premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If fred is both not old and not patient then john is either not curious or not happy.
If someone is strong or not happy then someone is funny.
If susan is either brave or patient then lucy is old or brave and vice versa.
If someone is not kind or calm then someone is not strong and vice versa.
If someone is not funny or generous then someone is both not kind and kind.
Everyone who is not kind is either humble or calm.
If fred is both patient and old then someone is not brave or patient and vice versa.
If someone is not rich then someone is not quiet and vice versa.
If susan is both creative and not brave then someone is either not tall or calm and vice versa.
Everyone who is either not quiet or quiet is both brave and kind and vice versa.
If fred is humble or quiet then someone is either not happy or not generous and vice versa.
If someone is not quiet then someone is not patient or not quiet.
Everyone who is not brave is either old or calm and vice versa.
If someone is either not generous or not calm then fred is either kind or brave.
If someone is both not patient and not curious then someone is both kind and funny and vice versa.
If lucy is strong or humble then someone is both tall and not rich.
Someone is both not happy and curious.
Mary is both happy and kind.
Someone is not rich.
Alice is not quiet.
Lucy is both curious and not humble.
Someone is either not strong or humble. | Lucy is not patient. | entailment | (((~old(fred)&~patient(fred)))=>((~curious(john)<~>~happy(john))))&
((?[X]:((strong(X)|~happy(X))))=>(?[X]:(funny(X))))&
(((brave(susan)<~>patient(susan)))<=>((old(lucy)|brave(lucy))))&
((?[X]:((~kind(X)|calm(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~funny(X)|generous(X))))=>(?[X]:((~kind(X)&kind(X)))))&
(![X]:(~kind(X)=>(humble(X)<~>calm(X))))&
(((patient(fred)&old(fred)))<=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:(~quiet(X))))&
(((creative(susan)&~brave(susan)))<=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(brave(X)&kind(X))))&
(((humble(fred)|quiet(fred)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((~patient(X)|~quiet(X)))))&
(![X]:(~brave(X)<=>(old(X)<~>calm(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>((kind(fred)<~>brave(fred))))&
((?[X]:((~patient(X)&~curious(X))))<=>(?[X]:((kind(X)&funny(X)))))&
(((strong(lucy)|humble(lucy)))=>(?[X]:((tall(X)&~rich(X)))))&
(?[X]:((~happy(X)&curious(X))))&
((happy(mary)&kind(mary)))&
(?[X]:(~rich(X)))&
(~quiet(alice))&
((curious(lucy)&~humble(lucy)))&
(?[X]:((~strong(X)<~>humble(X)))) | ~patient(lucy) | [
"p4",
"p6",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4820648833334708213976679
% SZS output start Proof for 4820648833334708213976679
5. ? [X0] : (generous(X0) | ~funny(X0)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p4]
7. (old(fred) & patient(fred)) <=> ? [X0] : (patient(X0) | ~brave(X0)) [input p6]
10. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> (kind(X0) & brave(X0))) [input p9]
13. ! [X0] : (~brave(X0) <=> (old(X0) <~> calm(X0))) [input p12]
14. ? [X0] : (~generous(X0) <~> ~calm(X0)) => (kind(fred) <~> brave(fred)) [input p13]
23. patient(lucy) [input hypothesis]
26. ? [X0] : (generous(X0) | ~funny(X0)) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 5]
33. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : (~generous(X0) & funny(X0)) [ennf transformation 26]
36. (kind(fred) <~> brave(fred)) | ! [X0] : (~generous(X0) <=> ~calm(X0)) [ennf transformation 14]
49. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : (~generous(X1) & funny(X1)) [rectify 33]
50. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK3) & ~kind(sK3)) [choice axiom]
51. (kind(sK3) & ~kind(sK3)) | ! [X1] : (~generous(X1) & funny(X1)) [skolemisation 49,50]
53. ((old(fred) & patient(fred)) | ! [X0] : (~patient(X0) & brave(X0))) & (? [X0] : (patient(X0) | ~brave(X0)) | (~old(fred) | ~patient(fred))) [nnf transformation 7]
54. ((old(fred) & patient(fred)) | ! [X0] : (~patient(X0) & brave(X0))) & (? [X0] : (patient(X0) | ~brave(X0)) | ~old(fred) | ~patient(fred)) [flattening 53]
55. ((old(fred) & patient(fred)) | ! [X0] : (~patient(X0) & brave(X0))) & (? [X1] : (patient(X1) | ~brave(X1)) | ~old(fred) | ~patient(fred)) [rectify 54]
56. ? [X1] : (patient(X1) | ~brave(X1)) => (patient(sK4) | ~brave(sK4)) [choice axiom]
57. ((old(fred) & patient(fred)) | ! [X0] : (~patient(X0) & brave(X0))) & ((patient(sK4) | ~brave(sK4)) | ~old(fred) | ~patient(fred)) [skolemisation 55,56]
68. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 10]
69. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [flattening 68]
78. ! [X0] : ((~brave(X0) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | brave(X0))) [nnf transformation 13]
79. ((~brave(fred) | ~kind(fred)) & (brave(fred) | kind(fred))) | ! [X0] : ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))) [nnf transformation 36]
108. ~kind(sK3) | ~generous(X1) [cnf transformation 51]
110. kind(sK3) | ~generous(X1) [cnf transformation 51]
117. old(fred) | ~patient(X0) [cnf transformation 57]
126. brave(X0) | quiet(X0) | quiet(X0) [cnf transformation 69]
127. brave(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 69]
128. kind(X0) | quiet(X0) | quiet(X0) [cnf transformation 69]
129. kind(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 69]
141. ~brave(X0) | calm(X0) | ~old(X0) [cnf transformation 78]
145. ~brave(fred) | ~kind(fred) | ~calm(X0) | generous(X0) [cnf transformation 79]
165. patient(lucy) [cnf transformation 23]
166. brave(X0) | quiet(X0) [duplicate literal removal 126]
167. ~quiet(X0) | brave(X0) [duplicate literal removal 127]
168. kind(X0) | quiet(X0) [duplicate literal removal 128]
169. ~quiet(X0) | kind(X0) [duplicate literal removal 129]
171. 1 <=> old(fred) [avatar definition]
173. old(fred) <- (1) [avatar component clause 171]
235. 15 <=> ! [X3] : ~calm(X3) [avatar definition]
236. ~calm(X3) <- (15) [avatar component clause 235]
243. 17 <=> ! [X3] : kind(X3) [avatar definition]
244. kind(X3) <- (17) [avatar component clause 243]
247. 18 <=> ! [X1] : ~generous(X1) [avatar definition]
248. ~generous(X1) <- (18) [avatar component clause 247]
250. 19 <=> kind(sK3) [avatar definition]
253. 18 | 19 [avatar split clause 110,250,247]
258. 18 | ~19 [avatar split clause 108,250,247]
261. 21 <=> ! [X0] : ~patient(X0) [avatar definition]
262. ~patient(X0) <- (21) [avatar component clause 261]
263. 21 | 1 [avatar split clause 117,171,261]
265. 22 <=> ! [X0] : brave(X0) [avatar definition]
266. brave(X0) <- (22) [avatar component clause 265]
319. kind(X0) [subsumption resolution 168,169]
320. 17 [avatar split clause 319,243]
321. brave(X0) [subsumption resolution 166,167]
322. 22 [avatar split clause 321,265]
364. 43 <=> kind(fred) [avatar definition]
366. ~kind(fred) <- (~43) [avatar component clause 364]
368. 44 <=> brave(fred) [avatar definition]
370. ~brave(fred) <- (~44) [avatar component clause 368]
373. 45 <=> ! [X0] : (~calm(X0) | generous(X0)) [avatar definition]
374. ~calm(X0) | generous(X0) <- (45) [avatar component clause 373]
375. 45 | ~43 | ~44 [avatar split clause 145,368,364,373]
443. $false <- (21) [resolution 262,165]
444. ~21 [avatar contradiction clause 443]
447. $false <- (22, ~44) [resolution 370,266]
448. ~22 | 44 [avatar contradiction clause 447]
449. $false <- (17, ~43) [subsumption resolution 366,244]
450. ~17 | 43 [avatar contradiction clause 449]
451. ~calm(X0) <- (18, 45) [subsumption resolution 374,248]
452. 15 | ~18 | ~45 [avatar split clause 451,373,247,235]
478. calm(X0) | ~old(X0) <- (22) [resolution 141,266]
479. ~old(X0) <- (15, 22) [subsumption resolution 478,236]
482. $false <- (1, 15, 22) [resolution 479,173]
483. ~1 | ~15 | ~22 [avatar contradiction clause 482]
484. $false [avatar sat refutation 253,258,263,320,322,375,444,448,450,452,483]
% SZS output end Proof for 4820648833334708213976679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either not kind or not humble and vice versa.
If someone is brave then paul is either not funny or not calm and vice versa.
If someone is not tall then someone is funny or brave.
Everyone who is patient or not quiet is both not brave and curious.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Everyone who is either curious or kind is not old and vice versa.
Someone is either quiet or strong.
Someone is not brave or creative.
Someone is not rich.
Someone is both strong and not rich.
Someone is not creative. | Susan is quiet. | entailment | (![X]:(~funny(X)<=>(~kind(X)<~>~humble(X))))&
((?[X]:(brave(X)))<=>((~funny(paul)<~>~calm(paul))))&
((?[X]:(~tall(X)))=>(?[X]:((funny(X)|brave(X)))))&
(![X]:((patient(X)|~quiet(X))=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(![X]:((curious(X)<~>kind(X))<=>~old(X)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:(~creative(X))) | quiet(susan) | [
"p3",
"p4",
"p5",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2931761316259055524741147
% SZS output start Proof for 2931761316259055524741147
4. ! [X0] : ((~quiet(X0) | patient(X0)) => (curious(X0) & ~brave(X0))) [input p3]
5. (calm(susan) & ~curious(susan)) <=> ? [X0] : (~rich(X0) & ~patient(X0)) [input p4]
6. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X0] : (~funny(X0) | patient(X0)) [input p5]
9. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p8]
18. ? [X0] : ~rich(X0) [input p17]
21. ~quiet(susan) [input hypothesis]
23. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X1] : (~funny(X1) | patient(X1)) [rectify 6]
29. ! [X0] : ((curious(X0) & ~brave(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 4]
31. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 9]
39. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X0] : (~rich(X0) & ~patient(X0)) | (~calm(susan) | curious(susan))) [nnf transformation 5]
40. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X0] : (~rich(X0) & ~patient(X0)) | ~calm(susan) | curious(susan)) [flattening 39]
41. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X1] : (~rich(X1) & ~patient(X1)) | ~calm(susan) | curious(susan)) [rectify 40]
42. ? [X1] : (~rich(X1) & ~patient(X1)) => (~rich(sK1) & ~patient(sK1)) [choice axiom]
43. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & ((~rich(sK1) & ~patient(sK1)) | ~calm(susan) | curious(susan)) [skolemisation 41,42]
44. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X1] : (~funny(X1) | patient(X1)) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 23]
45. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X2] : (~funny(X2) | patient(X2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [rectify 44]
46. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK2) & creative(sK2)) [choice axiom]
47. ? [X2] : (~funny(X2) | patient(X2)) => (~funny(sK3) | patient(sK3)) [choice axiom]
48. ((curious(sK2) & creative(sK2)) | ! [X1] : (funny(X1) & ~patient(X1))) & ((~funny(sK3) | patient(sK3)) | ! [X3] : (~curious(X3) | ~creative(X3))) [skolemisation 45,47,46]
67. ? [X0] : ~rich(X0) => ~rich(sK8) [choice axiom]
68. ~rich(sK8) [skolemisation 18,67]
84. curious(X0) | quiet(X0) [cnf transformation 29]
87. ~curious(susan) | rich(X0) | patient(X0) [cnf transformation 43]
90. creative(sK2) | ~patient(X1) [cnf transformation 48]
101. ~creative(X0) | ~creative(X0) [cnf transformation 31]
128. ~rich(sK8) [cnf transformation 68]
132. ~quiet(susan) [cnf transformation 21]
135. ~creative(X0) [duplicate literal removal 101]
156. 5 <=> ! [X0] : (rich(X0) | patient(X0)) [avatar definition]
157. rich(X0) | patient(X0) <- (5) [avatar component clause 156]
164. 7 <=> curious(susan) [avatar definition]
166. ~curious(susan) <- (~7) [avatar component clause 164]
167. 5 | ~7 [avatar split clause 87,164,156]
187. 12 <=> ! [X1] : ~patient(X1) [avatar definition]
188. ~patient(X1) <- (12) [avatar component clause 187]
191. 13 <=> creative(sK2) [avatar definition]
193. creative(sK2) <- (13) [avatar component clause 191]
195. 12 | 13 [avatar split clause 90,191,187]
276. $false <- (13) [subsumption resolution 193,135]
277. ~13 [avatar contradiction clause 276]
283. quiet(susan) <- (~7) [resolution 84,166]
284. $false <- (~7) [subsumption resolution 283,132]
285. 7 [avatar contradiction clause 284]
288. rich(X0) <- (5, 12) [subsumption resolution 157,188]
289. $false <- (5, 12) [resolution 288,128]
294. ~5 | ~12 [avatar contradiction clause 289]
295. $false [avatar sat refutation 167,195,277,285,294]
% SZS output end Proof for 2931761316259055524741147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is happy then lucy is either humble or not humble and vice versa.
If someone is either funny or not humble then alice is not old and vice versa.
If john is not brave then susan is either strong or generous and vice versa.
If someone is either not happy or not kind then fred is creative or happy and vice versa.
Everyone who is not brave is both not quiet and quiet and vice versa.
Everyone who is not old or not calm is not patient or happy.
Everyone who is not funny is quiet and vice versa.
Everyone who is either creative or not rich is either not humble or old.
Everyone who is either not generous or not curious is not curious and vice versa.
If paul is either old or not generous then someone is both tall and humble.
If someone is not curious then susan is kind.
Everyone who is both funny and not generous is calm.
If someone is not wise or funny then mary is both humble and not creative and vice versa.
If fred is both not brave and not wise then alice is either not wise or not brave and vice versa.
If mary is patient or not rich then someone is either rich or wise.
Everyone who is either not quiet or strong is either not generous or tall.
Someone is either creative or brave.
Alice is old.
Someone is both not wise and not calm.
Someone is kind or quiet.
John is humble or brave.
Someone is both quiet and not strong.
Fred is curious.
Someone is both not humble and not patient. | Fred is funny. | neutral | ((happy(john))<=>((humble(lucy)<~>~humble(lucy))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(~old(alice)))&
((~brave(john))<=>((strong(susan)<~>generous(susan))))&
((?[X]:((~happy(X)<~>~kind(X))))<=>((creative(fred)|happy(fred))))&
(![X]:(~brave(X)<=>(~quiet(X)&quiet(X))))&
(![X]:((~old(X)|~calm(X))=>(~patient(X)|happy(X))))&
(![X]:(~funny(X)<=>quiet(X)))&
(![X]:((creative(X)<~>~rich(X))=>(~humble(X)<~>old(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>~curious(X)))&
(((old(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&humble(X)))))&
((?[X]:(~curious(X)))=>(kind(susan)))&
(![X]:((funny(X)&~generous(X))=>calm(X)))&
((?[X]:((~wise(X)|funny(X))))<=>((humble(mary)&~creative(mary))))&
(((~brave(fred)&~wise(fred)))<=>((~wise(alice)<~>~brave(alice))))&
(((patient(mary)|~rich(mary)))=>(?[X]:((rich(X)<~>wise(X)))))&
(![X]:((~quiet(X)<~>strong(X))=>(~generous(X)<~>tall(X))))&
(?[X]:((creative(X)<~>brave(X))))&
(old(alice))&
(?[X]:((~wise(X)&~calm(X))))&
(?[X]:((kind(X)|quiet(X))))&
((humble(john)|brave(john)))&
(?[X]:((quiet(X)&~strong(X))))&
(curious(fred))&
(?[X]:((~humble(X)&~patient(X)))) | funny(fred) | [] | null | 0 |
If someone is both quiet and not brave then someone is either quiet or patient and vice versa.
Everyone who is not funny or patient is not strong or funny and vice versa.
Everyone who is both not old and not patient is both not tall and not happy.
If susan is either not creative or creative then someone is either strong or calm and vice versa.
If someone is both wise and quiet then someone is creative or brave.
If someone is not wise or not creative then someone is calm and vice versa.
Everyone who is not curious is both not humble and generous and vice versa.
If someone is patient then someone is strong or humble and vice versa.
Everyone who is both not creative and not calm is either happy or not wise and vice versa.
Everyone who is both not old and happy is not curious and vice versa.
Everyone who is brave or not patient is tall and vice versa.
Everyone who is tall or old is either not kind or not wise.
Everyone who is both not old and not strong is either generous or not patient and vice versa.
Everyone who is both humble and not generous is either not quiet or patient.
Everyone who is either not rich or not strong is either patient or not patient.
Everyone who is both not strong and patient is not humble or patient and vice versa.
Fred is not curious.
Someone is either wise or creative.
Someone is not funny or not strong.
Lucy is both not tall and happy.
Alice is curious.
Someone is either funny or not rich. | Lucy is calm. | neutral | ((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:((~funny(X)|patient(X))<=>(~strong(X)|funny(X))))&
(![X]:((~old(X)&~patient(X))=>(~tall(X)&~happy(X))))&
(((~creative(susan)<~>creative(susan)))<=>(?[X]:((strong(X)<~>calm(X)))))&
((?[X]:((wise(X)&quiet(X))))=>(?[X]:((creative(X)|brave(X)))))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:(calm(X))))&
(![X]:(~curious(X)<=>(~humble(X)&generous(X))))&
((?[X]:(patient(X)))<=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((~old(X)&happy(X))<=>~curious(X)))&
(![X]:((brave(X)|~patient(X))<=>tall(X)))&
(![X]:((tall(X)|old(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((~old(X)&~strong(X))<=>(generous(X)<~>~patient(X))))&
(![X]:((humble(X)&~generous(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(patient(X)<~>~patient(X))))&
(![X]:((~strong(X)&patient(X))<=>(~humble(X)|patient(X))))&
(~curious(fred))&
(?[X]:((wise(X)<~>creative(X))))&
(?[X]:((~funny(X)|~strong(X))))&
((~tall(lucy)&happy(lucy)))&
(curious(alice))&
(?[X]:((funny(X)<~>~rich(X)))) | calm(lucy) | [] | null | 0 |
If someone is strong then paul is not humble and vice versa. Everyone who is not kind is both not tall and not patient and vice versa. Everyone who is both quiet and not kind is generous or not kind and vice versa. Everyone who is either not strong or not generous is not brave. If someone is either not happy or not rich then john is not funny and vice versa. Everyone who is strong or quiet is generous. Everyone who is not humble is both rich and not patient and vice versa. If someone is both happy and rich then someone is old and vice versa. Everyone who is either old or calm is either not strong or tall. Everyone who is either patient or not funny is calm. Everyone who is both not quiet and happy is not brave and vice versa. Everyone who is not happy is not quiet or humble. Everyone who is not creative is both not tall and not old. If susan is not happy or humble then someone is happy. Everyone who is patient or rich is not kind or not strong and vice versa. Everyone who is funny is either not creative or not funny. Someone is either tall or not wise. John is either rich or not happy. Susan is not brave. Fred is humble or happy. Mary is old or generous. Paul is either not rich or old. Someone is either not wise or not tall. | Susan is strong. | contradiction | ((?[X]:(strong(X)))<=>(~humble(paul)))&
(![X]:(~kind(X)<=>(~tall(X)&~patient(X))))&
(![X]:((quiet(X)&~kind(X))<=>(generous(X)|~kind(X))))&
(![X]:((~strong(X)<~>~generous(X))=>~brave(X)))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(~funny(john)))&
(![X]:((strong(X)|quiet(X))=>generous(X)))&
(![X]:(~humble(X)<=>(rich(X)&~patient(X))))&
((?[X]:((happy(X)&rich(X))))<=>(?[X]:(old(X))))&
(![X]:((old(X)<~>calm(X))=>(~strong(X)<~>tall(X))))&
(![X]:((patient(X)<~>~funny(X))=>calm(X)))&
(![X]:((~quiet(X)&happy(X))<=>~brave(X)))&
(![X]:(~happy(X)=>(~quiet(X)|humble(X))))&
(![X]:(~creative(X)=>(~tall(X)&~old(X))))&
(((~happy(susan)|humble(susan)))=>(?[X]:(happy(X))))&
(![X]:((patient(X)|rich(X))<=>(~kind(X)|~strong(X))))&
(![X]:(funny(X)=>(~creative(X)<~>~funny(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
((rich(john)<~>~happy(john)))&
(~brave(susan))&
((humble(fred)|happy(fred)))&
((old(mary)|generous(mary)))&
((~rich(paul)<~>old(paul)))&
(?[X]:((~wise(X)<~>~tall(X)))) | strong(susan) | [
"p2",
"p5",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 286586380826582149760203
% SZS output start Proof for 286586380826582149760203
3. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~kind(X0) | generous(X0))) [input p2]
6. ! [X0] : ((quiet(X0) | strong(X0)) => generous(X0)) [input p5]
11. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> ~brave(X0)) [input p10]
19. ~brave(susan) [input p18]
24. strong(susan) [input hypothesis]
26. ! [X0] : (~brave(X0) => (happy(X0) & ~quiet(X0))) [unused predicate definition removal 11]
28. ! [X0] : (generous(X0) | (~quiet(X0) & ~strong(X0))) [ennf transformation 6]
31. ! [X0] : ((happy(X0) & ~quiet(X0)) | brave(X0)) [ennf transformation 26]
43. ! [X0] : (((~kind(X0) & quiet(X0)) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | (kind(X0) | ~quiet(X0)))) [nnf transformation 3]
44. ! [X0] : (((~kind(X0) & quiet(X0)) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | kind(X0) | ~quiet(X0))) [flattening 43]
78. ~generous(X0) | quiet(X0) [cnf transformation 44]
88. ~strong(X0) | generous(X0) [cnf transformation 28]
102. ~quiet(X0) | brave(X0) [cnf transformation 31]
119. ~brave(susan) [cnf transformation 19]
126. strong(susan) [cnf transformation 24]
260. generous(susan) [resolution 88,126]
264. quiet(susan) [resolution 260,78]
319. brave(susan) [resolution 264,102]
321. $false [subsumption resolution 319,119]
% SZS output end Proof for 286586380826582149760203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not funny is either funny or not curious and vice versa.
If someone is not kind then someone is humble or not calm.
Everyone who is not patient is not funny and vice versa.
If someone is calm then susan is strong or quiet and vice versa.
If someone is curious then someone is either not old or not strong.
Everyone who is old is both not patient and old.
Everyone who is brave is both not creative and not wise and vice versa.
Everyone who is both funny and not quiet is either not quiet or not curious.
If john is both not wise and strong then fred is tall and vice versa.
If paul is not generous or not humble then someone is not patient.
If alice is either funny or not wise then someone is both not strong and humble and vice versa.
Everyone who is not patient is both not wise and curious and vice versa.
If someone is both not old and not kind then someone is kind and vice versa.
If lucy is humble or old then someone is not calm or not tall and vice versa.
If someone is either calm or not rich then someone is either not tall or not wise and vice versa.
If someone is not funny or rich then susan is not humble or old and vice versa.
Someone is generous.
Someone is brave.
Someone is either not humble or not rich.
Someone is brave or patient.
Someone is both not calm and rich.
Someone is both curious and humble.
Someone is either not old or not kind.
Susan is not wise. | Paul is old. | contradiction | (![X]:((~rich(X)|~funny(X))<=>(funny(X)<~>~curious(X))))&
((?[X]:(~kind(X)))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(~patient(X)<=>~funny(X)))&
((?[X]:(calm(X)))<=>((strong(susan)|quiet(susan))))&
((?[X]:(curious(X)))=>(?[X]:((~old(X)<~>~strong(X)))))&
(![X]:(old(X)=>(~patient(X)&old(X))))&
(![X]:(brave(X)<=>(~creative(X)&~wise(X))))&
(![X]:((funny(X)&~quiet(X))=>(~quiet(X)<~>~curious(X))))&
(((~wise(john)&strong(john)))<=>(tall(fred)))&
(((~generous(paul)|~humble(paul)))=>(?[X]:(~patient(X))))&
(((funny(alice)<~>~wise(alice)))<=>(?[X]:((~strong(X)&humble(X)))))&
(![X]:(~patient(X)<=>(~wise(X)&curious(X))))&
((?[X]:((~old(X)&~kind(X))))<=>(?[X]:(kind(X))))&
(((humble(lucy)|old(lucy)))<=>(?[X]:((~calm(X)|~tall(X)))))&
((?[X]:((calm(X)<~>~rich(X))))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((~funny(X)|rich(X))))<=>((~humble(susan)|old(susan))))&
(?[X]:(generous(X)))&
(?[X]:(brave(X)))&
(?[X]:((~humble(X)<~>~rich(X))))&
(?[X]:((brave(X)|patient(X))))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((curious(X)&humble(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan)) | old(paul) | [
"p0",
"p2",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 26762546866089091946734
% SZS output start Proof for 26762546866089091946734
1. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> (funny(X0) <~> ~curious(X0))) [input p0]
3. ! [X0] : (~patient(X0) <=> ~funny(X0)) [input p2]
6. ! [X0] : (old(X0) => (old(X0) & ~patient(X0))) [input p5]
12. ! [X0] : (~patient(X0) <=> (curious(X0) & ~wise(X0))) [input p11]
25. old(paul) [input hypothesis]
36. ! [X0] : ((old(X0) & ~patient(X0)) | ~old(X0)) [ennf transformation 6]
41. ! [X0] : (((~funny(X0) | ~rich(X0)) | ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) & (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | (funny(X0) & rich(X0)))) [nnf transformation 1]
42. ! [X0] : ((~funny(X0) | ~rich(X0) | ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) & (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | (funny(X0) & rich(X0)))) [flattening 41]
46. ! [X0] : ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))) [nnf transformation 3]
65. ! [X0] : ((~patient(X0) | (~curious(X0) | wise(X0))) & ((curious(X0) & ~wise(X0)) | patient(X0))) [nnf transformation 12]
66. ! [X0] : ((~patient(X0) | ~curious(X0) | wise(X0)) & ((curious(X0) & ~wise(X0)) | patient(X0))) [flattening 65]
102. ~curious(X0) | funny(X0) | funny(X0) [cnf transformation 42]
108. ~funny(X0) | patient(X0) [cnf transformation 46]
109. ~patient(X0) | funny(X0) [cnf transformation 46]
115. ~old(X0) | ~patient(X0) [cnf transformation 36]
131. patient(X0) | curious(X0) [cnf transformation 66]
163. old(paul) [cnf transformation 25]
165. ~curious(X0) | funny(X0) [duplicate literal removal 102]
365. 45 <=> ! [X1] : funny(X1) [avatar definition]
366. funny(X1) <- (45) [avatar component clause 365]
401. ~patient(paul) [resolution 115,163]
404. curious(X0) | funny(X0) [resolution 131,109]
408. funny(X0) [subsumption resolution 404,165]
409. 45 [avatar split clause 408,365]
411. patient(X0) <- (45) [resolution 366,108]
420. $false <- (45) [resolution 411,401]
427. ~45 [avatar contradiction clause 420]
428. $false [avatar sat refutation 409,427]
% SZS output end Proof for 26762546866089091946734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or old then susan is both strong and kind and vice versa.
If someone is not brave then someone is calm.
If someone is not rich or old then someone is not rich and vice versa.
If mary is both funny and not kind then someone is both brave and wise.
Everyone who is both kind and happy is either not funny or quiet.
If alice is not curious then someone is either not creative or happy and vice versa.
Everyone who is patient is curious.
Everyone who is either not curious or brave is both brave and not brave and vice versa.
If someone is not quiet then lucy is patient or funny.
Everyone who is patient or funny is either brave or not generous.
Everyone who is either strong or humble is both tall and not funny.
Everyone who is not rich is either not generous or humble and vice versa.
Everyone who is both brave and not wise is calm and vice versa.
If mary is either not old or calm then someone is both curious and generous.
If someone is happy then fred is either curious or brave and vice versa.
If lucy is not generous then someone is curious and vice versa.
Someone is both wise and generous.
Someone is either creative or not happy.
John is either rich or humble.
Someone is either not happy or not humble.
Someone is wise.
Susan is calm or not funny.
Someone is not funny. | Mary is tall. | neutral | ((?[X]:((~wise(X)<~>old(X))))<=>((strong(susan)&kind(susan))))&
((?[X]:(~brave(X)))=>(?[X]:(calm(X))))&
((?[X]:((~rich(X)|old(X))))<=>(?[X]:(~rich(X))))&
(((funny(mary)&~kind(mary)))=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((kind(X)&happy(X))=>(~funny(X)<~>quiet(X))))&
((~curious(alice))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:(patient(X)=>curious(X)))&
(![X]:((~curious(X)<~>brave(X))<=>(brave(X)&~brave(X))))&
((?[X]:(~quiet(X)))=>((patient(lucy)|funny(lucy))))&
(![X]:((patient(X)|funny(X))=>(brave(X)<~>~generous(X))))&
(![X]:((strong(X)<~>humble(X))=>(tall(X)&~funny(X))))&
(![X]:(~rich(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((brave(X)&~wise(X))<=>calm(X)))&
(((~old(mary)<~>calm(mary)))=>(?[X]:((curious(X)&generous(X)))))&
((?[X]:(happy(X)))<=>((curious(fred)<~>brave(fred))))&
((~generous(lucy))<=>(?[X]:(curious(X))))&
(?[X]:((wise(X)&generous(X))))&
(?[X]:((creative(X)<~>~happy(X))))&
((rich(john)<~>humble(john)))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:(wise(X)))&
((calm(susan)|~funny(susan)))&
(?[X]:(~funny(X))) | tall(mary) | [] | null | 0 |
Everyone who is either funny or not creative is creative or humble and vice versa. Everyone who is either tall or not happy is both brave and not generous. If fred is both not funny and not wise then john is either generous or not calm and vice versa. Everyone who is both not curious and tall is not calm or not rich and vice versa. Everyone who is old or not tall is either not strong or not funny. If fred is both generous and not tall then fred is not happy or humble. Everyone who is both brave and happy is not curious or not old and vice versa. If john is creative or not strong then lucy is not generous or not strong and vice versa. Everyone who is not patient is not quiet or not creative. If someone is both brave and not humble then someone is both creative and rich. Everyone who is not curious is both calm and rich. Everyone who is brave or rich is both funny and not wise. If alice is both not calm and not patient then lucy is both patient and not generous and vice versa. Everyone who is both not rich and not humble is either not creative or tall and vice versa. Everyone who is both tall and funny is patient or not generous and vice versa. If someone is old or patient then someone is either funny or patient. Someone is strong or rich. Alice is not kind. Someone is not generous. Someone is either not quiet or not calm. Someone is either not generous or not quiet. Someone is not creative or creative. Lucy is either not happy or patient. | Alice is not wise. | entailment | (![X]:((funny(X)<~>~creative(X))<=>(creative(X)|humble(X))))&
(![X]:((tall(X)<~>~happy(X))=>(brave(X)&~generous(X))))&
(((~funny(fred)&~wise(fred)))<=>((generous(john)<~>~calm(john))))&
(![X]:((~curious(X)&tall(X))<=>(~calm(X)|~rich(X))))&
(![X]:((old(X)|~tall(X))=>(~strong(X)<~>~funny(X))))&
(((generous(fred)&~tall(fred)))=>((~happy(fred)|humble(fred))))&
(![X]:((brave(X)&happy(X))<=>(~curious(X)|~old(X))))&
(((creative(john)|~strong(john)))<=>((~generous(lucy)|~strong(lucy))))&
(![X]:(~patient(X)=>(~quiet(X)|~creative(X))))&
((?[X]:((brave(X)&~humble(X))))=>(?[X]:((creative(X)&rich(X)))))&
(![X]:(~curious(X)=>(calm(X)&rich(X))))&
(![X]:((brave(X)|rich(X))=>(funny(X)&~wise(X))))&
(((~calm(alice)&~patient(alice)))<=>((patient(lucy)&~generous(lucy))))&
(![X]:((~rich(X)&~humble(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((tall(X)&funny(X))<=>(patient(X)|~generous(X))))&
((?[X]:((old(X)|patient(X))))=>(?[X]:((funny(X)<~>patient(X)))))&
(?[X]:((strong(X)|rich(X))))&
(~kind(alice))&
(?[X]:(~generous(X)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:((~generous(X)<~>~quiet(X))))&
(?[X]:((~creative(X)|creative(X))))&
((~happy(lucy)<~>patient(lucy))) | ~wise(alice) | [
"p3",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 448930613106049305815842
% SZS output start Proof for 448930613106049305815842
4. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~rich(X0) | ~calm(X0))) [input p3]
11. ! [X0] : (~curious(X0) => (rich(X0) & calm(X0))) [input p10]
12. ! [X0] : ((rich(X0) | brave(X0)) => (~wise(X0) & funny(X0))) [input p11]
24. wise(alice) [input hypothesis]
35. ! [X0] : ((rich(X0) & calm(X0)) | curious(X0)) [ennf transformation 11]
36. ! [X0] : ((~wise(X0) & funny(X0)) | (~rich(X0) & ~brave(X0))) [ennf transformation 12]
43. ! [X0] : (((tall(X0) & ~curious(X0)) | (rich(X0) & calm(X0))) & ((~rich(X0) | ~calm(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 4]
44. ! [X0] : (((tall(X0) & ~curious(X0)) | (rich(X0) & calm(X0))) & (~rich(X0) | ~calm(X0) | ~tall(X0) | curious(X0))) [flattening 43]
94. ~curious(X0) | rich(X0) [cnf transformation 44]
115. rich(X0) | curious(X0) [cnf transformation 35]
119. ~wise(X0) | ~rich(X0) [cnf transformation 36]
148. wise(alice) [cnf transformation 24]
221. rich(X0) [subsumption resolution 115,94]
223. ~wise(X0) [subsumption resolution 119,221]
270. $false [subsumption resolution 148,223]
% SZS output end Proof for 448930613106049305815842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is both rich and happy and vice versa. Everyone who is both not generous and not creative is not happy. Everyone who is either not curious or wise is rich or not wise and vice versa. If lucy is either strong or not humble then someone is not old or brave and vice versa. If someone is not creative then fred is not humble and vice versa. Everyone who is tall is brave. Everyone who is not wise is both wise and happy. If fred is either not kind or old then someone is both not quiet and creative. Everyone who is tall or old is not patient or brave. Everyone who is either funny or not happy is either not tall or patient and vice versa. Everyone who is not curious is either tall or happy. If alice is both not happy and old then john is both rich and brave and vice versa. If someone is either not strong or not patient then someone is not strong and vice versa. If john is either not tall or not creative then john is humble or not calm and vice versa. Everyone who is not wise or calm is funny. Everyone who is either quiet or not strong is not patient or not old and vice versa. Mary is either not calm or not happy. Paul is humble. Paul is either rich or patient. Paul is not kind. John is both not curious and not old. Lucy is both quiet and not creative. Lucy is happy. | John is wise. | entailment | (![X]:(tall(X)<=>(rich(X)&happy(X))))&
(![X]:((~generous(X)&~creative(X))=>~happy(X)))&
(![X]:((~curious(X)<~>wise(X))<=>(rich(X)|~wise(X))))&
(((strong(lucy)<~>~humble(lucy)))<=>(?[X]:((~old(X)|brave(X)))))&
((?[X]:(~creative(X)))<=>(~humble(fred)))&
(![X]:(tall(X)=>brave(X)))&
(![X]:(~wise(X)=>(wise(X)&happy(X))))&
(((~kind(fred)<~>old(fred)))=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((tall(X)|old(X))=>(~patient(X)|brave(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~tall(X)<~>patient(X))))&
(![X]:(~curious(X)=>(tall(X)<~>happy(X))))&
(((~happy(alice)&old(alice)))<=>((rich(john)&brave(john))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:(~strong(X))))&
(((~tall(john)<~>~creative(john)))<=>((humble(john)|~calm(john))))&
(![X]:((~wise(X)|calm(X))=>funny(X)))&
(![X]:((quiet(X)<~>~strong(X))<=>(~patient(X)|~old(X))))&
((~calm(mary)<~>~happy(mary)))&
(humble(paul))&
((rich(paul)<~>patient(paul)))&
(~kind(paul))&
((~curious(john)&~old(john)))&
((quiet(lucy)&~creative(lucy)))&
(happy(lucy)) | wise(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2944862740576143012673376
% SZS output start Proof for 2944862740576143012673376
7. ! [X0] : (~wise(X0) => (happy(X0) & wise(X0))) [input p6]
24. ~wise(john) [input hypothesis]
28. ! [X0] : ((happy(X0) & wise(X0)) | wise(X0)) [ennf transformation 7]
82. wise(X0) | wise(X0) [cnf transformation 28]
133. ~wise(john) [cnf transformation 24]
134. wise(X0) [duplicate literal removal 82]
292. $false [subsumption resolution 133,134]
% SZS output end Proof for 2944862740576143012673376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is not humble or not patient and vice versa.
Everyone who is rich is either rich or not humble and vice versa.
Everyone who is not curious is not creative and vice versa.
If susan is either not curious or not patient then someone is tall.
Everyone who is old or not curious is both not rich and brave and vice versa.
If fred is either creative or not brave then john is humble or funny.
Everyone who is either quiet or not quiet is rich and vice versa.
Everyone who is both brave and humble is humble or tall and vice versa.
Everyone who is either curious or not happy is either tall or generous and vice versa.
If fred is generous then someone is old and vice versa.
Everyone who is kind or not creative is either wise or not strong and vice versa.
If someone is both curious and not brave then someone is both not rich and not curious and vice versa.
If someone is happy or rich then someone is not quiet or not generous and vice versa.
Everyone who is not calm or quiet is both quiet and not creative and vice versa.
Everyone who is not kind is not generous or curious and vice versa.
Alice is either rich or not calm.
Paul is either patient or not curious.
John is either humble or funny. | John is not patient. | neutral | ((?[X]:(~old(X)))<=>(?[X]:((~humble(X)|~patient(X)))))&
(![X]:(rich(X)<=>(rich(X)<~>~humble(X))))&
(![X]:(~curious(X)<=>~creative(X)))&
(((~curious(susan)<~>~patient(susan)))=>(?[X]:(tall(X))))&
(![X]:((old(X)|~curious(X))<=>(~rich(X)&brave(X))))&
(((creative(fred)<~>~brave(fred)))=>((humble(john)|funny(john))))&
(![X]:((quiet(X)<~>~quiet(X))<=>rich(X)))&
(![X]:((brave(X)&humble(X))<=>(humble(X)|tall(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(tall(X)<~>generous(X))))&
((generous(fred))<=>(?[X]:(old(X))))&
(![X]:((kind(X)|~creative(X))<=>(wise(X)<~>~strong(X))))&
((?[X]:((curious(X)&~brave(X))))<=>(?[X]:((~rich(X)&~curious(X)))))&
((?[X]:((happy(X)|rich(X))))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(![X]:((~calm(X)|quiet(X))<=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>(~generous(X)|curious(X))))&
((rich(alice)<~>~calm(alice)))&
((patient(paul)<~>~curious(paul)))&
((humble(john)<~>funny(john))) | ~patient(john) | [] | null | 0 |
Everyone who is brave or not kind is either strong or happy and vice versa.
Everyone who is not old is not creative and vice versa.
If someone is either generous or not calm then susan is both humble and funny and vice versa.
Everyone who is generous or funny is either tall or not generous and vice versa.
If fred is both generous and humble then someone is not calm and vice versa.
If alice is either not patient or quiet then someone is both brave and not quiet and vice versa.
If someone is both strong and not happy then someone is creative or not quiet.
Everyone who is not tall is either not calm or not tall and vice versa.
If alice is either not patient or happy then someone is not tall and vice versa.
If someone is both not calm and not patient then paul is either not curious or calm and vice versa.
Everyone who is both quiet and calm is both not strong and happy and vice versa.
Everyone who is both not quiet and not creative is both not strong and not tall and vice versa.
Everyone who is not old or patient is not happy or brave.
Everyone who is both not tall and not patient is both not strong and not creative and vice versa.
If alice is rich or not patient then someone is curious or not quiet and vice versa.
Everyone who is either not brave or not kind is not strong or happy.
Someone is either funny or old.
Alice is funny or curious.
Someone is either wise or funny.
Someone is brave or curious.
Someone is not humble.
Fred is both quiet and brave.
Someone is old or not kind.
Mary is either humble or quiet. | Fred is tall. | entailment | (![X]:((brave(X)|~kind(X))<=>(strong(X)<~>happy(X))))&
(![X]:(~old(X)<=>~creative(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>((humble(susan)&funny(susan))))&
(![X]:((generous(X)|funny(X))<=>(tall(X)<~>~generous(X))))&
(((generous(fred)&humble(fred)))<=>(?[X]:(~calm(X))))&
(((~patient(alice)<~>quiet(alice)))<=>(?[X]:((brave(X)&~quiet(X)))))&
((?[X]:((strong(X)&~happy(X))))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(~tall(X)<=>(~calm(X)<~>~tall(X))))&
(((~patient(alice)<~>happy(alice)))<=>(?[X]:(~tall(X))))&
((?[X]:((~calm(X)&~patient(X))))<=>((~curious(paul)<~>calm(paul))))&
(![X]:((quiet(X)&calm(X))<=>(~strong(X)&happy(X))))&
(![X]:((~quiet(X)&~creative(X))<=>(~strong(X)&~tall(X))))&
(![X]:((~old(X)|patient(X))=>(~happy(X)|brave(X))))&
(![X]:((~tall(X)&~patient(X))<=>(~strong(X)&~creative(X))))&
(((rich(alice)|~patient(alice)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~strong(X)|happy(X))))&
(?[X]:((funny(X)<~>old(X))))&
((funny(alice)|curious(alice)))&
(?[X]:((wise(X)<~>funny(X))))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:(~humble(X)))&
((quiet(fred)&brave(fred)))&
(?[X]:((old(X)|~kind(X))))&
((humble(mary)<~>quiet(mary))) | tall(fred) | [
"p7",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 709943704624762615084940
% SZS output start Proof for 709943704624762615084940
8. ! [X0] : (~tall(X0) <=> (~calm(X0) <~> ~tall(X0))) [input p7]
11. ! [X0] : ((calm(X0) & quiet(X0)) <=> (happy(X0) & ~strong(X0))) [input p10]
12. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (~tall(X0) & ~strong(X0))) [input p11]
22. brave(fred) & quiet(fred) [input p21]
25. ~tall(fred) [input hypothesis]
54. ! [X0] : ((~tall(X0) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | tall(X0))) [nnf transformation 8]
63. ! [X0] : (((calm(X0) & quiet(X0)) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | (~calm(X0) | ~quiet(X0)))) [nnf transformation 11]
64. ! [X0] : (((calm(X0) & quiet(X0)) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | ~calm(X0) | ~quiet(X0))) [flattening 63]
65. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (tall(X0) | strong(X0))) & ((~tall(X0) & ~strong(X0)) | (creative(X0) | quiet(X0)))) [nnf transformation 12]
66. ! [X0] : (((~creative(X0) & ~quiet(X0)) | tall(X0) | strong(X0)) & ((~tall(X0) & ~strong(X0)) | creative(X0) | quiet(X0))) [flattening 65]
119. tall(X0) | calm(X0) | tall(X0) [cnf transformation 54]
120. ~tall(X0) | ~tall(X0) | calm(X0) [cnf transformation 54]
132. ~quiet(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 64]
138. ~quiet(X0) | tall(X0) | strong(X0) [cnf transformation 66]
159. quiet(fred) [cnf transformation 22]
164. ~tall(fred) [cnf transformation 25]
165. tall(X0) | calm(X0) [duplicate literal removal 119]
166. ~tall(X0) | calm(X0) [duplicate literal removal 120]
198. 7 <=> ! [X0] : calm(X0) [avatar definition]
199. calm(X0) <- (7) [avatar component clause 198]
252. calm(X0) [subsumption resolution 165,166]
253. 7 [avatar split clause 252,198]
388. 45 <=> strong(fred) [avatar definition]
433. ~calm(fred) | ~strong(fred) [resolution 132,159]
484. tall(fred) | strong(fred) [resolution 138,159]
486. strong(fred) [subsumption resolution 484,164]
492. 45 [avatar split clause 486,388]
493. ~strong(fred) <- (7) [subsumption resolution 433,199]
494. ~45 | ~7 [avatar split clause 493,198,388]
495. $false [avatar sat refutation 253,492,494]
% SZS output end Proof for 709943704624762615084940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not wise is not funny.
If mary is either not strong or humble then someone is either kind or not rich and vice versa.
Everyone who is not kind or not quiet is both not humble and not wise and vice versa.
Everyone who is either strong or quiet is curious.
If someone is happy or brave then someone is either patient or not tall and vice versa.
Everyone who is either tall or patient is both tall and not strong and vice versa.
Everyone who is both patient and not humble is kind or not quiet and vice versa.
If mary is brave then someone is either not tall or not old.
If mary is tall then someone is both not kind and not curious.
Everyone who is not strong is creative and vice versa.
If john is both not humble and strong then mary is old or not patient and vice versa.
If someone is not happy or curious then someone is either old or humble and vice versa.
If someone is both not tall and not happy then paul is both happy and tall.
If mary is not wise then mary is either not rich or funny and vice versa.
Everyone who is either not funny or not creative is not rich or curious and vice versa.
Everyone who is rich or old is rich or not strong and vice versa.
Someone is both rich and patient.
Someone is both not old and not rich.
Fred is not kind.
Mary is either patient or tall.
Paul is not brave.
Susan is not funny.
Susan is not rich.
Someone is both brave and funny. | Fred is humble. | contradiction | (![X]:((~humble(X)&~wise(X))=>~funny(X)))&
(((~strong(mary)<~>humble(mary)))<=>(?[X]:((kind(X)<~>~rich(X)))))&
(![X]:((~kind(X)|~quiet(X))<=>(~humble(X)&~wise(X))))&
(![X]:((strong(X)<~>quiet(X))=>curious(X)))&
((?[X]:((happy(X)|brave(X))))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>patient(X))<=>(tall(X)&~strong(X))))&
(![X]:((patient(X)&~humble(X))<=>(kind(X)|~quiet(X))))&
((brave(mary))=>(?[X]:((~tall(X)<~>~old(X)))))&
((tall(mary))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:(~strong(X)<=>creative(X)))&
(((~humble(john)&strong(john)))<=>((old(mary)|~patient(mary))))&
((?[X]:((~happy(X)|curious(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
((?[X]:((~tall(X)&~happy(X))))=>((happy(paul)&tall(paul))))&
((~wise(mary))<=>((~rich(mary)<~>funny(mary))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~rich(X)|curious(X))))&
(![X]:((rich(X)|old(X))<=>(rich(X)|~strong(X))))&
(?[X]:((rich(X)&patient(X))))&
(?[X]:((~old(X)&~rich(X))))&
(~kind(fred))&
((patient(mary)<~>tall(mary)))&
(~brave(paul))&
(~funny(susan))&
(~rich(susan))&
(?[X]:((brave(X)&funny(X)))) | humble(fred) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1178495094482349520612487
% SZS output start Proof for 1178495094482349520612487
3. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (~wise(X0) & ~humble(X0))) [input p2]
7. ! [X0] : ((~humble(X0) & patient(X0)) <=> (~quiet(X0) | kind(X0))) [input p6]
25. humble(fred) [input hypothesis]
38. ! [X0] : (((~quiet(X0) | ~kind(X0)) | (wise(X0) | humble(X0))) & ((~wise(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [nnf transformation 3]
39. ! [X0] : ((~quiet(X0) | ~kind(X0) | wise(X0) | humble(X0)) & ((~wise(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [flattening 38]
48. ! [X0] : (((~humble(X0) & patient(X0)) | (quiet(X0) & ~kind(X0))) & ((~quiet(X0) | kind(X0)) | (humble(X0) | ~patient(X0)))) [nnf transformation 7]
49. ! [X0] : (((~humble(X0) & patient(X0)) | (quiet(X0) & ~kind(X0))) & (~quiet(X0) | kind(X0) | humble(X0) | ~patient(X0))) [flattening 48]
84. ~humble(X0) | kind(X0) [cnf transformation 39]
106. ~humble(X0) | ~kind(X0) [cnf transformation 49]
153. humble(fred) [cnf transformation 25]
220. ~humble(X0) [subsumption resolution 106,84]
326. $false [subsumption resolution 153,220]
% SZS output end Proof for 1178495094482349520612487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not patient is not tall or quiet.
If someone is either not humble or not wise then someone is rich and vice versa.
If susan is either patient or not creative then mary is either not creative or not happy and vice versa.
Everyone who is both strong and humble is brave.
Everyone who is both not wise and not kind is not quiet or brave and vice versa.
Everyone who is wise is both patient and not tall and vice versa.
Everyone who is both funny and not wise is both generous and not tall.
Everyone who is not patient is rich or brave and vice versa.
Everyone who is both not curious and patient is old or rich and vice versa.
If someone is not kind then someone is funny or not funny.
If alice is either not old or not wise then lucy is either tall or humble and vice versa.
Everyone who is either brave or wise is not patient.
If someone is wise or not brave then susan is either not strong or old.
Everyone who is wise or not quiet is either curious or patient and vice versa.
Everyone who is creative or not funny is either patient or not kind and vice versa.
Everyone who is not creative or not funny is either not funny or calm and vice versa.
Someone is either strong or patient.
Someone is generous or not quiet.
Paul is either strong or not calm.
Someone is not funny.
Someone is not happy or not generous.
Lucy is generous.
Someone is tall. | Lucy is tall. | contradiction | (![X]:((strong(X)<~>~patient(X))=>(~tall(X)|quiet(X))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(?[X]:(rich(X))))&
(((patient(susan)<~>~creative(susan)))<=>((~creative(mary)<~>~happy(mary))))&
(![X]:((strong(X)&humble(X))=>brave(X)))&
(![X]:((~wise(X)&~kind(X))<=>(~quiet(X)|brave(X))))&
(![X]:(wise(X)<=>(patient(X)&~tall(X))))&
(![X]:((funny(X)&~wise(X))=>(generous(X)&~tall(X))))&
(![X]:(~patient(X)<=>(rich(X)|brave(X))))&
(![X]:((~curious(X)&patient(X))<=>(old(X)|rich(X))))&
((?[X]:(~kind(X)))=>(?[X]:((funny(X)|~funny(X)))))&
(((~old(alice)<~>~wise(alice)))<=>((tall(lucy)<~>humble(lucy))))&
(![X]:((brave(X)<~>wise(X))=>~patient(X)))&
((?[X]:((wise(X)|~brave(X))))=>((~strong(susan)<~>old(susan))))&
(![X]:((wise(X)|~quiet(X))<=>(curious(X)<~>patient(X))))&
(![X]:((creative(X)|~funny(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((~creative(X)|~funny(X))<=>(~funny(X)<~>calm(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((strong(paul)<~>~calm(paul)))&
(?[X]:(~funny(X)))&
(?[X]:((~happy(X)|~generous(X))))&
(generous(lucy))&
(?[X]:(tall(X))) | tall(lucy) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2724813308770869715142150
% SZS output start Proof for 2724813308770869715142150
2. ? [X0] : (~humble(X0) <~> ~wise(X0)) <=> ? [X0] : rich(X0) [input p1]
5. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> (brave(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : (wise(X0) <=> (~tall(X0) & patient(X0))) [input p5]
7. ! [X0] : ((~wise(X0) & funny(X0)) => (~tall(X0) & generous(X0))) [input p6]
8. ! [X0] : (~patient(X0) <=> (brave(X0) | rich(X0))) [input p7]
9. ! [X0] : ((patient(X0) & ~curious(X0)) <=> (rich(X0) | old(X0))) [input p8]
11. (~old(alice) <~> ~wise(alice)) <=> (tall(lucy) <~> humble(lucy)) [input p10]
12. ! [X0] : ((brave(X0) <~> wise(X0)) => ~patient(X0)) [input p11]
14. ! [X0] : ((~quiet(X0) | wise(X0)) <=> (curious(X0) <~> patient(X0))) [input p13]
15. ! [X0] : ((~funny(X0) | creative(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p14]
24. tall(lucy) [input hypothesis]
25. ? [X0] : (~humble(X0) <~> ~wise(X0)) <=> ? [X1] : rich(X1) [rectify 2]
31. ! [X0] : ((~tall(X0) & generous(X0)) | (wise(X0) | ~funny(X0))) [ennf transformation 7]
32. ! [X0] : ((~tall(X0) & generous(X0)) | wise(X0) | ~funny(X0)) [flattening 31]
34. ! [X0] : (~patient(X0) | (brave(X0) <=> wise(X0))) [ennf transformation 12]
37. (? [X0] : ((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0)))) [nnf transformation 25]
38. (? [X0] : ((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : ((~humble(X3) | wise(X3)) & (~wise(X3) | humble(X3)))) [rectify 37]
39. ? [X0] : ((wise(X0) | humble(X0)) & (~wise(X0) | ~humble(X0))) => ((wise(sK0) | humble(sK0)) & (~wise(sK0) | ~humble(sK0))) [choice axiom]
40. ? [X2] : rich(X2) => rich(sK1) [choice axiom]
41. (((wise(sK0) | humble(sK0)) & (~wise(sK0) | ~humble(sK0))) | ! [X1] : ~rich(X1)) & (rich(sK1) | ! [X3] : ((~humble(X3) | wise(X3)) & (~wise(X3) | humble(X3)))) [skolemisation 38,40,39]
43. ! [X0] : (((~kind(X0) & ~wise(X0)) | (~brave(X0) & quiet(X0))) & ((brave(X0) | ~quiet(X0)) | (kind(X0) | wise(X0)))) [nnf transformation 5]
44. ! [X0] : (((~kind(X0) & ~wise(X0)) | (~brave(X0) & quiet(X0))) & (brave(X0) | ~quiet(X0) | kind(X0) | wise(X0))) [flattening 43]
45. ! [X0] : ((wise(X0) | (tall(X0) | ~patient(X0))) & ((~tall(X0) & patient(X0)) | ~wise(X0))) [nnf transformation 6]
46. ! [X0] : ((wise(X0) | tall(X0) | ~patient(X0)) & ((~tall(X0) & patient(X0)) | ~wise(X0))) [flattening 45]
47. ! [X0] : ((~patient(X0) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | patient(X0))) [nnf transformation 8]
48. ! [X0] : ((~patient(X0) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | patient(X0))) [flattening 47]
49. ! [X0] : (((patient(X0) & ~curious(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (~patient(X0) | curious(X0)))) [nnf transformation 9]
50. ! [X0] : (((patient(X0) & ~curious(X0)) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | ~patient(X0) | curious(X0))) [flattening 49]
54. (((wise(alice) | old(alice)) & (~wise(alice) | ~old(alice))) | ((tall(lucy) | ~humble(lucy)) & (humble(lucy) | ~tall(lucy)))) & (((~humble(lucy) | ~tall(lucy)) & (humble(lucy) | tall(lucy))) | ((~old(alice) | wise(alice)) & (~wise(alice) | old(alice)))) [nnf transformation 11]
55. ! [X0] : (~patient(X0) | ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) [nnf transformation 34]
57. ! [X0] : (((~quiet(X0) | wise(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0)))) & (((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~wise(X0)))) [nnf transformation 14]
58. ! [X0] : ((~quiet(X0) | wise(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0)))) & (((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~wise(X0)))) [flattening 57]
59. ! [X0] : (((~funny(X0) | creative(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (funny(X0) & ~creative(X0)))) [nnf transformation 15]
60. ! [X0] : ((~funny(X0) | creative(X0) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (funny(X0) & ~creative(X0)))) [flattening 59]
78. rich(sK1) | ~humble(X3) | wise(X3) [cnf transformation 41]
92. ~brave(X0) | ~wise(X0) [cnf transformation 44]
93. ~kind(X0) | quiet(X0) [cnf transformation 44]
95. ~wise(X0) | patient(X0) [cnf transformation 46]
96. ~wise(X0) | ~tall(X0) [cnf transformation 46]
97. ~patient(X0) | tall(X0) | wise(X0) [cnf transformation 46]
99. ~tall(X0) | wise(X0) | ~funny(X0) [cnf transformation 32]
101. ~rich(X0) | ~patient(X0) [cnf transformation 48]
104. ~old(X0) | ~curious(X0) [cnf transformation 50]
106. ~old(X0) | patient(X0) [cnf transformation 50]
107. patient(X0) | ~rich(X0) [cnf transformation 50]
115. wise(alice) | old(alice) | humble(lucy) | ~tall(lucy) [cnf transformation 54]
118. ~patient(X0) | brave(X0) | ~wise(X0) [cnf transformation 55]
128. ~quiet(X0) | wise(X0) | curious(X0) | ~patient(X0) [cnf transformation 58]
132. ~patient(X0) | kind(X0) | funny(X0) [cnf transformation 60]
150. tall(lucy) [cnf transformation 24]
154. 1 <=> ! [X1] : ~rich(X1) [avatar definition]
155. ~rich(X1) <- (1) [avatar component clause 154]
167. 4 <=> ! [X3] : (~humble(X3) | wise(X3)) [avatar definition]
168. ~humble(X3) | wise(X3) <- (4) [avatar component clause 167]
170. 5 <=> rich(sK1) [avatar definition]
172. rich(sK1) <- (5) [avatar component clause 170]
173. 4 | 5 [avatar split clause 78,170,167]
202. ~funny(X0) | ~tall(X0) [subsumption resolution 99,96]
203. ~rich(X0) [subsumption resolution 107,101]
204. 1 [avatar split clause 203,154]
207. 11 <=> humble(lucy) [avatar definition]
208. humble(lucy) <- (11) [avatar component clause 207]
211. 12 <=> tall(lucy) [avatar definition]
215. 13 <=> old(alice) [avatar definition]
217. old(alice) <- (13) [avatar component clause 215]
219. 14 <=> wise(alice) [avatar definition]
221. wise(alice) <- (14) [avatar component clause 219]
223. ~12 | 11 | 13 | 14 [avatar split clause 115,219,215,207,211]
230. brave(X0) | ~wise(X0) [subsumption resolution 118,95]
231. ~wise(X0) [subsumption resolution 230,92]
245. ~quiet(X0) | curious(X0) | ~patient(X0) [subsumption resolution 128,231]
285. 12 [avatar split clause 150,211]
286. $false <- (1, 5) [resolution 172,155]
287. ~1 | ~5 [avatar contradiction clause 286]
288. ~humble(X3) <- (4) [subsumption resolution 168,231]
289. $false <- (4, 11) [resolution 288,208]
290. ~4 | ~11 [avatar contradiction clause 289]
303. 26 <=> funny(alice) [avatar definition]
305. funny(alice) <- (26) [avatar component clause 303]
307. 27 <=> kind(alice) [avatar definition]
309. kind(alice) <- (27) [avatar component clause 307]
311. $false <- (14) [subsumption resolution 221,231]
312. ~14 [avatar contradiction clause 311]
313. patient(alice) <- (13) [resolution 217,106]
314. ~curious(alice) <- (13) [resolution 217,104]
315. kind(alice) | funny(alice) <- (13) [resolution 313,132]
316. tall(alice) | wise(alice) <- (13) [resolution 313,97]
317. tall(alice) <- (13) [subsumption resolution 316,231]
321. ~tall(alice) <- (26) [resolution 305,202]
332. $false <- (13, 26) [subsumption resolution 321,317]
333. ~13 | ~26 [avatar contradiction clause 332]
334. 26 | 27 | ~13 [avatar split clause 315,215,307,303]
339. quiet(alice) <- (27) [resolution 309,93]
381. curious(alice) | ~patient(alice) <- (27) [resolution 339,245]
382. ~patient(alice) <- (13, 27) [subsumption resolution 381,314]
383. $false <- (13, 27) [subsumption resolution 382,313]
384. ~13 | ~27 [avatar contradiction clause 383]
385. $false [avatar sat refutation 173,204,223,285,287,290,312,333,334,384]
% SZS output end Proof for 2724813308770869715142150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If john is humble then someone is calm or funny and vice versa.
If someone is either not wise or not quiet then someone is either not brave or not calm and vice versa.
Everyone who is not calm or humble is not humble or not quiet and vice versa.
Everyone who is quiet or wise is either creative or strong.
Everyone who is both not old and not strong is strong or curious and vice versa.
Everyone who is both quiet and not happy is either not curious or tall and vice versa.
Everyone who is not patient or humble is wise or not humble.
If someone is quiet then someone is both not funny and humble.
If someone is either not funny or not wise then someone is wise or kind.
If someone is either not funny or not generous then someone is tall or calm.
If someone is not brave then someone is not funny.
Everyone who is both calm and not old is tall or not strong.
Everyone who is calm is not old and vice versa.
If alice is kind or not tall then someone is strong and vice versa.
Everyone who is funny or not happy is not quiet or not strong and vice versa.
Everyone who is both not creative and not old is either not curious or brave.
Someone is rich or not strong.
Someone is either not funny or tall.
Susan is either funny or not rich.
Someone is not kind or wise.
Someone is not generous or not tall.
Someone is kind.
Someone is either calm or not funny. | Alice is generous. | neutral | ((humble(john))<=>(?[X]:((calm(X)|funny(X)))))&
((?[X]:((~wise(X)<~>~quiet(X))))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((quiet(X)|wise(X))=>(creative(X)<~>strong(X))))&
(![X]:((~old(X)&~strong(X))<=>(strong(X)|curious(X))))&
(![X]:((quiet(X)&~happy(X))<=>(~curious(X)<~>tall(X))))&
(![X]:((~patient(X)|humble(X))=>(wise(X)|~humble(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~funny(X)&humble(X)))))&
((?[X]:((~funny(X)<~>~wise(X))))=>(?[X]:((wise(X)|kind(X)))))&
((?[X]:((~funny(X)<~>~generous(X))))=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(~funny(X))))&
(![X]:((calm(X)&~old(X))=>(tall(X)|~strong(X))))&
(![X]:(calm(X)<=>~old(X)))&
(((kind(alice)|~tall(alice)))<=>(?[X]:(strong(X))))&
(![X]:((funny(X)|~happy(X))<=>(~quiet(X)|~strong(X))))&
(![X]:((~creative(X)&~old(X))=>(~curious(X)<~>brave(X))))&
(?[X]:((rich(X)|~strong(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
((funny(susan)<~>~rich(susan)))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)<~>~funny(X)))) | generous(alice) | [] | null | 0 |
If john is either not brave or curious then fred is quiet and vice versa. Everyone who is not brave or not calm is both humble and not happy. Everyone who is happy is not curious or not creative. Everyone who is either kind or not wise is both not old and strong. Everyone who is both not wise and curious is not strong or not wise and vice versa. If fred is either tall or strong then someone is not funny or happy. If someone is both not generous and not strong then fred is either old or happy and vice versa. If someone is not humble or patient then someone is either not quiet or old. If lucy is calm or not generous then john is funny or not curious. If someone is not patient then someone is either old or kind. Everyone who is both not calm and not humble is either old or not curious and vice versa. If someone is both not happy and not tall then someone is either not quiet or happy and vice versa. Everyone who is both not tall and curious is calm or brave and vice versa. Everyone who is both old and not tall is not kind. If someone is not curious or happy then fred is calm. Everyone who is either not rich or not funny is either wise or not generous. Someone is not rich or generous. Mary is happy. Alice is both not old and wise. Someone is happy or not calm. Someone is happy or not quiet. Someone is both brave and wise. John is both not curious and not funny. Lucy is either rich or not kind. | Mary is not happy. | contradiction | (((~brave(john)<~>curious(john)))<=>(quiet(fred)))&
(![X]:((~brave(X)|~calm(X))=>(humble(X)&~happy(X))))&
(![X]:(happy(X)=>(~curious(X)|~creative(X))))&
(![X]:((kind(X)<~>~wise(X))=>(~old(X)&strong(X))))&
(![X]:((~wise(X)&curious(X))<=>(~strong(X)|~wise(X))))&
(((tall(fred)<~>strong(fred)))=>(?[X]:((~funny(X)|happy(X)))))&
((?[X]:((~generous(X)&~strong(X))))<=>((old(fred)<~>happy(fred))))&
((?[X]:((~humble(X)|patient(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
(((calm(lucy)|~generous(lucy)))=>((funny(john)|~curious(john))))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)<~>kind(X)))))&
(![X]:((~calm(X)&~humble(X))<=>(old(X)<~>~curious(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~tall(X)&curious(X))<=>(calm(X)|brave(X))))&
(![X]:((old(X)&~tall(X))=>~kind(X)))&
((?[X]:((~curious(X)|happy(X))))=>(calm(fred)))&
(![X]:((~rich(X)<~>~funny(X))=>(wise(X)<~>~generous(X))))&
(?[X]:((~rich(X)|generous(X))))&
(happy(mary))&
((~old(alice)&wise(alice)))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((happy(X)|~quiet(X))))&
(?[X]:((brave(X)&wise(X))))&
((~curious(john)&~funny(john)))&
((rich(lucy)<~>~kind(lucy))) | ~happy(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3242518864839743305804987
% SZS output start Proof for 3242518864839743305804987
18. happy(mary) [input p17]
25. ~happy(mary) [input hypothesis]
137. happy(mary) [cnf transformation 18]
148. ~happy(mary) [cnf transformation 25]
335. $false [subsumption resolution 148,137]
% SZS output end Proof for 3242518864839743305804987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not calm is both not patient and not calm and vice versa. If someone is both not happy and old then alice is both strong and not tall and vice versa. Everyone who is either strong or not happy is not brave or strong and vice versa. If someone is both tall and strong then someone is not old or funny. Everyone who is both not kind and kind is both not calm and strong and vice versa. If someone is curious or happy then someone is either not strong or tall. Everyone who is patient or not brave is both generous and old and vice versa. Everyone who is rich or quiet is patient and vice versa. Everyone who is either wise or kind is funny or brave. Everyone who is both tall and not happy is old. If mary is either kind or strong then someone is either not strong or funny. Everyone who is calm or not quiet is both calm and funny. If paul is calm then someone is both calm and creative and vice versa. Everyone who is not quiet or not patient is old or humble and vice versa. Everyone who is humble or wise is either not curious or not generous and vice versa. If mary is not calm or curious then john is not strong or not old and vice versa. Someone is both not curious and happy. Alice is humble. Someone is not strong or not kind. Alice is not creative or calm. Someone is both not old and brave. John is tall. Someone is both not creative and not happy. | John is funny. | entailment | (![X]:((~funny(X)&~calm(X))<=>(~patient(X)&~calm(X))))&
((?[X]:((~happy(X)&old(X))))<=>((strong(alice)&~tall(alice))))&
(![X]:((strong(X)<~>~happy(X))<=>(~brave(X)|strong(X))))&
((?[X]:((tall(X)&strong(X))))=>(?[X]:((~old(X)|funny(X)))))&
(![X]:((~kind(X)&kind(X))<=>(~calm(X)&strong(X))))&
((?[X]:((curious(X)|happy(X))))=>(?[X]:((~strong(X)<~>tall(X)))))&
(![X]:((patient(X)|~brave(X))<=>(generous(X)&old(X))))&
(![X]:((rich(X)|quiet(X))<=>patient(X)))&
(![X]:((wise(X)<~>kind(X))=>(funny(X)|brave(X))))&
(![X]:((tall(X)&~happy(X))=>old(X)))&
(((kind(mary)<~>strong(mary)))=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((calm(X)|~quiet(X))=>(calm(X)&funny(X))))&
((calm(paul))<=>(?[X]:((calm(X)&creative(X)))))&
(![X]:((~quiet(X)|~patient(X))<=>(old(X)|humble(X))))&
(![X]:((humble(X)|wise(X))<=>(~curious(X)<~>~generous(X))))&
(((~calm(mary)|curious(mary)))<=>((~strong(john)|~old(john))))&
(?[X]:((~curious(X)&happy(X))))&
(humble(alice))&
(?[X]:((~strong(X)|~kind(X))))&
((~creative(alice)|calm(alice)))&
(?[X]:((~old(X)&brave(X))))&
(tall(john))&
(?[X]:((~creative(X)&~happy(X)))) | funny(john) | [
"p6",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5097864970415948892137011
% SZS output start Proof for 5097864970415948892137011
7. ! [X0] : ((~brave(X0) | patient(X0)) <=> (old(X0) & generous(X0))) [input p6]
8. ! [X0] : ((quiet(X0) | rich(X0)) <=> patient(X0)) [input p7]
12. ! [X0] : ((~quiet(X0) | calm(X0)) => (funny(X0) & calm(X0))) [input p11]
14. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (humble(X0) | old(X0))) [input p13]
24. ~funny(john) [input hypothesis]
34. ! [X0] : ((funny(X0) & calm(X0)) | (quiet(X0) & ~calm(X0))) [ennf transformation 12]
53. ! [X0] : (((~brave(X0) | patient(X0)) | (~old(X0) | ~generous(X0))) & ((old(X0) & generous(X0)) | (brave(X0) & ~patient(X0)))) [nnf transformation 7]
54. ! [X0] : ((~brave(X0) | patient(X0) | ~old(X0) | ~generous(X0)) & ((old(X0) & generous(X0)) | (brave(X0) & ~patient(X0)))) [flattening 53]
55. ! [X0] : (((quiet(X0) | rich(X0)) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & ~rich(X0)))) [nnf transformation 8]
56. ! [X0] : ((quiet(X0) | rich(X0) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & ~rich(X0)))) [flattening 55]
65. ! [X0] : (((~patient(X0) | ~quiet(X0)) | (~humble(X0) & ~old(X0))) & ((humble(X0) | old(X0)) | (patient(X0) & quiet(X0)))) [nnf transformation 14]
66. ! [X0] : ((~patient(X0) | ~quiet(X0) | (~humble(X0) & ~old(X0))) & (humble(X0) | old(X0) | (patient(X0) & quiet(X0)))) [flattening 65]
104. ~patient(X0) | old(X0) [cnf transformation 54]
108. ~quiet(X0) | patient(X0) [cnf transformation 56]
120. quiet(X0) | funny(X0) [cnf transformation 34]
125. humble(X0) | old(X0) | patient(X0) [cnf transformation 66]
126. ~patient(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 66]
127. ~patient(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 66]
148. ~funny(john) [cnf transformation 24]
244. ~humble(X0) | ~quiet(X0) [subsumption resolution 127,108]
245. ~quiet(X0) | ~old(X0) [subsumption resolution 126,108]
246. humble(X0) | old(X0) [subsumption resolution 125,104]
301. old(X0) | ~quiet(X0) [resolution 246,244]
302. ~quiet(X0) [subsumption resolution 301,245]
303. funny(X0) [resolution 302,120]
306. $false [resolution 303,148]
% SZS output end Proof for 5097864970415948892137011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not patient is calm or not rich and vice versa.
If someone is either not creative or not tall then someone is either not rich or not curious and vice versa.
If someone is both strong and wise then mary is both not humble and not generous and vice versa.
If someone is either creative or not creative then mary is generous and vice versa.
If lucy is either generous or rich then alice is both not generous and curious.
If paul is both humble and not calm then someone is either not patient or not humble.
If alice is both not creative and not patient then someone is either brave or wise and vice versa.
Everyone who is either wise or not rich is patient.
Everyone who is both not tall and wise is either curious or creative.
Everyone who is both wise and humble is both not tall and rich and vice versa.
If john is both kind and not rich then john is not creative.
If someone is either kind or generous then someone is not brave.
Everyone who is not old or creative is old or not wise and vice versa.
Everyone who is not wise is both not calm and not tall and vice versa.
Everyone who is not quiet is both not funny and kind.
Everyone who is both patient and creative is both not creative and old and vice versa.
Someone is both curious and creative.
Someone is not generous.
Alice is both not patient and old.
Someone is funny.
Someone is either not quiet or old.
Paul is both generous and calm. | John is generous. | contradiction | (![X]:((old(X)|~patient(X))<=>(calm(X)|~rich(X))))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:((strong(X)&wise(X))))<=>((~humble(mary)&~generous(mary))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(generous(mary)))&
(((generous(lucy)<~>rich(lucy)))=>((~generous(alice)&curious(alice))))&
(((humble(paul)&~calm(paul)))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(((~creative(alice)&~patient(alice)))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~rich(X))=>patient(X)))&
(![X]:((~tall(X)&wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((wise(X)&humble(X))<=>(~tall(X)&rich(X))))&
(((kind(john)&~rich(john)))=>(~creative(john)))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|creative(X))<=>(old(X)|~wise(X))))&
(![X]:(~wise(X)<=>(~calm(X)&~tall(X))))&
(![X]:(~quiet(X)=>(~funny(X)&kind(X))))&
(![X]:((patient(X)&creative(X))<=>(~creative(X)&old(X))))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:(~generous(X)))&
((~patient(alice)&old(alice)))&
(?[X]:(funny(X)))&
(?[X]:((~quiet(X)<~>old(X))))&
((generous(paul)&calm(paul))) | generous(john) | [
"p0",
"p6",
"p7",
"p9",
"p10",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9130890892551105470710012
% SZS output start Proof for 9130890892551105470710012
1. ! [X0] : ((~patient(X0) | old(X0)) <=> (~rich(X0) | calm(X0))) [input p0]
7. (~patient(alice) & ~creative(alice)) <=> ? [X0] : (brave(X0) <~> wise(X0)) [input p6]
8. ! [X0] : ((wise(X0) <~> ~rich(X0)) => patient(X0)) [input p7]
10. ! [X0] : ((humble(X0) & wise(X0)) <=> (rich(X0) & ~tall(X0))) [input p9]
11. (~rich(john) & kind(john)) => ~creative(john) [input p10]
12. ? [X0] : (kind(X0) <~> generous(X0)) => ? [X0] : ~brave(X0) [input p11]
13. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~wise(X0) | old(X0))) [input p12]
14. ! [X0] : (~wise(X0) <=> (~tall(X0) & ~calm(X0))) [input p13]
16. ! [X0] : ((creative(X0) & patient(X0)) <=> (old(X0) & ~creative(X0))) [input p15]
23. generous(john) [input hypothesis]
25. ? [X0] : (kind(X0) <~> generous(X0)) => ? [X1] : ~brave(X1) [rectify 12]
29. ! [X0] : (patient(X0) | (wise(X0) <=> ~rich(X0))) [ennf transformation 8]
32. ~creative(john) | (rich(john) | ~kind(john)) [ennf transformation 11]
33. ~creative(john) | rich(john) | ~kind(john) [flattening 32]
34. ? [X1] : ~brave(X1) | ! [X0] : (kind(X0) <=> generous(X0)) [ennf transformation 25]
36. ! [X0] : (((~patient(X0) | old(X0)) | (rich(X0) & ~calm(X0))) & ((~rich(X0) | calm(X0)) | (patient(X0) & ~old(X0)))) [nnf transformation 1]
37. ! [X0] : ((~patient(X0) | old(X0) | (rich(X0) & ~calm(X0))) & (~rich(X0) | calm(X0) | (patient(X0) & ~old(X0)))) [flattening 36]
56. ((~patient(alice) & ~creative(alice)) | ! [X0] : ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (? [X0] : ((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | (patient(alice) | creative(alice))) [nnf transformation 7]
57. ((~patient(alice) & ~creative(alice)) | ! [X0] : ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (? [X0] : ((~wise(X0) | ~brave(X0)) & (wise(X0) | brave(X0))) | patient(alice) | creative(alice)) [flattening 56]
58. ((~patient(alice) & ~creative(alice)) | ! [X0] : ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (? [X1] : ((~wise(X1) | ~brave(X1)) & (wise(X1) | brave(X1))) | patient(alice) | creative(alice)) [rectify 57]
59. ? [X1] : ((~wise(X1) | ~brave(X1)) & (wise(X1) | brave(X1))) => ((~wise(sK5) | ~brave(sK5)) & (wise(sK5) | brave(sK5))) [choice axiom]
60. ((~patient(alice) & ~creative(alice)) | ! [X0] : ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0)))) & (((~wise(sK5) | ~brave(sK5)) & (wise(sK5) | brave(sK5))) | patient(alice) | creative(alice)) [skolemisation 58,59]
61. ! [X0] : (patient(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) [nnf transformation 29]
63. ! [X0] : (((humble(X0) & wise(X0)) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | (~humble(X0) | ~wise(X0)))) [nnf transformation 10]
64. ! [X0] : (((humble(X0) & wise(X0)) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | ~humble(X0) | ~wise(X0))) [flattening 63]
65. ? [X1] : ~brave(X1) | ! [X0] : ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0))) [nnf transformation 34]
66. ? [X0] : ~brave(X0) | ! [X1] : ((kind(X1) | ~generous(X1)) & (generous(X1) | ~kind(X1))) [rectify 65]
67. ? [X0] : ~brave(X0) => ~brave(sK6) [choice axiom]
68. ~brave(sK6) | ! [X1] : ((kind(X1) | ~generous(X1)) & (generous(X1) | ~kind(X1))) [skolemisation 66,67]
69. ! [X0] : (((creative(X0) | ~old(X0)) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 13]
70. ! [X0] : ((creative(X0) | ~old(X0) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | (~creative(X0) & old(X0)))) [flattening 69]
71. ! [X0] : ((~wise(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [nnf transformation 14]
72. ! [X0] : ((~wise(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [flattening 71]
73. ! [X0] : (((creative(X0) & patient(X0)) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | (~creative(X0) | ~patient(X0)))) [nnf transformation 16]
74. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | ~creative(X0) | ~patient(X0))) [flattening 73]
85. ~rich(X0) | calm(X0) | patient(X0) [cnf transformation 37]
87. ~patient(X0) | old(X0) | rich(X0) [cnf transformation 37]
113. ~creative(alice) | brave(X0) | ~wise(X0) [cnf transformation 60]
116. ~wise(X0) | ~rich(X0) | patient(X0) [cnf transformation 61]
117. wise(X0) | patient(X0) | rich(X0) [cnf transformation 61]
122. ~rich(X0) | wise(X0) | tall(X0) [cnf transformation 64]
124. ~creative(john) | rich(john) | ~kind(john) [cnf transformation 33]
126. ~brave(sK6) | kind(X1) | ~generous(X1) [cnf transformation 68]
127. ~wise(X0) | old(X0) | old(X0) [cnf transformation 70]
129. creative(X0) | ~old(X0) | ~old(X0) [cnf transformation 70]
131. ~calm(X0) | wise(X0) [cnf transformation 72]
132. ~tall(X0) | wise(X0) [cnf transformation 72]
136. ~creative(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 74]
150. generous(john) [cnf transformation 23]
151. ~creative(X0) | ~patient(X0) [duplicate literal removal 136]
153. ~wise(X0) | old(X0) [duplicate literal removal 127]
154. ~old(X0) | creative(X0) [duplicate literal removal 129]
217. 14 <=> ! [X1] : creative(X1) [avatar definition]
218. creative(X1) <- (14) [avatar component clause 217]
263. 24 <=> ! [X0] : (brave(X0) | ~wise(X0)) [avatar definition]
264. ~wise(X0) | brave(X0) <- (24) [avatar component clause 263]
275. 27 <=> creative(alice) [avatar definition]
277. ~creative(alice) <- (~27) [avatar component clause 275]
278. 24 | ~27 [avatar split clause 113,275,263]
291. 30 <=> kind(john) [avatar definition]
295. 31 <=> rich(john) [avatar definition]
297. rich(john) <- (31) [avatar component clause 295]
299. 32 <=> creative(john) [avatar definition]
301. ~creative(john) <- (~32) [avatar component clause 299]
302. ~30 | 31 | ~32 [avatar split clause 124,299,295,291]
304. 33 <=> ! [X1] : (kind(X1) | ~generous(X1)) [avatar definition]
305. ~generous(X1) | kind(X1) <- (33) [avatar component clause 304]
307. 34 <=> brave(sK6) [avatar definition]
309. ~brave(sK6) <- (~34) [avatar component clause 307]
310. 33 | ~34 [avatar split clause 126,307,304]
362. patient(X3) | rich(X3) | old(X3) [resolution 117,153]
364. rich(X3) | old(X3) [subsumption resolution 362,87]
374. wise(X0) | tall(X0) | old(X0) [resolution 122,364]
375. wise(X0) | old(X0) [subsumption resolution 374,132]
376. old(X0) [subsumption resolution 375,153]
389. creative(X1) [resolution 376,154]
391. 14 [avatar split clause 389,217]
392. ~patient(X0) <- (14) [resolution 218,151]
447. $false <- (14, ~27) [subsumption resolution 277,218]
448. ~14 | 27 [avatar contradiction clause 447]
458. brave(X1) | patient(X1) | rich(X1) <- (24) [resolution 264,117]
459. brave(X1) | rich(X1) <- (14, 24) [subsumption resolution 458,392]
501. kind(john) <- (33) [resolution 305,150]
505. 30 | ~33 [avatar split clause 501,304,291]
506. $false <- (14, ~32) [subsumption resolution 301,218]
507. ~14 | 32 [avatar contradiction clause 506]
509. wise(john) | tall(john) <- (31) [resolution 297,122]
521. wise(john) <- (31) [subsumption resolution 509,132]
539. 52 <=> calm(sK6) [avatar definition]
541. calm(sK6) <- (52) [avatar component clause 539]
548. ~rich(john) | patient(john) <- (31) [resolution 521,116]
556. patient(john) <- (31) [subsumption resolution 548,297]
557. $false <- (14, 31) [subsumption resolution 556,392]
558. ~14 | ~31 [avatar contradiction clause 557]
561. rich(sK6) <- (14, 24, ~34) [resolution 459,309]
588. wise(sK6) <- (52) [resolution 541,131]
599. calm(sK6) | patient(sK6) <- (14, 24, ~34) [resolution 561,85]
645. brave(sK6) <- (24, 52) [resolution 588,264]
649. $false <- (24, ~34, 52) [subsumption resolution 645,309]
650. ~24 | 34 | ~52 [avatar contradiction clause 649]
653. calm(sK6) <- (14, 24, ~34) [subsumption resolution 599,392]
654. 52 | ~14 | ~24 | 34 [avatar split clause 653,307,263,217,539]
655. $false [avatar sat refutation 278,302,310,391,448,505,507,558,650,654]
% SZS output end Proof for 9130890892551105470710012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not funny and not generous. Everyone who is not happy is not curious and vice versa. If susan is either not funny or humble then fred is generous or wise and vice versa. If someone is not tall then someone is not creative or wise. If susan is quiet or not brave then someone is not kind and vice versa. Everyone who is both not curious and kind is either not wise or creative and vice versa. Everyone who is not quiet is both calm and not humble. Everyone who is creative or strong is not tall and vice versa. If paul is either not happy or not tall then someone is not generous and vice versa. If someone is not curious then someone is not quiet and vice versa. Everyone who is both not wise and brave is either happy or patient. Everyone who is rich or not tall is both humble and funny. Everyone who is either kind or strong is both not kind and funny and vice versa. If susan is not calm or curious then someone is not patient or not old. Everyone who is generous is both not kind and not happy and vice versa. If someone is brave then someone is not funny or tall. John is both strong and not kind. Someone is both not creative and old. Someone is wise or not happy. Someone is either not calm or not rich. Someone is either not rich or brave. | Fred is not happy. | contradiction | (![X]:(~curious(X)=>(~funny(X)&~generous(X))))&
(![X]:(~happy(X)<=>~curious(X)))&
(((~funny(susan)<~>humble(susan)))<=>((generous(fred)|wise(fred))))&
((?[X]:(~tall(X)))=>(?[X]:((~creative(X)|wise(X)))))&
(((quiet(susan)|~brave(susan)))<=>(?[X]:(~kind(X))))&
(![X]:((~curious(X)&kind(X))<=>(~wise(X)<~>creative(X))))&
(![X]:(~quiet(X)=>(calm(X)&~humble(X))))&
(![X]:((creative(X)|strong(X))<=>~tall(X)))&
(((~happy(paul)<~>~tall(paul)))<=>(?[X]:(~generous(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&brave(X))=>(happy(X)<~>patient(X))))&
(![X]:((rich(X)|~tall(X))=>(humble(X)&funny(X))))&
(![X]:((kind(X)<~>strong(X))<=>(~kind(X)&funny(X))))&
(((~calm(susan)|curious(susan)))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(generous(X)<=>(~kind(X)&~happy(X))))&
((?[X]:(brave(X)))=>(?[X]:((~funny(X)|tall(X)))))&
((strong(john)&~kind(john)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((wise(X)|~happy(X))))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~rich(X)<~>brave(X)))) | ~happy(fred) | [
"p0",
"p1",
"p7",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7031920167177624925496723
% SZS output start Proof for 7031920167177624925496723
1. ! [X0] : (~curious(X0) => (~generous(X0) & ~funny(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> ~curious(X0)) [input p1]
8. ! [X0] : ((strong(X0) | creative(X0)) <=> ~tall(X0)) [input p7]
12. ! [X0] : ((~tall(X0) | rich(X0)) => (funny(X0) & humble(X0))) [input p11]
13. ! [X0] : ((kind(X0) <~> strong(X0)) <=> (funny(X0) & ~kind(X0))) [input p12]
15. ! [X0] : (generous(X0) <=> (~happy(X0) & ~kind(X0))) [input p14]
22. ~happy(fred) [input hypothesis]
26. ! [X0] : ((~generous(X0) & ~funny(X0)) | curious(X0)) [ennf transformation 1]
31. ! [X0] : ((funny(X0) & humble(X0)) | (tall(X0) & ~rich(X0))) [ennf transformation 12]
34. ! [X0] : ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))) [nnf transformation 2]
47. ! [X0] : (((strong(X0) | creative(X0)) | tall(X0)) & (~tall(X0) | (~strong(X0) & ~creative(X0)))) [nnf transformation 8]
48. ! [X0] : ((strong(X0) | creative(X0) | tall(X0)) & (~tall(X0) | (~strong(X0) & ~creative(X0)))) [flattening 47]
59. ! [X0] : ((((~strong(X0) | ~kind(X0)) & (strong(X0) | kind(X0))) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0))))) [nnf transformation 13]
60. ! [X0] : ((((~strong(X0) | ~kind(X0)) & (strong(X0) | kind(X0))) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0))))) [flattening 59]
63. ! [X0] : ((generous(X0) | (happy(X0) | kind(X0))) & ((~happy(X0) & ~kind(X0)) | ~generous(X0))) [nnf transformation 15]
64. ! [X0] : ((generous(X0) | happy(X0) | kind(X0)) & ((~happy(X0) & ~kind(X0)) | ~generous(X0))) [flattening 63]
78. ~funny(X0) | curious(X0) [cnf transformation 26]
79. ~generous(X0) | curious(X0) [cnf transformation 26]
80. ~curious(X0) | happy(X0) [cnf transformation 34]
81. ~happy(X0) | curious(X0) [cnf transformation 34]
101. ~strong(X0) | ~tall(X0) [cnf transformation 48]
114. tall(X0) | funny(X0) [cnf transformation 31]
115. ~kind(X0) | strong(X0) | ~kind(X0) [cnf transformation 60]
125. kind(X0) | happy(X0) | generous(X0) [cnf transformation 64]
136. ~happy(fred) [cnf transformation 22]
137. ~kind(X0) | strong(X0) [duplicate literal removal 115]
219. 18 <=> ! [X3] : curious(X3) [avatar definition]
220. curious(X3) <- (18) [avatar component clause 219]
376. strong(X1) | generous(X1) | happy(X1) [resolution 125,137]
431. ~tall(X1) | happy(X1) | generous(X1) [resolution 376,101]
464. happy(X0) | generous(X0) | funny(X0) [resolution 431,114]
519. generous(X1) | funny(X1) | curious(X1) [resolution 464,81]
522. funny(X1) | curious(X1) [subsumption resolution 519,79]
523. curious(X1) [subsumption resolution 522,78]
524. 18 [avatar split clause 523,219]
535. happy(X1) <- (18) [resolution 220,80]
542. $false <- (18) [resolution 535,136]
545. ~18 [avatar contradiction clause 542]
546. $false [avatar sat refutation 524,545]
% SZS output end Proof for 7031920167177624925496723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or not generous then paul is not generous and vice versa.
If lucy is both creative and not humble then someone is not wise or tall and vice versa.
If susan is strong or rich then susan is both rich and not curious and vice versa.
If alice is humble or strong then lucy is not patient or not wise.
If mary is not strong or not wise then mary is old or strong and vice versa.
If lucy is not generous or not humble then someone is both kind and creative.
Everyone who is both strong and humble is not humble or kind.
If john is either not rich or not generous then mary is happy and vice versa.
Everyone who is humble is brave and vice versa.
Everyone who is either not kind or not curious is curious and vice versa.
If fred is kind or happy then someone is both curious and generous.
Everyone who is either rich or calm is not calm.
If someone is not rich then someone is both not strong and not quiet and vice versa.
If john is either not calm or creative then susan is either calm or happy.
Someone is either not wise or not old.
Someone is both humble and not tall.
Someone is humble or not wise.
Someone is both strong and not brave.
Someone is patient or kind.
Someone is both not tall and not old.
Someone is calm.
Alice is wise or quiet. | Mary is not creative. | neutral | ((?[X]:((happy(X)<~>~generous(X))))<=>(~generous(paul)))&
(((creative(lucy)&~humble(lucy)))<=>(?[X]:((~wise(X)|tall(X)))))&
(((strong(susan)|rich(susan)))<=>((rich(susan)&~curious(susan))))&
(((humble(alice)|strong(alice)))=>((~patient(lucy)|~wise(lucy))))&
(((~strong(mary)|~wise(mary)))<=>((old(mary)|strong(mary))))&
(((~generous(lucy)|~humble(lucy)))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:((strong(X)&humble(X))=>(~humble(X)|kind(X))))&
(((~rich(john)<~>~generous(john)))<=>(happy(mary)))&
(![X]:(humble(X)<=>brave(X)))&
(![X]:((~kind(X)<~>~curious(X))<=>curious(X)))&
(((kind(fred)|happy(fred)))=>(?[X]:((curious(X)&generous(X)))))&
(![X]:((rich(X)<~>calm(X))=>~calm(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(((~calm(john)<~>creative(john)))=>((calm(susan)<~>happy(susan))))&
(?[X]:((~wise(X)<~>~old(X))))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((humble(X)|~wise(X))))&
(?[X]:((strong(X)&~brave(X))))&
(?[X]:((patient(X)|kind(X))))&
(?[X]:((~tall(X)&~old(X))))&
(?[X]:(calm(X)))&
((wise(alice)|quiet(alice))) | ~creative(mary) | [] | null | 0 |
If paul is both quiet and not old then someone is both humble and not old and vice versa. Everyone who is not strong is not kind or happy and vice versa. If someone is not funny or creative then someone is both kind and tall and vice versa. Everyone who is both generous and not calm is both not quiet and calm. Everyone who is not rich or funny is not old. Everyone who is either brave or not old is either not quiet or funny. Everyone who is not wise or not brave is both not patient and not humble and vice versa. If someone is both not humble and not kind then fred is not quiet or old and vice versa. If someone is rich or not calm then fred is either not humble or old and vice versa. Everyone who is generous or humble is either not funny or patient and vice versa. If someone is old then someone is both brave and not old. If someone is both happy and wise then someone is both not generous and funny. If alice is either humble or funny then alice is quiet or kind. Everyone who is not curious or not quiet is not strong and vice versa. Everyone who is not creative is both not patient and happy and vice versa. Everyone who is rich or happy is not creative or kind and vice versa. Someone is funny or not creative. Alice is patient. Someone is curious. Fred is tall. Fred is kind. Alice is not strong. Alice is not rich or not old. | Fred is quiet. | neutral | (((quiet(paul)&~old(paul)))<=>(?[X]:((humble(X)&~old(X)))))&
(![X]:(~strong(X)<=>(~kind(X)|happy(X))))&
((?[X]:((~funny(X)|creative(X))))<=>(?[X]:((kind(X)&tall(X)))))&
(![X]:((generous(X)&~calm(X))=>(~quiet(X)&calm(X))))&
(![X]:((~rich(X)|funny(X))=>~old(X)))&
(![X]:((brave(X)<~>~old(X))=>(~quiet(X)<~>funny(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~quiet(fred)|old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>((~humble(fred)<~>old(fred))))&
(![X]:((generous(X)|humble(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((humble(alice)<~>funny(alice)))=>((quiet(alice)|kind(alice))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(![X]:((rich(X)|happy(X))<=>(~creative(X)|kind(X))))&
(?[X]:((funny(X)|~creative(X))))&
(patient(alice))&
(?[X]:(curious(X)))&
(tall(fred))&
(kind(fred))&
(~strong(alice))&
((~rich(alice)|~old(alice))) | quiet(fred) | [] | null | 0 |
Everyone who is generous is both creative and not old.
Everyone who is not tall is either not creative or not quiet and vice versa.
Everyone who is both generous and funny is either not tall or patient and vice versa.
Everyone who is not kind or quiet is calm and vice versa.
Everyone who is either creative or strong is calm or not happy and vice versa.
Everyone who is either not patient or generous is calm.
Everyone who is not old is both not wise and not happy.
If someone is both not wise and not creative then lucy is old or wise and vice versa.
Everyone who is both wise and creative is either wise or quiet and vice versa.
Everyone who is calm or not strong is either happy or not quiet and vice versa.
Everyone who is not humble is either not funny or happy and vice versa.
If someone is calm or not strong then someone is not wise.
Everyone who is either tall or curious is patient or tall and vice versa.
If john is either generous or not funny then mary is both not curious and kind.
Everyone who is not kind is both not funny and creative and vice versa.
If fred is not kind then someone is quiet or rich.
Mary is both curious and old.
Someone is humble or not happy.
Someone is happy or wise.
Someone is not happy or patient.
Someone is creative or quiet.
John is not tall or tall.
Susan is both curious and rich.
Someone is not quiet or not generous. | Lucy is not old. | entailment | (![X]:(generous(X)=>(creative(X)&~old(X))))&
(![X]:(~tall(X)<=>(~creative(X)<~>~quiet(X))))&
(![X]:((generous(X)&funny(X))<=>(~tall(X)<~>patient(X))))&
(![X]:((~kind(X)|quiet(X))<=>calm(X)))&
(![X]:((creative(X)<~>strong(X))<=>(calm(X)|~happy(X))))&
(![X]:((~patient(X)<~>generous(X))=>calm(X)))&
(![X]:(~old(X)=>(~wise(X)&~happy(X))))&
((?[X]:((~wise(X)&~creative(X))))<=>((old(lucy)|wise(lucy))))&
(![X]:((wise(X)&creative(X))<=>(wise(X)<~>quiet(X))))&
(![X]:((calm(X)|~strong(X))<=>(happy(X)<~>~quiet(X))))&
(![X]:(~humble(X)<=>(~funny(X)<~>happy(X))))&
((?[X]:((calm(X)|~strong(X))))=>(?[X]:(~wise(X))))&
(![X]:((tall(X)<~>curious(X))<=>(patient(X)|tall(X))))&
(((generous(john)<~>~funny(john)))=>((~curious(mary)&kind(mary))))&
(![X]:(~kind(X)<=>(~funny(X)&creative(X))))&
((~kind(fred))=>(?[X]:((quiet(X)|rich(X)))))&
((curious(mary)&old(mary)))&
(?[X]:((humble(X)|~happy(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~happy(X)|patient(X))))&
(?[X]:((creative(X)|quiet(X))))&
((~tall(john)|tall(john)))&
((curious(susan)&rich(susan)))&
(?[X]:((~quiet(X)|~generous(X)))) | ~old(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1545653290763496806655319
% SZS output start Proof for 1545653290763496806655319
1. ! [X0] : (generous(X0) => (~old(X0) & creative(X0))) [input p0]
2. ! [X0] : (~tall(X0) <=> (~creative(X0) <~> ~quiet(X0))) [input p1]
3. ! [X0] : ((funny(X0) & generous(X0)) <=> (~tall(X0) <~> patient(X0))) [input p2]
4. ! [X0] : ((quiet(X0) | ~kind(X0)) <=> calm(X0)) [input p3]
6. ! [X0] : ((~patient(X0) <~> generous(X0)) => calm(X0)) [input p5]
8. ? [X0] : (~creative(X0) & ~wise(X0)) <=> (wise(lucy) | old(lucy)) [input p7]
9. ! [X0] : ((creative(X0) & wise(X0)) <=> (wise(X0) <~> quiet(X0))) [input p8]
15. ! [X0] : (~kind(X0) <=> (creative(X0) & ~funny(X0))) [input p14]
25. old(lucy) [input hypothesis]
30. ! [X0] : ((~old(X0) & creative(X0)) | ~generous(X0)) [ennf transformation 1]
31. ! [X0] : (calm(X0) | (~patient(X0) <=> generous(X0))) [ennf transformation 6]
36. ! [X0] : ((~tall(X0) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | tall(X0))) [nnf transformation 2]
37. ! [X0] : (((funny(X0) & generous(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | (~funny(X0) | ~generous(X0)))) [nnf transformation 3]
38. ! [X0] : (((funny(X0) & generous(X0)) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ~funny(X0) | ~generous(X0))) [flattening 37]
39. ! [X0] : (((quiet(X0) | ~kind(X0)) | ~calm(X0)) & (calm(X0) | (~quiet(X0) & kind(X0)))) [nnf transformation 4]
40. ! [X0] : ((quiet(X0) | ~kind(X0) | ~calm(X0)) & (calm(X0) | (~quiet(X0) & kind(X0)))) [flattening 39]
43. ! [X0] : (calm(X0) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) [nnf transformation 31]
44. (? [X0] : (~creative(X0) & ~wise(X0)) | (~wise(lucy) & ~old(lucy))) & ((wise(lucy) | old(lucy)) | ! [X0] : (creative(X0) | wise(X0))) [nnf transformation 8]
45. (? [X0] : (~creative(X0) & ~wise(X0)) | (~wise(lucy) & ~old(lucy))) & (wise(lucy) | old(lucy) | ! [X0] : (creative(X0) | wise(X0))) [flattening 44]
46. (? [X0] : (~creative(X0) & ~wise(X0)) | (~wise(lucy) & ~old(lucy))) & (wise(lucy) | old(lucy) | ! [X1] : (creative(X1) | wise(X1))) [rectify 45]
47. ? [X0] : (~creative(X0) & ~wise(X0)) => (~creative(sK0) & ~wise(sK0)) [choice axiom]
48. ((~creative(sK0) & ~wise(sK0)) | (~wise(lucy) & ~old(lucy))) & (wise(lucy) | old(lucy) | ! [X1] : (creative(X1) | wise(X1))) [skolemisation 46,47]
49. ! [X0] : (((creative(X0) & wise(X0)) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) & (((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | (~creative(X0) | ~wise(X0)))) [nnf transformation 9]
50. ! [X0] : (((creative(X0) & wise(X0)) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) & (((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ~creative(X0) | ~wise(X0))) [flattening 49]
60. ! [X0] : ((~kind(X0) | (~creative(X0) | funny(X0))) & ((creative(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 15]
61. ! [X0] : ((~kind(X0) | ~creative(X0) | funny(X0)) & ((creative(X0) & ~funny(X0)) | kind(X0))) [flattening 60]
72. ~generous(X0) | creative(X0) [cnf transformation 30]
75. quiet(X0) | creative(X0) | tall(X0) [cnf transformation 36]
77. ~tall(X0) | ~creative(X0) | quiet(X0) [cnf transformation 36]
81. ~patient(X0) | ~tall(X0) | generous(X0) [cnf transformation 38]
86. ~calm(X0) | ~kind(X0) | quiet(X0) [cnf transformation 40]
93. calm(X0) | generous(X0) | patient(X0) [cnf transformation 43]
98. ~wise(sK0) | ~old(lucy) [cnf transformation 48]
100. ~creative(sK0) | ~old(lucy) [cnf transformation 48]
105. wise(X0) | wise(X0) | ~quiet(X0) [cnf transformation 50]
129. kind(X0) | creative(X0) [cnf transformation 61]
140. old(lucy) [cnf transformation 25]
144. ~quiet(X0) | wise(X0) [duplicate literal removal 105]
150. 2 <=> creative(sK0) [avatar definition]
152. ~creative(sK0) <- (~2) [avatar component clause 150]
155. 3 <=> old(lucy) [avatar definition]
158. ~3 | ~2 [avatar split clause 100,150,155]
160. 4 <=> wise(sK0) [avatar definition]
162. ~wise(sK0) <- (~4) [avatar component clause 160]
164. ~3 | ~4 [avatar split clause 98,160,155]
252. 3 [avatar split clause 140,155]
266. wise(X3) | tall(X3) | creative(X3) [resolution 75,144]
353. ~kind(X1) | patient(X1) | generous(X1) | quiet(X1) [resolution 93,86]
565. tall(sK0) | creative(sK0) <- (~4) [resolution 266,162]
570. tall(sK0) <- (~2, ~4) [subsumption resolution 565,152]
604. patient(X0) | generous(X0) | quiet(X0) | creative(X0) [resolution 353,129]
615. patient(X0) | quiet(X0) | creative(X0) [subsumption resolution 604,72]
695. quiet(X4) | creative(X4) | ~tall(X4) | generous(X4) [resolution 615,81]
697. ~tall(X4) | quiet(X4) | generous(X4) [subsumption resolution 695,77]
752. 57 <=> quiet(sK0) [avatar definition]
754. quiet(sK0) <- (57) [avatar component clause 752]
760. 58 <=> generous(sK0) [avatar definition]
761. generous(sK0) <- (58) [avatar component clause 760]
768. quiet(sK0) | generous(sK0) <- (~2, ~4) [resolution 697,570]
777. wise(sK0) <- (57) [resolution 754,144]
795. $false <- (~4, 57) [subsumption resolution 777,162]
796. 4 | ~57 [avatar contradiction clause 795]
798. 58 | 57 | 2 | 4 [avatar split clause 768,160,150,752,760]
804. creative(sK0) <- (58) [resolution 761,72]
805. $false <- (~2, 58) [subsumption resolution 804,152]
806. 2 | ~58 [avatar contradiction clause 805]
807. $false [avatar sat refutation 158,164,252,796,798,806]
% SZS output end Proof for 1545653290763496806655319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or not happy then alice is either not happy or not calm and vice versa. If mary is creative then paul is tall. Everyone who is both not calm and brave is brave or not brave. If susan is either not rich or not quiet then someone is not generous or curious and vice versa. Everyone who is either not humble or not creative is either not brave or not wise. If fred is not happy then alice is happy or not quiet. If fred is strong or tall then someone is not calm or kind and vice versa. Everyone who is either patient or not calm is either not funny or not old. Everyone who is tall is either not creative or strong. Everyone who is either not rich or not happy is not funny or calm. Everyone who is both not curious and brave is wise or tall. If john is not generous or not brave then alice is rich. If someone is creative or not humble then someone is funny or wise and vice versa. Everyone who is kind is not happy or not curious. Everyone who is not patient or not happy is rich or kind and vice versa. Everyone who is creative or not happy is both strong and not generous. Someone is both not happy and not old. Fred is not funny or humble. Paul is either happy or not funny. Paul is not wise. Fred is not kind. Someone is not old. Someone is either not creative or strong. Fred is not funny. | Susan is not brave. | neutral | ((?[X]:((curious(X)<~>~happy(X))))<=>((~happy(alice)<~>~calm(alice))))&
((creative(mary))=>(tall(paul)))&
(![X]:((~calm(X)&brave(X))=>(brave(X)|~brave(X))))&
(((~rich(susan)<~>~quiet(susan)))<=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~humble(X)<~>~creative(X))=>(~brave(X)<~>~wise(X))))&
((~happy(fred))=>((happy(alice)|~quiet(alice))))&
(((strong(fred)|tall(fred)))<=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((patient(X)<~>~calm(X))=>(~funny(X)<~>~old(X))))&
(![X]:(tall(X)=>(~creative(X)<~>strong(X))))&
(![X]:((~rich(X)<~>~happy(X))=>(~funny(X)|calm(X))))&
(![X]:((~curious(X)&brave(X))=>(wise(X)|tall(X))))&
(((~generous(john)|~brave(john)))=>(rich(alice)))&
((?[X]:((creative(X)|~humble(X))))<=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(kind(X)=>(~happy(X)|~curious(X))))&
(![X]:((~patient(X)|~happy(X))<=>(rich(X)|kind(X))))&
(![X]:((creative(X)|~happy(X))=>(strong(X)&~generous(X))))&
(?[X]:((~happy(X)&~old(X))))&
((~funny(fred)|humble(fred)))&
((happy(paul)<~>~funny(paul)))&
(~wise(paul))&
(~kind(fred))&
(?[X]:(~old(X)))&
(?[X]:((~creative(X)<~>strong(X))))&
(~funny(fred)) | ~brave(susan) | [] | null | 0 |
Everyone who is not patient is old or not rich.
Everyone who is patient is both not wise and old and vice versa.
Everyone who is old is either not kind or not old.
If someone is both not humble and not curious then someone is both not kind and not patient and vice versa.
If lucy is both not creative and generous then someone is either not calm or rich.
If susan is both not patient and curious then alice is either not patient or generous and vice versa.
If someone is both not generous and not old then mary is both not funny and not humble.
If fred is both not brave and wise then mary is either not quiet or calm.
Everyone who is patient or not brave is both kind and curious and vice versa.
Everyone who is not brave is both not strong and tall.
If someone is old or brave then john is not creative or patient and vice versa.
If someone is both not calm and not kind then someone is either curious or patient and vice versa.
If someone is both not happy and not funny then fred is both funny and not funny and vice versa.
Everyone who is not quiet or not brave is either happy or wise.
If paul is rich then susan is not wise or not brave and vice versa.
If paul is both not quiet and happy then paul is either humble or not calm.
Someone is both not brave and not generous.
Alice is either quiet or not old.
Alice is not humble.
Fred is either strong or not patient.
Someone is either quiet or wise.
Mary is rich.
Mary is both creative and wise.
Lucy is either brave or not funny. | Mary is not quiet. | contradiction | (![X]:(~patient(X)=>(old(X)|~rich(X))))&
(![X]:(patient(X)<=>(~wise(X)&old(X))))&
(![X]:(old(X)=>(~kind(X)<~>~old(X))))&
((?[X]:((~humble(X)&~curious(X))))<=>(?[X]:((~kind(X)&~patient(X)))))&
(((~creative(lucy)&generous(lucy)))=>(?[X]:((~calm(X)<~>rich(X)))))&
(((~patient(susan)&curious(susan)))<=>((~patient(alice)<~>generous(alice))))&
((?[X]:((~generous(X)&~old(X))))=>((~funny(mary)&~humble(mary))))&
(((~brave(fred)&wise(fred)))=>((~quiet(mary)<~>calm(mary))))&
(![X]:((patient(X)|~brave(X))<=>(kind(X)&curious(X))))&
(![X]:(~brave(X)=>(~strong(X)&tall(X))))&
((?[X]:((old(X)|brave(X))))<=>((~creative(john)|patient(john))))&
((?[X]:((~calm(X)&~kind(X))))<=>(?[X]:((curious(X)<~>patient(X)))))&
((?[X]:((~happy(X)&~funny(X))))<=>((funny(fred)&~funny(fred))))&
(![X]:((~quiet(X)|~brave(X))=>(happy(X)<~>wise(X))))&
((rich(paul))<=>((~wise(susan)|~brave(susan))))&
(((~quiet(paul)&happy(paul)))=>((humble(paul)<~>~calm(paul))))&
(?[X]:((~brave(X)&~generous(X))))&
((quiet(alice)<~>~old(alice)))&
(~humble(alice))&
((strong(fred)<~>~patient(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(rich(mary))&
((creative(mary)&wise(mary)))&
((brave(lucy)<~>~funny(lucy))) | ~quiet(mary) | [
"p2",
"p6",
"p8",
"p12",
"p13",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1248098481239807170316998
% SZS output start Proof for 1248098481239807170316998
3. ! [X0] : (old(X0) => (~kind(X0) <~> ~old(X0))) [input p2]
7. ? [X0] : (~old(X0) & ~generous(X0)) => (~humble(mary) & ~funny(mary)) [input p6]
9. ! [X0] : ((~brave(X0) | patient(X0)) <=> (curious(X0) & kind(X0))) [input p8]
13. ? [X0] : (~funny(X0) & ~happy(X0)) <=> (~funny(fred) & funny(fred)) [input p12]
14. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (happy(X0) <~> wise(X0))) [input p13]
17. ? [X0] : (~generous(X0) & ~brave(X0)) [input p16]
23. wise(mary) & creative(mary) [input p22]
25. ~quiet(mary) [input hypothesis]
31. ! [X0] : ((~kind(X0) <~> ~old(X0)) | ~old(X0)) [ennf transformation 3]
34. (~humble(mary) & ~funny(mary)) | ! [X0] : (old(X0) | generous(X0)) [ennf transformation 7]
38. ! [X0] : ((happy(X0) <~> wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 14]
43. ! [X0] : (((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | ~old(X0)) [nnf transformation 31]
55. ! [X0] : (((~brave(X0) | patient(X0)) | (~curious(X0) | ~kind(X0))) & ((curious(X0) & kind(X0)) | (brave(X0) & ~patient(X0)))) [nnf transformation 9]
56. ! [X0] : ((~brave(X0) | patient(X0) | ~curious(X0) | ~kind(X0)) & ((curious(X0) & kind(X0)) | (brave(X0) & ~patient(X0)))) [flattening 55]
67. (? [X0] : (~funny(X0) & ~happy(X0)) | (funny(fred) | ~funny(fred))) & ((~funny(fred) & funny(fred)) | ! [X0] : (funny(X0) | happy(X0))) [nnf transformation 13]
68. (? [X0] : (~funny(X0) & ~happy(X0)) | funny(fred) | ~funny(fred)) & ((~funny(fred) & funny(fred)) | ! [X0] : (funny(X0) | happy(X0))) [flattening 67]
69. (? [X0] : (~funny(X0) & ~happy(X0)) | funny(fred) | ~funny(fred)) & ((~funny(fred) & funny(fred)) | ! [X1] : (funny(X1) | happy(X1))) [rectify 68]
70. ? [X0] : (~funny(X0) & ~happy(X0)) => (~funny(sK6) & ~happy(sK6)) [choice axiom]
71. ((~funny(sK6) & ~happy(sK6)) | funny(fred) | ~funny(fred)) & ((~funny(fred) & funny(fred)) | ! [X1] : (funny(X1) | happy(X1))) [skolemisation 69,70]
72. ! [X0] : (((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | (brave(X0) & quiet(X0))) [nnf transformation 38]
76. ? [X0] : (~generous(X0) & ~brave(X0)) => (~generous(sK7) & ~brave(sK7)) [choice axiom]
77. ~generous(sK7) & ~brave(sK7) [skolemisation 17,76]
88. ~old(X0) | ~kind(X0) | ~old(X0) [cnf transformation 43]
102. ~funny(mary) | old(X0) | generous(X0) [cnf transformation 34]
107. brave(X0) | kind(X0) [cnf transformation 56]
122. funny(fred) | funny(X1) | happy(X1) [cnf transformation 71]
123. ~funny(fred) | funny(X1) | happy(X1) [cnf transformation 71]
128. ~happy(X0) | ~wise(X0) | quiet(X0) [cnf transformation 72]
135. ~brave(sK7) [cnf transformation 77]
136. ~generous(sK7) [cnf transformation 77]
146. wise(mary) [cnf transformation 23]
149. ~quiet(mary) [cnf transformation 25]
150. ~kind(X0) | ~old(X0) [duplicate literal removal 88]
218. 15 <=> ! [X0] : (old(X0) | generous(X0)) [avatar definition]
219. generous(X0) | old(X0) <- (15) [avatar component clause 218]
226. 17 <=> funny(mary) [avatar definition]
229. 15 | ~17 [avatar split clause 102,226,218]
239. 20 <=> quiet(mary) [avatar definition]
240. ~quiet(mary) <- (~20) [avatar component clause 239]
303. 34 <=> ! [X1] : (funny(X1) | happy(X1)) [avatar definition]
304. happy(X1) | funny(X1) <- (34) [avatar component clause 303]
306. 35 <=> funny(fred) [avatar definition]
309. 34 | ~35 [avatar split clause 123,306,303]
310. 34 | 35 [avatar split clause 122,306,303]
384. ~20 [avatar split clause 149,239]
386. kind(sK7) [resolution 107,135]
390. ~old(sK7) [resolution 150,386]
441. ~wise(X2) | quiet(X2) | funny(X2) <- (34) [resolution 128,304]
469. quiet(mary) | funny(mary) <- (34) [resolution 441,146]
471. funny(mary) <- (~20, 34) [subsumption resolution 469,240]
483. 17 | 20 | ~34 [avatar split clause 471,303,239,226]
490. old(sK7) <- (15) [resolution 219,136]
492. $false <- (15) [subsumption resolution 490,390]
493. ~15 [avatar contradiction clause 492]
496. $false [avatar sat refutation 229,309,310,384,483,493]
% SZS output end Proof for 1248098481239807170316998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or old is not funny or not humble.
Everyone who is not quiet is both not brave and generous and vice versa.
If alice is not patient or not tall then someone is both curious and not strong.
If someone is not strong then someone is either rich or not quiet and vice versa.
Everyone who is not funny is either rich or brave and vice versa.
If john is not funny or tall then someone is not brave or generous and vice versa.
Everyone who is not curious or not wise is both brave and not strong and vice versa.
If someone is not brave or not strong then someone is both not tall and wise.
Everyone who is either not tall or strong is tall.
If lucy is both not kind and funny then someone is both not wise and humble.
Everyone who is kind or not tall is not old or not strong.
If mary is either old or quiet then lucy is not humble or kind.
Everyone who is either calm or funny is quiet and vice versa.
If lucy is funny then someone is not old and vice versa.
If alice is either not strong or not calm then paul is calm or funny and vice versa.
Everyone who is not strong or calm is either not humble or creative and vice versa.
Someone is either not old or happy.
Someone is both not quiet and not patient.
Paul is either quiet or strong.
Paul is humble.
Someone is either strong or humble.
Someone is both strong and rich.
Alice is not patient or not kind.
Lucy is not curious. | Lucy is brave. | entailment | (![X]:((tall(X)|old(X))=>(~funny(X)|~humble(X))))&
(![X]:(~quiet(X)<=>(~brave(X)&generous(X))))&
(((~patient(alice)|~tall(alice)))=>(?[X]:((curious(X)&~strong(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:(~funny(X)<=>(rich(X)<~>brave(X))))&
(((~funny(john)|tall(john)))<=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:((~curious(X)|~wise(X))<=>(brave(X)&~strong(X))))&
((?[X]:((~brave(X)|~strong(X))))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~tall(X)<~>strong(X))=>tall(X)))&
(((~kind(lucy)&funny(lucy)))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:((kind(X)|~tall(X))=>(~old(X)|~strong(X))))&
(((old(mary)<~>quiet(mary)))=>((~humble(lucy)|kind(lucy))))&
(![X]:((calm(X)<~>funny(X))<=>quiet(X)))&
((funny(lucy))<=>(?[X]:(~old(X))))&
(((~strong(alice)<~>~calm(alice)))<=>((calm(paul)|funny(paul))))&
(![X]:((~strong(X)|calm(X))<=>(~humble(X)<~>creative(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:((~quiet(X)&~patient(X))))&
((quiet(paul)<~>strong(paul)))&
(humble(paul))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:((strong(X)&rich(X))))&
((~patient(alice)|~kind(alice)))&
(~curious(lucy)) | brave(lucy) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1436426645931757376814491
% SZS output start Proof for 1436426645931757376814491
7. ! [X0] : ((~wise(X0) | ~curious(X0)) <=> (~strong(X0) & brave(X0))) [input p6]
24. ~curious(lucy) [input p23]
25. ~brave(lucy) [input hypothesis]
54. ! [X0] : (((~wise(X0) | ~curious(X0)) | (strong(X0) | ~brave(X0))) & ((~strong(X0) & brave(X0)) | (wise(X0) & curious(X0)))) [nnf transformation 7]
55. ! [X0] : ((~wise(X0) | ~curious(X0) | strong(X0) | ~brave(X0)) & ((~strong(X0) & brave(X0)) | (wise(X0) & curious(X0)))) [flattening 54]
104. curious(X0) | brave(X0) [cnf transformation 55]
151. ~curious(lucy) [cnf transformation 24]
152. ~brave(lucy) [cnf transformation 25]
342. brave(lucy) [resolution 104,151]
343. $false [subsumption resolution 342,152]
% SZS output end Proof for 1436426645931757376814491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not funny is both creative and strong.
Everyone who is both not generous and not patient is either old or generous and vice versa.
Everyone who is either not old or happy is either curious or not humble and vice versa.
Everyone who is happy or not strong is not happy or calm.
Everyone who is either wise or not creative is either not brave or funny.
If someone is quiet then someone is calm.
Everyone who is either wise or not quiet is both not old and not generous and vice versa.
Everyone who is both not strong and funny is generous.
If someone is either not strong or not wise then fred is either not quiet or patient and vice versa.
If someone is both creative and kind then someone is not tall.
If someone is both not curious and not strong then fred is both not generous and not wise.
Everyone who is either tall or calm is either rich or generous.
If lucy is either not kind or not funny then someone is either strong or not tall.
Everyone who is not happy or rich is both curious and generous.
Everyone who is not wise or quiet is old and vice versa.
Everyone who is not tall or not old is either not creative or humble and vice versa.
John is either not strong or old.
John is either strong or not calm.
Someone is generous or wise.
Someone is either calm or not kind.
Someone is creative.
Someone is generous. | Lucy is not quiet. | contradiction | (![X]:((~generous(X)&~funny(X))=>(creative(X)&strong(X))))&
(![X]:((~generous(X)&~patient(X))<=>(old(X)<~>generous(X))))&
(![X]:((~old(X)<~>happy(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((happy(X)|~strong(X))=>(~happy(X)|calm(X))))&
(![X]:((wise(X)<~>~creative(X))=>(~brave(X)<~>funny(X))))&
((?[X]:(quiet(X)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~old(X)&~generous(X))))&
(![X]:((~strong(X)&funny(X))=>generous(X)))&
((?[X]:((~strong(X)<~>~wise(X))))<=>((~quiet(fred)<~>patient(fred))))&
((?[X]:((creative(X)&kind(X))))=>(?[X]:(~tall(X))))&
((?[X]:((~curious(X)&~strong(X))))=>((~generous(fred)&~wise(fred))))&
(![X]:((tall(X)<~>calm(X))=>(rich(X)<~>generous(X))))&
(((~kind(lucy)<~>~funny(lucy)))=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((~happy(X)|rich(X))=>(curious(X)&generous(X))))&
(![X]:((~wise(X)|quiet(X))<=>old(X)))&
(![X]:((~tall(X)|~old(X))<=>(~creative(X)<~>humble(X))))&
((~strong(john)<~>old(john)))&
((strong(john)<~>~calm(john)))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:(creative(X)))&
(?[X]:(generous(X))) | ~quiet(lucy) | [
"p1",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5331609250788703886773526
% SZS output start Proof for 5331609250788703886773526
2. ! [X0] : ((~patient(X0) & ~generous(X0)) <=> (old(X0) <~> generous(X0))) [input p1]
7. ! [X0] : ((wise(X0) <~> ~quiet(X0)) <=> (~generous(X0) & ~old(X0))) [input p6]
15. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> old(X0)) [input p14]
23. ~quiet(lucy) [input hypothesis]
39. ! [X0] : (((~patient(X0) & ~generous(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) & (((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (patient(X0) | generous(X0)))) [nnf transformation 2]
40. ! [X0] : (((~patient(X0) & ~generous(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) & (((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | patient(X0) | generous(X0))) [flattening 39]
46. ! [X0] : ((((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0))))) [nnf transformation 7]
47. ! [X0] : ((((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0))))) [flattening 46]
59. ! [X0] : (((quiet(X0) | ~wise(X0)) | ~old(X0)) & (old(X0) | (~quiet(X0) & wise(X0)))) [nnf transformation 15]
60. ! [X0] : ((quiet(X0) | ~wise(X0) | ~old(X0)) & (old(X0) | (~quiet(X0) & wise(X0)))) [flattening 59]
79. ~generous(X0) | old(X0) | ~generous(X0) [cnf transformation 40]
98. ~old(X0) | wise(X0) | quiet(X0) [cnf transformation 47]
102. quiet(X0) | ~wise(X0) | generous(X0) | old(X0) [cnf transformation 47]
127. wise(X0) | old(X0) [cnf transformation 60]
128. ~quiet(X0) | old(X0) [cnf transformation 60]
129. quiet(X0) | ~wise(X0) | ~old(X0) [cnf transformation 60]
145. ~quiet(lucy) [cnf transformation 23]
148. ~generous(X0) | old(X0) [duplicate literal removal 79]
158. quiet(X0) | ~wise(X0) | old(X0) [subsumption resolution 102,148]
232. ~wise(X0) | quiet(X0) [subsumption resolution 129,158]
275. quiet(X0) | old(X0) [resolution 232,127]
276. old(X0) [subsumption resolution 275,128]
290. wise(X0) | quiet(X0) [resolution 98,276]
296. quiet(X0) [subsumption resolution 290,232]
297. $false [resolution 296,145]
% SZS output end Proof for 5331609250788703886773526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or strong is either not calm or not brave and vice versa.
Everyone who is not tall or creative is both not happy and not calm.
Everyone who is either not creative or quiet is old or not generous.
If someone is creative or patient then someone is both not humble and wise.
Everyone who is not kind is either tall or rich and vice versa.
If fred is both not funny and not generous then someone is both not wise and not humble and vice versa.
Everyone who is both not brave and rich is not wise or not generous.
If fred is not tall then someone is both not wise and tall and vice versa.
If alice is happy then mary is generous or not generous.
Everyone who is funny or brave is not brave or not humble.
Everyone who is not brave is not calm or not funny.
Everyone who is strong or not curious is both not humble and creative.
If someone is not kind then someone is either curious or not rich and vice versa.
If john is both not patient and brave then someone is both not kind and not old.
Everyone who is either not kind or not patient is not funny or old and vice versa.
Everyone who is patient or not happy is both calm and tall and vice versa.
John is not brave or creative.
Someone is not patient.
Lucy is old.
Someone is both not old and quiet.
Lucy is humble or generous. | Lucy is wise. | entailment | (![X]:((happy(X)|strong(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((~tall(X)|creative(X))=>(~happy(X)&~calm(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(old(X)|~generous(X))))&
((?[X]:((creative(X)|patient(X))))=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:(~kind(X)<=>(tall(X)<~>rich(X))))&
(((~funny(fred)&~generous(fred)))<=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~brave(X)&rich(X))=>(~wise(X)|~generous(X))))&
((~tall(fred))<=>(?[X]:((~wise(X)&tall(X)))))&
((happy(alice))=>((generous(mary)|~generous(mary))))&
(![X]:((funny(X)|brave(X))=>(~brave(X)|~humble(X))))&
(![X]:(~brave(X)=>(~calm(X)|~funny(X))))&
(![X]:((strong(X)|~curious(X))=>(~humble(X)&creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>~rich(X)))))&
(((~patient(john)&brave(john)))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~funny(X)|old(X))))&
(![X]:((patient(X)|~happy(X))<=>(calm(X)&tall(X))))&
((~brave(john)|creative(john)))&
(?[X]:(~patient(X)))&
(old(lucy))&
(?[X]:((~old(X)&quiet(X))))&
((humble(lucy)|generous(lucy))) | wise(lucy) | [
"p1",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4887404165411735920536765
% SZS output start Proof for 4887404165411735920536765
2. ! [X0] : ((creative(X0) | ~tall(X0)) => (~calm(X0) & ~happy(X0))) [input p1]
8. ~tall(fred) <=> ? [X0] : (tall(X0) & ~wise(X0)) [input p7]
16. ! [X0] : ((~happy(X0) | patient(X0)) <=> (tall(X0) & calm(X0))) [input p15]
22. ~wise(lucy) [input hypothesis]
25. ! [X0] : ((~calm(X0) & ~happy(X0)) | (~creative(X0) & tall(X0))) [ennf transformation 2]
52. (~tall(fred) | ! [X0] : (~tall(X0) | wise(X0))) & (? [X0] : (tall(X0) & ~wise(X0)) | tall(fred)) [nnf transformation 8]
53. (~tall(fred) | ! [X0] : (~tall(X0) | wise(X0))) & (? [X1] : (tall(X1) & ~wise(X1)) | tall(fred)) [rectify 52]
54. ? [X1] : (tall(X1) & ~wise(X1)) => (tall(sK2) & ~wise(sK2)) [choice axiom]
55. (~tall(fred) | ! [X0] : (~tall(X0) | wise(X0))) & ((tall(sK2) & ~wise(sK2)) | tall(fred)) [skolemisation 53,54]
65. ! [X0] : (((~happy(X0) | patient(X0)) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | (happy(X0) & ~patient(X0)))) [nnf transformation 16]
66. ! [X0] : ((~happy(X0) | patient(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | (happy(X0) & ~patient(X0)))) [flattening 65]
77. ~happy(X0) | tall(X0) [cnf transformation 25]
98. ~tall(fred) | ~tall(X0) | wise(X0) [cnf transformation 55]
122. tall(X0) | happy(X0) [cnf transformation 66]
130. ~wise(lucy) [cnf transformation 22]
174. 10 <=> ! [X0] : (~tall(X0) | wise(X0)) [avatar definition]
175. ~tall(X0) | wise(X0) <- (10) [avatar component clause 174]
177. 11 <=> tall(fred) [avatar definition]
179. ~tall(fred) <- (~11) [avatar component clause 177]
180. 10 | ~11 [avatar split clause 98,177,174]
235. tall(X0) [subsumption resolution 122,77]
250. wise(X0) <- (10) [subsumption resolution 175,235]
253. $false <- (10) [resolution 250,130]
254. ~10 [avatar contradiction clause 253]
255. $false <- (~11) [subsumption resolution 179,235]
256. 11 [avatar contradiction clause 255]
257. $false [avatar sat refutation 180,254,256]
% SZS output end Proof for 4887404165411735920536765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not creative is curious or funny. Everyone who is both happy and brave is not rich or not creative. Everyone who is both not strong and wise is either calm or not old and vice versa. If paul is quiet then someone is either strong or humble. If someone is either not funny or happy then someone is either not generous or not kind. Everyone who is not brave is both not funny and not calm. If someone is both not generous and humble then john is both quiet and generous and vice versa. Everyone who is both happy and funny is not brave and vice versa. Everyone who is both wise and not wise is both not brave and not calm and vice versa. If paul is either wise or curious then someone is not humble or not kind. If someone is either not happy or not humble then someone is either not humble or not curious and vice versa. Everyone who is not curious or not tall is kind and vice versa. If lucy is both not happy and funny then alice is not kind and vice versa. Everyone who is not strong is calm. Everyone who is both rich and strong is either kind or not quiet. Everyone who is either kind or happy is not wise. Susan is both not patient and not happy. John is not happy or not creative. Fred is happy or kind. Someone is calm. Susan is both wise and not calm. Someone is happy or not creative. Someone is old or humble. Lucy is either curious or not funny. | Susan is tall. | entailment | (![X]:((~patient(X)|~creative(X))=>(curious(X)|funny(X))))&
(![X]:((happy(X)&brave(X))=>(~rich(X)|~creative(X))))&
(![X]:((~strong(X)&wise(X))<=>(calm(X)<~>~old(X))))&
((quiet(paul))=>(?[X]:((strong(X)<~>humble(X)))))&
((?[X]:((~funny(X)<~>happy(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(![X]:((happy(X)&funny(X))<=>~brave(X)))&
(![X]:((wise(X)&~wise(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~curious(X)|~tall(X))<=>kind(X)))&
(((~happy(lucy)&funny(lucy)))<=>(~kind(alice)))&
(![X]:(~strong(X)=>calm(X)))&
(![X]:((rich(X)&strong(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>happy(X))=>~wise(X)))&
((~patient(susan)&~happy(susan)))&
((~happy(john)|~creative(john)))&
((happy(fred)|kind(fred)))&
(?[X]:(calm(X)))&
((wise(susan)&~calm(susan)))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((old(X)|humble(X))))&
((curious(lucy)<~>~funny(lucy))) | tall(susan) | [
"p11",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3555431084794872047402213
% SZS output start Proof for 3555431084794872047402213
12. ! [X0] : ((~tall(X0) | ~curious(X0)) <=> kind(X0)) [input p11]
16. ! [X0] : ((kind(X0) <~> happy(X0)) => ~wise(X0)) [input p15]
17. ~happy(susan) & ~patient(susan) [input p16]
21. ~calm(susan) & wise(susan) [input p20]
25. ~tall(susan) [input hypothesis]
37. ! [X0] : (~wise(X0) | (kind(X0) <=> happy(X0))) [ennf transformation 16]
64. ! [X0] : (((~tall(X0) | ~curious(X0)) | ~kind(X0)) & (kind(X0) | (tall(X0) & curious(X0)))) [nnf transformation 12]
65. ! [X0] : ((~tall(X0) | ~curious(X0) | ~kind(X0)) & (kind(X0) | (tall(X0) & curious(X0)))) [flattening 64]
68. ! [X0] : (~wise(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) [nnf transformation 37]
114. tall(X0) | kind(X0) [cnf transformation 65]
120. ~kind(X0) | happy(X0) | ~wise(X0) [cnf transformation 68]
123. ~happy(susan) [cnf transformation 17]
127. wise(susan) [cnf transformation 21]
133. ~tall(susan) [cnf transformation 25]
305. kind(susan) [resolution 114,133]
370. happy(susan) | ~wise(susan) [resolution 120,305]
381. ~wise(susan) [subsumption resolution 370,123]
382. $false [subsumption resolution 381,127]
% SZS output end Proof for 3555431084794872047402213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and humble is not old and vice versa. If someone is both kind and not curious then alice is either not generous or old. Everyone who is not generous is rich or patient. If someone is not patient then mary is not patient or creative and vice versa. Everyone who is strong is old or tall and vice versa. Everyone who is not generous is not kind or quiet and vice versa. If fred is not curious or not quiet then john is not patient. Everyone who is either not kind or creative is both patient and humble. If someone is either wise or not old then someone is both not kind and not generous and vice versa. If john is either not funny or old then alice is not brave or not creative and vice versa. Everyone who is not brave or kind is both old and tall and vice versa. Everyone who is both quiet and funny is either kind or funny and vice versa. Everyone who is either happy or not patient is calm. Everyone who is either generous or old is not curious and vice versa. If alice is either not kind or not brave then paul is not happy or rich and vice versa. Everyone who is kind is either not quiet or not curious. Paul is not happy or wise. Paul is not happy or calm. Someone is funny or not brave. Mary is either generous or not strong. Someone is brave or not wise. Paul is not patient. Susan is not brave or not happy. Susan is both not generous and not quiet. | Alice is not happy. | neutral | (![X]:((wise(X)&humble(X))<=>~old(X)))&
((?[X]:((kind(X)&~curious(X))))=>((~generous(alice)<~>old(alice))))&
(![X]:(~generous(X)=>(rich(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((~patient(mary)|creative(mary))))&
(![X]:(strong(X)<=>(old(X)|tall(X))))&
(![X]:(~generous(X)<=>(~kind(X)|quiet(X))))&
(((~curious(fred)|~quiet(fred)))=>(~patient(john)))&
(![X]:((~kind(X)<~>creative(X))=>(patient(X)&humble(X))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~kind(X)&~generous(X)))))&
(((~funny(john)<~>old(john)))<=>((~brave(alice)|~creative(alice))))&
(![X]:((~brave(X)|kind(X))<=>(old(X)&tall(X))))&
(![X]:((quiet(X)&funny(X))<=>(kind(X)<~>funny(X))))&
(![X]:((happy(X)<~>~patient(X))=>calm(X)))&
(![X]:((generous(X)<~>old(X))<=>~curious(X)))&
(((~kind(alice)<~>~brave(alice)))<=>((~happy(paul)|rich(paul))))&
(![X]:(kind(X)=>(~quiet(X)<~>~curious(X))))&
((~happy(paul)|wise(paul)))&
((~happy(paul)|calm(paul)))&
(?[X]:((funny(X)|~brave(X))))&
((generous(mary)<~>~strong(mary)))&
(?[X]:((brave(X)|~wise(X))))&
(~patient(paul))&
((~brave(susan)|~happy(susan)))&
((~generous(susan)&~quiet(susan))) | ~happy(alice) | [] | null | 0 |
Everyone who is wise is funny.
If someone is both humble and curious then alice is either happy or not happy.
If fred is not generous then someone is not humble or not strong and vice versa.
If susan is not strong then john is kind.
If lucy is creative then someone is both happy and funny.
Everyone who is both quiet and humble is both not old and not funny and vice versa.
Everyone who is old is both humble and not tall and vice versa.
If mary is not curious or funny then john is either wise or kind and vice versa.
If alice is both wise and not calm then alice is funny.
Everyone who is calm is both not generous and curious and vice versa.
If someone is quiet then paul is generous or humble and vice versa.
Everyone who is quiet or not wise is old and vice versa.
Everyone who is not creative or creative is not old or quiet and vice versa.
Everyone who is quiet is curious or not brave and vice versa.
Everyone who is creative or not kind is not wise or not curious.
If lucy is wise or not brave then someone is not happy or not funny and vice versa.
Someone is not quiet or old.
Paul is funny.
Alice is either not wise or not kind.
Someone is tall.
Someone is either curious or humble. | Paul is calm. | contradiction | (![X]:(wise(X)=>funny(X)))&
((?[X]:((humble(X)&curious(X))))=>((happy(alice)<~>~happy(alice))))&
((~generous(fred))<=>(?[X]:((~humble(X)|~strong(X)))))&
((~strong(susan))=>(kind(john)))&
((creative(lucy))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((quiet(X)&humble(X))<=>(~old(X)&~funny(X))))&
(![X]:(old(X)<=>(humble(X)&~tall(X))))&
(((~curious(mary)|funny(mary)))<=>((wise(john)<~>kind(john))))&
(((wise(alice)&~calm(alice)))=>(funny(alice)))&
(![X]:(calm(X)<=>(~generous(X)&curious(X))))&
((?[X]:(quiet(X)))<=>((generous(paul)|humble(paul))))&
(![X]:((quiet(X)|~wise(X))<=>old(X)))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(((wise(lucy)|~brave(lucy)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(?[X]:((~quiet(X)|old(X))))&
(funny(paul))&
((~wise(alice)<~>~kind(alice)))&
(?[X]:(tall(X)))&
(?[X]:((curious(X)<~>humble(X)))) | calm(paul) | [
"p5",
"p6",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6886215346397336168770747
% SZS output start Proof for 6886215346397336168770747
6. ! [X0] : ((humble(X0) & quiet(X0)) <=> (~funny(X0) & ~old(X0))) [input p5]
7. ! [X0] : (old(X0) <=> (~tall(X0) & humble(X0))) [input p6]
10. ! [X0] : (calm(X0) <=> (curious(X0) & ~generous(X0))) [input p9]
11. ? [X0] : quiet(X0) <=> (humble(paul) | generous(paul)) [input p10]
12. ! [X0] : ((~wise(X0) | quiet(X0)) <=> old(X0)) [input p11]
14. ! [X0] : (quiet(X0) <=> (~brave(X0) | curious(X0))) [input p13]
22. calm(paul) [input hypothesis]
23. ! [X0] : (calm(X0) => (curious(X0) & ~generous(X0))) [unused predicate definition removal 10]
30. ! [X0] : ((curious(X0) & ~generous(X0)) | ~calm(X0)) [ennf transformation 23]
40. ! [X0] : (((humble(X0) & quiet(X0)) | (funny(X0) | old(X0))) & ((~funny(X0) & ~old(X0)) | (~humble(X0) | ~quiet(X0)))) [nnf transformation 6]
41. ! [X0] : (((humble(X0) & quiet(X0)) | funny(X0) | old(X0)) & ((~funny(X0) & ~old(X0)) | ~humble(X0) | ~quiet(X0))) [flattening 40]
42. ! [X0] : ((old(X0) | (tall(X0) | ~humble(X0))) & ((~tall(X0) & humble(X0)) | ~old(X0))) [nnf transformation 7]
43. ! [X0] : ((old(X0) | tall(X0) | ~humble(X0)) & ((~tall(X0) & humble(X0)) | ~old(X0))) [flattening 42]
46. (? [X0] : quiet(X0) | (~humble(paul) & ~generous(paul))) & ((humble(paul) | generous(paul)) | ! [X0] : ~quiet(X0)) [nnf transformation 11]
47. (? [X0] : quiet(X0) | (~humble(paul) & ~generous(paul))) & (humble(paul) | generous(paul) | ! [X0] : ~quiet(X0)) [flattening 46]
48. (? [X0] : quiet(X0) | (~humble(paul) & ~generous(paul))) & (humble(paul) | generous(paul) | ! [X1] : ~quiet(X1)) [rectify 47]
49. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
50. (quiet(sK2) | (~humble(paul) & ~generous(paul))) & (humble(paul) | generous(paul) | ! [X1] : ~quiet(X1)) [skolemisation 48,49]
51. ! [X0] : (((~wise(X0) | quiet(X0)) | ~old(X0)) & (old(X0) | (wise(X0) & ~quiet(X0)))) [nnf transformation 12]
52. ! [X0] : ((~wise(X0) | quiet(X0) | ~old(X0)) & (old(X0) | (wise(X0) & ~quiet(X0)))) [flattening 51]
55. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & ((~brave(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 14]
56. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & (~brave(X0) | curious(X0) | ~quiet(X0))) [flattening 55]
79. ~old(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 41]
83. ~old(X0) | humble(X0) [cnf transformation 43]
93. ~calm(X0) | ~generous(X0) [cnf transformation 30]
94. ~calm(X0) | curious(X0) [cnf transformation 30]
95. humble(paul) | generous(paul) | ~quiet(X1) [cnf transformation 50]
97. quiet(sK2) | ~humble(paul) [cnf transformation 50]
98. ~quiet(X0) | old(X0) [cnf transformation 52]
106. ~curious(X0) | quiet(X0) [cnf transformation 56]
121. calm(paul) [cnf transformation 22]
185. 14 <=> humble(paul) [avatar definition]
189. 15 <=> quiet(sK2) [avatar definition]
191. quiet(sK2) <- (15) [avatar component clause 189]
192. ~14 | 15 [avatar split clause 97,189,185]
194. 16 <=> generous(paul) [avatar definition]
199. 17 <=> ! [X1] : ~quiet(X1) [avatar definition]
200. ~quiet(X1) <- (17) [avatar component clause 199]
201. 17 | 16 | 14 [avatar split clause 95,185,194,199]
251. ~generous(paul) [resolution 93,121]
252. ~16 [avatar split clause 251,194]
253. curious(paul) [resolution 94,121]
254. old(sK2) <- (15) [resolution 98,191]
257. humble(sK2) <- (15) [resolution 254,83]
259. quiet(paul) [resolution 106,253]
267. ~humble(sK2) | ~quiet(sK2) <- (15) [resolution 79,254]
270. ~quiet(sK2) <- (15) [subsumption resolution 267,257]
271. $false <- (15) [subsumption resolution 270,191]
272. ~15 [avatar contradiction clause 271]
289. $false <- (17) [resolution 259,200]
291. ~17 [avatar contradiction clause 289]
292. $false [avatar sat refutation 192,201,252,272,291]
% SZS output end Proof for 6886215346397336168770747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then mary is either not curious or humble.
Everyone who is both not tall and kind is wise.
If someone is both quiet and funny then mary is either not wise or not strong.
If someone is kind or not old then mary is either creative or brave and vice versa.
Everyone who is not kind is both creative and not creative.
Everyone who is creative or tall is both happy and not generous.
Everyone who is not wise or not patient is happy or not humble and vice versa.
Everyone who is either not tall or not happy is not wise or not patient.
Everyone who is brave is either curious or patient.
Everyone who is either not strong or old is both patient and generous.
If fred is either not strong or tall then susan is curious.
Everyone who is either curious or brave is both not curious and generous and vice versa.
Everyone who is quiet is either brave or not patient.
Everyone who is not wise is not happy and vice versa.
If someone is not humble or not kind then alice is happy or old and vice versa.
Everyone who is not humble or patient is not curious or not creative.
Someone is not brave.
Someone is either old or brave.
Someone is either not calm or rich.
Fred is curious or tall.
Mary is either not happy or humble. | Susan is not quiet. | neutral | ((?[X]:(tall(X)))=>((~curious(mary)<~>humble(mary))))&
(![X]:((~tall(X)&kind(X))=>wise(X)))&
((?[X]:((quiet(X)&funny(X))))=>((~wise(mary)<~>~strong(mary))))&
((?[X]:((kind(X)|~old(X))))<=>((creative(mary)<~>brave(mary))))&
(![X]:(~kind(X)=>(creative(X)&~creative(X))))&
(![X]:((creative(X)|tall(X))=>(happy(X)&~generous(X))))&
(![X]:((~wise(X)|~patient(X))<=>(happy(X)|~humble(X))))&
(![X]:((~tall(X)<~>~happy(X))=>(~wise(X)|~patient(X))))&
(![X]:(brave(X)=>(curious(X)<~>patient(X))))&
(![X]:((~strong(X)<~>old(X))=>(patient(X)&generous(X))))&
(((~strong(fred)<~>tall(fred)))=>(curious(susan)))&
(![X]:((curious(X)<~>brave(X))<=>(~curious(X)&generous(X))))&
(![X]:(quiet(X)=>(brave(X)<~>~patient(X))))&
(![X]:(~wise(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~kind(X))))<=>((happy(alice)|old(alice))))&
(![X]:((~humble(X)|patient(X))=>(~curious(X)|~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:((old(X)<~>brave(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
((curious(fred)|tall(fred)))&
((~happy(mary)<~>humble(mary))) | ~quiet(susan) | [] | null | 0 |
Everyone who is both wise and not old is not generous.
Everyone who is not patient is happy.
If paul is not humble or not rich then mary is funny and vice versa.
Everyone who is either humble or not tall is not happy or happy and vice versa.
Everyone who is funny or strong is either generous or not happy and vice versa.
Everyone who is either tall or wise is both wise and not calm and vice versa.
If someone is quiet then someone is brave.
If someone is either not creative or patient then paul is not calm and vice versa.
If someone is either generous or curious then someone is either curious or not humble.
If someone is both calm and not humble then someone is both happy and not generous and vice versa.
If someone is generous then susan is both not curious and not funny and vice versa.
Everyone who is not brave is both humble and funny and vice versa.
If fred is either not tall or wise then john is either not rich or not wise.
Everyone who is both not happy and happy is not quiet or not rich.
If john is brave then mary is both not quiet and calm and vice versa.
If mary is both not curious and old then paul is either not wise or strong.
Alice is either kind or not kind.
Someone is kind.
Someone is either creative or old.
Someone is either not old or calm.
Someone is rich.
Someone is either kind or not patient.
Someone is patient or happy. | Susan is not curious. | neutral | (![X]:((wise(X)&~old(X))=>~generous(X)))&
(![X]:(~patient(X)=>happy(X)))&
(((~humble(paul)|~rich(paul)))<=>(funny(mary)))&
(![X]:((humble(X)<~>~tall(X))<=>(~happy(X)|happy(X))))&
(![X]:((funny(X)|strong(X))<=>(generous(X)<~>~happy(X))))&
(![X]:((tall(X)<~>wise(X))<=>(wise(X)&~calm(X))))&
((?[X]:(quiet(X)))=>(?[X]:(brave(X))))&
((?[X]:((~creative(X)<~>patient(X))))<=>(~calm(paul)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:((curious(X)<~>~humble(X)))))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((happy(X)&~generous(X)))))&
((?[X]:(generous(X)))<=>((~curious(susan)&~funny(susan))))&
(![X]:(~brave(X)<=>(humble(X)&funny(X))))&
(((~tall(fred)<~>wise(fred)))=>((~rich(john)<~>~wise(john))))&
(![X]:((~happy(X)&happy(X))=>(~quiet(X)|~rich(X))))&
((brave(john))<=>((~quiet(mary)&calm(mary))))&
(((~curious(mary)&old(mary)))=>((~wise(paul)<~>strong(paul))))&
((kind(alice)<~>~kind(alice)))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>old(X))))&
(?[X]:((~old(X)<~>calm(X))))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((patient(X)|happy(X)))) | ~curious(susan) | [] | null | 0 |
If mary is both creative and patient then someone is either not happy or funny.
Everyone who is either not creative or funny is both not rich and happy.
Everyone who is patient is quiet.
Everyone who is not humble or old is either calm or not strong.
If alice is both happy and tall then john is either calm or not generous.
Everyone who is calm or not humble is not curious.
If mary is either tall or happy then alice is both wise and not creative.
Everyone who is both generous and kind is not brave or not creative and vice versa.
Everyone who is not rich or patient is not creative or happy and vice versa.
If someone is either not humble or kind then paul is both kind and not strong and vice versa.
If alice is either rich or not rich then someone is strong or rich and vice versa.
Everyone who is generous is both kind and happy and vice versa.
Everyone who is either not rich or not humble is not happy or not rich.
Everyone who is not rich or funny is not brave or creative.
If someone is either not patient or creative then mary is both not creative and not strong and vice versa.
Everyone who is either funny or tall is both not creative and tall.
Paul is patient.
Susan is not generous.
Someone is not brave or not rich.
Someone is rich.
Someone is old or humble.
Lucy is both not wise and happy. | John is not funny. | neutral | (((creative(mary)&patient(mary)))=>(?[X]:((~happy(X)<~>funny(X)))))&
(![X]:((~creative(X)<~>funny(X))=>(~rich(X)&happy(X))))&
(![X]:(patient(X)=>quiet(X)))&
(![X]:((~humble(X)|old(X))=>(calm(X)<~>~strong(X))))&
(((happy(alice)&tall(alice)))=>((calm(john)<~>~generous(john))))&
(![X]:((calm(X)|~humble(X))=>~curious(X)))&
(((tall(mary)<~>happy(mary)))=>((wise(alice)&~creative(alice))))&
(![X]:((generous(X)&kind(X))<=>(~brave(X)|~creative(X))))&
(![X]:((~rich(X)|patient(X))<=>(~creative(X)|happy(X))))&
((?[X]:((~humble(X)<~>kind(X))))<=>((kind(paul)&~strong(paul))))&
(((rich(alice)<~>~rich(alice)))<=>(?[X]:((strong(X)|rich(X)))))&
(![X]:(generous(X)<=>(kind(X)&happy(X))))&
(![X]:((~rich(X)<~>~humble(X))=>(~happy(X)|~rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~brave(X)|creative(X))))&
((?[X]:((~patient(X)<~>creative(X))))<=>((~creative(mary)&~strong(mary))))&
(![X]:((funny(X)<~>tall(X))=>(~creative(X)&tall(X))))&
(patient(paul))&
(~generous(susan))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((old(X)|humble(X))))&
((~wise(lucy)&happy(lucy))) | ~funny(john) | [] | null | 0 |
If paul is generous then alice is both quiet and not happy.
If someone is rich or creative then someone is not strong.
If lucy is either not tall or funny then lucy is either not rich or not happy and vice versa.
Everyone who is both old and not happy is both humble and not generous.
If someone is either not tall or tall then paul is both not creative and not quiet.
If paul is both not funny and humble then someone is both not rich and not curious and vice versa.
If someone is either brave or funny then someone is humble or funny.
If lucy is not old then john is wise and vice versa.
Everyone who is either not happy or not curious is quiet and vice versa.
Everyone who is strong is either not curious or tall and vice versa.
Everyone who is either not patient or not humble is both tall and not quiet and vice versa.
Everyone who is not quiet or humble is strong.
Everyone who is both creative and kind is both kind and not humble.
If john is not calm or rich then someone is not tall.
Everyone who is not kind or not curious is either wise or patient and vice versa.
Everyone who is either funny or tall is not generous and vice versa.
Someone is happy.
Susan is not tall or not rich.
Susan is both not calm and not happy.
Lucy is either creative or brave.
John is both not creative and patient.
Someone is not rich or generous.
Lucy is either not calm or not rich.
Someone is not creative. | Paul is not strong. | contradiction | ((generous(paul))=>((quiet(alice)&~happy(alice))))&
((?[X]:((rich(X)|creative(X))))=>(?[X]:(~strong(X))))&
(((~tall(lucy)<~>funny(lucy)))<=>((~rich(lucy)<~>~happy(lucy))))&
(![X]:((old(X)&~happy(X))=>(humble(X)&~generous(X))))&
((?[X]:((~tall(X)<~>tall(X))))=>((~creative(paul)&~quiet(paul))))&
(((~funny(paul)&humble(paul)))<=>(?[X]:((~rich(X)&~curious(X)))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:((humble(X)|funny(X)))))&
((~old(lucy))<=>(wise(john)))&
(![X]:((~happy(X)<~>~curious(X))<=>quiet(X)))&
(![X]:(strong(X)<=>(~curious(X)<~>tall(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(tall(X)&~quiet(X))))&
(![X]:((~quiet(X)|humble(X))=>strong(X)))&
(![X]:((creative(X)&kind(X))=>(kind(X)&~humble(X))))&
(((~calm(john)|rich(john)))=>(?[X]:(~tall(X))))&
(![X]:((~kind(X)|~curious(X))<=>(wise(X)<~>patient(X))))&
(![X]:((funny(X)<~>tall(X))<=>~generous(X)))&
(?[X]:(happy(X)))&
((~tall(susan)|~rich(susan)))&
((~calm(susan)&~happy(susan)))&
((creative(lucy)<~>brave(lucy)))&
((~creative(john)&patient(john)))&
(?[X]:((~rich(X)|generous(X))))&
((~calm(lucy)<~>~rich(lucy)))&
(?[X]:(~creative(X))) | ~strong(paul) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1988725842824691718674711
% SZS output start Proof for 1988725842824691718674711
5. ? [X0] : (~tall(X0) <~> tall(X0)) => (~quiet(paul) & ~creative(paul)) [input p4]
12. ! [X0] : ((humble(X0) | ~quiet(X0)) => strong(X0)) [input p11]
25. ~strong(paul) [input hypothesis]
32. (~quiet(paul) & ~creative(paul)) | ! [X0] : (~tall(X0) <=> tall(X0)) [ennf transformation 5]
34. ! [X0] : (strong(X0) | (~humble(X0) & quiet(X0))) [ennf transformation 12]
42. (~quiet(paul) & ~creative(paul)) | ! [X0] : ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))) [nnf transformation 32]
86. ~quiet(paul) | tall(X0) | tall(X0) [cnf transformation 42]
87. ~quiet(paul) | ~tall(X0) | ~tall(X0) [cnf transformation 42]
110. strong(X0) | quiet(X0) [cnf transformation 34]
138. ~strong(paul) [cnf transformation 25]
141. ~quiet(paul) | tall(X0) [duplicate literal removal 86]
142. ~quiet(paul) | ~tall(X0) [duplicate literal removal 87]
194. 11 <=> ! [X0] : ~tall(X0) [avatar definition]
195. ~tall(X0) <- (11) [avatar component clause 194]
197. 12 <=> quiet(paul) [avatar definition]
200. 11 | ~12 [avatar split clause 142,197,194]
202. 13 <=> ! [X0] : tall(X0) [avatar definition]
203. tall(X0) <- (13) [avatar component clause 202]
204. 13 | ~12 [avatar split clause 141,197,202]
308. quiet(paul) [resolution 110,138]
312. 12 [avatar split clause 308,197]
313. $false <- (11, 13) [subsumption resolution 195,203]
314. ~11 | ~13 [avatar contradiction clause 313]
315. $false [avatar sat refutation 200,204,312,314]
% SZS output end Proof for 1988725842824691718674711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is strong or tall then susan is not patient or not generous. Everyone who is not patient is old or not calm. If someone is brave then someone is both kind and not rich and vice versa. Everyone who is funny or not old is both kind and not calm and vice versa. Everyone who is generous or not brave is not patient and vice versa. Everyone who is rich is either not kind or brave. If someone is both not patient and not curious then someone is calm or strong and vice versa. If alice is either rich or not creative then alice is both curious and funny and vice versa. Everyone who is either wise or happy is either not curious or not happy. Everyone who is both not humble and not creative is not rich or not tall and vice versa. If someone is both not generous and not tall then lucy is patient. Everyone who is not strong or old is both tall and patient and vice versa. Everyone who is funny or curious is not rich. Everyone who is not happy or not patient is either rich or funny and vice versa. If someone is kind then someone is wise or rich and vice versa. If someone is either not curious or rich then someone is both kind and creative. Someone is both generous and not quiet. Someone is either not calm or not strong. Someone is calm or not brave. John is both not quiet and not curious. Someone is either not calm or calm. Lucy is not kind. Alice is generous or not wise. | Alice is happy. | neutral | (((strong(john)|tall(john)))=>((~patient(susan)|~generous(susan))))&
(![X]:(~patient(X)=>(old(X)|~calm(X))))&
((?[X]:(brave(X)))<=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((funny(X)|~old(X))<=>(kind(X)&~calm(X))))&
(![X]:((generous(X)|~brave(X))<=>~patient(X)))&
(![X]:(rich(X)=>(~kind(X)<~>brave(X))))&
((?[X]:((~patient(X)&~curious(X))))<=>(?[X]:((calm(X)|strong(X)))))&
(((rich(alice)<~>~creative(alice)))<=>((curious(alice)&funny(alice))))&
(![X]:((wise(X)<~>happy(X))=>(~curious(X)<~>~happy(X))))&
(![X]:((~humble(X)&~creative(X))<=>(~rich(X)|~tall(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(patient(lucy)))&
(![X]:((~strong(X)|old(X))<=>(tall(X)&patient(X))))&
(![X]:((funny(X)|curious(X))=>~rich(X)))&
(![X]:((~happy(X)|~patient(X))<=>(rich(X)<~>funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)|rich(X)))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((kind(X)&creative(X)))))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
(?[X]:((calm(X)|~brave(X))))&
((~quiet(john)&~curious(john)))&
(?[X]:((~calm(X)<~>calm(X))))&
(~kind(lucy))&
((generous(alice)|~wise(alice))) | happy(alice) | [] | null | 0 |
Everyone who is either not creative or not wise is both not quiet and calm.
If someone is generous or funny then fred is both not rich and happy and vice versa.
Everyone who is patient is quiet.
Everyone who is not humble or old is either calm or not strong.
If alice is both happy and tall then john is either calm or not generous.
Everyone who is calm or not humble is not curious.
If mary is either tall or happy then alice is both wise and not creative.
Everyone who is both generous and kind is not brave or not creative and vice versa.
Everyone who is not rich or patient is not creative or happy and vice versa.
If someone is either not humble or kind then paul is both kind and not strong and vice versa.
If alice is either rich or not rich then someone is strong or rich and vice versa.
Everyone who is generous is both kind and happy and vice versa.
Everyone who is either not rich or not humble is not happy or not rich.
Everyone who is not rich or funny is not brave or creative.
If someone is either not patient or creative then mary is both not creative and not strong and vice versa.
Everyone who is either funny or tall is both not creative and tall.
Paul is patient.
Susan is not generous.
Someone is not brave or not rich.
Someone is rich.
Someone is old or humble.
Lucy is both not wise and happy. | Mary is patient. | neutral | (![X]:((~creative(X)<~>~wise(X))=>(~quiet(X)&calm(X))))&
((?[X]:((generous(X)|funny(X))))<=>((~rich(fred)&happy(fred))))&
(![X]:(patient(X)=>quiet(X)))&
(![X]:((~humble(X)|old(X))=>(calm(X)<~>~strong(X))))&
(((happy(alice)&tall(alice)))=>((calm(john)<~>~generous(john))))&
(![X]:((calm(X)|~humble(X))=>~curious(X)))&
(((tall(mary)<~>happy(mary)))=>((wise(alice)&~creative(alice))))&
(![X]:((generous(X)&kind(X))<=>(~brave(X)|~creative(X))))&
(![X]:((~rich(X)|patient(X))<=>(~creative(X)|happy(X))))&
((?[X]:((~humble(X)<~>kind(X))))<=>((kind(paul)&~strong(paul))))&
(((rich(alice)<~>~rich(alice)))<=>(?[X]:((strong(X)|rich(X)))))&
(![X]:(generous(X)<=>(kind(X)&happy(X))))&
(![X]:((~rich(X)<~>~humble(X))=>(~happy(X)|~rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~brave(X)|creative(X))))&
((?[X]:((~patient(X)<~>creative(X))))<=>((~creative(mary)&~strong(mary))))&
(![X]:((funny(X)<~>tall(X))=>(~creative(X)&tall(X))))&
(patient(paul))&
(~generous(susan))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((old(X)|humble(X))))&
((~wise(lucy)&happy(lucy))) | patient(mary) | [] | null | 0 |
If someone is either not curious or old then susan is both happy and wise and vice versa.
If mary is either not creative or not funny then fred is both old and not wise and vice versa.
Everyone who is not wise is both not humble and brave.
Everyone who is not tall or not wise is tall.
If lucy is both quiet and not old then someone is both calm and brave and vice versa.
If lucy is both not strong and not patient then someone is both old and not old and vice versa.
If someone is both calm and not old then paul is strong and vice versa.
If john is both not creative and not wise then someone is either tall or not rich.
Everyone who is both not curious and not humble is either strong or calm.
If someone is either not strong or curious then john is kind or not patient and vice versa.
Everyone who is both not strong and not brave is not humble and vice versa.
If someone is either humble or not curious then someone is both happy and wise.
If john is either old or happy then susan is either old or not quiet.
If someone is calm or not wise then someone is not wise or brave and vice versa.
Everyone who is both not tall and brave is creative and vice versa.
Everyone who is both not strong and not generous is not brave.
John is either not rich or calm.
Someone is both not strong and not happy.
Someone is not quiet.
Lucy is either not curious or tall.
Someone is rich.
Alice is either not strong or not patient.
Fred is either not happy or not humble. | Susan is not strong. | neutral | ((?[X]:((~curious(X)<~>old(X))))<=>((happy(susan)&wise(susan))))&
(((~creative(mary)<~>~funny(mary)))<=>((old(fred)&~wise(fred))))&
(![X]:(~wise(X)=>(~humble(X)&brave(X))))&
(![X]:((~tall(X)|~wise(X))=>tall(X)))&
(((quiet(lucy)&~old(lucy)))<=>(?[X]:((calm(X)&brave(X)))))&
(((~strong(lucy)&~patient(lucy)))<=>(?[X]:((old(X)&~old(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(strong(paul)))&
(((~creative(john)&~wise(john)))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((~curious(X)&~humble(X))=>(strong(X)<~>calm(X))))&
((?[X]:((~strong(X)<~>curious(X))))<=>((kind(john)|~patient(john))))&
(![X]:((~strong(X)&~brave(X))<=>~humble(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>(?[X]:((happy(X)&wise(X)))))&
(((old(john)<~>happy(john)))=>((old(susan)<~>~quiet(susan))))&
((?[X]:((calm(X)|~wise(X))))<=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:((~tall(X)&brave(X))<=>creative(X)))&
(![X]:((~strong(X)&~generous(X))=>~brave(X)))&
((~rich(john)<~>calm(john)))&
(?[X]:((~strong(X)&~happy(X))))&
(?[X]:(~quiet(X)))&
((~curious(lucy)<~>tall(lucy)))&
(?[X]:(rich(X)))&
((~strong(alice)<~>~patient(alice)))&
((~happy(fred)<~>~humble(fred))) | ~strong(susan) | [] | null | 0 |
If fred is humble or not kind then lucy is happy and vice versa. Everyone who is not strong is either not quiet or happy. Everyone who is both not curious and brave is not creative or not curious. If fred is both strong and not kind then mary is not quiet or not funny. Everyone who is either curious or not patient is curious or not wise and vice versa. If fred is quiet then susan is either not happy or not tall and vice versa. Everyone who is curious or not old is both rich and not funny. Everyone who is either not old or creative is old or not wise. If paul is both brave and not generous then someone is either not funny or not humble. If susan is rich or creative then someone is not strong or not kind. Everyone who is not strong or brave is strong and vice versa. If someone is either not patient or not generous then someone is not patient. Everyone who is not quiet or strong is both not humble and not creative and vice versa. Everyone who is both kind and wise is either not creative or not patient. Everyone who is not quiet is calm or funny and vice versa. Everyone who is not old is both not creative and not calm and vice versa. Lucy is calm. Someone is generous or not generous. Someone is either not generous or not strong. Mary is not tall or creative. Paul is curious or not funny. Someone is quiet or not strong. | Paul is not quiet. | neutral | (((humble(fred)|~kind(fred)))<=>(happy(lucy)))&
(![X]:(~strong(X)=>(~quiet(X)<~>happy(X))))&
(![X]:((~curious(X)&brave(X))=>(~creative(X)|~curious(X))))&
(((strong(fred)&~kind(fred)))=>((~quiet(mary)|~funny(mary))))&
(![X]:((curious(X)<~>~patient(X))<=>(curious(X)|~wise(X))))&
((quiet(fred))<=>((~happy(susan)<~>~tall(susan))))&
(![X]:((curious(X)|~old(X))=>(rich(X)&~funny(X))))&
(![X]:((~old(X)<~>creative(X))=>(old(X)|~wise(X))))&
(((brave(paul)&~generous(paul)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((rich(susan)|creative(susan)))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((~strong(X)|brave(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(~patient(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~humble(X)&~creative(X))))&
(![X]:((kind(X)&wise(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(~quiet(X)<=>(calm(X)|funny(X))))&
(![X]:(~old(X)<=>(~creative(X)&~calm(X))))&
(calm(lucy))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((~generous(X)<~>~strong(X))))&
((~tall(mary)|creative(mary)))&
((curious(paul)|~funny(paul)))&
(?[X]:((quiet(X)|~strong(X)))) | ~quiet(paul) | [] | null | 0 |
If lucy is both kind and not happy then someone is calm or not brave.
If someone is both kind and not curious then mary is not generous and vice versa.
Everyone who is both not generous and not quiet is not funny and vice versa.
If someone is either wise or quiet then mary is not humble and vice versa.
Everyone who is both not funny and not strong is not kind and vice versa.
Everyone who is both not old and not kind is generous or not wise and vice versa.
If someone is not calm or not kind then paul is both humble and generous.
If someone is either funny or not tall then paul is strong.
If someone is old then alice is either not funny or wise and vice versa.
Everyone who is both not curious and not brave is calm or not quiet.
If someone is calm then susan is happy or tall and vice versa.
Everyone who is curious is both not strong and tall.
Everyone who is rich is both wise and strong and vice versa.
Everyone who is creative is both not wise and strong and vice versa.
If someone is wise or quiet then fred is not humble or not generous and vice versa.
Everyone who is not quiet or not tall is both not brave and not old.
Someone is either not kind or not funny.
Someone is not brave or patient.
Lucy is both not tall and not happy.
Fred is either not old or generous.
Someone is either not curious or not creative.
John is strong or not curious.
Paul is brave. | Fred is rich. | neutral | (((kind(lucy)&~happy(lucy)))=>(?[X]:((calm(X)|~brave(X)))))&
((?[X]:((kind(X)&~curious(X))))<=>(~generous(mary)))&
(![X]:((~generous(X)&~quiet(X))<=>~funny(X)))&
((?[X]:((wise(X)<~>quiet(X))))<=>(~humble(mary)))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(![X]:(creative(X)<=>(~wise(X)&strong(X))))&
((?[X]:((wise(X)|quiet(X))))<=>((~humble(fred)|~generous(fred))))&
(![X]:((~quiet(X)|~tall(X))=>(~brave(X)&~old(X))))&
(?[X]:((~kind(X)<~>~funny(X))))&
(?[X]:((~brave(X)|patient(X))))&
((~tall(lucy)&~happy(lucy)))&
((~old(fred)<~>generous(fred)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((strong(john)|~curious(john)))&
(brave(paul)) | rich(fred) | [] | null | 0 |
If someone is either kind or not creative then mary is either not kind or not humble. If someone is both not strong and not kind then someone is both not patient and not rich and vice versa. Everyone who is both old and creative is strong and vice versa. If someone is either not patient or happy then susan is either happy or patient. Everyone who is kind is not curious. If mary is either not rich or funny then paul is not happy and vice versa. If someone is not generous then someone is both happy and wise and vice versa. Everyone who is patient is strong. Everyone who is patient is not rich. If someone is both not creative and not tall then fred is both not brave and not patient. Everyone who is wise is both not quiet and kind. Everyone who is wise or not funny is creative and vice versa. Everyone who is quiet is calm and vice versa. Everyone who is both generous and not curious is not strong. If someone is happy then someone is brave and vice versa. Everyone who is either patient or old is patient and vice versa. Someone is either not funny or happy. Someone is not quiet or happy. Someone is not kind. Fred is funny. Mary is either calm or not patient. Someone is wise. | Mary is old. | contradiction | ((?[X]:((kind(X)<~>~creative(X))))=>((~kind(mary)<~>~humble(mary))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((old(X)&creative(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>happy(X))))=>((happy(susan)<~>patient(susan))))&
(![X]:(kind(X)=>~curious(X)))&
(((~rich(mary)<~>funny(mary)))<=>(~happy(paul)))&
((?[X]:(~generous(X)))<=>(?[X]:((happy(X)&wise(X)))))&
(![X]:(patient(X)=>strong(X)))&
(![X]:(patient(X)=>~rich(X)))&
((?[X]:((~creative(X)&~tall(X))))=>((~brave(fred)&~patient(fred))))&
(![X]:(wise(X)=>(~quiet(X)&kind(X))))&
(![X]:((wise(X)|~funny(X))<=>creative(X)))&
(![X]:(quiet(X)<=>calm(X)))&
(![X]:((generous(X)&~curious(X))=>~strong(X)))&
((?[X]:(happy(X)))<=>(?[X]:(brave(X))))&
(![X]:((patient(X)<~>old(X))<=>patient(X)))&
(?[X]:((~funny(X)<~>happy(X))))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:(~kind(X)))&
(funny(fred))&
((calm(mary)<~>~patient(mary)))&
(?[X]:(wise(X))) | old(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 197560378046570313998308
% SZS output start Proof for 197560378046570313998308
16. ! [X0] : ((patient(X0) <~> old(X0)) <=> patient(X0)) [input p15]
23. old(mary) [input hypothesis]
60. ! [X0] : ((((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ~patient(X0)) & (patient(X0) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0))))) [nnf transformation 16]
106. patient(X0) | patient(X0) | ~old(X0) [cnf transformation 60]
108. ~old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 60]
117. old(mary) [cnf transformation 23]
118. patient(X0) | ~old(X0) [duplicate literal removal 106]
119. ~old(X0) | ~patient(X0) [duplicate literal removal 108]
235. ~old(X0) [subsumption resolution 118,119]
265. $false [subsumption resolution 117,235]
% SZS output end Proof for 197560378046570313998308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not strong then someone is either funny or not funny and vice versa.
If mary is either rich or brave then someone is either patient or not happy.
Everyone who is happy is either not patient or patient and vice versa.
Everyone who is either generous or brave is either not tall or calm.
Everyone who is either not kind or curious is both not calm and patient.
If paul is not funny or calm then alice is both not quiet and rich and vice versa.
If mary is either not creative or not patient then john is both calm and happy and vice versa.
Everyone who is both not calm and rich is both not kind and not quiet.
Everyone who is either funny or not brave is both not creative and not humble.
Everyone who is either not quiet or not calm is not generous.
If someone is humble or kind then john is either not funny or not wise and vice versa.
Everyone who is not generous or not rich is either not old or not humble.
If paul is either old or kind then someone is either curious or happy.
If someone is not wise then susan is both tall and not tall and vice versa.
Everyone who is tall is either not brave or not patient and vice versa.
Everyone who is both not quiet and not brave is not happy and vice versa.
Someone is brave.
Someone is both not creative and not curious.
Fred is not strong or happy.
Someone is either wise or strong.
Paul is calm.
Susan is calm or not happy.
Someone is either not quiet or not funny.
Someone is either patient or strong. | Mary is wise. | entailment | ((?[X]:((~rich(X)|~strong(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
(((rich(mary)<~>brave(mary)))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:(happy(X)<=>(~patient(X)<~>patient(X))))&
(![X]:((generous(X)<~>brave(X))=>(~tall(X)<~>calm(X))))&
(![X]:((~kind(X)<~>curious(X))=>(~calm(X)&patient(X))))&
(((~funny(paul)|calm(paul)))<=>((~quiet(alice)&rich(alice))))&
(((~creative(mary)<~>~patient(mary)))<=>((calm(john)&happy(john))))&
(![X]:((~calm(X)&rich(X))=>(~kind(X)&~quiet(X))))&
(![X]:((funny(X)<~>~brave(X))=>(~creative(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>~generous(X)))&
((?[X]:((humble(X)|kind(X))))<=>((~funny(john)<~>~wise(john))))&
(![X]:((~generous(X)|~rich(X))=>(~old(X)<~>~humble(X))))&
(((old(paul)<~>kind(paul)))=>(?[X]:((curious(X)<~>happy(X)))))&
((?[X]:(~wise(X)))<=>((tall(susan)&~tall(susan))))&
(![X]:(tall(X)<=>(~brave(X)<~>~patient(X))))&
(![X]:((~quiet(X)&~brave(X))<=>~happy(X)))&
(?[X]:(brave(X)))&
(?[X]:((~creative(X)&~curious(X))))&
((~strong(fred)|happy(fred)))&
(?[X]:((wise(X)<~>strong(X))))&
(calm(paul))&
((calm(susan)|~happy(susan)))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((patient(X)<~>strong(X)))) | wise(mary) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5900091727681323307295842
% SZS output start Proof for 5900091727681323307295842
14. ? [X0] : ~wise(X0) <=> (~tall(susan) & tall(susan)) [input p13]
25. ~wise(mary) [input hypothesis]
61. (? [X0] : ~wise(X0) | (tall(susan) | ~tall(susan))) & ((~tall(susan) & tall(susan)) | ! [X0] : wise(X0)) [nnf transformation 14]
62. (? [X0] : ~wise(X0) | tall(susan) | ~tall(susan)) & ((~tall(susan) & tall(susan)) | ! [X0] : wise(X0)) [flattening 61]
63. (? [X0] : ~wise(X0) | tall(susan) | ~tall(susan)) & ((~tall(susan) & tall(susan)) | ! [X1] : wise(X1)) [rectify 62]
64. ? [X0] : ~wise(X0) => ~wise(sK5) [choice axiom]
65. (~wise(sK5) | tall(susan) | ~tall(susan)) & ((~tall(susan) & tall(susan)) | ! [X1] : wise(X1)) [skolemisation 63,64]
137. tall(susan) | wise(X1) [cnf transformation 65]
138. ~tall(susan) | wise(X1) [cnf transformation 65]
159. ~wise(mary) [cnf transformation 25]
285. 25 <=> ! [X1] : wise(X1) [avatar definition]
286. wise(X1) <- (25) [avatar component clause 285]
288. 26 <=> tall(susan) [avatar definition]
291. 25 | ~26 [avatar split clause 138,288,285]
292. 25 | 26 [avatar split clause 137,288,285]
326. $false <- (25) [resolution 286,159]
327. ~25 [avatar contradiction clause 326]
328. $false [avatar sat refutation 291,292,327]
% SZS output end Proof for 5900091727681323307295842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is not quiet or old and vice versa.
Everyone who is both patient and kind is not rich and vice versa.
Everyone who is patient is both not happy and not old.
If john is wise or old then someone is either not brave or old and vice versa.
Everyone who is not creative or funny is both generous and not happy and vice versa.
If someone is either quiet or curious then susan is either kind or not rich.
If someone is funny then someone is both not curious and not funny and vice versa.
Everyone who is both rich and not curious is not happy and vice versa.
If someone is not quiet then someone is both tall and quiet.
Everyone who is not happy or not wise is rich or tall and vice versa.
If someone is either tall or not strong then mary is both not tall and funny.
If someone is not wise or not kind then someone is not rich.
If someone is brave or curious then fred is either not happy or not brave.
If john is both patient and not funny then someone is not old or not tall and vice versa.
Everyone who is both not brave and happy is humble or not tall and vice versa.
If john is both brave and generous then susan is not funny.
Susan is not rich or tall.
Someone is quiet or old.
Paul is both quiet and old.
Mary is both not happy and brave.
Someone is either not wise or not curious.
Someone is not tall or funny.
Susan is not strong. | Susan is not wise. | contradiction | (![X]:(~patient(X)<=>(~quiet(X)|old(X))))&
(![X]:((patient(X)&kind(X))<=>~rich(X)))&
(![X]:(patient(X)=>(~happy(X)&~old(X))))&
(((wise(john)|old(john)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~creative(X)|funny(X))<=>(generous(X)&~happy(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>((kind(susan)<~>~rich(susan))))&
((?[X]:(funny(X)))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((rich(X)&~curious(X))<=>~happy(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((~happy(X)|~wise(X))<=>(rich(X)|tall(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>((~tall(mary)&funny(mary))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((patient(john)&~funny(john)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~brave(X)&happy(X))<=>(humble(X)|~tall(X))))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
((~rich(susan)|tall(susan)))&
(?[X]:((quiet(X)|old(X))))&
((quiet(paul)&old(paul)))&
((~happy(mary)&brave(mary)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((~tall(X)|funny(X))))&
(~strong(susan)) | ~wise(susan) | [
"p1",
"p2",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6836023118418707146599776
% SZS output start Proof for 6836023118418707146599776
2. ! [X0] : ((kind(X0) & patient(X0)) <=> ~rich(X0)) [input p1]
3. ! [X0] : (patient(X0) => (~old(X0) & ~happy(X0))) [input p2]
8. ! [X0] : ((~curious(X0) & rich(X0)) <=> ~happy(X0)) [input p7]
12. ? [X0] : (~kind(X0) | ~wise(X0)) => ? [X0] : ~rich(X0) [input p11]
24. ~wise(susan) [input hypothesis]
27. ? [X0] : (~kind(X0) | ~wise(X0)) => ? [X1] : ~rich(X1) [rectify 12]
28. ! [X0] : ((~old(X0) & ~happy(X0)) | ~patient(X0)) [ennf transformation 3]
32. ? [X1] : ~rich(X1) | ! [X0] : (kind(X0) & wise(X0)) [ennf transformation 27]
38. ! [X0] : (((kind(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | (~kind(X0) | ~patient(X0)))) [nnf transformation 2]
39. ! [X0] : (((kind(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | ~kind(X0) | ~patient(X0))) [flattening 38]
53. ! [X0] : (((~curious(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) | ~rich(X0)))) [nnf transformation 8]
54. ! [X0] : (((~curious(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | curious(X0) | ~rich(X0))) [flattening 53]
61. ? [X0] : ~rich(X0) | ! [X1] : (kind(X1) & wise(X1)) [rectify 32]
62. ? [X0] : ~rich(X0) => ~rich(sK4) [choice axiom]
63. ~rich(sK4) | ! [X1] : (kind(X1) & wise(X1)) [skolemisation 61,62]
83. rich(X0) | patient(X0) [cnf transformation 39]
85. ~happy(X0) | ~patient(X0) [cnf transformation 28]
106. happy(X0) | rich(X0) [cnf transformation 54]
118. ~rich(sK4) | wise(X1) [cnf transformation 63]
145. ~wise(susan) [cnf transformation 24]
252. 24 <=> rich(sK4) [avatar definition]
254. ~rich(sK4) <- (~24) [avatar component clause 252]
257. 25 <=> ! [X1] : wise(X1) [avatar definition]
258. wise(X1) <- (25) [avatar component clause 257]
259. 25 | ~24 [avatar split clause 118,252,257]
386. rich(X1) | ~patient(X1) [resolution 106,85]
387. rich(X1) [subsumption resolution 386,83]
390. $false <- (~24) [resolution 387,254]
391. 24 [avatar contradiction clause 390]
392. $false <- (25) [resolution 258,145]
393. ~25 [avatar contradiction clause 392]
394. $false [avatar sat refutation 259,391,393]
% SZS output end Proof for 6836023118418707146599776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or kind is both not strong and strong and vice versa. Everyone who is not generous or not quiet is either strong or kind and vice versa. Everyone who is not wise or not creative is both not funny and strong and vice versa. If mary is kind or not patient then alice is either tall or curious and vice versa. Everyone who is not creative is both brave and kind and vice versa. Everyone who is not funny or not patient is not rich and vice versa. Everyone who is not patient or not curious is not happy and vice versa. If john is happy or not creative then someone is wise. Everyone who is not tall or rich is not rich and vice versa. Everyone who is either not happy or not old is calm and vice versa. If mary is both brave and old then someone is either not strong or brave and vice versa. Everyone who is funny is not creative or kind and vice versa. If someone is both creative and calm then someone is either quiet or not calm and vice versa. Everyone who is either not humble or not brave is not strong and vice versa. If john is funny or humble then mary is either quiet or old and vice versa. Everyone who is calm or not brave is either not tall or not happy and vice versa. Someone is not wise. Someone is brave. Someone is both not kind and not rich. Someone is creative or not humble. Someone is patient. | Alice is generous. | entailment | (![X]:((humble(X)<~>kind(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(strong(X)<~>kind(X))))&
(![X]:((~wise(X)|~creative(X))<=>(~funny(X)&strong(X))))&
(((kind(mary)|~patient(mary)))<=>((tall(alice)<~>curious(alice))))&
(![X]:(~creative(X)<=>(brave(X)&kind(X))))&
(![X]:((~funny(X)|~patient(X))<=>~rich(X)))&
(![X]:((~patient(X)|~curious(X))<=>~happy(X)))&
(((happy(john)|~creative(john)))=>(?[X]:(wise(X))))&
(![X]:((~tall(X)|rich(X))<=>~rich(X)))&
(![X]:((~happy(X)<~>~old(X))<=>calm(X)))&
(((brave(mary)&old(mary)))<=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:(funny(X)<=>(~creative(X)|kind(X))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>~brave(X))<=>~strong(X)))&
(((funny(john)|humble(john)))<=>((quiet(mary)<~>old(mary))))&
(![X]:((calm(X)|~brave(X))<=>(~tall(X)<~>~happy(X))))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X)))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((creative(X)|~humble(X))))&
(?[X]:(patient(X))) | generous(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4696725175445021573991741
% SZS output start Proof for 4696725175445021573991741
1. ! [X0] : ((humble(X0) <~> kind(X0)) <=> (strong(X0) & ~strong(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (strong(X0) <~> kind(X0))) [input p1]
3. ! [X0] : ((~creative(X0) | ~wise(X0)) <=> (strong(X0) & ~funny(X0))) [input p2]
4. (~patient(mary) | kind(mary)) <=> (tall(alice) <~> curious(alice)) [input p3]
5. ! [X0] : (~creative(X0) <=> (kind(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> ~rich(X0)) [input p5]
7. ! [X0] : ((~curious(X0) | ~patient(X0)) <=> ~happy(X0)) [input p6]
9. ! [X0] : ((rich(X0) | ~tall(X0)) <=> ~rich(X0)) [input p8]
10. ! [X0] : ((~happy(X0) <~> ~old(X0)) <=> calm(X0)) [input p9]
11. (old(mary) & brave(mary)) <=> ? [X0] : (~strong(X0) <~> brave(X0)) [input p10]
12. ! [X0] : (funny(X0) <=> (kind(X0) | ~creative(X0))) [input p11]
14. ! [X0] : ((~humble(X0) <~> ~brave(X0)) <=> ~strong(X0)) [input p13]
15. (humble(john) | funny(john)) <=> (quiet(mary) <~> old(mary)) [input p14]
16. ! [X0] : ((~brave(X0) | calm(X0)) <=> (~tall(X0) <~> ~happy(X0))) [input p15]
22. ~generous(alice) [input hypothesis]
25. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 1]
26. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [flattening 25]
27. ! [X0] : (((~quiet(X0) | ~generous(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (quiet(X0) & generous(X0)))) [nnf transformation 2]
28. ! [X0] : ((~quiet(X0) | ~generous(X0) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (quiet(X0) & generous(X0)))) [flattening 27]
29. ! [X0] : (((~creative(X0) | ~wise(X0)) | (~strong(X0) | funny(X0))) & ((strong(X0) & ~funny(X0)) | (creative(X0) & wise(X0)))) [nnf transformation 3]
30. ! [X0] : ((~creative(X0) | ~wise(X0) | ~strong(X0) | funny(X0)) & ((strong(X0) & ~funny(X0)) | (creative(X0) & wise(X0)))) [flattening 29]
31. ((~patient(mary) | kind(mary)) | ((tall(alice) | ~curious(alice)) & (curious(alice) | ~tall(alice)))) & (((~curious(alice) | ~tall(alice)) & (curious(alice) | tall(alice))) | (patient(mary) & ~kind(mary))) [nnf transformation 4]
32. (~patient(mary) | kind(mary) | ((tall(alice) | ~curious(alice)) & (curious(alice) | ~tall(alice)))) & (((~curious(alice) | ~tall(alice)) & (curious(alice) | tall(alice))) | (patient(mary) & ~kind(mary))) [flattening 31]
33. ! [X0] : ((~creative(X0) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | creative(X0))) [nnf transformation 5]
34. ! [X0] : ((~creative(X0) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | creative(X0))) [flattening 33]
35. ! [X0] : (((~patient(X0) | ~funny(X0)) | rich(X0)) & (~rich(X0) | (patient(X0) & funny(X0)))) [nnf transformation 6]
36. ! [X0] : ((~patient(X0) | ~funny(X0) | rich(X0)) & (~rich(X0) | (patient(X0) & funny(X0)))) [flattening 35]
37. ! [X0] : (((~curious(X0) | ~patient(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & patient(X0)))) [nnf transformation 7]
38. ! [X0] : ((~curious(X0) | ~patient(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & patient(X0)))) [flattening 37]
41. ! [X0] : (((rich(X0) | ~tall(X0)) | rich(X0)) & (~rich(X0) | (~rich(X0) & tall(X0)))) [nnf transformation 9]
42. ! [X0] : ((rich(X0) | ~tall(X0) | rich(X0)) & (~rich(X0) | (~rich(X0) & tall(X0)))) [flattening 41]
43. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | ~calm(X0)) & (calm(X0) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [nnf transformation 10]
44. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (? [X0] : ((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~old(mary) | ~brave(mary))) [nnf transformation 11]
45. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (? [X0] : ((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | ~old(mary) | ~brave(mary)) [flattening 44]
46. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (? [X1] : ((~brave(X1) | strong(X1)) & (brave(X1) | ~strong(X1))) | ~old(mary) | ~brave(mary)) [rectify 45]
47. ? [X1] : ((~brave(X1) | strong(X1)) & (brave(X1) | ~strong(X1))) => ((~brave(sK1) | strong(sK1)) & (brave(sK1) | ~strong(sK1))) [choice axiom]
48. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (((~brave(sK1) | strong(sK1)) & (brave(sK1) | ~strong(sK1))) | ~old(mary) | ~brave(mary)) [skolemisation 46,47]
49. ! [X0] : ((funny(X0) | (~kind(X0) & creative(X0))) & ((kind(X0) | ~creative(X0)) | ~funny(X0))) [nnf transformation 12]
50. ! [X0] : ((funny(X0) | (~kind(X0) & creative(X0))) & (kind(X0) | ~creative(X0) | ~funny(X0))) [flattening 49]
56. ! [X0] : ((((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | strong(X0)) & (~strong(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0))))) [nnf transformation 14]
57. ((humble(john) | funny(john)) | ((quiet(mary) | ~old(mary)) & (old(mary) | ~quiet(mary)))) & (((~old(mary) | ~quiet(mary)) & (old(mary) | quiet(mary))) | (~humble(john) & ~funny(john))) [nnf transformation 15]
58. (humble(john) | funny(john) | ((quiet(mary) | ~old(mary)) & (old(mary) | ~quiet(mary)))) & (((~old(mary) | ~quiet(mary)) & (old(mary) | quiet(mary))) | (~humble(john) & ~funny(john))) [flattening 57]
59. ! [X0] : (((~brave(X0) | calm(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (brave(X0) & ~calm(X0)))) [nnf transformation 16]
60. ! [X0] : ((~brave(X0) | calm(X0) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (brave(X0) & ~calm(X0)))) [flattening 59]
71. ~strong(X0) | kind(X0) | ~humble(X0) [cnf transformation 26]
73. ~humble(X0) | kind(X0) | strong(X0) [cnf transformation 26]
77. generous(X0) | strong(X0) | kind(X0) [cnf transformation 28]
78. quiet(X0) | strong(X0) | kind(X0) [cnf transformation 28]
79. ~strong(X0) | ~kind(X0) | generous(X0) [cnf transformation 28]
84. ~funny(X0) | creative(X0) [cnf transformation 30]
93. ~patient(mary) | kind(mary) | tall(alice) | ~curious(alice) [cnf transformation 32]
96. ~brave(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 34]
99. ~patient(X0) | ~funny(X0) | rich(X0) [cnf transformation 36]
100. ~happy(X0) | patient(X0) [cnf transformation 38]
101. ~happy(X0) | curious(X0) [cnf transformation 38]
106. ~rich(X0) | ~rich(X0) [cnf transformation 42]
107. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 42]
108. ~old(X0) | calm(X0) | happy(X0) [cnf transformation 43]
110. ~calm(X0) | ~happy(X0) | ~old(X0) [cnf transformation 43]
114. brave(mary) | brave(X0) | strong(X0) [cnf transformation 48]
115. brave(mary) | ~strong(X0) | ~brave(X0) [cnf transformation 48]
116. old(mary) | brave(X0) | strong(X0) [cnf transformation 48]
117. old(mary) | ~strong(X0) | ~brave(X0) [cnf transformation 48]
118. kind(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 50]
119. funny(X0) | creative(X0) [cnf transformation 50]
120. ~kind(X0) | funny(X0) [cnf transformation 50]
127. ~brave(X0) | ~strong(X0) | humble(X0) [cnf transformation 56]
129. ~brave(X0) | ~humble(X0) | strong(X0) [cnf transformation 56]
135. humble(john) | funny(john) | old(mary) | ~quiet(mary) [cnf transformation 58]
139. ~calm(X0) | tall(X0) | happy(X0) [cnf transformation 60]
140. happy(X0) | tall(X0) | brave(X0) [cnf transformation 60]
141. ~happy(X0) | calm(X0) | ~brave(X0) | tall(X0) [cnf transformation 60]
149. ~generous(alice) [cnf transformation 22]
150. ~rich(X0) [duplicate literal removal 106]
151. ~tall(X0) | rich(X0) [duplicate literal removal 107]
153. ~humble(X0) | kind(X0) [subsumption resolution 71,73]
155. 1 <=> curious(alice) [avatar definition]
159. 2 <=> tall(alice) [avatar definition]
160. ~tall(alice) <- (~2) [avatar component clause 159]
161. tall(alice) <- (2) [avatar component clause 159]
163. 3 <=> kind(mary) [avatar definition]
164. ~kind(mary) <- (~3) [avatar component clause 163]
165. kind(mary) <- (3) [avatar component clause 163]
167. 4 <=> patient(mary) [avatar definition]
168. patient(mary) <- (4) [avatar component clause 167]
170. ~1 | 2 | 3 | ~4 [avatar split clause 93,167,163,159,155]
186. 7 <=> happy(john) [avatar definition]
187. happy(john) <- (7) [avatar component clause 186]
188. ~happy(john) <- (~7) [avatar component clause 186]
191. 8 <=> ! [X0] : (~strong(X0) | ~brave(X0)) [avatar definition]
192. ~brave(X0) | ~strong(X0) <- (8) [avatar component clause 191]
194. 9 <=> old(mary) [avatar definition]
196. old(mary) <- (9) [avatar component clause 194]
197. 8 | 9 [avatar split clause 117,194,191]
199. 10 <=> ! [X0] : (brave(X0) | strong(X0)) [avatar definition]
200. brave(X0) | strong(X0) <- (10) [avatar component clause 199]
201. 10 | 9 [avatar split clause 116,194,199]
203. 11 <=> brave(mary) [avatar definition]
204. ~brave(mary) <- (~11) [avatar component clause 203]
205. brave(mary) <- (11) [avatar component clause 203]
206. 8 | 11 [avatar split clause 115,203,191]
207. 10 | 11 [avatar split clause 114,203,199]
218. creative(X0) [subsumption resolution 119,84]
219. ~funny(X0) | kind(X0) [subsumption resolution 118,218]
248. 20 <=> quiet(mary) [avatar definition]
249. ~quiet(mary) <- (~20) [avatar component clause 248]
252. 21 <=> funny(john) [avatar definition]
254. funny(john) <- (21) [avatar component clause 252]
256. 22 <=> humble(john) [avatar definition]
258. humble(john) <- (22) [avatar component clause 256]
260. ~20 | 9 | 21 | 22 [avatar split clause 135,256,252,194,248]
266. rich(alice) <- (2) [resolution 151,161]
267. $false <- (2) [subsumption resolution 266,150]
268. ~2 [avatar contradiction clause 267]
272. strong(alice) | kind(alice) [resolution 77,149]
274. 23 <=> kind(alice) [avatar definition]
276. kind(alice) <- (23) [avatar component clause 274]
278. 24 <=> strong(alice) [avatar definition]
280. strong(alice) <- (24) [avatar component clause 278]
281. 23 | 24 [avatar split clause 272,278,274]
283. strong(mary) | kind(mary) <- (~20) [resolution 78,249]
293. strong(mary) <- (~3, ~20) [subsumption resolution 283,164]
329. ~kind(X0) | ~creative(X0) | strong(X0) <- (10) [resolution 96,200]
332. ~kind(X0) | strong(X0) <- (10) [subsumption resolution 329,218]
384. 36 <=> humble(mary) [avatar definition]
419. tall(john) | brave(john) <- (~7) [resolution 140,188]
422. brave(X2) | tall(X2) | curious(X2) [resolution 140,101]
423. brave(X3) | tall(X3) | patient(X3) [resolution 140,100]
426. 38 <=> brave(john) [avatar definition]
428. brave(john) <- (38) [avatar component clause 426]
430. 39 <=> tall(john) [avatar definition]
432. tall(john) <- (39) [avatar component clause 430]
433. 38 | 39 | 7 [avatar split clause 419,186,430,426]
459. ~kind(john) | ~creative(john) <- (38) [resolution 428,96]
462. ~kind(john) <- (38) [subsumption resolution 459,218]
488. strong(alice) <- (10, 23) [resolution 332,276]
489. 24 | ~10 | ~23 [avatar split clause 488,274,199,278]
492. ~kind(alice) | generous(alice) <- (24) [resolution 280,79]
495. generous(alice) <- (23, 24) [subsumption resolution 492,276]
496. $false <- (23, 24) [subsumption resolution 495,149]
497. ~23 | ~24 [avatar contradiction clause 496]
513. calm(mary) | happy(mary) <- (9) [resolution 196,108]
515. 47 <=> happy(mary) [avatar definition]
516. ~happy(mary) <- (~47) [avatar component clause 515]
517. happy(mary) <- (47) [avatar component clause 515]
519. 48 <=> calm(mary) [avatar definition]
521. calm(mary) <- (48) [avatar component clause 519]
522. 47 | 48 | ~9 [avatar split clause 513,194,519,515]
524. ~humble(mary) | strong(mary) <- (11) [resolution 205,129]
525. ~strong(mary) | humble(mary) <- (11) [resolution 205,127]
527. humble(mary) <- (~3, 11, ~20) [subsumption resolution 525,293]
530. 36 | 3 | ~11 | 20 [avatar split clause 527,248,203,163,384]
544. kind(john) <- (21) [resolution 254,219]
547. $false <- (21, 38) [subsumption resolution 544,462]
548. ~21 | ~38 [avatar contradiction clause 547]
550. kind(john) <- (22) [resolution 258,153]
554. rich(john) <- (39) [resolution 432,151]
555. $false <- (39) [subsumption resolution 554,150]
556. ~39 [avatar contradiction clause 555]
561. patient(john) <- (7) [resolution 187,100]
577. 51 <=> tall(mary) [avatar definition]
578. ~tall(mary) <- (~51) [avatar component clause 577]
579. tall(mary) <- (51) [avatar component clause 577]
584. ~happy(mary) | ~old(mary) <- (48) [resolution 521,110]
587. ~old(mary) <- (47, 48) [subsumption resolution 584,517]
588. $false <- (9, 47, 48) [subsumption resolution 587,196]
589. ~9 | ~47 | ~48 [avatar contradiction clause 588]
599. funny(john) <- (22) [resolution 550,120]
600. 21 | ~22 [avatar split clause 599,256,252]
605. ~funny(john) | rich(john) <- (7) [resolution 561,99]
610. ~funny(john) <- (7) [subsumption resolution 605,150]
611. ~21 | ~7 [avatar split clause 610,186,252]
626. 52 <=> strong(mary) [avatar definition]
627. strong(mary) <- (52) [avatar component clause 626]
635. 52 | ~36 | ~11 [avatar split clause 524,203,384,626]
705. rich(mary) <- (51) [resolution 579,151]
706. $false <- (51) [subsumption resolution 705,150]
707. ~51 [avatar contradiction clause 706]
710. tall(mary) | happy(mary) <- (48) [resolution 521,139]
714. happy(mary) <- (48, ~51) [subsumption resolution 710,578]
715. $false <- (~47, 48, ~51) [subsumption resolution 714,516]
716. 47 | ~48 | 51 [avatar contradiction clause 715]
719. tall(mary) | patient(mary) <- (~11) [resolution 204,423]
728. ~strong(X0) | tall(X0) | patient(X0) <- (8) [resolution 192,423]
729. ~strong(X1) | tall(X1) | curious(X1) <- (8) [resolution 192,422]
740. strong(X4) | ~kind(X4) | ~creative(X4) <- (10) [resolution 200,96]
745. ~kind(X4) | strong(X4) <- (10) [subsumption resolution 740,218]
765. calm(mary) | ~brave(mary) | tall(mary) <- (47) [resolution 517,141]
769. patient(mary) <- (47) [resolution 517,100]
778. tall(mary) | patient(mary) <- (8, 52) [resolution 728,627]
793. tall(alice) | curious(alice) <- (8, 24) [resolution 729,280]
796. curious(alice) <- (~2, 8, 24) [subsumption resolution 793,160]
799. 1 | 2 | ~8 | ~24 [avatar split clause 796,278,191,159,155]
800. patient(mary) <- (8, ~51, 52) [subsumption resolution 778,578]
801. 4 | ~8 | 51 | ~52 [avatar split clause 800,626,577,191,167]
802. 4 | ~47 [avatar split clause 769,515,167]
803. patient(mary) <- (~11, ~51) [subsumption resolution 719,578]
804. 4 | 11 | 51 [avatar split clause 803,577,203,167]
813. strong(mary) <- (3, 10) [resolution 165,745]
816. funny(mary) <- (3) [resolution 165,120]
822. 52 | ~3 | ~10 [avatar split clause 813,199,163,626]
826. calm(mary) | ~brave(mary) <- (47, ~51) [subsumption resolution 765,578]
827. ~11 | 48 | ~47 | 51 [avatar split clause 826,577,515,519,203]
828. ~funny(mary) | rich(mary) <- (4) [resolution 168,99]
829. rich(mary) <- (3, 4) [subsumption resolution 828,816]
830. $false <- (3, 4) [subsumption resolution 829,150]
831. ~3 | ~4 [avatar contradiction clause 830]
832. $false [avatar sat refutation 170,197,201,206,207,260,268,281,433,489,497,522,530,548,556,589,600,611,635,707,716,799,801,802,804,822,827,831]
% SZS output end Proof for 4696725175445021573991741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then susan is generous or kind and vice versa. Everyone who is not patient is either wise or strong and vice versa. Everyone who is calm is both not wise and not funny. Everyone who is both not curious and not rich is rich and vice versa. If someone is not old or not calm then lucy is funny or happy and vice versa. If mary is either not creative or not funny then alice is both strong and not quiet. If someone is both strong and not curious then someone is not wise or kind. Everyone who is not kind is not curious. If someone is both not old and quiet then someone is not wise or humble. If alice is funny then fred is wise or not kind. If alice is either kind or rich then susan is humble or old and vice versa. If susan is not old or not wise then someone is rich or happy and vice versa. Everyone who is humble or curious is not wise. If alice is either not calm or wise then someone is not generous or not patient and vice versa. Everyone who is not funny is not creative. Everyone who is either old or funny is either strong or rich. Someone is both quiet and creative. Someone is either old or funny. Someone is either brave or not quiet. Someone is strong. Someone is both not old and not calm. Someone is both generous and strong. Someone is quiet or creative. Someone is both not old and creative. | Fred is not rich. | entailment | ((?[X]:(~tall(X)))<=>((generous(susan)|kind(susan))))&
(![X]:(~patient(X)<=>(wise(X)<~>strong(X))))&
(![X]:(calm(X)=>(~wise(X)&~funny(X))))&
(![X]:((~curious(X)&~rich(X))<=>rich(X)))&
((?[X]:((~old(X)|~calm(X))))<=>((funny(lucy)|happy(lucy))))&
(((~creative(mary)<~>~funny(mary)))=>((strong(alice)&~quiet(alice))))&
((?[X]:((strong(X)&~curious(X))))=>(?[X]:((~wise(X)|kind(X)))))&
(![X]:(~kind(X)=>~curious(X)))&
((?[X]:((~old(X)&quiet(X))))=>(?[X]:((~wise(X)|humble(X)))))&
((funny(alice))=>((wise(fred)|~kind(fred))))&
(((kind(alice)<~>rich(alice)))<=>((humble(susan)|old(susan))))&
(((~old(susan)|~wise(susan)))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((humble(X)|curious(X))=>~wise(X)))&
(((~calm(alice)<~>wise(alice)))<=>(?[X]:((~generous(X)|~patient(X)))))&
(![X]:(~funny(X)=>~creative(X)))&
(![X]:((old(X)<~>funny(X))=>(strong(X)<~>rich(X))))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)&~calm(X))))&
(?[X]:((generous(X)&strong(X))))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((~old(X)&creative(X)))) | ~rich(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3742426883280214647647658
% SZS output start Proof for 3742426883280214647647658
4. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> rich(X0)) [input p3]
25. rich(fred) [input hypothesis]
44. ! [X0] : (((~rich(X0) & ~curious(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) | curious(X0)))) [nnf transformation 4]
45. ! [X0] : (((~rich(X0) & ~curious(X0)) | ~rich(X0)) & (rich(X0) | rich(X0) | curious(X0))) [flattening 44]
99. ~rich(X0) | ~rich(X0) [cnf transformation 45]
149. rich(fred) [cnf transformation 25]
151. ~rich(X0) [duplicate literal removal 99]
323. $false [subsumption resolution 149,151]
% SZS output end Proof for 3742426883280214647647658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not creative is calm and vice versa.
Everyone who is both strong and kind is either calm or not funny.
If someone is brave or not strong then fred is both not calm and humble.
If susan is both not brave and not old then paul is either not patient or not curious and vice versa.
If mary is either not brave or brave then someone is either curious or happy and vice versa.
If mary is either curious or humble then paul is not wise and vice versa.
Everyone who is either rich or humble is both creative and not curious.
If susan is quiet or curious then fred is both not quiet and not patient and vice versa.
If someone is either not funny or not brave then paul is both not funny and humble and vice versa.
If someone is strong then someone is both not humble and humble.
Everyone who is not curious or brave is either curious or tall and vice versa.
If someone is both not patient and not tall then someone is either old or brave.
Everyone who is either strong or creative is not funny and vice versa.
Everyone who is both creative and not creative is both humble and not generous.
Everyone who is either rich or kind is quiet or not humble and vice versa.
Everyone who is either not brave or not creative is both not old and not brave and vice versa.
Fred is wise.
Paul is either not old or wise.
Mary is either not funny or old.
Someone is not tall or happy.
Lucy is either not strong or not wise.
John is not strong.
Paul is patient. | Paul is not patient. | contradiction | (![X]:((~old(X)<~>~creative(X))<=>calm(X)))&
(![X]:((strong(X)&kind(X))=>(calm(X)<~>~funny(X))))&
((?[X]:((brave(X)|~strong(X))))=>((~calm(fred)&humble(fred))))&
(((~brave(susan)&~old(susan)))<=>((~patient(paul)<~>~curious(paul))))&
(((~brave(mary)<~>brave(mary)))<=>(?[X]:((curious(X)<~>happy(X)))))&
(((curious(mary)<~>humble(mary)))<=>(~wise(paul)))&
(![X]:((rich(X)<~>humble(X))=>(creative(X)&~curious(X))))&
(((quiet(susan)|curious(susan)))<=>((~quiet(fred)&~patient(fred))))&
((?[X]:((~funny(X)<~>~brave(X))))<=>((~funny(paul)&humble(paul))))&
((?[X]:(strong(X)))=>(?[X]:((~humble(X)&humble(X)))))&
(![X]:((~curious(X)|brave(X))<=>(curious(X)<~>tall(X))))&
((?[X]:((~patient(X)&~tall(X))))=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:((strong(X)<~>creative(X))<=>~funny(X)))&
(![X]:((creative(X)&~creative(X))=>(humble(X)&~generous(X))))&
(![X]:((rich(X)<~>kind(X))<=>(quiet(X)|~humble(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>(~old(X)&~brave(X))))&
(wise(fred))&
((~old(paul)<~>wise(paul)))&
((~funny(mary)<~>old(mary)))&
(?[X]:((~tall(X)|happy(X))))&
((~strong(lucy)<~>~wise(lucy)))&
(~strong(john))&
(patient(paul)) | ~patient(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 717524794848894885119816
% SZS output start Proof for 717524794848894885119816
23. patient(paul) [input p22]
24. ~patient(paul) [input hypothesis]
151. patient(paul) [cnf transformation 23]
152. ~patient(paul) [cnf transformation 24]
184. 6 <=> patient(paul) [avatar definition]
339. 6 [avatar split clause 151,184]
340. ~6 [avatar split clause 152,184]
341. $false [avatar sat refutation 339,340]
% SZS output end Proof for 717524794848894885119816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or tall then paul is curious.
Everyone who is not wise is quiet.
If paul is both brave and not generous then susan is not calm and vice versa.
Everyone who is both not tall and not creative is not old.
If someone is kind then someone is brave or not wise and vice versa.
If someone is either generous or not calm then alice is not strong or not brave.
Everyone who is both rich and not creative is not happy or humble and vice versa.
If mary is both not quiet and not generous then someone is tall or generous and vice versa.
If someone is either quiet or funny then someone is either not creative or not quiet and vice versa.
Everyone who is either not curious or not happy is not old or old.
Everyone who is not patient is either not kind or tall.
Everyone who is happy or curious is generous or quiet and vice versa.
If someone is either funny or not strong then someone is not wise.
If mary is quiet or not tall then lucy is either not humble or curious.
If someone is old or not happy then someone is not wise or not happy and vice versa.
If someone is both not old and brave then alice is humble.
Someone is both creative and not funny.
Paul is both brave and not rich.
Paul is both not old and not calm.
Someone is either not rich or old.
Someone is either brave or not generous.
John is either wise or not strong.
Someone is both not generous and creative.
Paul is old or curious. | Alice is creative. | contradiction | (((~humble(fred)|tall(fred)))=>(curious(paul)))&
(![X]:(~wise(X)=>quiet(X)))&
(((brave(paul)&~generous(paul)))<=>(~calm(susan)))&
(![X]:((~tall(X)&~creative(X))=>~old(X)))&
((?[X]:(kind(X)))<=>(?[X]:((brave(X)|~wise(X)))))&
((?[X]:((generous(X)<~>~calm(X))))=>((~strong(alice)|~brave(alice))))&
(![X]:((rich(X)&~creative(X))<=>(~happy(X)|humble(X))))&
(((~quiet(mary)&~generous(mary)))<=>(?[X]:((tall(X)|generous(X)))))&
((?[X]:((quiet(X)<~>funny(X))))<=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((~curious(X)<~>~happy(X))=>(~old(X)|old(X))))&
(![X]:(~patient(X)=>(~kind(X)<~>tall(X))))&
(![X]:((happy(X)|curious(X))<=>(generous(X)|quiet(X))))&
((?[X]:((funny(X)<~>~strong(X))))=>(?[X]:(~wise(X))))&
(((quiet(mary)|~tall(mary)))=>((~humble(lucy)<~>curious(lucy))))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:((~wise(X)|~happy(X)))))&
((?[X]:((~old(X)&brave(X))))=>(humble(alice)))&
(?[X]:((creative(X)&~funny(X))))&
((brave(paul)&~rich(paul)))&
((~old(paul)&~calm(paul)))&
(?[X]:((~rich(X)<~>old(X))))&
(?[X]:((brave(X)<~>~generous(X))))&
((wise(john)<~>~strong(john)))&
(?[X]:((~generous(X)&creative(X))))&
((old(paul)|curious(paul))) | creative(alice) | [
"p6",
"p15",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6505728849488134596336440
% SZS output start Proof for 6505728849488134596336440
7. ! [X0] : ((~creative(X0) & rich(X0)) <=> (humble(X0) | ~happy(X0))) [input p6]
16. ? [X0] : (brave(X0) & ~old(X0)) => humble(alice) [input p15]
18. ~rich(paul) & brave(paul) [input p17]
19. ~calm(paul) & ~old(paul) [input p18]
25. creative(alice) [input hypothesis]
41. humble(alice) | ! [X0] : (~brave(X0) | old(X0)) [ennf transformation 16]
50. ! [X0] : (((~creative(X0) & rich(X0)) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | (creative(X0) | ~rich(X0)))) [nnf transformation 7]
51. ! [X0] : (((~creative(X0) & rich(X0)) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | creative(X0) | ~rich(X0))) [flattening 50]
102. ~creative(X0) | ~humble(X0) [cnf transformation 51]
132. humble(alice) | ~brave(X0) | old(X0) [cnf transformation 41]
135. brave(paul) [cnf transformation 18]
137. ~old(paul) [cnf transformation 19]
148. creative(alice) [cnf transformation 25]
173. 6 <=> brave(paul) [avatar definition]
175. brave(paul) <- (6) [avatar component clause 173]
336. 43 <=> ! [X0] : (~brave(X0) | old(X0)) [avatar definition]
337. ~brave(X0) | old(X0) <- (43) [avatar component clause 336]
339. 44 <=> humble(alice) [avatar definition]
342. 43 | 44 [avatar split clause 132,339,336]
343. 6 [avatar split clause 135,173]
384. ~humble(alice) [resolution 102,148]
388. ~44 [avatar split clause 384,339]
389. old(paul) <- (6, 43) [resolution 337,175]
390. $false <- (6, 43) [subsumption resolution 389,137]
391. ~6 | ~43 [avatar contradiction clause 390]
392. $false [avatar sat refutation 342,343,388,391]
% SZS output end Proof for 6505728849488134596336440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not tall is either creative or not quiet.
If john is both not patient and not creative then someone is calm or humble.
Everyone who is either not strong or wise is tall and vice versa.
Everyone who is both not rich and not patient is both not wise and not calm and vice versa.
If paul is both calm and creative then someone is happy or quiet and vice versa.
If fred is rich then someone is either generous or not happy.
Everyone who is curious is either not curious or strong.
If someone is not funny then someone is both rich and not brave and vice versa.
Everyone who is both calm and humble is creative or not strong and vice versa.
If someone is either rich or not kind then someone is either not generous or not humble.
Everyone who is wise is both not brave and creative.
If alice is not strong then alice is either generous or curious.
Everyone who is either not kind or brave is kind or rich.
If paul is either calm or not funny then someone is both rich and strong and vice versa.
Everyone who is strong or rich is patient or not kind and vice versa.
Everyone who is not curious or creative is both not happy and not rich.
Fred is both patient and brave.
Someone is curious or not strong.
Someone is rich.
Someone is either wise or not quiet.
Someone is not curious.
John is either not funny or generous.
Alice is either not curious or rich.
Lucy is not calm. | Fred is tall. | contradiction | (![X]:((~quiet(X)|~tall(X))=>(creative(X)<~>~quiet(X))))&
(((~patient(john)&~creative(john)))=>(?[X]:((calm(X)|humble(X)))))&
(![X]:((~strong(X)<~>wise(X))<=>tall(X)))&
(![X]:((~rich(X)&~patient(X))<=>(~wise(X)&~calm(X))))&
(((calm(paul)&creative(paul)))<=>(?[X]:((happy(X)|quiet(X)))))&
((rich(fred))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(curious(X)=>(~curious(X)<~>strong(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((rich(X)&~brave(X)))))&
(![X]:((calm(X)&humble(X))<=>(creative(X)|~strong(X))))&
((?[X]:((rich(X)<~>~kind(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:(wise(X)=>(~brave(X)&creative(X))))&
((~strong(alice))=>((generous(alice)<~>curious(alice))))&
(![X]:((~kind(X)<~>brave(X))=>(kind(X)|rich(X))))&
(((calm(paul)<~>~funny(paul)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((strong(X)|rich(X))<=>(patient(X)|~kind(X))))&
(![X]:((~curious(X)|creative(X))=>(~happy(X)&~rich(X))))&
((patient(fred)&brave(fred)))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)<~>~quiet(X))))&
(?[X]:(~curious(X)))&
((~funny(john)<~>generous(john)))&
((~curious(alice)<~>rich(alice)))&
(~calm(lucy)) | tall(fred) | [
"p2",
"p6",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7919578214748866785697790
% SZS output start Proof for 7919578214748866785697790
3. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> tall(X0)) [input p2]
7. ! [X0] : (curious(X0) => (~curious(X0) <~> strong(X0))) [input p6]
11. ! [X0] : (wise(X0) => (creative(X0) & ~brave(X0))) [input p10]
15. ! [X0] : ((rich(X0) | strong(X0)) <=> (~kind(X0) | patient(X0))) [input p14]
16. ! [X0] : ((creative(X0) | ~curious(X0)) => (~rich(X0) & ~happy(X0))) [input p15]
17. brave(fred) & patient(fred) [input p16]
25. tall(fred) [input hypothesis]
28. ! [X0] : (tall(X0) => (~strong(X0) <~> wise(X0))) [unused predicate definition removal 3]
32. ! [X0] : ((~strong(X0) <~> wise(X0)) | ~tall(X0)) [ennf transformation 28]
34. ! [X0] : ((~curious(X0) <~> strong(X0)) | ~curious(X0)) [ennf transformation 7]
36. ! [X0] : ((creative(X0) & ~brave(X0)) | ~wise(X0)) [ennf transformation 11]
40. ! [X0] : ((~rich(X0) & ~happy(X0)) | (~creative(X0) & curious(X0))) [ennf transformation 16]
44. ! [X0] : (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~tall(X0)) [nnf transformation 32]
55. ! [X0] : (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ~curious(X0)) [nnf transformation 34]
73. ! [X0] : (((rich(X0) | strong(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (~rich(X0) & ~strong(X0)))) [nnf transformation 15]
74. ! [X0] : ((rich(X0) | strong(X0) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | (~rich(X0) & ~strong(X0)))) [flattening 73]
91. ~strong(X0) | wise(X0) | ~tall(X0) [cnf transformation 44]
104. strong(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 55]
118. ~brave(X0) | ~wise(X0) [cnf transformation 36]
132. ~patient(X0) | strong(X0) | rich(X0) [cnf transformation 74]
136. ~rich(X0) | curious(X0) [cnf transformation 40]
138. patient(fred) [cnf transformation 17]
139. brave(fred) [cnf transformation 17]
150. tall(fred) [cnf transformation 25]
152. ~curious(X0) | strong(X0) [duplicate literal removal 104]
199. 11 <=> rich(fred) [avatar definition]
200. rich(fred) <- (11) [avatar component clause 199]
328. ~wise(fred) [resolution 118,139]
445. strong(fred) | rich(fred) [resolution 132,138]
482. 57 <=> strong(fred) [avatar definition]
484. strong(fred) <- (57) [avatar component clause 482]
485. 11 | 57 [avatar split clause 445,482,199]
488. curious(fred) <- (11) [resolution 200,136]
546. strong(fred) <- (11) [resolution 488,152]
547. 57 | ~11 [avatar split clause 546,199,482]
549. wise(fred) | ~tall(fred) <- (57) [resolution 484,91]
552. ~tall(fred) <- (57) [subsumption resolution 549,328]
553. $false <- (57) [subsumption resolution 552,150]
554. ~57 [avatar contradiction clause 553]
555. $false [avatar sat refutation 485,547,554]
% SZS output end Proof for 7919578214748866785697790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or kind is brave or not quiet and vice versa. Everyone who is calm or not happy is either not creative or not strong and vice versa. Everyone who is both wise and creative is not generous. If alice is both not generous and wise then someone is both not happy and not funny and vice versa. If someone is generous or not humble then fred is not brave or not wise and vice versa. Everyone who is rich is both happy and not tall. Everyone who is either generous or not patient is generous. Everyone who is both not creative and not wise is not rich and vice versa. Everyone who is wise or not humble is not happy. Everyone who is patient or wise is both strong and generous and vice versa. Everyone who is both not funny and not wise is either creative or patient and vice versa. If someone is either not happy or creative then john is both rich and not calm and vice versa. Everyone who is either not tall or old is not tall or generous. If susan is either tall or humble then paul is either rich or not patient and vice versa. Everyone who is either calm or not rich is both not brave and generous and vice versa. Someone is funny or not curious. Paul is either not old or not creative. Someone is not brave or not curious. Fred is either humble or not kind. Someone is either not humble or calm. | Paul is humble. | entailment | (![X]:((~funny(X)<~>kind(X))<=>(brave(X)|~quiet(X))))&
(![X]:((calm(X)|~happy(X))<=>(~creative(X)<~>~strong(X))))&
(![X]:((wise(X)&creative(X))=>~generous(X)))&
(((~generous(alice)&wise(alice)))<=>(?[X]:((~happy(X)&~funny(X)))))&
((?[X]:((generous(X)|~humble(X))))<=>((~brave(fred)|~wise(fred))))&
(![X]:(rich(X)=>(happy(X)&~tall(X))))&
(![X]:((generous(X)<~>~patient(X))=>generous(X)))&
(![X]:((~creative(X)&~wise(X))<=>~rich(X)))&
(![X]:((wise(X)|~humble(X))=>~happy(X)))&
(![X]:((patient(X)|wise(X))<=>(strong(X)&generous(X))))&
(![X]:((~funny(X)&~wise(X))<=>(creative(X)<~>patient(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((rich(john)&~calm(john))))&
(![X]:((~tall(X)<~>old(X))=>(~tall(X)|generous(X))))&
(((tall(susan)<~>humble(susan)))<=>((rich(paul)<~>~patient(paul))))&
(![X]:((calm(X)<~>~rich(X))<=>(~brave(X)&generous(X))))&
(?[X]:((funny(X)|~curious(X))))&
((~old(paul)<~>~creative(paul)))&
(?[X]:((~brave(X)|~curious(X))))&
((humble(fred)<~>~kind(fred)))&
(?[X]:((~humble(X)<~>calm(X)))) | humble(paul) | [
"p1",
"p3",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1527974179869944405285265
% SZS output start Proof for 1527974179869944405285265
2. ! [X0] : ((~happy(X0) | calm(X0)) <=> (~creative(X0) <~> ~strong(X0))) [input p1]
4. (wise(alice) & ~generous(alice)) <=> ? [X0] : (~funny(X0) & ~happy(X0)) [input p3]
6. ! [X0] : (rich(X0) => (~tall(X0) & happy(X0))) [input p5]
7. ! [X0] : ((generous(X0) <~> ~patient(X0)) => generous(X0)) [input p6]
8. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> ~rich(X0)) [input p7]
9. ! [X0] : ((~humble(X0) | wise(X0)) => ~happy(X0)) [input p8]
10. ! [X0] : ((wise(X0) | patient(X0)) <=> (generous(X0) & strong(X0))) [input p9]
11. ! [X0] : ((~wise(X0) & ~funny(X0)) <=> (creative(X0) <~> patient(X0))) [input p10]
21. ~humble(paul) [input hypothesis]
26. ! [X0] : ((~tall(X0) & happy(X0)) | ~rich(X0)) [ennf transformation 6]
27. ! [X0] : (generous(X0) | (generous(X0) <=> ~patient(X0))) [ennf transformation 7]
28. ! [X0] : (~happy(X0) | (humble(X0) & ~wise(X0))) [ennf transformation 9]
33. ! [X0] : (((~happy(X0) | calm(X0)) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0)))) & (((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | (happy(X0) & ~calm(X0)))) [nnf transformation 2]
34. ! [X0] : ((~happy(X0) | calm(X0) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0)))) & (((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | (happy(X0) & ~calm(X0)))) [flattening 33]
35. ((wise(alice) & ~generous(alice)) | ! [X0] : (funny(X0) | happy(X0))) & (? [X0] : (~funny(X0) & ~happy(X0)) | (~wise(alice) | generous(alice))) [nnf transformation 4]
36. ((wise(alice) & ~generous(alice)) | ! [X0] : (funny(X0) | happy(X0))) & (? [X0] : (~funny(X0) & ~happy(X0)) | ~wise(alice) | generous(alice)) [flattening 35]
37. ((wise(alice) & ~generous(alice)) | ! [X0] : (funny(X0) | happy(X0))) & (? [X1] : (~funny(X1) & ~happy(X1)) | ~wise(alice) | generous(alice)) [rectify 36]
38. ? [X1] : (~funny(X1) & ~happy(X1)) => (~funny(sK0) & ~happy(sK0)) [choice axiom]
39. ((wise(alice) & ~generous(alice)) | ! [X0] : (funny(X0) | happy(X0))) & ((~funny(sK0) & ~happy(sK0)) | ~wise(alice) | generous(alice)) [skolemisation 37,38]
45. ! [X0] : (generous(X0) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0)))) [nnf transformation 27]
46. ! [X0] : (((~wise(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | (wise(X0) | creative(X0)))) [nnf transformation 8]
47. ! [X0] : (((~wise(X0) & ~creative(X0)) | rich(X0)) & (~rich(X0) | wise(X0) | creative(X0))) [flattening 46]
48. ! [X0] : (((wise(X0) | patient(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 10]
49. ! [X0] : ((wise(X0) | patient(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (~wise(X0) & ~patient(X0)))) [flattening 48]
50. ! [X0] : (((~wise(X0) & ~funny(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (wise(X0) | funny(X0)))) [nnf transformation 11]
51. ! [X0] : (((~wise(X0) & ~funny(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | wise(X0) | funny(X0))) [flattening 50]
75. strong(X0) | creative(X0) | happy(X0) [cnf transformation 34]
81. ~generous(alice) | funny(X0) | happy(X0) [cnf transformation 39]
87. ~rich(X0) | happy(X0) [cnf transformation 26]
90. generous(X0) | generous(X0) | patient(X0) [cnf transformation 45]
92. ~creative(X0) | rich(X0) [cnf transformation 47]
93. ~wise(X0) | rich(X0) [cnf transformation 47]
95. ~happy(X0) | humble(X0) [cnf transformation 28]
98. generous(X0) | ~patient(X0) [cnf transformation 49]
100. wise(X0) | patient(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 49]
104. ~patient(X0) | creative(X0) | ~funny(X0) [cnf transformation 51]
135. ~humble(paul) [cnf transformation 21]
137. patient(X0) | generous(X0) [duplicate literal removal 90]
139. 1 <=> ! [X0] : (funny(X0) | happy(X0)) [avatar definition]
140. happy(X0) | funny(X0) <- (1) [avatar component clause 139]
147. 3 <=> generous(alice) [avatar definition]
149. ~generous(alice) <- (~3) [avatar component clause 147]
150. 1 | ~3 [avatar split clause 81,147,139]
180. 10 <=> ! [X1] : humble(X1) [avatar definition]
181. humble(X1) <- (10) [avatar component clause 180]
187. ~strong(X0) | patient(X0) | wise(X0) [subsumption resolution 100,137]
188. generous(X0) [subsumption resolution 98,137]
273. $false <- (~3) [subsumption resolution 149,188]
274. 3 [avatar contradiction clause 273]
414. patient(X0) | wise(X0) | creative(X0) | happy(X0) [resolution 187,75]
524. $false <- (10) [resolution 181,135]
527. ~10 [avatar contradiction clause 524]
563. wise(X2) | creative(X2) | happy(X2) | creative(X2) | ~funny(X2) [resolution 414,104]
566. wise(X2) | creative(X2) | happy(X2) | ~funny(X2) [duplicate literal removal 563]
569. wise(X2) | creative(X2) | happy(X2) <- (1) [subsumption resolution 566,140]
587. creative(X5) | happy(X5) | rich(X5) <- (1) [resolution 569,93]
591. happy(X5) | rich(X5) <- (1) [subsumption resolution 587,92]
592. happy(X5) <- (1) [subsumption resolution 591,87]
593. humble(X0) <- (1) [resolution 592,95]
596. 10 | ~1 [avatar split clause 593,139,180]
597. $false [avatar sat refutation 150,274,527,596]
% SZS output end Proof for 1527974179869944405285265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not patient is patient.
Everyone who is patient is either not creative or tall.
Everyone who is both kind and old is not generous or not rich.
Everyone who is either quiet or wise is tall or not happy and vice versa.
If lucy is not creative then someone is both old and not creative and vice versa.
Everyone who is not brave or generous is not calm or tall and vice versa.
If someone is either not old or old then someone is not curious.
Everyone who is happy is quiet.
If someone is both brave and not curious then someone is both creative and humble and vice versa.
Everyone who is either strong or wise is quiet and vice versa.
Everyone who is both patient and not patient is not humble.
If someone is either not happy or quiet then john is old or not happy.
If someone is quiet then paul is either not rich or not humble and vice versa.
If paul is funny or not curious then someone is not patient or not kind and vice versa.
Everyone who is not happy or not curious is either brave or kind and vice versa.
If mary is not happy or not tall then lucy is either humble or not wise and vice versa.
Someone is either creative or brave.
Lucy is not quiet or not brave.
Someone is calm or humble.
Lucy is not funny.
Someone is not quiet.
Paul is either not tall or generous.
Someone is either not happy or quiet. | Mary is not generous. | neutral | (![X]:((brave(X)&~patient(X))=>patient(X)))&
(![X]:(patient(X)=>(~creative(X)<~>tall(X))))&
(![X]:((kind(X)&old(X))=>(~generous(X)|~rich(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(tall(X)|~happy(X))))&
((~creative(lucy))<=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~calm(X)|tall(X))))&
((?[X]:((~old(X)<~>old(X))))=>(?[X]:(~curious(X))))&
(![X]:(happy(X)=>quiet(X)))&
((?[X]:((brave(X)&~curious(X))))<=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((strong(X)<~>wise(X))<=>quiet(X)))&
(![X]:((patient(X)&~patient(X))=>~humble(X)))&
((?[X]:((~happy(X)<~>quiet(X))))=>((old(john)|~happy(john))))&
((?[X]:(quiet(X)))<=>((~rich(paul)<~>~humble(paul))))&
(((funny(paul)|~curious(paul)))<=>(?[X]:((~patient(X)|~kind(X)))))&
(![X]:((~happy(X)|~curious(X))<=>(brave(X)<~>kind(X))))&
(((~happy(mary)|~tall(mary)))<=>((humble(lucy)<~>~wise(lucy))))&
(?[X]:((creative(X)<~>brave(X))))&
((~quiet(lucy)|~brave(lucy)))&
(?[X]:((calm(X)|humble(X))))&
(~funny(lucy))&
(?[X]:(~quiet(X)))&
((~tall(paul)<~>generous(paul)))&
(?[X]:((~happy(X)<~>quiet(X)))) | ~generous(mary) | [] | null | 0 |
Everyone who is not happy or patient is not kind or kind.
Everyone who is either not brave or not generous is both happy and patient and vice versa.
Everyone who is either not wise or curious is calm.
Everyone who is wise is either not wise or not calm and vice versa.
If mary is either not brave or not rich then someone is either humble or patient and vice versa.
Everyone who is both generous and tall is patient or calm and vice versa.
If mary is humble then alice is not tall or not kind and vice versa.
If lucy is either not calm or creative then susan is strong or not kind and vice versa.
Everyone who is either patient or not strong is both strong and generous and vice versa.
If someone is not old or not humble then someone is both quiet and wise.
Everyone who is both not generous and not curious is either not curious or creative.
Everyone who is both tall and not old is not humble.
Everyone who is wise or old is not happy.
If paul is both wise and not curious then susan is strong or quiet.
Everyone who is brave is not brave or tall.
Everyone who is tall or not kind is funny and vice versa.
Someone is rich or wise.
Someone is not rich or not wise.
John is either wise or patient.
Someone is both not happy and rich.
Someone is not patient or not calm.
Someone is either not old or not creative.
Alice is not generous.
Someone is either not rich or strong. | John is wise. | neutral | (![X]:((~happy(X)|patient(X))=>(~kind(X)|kind(X))))&
(![X]:((~brave(X)<~>~generous(X))<=>(happy(X)&patient(X))))&
(![X]:((~wise(X)<~>curious(X))=>calm(X)))&
(![X]:(wise(X)<=>(~wise(X)<~>~calm(X))))&
(((~brave(mary)<~>~rich(mary)))<=>(?[X]:((humble(X)<~>patient(X)))))&
(![X]:((generous(X)&tall(X))<=>(patient(X)|calm(X))))&
((humble(mary))<=>((~tall(alice)|~kind(alice))))&
(((~calm(lucy)<~>creative(lucy)))<=>((strong(susan)|~kind(susan))))&
(![X]:((patient(X)<~>~strong(X))<=>(strong(X)&generous(X))))&
((?[X]:((~old(X)|~humble(X))))=>(?[X]:((quiet(X)&wise(X)))))&
(![X]:((~generous(X)&~curious(X))=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)&~old(X))=>~humble(X)))&
(![X]:((wise(X)|old(X))=>~happy(X)))&
(((wise(paul)&~curious(paul)))=>((strong(susan)|quiet(susan))))&
(![X]:(brave(X)=>(~brave(X)|tall(X))))&
(![X]:((tall(X)|~kind(X))<=>funny(X)))&
(?[X]:((rich(X)|wise(X))))&
(?[X]:((~rich(X)|~wise(X))))&
((wise(john)<~>patient(john)))&
(?[X]:((~happy(X)&rich(X))))&
(?[X]:((~patient(X)|~calm(X))))&
(?[X]:((~old(X)<~>~creative(X))))&
(~generous(alice))&
(?[X]:((~rich(X)<~>strong(X)))) | wise(john) | [] | null | 0 |
If lucy is funny or brave then someone is rich or brave and vice versa. Everyone who is both kind and wise is both kind and not old. Everyone who is creative is curious and vice versa. If mary is humble or not curious then someone is not calm. Everyone who is strong or not quiet is both not creative and happy. Everyone who is wise is either not strong or not old. Everyone who is happy is both not curious and not calm. Everyone who is not funny is either not strong or not kind and vice versa. Everyone who is funny is either creative or happy and vice versa. Everyone who is both not happy and patient is both old and not brave. If someone is either curious or not creative then someone is both not patient and tall. If someone is either not humble or not patient then someone is both patient and happy and vice versa. Everyone who is not kind is both humble and strong and vice versa. If someone is either not quiet or not happy then fred is both not curious and not creative and vice versa. Everyone who is calm is strong or not rich. If alice is both strong and not curious then paul is either not wise or curious and vice versa. John is humble. Lucy is not wise. Alice is both not happy and not curious. Someone is both quiet and old. Someone is tall or wise. Fred is both not wise and not humble. | Mary is creative. | contradiction | (((funny(lucy)|brave(lucy)))<=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((kind(X)&wise(X))=>(kind(X)&~old(X))))&
(![X]:(creative(X)<=>curious(X)))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)|~quiet(X))=>(~creative(X)&happy(X))))&
(![X]:(wise(X)=>(~strong(X)<~>~old(X))))&
(![X]:(happy(X)=>(~curious(X)&~calm(X))))&
(![X]:(~funny(X)<=>(~strong(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(creative(X)<~>happy(X))))&
(![X]:((~happy(X)&patient(X))=>(old(X)&~brave(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:((~patient(X)&tall(X)))))&
((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(![X]:(~kind(X)<=>(humble(X)&strong(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>((~curious(fred)&~creative(fred))))&
(![X]:(calm(X)=>(strong(X)|~rich(X))))&
(((strong(alice)&~curious(alice)))<=>((~wise(paul)<~>curious(paul))))&
(humble(john))&
(~wise(lucy))&
((~happy(alice)&~curious(alice)))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((tall(X)|wise(X))))&
((~wise(fred)&~humble(fred))) | creative(mary) | [
"p2",
"p4",
"p6",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6132823431553826229636749
% SZS output start Proof for 6132823431553826229636749
3. ! [X0] : (creative(X0) <=> curious(X0)) [input p2]
5. ! [X0] : ((~quiet(X0) | strong(X0)) => (happy(X0) & ~creative(X0))) [input p4]
7. ! [X0] : (happy(X0) => (~calm(X0) & ~curious(X0))) [input p6]
8. ! [X0] : (~funny(X0) <=> (~strong(X0) <~> ~kind(X0))) [input p7]
9. ! [X0] : (funny(X0) <=> (creative(X0) <~> happy(X0))) [input p8]
13. ! [X0] : (~kind(X0) <=> (strong(X0) & humble(X0))) [input p12]
23. creative(mary) [input hypothesis]
28. ! [X0] : (happy(X0) => ~curious(X0)) [pure predicate removal 7]
33. ! [X0] : ((happy(X0) & ~creative(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 5]
35. ! [X0] : (~curious(X0) | ~happy(X0)) [ennf transformation 28]
44. ! [X0] : ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))) [nnf transformation 3]
46. ! [X0] : ((~funny(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | funny(X0))) [nnf transformation 8]
47. ! [X0] : ((funny(X0) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0)))) & (((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | ~funny(X0))) [nnf transformation 9]
57. ! [X0] : ((~kind(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | kind(X0))) [nnf transformation 13]
58. ! [X0] : ((~kind(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | kind(X0))) [flattening 57]
74. ~creative(X0) | curious(X0) [cnf transformation 44]
76. ~strong(X0) | ~creative(X0) [cnf transformation 33]
82. ~happy(X0) | ~curious(X0) [cnf transformation 35]
85. ~kind(X0) | ~funny(X0) | strong(X0) [cnf transformation 46]
89. ~creative(X0) | happy(X0) | funny(X0) [cnf transformation 47]
102. strong(X0) | kind(X0) [cnf transformation 58]
124. creative(mary) [cnf transformation 23]
251. curious(mary) [resolution 74,124]
262. ~creative(X1) | kind(X1) [resolution 102,76]
320. kind(mary) [resolution 262,124]
322. happy(mary) | funny(mary) [resolution 89,124]
325. 33 <=> funny(mary) [avatar definition]
327. funny(mary) <- (33) [avatar component clause 325]
329. 34 <=> happy(mary) [avatar definition]
331. happy(mary) <- (34) [avatar component clause 329]
332. 33 | 34 [avatar split clause 322,329,325]
348. ~funny(mary) | strong(mary) [resolution 320,85]
349. strong(mary) <- (33) [subsumption resolution 348,327]
376. ~creative(mary) <- (33) [resolution 349,76]
379. $false <- (33) [subsumption resolution 376,124]
380. ~33 [avatar contradiction clause 379]
383. ~curious(mary) <- (34) [resolution 331,82]
384. $false <- (34) [subsumption resolution 383,251]
385. ~34 [avatar contradiction clause 384]
386. $false [avatar sat refutation 332,380,385]
% SZS output end Proof for 6132823431553826229636749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous or not tall then mary is not creative or not generous and vice versa. If someone is not patient or not quiet then someone is both not funny and kind. Everyone who is either not calm or curious is both calm and not generous and vice versa. Everyone who is not humble or strong is both not brave and not calm. If someone is both calm and curious then someone is old or patient and vice versa. Everyone who is not generous is not happy. If lucy is either not tall or not happy then mary is both not brave and not quiet. Everyone who is humble or not brave is funny or not wise. Everyone who is not quiet is not patient or brave and vice versa. If fred is either not old or not quiet then mary is either not patient or not old and vice versa. Everyone who is either not calm or not rich is not kind or not quiet and vice versa. Everyone who is either not patient or old is not quiet and vice versa. Everyone who is both tall and not humble is tall and vice versa. Everyone who is humble or strong is both tall and kind and vice versa. If someone is brave then someone is either tall or not old. Everyone who is either humble or not funny is either generous or not old and vice versa. Mary is wise. Someone is both kind and not wise. Susan is either curious or wise. Alice is either wise or generous. Lucy is not calm or not quiet. Lucy is both wise and not brave. Susan is not happy or not rich. Lucy is both creative and not patient. | Lucy is not generous. | contradiction | ((?[X]:((~generous(X)|~tall(X))))<=>((~creative(mary)|~generous(mary))))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:((~funny(X)&kind(X)))))&
(![X]:((~calm(X)<~>curious(X))<=>(calm(X)&~generous(X))))&
(![X]:((~humble(X)|strong(X))=>(~brave(X)&~calm(X))))&
((?[X]:((calm(X)&curious(X))))<=>(?[X]:((old(X)|patient(X)))))&
(![X]:(~generous(X)=>~happy(X)))&
(((~tall(lucy)<~>~happy(lucy)))=>((~brave(mary)&~quiet(mary))))&
(![X]:((humble(X)|~brave(X))=>(funny(X)|~wise(X))))&
(![X]:(~quiet(X)<=>(~patient(X)|brave(X))))&
(((~old(fred)<~>~quiet(fred)))<=>((~patient(mary)<~>~old(mary))))&
(![X]:((~calm(X)<~>~rich(X))<=>(~kind(X)|~quiet(X))))&
(![X]:((~patient(X)<~>old(X))<=>~quiet(X)))&
(![X]:((tall(X)&~humble(X))<=>tall(X)))&
(![X]:((humble(X)|strong(X))<=>(tall(X)&kind(X))))&
((?[X]:(brave(X)))=>(?[X]:((tall(X)<~>~old(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(generous(X)<~>~old(X))))&
(wise(mary))&
(?[X]:((kind(X)&~wise(X))))&
((curious(susan)<~>wise(susan)))&
((wise(alice)<~>generous(alice)))&
((~calm(lucy)|~quiet(lucy)))&
((wise(lucy)&~brave(lucy)))&
((~happy(susan)|~rich(susan)))&
((creative(lucy)&~patient(lucy))) | ~generous(lucy) | [
"p3",
"p4",
"p7",
"p12",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1430207521020229591343575
% SZS output start Proof for 1430207521020229591343575
4. ! [X0] : ((strong(X0) | ~humble(X0)) => (~calm(X0) & ~brave(X0))) [input p3]
5. ? [X0] : (curious(X0) & calm(X0)) <=> ? [X0] : (patient(X0) | old(X0)) [input p4]
8. ! [X0] : ((~brave(X0) | humble(X0)) => (~wise(X0) | funny(X0))) [input p7]
13. ! [X0] : ((~humble(X0) & tall(X0)) <=> tall(X0)) [input p12]
14. ! [X0] : ((strong(X0) | humble(X0)) <=> (kind(X0) & tall(X0))) [input p13]
16. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (generous(X0) <~> ~old(X0))) [input p15]
22. ~brave(lucy) & wise(lucy) [input p21]
25. ~generous(lucy) [input hypothesis]
27. ? [X0] : (curious(X0) & calm(X0)) <=> ? [X1] : (patient(X1) | old(X1)) [rectify 5]
30. ! [X0] : ((~calm(X0) & ~brave(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 4]
33. ! [X0] : ((~wise(X0) | funny(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 8]
34. ! [X0] : (~wise(X0) | funny(X0) | (brave(X0) & ~humble(X0))) [flattening 33]
46. (? [X0] : (curious(X0) & calm(X0)) | ! [X1] : (~patient(X1) & ~old(X1))) & (? [X1] : (patient(X1) | old(X1)) | ! [X0] : (~curious(X0) | ~calm(X0))) [nnf transformation 27]
47. (? [X0] : (curious(X0) & calm(X0)) | ! [X1] : (~patient(X1) & ~old(X1))) & (? [X2] : (patient(X2) | old(X2)) | ! [X3] : (~curious(X3) | ~calm(X3))) [rectify 46]
48. ? [X0] : (curious(X0) & calm(X0)) => (curious(sK2) & calm(sK2)) [choice axiom]
49. ? [X2] : (patient(X2) | old(X2)) => (patient(sK3) | old(sK3)) [choice axiom]
50. ((curious(sK2) & calm(sK2)) | ! [X1] : (~patient(X1) & ~old(X1))) & ((patient(sK3) | old(sK3)) | ! [X3] : (~curious(X3) | ~calm(X3))) [skolemisation 47,49,48]
58. ! [X0] : (((~humble(X0) & tall(X0)) | ~tall(X0)) & (tall(X0) | (humble(X0) | ~tall(X0)))) [nnf transformation 13]
59. ! [X0] : (((~humble(X0) & tall(X0)) | ~tall(X0)) & (tall(X0) | humble(X0) | ~tall(X0))) [flattening 58]
60. ! [X0] : (((strong(X0) | humble(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (~strong(X0) & ~humble(X0)))) [nnf transformation 14]
61. ! [X0] : ((strong(X0) | humble(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (~strong(X0) & ~humble(X0)))) [flattening 60]
66. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 16]
87. ~calm(X0) | humble(X0) [cnf transformation 30]
90. calm(sK2) | ~old(X1) [cnf transformation 50]
100. ~wise(X0) | funny(X0) | brave(X0) [cnf transformation 34]
124. ~humble(X0) | ~tall(X0) [cnf transformation 59]
125. tall(X0) | ~humble(X0) [cnf transformation 61]
137. ~funny(X0) | humble(X0) | generous(X0) | old(X0) [cnf transformation 66]
148. wise(lucy) [cnf transformation 22]
149. ~brave(lucy) [cnf transformation 22]
153. ~generous(lucy) [cnf transformation 25]
209. 13 <=> ! [X1] : ~old(X1) [avatar definition]
210. ~old(X1) <- (13) [avatar component clause 209]
213. 14 <=> calm(sK2) [avatar definition]
215. calm(sK2) <- (14) [avatar component clause 213]
217. 13 | 14 [avatar split clause 90,213,209]
277. ~humble(X0) [subsumption resolution 125,124]
291. ~funny(X0) | generous(X0) | old(X0) [subsumption resolution 137,277]
341. funny(lucy) | brave(lucy) [resolution 100,148]
348. funny(lucy) [subsumption resolution 341,149]
392. generous(lucy) | old(lucy) [resolution 291,348]
396. old(lucy) [subsumption resolution 392,153]
397. $false <- (13) [subsumption resolution 396,210]
398. ~13 [avatar contradiction clause 397]
417. humble(sK2) <- (14) [resolution 215,87]
418. $false <- (14) [subsumption resolution 417,277]
419. ~14 [avatar contradiction clause 418]
420. $false [avatar sat refutation 217,398,419]
% SZS output end Proof for 1430207521020229591343575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not curious is rich and vice versa. Everyone who is curious is wise or brave and vice versa. Everyone who is calm is not generous. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Everyone who is either wise or happy is happy. If someone is not rich or kind then lucy is curious and vice versa. Everyone who is either not strong or not quiet is not rich and vice versa. Everyone who is not curious is creative or not patient and vice versa. Someone is not tall or old. John is either not humble or patient. Someone is either funny or not kind. Alice is funny or old. Lucy is either not curious or brave. Susan is either funny or not calm. Fred is not kind. Paul is tall or brave. | Lucy is not generous. | neutral | (![X]:((tall(X)&~curious(X))<=>rich(X)))&
(![X]:(curious(X)<=>(wise(X)|brave(X))))&
(![X]:(calm(X)=>~generous(X)))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(?[X]:((~tall(X)|old(X))))&
((~humble(john)<~>patient(john)))&
(?[X]:((funny(X)<~>~kind(X))))&
((funny(alice)|old(alice)))&
((~curious(lucy)<~>brave(lucy)))&
((funny(susan)<~>~calm(susan)))&
(~kind(fred))&
((tall(paul)|brave(paul))) | ~generous(lucy) | [] | null | 0 |
Everyone who is either not generous or humble is both not funny and not patient and vice versa.
If someone is curious or not brave then someone is not humble.
If someone is both patient and brave then susan is not funny.
If john is both kind and not kind then someone is old and vice versa.
Everyone who is either not quiet or curious is both patient and not funny and vice versa.
Everyone who is either rich or not strong is wise or patient and vice versa.
Everyone who is curious is not wise or not strong.
Everyone who is not tall or not generous is both tall and not old and vice versa.
Everyone who is tall or generous is both not generous and rich.
Everyone who is strong or not quiet is either generous or not strong and vice versa.
If fred is not humble or not generous then mary is either not wise or patient.
Everyone who is not rich is funny and vice versa.
Everyone who is not creative is old or not happy and vice versa.
If mary is kind or not curious then mary is either not strong or not rich and vice versa.
Someone is both not strong and not funny.
Paul is either kind or patient.
Alice is either not calm or not patient.
Someone is either calm or not happy.
Fred is curious or not strong. | Alice is creative. | neutral | (![X]:((~generous(X)<~>humble(X))<=>(~funny(X)&~patient(X))))&
((?[X]:((curious(X)|~brave(X))))=>(?[X]:(~humble(X))))&
((?[X]:((patient(X)&brave(X))))=>(~funny(susan)))&
(((kind(john)&~kind(john)))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(patient(X)&~funny(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)=>(~wise(X)|~strong(X))))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)&~old(X))))&
(![X]:((tall(X)|generous(X))=>(~generous(X)&rich(X))))&
(![X]:((strong(X)|~quiet(X))<=>(generous(X)<~>~strong(X))))&
(((~humble(fred)|~generous(fred)))=>((~wise(mary)<~>patient(mary))))&
(![X]:(~rich(X)<=>funny(X)))&
(![X]:(~creative(X)<=>(old(X)|~happy(X))))&
(((kind(mary)|~curious(mary)))<=>((~strong(mary)<~>~rich(mary))))&
(?[X]:((~strong(X)&~funny(X))))&
((kind(paul)<~>patient(paul)))&
((~calm(alice)<~>~patient(alice)))&
(?[X]:((calm(X)<~>~happy(X))))&
((curious(fred)|~strong(fred))) | creative(alice) | [] | null | 0 |
Everyone who is either brave or not quiet is both not tall and old and vice versa.
Everyone who is both rich and not quiet is calm or rich and vice versa.
Everyone who is not strong or rich is not creative.
Everyone who is not tall is either quiet or curious.
If alice is not tall then alice is not kind and vice versa.
Everyone who is both humble and not strong is generous or calm and vice versa.
Everyone who is both not old and not generous is happy or not strong and vice versa.
If someone is old or not brave then paul is happy or not kind.
Everyone who is either not patient or not curious is funny or not generous and vice versa.
If someone is both not generous and not wise then alice is either not brave or not strong and vice versa.
If john is not happy or old then someone is not old.
If someone is not creative then someone is both not patient and rich and vice versa.
Everyone who is both not patient and calm is both not happy and strong.
If someone is not brave or not patient then paul is not curious.
If someone is brave then john is both not wise and generous.
If john is not wise then someone is not calm or kind and vice versa.
Alice is not rich or not patient.
Someone is not happy.
Someone is not quiet or funny.
Lucy is strong.
Someone is both not curious and tall.
Someone is either not wise or curious.
Someone is both not kind and not tall.
Someone is both creative and not patient. | Paul is not brave. | entailment | (![X]:((brave(X)<~>~quiet(X))<=>(~tall(X)&old(X))))&
(![X]:((rich(X)&~quiet(X))<=>(calm(X)|rich(X))))&
(![X]:((~strong(X)|rich(X))=>~creative(X)))&
(![X]:(~tall(X)=>(quiet(X)<~>curious(X))))&
((~tall(alice))<=>(~kind(alice)))&
(![X]:((humble(X)&~strong(X))<=>(generous(X)|calm(X))))&
(![X]:((~old(X)&~generous(X))<=>(happy(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))=>((happy(paul)|~kind(paul))))&
(![X]:((~patient(X)<~>~curious(X))<=>(funny(X)|~generous(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>((~brave(alice)<~>~strong(alice))))&
(((~happy(john)|old(john)))=>(?[X]:(~old(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((~patient(X)&calm(X))=>(~happy(X)&strong(X))))&
((?[X]:((~brave(X)|~patient(X))))=>(~curious(paul)))&
((?[X]:(brave(X)))=>((~wise(john)&generous(john))))&
((~wise(john))<=>(?[X]:((~calm(X)|kind(X)))))&
((~rich(alice)|~patient(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((~quiet(X)|funny(X))))&
(strong(lucy))&
(?[X]:((~curious(X)&tall(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:((creative(X)&~patient(X)))) | ~brave(paul) | [
"p5",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2001247661047326432102962
% SZS output start Proof for 2001247661047326432102962
6. ! [X0] : ((~strong(X0) & humble(X0)) <=> (calm(X0) | generous(X0))) [input p5]
7. ! [X0] : ((~generous(X0) & ~old(X0)) <=> (~strong(X0) | happy(X0))) [input p6]
15. ? [X0] : brave(X0) => (generous(john) & ~wise(john)) [input p14]
25. brave(paul) [input hypothesis]
35. (generous(john) & ~wise(john)) | ! [X0] : ~brave(X0) [ennf transformation 15]
42. ! [X0] : (((~strong(X0) & humble(X0)) | (~calm(X0) & ~generous(X0))) & ((calm(X0) | generous(X0)) | (strong(X0) | ~humble(X0)))) [nnf transformation 6]
43. ! [X0] : (((~strong(X0) & humble(X0)) | (~calm(X0) & ~generous(X0))) & (calm(X0) | generous(X0) | strong(X0) | ~humble(X0))) [flattening 42]
44. ! [X0] : (((~generous(X0) & ~old(X0)) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | (generous(X0) | old(X0)))) [nnf transformation 7]
45. ! [X0] : (((~generous(X0) & ~old(X0)) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | generous(X0) | old(X0))) [flattening 44]
96. ~strong(X0) | ~generous(X0) [cnf transformation 43]
102. ~generous(X0) | strong(X0) [cnf transformation 45]
127. generous(john) | ~brave(X0) [cnf transformation 35]
143. brave(paul) [cnf transformation 25]
154. ~generous(X0) [subsumption resolution 102,96]
240. ~brave(X0) [subsumption resolution 127,154]
290. $false [subsumption resolution 143,240]
% SZS output end Proof for 2001247661047326432102962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not rich or not generous is either not tall or creative.
Everyone who is both not brave and not rich is not humble and vice versa.
If someone is either kind or not calm then susan is either not patient or not quiet.
If john is either not old or strong then someone is quiet.
Everyone who is either not generous or not rich is both quiet and curious.
Everyone who is either not creative or not patient is happy or funny and vice versa.
If someone is both not old and brave then lucy is both not calm and not kind and vice versa.
If someone is either tall or not quiet then john is not tall or not old.
Everyone who is either humble or not curious is not wise or not quiet and vice versa.
Everyone who is rich or not kind is both funny and kind.
Everyone who is both not wise and wise is either not humble or not kind.
Everyone who is both kind and not curious is either patient or not generous.
Everyone who is both not wise and generous is both not strong and rich and vice versa.
Everyone who is not creative or brave is not strong.
Everyone who is both not kind and wise is not rich and vice versa.
If someone is either not curious or not quiet then fred is both not strong and not patient.
Someone is not funny or wise.
Someone is either humble or not tall.
Someone is rich or happy.
John is kind or creative.
Alice is either curious or brave.
John is either not strong or rich. | Alice is not brave. | entailment | (![X]:((~rich(X)<~>~generous(X))=>(~tall(X)<~>creative(X))))&
(![X]:((~brave(X)&~rich(X))<=>~humble(X)))&
((?[X]:((kind(X)<~>~calm(X))))=>((~patient(susan)<~>~quiet(susan))))&
(((~old(john)<~>strong(john)))=>(?[X]:(quiet(X))))&
(![X]:((~generous(X)<~>~rich(X))=>(quiet(X)&curious(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>(happy(X)|funny(X))))&
((?[X]:((~old(X)&brave(X))))<=>((~calm(lucy)&~kind(lucy))))&
((?[X]:((tall(X)<~>~quiet(X))))=>((~tall(john)|~old(john))))&
(![X]:((humble(X)<~>~curious(X))<=>(~wise(X)|~quiet(X))))&
(![X]:((rich(X)|~kind(X))=>(funny(X)&kind(X))))&
(![X]:((~wise(X)&wise(X))=>(~humble(X)<~>~kind(X))))&
(![X]:((kind(X)&~curious(X))=>(patient(X)<~>~generous(X))))&
(![X]:((~wise(X)&generous(X))<=>(~strong(X)&rich(X))))&
(![X]:((~creative(X)|brave(X))=>~strong(X)))&
(![X]:((~kind(X)&wise(X))<=>~rich(X)))&
((?[X]:((~curious(X)<~>~quiet(X))))=>((~strong(fred)&~patient(fred))))&
(?[X]:((~funny(X)|wise(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:((rich(X)|happy(X))))&
((kind(john)|creative(john)))&
((curious(alice)<~>brave(alice)))&
((~strong(john)<~>rich(john))) | ~brave(alice) | [
"p1",
"p4",
"p5",
"p8",
"p9",
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8344693405978091632872974
% SZS output start Proof for 8344693405978091632872974
2. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> ~humble(X0)) [input p1]
5. ! [X0] : ((~generous(X0) <~> ~rich(X0)) => (curious(X0) & quiet(X0))) [input p4]
6. ! [X0] : ((~creative(X0) <~> ~patient(X0)) <=> (funny(X0) | happy(X0))) [input p5]
9. ! [X0] : ((humble(X0) <~> ~curious(X0)) <=> (~quiet(X0) | ~wise(X0))) [input p8]
10. ! [X0] : ((~kind(X0) | rich(X0)) => (kind(X0) & funny(X0))) [input p9]
12. ! [X0] : ((~curious(X0) & kind(X0)) => (patient(X0) <~> ~generous(X0))) [input p11]
13. ! [X0] : ((generous(X0) & ~wise(X0)) <=> (rich(X0) & ~strong(X0))) [input p12]
14. ! [X0] : ((brave(X0) | ~creative(X0)) => ~strong(X0)) [input p13]
15. ! [X0] : ((wise(X0) & ~kind(X0)) <=> ~rich(X0)) [input p14]
21. curious(alice) <~> brave(alice) [input p20]
23. brave(alice) [input hypothesis]
27. ! [X0] : ((curious(X0) & quiet(X0)) | (~generous(X0) <=> ~rich(X0))) [ennf transformation 5]
30. ! [X0] : ((kind(X0) & funny(X0)) | (kind(X0) & ~rich(X0))) [ennf transformation 10]
33. ! [X0] : ((patient(X0) <~> ~generous(X0)) | (curious(X0) | ~kind(X0))) [ennf transformation 12]
34. ! [X0] : ((patient(X0) <~> ~generous(X0)) | curious(X0) | ~kind(X0)) [flattening 33]
35. ! [X0] : (~strong(X0) | (~brave(X0) & creative(X0))) [ennf transformation 14]
38. ! [X0] : (((~rich(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) | brave(X0)))) [nnf transformation 2]
39. ! [X0] : (((~rich(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | rich(X0) | brave(X0))) [flattening 38]
44. ! [X0] : ((curious(X0) & quiet(X0)) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0)))) [nnf transformation 27]
45. ! [X0] : ((((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0))))) [nnf transformation 6]
46. ! [X0] : ((((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0))))) [flattening 45]
53. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) & ((~quiet(X0) | ~wise(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [nnf transformation 9]
54. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) & (~quiet(X0) | ~wise(X0) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [flattening 53]
56. ! [X0] : (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | curious(X0) | ~kind(X0)) [nnf transformation 34]
57. ! [X0] : (((generous(X0) & ~wise(X0)) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | (~generous(X0) | wise(X0)))) [nnf transformation 13]
58. ! [X0] : (((generous(X0) & ~wise(X0)) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | ~generous(X0) | wise(X0))) [flattening 57]
59. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 15]
60. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0)) & (~rich(X0) | ~wise(X0) | kind(X0))) [flattening 59]
69. (~brave(alice) | ~curious(alice)) & (brave(alice) | curious(alice)) [nnf transformation 21]
77. ~rich(X0) | humble(X0) [cnf transformation 39]
86. ~rich(X0) | curious(X0) | generous(X0) [cnf transformation 44]
91. ~funny(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 46]
104. ~humble(X0) | curious(X0) | wise(X0) [cnf transformation 54]
106. ~rich(X0) | funny(X0) [cnf transformation 30]
109. kind(X0) | kind(X0) [cnf transformation 30]
112. ~generous(X0) | patient(X0) | curious(X0) | ~kind(X0) [cnf transformation 56]
116. ~wise(X0) | ~rich(X0) | strong(X0) [cnf transformation 58]
118. ~strong(X0) | creative(X0) [cnf transformation 35]
121. ~kind(X0) | rich(X0) [cnf transformation 60]
133. ~brave(alice) | ~curious(alice) [cnf transformation 69]
136. brave(alice) [cnf transformation 23]
137. kind(X0) [duplicate literal removal 109]
206. ~generous(X0) | patient(X0) | curious(X0) [subsumption resolution 112,137]
207. rich(X0) [subsumption resolution 121,137]
246. 24 <=> curious(alice) [avatar definition]
248. ~curious(alice) <- (~24) [avatar component clause 246]
250. 25 <=> brave(alice) [avatar definition]
253. ~24 | ~25 [avatar split clause 133,250,246]
257. 25 [avatar split clause 136,250]
262. humble(X0) [resolution 77,207]
263. funny(X0) [resolution 106,207]
278. curious(X0) | generous(X0) [resolution 86,207]
281. generous(alice) <- (~24) [resolution 278,248]
284. ~patient(X0) | ~creative(X0) [resolution 91,263]
291. wise(X0) | curious(X0) [resolution 104,262]
312. ~rich(X0) | strong(X0) | curious(X0) [resolution 116,291]
315. curious(X0) | strong(X0) [subsumption resolution 312,207]
323. patient(alice) | curious(alice) <- (~24) [resolution 206,281]
324. patient(alice) <- (~24) [subsumption resolution 323,248]
327. ~creative(alice) <- (~24) [resolution 324,284]
452. strong(alice) <- (~24) [resolution 315,248]
476. creative(alice) <- (~24) [resolution 452,118]
480. $false <- (~24) [subsumption resolution 476,327]
481. 24 [avatar contradiction clause 480]
482. $false [avatar sat refutation 253,257,481]
% SZS output end Proof for 8344693405978091632872974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or creative is either not curious or quiet.
Everyone who is strong is not strong or not curious.
Everyone who is both kind and curious is patient and vice versa.
Everyone who is both kind and not humble is creative.
If lucy is not funny then someone is not old and vice versa.
Everyone who is either funny or brave is not brave and vice versa.
If alice is rich or not rich then john is old.
Everyone who is either happy or not strong is either creative or rich.
Everyone who is not old or patient is not quiet or not humble and vice versa.
If susan is either not old or happy then lucy is calm or creative.
If someone is not strong or not kind then someone is not patient and vice versa.
If alice is old or not old then susan is not humble or not funny.
Everyone who is both not patient and not curious is both not patient and generous and vice versa.
If someone is not curious or rich then someone is both wise and tall and vice versa.
If someone is not tall or not calm then lucy is patient and vice versa.
Someone is either not curious or curious.
Paul is kind or curious.
Someone is not generous or rich.
Lucy is either quiet or not kind.
Someone is brave.
Susan is funny or wise. | Lucy is not kind. | contradiction | (![X]:((~creative(X)|creative(X))=>(~curious(X)<~>quiet(X))))&
(![X]:(strong(X)=>(~strong(X)|~curious(X))))&
(![X]:((kind(X)&curious(X))<=>patient(X)))&
(![X]:((kind(X)&~humble(X))=>creative(X)))&
((~funny(lucy))<=>(?[X]:(~old(X))))&
(![X]:((funny(X)<~>brave(X))<=>~brave(X)))&
(((rich(alice)|~rich(alice)))=>(old(john)))&
(![X]:((happy(X)<~>~strong(X))=>(creative(X)<~>rich(X))))&
(![X]:((~old(X)|patient(X))<=>(~quiet(X)|~humble(X))))&
(((~old(susan)<~>happy(susan)))=>((calm(lucy)|creative(lucy))))&
((?[X]:((~strong(X)|~kind(X))))<=>(?[X]:(~patient(X))))&
(((old(alice)|~old(alice)))=>((~humble(susan)|~funny(susan))))&
(![X]:((~patient(X)&~curious(X))<=>(~patient(X)&generous(X))))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((wise(X)&tall(X)))))&
((?[X]:((~tall(X)|~calm(X))))<=>(patient(lucy)))&
(?[X]:((~curious(X)<~>curious(X))))&
((kind(paul)|curious(paul)))&
(?[X]:((~generous(X)|rich(X))))&
((quiet(lucy)<~>~kind(lucy)))&
(?[X]:(brave(X)))&
((funny(susan)|wise(susan))) | ~kind(lucy) | [
"p0",
"p2",
"p4",
"p5",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7862598041183990885235154
% SZS output start Proof for 7862598041183990885235154
1. ! [X0] : ((creative(X0) | ~creative(X0)) => (~curious(X0) <~> quiet(X0))) [input p0]
3. ! [X0] : ((curious(X0) & kind(X0)) <=> patient(X0)) [input p2]
5. ~funny(lucy) <=> ? [X0] : ~old(X0) [input p4]
6. ! [X0] : ((funny(X0) <~> brave(X0)) <=> ~brave(X0)) [input p5]
9. ! [X0] : ((patient(X0) | ~old(X0)) <=> (~humble(X0) | ~quiet(X0))) [input p8]
19. quiet(lucy) <~> ~kind(lucy) [input p18]
22. ~kind(lucy) [input hypothesis]
25. ! [X0] : ((~curious(X0) <~> quiet(X0)) | (~creative(X0) & creative(X0))) [ennf transformation 1]
36. ! [X0] : (((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | (~creative(X0) & creative(X0))) [nnf transformation 25]
37. ! [X0] : (((curious(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | (~curious(X0) | ~kind(X0)))) [nnf transformation 3]
38. ! [X0] : (((curious(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | ~curious(X0) | ~kind(X0))) [flattening 37]
39. (~funny(lucy) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | funny(lucy)) [nnf transformation 5]
40. (~funny(lucy) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | funny(lucy)) [rectify 39]
41. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
42. (~funny(lucy) | ! [X0] : old(X0)) & (~old(sK0) | funny(lucy)) [skolemisation 40,41]
43. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | brave(X0)) & (~brave(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 6]
45. ! [X0] : (((patient(X0) | ~old(X0)) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 9]
46. ! [X0] : ((patient(X0) | ~old(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | (~patient(X0) & old(X0)))) [flattening 45]
69. (kind(lucy) | ~quiet(lucy)) & (~kind(lucy) | quiet(lucy)) [nnf transformation 19]
72. quiet(X0) | ~curious(X0) | creative(X0) [cnf transformation 36]
73. ~curious(X0) | quiet(X0) | ~creative(X0) [cnf transformation 36]
79. ~patient(X0) | curious(X0) [cnf transformation 38]
82. ~funny(lucy) | old(X0) [cnf transformation 42]
84. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 43]
85. brave(X0) | funny(X0) | brave(X0) [cnf transformation 43]
95. ~old(X0) | patient(X0) | quiet(X0) [cnf transformation 46]
121. kind(lucy) | ~quiet(lucy) [cnf transformation 69]
124. ~kind(lucy) [cnf transformation 22]
125. ~brave(X0) | funny(X0) [duplicate literal removal 84]
126. brave(X0) | funny(X0) [duplicate literal removal 85]
129. ~curious(X0) | quiet(X0) [subsumption resolution 72,73]
131. 1 <=> ! [X0] : old(X0) [avatar definition]
132. old(X0) <- (1) [avatar component clause 131]
134. 2 <=> funny(lucy) [avatar definition]
136. ~funny(lucy) <- (~2) [avatar component clause 134]
137. 1 | ~2 [avatar split clause 82,134,131]
143. funny(X0) [subsumption resolution 125,126]
279. 34 <=> quiet(lucy) [avatar definition]
281. ~quiet(lucy) <- (~34) [avatar component clause 279]
283. 35 <=> kind(lucy) [avatar definition]
286. ~34 | 35 [avatar split clause 121,283,279]
288. ~35 [avatar split clause 124,283]
291. $false <- (~2) [subsumption resolution 136,143]
292. 2 [avatar contradiction clause 291]
343. patient(X0) | quiet(X0) <- (1) [resolution 95,132]
348. quiet(X0) | curious(X0) <- (1) [resolution 343,79]
351. quiet(X0) <- (1) [subsumption resolution 348,129]
373. $false <- (1, ~34) [resolution 351,281]
376. ~1 | 34 [avatar contradiction clause 373]
378. $false [avatar sat refutation 137,286,288,292,376]
% SZS output end Proof for 7862598041183990885235154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is old or not kind then susan is brave or rich and vice versa. If someone is both not generous and not calm then lucy is either not strong or not tall and vice versa. If someone is either not strong or not funny then alice is not funny or not patient. If mary is brave then someone is old or not old. Everyone who is not happy is not creative. If someone is brave then mary is not creative. If someone is not generous or not rich then lucy is not brave and vice versa. Everyone who is either not creative or not strong is either strong or not rich. If paul is not patient or brave then someone is kind. If paul is both quiet and not curious then alice is both calm and old. Everyone who is not tall or calm is both not strong and not calm and vice versa. Everyone who is both not old and not kind is either calm or not generous. Everyone who is generous or wise is not old or not generous. Everyone who is either rich or old is not funny. If someone is either calm or happy then someone is either not funny or not curious and vice versa. If someone is brave then someone is curious and vice versa. John is both strong and creative. Someone is not creative. Someone is brave or quiet. Someone is not humble. Someone is either generous or happy. Susan is both not creative and patient. Someone is tall. | Mary is generous. | entailment | (((old(paul)|~kind(paul)))<=>((brave(susan)|rich(susan))))&
((?[X]:((~generous(X)&~calm(X))))<=>((~strong(lucy)<~>~tall(lucy))))&
((?[X]:((~strong(X)<~>~funny(X))))=>((~funny(alice)|~patient(alice))))&
((brave(mary))=>(?[X]:((old(X)|~old(X)))))&
(![X]:(~happy(X)=>~creative(X)))&
((?[X]:(brave(X)))=>(~creative(mary)))&
((?[X]:((~generous(X)|~rich(X))))<=>(~brave(lucy)))&
(![X]:((~creative(X)<~>~strong(X))=>(strong(X)<~>~rich(X))))&
(((~patient(paul)|brave(paul)))=>(?[X]:(kind(X))))&
(((quiet(paul)&~curious(paul)))=>((calm(alice)&old(alice))))&
(![X]:((~tall(X)|calm(X))<=>(~strong(X)&~calm(X))))&
(![X]:((~old(X)&~kind(X))=>(calm(X)<~>~generous(X))))&
(![X]:((generous(X)|wise(X))=>(~old(X)|~generous(X))))&
(![X]:((rich(X)<~>old(X))=>~funny(X)))&
((?[X]:((calm(X)<~>happy(X))))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
((?[X]:(brave(X)))<=>(?[X]:(curious(X))))&
((strong(john)&creative(john)))&
(?[X]:(~creative(X)))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:(~humble(X)))&
(?[X]:((generous(X)<~>happy(X))))&
((~creative(susan)&patient(susan)))&
(?[X]:(tall(X))) | generous(mary) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8986215082508466113517172
% SZS output start Proof for 8986215082508466113517172
2. ? [X0] : (~calm(X0) & ~generous(X0)) <=> (~strong(lucy) <~> ~tall(lucy)) [input p1]
11. ! [X0] : ((calm(X0) | ~tall(X0)) <=> (~calm(X0) & ~strong(X0))) [input p10]
24. ~generous(mary) [input hypothesis]
45. (? [X0] : (~calm(X0) & ~generous(X0)) | ((~strong(lucy) | tall(lucy)) & (~tall(lucy) | strong(lucy)))) & (((tall(lucy) | strong(lucy)) & (~tall(lucy) | ~strong(lucy))) | ! [X0] : (calm(X0) | generous(X0))) [nnf transformation 2]
46. (? [X0] : (~calm(X0) & ~generous(X0)) | ((~strong(lucy) | tall(lucy)) & (~tall(lucy) | strong(lucy)))) & (((tall(lucy) | strong(lucy)) & (~tall(lucy) | ~strong(lucy))) | ! [X1] : (calm(X1) | generous(X1))) [rectify 45]
47. ? [X0] : (~calm(X0) & ~generous(X0)) => (~calm(sK0) & ~generous(sK0)) [choice axiom]
48. ((~calm(sK0) & ~generous(sK0)) | ((~strong(lucy) | tall(lucy)) & (~tall(lucy) | strong(lucy)))) & (((tall(lucy) | strong(lucy)) & (~tall(lucy) | ~strong(lucy))) | ! [X1] : (calm(X1) | generous(X1))) [skolemisation 46,47]
59. ! [X0] : (((calm(X0) | ~tall(X0)) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | (~calm(X0) & tall(X0)))) [nnf transformation 11]
60. ! [X0] : ((calm(X0) | ~tall(X0) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | (~calm(X0) & tall(X0)))) [flattening 59]
86. ~tall(lucy) | ~strong(lucy) | calm(X1) | generous(X1) [cnf transformation 48]
87. tall(lucy) | strong(lucy) | calm(X1) | generous(X1) [cnf transformation 48]
108. ~strong(X0) | tall(X0) [cnf transformation 60]
111. ~calm(X0) | ~calm(X0) [cnf transformation 60]
112. calm(X0) | ~tall(X0) | calm(X0) | strong(X0) [cnf transformation 60]
137. ~generous(mary) [cnf transformation 24]
139. ~calm(X0) [duplicate literal removal 111]
140. ~tall(X0) | calm(X0) | strong(X0) [duplicate literal removal 112]
164. 5 <=> tall(lucy) [avatar definition]
166. tall(lucy) <- (5) [avatar component clause 164]
168. 6 <=> strong(lucy) [avatar definition]
169. strong(lucy) <- (6) [avatar component clause 168]
184. 9 <=> ! [X1] : (calm(X1) | generous(X1)) [avatar definition]
185. calm(X1) | generous(X1) <- (9) [avatar component clause 184]
186. 9 | 6 | 5 [avatar split clause 87,164,168,184]
187. 9 | ~6 | ~5 [avatar split clause 86,164,168,184]
230. 20 <=> ! [X1] : generous(X1) [avatar definition]
231. generous(X1) <- (20) [avatar component clause 230]
370. calm(lucy) | strong(lucy) <- (5) [resolution 140,166]
373. strong(lucy) <- (5) [subsumption resolution 370,139]
376. 6 | ~5 [avatar split clause 373,164,168]
377. generous(X1) <- (9) [subsumption resolution 185,139]
378. 20 | ~9 [avatar split clause 377,184,230]
379. tall(lucy) <- (6) [resolution 169,108]
380. $false <- (20) [resolution 231,137]
384. ~20 [avatar contradiction clause 380]
385. 5 | ~6 [avatar split clause 379,168,164]
386. $false [avatar sat refutation 186,187,376,378,384,385]
% SZS output end Proof for 8986215082508466113517172
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm and not rich then paul is either not old or funny and vice versa. If someone is not quiet then alice is happy or not patient and vice versa. Everyone who is either not funny or not brave is not calm or not quiet and vice versa. Everyone who is tall or funny is both not calm and not patient. Everyone who is both quiet and not funny is both not rich and not funny and vice versa. Everyone who is both wise and tall is both not calm and not kind and vice versa. If someone is not tall then someone is both not wise and humble. Everyone who is not creative is not brave or funny and vice versa. Everyone who is either kind or quiet is not brave or quiet and vice versa. Everyone who is both not happy and not old is not happy. Everyone who is both not brave and not strong is calm. Everyone who is wise is either not patient or kind. Everyone who is either not rich or not brave is kind or not quiet and vice versa. Everyone who is patient or generous is not curious or not brave. Everyone who is funny is creative. If susan is either not old or not funny then mary is either not happy or not tall. Paul is not wise or patient. Alice is either not wise or kind. John is both quiet and happy. Lucy is either not humble or not quiet. John is not generous. | Susan is not curious. | neutral | ((?[X]:((~calm(X)&~rich(X))))<=>((~old(paul)<~>funny(paul))))&
((?[X]:(~quiet(X)))<=>((happy(alice)|~patient(alice))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~calm(X)|~quiet(X))))&
(![X]:((tall(X)|funny(X))=>(~calm(X)&~patient(X))))&
(![X]:((quiet(X)&~funny(X))<=>(~rich(X)&~funny(X))))&
(![X]:((wise(X)&tall(X))<=>(~calm(X)&~kind(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:(~creative(X)<=>(~brave(X)|funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>(~brave(X)|quiet(X))))&
(![X]:((~happy(X)&~old(X))=>~happy(X)))&
(![X]:((~brave(X)&~strong(X))=>calm(X)))&
(![X]:(wise(X)=>(~patient(X)<~>kind(X))))&
(![X]:((~rich(X)<~>~brave(X))<=>(kind(X)|~quiet(X))))&
(![X]:((patient(X)|generous(X))=>(~curious(X)|~brave(X))))&
(![X]:(funny(X)=>creative(X)))&
(((~old(susan)<~>~funny(susan)))=>((~happy(mary)<~>~tall(mary))))&
((~wise(paul)|patient(paul)))&
((~wise(alice)<~>kind(alice)))&
((quiet(john)&happy(john)))&
((~humble(lucy)<~>~quiet(lucy)))&
(~generous(john)) | ~curious(susan) | [] | null | 0 |
If mary is tall or not patient then alice is either not humble or curious.
Everyone who is not calm is either generous or not strong and vice versa.
Everyone who is old or not tall is curious or wise and vice versa.
If susan is not kind or quiet then someone is not patient and vice versa.
Everyone who is not quiet is strong or not tall and vice versa.
If paul is either tall or happy then someone is not generous and vice versa.
Everyone who is either not generous or not strong is not old.
Everyone who is not kind is funny or not rich.
Everyone who is happy or rich is not happy and vice versa.
If fred is humble or funny then someone is rich.
If someone is not creative or funny then someone is wise or not wise and vice versa.
If someone is both not generous and not calm then john is funny.
Everyone who is either creative or humble is either not kind or not brave and vice versa.
Everyone who is both calm and humble is not calm and vice versa.
If alice is both generous and not generous then someone is not patient or generous and vice versa.
If mary is both not strong and not rich then john is either rich or not happy and vice versa.
Susan is either wise or curious.
Someone is either quiet or not happy.
John is patient or calm.
Alice is kind.
Someone is not kind.
Someone is strong.
Someone is not brave. | Alice is not happy. | entailment | (((tall(mary)|~patient(mary)))=>((~humble(alice)<~>curious(alice))))&
(![X]:(~calm(X)<=>(generous(X)<~>~strong(X))))&
(![X]:((old(X)|~tall(X))<=>(curious(X)|wise(X))))&
(((~kind(susan)|quiet(susan)))<=>(?[X]:(~patient(X))))&
(![X]:(~quiet(X)<=>(strong(X)|~tall(X))))&
(((tall(paul)<~>happy(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)<~>~strong(X))=>~old(X)))&
(![X]:(~kind(X)=>(funny(X)|~rich(X))))&
(![X]:((happy(X)|rich(X))<=>~happy(X)))&
(((humble(fred)|funny(fred)))=>(?[X]:(rich(X))))&
((?[X]:((~creative(X)|funny(X))))<=>(?[X]:((wise(X)|~wise(X)))))&
((?[X]:((~generous(X)&~calm(X))))=>(funny(john)))&
(![X]:((creative(X)<~>humble(X))<=>(~kind(X)<~>~brave(X))))&
(![X]:((calm(X)&humble(X))<=>~calm(X)))&
(((generous(alice)&~generous(alice)))<=>(?[X]:((~patient(X)|generous(X)))))&
(((~strong(mary)&~rich(mary)))<=>((rich(john)<~>~happy(john))))&
((wise(susan)<~>curious(susan)))&
(?[X]:((quiet(X)<~>~happy(X))))&
((patient(john)|calm(john)))&
(kind(alice))&
(?[X]:(~kind(X)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X))) | ~happy(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2444170015504662027423939
% SZS output start Proof for 2444170015504662027423939
9. ! [X0] : ((rich(X0) | happy(X0)) <=> ~happy(X0)) [input p8]
24. happy(alice) [input hypothesis]
48. ! [X0] : (((rich(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (~rich(X0) & ~happy(X0)))) [nnf transformation 9]
49. ! [X0] : ((rich(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (~rich(X0) & ~happy(X0)))) [flattening 48]
102. ~happy(X0) | ~happy(X0) [cnf transformation 49]
143. happy(alice) [cnf transformation 24]
146. ~happy(X0) [duplicate literal removal 102]
280. $false [subsumption resolution 143,146]
% SZS output end Proof for 2444170015504662027423939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either rich or not tall then mary is generous. If someone is not kind or not creative then susan is not brave or curious. Everyone who is not patient is not humble or not creative and vice versa. Everyone who is not rich or quiet is not old or not strong and vice versa. If susan is calm then mary is both strong and not curious and vice versa. If alice is not tall or calm then someone is quiet. If someone is not happy then someone is not wise or patient. Everyone who is both not brave and not wise is either happy or not wise and vice versa. If someone is not creative or quiet then someone is either not patient or not creative. Everyone who is old is both not old and tall. If someone is not happy then someone is not wise. If someone is either calm or not generous then someone is not wise and vice versa. Everyone who is funny or not patient is either tall or wise. Everyone who is both old and not creative is curious or calm and vice versa. If susan is either calm or old then mary is either not funny or not patient. Everyone who is not brave or not patient is both calm and not patient. Someone is humble. Alice is either creative or not generous. Mary is both not tall and not calm. Someone is kind. Someone is either not rich or not brave. | Mary is patient. | entailment | (((rich(fred)<~>~tall(fred)))=>(generous(mary)))&
((?[X]:((~kind(X)|~creative(X))))=>((~brave(susan)|curious(susan))))&
(![X]:(~patient(X)<=>(~humble(X)|~creative(X))))&
(![X]:((~rich(X)|quiet(X))<=>(~old(X)|~strong(X))))&
((calm(susan))<=>((strong(mary)&~curious(mary))))&
(((~tall(alice)|calm(alice)))=>(?[X]:(quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:(old(X)=>(~old(X)&tall(X))))&
((?[X]:(~happy(X)))=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)|~patient(X))=>(tall(X)<~>wise(X))))&
(![X]:((old(X)&~creative(X))<=>(curious(X)|calm(X))))&
(((calm(susan)<~>old(susan)))=>((~funny(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|~patient(X))=>(calm(X)&~patient(X))))&
(?[X]:(humble(X)))&
((creative(alice)<~>~generous(alice)))&
((~tall(mary)&~calm(mary)))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)<~>~brave(X)))) | patient(mary) | [
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8860168664577880512870799
% SZS output start Proof for 8860168664577880512870799
10. ! [X0] : (old(X0) => (tall(X0) & ~old(X0))) [input p9]
14. ! [X0] : ((~creative(X0) & old(X0)) <=> (calm(X0) | curious(X0))) [input p13]
16. ! [X0] : ((~patient(X0) | ~brave(X0)) => (~patient(X0) & calm(X0))) [input p15]
22. ~patient(mary) [input hypothesis]
35. ! [X0] : ((tall(X0) & ~old(X0)) | ~old(X0)) [ennf transformation 10]
39. ! [X0] : ((~patient(X0) & calm(X0)) | (patient(X0) & brave(X0))) [ennf transformation 16]
67. ! [X0] : (((~creative(X0) & old(X0)) | (~calm(X0) & ~curious(X0))) & ((calm(X0) | curious(X0)) | (creative(X0) | ~old(X0)))) [nnf transformation 14]
68. ! [X0] : (((~creative(X0) & old(X0)) | (~calm(X0) & ~curious(X0))) & (calm(X0) | curious(X0) | creative(X0) | ~old(X0))) [flattening 67]
102. ~old(X0) | ~old(X0) [cnf transformation 35]
115. old(X0) | ~calm(X0) [cnf transformation 68]
123. calm(X0) | patient(X0) [cnf transformation 39]
133. ~patient(mary) [cnf transformation 22]
134. ~old(X0) [duplicate literal removal 102]
254. ~calm(X0) [subsumption resolution 115,134]
256. patient(X0) [subsumption resolution 123,254]
269. $false [subsumption resolution 133,256]
% SZS output end Proof for 8860168664577880512870799
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or funny is both not generous and not kind and vice versa. If lucy is not happy then mary is not old or not tall. Everyone who is either funny or generous is not patient or tall and vice versa. If paul is both not strong and not wise then mary is either not old or generous and vice versa. Everyone who is either not old or strong is either patient or funny and vice versa. Everyone who is patient or not old is both not strong and not humble. If someone is both not quiet and humble then someone is not wise. If susan is patient or generous then someone is both not brave and not quiet. If alice is either happy or calm then susan is both not quiet and quiet. If john is either humble or not humble then someone is not generous and vice versa. Everyone who is not old is both funny and not patient. Everyone who is not kind or not generous is both tall and kind and vice versa. If someone is either tall or calm then mary is creative or not strong and vice versa. Everyone who is quiet is not generous or not kind and vice versa. If someone is either brave or not humble then mary is creative and vice versa. Everyone who is either old or curious is either calm or curious and vice versa. Someone is both rich and old. Alice is not happy or old. Someone is either generous or brave. Someone is curious or quiet. John is both humble and not patient. Fred is old. Someone is not generous. John is not kind or not quiet. | John is funny. | contradiction | (![X]:((~calm(X)<~>funny(X))<=>(~generous(X)&~kind(X))))&
((~happy(lucy))=>((~old(mary)|~tall(mary))))&
(![X]:((funny(X)<~>generous(X))<=>(~patient(X)|tall(X))))&
(((~strong(paul)&~wise(paul)))<=>((~old(mary)<~>generous(mary))))&
(![X]:((~old(X)<~>strong(X))<=>(patient(X)<~>funny(X))))&
(![X]:((patient(X)|~old(X))=>(~strong(X)&~humble(X))))&
((?[X]:((~quiet(X)&humble(X))))=>(?[X]:(~wise(X))))&
(((patient(susan)|generous(susan)))=>(?[X]:((~brave(X)&~quiet(X)))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(?[X]:((rich(X)&old(X))))&
((~happy(alice)|old(alice)))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((humble(john)&~patient(john)))&
(old(fred))&
(?[X]:(~generous(X)))&
((~kind(john)|~quiet(john))) | funny(john) | [
"p0",
"p5",
"p11",
"p13",
"p15",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1102243763763826454943564
% SZS output start Proof for 1102243763763826454943564
1. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> (~kind(X0) & ~generous(X0))) [input p0]
6. ! [X0] : ((~old(X0) | patient(X0)) => (~humble(X0) & ~strong(X0))) [input p5]
12. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p11]
14. ! [X0] : (quiet(X0) <=> (~kind(X0) | ~generous(X0))) [input p13]
16. ! [X0] : ((old(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p15]
21. ~patient(john) & humble(john) [input p20]
24. ~quiet(john) | ~kind(john) [input p23]
25. funny(john) [input hypothesis]
30. ! [X0] : ((~humble(X0) & ~strong(X0)) | (old(X0) & ~patient(X0))) [ennf transformation 6]
35. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (kind(X0) | generous(X0))) & ((~kind(X0) & ~generous(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | kind(X0) | generous(X0)) & ((~kind(X0) & ~generous(X0)) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [flattening 35]
52. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 12]
53. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 52]
59. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ~quiet(X0))) [nnf transformation 14]
60. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ~quiet(X0))) [flattening 59]
65. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 16]
76. ~generous(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 36]
105. ~humble(X0) | old(X0) [cnf transformation 30]
123. kind(X0) | kind(X0) [cnf transformation 53]
133. quiet(X0) | generous(X0) [cnf transformation 60]
139. curious(X0) | calm(X0) | curious(X0) | ~old(X0) [cnf transformation 65]
146. ~curious(X0) | ~old(X0) | calm(X0) | ~curious(X0) [cnf transformation 65]
152. humble(john) [cnf transformation 21]
156. ~quiet(john) | ~kind(john) [cnf transformation 24]
157. funny(john) [cnf transformation 25]
158. curious(X0) | calm(X0) | ~old(X0) [duplicate literal removal 139]
161. ~curious(X0) | ~old(X0) | calm(X0) [duplicate literal removal 146]
162. kind(X0) [duplicate literal removal 123]
242. 16 <=> humble(john) [avatar definition]
244. humble(john) <- (16) [avatar component clause 242]
299. ~old(X0) | calm(X0) [subsumption resolution 158,161]
324. 16 [avatar split clause 152,242]
325. ~quiet(john) [subsumption resolution 156,162]
327. old(john) <- (16) [resolution 105,244]
330. generous(john) [resolution 133,325]
333. calm(john) <- (16) [resolution 299,327]
343. ~calm(john) | ~funny(john) [resolution 76,330]
362. ~funny(john) <- (16) [subsumption resolution 343,333]
363. $false <- (16) [subsumption resolution 362,157]
364. ~16 [avatar contradiction clause 363]
365. $false [avatar sat refutation 324,364]
% SZS output end Proof for 1102243763763826454943564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or funny then susan is either not rich or humble and vice versa. Everyone who is both rich and creative is not patient. If alice is both not quiet and not tall then someone is kind. If mary is wise or brave then paul is not brave. Everyone who is both kind and not tall is either not wise or humble and vice versa. Everyone who is both not calm and old is old or curious and vice versa. Everyone who is both not old and creative is both not curious and kind and vice versa. If susan is both old and not curious then paul is happy or not generous and vice versa. If mary is both not generous and tall then someone is either not curious or not happy. Everyone who is not curious or not old is both calm and creative and vice versa. If fred is tall or not patient then mary is not rich and vice versa. Everyone who is not generous or generous is either not kind or rich and vice versa. Everyone who is calm is patient and vice versa. If someone is not wise or kind then someone is either happy or wise and vice versa. If someone is not strong or wise then paul is both not tall and humble. If fred is both strong and funny then susan is not quiet and vice versa. Someone is both not brave and not wise. Someone is both not wise and creative. Lucy is either old or not strong. Someone is both strong and not brave. Lucy is not quiet. Someone is either not tall or generous. | Mary is curious. | entailment | ((?[X]:((old(X)<~>funny(X))))<=>((~rich(susan)<~>humble(susan))))&
(![X]:((rich(X)&creative(X))=>~patient(X)))&
(((~quiet(alice)&~tall(alice)))=>(?[X]:(kind(X))))&
(((wise(mary)|brave(mary)))=>(~brave(paul)))&
(![X]:((kind(X)&~tall(X))<=>(~wise(X)<~>humble(X))))&
(![X]:((~calm(X)&old(X))<=>(old(X)|curious(X))))&
(![X]:((~old(X)&creative(X))<=>(~curious(X)&kind(X))))&
(((old(susan)&~curious(susan)))<=>((happy(paul)|~generous(paul))))&
(((~generous(mary)&tall(mary)))=>(?[X]:((~curious(X)<~>~happy(X)))))&
(![X]:((~curious(X)|~old(X))<=>(calm(X)&creative(X))))&
(((tall(fred)|~patient(fred)))<=>(~rich(mary)))&
(![X]:((~generous(X)|generous(X))<=>(~kind(X)<~>rich(X))))&
(![X]:(calm(X)<=>patient(X)))&
((?[X]:((~wise(X)|kind(X))))<=>(?[X]:((happy(X)<~>wise(X)))))&
((?[X]:((~strong(X)|wise(X))))=>((~tall(paul)&humble(paul))))&
(((strong(fred)&funny(fred)))<=>(~quiet(susan)))&
(?[X]:((~brave(X)&~wise(X))))&
(?[X]:((~wise(X)&creative(X))))&
((old(lucy)<~>~strong(lucy)))&
(?[X]:((strong(X)&~brave(X))))&
(~quiet(lucy))&
(?[X]:((~tall(X)<~>generous(X)))) | curious(mary) | [
"p1",
"p5",
"p6",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8705601286710062509940107
% SZS output start Proof for 8705601286710062509940107
2. ! [X0] : ((creative(X0) & rich(X0)) => ~patient(X0)) [input p1]
6. ! [X0] : ((old(X0) & ~calm(X0)) <=> (curious(X0) | old(X0))) [input p5]
7. ! [X0] : ((creative(X0) & ~old(X0)) <=> (kind(X0) & ~curious(X0))) [input p6]
10. ! [X0] : ((~old(X0) | ~curious(X0)) <=> (creative(X0) & calm(X0))) [input p9]
12. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (~kind(X0) <~> rich(X0))) [input p11]
13. ! [X0] : (calm(X0) <=> patient(X0)) [input p12]
23. ~curious(mary) [input hypothesis]
28. ! [X0] : (~patient(X0) | (~creative(X0) | ~rich(X0))) [ennf transformation 2]
29. ! [X0] : (~patient(X0) | ~creative(X0) | ~rich(X0)) [flattening 28]
43. ! [X0] : (((old(X0) & ~calm(X0)) | (~curious(X0) & ~old(X0))) & ((curious(X0) | old(X0)) | (~old(X0) | calm(X0)))) [nnf transformation 6]
44. ! [X0] : (((old(X0) & ~calm(X0)) | (~curious(X0) & ~old(X0))) & (curious(X0) | old(X0) | ~old(X0) | calm(X0))) [flattening 43]
45. ! [X0] : (((creative(X0) & ~old(X0)) | (~kind(X0) | curious(X0))) & ((kind(X0) & ~curious(X0)) | (~creative(X0) | old(X0)))) [nnf transformation 7]
46. ! [X0] : (((creative(X0) & ~old(X0)) | ~kind(X0) | curious(X0)) & ((kind(X0) & ~curious(X0)) | ~creative(X0) | old(X0))) [flattening 45]
52. ! [X0] : (((~old(X0) | ~curious(X0)) | (~creative(X0) | ~calm(X0))) & ((creative(X0) & calm(X0)) | (old(X0) & curious(X0)))) [nnf transformation 10]
53. ! [X0] : ((~old(X0) | ~curious(X0) | ~creative(X0) | ~calm(X0)) & ((creative(X0) & calm(X0)) | (old(X0) & curious(X0)))) [flattening 52]
56. ! [X0] : (((generous(X0) | ~generous(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (~generous(X0) & generous(X0)))) [nnf transformation 12]
57. ! [X0] : ((generous(X0) | ~generous(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (~generous(X0) & generous(X0)))) [flattening 56]
58. ! [X0] : ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))) [nnf transformation 13]
84. ~patient(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 29]
93. ~calm(X0) | ~old(X0) [cnf transformation 44]
98. ~creative(X0) | kind(X0) | old(X0) [cnf transformation 46]
108. curious(X0) | calm(X0) [cnf transformation 53]
110. curious(X0) | creative(X0) [cnf transformation 53]
116. rich(X0) | ~kind(X0) | generous(X0) [cnf transformation 57]
117. ~generous(X0) | ~kind(X0) | rich(X0) [cnf transformation 57]
122. ~calm(X0) | patient(X0) [cnf transformation 58]
146. ~curious(mary) [cnf transformation 23]
230. 18 <=> rich(mary) [avatar definition]
245. ~kind(X0) | rich(X0) [subsumption resolution 116,117]
333. calm(mary) [resolution 108,146]
336. ~old(mary) [resolution 333,93]
338. creative(mary) [resolution 110,146]
341. patient(mary) [resolution 122,333]
344. ~creative(mary) | ~rich(mary) [resolution 84,341]
393. kind(mary) | old(mary) [resolution 98,338]
396. kind(mary) [subsumption resolution 393,336]
437. rich(mary) [resolution 396,245]
440. 18 [avatar split clause 437,230]
441. ~rich(mary) [subsumption resolution 344,338]
442. ~18 [avatar split clause 441,230]
443. $false [avatar sat refutation 440,442]
% SZS output end Proof for 8705601286710062509940107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not curious and not kind then someone is both not strong and not generous.
If someone is not kind or old then someone is generous.
Everyone who is not curious or tall is happy or not humble.
Everyone who is both not old and humble is both not humble and generous and vice versa.
Everyone who is strong is not old.
Everyone who is not generous is creative or not quiet and vice versa.
Everyone who is both not happy and not generous is not wise or not creative.
If someone is both not wise and wise then susan is happy or not kind.
If someone is both curious and calm then lucy is strong or rich.
If someone is rich then someone is both not wise and not brave and vice versa.
Everyone who is not rich or happy is both not kind and not strong and vice versa.
If someone is not patient or not happy then mary is not quiet or kind.
Everyone who is generous or not funny is both kind and brave.
Everyone who is funny or not generous is both not old and not brave and vice versa.
If fred is old then someone is not humble or not creative and vice versa.
Someone is creative or kind.
Alice is either not funny or not calm.
Paul is either patient or kind.
Someone is not brave or creative.
Someone is either rich or not strong. | Fred is kind. | entailment | (((~curious(alice)&~kind(alice)))=>(?[X]:((~strong(X)&~generous(X)))))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(generous(X))))&
(![X]:((~curious(X)|tall(X))=>(happy(X)|~humble(X))))&
(![X]:((~old(X)&humble(X))<=>(~humble(X)&generous(X))))&
(![X]:(strong(X)=>~old(X)))&
(![X]:(~generous(X)<=>(creative(X)|~quiet(X))))&
(![X]:((~happy(X)&~generous(X))=>(~wise(X)|~creative(X))))&
((?[X]:((~wise(X)&wise(X))))=>((happy(susan)|~kind(susan))))&
((?[X]:((curious(X)&calm(X))))=>((strong(lucy)|rich(lucy))))&
((?[X]:(rich(X)))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~rich(X)|happy(X))<=>(~kind(X)&~strong(X))))&
((?[X]:((~patient(X)|~happy(X))))=>((~quiet(mary)|kind(mary))))&
(![X]:((generous(X)|~funny(X))=>(kind(X)&brave(X))))&
(![X]:((funny(X)|~generous(X))<=>(~old(X)&~brave(X))))&
((old(fred))<=>(?[X]:((~humble(X)|~creative(X)))))&
(?[X]:((creative(X)|kind(X))))&
((~funny(alice)<~>~calm(alice)))&
((patient(paul)<~>kind(paul)))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((rich(X)<~>~strong(X)))) | kind(fred) | [
"p1",
"p5",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 892531507289266407920591
% SZS output start Proof for 892531507289266407920591
2. ? [X0] : (old(X0) | ~kind(X0)) => ? [X0] : generous(X0) [input p1]
6. ! [X0] : (~generous(X0) <=> (~quiet(X0) | creative(X0))) [input p5]
13. ! [X0] : ((~funny(X0) | generous(X0)) => (brave(X0) & kind(X0))) [input p12]
14. ! [X0] : ((~generous(X0) | funny(X0)) <=> (~brave(X0) & ~old(X0))) [input p13]
15. old(fred) <=> ? [X0] : (~creative(X0) | ~humble(X0)) [input p14]
21. ~kind(fred) [input hypothesis]
22. ? [X0] : (old(X0) | ~kind(X0)) => ? [X1] : generous(X1) [rectify 2]
27. ? [X1] : generous(X1) | ! [X0] : (~old(X0) & kind(X0)) [ennf transformation 22]
39. ! [X0] : ((brave(X0) & kind(X0)) | (funny(X0) & ~generous(X0))) [ennf transformation 13]
42. ? [X0] : generous(X0) | ! [X1] : (~old(X1) & kind(X1)) [rectify 27]
43. ? [X0] : generous(X0) => generous(sK1) [choice axiom]
44. generous(sK1) | ! [X1] : (~old(X1) & kind(X1)) [skolemisation 42,43]
47. ! [X0] : ((~generous(X0) | (quiet(X0) & ~creative(X0))) & ((~quiet(X0) | creative(X0)) | generous(X0))) [nnf transformation 6]
48. ! [X0] : ((~generous(X0) | (quiet(X0) & ~creative(X0))) & (~quiet(X0) | creative(X0) | generous(X0))) [flattening 47]
56. ! [X0] : (((~generous(X0) | funny(X0)) | (brave(X0) | old(X0))) & ((~brave(X0) & ~old(X0)) | (generous(X0) & ~funny(X0)))) [nnf transformation 14]
57. ! [X0] : ((~generous(X0) | funny(X0) | brave(X0) | old(X0)) & ((~brave(X0) & ~old(X0)) | (generous(X0) & ~funny(X0)))) [flattening 56]
58. (old(fred) | ! [X0] : (creative(X0) & humble(X0))) & (? [X0] : (~creative(X0) | ~humble(X0)) | ~old(fred)) [nnf transformation 15]
59. (old(fred) | ! [X0] : (creative(X0) & humble(X0))) & (? [X1] : (~creative(X1) | ~humble(X1)) | ~old(fred)) [rectify 58]
60. ? [X1] : (~creative(X1) | ~humble(X1)) => (~creative(sK4) | ~humble(sK4)) [choice axiom]
61. (old(fred) | ! [X0] : (creative(X0) & humble(X0))) & ((~creative(sK4) | ~humble(sK4)) | ~old(fred)) [skolemisation 59,60]
73. generous(sK1) | kind(X1) [cnf transformation 44]
82. ~creative(X0) | ~generous(X0) [cnf transformation 48]
97. ~generous(X0) | kind(X0) [cnf transformation 39]
102. ~old(X0) | generous(X0) [cnf transformation 57]
108. old(fred) | creative(X0) [cnf transformation 61]
117. ~kind(fred) [cnf transformation 21]
142. 6 <=> generous(sK1) [avatar definition]
144. generous(sK1) <- (6) [avatar component clause 142]
147. 7 <=> ! [X1] : kind(X1) [avatar definition]
148. kind(X1) <- (7) [avatar component clause 147]
149. 7 | 6 [avatar split clause 73,142,147]
201. 20 <=> ! [X0] : creative(X0) [avatar definition]
202. creative(X0) <- (20) [avatar component clause 201]
204. 21 <=> old(fred) [avatar definition]
206. old(fred) <- (21) [avatar component clause 204]
207. 20 | 21 [avatar split clause 108,204,201]
277. generous(fred) <- (21) [resolution 102,206]
279. kind(fred) <- (21) [resolution 277,97]
281. $false <- (21) [subsumption resolution 279,117]
282. ~21 [avatar contradiction clause 281]
284. ~generous(X0) <- (20) [resolution 202,82]
286. $false <- (6, 20) [resolution 284,144]
287. ~6 | ~20 [avatar contradiction clause 286]
288. $false <- (7) [resolution 148,117]
292. ~7 [avatar contradiction clause 288]
293. $false [avatar sat refutation 149,207,282,287,292]
% SZS output end Proof for 892531507289266407920591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is brave.
Everyone who is both not wise and humble is generous.
Everyone who is both curious and not wise is both creative and not generous.
Everyone who is either patient or quiet is either not creative or not brave and vice versa.
If someone is either not kind or not quiet then mary is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
If lucy is both not patient and happy then paul is not generous or not calm.
If someone is creative then paul is both brave and rich and vice versa.
If someone is not humble then paul is both quiet and wise.
Someone is not brave.
Someone is not kind or not funny.
Someone is not humble or generous.
Someone is old.
Paul is not calm.
Lucy is funny.
Someone is not rich or not old.
Someone is either humble or not calm. | Paul is tall. | entailment | (![X]:(generous(X)=>brave(X)))&
(![X]:((~wise(X)&humble(X))=>generous(X)))&
(![X]:((curious(X)&~wise(X))=>(creative(X)&~generous(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~creative(X)<~>~brave(X))))&
((?[X]:((~kind(X)<~>~quiet(X))))=>(~calm(mary)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
(((~patient(lucy)&happy(lucy)))=>((~generous(paul)|~calm(paul))))&
((?[X]:(creative(X)))<=>((brave(paul)&rich(paul))))&
((?[X]:(~humble(X)))=>((quiet(paul)&wise(paul))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(old(X)))&
(~calm(paul))&
(funny(lucy))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((humble(X)<~>~calm(X)))) | tall(paul) | [
"p0",
"p1",
"p5",
"p7",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2106585288870231440713400
% SZS output start Proof for 2106585288870231440713400
1. ! [X0] : (generous(X0) => brave(X0)) [input p0]
2. ! [X0] : ((humble(X0) & ~wise(X0)) => generous(X0)) [input p1]
6. ! [X0] : (tall(X0) <=> (wise(X0) | rich(X0))) [input p5]
8. ! [X0] : ((~happy(X0) & calm(X0)) <=> (strong(X0) | brave(X0))) [input p7]
16. ? [X0] : ~humble(X0) => (wise(paul) & quiet(paul)) [input p15]
21. ~calm(paul) [input p20]
25. ~tall(paul) [input hypothesis]
28. ! [X0] : (brave(X0) | ~generous(X0)) [ennf transformation 1]
29. ! [X0] : (generous(X0) | (~humble(X0) | wise(X0))) [ennf transformation 2]
30. ! [X0] : (generous(X0) | ~humble(X0) | wise(X0)) [flattening 29]
40. (wise(paul) & quiet(paul)) | ! [X0] : humble(X0) [ennf transformation 16]
43. ! [X0] : ((tall(X0) | (~wise(X0) & ~rich(X0))) & ((wise(X0) | rich(X0)) | ~tall(X0))) [nnf transformation 6]
44. ! [X0] : ((tall(X0) | (~wise(X0) & ~rich(X0))) & (wise(X0) | rich(X0) | ~tall(X0))) [flattening 43]
45. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | (happy(X0) | ~calm(X0)))) [nnf transformation 8]
46. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | happy(X0) | ~calm(X0))) [flattening 45]
76. ~generous(X0) | brave(X0) [cnf transformation 28]
77. ~humble(X0) | generous(X0) | wise(X0) [cnf transformation 30]
90. ~wise(X0) | tall(X0) [cnf transformation 44]
94. ~brave(X0) | calm(X0) [cnf transformation 46]
118. wise(paul) | humble(X0) [cnf transformation 40]
123. ~calm(paul) [cnf transformation 21]
128. ~tall(paul) [cnf transformation 25]
233. 24 <=> generous(paul) [avatar definition]
234. generous(paul) <- (24) [avatar component clause 233]
237. 25 <=> calm(paul) [avatar definition]
239. ~calm(paul) <- (~25) [avatar component clause 237]
242. 26 <=> brave(paul) [avatar definition]
243. brave(paul) <- (26) [avatar component clause 242]
244. ~brave(paul) <- (~26) [avatar component clause 242]
260. 30 <=> ! [X0] : humble(X0) [avatar definition]
261. humble(X0) <- (30) [avatar component clause 260]
263. 31 <=> wise(paul) [avatar definition]
264. ~wise(paul) <- (~31) [avatar component clause 263]
265. wise(paul) <- (31) [avatar component clause 263]
266. 30 | 31 [avatar split clause 118,263,260]
290. ~25 [avatar split clause 123,237]
323. tall(paul) <- (31) [resolution 90,265]
324. $false <- (31) [subsumption resolution 323,128]
325. ~31 [avatar contradiction clause 324]
329. calm(paul) <- (26) [resolution 94,243]
330. $false <- (~25, 26) [subsumption resolution 329,239]
331. 25 | ~26 [avatar contradiction clause 330]
338. wise(X0) | generous(X0) <- (30) [resolution 77,261]
355. generous(paul) <- (30, ~31) [resolution 338,264]
356. 24 | ~30 | 31 [avatar split clause 355,263,260,233]
357. brave(paul) <- (24) [resolution 234,76]
358. $false <- (24, ~26) [subsumption resolution 357,244]
359. ~24 | 26 [avatar contradiction clause 358]
360. $false [avatar sat refutation 266,290,325,331,356,359]
% SZS output end Proof for 2106585288870231440713400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is rich then someone is kind or not patient.
Everyone who is both not brave and patient is happy or funny and vice versa.
Everyone who is calm is tall.
If fred is either kind or not strong then someone is either not kind or curious and vice versa.
If someone is both quiet and generous then someone is either rich or quiet.
If someone is both calm and strong then mary is both not humble and wise and vice versa.
Everyone who is either not funny or strong is not creative or funny.
If someone is creative or kind then someone is either rich or not curious.
If susan is either not tall or not wise then someone is not patient and vice versa.
If someone is either humble or not old then lucy is both old and funny and vice versa.
Everyone who is not brave or not curious is both tall and humble and vice versa.
If someone is not wise or not brave then someone is curious or happy and vice versa.
Everyone who is not happy is both quiet and curious and vice versa.
Everyone who is both curious and strong is both creative and not strong.
If someone is patient or calm then someone is funny or not rich.
If alice is brave or not generous then fred is curious and vice versa.
Susan is not curious or curious.
Someone is not brave.
John is tall or not brave.
Fred is both generous and not tall.
Paul is tall.
Susan is either quiet or not happy.
Someone is not happy or kind.
Lucy is both wise and happy. | Fred is strong. | contradiction | ((rich(mary))=>(?[X]:((kind(X)|~patient(X)))))&
(![X]:((~brave(X)&patient(X))<=>(happy(X)|funny(X))))&
(![X]:(calm(X)=>tall(X)))&
(((kind(fred)<~>~strong(fred)))<=>(?[X]:((~kind(X)<~>curious(X)))))&
((?[X]:((quiet(X)&generous(X))))=>(?[X]:((rich(X)<~>quiet(X)))))&
((?[X]:((calm(X)&strong(X))))<=>((~humble(mary)&wise(mary))))&
(![X]:((~funny(X)<~>strong(X))=>(~creative(X)|funny(X))))&
((?[X]:((creative(X)|kind(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(((~tall(susan)<~>~wise(susan)))<=>(?[X]:(~patient(X))))&
((?[X]:((humble(X)<~>~old(X))))<=>((old(lucy)&funny(lucy))))&
(![X]:((~brave(X)|~curious(X))<=>(tall(X)&humble(X))))&
((?[X]:((~wise(X)|~brave(X))))<=>(?[X]:((curious(X)|happy(X)))))&
(![X]:(~happy(X)<=>(quiet(X)&curious(X))))&
(![X]:((curious(X)&strong(X))=>(creative(X)&~strong(X))))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:((funny(X)|~rich(X)))))&
(((brave(alice)|~generous(alice)))<=>(curious(fred)))&
((~curious(susan)|curious(susan)))&
(?[X]:(~brave(X)))&
((tall(john)|~brave(john)))&
((generous(fred)&~tall(fred)))&
(tall(paul))&
((quiet(susan)<~>~happy(susan)))&
(?[X]:((~happy(X)|kind(X))))&
((wise(lucy)&happy(lucy))) | strong(fred) | [
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5160998424760981061579560
% SZS output start Proof for 5160998424760981061579560
11. ! [X0] : ((~curious(X0) | ~brave(X0)) <=> (humble(X0) & tall(X0))) [input p10]
14. ! [X0] : ((strong(X0) & curious(X0)) => (~strong(X0) & creative(X0))) [input p13]
20. ~tall(fred) & generous(fred) [input p19]
25. strong(fred) [input hypothesis]
36. ! [X0] : ((~strong(X0) & creative(X0)) | (~strong(X0) | ~curious(X0))) [ennf transformation 14]
37. ! [X0] : ((~strong(X0) & creative(X0)) | ~strong(X0) | ~curious(X0)) [flattening 36]
70. ! [X0] : (((~curious(X0) | ~brave(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (curious(X0) & brave(X0)))) [nnf transformation 11]
71. ! [X0] : ((~curious(X0) | ~brave(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | (curious(X0) & brave(X0)))) [flattening 70]
127. curious(X0) | tall(X0) [cnf transformation 71]
139. ~strong(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 37]
149. ~tall(fred) [cnf transformation 20]
156. strong(fred) [cnf transformation 25]
157. ~curious(X0) | ~strong(X0) [duplicate literal removal 139]
180. 6 <=> strong(fred) [avatar definition]
182. strong(fred) <- (6) [avatar component clause 180]
352. 44 <=> curious(fred) [avatar definition]
353. curious(fred) <- (44) [avatar component clause 352]
354. ~curious(fred) <- (~44) [avatar component clause 352]
378. 6 [avatar split clause 156,180]
401. ~strong(fred) <- (44) [resolution 157,353]
404. $false <- (6, 44) [subsumption resolution 401,182]
405. ~6 | ~44 [avatar contradiction clause 404]
407. tall(fred) <- (~44) [resolution 354,127]
408. $false <- (~44) [subsumption resolution 407,149]
409. 44 [avatar contradiction clause 408]
410. $false [avatar sat refutation 378,405,409]
% SZS output end Proof for 5160998424760981061579560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both quiet and not strong then lucy is both calm and quiet and vice versa.
If someone is not funny then paul is humble and vice versa.
Everyone who is not quiet or not strong is not old or not brave.
Everyone who is either not rich or not generous is not calm or not curious.
If paul is both not generous and not strong then lucy is either patient or not strong.
Everyone who is not generous is not funny or not strong and vice versa.
If someone is not strong or not happy then someone is both patient and curious.
If john is not calm or rich then lucy is both brave and not kind.
Everyone who is not kind or generous is generous or patient and vice versa.
Everyone who is not patient is both not strong and not patient.
Everyone who is both tall and not wise is brave or calm and vice versa.
If lucy is kind then mary is tall.
If alice is not curious or not tall then susan is not quiet and vice versa.
Everyone who is either kind or patient is both not rich and kind and vice versa.
Everyone who is not funny is either strong or not wise and vice versa.
If someone is either curious or not patient then someone is brave and vice versa.
Someone is both generous and not humble.
Fred is patient.
Paul is strong or not happy.
Someone is either not strong or not humble.
John is not patient.
Fred is not patient or humble.
Mary is both kind and not funny.
Alice is patient. | Paul is not patient. | neutral | (((quiet(mary)&~strong(mary)))<=>((calm(lucy)&quiet(lucy))))&
((?[X]:(~funny(X)))<=>(humble(paul)))&
(![X]:((~quiet(X)|~strong(X))=>(~old(X)|~brave(X))))&
(![X]:((~rich(X)<~>~generous(X))=>(~calm(X)|~curious(X))))&
(((~generous(paul)&~strong(paul)))=>((patient(lucy)<~>~strong(lucy))))&
(![X]:(~generous(X)<=>(~funny(X)|~strong(X))))&
((?[X]:((~strong(X)|~happy(X))))=>(?[X]:((patient(X)&curious(X)))))&
(((~calm(john)|rich(john)))=>((brave(lucy)&~kind(lucy))))&
(![X]:((~kind(X)|generous(X))<=>(generous(X)|patient(X))))&
(![X]:(~patient(X)=>(~strong(X)&~patient(X))))&
(![X]:((tall(X)&~wise(X))<=>(brave(X)|calm(X))))&
((kind(lucy))=>(tall(mary)))&
(((~curious(alice)|~tall(alice)))<=>(~quiet(susan)))&
(![X]:((kind(X)<~>patient(X))<=>(~rich(X)&kind(X))))&
(![X]:(~funny(X)<=>(strong(X)<~>~wise(X))))&
((?[X]:((curious(X)<~>~patient(X))))<=>(?[X]:(brave(X))))&
(?[X]:((generous(X)&~humble(X))))&
(patient(fred))&
((strong(paul)|~happy(paul)))&
(?[X]:((~strong(X)<~>~humble(X))))&
(~patient(john))&
((~patient(fred)|humble(fred)))&
((kind(mary)&~funny(mary)))&
(patient(alice)) | ~patient(paul) | [] | null | 0 |
If someone is quiet then paul is not humble. Everyone who is both funny and not brave is both not old and creative and vice versa. Everyone who is both happy and tall is patient. If someone is both curious and generous then lucy is generous. If someone is old or not curious then john is old or not generous. Everyone who is rich is happy or funny and vice versa. If alice is both not curious and not brave then someone is either not patient or not rich. If paul is curious or funny then someone is wise or not generous and vice versa. If someone is not happy then someone is both calm and not brave. Everyone who is not humble is both funny and not brave. Everyone who is both not calm and happy is both patient and funny. Everyone who is either not curious or generous is not wise and vice versa. If someone is both generous and not creative then alice is both not humble and calm and vice versa. Everyone who is either patient or not rich is either not tall or not wise. If alice is not old then someone is humble or not creative and vice versa. Everyone who is quiet is not old and vice versa. John is quiet or curious. Someone is calm or not brave. Someone is either not curious or not funny. Someone is quiet. Mary is either brave or rich. Mary is not old. Someone is either humble or not creative. Someone is not calm. | Paul is not rich. | contradiction | ((?[X]:(quiet(X)))=>(~humble(paul)))&
(![X]:((funny(X)&~brave(X))<=>(~old(X)&creative(X))))&
(![X]:((happy(X)&tall(X))=>patient(X)))&
((?[X]:((curious(X)&generous(X))))=>(generous(lucy)))&
((?[X]:((old(X)|~curious(X))))=>((old(john)|~generous(john))))&
(![X]:(rich(X)<=>(happy(X)|funny(X))))&
(((~curious(alice)&~brave(alice)))=>(?[X]:((~patient(X)<~>~rich(X)))))&
(((curious(paul)|funny(paul)))<=>(?[X]:((wise(X)|~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:(~humble(X)=>(funny(X)&~brave(X))))&
(![X]:((~calm(X)&happy(X))=>(patient(X)&funny(X))))&
(![X]:((~curious(X)<~>generous(X))<=>~wise(X)))&
((?[X]:((generous(X)&~creative(X))))<=>((~humble(alice)&calm(alice))))&
(![X]:((patient(X)<~>~rich(X))=>(~tall(X)<~>~wise(X))))&
((~old(alice))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:(quiet(X)<=>~old(X)))&
((quiet(john)|curious(john)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
(?[X]:(quiet(X)))&
((brave(mary)<~>rich(mary)))&
(~old(mary))&
(?[X]:((humble(X)<~>~creative(X))))&
(?[X]:(~calm(X))) | ~rich(paul) | [
"p0",
"p5",
"p9",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2429753525737411228771013
% SZS output start Proof for 2429753525737411228771013
1. ? [X0] : quiet(X0) => ~humble(paul) [input p0]
6. ! [X0] : (rich(X0) <=> (funny(X0) | happy(X0))) [input p5]
10. ! [X0] : (~humble(X0) => (~brave(X0) & funny(X0))) [input p9]
16. ! [X0] : (quiet(X0) <=> ~old(X0)) [input p15]
22. ~old(mary) [input p21]
25. ~rich(paul) [input hypothesis]
27. ~humble(paul) | ! [X0] : ~quiet(X0) [ennf transformation 1]
36. ! [X0] : ((~brave(X0) & funny(X0)) | humble(X0)) [ennf transformation 10]
42. ! [X0] : ((rich(X0) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | ~rich(X0))) [nnf transformation 6]
43. ! [X0] : ((rich(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | ~rich(X0))) [flattening 42]
66. ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))) [nnf transformation 16]
80. ~humble(paul) | ~quiet(X0) [cnf transformation 27]
91. ~funny(X0) | rich(X0) [cnf transformation 43]
100. funny(X0) | humble(X0) [cnf transformation 36]
120. old(X0) | quiet(X0) [cnf transformation 66]
128. ~old(mary) [cnf transformation 22]
132. ~rich(paul) [cnf transformation 25]
134. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
135. ~quiet(X0) <- (1) [avatar component clause 134]
137. 2 <=> humble(paul) [avatar definition]
140. 1 | ~2 [avatar split clause 80,137,134]
320. rich(X0) | humble(X0) [resolution 100,91]
322. quiet(mary) [resolution 120,128]
329. humble(paul) [resolution 320,132]
333. 2 [avatar split clause 329,137]
336. $false <- (1) [resolution 135,322]
339. ~1 [avatar contradiction clause 336]
342. $false [avatar sat refutation 140,333,339]
% SZS output end Proof for 2429753525737411228771013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not humble or creative. If paul is not calm or not old then someone is not strong or patient. Everyone who is humble is both not brave and not happy. Everyone who is not creative or tall is either not patient or old and vice versa. Everyone who is creative is not rich and vice versa. If someone is both not patient and rich then lucy is either happy or funny. Everyone who is strong or not tall is happy and vice versa. If alice is not brave or curious then someone is patient and vice versa. Everyone who is either not calm or kind is either not curious or not patient. Everyone who is either patient or not old is both patient and not patient. Everyone who is not funny is both happy and not calm. If someone is either not kind or kind then someone is both strong and not old and vice versa. If someone is either not patient or brave then fred is either kind or not humble. If someone is either not wise or not humble then john is not humble and vice versa. If paul is either not rich or happy then someone is either kind or not happy. If lucy is not calm then susan is old. Someone is either creative or old. John is both happy and quiet. Someone is both not curious and wise. Alice is either humble or happy. Fred is curious. Lucy is happy. Someone is either humble or not generous. | John is humble. | contradiction | (![X]:(strong(X)=>(~humble(X)|creative(X))))&
(((~calm(paul)|~old(paul)))=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:(humble(X)=>(~brave(X)&~happy(X))))&
(![X]:((~creative(X)|tall(X))<=>(~patient(X)<~>old(X))))&
(![X]:(creative(X)<=>~rich(X)))&
((?[X]:((~patient(X)&rich(X))))=>((happy(lucy)<~>funny(lucy))))&
(![X]:((strong(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((patient(X)<~>~old(X))=>(patient(X)&~patient(X))))&
(![X]:(~funny(X)=>(happy(X)&~calm(X))))&
((?[X]:((~kind(X)<~>kind(X))))<=>(?[X]:((strong(X)&~old(X)))))&
((?[X]:((~patient(X)<~>brave(X))))=>((kind(fred)<~>~humble(fred))))&
((?[X]:((~wise(X)<~>~humble(X))))<=>(~humble(john)))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((kind(X)<~>~happy(X)))))&
((~calm(lucy))=>(old(susan)))&
(?[X]:((creative(X)<~>old(X))))&
((happy(john)&quiet(john)))&
(?[X]:((~curious(X)&wise(X))))&
((humble(alice)<~>happy(alice)))&
(curious(fred))&
(happy(lucy))&
(?[X]:((humble(X)<~>~generous(X)))) | humble(john) | [
"p2",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 246482005940641061121827
% SZS output start Proof for 246482005940641061121827
3. ! [X0] : (humble(X0) => (~happy(X0) & ~brave(X0))) [input p2]
18. quiet(john) & happy(john) [input p17]
24. humble(john) [input hypothesis]
26. happy(john) [pure predicate removal 18]
30. ! [X0] : ((~happy(X0) & ~brave(X0)) | ~humble(X0)) [ennf transformation 3]
79. ~happy(X0) | ~humble(X0) [cnf transformation 30]
127. happy(john) [cnf transformation 26]
136. humble(john) [cnf transformation 24]
229. 20 <=> humble(john) [avatar definition]
231. humble(john) <- (20) [avatar component clause 229]
309. 20 [avatar split clause 136,229]
321. ~humble(john) [resolution 79,127]
324. $false <- (20) [subsumption resolution 321,231]
325. ~20 [avatar contradiction clause 324]
326. $false [avatar sat refutation 309,325]
% SZS output end Proof for 246482005940641061121827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
If someone is not calm or not happy then susan is either not rich or creative and vice versa.
Everyone who is either creative or not curious is both not rich and happy and vice versa.
Everyone who is kind is either generous or not quiet.
Everyone who is patient or wise is tall or not rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is generous is either calm or kind and vice versa.
Everyone who is calm or not kind is both not generous and generous.
Everyone who is not brave is either not calm or brave and vice versa.
If someone is either not rich or generous then someone is either quiet or brave.
Everyone who is old is both not happy and tall.
Someone is not happy.
Someone is not humble.
Someone is either not creative or not curious.
Someone is either humble or not old.
Someone is either not humble or happy.
Someone is not strong. | Lucy is old. | neutral | (((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
((?[X]:((~calm(X)|~happy(X))))<=>((~rich(susan)<~>creative(susan))))&
(![X]:((creative(X)<~>~curious(X))<=>(~rich(X)&happy(X))))&
(![X]:(kind(X)=>(generous(X)<~>~quiet(X))))&
(![X]:((patient(X)|wise(X))<=>(tall(X)|~rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(generous(X)<=>(calm(X)<~>kind(X))))&
(![X]:((calm(X)|~kind(X))=>(~generous(X)&generous(X))))&
(![X]:(~brave(X)<=>(~calm(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>generous(X))))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(old(X)=>(~happy(X)&tall(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
(?[X]:(~strong(X))) | old(lucy) | [] | null | 0 |
Everyone who is both curious and not tall is both not calm and not quiet and vice versa.
Everyone who is generous is not old and vice versa.
Everyone who is both rich and kind is either wise or funny and vice versa.
If mary is old or not wise then someone is either not tall or old and vice versa.
If someone is wise then someone is not strong and vice versa.
Everyone who is patient or calm is either kind or not funny and vice versa.
Everyone who is either not tall or calm is quiet or not quiet and vice versa.
If mary is both happy and not funny then fred is creative and vice versa.
Everyone who is either not brave or humble is not tall or not strong and vice versa.
Everyone who is calm or generous is wise or not brave and vice versa.
Everyone who is either wise or not brave is either not generous or patient.
Everyone who is kind or tall is not brave and vice versa.
Everyone who is strong or old is either patient or not tall.
If someone is old then lucy is not happy and vice versa.
If lucy is either not rich or not funny then mary is either not humble or not wise and vice versa.
If mary is strong then someone is curious or funny.
Someone is either not humble or not strong.
Someone is generous or not creative.
Someone is both old and not generous.
Someone is both wise and not rich.
Mary is kind.
Susan is not kind or not happy.
Someone is curious.
Someone is strong. | Susan is creative. | neutral | (![X]:((curious(X)&~tall(X))<=>(~calm(X)&~quiet(X))))&
(![X]:(generous(X)<=>~old(X)))&
(![X]:((rich(X)&kind(X))<=>(wise(X)<~>funny(X))))&
(((old(mary)|~wise(mary)))<=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:(wise(X)))<=>(?[X]:(~strong(X))))&
(![X]:((patient(X)|calm(X))<=>(kind(X)<~>~funny(X))))&
(![X]:((~tall(X)<~>calm(X))<=>(quiet(X)|~quiet(X))))&
(((happy(mary)&~funny(mary)))<=>(creative(fred)))&
(![X]:((~brave(X)<~>humble(X))<=>(~tall(X)|~strong(X))))&
(![X]:((calm(X)|generous(X))<=>(wise(X)|~brave(X))))&
(![X]:((wise(X)<~>~brave(X))=>(~generous(X)<~>patient(X))))&
(![X]:((kind(X)|tall(X))<=>~brave(X)))&
(![X]:((strong(X)|old(X))=>(patient(X)<~>~tall(X))))&
((?[X]:(old(X)))<=>(~happy(lucy)))&
(((~rich(lucy)<~>~funny(lucy)))<=>((~humble(mary)<~>~wise(mary))))&
((strong(mary))=>(?[X]:((curious(X)|funny(X)))))&
(?[X]:((~humble(X)<~>~strong(X))))&
(?[X]:((generous(X)|~creative(X))))&
(?[X]:((old(X)&~generous(X))))&
(?[X]:((wise(X)&~rich(X))))&
(kind(mary))&
((~kind(susan)|~happy(susan)))&
(?[X]:(curious(X)))&
(?[X]:(strong(X))) | creative(susan) | [] | null | 0 |
Everyone who is not creative is not wise or strong and vice versa.
If susan is not wise then someone is wise and vice versa.
Everyone who is not brave is either not generous or creative and vice versa.
If someone is not patient then someone is calm or curious.
Everyone who is both not wise and not funny is not generous or not curious.
Everyone who is either patient or old is both not curious and not humble and vice versa.
If susan is both not curious and curious then susan is quiet or not old.
If paul is calm then john is old and vice versa.
If someone is both tall and not old then alice is both not quiet and quiet and vice versa.
If someone is not wise then paul is either not old or rich and vice versa.
Everyone who is either humble or not rich is both not rich and not wise and vice versa.
Everyone who is strong is either not old or kind.
Everyone who is quiet is not creative.
Everyone who is creative or generous is humble or calm and vice versa.
If alice is both kind and not brave then someone is both not strong and not kind.
Everyone who is either not strong or not calm is not old or strong and vice versa.
Alice is not happy or not old.
Lucy is not patient.
Lucy is both curious and happy.
Someone is either kind or strong.
Alice is either not patient or funny.
Someone is both humble and not funny.
Alice is not happy. | Lucy is not tall. | entailment | (![X]:(~creative(X)<=>(~wise(X)|strong(X))))&
((~wise(susan))<=>(?[X]:(wise(X))))&
(![X]:(~brave(X)<=>(~generous(X)<~>creative(X))))&
((?[X]:(~patient(X)))=>(?[X]:((calm(X)|curious(X)))))&
(![X]:((~wise(X)&~funny(X))=>(~generous(X)|~curious(X))))&
(![X]:((patient(X)<~>old(X))<=>(~curious(X)&~humble(X))))&
(((~curious(susan)&curious(susan)))=>((quiet(susan)|~old(susan))))&
((calm(paul))<=>(old(john)))&
((?[X]:((tall(X)&~old(X))))<=>((~quiet(alice)&quiet(alice))))&
((?[X]:(~wise(X)))<=>((~old(paul)<~>rich(paul))))&
(![X]:((humble(X)<~>~rich(X))<=>(~rich(X)&~wise(X))))&
(![X]:(strong(X)=>(~old(X)<~>kind(X))))&
(![X]:(quiet(X)=>~creative(X)))&
(![X]:((creative(X)|generous(X))<=>(humble(X)|calm(X))))&
(((kind(alice)&~brave(alice)))=>(?[X]:((~strong(X)&~kind(X)))))&
(![X]:((~strong(X)<~>~calm(X))<=>(~old(X)|strong(X))))&
((~happy(alice)|~old(alice)))&
(~patient(lucy))&
((curious(lucy)&happy(lucy)))&
(?[X]:((kind(X)<~>strong(X))))&
((~patient(alice)<~>funny(alice)))&
(?[X]:((humble(X)&~funny(X))))&
(~happy(alice)) | ~tall(lucy) | [
"p5",
"p8",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4301130083015723716839384
% SZS output start Proof for 4301130083015723716839384
6. ! [X0] : ((patient(X0) <~> old(X0)) <=> (~humble(X0) & ~curious(X0))) [input p5]
9. ? [X0] : (~old(X0) & tall(X0)) <=> (quiet(alice) & ~quiet(alice)) [input p8]
18. ~patient(lucy) [input p17]
19. happy(lucy) & curious(lucy) [input p18]
24. tall(lucy) [input hypothesis]
47. ! [X0] : ((((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (humble(X0) | curious(X0))) & ((~humble(X0) & ~curious(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0))))) [nnf transformation 6]
48. ! [X0] : ((((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | humble(X0) | curious(X0)) & ((~humble(X0) & ~curious(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0))))) [flattening 47]
50. (? [X0] : (~old(X0) & tall(X0)) | (~quiet(alice) | quiet(alice))) & ((quiet(alice) & ~quiet(alice)) | ! [X0] : (old(X0) | ~tall(X0))) [nnf transformation 9]
51. (? [X0] : (~old(X0) & tall(X0)) | ~quiet(alice) | quiet(alice)) & ((quiet(alice) & ~quiet(alice)) | ! [X0] : (old(X0) | ~tall(X0))) [flattening 50]
52. (? [X0] : (~old(X0) & tall(X0)) | ~quiet(alice) | quiet(alice)) & ((quiet(alice) & ~quiet(alice)) | ! [X1] : (old(X1) | ~tall(X1))) [rectify 51]
53. ? [X0] : (~old(X0) & tall(X0)) => (~old(sK2) & tall(sK2)) [choice axiom]
54. ((~old(sK2) & tall(sK2)) | ~quiet(alice) | quiet(alice)) & ((quiet(alice) & ~quiet(alice)) | ! [X1] : (old(X1) | ~tall(X1))) [skolemisation 52,53]
84. ~old(X0) | patient(X0) | ~curious(X0) [cnf transformation 48]
92. ~quiet(alice) | old(X1) | ~tall(X1) [cnf transformation 54]
93. quiet(alice) | old(X1) | ~tall(X1) [cnf transformation 54]
122. ~patient(lucy) [cnf transformation 18]
123. curious(lucy) [cnf transformation 19]
132. tall(lucy) [cnf transformation 24]
173. 9 <=> ! [X1] : (old(X1) | ~tall(X1)) [avatar definition]
174. ~tall(X1) | old(X1) <- (9) [avatar component clause 173]
176. 10 <=> quiet(alice) [avatar definition]
179. 9 | 10 [avatar split clause 93,176,173]
180. 9 | ~10 [avatar split clause 92,176,173]
252. old(lucy) <- (9) [resolution 174,132]
266. patient(lucy) | ~curious(lucy) <- (9) [resolution 84,252]
267. ~curious(lucy) <- (9) [subsumption resolution 266,122]
268. $false <- (9) [subsumption resolution 267,123]
269. ~9 [avatar contradiction clause 268]
270. $false [avatar sat refutation 179,180,269]
% SZS output end Proof for 4301130083015723716839384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not quiet or wise then someone is either wise or old.
Everyone who is generous or calm is both rich and not wise.
If someone is not generous or not calm then someone is rich or happy and vice versa.
Everyone who is both quiet and brave is creative and vice versa.
If someone is both not humble and not creative then someone is generous or rich.
If someone is either not quiet or not patient then fred is brave and vice versa.
Everyone who is not quiet is either generous or not old and vice versa.
Everyone who is both not tall and generous is funny or quiet.
Everyone who is creative is not quiet.
If lucy is not strong or not funny then someone is not humble.
Everyone who is not humble or not wise is either not happy or not calm.
If paul is either not curious or wise then someone is either not kind or generous.
Everyone who is either not creative or not brave is generous and vice versa.
If john is both not quiet and not generous then someone is either tall or rich and vice versa.
Everyone who is either calm or wise is old or strong and vice versa.
Everyone who is both funny and brave is not tall.
Susan is either not funny or wise.
Mary is both quiet and happy.
Alice is old.
Someone is not old or not creative.
Susan is not generous or not funny.
Someone is either not quiet or funny.
Someone is either strong or wise.
Someone is tall. | Mary is not old. | contradiction | (((~quiet(fred)<~>wise(fred)))=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((generous(X)|calm(X))=>(rich(X)&~wise(X))))&
((?[X]:((~generous(X)|~calm(X))))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((quiet(X)&brave(X))<=>creative(X)))&
((?[X]:((~humble(X)&~creative(X))))=>(?[X]:((generous(X)|rich(X)))))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>(brave(fred)))&
(![X]:(~quiet(X)<=>(generous(X)<~>~old(X))))&
(![X]:((~tall(X)&generous(X))=>(funny(X)|quiet(X))))&
(![X]:(creative(X)=>~quiet(X)))&
(((~strong(lucy)|~funny(lucy)))=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|~wise(X))=>(~happy(X)<~>~calm(X))))&
(((~curious(paul)<~>wise(paul)))=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:((~creative(X)<~>~brave(X))<=>generous(X)))&
(((~quiet(john)&~generous(john)))<=>(?[X]:((tall(X)<~>rich(X)))))&
(![X]:((calm(X)<~>wise(X))<=>(old(X)|strong(X))))&
(![X]:((funny(X)&brave(X))=>~tall(X)))&
((~funny(susan)<~>wise(susan)))&
((quiet(mary)&happy(mary)))&
(old(alice))&
(?[X]:((~old(X)|~creative(X))))&
((~generous(susan)|~funny(susan)))&
(?[X]:((~quiet(X)<~>funny(X))))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:(tall(X))) | ~old(mary) | [
"p3",
"p6",
"p8",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4820758626512301714281888
% SZS output start Proof for 4820758626512301714281888
4. ! [X0] : ((brave(X0) & quiet(X0)) <=> creative(X0)) [input p3]
7. ! [X0] : (~quiet(X0) <=> (generous(X0) <~> ~old(X0))) [input p6]
9. ! [X0] : (creative(X0) => ~quiet(X0)) [input p8]
13. ! [X0] : ((~creative(X0) <~> ~brave(X0)) <=> generous(X0)) [input p12]
18. happy(mary) & quiet(mary) [input p17]
25. ~old(mary) [input hypothesis]
33. ! [X0] : (~quiet(X0) | ~creative(X0)) [ennf transformation 9]
47. ! [X0] : (((brave(X0) & quiet(X0)) | ~creative(X0)) & (creative(X0) | (~brave(X0) | ~quiet(X0)))) [nnf transformation 4]
48. ! [X0] : (((brave(X0) & quiet(X0)) | ~creative(X0)) & (creative(X0) | ~brave(X0) | ~quiet(X0))) [flattening 47]
56. ! [X0] : ((~quiet(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | quiet(X0))) [nnf transformation 7]
63. ! [X0] : ((((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ~generous(X0)) & (generous(X0) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0))))) [nnf transformation 13]
94. ~brave(X0) | creative(X0) | ~quiet(X0) [cnf transformation 48]
95. ~creative(X0) | quiet(X0) [cnf transformation 48]
105. ~quiet(X0) | generous(X0) | old(X0) [cnf transformation 56]
107. ~quiet(X0) | ~creative(X0) [cnf transformation 33]
121. brave(X0) | creative(X0) | ~generous(X0) [cnf transformation 63]
137. quiet(mary) [cnf transformation 18]
147. ~old(mary) [cnf transformation 25]
231. ~creative(X0) [subsumption resolution 107,95]
267. ~generous(X0) | brave(X0) [subsumption resolution 121,231]
382. generous(mary) | old(mary) [resolution 105,137]
385. generous(mary) [subsumption resolution 382,147]
397. brave(mary) [resolution 385,267]
477. creative(mary) | ~quiet(mary) [resolution 397,94]
479. ~quiet(mary) [subsumption resolution 477,231]
480. $false [subsumption resolution 479,137]
% SZS output end Proof for 4820758626512301714281888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or not quiet then someone is both not rich and wise.
Everyone who is not quiet is rich.
If paul is both not quiet and happy then someone is both not happy and quiet and vice versa.
If john is both not wise and rich then fred is either strong or tall.
Everyone who is generous or wise is quiet.
If someone is tall or funny then susan is both not tall and not rich and vice versa.
If someone is both old and curious then mary is both creative and not patient.
If someone is tall or not humble then alice is not quiet and vice versa.
Everyone who is either strong or creative is both not rich and humble.
If someone is either not quiet or happy then susan is not brave.
Everyone who is either not patient or not quiet is either old or strong and vice versa.
Everyone who is not brave or not happy is either not brave or generous and vice versa.
Everyone who is not brave or kind is brave and vice versa.
If someone is not tall then someone is both creative and not calm.
Everyone who is either calm or not rich is happy and vice versa.
If someone is both not humble and not wise then alice is either not strong or curious and vice versa.
John is either brave or funny.
Susan is either not patient or not generous.
Someone is not brave or not funny.
Mary is happy or tall.
Someone is old or humble.
Mary is both happy and not humble.
Fred is either kind or old.
Someone is kind or not creative. | Alice is calm. | entailment | ((?[X]:((funny(X)<~>~quiet(X))))=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:(~quiet(X)=>rich(X)))&
(((~quiet(paul)&happy(paul)))<=>(?[X]:((~happy(X)&quiet(X)))))&
(((~wise(john)&rich(john)))=>((strong(fred)<~>tall(fred))))&
(![X]:((generous(X)|wise(X))=>quiet(X)))&
((?[X]:((tall(X)|funny(X))))<=>((~tall(susan)&~rich(susan))))&
((?[X]:((old(X)&curious(X))))=>((creative(mary)&~patient(mary))))&
((?[X]:((tall(X)|~humble(X))))<=>(~quiet(alice)))&
(![X]:((strong(X)<~>creative(X))=>(~rich(X)&humble(X))))&
((?[X]:((~quiet(X)<~>happy(X))))=>(~brave(susan)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(old(X)<~>strong(X))))&
(![X]:((~brave(X)|~happy(X))<=>(~brave(X)<~>generous(X))))&
(![X]:((~brave(X)|kind(X))<=>brave(X)))&
((?[X]:(~tall(X)))=>(?[X]:((creative(X)&~calm(X)))))&
(![X]:((calm(X)<~>~rich(X))<=>happy(X)))&
((?[X]:((~humble(X)&~wise(X))))<=>((~strong(alice)<~>curious(alice))))&
((brave(john)<~>funny(john)))&
((~patient(susan)<~>~generous(susan)))&
(?[X]:((~brave(X)|~funny(X))))&
((happy(mary)|tall(mary)))&
(?[X]:((old(X)|humble(X))))&
((happy(mary)&~humble(mary)))&
((kind(fred)<~>old(fred)))&
(?[X]:((kind(X)|~creative(X)))) | calm(alice) | [
"p1",
"p7",
"p9",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 193297276576667575637555
% SZS output start Proof for 193297276576667575637555
2. ! [X0] : (~quiet(X0) => rich(X0)) [input p1]
8. ? [X0] : (~humble(X0) | tall(X0)) <=> ~quiet(alice) [input p7]
10. ? [X0] : (~quiet(X0) <~> happy(X0)) => ~brave(susan) [input p9]
13. ! [X0] : ((kind(X0) | ~brave(X0)) <=> brave(X0)) [input p12]
15. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> happy(X0)) [input p14]
22. ~humble(mary) & happy(mary) [input p21]
25. ~calm(alice) [input hypothesis]
29. ! [X0] : (rich(X0) | quiet(X0)) [ennf transformation 2]
35. ~brave(susan) | ! [X0] : (~quiet(X0) <=> happy(X0)) [ennf transformation 10]
52. (? [X0] : (~humble(X0) | tall(X0)) | quiet(alice)) & (~quiet(alice) | ! [X0] : (humble(X0) & ~tall(X0))) [nnf transformation 8]
53. (? [X0] : (~humble(X0) | tall(X0)) | quiet(alice)) & (~quiet(alice) | ! [X1] : (humble(X1) & ~tall(X1))) [rectify 52]
54. ? [X0] : (~humble(X0) | tall(X0)) => (~humble(sK3) | tall(sK3)) [choice axiom]
55. ((~humble(sK3) | tall(sK3)) | quiet(alice)) & (~quiet(alice) | ! [X1] : (humble(X1) & ~tall(X1))) [skolemisation 53,54]
57. ~brave(susan) | ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))) [nnf transformation 35]
61. ! [X0] : (((kind(X0) | ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~kind(X0) & brave(X0)))) [nnf transformation 13]
62. ! [X0] : ((kind(X0) | ~brave(X0) | ~brave(X0)) & (brave(X0) | (~kind(X0) & brave(X0)))) [flattening 61]
66. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ~happy(X0)) & (happy(X0) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 15]
84. rich(X0) | quiet(X0) [cnf transformation 29]
101. ~quiet(alice) | humble(X1) [cnf transformation 55]
107. ~brave(susan) | happy(X0) | quiet(X0) [cnf transformation 57]
123. brave(X0) | brave(X0) [cnf transformation 62]
130. ~happy(X0) | calm(X0) | ~rich(X0) [cnf transformation 66]
146. ~humble(mary) [cnf transformation 22]
150. ~calm(alice) [cnf transformation 25]
151. brave(X0) [duplicate literal removal 123]
255. 23 <=> quiet(alice) [avatar definition]
256. ~quiet(alice) <- (~23) [avatar component clause 255]
268. 26 <=> ! [X1] : humble(X1) [avatar definition]
269. humble(X1) <- (26) [avatar component clause 268]
270. 26 | ~23 [avatar split clause 101,255,268]
276. 28 <=> brave(susan) [avatar definition]
278. ~brave(susan) <- (~28) [avatar component clause 276]
281. 29 <=> ! [X0] : (happy(X0) | quiet(X0)) [avatar definition]
282. happy(X0) | quiet(X0) <- (29) [avatar component clause 281]
283. 29 | ~28 [avatar split clause 107,276,281]
372. $false <- (~28) [subsumption resolution 278,151]
373. 28 [avatar contradiction clause 372]
433. 51 <=> rich(alice) [avatar definition]
434. ~rich(alice) <- (~51) [avatar component clause 433]
437. 52 <=> happy(alice) [avatar definition]
438. ~happy(alice) <- (~52) [avatar component clause 437]
439. happy(alice) <- (52) [avatar component clause 437]
446. calm(alice) | ~rich(alice) <- (52) [resolution 130,439]
466. ~rich(alice) <- (52) [subsumption resolution 446,150]
467. ~51 | ~52 [avatar split clause 466,437,433]
468. quiet(alice) <- (~51) [resolution 434,84]
469. $false <- (~23, ~51) [subsumption resolution 468,256]
470. 23 | 51 [avatar contradiction clause 469]
474. quiet(alice) <- (29, ~52) [resolution 438,282]
477. 23 | ~29 | 52 [avatar split clause 474,437,281,255]
480. $false <- (26) [resolution 269,146]
485. ~26 [avatar contradiction clause 480]
486. $false [avatar sat refutation 270,283,373,467,470,477,485]
% SZS output end Proof for 193297276576667575637555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble is either not old or not humble and vice versa.
Everyone who is both not old and not funny is both not kind and curious.
If lucy is happy or patient then someone is both not generous and not patient and vice versa.
Everyone who is not happy or tall is both not happy and brave.
If someone is not humble or tall then someone is not wise or creative and vice versa.
Everyone who is both brave and old is not generous or not creative and vice versa.
Everyone who is both wise and not happy is brave and vice versa.
If lucy is wise or funny then alice is wise.
If paul is humble then paul is not tall or not kind.
Everyone who is both not brave and funny is both not curious and not calm and vice versa.
Everyone who is either not curious or not happy is either generous or wise.
Everyone who is tall is humble and vice versa.
Everyone who is both kind and wise is both quiet and brave and vice versa.
Everyone who is either not quiet or not generous is not old or not funny and vice versa.
Everyone who is not generous or generous is either old or humble.
Everyone who is either not old or patient is both wise and not wise and vice versa.
Lucy is not happy.
Paul is not happy.
Mary is both funny and not brave.
Someone is not wise or funny.
Someone is not curious or happy.
Mary is either not patient or not funny.
Someone is not old or generous. | Paul is generous. | entailment | (![X]:(~humble(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~old(X)&~funny(X))=>(~kind(X)&curious(X))))&
(((happy(lucy)|patient(lucy)))<=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~happy(X)|tall(X))=>(~happy(X)&brave(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:((brave(X)&old(X))<=>(~generous(X)|~creative(X))))&
(![X]:((wise(X)&~happy(X))<=>brave(X)))&
(((wise(lucy)|funny(lucy)))=>(wise(alice)))&
((humble(paul))=>((~tall(paul)|~kind(paul))))&
(![X]:((~brave(X)&funny(X))<=>(~curious(X)&~calm(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(generous(X)<~>wise(X))))&
(![X]:(tall(X)<=>humble(X)))&
(![X]:((kind(X)&wise(X))<=>(quiet(X)&brave(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~old(X)|~funny(X))))&
(![X]:((~generous(X)|generous(X))=>(old(X)<~>humble(X))))&
(![X]:((~old(X)<~>patient(X))<=>(wise(X)&~wise(X))))&
(~happy(lucy))&
(~happy(paul))&
((funny(mary)&~brave(mary)))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((~curious(X)|happy(X))))&
((~patient(mary)<~>~funny(mary)))&
(?[X]:((~old(X)|generous(X)))) | generous(paul) | [
"p0",
"p2",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 942163682879793904885898
% SZS output start Proof for 942163682879793904885898
1. ! [X0] : (~humble(X0) <=> (~old(X0) <~> ~humble(X0))) [input p0]
3. (patient(lucy) | happy(lucy)) <=> ? [X0] : (~patient(X0) & ~generous(X0)) [input p2]
16. ! [X0] : ((~old(X0) <~> patient(X0)) <=> (~wise(X0) & wise(X0))) [input p15]
17. ~happy(lucy) [input p16]
24. ~generous(paul) [input hypothesis]
34. ! [X0] : ((~humble(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0)))) & (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | humble(X0))) [nnf transformation 1]
35. ((patient(lucy) | happy(lucy)) | ! [X0] : (patient(X0) | generous(X0))) & (? [X0] : (~patient(X0) & ~generous(X0)) | (~patient(lucy) & ~happy(lucy))) [nnf transformation 3]
36. (patient(lucy) | happy(lucy) | ! [X0] : (patient(X0) | generous(X0))) & (? [X0] : (~patient(X0) & ~generous(X0)) | (~patient(lucy) & ~happy(lucy))) [flattening 35]
37. (patient(lucy) | happy(lucy) | ! [X0] : (patient(X0) | generous(X0))) & (? [X1] : (~patient(X1) & ~generous(X1)) | (~patient(lucy) & ~happy(lucy))) [rectify 36]
38. ? [X1] : (~patient(X1) & ~generous(X1)) => (~patient(sK0) & ~generous(sK0)) [choice axiom]
39. (patient(lucy) | happy(lucy) | ! [X0] : (patient(X0) | generous(X0))) & ((~patient(sK0) & ~generous(sK0)) | (~patient(lucy) & ~happy(lucy))) [skolemisation 37,38]
58. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | (wise(X0) | ~wise(X0))) & ((~wise(X0) & wise(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [nnf transformation 16]
59. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | wise(X0) | ~wise(X0)) & ((~wise(X0) & wise(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [flattening 58]
68. humble(X0) | old(X0) | humble(X0) [cnf transformation 34]
69. ~humble(X0) | ~humble(X0) | old(X0) [cnf transformation 34]
77. patient(lucy) | happy(lucy) | patient(X0) | generous(X0) [cnf transformation 39]
122. wise(X0) | ~old(X0) | ~patient(X0) [cnf transformation 59]
124. ~wise(X0) | ~old(X0) | ~patient(X0) [cnf transformation 59]
127. ~happy(lucy) [cnf transformation 17]
136. ~generous(paul) [cnf transformation 24]
137. humble(X0) | old(X0) [duplicate literal removal 68]
138. ~humble(X0) | old(X0) [duplicate literal removal 69]
139. old(X0) [subsumption resolution 137,138]
141. 1 <=> ! [X0] : (patient(X0) | generous(X0)) [avatar definition]
142. patient(X0) | generous(X0) <- (1) [avatar component clause 141]
144. 2 <=> happy(lucy) [avatar definition]
148. 3 <=> patient(lucy) [avatar definition]
150. patient(lucy) <- (3) [avatar component clause 148]
151. 1 | 2 | 3 [avatar split clause 77,148,144,141]
229. ~wise(X0) | ~patient(X0) [subsumption resolution 124,139]
230. wise(X0) | ~patient(X0) [subsumption resolution 122,139]
231. ~patient(X0) [subsumption resolution 230,229]
232. ~2 [avatar split clause 127,144]
252. $false <- (3) [subsumption resolution 150,231]
253. ~3 [avatar contradiction clause 252]
254. generous(X0) <- (1) [subsumption resolution 142,231]
255. $false <- (1) [resolution 254,136]
258. ~1 [avatar contradiction clause 255]
259. $false [avatar sat refutation 151,232,253,258]
% SZS output end Proof for 942163682879793904885898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not patient and creative then mary is both not brave and strong.
Everyone who is both not wise and not tall is happy or not tall.
If paul is not kind then paul is not generous or not kind and vice versa.
Everyone who is either quiet or not humble is humble.
Everyone who is creative or not strong is not strong or creative and vice versa.
Everyone who is not tall or tall is both tall and not rich and vice versa.
If susan is either humble or calm then someone is both not brave and not curious and vice versa.
If paul is not old or not kind then susan is not funny or rich and vice versa.
Everyone who is funny is both not creative and creative and vice versa.
If lucy is not strong then someone is strong and vice versa.
Everyone who is strong or not rich is either rich or not patient and vice versa.
Everyone who is not old is either rich or wise.
Everyone who is not rich or quiet is either old or not calm.
If fred is funny then susan is both generous and happy and vice versa.
Everyone who is wise or quiet is both not kind and not brave and vice versa.
Everyone who is not strong or not old is either not happy or curious and vice versa.
Susan is not calm.
Someone is not wise.
Paul is either calm or not patient.
Someone is not kind.
Fred is calm or quiet.
Someone is both not curious and humble.
Someone is funny or not humble.
Fred is curious. | Mary is not happy. | neutral | ((?[X]:((~patient(X)&creative(X))))=>((~brave(mary)&strong(mary))))&
(![X]:((~wise(X)&~tall(X))=>(happy(X)|~tall(X))))&
((~kind(paul))<=>((~generous(paul)|~kind(paul))))&
(![X]:((quiet(X)<~>~humble(X))=>humble(X)))&
(![X]:((creative(X)|~strong(X))<=>(~strong(X)|creative(X))))&
(![X]:((~tall(X)|tall(X))<=>(tall(X)&~rich(X))))&
(((humble(susan)<~>calm(susan)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(((~old(paul)|~kind(paul)))<=>((~funny(susan)|rich(susan))))&
(![X]:(funny(X)<=>(~creative(X)&creative(X))))&
((~strong(lucy))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)|~rich(X))<=>(rich(X)<~>~patient(X))))&
(![X]:(~old(X)=>(rich(X)<~>wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(old(X)<~>~calm(X))))&
((funny(fred))<=>((generous(susan)&happy(susan))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~strong(X)|~old(X))<=>(~happy(X)<~>curious(X))))&
(~calm(susan))&
(?[X]:(~wise(X)))&
((calm(paul)<~>~patient(paul)))&
(?[X]:(~kind(X)))&
((calm(fred)|quiet(fred)))&
(?[X]:((~curious(X)&humble(X))))&
(?[X]:((funny(X)|~humble(X))))&
(curious(fred)) | ~happy(mary) | [] | null | 0 |
Everyone who is not funny is either patient or not curious and vice versa.
If someone is both not wise and not strong then someone is quiet and vice versa.
Everyone who is either calm or strong is both rich and not kind.
If paul is both not patient and not old then someone is not tall.
Everyone who is both not strong and not curious is both generous and quiet.
Everyone who is not strong is both old and not quiet.
If susan is wise then someone is both kind and not creative and vice versa.
Everyone who is calm is happy or not quiet and vice versa.
Everyone who is both humble and not wise is either not generous or humble.
Everyone who is not rich or patient is not wise.
If john is not generous then alice is both not happy and creative.
Everyone who is not kind is either strong or not happy and vice versa.
If someone is either old or not quiet then lucy is not wise or strong and vice versa.
Everyone who is patient or happy is either happy or rich and vice versa.
If someone is kind then susan is quiet or calm.
Everyone who is both patient and not creative is curious or old and vice versa.
Alice is tall.
Susan is not quiet or wise.
Someone is not kind.
Someone is both funny and not quiet.
Lucy is either calm or kind.
Someone is not old or generous.
Fred is both not old and kind.
Susan is not rich or not strong. | Fred is calm. | entailment | (![X]:(~funny(X)<=>(patient(X)<~>~curious(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
(![X]:((calm(X)<~>strong(X))=>(rich(X)&~kind(X))))&
(((~patient(paul)&~old(paul)))=>(?[X]:(~tall(X))))&
(![X]:((~strong(X)&~curious(X))=>(generous(X)&quiet(X))))&
(![X]:(~strong(X)=>(old(X)&~quiet(X))))&
((wise(susan))<=>(?[X]:((kind(X)&~creative(X)))))&
(![X]:(calm(X)<=>(happy(X)|~quiet(X))))&
(![X]:((humble(X)&~wise(X))=>(~generous(X)<~>humble(X))))&
(![X]:((~rich(X)|patient(X))=>~wise(X)))&
((~generous(john))=>((~happy(alice)&creative(alice))))&
(![X]:(~kind(X)<=>(strong(X)<~>~happy(X))))&
((?[X]:((old(X)<~>~quiet(X))))<=>((~wise(lucy)|strong(lucy))))&
(![X]:((patient(X)|happy(X))<=>(happy(X)<~>rich(X))))&
((?[X]:(kind(X)))=>((quiet(susan)|calm(susan))))&
(![X]:((patient(X)&~creative(X))<=>(curious(X)|old(X))))&
(tall(alice))&
((~quiet(susan)|wise(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)&~quiet(X))))&
((calm(lucy)<~>kind(lucy)))&
(?[X]:((~old(X)|generous(X))))&
((~old(fred)&kind(fred)))&
((~rich(susan)|~strong(susan))) | calm(fred) | [
"p2",
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9181903141845823612394762
% SZS output start Proof for 9181903141845823612394762
3. ! [X0] : ((calm(X0) <~> strong(X0)) => (~kind(X0) & rich(X0))) [input p2]
6. ! [X0] : (~strong(X0) => (~quiet(X0) & old(X0))) [input p5]
23. kind(fred) & ~old(fred) [input p22]
25. ~calm(fred) [input hypothesis]
29. ! [X0] : ((~kind(X0) & rich(X0)) | (calm(X0) <=> strong(X0))) [ennf transformation 3]
34. ! [X0] : ((~quiet(X0) & old(X0)) | strong(X0)) [ennf transformation 6]
47. ! [X0] : ((~kind(X0) & rich(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) [nnf transformation 29]
82. ~kind(X0) | calm(X0) | ~strong(X0) [cnf transformation 47]
86. old(X0) | strong(X0) [cnf transformation 34]
130. ~old(fred) [cnf transformation 23]
131. kind(fred) [cnf transformation 23]
133. ~calm(fred) [cnf transformation 25]
264. strong(fred) [resolution 86,130]
334. calm(fred) | ~strong(fred) [resolution 82,131]
335. ~strong(fred) [subsumption resolution 334,133]
336. $false [subsumption resolution 335,264]
% SZS output end Proof for 9181903141845823612394762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not generous is not curious or wise.
Everyone who is either not humble or not generous is either humble or old and vice versa.
Everyone who is patient is brave.
If mary is both curious and not rich then someone is calm.
If susan is both not generous and not humble then susan is both not humble and generous.
If lucy is creative or not curious then susan is curious.
Everyone who is humble is curious or kind and vice versa.
Everyone who is not strong or not wise is either generous or not generous and vice versa.
Everyone who is both not wise and not tall is not calm.
If alice is both kind and not patient then someone is not quiet or not humble and vice versa.
Everyone who is curious or not patient is happy and vice versa.
Everyone who is both not old and not patient is generous or tall and vice versa.
If someone is not curious or not calm then john is generous.
Everyone who is either not creative or not curious is not curious or rich and vice versa.
Everyone who is both not patient and not strong is not tall or not strong.
If someone is generous then fred is either not curious or not strong.
Someone is either not brave or not happy.
Paul is both humble and not funny.
Someone is happy.
Someone is either brave or not patient.
Mary is either not patient or curious.
Someone is not creative or not old.
Someone is both not patient and rich. | Paul is not wise. | contradiction | (![X]:((~calm(X)|~generous(X))=>(~curious(X)|wise(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(humble(X)<~>old(X))))&
(![X]:(patient(X)=>brave(X)))&
(((curious(mary)&~rich(mary)))=>(?[X]:(calm(X))))&
(((~generous(susan)&~humble(susan)))=>((~humble(susan)&generous(susan))))&
(((creative(lucy)|~curious(lucy)))=>(curious(susan)))&
(![X]:(humble(X)<=>(curious(X)|kind(X))))&
(![X]:((~strong(X)|~wise(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~wise(X)&~tall(X))=>~calm(X)))&
(((kind(alice)&~patient(alice)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((curious(X)|~patient(X))<=>happy(X)))&
(![X]:((~old(X)&~patient(X))<=>(generous(X)|tall(X))))&
((?[X]:((~curious(X)|~calm(X))))=>(generous(john)))&
(![X]:((~creative(X)<~>~curious(X))<=>(~curious(X)|rich(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)|~strong(X))))&
((?[X]:(generous(X)))=>((~curious(fred)<~>~strong(fred))))&
(?[X]:((~brave(X)<~>~happy(X))))&
((humble(paul)&~funny(paul)))&
(?[X]:(happy(X)))&
(?[X]:((brave(X)<~>~patient(X))))&
((~patient(mary)<~>curious(mary)))&
(?[X]:((~creative(X)|~old(X))))&
(?[X]:((~patient(X)&rich(X)))) | ~wise(paul) | [
"p0",
"p1",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6120621170979506322990339
% SZS output start Proof for 6120621170979506322990339
1. ! [X0] : ((~generous(X0) | ~calm(X0)) => (wise(X0) | ~curious(X0))) [input p0]
2. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (humble(X0) <~> old(X0))) [input p1]
12. ! [X0] : ((~patient(X0) & ~old(X0)) <=> (tall(X0) | generous(X0))) [input p11]
13. ? [X0] : (~calm(X0) | ~curious(X0)) => generous(john) [input p12]
24. ~wise(paul) [input hypothesis]
26. ! [X0] : ((wise(X0) | ~curious(X0)) | (generous(X0) & calm(X0))) [ennf transformation 1]
27. ! [X0] : (wise(X0) | ~curious(X0) | (generous(X0) & calm(X0))) [flattening 26]
36. generous(john) | ! [X0] : (calm(X0) & curious(X0)) [ennf transformation 13]
40. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0)))) & (((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 2]
54. ! [X0] : (((~patient(X0) & ~old(X0)) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | (patient(X0) | old(X0)))) [nnf transformation 12]
55. ! [X0] : (((~patient(X0) & ~old(X0)) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | patient(X0) | old(X0))) [flattening 54]
73. ~curious(X0) | wise(X0) | generous(X0) [cnf transformation 27]
74. old(X0) | humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 40]
77. ~old(X0) | ~humble(X0) | ~humble(X0) | generous(X0) [cnf transformation 40]
78. ~generous(X0) | ~humble(X0) | old(X0) | ~humble(X0) [cnf transformation 40]
81. generous(X0) | humble(X0) | humble(X0) | ~old(X0) [cnf transformation 40]
107. ~old(X0) | ~generous(X0) [cnf transformation 55]
111. generous(john) | curious(X0) [cnf transformation 36]
133. ~wise(paul) [cnf transformation 24]
139. old(X0) | humble(X0) | ~generous(X0) [duplicate literal removal 74]
140. ~old(X0) | ~humble(X0) | generous(X0) [duplicate literal removal 77]
141. ~humble(X0) | ~generous(X0) | old(X0) [duplicate literal removal 78]
142. generous(X0) | humble(X0) | ~old(X0) [duplicate literal removal 81]
143. ~old(X0) | generous(X0) [subsumption resolution 140,142]
144. ~generous(X0) | old(X0) [subsumption resolution 139,141]
209. ~old(X0) [subsumption resolution 107,143]
215. 16 <=> generous(john) [avatar definition]
217. generous(john) <- (16) [avatar component clause 215]
220. 17 <=> ! [X0] : curious(X0) [avatar definition]
221. curious(X0) <- (17) [avatar component clause 220]
222. 17 | 16 [avatar split clause 111,215,220]
274. old(john) <- (16) [resolution 144,217]
275. $false <- (16) [subsumption resolution 274,209]
276. ~16 [avatar contradiction clause 275]
289. wise(X0) | generous(X0) <- (17) [resolution 73,221]
332. generous(paul) <- (17) [resolution 289,133]
335. old(paul) <- (17) [resolution 332,144]
336. $false <- (17) [subsumption resolution 335,209]
337. ~17 [avatar contradiction clause 336]
338. $false [avatar sat refutation 222,276,337]
% SZS output end Proof for 6120621170979506322990339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either humble or brave then someone is not tall and vice versa.
If someone is not rich then someone is either not humble or kind.
If someone is not quiet or not curious then fred is kind or humble and vice versa.
Everyone who is either quiet or not rich is not strong or not quiet and vice versa.
If susan is both not funny and humble then john is either wise or happy.
Everyone who is both not generous and not humble is curious or kind and vice versa.
Everyone who is either funny or curious is not creative or not wise and vice versa.
If mary is not funny or not calm then someone is not wise or not brave and vice versa.
If someone is calm or not quiet then someone is either not strong or wise.
Everyone who is not funny or not strong is either happy or tall and vice versa.
Everyone who is funny is strong or tall.
Everyone who is generous or wise is either not creative or generous.
If someone is not humble or not patient then someone is both not kind and kind.
Everyone who is not quiet or creative is not rich.
Everyone who is either not happy or old is not kind or not humble.
Someone is not creative.
Fred is not kind. | Susan is not tall. | contradiction | (((humble(paul)<~>brave(paul)))<=>(?[X]:(~tall(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~humble(X)<~>kind(X)))))&
((?[X]:((~quiet(X)|~curious(X))))<=>((kind(fred)|humble(fred))))&
(![X]:((quiet(X)<~>~rich(X))<=>(~strong(X)|~quiet(X))))&
(((~funny(susan)&humble(susan)))=>((wise(john)<~>happy(john))))&
(![X]:((~generous(X)&~humble(X))<=>(curious(X)|kind(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~wise(X))))&
(((~funny(mary)|~calm(mary)))<=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((~funny(X)|~strong(X))<=>(happy(X)<~>tall(X))))&
(![X]:(funny(X)=>(strong(X)|tall(X))))&
(![X]:((generous(X)|wise(X))=>(~creative(X)<~>generous(X))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)&kind(X)))))&
(![X]:((~quiet(X)|creative(X))=>~rich(X)))&
(![X]:((~happy(X)<~>old(X))=>(~kind(X)|~humble(X))))&
(?[X]:(~creative(X)))&
(~kind(fred)) | ~tall(susan) | [
"p1",
"p3",
"p5",
"p6",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3928974261926161504159901
% SZS output start Proof for 3928974261926161504159901
2. ? [X0] : ~rich(X0) => ? [X0] : (~humble(X0) <~> kind(X0)) [input p1]
4. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p3]
6. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (kind(X0) | curious(X0))) [input p5]
7. ! [X0] : ((funny(X0) <~> curious(X0)) <=> (~wise(X0) | ~creative(X0))) [input p6]
11. ! [X0] : (funny(X0) => (tall(X0) | strong(X0))) [input p10]
13. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p12]
14. ! [X0] : ((creative(X0) | ~quiet(X0)) => ~rich(X0)) [input p13]
18. ~tall(susan) [input hypothesis]
19. ? [X0] : ~rich(X0) => ? [X1] : (~humble(X1) <~> kind(X1)) [rectify 2]
21. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 13]
22. ? [X0] : ~humble(X0) => ? [X1] : (kind(X1) & ~kind(X1)) [pure predicate removal 21]
23. ? [X1] : (~humble(X1) <~> kind(X1)) | ! [X0] : rich(X0) [ennf transformation 19]
27. ! [X0] : ((tall(X0) | strong(X0)) | ~funny(X0)) [ennf transformation 11]
28. ! [X0] : (tall(X0) | strong(X0) | ~funny(X0)) [flattening 27]
30. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : humble(X0) [ennf transformation 22]
31. ! [X0] : (~rich(X0) | (~creative(X0) & quiet(X0))) [ennf transformation 14]
38. ? [X1] : ((~kind(X1) | humble(X1)) & (kind(X1) | ~humble(X1))) | ! [X0] : rich(X0) [nnf transformation 23]
39. ? [X0] : ((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | ! [X1] : rich(X1) [rectify 38]
40. ? [X0] : ((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) => ((~kind(sK1) | humble(sK1)) & (kind(sK1) | ~humble(sK1))) [choice axiom]
41. ((~kind(sK1) | humble(sK1)) & (kind(sK1) | ~humble(sK1))) | ! [X1] : rich(X1) [skolemisation 39,40]
47. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 4]
48. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [flattening 47]
50. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 6]
51. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | humble(X0) | generous(X0))) [flattening 50]
52. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (wise(X0) & creative(X0))) & ((~wise(X0) | ~creative(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 7]
53. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (wise(X0) & creative(X0))) & (~wise(X0) | ~creative(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [flattening 52]
66. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : humble(X1) [rectify 30]
67. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK5) & ~kind(sK5)) [choice axiom]
68. (kind(sK5) & ~kind(sK5)) | ! [X1] : humble(X1) [skolemisation 66,67]
76. kind(sK1) | ~humble(sK1) | rich(X1) [cnf transformation 41]
82. ~quiet(X0) | ~strong(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 48]
85. ~rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 48]
93. ~curious(X0) | ~humble(X0) [cnf transformation 51]
94. ~kind(X0) | ~humble(X0) [cnf transformation 51]
97. creative(X0) | funny(X0) | curious(X0) [cnf transformation 53]
115. ~funny(X0) | strong(X0) | tall(X0) [cnf transformation 28]
120. ~kind(sK5) | humble(X1) [cnf transformation 68]
121. kind(sK5) | humble(X1) [cnf transformation 68]
123. ~creative(X0) | ~rich(X0) [cnf transformation 31]
128. ~tall(susan) [cnf transformation 18]
130. ~quiet(X0) | ~strong(X0) | ~rich(X0) [duplicate literal removal 82]
131. ~rich(X0) | quiet(X0) [duplicate literal removal 85]
152. 5 <=> ! [X1] : rich(X1) [avatar definition]
153. rich(X1) <- (5) [avatar component clause 152]
155. 6 <=> humble(sK1) [avatar definition]
156. ~humble(sK1) <- (~6) [avatar component clause 155]
159. 7 <=> kind(sK1) [avatar definition]
160. kind(sK1) <- (7) [avatar component clause 159]
163. 5 | ~6 | 7 [avatar split clause 76,159,155,152]
190. ~strong(X0) | ~rich(X0) [subsumption resolution 130,131]
192. 14 <=> funny(susan) [avatar definition]
193. ~funny(susan) <- (~14) [avatar component clause 192]
194. funny(susan) <- (14) [avatar component clause 192]
251. 27 <=> ! [X1] : humble(X1) [avatar definition]
252. humble(X1) <- (27) [avatar component clause 251]
254. 28 <=> kind(sK5) [avatar definition]
257. 27 | 28 [avatar split clause 121,254,251]
258. 27 | ~28 [avatar split clause 120,254,251]
262. $false <- (~6, 27) [subsumption resolution 156,252]
263. 6 | ~27 [avatar contradiction clause 262]
268. ~rich(X0) | curious(X0) | funny(X0) [resolution 97,123]
289. 32 <=> curious(susan) [avatar definition]
290. curious(susan) <- (32) [avatar component clause 289]
314. ~humble(sK1) <- (7) [resolution 160,94]
315. $false <- (7, 27) [subsumption resolution 314,252]
316. ~7 | ~27 [avatar contradiction clause 315]
342. strong(susan) | tall(susan) <- (14) [resolution 115,194]
345. strong(susan) <- (14) [subsumption resolution 342,128]
364. ~rich(susan) <- (14) [resolution 345,190]
365. $false <- (5, 14) [subsumption resolution 364,153]
366. ~5 | ~14 [avatar contradiction clause 365]
440. funny(X0) | curious(X0) <- (5) [resolution 268,153]
450. curious(susan) <- (5, ~14) [resolution 440,193]
453. 32 | ~5 | 14 [avatar split clause 450,192,152,289]
454. ~humble(susan) <- (32) [resolution 290,93]
455. $false <- (27, 32) [subsumption resolution 454,252]
456. ~27 | ~32 [avatar contradiction clause 455]
457. $false [avatar sat refutation 163,257,258,263,316,366,453,456]
% SZS output end Proof for 3928974261926161504159901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not quiet then john is humble or not curious and vice versa.
Everyone who is either old or not quiet is either not quiet or not creative.
Everyone who is not quiet or not creative is both strong and not wise and vice versa.
Everyone who is both not brave and kind is either not funny or not creative.
If mary is strong then someone is both not tall and not curious.
Everyone who is either not patient or calm is generous or not funny.
If someone is either quiet or not calm then someone is kind or rich.
Everyone who is not funny or not wise is both old and kind.
Everyone who is both strong and tall is not happy and vice versa.
If alice is both funny and not calm then lucy is both not humble and wise.
If someone is either brave or calm then susan is both not quiet and not wise.
If someone is either quiet or not generous then someone is not tall or quiet.
If someone is not creative then someone is both not funny and brave and vice versa.
Everyone who is not funny is both tall and not calm.
If mary is not generous then susan is not curious.
Everyone who is rich or generous is quiet.
Someone is funny.
Someone is curious or quiet.
Someone is kind.
Someone is both not strong and patient.
Susan is kind or not calm.
Mary is both quiet and not funny.
Susan is calm or not humble.
John is both happy and not quiet. | Susan is quiet. | contradiction | ((?[X]:((~humble(X)|~quiet(X))))<=>((humble(john)|~curious(john))))&
(![X]:((old(X)<~>~quiet(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~creative(X))<=>(strong(X)&~wise(X))))&
(![X]:((~brave(X)&kind(X))=>(~funny(X)<~>~creative(X))))&
((strong(mary))=>(?[X]:((~tall(X)&~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>(generous(X)|~funny(X))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~funny(X)|~wise(X))=>(old(X)&kind(X))))&
(![X]:((strong(X)&tall(X))<=>~happy(X)))&
(((funny(alice)&~calm(alice)))=>((~humble(lucy)&wise(lucy))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(?[X]:(funny(X)))&
(?[X]:((curious(X)|quiet(X))))&
(?[X]:(kind(X)))&
(?[X]:((~strong(X)&patient(X))))&
((kind(susan)|~calm(susan)))&
((quiet(mary)&~funny(mary)))&
((calm(susan)|~humble(susan)))&
((happy(john)&~quiet(john))) | quiet(susan) | [
"p1",
"p7",
"p10",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2351026587598101695880887
% SZS output start Proof for 2351026587598101695880887
2. ! [X0] : ((old(X0) <~> ~quiet(X0)) => (~quiet(X0) <~> ~creative(X0))) [input p1]
8. ! [X0] : ((~wise(X0) | ~funny(X0)) => (kind(X0) & old(X0))) [input p7]
11. ? [X0] : (brave(X0) <~> calm(X0)) => (~wise(susan) & ~quiet(susan)) [input p10]
13. ? [X0] : ~creative(X0) <=> ? [X0] : (brave(X0) & ~funny(X0)) [input p12]
14. ! [X0] : (~funny(X0) => (~calm(X0) & tall(X0))) [input p13]
22. ~funny(mary) & quiet(mary) [input p21]
25. quiet(susan) [input hypothesis]
28. ? [X0] : ~creative(X0) <=> ? [X1] : (brave(X1) & ~funny(X1)) [rectify 13]
30. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) | (old(X0) <=> ~quiet(X0))) [ennf transformation 2]
37. ! [X0] : ((kind(X0) & old(X0)) | (wise(X0) & funny(X0))) [ennf transformation 8]
42. (~wise(susan) & ~quiet(susan)) | ! [X0] : (brave(X0) <=> calm(X0)) [ennf transformation 11]
44. ! [X0] : ((~calm(X0) & tall(X0)) | funny(X0)) [ennf transformation 14]
52. ! [X0] : (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) [nnf transformation 30]
63. (~wise(susan) & ~quiet(susan)) | ! [X0] : ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))) [nnf transformation 42]
68. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X1] : (brave(X1) & ~funny(X1)) | ! [X0] : creative(X0)) [nnf transformation 28]
69. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X2] : (brave(X2) & ~funny(X2)) | ! [X3] : creative(X3)) [rectify 68]
70. ? [X0] : ~creative(X0) => ~creative(sK4) [choice axiom]
71. ? [X2] : (brave(X2) & ~funny(X2)) => (brave(sK5) & ~funny(sK5)) [choice axiom]
72. (~creative(sK4) | ! [X1] : (~brave(X1) | funny(X1))) & ((brave(sK5) & ~funny(sK5)) | ! [X3] : creative(X3)) [skolemisation 69,71,70]
85. ~creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 52]
102. funny(X0) | old(X0) [cnf transformation 37]
109. ~quiet(susan) | calm(X0) | ~brave(X0) [cnf transformation 63]
115. ~funny(sK5) | creative(X3) [cnf transformation 72]
116. brave(sK5) | creative(X3) [cnf transformation 72]
119. ~calm(X0) | funny(X0) [cnf transformation 44]
129. quiet(mary) [cnf transformation 22]
130. ~funny(mary) [cnf transformation 22]
134. quiet(susan) [cnf transformation 25]
135. ~creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 85]
220. 20 <=> ! [X0] : (calm(X0) | ~brave(X0)) [avatar definition]
221. ~brave(X0) | calm(X0) <- (20) [avatar component clause 220]
224. 21 <=> quiet(susan) [avatar definition]
228. 20 | ~21 [avatar split clause 109,224,220]
254. 28 <=> ! [X3] : creative(X3) [avatar definition]
255. creative(X3) <- (28) [avatar component clause 254]
257. 29 <=> brave(sK5) [avatar definition]
259. brave(sK5) <- (29) [avatar component clause 257]
260. 28 | 29 [avatar split clause 116,257,254]
262. 30 <=> funny(sK5) [avatar definition]
264. ~funny(sK5) <- (~30) [avatar component clause 262]
265. 28 | ~30 [avatar split clause 115,262,254]
298. 21 [avatar split clause 134,224]
305. old(mary) [resolution 102,130]
326. ~old(X0) | ~quiet(X0) <- (28) [resolution 135,255]
422. ~quiet(mary) <- (28) [resolution 326,305]
425. $false <- (28) [subsumption resolution 422,129]
426. ~28 [avatar contradiction clause 425]
507. calm(sK5) <- (20, 29) [resolution 259,221]
545. funny(sK5) <- (20, 29) [resolution 507,119]
546. $false <- (20, 29, ~30) [subsumption resolution 545,264]
547. ~20 | ~29 | 30 [avatar contradiction clause 546]
548. $false [avatar sat refutation 228,260,265,298,426,547]
% SZS output end Proof for 2351026587598101695880887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both not happy and not tall.
If mary is not wise or not happy then someone is not funny and vice versa.
Everyone who is not rich is curious or quiet and vice versa.
If fred is both not calm and tall then susan is either not funny or not happy and vice versa.
If mary is either brave or not rich then someone is not rich or patient.
If someone is either not happy or brave then someone is either kind or generous.
Everyone who is both curious and humble is either creative or happy and vice versa.
Everyone who is old is either wise or happy.
Everyone who is both tall and not quiet is both not wise and not patient and vice versa.
If someone is either strong or not happy then susan is both funny and not wise and vice versa.
If someone is strong then mary is either rich or calm.
Everyone who is both rich and not old is either brave or not brave and vice versa.
If someone is kind then mary is not wise.
If someone is kind or not calm then someone is kind and vice versa.
If fred is either not funny or not patient then lucy is brave or not patient.
Everyone who is either kind or old is either not patient or not wise and vice versa.
Someone is either not rich or not patient.
Mary is either not calm or not curious.
Paul is generous or not tall.
Someone is either kind or tall.
Someone is either not funny or not humble.
Fred is not creative or not rich.
Susan is not curious. | Mary is creative. | contradiction | (![X]:(calm(X)=>(~happy(X)&~tall(X))))&
(((~wise(mary)|~happy(mary)))<=>(?[X]:(~funny(X))))&
(![X]:(~rich(X)<=>(curious(X)|quiet(X))))&
(((~calm(fred)&tall(fred)))<=>((~funny(susan)<~>~happy(susan))))&
(((brave(mary)<~>~rich(mary)))=>(?[X]:((~rich(X)|patient(X)))))&
((?[X]:((~happy(X)<~>brave(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((curious(X)&humble(X))<=>(creative(X)<~>happy(X))))&
(![X]:(old(X)=>(wise(X)<~>happy(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~wise(X)&~patient(X))))&
((?[X]:((strong(X)<~>~happy(X))))<=>((funny(susan)&~wise(susan))))&
((?[X]:(strong(X)))=>((rich(mary)<~>calm(mary))))&
(![X]:((rich(X)&~old(X))<=>(brave(X)<~>~brave(X))))&
((?[X]:(kind(X)))=>(~wise(mary)))&
((?[X]:((kind(X)|~calm(X))))<=>(?[X]:(kind(X))))&
(((~funny(fred)<~>~patient(fred)))=>((brave(lucy)|~patient(lucy))))&
(![X]:((kind(X)<~>old(X))<=>(~patient(X)<~>~wise(X))))&
(?[X]:((~rich(X)<~>~patient(X))))&
((~calm(mary)<~>~curious(mary)))&
((generous(paul)|~tall(paul)))&
(?[X]:((kind(X)<~>tall(X))))&
(?[X]:((~funny(X)<~>~humble(X))))&
((~creative(fred)|~rich(fred)))&
(~curious(susan)) | creative(mary) | [
"p0",
"p2",
"p6",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3144538721807415557275761
% SZS output start Proof for 3144538721807415557275761
1. ! [X0] : (calm(X0) => (~tall(X0) & ~happy(X0))) [input p0]
3. ! [X0] : (~rich(X0) <=> (quiet(X0) | curious(X0))) [input p2]
7. ! [X0] : ((humble(X0) & curious(X0)) <=> (creative(X0) <~> happy(X0))) [input p6]
12. ! [X0] : ((~old(X0) & rich(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p11]
18. ~calm(mary) <~> ~curious(mary) [input p17]
24. creative(mary) [input hypothesis]
27. ! [X0] : ((~tall(X0) & ~happy(X0)) | ~calm(X0)) [ennf transformation 1]
40. ! [X0] : ((~rich(X0) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | rich(X0))) [nnf transformation 3]
41. ! [X0] : ((~rich(X0) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | rich(X0))) [flattening 40]
51. ! [X0] : (((humble(X0) & curious(X0)) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0)))) & (((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | (~humble(X0) | ~curious(X0)))) [nnf transformation 7]
52. ! [X0] : (((humble(X0) & curious(X0)) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0)))) & (((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | ~humble(X0) | ~curious(X0))) [flattening 51]
62. ! [X0] : (((~old(X0) & rich(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (old(X0) | ~rich(X0)))) [nnf transformation 12]
63. ! [X0] : (((~old(X0) & rich(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | old(X0) | ~rich(X0))) [flattening 62]
74. (curious(mary) | calm(mary)) & (~curious(mary) | ~calm(mary)) [nnf transformation 18]
81. ~happy(X0) | ~calm(X0) [cnf transformation 27]
87. ~curious(X0) | ~rich(X0) [cnf transformation 41]
103. ~creative(X0) | happy(X0) | curious(X0) [cnf transformation 52]
123. rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 63]
124. rich(X0) | brave(X0) | brave(X0) [cnf transformation 63]
144. curious(mary) | calm(mary) [cnf transformation 74]
152. creative(mary) [cnf transformation 24]
153. rich(X0) | ~brave(X0) [duplicate literal removal 123]
154. brave(X0) | rich(X0) [duplicate literal removal 124]
165. 3 <=> happy(mary) [avatar definition]
166. happy(mary) <- (3) [avatar component clause 165]
263. 23 <=> calm(mary) [avatar definition]
264. calm(mary) <- (23) [avatar component clause 263]
269. rich(X0) [subsumption resolution 153,154]
316. 33 <=> curious(mary) [avatar definition]
317. ~curious(mary) <- (~33) [avatar component clause 316]
318. curious(mary) <- (33) [avatar component clause 316]
319. 23 | 33 [avatar split clause 144,316,263]
379. ~rich(mary) <- (33) [resolution 87,318]
380. $false <- (33) [subsumption resolution 379,269]
381. ~33 [avatar contradiction clause 380]
387. happy(mary) | curious(mary) [resolution 103,152]
388. happy(mary) <- (~33) [subsumption resolution 387,317]
389. 3 | 33 [avatar split clause 388,316,165]
390. ~calm(mary) <- (3) [resolution 166,81]
391. $false <- (3, 23) [subsumption resolution 390,264]
392. ~3 | ~23 [avatar contradiction clause 391]
393. $false [avatar sat refutation 319,381,389,392]
% SZS output end Proof for 3144538721807415557275761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not quiet or calm.
Everyone who is not creative or brave is either happy or not happy and vice versa.
If someone is not brave or rich then fred is strong and vice versa.
Everyone who is kind or not quiet is either rich or curious and vice versa.
If fred is either tall or strong then someone is both rich and humble.
Everyone who is both patient and not rich is generous or not calm and vice versa.
If susan is creative then someone is both old and humble.
If someone is quiet then lucy is not rich or not strong.
Everyone who is both not patient and not old is either not curious or curious and vice versa.
If someone is both wise and not happy then someone is both rich and not kind.
If mary is both funny and creative then alice is not funny.
If someone is curious or patient then john is either humble or not rich.
Everyone who is either creative or not quiet is either not creative or not humble.
Everyone who is not creative or rich is not funny.
Everyone who is brave or quiet is both not creative and quiet.
If someone is brave or creative then someone is either not happy or not old and vice versa.
John is not happy.
Fred is not tall.
Lucy is tall or not rich.
Lucy is not calm or not kind.
Lucy is patient or not wise.
Someone is not generous. | Alice is quiet. | entailment | (![X]:(~quiet(X)=>(~quiet(X)<~>calm(X))))&
(![X]:((~creative(X)|brave(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:((~brave(X)|rich(X))))<=>(strong(fred)))&
(![X]:((kind(X)|~quiet(X))<=>(rich(X)<~>curious(X))))&
(((tall(fred)<~>strong(fred)))=>(?[X]:((rich(X)&humble(X)))))&
(![X]:((patient(X)&~rich(X))<=>(generous(X)|~calm(X))))&
((creative(susan))=>(?[X]:((old(X)&humble(X)))))&
((?[X]:(quiet(X)))=>((~rich(lucy)|~strong(lucy))))&
(![X]:((~patient(X)&~old(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((wise(X)&~happy(X))))=>(?[X]:((rich(X)&~kind(X)))))&
(((funny(mary)&creative(mary)))=>(~funny(alice)))&
((?[X]:((curious(X)|patient(X))))=>((humble(john)<~>~rich(john))))&
(![X]:((creative(X)<~>~quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((~creative(X)|rich(X))=>~funny(X)))&
(![X]:((brave(X)|quiet(X))=>(~creative(X)&quiet(X))))&
((?[X]:((brave(X)|creative(X))))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(~happy(john))&
(~tall(fred))&
((tall(lucy)|~rich(lucy)))&
((~calm(lucy)|~kind(lucy)))&
((patient(lucy)|~wise(lucy)))&
(?[X]:(~generous(X))) | quiet(alice) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 89788382183618062345652
% SZS output start Proof for 89788382183618062345652
1. ! [X0] : (~quiet(X0) => (~quiet(X0) <~> calm(X0))) [input p0]
6. ! [X0] : ((~rich(X0) & patient(X0)) <=> (~calm(X0) | generous(X0))) [input p5]
9. ! [X0] : ((~old(X0) & ~patient(X0)) <=> (~curious(X0) <~> curious(X0))) [input p8]
23. ~quiet(alice) [input hypothesis]
30. ! [X0] : ((~quiet(X0) <~> calm(X0)) | quiet(X0)) [ennf transformation 1]
38. ! [X0] : (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | quiet(X0)) [nnf transformation 30]
50. ! [X0] : (((~rich(X0) & patient(X0)) | (calm(X0) & ~generous(X0))) & ((~calm(X0) | generous(X0)) | (rich(X0) | ~patient(X0)))) [nnf transformation 6]
51. ! [X0] : (((~rich(X0) & patient(X0)) | (calm(X0) & ~generous(X0))) & (~calm(X0) | generous(X0) | rich(X0) | ~patient(X0))) [flattening 50]
54. ! [X0] : (((~old(X0) & ~patient(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | (old(X0) | patient(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~patient(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | old(X0) | patient(X0))) [flattening 54]
66. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
88. patient(X0) | calm(X0) [cnf transformation 51]
96. ~patient(X0) | curious(X0) | curious(X0) [cnf transformation 55]
97. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 55]
123. ~quiet(alice) [cnf transformation 23]
126. ~patient(X0) | curious(X0) [duplicate literal removal 96]
127. ~patient(X0) | ~curious(X0) [duplicate literal removal 97]
132. ~calm(X0) | quiet(X0) [duplicate literal removal 66]
198. ~patient(X0) [subsumption resolution 126,127]
251. calm(X0) [resolution 88,198]
260. quiet(X0) [resolution 132,251]
261. $false [resolution 260,123]
% SZS output end Proof for 89788382183618062345652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not creative or not brave. If someone is either not brave or calm then someone is either patient or not calm. If alice is either not brave or not happy then susan is either not patient or funny. Everyone who is happy or rich is not generous and vice versa. Everyone who is either happy or strong is not creative. Everyone who is both not brave and not calm is kind and vice versa. Everyone who is both wise and not calm is either not brave or not curious and vice versa. Everyone who is both not generous and brave is either generous or not rich. If someone is not quiet then susan is not rich. If fred is both not quiet and not curious then someone is both not old and quiet. If someone is old or not generous then someone is both wise and not quiet and vice versa. Everyone who is either tall or not generous is both not kind and funny. If lucy is old or generous then fred is either tall or curious and vice versa. If someone is not curious or rich then alice is either generous or old and vice versa. Everyone who is not kind or not quiet is either not quiet or rich. Everyone who is not creative or calm is both not rich and not humble. Mary is either brave or not rich. Fred is strong. Paul is both strong and not calm. Someone is rich. Someone is brave or rich. Someone is curious. Someone is either not calm or happy. Mary is both not tall and curious. | Mary is calm. | contradiction | (![X]:(humble(X)=>(~creative(X)|~brave(X))))&
((?[X]:((~brave(X)<~>calm(X))))=>(?[X]:((patient(X)<~>~calm(X)))))&
(((~brave(alice)<~>~happy(alice)))=>((~patient(susan)<~>funny(susan))))&
(![X]:((happy(X)|rich(X))<=>~generous(X)))&
(![X]:((happy(X)<~>strong(X))=>~creative(X)))&
(![X]:((~brave(X)&~calm(X))<=>kind(X)))&
(![X]:((wise(X)&~calm(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((~generous(X)&brave(X))=>(generous(X)<~>~rich(X))))&
((?[X]:(~quiet(X)))=>(~rich(susan)))&
(((~quiet(fred)&~curious(fred)))=>(?[X]:((~old(X)&quiet(X)))))&
((?[X]:((old(X)|~generous(X))))<=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:((tall(X)<~>~generous(X))=>(~kind(X)&funny(X))))&
(((old(lucy)|generous(lucy)))<=>((tall(fred)<~>curious(fred))))&
((?[X]:((~curious(X)|rich(X))))<=>((generous(alice)<~>old(alice))))&
(![X]:((~kind(X)|~quiet(X))=>(~quiet(X)<~>rich(X))))&
(![X]:((~creative(X)|calm(X))=>(~rich(X)&~humble(X))))&
((brave(mary)<~>~rich(mary)))&
(strong(fred))&
((strong(paul)&~calm(paul)))&
(?[X]:(rich(X)))&
(?[X]:((brave(X)|rich(X))))&
(?[X]:(curious(X)))&
(?[X]:((~calm(X)<~>happy(X))))&
((~tall(mary)&curious(mary))) | calm(mary) | [
"p3",
"p6",
"p7",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3076798554315507638892905
% SZS output start Proof for 3076798554315507638892905
4. ! [X0] : ((rich(X0) | happy(X0)) <=> ~generous(X0)) [input p3]
7. ! [X0] : ((~calm(X0) & wise(X0)) <=> (~brave(X0) <~> ~curious(X0))) [input p6]
8. ! [X0] : ((brave(X0) & ~generous(X0)) => (generous(X0) <~> ~rich(X0))) [input p7]
17. brave(mary) <~> ~rich(mary) [input p16]
24. curious(mary) & ~tall(mary) [input p23]
25. calm(mary) [input hypothesis]
33. ! [X0] : ((generous(X0) <~> ~rich(X0)) | (~brave(X0) | generous(X0))) [ennf transformation 8]
34. ! [X0] : ((generous(X0) <~> ~rich(X0)) | ~brave(X0) | generous(X0)) [flattening 33]
46. ! [X0] : (((rich(X0) | happy(X0)) | generous(X0)) & (~generous(X0) | (~rich(X0) & ~happy(X0)))) [nnf transformation 4]
47. ! [X0] : ((rich(X0) | happy(X0) | generous(X0)) & (~generous(X0) | (~rich(X0) & ~happy(X0)))) [flattening 46]
51. ! [X0] : (((~calm(X0) & wise(X0)) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) & (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | (calm(X0) | ~wise(X0)))) [nnf transformation 7]
52. ! [X0] : (((~calm(X0) & wise(X0)) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) & (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | calm(X0) | ~wise(X0))) [flattening 51]
53. ! [X0] : (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ~brave(X0) | generous(X0)) [nnf transformation 34]
69. (rich(mary) | ~brave(mary)) & (~rich(mary) | brave(mary)) [nnf transformation 17]
88. ~generous(X0) | ~rich(X0) [cnf transformation 47]
99. ~curious(X0) | ~calm(X0) | brave(X0) [cnf transformation 52]
101. ~rich(X0) | generous(X0) | ~brave(X0) | generous(X0) [cnf transformation 53]
134. rich(mary) | ~brave(mary) [cnf transformation 69]
144. curious(mary) [cnf transformation 24]
145. calm(mary) [cnf transformation 25]
147. ~rich(X0) | generous(X0) | ~brave(X0) [duplicate literal removal 101]
186. ~rich(X0) | ~brave(X0) [subsumption resolution 147,88]
289. ~brave(mary) [subsumption resolution 134,186]
407. ~calm(mary) | brave(mary) [resolution 99,144]
408. brave(mary) [subsumption resolution 407,145]
409. $false [subsumption resolution 408,289]
% SZS output end Proof for 3076798554315507638892905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not rich then mary is quiet or not old and vice versa. Everyone who is both not patient and quiet is not happy. Everyone who is old or kind 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 either not generous or quiet. | John is not funny. | entailment | ((?[X]:((~brave(X)<~>~rich(X))))<=>((quiet(mary)|~old(mary))))&
(![X]:((~patient(X)&quiet(X))=>~happy(X)))&
(![X]:((old(X)|kind(X))<=>old(X)))&
(((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)<~>quiet(X)))) | ~funny(john) | [
"p2",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7268580374031668280548739
% SZS output start Proof for 7268580374031668280548739
3. ! [X0] : ((kind(X0) | old(X0)) <=> old(X0)) [input p2]
14. ! [X0] : (old(X0) => (~funny(X0) & ~humble(X0))) [input p13]
16. ! [X0] : (old(X0) <=> (~kind(X0) | happy(X0))) [input p15]
23. funny(john) [input hypothesis]
34. ! [X0] : ((~funny(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 14]
41. ! [X0] : (((kind(X0) | old(X0)) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [nnf transformation 3]
42. ! [X0] : ((kind(X0) | old(X0) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [flattening 41]
60. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ~old(X0))) [nnf transformation 16]
61. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ~old(X0))) [flattening 60]
79. ~kind(X0) | old(X0) [cnf transformation 42]
110. ~funny(X0) | ~old(X0) [cnf transformation 34]
114. old(X0) | kind(X0) [cnf transformation 61]
124. funny(john) [cnf transformation 23]
249. old(X0) [subsumption resolution 114,79]
308. ~old(john) [resolution 110,124]
309. $false [subsumption resolution 308,249]
% SZS output end Proof for 7268580374031668280548739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or tall then mary is not wise or strong. If susan is either strong or not generous then mary is wise. If someone is kind then fred is patient or creative. Everyone who is calm is both old and not calm and vice versa. Everyone who is both strong and not generous is strong or brave. Everyone who is either generous or rich is both creative and rich. Everyone who is not wise or wise is not old or calm. If someone is either strong or not kind then john is not quiet and vice versa. Everyone who is wise is rich. Everyone who is either funny or wise is both creative and not patient. If someone is either rich or creative then fred is strong or not tall and vice versa. Everyone who is not generous or not happy is both not tall and not brave. If someone is wise or not old then john is either not creative or strong and vice versa. Everyone who is either wise or rich is happy or rich and vice versa. If someone is patient or quiet then mary is either not tall or strong and vice versa. Everyone who is not old is not generous or not rich. Someone is not kind. Alice is either calm or not rich. Someone is strong or not happy. Someone is either happy or humble. Susan is happy. Fred is either not old or not funny. | Fred is not patient. | entailment | (((~tall(paul)|tall(paul)))=>((~wise(mary)|strong(mary))))&
(((strong(susan)<~>~generous(susan)))=>(wise(mary)))&
((?[X]:(kind(X)))=>((patient(fred)|creative(fred))))&
(![X]:(calm(X)<=>(old(X)&~calm(X))))&
(![X]:((strong(X)&~generous(X))=>(strong(X)|brave(X))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)&rich(X))))&
(![X]:((~wise(X)|wise(X))=>(~old(X)|calm(X))))&
((?[X]:((strong(X)<~>~kind(X))))<=>(~quiet(john)))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((funny(X)<~>wise(X))=>(creative(X)&~patient(X))))&
((?[X]:((rich(X)<~>creative(X))))<=>((strong(fred)|~tall(fred))))&
(![X]:((~generous(X)|~happy(X))=>(~tall(X)&~brave(X))))&
((?[X]:((wise(X)|~old(X))))<=>((~creative(john)<~>strong(john))))&
(![X]:((wise(X)<~>rich(X))<=>(happy(X)|rich(X))))&
((?[X]:((patient(X)|quiet(X))))<=>((~tall(mary)<~>strong(mary))))&
(![X]:(~old(X)=>(~generous(X)|~rich(X))))&
(?[X]:(~kind(X)))&
((calm(alice)<~>~rich(alice)))&
(?[X]:((strong(X)|~happy(X))))&
(?[X]:((happy(X)<~>humble(X))))&
(happy(susan))&
((~old(fred)<~>~funny(fred))) | ~patient(fred) | [
"p3",
"p8",
"p9",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6211282122998077606586268
% SZS output start Proof for 6211282122998077606586268
4. ! [X0] : (calm(X0) <=> (~calm(X0) & old(X0))) [input p3]
9. ! [X0] : (wise(X0) => rich(X0)) [input p8]
10. ! [X0] : ((funny(X0) <~> wise(X0)) => (~patient(X0) & creative(X0))) [input p9]
14. ! [X0] : ((wise(X0) <~> rich(X0)) <=> (rich(X0) | happy(X0))) [input p13]
22. ~old(fred) <~> ~funny(fred) [input p21]
23. patient(fred) [input hypothesis]
34. ! [X0] : (rich(X0) | ~wise(X0)) [ennf transformation 9]
35. ! [X0] : ((~patient(X0) & creative(X0)) | (funny(X0) <=> wise(X0))) [ennf transformation 10]
40. ! [X0] : ((calm(X0) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | ~calm(X0))) [nnf transformation 4]
41. ! [X0] : ((calm(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | ~calm(X0))) [flattening 40]
47. ! [X0] : ((~patient(X0) & creative(X0)) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0)))) [nnf transformation 35]
57. ! [X0] : ((((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))))) [nnf transformation 14]
58. ! [X0] : ((((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0))))) [flattening 57]
71. (funny(fred) | old(fred)) & (~funny(fred) | ~old(fred)) [nnf transformation 22]
78. ~calm(X0) | ~calm(X0) [cnf transformation 41]
79. calm(X0) | calm(X0) | ~old(X0) [cnf transformation 41]
91. ~wise(X0) | rich(X0) [cnf transformation 34]
94. ~funny(X0) | wise(X0) | ~patient(X0) [cnf transformation 47]
117. ~rich(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 58]
133. funny(fred) | old(fred) [cnf transformation 71]
134. patient(fred) [cnf transformation 23]
136. ~rich(X0) | ~wise(X0) [duplicate literal removal 117]
138. ~calm(X0) [duplicate literal removal 78]
139. ~old(X0) | calm(X0) [duplicate literal removal 79]
168. 7 <=> patient(fred) [avatar definition]
170. patient(fred) <- (7) [avatar component clause 168]
249. 25 <=> ! [X1] : ~wise(X1) [avatar definition]
250. ~wise(X1) <- (25) [avatar component clause 249]
254. ~wise(X0) [subsumption resolution 136,91]
255. 25 [avatar split clause 254,249]
304. 35 <=> old(fred) [avatar definition]
306. old(fred) <- (35) [avatar component clause 304]
308. 36 <=> funny(fred) [avatar definition]
310. funny(fred) <- (36) [avatar component clause 308]
311. 35 | 36 [avatar split clause 133,308,304]
313. 7 [avatar split clause 134,168]
315. calm(fred) <- (35) [resolution 139,306]
316. $false <- (35) [subsumption resolution 315,138]
317. ~35 [avatar contradiction clause 316]
344. wise(fred) | ~patient(fred) <- (36) [resolution 94,310]
345. ~patient(fred) <- (25, 36) [subsumption resolution 344,250]
346. $false <- (7, 25, 36) [subsumption resolution 345,170]
347. ~7 | ~25 | ~36 [avatar contradiction clause 346]
348. $false [avatar sat refutation 255,311,313,317,347]
% SZS output end Proof for 6211282122998077606586268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then fred is either not old or funny.
If someone is both humble and generous then mary is both brave and not quiet and vice versa.
Everyone who is not strong is not wise and vice versa.
Everyone who is not quiet or not happy is both creative and not funny.
If someone is both quiet and not patient then fred is not humble.
Everyone who is both creative and tall is not kind or not happy and vice versa.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old.
Mary is either not patient or not wise.
Someone is not funny or kind. | Mary is rich. | contradiction | ((?[X]:(kind(X)))=>((~old(fred)<~>funny(fred))))&
((?[X]:((humble(X)&generous(X))))<=>((brave(mary)&~quiet(mary))))&
(![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~quiet(X)|~happy(X))=>(creative(X)&~funny(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(~humble(fred)))&
(![X]:((creative(X)&tall(X))<=>(~kind(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan)))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X)))) | rich(mary) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1583093802018593425650734
% SZS output start Proof for 1583093802018593425650734
2. ? [X0] : (generous(X0) & humble(X0)) <=> (~quiet(mary) & brave(mary)) [input p1]
3. ! [X0] : (~strong(X0) <=> ~wise(X0)) [input p2]
4. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (~funny(X0) & creative(X0))) [input p3]
6. ! [X0] : ((tall(X0) & creative(X0)) <=> (~happy(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((creative(X0) <~> rich(X0)) <=> (old(X0) | ~funny(X0))) [input p8]
10. ! [X0] : ((~tall(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~strong(X0))) [input p9]
11. (generous(susan) & curious(susan)) <=> ? [X0] : curious(X0) [input p10]
12. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p11]
14. ! [X0] : ((strong(X0) <~> creative(X0)) => (curious(X0) & generous(X0))) [input p13]
21. rich(mary) [input hypothesis]
23. ! [X0] : ((~funny(X0) & creative(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 4]
25. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 7]
26. ! [X0] : ((curious(X0) & generous(X0)) | (strong(X0) <=> creative(X0))) [ennf transformation 14]
28. (? [X0] : (generous(X0) & humble(X0)) | (quiet(mary) | ~brave(mary))) & ((~quiet(mary) & brave(mary)) | ! [X0] : (~generous(X0) | ~humble(X0))) [nnf transformation 2]
29. (? [X0] : (generous(X0) & humble(X0)) | quiet(mary) | ~brave(mary)) & ((~quiet(mary) & brave(mary)) | ! [X0] : (~generous(X0) | ~humble(X0))) [flattening 28]
30. (? [X0] : (generous(X0) & humble(X0)) | quiet(mary) | ~brave(mary)) & ((~quiet(mary) & brave(mary)) | ! [X1] : (~generous(X1) | ~humble(X1))) [rectify 29]
31. ? [X0] : (generous(X0) & humble(X0)) => (generous(sK0) & humble(sK0)) [choice axiom]
32. ((generous(sK0) & humble(sK0)) | quiet(mary) | ~brave(mary)) & ((~quiet(mary) & brave(mary)) | ! [X1] : (~generous(X1) | ~humble(X1))) [skolemisation 30,31]
33. ! [X0] : ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))) [nnf transformation 3]
34. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 6]
35. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~tall(X0) | ~creative(X0))) [flattening 34]
41. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [nnf transformation 9]
42. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [flattening 41]
43. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [nnf transformation 10]
44. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [flattening 43]
45. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~generous(susan) | ~curious(susan))) [nnf transformation 11]
46. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ~generous(susan) | ~curious(susan)) [flattening 45]
47. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ~generous(susan) | ~curious(susan)) [rectify 46]
48. ? [X1] : curious(X1) => curious(sK2) [choice axiom]
49. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (curious(sK2) | ~generous(susan) | ~curious(susan)) [skolemisation 47,48]
50. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 12]
51. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 50]
54. ! [X0] : ((curious(X0) & generous(X0)) | ((strong(X0) | ~creative(X0)) & (creative(X0) | ~strong(X0)))) [nnf transformation 26]
68. ~quiet(mary) | ~generous(X1) | ~humble(X1) [cnf transformation 32]
71. ~wise(X0) | strong(X0) [cnf transformation 33]
72. ~strong(X0) | wise(X0) [cnf transformation 33]
73. creative(X0) | quiet(X0) [cnf transformation 23]
75. ~funny(X0) | quiet(X0) [cnf transformation 23]
76. ~funny(X0) | happy(X0) [cnf transformation 23]
78. ~tall(X0) | ~kind(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 35]
81. tall(X0) | kind(X0) [cnf transformation 35]
85. ~generous(X0) | wise(X0) [cnf transformation 25]
97. ~rich(X0) | ~creative(X0) | funny(X0) [cnf transformation 42]
99. ~strong(X0) | ~kind(X0) | tall(X0) [cnf transformation 44]
100. ~strong(X0) | ~tall(X0) | kind(X0) [cnf transformation 44]
107. generous(susan) | ~curious(X0) [cnf transformation 49]
108. ~strong(X0) | humble(X0) | ~generous(X0) [cnf transformation 51]
109. strong(X0) | generous(X0) [cnf transformation 51]
117. generous(X0) | creative(X0) | ~strong(X0) [cnf transformation 54]
119. ~strong(X0) | creative(X0) | curious(X0) [cnf transformation 54]
131. rich(mary) [cnf transformation 21]
150. 5 <=> quiet(mary) [avatar definition]
164. 8 <=> ! [X1] : (~generous(X1) | ~humble(X1)) [avatar definition]
165. ~generous(X1) | ~humble(X1) <- (8) [avatar component clause 164]
166. 8 | ~5 [avatar split clause 68,150,164]
206. ~strong(X0) | kind(X0) [subsumption resolution 100,81]
207. ~strong(X0) | tall(X0) [subsumption resolution 99,81]
209. 17 <=> ! [X0] : ~curious(X0) [avatar definition]
210. ~curious(X0) <- (17) [avatar component clause 209]
212. 18 <=> generous(susan) [avatar definition]
214. generous(susan) <- (18) [avatar component clause 212]
215. 17 | 18 [avatar split clause 107,212,209]
226. creative(X0) | generous(X0) [subsumption resolution 117,109]
238. 23 <=> generous(mary) [avatar definition]
239. ~generous(mary) <- (~23) [avatar component clause 238]
240. generous(mary) <- (23) [avatar component clause 238]
283. wise(susan) <- (18) [resolution 85,214]
284. strong(susan) <- (18) [resolution 283,71]
288. generous(X0) | wise(X0) [resolution 109,72]
289. wise(X0) [subsumption resolution 288,85]
291. strong(X0) [resolution 289,71]
294. ~humble(susan) <- (8, 18) [resolution 165,214]
301. kind(X0) [resolution 206,291]
304. tall(X0) [resolution 207,291]
311. ~creative(mary) | funny(mary) [resolution 97,131]
315. 30 <=> funny(mary) [avatar definition]
317. funny(mary) <- (30) [avatar component clause 315]
319. 31 <=> creative(mary) [avatar definition]
321. ~creative(mary) <- (~31) [avatar component clause 319]
322. 30 | ~31 [avatar split clause 311,319,315]
323. generous(mary) <- (~31) [resolution 321,226]
327. $false <- (~23, ~31) [subsumption resolution 323,239]
328. 23 | 31 [avatar contradiction clause 327]
333. quiet(mary) <- (30) [resolution 317,75]
334. humble(susan) | ~generous(susan) <- (18) [resolution 108,284]
335. humble(X0) | ~generous(X0) [resolution 108,291]
337. ~generous(susan) <- (8, 18) [subsumption resolution 334,294]
338. $false <- (8, 18) [subsumption resolution 337,214]
339. ~8 | ~18 [avatar contradiction clause 338]
341. 5 | ~30 [avatar split clause 333,315,150]
357. quiet(mary) <- (~31) [resolution 321,73]
360. 5 | 31 [avatar split clause 357,319,150]
361. ~generous(X1) <- (8) [subsumption resolution 165,335]
366. $false <- (8, 23) [resolution 361,240]
371. ~8 | ~23 [avatar contradiction clause 366]
376. happy(mary) <- (30) [resolution 317,76]
386. creative(X0) | curious(X0) [resolution 119,291]
388. creative(X0) <- (17) [subsumption resolution 386,210]
398. ~kind(X0) | ~happy(X0) | ~creative(X0) [resolution 78,304]
401. ~happy(X0) | ~creative(X0) [subsumption resolution 398,301]
402. ~happy(X0) <- (17) [subsumption resolution 401,388]
403. $false <- (17, 30) [resolution 402,376]
404. ~17 | ~30 [avatar contradiction clause 403]
405. $false [avatar sat refutation 166,215,322,328,339,341,360,371,404]
% SZS output end Proof for 1583093802018593425650734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not calm is not rich. Everyone who is either calm or not quiet is either not strong or not creative and vice versa. If alice is either not quiet or not wise then john is both wise and curious. If someone is not old or not wise then someone is not kind and vice versa. Everyone who is either not humble or wise is not brave and vice versa. Everyone who is both not old and not happy is both not strong and curious and vice versa. Everyone who is not generous is either not curious or humble. Everyone who is happy or calm is both humble and not happy and vice versa. If someone is either quiet or not rich then susan is either wise or brave. If paul is tall then john is both not tall and not rich and vice versa. Everyone who is either not calm or strong is wise. If someone is both tall and not funny then someone is not brave or rich. Everyone who is patient or strong is rich and vice versa. Everyone who is creative or not strong is both not calm and strong and vice versa. If fred is both not rich and not humble then susan is both not funny and quiet and vice versa. Everyone who is strong is tall or not funny. Susan is patient or creative. Alice is both not kind and strong. Someone is both calm and tall. Fred is either not kind or not creative. John is either brave or generous. Alice is curious or tall. Someone is not happy. | Paul is funny. | contradiction | (![X]:((~funny(X)&~calm(X))=>~rich(X)))&
(![X]:((calm(X)<~>~quiet(X))<=>(~strong(X)<~>~creative(X))))&
(((~quiet(alice)<~>~wise(alice)))=>((wise(john)&curious(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~brave(X)))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&curious(X))))&
(![X]:(~generous(X)=>(~curious(X)<~>humble(X))))&
(![X]:((happy(X)|calm(X))<=>(humble(X)&~happy(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>((wise(susan)<~>brave(susan))))&
((tall(paul))<=>((~tall(john)&~rich(john))))&
(![X]:((~calm(X)<~>strong(X))=>wise(X)))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(![X]:((patient(X)|strong(X))<=>rich(X)))&
(![X]:((creative(X)|~strong(X))<=>(~calm(X)&strong(X))))&
(((~rich(fred)&~humble(fred)))<=>((~funny(susan)&quiet(susan))))&
(![X]:(strong(X)=>(tall(X)|~funny(X))))&
((patient(susan)|creative(susan)))&
((~kind(alice)&strong(alice)))&
(?[X]:((calm(X)&tall(X))))&
((~kind(fred)<~>~creative(fred)))&
((brave(john)<~>generous(john)))&
((curious(alice)|tall(alice)))&
(?[X]:(~happy(X))) | funny(paul) | [
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2159971507035576507460645
% SZS output start Proof for 2159971507035576507460645
10. tall(paul) <=> (~rich(john) & ~tall(john)) [input p9]
13. ! [X0] : ((strong(X0) | patient(X0)) <=> rich(X0)) [input p12]
14. ! [X0] : ((~strong(X0) | creative(X0)) <=> (strong(X0) & ~calm(X0))) [input p13]
16. ! [X0] : (strong(X0) => (~funny(X0) | tall(X0))) [input p15]
24. funny(paul) [input hypothesis]
34. ! [X0] : ((~funny(X0) | tall(X0)) | ~strong(X0)) [ennf transformation 16]
35. ! [X0] : (~funny(X0) | tall(X0) | ~strong(X0)) [flattening 34]
50. (tall(paul) | (rich(john) | tall(john))) & ((~rich(john) & ~tall(john)) | ~tall(paul)) [nnf transformation 10]
51. (tall(paul) | rich(john) | tall(john)) & ((~rich(john) & ~tall(john)) | ~tall(paul)) [flattening 50]
56. ! [X0] : (((strong(X0) | patient(X0)) | ~rich(X0)) & (rich(X0) | (~strong(X0) & ~patient(X0)))) [nnf transformation 13]
57. ! [X0] : ((strong(X0) | patient(X0) | ~rich(X0)) & (rich(X0) | (~strong(X0) & ~patient(X0)))) [flattening 56]
58. ! [X0] : (((~strong(X0) | creative(X0)) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 14]
59. ! [X0] : ((~strong(X0) | creative(X0) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [flattening 58]
104. ~rich(john) | ~tall(paul) [cnf transformation 51]
110. ~strong(X0) | rich(X0) [cnf transformation 57]
115. strong(X0) | strong(X0) [cnf transformation 59]
121. ~funny(X0) | tall(X0) | ~strong(X0) [cnf transformation 35]
133. funny(paul) [cnf transformation 24]
134. strong(X0) [duplicate literal removal 115]
205. 16 <=> rich(john) [avatar definition]
206. ~rich(john) <- (~16) [avatar component clause 205]
209. 17 <=> tall(paul) [avatar definition]
213. ~17 | ~16 [avatar split clause 104,205,209]
247. ~funny(X0) | tall(X0) [subsumption resolution 121,134]
288. rich(X0) [resolution 110,134]
291. tall(paul) [resolution 247,133]
295. 17 [avatar split clause 291,209]
296. $false <- (~16) [subsumption resolution 206,288]
297. 16 [avatar contradiction clause 296]
298. $false [avatar sat refutation 213,295,297]
% SZS output end Proof for 2159971507035576507460645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not brave is happy. If john is not funny or rich then someone is either funny or not humble. If someone is either not generous or wise then someone is both kind and calm. Everyone who is both generous and not creative is strong or not funny and vice versa. Everyone who is both not old and not patient is rich. Everyone who is both not strong and calm is not calm and vice versa. If susan is strong then someone is old. If someone is both not rich and strong then someone is either brave or not generous. Everyone who is both not happy and not creative is not humble. If someone is kind or humble then paul is both not quiet and humble. If someone is both kind and brave then someone is not patient and vice versa. Everyone who is either not wise or tall is either not tall or kind and vice versa. Everyone who is either patient or not creative is not curious or brave and vice versa. If john is either not quiet or old then susan is old. Everyone who is either brave or tall is generous. Mary is either patient or not rich. Lucy is either generous or kind. Lucy is both not rich and not quiet. Mary is either generous or not curious. Mary is either patient or not funny. Someone is either not rich or funny. Fred is not patient. Someone is both strong and tall. | Fred is not generous. | contradiction | (![X]:((brave(X)<~>~brave(X))=>happy(X)))&
(((~funny(john)|rich(john)))=>(?[X]:((funny(X)<~>~humble(X)))))&
((?[X]:((~generous(X)<~>wise(X))))=>(?[X]:((kind(X)&calm(X)))))&
(![X]:((generous(X)&~creative(X))<=>(strong(X)|~funny(X))))&
(![X]:((~old(X)&~patient(X))=>rich(X)))&
(![X]:((~strong(X)&calm(X))<=>~calm(X)))&
((strong(susan))=>(?[X]:(old(X))))&
((?[X]:((~rich(X)&strong(X))))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~happy(X)&~creative(X))=>~humble(X)))&
((?[X]:((kind(X)|humble(X))))=>((~quiet(paul)&humble(paul))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~wise(X)<~>tall(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~curious(X)|brave(X))))&
(((~quiet(john)<~>old(john)))=>(old(susan)))&
(![X]:((brave(X)<~>tall(X))=>generous(X)))&
((patient(mary)<~>~rich(mary)))&
((generous(lucy)<~>kind(lucy)))&
((~rich(lucy)&~quiet(lucy)))&
((generous(mary)<~>~curious(mary)))&
((patient(mary)<~>~funny(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(~patient(fred))&
(?[X]:((strong(X)&tall(X)))) | ~generous(fred) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 32334182379503694715476
% SZS output start Proof for 32334182379503694715476
4. ! [X0] : ((~creative(X0) & generous(X0)) <=> (~funny(X0) | strong(X0))) [input p3]
6. ! [X0] : ((calm(X0) & ~strong(X0)) <=> ~calm(X0)) [input p5]
24. ~generous(fred) [input hypothesis]
46. ! [X0] : (((~creative(X0) & generous(X0)) | (funny(X0) & ~strong(X0))) & ((~funny(X0) | strong(X0)) | (creative(X0) | ~generous(X0)))) [nnf transformation 4]
47. ! [X0] : (((~creative(X0) & generous(X0)) | (funny(X0) & ~strong(X0))) & (~funny(X0) | strong(X0) | creative(X0) | ~generous(X0))) [flattening 46]
48. ! [X0] : (((calm(X0) & ~strong(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) | strong(X0)))) [nnf transformation 6]
49. ! [X0] : (((calm(X0) & ~strong(X0)) | calm(X0)) & (~calm(X0) | ~calm(X0) | strong(X0))) [flattening 48]
84. ~strong(X0) | generous(X0) [cnf transformation 47]
89. ~calm(X0) | ~calm(X0) | strong(X0) [cnf transformation 49]
91. calm(X0) | calm(X0) [cnf transformation 49]
135. ~generous(fred) [cnf transformation 24]
140. ~calm(X0) | strong(X0) [duplicate literal removal 89]
141. calm(X0) [duplicate literal removal 91]
180. strong(X0) [subsumption resolution 140,141]
300. generous(X0) [resolution 84,180]
307. $false [resolution 300,135]
% SZS output end Proof for 32334182379503694715476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is both not curious and rich and vice versa. If susan is both curious and not calm then john is both calm and strong and vice versa. Everyone who is either kind or generous is either creative or not old. If someone is rich then paul is either not rich or funny and vice versa. Everyone who is both not rich and not humble is both not kind and creative and vice versa. If susan is funny then susan is either not wise or not patient and vice versa. Everyone who is either not calm or funny is not brave. Everyone who is humble or not generous is both not happy and creative and vice versa. Everyone who is strong is either not funny or wise. If someone is either generous or patient then someone is not generous or happy. Everyone who is either not calm or brave is brave and vice versa. Everyone who is either not old or not happy is either kind or not curious. If someone is both not patient and not generous then someone is humble or not kind and vice versa. Everyone who is not kind is strong or rich. If paul is both creative and curious then susan is not funny and vice versa. Everyone who is quiet or tall is either not creative or not brave and vice versa. Alice is not funny. Someone is not calm or not patient. Someone is not happy or not curious. Someone is patient or rich. Someone is both creative and not humble. Paul is both curious and not kind. Susan is generous or quiet. Someone is wise or patient. | John is calm. | entailment | (![X]:(brave(X)<=>(~curious(X)&rich(X))))&
(((curious(susan)&~calm(susan)))<=>((calm(john)&strong(john))))&
(![X]:((kind(X)<~>generous(X))=>(creative(X)<~>~old(X))))&
((?[X]:(rich(X)))<=>((~rich(paul)<~>funny(paul))))&
(![X]:((~rich(X)&~humble(X))<=>(~kind(X)&creative(X))))&
((funny(susan))<=>((~wise(susan)<~>~patient(susan))))&
(![X]:((~calm(X)<~>funny(X))=>~brave(X)))&
(![X]:((humble(X)|~generous(X))<=>(~happy(X)&creative(X))))&
(![X]:(strong(X)=>(~funny(X)<~>wise(X))))&
((?[X]:((generous(X)<~>patient(X))))=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~calm(X)<~>brave(X))<=>brave(X)))&
(![X]:((~old(X)<~>~happy(X))=>(kind(X)<~>~curious(X))))&
((?[X]:((~patient(X)&~generous(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:(~kind(X)=>(strong(X)|rich(X))))&
(((creative(paul)&curious(paul)))<=>(~funny(susan)))&
(![X]:((quiet(X)|tall(X))<=>(~creative(X)<~>~brave(X))))&
(~funny(alice))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((~happy(X)|~curious(X))))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((creative(X)&~humble(X))))&
((curious(paul)&~kind(paul)))&
((generous(susan)|quiet(susan)))&
(?[X]:((wise(X)|patient(X)))) | calm(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6515514934452944649552395
% SZS output start Proof for 6515514934452944649552395
11. ! [X0] : ((~calm(X0) <~> brave(X0)) <=> brave(X0)) [input p10]
25. ~calm(john) [input hypothesis]
55. ! [X0] : ((((~brave(X0) | calm(X0)) & (brave(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))))) [nnf transformation 11]
110. brave(X0) | brave(X0) | calm(X0) [cnf transformation 55]
113. ~brave(X0) | calm(X0) | ~brave(X0) [cnf transformation 55]
143. ~calm(john) [cnf transformation 25]
144. brave(X0) | calm(X0) [duplicate literal removal 110]
145. ~brave(X0) | calm(X0) [duplicate literal removal 113]
217. calm(X0) [subsumption resolution 144,145]
297. $false [subsumption resolution 143,217]
% SZS output end Proof for 6515514934452944649552395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not wise or funny and vice versa.
If someone is not tall then someone is both patient and not creative and vice versa.
Everyone who is creative or humble is both not brave and not patient.
If someone is not rich then alice is not quiet or calm.
Everyone who is both funny and humble is both humble and not quiet and vice versa.
Everyone who is either humble or not patient is not generous or curious.
Everyone who is both kind and generous is not funny or not tall and vice versa.
If susan is either rich or not calm then mary is tall or not humble.
If someone is tall or not humble then lucy is rich.
If paul is either happy or generous then someone is both patient and humble and vice versa.
If someone is not patient then john is both humble and not funny and vice versa.
If lucy is not happy then someone is generous.
Everyone who is not happy or creative is brave or not quiet.
Everyone who is not brave is both not happy and strong.
Everyone who is both not happy and not brave is strong and vice versa.
Susan is not curious or generous.
Someone is either tall or humble.
Someone is kind or not brave.
John is not wise.
Someone is calm or curious. | Alice is not strong. | neutral | (![X]:(rich(X)<=>(~wise(X)|funny(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((creative(X)|humble(X))=>(~brave(X)&~patient(X))))&
((?[X]:(~rich(X)))=>((~quiet(alice)|calm(alice))))&
(![X]:((funny(X)&humble(X))<=>(humble(X)&~quiet(X))))&
(![X]:((humble(X)<~>~patient(X))=>(~generous(X)|curious(X))))&
(![X]:((kind(X)&generous(X))<=>(~funny(X)|~tall(X))))&
(((rich(susan)<~>~calm(susan)))=>((tall(mary)|~humble(mary))))&
((?[X]:((tall(X)|~humble(X))))=>(rich(lucy)))&
(((happy(paul)<~>generous(paul)))<=>(?[X]:((patient(X)&humble(X)))))&
((?[X]:(~patient(X)))<=>((humble(john)&~funny(john))))&
((~happy(lucy))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)|creative(X))=>(brave(X)|~quiet(X))))&
(![X]:(~brave(X)=>(~happy(X)&strong(X))))&
(![X]:((~happy(X)&~brave(X))<=>strong(X)))&
((~curious(susan)|generous(susan)))&
(?[X]:((tall(X)<~>humble(X))))&
(?[X]:((kind(X)|~brave(X))))&
(~wise(john))&
(?[X]:((calm(X)|curious(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is not tall or not calm is rich.
Everyone who is calm is brave and vice versa.
If someone is both not rich and not brave then john is not calm or quiet.
If paul is not generous then paul is not calm and vice versa.
If john is curious then someone is rich.
If someone is strong or brave then mary is either not strong or not curious and vice versa.
If paul is quiet then someone is either not strong or not rich.
If someone is either curious or not old then paul is either brave or generous and vice versa.
If fred is not old or happy then mary is curious or strong and vice versa.
If someone is rich then john is both not funny and not curious.
Everyone who is either not curious or happy is brave or old and vice versa.
If fred is creative or strong then john is either not patient or brave.
Everyone who is kind or not humble is both quiet and not brave and vice versa.
If someone is either strong or not curious then someone is either not tall or not humble and vice versa.
Everyone who is generous is either old or not happy and vice versa.
Paul is humble.
Mary is brave or wise.
John is humble or happy.
Someone is not happy.
Someone is either not generous or not happy.
Mary is both strong and not tall. | Mary is generous. | contradiction | (![X]:((~tall(X)|~calm(X))=>rich(X)))&
(![X]:(calm(X)<=>brave(X)))&
((?[X]:((~rich(X)&~brave(X))))=>((~calm(john)|quiet(john))))&
((~generous(paul))<=>(~calm(paul)))&
((curious(john))=>(?[X]:(rich(X))))&
((?[X]:((strong(X)|brave(X))))<=>((~strong(mary)<~>~curious(mary))))&
((quiet(paul))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((?[X]:((curious(X)<~>~old(X))))<=>((brave(paul)<~>generous(paul))))&
(((~old(fred)|happy(fred)))<=>((curious(mary)|strong(mary))))&
((?[X]:(rich(X)))=>((~funny(john)&~curious(john))))&
(![X]:((~curious(X)<~>happy(X))<=>(brave(X)|old(X))))&
(((creative(fred)|strong(fred)))=>((~patient(john)<~>brave(john))))&
(![X]:((kind(X)|~humble(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~happy(X))))&
(humble(paul))&
((brave(mary)|wise(mary)))&
((humble(john)|happy(john)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)<~>~happy(X))))&
((strong(mary)&~tall(mary))) | generous(mary) | [
"p1",
"p3",
"p5",
"p7",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 885872181432967448517587
% SZS output start Proof for 885872181432967448517587
2. ! [X0] : (calm(X0) <=> brave(X0)) [input p1]
4. ~generous(paul) <=> ~calm(paul) [input p3]
6. ? [X0] : (brave(X0) | strong(X0)) <=> (~strong(mary) <~> ~curious(mary)) [input p5]
8. ? [X0] : (curious(X0) <~> ~old(X0)) <=> (brave(paul) <~> generous(paul)) [input p7]
11. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (old(X0) | brave(X0))) [input p10]
15. ! [X0] : (generous(X0) <=> (old(X0) <~> ~happy(X0))) [input p14]
21. ~tall(mary) & strong(mary) [input p20]
22. generous(mary) [input hypothesis]
34. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 2]
35. (~generous(paul) | calm(paul)) & (~calm(paul) | generous(paul)) [nnf transformation 4]
38. (? [X0] : (brave(X0) | strong(X0)) | ((~strong(mary) | curious(mary)) & (~curious(mary) | strong(mary)))) & (((curious(mary) | strong(mary)) & (~curious(mary) | ~strong(mary))) | ! [X0] : (~brave(X0) & ~strong(X0))) [nnf transformation 6]
39. (? [X0] : (brave(X0) | strong(X0)) | ((~strong(mary) | curious(mary)) & (~curious(mary) | strong(mary)))) & (((curious(mary) | strong(mary)) & (~curious(mary) | ~strong(mary))) | ! [X1] : (~brave(X1) & ~strong(X1))) [rectify 38]
40. ? [X0] : (brave(X0) | strong(X0)) => (brave(sK1) | strong(sK1)) [choice axiom]
41. ((brave(sK1) | strong(sK1)) | ((~strong(mary) | curious(mary)) & (~curious(mary) | strong(mary)))) & (((curious(mary) | strong(mary)) & (~curious(mary) | ~strong(mary))) | ! [X1] : (~brave(X1) & ~strong(X1))) [skolemisation 39,40]
45. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 8]
46. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [rectify 45]
47. ? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) => ((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) [choice axiom]
48. (((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [skolemisation 46,47]
51. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 11]
52. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 51]
61. ! [X0] : ((generous(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | ~generous(X0))) [nnf transformation 15]
69. ~calm(X0) | brave(X0) [cnf transformation 34]
70. ~brave(X0) | calm(X0) [cnf transformation 34]
72. ~calm(paul) | generous(paul) [cnf transformation 35]
73. ~generous(paul) | calm(paul) [cnf transformation 35]
75. ~curious(mary) | ~strong(mary) | ~strong(X1) [cnf transformation 41]
84. generous(paul) | brave(paul) | curious(X1) | old(X1) [cnf transformation 48]
86. ~generous(paul) | ~brave(paul) | curious(X1) | old(X1) [cnf transformation 48]
101. ~happy(X0) | curious(X0) | ~old(X0) [cnf transformation 52]
117. ~happy(X0) | old(X0) | ~generous(X0) [cnf transformation 61]
118. ~old(X0) | happy(X0) | ~generous(X0) [cnf transformation 61]
126. strong(mary) [cnf transformation 21]
128. generous(mary) [cnf transformation 22]
142. 4 <=> calm(paul) [avatar definition]
143. ~calm(paul) <- (~4) [avatar component clause 142]
144. calm(paul) <- (4) [avatar component clause 142]
146. 5 <=> generous(paul) [avatar definition]
149. 4 | ~5 [avatar split clause 73,146,142]
150. 5 | ~4 [avatar split clause 72,142,146]
161. 8 <=> curious(mary) [avatar definition]
162. ~curious(mary) <- (~8) [avatar component clause 161]
165. 9 <=> strong(mary) [avatar definition]
166. strong(mary) <- (9) [avatar component clause 165]
183. 13 <=> ! [X1] : ~strong(X1) [avatar definition]
184. ~strong(X1) <- (13) [avatar component clause 183]
187. 13 | ~9 | ~8 [avatar split clause 75,161,165,183]
203. 17 <=> brave(paul) [avatar definition]
204. ~brave(paul) <- (~17) [avatar component clause 203]
205. brave(paul) <- (17) [avatar component clause 203]
219. 20 <=> ! [X1] : (curious(X1) | old(X1)) [avatar definition]
220. old(X1) | curious(X1) <- (20) [avatar component clause 219]
221. 20 | ~17 | ~5 [avatar split clause 86,146,203,219]
226. 20 | 17 | 5 [avatar split clause 84,146,203,219]
313. 9 [avatar split clause 126,165]
314. brave(paul) <- (4) [resolution 69,144]
315. $false <- (4, ~17) [subsumption resolution 314,204]
316. ~4 | 17 [avatar contradiction clause 315]
317. calm(paul) <- (17) [resolution 70,205]
318. $false <- (~4, 17) [subsumption resolution 317,143]
319. 4 | ~17 [avatar contradiction clause 318]
344. ~generous(X0) | happy(X0) | curious(X0) <- (20) [resolution 118,220]
376. happy(mary) | curious(mary) <- (20) [resolution 344,128]
379. happy(mary) <- (~8, 20) [subsumption resolution 376,162]
400. old(mary) | ~generous(mary) <- (~8, 20) [resolution 379,117]
401. curious(mary) | ~old(mary) <- (~8, 20) [resolution 379,101]
403. old(mary) <- (~8, 20) [subsumption resolution 400,128]
404. ~old(mary) <- (~8, 20) [subsumption resolution 401,162]
405. $false <- (~8, 20) [subsumption resolution 404,403]
406. 8 | ~20 [avatar contradiction clause 405]
414. $false <- (9, 13) [resolution 184,166]
417. ~9 | ~13 [avatar contradiction clause 414]
418. $false [avatar sat refutation 149,150,187,221,226,313,316,319,406,417]
% SZS output end Proof for 885872181432967448517587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is strong or not brave.
If someone is both not patient and not happy then someone is both not funny and not tall and vice versa.
Everyone who is not brave is rich and vice versa.
If susan is rich then someone is either wise or not creative and vice versa.
If susan is humble or patient then someone is both happy and not curious.
If someone is not calm then mary is either curious or not patient.
Everyone who is creative or not patient is either brave or creative.
Everyone who is generous or humble is tall.
Everyone who is not rich or not old is patient and vice versa.
If someone is not tall or brave then someone is either quiet or not calm.
Everyone who is not creative is either patient or not creative and vice versa.
If paul is both not curious and not creative then alice is both not funny and wise.
If someone is either curious or old then someone is both not kind and not generous.
Everyone who is tall is not generous and vice versa.
Everyone who is either patient or not strong is both not funny and creative and vice versa.
If lucy is both patient and strong then someone is either creative or not strong and vice versa.
Paul is either kind or curious.
Susan is either tall or not calm.
Someone is happy or not old.
Someone is both wise and calm.
Alice is not funny or humble. | Alice is not tall. | contradiction | (![X]:((~humble(X)&happy(X))=>(strong(X)|~brave(X))))&
((?[X]:((~patient(X)&~happy(X))))<=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:(~brave(X)<=>rich(X)))&
((rich(susan))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(((humble(susan)|patient(susan)))=>(?[X]:((happy(X)&~curious(X)))))&
((?[X]:(~calm(X)))=>((curious(mary)<~>~patient(mary))))&
(![X]:((creative(X)|~patient(X))=>(brave(X)<~>creative(X))))&
(![X]:((generous(X)|humble(X))=>tall(X)))&
(![X]:((~rich(X)|~old(X))<=>patient(X)))&
((?[X]:((~tall(X)|brave(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:(~creative(X)<=>(patient(X)<~>~creative(X))))&
(((~curious(paul)&~creative(paul)))=>((~funny(alice)&wise(alice))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~funny(X)&creative(X))))&
(((patient(lucy)&strong(lucy)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
((kind(paul)<~>curious(paul)))&
((tall(susan)<~>~calm(susan)))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:((wise(X)&calm(X))))&
((~funny(alice)|humble(alice))) | ~tall(alice) | [
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3851347426313404646621445
% SZS output start Proof for 3851347426313404646621445
8. ! [X0] : ((humble(X0) | generous(X0)) => tall(X0)) [input p7]
14. ! [X0] : (tall(X0) <=> ~generous(X0)) [input p13]
22. ~tall(alice) [input hypothesis]
31. ! [X0] : (tall(X0) | (~humble(X0) & ~generous(X0))) [ennf transformation 8]
61. ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))) [nnf transformation 14]
96. tall(X0) | ~generous(X0) [cnf transformation 31]
116. tall(X0) | generous(X0) [cnf transformation 61]
137. ~tall(alice) [cnf transformation 22]
235. 22 <=> ! [X1] : tall(X1) [avatar definition]
236. tall(X1) <- (22) [avatar component clause 235]
277. tall(X0) [subsumption resolution 116,96]
278. 22 [avatar split clause 277,235]
326. $false <- (22) [resolution 236,137]
327. ~22 [avatar contradiction clause 326]
328. $false [avatar sat refutation 278,327]
% SZS output end Proof for 3851347426313404646621445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or calm is humble and vice versa.
If mary is either kind or not calm then alice is curious or not kind and vice versa.
If someone is either funny or old then mary is either wise or not humble and vice versa.
If alice is not brave then someone is not strong or quiet.
Everyone who is tall or old is not kind.
Everyone who is both not curious and not quiet is either not humble or quiet and vice versa.
Everyone who is both calm and not generous is both brave and not humble.
If someone is both not rich and curious then someone is either strong or not rich and vice versa.
If fred is both not humble and not calm then someone is both not brave and not rich.
If fred is not curious or old then paul is either not humble or not quiet.
Everyone who is either not happy or patient is either not patient or not rich.
Everyone who is both not funny and not calm is not tall or not rich.
Everyone who is either curious or happy is both not humble and not strong and vice versa.
Everyone who is not rich is not patient and vice versa.
Everyone who is not kind is both rich and wise and vice versa.
Everyone who is either not creative or not strong is either brave or old and vice versa.
Paul is either rich or not kind.
Fred is either curious or generous.
Someone is old.
Someone is not funny.
John is either not calm or quiet.
Mary is both happy and strong.
Someone is not rich or not funny. | Mary is tall. | contradiction | (![X]:((brave(X)<~>calm(X))<=>humble(X)))&
(((kind(mary)<~>~calm(mary)))<=>((curious(alice)|~kind(alice))))&
((?[X]:((funny(X)<~>old(X))))<=>((wise(mary)<~>~humble(mary))))&
((~brave(alice))=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:((tall(X)|old(X))=>~kind(X)))&
(![X]:((~curious(X)&~quiet(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:((calm(X)&~generous(X))=>(brave(X)&~humble(X))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(((~humble(fred)&~calm(fred)))=>(?[X]:((~brave(X)&~rich(X)))))&
(((~curious(fred)|old(fred)))=>((~humble(paul)<~>~quiet(paul))))&
(![X]:((~happy(X)<~>patient(X))=>(~patient(X)<~>~rich(X))))&
(![X]:((~funny(X)&~calm(X))=>(~tall(X)|~rich(X))))&
(![X]:((curious(X)<~>happy(X))<=>(~humble(X)&~strong(X))))&
(![X]:(~rich(X)<=>~patient(X)))&
(![X]:(~kind(X)<=>(rich(X)&wise(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>(brave(X)<~>old(X))))&
((rich(paul)<~>~kind(paul)))&
((curious(fred)<~>generous(fred)))&
(?[X]:(old(X)))&
(?[X]:(~funny(X)))&
((~calm(john)<~>quiet(john)))&
((happy(mary)&strong(mary)))&
(?[X]:((~rich(X)|~funny(X)))) | tall(mary) | [
"p4",
"p10",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8516257766235370326375335
% SZS output start Proof for 8516257766235370326375335
5. ! [X0] : ((old(X0) | tall(X0)) => ~kind(X0)) [input p4]
11. ! [X0] : ((~happy(X0) <~> patient(X0)) => (~patient(X0) <~> ~rich(X0))) [input p10]
14. ! [X0] : (~rich(X0) <=> ~patient(X0)) [input p13]
15. ! [X0] : (~kind(X0) <=> (wise(X0) & rich(X0))) [input p14]
22. strong(mary) & happy(mary) [input p21]
24. tall(mary) [input hypothesis]
27. ! [X0] : (~kind(X0) | (~old(X0) & ~tall(X0))) [ennf transformation 5]
33. ! [X0] : ((~patient(X0) <~> ~rich(X0)) | (~happy(X0) <=> patient(X0))) [ennf transformation 11]
55. ! [X0] : (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) [nnf transformation 33]
58. ! [X0] : ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))) [nnf transformation 14]
59. ! [X0] : ((~kind(X0) | (~wise(X0) | ~rich(X0))) & ((wise(X0) & rich(X0)) | kind(X0))) [nnf transformation 15]
60. ! [X0] : ((~kind(X0) | ~wise(X0) | ~rich(X0)) & ((wise(X0) & rich(X0)) | kind(X0))) [flattening 59]
90. ~tall(X0) | ~kind(X0) [cnf transformation 27]
113. ~rich(X0) | ~patient(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 55]
124. ~rich(X0) | patient(X0) [cnf transformation 58]
125. rich(X0) | kind(X0) [cnf transformation 60]
144. happy(mary) [cnf transformation 22]
147. tall(mary) [cnf transformation 24]
148. ~patient(X0) | ~rich(X0) | ~happy(X0) [duplicate literal removal 113]
157. 2 <=> kind(mary) [avatar definition]
159. ~kind(mary) <- (~2) [avatar component clause 157]
314. ~kind(mary) [resolution 90,147]
318. patient(X0) | kind(X0) [resolution 125,124]
326. ~2 [avatar split clause 314,157]
380. ~rich(X0) | ~happy(X0) | kind(X0) [resolution 148,318]
382. ~happy(X0) | kind(X0) [subsumption resolution 380,125]
440. kind(mary) [resolution 382,144]
444. $false <- (~2) [subsumption resolution 440,159]
445. 2 [avatar contradiction clause 444]
446. $false [avatar sat refutation 326,445]
% SZS output end Proof for 8516257766235370326375335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not humble is either quiet or wise.
If susan is not calm then someone is either curious or rich.
If someone is either not brave or not quiet then susan is either not curious or kind.
Everyone who is not happy or not curious is not funny or patient and vice versa.
If susan is not happy then someone is funny or quiet.
Everyone who is not curious is both not creative and brave and vice versa.
Everyone who is either tall or kind is generous and vice versa.
If john is kind then lucy is not old and vice versa.
If mary is both not curious and not patient then susan is not calm.
If someone is either generous or calm then someone is either not old or not wise.
If someone is both patient and not tall then someone is not humble and vice versa.
Everyone who is both curious and quiet is not kind.
If someone is not tall then susan is curious.
Everyone who is not kind is both rich and strong.
Everyone who is both not calm and calm is humble or creative and vice versa.
Everyone who is both not funny and not patient is not kind or not patient.
Someone is either strong or not patient.
Someone is quiet or not old.
Someone is humble or not brave.
Paul is tall or brave.
Alice is either creative or not patient.
Someone is funny.
Someone is either not quiet or not humble. | John is creative. | contradiction | (![X]:((~tall(X)<~>~humble(X))=>(quiet(X)<~>wise(X))))&
((~calm(susan))=>(?[X]:((curious(X)<~>rich(X)))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>((~curious(susan)<~>kind(susan))))&
(![X]:((~happy(X)|~curious(X))<=>(~funny(X)|patient(X))))&
((~happy(susan))=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:(~curious(X)<=>(~creative(X)&brave(X))))&
(![X]:((tall(X)<~>kind(X))<=>generous(X)))&
((kind(john))<=>(~old(lucy)))&
(((~curious(mary)&~patient(mary)))=>(~calm(susan)))&
((?[X]:((generous(X)<~>calm(X))))=>(?[X]:((~old(X)<~>~wise(X)))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~humble(X))))&
(![X]:((curious(X)&quiet(X))=>~kind(X)))&
((?[X]:(~tall(X)))=>(curious(susan)))&
(![X]:(~kind(X)=>(rich(X)&strong(X))))&
(![X]:((~calm(X)&calm(X))<=>(humble(X)|creative(X))))&
(![X]:((~funny(X)&~patient(X))=>(~kind(X)|~patient(X))))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((quiet(X)|~old(X))))&
(?[X]:((humble(X)|~brave(X))))&
((tall(paul)|brave(paul)))&
((creative(alice)<~>~patient(alice)))&
(?[X]:(funny(X)))&
(?[X]:((~quiet(X)<~>~humble(X)))) | creative(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3432548377944036064177044
% SZS output start Proof for 3432548377944036064177044
15. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (creative(X0) | humble(X0))) [input p14]
24. creative(john) [input hypothesis]
62. ! [X0] : (((calm(X0) & ~calm(X0)) | (~creative(X0) & ~humble(X0))) & ((creative(X0) | humble(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 15]
63. ! [X0] : (((calm(X0) & ~calm(X0)) | (~creative(X0) & ~humble(X0))) & (creative(X0) | humble(X0) | ~calm(X0) | calm(X0))) [flattening 62]
115. ~calm(X0) | ~creative(X0) [cnf transformation 63]
117. calm(X0) | ~creative(X0) [cnf transformation 63]
129. creative(john) [cnf transformation 24]
237. ~creative(X0) [subsumption resolution 115,117]
270. $false [subsumption resolution 129,237]
% SZS output end Proof for 3432548377944036064177044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or kind then someone is both not strong and quiet. Everyone who is either not generous or not patient is strong or not patient and vice versa. Everyone who is either not tall or tall is both not happy and wise and vice versa. Everyone who is kind is both not rich and not quiet. Everyone who is both wise and patient is not strong and vice versa. If someone is both not tall and not old then someone is not creative. Everyone who is not rich is quiet or strong. Everyone who is not tall or not generous is not quiet and vice versa. If someone is both not old and not humble then mary is either funny or not brave and vice versa. Everyone who is not strong is kind or not rich and vice versa. If someone is brave then john is both kind and funny and vice versa. If fred is not patient or not wise then alice is both not patient and old and vice versa. If fred is both not tall and rich then someone is both not wise and creative. Everyone who is either patient or old is both wise and not humble and vice versa. If someone is not humble or not rich then someone is not old or creative. If someone is not calm or not quiet then john is not calm or not happy and vice versa. Someone is both quiet and funny. Paul is not brave or patient. Someone is both not tall and not happy. Someone is both not patient and rich. Someone is not old. Alice is rich or not happy. John is either not curious or generous. Someone is generous. | Paul is not brave. | entailment | ((?[X]:((happy(X)<~>kind(X))))=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((~generous(X)<~>~patient(X))<=>(strong(X)|~patient(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~happy(X)&wise(X))))&
(![X]:(kind(X)=>(~rich(X)&~quiet(X))))&
(![X]:((wise(X)&patient(X))<=>~strong(X)))&
((?[X]:((~tall(X)&~old(X))))=>(?[X]:(~creative(X))))&
(![X]:(~rich(X)=>(quiet(X)|strong(X))))&
(![X]:((~tall(X)|~generous(X))<=>~quiet(X)))&
((?[X]:((~old(X)&~humble(X))))<=>((funny(mary)<~>~brave(mary))))&
(![X]:(~strong(X)<=>(kind(X)|~rich(X))))&
((?[X]:(brave(X)))<=>((kind(john)&funny(john))))&
(((~patient(fred)|~wise(fred)))<=>((~patient(alice)&old(alice))))&
(((~tall(fred)&rich(fred)))=>(?[X]:((~wise(X)&creative(X)))))&
(![X]:((patient(X)<~>old(X))<=>(wise(X)&~humble(X))))&
((?[X]:((~humble(X)|~rich(X))))=>(?[X]:((~old(X)|creative(X)))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((~calm(john)|~happy(john))))&
(?[X]:((quiet(X)&funny(X))))&
((~brave(paul)|patient(paul)))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((~patient(X)&rich(X))))&
(?[X]:(~old(X)))&
((rich(alice)|~happy(alice)))&
((~curious(john)<~>generous(john)))&
(?[X]:(generous(X))) | ~brave(paul) | [
"p3",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 548337196189156548168249
% SZS output start Proof for 548337196189156548168249
4. ! [X0] : (kind(X0) => (~quiet(X0) & ~rich(X0))) [input p3]
7. ! [X0] : (~rich(X0) => (strong(X0) | quiet(X0))) [input p6]
10. ! [X0] : (~strong(X0) <=> (~rich(X0) | kind(X0))) [input p9]
11. ? [X0] : brave(X0) <=> (funny(john) & kind(john)) [input p10]
25. brave(paul) [input hypothesis]
30. ! [X0] : ((~quiet(X0) & ~rich(X0)) | ~kind(X0)) [ennf transformation 4]
32. ! [X0] : ((strong(X0) | quiet(X0)) | rich(X0)) [ennf transformation 7]
33. ! [X0] : (strong(X0) | quiet(X0) | rich(X0)) [flattening 32]
56. ! [X0] : ((~strong(X0) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
57. ! [X0] : ((~strong(X0) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | strong(X0))) [flattening 56]
58. (? [X0] : brave(X0) | (~funny(john) | ~kind(john))) & ((funny(john) & kind(john)) | ! [X0] : ~brave(X0)) [nnf transformation 11]
59. (? [X0] : brave(X0) | ~funny(john) | ~kind(john)) & ((funny(john) & kind(john)) | ! [X0] : ~brave(X0)) [flattening 58]
60. (? [X0] : brave(X0) | ~funny(john) | ~kind(john)) & ((funny(john) & kind(john)) | ! [X1] : ~brave(X1)) [rectify 59]
61. ? [X0] : brave(X0) => brave(sK3) [choice axiom]
62. (brave(sK3) | ~funny(john) | ~kind(john)) & ((funny(john) & kind(john)) | ! [X1] : ~brave(X1)) [skolemisation 60,61]
104. ~rich(X0) | ~kind(X0) [cnf transformation 30]
105. ~quiet(X0) | ~kind(X0) [cnf transformation 30]
110. rich(X0) | quiet(X0) | strong(X0) [cnf transformation 33]
120. ~rich(X0) | kind(X0) | strong(X0) [cnf transformation 57]
121. ~strong(X0) | ~kind(X0) [cnf transformation 57]
123. kind(john) | ~brave(X1) [cnf transformation 62]
157. brave(paul) [cnf transformation 25]
219. ~rich(X0) | strong(X0) [subsumption resolution 120,104]
221. 12 <=> kind(john) [avatar definition]
222. kind(john) <- (12) [avatar component clause 221]
234. 15 <=> ! [X1] : ~brave(X1) [avatar definition]
235. ~brave(X1) <- (15) [avatar component clause 234]
237. 15 | 12 [avatar split clause 123,221,234]
303. 29 <=> brave(paul) [avatar definition]
304. brave(paul) <- (29) [avatar component clause 303]
321. 29 [avatar split clause 157,303]
358. $false <- (15, 29) [resolution 235,304]
359. ~15 | ~29 [avatar contradiction clause 358]
368. quiet(X0) | strong(X0) | strong(X0) [resolution 110,219]
370. quiet(X0) | strong(X0) [duplicate literal removal 368]
383. strong(X2) | ~kind(X2) [resolution 370,105]
384. ~kind(X2) [subsumption resolution 383,121]
398. $false <- (12) [resolution 384,222]
399. ~12 [avatar contradiction clause 398]
400. $false [avatar sat refutation 237,321,359,399]
% SZS output end Proof for 548337196189156548168249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and generous then someone is both strong and happy. Everyone who is not funny or not creative is not rich or not kind and vice versa. Everyone who is not calm or not happy is both not wise and not brave. Everyone who is patient is wise or strong and vice versa. Everyone who is either rich or curious is either not strong or humble and vice versa. Everyone who is not humble is either not calm or not funny. Everyone who is both brave and not old is both wise and not creative. Everyone who is generous is not strong or not funny and vice versa. Everyone who is brave is both kind and not tall and vice versa. Everyone who is either wise or not strong is either kind or not humble and vice versa. Everyone who is funny or not brave is funny and vice versa. If paul is both not calm and calm then someone is quiet or generous and vice versa. Everyone who is tall is either not happy or brave. Everyone who is quiet is either old or wise. If alice is not old or rich then someone is both not tall and not kind. Everyone who is not old is either tall or calm and vice versa. Lucy is wise. Paul is rich. Susan is either rich or not curious. Mary is either generous or not tall. Someone is not brave or not strong. | Susan is old. | contradiction | ((?[X]:((~quiet(X)&generous(X))))=>(?[X]:((strong(X)&happy(X)))))&
(![X]:((~funny(X)|~creative(X))<=>(~rich(X)|~kind(X))))&
(![X]:((~calm(X)|~happy(X))=>(~wise(X)&~brave(X))))&
(![X]:(patient(X)<=>(wise(X)|strong(X))))&
(![X]:((rich(X)<~>curious(X))<=>(~strong(X)<~>humble(X))))&
(![X]:(~humble(X)=>(~calm(X)<~>~funny(X))))&
(![X]:((brave(X)&~old(X))=>(wise(X)&~creative(X))))&
(![X]:(generous(X)<=>(~strong(X)|~funny(X))))&
(![X]:(brave(X)<=>(kind(X)&~tall(X))))&
(![X]:((wise(X)<~>~strong(X))<=>(kind(X)<~>~humble(X))))&
(![X]:((funny(X)|~brave(X))<=>funny(X)))&
(((~calm(paul)&calm(paul)))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:(tall(X)=>(~happy(X)<~>brave(X))))&
(![X]:(quiet(X)=>(old(X)<~>wise(X))))&
(((~old(alice)|rich(alice)))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(~old(X)<=>(tall(X)<~>calm(X))))&
(wise(lucy))&
(rich(paul))&
((rich(susan)<~>~curious(susan)))&
((generous(mary)<~>~tall(mary)))&
(?[X]:((~brave(X)|~strong(X)))) | old(susan) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p9",
"p11",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3023242531583544528433659
% SZS output start Proof for 3023242531583544528433659
3. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~brave(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (~strong(X0) <~> humble(X0))) [input p4]
6. ! [X0] : (~humble(X0) => (~calm(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : (generous(X0) <=> (~funny(X0) | ~strong(X0))) [input p7]
9. ! [X0] : (brave(X0) <=> (~tall(X0) & kind(X0))) [input p8]
10. ! [X0] : ((wise(X0) <~> ~strong(X0)) <=> (kind(X0) <~> ~humble(X0))) [input p9]
12. (calm(paul) & ~calm(paul)) <=> ? [X0] : (generous(X0) | quiet(X0)) [input p11]
13. ! [X0] : (tall(X0) => (~happy(X0) <~> brave(X0))) [input p12]
16. ! [X0] : (~old(X0) <=> (tall(X0) <~> calm(X0))) [input p15]
19. rich(susan) <~> ~curious(susan) [input p18]
22. old(susan) [input hypothesis]
25. ! [X0] : ((~brave(X0) & ~wise(X0)) | (happy(X0) & calm(X0))) [ennf transformation 3]
26. ! [X0] : ((~calm(X0) <~> ~funny(X0)) | humble(X0)) [ennf transformation 6]
29. ! [X0] : ((~happy(X0) <~> brave(X0)) | ~tall(X0)) [ennf transformation 13]
37. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 5]
38. ! [X0] : (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | humble(X0)) [nnf transformation 26]
39. ! [X0] : ((generous(X0) | (funny(X0) & strong(X0))) & ((~funny(X0) | ~strong(X0)) | ~generous(X0))) [nnf transformation 8]
40. ! [X0] : ((generous(X0) | (funny(X0) & strong(X0))) & (~funny(X0) | ~strong(X0) | ~generous(X0))) [flattening 39]
41. ! [X0] : ((brave(X0) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | ~brave(X0))) [nnf transformation 9]
42. ! [X0] : ((brave(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | ~brave(X0))) [flattening 41]
43. ! [X0] : ((((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) & (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))))) [nnf transformation 10]
46. ((calm(paul) & ~calm(paul)) | ! [X0] : (~generous(X0) & ~quiet(X0))) & (? [X0] : (generous(X0) | quiet(X0)) | (~calm(paul) | calm(paul))) [nnf transformation 12]
47. ((calm(paul) & ~calm(paul)) | ! [X0] : (~generous(X0) & ~quiet(X0))) & (? [X0] : (generous(X0) | quiet(X0)) | ~calm(paul) | calm(paul)) [flattening 46]
48. ((calm(paul) & ~calm(paul)) | ! [X0] : (~generous(X0) & ~quiet(X0))) & (? [X1] : (generous(X1) | quiet(X1)) | ~calm(paul) | calm(paul)) [rectify 47]
49. ? [X1] : (generous(X1) | quiet(X1)) => (generous(sK1) | quiet(sK1)) [choice axiom]
50. ((calm(paul) & ~calm(paul)) | ! [X0] : (~generous(X0) & ~quiet(X0))) & ((generous(sK1) | quiet(sK1)) | ~calm(paul) | calm(paul)) [skolemisation 48,49]
51. ! [X0] : (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~tall(X0)) [nnf transformation 29]
55. ! [X0] : ((~old(X0) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0)))) & (((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | old(X0))) [nnf transformation 16]
56. (curious(susan) | ~rich(susan)) & (~curious(susan) | rich(susan)) [nnf transformation 19]
66. ~wise(X0) | calm(X0) [cnf transformation 25]
67. ~wise(X0) | happy(X0) [cnf transformation 25]
68. ~brave(X0) | calm(X0) [cnf transformation 25]
75. ~humble(X0) | rich(X0) | ~strong(X0) | curious(X0) [cnf transformation 37]
77. ~humble(X0) | ~rich(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 37]
78. ~calm(X0) | ~funny(X0) | humble(X0) [cnf transformation 38]
83. strong(X0) | generous(X0) [cnf transformation 40]
84. funny(X0) | generous(X0) [cnf transformation 40]
86. ~tall(X0) | ~brave(X0) [cnf transformation 42]
87. ~kind(X0) | tall(X0) | brave(X0) [cnf transformation 42]
92. ~humble(X0) | wise(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 43]
93. ~strong(X0) | wise(X0) | kind(X0) | humble(X0) [cnf transformation 43]
101. ~calm(paul) | ~generous(X0) [cnf transformation 50]
103. calm(paul) | ~generous(X0) [cnf transformation 50]
104. brave(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 51]
114. ~tall(X0) | calm(X0) | ~old(X0) [cnf transformation 55]
115. ~old(X0) | tall(X0) | ~calm(X0) [cnf transformation 55]
118. ~curious(susan) | rich(susan) [cnf transformation 56]
119. curious(susan) | ~rich(susan) [cnf transformation 56]
123. old(susan) [cnf transformation 22]
138. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
139. ~generous(X0) <- (4) [avatar component clause 138]
141. 5 <=> calm(paul) [avatar definition]
144. 4 | 5 [avatar split clause 103,141,138]
149. 4 | ~5 [avatar split clause 101,141,138]
151. ~tall(X0) | ~happy(X0) [subsumption resolution 104,86]
173. 11 <=> rich(susan) [avatar definition]
174. rich(susan) <- (11) [avatar component clause 173]
175. ~rich(susan) <- (~11) [avatar component clause 173]
177. 12 <=> curious(susan) [avatar definition]
178. ~curious(susan) <- (~12) [avatar component clause 177]
179. curious(susan) <- (12) [avatar component clause 177]
180. ~11 | 12 [avatar split clause 119,177,173]
181. 11 | ~12 [avatar split clause 118,177,173]
275. tall(susan) | ~calm(susan) [resolution 115,123]
278. 23 <=> calm(susan) [avatar definition]
279. calm(susan) <- (23) [avatar component clause 278]
280. ~calm(susan) <- (~23) [avatar component clause 278]
282. 24 <=> tall(susan) [avatar definition]
284. tall(susan) <- (24) [avatar component clause 282]
285. ~23 | 24 [avatar split clause 275,282,278]
371. wise(X0) | kind(X0) | humble(X0) | generous(X0) [resolution 93,83]
386. humble(X0) | kind(X0) | wise(X0) <- (4) [subsumption resolution 371,139]
479. ~curious(X3) | wise(X3) | ~rich(X3) | ~strong(X3) | kind(X3) <- (4) [resolution 386,77]
592. 46 <=> kind(susan) [avatar definition]
594. kind(susan) <- (46) [avatar component clause 592]
596. 47 <=> wise(susan) [avatar definition]
598. wise(susan) <- (47) [avatar component clause 596]
647. tall(susan) | brave(susan) <- (46) [resolution 594,87]
651. 52 <=> strong(susan) [avatar definition]
652. ~strong(susan) <- (~52) [avatar component clause 651]
653. strong(susan) <- (52) [avatar component clause 651]
655. 53 <=> humble(susan) [avatar definition]
656. ~humble(susan) <- (~53) [avatar component clause 655]
657. humble(susan) <- (53) [avatar component clause 655]
660. 54 <=> brave(susan) [avatar definition]
662. brave(susan) <- (54) [avatar component clause 660]
663. 54 | 24 | ~46 [avatar split clause 647,592,282,660]
711. rich(susan) | ~strong(susan) | curious(susan) <- (53) [resolution 657,75]
715. wise(susan) | ~strong(susan) | ~kind(susan) <- (53) [resolution 657,92]
717. ~strong(susan) | curious(susan) <- (~11, 53) [subsumption resolution 711,175]
718. ~strong(susan) <- (~11, ~12, 53) [subsumption resolution 717,178]
719. ~52 | 11 | 12 | ~53 [avatar split clause 718,655,177,173,651]
720. wise(susan) | ~strong(susan) <- (46, 53) [subsumption resolution 715,594]
721. ~52 | 47 | ~46 | ~53 [avatar split clause 720,655,592,596,651]
727. generous(susan) <- (~52) [resolution 652,83]
728. $false <- (4, ~52) [subsumption resolution 727,139]
729. ~4 | 52 [avatar contradiction clause 728]
767. kind(susan) | wise(susan) <- (4, ~53) [resolution 656,386]
788. calm(susan) <- (54) [resolution 662,68]
789. $false <- (~23, 54) [subsumption resolution 788,280]
790. 23 | ~54 [avatar contradiction clause 789]
791. 47 | 46 | ~4 | 53 [avatar split clause 767,655,138,592,596]
798. calm(susan) <- (47) [resolution 598,66]
799. $false <- (~23, 47) [subsumption resolution 798,280]
800. 23 | ~47 [avatar contradiction clause 799]
803. wise(susan) | ~rich(susan) | ~strong(susan) | kind(susan) <- (4, 12) [resolution 179,479]
811. wise(susan) | ~strong(susan) | kind(susan) <- (4, 11, 12) [subsumption resolution 803,174]
812. wise(susan) | kind(susan) <- (4, 11, 12, 52) [subsumption resolution 811,653]
816. calm(susan) | ~old(susan) <- (24) [resolution 284,114]
818. ~happy(susan) <- (24) [resolution 284,151]
819. ~brave(susan) <- (24) [resolution 284,86]
823. happy(susan) <- (47) [resolution 598,67]
825. $false <- (24, 47) [subsumption resolution 823,818]
826. ~24 | ~47 [avatar contradiction clause 825]
827. 46 | 47 | ~4 | ~11 | ~12 | ~52 [avatar split clause 812,651,177,173,138,596,592]
830. calm(susan) <- (24) [subsumption resolution 816,123]
831. 23 | ~24 [avatar split clause 830,282,278]
832. ~54 | ~24 [avatar split clause 819,282,660]
836. ~funny(susan) | humble(susan) <- (23) [resolution 279,78]
837. ~funny(susan) <- (23, ~53) [subsumption resolution 836,656]
839. generous(susan) <- (23, ~53) [resolution 837,84]
842. $false <- (4, 23, ~53) [subsumption resolution 839,139]
843. ~4 | ~23 | 53 [avatar contradiction clause 842]
844. $false [avatar sat refutation 144,149,180,181,285,663,719,721,729,790,791,800,826,827,831,832,843]
% SZS output end Proof for 3023242531583544528433659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or not strong then someone is both not tall and brave and vice versa.
If someone is humble or quiet then mary is either not curious or tall and vice versa.
If fred is brave or not old then fred is strong.
If someone is brave or not happy then someone is either humble or not calm and vice versa.
Everyone who is either not humble or rich is both calm and strong and vice versa.
If someone is wise then lucy is either not calm or not old and vice versa.
Everyone who is either not generous or not quiet is either brave or not quiet and vice versa.
If someone is not quiet or wise then mary is either kind or tall.
If alice is not patient or not happy then john is brave and vice versa.
Everyone who is not calm is both not strong and not wise and vice versa.
If someone is not patient then fred is either not quiet or wise.
Everyone who is kind or generous is not rich or wise.
If fred is either not patient or not funny then someone is wise and vice versa.
Everyone who is either not tall or not strong is both not creative and calm.
Everyone who is both tall and calm is not tall or not funny and vice versa.
Someone is either not curious or not rich.
Someone is either humble or not patient.
Lucy is kind.
Someone is not wise.
Paul is not old.
Lucy is old or funny.
Someone is not patient or not curious.
Susan is not curious or not patient. | Fred is not quiet. | entailment | ((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((~tall(X)&brave(X)))))&
((?[X]:((humble(X)|quiet(X))))<=>((~curious(mary)<~>tall(mary))))&
(((brave(fred)|~old(fred)))=>(strong(fred)))&
((?[X]:((brave(X)|~happy(X))))<=>(?[X]:((humble(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>rich(X))<=>(calm(X)&strong(X))))&
((?[X]:(wise(X)))<=>((~calm(lucy)<~>~old(lucy))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(brave(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)|wise(X))))=>((kind(mary)<~>tall(mary))))&
(((~patient(alice)|~happy(alice)))<=>(brave(john)))&
(![X]:(~calm(X)<=>(~strong(X)&~wise(X))))&
((?[X]:(~patient(X)))=>((~quiet(fred)<~>wise(fred))))&
(![X]:((kind(X)|generous(X))=>(~rich(X)|wise(X))))&
(((~patient(fred)<~>~funny(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~creative(X)&calm(X))))&
(![X]:((tall(X)&calm(X))<=>(~tall(X)|~funny(X))))&
(?[X]:((~curious(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
(kind(lucy))&
(?[X]:(~wise(X)))&
(~old(paul))&
((old(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|~curious(X))))&
((~curious(susan)|~patient(susan))) | ~quiet(fred) | [
"p5",
"p9",
"p10",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6702776766365506837212393
% SZS output start Proof for 6702776766365506837212393
6. ? [X0] : wise(X0) <=> (~calm(lucy) <~> ~old(lucy)) [input p5]
10. ! [X0] : (~calm(X0) <=> (~wise(X0) & ~strong(X0))) [input p9]
11. ? [X0] : ~patient(X0) => (~quiet(fred) <~> wise(fred)) [input p10]
13. (~patient(fred) <~> ~funny(fred)) <=> ? [X0] : wise(X0) [input p12]
14. ! [X0] : ((~tall(X0) <~> ~strong(X0)) => (calm(X0) & ~creative(X0))) [input p13]
15. ! [X0] : ((calm(X0) & tall(X0)) <=> (~funny(X0) | ~tall(X0))) [input p14]
21. funny(lucy) | old(lucy) [input p20]
24. quiet(fred) [input hypothesis]
27. ! [X0] : ((~tall(X0) <~> ~strong(X0)) => calm(X0)) [pure predicate removal 14]
30. (~quiet(fred) <~> wise(fred)) | ! [X0] : patient(X0) [ennf transformation 11]
33. ! [X0] : (calm(X0) | (~tall(X0) <=> ~strong(X0))) [ennf transformation 27]
50. (? [X0] : wise(X0) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X0] : ~wise(X0)) [nnf transformation 6]
51. (? [X0] : wise(X0) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X1] : ~wise(X1)) [rectify 50]
52. ? [X0] : wise(X0) => wise(sK5) [choice axiom]
53. (wise(sK5) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X1] : ~wise(X1)) [skolemisation 51,52]
58. ! [X0] : ((~calm(X0) | (wise(X0) | strong(X0))) & ((~wise(X0) & ~strong(X0)) | calm(X0))) [nnf transformation 10]
59. ! [X0] : ((~calm(X0) | wise(X0) | strong(X0)) & ((~wise(X0) & ~strong(X0)) | calm(X0))) [flattening 58]
60. ((~wise(fred) | quiet(fred)) & (wise(fred) | ~quiet(fred))) | ! [X0] : patient(X0) [nnf transformation 30]
61. (((funny(fred) | patient(fred)) & (~funny(fred) | ~patient(fred))) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | ((~patient(fred) | funny(fred)) & (~funny(fred) | patient(fred)))) [nnf transformation 13]
62. (((funny(fred) | patient(fred)) & (~funny(fred) | ~patient(fred))) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | ((~patient(fred) | funny(fred)) & (~funny(fred) | patient(fred)))) [rectify 61]
63. ? [X1] : wise(X1) => wise(sK6) [choice axiom]
64. (((funny(fred) | patient(fred)) & (~funny(fred) | ~patient(fred))) | ! [X0] : ~wise(X0)) & (wise(sK6) | ((~patient(fred) | funny(fred)) & (~funny(fred) | patient(fred)))) [skolemisation 62,63]
65. ! [X0] : (calm(X0) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 33]
66. ! [X0] : (((calm(X0) & tall(X0)) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | (~calm(X0) | ~tall(X0)))) [nnf transformation 15]
67. ! [X0] : (((calm(X0) & tall(X0)) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | ~calm(X0) | ~tall(X0))) [flattening 66]
104. ~old(lucy) | ~calm(lucy) | ~wise(X1) [cnf transformation 53]
123. ~strong(X0) | calm(X0) [cnf transformation 59]
126. wise(fred) | ~quiet(fred) | patient(X0) [cnf transformation 60]
131. wise(sK6) | ~patient(fred) | funny(fred) [cnf transformation 64]
135. calm(X0) | ~tall(X0) | strong(X0) [cnf transformation 65]
136. ~funny(X0) | ~tall(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 67]
137. tall(X0) | tall(X0) [cnf transformation 67]
139. calm(X0) | tall(X0) [cnf transformation 67]
148. funny(lucy) | old(lucy) [cnf transformation 21]
151. quiet(fred) [cnf transformation 24]
152. ~funny(X0) | ~tall(X0) | ~calm(X0) [duplicate literal removal 136]
153. tall(X0) [duplicate literal removal 137]
266. 25 <=> old(lucy) [avatar definition]
270. 26 <=> calm(lucy) [avatar definition]
272. ~calm(lucy) <- (~26) [avatar component clause 270]
280. 28 <=> ! [X1] : ~wise(X1) [avatar definition]
281. ~wise(X1) <- (28) [avatar component clause 280]
283. 28 | ~26 | ~25 [avatar split clause 104,266,270,280]
313. 34 <=> ! [X0] : patient(X0) [avatar definition]
314. patient(X0) <- (34) [avatar component clause 313]
316. 35 <=> quiet(fred) [avatar definition]
320. 36 <=> wise(fred) [avatar definition]
321. wise(fred) <- (36) [avatar component clause 320]
324. 34 | ~35 | 36 [avatar split clause 126,320,316,313]
326. 37 <=> patient(fred) [avatar definition]
327. ~patient(fred) <- (~37) [avatar component clause 326]
330. 38 <=> funny(fred) [avatar definition]
332. funny(fred) <- (38) [avatar component clause 330]
336. 39 <=> wise(sK6) [avatar definition]
338. wise(sK6) <- (39) [avatar component clause 336]
339. 38 | ~37 | 39 [avatar split clause 131,336,326,330]
341. calm(X0) | ~tall(X0) [subsumption resolution 135,123]
342. calm(X0) [subsumption resolution 139,341]
343. ~funny(X0) | ~calm(X0) [subsumption resolution 152,153]
344. ~funny(X0) [subsumption resolution 343,342]
365. old(lucy) [subsumption resolution 148,344]
366. 25 [avatar split clause 365,266]
385. 35 [avatar split clause 151,316]
391. $false <- (34, ~37) [resolution 327,314]
392. ~34 | 37 [avatar contradiction clause 391]
393. $false <- (28, 36) [subsumption resolution 321,281]
394. ~28 | ~36 [avatar contradiction clause 393]
395. $false <- (38) [subsumption resolution 332,344]
396. ~38 [avatar contradiction clause 395]
397. $false <- (28, 39) [subsumption resolution 338,281]
398. ~28 | ~39 [avatar contradiction clause 397]
399. $false <- (~26) [subsumption resolution 272,342]
400. 26 [avatar contradiction clause 399]
401. $false [avatar sat refutation 283,324,339,366,385,392,394,396,398,400]
% SZS output end Proof for 6702776766365506837212393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either humble or not calm then someone is not generous and vice versa.
If lucy is not rich then someone is either not generous or calm and vice versa.
Everyone who is both tall and not curious is either not old or not patient and vice versa.
Everyone who is wise is not kind and vice versa.
Everyone who is both not quiet and rich is not quiet.
If someone is not calm then alice is both not patient and happy.
If fred is not brave or curious then someone is not tall or not patient.
Everyone who is kind or not brave is both not funny and not creative.
Everyone who is happy or curious is not happy.
Everyone who is generous or old is not old or rich and vice versa.
Everyone who is either wise or funny is kind or patient and vice versa.
If someone is both old and not creative then alice is not old.
Everyone who is either creative or tall is not tall.
Everyone who is both tall and creative is not humble or not brave.
Everyone who is not old or not funny is both generous and not tall.
If someone is not brave then someone is not strong or curious and vice versa.
Someone is quiet.
Someone is not generous.
Mary is either not generous or not creative.
Alice is either quiet or strong.
Susan is not brave or not tall. | Mary is not creative. | entailment | (((humble(mary)<~>~calm(mary)))<=>(?[X]:(~generous(X))))&
((~rich(lucy))<=>(?[X]:((~generous(X)<~>calm(X)))))&
(![X]:((tall(X)&~curious(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(wise(X)<=>~kind(X)))&
(![X]:((~quiet(X)&rich(X))=>~quiet(X)))&
((?[X]:(~calm(X)))=>((~patient(alice)&happy(alice))))&
(((~brave(fred)|curious(fred)))=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((kind(X)|~brave(X))=>(~funny(X)&~creative(X))))&
(![X]:((happy(X)|curious(X))=>~happy(X)))&
(![X]:((generous(X)|old(X))<=>(~old(X)|rich(X))))&
(![X]:((wise(X)<~>funny(X))<=>(kind(X)|patient(X))))&
((?[X]:((old(X)&~creative(X))))=>(~old(alice)))&
(![X]:((creative(X)<~>tall(X))=>~tall(X)))&
(![X]:((tall(X)&creative(X))=>(~humble(X)|~brave(X))))&
(![X]:((~old(X)|~funny(X))=>(generous(X)&~tall(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((~strong(X)|curious(X)))))&
(?[X]:(quiet(X)))&
(?[X]:(~generous(X)))&
((~generous(mary)<~>~creative(mary)))&
((quiet(alice)<~>strong(alice)))&
((~brave(susan)|~tall(susan))) | ~creative(mary) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p12",
"p13",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 81857982526548892379241
% SZS output start Proof for 81857982526548892379241
1. (humble(mary) <~> ~calm(mary)) <=> ? [X0] : ~generous(X0) [input p0]
3. ! [X0] : ((~curious(X0) & tall(X0)) <=> (~old(X0) <~> ~patient(X0))) [input p2]
4. ! [X0] : (wise(X0) <=> ~kind(X0)) [input p3]
6. ? [X0] : ~calm(X0) => (happy(alice) & ~patient(alice)) [input p5]
8. ! [X0] : ((~brave(X0) | kind(X0)) => (~creative(X0) & ~funny(X0))) [input p7]
9. ! [X0] : ((curious(X0) | happy(X0)) => ~happy(X0)) [input p8]
10. ! [X0] : ((old(X0) | generous(X0)) <=> (rich(X0) | ~old(X0))) [input p9]
11. ! [X0] : ((wise(X0) <~> funny(X0)) <=> (patient(X0) | kind(X0))) [input p10]
13. ! [X0] : ((creative(X0) <~> tall(X0)) => ~tall(X0)) [input p12]
14. ! [X0] : ((creative(X0) & tall(X0)) => (~brave(X0) | ~humble(X0))) [input p13]
15. ! [X0] : ((~funny(X0) | ~old(X0)) => (~tall(X0) & generous(X0))) [input p14]
18. ? [X0] : ~generous(X0) [input p17]
19. ~generous(mary) <~> ~creative(mary) [input p18]
22. creative(mary) [input hypothesis]
26. (happy(alice) & ~patient(alice)) | ! [X0] : calm(X0) [ennf transformation 6]
28. ! [X0] : ((~creative(X0) & ~funny(X0)) | (brave(X0) & ~kind(X0))) [ennf transformation 8]
29. ! [X0] : (~happy(X0) | (~curious(X0) & ~happy(X0))) [ennf transformation 9]
31. ! [X0] : (~tall(X0) | (creative(X0) <=> tall(X0))) [ennf transformation 13]
32. ! [X0] : ((~brave(X0) | ~humble(X0)) | (~creative(X0) | ~tall(X0))) [ennf transformation 14]
33. ! [X0] : (~brave(X0) | ~humble(X0) | ~creative(X0) | ~tall(X0)) [flattening 32]
34. ! [X0] : ((~tall(X0) & generous(X0)) | (funny(X0) & old(X0))) [ennf transformation 15]
35. (((calm(mary) | ~humble(mary)) & (~calm(mary) | humble(mary))) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ((humble(mary) | calm(mary)) & (~calm(mary) | ~humble(mary)))) [nnf transformation 1]
36. (((calm(mary) | ~humble(mary)) & (~calm(mary) | humble(mary))) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ((humble(mary) | calm(mary)) & (~calm(mary) | ~humble(mary)))) [rectify 35]
37. ? [X1] : ~generous(X1) => ~generous(sK0) [choice axiom]
38. (((calm(mary) | ~humble(mary)) & (~calm(mary) | humble(mary))) | ! [X0] : generous(X0)) & (~generous(sK0) | ((humble(mary) | calm(mary)) & (~calm(mary) | ~humble(mary)))) [skolemisation 36,37]
43. ! [X0] : (((~curious(X0) & tall(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (curious(X0) | ~tall(X0)))) [nnf transformation 3]
44. ! [X0] : (((~curious(X0) & tall(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | curious(X0) | ~tall(X0))) [flattening 43]
45. ! [X0] : ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0))) [nnf transformation 4]
48. ! [X0] : (((old(X0) | generous(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (~old(X0) & ~generous(X0)))) [nnf transformation 10]
49. ! [X0] : ((old(X0) | generous(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | (~old(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 11]
51. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [flattening 50]
52. ! [X0] : (~tall(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) [nnf transformation 31]
60. ? [X0] : ~generous(X0) => ~generous(sK6) [choice axiom]
61. ~generous(sK6) [skolemisation 18,60]
62. (creative(mary) | generous(mary)) & (~creative(mary) | ~generous(mary)) [nnf transformation 19]
66. ~calm(mary) | humble(mary) | generous(X0) [cnf transformation 38]
75. ~old(X0) | tall(X0) | patient(X0) [cnf transformation 44]
78. ~kind(X0) | ~wise(X0) [cnf transformation 45]
79. kind(X0) | wise(X0) [cnf transformation 45]
82. happy(alice) | calm(X0) [cnf transformation 26]
85. ~funny(X0) | ~kind(X0) [cnf transformation 28]
88. ~creative(X0) | brave(X0) [cnf transformation 28]
89. ~happy(X0) | ~happy(X0) [cnf transformation 29]
93. old(X0) | generous(X0) | old(X0) [cnf transformation 49]
97. funny(X0) | wise(X0) | ~kind(X0) [cnf transformation 51]
100. ~funny(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 51]
103. ~tall(X0) | creative(X0) | ~tall(X0) [cnf transformation 52]
104. ~brave(X0) | ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 33]
106. funny(X0) | generous(X0) [cnf transformation 34]
113. ~generous(sK6) [cnf transformation 61]
114. ~creative(mary) | ~generous(mary) [cnf transformation 62]
119. creative(mary) [cnf transformation 22]
120. ~tall(X0) | creative(X0) [duplicate literal removal 103]
122. old(X0) | generous(X0) [duplicate literal removal 93]
123. ~happy(X0) [duplicate literal removal 89]
125. 1 <=> ! [X0] : generous(X0) [avatar definition]
126. generous(X0) <- (1) [avatar component clause 125]
128. 2 <=> humble(mary) [avatar definition]
129. humble(mary) <- (2) [avatar component clause 128]
132. 3 <=> calm(mary) [avatar definition]
133. ~calm(mary) <- (~3) [avatar component clause 132]
136. 1 | 2 | ~3 [avatar split clause 66,132,128,125]
166. 10 <=> ! [X0] : calm(X0) [avatar definition]
167. calm(X0) <- (10) [avatar component clause 166]
169. 11 <=> happy(alice) [avatar definition]
171. happy(alice) <- (11) [avatar component clause 169]
172. 10 | 11 [avatar split clause 82,169,166]
196. wise(X0) | ~kind(X0) [subsumption resolution 97,85]
197. ~kind(X0) [subsumption resolution 196,78]
207. ~humble(X0) | ~creative(X0) | ~tall(X0) [subsumption resolution 104,88]
208. ~tall(X0) | ~humble(X0) [subsumption resolution 207,120]
234. 25 <=> generous(mary) [avatar definition]
235. ~generous(mary) <- (~25) [avatar component clause 234]
238. 26 <=> creative(mary) [avatar definition]
242. ~25 | ~26 [avatar split clause 114,238,234]
262. 26 [avatar split clause 119,238]
265. $false <- (~3, 10) [subsumption resolution 133,167]
266. 3 | ~10 [avatar contradiction clause 265]
267. $false <- (11) [subsumption resolution 171,123]
268. ~11 [avatar contradiction clause 267]
271. wise(X1) [resolution 79,197]
281. patient(X0) | tall(X0) | generous(X0) [resolution 75,122]
286. ~wise(X0) | ~patient(X0) | generous(X0) [resolution 100,106]
287. ~patient(X0) | generous(X0) [subsumption resolution 286,271]
321. tall(X1) | generous(X1) | generous(X1) [resolution 281,287]
326. tall(X1) | generous(X1) [duplicate literal removal 321]
330. ~humble(X1) | generous(X1) [resolution 326,208]
334. generous(mary) <- (2) [resolution 330,129]
335. $false <- (2, ~25) [subsumption resolution 334,235]
336. ~2 | 25 [avatar contradiction clause 335]
339. $false <- (1) [resolution 126,113]
340. ~1 [avatar contradiction clause 339]
343. $false [avatar sat refutation 136,172,242,262,266,268,336,340]
% SZS output end Proof for 81857982526548892379241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and rich then fred is not calm or old and vice versa.
Everyone who is humble is not quiet.
Everyone who is not funny is happy and vice versa.
Everyone who is both wise and not quiet is not curious.
Everyone who is not kind or not funny is both rich and calm.
If lucy is not wise or not quiet then mary is both creative and not patient.
If paul is both not generous and not wise then someone is either not funny or patient and vice versa.
Everyone who is not calm is wise.
Everyone who is either kind or not patient is either not quiet or kind.
If someone is not funny then someone is either funny or not patient and vice versa.
If someone is either not rich or old then someone is either kind or calm.
Everyone who is not patient is both brave and old.
Everyone who is both rich and not rich is both rich and old and vice versa.
Everyone who is generous or funny is not rich and vice versa.
If someone is not calm then alice is both not calm and not old.
Everyone who is creative is not calm.
John is either not funny or not strong.
John is not old or wise.
Someone is either not happy or quiet.
Someone is not kind.
Fred is not tall.
Someone is both wise and not happy.
Someone is not funny.
Fred is either not old or not curious. | Paul is creative. | contradiction | ((?[X]:((~calm(X)&rich(X))))<=>((~calm(fred)|old(fred))))&
(![X]:(humble(X)=>~quiet(X)))&
(![X]:(~funny(X)<=>happy(X)))&
(![X]:((wise(X)&~quiet(X))=>~curious(X)))&
(![X]:((~kind(X)|~funny(X))=>(rich(X)&calm(X))))&
(((~wise(lucy)|~quiet(lucy)))=>((creative(mary)&~patient(mary))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(~calm(X)=>wise(X)))&
(![X]:((kind(X)<~>~patient(X))=>(~quiet(X)<~>kind(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((funny(X)<~>~patient(X)))))&
((?[X]:((~rich(X)<~>old(X))))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:(~patient(X)=>(brave(X)&old(X))))&
(![X]:((rich(X)&~rich(X))<=>(rich(X)&old(X))))&
(![X]:((generous(X)|funny(X))<=>~rich(X)))&
((?[X]:(~calm(X)))=>((~calm(alice)&~old(alice))))&
(![X]:(creative(X)=>~calm(X)))&
((~funny(john)<~>~strong(john)))&
((~old(john)|wise(john)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:(~kind(X)))&
(~tall(fred))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:(~funny(X)))&
((~old(fred)<~>~curious(fred))) | creative(paul) | [
"p6",
"p7",
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9093505150131954599725539
% SZS output start Proof for 9093505150131954599725539
7. (~wise(paul) & ~generous(paul)) <=> ? [X0] : (~funny(X0) <~> patient(X0)) [input p6]
8. ! [X0] : (~calm(X0) => wise(X0)) [input p7]
10. ? [X0] : ~funny(X0) <=> ? [X0] : (funny(X0) <~> ~patient(X0)) [input p9]
16. ! [X0] : (creative(X0) => ~calm(X0)) [input p15]
23. ? [X0] : ~funny(X0) [input p22]
25. creative(paul) [input hypothesis]
26. ? [X0] : ~funny(X0) <=> ? [X1] : (funny(X1) <~> ~patient(X1)) [rectify 10]
35. ! [X0] : (wise(X0) | calm(X0)) [ennf transformation 8]
40. ! [X0] : (~calm(X0) | ~creative(X0)) [ennf transformation 16]
47. ((~wise(paul) & ~generous(paul)) | ! [X0] : ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (? [X0] : ((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (wise(paul) | generous(paul))) [nnf transformation 7]
48. ((~wise(paul) & ~generous(paul)) | ! [X0] : ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (? [X0] : ((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | wise(paul) | generous(paul)) [flattening 47]
49. ((~wise(paul) & ~generous(paul)) | ! [X0] : ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (? [X1] : ((~patient(X1) | funny(X1)) & (patient(X1) | ~funny(X1))) | wise(paul) | generous(paul)) [rectify 48]
50. ? [X1] : ((~patient(X1) | funny(X1)) & (patient(X1) | ~funny(X1))) => ((~patient(sK1) | funny(sK1)) & (patient(sK1) | ~funny(sK1))) [choice axiom]
51. ((~wise(paul) & ~generous(paul)) | ! [X0] : ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(sK1) | funny(sK1)) & (patient(sK1) | ~funny(sK1))) | wise(paul) | generous(paul)) [skolemisation 49,50]
53. (? [X0] : ~funny(X0) | ! [X1] : ((funny(X1) | patient(X1)) & (~patient(X1) | ~funny(X1)))) & (? [X1] : ((patient(X1) | ~funny(X1)) & (~patient(X1) | funny(X1))) | ! [X0] : funny(X0)) [nnf transformation 26]
54. (? [X0] : ~funny(X0) | ! [X1] : ((funny(X1) | patient(X1)) & (~patient(X1) | ~funny(X1)))) & (? [X2] : ((patient(X2) | ~funny(X2)) & (~patient(X2) | funny(X2))) | ! [X3] : funny(X3)) [rectify 53]
55. ? [X0] : ~funny(X0) => ~funny(sK2) [choice axiom]
56. ? [X2] : ((patient(X2) | ~funny(X2)) & (~patient(X2) | funny(X2))) => ((patient(sK3) | ~funny(sK3)) & (~patient(sK3) | funny(sK3))) [choice axiom]
57. (~funny(sK2) | ! [X1] : ((funny(X1) | patient(X1)) & (~patient(X1) | ~funny(X1)))) & (((patient(sK3) | ~funny(sK3)) & (~patient(sK3) | funny(sK3))) | ! [X3] : funny(X3)) [skolemisation 54,56,55]
74. ? [X0] : ~funny(X0) => ~funny(sK8) [choice axiom]
75. ~funny(sK8) [skolemisation 23,74]
97. ~wise(paul) | patient(X0) | funny(X0) [cnf transformation 51]
98. ~wise(paul) | ~funny(X0) | ~patient(X0) [cnf transformation 51]
99. wise(X0) | calm(X0) [cnf transformation 35]
104. ~patient(sK3) | funny(sK3) | funny(X3) [cnf transformation 57]
105. patient(sK3) | ~funny(sK3) | funny(X3) [cnf transformation 57]
122. ~creative(X0) | ~calm(X0) [cnf transformation 40]
131. ~funny(sK8) [cnf transformation 75]
134. creative(paul) [cnf transformation 25]
184. 10 <=> ! [X0] : (~funny(X0) | ~patient(X0)) [avatar definition]
185. ~patient(X0) | ~funny(X0) <- (10) [avatar component clause 184]
187. 11 <=> wise(paul) [avatar definition]
189. ~wise(paul) <- (~11) [avatar component clause 187]
190. 10 | ~11 [avatar split clause 98,187,184]
192. 12 <=> ! [X0] : (patient(X0) | funny(X0)) [avatar definition]
193. patient(X0) | funny(X0) <- (12) [avatar component clause 192]
194. 12 | ~11 [avatar split clause 97,187,192]
218. 17 <=> ! [X3] : funny(X3) [avatar definition]
219. funny(X3) <- (17) [avatar component clause 218]
221. 18 <=> funny(sK3) [avatar definition]
222. funny(sK3) <- (18) [avatar component clause 221]
225. 19 <=> patient(sK3) [avatar definition]
226. ~patient(sK3) <- (~19) [avatar component clause 225]
227. patient(sK3) <- (19) [avatar component clause 225]
228. 17 | ~18 | 19 [avatar split clause 105,225,221,218]
229. 17 | 18 | ~19 [avatar split clause 104,225,221,218]
308. calm(paul) <- (~11) [resolution 99,189]
317. ~calm(paul) [resolution 122,134]
318. $false <- (~11) [subsumption resolution 317,308]
319. 11 [avatar contradiction clause 318]
331. funny(sK3) <- (12, ~19) [resolution 193,226]
338. 18 | ~12 | 19 [avatar split clause 331,225,192,221]
341. $false <- (17) [resolution 219,131]
342. ~17 [avatar contradiction clause 341]
346. ~funny(sK3) <- (10, 19) [resolution 227,185]
347. $false <- (10, 18, 19) [subsumption resolution 346,222]
348. ~10 | ~18 | ~19 [avatar contradiction clause 347]
349. $false [avatar sat refutation 190,194,228,229,319,338,342,348]
% SZS output end Proof for 9093505150131954599725539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not rich is funny and vice versa. Everyone who is either generous or not old is both not humble and old. If mary is either not strong or not generous then paul is either generous or wise. If john is not generous or wise then someone is both not quiet and not strong and vice versa. Everyone who is both kind and not quiet is both not kind and funny. Everyone who is either old or not curious is strong. If paul is both not strong and generous then john is not strong or not wise and vice versa. Everyone who is either calm or not calm is both not tall and curious and vice versa. If paul is both kind and not quiet then someone is not rich and vice versa. If fred is either tall or not calm then someone is both old and not tall and vice versa. Everyone who is both not quiet and strong is both not curious and not brave. Everyone who is creative is both not calm and not patient and vice versa. Everyone who is generous is kind or not humble and vice versa. Everyone who is both brave and funny is patient or not wise. Everyone who is rich is either generous or calm and vice versa. Someone is not funny. Lucy is not strong. Susan is not generous. Someone is strong. Someone is either brave or generous. | Fred is not calm. | entailment | (![X]:((~wise(X)&~rich(X))<=>funny(X)))&
(![X]:((generous(X)<~>~old(X))=>(~humble(X)&old(X))))&
(((~strong(mary)<~>~generous(mary)))=>((generous(paul)<~>wise(paul))))&
(((~generous(john)|wise(john)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((kind(X)&~quiet(X))=>(~kind(X)&funny(X))))&
(![X]:((old(X)<~>~curious(X))=>strong(X)))&
(((~strong(paul)&generous(paul)))<=>((~strong(john)|~wise(john))))&
(![X]:((calm(X)<~>~calm(X))<=>(~tall(X)&curious(X))))&
(((kind(paul)&~quiet(paul)))<=>(?[X]:(~rich(X))))&
(((tall(fred)<~>~calm(fred)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~curious(X)&~brave(X))))&
(![X]:(creative(X)<=>(~calm(X)&~patient(X))))&
(![X]:(generous(X)<=>(kind(X)|~humble(X))))&
(![X]:((brave(X)&funny(X))=>(patient(X)|~wise(X))))&
(![X]:(rich(X)<=>(generous(X)<~>calm(X))))&
(?[X]:(~funny(X)))&
(~strong(lucy))&
(~generous(susan))&
(?[X]:(strong(X)))&
(?[X]:((brave(X)<~>generous(X)))) | ~calm(fred) | [
"p1",
"p7",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5301611558709728618158723
% SZS output start Proof for 5301611558709728618158723
2. ! [X0] : ((generous(X0) <~> ~old(X0)) => (old(X0) & ~humble(X0))) [input p1]
8. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> (curious(X0) & ~tall(X0))) [input p7]
10. (tall(fred) <~> ~calm(fred)) <=> ? [X0] : (~tall(X0) & old(X0)) [input p9]
18. ~generous(susan) [input p17]
21. calm(fred) [input hypothesis]
23. ! [X0] : ((old(X0) & ~humble(X0)) | (generous(X0) <=> ~old(X0))) [ennf transformation 2]
32. ! [X0] : ((old(X0) & ~humble(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 23]
42. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | (~curious(X0) | tall(X0))) & ((curious(X0) & ~tall(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 8]
43. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ~curious(X0) | tall(X0)) & ((curious(X0) & ~tall(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [flattening 42]
49. (((calm(fred) | ~tall(fred)) & (~calm(fred) | tall(fred))) | ! [X0] : (tall(X0) | ~old(X0))) & (? [X0] : (~tall(X0) & old(X0)) | ((tall(fred) | calm(fred)) & (~calm(fred) | ~tall(fred)))) [nnf transformation 10]
50. (((calm(fred) | ~tall(fred)) & (~calm(fred) | tall(fred))) | ! [X0] : (tall(X0) | ~old(X0))) & (? [X1] : (~tall(X1) & old(X1)) | ((tall(fred) | calm(fred)) & (~calm(fred) | ~tall(fred)))) [rectify 49]
51. ? [X1] : (~tall(X1) & old(X1)) => (~tall(sK2) & old(sK2)) [choice axiom]
52. (((calm(fred) | ~tall(fred)) & (~calm(fred) | tall(fred))) | ! [X0] : (tall(X0) | ~old(X0))) & ((~tall(sK2) & old(sK2)) | ((tall(fred) | calm(fred)) & (~calm(fred) | ~tall(fred)))) [skolemisation 50,51]
69. old(X0) | generous(X0) | old(X0) [cnf transformation 32]
88. ~tall(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 43]
89. ~tall(X0) | calm(X0) | calm(X0) [cnf transformation 43]
101. ~calm(fred) | tall(fred) | tall(X0) | ~old(X0) [cnf transformation 52]
114. ~generous(susan) [cnf transformation 18]
118. calm(fred) [cnf transformation 21]
119. ~tall(X0) | ~calm(X0) [duplicate literal removal 88]
120. ~tall(X0) | calm(X0) [duplicate literal removal 89]
124. old(X0) | generous(X0) [duplicate literal removal 69]
183. ~tall(X0) [subsumption resolution 119,120]
197. ~calm(fred) | tall(X0) | ~old(X0) [subsumption resolution 101,183]
198. ~calm(fred) | ~old(X0) [subsumption resolution 197,183]
200. 15 <=> ! [X0] : ~old(X0) [avatar definition]
201. ~old(X0) <- (15) [avatar component clause 200]
203. 16 <=> calm(fred) [avatar definition]
206. 15 | ~16 [avatar split clause 198,203,200]
224. 16 [avatar split clause 118,203]
225. generous(X0) <- (15) [resolution 124,201]
226. $false <- (15) [resolution 225,114]
231. ~15 [avatar contradiction clause 226]
232. $false [avatar sat refutation 206,224,231]
% SZS output end Proof for 5301611558709728618158723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either brave or not rich and vice versa.
Everyone who is not quiet is both not brave and curious.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
If someone is quiet or not kind then someone is either not humble or not patient and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Everyone who is either curious or kind is not old and vice versa.
If mary is both not happy and not humble then fred is both calm and not strong.
If lucy is both not happy and not strong then someone is both not wise and not kind and vice versa.
Mary is strong.
Someone is either not rich or not brave.
Paul is both not old and not quiet.
Alice is humble or not tall.
Fred is not patient.
Lucy is not curious or patient.
Lucy is not creative or humble.
John is not tall or not patient. | Susan is not patient. | entailment | (![X]:(wise(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(~quiet(X)=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(![X]:((curious(X)<~>kind(X))<=>~old(X)))&
(((~happy(mary)&~humble(mary)))=>((calm(fred)&~strong(fred))))&
(((~happy(lucy)&~strong(lucy)))<=>(?[X]:((~wise(X)&~kind(X)))))&
(strong(mary))&
(?[X]:((~rich(X)<~>~brave(X))))&
((~old(paul)&~quiet(paul)))&
((humble(alice)|~tall(alice)))&
(~patient(fred))&
((~curious(lucy)|patient(lucy)))&
((~creative(lucy)|humble(lucy)))&
((~tall(john)|~patient(john))) | ~patient(susan) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2719567830827708457699383
% SZS output start Proof for 2719567830827708457699383
4. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X0] : (~funny(X0) | patient(X0)) [input p3]
7. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p6]
25. patient(susan) [input hypothesis]
26. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X1] : (~funny(X1) | patient(X1)) [rectify 4]
31. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 7]
43. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X1] : (~funny(X1) | patient(X1)) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 26]
44. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X2] : (~funny(X2) | patient(X2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [rectify 43]
45. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK1) & creative(sK1)) [choice axiom]
46. ? [X2] : (~funny(X2) | patient(X2)) => (~funny(sK2) | patient(sK2)) [choice axiom]
47. ((curious(sK1) & creative(sK1)) | ! [X1] : (funny(X1) & ~patient(X1))) & ((~funny(sK2) | patient(sK2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [skolemisation 44,46,45]
85. creative(sK1) | ~patient(X1) [cnf transformation 47]
98. ~creative(X0) | ~creative(X0) [cnf transformation 31]
146. patient(susan) [cnf transformation 25]
149. ~creative(X0) [duplicate literal removal 98]
182. 8 <=> ! [X1] : ~patient(X1) [avatar definition]
183. ~patient(X1) <- (8) [avatar component clause 182]
186. 9 <=> creative(sK1) [avatar definition]
188. creative(sK1) <- (9) [avatar component clause 186]
190. 8 | 9 [avatar split clause 85,186,182]
351. $false <- (8) [resolution 183,146]
352. ~8 [avatar contradiction clause 351]
353. $false <- (9) [subsumption resolution 188,149]
354. ~9 [avatar contradiction clause 353]
355. $false [avatar sat refutation 190,352,354]
% SZS output end Proof for 2719567830827708457699383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits