
(![X]:((quiet(X)&rich(X))=>(~calm(X)|kind(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>(?[X]:((~brave(X)<~>humble(X)))))&
(![X]:((~curious(X)&strong(X))=>(old(X)|generous(X))))&
(![X]:((rich(X)|wise(X))=>(~humble(X)<~>~funny(X))))&
(![X]:((tall(X)|~tall(X))<=>(~creative(X)<~>~patient(X))))&
(((happy(fred)|~curious(fred)))=>((kind(alice)<~>~old(alice))))&
(((curious(susan)&~funny(susan)))<=>((generous(fred)&wise(fred))))&
((patient(fred)&calm(fred)))&
((curious(fred)|humble(fred)))&
((~old(fred)|~tall(fred)))&
((~old(fred)&funny(fred)))&
(?[X]:((curious(X)|~calm(X))))&
(~wise(alice))&
((patient(alice)<~>~curious(alice))) | ~creative(fred) | [
"p5",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8197271312203945645409929
% SZS output start Proof for 8197271312203945645409929
6. ! [X0] : ((~humble(X0) | ~patient(X0)) <=> patient(X0)) [input p5]
7. ! [X0] : ((~strong(X0) | wise(X0)) <=> ~patient(X0)) [input p6]
8. ! [X0] : ((~wise(X0) | happy(X0)) <=> tall(X0)) [input p7]
14. ! [X0] : ((~tall(X0) | tall(X0)) <=> (~creative(X0) <~> ~patient(X0))) [input p13]
24. creative(fred) [input hypothesis]
47. ! [X0] : (((~humble(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [nnf transformation 6]
48. ! [X0] : ((~humble(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [flattening 47]
49. ! [X0] : (((~strong(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [nnf transformation 7]
50. ! [X0] : ((~strong(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [flattening 49]
51. ! [X0] : (((~wise(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (wise(X0) & ~happy(X0)))) [nnf transformation 8]
52. ! [X0] : ((~wise(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (wise(X0) & ~happy(X0)))) [flattening 51]
61. ! [X0] : (((~tall(X0) | tall(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (tall(X0) & ~tall(X0)))) [nnf transformation 14]
62. ! [X0] : ((~tall(X0) | tall(X0) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (tall(X0) & ~tall(X0)))) [flattening 61]
81. patient(X0) | patient(X0) [cnf transformation 48]
84. ~patient(X0) | ~wise(X0) [cnf transformation 50]
88. tall(X0) | wise(X0) [cnf transformation 52]
110. ~patient(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 62]
134. creative(fred) [cnf transformation 24]
135. patient(X0) [duplicate literal removal 81]
165. ~wise(X0) [subsumption resolution 84,135]
166. tall(X0) [subsumption resolution 88,165]
204. ~creative(X0) | ~tall(X0) [subsumption resolution 110,135]
205. ~creative(X0) [subsumption resolution 204,166]
257. $false [subsumption resolution 134,205]
% SZS output end Proof for 8197271312203945645409929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is not curious and vice versa.
Everyone who is both funny and strong is either patient or generous and vice versa.
Everyone who is both strong and not kind is either brave or kind.
If paul is both not funny and kind then john is either strong or quiet.
If someone is either rich or generous then someone is rich and vice versa.
Everyone who is strong is both not strong and not generous.
Everyone who is either not tall or old is calm.
Everyone who is both rich and not patient is not funny.
Everyone who is both kind and not curious is not funny and vice versa.
Everyone who is patient is happy or not patient.
Everyone who is both not curious and creative is either creative or not patient and vice versa.
If alice is not curious or humble then paul is not quiet and vice versa.
Everyone who is not funny or curious is not wise or not kind.
Everyone who is both curious and not funny is either not quiet or creative.
If fred is not humble then someone is humble or not kind and vice versa.
Everyone who is not generous is both old and tall and vice versa.
Someone is generous or not wise.
Mary is rich.
Someone is humble.
John is curious or not old.
Mary is not rich or rich.
Someone is not humble.
Alice is funny or not strong. | Mary is patient. | entailment | (![X]:(~happy(X)<=>~curious(X)))&
(![X]:((funny(X)&strong(X))<=>(patient(X)<~>generous(X))))&
(![X]:((strong(X)&~kind(X))=>(brave(X)<~>kind(X))))&
(((~funny(paul)&kind(paul)))=>((strong(john)<~>quiet(john))))&
((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:(rich(X))))&
(![X]:(strong(X)=>(~strong(X)&~generous(X))))&
(![X]:((~tall(X)<~>old(X))=>calm(X)))&
(![X]:((rich(X)&~patient(X))=>~funny(X)))&
(![X]:((kind(X)&~curious(X))<=>~funny(X)))&
(![X]:(patient(X)=>(happy(X)|~patient(X))))&
(![X]:((~curious(X)&creative(X))<=>(creative(X)<~>~patient(X))))&
(((~curious(alice)|humble(alice)))<=>(~quiet(paul)))&
(![X]:((~funny(X)|curious(X))=>(~wise(X)|~kind(X))))&
(![X]:((curious(X)&~funny(X))=>(~quiet(X)<~>creative(X))))&
((~humble(fred))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:(~generous(X)<=>(old(X)&tall(X))))&
(?[X]:((generous(X)|~wise(X))))&
(rich(mary))&
(?[X]:(humble(X)))&
((curious(john)|~old(john)))&
((~rich(mary)|rich(mary)))&
(?[X]:(~humble(X)))&
((funny(alice)|~strong(alice))) | patient(mary) | [
"p7",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5540873475809128738771091
% SZS output start Proof for 5540873475809128738771091
8. ! [X0] : ((~patient(X0) & rich(X0)) => ~funny(X0)) [input p7]
9. ! [X0] : ((~curious(X0) & kind(X0)) <=> ~funny(X0)) [input p8]
11. ! [X0] : ((creative(X0) & ~curious(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p10]
18. rich(mary) [input p17]
24. ~patient(mary) [input hypothesis]
36. ! [X0] : (~funny(X0) | (patient(X0) | ~rich(X0))) [ennf transformation 8]
37. ! [X0] : (~funny(X0) | patient(X0) | ~rich(X0)) [flattening 36]
51. ! [X0] : (((~curious(X0) & kind(X0)) | funny(X0)) & (~funny(X0) | (curious(X0) | ~kind(X0)))) [nnf transformation 9]
52. ! [X0] : (((~curious(X0) & kind(X0)) | funny(X0)) & (~funny(X0) | curious(X0) | ~kind(X0))) [flattening 51]
53. ! [X0] : (((creative(X0) & ~curious(X0)) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (~creative(X0) | curious(X0)))) [nnf transformation 11]
54. ! [X0] : (((creative(X0) & ~curious(X0)) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | ~creative(X0) | curious(X0))) [flattening 53]
85. ~rich(X0) | patient(X0) | ~funny(X0) [cnf transformation 37]
88. ~curious(X0) | funny(X0) [cnf transformation 52]
91. patient(X0) | ~creative(X0) | ~creative(X0) | curious(X0) [cnf transformation 54]
95. creative(X0) | creative(X0) | patient(X0) [cnf transformation 54]
107. rich(mary) [cnf transformation 18]
113. ~patient(mary) [cnf transformation 24]
114. patient(X0) | ~creative(X0) | curious(X0) [duplicate literal removal 91]
115. creative(X0) | patient(X0) [duplicate literal removal 95]
162. patient(X0) | curious(X0) [subsumption resolution 114,115]
217. curious(mary) [resolution 162,113]
220. funny(mary) [resolution 217,88]
232. patient(mary) | ~funny(mary) [resolution 85,107]
235. ~funny(mary) [subsumption resolution 232,113]
236. $false [subsumption resolution 235,220]
% SZS output end Proof for 5540873475809128738771091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not generous then someone is both curious and rich.
If alice is wise then fred is either curious or brave.
If someone is quiet or curious then alice is either not funny or brave.
Everyone who is both tall and brave is both kind and strong and vice versa.
If someone is not brave then someone is brave or old.
Everyone who is not strong or not brave is either wise or happy.
Everyone who is not wise or old is not wise or generous and vice versa.
If mary is not humble then someone is quiet.
If susan is kind then paul is kind and vice versa.
Everyone who is both not curious and rich is both old and not old and vice versa.
Everyone who is not brave or not kind is not wise or not rich.
Everyone who is both wise and old is calm or rich and vice versa.
If someone is not kind or not tall then someone is old or brave and vice versa.
If mary is quiet then someone is both funny and wise and vice versa.
Everyone who is both not calm and kind is humble or not old.
If lucy is quiet or kind then mary is either humble or not strong.
Someone is not humble or generous.
Someone is both rich and kind.
Lucy is happy or strong.
Paul is old or not strong.
John is curious or old.
Mary is calm or funny.
Someone is not happy. | Alice is not curious. | neutral | ((?[X]:((kind(X)|~generous(X))))=>(?[X]:((curious(X)&rich(X)))))&
((wise(alice))=>((curious(fred)<~>brave(fred))))&
((?[X]:((quiet(X)|curious(X))))=>((~funny(alice)<~>brave(alice))))&
(![X]:((tall(X)&brave(X))<=>(kind(X)&strong(X))))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)|old(X)))))&
(![X]:((~strong(X)|~brave(X))=>(wise(X)<~>happy(X))))&
(![X]:((~wise(X)|old(X))<=>(~wise(X)|generous(X))))&
((~humble(mary))=>(?[X]:(quiet(X))))&
((kind(susan))<=>(kind(paul)))&
(![X]:((~curious(X)&rich(X))<=>(old(X)&~old(X))))&
(![X]:((~brave(X)|~kind(X))=>(~wise(X)|~rich(X))))&
(![X]:((wise(X)&old(X))<=>(calm(X)|rich(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>(?[X]:((old(X)|brave(X)))))&
((quiet(mary))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((~calm(X)&kind(X))=>(humble(X)|~old(X))))&
(((quiet(lucy)|kind(lucy)))=>((humble(mary)<~>~strong(mary))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:((rich(X)&kind(X))))&
((happy(lucy)|strong(lucy)))&
((old(paul)|~strong(paul)))&
((curious(john)|old(john)))&
((calm(mary)|funny(mary)))&
(?[X]:(~happy(X))) | ~curious(alice) | [] | null | 0 |
If paul is both not humble and patient then someone is either patient or not wise. If paul is either not kind or not curious then lucy is humble or not curious. Everyone who is both wise and not patient is not generous and vice versa. Everyone who is not old or happy is creative and vice versa. If someone is both not kind and wise then someone is both not happy and generous. Everyone who is not old or not funny is either not funny or not old. If someone is not brave or not curious then mary is calm and vice versa. If someone is not generous or creative then susan is both not humble and creative and vice versa. Everyone who is either quiet or not curious is patient or not funny and vice versa. If someone is curious or not brave then mary is either rich or not patient. If someone is either rich or wise then susan is funny or not old and vice versa. Everyone who is generous is both not happy and curious and vice versa. Everyone who is either patient or strong is not funny or not tall. Everyone who is either not kind or kind is both rich and quiet. If mary is humble then someone is not rich and vice versa. Everyone who is both not kind and funny is either generous or patient. Susan is not creative or tall. Someone is strong. Lucy is not brave or not strong. | Mary is rich. | entailment | (((~humble(paul)&patient(paul)))=>(?[X]:((patient(X)<~>~wise(X)))))&
(((~kind(paul)<~>~curious(paul)))=>((humble(lucy)|~curious(lucy))))&
(![X]:((wise(X)&~patient(X))<=>~generous(X)))&
(![X]:((~old(X)|happy(X))<=>creative(X)))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:((~old(X)|~funny(X))=>(~funny(X)<~>~old(X))))&
((?[X]:((~brave(X)|~curious(X))))<=>(calm(mary)))&
((?[X]:((~generous(X)|creative(X))))<=>((~humble(susan)&creative(susan))))&
(![X]:((quiet(X)<~>~curious(X))<=>(patient(X)|~funny(X))))&
((?[X]:((curious(X)|~brave(X))))=>((rich(mary)<~>~patient(mary))))&
((?[X]:((rich(X)<~>wise(X))))<=>((funny(susan)|~old(susan))))&
(![X]:(generous(X)<=>(~happy(X)&curious(X))))&
(![X]:((patient(X)<~>strong(X))=>(~funny(X)|~tall(X))))&
(![X]:((~kind(X)<~>kind(X))=>(rich(X)&quiet(X))))&
((humble(mary))<=>(?[X]:(~rich(X))))&
(![X]:((~kind(X)&funny(X))=>(generous(X)<~>patient(X))))&
((~creative(susan)|tall(susan)))&
(?[X]:(strong(X)))&
((~brave(lucy)|~strong(lucy))) | rich(mary) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3540448730065852491438228
% SZS output start Proof for 3540448730065852491438228
14. ! [X0] : ((~kind(X0) <~> kind(X0)) => (quiet(X0) & rich(X0))) [input p13]
20. ~rich(mary) [input hypothesis]
31. ! [X0] : ((quiet(X0) & rich(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 14]
66. ! [X0] : ((quiet(X0) & rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 31]
119. rich(X0) | kind(X0) | kind(X0) [cnf transformation 66]
120. rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 66]
130. ~rich(mary) [cnf transformation 20]
131. rich(X0) | kind(X0) [duplicate literal removal 119]
132. rich(X0) | ~kind(X0) [duplicate literal removal 120]
280. rich(X0) [subsumption resolution 131,132]
298. $false [subsumption resolution 130,280]
% SZS output end Proof for 3540448730065852491438228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not calm is either not tall or not happy and vice versa.
Everyone who is not kind or not funny is either wise or not funny and vice versa.
Everyone who is either quiet or not kind is quiet or kind.
If alice is not patient then mary is either creative or not brave.
Everyone who is both tall and strong is both brave and generous and vice versa.
Everyone who is funny or not wise is both tall and rich and vice versa.
Everyone who is happy or not patient is patient.
Everyone who is tall is both strong and humble and vice versa.
If someone is either happy or brave then someone is not patient and vice versa.
If someone is not kind then someone is brave or not creative.
If lucy is brave or old then someone is either not strong or patient and vice versa.
If alice is both not brave and humble then alice is either quiet or calm.
If someone is either happy or not creative then someone is either not humble or patient.
If paul is curious then susan is either not humble or old and vice versa.
Everyone who is both rich and not creative is either not happy or curious.
Everyone who is rich is not curious or creative.
Someone is not rich or calm.
Lucy is funny.
Someone is either not old or brave.
Alice is either tall or kind.
Mary is brave or not quiet.
Someone is tall. | Lucy is not creative. | contradiction | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(quiet(X)|kind(X))))&
((~patient(alice))=>((creative(mary)<~>~brave(mary))))&
(![X]:((tall(X)&strong(X))<=>(brave(X)&generous(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)&rich(X))))&
(![X]:((happy(X)|~patient(X))=>patient(X)))&
(![X]:(tall(X)<=>(strong(X)&humble(X))))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((brave(X)|~creative(X)))))&
(((brave(lucy)|old(lucy)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~brave(alice)&humble(alice)))=>((quiet(alice)<~>calm(alice))))&
((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>patient(X)))))&
((curious(paul))<=>((~humble(susan)<~>old(susan))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)<~>curious(X))))&
(![X]:(rich(X)=>(~curious(X)|creative(X))))&
(?[X]:((~rich(X)|calm(X))))&
(funny(lucy))&
(?[X]:((~old(X)<~>brave(X))))&
((tall(alice)<~>kind(alice)))&
((brave(mary)|~quiet(mary)))&
(?[X]:(tall(X))) | ~creative(lucy) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4354676050130432775470676
% SZS output start Proof for 4354676050130432775470676
5. ! [X0] : ((strong(X0) & tall(X0)) <=> (generous(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | funny(X0)) <=> (rich(X0) & tall(X0))) [input p5]
7. ! [X0] : ((~patient(X0) | happy(X0)) => patient(X0)) [input p6]
8. ! [X0] : (tall(X0) <=> (humble(X0) & strong(X0))) [input p7]
9. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X0] : ~patient(X0) [input p8]
15. ! [X0] : ((~creative(X0) & rich(X0)) => (~happy(X0) <~> curious(X0))) [input p14]
16. ! [X0] : (rich(X0) => (creative(X0) | ~curious(X0))) [input p15]
18. funny(lucy) [input p17]
23. ~creative(lucy) [input hypothesis]
24. ? [X0] : (happy(X0) <~> brave(X0)) <=> ? [X1] : ~patient(X1) [rectify 9]
30. ! [X0] : (patient(X0) | (patient(X0) & ~happy(X0))) [ennf transformation 7]
35. ! [X0] : ((~happy(X0) <~> curious(X0)) | (creative(X0) | ~rich(X0))) [ennf transformation 15]
36. ! [X0] : ((~happy(X0) <~> curious(X0)) | creative(X0) | ~rich(X0)) [flattening 35]
37. ! [X0] : ((creative(X0) | ~curious(X0)) | ~rich(X0)) [ennf transformation 16]
38. ! [X0] : (creative(X0) | ~curious(X0) | ~rich(X0)) [flattening 37]
45. ! [X0] : (((strong(X0) & tall(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((strong(X0) & tall(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~strong(X0) | ~tall(X0))) [flattening 45]
47. ! [X0] : (((~wise(X0) | funny(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [nnf transformation 6]
48. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (wise(X0) & ~funny(X0)))) [flattening 47]
49. ! [X0] : ((tall(X0) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | ~tall(X0))) [nnf transformation 8]
50. ! [X0] : ((tall(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | ~tall(X0))) [flattening 49]
51. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) [nnf transformation 24]
52. (? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [rectify 51]
53. ? [X0] : ((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) => ((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) [choice axiom]
54. ? [X2] : ~patient(X2) => ~patient(sK1) [choice axiom]
55. (((~brave(sK0) | ~happy(sK0)) & (brave(sK0) | happy(sK0))) | ! [X1] : patient(X1)) & (~patient(sK1) | ! [X3] : ((happy(X3) | ~brave(X3)) & (brave(X3) | ~happy(X3)))) [skolemisation 52,54,53]
70. ! [X0] : (((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | creative(X0) | ~rich(X0)) [nnf transformation 36]
95. ~strong(X0) | brave(X0) | ~tall(X0) [cnf transformation 46]
99. ~funny(X0) | tall(X0) [cnf transformation 48]
101. ~funny(X0) | rich(X0) [cnf transformation 48]
105. patient(X0) | patient(X0) [cnf transformation 30]
106. ~tall(X0) | strong(X0) [cnf transformation 50]
110. ~patient(sK1) | happy(X3) | ~brave(X3) [cnf transformation 55]
130. ~rich(X0) | ~happy(X0) | creative(X0) | curious(X0) [cnf transformation 70]
132. ~curious(X0) | creative(X0) | ~rich(X0) [cnf transformation 38]
134. funny(lucy) [cnf transformation 18]
141. ~creative(lucy) [cnf transformation 23]
142. patient(X0) [duplicate literal removal 105]
160. ~brave(X3) | happy(X3) [subsumption resolution 110,142]
179. 8 <=> brave(lucy) [avatar definition]
181. brave(lucy) <- (8) [avatar component clause 179]
277. tall(lucy) [resolution 99,134]
278. rich(lucy) [resolution 101,134]
282. strong(lucy) [resolution 106,277]
329. brave(lucy) | ~tall(lucy) [resolution 95,282]
337. brave(lucy) [subsumption resolution 329,277]
338. 8 [avatar split clause 337,179]
339. happy(lucy) <- (8) [resolution 181,160]
392. ~happy(lucy) | creative(lucy) | curious(lucy) [resolution 130,278]
394. creative(lucy) | curious(lucy) <- (8) [subsumption resolution 392,339]
395. curious(lucy) <- (8) [subsumption resolution 394,141]
441. creative(lucy) | ~rich(lucy) <- (8) [resolution 395,132]
442. ~rich(lucy) <- (8) [subsumption resolution 441,141]
443. $false <- (8) [subsumption resolution 442,278]
444. ~8 [avatar contradiction clause 443]
445. $false [avatar sat refutation 338,444]
% SZS output end Proof for 4354676050130432775470676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either wise or not funny then mary is not creative and vice versa.
Everyone who is either calm or not rich is not old.
If someone is both not funny and not patient then someone is not kind or tall.
If someone is either funny or wise then someone is either not kind or not strong.
Everyone who is curious is not funny or tall and vice versa.
Everyone who is curious or not calm is both wise and creative.
If alice is not generous then someone is not humble or not strong and vice versa.
Everyone who is either old or patient is both not humble and happy.
Everyone who is not generous or funny is both curious and not tall and vice versa.
Everyone who is not creative or not wise is not rich or not kind and vice versa.
If paul is either brave or not wise then someone is both not rich and tall and vice versa.
If someone is either not brave or calm then someone is patient or humble and vice versa.
Everyone who is both not strong and curious is either happy or not creative.
Everyone who is creative or quiet is either not calm or quiet.
Everyone who is not calm or not old is wise or not creative.
Everyone who is generous or quiet is not quiet or calm.
Someone is either not calm or strong.
Someone is either tall or funny.
Lucy is quiet.
Someone is both patient and creative.
Alice is either not curious or old.
Someone is either not humble or not brave.
Someone is both creative and not old.
Someone is not funny or not creative. | Lucy is wise. | entailment | (((wise(john)<~>~funny(john)))<=>(~creative(mary)))&
(![X]:((calm(X)<~>~rich(X))=>~old(X)))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((funny(X)<~>wise(X))))=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:(curious(X)<=>(~funny(X)|tall(X))))&
(![X]:((curious(X)|~calm(X))=>(wise(X)&creative(X))))&
((~generous(alice))<=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((old(X)<~>patient(X))=>(~humble(X)&happy(X))))&
(![X]:((~generous(X)|funny(X))<=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)|~wise(X))<=>(~rich(X)|~kind(X))))&
(((brave(paul)<~>~wise(paul)))<=>(?[X]:((~rich(X)&tall(X)))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((~strong(X)&curious(X))=>(happy(X)<~>~creative(X))))&
(![X]:((creative(X)|quiet(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)|~creative(X))))&
(![X]:((generous(X)|quiet(X))=>(~quiet(X)|calm(X))))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(quiet(lucy))&
(?[X]:((patient(X)&creative(X))))&
((~curious(alice)<~>old(alice)))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((~funny(X)|~creative(X)))) | wise(lucy) | [
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6619642715354458844281364
% SZS output start Proof for 6619642715354458844281364
5. ! [X0] : (curious(X0) <=> (tall(X0) | ~funny(X0))) [input p4]
6. ! [X0] : ((~calm(X0) | curious(X0)) => (creative(X0) & wise(X0))) [input p5]
9. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~tall(X0) & curious(X0))) [input p8]
25. ~wise(lucy) [input hypothesis]
32. ! [X0] : ((creative(X0) & wise(X0)) | (calm(X0) & ~curious(X0))) [ennf transformation 6]
50. ! [X0] : ((curious(X0) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ~curious(X0))) [nnf transformation 5]
51. ! [X0] : ((curious(X0) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~curious(X0))) [flattening 50]
57. ! [X0] : (((funny(X0) | ~generous(X0)) | (tall(X0) | ~curious(X0))) & ((~tall(X0) & curious(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 9]
58. ! [X0] : ((funny(X0) | ~generous(X0) | tall(X0) | ~curious(X0)) & ((~tall(X0) & curious(X0)) | (~funny(X0) & generous(X0)))) [flattening 57]
100. curious(X0) | funny(X0) [cnf transformation 51]
102. ~curious(X0) | wise(X0) [cnf transformation 32]
114. curious(X0) | ~funny(X0) [cnf transformation 58]
158. ~wise(lucy) [cnf transformation 25]
229. curious(X0) [subsumption resolution 114,100]
331. wise(X1) [resolution 102,229]
332. $false [resolution 331,158]
% SZS output end Proof for 6619642715354458844281364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall or calm then john is both brave and kind.
Everyone who is not brave or not patient is funny or quiet and vice versa.
Everyone who is old or not happy is creative or calm.
If someone is either not brave or quiet then mary is both curious and humble and vice versa.
Everyone who is either calm or kind is not generous or not kind and vice versa.
Everyone who is not calm or happy is either strong or quiet and vice versa.
Everyone who is either tall or strong is strong or not brave and vice versa.
Everyone who is patient is either not brave or not strong and vice versa.
Everyone who is both not calm and calm is funny and vice versa.
Everyone who is old is both not funny and patient and vice versa.
If fred is both not creative and calm then mary is kind and vice versa.
If someone is not old or not strong then lucy is old.
Everyone who is both not creative and generous is strong.
If susan is not humble then someone is not wise or not humble and vice versa.
If someone is strong or brave then john is strong or not patient and vice versa.
If paul is not strong or not wise then someone is patient.
Mary is both not brave and wise.
Someone is either not funny or not curious.
Fred is either not tall or not calm.
Someone is either wise or not kind.
Someone is either quiet or not calm.
Someone is not creative or not humble.
John is creative.
Someone is either not patient or rich. | John is not brave. | contradiction | ((?[X]:((tall(X)|calm(X))))=>((brave(john)&kind(john))))&
(![X]:((~brave(X)|~patient(X))<=>(funny(X)|quiet(X))))&
(![X]:((old(X)|~happy(X))=>(creative(X)|calm(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((curious(mary)&humble(mary))))&
(![X]:((calm(X)<~>kind(X))<=>(~generous(X)|~kind(X))))&
(![X]:((~calm(X)|happy(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)<~>strong(X))<=>(strong(X)|~brave(X))))&
(![X]:(patient(X)<=>(~brave(X)<~>~strong(X))))&
(![X]:((~calm(X)&calm(X))<=>funny(X)))&
(![X]:(old(X)<=>(~funny(X)&patient(X))))&
(((~creative(fred)&calm(fred)))<=>(kind(mary)))&
((?[X]:((~old(X)|~strong(X))))=>(old(lucy)))&
(![X]:((~creative(X)&generous(X))=>strong(X)))&
((~humble(susan))<=>(?[X]:((~wise(X)|~humble(X)))))&
((?[X]:((strong(X)|brave(X))))<=>((strong(john)|~patient(john))))&
(((~strong(paul)|~wise(paul)))=>(?[X]:(patient(X))))&
((~brave(mary)&wise(mary)))&
(?[X]:((~funny(X)<~>~curious(X))))&
((~tall(fred)<~>~calm(fred)))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((quiet(X)<~>~calm(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(creative(john))&
(?[X]:((~patient(X)<~>rich(X)))) | ~brave(john) | [
"p0",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 469600728966310377363485
% SZS output start Proof for 469600728966310377363485
1. ? [X0] : (calm(X0) | tall(X0)) => (kind(john) & brave(john)) [input p0]
19. ~tall(fred) <~> ~calm(fred) [input p18]
25. ~brave(john) [input hypothesis]
26. (kind(john) & brave(john)) | ! [X0] : (~calm(X0) & ~tall(X0)) [ennf transformation 1]
67. (calm(fred) | tall(fred)) & (~calm(fred) | ~tall(fred)) [nnf transformation 19]
79. brave(john) | ~tall(X0) [cnf transformation 26]
80. brave(john) | ~calm(X0) [cnf transformation 26]
143. calm(fred) | tall(fred) [cnf transformation 67]
152. ~brave(john) [cnf transformation 25]
158. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
159. ~calm(X0) <- (1) [avatar component clause 158]
166. 3 <=> ! [X0] : ~tall(X0) [avatar definition]
167. ~tall(X0) <- (3) [avatar component clause 166]
170. 4 <=> brave(john) [avatar definition]
173. 1 | 4 [avatar split clause 80,170,158]
174. 3 | 4 [avatar split clause 79,170,166]
212. 12 <=> calm(fred) [avatar definition]
214. calm(fred) <- (12) [avatar component clause 212]
297. 31 <=> tall(fred) [avatar definition]
299. tall(fred) <- (31) [avatar component clause 297]
300. 31 | 12 [avatar split clause 143,212,297]
341. ~4 [avatar split clause 152,170]
342. $false <- (1, 12) [resolution 214,159]
343. ~1 | ~12 [avatar contradiction clause 342]
344. $false <- (3, 31) [subsumption resolution 299,167]
345. ~3 | ~31 [avatar contradiction clause 344]
346. $false [avatar sat refutation 173,174,300,341,343,345]
% SZS output end Proof for 469600728966310377363485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and patient then someone is both rich and old and vice versa. Everyone who is both kind and not wise is either quiet or creative and vice versa. Everyone who is strong is both patient and not happy and vice versa. Everyone who is not funny is both not humble and not curious and vice versa. Everyone who is funny is not quiet or creative and vice versa. Everyone who is either funny or not creative is generous or kind. Everyone who is either not strong or not old is calm. Everyone who is rich or not calm is not patient. If mary is strong or generous then paul is either rich or not kind. Everyone who is not patient or not rich is both not wise and not quiet. Everyone who is not tall or calm is either not creative or not wise and vice versa. If someone is patient or not funny then someone is not patient. Everyone who is strong is humble. If someone is not happy or funny then mary is not tall. Everyone who is quiet is either not tall or not curious. If someone is either rich or not generous then someone is not patient or rich and vice versa. Alice is both not quiet and not tall. Someone is either not calm or not creative. Lucy is not humble or not rich. Fred is not calm or patient. John is both not happy and not rich. Someone is patient or old. Someone is either not quiet or not brave. | Fred is funny. | entailment | ((?[X]:((~happy(X)&patient(X))))<=>(?[X]:((rich(X)&old(X)))))&
(![X]:((kind(X)&~wise(X))<=>(quiet(X)<~>creative(X))))&
(![X]:(strong(X)<=>(patient(X)&~happy(X))))&
(![X]:(~funny(X)<=>(~humble(X)&~curious(X))))&
(![X]:(funny(X)<=>(~quiet(X)|creative(X))))&
(![X]:((funny(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((~strong(X)<~>~old(X))=>calm(X)))&
(![X]:((rich(X)|~calm(X))=>~patient(X)))&
(((strong(mary)|generous(mary)))=>((rich(paul)<~>~kind(paul))))&
(![X]:((~patient(X)|~rich(X))=>(~wise(X)&~quiet(X))))&
(![X]:((~tall(X)|calm(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:(~patient(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~happy(X)|funny(X))))=>(~tall(mary)))&
(![X]:(quiet(X)=>(~tall(X)<~>~curious(X))))&
((?[X]:((rich(X)<~>~generous(X))))<=>(?[X]:((~patient(X)|rich(X)))))&
((~quiet(alice)&~tall(alice)))&
(?[X]:((~calm(X)<~>~creative(X))))&
((~humble(lucy)|~rich(lucy)))&
((~calm(fred)|patient(fred)))&
((~happy(john)&~rich(john)))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~quiet(X)<~>~brave(X)))) | funny(fred) | [
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 9002063664968226287107680
% SZS output start Proof for 9002063664968226287107680
5. ! [X0] : (funny(X0) <=> (creative(X0) | ~quiet(X0))) [input p4]
8. ! [X0] : ((~calm(X0) | rich(X0)) => ~patient(X0)) [input p7]
10. ! [X0] : ((~rich(X0) | ~patient(X0)) => (~quiet(X0) & ~wise(X0))) [input p9]
24. ~funny(fred) [input hypothesis]
31. ! [X0] : (~patient(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 8]
33. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (rich(X0) & patient(X0))) [ennf transformation 10]
49. ! [X0] : ((funny(X0) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ~funny(X0))) [nnf transformation 5]
50. ! [X0] : ((funny(X0) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ~funny(X0))) [flattening 49]
90. funny(X0) | quiet(X0) [cnf transformation 50]
96. ~rich(X0) | ~patient(X0) [cnf transformation 31]
104. ~quiet(X0) | patient(X0) [cnf transformation 33]
105. ~quiet(X0) | rich(X0) [cnf transformation 33]
136. ~funny(fred) [cnf transformation 24]
265. 29 <=> patient(fred) [avatar definition]
267. patient(fred) <- (29) [avatar component clause 265]
288. quiet(fred) [resolution 90,136]
292. patient(fred) [resolution 104,288]
293. 29 [avatar split clause 292,265]
299. rich(fred) [resolution 105,288]
319. ~patient(fred) [resolution 299,96]
320. $false <- (29) [subsumption resolution 319,267]
321. ~29 [avatar contradiction clause 320]
322. $false [avatar sat refutation 293,321]
% SZS output end Proof for 9002063664968226287107680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and not creative then paul is not funny or not quiet and vice versa. Everyone who is humble or not kind is both not funny and brave and vice versa. Everyone who is rich or not humble is both happy and old. If lucy is curious or wise then someone is either not tall or not brave and vice versa. If someone is old or not strong then someone is either generous or humble. Everyone who is not quiet or patient is both not curious and not humble and vice versa. If someone is both funny and not humble then john is both humble and not generous and vice versa. Everyone who is either quiet or not creative is both not old and quiet and vice versa. Everyone who is both not old and funny is either rich or not tall. If someone is not creative or generous then john is either not rich or rich. Everyone who is strong is not patient or not strong. Everyone who is either happy or not tall is humble. If fred is either not patient or curious then someone is both wise and kind. Everyone who is both not kind and patient is both generous and not calm. If someone is either not happy or not humble then john is both not old and humble. If someone is not old then john is either not patient or not kind. Lucy is both brave and not tall. John is happy. Mary is either wise or strong. Alice is old or rich. Someone is either not curious or not brave. Susan is both curious and brave. | John is generous. | neutral | ((?[X]:((brave(X)&~creative(X))))<=>((~funny(paul)|~quiet(paul))))&
(![X]:((humble(X)|~kind(X))<=>(~funny(X)&brave(X))))&
(![X]:((rich(X)|~humble(X))=>(happy(X)&old(X))))&
(((curious(lucy)|wise(lucy)))<=>(?[X]:((~tall(X)<~>~brave(X)))))&
((?[X]:((old(X)|~strong(X))))=>(?[X]:((generous(X)<~>humble(X)))))&
(![X]:((~quiet(X)|patient(X))<=>(~curious(X)&~humble(X))))&
((?[X]:((funny(X)&~humble(X))))<=>((humble(john)&~generous(john))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~old(X)&quiet(X))))&
(![X]:((~old(X)&funny(X))=>(rich(X)<~>~tall(X))))&
((?[X]:((~creative(X)|generous(X))))=>((~rich(john)<~>rich(john))))&
(![X]:(strong(X)=>(~patient(X)|~strong(X))))&
(![X]:((happy(X)<~>~tall(X))=>humble(X)))&
(((~patient(fred)<~>curious(fred)))=>(?[X]:((wise(X)&kind(X)))))&
(![X]:((~kind(X)&patient(X))=>(generous(X)&~calm(X))))&
((?[X]:((~happy(X)<~>~humble(X))))=>((~old(john)&humble(john))))&
((?[X]:(~old(X)))=>((~patient(john)<~>~kind(john))))&
((brave(lucy)&~tall(lucy)))&
(happy(john))&
((wise(mary)<~>strong(mary)))&
((old(alice)|rich(alice)))&
(?[X]:((~curious(X)<~>~brave(X))))&
((curious(susan)&brave(susan))) | generous(john) | [] | null | 0 |
Everyone who is curious is strong. Everyone who is not old is either not funny or not tall and vice versa. Everyone who is not generous is not strong and vice versa. Everyone who is not funny is both not wise and not happy. If alice is either not creative or not strong then mary is strong or tall. If someone is either calm or not old then john is not generous. Everyone who is kind or not old is either tall or calm. If someone is either not old or not calm then someone is not humble. Everyone who is both not kind and humble is either generous or not humble and vice versa. Everyone who is strong is not humble. Everyone who is not curious is not brave or not calm. If susan is both not happy and kind then someone is not funny or tall. If susan is not happy then paul is humble. Everyone who is both not strong and not tall is quiet or patient and vice versa. Everyone who is not tall is creative or not humble. Everyone who is not patient is either tall or not calm. Someone is either not brave or not old. Lucy is both not generous and not curious. Fred is wise. Susan is both not funny and kind. Alice is funny or not brave. Someone is kind. | Lucy is generous. | contradiction | (![X]:(curious(X)=>strong(X)))&
(![X]:(~old(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:(~funny(X)=>(~wise(X)&~happy(X))))&
(((~creative(alice)<~>~strong(alice)))=>((strong(mary)|tall(mary))))&
((?[X]:((calm(X)<~>~old(X))))=>(~generous(john)))&
(![X]:((kind(X)|~old(X))=>(tall(X)<~>calm(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>(?[X]:(~humble(X))))&
(![X]:((~kind(X)&humble(X))<=>(generous(X)<~>~humble(X))))&
(![X]:(strong(X)=>~humble(X)))&
(![X]:(~curious(X)=>(~brave(X)|~calm(X))))&
(((~happy(susan)&kind(susan)))=>(?[X]:((~funny(X)|tall(X)))))&
((~happy(susan))=>(humble(paul)))&
(![X]:((~strong(X)&~tall(X))<=>(quiet(X)|patient(X))))&
(![X]:(~tall(X)=>(creative(X)|~humble(X))))&
(![X]:(~patient(X)=>(tall(X)<~>~calm(X))))&
(?[X]:((~brave(X)<~>~old(X))))&
((~generous(lucy)&~curious(lucy)))&
(wise(fred))&
((~funny(susan)&kind(susan)))&
((funny(alice)|~brave(alice)))&
(?[X]:(kind(X))) | generous(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3441149166446048173501630
% SZS output start Proof for 3441149166446048173501630
18. ~curious(lucy) & ~generous(lucy) [input p17]
23. generous(lucy) [input hypothesis]
101. ~generous(lucy) [cnf transformation 18]
108. generous(lucy) [cnf transformation 23]
197. $false [subsumption resolution 108,101]
% SZS output end Proof for 3441149166446048173501630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Subsets and Splits