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 not strong or patient then alice is both curious and strong and vice versa. Everyone who is calm or not brave is both humble and not funny. Everyone who is both funny and not curious is wise and vice versa. If someone is either kind or not rich then susan is humble and vice versa. If alice is both kind and tall then someone is either funny or not strong and vice versa. Everyone who is both not creative and funny is both happy and not quiet and vice versa. If fred is both not kind and not generous then paul is patient. Everyone who is either not kind or patient is either quiet or not happy and vice versa. Everyone who is both funny and not wise is either rich or tall and vice versa. Everyone who is not rich or not quiet is both not old and calm. If someone is not tall then someone is either not brave or not happy and vice versa. If susan is either humble or patient then alice is both not rich and generous. Everyone who is either generous or calm is not patient or funny. Everyone who is either not calm or rich is either funny or humble. Everyone who is happy is both not humble and not quiet. Everyone who is brave or calm is not happy or happy. Someone is both brave and curious. Someone is either not kind or curious. Fred is not generous or not kind. John is not tall or curious. Mary is either not calm or funny. Fred is either wise or strong. Someone is both kind and wise. Someone is not kind. | John is not wise. | entailment | (((~strong(fred)|patient(fred)))<=>((curious(alice)&strong(alice))))&
(![X]:((calm(X)|~brave(X))=>(humble(X)&~funny(X))))&
(![X]:((funny(X)&~curious(X))<=>wise(X)))&
((?[X]:((kind(X)<~>~rich(X))))<=>(humble(susan)))&
(((kind(alice)&tall(alice)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:((~creative(X)&funny(X))<=>(happy(X)&~quiet(X))))&
(((~kind(fred)&~generous(fred)))=>(patient(paul)))&
(![X]:((~kind(X)<~>patient(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((funny(X)&~wise(X))<=>(rich(X)<~>tall(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~old(X)&calm(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
(((humble(susan)<~>patient(susan)))=>((~rich(alice)&generous(alice))))&
(![X]:((generous(X)<~>calm(X))=>(~patient(X)|funny(X))))&
(![X]:((~calm(X)<~>rich(X))=>(funny(X)<~>humble(X))))&
(![X]:(happy(X)=>(~humble(X)&~quiet(X))))&
(![X]:((brave(X)|calm(X))=>(~happy(X)|happy(X))))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
((~generous(fred)|~kind(fred)))&
((~tall(john)|curious(john)))&
((~calm(mary)<~>funny(mary)))&
((wise(fred)<~>strong(fred)))&
(?[X]:((kind(X)&wise(X))))&
(?[X]:(~kind(X))) | ~wise(john) | [
"p1",
"p2",
"p8",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6632696136454386142599267
% SZS output start Proof for 6632696136454386142599267
2. ! [X0] : ((~brave(X0) | calm(X0)) => (~funny(X0) & humble(X0))) [input p1]
3. ! [X0] : ((~curious(X0) & funny(X0)) <=> wise(X0)) [input p2]
9. ! [X0] : ((~wise(X0) & funny(X0)) <=> (rich(X0) <~> tall(X0))) [input p8]
10. ! [X0] : ((~quiet(X0) | ~rich(X0)) => (calm(X0) & ~old(X0))) [input p9]
20. curious(john) | ~tall(john) [input p19]
25. wise(john) [input hypothesis]
27. ! [X0] : ((~quiet(X0) | ~rich(X0)) => calm(X0)) [pure predicate removal 10]
28. ! [X0] : ((~funny(X0) & humble(X0)) | (brave(X0) & ~calm(X0))) [ennf transformation 2]
31. ! [X0] : (calm(X0) | (quiet(X0) & rich(X0))) [ennf transformation 27]
41. ! [X0] : (((~curious(X0) & funny(X0)) | ~wise(X0)) & (wise(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 3]
42. ! [X0] : (((~curious(X0) & funny(X0)) | ~wise(X0)) & (wise(X0) | curious(X0) | ~funny(X0))) [flattening 41]
55. ! [X0] : (((~wise(X0) & funny(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (wise(X0) | ~funny(X0)))) [nnf transformation 9]
56. ! [X0] : (((~wise(X0) & funny(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | wise(X0) | ~funny(X0))) [flattening 55]
83. ~funny(X0) | ~calm(X0) [cnf transformation 28]
86. ~wise(X0) | funny(X0) [cnf transformation 42]
87. ~wise(X0) | ~curious(X0) [cnf transformation 42]
115. ~rich(X0) | tall(X0) | ~wise(X0) [cnf transformation 56]
117. rich(X0) | calm(X0) [cnf transformation 31]
142. curious(john) | ~tall(john) [cnf transformation 20]
150. wise(john) [cnf transformation 25]
289. 30 <=> tall(john) [avatar definition]
291. ~tall(john) <- (~30) [avatar component clause 289]
293. 31 <=> curious(john) [avatar definition]
296. ~30 | 31 [avatar split clause 142,293,289]
313. funny(john) [resolution 86,150]
315. ~curious(john) [resolution 87,150]
316. ~31 [avatar split clause 315,293]
320. ~calm(john) [resolution 313,83]
407. ~wise(X1) | tall(X1) | calm(X1) [resolution 115,117]
681. tall(john) | calm(john) [resolution 407,150]
687. calm(john) <- (~30) [subsumption resolution 681,291]
688. $false <- (~30) [subsumption resolution 687,320]
689. 30 [avatar contradiction clause 688]
691. $false [avatar sat refutation 296,316,689]
% SZS output end Proof for 6632696136454386142599267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not patient is both not brave and not rich and vice versa.
Everyone who is both rich and not strong is old and vice versa.
Everyone who is both not brave and funny is kind or curious and vice versa.
If someone is brave then mary is both old and patient.
Everyone who is not happy is either funny or not brave and vice versa.
Everyone who is both not creative and not curious is not patient or not old.
Everyone who is strong is not strong or patient and vice versa.
Everyone who is kind or happy is quiet and vice versa.
Everyone who is not funny is wise and vice versa.
Everyone who is kind or rich is patient or quiet.
If someone is both old and generous then someone is not generous.
Everyone who is not rich is quiet or strong.
Everyone who is creative or humble is kind or happy and vice versa.
If someone is both not wise and curious then mary is both strong and creative and vice versa.
If lucy is either quiet or kind then paul is both not creative and not wise.
If alice is not quiet or quiet then paul is either brave or not calm and vice versa.
Alice is strong.
Someone is either not tall or not creative.
Susan is either not kind or not rich.
Lucy is both rich and not creative.
Someone is either creative or not wise.
Someone is quiet or brave. | Mary is not quiet. | neutral | (![X]:((kind(X)|~patient(X))<=>(~brave(X)&~rich(X))))&
(![X]:((rich(X)&~strong(X))<=>old(X)))&
(![X]:((~brave(X)&funny(X))<=>(kind(X)|curious(X))))&
((?[X]:(brave(X)))=>((old(mary)&patient(mary))))&
(![X]:(~happy(X)<=>(funny(X)<~>~brave(X))))&
(![X]:((~creative(X)&~curious(X))=>(~patient(X)|~old(X))))&
(![X]:(strong(X)<=>(~strong(X)|patient(X))))&
(![X]:((kind(X)|happy(X))<=>quiet(X)))&
(![X]:(~funny(X)<=>wise(X)))&
(![X]:((kind(X)|rich(X))=>(patient(X)|quiet(X))))&
((?[X]:((old(X)&generous(X))))=>(?[X]:(~generous(X))))&
(![X]:(~rich(X)=>(quiet(X)|strong(X))))&
(![X]:((creative(X)|humble(X))<=>(kind(X)|happy(X))))&
((?[X]:((~wise(X)&curious(X))))<=>((strong(mary)&creative(mary))))&
(((quiet(lucy)<~>kind(lucy)))=>((~creative(paul)&~wise(paul))))&
(((~quiet(alice)|quiet(alice)))<=>((brave(paul)<~>~calm(paul))))&
(strong(alice))&
(?[X]:((~tall(X)<~>~creative(X))))&
((~kind(susan)<~>~rich(susan)))&
((rich(lucy)&~creative(lucy)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((quiet(X)|brave(X)))) | ~quiet(mary) | [] | null | 0 |
If someone is either not calm or wise then alice is both patient and creative and vice versa. If someone is both curious and tall then someone is both rich and not rich. Everyone who is not happy is quiet or not quiet and vice versa. Everyone who is not strong or rich is both not curious and not kind and vice versa. If susan is both wise and kind then susan is not strong or curious. Everyone who is not wise or not quiet is either wise or not brave and vice versa. Everyone who is either brave or not creative is not kind. If someone is either not tall or not kind then someone is either not wise or strong and vice versa. If someone is either quiet or creative then someone is not tall. If someone is not strong then someone is both not tall and not wise and vice versa. Everyone who is either not brave or not tall is either rich or not brave and vice versa. Everyone who is not wise is either not generous or not strong. Everyone who is not funny or not old is both strong and tall. Everyone who is happy or not creative is either not tall or generous and vice versa. Everyone who is both old and not happy is not brave or not quiet and vice versa. Everyone who is not kind is either not tall or rich and vice versa. Mary is humble or not humble. Paul is kind or not humble. Someone is not humble. Someone is calm or quiet. | Paul is generous. | contradiction | ((?[X]:((~calm(X)<~>wise(X))))<=>((patient(alice)&creative(alice))))&
((?[X]:((curious(X)&tall(X))))=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:(~happy(X)<=>(quiet(X)|~quiet(X))))&
(![X]:((~strong(X)|rich(X))<=>(~curious(X)&~kind(X))))&
(((wise(susan)&kind(susan)))=>((~strong(susan)|curious(susan))))&
(![X]:((~wise(X)|~quiet(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((brave(X)<~>~creative(X))=>~kind(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
((?[X]:((quiet(X)<~>creative(X))))=>(?[X]:(~tall(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:((~brave(X)<~>~tall(X))<=>(rich(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(~generous(X)<~>~strong(X))))&
(![X]:((~funny(X)|~old(X))=>(strong(X)&tall(X))))&
(![X]:((happy(X)|~creative(X))<=>(~tall(X)<~>generous(X))))&
(![X]:((old(X)&~happy(X))<=>(~brave(X)|~quiet(X))))&
(![X]:(~kind(X)<=>(~tall(X)<~>rich(X))))&
((humble(mary)|~humble(mary)))&
((kind(paul)|~humble(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)|quiet(X)))) | generous(paul) | [
"p3",
"p7",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7278906861841845040147172
% SZS output start Proof for 7278906861841845040147172
4. ! [X0] : ((rich(X0) | ~strong(X0)) <=> (~kind(X0) & ~curious(X0))) [input p3]
8. ? [X0] : (~tall(X0) <~> ~kind(X0)) <=> ? [X0] : (~wise(X0) <~> strong(X0)) [input p7]
11. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (rich(X0) <~> ~brave(X0))) [input p10]
12. ! [X0] : (~wise(X0) => (~generous(X0) <~> ~strong(X0))) [input p11]
16. ! [X0] : (~kind(X0) <=> (~tall(X0) <~> rich(X0))) [input p15]
21. generous(paul) [input hypothesis]
23. ? [X0] : (~tall(X0) <~> ~kind(X0)) <=> ? [X1] : (~wise(X1) <~> strong(X1)) [rectify 8]
32. ! [X0] : ((~generous(X0) <~> ~strong(X0)) | wise(X0)) [ennf transformation 12]
44. ! [X0] : (((rich(X0) | ~strong(X0)) | (kind(X0) | curious(X0))) & ((~kind(X0) & ~curious(X0)) | (~rich(X0) & strong(X0)))) [nnf transformation 4]
45. ! [X0] : ((rich(X0) | ~strong(X0) | kind(X0) | curious(X0)) & ((~kind(X0) & ~curious(X0)) | (~rich(X0) & strong(X0)))) [flattening 44]
49. (? [X0] : ((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | ! [X1] : ((~wise(X1) | ~strong(X1)) & (strong(X1) | wise(X1)))) & (? [X1] : ((~strong(X1) | wise(X1)) & (strong(X1) | ~wise(X1))) | ! [X0] : ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0)))) [nnf transformation 23]
50. (? [X0] : ((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | ! [X1] : ((~wise(X1) | ~strong(X1)) & (strong(X1) | wise(X1)))) & (? [X2] : ((~strong(X2) | wise(X2)) & (strong(X2) | ~wise(X2))) | ! [X3] : ((~tall(X3) | kind(X3)) & (~kind(X3) | tall(X3)))) [rectify 49]
51. ? [X0] : ((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) => ((kind(sK2) | tall(sK2)) & (~kind(sK2) | ~tall(sK2))) [choice axiom]
52. ? [X2] : ((~strong(X2) | wise(X2)) & (strong(X2) | ~wise(X2))) => ((~strong(sK3) | wise(sK3)) & (strong(sK3) | ~wise(sK3))) [choice axiom]
53. (((kind(sK2) | tall(sK2)) & (~kind(sK2) | ~tall(sK2))) | ! [X1] : ((~wise(X1) | ~strong(X1)) & (strong(X1) | wise(X1)))) & (((~strong(sK3) | wise(sK3)) & (strong(sK3) | ~wise(sK3))) | ! [X3] : ((~tall(X3) | kind(X3)) & (~kind(X3) | tall(X3)))) [skolemisation 50,52,51]
63. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | ((rich(X0) | brave(X0)) & (~brave(X0) | ~rich(X0)))) & (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 11]
64. ! [X0] : (((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | wise(X0)) [nnf transformation 32]
69. ! [X0] : ((~kind(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | kind(X0))) [nnf transformation 16]
87. ~kind(X0) | strong(X0) [cnf transformation 45]
88. ~kind(X0) | ~rich(X0) [cnf transformation 45]
104. ~kind(sK2) | ~tall(sK2) | ~wise(X1) | ~strong(X1) [cnf transformation 53]
113. ~brave(X0) | rich(X0) | ~brave(X0) | tall(X0) [cnf transformation 63]
114. brave(X0) | ~rich(X0) | ~tall(X0) | brave(X0) [cnf transformation 63]
116. ~tall(X0) | ~brave(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 63]
119. tall(X0) | brave(X0) | rich(X0) | brave(X0) [cnf transformation 63]
120. ~generous(X0) | ~strong(X0) | wise(X0) [cnf transformation 64]
135. rich(X0) | ~tall(X0) | kind(X0) [cnf transformation 69]
136. ~rich(X0) | tall(X0) | kind(X0) [cnf transformation 69]
143. generous(paul) [cnf transformation 21]
144. ~brave(X0) | rich(X0) | tall(X0) [duplicate literal removal 113]
145. brave(X0) | ~rich(X0) | ~tall(X0) [duplicate literal removal 114]
146. ~tall(X0) | ~brave(X0) | ~rich(X0) [duplicate literal removal 116]
147. tall(X0) | brave(X0) | rich(X0) [duplicate literal removal 119]
203. 12 <=> ! [X1] : (~wise(X1) | ~strong(X1)) [avatar definition]
204. ~wise(X1) | ~strong(X1) <- (12) [avatar component clause 203]
206. 13 <=> tall(sK2) [avatar definition]
207. ~tall(sK2) <- (~13) [avatar component clause 206]
210. 14 <=> kind(sK2) [avatar definition]
211. ~kind(sK2) <- (~14) [avatar component clause 210]
218. 12 | ~13 | ~14 [avatar split clause 104,210,206,203]
259. 25 <=> ! [X3] : strong(X3) [avatar definition]
260. strong(X3) <- (25) [avatar component clause 259]
271. ~rich(X0) | ~tall(X0) [subsumption resolution 145,146]
272. rich(X0) | tall(X0) [subsumption resolution 144,147]
276. kind(X0) | tall(X0) [subsumption resolution 136,272]
277. kind(X0) | rich(X0) [subsumption resolution 135,276]
305. tall(X0) | ~rich(X0) [resolution 276,88]
307. ~rich(X0) [subsumption resolution 305,271]
308. rich(sK2) <- (~14) [resolution 277,211]
310. rich(X1) | strong(X1) [resolution 277,87]
311. $false <- (~14) [subsumption resolution 308,307]
312. 14 [avatar contradiction clause 311]
313. strong(X1) [subsumption resolution 310,307]
314. 25 [avatar split clause 313,259]
330. tall(X0) [resolution 307,272]
368. ~wise(X1) <- (12, 25) [subsumption resolution 204,260]
389. ~strong(paul) | wise(paul) [resolution 120,143]
390. wise(paul) <- (25) [subsumption resolution 389,260]
391. $false <- (12, 25) [subsumption resolution 390,368]
392. ~12 | ~25 [avatar contradiction clause 391]
393. $false <- (~13) [subsumption resolution 207,330]
394. 13 [avatar contradiction clause 393]
395. $false [avatar sat refutation 218,312,314,392,394]
% SZS output end Proof for 7278906861841845040147172
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is both not happy and calm.
Everyone who is both patient and old is both curious and calm.
Everyone who is not brave or quiet is not strong and vice versa.
If fred is either not quiet or not kind then susan is either kind or not humble and vice versa.
If john is not happy then someone is both not happy and rich.
Everyone who is both not tall and quiet is both rich and not curious.
If paul is either not wise or not kind then someone is both wise and not kind and vice versa.
If someone is creative or not funny then someone is both not patient and strong and vice versa.
If susan is both not tall and not calm then someone is calm and vice versa.
Everyone who is not humble or patient is funny.
Everyone who is not rich or not quiet is not happy or not funny.
Everyone who is both strong and not tall is either kind or generous.
Everyone who is rich is not old or not quiet and vice versa.
Everyone who is either patient or happy is either brave or generous and vice versa.
Everyone who is tall is not rich or not kind.
Everyone who is not old is not curious.
Paul is either kind or happy.
Susan is not rich.
Susan is patient or not strong.
Someone is generous.
Someone is kind or quiet.
Susan is not creative or not funny.
John is not tall.
Alice is tall. | Susan is patient. | contradiction | (![X]:((~calm(X)<~>quiet(X))=>(~happy(X)&calm(X))))&
(![X]:((patient(X)&old(X))=>(curious(X)&calm(X))))&
(![X]:((~brave(X)|quiet(X))<=>~strong(X)))&
(((~quiet(fred)<~>~kind(fred)))<=>((kind(susan)<~>~humble(susan))))&
((~happy(john))=>(?[X]:((~happy(X)&rich(X)))))&
(![X]:((~tall(X)&quiet(X))=>(rich(X)&~curious(X))))&
(((~wise(paul)<~>~kind(paul)))<=>(?[X]:((wise(X)&~kind(X)))))&
((?[X]:((creative(X)|~funny(X))))<=>(?[X]:((~patient(X)&strong(X)))))&
(((~tall(susan)&~calm(susan)))<=>(?[X]:(calm(X))))&
(![X]:((~humble(X)|patient(X))=>funny(X)))&
(![X]:((~rich(X)|~quiet(X))=>(~happy(X)|~funny(X))))&
(![X]:((strong(X)&~tall(X))=>(kind(X)<~>generous(X))))&
(![X]:(rich(X)<=>(~old(X)|~quiet(X))))&
(![X]:((patient(X)<~>happy(X))<=>(brave(X)<~>generous(X))))&
(![X]:(tall(X)=>(~rich(X)|~kind(X))))&
(![X]:(~old(X)=>~curious(X)))&
((kind(paul)<~>happy(paul)))&
(~rich(susan))&
((patient(susan)|~strong(susan)))&
(?[X]:(generous(X)))&
(?[X]:((kind(X)|quiet(X))))&
((~creative(susan)|~funny(susan)))&
(~tall(john))&
(tall(alice)) | patient(susan) | [
"p1",
"p8",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1665556959122034728886000
% SZS output start Proof for 1665556959122034728886000
2. ! [X0] : ((old(X0) & patient(X0)) => (calm(X0) & curious(X0))) [input p1]
9. (~calm(susan) & ~tall(susan)) <=> ? [X0] : calm(X0) [input p8]
13. ! [X0] : (rich(X0) <=> (~quiet(X0) | ~old(X0))) [input p12]
18. ~rich(susan) [input p17]
25. patient(susan) [input hypothesis]
28. ! [X0] : ((calm(X0) & curious(X0)) | (~old(X0) | ~patient(X0))) [ennf transformation 2]
29. ! [X0] : ((calm(X0) & curious(X0)) | ~old(X0) | ~patient(X0)) [flattening 28]
56. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (calm(susan) | tall(susan))) [nnf transformation 9]
57. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | calm(susan) | tall(susan)) [flattening 56]
58. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | calm(susan) | tall(susan)) [rectify 57]
59. ? [X1] : calm(X1) => calm(sK4) [choice axiom]
60. ((~calm(susan) & ~tall(susan)) | ! [X0] : ~calm(X0)) & (calm(sK4) | calm(susan) | tall(susan)) [skolemisation 58,59]
62. ! [X0] : ((rich(X0) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | ~rich(X0))) [nnf transformation 13]
63. ! [X0] : ((rich(X0) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | ~rich(X0))) [flattening 62]
75. ~old(X0) | calm(X0) | ~patient(X0) [cnf transformation 29]
104. ~calm(susan) | ~calm(X0) [cnf transformation 60]
112. rich(X0) | old(X0) [cnf transformation 63]
126. ~rich(susan) [cnf transformation 18]
133. patient(susan) [cnf transformation 25]
229. 20 <=> ! [X0] : ~calm(X0) [avatar definition]
230. ~calm(X0) <- (20) [avatar component clause 229]
232. 21 <=> calm(susan) [avatar definition]
235. 20 | ~21 [avatar split clause 104,232,229]
253. 25 <=> patient(susan) [avatar definition]
255. patient(susan) <- (25) [avatar component clause 253]
279. 25 [avatar split clause 133,253]
287. old(susan) [resolution 112,126]
302. calm(susan) | ~patient(susan) [resolution 75,287]
303. ~patient(susan) <- (20) [subsumption resolution 302,230]
304. $false <- (20, 25) [subsumption resolution 303,255]
305. ~20 | ~25 [avatar contradiction clause 304]
306. calm(susan) <- (25) [subsumption resolution 302,255]
307. 21 | ~25 [avatar split clause 306,253,232]
317. $false [avatar sat refutation 235,279,305,307]
% SZS output end Proof for 1665556959122034728886000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or old is strong or calm and vice versa.
Everyone who is not strong or curious is both not tall and not brave and vice versa.
Everyone who is both not tall and creative is either not patient or not funny and vice versa.
Everyone who is both funny and not creative is either not old or quiet and vice versa.
If mary is not rich or humble then someone is both not old and tall and vice versa.
If someone is kind then paul is creative.
Everyone who is happy is patient or calm.
Everyone who is both not creative and not generous is both not humble and not wise and vice versa.
Everyone who is either curious or happy is both generous and not funny.
Everyone who is old or funny is not creative or curious.
Everyone who is not funny or not kind is either tall or funny and vice versa.
If someone is not brave then lucy is either not rich or not old and vice versa.
Everyone who is not kind is not old.
If lucy is not humble then paul is either rich or not curious and vice versa.
If someone is not humble or generous then someone is either not rich or not wise.
Everyone who is both not rich and wise is happy.
Someone is both not humble and not patient.
Someone is not rich or not curious.
Someone is not tall.
Someone is either happy or not curious.
John is funny.
Lucy is both rich and wise.
Lucy is both humble and not funny. | Paul is not quiet. | contradiction | (![X]:((~humble(X)<~>old(X))<=>(strong(X)|calm(X))))&
(![X]:((~strong(X)|curious(X))<=>(~tall(X)&~brave(X))))&
(![X]:((~tall(X)&creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((funny(X)&~creative(X))<=>(~old(X)<~>quiet(X))))&
(((~rich(mary)|humble(mary)))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(kind(X)))=>(creative(paul)))&
(![X]:(happy(X)=>(patient(X)|calm(X))))&
(![X]:((~creative(X)&~generous(X))<=>(~humble(X)&~wise(X))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~funny(X))))&
(![X]:((old(X)|funny(X))=>(~creative(X)|curious(X))))&
(![X]:((~funny(X)|~kind(X))<=>(tall(X)<~>funny(X))))&
((?[X]:(~brave(X)))<=>((~rich(lucy)<~>~old(lucy))))&
(![X]:(~kind(X)=>~old(X)))&
((~humble(lucy))<=>((rich(paul)<~>~curious(paul))))&
((?[X]:((~humble(X)|generous(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~rich(X)&wise(X))=>happy(X)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(funny(john))&
((rich(lucy)&wise(lucy)))&
((humble(lucy)&~funny(lucy))) | ~quiet(paul) | [
"p0",
"p1",
"p3",
"p5",
"p9",
"p10",
"p11",
"p12",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3960419319559562761718668
% SZS output start Proof for 3960419319559562761718668
1. ! [X0] : ((~humble(X0) <~> old(X0)) <=> (calm(X0) | strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~brave(X0) & ~tall(X0))) [input p1]
4. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~old(X0) <~> quiet(X0))) [input p3]
6. ? [X0] : kind(X0) => creative(paul) [input p5]
10. ! [X0] : ((funny(X0) | old(X0)) => (curious(X0) | ~creative(X0))) [input p9]
11. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (tall(X0) <~> funny(X0))) [input p10]
12. ? [X0] : ~brave(X0) <=> (~rich(lucy) <~> ~old(lucy)) [input p11]
13. ! [X0] : (~kind(X0) => ~old(X0)) [input p12]
22. wise(lucy) & rich(lucy) [input p21]
23. ~funny(lucy) & humble(lucy) [input p22]
24. ~quiet(paul) [input hypothesis]
26. creative(paul) | ! [X0] : ~kind(X0) [ennf transformation 6]
30. ! [X0] : ((curious(X0) | ~creative(X0)) | (~funny(X0) & ~old(X0))) [ennf transformation 10]
31. ! [X0] : (curious(X0) | ~creative(X0) | (~funny(X0) & ~old(X0))) [flattening 30]
32. ! [X0] : (~old(X0) | kind(X0)) [ennf transformation 13]
36. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [flattening 36]
38. ! [X0] : (((curious(X0) | ~strong(X0)) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~strong(X0) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [flattening 38]
42. ! [X0] : (((~creative(X0) & funny(X0)) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) & (((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | (creative(X0) | ~funny(X0)))) [nnf transformation 4]
43. ! [X0] : (((~creative(X0) & funny(X0)) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) & (((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | creative(X0) | ~funny(X0))) [flattening 42]
52. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 11]
53. ! [X0] : ((~kind(X0) | ~funny(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [flattening 52]
54. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X0] : brave(X0)) [nnf transformation 12]
55. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [rectify 54]
56. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
57. (~brave(sK1) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [skolemisation 55,56]
74. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 37]
78. ~tall(X0) | strong(X0) [cnf transformation 39]
81. ~brave(X0) | ~curious(X0) [cnf transformation 39]
93. ~creative(X0) | quiet(X0) | old(X0) [cnf transformation 43]
100. creative(paul) | ~kind(X0) [cnf transformation 26]
110. ~creative(X0) | curious(X0) | ~old(X0) [cnf transformation 31]
112. funny(X0) | tall(X0) | funny(X0) [cnf transformation 53]
118. ~old(lucy) | ~rich(lucy) | brave(X1) [cnf transformation 57]
122. ~old(X0) | kind(X0) [cnf transformation 32]
139. rich(lucy) [cnf transformation 22]
141. humble(lucy) [cnf transformation 23]
142. ~funny(lucy) [cnf transformation 23]
143. ~quiet(paul) [cnf transformation 24]
144. funny(X0) | tall(X0) [duplicate literal removal 112]
171. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
172. ~kind(X0) <- (6) [avatar component clause 171]
174. 7 <=> creative(paul) [avatar definition]
176. creative(paul) <- (7) [avatar component clause 174]
177. 6 | 7 [avatar split clause 100,174,171]
179. 8 <=> old(lucy) [avatar definition]
181. old(lucy) <- (8) [avatar component clause 179]
183. 9 <=> rich(lucy) [avatar definition]
193. 11 <=> ! [X1] : brave(X1) [avatar definition]
194. brave(X1) <- (11) [avatar component clause 193]
196. 11 | ~9 | ~8 [avatar split clause 118,179,183,193]
206. 14 <=> humble(lucy) [avatar definition]
207. humble(lucy) <- (14) [avatar component clause 206]
250. 9 [avatar split clause 139,183]
251. 14 [avatar split clause 141,206]
254. tall(lucy) [resolution 144,142]
258. strong(lucy) [resolution 254,78]
261. ~humble(lucy) | old(lucy) [resolution 258,74]
262. old(lucy) <- (14) [subsumption resolution 261,207]
265. 8 | ~14 [avatar split clause 262,206,179]
266. kind(lucy) <- (8) [resolution 181,122]
267. $false <- (6, 8) [subsumption resolution 266,172]
268. ~6 | ~8 [avatar contradiction clause 267]
270. ~curious(X0) <- (11) [resolution 194,81]
300. 26 <=> old(paul) [avatar definition]
312. quiet(paul) | old(paul) <- (7) [resolution 93,176]
347. curious(paul) | ~old(paul) <- (7) [resolution 110,176]
349. ~old(paul) <- (7, 11) [subsumption resolution 347,270]
355. ~26 | ~7 | ~11 [avatar split clause 349,193,174,300]
365. old(paul) <- (7) [subsumption resolution 312,143]
366. 26 | ~7 [avatar split clause 365,174,300]
368. $false [avatar sat refutation 177,196,250,251,265,268,355,366]
% SZS output end Proof for 3960419319559562761718668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not humble is either not funny or humble.
If someone is happy or not old then someone is wise or not creative and vice versa.
Everyone who is old is both not rich and not curious and vice versa.
Everyone who is both strong and not patient is not rich or not tall and vice versa.
Everyone who is either not wise or tall is both not happy and generous and vice versa.
If someone is either calm or not kind then lucy is not brave or patient.
If someone is not humble or patient then paul is both curious and not patient and vice versa.
Everyone who is not funny is both brave and not curious.
If someone is calm then someone is either not old or funny and vice versa.
Everyone who is either creative or not happy is both humble and not old.
Everyone who is both not funny and happy is not kind or happy.
Everyone who is both not wise and curious is either not creative or creative and vice versa.
Everyone who is creative is either not patient or not brave and vice versa.
Everyone who is either not kind or not old is either kind or brave and vice versa.
Everyone who is not humble is funny or calm.
Everyone who is quiet or not rich is both not patient and not generous.
Someone is not curious or tall.
Someone is generous.
Someone is both rich and patient.
Someone is either generous or rich.
Someone is not humble or not quiet.
Someone is both kind and rich. | Lucy is curious. | entailment | (![X]:((~generous(X)|~humble(X))=>(~funny(X)<~>humble(X))))&
((?[X]:((happy(X)|~old(X))))<=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:(old(X)<=>(~rich(X)&~curious(X))))&
(![X]:((strong(X)&~patient(X))<=>(~rich(X)|~tall(X))))&
(![X]:((~wise(X)<~>tall(X))<=>(~happy(X)&generous(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((~brave(lucy)|patient(lucy))))&
((?[X]:((~humble(X)|patient(X))))<=>((curious(paul)&~patient(paul))))&
(![X]:(~funny(X)=>(brave(X)&~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((creative(X)<~>~happy(X))=>(humble(X)&~old(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)|happy(X))))&
(![X]:((~wise(X)&curious(X))<=>(~creative(X)<~>creative(X))))&
(![X]:(creative(X)<=>(~patient(X)<~>~brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(kind(X)<~>brave(X))))&
(![X]:(~humble(X)=>(funny(X)|calm(X))))&
(![X]:((quiet(X)|~rich(X))=>(~patient(X)&~generous(X))))&
(?[X]:((~curious(X)|tall(X))))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)&patient(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((~humble(X)|~quiet(X))))&
(?[X]:((kind(X)&rich(X)))) | curious(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 769510593366047079817208
% SZS output start Proof for 769510593366047079817208
12. ! [X0] : ((curious(X0) & ~wise(X0)) <=> (~creative(X0) <~> creative(X0))) [input p11]
23. ~curious(lucy) [input hypothesis]
62. ! [X0] : (((curious(X0) & ~wise(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~curious(X0) | wise(X0)))) [nnf transformation 12]
63. ! [X0] : (((curious(X0) & ~wise(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~curious(X0) | wise(X0))) [flattening 62]
121. curious(X0) | creative(X0) | creative(X0) [cnf transformation 63]
122. curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 63]
146. ~curious(lucy) [cnf transformation 23]
153. curious(X0) | creative(X0) [duplicate literal removal 121]
154. curious(X0) | ~creative(X0) [duplicate literal removal 122]
256. curious(X0) [subsumption resolution 153,154]
265. $false [subsumption resolution 146,256]
% SZS output end Proof for 769510593366047079817208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or calm is creative and vice versa.
If someone is either brave or patient then someone is both patient and not humble.
If mary is kind then someone is either not brave or not quiet and vice versa.
Everyone who is not humble or curious is not wise or creative and vice versa.
Everyone who is not happy is curious or not brave.
Everyone who is not funny or not wise is not rich or not funny.
Everyone who is both not quiet and humble is both funny and strong and vice versa.
Everyone who is both not rich and strong is quiet or old and vice versa.
Everyone who is curious or calm is not wise.
Everyone who is both not funny and not generous is both not brave and patient and vice versa.
If someone is strong or happy then mary is either rich or funny and vice versa.
Everyone who is both not kind and not brave is not kind or not calm.
If fred is both wise and not tall then someone is not patient and vice versa.
Everyone who is both creative and curious is either happy or strong.
Everyone who is not curious or not funny is rich and vice versa.
If someone is either rich or not funny then paul is both not generous and rich and vice versa.
Fred is strong.
Someone is either strong or funny.
Someone is either not rich or curious.
Alice is either not generous or not happy.
Paul is not strong.
Someone is patient or not tall.
Mary is either not quiet or not brave.
Someone is not tall. | Mary is not patient. | contradiction | (![X]:((funny(X)<~>calm(X))<=>creative(X)))&
((?[X]:((brave(X)<~>patient(X))))=>(?[X]:((patient(X)&~humble(X)))))&
((kind(mary))<=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((~humble(X)|curious(X))<=>(~wise(X)|creative(X))))&
(![X]:(~happy(X)=>(curious(X)|~brave(X))))&
(![X]:((~funny(X)|~wise(X))=>(~rich(X)|~funny(X))))&
(![X]:((~quiet(X)&humble(X))<=>(funny(X)&strong(X))))&
(![X]:((~rich(X)&strong(X))<=>(quiet(X)|old(X))))&
(![X]:((curious(X)|calm(X))=>~wise(X)))&
(![X]:((~funny(X)&~generous(X))<=>(~brave(X)&patient(X))))&
((?[X]:((strong(X)|happy(X))))<=>((rich(mary)<~>funny(mary))))&
(![X]:((~kind(X)&~brave(X))=>(~kind(X)|~calm(X))))&
(((wise(fred)&~tall(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((creative(X)&curious(X))=>(happy(X)<~>strong(X))))&
(![X]:((~curious(X)|~funny(X))<=>rich(X)))&
((?[X]:((rich(X)<~>~funny(X))))<=>((~generous(paul)&rich(paul))))&
(strong(fred))&
(?[X]:((strong(X)<~>funny(X))))&
(?[X]:((~rich(X)<~>curious(X))))&
((~generous(alice)<~>~happy(alice)))&
(~strong(paul))&
(?[X]:((patient(X)|~tall(X))))&
((~quiet(mary)<~>~brave(mary)))&
(?[X]:(~tall(X))) | ~patient(mary) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5749232736184218507613313
% SZS output start Proof for 5749232736184218507613313
1. ! [X0] : ((funny(X0) <~> calm(X0)) <=> creative(X0)) [input p0]
4. ! [X0] : ((curious(X0) | ~humble(X0)) <=> (creative(X0) | ~wise(X0))) [input p3]
7. ! [X0] : ((humble(X0) & ~quiet(X0)) <=> (strong(X0) & funny(X0))) [input p6]
8. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (old(X0) | quiet(X0))) [input p7]
9. ! [X0] : ((calm(X0) | curious(X0)) => ~wise(X0)) [input p8]
13. (~tall(fred) & wise(fred)) <=> ? [X0] : ~patient(X0) [input p12]
15. ! [X0] : ((~funny(X0) | ~curious(X0)) <=> rich(X0)) [input p14]
17. strong(fred) [input p16]
25. ~patient(mary) [input hypothesis]
32. ! [X0] : (~wise(X0) | (~calm(X0) & ~curious(X0))) [ennf transformation 9]
37. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | ~creative(X0)) & (creative(X0) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [nnf transformation 1]
46. ! [X0] : (((curious(X0) | ~humble(X0)) | (~creative(X0) & wise(X0))) & ((creative(X0) | ~wise(X0)) | (~curious(X0) & humble(X0)))) [nnf transformation 4]
47. ! [X0] : ((curious(X0) | ~humble(X0) | (~creative(X0) & wise(X0))) & (creative(X0) | ~wise(X0) | (~curious(X0) & humble(X0)))) [flattening 46]
48. ! [X0] : (((humble(X0) & ~quiet(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (~humble(X0) | quiet(X0)))) [nnf transformation 7]
49. ! [X0] : (((humble(X0) & ~quiet(X0)) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | ~humble(X0) | quiet(X0))) [flattening 48]
50. ! [X0] : (((strong(X0) & ~rich(X0)) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | (~strong(X0) | rich(X0)))) [nnf transformation 8]
51. ! [X0] : (((strong(X0) & ~rich(X0)) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | ~strong(X0) | rich(X0))) [flattening 50]
58. ((~tall(fred) & wise(fred)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (tall(fred) | ~wise(fred))) [nnf transformation 13]
59. ((~tall(fred) & wise(fred)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | tall(fred) | ~wise(fred)) [flattening 58]
60. ((~tall(fred) & wise(fred)) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | tall(fred) | ~wise(fred)) [rectify 59]
61. ? [X1] : ~patient(X1) => ~patient(sK3) [choice axiom]
62. ((~tall(fred) & wise(fred)) | ! [X0] : patient(X0)) & (~patient(sK3) | tall(fred) | ~wise(fred)) [skolemisation 60,61]
64. ! [X0] : (((~funny(X0) | ~curious(X0)) | ~rich(X0)) & (rich(X0) | (funny(X0) & curious(X0)))) [nnf transformation 15]
65. ! [X0] : ((~funny(X0) | ~curious(X0) | ~rich(X0)) & (rich(X0) | (funny(X0) & curious(X0)))) [flattening 64]
83. ~funny(X0) | calm(X0) | creative(X0) [cnf transformation 37]
85. ~creative(X0) | funny(X0) | calm(X0) [cnf transformation 37]
95. ~wise(X0) | creative(X0) | humble(X0) [cnf transformation 47]
98. ~humble(X0) | curious(X0) | ~creative(X0) [cnf transformation 47]
102. ~humble(X0) | funny(X0) | quiet(X0) [cnf transformation 49]
105. ~strong(X0) | humble(X0) | ~funny(X0) [cnf transformation 49]
107. ~rich(X0) | ~quiet(X0) [cnf transformation 51]
111. ~wise(X0) | ~curious(X0) [cnf transformation 32]
112. ~wise(X0) | ~calm(X0) [cnf transformation 32]
125. wise(fred) | patient(X0) [cnf transformation 62]
130. rich(X0) | funny(X0) [cnf transformation 65]
138. strong(fred) [cnf transformation 17]
150. ~patient(mary) [cnf transformation 25]
220. 16 <=> ! [X0] : patient(X0) [avatar definition]
221. patient(X0) <- (16) [avatar component clause 220]
228. 18 <=> wise(fred) [avatar definition]
230. wise(fred) <- (18) [avatar component clause 228]
231. 16 | 18 [avatar split clause 125,228,220]
303. $false <- (16) [resolution 221,150]
304. ~16 [avatar contradiction clause 303]
309. ~curious(fred) <- (18) [resolution 111,230]
310. ~calm(fred) <- (18) [resolution 112,230]
314. ~quiet(X0) | funny(X0) [resolution 130,107]
344. creative(fred) | humble(fred) <- (18) [resolution 95,230]
346. 37 <=> humble(fred) [avatar definition]
348. humble(fred) <- (37) [avatar component clause 346]
350. 38 <=> creative(fred) [avatar definition]
351. ~creative(fred) <- (~38) [avatar component clause 350]
352. creative(fred) <- (38) [avatar component clause 350]
353. 37 | 38 | ~18 [avatar split clause 344,228,350,346]
355. funny(fred) | calm(fred) <- (38) [resolution 352,85]
356. funny(fred) <- (18, 38) [subsumption resolution 355,310]
444. humble(fred) | ~funny(fred) [resolution 105,138]
447. humble(fred) <- (18, 38) [subsumption resolution 444,356]
448. 37 | ~18 | ~38 [avatar split clause 447,350,228,346]
459. funny(fred) | quiet(fred) <- (37) [resolution 348,102]
460. curious(fred) | ~creative(fred) <- (37) [resolution 348,98]
462. ~creative(fred) <- (18, 37) [subsumption resolution 460,309]
465. ~38 | ~18 | ~37 [avatar split clause 462,346,228,350]
466. funny(fred) <- (37) [subsumption resolution 459,314]
671. calm(fred) | creative(fred) <- (37) [resolution 466,83]
672. creative(fred) <- (18, 37) [subsumption resolution 671,310]
673. $false <- (18, 37, ~38) [subsumption resolution 672,351]
674. ~18 | ~37 | 38 [avatar contradiction clause 673]
675. $false [avatar sat refutation 231,304,353,448,465,674]
% SZS output end Proof for 5749232736184218507613313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not old or curious then someone is either not curious or humble and vice versa.
If lucy is either not calm or old then someone is both curious and calm.
If susan is both curious and not patient then someone is wise.
If someone is patient or not tall then someone is either not strong or not kind and vice versa.
Everyone who is not generous or not humble is not kind or not creative.
Everyone who is creative or not curious is both patient and not old.
If alice is not calm then mary is calm.
Everyone who is old or not humble is not curious and vice versa.
If mary is either generous or creative then paul is both not happy and not wise.
Everyone who is both rich and curious is not generous and vice versa.
Everyone who is not patient or calm is wise or not generous.
If someone is both not rich and not kind then someone is both funny and not wise.
Everyone who is not calm is either curious or not strong and vice versa.
Everyone who is either not calm or not generous is not brave or not rich and vice versa.
If lucy is not old then someone is not kind and vice versa.
Everyone who is either happy or not humble is not happy and vice versa.
Mary is both not brave and not funny.
Someone is either brave or quiet.
Someone is both not kind and not strong.
Someone is both quiet and not kind.
Someone is not curious or not strong.
Someone is either not happy or generous.
Lucy is kind. | Lucy is not generous. | contradiction | (((~old(alice)<~>curious(alice)))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(((~calm(lucy)<~>old(lucy)))=>(?[X]:((curious(X)&calm(X)))))&
(((curious(susan)&~patient(susan)))=>(?[X]:(wise(X))))&
((?[X]:((patient(X)|~tall(X))))<=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~generous(X)|~humble(X))=>(~kind(X)|~creative(X))))&
(![X]:((creative(X)|~curious(X))=>(patient(X)&~old(X))))&
((~calm(alice))=>(calm(mary)))&
(![X]:((old(X)|~humble(X))<=>~curious(X)))&
(((generous(mary)<~>creative(mary)))=>((~happy(paul)&~wise(paul))))&
(![X]:((rich(X)&curious(X))<=>~generous(X)))&
(![X]:((~patient(X)|calm(X))=>(wise(X)|~generous(X))))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:(~calm(X)<=>(curious(X)<~>~strong(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~brave(X)|~rich(X))))&
((~old(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~happy(X)))&
((~brave(mary)&~funny(mary)))&
(?[X]:((brave(X)<~>quiet(X))))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(?[X]:((~happy(X)<~>generous(X))))&
(kind(lucy)) | ~generous(lucy) | [
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8660874801874782065544962
% SZS output start Proof for 8660874801874782065544962
8. ! [X0] : ((~humble(X0) | old(X0)) <=> ~curious(X0)) [input p7]
10. ! [X0] : ((curious(X0) & rich(X0)) <=> ~generous(X0)) [input p9]
16. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> ~happy(X0)) [input p15]
24. ~generous(lucy) [input hypothesis]
52. ! [X0] : (((~humble(X0) | old(X0)) | curious(X0)) & (~curious(X0) | (humble(X0) & ~old(X0)))) [nnf transformation 8]
53. ! [X0] : ((~humble(X0) | old(X0) | curious(X0)) & (~curious(X0) | (humble(X0) & ~old(X0)))) [flattening 52]
55. ! [X0] : (((curious(X0) & rich(X0)) | generous(X0)) & (~generous(X0) | (~curious(X0) | ~rich(X0)))) [nnf transformation 10]
56. ! [X0] : (((curious(X0) & rich(X0)) | generous(X0)) & (~generous(X0) | ~curious(X0) | ~rich(X0))) [flattening 55]
67. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | happy(X0)) & (~happy(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 16]
107. ~curious(X0) | humble(X0) [cnf transformation 53]
115. generous(X0) | curious(X0) [cnf transformation 56]
132. ~happy(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 67]
134. ~humble(X0) | happy(X0) | happy(X0) [cnf transformation 67]
148. ~generous(lucy) [cnf transformation 24]
149. ~happy(X0) | ~humble(X0) [duplicate literal removal 132]
150. ~humble(X0) | happy(X0) [duplicate literal removal 134]
295. ~humble(X0) [subsumption resolution 149,150]
327. curious(lucy) [resolution 115,148]
330. humble(lucy) [resolution 327,107]
331. $false [subsumption resolution 330,295]
% SZS output end Proof for 8660874801874782065544962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not old then alice is both quiet and tall and vice versa.
Everyone who is both not patient and not strong is generous and vice versa.
If someone is calm or not curious then someone is not patient and vice versa.
If fred is generous then mary is not curious or strong.
Everyone who is rich is both funny and happy.
If someone is not quiet or not creative then someone is either tall or not old.
If john is either not brave or creative then someone is rich and vice versa.
If someone is either not kind or not strong then fred is old or not humble.
Everyone who is both not wise and humble is patient.
If paul is both calm and not old then mary is either not humble or not patient.
Everyone who is old is both patient and humble and vice versa.
Everyone who is not strong is happy and vice versa.
Everyone who is creative or not wise is kind and vice versa.
Everyone who is both not happy and not tall is both wise and quiet.
If someone is not strong or not patient then john is both generous and old.
If someone is not wise or not rich then alice is quiet and vice versa.
Susan is either not patient or not funny.
Susan is not strong or patient.
Someone is not funny or not generous.
Paul is either not quiet or funny.
Someone is not old or not curious.
John is kind or not rich.
Someone is not humble or not happy. | Paul is patient. | entailment | ((?[X]:((quiet(X)&~old(X))))<=>((quiet(alice)&tall(alice))))&
(![X]:((~patient(X)&~strong(X))<=>generous(X)))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:(~patient(X))))&
((generous(fred))=>((~curious(mary)|strong(mary))))&
(![X]:(rich(X)=>(funny(X)&happy(X))))&
((?[X]:((~quiet(X)|~creative(X))))=>(?[X]:((tall(X)<~>~old(X)))))&
(((~brave(john)<~>creative(john)))<=>(?[X]:(rich(X))))&
((?[X]:((~kind(X)<~>~strong(X))))=>((old(fred)|~humble(fred))))&
(![X]:((~wise(X)&humble(X))=>patient(X)))&
(((calm(paul)&~old(paul)))=>((~humble(mary)<~>~patient(mary))))&
(![X]:(old(X)<=>(patient(X)&humble(X))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:((creative(X)|~wise(X))<=>kind(X)))&
(![X]:((~happy(X)&~tall(X))=>(wise(X)&quiet(X))))&
((?[X]:((~strong(X)|~patient(X))))=>((generous(john)&old(john))))&
((?[X]:((~wise(X)|~rich(X))))<=>(quiet(alice)))&
((~patient(susan)<~>~funny(susan)))&
((~strong(susan)|patient(susan)))&
(?[X]:((~funny(X)|~generous(X))))&
((~quiet(paul)<~>funny(paul)))&
(?[X]:((~old(X)|~curious(X))))&
((kind(john)|~rich(john)))&
(?[X]:((~humble(X)|~happy(X)))) | patient(paul) | [
"p1",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7208155652608825183783586
% SZS output start Proof for 7208155652608825183783586
2. ! [X0] : ((~strong(X0) & ~patient(X0)) <=> generous(X0)) [input p1]
11. ! [X0] : (old(X0) <=> (humble(X0) & patient(X0))) [input p10]
15. ? [X0] : (~patient(X0) | ~strong(X0)) => (old(john) & generous(john)) [input p14]
24. ~patient(paul) [input hypothesis]
39. (old(john) & generous(john)) | ! [X0] : (patient(X0) & strong(X0)) [ennf transformation 15]
45. ! [X0] : (((~strong(X0) & ~patient(X0)) | ~generous(X0)) & (generous(X0) | (strong(X0) | patient(X0)))) [nnf transformation 2]
46. ! [X0] : (((~strong(X0) & ~patient(X0)) | ~generous(X0)) & (generous(X0) | strong(X0) | patient(X0))) [flattening 45]
62. ! [X0] : ((old(X0) | (~humble(X0) | ~patient(X0))) & ((humble(X0) & patient(X0)) | ~old(X0))) [nnf transformation 11]
63. ! [X0] : ((old(X0) | ~humble(X0) | ~patient(X0)) & ((humble(X0) & patient(X0)) | ~old(X0))) [flattening 62]
84. ~generous(X0) | ~patient(X0) [cnf transformation 46]
85. ~generous(X0) | ~strong(X0) [cnf transformation 46]
105. ~old(X0) | patient(X0) [cnf transformation 63]
116. generous(john) | patient(X0) [cnf transformation 39]
117. old(john) | strong(X0) [cnf transformation 39]
131. ~patient(paul) [cnf transformation 24]
156. 6 <=> ! [X1] : patient(X1) [avatar definition]
157. patient(X1) <- (6) [avatar component clause 156]
264. 31 <=> old(john) [avatar definition]
266. old(john) <- (31) [avatar component clause 264]
269. 32 <=> ! [X0] : strong(X0) [avatar definition]
270. strong(X0) <- (32) [avatar component clause 269]
271. 32 | 31 [avatar split clause 117,264,269]
273. 33 <=> generous(john) [avatar definition]
275. generous(john) <- (33) [avatar component clause 273]
276. 6 | 33 [avatar split clause 116,273,156]
358. $false <- (6) [resolution 157,131]
359. ~6 [avatar contradiction clause 358]
362. ~patient(john) <- (33) [resolution 84,275]
363. ~strong(john) <- (33) [resolution 85,275]
364. $false <- (32, 33) [subsumption resolution 363,270]
365. ~32 | ~33 [avatar contradiction clause 364]
368. patient(john) <- (31) [resolution 105,266]
369. $false <- (31, 33) [subsumption resolution 368,362]
370. ~31 | ~33 [avatar contradiction clause 369]
371. $false [avatar sat refutation 271,276,359,365,370]
% SZS output end Proof for 7208155652608825183783586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and quiet then someone is both not creative and not rich and vice versa.
If someone is either old or not creative then someone is either strong or not tall and vice versa.
Everyone who is either tall or not quiet is either humble or generous and vice versa.
Everyone who is both not humble and old is both not quiet and curious and vice versa.
Everyone who is not brave is not happy.
Everyone who is curious is both not funny and not old.
If susan is both happy and not wise then someone is both not strong and not curious.
Everyone who is either not quiet or rich is wise or patient and vice versa.
Everyone who is either curious or old is kind or not happy.
Everyone who is both old and not brave is both not humble and quiet and vice versa.
Everyone who is either not brave or brave is not patient or not funny and vice versa.
If someone is both not happy and kind then mary is not patient or not strong and vice versa.
Everyone who is not tall is not curious or not patient.
Everyone who is wise is either not rich or not old and vice versa.
Everyone who is both not quiet and not brave is both not quiet and not creative and vice versa.
If paul is either not tall or not happy then someone is either not tall or not strong.
Someone is either not rich or not kind.
Mary is not generous or not tall.
Fred is tall or generous.
Paul is old.
Someone is funny.
Fred is either not humble or creative.
Someone is either not humble or happy.
Someone is both not patient and not kind. | Mary is not creative. | neutral | ((?[X]:((patient(X)&quiet(X))))<=>(?[X]:((~creative(X)&~rich(X)))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~humble(X)&old(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~brave(X)=>~happy(X)))&
(![X]:(curious(X)=>(~funny(X)&~old(X))))&
(((happy(susan)&~wise(susan)))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~quiet(X)<~>rich(X))<=>(wise(X)|patient(X))))&
(![X]:((curious(X)<~>old(X))=>(kind(X)|~happy(X))))&
(![X]:((old(X)&~brave(X))<=>(~humble(X)&quiet(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(~patient(X)|~funny(X))))&
((?[X]:((~happy(X)&kind(X))))<=>((~patient(mary)|~strong(mary))))&
(![X]:(~tall(X)=>(~curious(X)|~patient(X))))&
(![X]:(wise(X)<=>(~rich(X)<~>~old(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(~quiet(X)&~creative(X))))&
(((~tall(paul)<~>~happy(paul)))=>(?[X]:((~tall(X)<~>~strong(X)))))&
(?[X]:((~rich(X)<~>~kind(X))))&
((~generous(mary)|~tall(mary)))&
((tall(fred)|generous(fred)))&
(old(paul))&
(?[X]:(funny(X)))&
((~humble(fred)<~>creative(fred)))&
(?[X]:((~humble(X)<~>happy(X))))&
(?[X]:((~patient(X)&~kind(X)))) | ~creative(mary) | [] | null | 0 |
If john is not old or brave then susan is both not calm and humble.
Everyone who is old or calm is not wise and vice versa.
Everyone who is not patient is either creative or not calm.
If lucy is not happy then alice is not creative or not generous.
Everyone who is not curious is both not rich and funny and vice versa.
If mary is not happy then someone is not wise or not rich.
If someone is not happy then someone is brave or not quiet.
Everyone who is brave or strong is either not creative or not humble.
Everyone who is strong or not wise is both patient and not brave and vice versa.
If john is both not quiet and humble then mary is either funny or not calm and vice versa.
If someone is both generous and funny then lucy is patient.
Everyone who is not rich or not old is not funny.
Everyone who is either not kind or not generous is not old or not strong and vice versa.
Everyone who is both curious and not calm is rich or curious and vice versa.
Everyone who is brave or rich is both not quiet and quiet.
Fred is both old and not tall.
Susan is happy.
Someone is both wise and tall.
Paul is not generous.
Mary is not old.
Someone is either funny or humble. | Fred is calm. | contradiction | (((~old(john)|brave(john)))=>((~calm(susan)&humble(susan))))&
(![X]:((old(X)|calm(X))<=>~wise(X)))&
(![X]:(~patient(X)=>(creative(X)<~>~calm(X))))&
((~happy(lucy))=>((~creative(alice)|~generous(alice))))&
(![X]:(~curious(X)<=>(~rich(X)&funny(X))))&
((~happy(mary))=>(?[X]:((~wise(X)|~rich(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((brave(X)|strong(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((strong(X)|~wise(X))<=>(patient(X)&~brave(X))))&
(((~quiet(john)&humble(john)))<=>((funny(mary)<~>~calm(mary))))&
((?[X]:((generous(X)&funny(X))))=>(patient(lucy)))&
(![X]:((~rich(X)|~old(X))=>~funny(X)))&
(![X]:((~kind(X)<~>~generous(X))<=>(~old(X)|~strong(X))))&
(![X]:((curious(X)&~calm(X))<=>(rich(X)|curious(X))))&
(![X]:((brave(X)|rich(X))=>(~quiet(X)&quiet(X))))&
((old(fred)&~tall(fred)))&
(happy(susan))&
(?[X]:((wise(X)&tall(X))))&
(~generous(paul))&
(~old(mary))&
(?[X]:((funny(X)<~>humble(X)))) | calm(fred) | [
"p4",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3745672150413294078812414
% SZS output start Proof for 3745672150413294078812414
5. ! [X0] : (~curious(X0) <=> (funny(X0) & ~rich(X0))) [input p4]
12. ! [X0] : ((~old(X0) | ~rich(X0)) => ~funny(X0)) [input p11]
14. ! [X0] : ((~calm(X0) & curious(X0)) <=> (curious(X0) | rich(X0))) [input p13]
15. ! [X0] : ((rich(X0) | brave(X0)) => (quiet(X0) & ~quiet(X0))) [input p14]
22. calm(fred) [input hypothesis]
32. ! [X0] : (~funny(X0) | (old(X0) & rich(X0))) [ennf transformation 12]
33. ! [X0] : ((quiet(X0) & ~quiet(X0)) | (~rich(X0) & ~brave(X0))) [ennf transformation 15]
37. ! [X0] : ((~curious(X0) | (~funny(X0) | rich(X0))) & ((funny(X0) & ~rich(X0)) | curious(X0))) [nnf transformation 5]
38. ! [X0] : ((~curious(X0) | ~funny(X0) | rich(X0)) & ((funny(X0) & ~rich(X0)) | curious(X0))) [flattening 37]
46. ! [X0] : (((~calm(X0) & curious(X0)) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | (calm(X0) | ~curious(X0)))) [nnf transformation 14]
47. ! [X0] : (((~calm(X0) & curious(X0)) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | calm(X0) | ~curious(X0))) [flattening 46]
63. funny(X0) | curious(X0) [cnf transformation 38]
81. ~funny(X0) | rich(X0) [cnf transformation 32]
93. ~curious(X0) | ~calm(X0) [cnf transformation 47]
95. ~quiet(X0) | ~rich(X0) [cnf transformation 33]
97. quiet(X0) | ~rich(X0) [cnf transformation 33]
106. calm(fred) [cnf transformation 22]
157. ~rich(X0) [subsumption resolution 95,97]
173. rich(X0) | curious(X0) [resolution 81,63]
176. curious(X0) [subsumption resolution 173,157]
180. ~calm(X0) [resolution 93,176]
190. $false [resolution 180,106]
% SZS output end Proof for 3745672150413294078812414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not creative or not quiet then john is both tall and not strong. Everyone who is either old or quiet is not old or not kind. If someone is both not patient and strong then paul is quiet or funny and vice versa. Everyone who is either not tall or funny is not funny or not tall and vice versa. Everyone who is either old or not wise is either kind or not tall and vice versa. Everyone who is both not happy and old is both not brave and not wise. Everyone who is not brave is either humble or funny. Everyone who is either not wise or patient is both old and patient. Everyone who is both wise and not kind is brave or not funny and vice versa. If alice is either generous or strong then lucy is either not brave or not happy and vice versa. Everyone who is not calm is either not curious or not generous. Everyone who is either not patient or not tall is old and vice versa. Everyone who is either patient or not tall is humble or not humble. Everyone who is generous or strong is either not happy or not creative and vice versa. Everyone who is humble is strong. Someone is both patient and not generous. Alice is either not tall or tall. Someone is creative. Someone is either not patient or brave. Mary is rich. | Alice is not patient. | contradiction | (((~creative(lucy)<~>~quiet(lucy)))=>((tall(john)&~strong(john))))&
(![X]:((old(X)<~>quiet(X))=>(~old(X)|~kind(X))))&
((?[X]:((~patient(X)&strong(X))))<=>((quiet(paul)|funny(paul))))&
(![X]:((~tall(X)<~>funny(X))<=>(~funny(X)|~tall(X))))&
(![X]:((old(X)<~>~wise(X))<=>(kind(X)<~>~tall(X))))&
(![X]:((~happy(X)&old(X))=>(~brave(X)&~wise(X))))&
(![X]:(~brave(X)=>(humble(X)<~>funny(X))))&
(![X]:((~wise(X)<~>patient(X))=>(old(X)&patient(X))))&
(![X]:((wise(X)&~kind(X))<=>(brave(X)|~funny(X))))&
(((generous(alice)<~>strong(alice)))<=>((~brave(lucy)<~>~happy(lucy))))&
(![X]:(~calm(X)=>(~curious(X)<~>~generous(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>old(X)))&
(![X]:((patient(X)<~>~tall(X))=>(humble(X)|~humble(X))))&
(![X]:((generous(X)|strong(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(humble(X)=>strong(X)))&
(?[X]:((patient(X)&~generous(X))))&
((~tall(alice)<~>tall(alice)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)<~>brave(X))))&
(rich(mary)) | ~patient(alice) | [
"p3",
"p4",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3533243955599546435601716
% SZS output start Proof for 3533243955599546435601716
4. ! [X0] : ((~tall(X0) <~> funny(X0)) <=> (~tall(X0) | ~funny(X0))) [input p3]
5. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (kind(X0) <~> ~tall(X0))) [input p4]
8. ! [X0] : ((~wise(X0) <~> patient(X0)) => (patient(X0) & old(X0))) [input p7]
9. ! [X0] : ((~kind(X0) & wise(X0)) <=> (~funny(X0) | brave(X0))) [input p8]
12. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> old(X0)) [input p11]
21. ~patient(alice) [input hypothesis]
30. ! [X0] : ((patient(X0) & old(X0)) | (~wise(X0) <=> patient(X0))) [ennf transformation 8]
41. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [flattening 41]
43. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0)))) & (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 5]
45. ! [X0] : ((patient(X0) & old(X0)) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) [nnf transformation 30]
46. ! [X0] : (((~kind(X0) & wise(X0)) | (funny(X0) & ~brave(X0))) & ((~funny(X0) | brave(X0)) | (kind(X0) | ~wise(X0)))) [nnf transformation 9]
47. ! [X0] : (((~kind(X0) & wise(X0)) | (funny(X0) & ~brave(X0))) & (~funny(X0) | brave(X0) | kind(X0) | ~wise(X0))) [flattening 46]
49. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ~old(X0)) & (old(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 12]
73. ~tall(X0) | ~funny(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 42]
74. funny(X0) | ~tall(X0) | funny(X0) [cnf transformation 42]
77. ~funny(X0) | tall(X0) | tall(X0) [cnf transformation 42]
83. ~wise(X0) | old(X0) | kind(X0) | tall(X0) [cnf transformation 43]
92. patient(X0) | patient(X0) | wise(X0) [cnf transformation 45]
98. ~kind(X0) | funny(X0) [cnf transformation 47]
110. ~old(X0) | patient(X0) | tall(X0) [cnf transformation 49]
127. ~patient(alice) [cnf transformation 21]
128. wise(X0) | patient(X0) [duplicate literal removal 92]
129. ~tall(X0) | ~funny(X0) [duplicate literal removal 73]
130. ~tall(X0) | funny(X0) [duplicate literal removal 74]
131. ~funny(X0) | tall(X0) [duplicate literal removal 77]
177. ~funny(X0) [subsumption resolution 129,131]
179. ~kind(X0) [subsumption resolution 98,177]
313. old(X0) | kind(X0) | tall(X0) | patient(X0) [resolution 83,128]
315. old(X0) | tall(X0) | patient(X0) [subsumption resolution 313,179]
316. patient(X0) | tall(X0) [subsumption resolution 315,110]
321. tall(alice) [resolution 316,127]
326. funny(alice) [resolution 321,130]
328. $false [subsumption resolution 326,177]
% SZS output end Proof for 3533243955599546435601716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not happy or creative.
If someone is either old or not wise then someone is tall and vice versa.
If mary is rich then someone is rich and vice versa.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
If john is kind or not patient then someone is not creative or not strong and vice versa.
If john is not strong or rich then someone is either not kind or old and vice versa.
Everyone who is both strong and not wise is both not happy and calm and vice versa.
Everyone who is not wise or not patient is either humble or not strong.
If john is both not kind and strong then john is both quiet and not brave.
Someone is both tall and calm.
John is tall.
Someone is either not tall or not happy.
Alice is both not tall and not happy.
Someone is either not kind or brave.
Lucy is both not calm and brave.
Someone is brave or patient.
John is funny or quiet. | Alice is humble. | entailment | (![X]:(tall(X)=>(~happy(X)|creative(X))))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:(tall(X))))&
((rich(mary))<=>(?[X]:(rich(X))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
(((kind(john)|~patient(john)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(((~strong(john)|rich(john)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((strong(X)&~wise(X))<=>(~happy(X)&calm(X))))&
(![X]:((~wise(X)|~patient(X))=>(humble(X)<~>~strong(X))))&
(((~kind(john)&strong(john)))=>((quiet(john)&~brave(john))))&
(?[X]:((tall(X)&calm(X))))&
(tall(john))&
(?[X]:((~tall(X)<~>~happy(X))))&
((~tall(alice)&~happy(alice)))&
(?[X]:((~kind(X)<~>brave(X))))&
((~calm(lucy)&brave(lucy)))&
(?[X]:((brave(X)|patient(X))))&
((funny(john)|quiet(john))) | humble(alice) | [
"p9",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8327063306914339500190377
% SZS output start Proof for 8327063306914339500190377
10. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> happy(X0)) [input p9]
14. ! [X0] : ((~wise(X0) & strong(X0)) <=> (calm(X0) & ~happy(X0))) [input p13]
15. ! [X0] : ((~patient(X0) | ~wise(X0)) => (humble(X0) <~> ~strong(X0))) [input p14]
20. ~happy(alice) & ~tall(alice) [input p19]
25. ~humble(alice) [input hypothesis]
35. ! [X0] : ((humble(X0) <~> ~strong(X0)) | (patient(X0) & wise(X0))) [ennf transformation 15]
65. ! [X0] : (((~rich(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [nnf transformation 10]
66. ! [X0] : ((~rich(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & calm(X0)))) [flattening 65]
77. ! [X0] : (((~wise(X0) & strong(X0)) | (~calm(X0) | happy(X0))) & ((calm(X0) & ~happy(X0)) | (wise(X0) | ~strong(X0)))) [nnf transformation 14]
78. ! [X0] : (((~wise(X0) & strong(X0)) | ~calm(X0) | happy(X0)) & ((calm(X0) & ~happy(X0)) | wise(X0) | ~strong(X0))) [flattening 77]
79. ! [X0] : (((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | (patient(X0) & wise(X0))) [nnf transformation 35]
116. calm(X0) | happy(X0) [cnf transformation 66]
132. strong(X0) | ~calm(X0) | happy(X0) [cnf transformation 78]
133. ~wise(X0) | ~calm(X0) | happy(X0) [cnf transformation 78]
134. ~strong(X0) | humble(X0) | wise(X0) [cnf transformation 79]
146. ~happy(alice) [cnf transformation 20]
153. ~humble(alice) [cnf transformation 25]
319. ~wise(X0) | happy(X0) [subsumption resolution 133,116]
320. strong(X0) | happy(X0) [subsumption resolution 132,116]
456. humble(X0) | wise(X0) | happy(X0) [resolution 134,320]
458. humble(X0) | happy(X0) [subsumption resolution 456,319]
466. happy(alice) [resolution 458,153]
467. $false [subsumption resolution 466,146]
% SZS output end Proof for 8327063306914339500190377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is rich.
If susan is creative or humble then someone is tall and vice versa.
Everyone who is tall or funny is not tall.
If john is either humble or quiet then alice is strong and vice versa.
If someone is not strong or not patient then susan is old and vice versa.
Everyone who is either humble or curious is tall.
If someone is tall then someone is both calm and brave and vice versa.
If lucy is either tall or rich then someone is either kind or not generous and vice versa.
If someone is strong or not humble then someone is happy or not generous.
If susan is both curious and not kind then someone is both not funny and not wise and vice versa.
Everyone who is either not kind or not tall is either not creative or not rich.
Everyone who is not tall is not kind or old.
If mary is not quiet then someone is not tall.
Everyone who is both creative and not old is humble.
If lucy is either not old or generous then someone is either not happy or not generous and vice versa.
If someone is both not patient and not old then someone is not humble or brave.
Someone is both funny and patient.
Someone is either not funny or tall.
Someone is brave or not wise.
Someone is not strong or not humble.
Someone is not rich.
Someone is both not funny and happy.
Someone is creative or not calm.
Someone is generous or curious. | Susan is not curious. | entailment | (![X]:(patient(X)=>rich(X)))&
(((creative(susan)|humble(susan)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)|funny(X))=>~tall(X)))&
(((humble(john)<~>quiet(john)))<=>(strong(alice)))&
((?[X]:((~strong(X)|~patient(X))))<=>(old(susan)))&
(![X]:((humble(X)<~>curious(X))=>tall(X)))&
((?[X]:(tall(X)))<=>(?[X]:((calm(X)&brave(X)))))&
(((tall(lucy)<~>rich(lucy)))<=>(?[X]:((kind(X)<~>~generous(X)))))&
((?[X]:((strong(X)|~humble(X))))=>(?[X]:((happy(X)|~generous(X)))))&
(((curious(susan)&~kind(susan)))<=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~kind(X)<~>~tall(X))=>(~creative(X)<~>~rich(X))))&
(![X]:(~tall(X)=>(~kind(X)|old(X))))&
((~quiet(mary))=>(?[X]:(~tall(X))))&
(![X]:((creative(X)&~old(X))=>humble(X)))&
(((~old(lucy)<~>generous(lucy)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
((?[X]:((~patient(X)&~old(X))))=>(?[X]:((~humble(X)|brave(X)))))&
(?[X]:((funny(X)&patient(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((brave(X)|~wise(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~funny(X)&happy(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((generous(X)|curious(X)))) | ~curious(susan) | [
"p1",
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4969022978591395112407987
% SZS output start Proof for 4969022978591395112407987
2. (humble(susan) | creative(susan)) <=> ? [X0] : tall(X0) [input p1]
3. ! [X0] : ((funny(X0) | tall(X0)) => ~tall(X0)) [input p2]
6. ! [X0] : ((humble(X0) <~> curious(X0)) => tall(X0)) [input p5]
25. curious(susan) [input hypothesis]
30. ! [X0] : (~tall(X0) | (~funny(X0) & ~tall(X0))) [ennf transformation 3]
31. ! [X0] : (tall(X0) | (humble(X0) <=> curious(X0))) [ennf transformation 6]
40. ((humble(susan) | creative(susan)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (~humble(susan) & ~creative(susan))) [nnf transformation 2]
41. (humble(susan) | creative(susan) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (~humble(susan) & ~creative(susan))) [flattening 40]
42. (humble(susan) | creative(susan) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | (~humble(susan) & ~creative(susan))) [rectify 41]
43. ? [X1] : tall(X1) => tall(sK0) [choice axiom]
44. (humble(susan) | creative(susan) | ! [X0] : ~tall(X0)) & (tall(sK0) | (~humble(susan) & ~creative(susan))) [skolemisation 42,43]
50. ! [X0] : (tall(X0) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0)))) [nnf transformation 31]
97. tall(sK0) | ~humble(susan) [cnf transformation 44]
99. ~tall(X0) | ~tall(X0) [cnf transformation 30]
109. ~curious(X0) | humble(X0) | tall(X0) [cnf transformation 50]
154. curious(susan) [cnf transformation 25]
155. ~tall(X0) [duplicate literal removal 99]
157. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
158. ~tall(X0) <- (1) [avatar component clause 157]
164. 3 <=> humble(susan) [avatar definition]
169. 4 <=> tall(sK0) [avatar definition]
171. tall(sK0) <- (4) [avatar component clause 169]
172. ~3 | 4 [avatar split clause 97,169,164]
174. 1 [avatar split clause 155,157]
285. 29 <=> curious(susan) [avatar definition]
287. curious(susan) <- (29) [avatar component clause 285]
388. 29 [avatar split clause 154,285]
397. humble(susan) | tall(susan) <- (29) [resolution 109,287]
401. humble(susan) <- (1, 29) [subsumption resolution 397,158]
402. 3 | ~1 | ~29 [avatar split clause 401,285,157,164]
403. $false <- (1, 4) [subsumption resolution 171,158]
404. ~1 | ~4 [avatar contradiction clause 403]
405. $false [avatar sat refutation 172,174,388,402,404]
% SZS output end Proof for 4969022978591395112407987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or tall then someone is not wise or curious.
Everyone who is either not wise or patient is strong and vice versa.
If someone is not tall then alice is either creative or not old and vice versa.
If someone is not creative then susan is both not kind and rich.
If someone is not tall or not curious then someone is not kind or funny.
If someone is not generous or happy then fred is funny.
Everyone who is strong or calm is both happy and old.
Everyone who is old is strong and vice versa.
Everyone who is both not brave and not curious is both strong and happy and vice versa.
Everyone who is both not humble and tall is both not kind and not humble.
Everyone who is not strong is patient or not curious.
Everyone who is not calm or not curious is both not humble and brave.
Everyone who is old is both not rich and not tall.
Everyone who is either old or not generous is either tall or curious and vice versa.
If someone is either not happy or old then lucy is either not generous or patient.
Everyone who is wise or not brave is either patient or quiet and vice versa.
Someone is both kind and not generous.
Someone is either generous or rich.
Someone is either generous or brave.
John is either not funny or happy. | Fred is quiet. | entailment | ((?[X]:((~strong(X)|tall(X))))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((~wise(X)<~>patient(X))<=>strong(X)))&
((?[X]:(~tall(X)))<=>((creative(alice)<~>~old(alice))))&
((?[X]:(~creative(X)))=>((~kind(susan)&rich(susan))))&
((?[X]:((~tall(X)|~curious(X))))=>(?[X]:((~kind(X)|funny(X)))))&
((?[X]:((~generous(X)|happy(X))))=>(funny(fred)))&
(![X]:((strong(X)|calm(X))=>(happy(X)&old(X))))&
(![X]:(old(X)<=>strong(X)))&
(![X]:((~brave(X)&~curious(X))<=>(strong(X)&happy(X))))&
(![X]:((~humble(X)&tall(X))=>(~kind(X)&~humble(X))))&
(![X]:(~strong(X)=>(patient(X)|~curious(X))))&
(![X]:((~calm(X)|~curious(X))=>(~humble(X)&brave(X))))&
(![X]:(old(X)=>(~rich(X)&~tall(X))))&
(![X]:((old(X)<~>~generous(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((~happy(X)<~>old(X))))=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((wise(X)|~brave(X))<=>(patient(X)<~>quiet(X))))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((generous(X)<~>brave(X))))&
((~funny(john)<~>happy(john))) | quiet(fred) | [
"p1",
"p6",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2831713165395323253805111
% SZS output start Proof for 2831713165395323253805111
2. ! [X0] : ((~wise(X0) <~> patient(X0)) <=> strong(X0)) [input p1]
7. ! [X0] : ((calm(X0) | strong(X0)) => (old(X0) & happy(X0))) [input p6]
8. ! [X0] : (old(X0) <=> strong(X0)) [input p7]
9. ! [X0] : ((~curious(X0) & ~brave(X0)) <=> (happy(X0) & strong(X0))) [input p8]
12. ! [X0] : ((~curious(X0) | ~calm(X0)) => (brave(X0) & ~humble(X0))) [input p11]
16. ! [X0] : ((~brave(X0) | wise(X0)) <=> (patient(X0) <~> quiet(X0))) [input p15]
21. ~quiet(fred) [input hypothesis]
28. ! [X0] : ((old(X0) & happy(X0)) | (~calm(X0) & ~strong(X0))) [ennf transformation 7]
33. ! [X0] : ((brave(X0) & ~humble(X0)) | (curious(X0) & calm(X0))) [ennf transformation 12]
39. ! [X0] : ((((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | ~strong(X0)) & (strong(X0) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0))))) [nnf transformation 2]
47. ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0))) [nnf transformation 8]
48. ! [X0] : (((~curious(X0) & ~brave(X0)) | (~happy(X0) | ~strong(X0))) & ((happy(X0) & strong(X0)) | (curious(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((~curious(X0) & ~brave(X0)) | ~happy(X0) | ~strong(X0)) & ((happy(X0) & strong(X0)) | curious(X0) | brave(X0))) [flattening 48]
52. ! [X0] : (((~brave(X0) | wise(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (brave(X0) & ~wise(X0)))) [nnf transformation 16]
53. ! [X0] : ((~brave(X0) | wise(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (brave(X0) & ~wise(X0)))) [flattening 52]
65. patient(X0) | strong(X0) | wise(X0) [cnf transformation 39]
66. ~patient(X0) | ~wise(X0) | strong(X0) [cnf transformation 39]
79. ~strong(X0) | happy(X0) [cnf transformation 28]
82. ~calm(X0) | old(X0) [cnf transformation 28]
83. ~old(X0) | strong(X0) [cnf transformation 47]
87. ~brave(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 49]
88. ~curious(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 49]
94. brave(X0) | calm(X0) [cnf transformation 33]
95. brave(X0) | curious(X0) [cnf transformation 33]
110. ~wise(X0) | patient(X0) | quiet(X0) [cnf transformation 53]
114. ~brave(X0) | wise(X0) | quiet(X0) | ~patient(X0) [cnf transformation 53]
124. ~quiet(fred) [cnf transformation 21]
198. ~curious(X0) | ~strong(X0) [subsumption resolution 88,79]
199. ~brave(X0) | ~strong(X0) [subsumption resolution 87,79]
268. ~strong(X0) | curious(X0) [resolution 199,95]
271. ~strong(X0) [subsumption resolution 268,198]
295. 28 <=> brave(fred) [avatar definition]
296. ~brave(fred) <- (~28) [avatar component clause 295]
297. brave(fred) <- (28) [avatar component clause 295]
299. 29 <=> patient(fred) [avatar definition]
300. ~patient(fred) <- (~29) [avatar component clause 299]
301. patient(fred) <- (29) [avatar component clause 299]
417. wise(fred) | quiet(fred) | ~patient(fred) <- (28) [resolution 114,297]
432. wise(fred) | ~patient(fred) <- (28) [subsumption resolution 417,124]
434. 46 <=> wise(fred) [avatar definition]
436. wise(fred) <- (46) [avatar component clause 434]
437. ~29 | 46 | ~28 [avatar split clause 432,295,434,299]
438. strong(fred) | wise(fred) <- (~29) [resolution 300,65]
439. wise(fred) <- (~29) [subsumption resolution 438,271]
440. 46 | 29 [avatar split clause 439,299,434]
466. patient(fred) | quiet(fred) <- (46) [resolution 436,110]
471. patient(fred) <- (46) [subsumption resolution 466,124]
472. 29 | ~46 [avatar split clause 471,434,299]
475. ~wise(fred) | strong(fred) <- (29) [resolution 301,66]
479. ~wise(fred) <- (29) [subsumption resolution 475,271]
480. ~46 | ~29 [avatar split clause 479,299,434]
484. calm(fred) <- (~28) [resolution 296,94]
514. old(fred) <- (~28) [resolution 484,82]
537. strong(fred) <- (~28) [resolution 514,83]
540. $false <- (~28) [subsumption resolution 537,271]
541. 28 [avatar contradiction clause 540]
542. $false [avatar sat refutation 437,440,472,480,541]
% SZS output end Proof for 2831713165395323253805111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is either not brave or not old and vice versa.
If mary is not wise then john is not kind and vice versa.
If john is both quiet and happy then fred is either wise or generous and vice versa.
Everyone who is both not humble and not generous is both not kind and not patient and vice versa.
Everyone who is tall is both not humble and humble.
If someone is both not strong and strong then lucy is either not creative or funny and vice versa.
Everyone who is rich is patient.
Everyone who is either not tall or tall is either not humble or quiet.
If fred is both happy and funny then lucy is both rich and old and vice versa.
Everyone who is either not kind or not calm is both not generous and quiet and vice versa.
Everyone who is kind or not calm is both not patient and quiet and vice versa.
If susan is not calm then fred is not kind or patient.
If someone is either not patient or curious then alice is both not tall and quiet and vice versa.
Everyone who is either curious or kind is either humble or not creative and vice versa.
If someone is not creative then someone is not calm and vice versa.
If fred is either not wise or not humble then susan is brave and vice versa.
Someone is either not calm or not rich.
Someone is not quiet or calm.
Fred is both humble and not generous.
Susan is both creative and wise.
Someone is humble.
Paul is creative or not patient.
Someone is either not calm or kind.
Alice is either not curious or not calm. | John is kind. | neutral | (![X]:(funny(X)<=>(~brave(X)<~>~old(X))))&
((~wise(mary))<=>(~kind(john)))&
(((quiet(john)&happy(john)))<=>((wise(fred)<~>generous(fred))))&
(![X]:((~humble(X)&~generous(X))<=>(~kind(X)&~patient(X))))&
(![X]:(tall(X)=>(~humble(X)&humble(X))))&
((?[X]:((~strong(X)&strong(X))))<=>((~creative(lucy)<~>funny(lucy))))&
(![X]:(rich(X)=>patient(X)))&
(![X]:((~tall(X)<~>tall(X))=>(~humble(X)<~>quiet(X))))&
(((happy(fred)&funny(fred)))<=>((rich(lucy)&old(lucy))))&
(![X]:((~kind(X)<~>~calm(X))<=>(~generous(X)&quiet(X))))&
(![X]:((kind(X)|~calm(X))<=>(~patient(X)&quiet(X))))&
((~calm(susan))=>((~kind(fred)|patient(fred))))&
((?[X]:((~patient(X)<~>curious(X))))<=>((~tall(alice)&quiet(alice))))&
(![X]:((curious(X)<~>kind(X))<=>(humble(X)<~>~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~calm(X))))&
(((~wise(fred)<~>~humble(fred)))<=>(brave(susan)))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((humble(fred)&~generous(fred)))&
((creative(susan)&wise(susan)))&
(?[X]:(humble(X)))&
((creative(paul)|~patient(paul)))&
(?[X]:((~calm(X)<~>kind(X))))&
((~curious(alice)<~>~calm(alice))) | kind(john) | [] | null | 0 |
Everyone who is both not wise and quiet is not calm and vice versa.
Everyone who is either quiet or not funny is both rich and not patient and vice versa.
Everyone who is not old or patient is both rich and happy and vice versa.
If someone is not old then alice is both wise and kind.
If someone is both not old and kind then someone is both not curious and not rich.
Everyone who is either generous or not kind is both not tall and brave and vice versa.
If alice is not tall then fred is tall and vice versa.
If lucy is either not happy or not strong then someone is either not funny or curious.
Everyone who is either not old or not wise is not rich.
If alice is both rich and not tall then paul is both not creative and not happy and vice versa.
Everyone who is both brave and generous is funny.
Everyone who is either generous or tall is not creative or not rich and vice versa.
If john is not quiet then someone is both patient and not creative and vice versa.
Everyone who is strong or brave is not kind and vice versa.
If john is generous or not old then someone is both creative and not kind and vice versa.
Everyone who is not generous or not rich is generous.
Someone is both not wise and generous.
Paul is not tall or not kind.
John is happy or generous.
Susan is both happy and not wise.
Fred is either funny or generous.
Someone is generous or not patient.
Mary is either not calm or old.
Alice is not quiet or patient. | Alice is generous. | entailment | (![X]:((~wise(X)&quiet(X))<=>~calm(X)))&
(![X]:((quiet(X)<~>~funny(X))<=>(rich(X)&~patient(X))))&
(![X]:((~old(X)|patient(X))<=>(rich(X)&happy(X))))&
((?[X]:(~old(X)))=>((wise(alice)&kind(alice))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~curious(X)&~rich(X)))))&
(![X]:((generous(X)<~>~kind(X))<=>(~tall(X)&brave(X))))&
((~tall(alice))<=>(tall(fred)))&
(((~happy(lucy)<~>~strong(lucy)))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~old(X)<~>~wise(X))=>~rich(X)))&
(((rich(alice)&~tall(alice)))<=>((~creative(paul)&~happy(paul))))&
(![X]:((brave(X)&generous(X))=>funny(X)))&
(![X]:((generous(X)<~>tall(X))<=>(~creative(X)|~rich(X))))&
((~quiet(john))<=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((strong(X)|brave(X))<=>~kind(X)))&
(((generous(john)|~old(john)))<=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:((~generous(X)|~rich(X))=>generous(X)))&
(?[X]:((~wise(X)&generous(X))))&
((~tall(paul)|~kind(paul)))&
((happy(john)|generous(john)))&
((happy(susan)&~wise(susan)))&
((funny(fred)<~>generous(fred)))&
(?[X]:((generous(X)|~patient(X))))&
((~calm(mary)<~>old(mary)))&
((~quiet(alice)|patient(alice))) | generous(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 409834169139251310314815
% SZS output start Proof for 409834169139251310314815
16. ! [X0] : ((~rich(X0) | ~generous(X0)) => generous(X0)) [input p15]
25. ~generous(alice) [input hypothesis]
33. ! [X0] : (generous(X0) | (rich(X0) & generous(X0))) [ennf transformation 16]
125. generous(X0) | generous(X0) [cnf transformation 33]
139. ~generous(alice) [cnf transformation 25]
140. generous(X0) [duplicate literal removal 125]
285. $false [subsumption resolution 139,140]
% SZS output end Proof for 409834169139251310314815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not happy is quiet and vice versa.
Everyone who is not creative is either generous or not calm and vice versa.
Everyone who is not tall is both strong and old.
Everyone who is curious is either not calm or generous and vice versa.
If susan is not strong or funny then john is either quiet or not patient.
Everyone who is not funny or curious is kind and vice versa.
If someone is not brave then someone is not brave or curious and vice versa.
Everyone who is not strong is both not wise and tall.
If someone is either kind or quiet then mary is not calm.
Everyone who is either not quiet or not funny is not funny or not happy and vice versa.
If someone is not quiet or patient then paul is not kind and vice versa.
If someone is wise or patient then someone is not kind or not humble and vice versa.
If alice is not patient then paul is both kind and not funny and vice versa.
If lucy is not strong or not generous then someone is rich and vice versa.
Everyone who is patient is both not happy and wise.
If susan is both not humble and not old then someone is both not curious and not strong and vice versa.
Fred is rich.
Someone is not tall or old.
Paul is both curious and not old.
Someone is patient or not happy.
Lucy is not tall.
Lucy is either not funny or brave.
Fred is both not calm and not wise. | Alice is patient. | contradiction | (![X]:((old(X)<~>~happy(X))<=>quiet(X)))&
(![X]:(~creative(X)<=>(generous(X)<~>~calm(X))))&
(![X]:(~tall(X)=>(strong(X)&old(X))))&
(![X]:(curious(X)<=>(~calm(X)<~>generous(X))))&
(((~strong(susan)|funny(susan)))=>((quiet(john)<~>~patient(john))))&
(![X]:((~funny(X)|curious(X))<=>kind(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~brave(X)|curious(X)))))&
(![X]:(~strong(X)=>(~wise(X)&tall(X))))&
((?[X]:((kind(X)<~>quiet(X))))=>(~calm(mary)))&
(![X]:((~quiet(X)<~>~funny(X))<=>(~funny(X)|~happy(X))))&
((?[X]:((~quiet(X)|patient(X))))<=>(~kind(paul)))&
((?[X]:((wise(X)|patient(X))))<=>(?[X]:((~kind(X)|~humble(X)))))&
((~patient(alice))<=>((kind(paul)&~funny(paul))))&
(((~strong(lucy)|~generous(lucy)))<=>(?[X]:(rich(X))))&
(![X]:(patient(X)=>(~happy(X)&wise(X))))&
(((~humble(susan)&~old(susan)))<=>(?[X]:((~curious(X)&~strong(X)))))&
(rich(fred))&
(?[X]:((~tall(X)|old(X))))&
((curious(paul)&~old(paul)))&
(?[X]:((patient(X)|~happy(X))))&
(~tall(lucy))&
((~funny(lucy)<~>brave(lucy)))&
((~calm(fred)&~wise(fred))) | patient(alice) | [
"p5",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8623909675702337644384217
% SZS output start Proof for 8623909675702337644384217
6. ! [X0] : ((curious(X0) | ~funny(X0)) <=> kind(X0)) [input p5]
11. ? [X0] : (patient(X0) | ~quiet(X0)) <=> ~kind(paul) [input p10]
19. ~old(paul) & curious(paul) [input p18]
24. patient(alice) [input hypothesis]
35. ! [X0] : (((curious(X0) | ~funny(X0)) | ~kind(X0)) & (kind(X0) | (~curious(X0) & funny(X0)))) [nnf transformation 6]
36. ! [X0] : ((curious(X0) | ~funny(X0) | ~kind(X0)) & (kind(X0) | (~curious(X0) & funny(X0)))) [flattening 35]
45. (? [X0] : (patient(X0) | ~quiet(X0)) | kind(paul)) & (~kind(paul) | ! [X0] : (~patient(X0) & quiet(X0))) [nnf transformation 11]
46. (? [X0] : (patient(X0) | ~quiet(X0)) | kind(paul)) & (~kind(paul) | ! [X1] : (~patient(X1) & quiet(X1))) [rectify 45]
47. ? [X0] : (patient(X0) | ~quiet(X0)) => (patient(sK2) | ~quiet(sK2)) [choice axiom]
48. ((patient(sK2) | ~quiet(sK2)) | kind(paul)) & (~kind(paul) | ! [X1] : (~patient(X1) & quiet(X1))) [skolemisation 46,47]
86. ~curious(X0) | kind(X0) [cnf transformation 36]
102. ~kind(paul) | ~patient(X1) [cnf transformation 48]
122. curious(paul) [cnf transformation 19]
130. patient(alice) [cnf transformation 24]
188. 13 <=> kind(paul) [avatar definition]
201. 16 <=> ! [X1] : ~patient(X1) [avatar definition]
202. ~patient(X1) <- (16) [avatar component clause 201]
203. 16 | ~13 [avatar split clause 102,188,201]
243. 26 <=> patient(alice) [avatar definition]
244. patient(alice) <- (26) [avatar component clause 243]
302. 26 [avatar split clause 130,243]
309. kind(paul) [resolution 86,122]
312. 13 [avatar split clause 309,188]
313. $false <- (16, 26) [resolution 202,244]
314. ~16 | ~26 [avatar contradiction clause 313]
315. $false [avatar sat refutation 203,302,312,314]
% SZS output end Proof for 8623909675702337644384217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or strong is both kind and old and vice versa.
Everyone who is not old is tall or not generous.
Everyone who is not rich is rich or not creative.
Everyone who is both not wise and funny is not quiet.
If someone is not quiet or brave then someone is not old and vice versa.
If paul is calm or not strong then alice is either not creative or patient.
Everyone who is old or not humble is not kind or not rich.
If alice is either curious or happy then someone is both creative and not kind and vice versa.
If someone is both not humble and kind then someone is not humble or funny.
Everyone who is not generous or not calm is strong.
Everyone who is either not happy or not strong is wise or not tall and vice versa.
Everyone who is strong is either not kind or creative.
Everyone who is either old or quiet is either not creative or calm and vice versa.
If paul is either not generous or not creative then someone is either not generous or rich.
Everyone who is tall or not funny is both not kind and generous and vice versa.
Someone is not rich.
Someone is either wise or not old.
John is both calm and not brave.
Someone is not brave.
Alice is either not quiet or not happy.
Lucy is both happy and generous.
John is not strong or patient. | Alice is calm. | entailment | (![X]:((~calm(X)|strong(X))<=>(kind(X)&old(X))))&
(![X]:(~old(X)=>(tall(X)|~generous(X))))&
(![X]:(~rich(X)=>(rich(X)|~creative(X))))&
(![X]:((~wise(X)&funny(X))=>~quiet(X)))&
((?[X]:((~quiet(X)|brave(X))))<=>(?[X]:(~old(X))))&
(((calm(paul)|~strong(paul)))=>((~creative(alice)<~>patient(alice))))&
(![X]:((old(X)|~humble(X))=>(~kind(X)|~rich(X))))&
(((curious(alice)<~>happy(alice)))<=>(?[X]:((creative(X)&~kind(X)))))&
((?[X]:((~humble(X)&kind(X))))=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((~generous(X)|~calm(X))=>strong(X)))&
(![X]:((~happy(X)<~>~strong(X))<=>(wise(X)|~tall(X))))&
(![X]:(strong(X)=>(~kind(X)<~>creative(X))))&
(![X]:((old(X)<~>quiet(X))<=>(~creative(X)<~>calm(X))))&
(((~generous(paul)<~>~creative(paul)))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))<=>(~kind(X)&generous(X))))&
(?[X]:(~rich(X)))&
(?[X]:((wise(X)<~>~old(X))))&
((calm(john)&~brave(john)))&
(?[X]:(~brave(X)))&
((~quiet(alice)<~>~happy(alice)))&
((happy(lucy)&generous(lucy)))&
((~strong(john)|patient(john))) | calm(alice) | [
"p0",
"p2",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8584424954590190483122778
% SZS output start Proof for 8584424954590190483122778
1. ! [X0] : ((strong(X0) | ~calm(X0)) <=> (old(X0) & kind(X0))) [input p0]
3. ! [X0] : (~rich(X0) => (~creative(X0) | rich(X0))) [input p2]
7. ! [X0] : ((~humble(X0) | old(X0)) => (~rich(X0) | ~kind(X0))) [input p6]
10. ! [X0] : ((~calm(X0) | ~generous(X0)) => strong(X0)) [input p9]
12. ! [X0] : (strong(X0) => (~kind(X0) <~> creative(X0))) [input p11]
23. ~calm(alice) [input hypothesis]
28. ! [X0] : ((~creative(X0) | rich(X0)) | rich(X0)) [ennf transformation 3]
29. ! [X0] : (~creative(X0) | rich(X0) | rich(X0)) [flattening 28]
33. ! [X0] : ((~rich(X0) | ~kind(X0)) | (humble(X0) & ~old(X0))) [ennf transformation 7]
34. ! [X0] : (~rich(X0) | ~kind(X0) | (humble(X0) & ~old(X0))) [flattening 33]
36. ! [X0] : (strong(X0) | (calm(X0) & generous(X0))) [ennf transformation 10]
37. ! [X0] : ((~kind(X0) <~> creative(X0)) | ~strong(X0)) [ennf transformation 12]
39. ! [X0] : (((strong(X0) | ~calm(X0)) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | (~strong(X0) & calm(X0)))) [nnf transformation 1]
40. ! [X0] : ((strong(X0) | ~calm(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | (~strong(X0) & calm(X0)))) [flattening 39]
56. ! [X0] : (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~strong(X0)) [nnf transformation 37]
72. ~strong(X0) | kind(X0) [cnf transformation 40]
74. ~strong(X0) | old(X0) [cnf transformation 40]
77. ~creative(X0) | rich(X0) | rich(X0) [cnf transformation 29]
86. ~rich(X0) | ~kind(X0) | ~old(X0) [cnf transformation 34]
96. strong(X0) | calm(X0) [cnf transformation 36]
103. creative(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 56]
133. ~calm(alice) [cnf transformation 23]
134. ~creative(X0) | rich(X0) [duplicate literal removal 77]
164. 8 <=> creative(alice) [avatar definition]
166. creative(alice) <- (8) [avatar component clause 164]
216. ~strong(X0) | creative(X0) [subsumption resolution 103,72]
338. 35 <=> strong(alice) [avatar definition]
339. strong(alice) <- (35) [avatar component clause 338]
340. ~strong(alice) <- (~35) [avatar component clause 338]
346. calm(alice) <- (~35) [resolution 340,96]
347. $false <- (~35) [subsumption resolution 346,133]
348. 35 [avatar contradiction clause 347]
360. creative(alice) <- (35) [resolution 339,216]
361. old(alice) <- (35) [resolution 339,74]
362. kind(alice) <- (35) [resolution 339,72]
365. 8 | ~35 [avatar split clause 360,338,164]
366. rich(alice) <- (8) [resolution 166,134]
392. ~kind(alice) | ~old(alice) <- (8) [resolution 366,86]
394. ~old(alice) <- (8, 35) [subsumption resolution 392,362]
395. $false <- (8, 35) [subsumption resolution 394,361]
396. ~8 | ~35 [avatar contradiction clause 395]
397. $false [avatar sat refutation 348,365,396]
% SZS output end Proof for 8584424954590190483122778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not old is either not creative or curious.
Everyone who is not patient or generous is not calm or not curious.
If someone is not tall or not happy then susan is both patient and quiet.
Everyone who is funny or patient is both calm and wise.
If someone is humble then someone is not patient.
If paul is curious or not funny then someone is either funny or not brave.
If john is both creative and wise then fred is not patient or not old.
Everyone who is not patient or not old is rich.
If mary is not kind or not wise then susan is both not quiet and generous.
Everyone who is both funny and creative is both not brave and rich.
If lucy is curious or not humble then someone is happy or patient and vice versa.
If someone is brave or not patient then someone is both wise and calm and vice versa.
Everyone who is both rich and kind is both kind and not brave.
Everyone who is both not strong and not calm is not tall or not creative and vice versa.
Everyone who is creative or not funny is patient and vice versa.
Everyone who is both not calm and not generous is generous.
Someone is not kind.
Someone is old or not kind.
Someone is either kind or generous.
Someone is calm.
Mary is either not creative or not kind.
Someone is wise.
Fred is tall or not curious. | John is creative. | entailment | (![X]:((generous(X)&~old(X))=>(~creative(X)<~>curious(X))))&
(![X]:((~patient(X)|generous(X))=>(~calm(X)|~curious(X))))&
((?[X]:((~tall(X)|~happy(X))))=>((patient(susan)&quiet(susan))))&
(![X]:((funny(X)|patient(X))=>(calm(X)&wise(X))))&
((?[X]:(humble(X)))=>(?[X]:(~patient(X))))&
(((curious(paul)|~funny(paul)))=>(?[X]:((funny(X)<~>~brave(X)))))&
(((creative(john)&wise(john)))=>((~patient(fred)|~old(fred))))&
(![X]:((~patient(X)|~old(X))=>rich(X)))&
(((~kind(mary)|~wise(mary)))=>((~quiet(susan)&generous(susan))))&
(![X]:((funny(X)&creative(X))=>(~brave(X)&rich(X))))&
(((curious(lucy)|~humble(lucy)))<=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((brave(X)|~patient(X))))<=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((rich(X)&kind(X))=>(kind(X)&~brave(X))))&
(![X]:((~strong(X)&~calm(X))<=>(~tall(X)|~creative(X))))&
(![X]:((creative(X)|~funny(X))<=>patient(X)))&
(![X]:((~calm(X)&~generous(X))=>generous(X)))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)|~kind(X))))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:(calm(X)))&
((~creative(mary)<~>~kind(mary)))&
(?[X]:(wise(X)))&
((tall(fred)|~curious(fred))) | creative(john) | [
"p3",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8619200601893245790376269
% SZS output start Proof for 8619200601893245790376269
4. ! [X0] : ((patient(X0) | funny(X0)) => (wise(X0) & calm(X0))) [input p3]
14. ! [X0] : ((~calm(X0) & ~strong(X0)) <=> (~creative(X0) | ~tall(X0))) [input p13]
15. ! [X0] : ((~funny(X0) | creative(X0)) <=> patient(X0)) [input p14]
24. ~creative(john) [input hypothesis]
32. ! [X0] : ((wise(X0) & calm(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 4]
62. ! [X0] : (((~calm(X0) & ~strong(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (calm(X0) | strong(X0)))) [nnf transformation 14]
63. ! [X0] : (((~calm(X0) & ~strong(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | calm(X0) | strong(X0))) [flattening 62]
64. ! [X0] : (((~funny(X0) | creative(X0)) | ~patient(X0)) & (patient(X0) | (funny(X0) & ~creative(X0)))) [nnf transformation 15]
65. ! [X0] : ((~funny(X0) | creative(X0) | ~patient(X0)) & (patient(X0) | (funny(X0) & ~creative(X0)))) [flattening 64]
86. ~funny(X0) | calm(X0) [cnf transformation 32]
87. ~patient(X0) | calm(X0) [cnf transformation 32]
119. ~calm(X0) | creative(X0) [cnf transformation 63]
121. funny(X0) | patient(X0) [cnf transformation 65]
133. ~creative(john) [cnf transformation 24]
182. 11 <=> creative(john) [avatar definition]
184. ~creative(john) <- (~11) [avatar component clause 182]
304. ~11 [avatar split clause 133,182]
323. patient(X1) | calm(X1) [resolution 121,86]
329. calm(X1) [subsumption resolution 323,87]
341. creative(X0) [resolution 329,119]
369. $false <- (~11) [resolution 341,184]
373. 11 [avatar contradiction clause 369]
375. $false [avatar sat refutation 304,373]
% SZS output end Proof for 8619200601893245790376269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or not happy and vice versa.
If someone is either not curious or not calm then lucy is both not kind and not old.
Everyone who is both not curious and creative is not funny or patient and vice versa.
Everyone who is tall or not strong is either patient or not old and vice versa.
If someone is not rich or not wise then someone is humble or not kind and vice versa.
If fred is not humble then someone is calm.
If someone is not curious then someone is not brave.
Everyone who is both not funny and rich is wise and vice versa.
If someone is funny then susan is both generous and not creative and vice versa.
If alice is either tall or not happy then susan is not patient or not tall.
Everyone who is either patient or rich is either patient or curious.
Everyone who is not generous or patient is not tall.
Everyone who is either not curious or not old is both not generous and wise and vice versa.
If susan is either not wise or patient then someone is either not rich or not generous.
Everyone who is both creative and not kind is wise or not old and vice versa.
Everyone who is either not generous or not calm is both not tall and not curious and vice versa.
Someone is patient or creative.
Fred is not tall or calm.
Alice is both not generous and curious.
Paul is both not strong and not curious.
Someone is not patient.
Fred is tall.
John is both old and happy. | Fred is patient. | contradiction | (![X]:(tall(X)<=>(wise(X)<~>~happy(X))))&
((?[X]:((~curious(X)<~>~calm(X))))=>((~kind(lucy)&~old(lucy))))&
(![X]:((~curious(X)&creative(X))<=>(~funny(X)|patient(X))))&
(![X]:((tall(X)|~strong(X))<=>(patient(X)<~>~old(X))))&
((?[X]:((~rich(X)|~wise(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
((~humble(fred))=>(?[X]:(calm(X))))&
((?[X]:(~curious(X)))=>(?[X]:(~brave(X))))&
(![X]:((~funny(X)&rich(X))<=>wise(X)))&
((?[X]:(funny(X)))<=>((generous(susan)&~creative(susan))))&
(((tall(alice)<~>~happy(alice)))=>((~patient(susan)|~tall(susan))))&
(![X]:((patient(X)<~>rich(X))=>(patient(X)<~>curious(X))))&
(![X]:((~generous(X)|patient(X))=>~tall(X)))&
(![X]:((~curious(X)<~>~old(X))<=>(~generous(X)&wise(X))))&
(((~wise(susan)<~>patient(susan)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((creative(X)&~kind(X))<=>(wise(X)|~old(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~tall(X)&~curious(X))))&
(?[X]:((patient(X)|creative(X))))&
((~tall(fred)|calm(fred)))&
((~generous(alice)&curious(alice)))&
((~strong(paul)&~curious(paul)))&
(?[X]:(~patient(X)))&
(tall(fred))&
((old(john)&happy(john))) | patient(fred) | [
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4977913470725500564946177
% SZS output start Proof for 4977913470725500564946177
12. ! [X0] : ((patient(X0) | ~generous(X0)) => ~tall(X0)) [input p11]
22. tall(fred) [input p21]
24. patient(fred) [input hypothesis]
33. ! [X0] : (~tall(X0) | (~patient(X0) & generous(X0))) [ennf transformation 12]
107. ~patient(X0) | ~tall(X0) [cnf transformation 33]
136. tall(fred) [cnf transformation 22]
139. patient(fred) [cnf transformation 24]
274. ~tall(fred) [resolution 107,139]
275. $false [subsumption resolution 274,136]
% SZS output end Proof for 4977913470725500564946177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and brave is not patient or old and vice versa.
If someone is both tall and generous then someone is either humble or not funny and vice versa.
If mary is both funny and not patient then mary is both patient and not brave.
If someone is patient then alice is both not brave and kind and vice versa.
If susan is not generous then someone is either not calm or strong.
Everyone who is not kind is either not brave or not kind and vice versa.
Everyone who is either humble or kind is either not quiet or brave.
If someone is quiet or not brave then alice is both not curious and happy.
Everyone who is calm is both strong and not generous.
Everyone who is happy or quiet is either humble or quiet.
If john is not humble or not curious then mary is kind or not generous.
Everyone who is both not strong and old is calm or not kind.
Everyone who is humble or strong is both wise and not curious and vice versa.
If someone is rich or not curious then john is not funny and vice versa.
Everyone who is not tall is not wise and vice versa.
Everyone who is either humble or not generous is rich.
Fred is either brave or quiet.
Someone is not brave or tall.
Someone is not old or kind.
Someone is either curious or not creative.
Alice is both not funny and not quiet. | Alice is not old. | neutral | (![X]:((humble(X)&brave(X))<=>(~patient(X)|old(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(((funny(mary)&~patient(mary)))=>((patient(mary)&~brave(mary))))&
((?[X]:(patient(X)))<=>((~brave(alice)&kind(alice))))&
((~generous(susan))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:(~kind(X)<=>(~brave(X)<~>~kind(X))))&
(![X]:((humble(X)<~>kind(X))=>(~quiet(X)<~>brave(X))))&
((?[X]:((quiet(X)|~brave(X))))=>((~curious(alice)&happy(alice))))&
(![X]:(calm(X)=>(strong(X)&~generous(X))))&
(![X]:((happy(X)|quiet(X))=>(humble(X)<~>quiet(X))))&
(((~humble(john)|~curious(john)))=>((kind(mary)|~generous(mary))))&
(![X]:((~strong(X)&old(X))=>(calm(X)|~kind(X))))&
(![X]:((humble(X)|strong(X))<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|~curious(X))))<=>(~funny(john)))&
(![X]:(~tall(X)<=>~wise(X)))&
(![X]:((humble(X)<~>~generous(X))=>rich(X)))&
((brave(fred)<~>quiet(fred)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~old(X)|kind(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
((~funny(alice)&~quiet(alice))) | ~old(alice) | [] | null | 0 |
Everyone who is not generous or kind is either not old or not kind.
Everyone who is not humble is not generous or not strong and vice versa.
If someone is either brave or old then lucy is both patient and kind and vice versa.
If john is not happy then someone is both generous and patient and vice versa.
If alice is curious then someone is strong or quiet.
Everyone who is either not quiet or not calm is both generous and not patient and vice versa.
Everyone who is either rich or not funny is calm and vice versa.
Everyone who is either curious or not rich is either not funny or not happy.
Everyone who is both brave and not rich is both not rich and not generous and vice versa.
If someone is both happy and not brave then someone is either not strong or not wise.
If someone is rich then susan is not wise or happy.
If mary is tall then alice is wise or generous.
Everyone who is not tall or not kind is patient or generous.
Everyone who is not kind is generous.
If paul is not calm then mary is not old or quiet.
If susan is both strong and not wise then someone is not rich or not calm and vice versa.
John is either not happy or not humble.
Fred is either not generous or not strong.
Someone is not brave or not curious.
Lucy is both not curious and not old.
Someone is both wise and not strong.
Someone is not quiet or calm.
Lucy is not happy.
Someone is either kind or humble. | Fred is not generous. | neutral | (![X]:((~generous(X)|kind(X))=>(~old(X)<~>~kind(X))))&
(![X]:(~humble(X)<=>(~generous(X)|~strong(X))))&
((?[X]:((brave(X)<~>old(X))))<=>((patient(lucy)&kind(lucy))))&
((~happy(john))<=>(?[X]:((generous(X)&patient(X)))))&
((curious(alice))=>(?[X]:((strong(X)|quiet(X)))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(generous(X)&~patient(X))))&
(![X]:((rich(X)<~>~funny(X))<=>calm(X)))&
(![X]:((curious(X)<~>~rich(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((brave(X)&~rich(X))<=>(~rich(X)&~generous(X))))&
((?[X]:((happy(X)&~brave(X))))=>(?[X]:((~strong(X)<~>~wise(X)))))&
((?[X]:(rich(X)))=>((~wise(susan)|happy(susan))))&
((tall(mary))=>((wise(alice)|generous(alice))))&
(![X]:((~tall(X)|~kind(X))=>(patient(X)|generous(X))))&
(![X]:(~kind(X)=>generous(X)))&
((~calm(paul))=>((~old(mary)|quiet(mary))))&
(((strong(susan)&~wise(susan)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((~happy(john)<~>~humble(john)))&
((~generous(fred)<~>~strong(fred)))&
(?[X]:((~brave(X)|~curious(X))))&
((~curious(lucy)&~old(lucy)))&
(?[X]:((wise(X)&~strong(X))))&
(?[X]:((~quiet(X)|calm(X))))&
(~happy(lucy))&
(?[X]:((kind(X)<~>humble(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is not wise is quiet or not happy.
Everyone who is not humble or not creative is both not old and kind.
If someone is not generous or not happy then fred is old or not humble.
Everyone who is humble or not old is either wise or calm.
If someone is not creative then someone is either not tall or rich and vice versa.
If lucy is either not strong or humble then someone is both patient and not calm and vice versa.
If someone is generous then someone is either not happy or strong and vice versa.
Everyone who is both creative and rich is calm or not creative and vice versa.
Everyone who is not strong or creative is both not curious and generous.
Everyone who is not calm is not patient or not calm and vice versa.
If someone is either not funny or not rich then someone is both happy and tall.
If someone is both curious and not wise then someone is both wise and not wise and vice versa.
Everyone who is both curious and creative is both calm and not generous.
If someone is not tall then susan is happy and vice versa.
If alice is curious or not brave then someone is either kind or calm and vice versa.
Everyone who is both not tall and creative is wise or strong and vice versa.
Someone is creative.
Alice is not curious.
Someone is patient.
John is generous or not generous.
Mary is either rich or happy. | Alice is calm. | entailment | (![X]:(~wise(X)=>(quiet(X)|~happy(X))))&
(![X]:((~humble(X)|~creative(X))=>(~old(X)&kind(X))))&
((?[X]:((~generous(X)|~happy(X))))=>((old(fred)|~humble(fred))))&
(![X]:((humble(X)|~old(X))=>(wise(X)<~>calm(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~tall(X)<~>rich(X)))))&
(((~strong(lucy)<~>humble(lucy)))<=>(?[X]:((patient(X)&~calm(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:((creative(X)&rich(X))<=>(calm(X)|~creative(X))))&
(![X]:((~strong(X)|creative(X))=>(~curious(X)&generous(X))))&
(![X]:(~calm(X)<=>(~patient(X)|~calm(X))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:((happy(X)&tall(X)))))&
((?[X]:((curious(X)&~wise(X))))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((curious(X)&creative(X))=>(calm(X)&~generous(X))))&
((?[X]:(~tall(X)))<=>(happy(susan)))&
(((curious(alice)|~brave(alice)))<=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((~tall(X)&creative(X))<=>(wise(X)|strong(X))))&
(?[X]:(creative(X)))&
(~curious(alice))&
(?[X]:(patient(X)))&
((generous(john)|~generous(john)))&
((rich(mary)<~>happy(mary))) | calm(alice) | [
"p1",
"p3",
"p4",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7083350658980781539941289
% SZS output start Proof for 7083350658980781539941289
2. ! [X0] : ((~creative(X0) | ~humble(X0)) => (kind(X0) & ~old(X0))) [input p1]
4. ! [X0] : ((~old(X0) | humble(X0)) => (wise(X0) <~> calm(X0))) [input p3]
5. ? [X0] : ~creative(X0) <=> ? [X0] : (~tall(X0) <~> rich(X0)) [input p4]
8. ! [X0] : ((rich(X0) & creative(X0)) <=> (~creative(X0) | calm(X0))) [input p7]
16. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (strong(X0) | wise(X0))) [input p15]
22. ~calm(alice) [input hypothesis]
23. ? [X0] : ~creative(X0) <=> ? [X1] : (~tall(X1) <~> rich(X1)) [rectify 5]
28. ! [X0] : ((kind(X0) & ~old(X0)) | (creative(X0) & humble(X0))) [ennf transformation 2]
31. ! [X0] : ((wise(X0) <~> calm(X0)) | (old(X0) & ~humble(X0))) [ennf transformation 4]
36. ! [X0] : (((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | (old(X0) & ~humble(X0))) [nnf transformation 31]
37. (? [X0] : ~creative(X0) | ! [X1] : ((~tall(X1) | ~rich(X1)) & (rich(X1) | tall(X1)))) & (? [X1] : ((~rich(X1) | tall(X1)) & (rich(X1) | ~tall(X1))) | ! [X0] : creative(X0)) [nnf transformation 23]
38. (? [X0] : ~creative(X0) | ! [X1] : ((~tall(X1) | ~rich(X1)) & (rich(X1) | tall(X1)))) & (? [X2] : ((~rich(X2) | tall(X2)) & (rich(X2) | ~tall(X2))) | ! [X3] : creative(X3)) [rectify 37]
39. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
40. ? [X2] : ((~rich(X2) | tall(X2)) & (rich(X2) | ~tall(X2))) => ((~rich(sK1) | tall(sK1)) & (rich(sK1) | ~tall(sK1))) [choice axiom]
41. (~creative(sK0) | ! [X1] : ((~tall(X1) | ~rich(X1)) & (rich(X1) | tall(X1)))) & (((~rich(sK1) | tall(sK1)) & (rich(sK1) | ~tall(sK1))) | ! [X3] : creative(X3)) [skolemisation 38,40,39]
51. ! [X0] : (((rich(X0) & creative(X0)) | (creative(X0) & ~calm(X0))) & ((~creative(X0) | calm(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 8]
52. ! [X0] : (((rich(X0) & creative(X0)) | (creative(X0) & ~calm(X0))) & (~creative(X0) | calm(X0) | ~rich(X0) | ~creative(X0))) [flattening 51]
73. ! [X0] : (((creative(X0) & ~tall(X0)) | (~strong(X0) & ~wise(X0))) & ((strong(X0) | wise(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 16]
74. ! [X0] : (((creative(X0) & ~tall(X0)) | (~strong(X0) & ~wise(X0))) & (strong(X0) | wise(X0) | ~creative(X0) | tall(X0))) [flattening 73]
80. ~old(X0) | humble(X0) [cnf transformation 28]
86. ~humble(X0) | wise(X0) | calm(X0) [cnf transformation 36]
87. calm(X0) | wise(X0) | old(X0) [cnf transformation 36]
92. ~creative(sK0) | rich(X1) | tall(X1) [cnf transformation 41]
104. ~creative(X0) | calm(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 52]
106. creative(X0) | creative(X0) [cnf transformation 52]
135. ~tall(X0) | ~wise(X0) [cnf transformation 74]
145. ~calm(alice) [cnf transformation 22]
146. ~rich(X0) | calm(X0) | ~creative(X0) [duplicate literal removal 104]
147. creative(X0) [duplicate literal removal 106]
168. 6 <=> creative(sK0) [avatar definition]
170. ~creative(sK0) <- (~6) [avatar component clause 168]
173. 7 <=> ! [X1] : (rich(X1) | tall(X1)) [avatar definition]
174. rich(X1) | tall(X1) <- (7) [avatar component clause 173]
175. 7 | ~6 [avatar split clause 92,168,173]
177. 8 <=> ! [X3] : creative(X3) [avatar definition]
178. creative(X3) <- (8) [avatar component clause 177]
239. 8 [avatar split clause 147,177]
319. $false <- (~6, 8) [subsumption resolution 170,178]
320. 6 | ~8 [avatar contradiction clause 319]
348. wise(alice) | old(alice) [resolution 87,145]
354. 39 <=> old(alice) [avatar definition]
356. old(alice) <- (39) [avatar component clause 354]
358. 40 <=> wise(alice) [avatar definition]
360. wise(alice) <- (40) [avatar component clause 358]
361. 39 | 40 [avatar split clause 348,358,354]
363. humble(alice) <- (39) [resolution 356,80]
375. wise(alice) | calm(alice) <- (39) [resolution 363,86]
376. wise(alice) <- (39) [subsumption resolution 375,145]
377. 40 | ~39 [avatar split clause 376,354,358]
388. calm(X0) | ~creative(X0) | tall(X0) <- (7) [resolution 146,174]
392. tall(X0) | calm(X0) <- (7, 8) [subsumption resolution 388,178]
438. ~wise(X0) | calm(X0) <- (7, 8) [resolution 392,135]
511. calm(alice) <- (7, 8, 40) [resolution 438,360]
512. $false <- (7, 8, 40) [subsumption resolution 511,145]
513. ~7 | ~8 | ~40 [avatar contradiction clause 512]
514. $false [avatar sat refutation 175,239,320,361,377,513]
% SZS output end Proof for 7083350658980781539941289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is not happy or not funny and vice versa.
Everyone who is either not generous or not curious is both not happy and patient and vice versa.
Everyone who is either not creative or not generous is both humble and not quiet.
If someone is both quiet and creative then someone is either not tall or generous and vice versa.
Everyone who is not wise or not old is either funny or not patient.
If susan is curious then someone is either patient or rich.
If alice is patient or not brave then someone is either creative or not wise and vice versa.
If lucy is both brave and quiet then someone is either not wise or humble.
If someone is either generous or strong then mary is both not calm and brave.
Everyone who is not brave is both not calm and not funny.
Everyone who is not tall is both creative and rich.
Everyone who is both not brave and happy is both not curious and not rich and vice versa.
Everyone who is not creative or not rich is humble or not calm and vice versa.
If someone is either happy or not humble then fred is not creative.
Everyone who is strong or calm is either not humble or not generous and vice versa.
Everyone who is generous is both not kind and not tall and vice versa.
Alice is both curious and rich.
Mary is both old and not humble.
Alice is not brave or rich.
Someone is kind.
Fred is not wise.
John is both humble and not happy.
John is both not creative and not calm.
Alice is both curious and not strong. | Alice is not patient. | contradiction | (![X]:(tall(X)<=>(~happy(X)|~funny(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~happy(X)&patient(X))))&
(![X]:((~creative(X)<~>~generous(X))=>(humble(X)&~quiet(X))))&
((?[X]:((quiet(X)&creative(X))))<=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:((~wise(X)|~old(X))=>(funny(X)<~>~patient(X))))&
((curious(susan))=>(?[X]:((patient(X)<~>rich(X)))))&
(((patient(alice)|~brave(alice)))<=>(?[X]:((creative(X)<~>~wise(X)))))&
(((brave(lucy)&quiet(lucy)))=>(?[X]:((~wise(X)<~>humble(X)))))&
((?[X]:((generous(X)<~>strong(X))))=>((~calm(mary)&brave(mary))))&
(![X]:(~brave(X)=>(~calm(X)&~funny(X))))&
(![X]:(~tall(X)=>(creative(X)&rich(X))))&
(![X]:((~brave(X)&happy(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~creative(X)|~rich(X))<=>(humble(X)|~calm(X))))&
((?[X]:((happy(X)<~>~humble(X))))=>(~creative(fred)))&
(![X]:((strong(X)|calm(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(~kind(X)&~tall(X))))&
((curious(alice)&rich(alice)))&
((old(mary)&~humble(mary)))&
((~brave(alice)|rich(alice)))&
(?[X]:(kind(X)))&
(~wise(fred))&
((humble(john)&~happy(john)))&
((~creative(john)&~calm(john)))&
((curious(alice)&~strong(alice))) | ~patient(alice) | [
"p0",
"p1",
"p4",
"p6",
"p9",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 63407014193753859849133
% SZS output start Proof for 63407014193753859849133
1. ! [X0] : (tall(X0) <=> (~funny(X0) | ~happy(X0))) [input p0]
2. ! [X0] : ((~generous(X0) <~> ~curious(X0)) <=> (patient(X0) & ~happy(X0))) [input p1]
5. ! [X0] : ((~old(X0) | ~wise(X0)) => (funny(X0) <~> ~patient(X0))) [input p4]
7. (~brave(alice) | patient(alice)) <=> ? [X0] : (creative(X0) <~> ~wise(X0)) [input p6]
10. ! [X0] : (~brave(X0) => (~funny(X0) & ~calm(X0))) [input p9]
11. ! [X0] : (~tall(X0) => (rich(X0) & creative(X0))) [input p10]
16. ! [X0] : (generous(X0) <=> (~tall(X0) & ~kind(X0))) [input p15]
17. rich(alice) & curious(alice) [input p16]
25. ~patient(alice) [input hypothesis]
28. ! [X0] : (~wise(X0) => (funny(X0) <~> ~patient(X0))) [pure predicate removal 5]
30. ! [X0] : ((funny(X0) <~> ~patient(X0)) | wise(X0)) [ennf transformation 28]
35. ! [X0] : ((~funny(X0) & ~calm(X0)) | brave(X0)) [ennf transformation 10]
36. ! [X0] : ((rich(X0) & creative(X0)) | tall(X0)) [ennf transformation 11]
38. ! [X0] : ((tall(X0) | (funny(X0) & happy(X0))) & ((~funny(X0) | ~happy(X0)) | ~tall(X0))) [nnf transformation 1]
39. ! [X0] : ((tall(X0) | (funny(X0) & happy(X0))) & (~funny(X0) | ~happy(X0) | ~tall(X0))) [flattening 38]
40. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [nnf transformation 2]
41. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [flattening 40]
48. ! [X0] : (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | wise(X0)) [nnf transformation 30]
52. ((~brave(alice) | patient(alice)) | ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (? [X0] : ((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (brave(alice) & ~patient(alice))) [nnf transformation 7]
53. (~brave(alice) | patient(alice) | ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (? [X0] : ((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (brave(alice) & ~patient(alice))) [flattening 52]
54. (~brave(alice) | patient(alice) | ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (? [X1] : ((wise(X1) | ~creative(X1)) & (~wise(X1) | creative(X1))) | (brave(alice) & ~patient(alice))) [rectify 53]
55. ? [X1] : ((wise(X1) | ~creative(X1)) & (~wise(X1) | creative(X1))) => ((wise(sK3) | ~creative(sK3)) & (~wise(sK3) | creative(sK3))) [choice axiom]
56. (~brave(alice) | patient(alice) | ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(sK3) | ~creative(sK3)) & (~wise(sK3) | creative(sK3))) | (brave(alice) & ~patient(alice))) [skolemisation 54,55]
68. ! [X0] : ((generous(X0) | (tall(X0) | kind(X0))) & ((~tall(X0) & ~kind(X0)) | ~generous(X0))) [nnf transformation 16]
69. ! [X0] : ((generous(X0) | tall(X0) | kind(X0)) & ((~tall(X0) & ~kind(X0)) | ~generous(X0))) [flattening 68]
74. funny(X0) | tall(X0) [cnf transformation 39]
77. ~curious(X0) | patient(X0) | generous(X0) [cnf transformation 41]
92. ~funny(X0) | patient(X0) | wise(X0) [cnf transformation 48]
99. ~brave(alice) | patient(alice) | ~wise(X0) | ~creative(X0) [cnf transformation 56]
108. ~funny(X0) | brave(X0) [cnf transformation 35]
109. creative(X0) | tall(X0) [cnf transformation 36]
128. ~tall(X0) | ~generous(X0) [cnf transformation 69]
130. curious(alice) [cnf transformation 17]
142. ~patient(alice) [cnf transformation 25]
144. 1 <=> ! [X1] : (~tall(X1) | ~generous(X1)) [avatar definition]
145. ~generous(X1) | ~tall(X1) <- (1) [avatar component clause 144]
192. 12 <=> patient(alice) [avatar definition]
193. ~patient(alice) <- (~12) [avatar component clause 192]
196. 13 <=> brave(alice) [avatar definition]
198. ~brave(alice) <- (~13) [avatar component clause 196]
201. 14 <=> ! [X0] : (~wise(X0) | ~creative(X0)) [avatar definition]
202. ~wise(X0) | ~creative(X0) <- (14) [avatar component clause 201]
203. 14 | 12 | ~13 [avatar split clause 99,196,192,201]
264. 1 [avatar split clause 128,144]
265. ~12 [avatar split clause 142,192]
267. brave(X0) | tall(X0) [resolution 108,74]
279. tall(alice) <- (~13) [resolution 267,198]
283. 28 <=> generous(alice) [avatar definition]
285. generous(alice) <- (28) [avatar component clause 283]
294. patient(alice) | generous(alice) [resolution 77,130]
295. generous(alice) <- (~12) [subsumption resolution 294,193]
296. 28 | 12 [avatar split clause 295,192,283]
298. ~tall(alice) <- (1, 28) [resolution 285,145]
299. $false <- (1, ~13, 28) [subsumption resolution 298,279]
300. ~1 | 13 | ~28 [avatar contradiction clause 299]
376. wise(X0) | patient(X0) | tall(X0) [resolution 92,74]
452. patient(X0) | tall(X0) | ~creative(X0) <- (14) [resolution 376,202]
453. patient(X0) | tall(X0) <- (14) [subsumption resolution 452,109]
454. tall(alice) <- (~12, 14) [resolution 453,193]
458. $false <- (1, ~12, 14, 28) [subsumption resolution 454,298]
459. ~1 | 12 | ~14 | ~28 [avatar contradiction clause 458]
460. $false [avatar sat refutation 203,264,265,296,300,459]
% SZS output end Proof for 63407014193753859849133
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then paul is calm and vice versa.
If someone is either old or not calm then susan is both patient and not tall and vice versa.
If fred is both generous and brave then someone is both not brave and kind and vice versa.
Everyone who is not tall is happy or generous and vice versa.
Everyone who is strong or not strong is funny.
If lucy is calm then john is not strong or not wise.
If someone is not brave then mary is happy or curious.
Everyone who is rich or kind is humble or curious.
Everyone who is either not kind or quiet is either humble or not happy.
If someone is generous then someone is both strong and not humble.
If someone is brave then fred is either brave or calm.
If someone is calm then alice is tall and vice versa.
Everyone who is both not curious and tall is not curious or kind.
Everyone who is happy is not patient and vice versa.
If someone is either not quiet or old then fred is not brave and vice versa.
Everyone who is brave is not curious or not kind and vice versa.
Someone is quiet.
Lucy is both curious and not humble.
Someone is either generous or strong.
Paul is both wise and not patient.
John is either not quiet or not generous.
Someone is either creative or not old.
Someone is not calm.
Someone is not tall or humble. | Lucy is calm. | neutral | ((?[X]:(~wise(X)))<=>(calm(paul)))&
((?[X]:((old(X)<~>~calm(X))))<=>((patient(susan)&~tall(susan))))&
(((generous(fred)&brave(fred)))<=>(?[X]:((~brave(X)&kind(X)))))&
(![X]:(~tall(X)<=>(happy(X)|generous(X))))&
(![X]:((strong(X)|~strong(X))=>funny(X)))&
((calm(lucy))=>((~strong(john)|~wise(john))))&
((?[X]:(~brave(X)))=>((happy(mary)|curious(mary))))&
(![X]:((rich(X)|kind(X))=>(humble(X)|curious(X))))&
(![X]:((~kind(X)<~>quiet(X))=>(humble(X)<~>~happy(X))))&
((?[X]:(generous(X)))=>(?[X]:((strong(X)&~humble(X)))))&
((?[X]:(brave(X)))=>((brave(fred)<~>calm(fred))))&
((?[X]:(calm(X)))<=>(tall(alice)))&
(![X]:((~curious(X)&tall(X))=>(~curious(X)|kind(X))))&
(![X]:(happy(X)<=>~patient(X)))&
((?[X]:((~quiet(X)<~>old(X))))<=>(~brave(fred)))&
(![X]:(brave(X)<=>(~curious(X)|~kind(X))))&
(?[X]:(quiet(X)))&
((curious(lucy)&~humble(lucy)))&
(?[X]:((generous(X)<~>strong(X))))&
((wise(paul)&~patient(paul)))&
((~quiet(john)<~>~generous(john)))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~tall(X)|humble(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is either not wise or not rich is either wise or not tall.
If mary is not patient then someone is not funny and vice versa.
Everyone who is both tall and not happy is not strong and vice versa.
If alice is either not quiet or kind then someone is both strong and tall and vice versa.
If someone is brave or not funny then someone is both generous and happy.
If someone is both not calm and not quiet then someone is old and vice versa.
If someone is either strong or not strong then alice is strong or curious and vice versa.
If someone is either not humble or happy then john is creative.
Everyone who is old or not kind is both not creative and generous and vice versa.
If john is old or not curious then someone is both quiet and not patient and vice versa.
If someone is either not calm or calm then someone is both not wise and calm and vice versa.
If someone is either calm or not kind then someone is patient.
If lucy is both creative and not strong then alice is not humble or tall and vice versa.
If someone is creative or not quiet then someone is either not rich or not strong and vice versa.
If someone is not tall then fred is humble or not brave.
Everyone who is either curious or humble is humble or curious.
Someone is either not happy or old.
Someone is both strong and quiet.
Fred is happy.
Susan is either generous or brave.
Lucy is either old or not wise.
Alice is either curious or not creative.
Fred is not kind or not strong.
Someone is strong or not happy. | Fred is not creative. | entailment | (![X]:((~wise(X)<~>~rich(X))=>(wise(X)<~>~tall(X))))&
((~patient(mary))<=>(?[X]:(~funny(X))))&
(![X]:((tall(X)&~happy(X))<=>~strong(X)))&
(((~quiet(alice)<~>kind(alice)))<=>(?[X]:((strong(X)&tall(X)))))&
((?[X]:((brave(X)|~funny(X))))=>(?[X]:((generous(X)&happy(X)))))&
((?[X]:((~calm(X)&~quiet(X))))<=>(?[X]:(old(X))))&
((?[X]:((strong(X)<~>~strong(X))))<=>((strong(alice)|curious(alice))))&
((?[X]:((~humble(X)<~>happy(X))))=>(creative(john)))&
(![X]:((old(X)|~kind(X))<=>(~creative(X)&generous(X))))&
(((old(john)|~curious(john)))<=>(?[X]:((quiet(X)&~patient(X)))))&
((?[X]:((~calm(X)<~>calm(X))))<=>(?[X]:((~wise(X)&calm(X)))))&
((?[X]:((calm(X)<~>~kind(X))))=>(?[X]:(patient(X))))&
(((creative(lucy)&~strong(lucy)))<=>((~humble(alice)|tall(alice))))&
((?[X]:((creative(X)|~quiet(X))))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
((?[X]:(~tall(X)))=>((humble(fred)|~brave(fred))))&
(![X]:((curious(X)<~>humble(X))=>(humble(X)|curious(X))))&
(?[X]:((~happy(X)<~>old(X))))&
(?[X]:((strong(X)&quiet(X))))&
(happy(fred))&
((generous(susan)<~>brave(susan)))&
((old(lucy)<~>~wise(lucy)))&
((curious(alice)<~>~creative(alice)))&
((~kind(fred)|~strong(fred)))&
(?[X]:((strong(X)|~happy(X)))) | ~creative(fred) | [
"p2",
"p8",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7092453433280084356511314
% SZS output start Proof for 7092453433280084356511314
3. ! [X0] : ((~happy(X0) & tall(X0)) <=> ~strong(X0)) [input p2]
9. ! [X0] : ((~kind(X0) | old(X0)) <=> (generous(X0) & ~creative(X0))) [input p8]
19. happy(fred) [input p18]
23. ~strong(fred) | ~kind(fred) [input p22]
25. creative(fred) [input hypothesis]
44. ! [X0] : (((~happy(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | (happy(X0) | ~tall(X0)))) [nnf transformation 3]
45. ! [X0] : (((~happy(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | happy(X0) | ~tall(X0))) [flattening 44]
64. ! [X0] : (((~kind(X0) | old(X0)) | (~generous(X0) | creative(X0))) & ((generous(X0) & ~creative(X0)) | (kind(X0) & ~old(X0)))) [nnf transformation 9]
65. ! [X0] : ((~kind(X0) | old(X0) | ~generous(X0) | creative(X0)) & ((generous(X0) & ~creative(X0)) | (kind(X0) & ~old(X0)))) [flattening 64]
106. ~happy(X0) | strong(X0) [cnf transformation 45]
129. ~creative(X0) | kind(X0) [cnf transformation 65]
164. happy(fred) [cnf transformation 19]
171. ~strong(fred) | ~kind(fred) [cnf transformation 23]
173. creative(fred) [cnf transformation 25]
444. 58 <=> kind(fred) [avatar definition]
446. ~kind(fred) <- (~58) [avatar component clause 444]
448. 59 <=> strong(fred) [avatar definition]
451. ~58 | ~59 [avatar split clause 171,448,444]
453. strong(fred) [resolution 106,164]
455. 59 [avatar split clause 453,448]
458. kind(fred) [resolution 129,173]
460. $false <- (~58) [subsumption resolution 458,446]
461. 58 [avatar contradiction clause 460]
462. $false [avatar sat refutation 451,455,461]
% SZS output end Proof for 7092453433280084356511314
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not brave is either quiet or not strong.
If lucy is not quiet then susan is not wise or not kind.
Everyone who is quiet or wise is either not funny or not generous and vice versa.
Everyone who is kind or not tall is calm or brave and vice versa.
If fred is either happy or old then susan is both happy and quiet.
If paul is both not quiet and not wise then fred is either not quiet or funny.
Everyone who is both not funny and kind is old or creative.
Everyone who is both not funny and brave is not curious.
If someone is humble or brave then susan is either quiet or not patient.
Everyone who is not old or not funny is both patient and funny and vice versa.
If someone is either not funny or not wise then someone is creative and vice versa.
If someone is happy then someone is calm.
Everyone who is either not calm or not curious is both not humble and humble.
If mary is not quiet then someone is both funny and not patient and vice versa.
If lucy is either not patient or happy then someone is not wise or not rich.
Everyone who is either creative or not funny is not calm or not patient and vice versa.
Paul is either happy or not brave.
Someone is calm.
Someone is not quiet or humble.
Mary is old.
Susan is rich.
Fred is curious.
Mary is creative or not wise.
Mary is both kind and not tall. | Lucy is funny. | entailment | (![X]:((curious(X)|~brave(X))=>(quiet(X)<~>~strong(X))))&
((~quiet(lucy))=>((~wise(susan)|~kind(susan))))&
(![X]:((quiet(X)|wise(X))<=>(~funny(X)<~>~generous(X))))&
(![X]:((kind(X)|~tall(X))<=>(calm(X)|brave(X))))&
(((happy(fred)<~>old(fred)))=>((happy(susan)&quiet(susan))))&
(((~quiet(paul)&~wise(paul)))=>((~quiet(fred)<~>funny(fred))))&
(![X]:((~funny(X)&kind(X))=>(old(X)|creative(X))))&
(![X]:((~funny(X)&brave(X))=>~curious(X)))&
((?[X]:((humble(X)|brave(X))))=>((quiet(susan)<~>~patient(susan))))&
(![X]:((~old(X)|~funny(X))<=>(patient(X)&funny(X))))&
((?[X]:((~funny(X)<~>~wise(X))))<=>(?[X]:(creative(X))))&
((?[X]:(happy(X)))=>(?[X]:(calm(X))))&
(![X]:((~calm(X)<~>~curious(X))=>(~humble(X)&humble(X))))&
((~quiet(mary))<=>(?[X]:((funny(X)&~patient(X)))))&
(((~patient(lucy)<~>happy(lucy)))=>(?[X]:((~wise(X)|~rich(X)))))&
(![X]:((creative(X)<~>~funny(X))<=>(~calm(X)|~patient(X))))&
((happy(paul)<~>~brave(paul)))&
(?[X]:(calm(X)))&
(?[X]:((~quiet(X)|humble(X))))&
(old(mary))&
(rich(susan))&
(curious(fred))&
((creative(mary)|~wise(mary)))&
((kind(mary)&~tall(mary))) | funny(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 762952488719391936481651
% SZS output start Proof for 762952488719391936481651
10. ! [X0] : ((~funny(X0) | ~old(X0)) <=> (funny(X0) & patient(X0))) [input p9]
25. ~funny(lucy) [input hypothesis]
50. ! [X0] : (((~funny(X0) | ~old(X0)) | (~funny(X0) | ~patient(X0))) & ((funny(X0) & patient(X0)) | (funny(X0) & old(X0)))) [nnf transformation 10]
51. ! [X0] : ((~funny(X0) | ~old(X0) | ~funny(X0) | ~patient(X0)) & ((funny(X0) & patient(X0)) | (funny(X0) & old(X0)))) [flattening 50]
105. funny(X0) | funny(X0) [cnf transformation 51]
137. ~funny(lucy) [cnf transformation 25]
138. funny(X0) [duplicate literal removal 105]
296. $false [subsumption resolution 137,138]
% SZS output end Proof for 762952488719391936481651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or brave is humble and vice versa. Everyone who is either not old or tall is both not quiet and wise and vice versa. Everyone who is both not brave and curious is either brave or wise. Everyone who is both rich and not generous is not curious and vice versa. If john is calm then someone is creative or not happy. If susan is funny then paul is quiet or not tall. Everyone who is not calm is happy or not creative and vice versa. Everyone who is either funny or generous is patient. Everyone who is not curious is both brave and not kind. Everyone who is both not wise and not humble is patient or rich and vice versa. If someone is not wise or brave then john is both strong and patient and vice versa. Everyone who is either not happy or wise is both not old and not humble. If someone is either tall or calm then lucy is happy and vice versa. If lucy is not wise then paul is not funny or not old and vice versa. Everyone who is not old is not tall or wise. Someone is both not happy and creative. Someone is either not strong or rich. Mary is either not humble or rich. Someone is generous or tall. Someone is not calm. | John is not brave. | entailment | (![X]:((funny(X)|brave(X))<=>humble(X)))&
(![X]:((~old(X)<~>tall(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~brave(X)&curious(X))=>(brave(X)<~>wise(X))))&
(![X]:((rich(X)&~generous(X))<=>~curious(X)))&
((calm(john))=>(?[X]:((creative(X)|~happy(X)))))&
((funny(susan))=>((quiet(paul)|~tall(paul))))&
(![X]:(~calm(X)<=>(happy(X)|~creative(X))))&
(![X]:((funny(X)<~>generous(X))=>patient(X)))&
(![X]:(~curious(X)=>(brave(X)&~kind(X))))&
(![X]:((~wise(X)&~humble(X))<=>(patient(X)|rich(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((strong(john)&patient(john))))&
(![X]:((~happy(X)<~>wise(X))=>(~old(X)&~humble(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(happy(lucy)))&
((~wise(lucy))<=>((~funny(paul)|~old(paul))))&
(![X]:(~old(X)=>(~tall(X)|wise(X))))&
(?[X]:((~happy(X)&creative(X))))&
(?[X]:((~strong(X)<~>rich(X))))&
((~humble(mary)<~>rich(mary)))&
(?[X]:((generous(X)|tall(X))))&
(?[X]:(~calm(X))) | ~brave(john) | [
"p0",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7784363864618504206104606
% SZS output start Proof for 7784363864618504206104606
1. ! [X0] : ((brave(X0) | funny(X0)) <=> humble(X0)) [input p0]
10. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (rich(X0) | patient(X0))) [input p9]
11. ? [X0] : (brave(X0) | ~wise(X0)) <=> (patient(john) & strong(john)) [input p10]
21. brave(john) [input hypothesis]
33. ! [X0] : (((brave(X0) | funny(X0)) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [nnf transformation 1]
34. ! [X0] : ((brave(X0) | funny(X0) | ~humble(X0)) & (humble(X0) | (~brave(X0) & ~funny(X0)))) [flattening 33]
45. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 10]
46. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | humble(X0) | wise(X0))) [flattening 45]
47. (? [X0] : (brave(X0) | ~wise(X0)) | (~patient(john) | ~strong(john))) & ((patient(john) & strong(john)) | ! [X0] : (~brave(X0) & wise(X0))) [nnf transformation 11]
48. (? [X0] : (brave(X0) | ~wise(X0)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X0] : (~brave(X0) & wise(X0))) [flattening 47]
49. (? [X0] : (brave(X0) | ~wise(X0)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X1] : (~brave(X1) & wise(X1))) [rectify 48]
50. ? [X0] : (brave(X0) | ~wise(X0)) => (brave(sK1) | ~wise(sK1)) [choice axiom]
51. ((brave(sK1) | ~wise(sK1)) | ~patient(john) | ~strong(john)) & ((patient(john) & strong(john)) | ! [X1] : (~brave(X1) & wise(X1))) [skolemisation 49,50]
70. ~brave(X0) | humble(X0) [cnf transformation 34]
94. ~patient(X0) | ~humble(X0) [cnf transformation 46]
99. patient(john) | ~brave(X1) [cnf transformation 51]
121. brave(john) [cnf transformation 21]
154. 8 <=> patient(john) [avatar definition]
155. patient(john) <- (8) [avatar component clause 154]
167. 11 <=> ! [X1] : ~brave(X1) [avatar definition]
168. ~brave(X1) <- (11) [avatar component clause 167]
169. 11 | 8 [avatar split clause 99,154,167]
235. humble(john) [resolution 70,121]
242. ~humble(john) <- (8) [resolution 94,155]
243. $false <- (8) [subsumption resolution 242,235]
244. ~8 [avatar contradiction clause 243]
245. $false <- (11) [resolution 168,121]
246. ~11 [avatar contradiction clause 245]
247. $false [avatar sat refutation 169,244,246]
% SZS output end Proof for 7784363864618504206104606
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not happy is either not curious or not calm and vice versa.
If fred is both not rich and not patient then susan is either not brave or not patient.
If someone is both old and funny then someone is both rich and kind and vice versa.
If someone is creative then someone is not tall or not brave and vice versa.
Everyone who is either not old or patient is kind and vice versa.
If someone is either not patient or not quiet then someone is both wise and not curious.
If lucy is not happy then someone is both not humble and not wise and vice versa.
Everyone who is not humble or not calm is either tall or brave.
If someone is both not tall and not quiet then someone is patient and vice versa.
If susan is not rich or not calm then someone is not quiet and vice versa.
If someone is not wise then someone is both curious and strong.
Everyone who is not quiet is both not wise and not brave.
Everyone who is both not tall and not brave is not kind or calm and vice versa.
Everyone who is both not humble and not kind is either rich or not funny and vice versa.
If someone is not funny or rich then john is either patient or curious.
Everyone who is creative is both strong and old and vice versa.
Someone is quiet.
Lucy is creative.
Mary is either strong or not strong.
Someone is both creative and tall.
Someone is tall or funny.
Fred is not patient.
Someone is both quiet and not curious.
Paul is both happy and not calm. | Fred is not quiet. | neutral | (![X]:((humble(X)&~happy(X))<=>(~curious(X)<~>~calm(X))))&
(((~rich(fred)&~patient(fred)))=>((~brave(susan)<~>~patient(susan))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:((rich(X)&kind(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:((~old(X)<~>patient(X))<=>kind(X)))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:((wise(X)&~curious(X)))))&
((~happy(lucy))<=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((~humble(X)|~calm(X))=>(tall(X)<~>brave(X))))&
((?[X]:((~tall(X)&~quiet(X))))<=>(?[X]:(patient(X))))&
(((~rich(susan)|~calm(susan)))<=>(?[X]:(~quiet(X))))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)&strong(X)))))&
(![X]:(~quiet(X)=>(~wise(X)&~brave(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~kind(X)|calm(X))))&
(![X]:((~humble(X)&~kind(X))<=>(rich(X)<~>~funny(X))))&
((?[X]:((~funny(X)|rich(X))))=>((patient(john)<~>curious(john))))&
(![X]:(creative(X)<=>(strong(X)&old(X))))&
(?[X]:(quiet(X)))&
(creative(lucy))&
((strong(mary)<~>~strong(mary)))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:((tall(X)|funny(X))))&
(~patient(fred))&
(?[X]:((quiet(X)&~curious(X))))&
((happy(paul)&~calm(paul))) | ~quiet(fred) | [] | null | 0 |
If someone is both funny and not quiet then someone is not funny or quiet.
Everyone who is either not humble or not rich is calm and vice versa.
Everyone who is either humble or calm is either strong or rich.
Everyone who is not happy is either not happy or not humble and vice versa.
Everyone who is both not humble and kind is both not humble and quiet and vice versa.
If fred is either humble or curious then someone is both not humble and not calm.
Everyone who is rich or not generous is old or not rich and vice versa.
Everyone who is not wise is curious.
Everyone who is both old and creative is both not rich and not old and vice versa.
If lucy is either not generous or generous then mary is both humble and not patient and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is old is either not tall or strong.
Everyone who is not rich or not old is creative or not old.
If mary is funny or not kind then john is not funny or humble and vice versa.
If someone is rich then someone is old and vice versa.
Everyone who is both not quiet and rich is strong and vice versa.
John is both rich and curious.
John is either brave or creative.
Someone is not funny.
Someone is not creative.
Someone is wise.
Paul is happy or not calm.
Paul is generous. | Mary is funny. | neutral | ((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~rich(X))<=>calm(X)))&
(![X]:((humble(X)<~>calm(X))=>(strong(X)<~>rich(X))))&
(![X]:(~happy(X)<=>(~happy(X)<~>~humble(X))))&
(![X]:((~humble(X)&kind(X))<=>(~humble(X)&quiet(X))))&
(((humble(fred)<~>curious(fred)))=>(?[X]:((~humble(X)&~calm(X)))))&
(![X]:((rich(X)|~generous(X))<=>(old(X)|~rich(X))))&
(![X]:(~wise(X)=>curious(X)))&
(![X]:((old(X)&creative(X))<=>(~rich(X)&~old(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>((humble(mary)&~patient(mary))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:(old(X)=>(~tall(X)<~>strong(X))))&
(![X]:((~rich(X)|~old(X))=>(creative(X)|~old(X))))&
(((funny(mary)|~kind(mary)))<=>((~funny(john)|humble(john))))&
((?[X]:(rich(X)))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)&rich(X))<=>strong(X)))&
((rich(john)&curious(john)))&
((brave(john)<~>creative(john)))&
(?[X]:(~funny(X)))&
(?[X]:(~creative(X)))&
(?[X]:(wise(X)))&
((happy(paul)|~calm(paul)))&
(generous(paul)) | funny(mary) | [] | null | 0 |
Everyone who is not calm or generous is not humble or not wise and vice versa. Everyone who is both rich and not curious is old or creative and vice versa. If someone is not old then fred is both old and patient. Everyone who is both not tall and not happy is not tall or strong. If fred is either wise or generous then someone is either old or calm and vice versa. If someone is not wise or not creative then someone is both happy and not old. If someone is not strong or not funny then fred is brave or not rich. Everyone who is both calm and not tall is funny and vice versa. If someone is either happy or tall then someone is both curious and not calm. If john is both not kind and humble then john is patient or not rich. Everyone who is either not generous or strong is not brave or quiet and vice versa. Everyone who is either generous or strong is not old or not tall. If someone is calm or not rich then someone is quiet or generous and vice versa. Everyone who is either calm or not brave is both old and not curious and vice versa. Everyone who is not patient is either not humble or not patient and vice versa. Everyone who is either not wise or not strong is both not humble and not happy. John is either patient or not old. Someone is either not tall or creative. Someone is creative or not calm. Someone is kind or not funny. Lucy is either calm or not brave. Alice is tall or not quiet. Someone is either not brave or curious. Fred is wise or not patient. | Fred is not tall. | entailment | (![X]:((~calm(X)|generous(X))<=>(~humble(X)|~wise(X))))&
(![X]:((rich(X)&~curious(X))<=>(old(X)|creative(X))))&
((?[X]:(~old(X)))=>((old(fred)&patient(fred))))&
(![X]:((~tall(X)&~happy(X))=>(~tall(X)|strong(X))))&
(((wise(fred)<~>generous(fred)))<=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((~wise(X)|~creative(X))))=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((~strong(X)|~funny(X))))=>((brave(fred)|~rich(fred))))&
(![X]:((calm(X)&~tall(X))<=>funny(X)))&
((?[X]:((happy(X)<~>tall(X))))=>(?[X]:((curious(X)&~calm(X)))))&
(((~kind(john)&humble(john)))=>((patient(john)|~rich(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)|quiet(X))))&
(![X]:((generous(X)<~>strong(X))=>(~old(X)|~tall(X))))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((calm(X)<~>~brave(X))<=>(old(X)&~curious(X))))&
(![X]:(~patient(X)<=>(~humble(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)&~happy(X))))&
((patient(john)<~>~old(john)))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((kind(X)|~funny(X))))&
((calm(lucy)<~>~brave(lucy)))&
((tall(alice)|~quiet(alice)))&
(?[X]:((~brave(X)<~>curious(X))))&
((wise(fred)|~patient(fred))) | ~tall(fred) | [
"p0",
"p2",
"p4",
"p5",
"p11",
"p14",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6622579482837000830432427
% SZS output start Proof for 6622579482837000830432427
1. ! [X0] : ((generous(X0) | ~calm(X0)) <=> (~wise(X0) | ~humble(X0))) [input p0]
3. ? [X0] : ~old(X0) => (patient(fred) & old(fred)) [input p2]
5. (wise(fred) <~> generous(fred)) <=> ? [X0] : (old(X0) <~> calm(X0)) [input p4]
6. ? [X0] : (~creative(X0) | ~wise(X0)) => ? [X0] : (~old(X0) & happy(X0)) [input p5]
12. ! [X0] : ((generous(X0) <~> strong(X0)) => (~tall(X0) | ~old(X0))) [input p11]
15. ! [X0] : (~patient(X0) <=> (~humble(X0) <~> ~patient(X0))) [input p14]
16. ! [X0] : ((~wise(X0) <~> ~strong(X0)) => (~happy(X0) & ~humble(X0))) [input p15]
24. ~patient(fred) | wise(fred) [input p23]
25. tall(fred) [input hypothesis]
26. ? [X0] : (~creative(X0) | ~wise(X0)) => ? [X1] : (~old(X1) & happy(X1)) [rectify 6]
32. (patient(fred) & old(fred)) | ! [X0] : old(X0) [ennf transformation 3]
35. ? [X1] : (~old(X1) & happy(X1)) | ! [X0] : (creative(X0) & wise(X0)) [ennf transformation 26]
40. ! [X0] : ((~tall(X0) | ~old(X0)) | (generous(X0) <=> strong(X0))) [ennf transformation 12]
41. ! [X0] : (~tall(X0) | ~old(X0) | (generous(X0) <=> strong(X0))) [flattening 40]
42. ! [X0] : ((~happy(X0) & ~humble(X0)) | (~wise(X0) <=> ~strong(X0))) [ennf transformation 16]
43. ! [X0] : (((generous(X0) | ~calm(X0)) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | (~generous(X0) & calm(X0)))) [nnf transformation 1]
44. ! [X0] : ((generous(X0) | ~calm(X0) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | (~generous(X0) & calm(X0)))) [flattening 43]
47. (((~generous(fred) | ~wise(fred)) & (generous(fred) | wise(fred))) | ! [X0] : ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (? [X0] : ((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | ((wise(fred) | ~generous(fred)) & (generous(fred) | ~wise(fred)))) [nnf transformation 5]
48. (((~generous(fred) | ~wise(fred)) & (generous(fred) | wise(fred))) | ! [X0] : ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (? [X1] : ((~calm(X1) | ~old(X1)) & (calm(X1) | old(X1))) | ((wise(fred) | ~generous(fred)) & (generous(fred) | ~wise(fred)))) [rectify 47]
49. ? [X1] : ((~calm(X1) | ~old(X1)) & (calm(X1) | old(X1))) => ((~calm(sK0) | ~old(sK0)) & (calm(sK0) | old(sK0))) [choice axiom]
50. (((~generous(fred) | ~wise(fred)) & (generous(fred) | wise(fred))) | ! [X0] : ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) & (((~calm(sK0) | ~old(sK0)) & (calm(sK0) | old(sK0))) | ((wise(fred) | ~generous(fred)) & (generous(fred) | ~wise(fred)))) [skolemisation 48,49]
51. ? [X0] : (~old(X0) & happy(X0)) | ! [X1] : (creative(X1) & wise(X1)) [rectify 35]
52. ? [X0] : (~old(X0) & happy(X0)) => (~old(sK1) & happy(sK1)) [choice axiom]
53. (~old(sK1) & happy(sK1)) | ! [X1] : (creative(X1) & wise(X1)) [skolemisation 51,52]
60. ! [X0] : (~tall(X0) | ~old(X0) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0)))) [nnf transformation 41]
68. ! [X0] : ((~patient(X0) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | patient(X0))) [nnf transformation 15]
69. ! [X0] : ((~happy(X0) & ~humble(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) [nnf transformation 42]
80. ~wise(X0) | ~humble(X0) | calm(X0) [cnf transformation 44]
81. ~wise(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 44]
89. old(fred) | old(X0) [cnf transformation 32]
90. patient(fred) | old(X0) [cnf transformation 32]
94. ~calm(sK0) | ~old(sK0) | generous(fred) | ~wise(fred) [cnf transformation 50]
102. ~old(sK1) | wise(X1) [cnf transformation 53]
119. ~strong(X0) | ~old(X0) | generous(X0) | ~tall(X0) [cnf transformation 60]
131. patient(X0) | humble(X0) | patient(X0) [cnf transformation 68]
132. ~patient(X0) | ~patient(X0) | humble(X0) [cnf transformation 68]
135. ~humble(X0) | ~wise(X0) | strong(X0) [cnf transformation 69]
148. ~patient(fred) | wise(fred) [cnf transformation 24]
149. tall(fred) [cnf transformation 25]
150. patient(X0) | humble(X0) [duplicate literal removal 131]
151. ~patient(X0) | humble(X0) [duplicate literal removal 132]
153. 1 <=> ! [X0] : old(X0) [avatar definition]
154. old(X0) <- (1) [avatar component clause 153]
156. 2 <=> patient(fred) [avatar definition]
159. 1 | 2 [avatar split clause 90,156,153]
161. 3 <=> old(fred) [avatar definition]
163. old(fred) <- (3) [avatar component clause 161]
164. 1 | 3 [avatar split clause 89,161,153]
169. 5 <=> wise(fred) [avatar definition]
170. wise(fred) <- (5) [avatar component clause 169]
171. ~wise(fred) <- (~5) [avatar component clause 169]
173. 6 <=> generous(fred) [avatar definition]
174. generous(fred) <- (6) [avatar component clause 173]
175. ~generous(fred) <- (~6) [avatar component clause 173]
184. 8 <=> old(sK0) [avatar definition]
186. ~old(sK0) <- (~8) [avatar component clause 184]
188. 9 <=> calm(sK0) [avatar definition]
190. ~calm(sK0) <- (~9) [avatar component clause 188]
192. ~5 | 6 | ~8 | ~9 [avatar split clause 94,188,184,173,169]
199. 11 <=> old(sK1) [avatar definition]
201. ~old(sK1) <- (~11) [avatar component clause 199]
204. 12 <=> ! [X1] : wise(X1) [avatar definition]
205. wise(X1) <- (12) [avatar component clause 204]
206. 12 | ~11 [avatar split clause 102,199,204]
281. humble(X0) [subsumption resolution 150,151]
282. ~wise(X0) | strong(X0) [subsumption resolution 135,281]
342. 5 | ~2 [avatar split clause 148,156,169]
362. ~humble(fred) | ~generous(fred) <- (5) [resolution 81,170]
363. ~generous(fred) <- (5) [subsumption resolution 362,281]
364. $false <- (5, 6) [subsumption resolution 363,174]
365. ~5 | ~6 [avatar contradiction clause 364]
367. $false <- (1, ~11) [resolution 154,201]
371. ~1 | 11 [avatar contradiction clause 367]
377. ~humble(X1) | calm(X1) <- (12) [resolution 205,80]
379. $false <- (~5, 12) [resolution 205,171]
380. 5 | ~12 [avatar contradiction clause 379]
383. $false <- (1, ~8) [subsumption resolution 186,154]
384. ~1 | 8 [avatar contradiction clause 383]
387. calm(X1) <- (12) [subsumption resolution 377,281]
398. $false <- (~9, 12) [resolution 387,190]
401. 9 | ~12 [avatar contradiction clause 398]
433. strong(fred) <- (5) [resolution 170,282]
576. ~old(fred) | generous(fred) | ~tall(fred) <- (5) [resolution 119,433]
578. generous(fred) | ~tall(fred) <- (3, 5) [subsumption resolution 576,163]
579. ~tall(fred) <- (3, 5, ~6) [subsumption resolution 578,175]
580. $false <- (3, 5, ~6) [subsumption resolution 579,149]
581. ~3 | ~5 | 6 [avatar contradiction clause 580]
592. $false [avatar sat refutation 159,164,192,206,342,365,371,380,384,401,581]
% SZS output end Proof for 6622579482837000830432427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is either creative or strong and vice versa.
If someone is funny or not rich then someone is either not wise or not old.
Everyone who is both wise and patient is not happy and vice versa.
If someone is not funny then someone is either patient or creative.
Everyone who is humble is both curious and not wise.
If someone is either old or not kind then susan is generous or quiet and vice versa.
Everyone who is wise or calm is both happy and brave.
Everyone who is either quiet or brave is both not quiet and not funny and vice versa.
Everyone who is either rich or generous is either happy or not strong.
Everyone who is not funny or wise is generous.
Everyone who is not creative or strong is either tall or rich and vice versa.
Everyone who is either not patient or not creative is either wise or not humble.
Everyone who is not strong or not creative is wise or generous.
If lucy is both creative and tall then susan is both creative and patient and vice versa.
Everyone who is patient is not patient or calm.
Everyone who is funny or old is humble and vice versa.
Alice is both not brave and funny.
Someone is not calm.
John is not kind or tall.
Susan is either brave or wise.
Someone is generous.
Lucy is funny or not patient.
Someone is tall or not rich.
Mary is not tall or not kind. | Susan is brave. | entailment | (![X]:(~wise(X)<=>(creative(X)<~>strong(X))))&
((?[X]:((funny(X)|~rich(X))))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((wise(X)&patient(X))<=>~happy(X)))&
((?[X]:(~funny(X)))=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:(humble(X)=>(curious(X)&~wise(X))))&
((?[X]:((old(X)<~>~kind(X))))<=>((generous(susan)|quiet(susan))))&
(![X]:((wise(X)|calm(X))=>(happy(X)&brave(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~quiet(X)&~funny(X))))&
(![X]:((rich(X)<~>generous(X))=>(happy(X)<~>~strong(X))))&
(![X]:((~funny(X)|wise(X))=>generous(X)))&
(![X]:((~creative(X)|strong(X))<=>(tall(X)<~>rich(X))))&
(![X]:((~patient(X)<~>~creative(X))=>(wise(X)<~>~humble(X))))&
(![X]:((~strong(X)|~creative(X))=>(wise(X)|generous(X))))&
(((creative(lucy)&tall(lucy)))<=>((creative(susan)&patient(susan))))&
(![X]:(patient(X)=>(~patient(X)|calm(X))))&
(![X]:((funny(X)|old(X))<=>humble(X)))&
((~brave(alice)&funny(alice)))&
(?[X]:(~calm(X)))&
((~kind(john)|tall(john)))&
((brave(susan)<~>wise(susan)))&
(?[X]:(generous(X)))&
((funny(lucy)|~patient(lucy)))&
(?[X]:((tall(X)|~rich(X))))&
((~tall(mary)|~kind(mary))) | brave(susan) | [
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7981528071022929988952382
% SZS output start Proof for 7981528071022929988952382
7. ! [X0] : ((calm(X0) | wise(X0)) => (brave(X0) & happy(X0))) [input p6]
20. brave(susan) <~> wise(susan) [input p19]
25. ~brave(susan) [input hypothesis]
32. ! [X0] : ((brave(X0) & happy(X0)) | (~calm(X0) & ~wise(X0))) [ennf transformation 7]
68. (~wise(susan) | ~brave(susan)) & (wise(susan) | brave(susan)) [nnf transformation 20]
95. brave(X0) | ~wise(X0) [cnf transformation 32]
133. wise(susan) | brave(susan) [cnf transformation 68]
134. ~wise(susan) | ~brave(susan) [cnf transformation 68]
139. ~brave(susan) [cnf transformation 25]
240. ~wise(susan) [subsumption resolution 134,95]
241. brave(susan) [subsumption resolution 133,240]
269. $false [subsumption resolution 139,241]
% SZS output end Proof for 7981528071022929988952382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or not quiet is both not happy and not calm and vice versa.
If someone is both strong and humble then someone is both not strong and brave and vice versa.
If lucy is either funny or tall then mary is both humble and curious and vice versa.
If someone is not brave or quiet then someone is not wise or rich.
If lucy is either not creative or curious then lucy is happy or tall.
If paul is both not curious and not wise then susan is not kind or not creative and vice versa.
If someone is both calm and humble then fred is both not old and quiet.
Everyone who is not curious or not rich is both humble and brave.
Everyone who is either not funny or not wise is either rich or not funny.
Everyone who is not humble is either not calm or happy and vice versa.
If john is both strong and brave then paul is both not humble and not strong and vice versa.
If someone is either calm or not wise then alice is not curious or funny.
Everyone who is not kind is wise or generous and vice versa.
If fred is either not curious or not rich then someone is generous or not wise.
Everyone who is either calm or quiet is both not funny and happy and vice versa.
Everyone who is either not humble or humble is not humble.
Someone is not strong or happy.
Someone is either not old or brave.
Susan is not tall.
Someone is not kind.
Someone is either tall or old.
Susan is both not humble and not wise.
Paul is either curious or not wise. | Paul is humble. | contradiction | (![X]:((~calm(X)<~>~quiet(X))<=>(~happy(X)&~calm(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((~strong(X)&brave(X)))))&
(((funny(lucy)<~>tall(lucy)))<=>((humble(mary)&curious(mary))))&
((?[X]:((~brave(X)|quiet(X))))=>(?[X]:((~wise(X)|rich(X)))))&
(((~creative(lucy)<~>curious(lucy)))=>((happy(lucy)|tall(lucy))))&
(((~curious(paul)&~wise(paul)))<=>((~kind(susan)|~creative(susan))))&
((?[X]:((calm(X)&humble(X))))=>((~old(fred)&quiet(fred))))&
(![X]:((~curious(X)|~rich(X))=>(humble(X)&brave(X))))&
(![X]:((~funny(X)<~>~wise(X))=>(rich(X)<~>~funny(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>happy(X))))&
(((strong(john)&brave(john)))<=>((~humble(paul)&~strong(paul))))&
((?[X]:((calm(X)<~>~wise(X))))=>((~curious(alice)|funny(alice))))&
(![X]:(~kind(X)<=>(wise(X)|generous(X))))&
(((~curious(fred)<~>~rich(fred)))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((calm(X)<~>quiet(X))<=>(~funny(X)&happy(X))))&
(![X]:((~humble(X)<~>humble(X))=>~humble(X)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~old(X)<~>brave(X))))&
(~tall(susan))&
(?[X]:(~kind(X)))&
(?[X]:((tall(X)<~>old(X))))&
((~humble(susan)&~wise(susan)))&
((curious(paul)<~>~wise(paul))) | humble(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3191615609641587706552349
% SZS output start Proof for 3191615609641587706552349
16. ! [X0] : ((~humble(X0) <~> humble(X0)) => ~humble(X0)) [input p15]
24. humble(paul) [input hypothesis]
36. ! [X0] : (~humble(X0) | (~humble(X0) <=> humble(X0))) [ennf transformation 16]
64. ! [X0] : (~humble(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 36]
133. ~humble(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 64]
145. humble(paul) [cnf transformation 24]
147. ~humble(X0) [duplicate literal removal 133]
352. $false [subsumption resolution 145,147]
% SZS output end Proof for 3191615609641587706552349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then susan is not quiet and vice versa. If someone is both not old and patient then lucy is not calm or brave. If someone is not creative or not tall then paul is both kind and not strong and vice versa. Everyone who is patient is quiet or not funny. If someone is quiet or not generous then lucy is either curious or not happy and vice versa. If someone is creative then paul is either humble or not humble and vice versa. If susan is either not brave or wise then someone is brave and vice versa. Everyone who is not kind or creative is both not funny and brave. If someone is either curious or not rich then lucy is not rich or not funny. If paul is not quiet or not calm then someone is either not patient or kind. If someone is both not quiet and not humble then fred is patient or calm and vice versa. If someone is both wise and funny then mary is both not tall and not humble and vice versa. Everyone who is patient or quiet is either not creative or quiet and vice versa. Everyone who is not strong is not kind. If susan is curious then someone is either tall or not quiet. If susan is brave or calm then someone is not wise. Someone is patient. Mary is rich. John is wise or brave. Someone is either not humble or old. Alice is tall. John is both not patient and strong. | Paul is not brave. | contradiction | ((?[X]:(old(X)))<=>(~quiet(susan)))&
((?[X]:((~old(X)&patient(X))))=>((~calm(lucy)|brave(lucy))))&
((?[X]:((~creative(X)|~tall(X))))<=>((kind(paul)&~strong(paul))))&
(![X]:(patient(X)=>(quiet(X)|~funny(X))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
(((~brave(susan)<~>wise(susan)))<=>(?[X]:(brave(X))))&
(![X]:((~kind(X)|creative(X))=>(~funny(X)&brave(X))))&
((?[X]:((curious(X)<~>~rich(X))))=>((~rich(lucy)|~funny(lucy))))&
(((~quiet(paul)|~calm(paul)))=>(?[X]:((~patient(X)<~>kind(X)))))&
((?[X]:((~quiet(X)&~humble(X))))<=>((patient(fred)|calm(fred))))&
((?[X]:((wise(X)&funny(X))))<=>((~tall(mary)&~humble(mary))))&
(![X]:((patient(X)|quiet(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:(~strong(X)=>~kind(X)))&
((curious(susan))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(((brave(susan)|calm(susan)))=>(?[X]:(~wise(X))))&
(?[X]:(patient(X)))&
(rich(mary))&
((wise(john)|brave(john)))&
(?[X]:((~humble(X)<~>old(X))))&
(tall(alice))&
((~patient(john)&strong(john))) | ~brave(paul) | [
"p2",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6459043448899971759372095
% SZS output start Proof for 6459043448899971759372095
3. ? [X0] : (~tall(X0) | ~creative(X0)) <=> (~strong(paul) & kind(paul)) [input p2]
8. ! [X0] : ((creative(X0) | ~kind(X0)) => (brave(X0) & ~funny(X0))) [input p7]
14. ! [X0] : (~strong(X0) => ~kind(X0)) [input p13]
23. ~brave(paul) [input hypothesis]
28. ! [X0] : ((brave(X0) & ~funny(X0)) | (~creative(X0) & kind(X0))) [ennf transformation 8]
32. ! [X0] : (~kind(X0) | strong(X0)) [ennf transformation 14]
39. (? [X0] : (~tall(X0) | ~creative(X0)) | (strong(paul) | ~kind(paul))) & ((~strong(paul) & kind(paul)) | ! [X0] : (tall(X0) & creative(X0))) [nnf transformation 3]
40. (? [X0] : (~tall(X0) | ~creative(X0)) | strong(paul) | ~kind(paul)) & ((~strong(paul) & kind(paul)) | ! [X0] : (tall(X0) & creative(X0))) [flattening 39]
41. (? [X0] : (~tall(X0) | ~creative(X0)) | strong(paul) | ~kind(paul)) & ((~strong(paul) & kind(paul)) | ! [X1] : (tall(X1) & creative(X1))) [rectify 40]
42. ? [X0] : (~tall(X0) | ~creative(X0)) => (~tall(sK1) | ~creative(sK1)) [choice axiom]
43. ((~tall(sK1) | ~creative(sK1)) | strong(paul) | ~kind(paul)) & ((~strong(paul) & kind(paul)) | ! [X1] : (tall(X1) & creative(X1))) [skolemisation 41,42]
87. ~strong(paul) | creative(X1) [cnf transformation 43]
107. kind(X0) | brave(X0) [cnf transformation 28]
108. ~creative(X0) | brave(X0) [cnf transformation 28]
130. ~kind(X0) | strong(X0) [cnf transformation 32]
143. ~brave(paul) [cnf transformation 23]
174. 7 <=> kind(paul) [avatar definition]
175. kind(paul) <- (7) [avatar component clause 174]
176. ~kind(paul) <- (~7) [avatar component clause 174]
178. 8 <=> strong(paul) [avatar definition]
179. ~strong(paul) <- (~8) [avatar component clause 178]
195. 12 <=> ! [X1] : creative(X1) [avatar definition]
196. creative(X1) <- (12) [avatar component clause 195]
197. 12 | ~8 [avatar split clause 87,178,195]
394. strong(paul) <- (7) [resolution 130,175]
397. $false <- (7, ~8) [subsumption resolution 394,179]
398. ~7 | 8 [avatar contradiction clause 397]
399. brave(paul) <- (~7) [resolution 176,107]
400. $false <- (~7) [subsumption resolution 399,143]
401. 7 [avatar contradiction clause 400]
408. brave(X0) <- (12) [resolution 196,108]
412. $false <- (12) [resolution 408,143]
415. ~12 [avatar contradiction clause 412]
416. $false [avatar sat refutation 197,398,401,415]
% SZS output end Proof for 6459043448899971759372095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not happy is not funny and vice versa.
Everyone who is kind is either old or not wise.
If someone is either tall or not quiet then someone is both not curious and not funny and vice versa.
If someone is both not happy and brave then fred is either not funny or not curious.
Everyone who is both not brave and not funny is patient or kind.
Everyone who is kind or not calm is not kind or tall.
Everyone who is both funny and not curious is not humble and vice versa.
If someone is both brave and wise then fred is either not wise or happy and vice versa.
If someone is creative then lucy is rich and vice versa.
If someone is either not funny or not old then someone is funny and vice versa.
Everyone who is wise is strong.
Everyone who is either humble or wise is both wise and generous and vice versa.
If mary is both happy and not wise then someone is either not generous or not rich and vice versa.
Everyone who is tall is both not wise and wise.
Everyone who is not humble or not old is not wise.
If someone is both kind and not happy then someone is both not patient and curious and vice versa.
Alice is either not generous or creative.
Someone is either calm or not calm.
John is either not calm or not curious.
Someone is happy or not wise.
Paul is not wise.
Alice is both happy and not tall.
Someone is either not rich or generous. | Paul is not happy. | contradiction | (![X]:((~funny(X)|~happy(X))<=>~funny(X)))&
(![X]:(kind(X)=>(old(X)<~>~wise(X))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>(?[X]:((~curious(X)&~funny(X)))))&
((?[X]:((~happy(X)&brave(X))))=>((~funny(fred)<~>~curious(fred))))&
(![X]:((~brave(X)&~funny(X))=>(patient(X)|kind(X))))&
(![X]:((kind(X)|~calm(X))=>(~kind(X)|tall(X))))&
(![X]:((funny(X)&~curious(X))<=>~humble(X)))&
((?[X]:((brave(X)&wise(X))))<=>((~wise(fred)<~>happy(fred))))&
((?[X]:(creative(X)))<=>(rich(lucy)))&
((?[X]:((~funny(X)<~>~old(X))))<=>(?[X]:(funny(X))))&
(![X]:(wise(X)=>strong(X)))&
(![X]:((humble(X)<~>wise(X))<=>(wise(X)&generous(X))))&
(((happy(mary)&~wise(mary)))<=>(?[X]:((~generous(X)<~>~rich(X)))))&
(![X]:(tall(X)=>(~wise(X)&wise(X))))&
(![X]:((~humble(X)|~old(X))=>~wise(X)))&
((?[X]:((kind(X)&~happy(X))))<=>(?[X]:((~patient(X)&curious(X)))))&
((~generous(alice)<~>creative(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~calm(john)<~>~curious(john)))&
(?[X]:((happy(X)|~wise(X))))&
(~wise(paul))&
((happy(alice)&~tall(alice)))&
(?[X]:((~rich(X)<~>generous(X)))) | ~happy(paul) | [
"p0",
"p6",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 545338046625449066620299
% SZS output start Proof for 545338046625449066620299
1. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> ~funny(X0)) [input p0]
7. ! [X0] : ((~curious(X0) & funny(X0)) <=> ~humble(X0)) [input p6]
12. ! [X0] : ((humble(X0) <~> wise(X0)) <=> (generous(X0) & wise(X0))) [input p11]
21. ~wise(paul) [input p20]
24. ~happy(paul) [input hypothesis]
37. ! [X0] : (((~happy(X0) | ~funny(X0)) | funny(X0)) & (~funny(X0) | (happy(X0) & funny(X0)))) [nnf transformation 1]
38. ! [X0] : ((~happy(X0) | ~funny(X0) | funny(X0)) & (~funny(X0) | (happy(X0) & funny(X0)))) [flattening 37]
46. ! [X0] : (((~curious(X0) & funny(X0)) | humble(X0)) & (~humble(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 7]
47. ! [X0] : (((~curious(X0) & funny(X0)) | humble(X0)) & (~humble(X0) | curious(X0) | ~funny(X0))) [flattening 46]
61. ! [X0] : ((((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~generous(X0) | ~wise(X0))) & ((generous(X0) & wise(X0)) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0))))) [nnf transformation 12]
62. ! [X0] : ((((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | ~generous(X0) | ~wise(X0)) & ((generous(X0) & wise(X0)) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0))))) [flattening 61]
84. ~funny(X0) | happy(X0) [cnf transformation 38]
100. humble(X0) | funny(X0) [cnf transformation 47]
114. wise(X0) | wise(X0) | ~humble(X0) [cnf transformation 62]
141. ~wise(paul) [cnf transformation 21]
146. ~happy(paul) [cnf transformation 24]
147. ~humble(X0) | wise(X0) [duplicate literal removal 114]
357. wise(X0) | funny(X0) [resolution 147,100]
365. funny(paul) [resolution 357,141]
377. happy(paul) [resolution 365,84]
378. $false [subsumption resolution 377,146]
% SZS output end Proof for 545338046625449066620299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not creative is either tall or generous. If paul is either brave or not generous then john is not creative and vice versa. Everyone who is either not brave or not funny is not humble and vice versa. Everyone who is either curious or creative is both not quiet and curious and vice versa. Everyone who is not curious is not old or brave and vice versa. If someone is either quiet or creative then lucy is both not quiet and not generous. Everyone who is both not strong and tall is both not curious and funny. Everyone who is either generous or calm is both not calm and happy and vice versa. Everyone who is both tall and quiet is not patient or rich and vice versa. Everyone who is not kind is quiet or wise and vice versa. Everyone who is both not brave and not wise is either old or not generous and vice versa. Everyone who is not curious is old or not kind. Everyone who is both not old and not happy is both not old and not rich and vice versa. Everyone who is either curious or not humble is not generous and vice versa. If mary is both not creative and curious then mary is not happy. Everyone who is both curious and not kind is not funny. Someone is both not generous and brave. Paul is not kind. Someone is not strong. Fred is not curious or wise. Someone is either brave or not happy. Fred is patient or happy. Someone is humble. Someone is curious. | Fred is happy. | neutral | (![X]:((funny(X)&~creative(X))=>(tall(X)<~>generous(X))))&
(((brave(paul)<~>~generous(paul)))<=>(~creative(john)))&
(![X]:((~brave(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~curious(X)<=>(~old(X)|brave(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>((~quiet(lucy)&~generous(lucy))))&
(![X]:((~strong(X)&tall(X))=>(~curious(X)&funny(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~calm(X)&happy(X))))&
(![X]:((tall(X)&quiet(X))<=>(~patient(X)|rich(X))))&
(![X]:(~kind(X)<=>(quiet(X)|wise(X))))&
(![X]:((~brave(X)&~wise(X))<=>(old(X)<~>~generous(X))))&
(![X]:(~curious(X)=>(old(X)|~kind(X))))&
(![X]:((~old(X)&~happy(X))<=>(~old(X)&~rich(X))))&
(![X]:((curious(X)<~>~humble(X))<=>~generous(X)))&
(((~creative(mary)&curious(mary)))=>(~happy(mary)))&
(![X]:((curious(X)&~kind(X))=>~funny(X)))&
(?[X]:((~generous(X)&brave(X))))&
(~kind(paul))&
(?[X]:(~strong(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(fred)|happy(fred)))&
(?[X]:(humble(X)))&
(?[X]:(curious(X))) | happy(fred) | [] | null | 0 |
Everyone who is not quiet or creative is either creative or quiet and vice versa. Everyone who is not patient or wise is rich or strong. If fred is humble or not tall then lucy is patient or not calm. Everyone who is either not generous or tall is either not rich or old and vice versa. Everyone who is not generous or curious is either not wise or not quiet and vice versa. If someone is old or not funny then someone is not creative or not patient. If susan is not patient or not tall then someone is either wise or not humble and vice versa. Everyone who is either not brave or not quiet is not generous. Everyone who is generous is either funny or not humble and vice versa. Everyone who is generous is creative. If lucy is both not humble and not generous then someone is either not old or curious and vice versa. If someone is both not funny and not happy then paul is either brave or curious. If someone is not kind then susan is either not strong or rich and vice versa. If someone is not calm or not funny then someone is either not funny or not old and vice versa. If someone is either not funny or not brave then someone is either creative or not wise. If fred is both generous and old then john is both generous and patient. Paul is not brave. Susan is not wise or creative. Paul is both not funny and not calm. Someone is both patient and not calm. Someone is strong. Paul is both happy and not brave. Someone is either generous or not kind. Paul is curious or not calm. | Paul is happy. | entailment | (![X]:((~quiet(X)|creative(X))<=>(creative(X)<~>quiet(X))))&
(![X]:((~patient(X)|wise(X))=>(rich(X)|strong(X))))&
(((humble(fred)|~tall(fred)))=>((patient(lucy)|~calm(lucy))))&
(![X]:((~generous(X)<~>tall(X))<=>(~rich(X)<~>old(X))))&
(![X]:((~generous(X)|curious(X))<=>(~wise(X)<~>~quiet(X))))&
((?[X]:((old(X)|~funny(X))))=>(?[X]:((~creative(X)|~patient(X)))))&
(((~patient(susan)|~tall(susan)))<=>(?[X]:((wise(X)<~>~humble(X)))))&
(![X]:((~brave(X)<~>~quiet(X))=>~generous(X)))&
(![X]:(generous(X)<=>(funny(X)<~>~humble(X))))&
(![X]:(generous(X)=>creative(X)))&
(((~humble(lucy)&~generous(lucy)))<=>(?[X]:((~old(X)<~>curious(X)))))&
((?[X]:((~funny(X)&~happy(X))))=>((brave(paul)<~>curious(paul))))&
((?[X]:(~kind(X)))<=>((~strong(susan)<~>rich(susan))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~funny(X)<~>~old(X)))))&
((?[X]:((~funny(X)<~>~brave(X))))=>(?[X]:((creative(X)<~>~wise(X)))))&
(((generous(fred)&old(fred)))=>((generous(john)&patient(john))))&
(~brave(paul))&
((~wise(susan)|creative(susan)))&
((~funny(paul)&~calm(paul)))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(strong(X)))&
((happy(paul)&~brave(paul)))&
(?[X]:((generous(X)<~>~kind(X))))&
((curious(paul)|~calm(paul))) | happy(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1862724321095656063124509
% SZS output start Proof for 1862724321095656063124509
22. ~brave(paul) & happy(paul) [input p21]
25. ~happy(paul) [input hypothesis]
151. happy(paul) [cnf transformation 22]
156. ~happy(paul) [cnf transformation 25]
361. $false [subsumption resolution 156,151]
% SZS output end Proof for 1862724321095656063124509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not calm is both not wise and not funny.
If lucy is both not old and not rich then someone is curious or not curious.
Everyone who is not happy or funny is either funny or not calm.
If someone is both not generous and not curious then alice is both not kind and not tall.
Everyone who is either strong or not curious is not funny.
Everyone who is both not rich and funny is patient and vice versa.
Everyone who is old is either not brave or funny.
Everyone who is wise is wise or patient.
Everyone who is not funny or creative is not creative or not old.
Everyone who is funny or strong is strong and vice versa.
If alice is tall then mary is patient.
Everyone who is both not humble and not creative is humble.
Everyone who is creative is not funny.
Everyone who is either kind or wise is either generous or not calm.
If john is either not happy or not brave then someone is wise or tall.
If someone is both quiet and kind then someone is both patient and not old.
Someone is not humble.
Someone is not humble or humble.
Someone is creative or not rich.
Mary is either calm or brave.
Someone is either not funny or patient.
Someone is either not strong or strong.
Fred is curious.
Alice is not brave. | Mary is not kind. | neutral | (![X]:((humble(X)<~>~calm(X))=>(~wise(X)&~funny(X))))&
(((~old(lucy)&~rich(lucy)))=>(?[X]:((curious(X)|~curious(X)))))&
(![X]:((~happy(X)|funny(X))=>(funny(X)<~>~calm(X))))&
((?[X]:((~generous(X)&~curious(X))))=>((~kind(alice)&~tall(alice))))&
(![X]:((strong(X)<~>~curious(X))=>~funny(X)))&
(![X]:((~rich(X)&funny(X))<=>patient(X)))&
(![X]:(old(X)=>(~brave(X)<~>funny(X))))&
(![X]:(wise(X)=>(wise(X)|patient(X))))&
(![X]:((~funny(X)|creative(X))=>(~creative(X)|~old(X))))&
(![X]:((funny(X)|strong(X))<=>strong(X)))&
((tall(alice))=>(patient(mary)))&
(![X]:((~humble(X)&~creative(X))=>humble(X)))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((kind(X)<~>wise(X))=>(generous(X)<~>~calm(X))))&
(((~happy(john)<~>~brave(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((quiet(X)&kind(X))))=>(?[X]:((patient(X)&~old(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((creative(X)|~rich(X))))&
((calm(mary)<~>brave(mary)))&
(?[X]:((~funny(X)<~>patient(X))))&
(?[X]:((~strong(X)<~>strong(X))))&
(curious(fred))&
(~brave(alice)) | ~kind(mary) | [] | null | 0 |
Everyone who is both rich and kind is generous.
If someone is both happy and humble then someone is generous or not old and vice versa.
Everyone who is calm is curious.
If john is not funny or not wise then mary is either not brave or not happy and vice versa.
Everyone who is either wise or strong is both creative and not wise and vice versa.
Everyone who is not brave is not creative or not patient and vice versa.
If someone is either not generous or brave then susan is either not humble or strong and vice versa.
Everyone who is both not patient and strong is both creative and not generous and vice versa.
Everyone who is rich or not humble is either not generous or not quiet and vice versa.
If someone is either funny or happy then someone is either wise or old and vice versa.
Everyone who is both calm and not kind is both not rich and strong.
If someone is creative then mary is both calm and happy.
Everyone who is brave or not quiet is both not patient and not rich.
Everyone who is either patient or tall is wise or humble.
Everyone who is both not quiet and not generous is creative or curious and vice versa.
If john is either generous or kind then someone is kind and vice versa.
Susan is either funny or quiet.
Alice is either not calm or not quiet.
Alice is both creative and old.
Someone is tall.
John is not happy or humble.
Someone is not brave or not wise. | Susan is funny. | neutral | (![X]:((rich(X)&kind(X))=>generous(X)))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((generous(X)|~old(X)))))&
(![X]:(calm(X)=>curious(X)))&
(((~funny(john)|~wise(john)))<=>((~brave(mary)<~>~happy(mary))))&
(![X]:((wise(X)<~>strong(X))<=>(creative(X)&~wise(X))))&
(![X]:(~brave(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~generous(X)<~>brave(X))))<=>((~humble(susan)<~>strong(susan))))&
(![X]:((~patient(X)&strong(X))<=>(creative(X)&~generous(X))))&
(![X]:((rich(X)|~humble(X))<=>(~generous(X)<~>~quiet(X))))&
((?[X]:((funny(X)<~>happy(X))))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((calm(X)&~kind(X))=>(~rich(X)&strong(X))))&
((?[X]:(creative(X)))=>((calm(mary)&happy(mary))))&
(![X]:((brave(X)|~quiet(X))=>(~patient(X)&~rich(X))))&
(![X]:((patient(X)<~>tall(X))=>(wise(X)|humble(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(creative(X)|curious(X))))&
(((generous(john)<~>kind(john)))<=>(?[X]:(kind(X))))&
((funny(susan)<~>quiet(susan)))&
((~calm(alice)<~>~quiet(alice)))&
((creative(alice)&old(alice)))&
(?[X]:(tall(X)))&
((~happy(john)|humble(john)))&
(?[X]:((~brave(X)|~wise(X)))) | funny(susan) | [] | null | 0 |
Everyone who is both kind and not kind is both not tall and not brave and vice versa. If someone is either brave or not wise then someone is not patient and vice versa. Everyone who is not funny or funny is either wise or strong and vice versa. Everyone who is both tall and strong is either not calm or tall and vice versa. If someone is either funny or old then susan is brave or happy. Everyone who is either brave or tall is either quiet or not kind and vice versa. Everyone who is happy is both not wise and patient. Everyone who is either not old or not quiet is either not old or not curious and vice versa. If paul is both kind and not kind then someone is not generous or not tall. Everyone who is either not rich or not curious is old or not old and vice versa. Everyone who is either kind or brave is generous and vice versa. Everyone who is rich or funny is humble and vice versa. If someone is both happy and not patient then john is both generous and not funny. If someone is both not rich and happy then alice is both patient and calm. Everyone who is both not wise and not strong is both creative and not tall. If paul is strong or not kind then someone is either brave or not curious. Lucy is both tall and not kind. Mary is either not generous or tall. Fred is either not humble or wise. Someone is both not generous and not wise. Someone is quiet. Someone is both quiet and not old. Mary is not wise or curious. | John is not old. | neutral | (![X]:((kind(X)&~kind(X))<=>(~tall(X)&~brave(X))))&
((?[X]:((brave(X)<~>~wise(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~funny(X)|funny(X))<=>(wise(X)<~>strong(X))))&
(![X]:((tall(X)&strong(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:((funny(X)<~>old(X))))=>((brave(susan)|happy(susan))))&
(![X]:((brave(X)<~>tall(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:(happy(X)=>(~wise(X)&patient(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(~old(X)<~>~curious(X))))&
(((kind(paul)&~kind(paul)))=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:((~rich(X)<~>~curious(X))<=>(old(X)|~old(X))))&
(![X]:((kind(X)<~>brave(X))<=>generous(X)))&
(![X]:((rich(X)|funny(X))<=>humble(X)))&
((?[X]:((happy(X)&~patient(X))))=>((generous(john)&~funny(john))))&
((?[X]:((~rich(X)&happy(X))))=>((patient(alice)&calm(alice))))&
(![X]:((~wise(X)&~strong(X))=>(creative(X)&~tall(X))))&
(((strong(paul)|~kind(paul)))=>(?[X]:((brave(X)<~>~curious(X)))))&
((tall(lucy)&~kind(lucy)))&
((~generous(mary)<~>tall(mary)))&
((~humble(fred)<~>wise(fred)))&
(?[X]:((~generous(X)&~wise(X))))&
(?[X]:(quiet(X)))&
(?[X]:((quiet(X)&~old(X))))&
((~wise(mary)|curious(mary))) | ~old(john) | [] | null | 0 |
Everyone who is funny is not kind.
Everyone who is rich is either wise or not calm and vice versa.
If lucy is humble then lucy is both happy and not wise.
Everyone who is both not patient and not kind is not calm and vice versa.
If someone is curious or wise then someone is strong and vice versa.
Everyone who is either tall or not wise is not old or old and vice versa.
Everyone who is both patient and funny is brave and vice versa.
If alice is strong or not curious then lucy is both happy and not kind.
Everyone who is tall is not quiet or kind and vice versa.
Everyone who is quiet or not strong is not humble and vice versa.
Everyone who is both not calm and calm is tall or humble and vice versa.
If someone is both not old and not quiet then someone is not kind or creative.
If someone is both not patient and not quiet then paul is calm or not happy.
If susan is both not brave and tall then susan is both kind and tall and vice versa.
Everyone who is either not quiet or not patient is either happy or wise and vice versa.
Everyone who is both not quiet and not wise is funny.
John is both not generous and old.
Mary is either kind or not creative.
Someone is either not tall or not rich.
Lucy is quiet.
Lucy is not wise or not patient.
Someone is patient.
John is either funny or not calm. | Susan is not humble. | entailment | (![X]:(funny(X)=>~kind(X)))&
(![X]:(rich(X)<=>(wise(X)<~>~calm(X))))&
((humble(lucy))=>((happy(lucy)&~wise(lucy))))&
(![X]:((~patient(X)&~kind(X))<=>~calm(X)))&
((?[X]:((curious(X)|wise(X))))<=>(?[X]:(strong(X))))&
(![X]:((tall(X)<~>~wise(X))<=>(~old(X)|old(X))))&
(![X]:((patient(X)&funny(X))<=>brave(X)))&
(((strong(alice)|~curious(alice)))=>((happy(lucy)&~kind(lucy))))&
(![X]:(tall(X)<=>(~quiet(X)|kind(X))))&
(![X]:((quiet(X)|~strong(X))<=>~humble(X)))&
(![X]:((~calm(X)&calm(X))<=>(tall(X)|humble(X))))&
((?[X]:((~old(X)&~quiet(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:((~patient(X)&~quiet(X))))=>((calm(paul)|~happy(paul))))&
(((~brave(susan)&tall(susan)))<=>((kind(susan)&tall(susan))))&
(![X]:((~quiet(X)<~>~patient(X))<=>(happy(X)<~>wise(X))))&
(![X]:((~quiet(X)&~wise(X))=>funny(X)))&
((~generous(john)&old(john)))&
((kind(mary)<~>~creative(mary)))&
(?[X]:((~tall(X)<~>~rich(X))))&
(quiet(lucy))&
((~wise(lucy)|~patient(lucy)))&
(?[X]:(patient(X)))&
((funny(john)<~>~calm(john))) | ~humble(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3566137485789073199517842
% SZS output start Proof for 3566137485789073199517842
11. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (humble(X0) | tall(X0))) [input p10]
24. humble(susan) [input hypothesis]
52. ! [X0] : (((calm(X0) & ~calm(X0)) | (~humble(X0) & ~tall(X0))) & ((humble(X0) | tall(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 11]
53. ! [X0] : (((calm(X0) & ~calm(X0)) | (~humble(X0) & ~tall(X0))) & (humble(X0) | tall(X0) | ~calm(X0) | calm(X0))) [flattening 52]
101. ~calm(X0) | ~humble(X0) [cnf transformation 53]
103. calm(X0) | ~humble(X0) [cnf transformation 53]
129. humble(susan) [cnf transformation 24]
186. ~humble(X0) [subsumption resolution 101,103]
238. $false [subsumption resolution 129,186]
% SZS output end Proof for 3566137485789073199517842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and creative is old or quiet and vice versa. If alice is old then fred is not tall or not rich. If mary is calm then someone is not calm or rich and vice versa. Everyone who is not humble is not patient or not creative and vice versa. Everyone who is not patient is either creative or not calm. If someone is not funny or rich then john is not calm or creative. Everyone who is strong is not brave or not rich and vice versa. If paul is both calm and patient then someone is patient. If someone is either not kind or not brave then someone is both quiet and creative. Everyone who is either wise or not quiet is not rich or not patient. Everyone who is not tall is not funny and vice versa. If mary is either rich or generous then someone is not old or tall and vice versa. If someone is either patient or not creative then alice is not calm or creative and vice versa. If john is either not rich or patient then fred is not patient. If someone is not funny or not old then alice is both not wise and creative. If someone is either curious or quiet then someone is either not generous or funny. Someone is not calm. Someone is either not happy or not quiet. Mary is not quiet. Paul is generous or not patient. Mary is quiet or old. Someone is either not calm or quiet. Someone is creative or not old. | John is not calm. | neutral | (![X]:((tall(X)&creative(X))<=>(old(X)|quiet(X))))&
((old(alice))=>((~tall(fred)|~rich(fred))))&
((calm(mary))<=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:(~humble(X)<=>(~patient(X)|~creative(X))))&
(![X]:(~patient(X)=>(creative(X)<~>~calm(X))))&
((?[X]:((~funny(X)|rich(X))))=>((~calm(john)|creative(john))))&
(![X]:(strong(X)<=>(~brave(X)|~rich(X))))&
(((calm(paul)&patient(paul)))=>(?[X]:(patient(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((wise(X)<~>~quiet(X))=>(~rich(X)|~patient(X))))&
(![X]:(~tall(X)<=>~funny(X)))&
(((rich(mary)<~>generous(mary)))<=>(?[X]:((~old(X)|tall(X)))))&
((?[X]:((patient(X)<~>~creative(X))))<=>((~calm(alice)|creative(alice))))&
(((~rich(john)<~>patient(john)))=>(~patient(fred)))&
((?[X]:((~funny(X)|~old(X))))=>((~wise(alice)&creative(alice))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:((~generous(X)<~>funny(X)))))&
(?[X]:(~calm(X)))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(~quiet(mary))&
((generous(paul)|~patient(paul)))&
((quiet(mary)|old(mary)))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:((creative(X)|~old(X)))) | ~calm(john) | [] | null | 0 |
Everyone who is not strong or not calm is either not humble or curious. Everyone who is not old is either not humble or humble. Everyone who is tall is not generous. Everyone who is either creative or not kind is not old and vice versa. Everyone who is quiet or not strong is happy or kind. Everyone who is either wise or tall is either not creative or not strong. If susan is both not generous and not patient then paul is both not kind and not patient. Everyone who is not generous or generous is either not tall or humble and vice versa. Everyone who is humble or generous is happy or wise. If fred is either calm or creative then fred is either strong or creative and vice versa. Everyone who is either not calm or not happy is either funny or wise and vice versa. If someone is both kind and brave then someone is creative and vice versa. If alice is both generous and brave then someone is not rich. Everyone who is either quiet or strong is not quiet and vice versa. Everyone who is both rich and calm is happy or creative and vice versa. If paul is not rich then susan is strong. Someone is brave or not wise. Susan is both generous and rich. Alice is both not funny and humble. Someone is not calm or funny. Mary is funny. Paul is not old. John is both old and not creative. | Alice is tall. | entailment | (![X]:((~strong(X)|~calm(X))=>(~humble(X)<~>curious(X))))&
(![X]:(~old(X)=>(~humble(X)<~>humble(X))))&
(![X]:(tall(X)=>~generous(X)))&
(![X]:((creative(X)<~>~kind(X))<=>~old(X)))&
(![X]:((quiet(X)|~strong(X))=>(happy(X)|kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(~creative(X)<~>~strong(X))))&
(((~generous(susan)&~patient(susan)))=>((~kind(paul)&~patient(paul))))&
(![X]:((~generous(X)|generous(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)|generous(X))=>(happy(X)|wise(X))))&
(((calm(fred)<~>creative(fred)))<=>((strong(fred)<~>creative(fred))))&
(![X]:((~calm(X)<~>~happy(X))<=>(funny(X)<~>wise(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:(creative(X))))&
(((generous(alice)&brave(alice)))=>(?[X]:(~rich(X))))&
(![X]:((quiet(X)<~>strong(X))<=>~quiet(X)))&
(![X]:((rich(X)&calm(X))<=>(happy(X)|creative(X))))&
((~rich(paul))=>(strong(susan)))&
(?[X]:((brave(X)|~wise(X))))&
((generous(susan)&rich(susan)))&
((~funny(alice)&humble(alice)))&
(?[X]:((~calm(X)|funny(X))))&
(funny(mary))&
(~old(paul))&
((old(john)&~creative(john))) | tall(alice) | [
"p2",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 986872450789972843555379
% SZS output start Proof for 986872450789972843555379
3. ! [X0] : (tall(X0) => ~generous(X0)) [input p2]
8. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (~tall(X0) <~> humble(X0))) [input p7]
19. humble(alice) & ~funny(alice) [input p18]
24. ~tall(alice) [input hypothesis]
28. ! [X0] : (~generous(X0) | ~tall(X0)) [ennf transformation 3]
43. ! [X0] : (((generous(X0) | ~generous(X0)) | ((~tall(X0) | ~humble(X0)) & (humble(X0) | tall(X0)))) & (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | (~generous(X0) & generous(X0)))) [nnf transformation 8]
44. ! [X0] : ((generous(X0) | ~generous(X0) | ((~tall(X0) | ~humble(X0)) & (humble(X0) | tall(X0)))) & (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | (~generous(X0) & generous(X0)))) [flattening 43]
67. ~generous(X0) | ~tall(X0) [cnf transformation 28]
82. ~humble(X0) | tall(X0) | generous(X0) [cnf transformation 44]
83. ~humble(X0) | tall(X0) | ~generous(X0) [cnf transformation 44]
122. humble(alice) [cnf transformation 19]
128. ~tall(alice) [cnf transformation 24]
153. ~generous(X0) | ~humble(X0) [subsumption resolution 83,67]
154. ~humble(X0) | tall(X0) [subsumption resolution 82,153]
230. tall(alice) [resolution 154,122]
231. $false [subsumption resolution 230,128]
% SZS output end Proof for 986872450789972843555379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not curious is both rich and not rich and vice versa.
Everyone who is patient or quiet is either happy or brave and vice versa.
Everyone who is strong is tall.
If someone is either not happy or patient then someone is rich and vice versa.
If paul is creative or calm then someone is both not old and tall and vice versa.
Everyone who is both not wise and not brave is kind or not patient.
Everyone who is both tall and not old is both not generous and not patient.
If someone is not patient then paul is either not humble or brave and vice versa.
Everyone who is both generous and tall is patient and vice versa.
If someone is either not humble or patient then fred is either strong or tall.
If paul is generous or not happy then someone is generous.
Everyone who is either strong or not old is tall and vice versa.
Everyone who is not tall or not brave is brave or humble.
If susan is happy or not calm then someone is both not kind and not curious and vice versa.
If mary is both patient and not tall then someone is either strong or wise and vice versa.
Everyone who is calm is not calm or funny and vice versa.
Susan is either humble or not wise.
Mary is both old and not creative.
Someone is funny or creative.
Someone is both not creative and not brave.
John is both not quiet and not happy.
Someone is not strong or not generous.
Lucy is calm. | Mary is not tall. | neutral | (![X]:((tall(X)<~>~curious(X))<=>(rich(X)&~rich(X))))&
(![X]:((patient(X)|quiet(X))<=>(happy(X)<~>brave(X))))&
(![X]:(strong(X)=>tall(X)))&
((?[X]:((~happy(X)<~>patient(X))))<=>(?[X]:(rich(X))))&
(((creative(paul)|calm(paul)))<=>(?[X]:((~old(X)&tall(X)))))&
(![X]:((~wise(X)&~brave(X))=>(kind(X)|~patient(X))))&
(![X]:((tall(X)&~old(X))=>(~generous(X)&~patient(X))))&
((?[X]:(~patient(X)))<=>((~humble(paul)<~>brave(paul))))&
(![X]:((generous(X)&tall(X))<=>patient(X)))&
((?[X]:((~humble(X)<~>patient(X))))=>((strong(fred)<~>tall(fred))))&
(((generous(paul)|~happy(paul)))=>(?[X]:(generous(X))))&
(![X]:((strong(X)<~>~old(X))<=>tall(X)))&
(![X]:((~tall(X)|~brave(X))=>(brave(X)|humble(X))))&
(((happy(susan)|~calm(susan)))<=>(?[X]:((~kind(X)&~curious(X)))))&
(((patient(mary)&~tall(mary)))<=>(?[X]:((strong(X)<~>wise(X)))))&
(![X]:(calm(X)<=>(~calm(X)|funny(X))))&
((humble(susan)<~>~wise(susan)))&
((old(mary)&~creative(mary)))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((~creative(X)&~brave(X))))&
((~quiet(john)&~happy(john)))&
(?[X]:((~strong(X)|~generous(X))))&
(calm(lucy)) | ~tall(mary) | [] | null | 0 |
Everyone who is not humble or not wise is not old and vice versa.
Everyone who is either not rich or humble is not old or not generous and vice versa.
Everyone who is not old is both not tall and wise and vice versa.
If alice is not humble then someone is either old or curious and vice versa.
Everyone who is both not quiet and not humble is not humble.
Everyone who is not tall or not curious is either old or not creative.
Everyone who is not patient is both not generous and not happy and vice versa.
If lucy is generous or not rich then alice is either wise or not curious and vice versa.
If john is both old and not happy then someone is old and vice versa.
Everyone who is not rich or calm is generous or not humble and vice versa.
Everyone who is both not funny and happy is both not generous and humble and vice versa.
If someone is tall or not calm then susan is both not strong and old and vice versa.
If fred is both not happy and not rich then someone is calm or patient.
Everyone who is curious is not old.
Everyone who is rich or brave is not old or not curious.
Everyone who is either calm or rich is both not calm and not quiet.
Someone is generous.
Someone is kind.
Someone is either creative or curious.
Paul is either not curious or not tall.
John is either not quiet or not patient.
Someone is not patient or generous. | John is creative. | entailment | (![X]:((~humble(X)|~wise(X))<=>~old(X)))&
(![X]:((~rich(X)<~>humble(X))<=>(~old(X)|~generous(X))))&
(![X]:(~old(X)<=>(~tall(X)&wise(X))))&
((~humble(alice))<=>(?[X]:((old(X)<~>curious(X)))))&
(![X]:((~quiet(X)&~humble(X))=>~humble(X)))&
(![X]:((~tall(X)|~curious(X))=>(old(X)<~>~creative(X))))&
(![X]:(~patient(X)<=>(~generous(X)&~happy(X))))&
(((generous(lucy)|~rich(lucy)))<=>((wise(alice)<~>~curious(alice))))&
(((old(john)&~happy(john)))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)|calm(X))<=>(generous(X)|~humble(X))))&
(![X]:((~funny(X)&happy(X))<=>(~generous(X)&humble(X))))&
((?[X]:((tall(X)|~calm(X))))<=>((~strong(susan)&old(susan))))&
(((~happy(fred)&~rich(fred)))=>(?[X]:((calm(X)|patient(X)))))&
(![X]:(curious(X)=>~old(X)))&
(![X]:((rich(X)|brave(X))=>(~old(X)|~curious(X))))&
(![X]:((calm(X)<~>rich(X))=>(~calm(X)&~quiet(X))))&
(?[X]:(generous(X)))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>curious(X))))&
((~curious(paul)<~>~tall(paul)))&
((~quiet(john)<~>~patient(john)))&
(?[X]:((~patient(X)|generous(X)))) | creative(john) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p8",
"p11",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5067983935364555722807642
% SZS output start Proof for 5067983935364555722807642
1. ! [X0] : ((~wise(X0) | ~humble(X0)) <=> ~old(X0)) [input p0]
2. ! [X0] : ((~rich(X0) <~> humble(X0)) <=> (~generous(X0) | ~old(X0))) [input p1]
3. ! [X0] : (~old(X0) <=> (wise(X0) & ~tall(X0))) [input p2]
4. ~humble(alice) <=> ? [X0] : (old(X0) <~> curious(X0)) [input p3]
6. ! [X0] : ((~curious(X0) | ~tall(X0)) => (old(X0) <~> ~creative(X0))) [input p5]
9. (~happy(john) & old(john)) <=> ? [X0] : old(X0) [input p8]
12. ? [X0] : (~calm(X0) | tall(X0)) <=> (old(susan) & ~strong(susan)) [input p11]
14. ! [X0] : (curious(X0) => ~old(X0)) [input p13]
16. ! [X0] : ((calm(X0) <~> rich(X0)) => (~quiet(X0) & ~calm(X0))) [input p15]
19. ? [X0] : (creative(X0) <~> curious(X0)) [input p18]
23. ~creative(john) [input hypothesis]
28. ! [X0] : ((old(X0) <~> ~creative(X0)) | (curious(X0) & tall(X0))) [ennf transformation 6]
31. ! [X0] : (~old(X0) | ~curious(X0)) [ennf transformation 14]
34. ! [X0] : ((~quiet(X0) & ~calm(X0)) | (calm(X0) <=> rich(X0))) [ennf transformation 16]
35. ! [X0] : (((~wise(X0) | ~humble(X0)) | old(X0)) & (~old(X0) | (wise(X0) & humble(X0)))) [nnf transformation 1]
36. ! [X0] : ((~wise(X0) | ~humble(X0) | old(X0)) & (~old(X0) | (wise(X0) & humble(X0)))) [flattening 35]
37. ! [X0] : ((((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (generous(X0) & old(X0))) & ((~generous(X0) | ~old(X0)) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~humble(X0) | rich(X0)) & (humble(X0) | ~rich(X0))) | (generous(X0) & old(X0))) & (~generous(X0) | ~old(X0) | ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))))) [flattening 37]
39. ! [X0] : ((~old(X0) | (~wise(X0) | tall(X0))) & ((wise(X0) & ~tall(X0)) | old(X0))) [nnf transformation 3]
40. ! [X0] : ((~old(X0) | ~wise(X0) | tall(X0)) & ((wise(X0) & ~tall(X0)) | old(X0))) [flattening 39]
41. (~humble(alice) | ! [X0] : ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) & (? [X0] : ((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | humble(alice)) [nnf transformation 4]
42. (~humble(alice) | ! [X0] : ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) & (? [X1] : ((~curious(X1) | ~old(X1)) & (curious(X1) | old(X1))) | humble(alice)) [rectify 41]
43. ? [X1] : ((~curious(X1) | ~old(X1)) & (curious(X1) | old(X1))) => ((~curious(sK0) | ~old(sK0)) & (curious(sK0) | old(sK0))) [choice axiom]
44. (~humble(alice) | ! [X0] : ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) & (((~curious(sK0) | ~old(sK0)) & (curious(sK0) | old(sK0))) | humble(alice)) [skolemisation 42,43]
45. ! [X0] : (((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (curious(X0) & tall(X0))) [nnf transformation 28]
50. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (happy(john) | ~old(john))) [nnf transformation 9]
51. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | happy(john) | ~old(john)) [flattening 50]
52. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | happy(john) | ~old(john)) [rectify 51]
53. ? [X1] : old(X1) => old(sK1) [choice axiom]
54. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (old(sK1) | happy(john) | ~old(john)) [skolemisation 52,53]
59. (? [X0] : (~calm(X0) | tall(X0)) | (~old(susan) | strong(susan))) & ((old(susan) & ~strong(susan)) | ! [X0] : (calm(X0) & ~tall(X0))) [nnf transformation 12]
60. (? [X0] : (~calm(X0) | tall(X0)) | ~old(susan) | strong(susan)) & ((old(susan) & ~strong(susan)) | ! [X0] : (calm(X0) & ~tall(X0))) [flattening 59]
61. (? [X0] : (~calm(X0) | tall(X0)) | ~old(susan) | strong(susan)) & ((old(susan) & ~strong(susan)) | ! [X1] : (calm(X1) & ~tall(X1))) [rectify 60]
62. ? [X0] : (~calm(X0) | tall(X0)) => (~calm(sK2) | tall(sK2)) [choice axiom]
63. ((~calm(sK2) | tall(sK2)) | ~old(susan) | strong(susan)) & ((old(susan) & ~strong(susan)) | ! [X1] : (calm(X1) & ~tall(X1))) [skolemisation 61,62]
66. ! [X0] : ((~quiet(X0) & ~calm(X0)) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) [nnf transformation 34]
69. ? [X0] : ((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) [nnf transformation 19]
70. ? [X0] : ((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) => ((~curious(sK5) | ~creative(sK5)) & (curious(sK5) | creative(sK5))) [choice axiom]
71. (~curious(sK5) | ~creative(sK5)) & (curious(sK5) | creative(sK5)) [skolemisation 69,70]
76. ~old(X0) | humble(X0) [cnf transformation 36]
77. ~old(X0) | wise(X0) [cnf transformation 36]
81. humble(X0) | ~rich(X0) | old(X0) [cnf transformation 38]
85. ~tall(X0) | old(X0) [cnf transformation 40]
87. ~old(X0) | ~wise(X0) | tall(X0) [cnf transformation 40]
91. ~humble(alice) | old(X0) | ~curious(X0) [cnf transformation 44]
93. ~creative(X0) | old(X0) | tall(X0) [cnf transformation 45]
96. ~old(X0) | creative(X0) | curious(X0) [cnf transformation 45]
107. old(john) | ~old(X0) [cnf transformation 54]
120. old(susan) | calm(X1) [cnf transformation 63]
123. ~curious(X0) | ~old(X0) [cnf transformation 31]
125. ~calm(X0) | rich(X0) | ~calm(X0) [cnf transformation 66]
130. curious(sK5) | creative(sK5) [cnf transformation 71]
137. ~creative(john) [cnf transformation 23]
138. ~calm(X0) | rich(X0) [duplicate literal removal 125]
139. ~rich(X0) | humble(X0) [subsumption resolution 81,76]
141. ~old(X0) | tall(X0) [subsumption resolution 87,77]
144. 1 <=> ! [X0] : (old(X0) | ~curious(X0)) [avatar definition]
145. old(X0) | ~curious(X0) <- (1) [avatar component clause 144]
147. 2 <=> humble(alice) [avatar definition]
149. ~humble(alice) <- (~2) [avatar component clause 147]
150. 1 | ~2 [avatar split clause 91,147,144]
165. ~creative(X0) | tall(X0) [subsumption resolution 93,141]
185. 9 <=> ! [X0] : ~old(X0) [avatar definition]
186. ~old(X0) <- (9) [avatar component clause 185]
193. 11 <=> old(john) [avatar definition]
195. old(john) <- (11) [avatar component clause 193]
196. 9 | 11 [avatar split clause 107,193,185]
207. 14 <=> old(susan) [avatar definition]
208. old(susan) <- (14) [avatar component clause 207]
220. 17 <=> ! [X1] : calm(X1) [avatar definition]
221. calm(X1) <- (17) [avatar component clause 220]
222. 17 | 14 [avatar split clause 120,207,220]
247. 23 <=> creative(sK5) [avatar definition]
248. creative(sK5) <- (23) [avatar component clause 247]
251. 24 <=> curious(sK5) [avatar definition]
252. curious(sK5) <- (24) [avatar component clause 251]
255. 23 | 24 [avatar split clause 130,251,247]
287. $false <- (9, 14) [resolution 208,186]
288. ~9 | ~14 [avatar contradiction clause 287]
304. tall(sK5) <- (23) [resolution 165,248]
308. old(sK5) <- (23) [resolution 304,85]
345. $false <- (9, 23) [resolution 186,308]
346. ~9 | ~23 [avatar contradiction clause 345]
387. rich(X0) <- (17) [resolution 221,138]
392. humble(X1) <- (17) [resolution 387,139]
412. $false <- (~2, 17) [resolution 392,149]
416. 2 | ~17 [avatar contradiction clause 412]
417. ~curious(X0) <- (1, 9) [subsumption resolution 145,186]
421. $false <- (1, 9, 24) [resolution 417,252]
422. ~1 | ~9 | ~24 [avatar contradiction clause 421]
485. creative(john) | curious(john) <- (11) [resolution 195,96]
489. curious(john) <- (11) [subsumption resolution 485,137]
570. ~old(john) <- (11) [resolution 489,123]
571. $false <- (11) [subsumption resolution 570,195]
572. ~11 [avatar contradiction clause 571]
573. $false [avatar sat refutation 150,196,222,255,288,346,416,422,572]
% SZS output end Proof for 5067983935364555722807642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either not old or funny and vice versa.
If someone is either not wise or funny then someone is either calm or happy.
Everyone who is either creative or curious is not brave.
Everyone who is both not generous and happy is happy or not calm and vice versa.
If someone is not funny then lucy is rich or not tall.
Everyone who is not funny is both not funny and funny and vice versa.
Everyone who is not wise or not strong is both generous and not quiet.
If someone is not old or patient then someone is both humble and strong and vice versa.
Everyone who is generous or not patient is both funny and creative and vice versa.
Everyone who is both creative and rich is both strong and not creative and vice versa.
Everyone who is tall or not generous is generous.
Everyone who is either not rich or kind is not kind and vice versa.
If mary is both not creative and funny then fred is not wise or not happy.
Everyone who is either rich or old is not happy or quiet.
Everyone who is not quiet or generous is both not quiet and creative and vice versa.
Everyone who is tall is both calm and not rich.
Fred is both tall and not quiet.
Someone is brave.
Someone is both old and not kind.
Susan is humble or funny.
Paul is both creative and calm.
Alice is either not calm or calm. | Fred is brave. | neutral | (![X]:(~humble(X)<=>(~old(X)<~>funny(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((creative(X)<~>curious(X))=>~brave(X)))&
(![X]:((~generous(X)&happy(X))<=>(happy(X)|~calm(X))))&
((?[X]:(~funny(X)))=>((rich(lucy)|~tall(lucy))))&
(![X]:(~funny(X)<=>(~funny(X)&funny(X))))&
(![X]:((~wise(X)|~strong(X))=>(generous(X)&~quiet(X))))&
((?[X]:((~old(X)|patient(X))))<=>(?[X]:((humble(X)&strong(X)))))&
(![X]:((generous(X)|~patient(X))<=>(funny(X)&creative(X))))&
(![X]:((creative(X)&rich(X))<=>(strong(X)&~creative(X))))&
(![X]:((tall(X)|~generous(X))=>generous(X)))&
(![X]:((~rich(X)<~>kind(X))<=>~kind(X)))&
(((~creative(mary)&funny(mary)))=>((~wise(fred)|~happy(fred))))&
(![X]:((rich(X)<~>old(X))=>(~happy(X)|quiet(X))))&
(![X]:((~quiet(X)|generous(X))<=>(~quiet(X)&creative(X))))&
(![X]:(tall(X)=>(calm(X)&~rich(X))))&
((tall(fred)&~quiet(fred)))&
(?[X]:(brave(X)))&
(?[X]:((old(X)&~kind(X))))&
((humble(susan)|funny(susan)))&
((creative(paul)&calm(paul)))&
((~calm(alice)<~>calm(alice))) | brave(fred) | [] | null | 0 |
If susan is curious or not curious then mary is either not strong or not tall.
If someone is both not old and not calm then john is either funny or curious and vice versa.
If fred is both not kind and curious then paul is either not funny or not strong and vice versa.
Everyone who is brave or not old is either not strong or not quiet and vice versa.
Everyone who is either not old or not curious is both strong and wise and vice versa.
If fred is not creative then lucy is either calm or not calm.
Everyone who is not curious or funny is both kind and not calm and vice versa.
If fred is either rich or generous then paul is either funny or not creative.
Everyone who is old is not quiet.
If alice is not calm or not curious then mary is generous.
If someone is both not tall and old then paul is either strong or not patient and vice versa.
Everyone who is tall or not curious is not rich or not old.
Everyone who is not old or kind is not patient or not tall.
Everyone who is not curious is not old.
If susan is brave then fred is old or calm.
Everyone who is either brave or humble is both not generous and not kind.
Paul is not funny.
Someone is not humble.
Someone is not kind.
Fred is either not old or not wise.
John is both humble and creative.
Someone is creative.
Someone is funny or patient. | Alice is calm. | neutral | (((curious(susan)|~curious(susan)))=>((~strong(mary)<~>~tall(mary))))&
((?[X]:((~old(X)&~calm(X))))<=>((funny(john)<~>curious(john))))&
(((~kind(fred)&curious(fred)))<=>((~funny(paul)<~>~strong(paul))))&
(![X]:((brave(X)|~old(X))<=>(~strong(X)<~>~quiet(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(strong(X)&wise(X))))&
((~creative(fred))=>((calm(lucy)<~>~calm(lucy))))&
(![X]:((~curious(X)|funny(X))<=>(kind(X)&~calm(X))))&
(((rich(fred)<~>generous(fred)))=>((funny(paul)<~>~creative(paul))))&
(![X]:(old(X)=>~quiet(X)))&
(((~calm(alice)|~curious(alice)))=>(generous(mary)))&
((?[X]:((~tall(X)&old(X))))<=>((strong(paul)<~>~patient(paul))))&
(![X]:((tall(X)|~curious(X))=>(~rich(X)|~old(X))))&
(![X]:((~old(X)|kind(X))=>(~patient(X)|~tall(X))))&
(![X]:(~curious(X)=>~old(X)))&
((brave(susan))=>((old(fred)|calm(fred))))&
(![X]:((brave(X)<~>humble(X))=>(~generous(X)&~kind(X))))&
(~funny(paul))&
(?[X]:(~humble(X)))&
(?[X]:(~kind(X)))&
((~old(fred)<~>~wise(fred)))&
((humble(john)&creative(john)))&
(?[X]:(creative(X)))&
(?[X]:((funny(X)|patient(X)))) | calm(alice) | [] | null | 0 |
If someone is wise then someone is not old or not happy.
If mary is both wise and curious then mary is either not brave or happy and vice versa.
If lucy is either old or not quiet then someone is not happy.
If paul is both old and tall then paul is old or not brave.
Everyone who is both not patient and not funny is both tall and old.
If mary is both curious and not funny then fred is patient or not creative and vice versa.
Everyone who is both wise and not wise is both not humble and not generous.
If mary is either not creative or rich then john is funny and vice versa.
If mary is either not happy or not calm then someone is kind.
If john is not rich or not generous then someone is patient or not brave.
Everyone who is both not brave and curious is not rich or not strong.
If someone is both rich and old then fred is either not quiet or not rich.
Everyone who is either not generous or brave is either kind or not tall.
If john is patient or not curious then someone is either creative or not strong.
Everyone who is wise is either generous or old and vice versa.
Everyone who is both not kind and funny is either not calm or not curious.
Someone is either humble or patient.
Someone is both not humble and not funny.
Mary is not kind.
Someone is not happy or not curious.
Someone is both not brave and happy.
Mary is happy.
Mary is either happy or not happy.
Someone is both not calm and not strong. | Mary is happy. | entailment | ((?[X]:(wise(X)))=>(?[X]:((~old(X)|~happy(X)))))&
(((wise(mary)&curious(mary)))<=>((~brave(mary)<~>happy(mary))))&
(((old(lucy)<~>~quiet(lucy)))=>(?[X]:(~happy(X))))&
(((old(paul)&tall(paul)))=>((old(paul)|~brave(paul))))&
(![X]:((~patient(X)&~funny(X))=>(tall(X)&old(X))))&
(((curious(mary)&~funny(mary)))<=>((patient(fred)|~creative(fred))))&
(![X]:((wise(X)&~wise(X))=>(~humble(X)&~generous(X))))&
(((~creative(mary)<~>rich(mary)))<=>(funny(john)))&
(((~happy(mary)<~>~calm(mary)))=>(?[X]:(kind(X))))&
(((~rich(john)|~generous(john)))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:((~brave(X)&curious(X))=>(~rich(X)|~strong(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(fred)<~>~rich(fred))))&
(![X]:((~generous(X)<~>brave(X))=>(kind(X)<~>~tall(X))))&
(((patient(john)|~curious(john)))=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:(wise(X)<=>(generous(X)<~>old(X))))&
(![X]:((~kind(X)&funny(X))=>(~calm(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>patient(X))))&
(?[X]:((~humble(X)&~funny(X))))&
(~kind(mary))&
(?[X]:((~happy(X)|~curious(X))))&
(?[X]:((~brave(X)&happy(X))))&
(happy(mary))&
((happy(mary)<~>~happy(mary)))&
(?[X]:((~calm(X)&~strong(X)))) | happy(mary) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 781322547317703134188098
% SZS output start Proof for 781322547317703134188098
22. happy(mary) [input p21]
25. ~happy(mary) [input hypothesis]
131. happy(mary) [cnf transformation 22]
136. ~happy(mary) [cnf transformation 25]
150. 4 <=> happy(mary) [avatar definition]
298. 4 [avatar split clause 131,150]
299. ~4 [avatar split clause 136,150]
300. $false [avatar sat refutation 298,299]
% SZS output end Proof for 781322547317703134188098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or not funny then mary is funny.
Everyone who is not rich or humble is both brave and tall.
Everyone who is not strong is generous or not rich and vice versa.
If someone is both not tall and not calm then someone is calm.
Everyone who is calm or not brave is quiet.
If someone is both quiet and not brave then someone is either not funny or patient and vice versa.
Everyone who is both not rich and not curious is not funny or strong and vice versa.
If someone is quiet then john is either tall or not tall and vice versa.
If paul is both not creative and kind then susan is either kind or generous and vice versa.
Everyone who is both not rich and rich is humble.
If susan is either wise or old then john is not quiet and vice versa.
Everyone who is curious is either not strong or generous and vice versa.
Everyone who is not happy or not old is tall.
If mary is not rich or wise then someone is not kind and vice versa.
Everyone who is wise or not generous is either old or not strong and vice versa.
Everyone who is brave or patient is both funny and not kind and vice versa.
Mary is not kind or generous.
Someone is not rich.
Someone is curious or not kind.
Someone is both old and generous.
Someone is not wise or not strong.
Someone is not generous or calm. | Paul is not brave. | neutral | ((?[X]:((~quiet(X)<~>~funny(X))))=>(funny(mary)))&
(![X]:((~rich(X)|humble(X))=>(brave(X)&tall(X))))&
(![X]:(~strong(X)<=>(generous(X)|~rich(X))))&
((?[X]:((~tall(X)&~calm(X))))=>(?[X]:(calm(X))))&
(![X]:((calm(X)|~brave(X))=>quiet(X)))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~rich(X)&~curious(X))<=>(~funny(X)|strong(X))))&
((?[X]:(quiet(X)))<=>((tall(john)<~>~tall(john))))&
(((~creative(paul)&kind(paul)))<=>((kind(susan)<~>generous(susan))))&
(![X]:((~rich(X)&rich(X))=>humble(X)))&
(((wise(susan)<~>old(susan)))<=>(~quiet(john)))&
(![X]:(curious(X)<=>(~strong(X)<~>generous(X))))&
(![X]:((~happy(X)|~old(X))=>tall(X)))&
(((~rich(mary)|wise(mary)))<=>(?[X]:(~kind(X))))&
(![X]:((wise(X)|~generous(X))<=>(old(X)<~>~strong(X))))&
(![X]:((brave(X)|patient(X))<=>(funny(X)&~kind(X))))&
((~kind(mary)|generous(mary)))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~generous(X)|calm(X)))) | ~brave(paul) | [] | null | 0 |
Everyone who is both creative and not quiet is either happy or generous.
Everyone who is both not quiet and not brave is both calm and generous.
Everyone who is wise or patient is either not strong or happy and vice versa.
If someone is creative or not kind then alice is both not tall and not quiet.
Everyone who is humble is quiet or patient.
If susan is both humble and not brave then susan is wise or patient.
If someone is either creative or not brave then fred is not rich and vice versa.
If paul is either not humble or funny then lucy is either patient or strong and vice versa.
Everyone who is not curious or not kind is not strong or curious.
Everyone who is both not tall and creative is both calm and not calm.
Everyone who is either not wise or not quiet is both rich and generous.
If someone is both brave and not calm then fred is not creative or rich and vice versa.
If someone is humble or not tall then someone is generous and vice versa.
Everyone who is generous or kind is not tall.
Everyone who is both patient and not quiet is not patient and vice versa.
If john is both tall and curious then someone is not happy.
Someone is not curious or rich.
Paul is not rich.
Mary is not happy.
Someone is not creative or not generous. | Paul is funny. | neutral | (![X]:((creative(X)&~quiet(X))=>(happy(X)<~>generous(X))))&
(![X]:((~quiet(X)&~brave(X))=>(calm(X)&generous(X))))&
(![X]:((wise(X)|patient(X))<=>(~strong(X)<~>happy(X))))&
((?[X]:((creative(X)|~kind(X))))=>((~tall(alice)&~quiet(alice))))&
(![X]:(humble(X)=>(quiet(X)|patient(X))))&
(((humble(susan)&~brave(susan)))=>((wise(susan)|patient(susan))))&
((?[X]:((creative(X)<~>~brave(X))))<=>(~rich(fred)))&
(((~humble(paul)<~>funny(paul)))<=>((patient(lucy)<~>strong(lucy))))&
(![X]:((~curious(X)|~kind(X))=>(~strong(X)|curious(X))))&
(![X]:((~tall(X)&creative(X))=>(calm(X)&~calm(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(rich(X)&generous(X))))&
((?[X]:((brave(X)&~calm(X))))<=>((~creative(fred)|rich(fred))))&
((?[X]:((humble(X)|~tall(X))))<=>(?[X]:(generous(X))))&
(![X]:((generous(X)|kind(X))=>~tall(X)))&
(![X]:((patient(X)&~quiet(X))<=>~patient(X)))&
(((tall(john)&curious(john)))=>(?[X]:(~happy(X))))&
(?[X]:((~curious(X)|rich(X))))&
(~rich(paul))&
(~happy(mary))&
(?[X]:((~creative(X)|~generous(X)))) | funny(paul) | [] | null | 0 |
If someone is either not humble or not brave then fred is brave and vice versa.
If someone is patient or not generous then fred is happy and vice versa.
Everyone who is not patient is either not strong or funny.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
Alice is strong or curious.
Susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Someone is both not calm and creative.
Susan is not kind or curious. | Fred is not strong. | contradiction | ((?[X]:((~humble(X)<~>~brave(X))))<=>(brave(fred)))&
((?[X]:((patient(X)|~generous(X))))<=>(happy(fred)))&
(![X]:(~patient(X)=>(~strong(X)<~>funny(X))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
((strong(alice)|curious(alice)))&
((~happy(susan)|happy(susan)))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
(?[X]:((~calm(X)&creative(X))))&
((~kind(susan)|curious(susan))) | ~strong(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8965491613982452476751967
% SZS output start Proof for 8965491613982452476751967
10. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p9]
23. ~strong(fred) [input hypothesis]
49. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 10]
50. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 49]
93. strong(X0) | strong(X0) [cnf transformation 50]
124. ~strong(fred) [cnf transformation 23]
125. strong(X0) [duplicate literal removal 93]
267. $false [subsumption resolution 124,125]
% SZS output end Proof for 8965491613982452476751967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and not wise then someone is both not humble and old and vice versa. Everyone who is either funny or creative is both patient and not creative. If john is creative then susan is not creative or not funny and vice versa. Everyone who is both not wise and not humble is not humble or not patient and vice versa. If lucy is both not tall and not wise then someone is not creative or not patient and vice versa. Everyone who is both calm and not creative is both not curious and not strong. Everyone who is not kind is both tall and not funny and vice versa. Everyone who is both quiet and old is both humble and not quiet. Everyone who is kind or not curious is brave or tall and vice versa. If someone is both not kind and strong then paul is generous or calm and vice versa. If john is either humble or creative then mary is either wise or not calm and vice versa. If someone is brave or creative then someone is either not happy or wise. Everyone who is either not generous or not kind is both patient and wise and vice versa. If someone is happy then paul is generous or not generous. If fred is tall or strong then someone is both tall and rich and vice versa. John is not curious or not creative. Mary is not happy or funny. Susan is generous. Lucy is either not funny or not old. | Susan is patient. | neutral | ((?[X]:((~patient(X)&~wise(X))))<=>(?[X]:((~humble(X)&old(X)))))&
(![X]:((funny(X)<~>creative(X))=>(patient(X)&~creative(X))))&
((creative(john))<=>((~creative(susan)|~funny(susan))))&
(![X]:((~wise(X)&~humble(X))<=>(~humble(X)|~patient(X))))&
(((~tall(lucy)&~wise(lucy)))<=>(?[X]:((~creative(X)|~patient(X)))))&
(![X]:((calm(X)&~creative(X))=>(~curious(X)&~strong(X))))&
(![X]:(~kind(X)<=>(tall(X)&~funny(X))))&
(![X]:((quiet(X)&old(X))=>(humble(X)&~quiet(X))))&
(![X]:((kind(X)|~curious(X))<=>(brave(X)|tall(X))))&
((?[X]:((~kind(X)&strong(X))))<=>((generous(paul)|calm(paul))))&
(((humble(john)<~>creative(john)))<=>((wise(mary)<~>~calm(mary))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~happy(X)<~>wise(X)))))&
(![X]:((~generous(X)<~>~kind(X))<=>(patient(X)&wise(X))))&
((?[X]:(happy(X)))=>((generous(paul)|~generous(paul))))&
(((tall(fred)|strong(fred)))<=>(?[X]:((tall(X)&rich(X)))))&
((~curious(john)|~creative(john)))&
((~happy(mary)|funny(mary)))&
(generous(susan))&
((~funny(lucy)<~>~old(lucy))) | patient(susan) | [] | null | 0 |
If susan is not generous or not strong then alice is either curious or not rich and vice versa. Everyone who is either rich or patient is not calm or old. Everyone who is not old is both patient and not rich and vice versa. If alice is not quiet then susan is not creative. If someone is old or not quiet then fred is brave and vice versa. Everyone who is both not old and brave is tall and vice versa. Everyone who is both not rich and happy is both not humble and kind and vice versa. Everyone who is not patient or not brave is both not creative and not wise. Everyone who is either tall or wise is not tall or quiet and vice versa. If john is either calm or not rich then someone is both not tall and not patient and vice versa. Everyone who is not patient is both generous and quiet. Everyone who is happy or strong is either tall or not wise and vice versa. Everyone who is both not kind and not tall is both patient and not brave. Everyone who is creative is either not kind or not curious. Everyone who is strong or not curious is both wise and not tall. If someone is both creative and not strong then someone is either old or not humble. Lucy is both not old and happy. Alice is not funny. Someone is both wise and rich. Alice is not quiet. Someone is either generous or quiet. Mary is either not curious or not humble. Someone is either creative or not old. Someone is generous. | Alice is not happy. | entailment | (((~generous(susan)|~strong(susan)))<=>((curious(alice)<~>~rich(alice))))&
(![X]:((rich(X)<~>patient(X))=>(~calm(X)|old(X))))&
(![X]:(~old(X)<=>(patient(X)&~rich(X))))&
((~quiet(alice))=>(~creative(susan)))&
((?[X]:((old(X)|~quiet(X))))<=>(brave(fred)))&
(![X]:((~old(X)&brave(X))<=>tall(X)))&
(![X]:((~rich(X)&happy(X))<=>(~humble(X)&kind(X))))&
(![X]:((~patient(X)|~brave(X))=>(~creative(X)&~wise(X))))&
(![X]:((tall(X)<~>wise(X))<=>(~tall(X)|quiet(X))))&
(((calm(john)<~>~rich(john)))<=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:(~patient(X)=>(generous(X)&quiet(X))))&
(![X]:((happy(X)|strong(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~kind(X)&~tall(X))=>(patient(X)&~brave(X))))&
(![X]:(creative(X)=>(~kind(X)<~>~curious(X))))&
(![X]:((strong(X)|~curious(X))=>(wise(X)&~tall(X))))&
((?[X]:((creative(X)&~strong(X))))=>(?[X]:((old(X)<~>~humble(X)))))&
((~old(lucy)&happy(lucy)))&
(~funny(alice))&
(?[X]:((wise(X)&rich(X))))&
(~quiet(alice))&
(?[X]:((generous(X)<~>quiet(X))))&
((~curious(mary)<~>~humble(mary)))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:(generous(X))) | ~happy(alice) | [
"p0",
"p2",
"p5",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 820983165721230000862129
% SZS output start Proof for 820983165721230000862129
1. (~strong(susan) | ~generous(susan)) <=> (curious(alice) <~> ~rich(alice)) [input p0]
3. ! [X0] : (~old(X0) <=> (~rich(X0) & patient(X0))) [input p2]
6. ! [X0] : ((brave(X0) & ~old(X0)) <=> tall(X0)) [input p5]
9. ! [X0] : ((tall(X0) <~> wise(X0)) <=> (quiet(X0) | ~tall(X0))) [input p8]
12. ! [X0] : ((strong(X0) | happy(X0)) <=> (tall(X0) <~> ~wise(X0))) [input p11]
15. ! [X0] : ((~curious(X0) | strong(X0)) => (~tall(X0) & wise(X0))) [input p14]
25. happy(alice) [input hypothesis]
36. ! [X0] : ((~tall(X0) & wise(X0)) | (curious(X0) & ~strong(X0))) [ennf transformation 15]
38. ((~strong(susan) | ~generous(susan)) | ((curious(alice) | rich(alice)) & (~rich(alice) | ~curious(alice)))) & (((rich(alice) | ~curious(alice)) & (~rich(alice) | curious(alice))) | (strong(susan) & generous(susan))) [nnf transformation 1]
39. (~strong(susan) | ~generous(susan) | ((curious(alice) | rich(alice)) & (~rich(alice) | ~curious(alice)))) & (((rich(alice) | ~curious(alice)) & (~rich(alice) | curious(alice))) | (strong(susan) & generous(susan))) [flattening 38]
41. ! [X0] : ((~old(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | old(X0))) [nnf transformation 3]
42. ! [X0] : ((~old(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | old(X0))) [flattening 41]
47. ! [X0] : (((brave(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | (~brave(X0) | old(X0)))) [nnf transformation 6]
48. ! [X0] : (((brave(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | ~brave(X0) | old(X0))) [flattening 47]
51. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~quiet(X0) & tall(X0))) & ((quiet(X0) | ~tall(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [nnf transformation 9]
52. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~quiet(X0) & tall(X0))) & (quiet(X0) | ~tall(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [flattening 51]
57. ! [X0] : (((strong(X0) | happy(X0)) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~strong(X0) & ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : ((strong(X0) | happy(X0) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~strong(X0) & ~happy(X0)))) [flattening 57]
78. rich(alice) | ~curious(alice) | strong(susan) [cnf transformation 39]
84. ~rich(X0) | old(X0) [cnf transformation 42]
91. ~tall(X0) | ~old(X0) [cnf transformation 48]
103. wise(X0) | tall(X0) | tall(X0) [cnf transformation 52]
115. ~wise(X0) | tall(X0) | ~happy(X0) [cnf transformation 58]
116. ~wise(X0) | tall(X0) | ~strong(X0) [cnf transformation 58]
117. wise(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 58]
118. wise(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 58]
127. ~tall(X0) | ~strong(X0) [cnf transformation 36]
128. ~tall(X0) | curious(X0) [cnf transformation 36]
143. happy(alice) [cnf transformation 25]
145. wise(X0) | tall(X0) [duplicate literal removal 103]
147. 1 <=> rich(alice) [avatar definition]
149. rich(alice) <- (1) [avatar component clause 147]
151. 2 <=> curious(alice) [avatar definition]
159. 4 <=> strong(susan) [avatar definition]
160. strong(susan) <- (4) [avatar component clause 159]
164. 4 | ~2 | 1 [avatar split clause 78,147,151,159]
224. ~strong(X0) | wise(X0) [subsumption resolution 118,145]
225. ~happy(X0) | wise(X0) [subsumption resolution 117,145]
226. ~strong(X0) | tall(X0) [subsumption resolution 116,224]
227. ~happy(X0) | tall(X0) [subsumption resolution 115,225]
228. ~strong(X0) [subsumption resolution 127,226]
305. tall(alice) [resolution 227,143]
335. curious(alice) [resolution 305,128]
337. ~old(alice) [resolution 305,91]
340. 2 [avatar split clause 335,151]
341. old(alice) <- (1) [resolution 149,84]
342. $false <- (1) [subsumption resolution 341,337]
343. ~1 [avatar contradiction clause 342]
344. $false <- (4) [subsumption resolution 160,228]
345. ~4 [avatar contradiction clause 344]
346. $false [avatar sat refutation 164,340,343,345]
% SZS output end Proof for 820983165721230000862129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or old is both not quiet and patient.
Everyone who is both not quiet and funny is old or not kind and vice versa.
If fred is not strong then susan is quiet.
If someone is both happy and not wise then someone is funny and vice versa.
If john is either not strong or humble then someone is both not old and calm and vice versa.
If lucy is both generous and not brave then someone is either funny or wise.
Everyone who is both calm and not tall is either not brave or not humble and vice versa.
Everyone who is not brave or tall is brave and vice versa.
If someone is humble then mary is not generous.
Everyone who is patient is either quiet or not generous and vice versa.
Everyone who is both old and patient is humble.
If susan is not calm or not funny then someone is generous and vice versa.
Everyone who is both happy and not tall is brave.
Everyone who is both calm and not happy is either wise or humble and vice versa.
Everyone who is not curious or creative is quiet or calm.
If someone is humble or not curious then john is either brave or not tall and vice versa.
Lucy is both not generous and not curious.
Fred is either generous or curious.
Lucy is both not funny and not patient.
Someone is not old or generous.
Susan is either wise or strong.
Someone is not happy. | John is not strong. | neutral | (![X]:((~creative(X)<~>old(X))=>(~quiet(X)&patient(X))))&
(![X]:((~quiet(X)&funny(X))<=>(old(X)|~kind(X))))&
((~strong(fred))=>(quiet(susan)))&
((?[X]:((happy(X)&~wise(X))))<=>(?[X]:(funny(X))))&
(((~strong(john)<~>humble(john)))<=>(?[X]:((~old(X)&calm(X)))))&
(((generous(lucy)&~brave(lucy)))=>(?[X]:((funny(X)<~>wise(X)))))&
(![X]:((calm(X)&~tall(X))<=>(~brave(X)<~>~humble(X))))&
(![X]:((~brave(X)|tall(X))<=>brave(X)))&
((?[X]:(humble(X)))=>(~generous(mary)))&
(![X]:(patient(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((old(X)&patient(X))=>humble(X)))&
(((~calm(susan)|~funny(susan)))<=>(?[X]:(generous(X))))&
(![X]:((happy(X)&~tall(X))=>brave(X)))&
(![X]:((calm(X)&~happy(X))<=>(wise(X)<~>humble(X))))&
(![X]:((~curious(X)|creative(X))=>(quiet(X)|calm(X))))&
((?[X]:((humble(X)|~curious(X))))<=>((brave(john)<~>~tall(john))))&
((~generous(lucy)&~curious(lucy)))&
((generous(fred)<~>curious(fred)))&
((~funny(lucy)&~patient(lucy)))&
(?[X]:((~old(X)|generous(X))))&
((wise(susan)<~>strong(susan)))&
(?[X]:(~happy(X))) | ~strong(john) | [] | null | 0 |
Everyone who is both not happy and not humble is either not creative or not rich.
If someone is not creative then someone is both wise and calm.
If someone is both not creative and not funny then john is old.
Everyone who is both not strong and not patient is both not kind and not funny.
Everyone who is not rich is not kind or strong.
If someone is not happy then fred is humble or creative.
Everyone who is not humble or happy is both kind and patient.
Everyone who is not kind is not wise or not quiet.
If john is not old then someone is brave and vice versa.
Everyone who is either not quiet or old is not wise.
If alice is both humble and not kind then paul is not patient and vice versa.
If paul is not quiet or kind then someone is either creative or not strong and vice versa.
Everyone who is either kind or patient is kind and vice versa.
If someone is patient then john is not old.
If someone is rich or curious then someone is not calm.
Everyone who is not brave or not strong is either rich or not curious.
Alice is not old or kind.
Alice is both not strong and quiet.
Someone is either kind or not brave.
Lucy is both old and wise.
Someone is either rich or not brave.
Someone is calm.
Someone is either kind or calm. | Alice is humble. | entailment | (![X]:((~happy(X)&~humble(X))=>(~creative(X)<~>~rich(X))))&
((?[X]:(~creative(X)))=>(?[X]:((wise(X)&calm(X)))))&
((?[X]:((~creative(X)&~funny(X))))=>(old(john)))&
(![X]:((~strong(X)&~patient(X))=>(~kind(X)&~funny(X))))&
(![X]:(~rich(X)=>(~kind(X)|strong(X))))&
((?[X]:(~happy(X)))=>((humble(fred)|creative(fred))))&
(![X]:((~humble(X)|happy(X))=>(kind(X)&patient(X))))&
(![X]:(~kind(X)=>(~wise(X)|~quiet(X))))&
((~old(john))<=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)<~>old(X))=>~wise(X)))&
(((humble(alice)&~kind(alice)))<=>(~patient(paul)))&
(((~quiet(paul)|kind(paul)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>patient(X))<=>kind(X)))&
((?[X]:(patient(X)))=>(~old(john)))&
((?[X]:((rich(X)|curious(X))))=>(?[X]:(~calm(X))))&
(![X]:((~brave(X)|~strong(X))=>(rich(X)<~>~curious(X))))&
((~old(alice)|kind(alice)))&
((~strong(alice)&quiet(alice)))&
(?[X]:((kind(X)<~>~brave(X))))&
((old(lucy)&wise(lucy)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)<~>calm(X)))) | humble(alice) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5972692541456007955816062
% SZS output start Proof for 5972692541456007955816062
11. (~kind(alice) & humble(alice)) <=> ~patient(paul) [input p10]
13. ! [X0] : ((kind(X0) <~> patient(X0)) <=> kind(X0)) [input p12]
24. ~humble(alice) [input hypothesis]
53. ((~kind(alice) & humble(alice)) | patient(paul)) & (~patient(paul) | (kind(alice) | ~humble(alice))) [nnf transformation 11]
54. ((~kind(alice) & humble(alice)) | patient(paul)) & (~patient(paul) | kind(alice) | ~humble(alice)) [flattening 53]
60. ! [X0] : ((((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) | ~kind(X0)) & (kind(X0) | ((kind(X0) | ~patient(X0)) & (patient(X0) | ~kind(X0))))) [nnf transformation 13]
95. humble(alice) | patient(paul) [cnf transformation 54]
104. kind(X0) | kind(X0) | ~patient(X0) [cnf transformation 60]
106. ~patient(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 60]
126. ~humble(alice) [cnf transformation 24]
127. kind(X0) | ~patient(X0) [duplicate literal removal 104]
128. ~patient(X0) | ~kind(X0) [duplicate literal removal 106]
172. 11 <=> patient(paul) [avatar definition]
174. patient(paul) <- (11) [avatar component clause 172]
181. 13 <=> humble(alice) [avatar definition]
184. 11 | 13 [avatar split clause 95,181,172]
215. ~patient(X0) [subsumption resolution 127,128]
263. ~13 [avatar split clause 126,181]
264. $false <- (11) [subsumption resolution 174,215]
265. ~11 [avatar contradiction clause 264]
266. $false [avatar sat refutation 184,263,265]
% SZS output end Proof for 5972692541456007955816062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and strong then someone is both kind and not curious.
If fred is both curious and not rich then someone is quiet or not rich.
If mary is both strong and not wise then someone is either generous or not patient and vice versa.
If someone is either not humble or kind then paul is happy and vice versa.
Everyone who is not curious or patient is either not creative or quiet and vice versa.
Everyone who is calm is both not wise and patient.
If fred is either creative or patient then john is humble or tall.
If lucy is either humble or quiet then paul is not generous.
Everyone who is not calm or curious is both tall and strong.
If someone is quiet or wise then someone is strong.
Everyone who is rich or not strong is either not tall or brave and vice versa.
If john is both not rich and strong then someone is not generous or patient.
Everyone who is both not brave and not strong is not tall or rich.
Everyone who is both not patient and not brave is both rich and not old.
Everyone who is wise is quiet or not tall.
If john is funny then paul is both not wise and brave and vice versa.
Someone is both not funny and humble.
Fred is both wise and not patient.
Fred is either not generous or calm.
Mary is not patient.
Alice is calm or not humble.
Someone is either happy or rich.
Someone is both generous and not strong.
Someone is not brave or not curious. | Fred is rich. | entailment | ((?[X]:((~kind(X)&strong(X))))=>(?[X]:((kind(X)&~curious(X)))))&
(((curious(fred)&~rich(fred)))=>(?[X]:((quiet(X)|~rich(X)))))&
(((strong(mary)&~wise(mary)))<=>(?[X]:((generous(X)<~>~patient(X)))))&
((?[X]:((~humble(X)<~>kind(X))))<=>(happy(paul)))&
(![X]:((~curious(X)|patient(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:(calm(X)=>(~wise(X)&patient(X))))&
(((creative(fred)<~>patient(fred)))=>((humble(john)|tall(john))))&
(((humble(lucy)<~>quiet(lucy)))=>(~generous(paul)))&
(![X]:((~calm(X)|curious(X))=>(tall(X)&strong(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:(strong(X))))&
(![X]:((rich(X)|~strong(X))<=>(~tall(X)<~>brave(X))))&
(((~rich(john)&strong(john)))=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((~brave(X)&~strong(X))=>(~tall(X)|rich(X))))&
(![X]:((~patient(X)&~brave(X))=>(rich(X)&~old(X))))&
(![X]:(wise(X)=>(quiet(X)|~tall(X))))&
((funny(john))<=>((~wise(paul)&brave(paul))))&
(?[X]:((~funny(X)&humble(X))))&
((wise(fred)&~patient(fred)))&
((~generous(fred)<~>calm(fred)))&
(~patient(mary))&
((calm(alice)|~humble(alice)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:((~brave(X)|~curious(X)))) | rich(fred) | [
"p5",
"p8",
"p10",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 320945780619873992796390
% SZS output start Proof for 320945780619873992796390
6. ! [X0] : (calm(X0) => (patient(X0) & ~wise(X0))) [input p5]
9. ! [X0] : ((curious(X0) | ~calm(X0)) => (strong(X0) & tall(X0))) [input p8]
11. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~tall(X0) <~> brave(X0))) [input p10]
14. ! [X0] : ((~brave(X0) & ~patient(X0)) => (~old(X0) & rich(X0))) [input p13]
18. ~patient(fred) & wise(fred) [input p17]
25. ~rich(fred) [input hypothesis]
28. ! [X0] : ((~brave(X0) & ~patient(X0)) => rich(X0)) [pure predicate removal 14]
32. ! [X0] : ((patient(X0) & ~wise(X0)) | ~calm(X0)) [ennf transformation 6]
36. ! [X0] : ((strong(X0) & tall(X0)) | (~curious(X0) & calm(X0))) [ennf transformation 9]
42. ! [X0] : (rich(X0) | (brave(X0) | patient(X0))) [ennf transformation 28]
43. ! [X0] : (rich(X0) | brave(X0) | patient(X0)) [flattening 42]
67. ! [X0] : (((~strong(X0) | rich(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (strong(X0) & ~rich(X0)))) [nnf transformation 11]
68. ! [X0] : ((~strong(X0) | rich(X0) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (strong(X0) & ~rich(X0)))) [flattening 67]
103. ~calm(X0) | patient(X0) [cnf transformation 32]
108. tall(X0) | calm(X0) [cnf transformation 36]
110. calm(X0) | strong(X0) [cnf transformation 36]
119. ~brave(X0) | rich(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 68]
122. brave(X0) | rich(X0) | patient(X0) [cnf transformation 43]
130. ~patient(fred) [cnf transformation 18]
140. ~rich(fred) [cnf transformation 25]
159. 5 <=> rich(fred) [avatar definition]
160. ~rich(fred) <- (~5) [avatar component clause 159]
222. 19 <=> patient(fred) [avatar definition]
224. ~patient(fred) <- (~19) [avatar component clause 222]
297. ~19 [avatar split clause 130,222]
336. ~5 [avatar split clause 140,159]
338. patient(X0) | strong(X0) [resolution 110,103]
477. rich(X0) | ~tall(X0) | ~strong(X0) | rich(X0) | patient(X0) [resolution 119,122]
479. rich(X0) | ~tall(X0) | ~strong(X0) | patient(X0) [duplicate literal removal 477]
480. ~tall(X0) | rich(X0) | patient(X0) [subsumption resolution 479,338]
509. rich(X0) | patient(X0) | calm(X0) [resolution 480,108]
512. patient(X0) | rich(X0) [subsumption resolution 509,103]
546. rich(fred) <- (~19) [resolution 512,224]
548. $false <- (~5, ~19) [subsumption resolution 546,160]
549. 5 | 19 [avatar contradiction clause 548]
552. $false [avatar sat refutation 297,336,549]
% SZS output end Proof for 320945780619873992796390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both tall and not kind is either strong or curious.
Everyone who is both funny and not creative is not patient.
Everyone who is both not strong and not brave is either creative or not curious and vice versa.
Everyone who is either rich or kind is not kind or not creative.
If lucy is generous or not quiet then someone is tall or not generous and vice versa.
Everyone who is not strong or not brave is both not creative and humble and vice versa.
If mary is either brave or not humble then mary is humble or not tall and vice versa.
Everyone who is not kind or not generous is not quiet or generous.
If someone is calm or not brave then someone is both wise and brave.
Everyone who is not happy is either funny or not happy.
If someone is both not happy and wise then alice is both not patient and calm.
If susan is both rich and not tall then someone is both humble and wise and vice versa.
If someone is either brave or kind then someone is both brave and tall and vice versa.
Everyone who is both calm and curious is not wise or wise.
Everyone who is not creative is both tall and wise and vice versa.
Everyone who is not curious or wise is calm or tall and vice versa.
Someone is not strong.
Someone is either strong or tall.
Someone is either not old or not humble.
Susan is not generous.
Someone is either rich or kind.
Lucy is either humble or patient.
Someone is both not kind and quiet.
Someone is not wise. | Susan is not calm. | contradiction | (![X]:((tall(X)&~kind(X))=>(strong(X)<~>curious(X))))&
(![X]:((funny(X)&~creative(X))=>~patient(X)))&
(![X]:((~strong(X)&~brave(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((rich(X)<~>kind(X))=>(~kind(X)|~creative(X))))&
(((generous(lucy)|~quiet(lucy)))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((~strong(X)|~brave(X))<=>(~creative(X)&humble(X))))&
(((brave(mary)<~>~humble(mary)))<=>((humble(mary)|~tall(mary))))&
(![X]:((~kind(X)|~generous(X))=>(~quiet(X)|generous(X))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:((wise(X)&brave(X)))))&
(![X]:(~happy(X)=>(funny(X)<~>~happy(X))))&
((?[X]:((~happy(X)&wise(X))))=>((~patient(alice)&calm(alice))))&
(((rich(susan)&~tall(susan)))<=>(?[X]:((humble(X)&wise(X)))))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((calm(X)&curious(X))=>(~wise(X)|wise(X))))&
(![X]:(~creative(X)<=>(tall(X)&wise(X))))&
(![X]:((~curious(X)|wise(X))<=>(calm(X)|tall(X))))&
(?[X]:(~strong(X)))&
(?[X]:((strong(X)<~>tall(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
(~generous(susan))&
(?[X]:((rich(X)<~>kind(X))))&
((humble(lucy)<~>patient(lucy)))&
(?[X]:((~kind(X)&quiet(X))))&
(?[X]:(~wise(X))) | ~calm(susan) | [
"p2",
"p5",
"p11",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 543968753259149656052737
% SZS output start Proof for 543968753259149656052737
3. ! [X0] : ((~brave(X0) & ~strong(X0)) <=> (creative(X0) <~> ~curious(X0))) [input p2]
6. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> (humble(X0) & ~creative(X0))) [input p5]
12. (~tall(susan) & rich(susan)) <=> ? [X0] : (wise(X0) & humble(X0)) [input p11]
15. ! [X0] : (~creative(X0) <=> (wise(X0) & tall(X0))) [input p14]
16. ! [X0] : ((wise(X0) | ~curious(X0)) <=> (tall(X0) | calm(X0))) [input p15]
17. ? [X0] : ~strong(X0) [input p16]
25. ~calm(susan) [input hypothesis]
42. ! [X0] : (((~brave(X0) & ~strong(X0)) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | (brave(X0) | strong(X0)))) [nnf transformation 3]
43. ! [X0] : (((~brave(X0) & ~strong(X0)) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | brave(X0) | strong(X0))) [flattening 42]
50. ! [X0] : (((~brave(X0) | ~strong(X0)) | (~humble(X0) | creative(X0))) & ((humble(X0) & ~creative(X0)) | (brave(X0) & strong(X0)))) [nnf transformation 6]
51. ! [X0] : ((~brave(X0) | ~strong(X0) | ~humble(X0) | creative(X0)) & ((humble(X0) & ~creative(X0)) | (brave(X0) & strong(X0)))) [flattening 50]
58. ((~tall(susan) & rich(susan)) | ! [X0] : (~wise(X0) | ~humble(X0))) & (? [X0] : (wise(X0) & humble(X0)) | (tall(susan) | ~rich(susan))) [nnf transformation 12]
59. ((~tall(susan) & rich(susan)) | ! [X0] : (~wise(X0) | ~humble(X0))) & (? [X0] : (wise(X0) & humble(X0)) | tall(susan) | ~rich(susan)) [flattening 58]
60. ((~tall(susan) & rich(susan)) | ! [X0] : (~wise(X0) | ~humble(X0))) & (? [X1] : (wise(X1) & humble(X1)) | tall(susan) | ~rich(susan)) [rectify 59]
61. ? [X1] : (wise(X1) & humble(X1)) => (wise(sK2) & humble(sK2)) [choice axiom]
62. ((~tall(susan) & rich(susan)) | ! [X0] : (~wise(X0) | ~humble(X0))) & ((wise(sK2) & humble(sK2)) | tall(susan) | ~rich(susan)) [skolemisation 60,61]
68. ! [X0] : ((~creative(X0) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | creative(X0))) [nnf transformation 15]
69. ! [X0] : ((~creative(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | creative(X0))) [flattening 68]
70. ! [X0] : (((wise(X0) | ~curious(X0)) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | (~wise(X0) & curious(X0)))) [nnf transformation 16]
71. ! [X0] : ((wise(X0) | ~curious(X0) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | (~wise(X0) & curious(X0)))) [flattening 70]
72. ? [X0] : ~strong(X0) => ~strong(sK5) [choice axiom]
73. ~strong(sK5) [skolemisation 17,72]
93. ~creative(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 43]
103. ~creative(X0) | strong(X0) [cnf transformation 51]
105. humble(X0) | strong(X0) [cnf transformation 51]
127. ~tall(susan) | ~wise(X0) | ~humble(X0) [cnf transformation 62]
135. creative(X0) | tall(X0) [cnf transformation 69]
136. wise(X0) | creative(X0) [cnf transformation 69]
138. calm(X0) | tall(X0) | curious(X0) [cnf transformation 71]
142. ~strong(sK5) [cnf transformation 73]
155. ~calm(susan) [cnf transformation 25]
237. 17 <=> ! [X0] : (~wise(X0) | ~humble(X0)) [avatar definition]
238. ~wise(X0) | ~humble(X0) <- (17) [avatar component clause 237]
240. 18 <=> tall(susan) [avatar definition]
243. 17 | ~18 [avatar split clause 127,240,237]
333. strong(X1) | tall(X1) [resolution 135,103]
353. ~curious(X0) | ~strong(X0) | tall(X0) [resolution 93,135]
355. ~curious(X0) | tall(X0) [subsumption resolution 353,333]
401. tall(susan) | curious(susan) [resolution 138,155]
703. tall(susan) [subsumption resolution 401,355]
704. 18 [avatar split clause 703,240]
721. ~humble(X0) | creative(X0) <- (17) [resolution 238,136]
737. creative(X1) | strong(X1) <- (17) [resolution 721,105]
744. strong(X1) <- (17) [subsumption resolution 737,103]
824. $false <- (17) [resolution 744,142]
829. ~17 [avatar contradiction clause 824]
832. $false [avatar sat refutation 243,704,829]
% SZS output end Proof for 543968753259149656052737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not patient and vice versa. Everyone who is not old or not creative is both generous and not strong. Everyone who is both wise and strong is not funny and vice versa. Everyone who is not happy or creative is both curious and quiet and vice versa. Everyone who is either not happy or not calm is brave. If lucy is either not funny or not curious then susan is both funny and strong. Everyone who is either not strong or not tall is both patient and not strong. Everyone who is both funny and calm is happy. Everyone who is not funny is not tall and vice versa. Everyone who is either quiet or not old is either funny or not calm. If someone is both not tall and not curious then someone is kind and vice versa. Everyone who is either generous or not happy is not curious and vice versa. If mary is either strong or not calm then someone is either brave or not kind and vice versa. If someone is not calm or not humble then someone is both creative and not humble and vice versa. John is not creative or old. Someone is not kind. Someone is not funny or humble. | Mary is not calm. | contradiction | (![X]:(~strong(X)<=>~patient(X)))&
(![X]:((~old(X)|~creative(X))=>(generous(X)&~strong(X))))&
(![X]:((wise(X)&strong(X))<=>~funny(X)))&
(![X]:((~happy(X)|creative(X))<=>(curious(X)&quiet(X))))&
(![X]:((~happy(X)<~>~calm(X))=>brave(X)))&
(((~funny(lucy)<~>~curious(lucy)))=>((funny(susan)&strong(susan))))&
(![X]:((~strong(X)<~>~tall(X))=>(patient(X)&~strong(X))))&
(![X]:((funny(X)&calm(X))=>happy(X)))&
(![X]:(~funny(X)<=>~tall(X)))&
(![X]:((quiet(X)<~>~old(X))=>(funny(X)<~>~calm(X))))&
((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:(kind(X))))&
(![X]:((generous(X)<~>~happy(X))<=>~curious(X)))&
(((strong(mary)<~>~calm(mary)))<=>(?[X]:((brave(X)<~>~kind(X)))))&
((?[X]:((~calm(X)|~humble(X))))<=>(?[X]:((creative(X)&~humble(X)))))&
((~creative(john)|old(john)))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)|humble(X)))) | ~calm(mary) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1750286068837110309301083
% SZS output start Proof for 1750286068837110309301083
1. ! [X0] : (~strong(X0) <=> ~patient(X0)) [input p0]
2. ! [X0] : ((~creative(X0) | ~old(X0)) => (~strong(X0) & generous(X0))) [input p1]
3. ! [X0] : ((strong(X0) & wise(X0)) <=> ~funny(X0)) [input p2]
4. ! [X0] : ((creative(X0) | ~happy(X0)) <=> (quiet(X0) & curious(X0))) [input p3]
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => (~strong(X0) & patient(X0))) [input p6]
9. ! [X0] : (~funny(X0) <=> ~tall(X0)) [input p8]
10. ! [X0] : ((quiet(X0) <~> ~old(X0)) => (funny(X0) <~> ~calm(X0))) [input p9]
18. ~calm(mary) [input hypothesis]
21. ! [X0] : ((~strong(X0) & generous(X0)) | (creative(X0) & old(X0))) [ennf transformation 2]
24. ! [X0] : ((~strong(X0) & patient(X0)) | (~strong(X0) <=> ~tall(X0))) [ennf transformation 7]
27. ! [X0] : ((funny(X0) <~> ~calm(X0)) | (quiet(X0) <=> ~old(X0))) [ennf transformation 10]
28. ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))) [nnf transformation 1]
29. ! [X0] : (((strong(X0) & wise(X0)) | funny(X0)) & (~funny(X0) | (~strong(X0) | ~wise(X0)))) [nnf transformation 3]
30. ! [X0] : (((strong(X0) & wise(X0)) | funny(X0)) & (~funny(X0) | ~strong(X0) | ~wise(X0))) [flattening 29]
31. ! [X0] : (((creative(X0) | ~happy(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (~creative(X0) & happy(X0)))) [nnf transformation 4]
32. ! [X0] : ((creative(X0) | ~happy(X0) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | (~creative(X0) & happy(X0)))) [flattening 31]
35. ! [X0] : ((~strong(X0) & patient(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) [nnf transformation 24]
36. ! [X0] : ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0))) [nnf transformation 9]
37. ! [X0] : (((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) [nnf transformation 27]
57. ~patient(X0) | strong(X0) [cnf transformation 28]
58. ~strong(X0) | patient(X0) [cnf transformation 28]
61. ~strong(X0) | old(X0) [cnf transformation 21]
62. ~strong(X0) | creative(X0) [cnf transformation 21]
65. funny(X0) | strong(X0) [cnf transformation 30]
69. ~creative(X0) | quiet(X0) [cnf transformation 32]
77. patient(X0) | ~tall(X0) | strong(X0) [cnf transformation 35]
80. ~strong(X0) | ~strong(X0) | tall(X0) [cnf transformation 35]
82. ~tall(X0) | funny(X0) [cnf transformation 36]
83. ~funny(X0) | tall(X0) [cnf transformation 36]
86. ~quiet(X0) | ~funny(X0) | ~old(X0) | calm(X0) [cnf transformation 37]
111. ~calm(mary) [cnf transformation 18]
112. ~strong(X0) | tall(X0) [duplicate literal removal 80]
133. ~tall(X0) | patient(X0) [subsumption resolution 77,58]
165. 12 <=> calm(mary) [avatar definition]
166. ~calm(mary) <- (~12) [avatar component clause 165]
208. 21 <=> ! [X3] : calm(X3) [avatar definition]
209. calm(X3) <- (21) [avatar component clause 208]
235. ~12 [avatar split clause 111,165]
238. $false <- (~12, 21) [subsumption resolution 166,209]
239. 12 | ~21 [avatar contradiction clause 238]
256. tall(X0) | strong(X0) [resolution 83,65]
258. tall(X0) [subsumption resolution 256,112]
262. funny(X0) [resolution 258,82]
274. patient(X0) [resolution 133,258]
363. strong(X0) [resolution 274,57]
398. creative(X1) [resolution 363,62]
399. old(X2) [resolution 363,61]
402. quiet(X0) [resolution 398,69]
427. ~funny(X0) | ~old(X0) | calm(X0) [resolution 402,86]
429. ~old(X0) | calm(X0) [subsumption resolution 427,262]
430. calm(X0) [subsumption resolution 429,399]
431. 21 [avatar split clause 430,208]
432. $false [avatar sat refutation 235,239,431]
% SZS output end Proof for 1750286068837110309301083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then fred is not generous or not rich and vice versa. If mary is generous then someone is both quiet and tall. Everyone who is calm or quiet is both not patient and creative and vice versa. Everyone who is not calm is not creative or not happy. Everyone who is not happy or not curious is both calm and not rich. Everyone who is both not curious and not old is either not calm or not funny and vice versa. Everyone who is either tall or not tall is either not brave or not quiet and vice versa. If someone is old or quiet then fred is rich or curious and vice versa. Everyone who is curious is either rich or humble and vice versa. Everyone who is both brave and tall is not tall or not curious. Everyone who is humble is either old or not patient and vice versa. Everyone who is not wise or not funny is either not humble or not brave and vice versa. If john is either not humble or not generous then alice is tall. If paul is both not generous and not funny then john is either creative or not brave. Someone is not wise or curious. Alice is creative. Paul is strong. Someone is not tall or kind. Someone is kind or tall. Someone is tall. | Alice is not funny. | contradiction | ((?[X]:(old(X)))<=>((~generous(fred)|~rich(fred))))&
((generous(mary))=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(![X]:(~calm(X)=>(~creative(X)|~happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(calm(X)&~rich(X))))&
(![X]:((~curious(X)&~old(X))<=>(~calm(X)<~>~funny(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(?[X]:((~wise(X)|curious(X))))&
(creative(alice))&
(strong(paul))&
(?[X]:((~tall(X)|kind(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:(tall(X))) | ~funny(alice) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3655139078010507206826375
% SZS output start Proof for 3655139078010507206826375
3. ! [X0] : ((quiet(X0) | calm(X0)) <=> (creative(X0) & ~patient(X0))) [input p2]
4. ! [X0] : (~calm(X0) => (~happy(X0) | ~creative(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | ~happy(X0)) => (~rich(X0) & calm(X0))) [input p4]
6. ! [X0] : ((~old(X0) & ~curious(X0)) <=> (~calm(X0) <~> ~funny(X0))) [input p5]
9. ! [X0] : (curious(X0) <=> (rich(X0) <~> humble(X0))) [input p8]
11. ! [X0] : (humble(X0) <=> (old(X0) <~> ~patient(X0))) [input p10]
16. creative(alice) [input p15]
21. ~funny(alice) [input hypothesis]
26. ! [X0] : ((~happy(X0) | ~creative(X0)) | calm(X0)) [ennf transformation 4]
27. ! [X0] : (~happy(X0) | ~creative(X0) | calm(X0)) [flattening 26]
28. ! [X0] : ((~rich(X0) & calm(X0)) | (curious(X0) & happy(X0))) [ennf transformation 5]
41. ! [X0] : (((quiet(X0) | calm(X0)) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 3]
42. ! [X0] : ((quiet(X0) | calm(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 41]
43. ! [X0] : (((~old(X0) & ~curious(X0)) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) & (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | (old(X0) | curious(X0)))) [nnf transformation 6]
44. ! [X0] : (((~old(X0) & ~curious(X0)) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) & (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | old(X0) | curious(X0))) [flattening 43]
51. ! [X0] : ((curious(X0) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0)))) & (((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | ~curious(X0))) [nnf transformation 9]
52. ! [X0] : ((humble(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ~humble(X0))) [nnf transformation 11]
66. ~patient(X0) | ~calm(X0) [cnf transformation 42]
71. ~happy(X0) | ~creative(X0) | calm(X0) [cnf transformation 27]
72. happy(X0) | calm(X0) [cnf transformation 28]
75. ~rich(X0) | curious(X0) [cnf transformation 28]
79. ~curious(X0) | ~calm(X0) | funny(X0) [cnf transformation 44]
81. ~calm(X0) | ~old(X0) | funny(X0) [cnf transformation 44]
97. curious(X0) | rich(X0) | ~humble(X0) [cnf transformation 51]
102. humble(X0) | old(X0) | patient(X0) [cnf transformation 52]
114. creative(alice) [cnf transformation 16]
116. ~funny(alice) [cnf transformation 21]
179. ~humble(X0) | curious(X0) [subsumption resolution 97,75]
228. ~creative(X0) | calm(X0) | calm(X0) [resolution 71,72]
229. ~creative(X0) | calm(X0) [duplicate literal removal 228]
230. calm(alice) [resolution 229,114]
279. curious(X3) | patient(X3) | old(X3) [resolution 102,179]
469. patient(X1) | old(X1) | ~calm(X1) | funny(X1) [resolution 279,79]
472. patient(X1) | ~calm(X1) | funny(X1) [subsumption resolution 469,81]
473. ~calm(X1) | funny(X1) [subsumption resolution 472,66]
604. funny(alice) [resolution 473,230]
606. $false [subsumption resolution 604,116]
% SZS output end Proof for 3655139078010507206826375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not creative is kind and vice versa.
If mary is both curious and not kind then fred is not patient and vice versa.
Everyone who is not tall or not humble is both not generous and creative.
If someone is not funny then alice is either not brave or kind and vice versa.
Everyone who is not patient or not old is not kind or strong and vice versa.
Everyone who is either brave or patient is both kind and patient.
If fred is either generous or humble then someone is creative or not old and vice versa.
Everyone who is either not patient or tall is quiet or brave and vice versa.
If john is either funny or not happy then someone is kind and vice versa.
If someone is either not kind or tall then alice is not wise or wise.
Everyone who is both funny and rich is either not quiet or not patient and vice versa.
Everyone who is tall or not generous is not calm or creative.
Everyone who is not strong is not quiet and vice versa.
If someone is either generous or not humble then susan is not old and vice versa.
Everyone who is either happy or funny is curious or happy and vice versa.
Everyone who is either not calm or patient is generous.
Lucy is old.
Lucy is both creative and not generous.
Someone is both not rich and not curious.
Fred is both not curious and patient.
Someone is funny. | Mary is rich. | neutral | (![X]:((~humble(X)&~creative(X))<=>kind(X)))&
(((curious(mary)&~kind(mary)))<=>(~patient(fred)))&
(![X]:((~tall(X)|~humble(X))=>(~generous(X)&creative(X))))&
((?[X]:(~funny(X)))<=>((~brave(alice)<~>kind(alice))))&
(![X]:((~patient(X)|~old(X))<=>(~kind(X)|strong(X))))&
(![X]:((brave(X)<~>patient(X))=>(kind(X)&patient(X))))&
(((generous(fred)<~>humble(fred)))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~patient(X)<~>tall(X))<=>(quiet(X)|brave(X))))&
(((funny(john)<~>~happy(john)))<=>(?[X]:(kind(X))))&
((?[X]:((~kind(X)<~>tall(X))))=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(![X]:((~calm(X)<~>patient(X))=>generous(X)))&
(old(lucy))&
((creative(lucy)&~generous(lucy)))&
(?[X]:((~rich(X)&~curious(X))))&
((~curious(fred)&patient(fred)))&
(?[X]:(funny(X))) | rich(mary) | [] | null | 0 |
Everyone who is not old is not generous or not strong.
Everyone who is wise or generous is both not happy and kind and vice versa.
Everyone who is not brave or kind is funny or not humble and vice versa.
If fred is both not generous and not wise then paul is both rich and curious and vice versa.
If someone is humble then someone is either old or calm and vice versa.
Everyone who is not generous or not patient is either not rich or not tall.
If someone is both not happy and quiet then mary is wise and vice versa.
Everyone who is patient or wise is strong and vice versa.
Everyone who is both humble and not tall is not tall and vice versa.
If someone is funny or quiet then john is both kind and not wise.
If paul is both not calm and not tall then lucy is humble or not tall.
Everyone who is either brave or kind is either patient or not patient and vice versa.
If paul is both rich and not patient then alice is either old or rich and vice versa.
Everyone who is funny is both old and calm.
Everyone who is not strong is either not patient or brave and vice versa.
Everyone who is either patient or not rich is not humble.
Mary is not patient.
Fred is either not funny or not humble.
Someone is creative.
Lucy is either curious or generous.
John is not funny or quiet.
Paul is both not brave and not creative.
Someone is not strong.
Paul is rich. | Alice is not quiet. | neutral | (![X]:(~old(X)=>(~generous(X)|~strong(X))))&
(![X]:((wise(X)|generous(X))<=>(~happy(X)&kind(X))))&
(![X]:((~brave(X)|kind(X))<=>(funny(X)|~humble(X))))&
(((~generous(fred)&~wise(fred)))<=>((rich(paul)&curious(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((old(X)<~>calm(X)))))&
(![X]:((~generous(X)|~patient(X))=>(~rich(X)<~>~tall(X))))&
((?[X]:((~happy(X)&quiet(X))))<=>(wise(mary)))&
(![X]:((patient(X)|wise(X))<=>strong(X)))&
(![X]:((humble(X)&~tall(X))<=>~tall(X)))&
((?[X]:((funny(X)|quiet(X))))=>((kind(john)&~wise(john))))&
(((~calm(paul)&~tall(paul)))=>((humble(lucy)|~tall(lucy))))&
(![X]:((brave(X)<~>kind(X))<=>(patient(X)<~>~patient(X))))&
(((rich(paul)&~patient(paul)))<=>((old(alice)<~>rich(alice))))&
(![X]:(funny(X)=>(old(X)&calm(X))))&
(![X]:(~strong(X)<=>(~patient(X)<~>brave(X))))&
(![X]:((patient(X)<~>~rich(X))=>~humble(X)))&
(~patient(mary))&
((~funny(fred)<~>~humble(fred)))&
(?[X]:(creative(X)))&
((curious(lucy)<~>generous(lucy)))&
((~funny(john)|quiet(john)))&
((~brave(paul)&~creative(paul)))&
(?[X]:(~strong(X)))&
(rich(paul)) | ~quiet(alice) | [] | null | 0 |
Everyone who is not creative is either not tall or not humble and vice versa.
If someone is humble or not humble then someone is both humble and not funny and vice versa.
If mary is not brave or not strong then mary is both tall and not patient.
Everyone who is not rich is both not funny and funny and vice versa.
Everyone who is happy is either calm or kind.
If susan is not kind then alice is both patient and not humble and vice versa.
Everyone who is not creative is generous or creative and vice versa.
If lucy is either not creative or humble then mary is either not brave or not humble.
If john is not curious then someone is calm or not humble.
Everyone who is either kind or not generous is rich.
Everyone who is either not patient or not old is not generous and vice versa.
If someone is patient or not wise then someone is both not curious and not funny.
Everyone who is both curious and not calm is not patient and vice versa.
Everyone who is both quiet and calm is not humble and vice versa.
John is not brave.
Paul is both not happy and brave.
Mary is quiet.
John is both strong and not humble. | Alice is creative. | contradiction | (![X]:(~creative(X)<=>(~tall(X)<~>~humble(X))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:((humble(X)&~funny(X)))))&
(((~brave(mary)|~strong(mary)))=>((tall(mary)&~patient(mary))))&
(![X]:(~rich(X)<=>(~funny(X)&funny(X))))&
(![X]:(happy(X)=>(calm(X)<~>kind(X))))&
((~kind(susan))<=>((patient(alice)&~humble(alice))))&
(![X]:(~creative(X)<=>(generous(X)|creative(X))))&
(((~creative(lucy)<~>humble(lucy)))=>((~brave(mary)<~>~humble(mary))))&
((~curious(john))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((kind(X)<~>~generous(X))=>rich(X)))&
(![X]:((~patient(X)<~>~old(X))<=>~generous(X)))&
((?[X]:((patient(X)|~wise(X))))=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((curious(X)&~calm(X))<=>~patient(X)))&
(![X]:((quiet(X)&calm(X))<=>~humble(X)))&
(~brave(john))&
((~happy(paul)&brave(paul)))&
(quiet(mary))&
((strong(john)&~humble(john))) | creative(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8056593388588733389835663
% SZS output start Proof for 8056593388588733389835663
7. ! [X0] : (~creative(X0) <=> (creative(X0) | generous(X0))) [input p6]
19. creative(alice) [input hypothesis]
43. ! [X0] : ((~creative(X0) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | creative(X0))) [nnf transformation 7]
44. ! [X0] : ((~creative(X0) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | creative(X0))) [flattening 43]
74. ~creative(X0) | ~creative(X0) [cnf transformation 44]
98. creative(alice) [cnf transformation 19]
100. ~creative(X0) [duplicate literal removal 74]
190. $false [subsumption resolution 98,100]
% SZS output end Proof for 8056593388588733389835663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not curious is calm and vice versa. Everyone who is not tall is either not strong or patient. Everyone who is kind or not funny is both not kind and quiet and vice versa. Everyone who is either not rich or not wise is both generous and creative and vice versa. Everyone who is not wise is both not curious and not humble and vice versa. Everyone who is both brave and not brave is not old or kind and vice versa. Everyone who is not old is happy or calm and vice versa. If someone is either not patient or not wise then susan is not brave or not creative and vice versa. If someone is either not rich or funny then susan is brave and vice versa. Everyone who is calm or not rich is either generous or not humble and vice versa. If someone is kind or not strong then someone is either not kind or not happy and vice versa. Everyone who is both not brave and not tall is not creative and vice versa. If fred is brave then susan is funny. Everyone who is not tall is both not wise and not curious and vice versa. If john is not quiet or not curious then someone is not tall. Alice is either not quiet or strong. Susan is tall. Fred is either funny or not rich. Someone is tall. Someone is not creative or quiet. Someone is not quiet or strong. Someone is strong. | Fred is not brave. | neutral | (![X]:((happy(X)|~curious(X))<=>calm(X)))&
(![X]:(~tall(X)=>(~strong(X)<~>patient(X))))&
(![X]:((kind(X)|~funny(X))<=>(~kind(X)&quiet(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(generous(X)&creative(X))))&
(![X]:(~wise(X)<=>(~curious(X)&~humble(X))))&
(![X]:((brave(X)&~brave(X))<=>(~old(X)|kind(X))))&
(![X]:(~old(X)<=>(happy(X)|calm(X))))&
((?[X]:((~patient(X)<~>~wise(X))))<=>((~brave(susan)|~creative(susan))))&
((?[X]:((~rich(X)<~>funny(X))))<=>(brave(susan)))&
(![X]:((calm(X)|~rich(X))<=>(generous(X)<~>~humble(X))))&
((?[X]:((kind(X)|~strong(X))))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:((~brave(X)&~tall(X))<=>~creative(X)))&
((brave(fred))=>(funny(susan)))&
(![X]:(~tall(X)<=>(~wise(X)&~curious(X))))&
(((~quiet(john)|~curious(john)))=>(?[X]:(~tall(X))))&
((~quiet(alice)<~>strong(alice)))&
(tall(susan))&
((funny(fred)<~>~rich(fred)))&
(?[X]:(tall(X)))&
(?[X]:((~creative(X)|quiet(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:(strong(X))) | ~brave(fred) | [] | null | 0 |
Everyone who is both old and not patient is either humble or tall and vice versa. Everyone who is not generous is happy or not kind. Everyone who is either strong or tall is not calm or calm. If lucy is rich then alice is both not humble and curious and vice versa. Everyone who is either not creative or not curious is kind. Everyone who is patient or funny is either brave or not humble and vice versa. Everyone who is not humble or not curious is not tall. Everyone who is not old is both happy and not strong and vice versa. Everyone who is brave or not humble is kind. Everyone who is either not tall or quiet is strong. If someone is humble then lucy is both not funny and not calm and vice versa. Everyone who is either not funny or curious is patient or not wise. If someone is not generous or not tall then susan is either not old or patient and vice versa. If alice is either quiet or calm then someone is both generous and rich and vice versa. If someone is quiet then someone is not brave or not tall and vice versa. Everyone who is not calm or generous is curious. Paul is either kind or not strong. Someone is not patient or happy. Susan is not quiet. Someone is both happy and old. John is either funny or not funny. Fred is creative or tall. Someone is both not kind and quiet. John is wise. | Lucy is curious. | entailment | (![X]:((old(X)&~patient(X))<=>(humble(X)<~>tall(X))))&
(![X]:(~generous(X)=>(happy(X)|~kind(X))))&
(![X]:((strong(X)<~>tall(X))=>(~calm(X)|calm(X))))&
((rich(lucy))<=>((~humble(alice)&curious(alice))))&
(![X]:((~creative(X)<~>~curious(X))=>kind(X)))&
(![X]:((patient(X)|funny(X))<=>(brave(X)<~>~humble(X))))&
(![X]:((~humble(X)|~curious(X))=>~tall(X)))&
(![X]:(~old(X)<=>(happy(X)&~strong(X))))&
(![X]:((brave(X)|~humble(X))=>kind(X)))&
(![X]:((~tall(X)<~>quiet(X))=>strong(X)))&
((?[X]:(humble(X)))<=>((~funny(lucy)&~calm(lucy))))&
(![X]:((~funny(X)<~>curious(X))=>(patient(X)|~wise(X))))&
((?[X]:((~generous(X)|~tall(X))))<=>((~old(susan)<~>patient(susan))))&
(((quiet(alice)<~>calm(alice)))<=>(?[X]:((generous(X)&rich(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~calm(X)|generous(X))=>curious(X)))&
((kind(paul)<~>~strong(paul)))&
(?[X]:((~patient(X)|happy(X))))&
(~quiet(susan))&
(?[X]:((happy(X)&old(X))))&
((funny(john)<~>~funny(john)))&
((creative(fred)|tall(fred)))&
(?[X]:((~kind(X)&quiet(X))))&
(wise(john)) | curious(lucy) | [
"p8",
"p10",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3560524843106592678118460
% SZS output start Proof for 3560524843106592678118460
9. ! [X0] : ((~humble(X0) | brave(X0)) => kind(X0)) [input p8]
11. ? [X0] : humble(X0) <=> (~calm(lucy) & ~funny(lucy)) [input p10]
16. ! [X0] : ((generous(X0) | ~calm(X0)) => curious(X0)) [input p15]
23. ? [X0] : (quiet(X0) & ~kind(X0)) [input p22]
25. ~curious(lucy) [input hypothesis]
33. ! [X0] : (kind(X0) | (humble(X0) & ~brave(X0))) [ennf transformation 9]
37. ! [X0] : (curious(X0) | (~generous(X0) & calm(X0))) [ennf transformation 16]
49. (? [X0] : humble(X0) | (calm(lucy) | funny(lucy))) & ((~calm(lucy) & ~funny(lucy)) | ! [X0] : ~humble(X0)) [nnf transformation 11]
50. (? [X0] : humble(X0) | calm(lucy) | funny(lucy)) & ((~calm(lucy) & ~funny(lucy)) | ! [X0] : ~humble(X0)) [flattening 49]
51. (? [X0] : humble(X0) | calm(lucy) | funny(lucy)) & ((~calm(lucy) & ~funny(lucy)) | ! [X1] : ~humble(X1)) [rectify 50]
52. ? [X0] : humble(X0) => humble(sK0) [choice axiom]
53. (humble(sK0) | calm(lucy) | funny(lucy)) & ((~calm(lucy) & ~funny(lucy)) | ! [X1] : ~humble(X1)) [skolemisation 51,52]
74. ? [X0] : (quiet(X0) & ~kind(X0)) => (quiet(sK7) & ~kind(sK7)) [choice axiom]
75. quiet(sK7) & ~kind(sK7) [skolemisation 23,74]
102. kind(X0) | humble(X0) [cnf transformation 33]
106. ~calm(lucy) | ~humble(X1) [cnf transformation 53]
125. curious(X0) | calm(X0) [cnf transformation 37]
136. ~kind(sK7) [cnf transformation 75]
139. ~curious(lucy) [cnf transformation 25]
160. 5 <=> calm(lucy) [avatar definition]
169. 7 <=> ! [X1] : ~humble(X1) [avatar definition]
170. ~humble(X1) <- (7) [avatar component clause 169]
171. 7 | ~5 [avatar split clause 106,160,169]
275. humble(sK7) [resolution 102,136]
277. calm(lucy) [resolution 125,139]
283. 5 [avatar split clause 277,160]
287. $false <- (7) [resolution 275,170]
288. ~7 [avatar contradiction clause 287]
289. $false [avatar sat refutation 171,283,288]
% SZS output end Proof for 3560524843106592678118460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is patient and vice versa. If someone is not creative or generous then someone is not old. Everyone who is either not kind or not generous is not humble. If john is patient or rich then mary is either not old or not generous. Everyone who is not strong or tall is creative or not rich. Everyone who is either not brave or not old is brave or calm. Everyone who is both not generous and not funny is not generous. Everyone who is not happy or not generous is not kind or creative and vice versa. Everyone who is not curious is not quiet. Everyone who is both calm and not kind is humble or not strong and vice versa. Everyone who is both not funny and not brave is either not calm or not patient and vice versa. If someone is not humble then someone is both humble and not tall and vice versa. Everyone who is either generous or not patient is not creative and vice versa. Everyone who is not old or not humble is not generous or humble. Everyone who is either wise or not strong is both not curious and old. If someone is tall then someone is wise or brave. Someone is creative or curious. Paul is both not calm and not kind. Someone is both not calm and curious. Susan is both not strong and old. Fred is not happy or humble. Someone is either not calm or rich. Someone is brave or old. Someone is both happy and not humble. | Paul is not wise. | entailment | (![X]:(~humble(X)<=>patient(X)))&
((?[X]:((~creative(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((~kind(X)<~>~generous(X))=>~humble(X)))&
(((patient(john)|rich(john)))=>((~old(mary)<~>~generous(mary))))&
(![X]:((~strong(X)|tall(X))=>(creative(X)|~rich(X))))&
(![X]:((~brave(X)<~>~old(X))=>(brave(X)|calm(X))))&
(![X]:((~generous(X)&~funny(X))=>~generous(X)))&
(![X]:((~happy(X)|~generous(X))<=>(~kind(X)|creative(X))))&
(![X]:(~curious(X)=>~quiet(X)))&
(![X]:((calm(X)&~kind(X))<=>(humble(X)|~strong(X))))&
(![X]:((~funny(X)&~brave(X))<=>(~calm(X)<~>~patient(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)&~tall(X)))))&
(![X]:((generous(X)<~>~patient(X))<=>~creative(X)))&
(![X]:((~old(X)|~humble(X))=>(~generous(X)|humble(X))))&
(![X]:((wise(X)<~>~strong(X))=>(~curious(X)&old(X))))&
((?[X]:(tall(X)))=>(?[X]:((wise(X)|brave(X)))))&
(?[X]:((creative(X)|curious(X))))&
((~calm(paul)&~kind(paul)))&
(?[X]:((~calm(X)&curious(X))))&
((~strong(susan)&old(susan)))&
((~happy(fred)|humble(fred)))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:((brave(X)|old(X))))&
(?[X]:((happy(X)&~humble(X)))) | ~wise(paul) | [
"p0",
"p5",
"p9",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6665476298191032706392776
% SZS output start Proof for 6665476298191032706392776
1. ! [X0] : (~humble(X0) <=> patient(X0)) [input p0]
6. ! [X0] : ((~brave(X0) <~> ~old(X0)) => (calm(X0) | brave(X0))) [input p5]
10. ! [X0] : ((~kind(X0) & calm(X0)) <=> (~strong(X0) | humble(X0))) [input p9]
11. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p10]
15. ! [X0] : ((wise(X0) <~> ~strong(X0)) => (old(X0) & ~curious(X0))) [input p14]
18. ~kind(paul) & ~calm(paul) [input p17]
25. wise(paul) [input hypothesis]
35. ! [X0] : ((calm(X0) | brave(X0)) | (~brave(X0) <=> ~old(X0))) [ennf transformation 6]
36. ! [X0] : (calm(X0) | brave(X0) | (~brave(X0) <=> ~old(X0))) [flattening 35]
41. ! [X0] : ((old(X0) & ~curious(X0)) | (wise(X0) <=> ~strong(X0))) [ennf transformation 15]
43. ! [X0] : ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0))) [nnf transformation 1]
49. ! [X0] : (calm(X0) | brave(X0) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) [nnf transformation 36]
52. ! [X0] : (((~kind(X0) & calm(X0)) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | (kind(X0) | ~calm(X0)))) [nnf transformation 10]
53. ! [X0] : (((~kind(X0) & calm(X0)) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | kind(X0) | ~calm(X0))) [flattening 52]
54. ! [X0] : (((~brave(X0) & ~funny(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (brave(X0) | funny(X0)))) [nnf transformation 11]
55. ! [X0] : (((~brave(X0) & ~funny(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | brave(X0) | funny(X0))) [flattening 54]
62. ! [X0] : ((old(X0) & ~curious(X0)) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) [nnf transformation 41]
77. patient(X0) | humble(X0) [cnf transformation 43]
89. calm(X0) | brave(X0) | ~old(X0) | brave(X0) [cnf transformation 49]
97. ~humble(X0) | calm(X0) [cnf transformation 53]
98. calm(X0) | strong(X0) [cnf transformation 53]
105. ~brave(X0) | ~patient(X0) | calm(X0) [cnf transformation 55]
118. ~wise(X0) | ~strong(X0) | old(X0) [cnf transformation 62]
122. ~calm(paul) [cnf transformation 18]
134. wise(paul) [cnf transformation 25]
136. ~old(X0) | brave(X0) | calm(X0) [duplicate literal removal 89]
248. strong(paul) [resolution 98,122]
321. ~strong(paul) | old(paul) [resolution 118,134]
322. old(paul) [subsumption resolution 321,248]
327. brave(paul) | calm(paul) [resolution 136,322]
337. brave(paul) [subsumption resolution 327,122]
385. ~patient(paul) | calm(paul) [resolution 337,105]
386. ~patient(paul) [subsumption resolution 385,122]
409. humble(paul) [resolution 386,77]
420. calm(paul) [resolution 409,97]
421. $false [subsumption resolution 420,122]
% SZS output end Proof for 6665476298191032706392776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or calm then lucy is not quiet. Everyone who is both quiet and not happy is not happy and vice versa. Everyone who is creative is not wise or tall and vice versa. If john is not patient then susan is either not curious or creative and vice versa. If someone is both not funny and not generous then paul is strong or brave and vice versa. If someone is humble then someone is both kind and not funny and vice versa. Everyone who is not happy or strong is either not strong or not patient. Everyone who is not funny is either not patient or strong. Everyone who is not humble is calm or wise. Everyone who is brave is not creative. Everyone who is not happy is not strong or not calm and vice versa. Everyone who is both brave and not patient is wise or brave. If someone is not humble then someone is rich or generous. Everyone who is generous is not quiet. If alice is tall then fred is not quiet and vice versa. Someone is both not happy and tall. Fred is quiet. Someone is rich or not old. Paul is wise. Someone is either not funny or generous. Paul is creative. Fred is not kind. Alice is brave or not funny. | Paul is generous. | contradiction | ((?[X]:((~calm(X)|calm(X))))=>(~quiet(lucy)))&
(![X]:((quiet(X)&~happy(X))<=>~happy(X)))&
(![X]:(creative(X)<=>(~wise(X)|tall(X))))&
((~patient(john))<=>((~curious(susan)<~>creative(susan))))&
((?[X]:((~funny(X)&~generous(X))))<=>((strong(paul)|brave(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((~happy(X)|strong(X))=>(~strong(X)<~>~patient(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>strong(X))))&
(![X]:(~humble(X)=>(calm(X)|wise(X))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~calm(X))))&
(![X]:((brave(X)&~patient(X))=>(wise(X)|brave(X))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)|generous(X)))))&
(![X]:(generous(X)=>~quiet(X)))&
((tall(alice))<=>(~quiet(fred)))&
(?[X]:((~happy(X)&tall(X))))&
(quiet(fred))&
(?[X]:((rich(X)|~old(X))))&
(wise(paul))&
(?[X]:((~funny(X)<~>generous(X))))&
(creative(paul))&
(~kind(fred))&
((brave(alice)|~funny(alice))) | generous(paul) | [
"p1",
"p4",
"p6",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8477570819431685037908684
% SZS output start Proof for 8477570819431685037908684
2. ! [X0] : ((~happy(X0) & quiet(X0)) <=> ~happy(X0)) [input p1]
5. ? [X0] : (~generous(X0) & ~funny(X0)) <=> (brave(paul) | strong(paul)) [input p4]
7. ! [X0] : ((strong(X0) | ~happy(X0)) => (~strong(X0) <~> ~patient(X0))) [input p6]
8. ! [X0] : (~funny(X0) => (~patient(X0) <~> strong(X0))) [input p7]
11. ! [X0] : (~happy(X0) <=> (~calm(X0) | ~strong(X0))) [input p10]
14. ! [X0] : (generous(X0) => ~quiet(X0)) [input p13]
24. generous(paul) [input hypothesis]
30. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | (~strong(X0) & happy(X0))) [ennf transformation 7]
31. ! [X0] : ((~patient(X0) <~> strong(X0)) | funny(X0)) [ennf transformation 8]
37. ! [X0] : (~quiet(X0) | ~generous(X0)) [ennf transformation 14]
38. ! [X0] : (((~happy(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | (happy(X0) | ~quiet(X0)))) [nnf transformation 2]
39. ! [X0] : (((~happy(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | happy(X0) | ~quiet(X0))) [flattening 38]
43. (? [X0] : (~generous(X0) & ~funny(X0)) | (~brave(paul) & ~strong(paul))) & ((brave(paul) | strong(paul)) | ! [X0] : (generous(X0) | funny(X0))) [nnf transformation 5]
44. (? [X0] : (~generous(X0) & ~funny(X0)) | (~brave(paul) & ~strong(paul))) & (brave(paul) | strong(paul) | ! [X0] : (generous(X0) | funny(X0))) [flattening 43]
45. (? [X0] : (~generous(X0) & ~funny(X0)) | (~brave(paul) & ~strong(paul))) & (brave(paul) | strong(paul) | ! [X1] : (generous(X1) | funny(X1))) [rectify 44]
46. ? [X0] : (~generous(X0) & ~funny(X0)) => (~generous(sK0) & ~funny(sK0)) [choice axiom]
47. ((~generous(sK0) & ~funny(sK0)) | (~brave(paul) & ~strong(paul))) & (brave(paul) | strong(paul) | ! [X1] : (generous(X1) | funny(X1))) [skolemisation 45,46]
53. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~strong(X0) & happy(X0))) [nnf transformation 30]
54. ! [X0] : (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | funny(X0)) [nnf transformation 31]
55. ! [X0] : ((~happy(X0) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | happy(X0))) [nnf transformation 11]
56. ! [X0] : ((~happy(X0) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | happy(X0))) [flattening 55]
66. happy(X0) | quiet(X0) [cnf transformation 39]
76. ~funny(sK0) | ~strong(paul) [cnf transformation 47]
84. ~patient(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
85. strong(X0) | patient(X0) | happy(X0) [cnf transformation 53]
87. strong(X0) | ~patient(X0) | funny(X0) [cnf transformation 54]
88. ~strong(X0) | patient(X0) | funny(X0) [cnf transformation 54]
92. ~happy(X0) | strong(X0) [cnf transformation 56]
95. ~generous(X0) | ~quiet(X0) [cnf transformation 37]
107. generous(paul) [cnf transformation 24]
108. ~strong(X0) | ~patient(X0) [duplicate literal removal 84]
147. 9 <=> strong(paul) [avatar definition]
149. ~strong(paul) <- (~9) [avatar component clause 147]
152. 10 <=> funny(sK0) [avatar definition]
154. ~funny(sK0) <- (~10) [avatar component clause 152]
156. ~9 | ~10 [avatar split clause 76,152,147]
182. ~strong(X0) | funny(X0) [subsumption resolution 88,108]
183. ~patient(X0) | funny(X0) [subsumption resolution 87,108]
219. strong(X0) | quiet(X0) [resolution 92,66]
221. ~quiet(paul) [resolution 95,107]
228. patient(X0) | happy(X0) | funny(X0) [resolution 85,182]
230. funny(X0) | happy(X0) [subsumption resolution 228,183]
243. happy(sK0) <- (~10) [resolution 230,154]
259. strong(sK0) <- (~10) [resolution 243,92]
277. funny(sK0) <- (~10) [resolution 259,182]
279. $false <- (~10) [subsumption resolution 277,154]
280. 10 [avatar contradiction clause 279]
290. quiet(paul) <- (~9) [resolution 149,219]
292. $false <- (~9) [subsumption resolution 290,221]
293. 9 [avatar contradiction clause 292]
294. $false [avatar sat refutation 156,280,293]
% SZS output end Proof for 8477570819431685037908684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not funny then someone is both not curious and not calm.
If someone is either not calm or not curious then someone is both not strong and patient.
If someone is either happy or not humble then someone is either quiet or wise.
If someone is both not happy and not patient then alice is creative or not tall.
If someone is either humble or calm then lucy is calm or patient.
If someone is both not wise and strong then someone is both curious and humble and vice versa.
If someone is either kind or not strong then fred is both generous and not quiet and vice versa.
If mary is either calm or rich then someone is happy or brave.
Everyone who is old is brave or not generous.
Everyone who is either quiet or not creative is not humble or not curious and vice versa.
If someone is not tall then someone is funny or not rich and vice versa.
If someone is generous then someone is either humble or calm.
If someone is both not tall and old then alice is not curious and vice versa.
If fred is both not curious and happy then someone is either not old or not tall.
If someone is humble or not happy then john is curious and vice versa.
If alice is both not humble and quiet then mary is happy and vice versa.
John is not patient.
Someone is not old or not kind.
Paul is tall or not quiet.
Someone is old or happy.
Someone is not funny or funny.
Someone is both not curious and not happy.
John is both happy and not brave.
Alice is not patient or not quiet. | Alice is not quiet. | neutral | ((?[X]:((~strong(X)|~funny(X))))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((~strong(X)&patient(X)))))&
((?[X]:((happy(X)<~>~humble(X))))=>(?[X]:((quiet(X)<~>wise(X)))))&
((?[X]:((~happy(X)&~patient(X))))=>((creative(alice)|~tall(alice))))&
((?[X]:((humble(X)<~>calm(X))))=>((calm(lucy)|patient(lucy))))&
((?[X]:((~wise(X)&strong(X))))<=>(?[X]:((curious(X)&humble(X)))))&
((?[X]:((kind(X)<~>~strong(X))))<=>((generous(fred)&~quiet(fred))))&
(((calm(mary)<~>rich(mary)))=>(?[X]:((happy(X)|brave(X)))))&
(![X]:(old(X)=>(brave(X)|~generous(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~humble(X)|~curious(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((funny(X)|~rich(X)))))&
((?[X]:(generous(X)))=>(?[X]:((humble(X)<~>calm(X)))))&
((?[X]:((~tall(X)&old(X))))<=>(~curious(alice)))&
(((~curious(fred)&happy(fred)))=>(?[X]:((~old(X)<~>~tall(X)))))&
((?[X]:((humble(X)|~happy(X))))<=>(curious(john)))&
(((~humble(alice)&quiet(alice)))<=>(happy(mary)))&
(~patient(john))&
(?[X]:((~old(X)|~kind(X))))&
((tall(paul)|~quiet(paul)))&
(?[X]:((old(X)|happy(X))))&
(?[X]:((~funny(X)|funny(X))))&
(?[X]:((~curious(X)&~happy(X))))&
((happy(john)&~brave(john)))&
((~patient(alice)|~quiet(alice))) | ~quiet(alice) | [] | null | 0 |
Everyone who is both not patient and not quiet is not tall or not rich.
Everyone who is not calm or old is both brave and tall and vice versa.
Everyone who is kind is both not kind and humble.
Everyone who is happy or strong is kind.
Everyone who is happy or funny is both not tall and brave.
Everyone who is old is both not patient and patient and vice versa.
Everyone who is either patient or not funny is patient.
If john is not tall then someone is either not rich or not happy.
If paul is either not kind or not brave then someone is either not brave or funny.
If someone is not quiet then john is either not kind or not quiet and vice versa.
Everyone who is either generous or happy is happy or kind and vice versa.
If someone is humble or not tall then fred is both not kind and not wise and vice versa.
Everyone who is rich is either not generous or curious and vice versa.
Everyone who is humble or not rich is both rich and calm.
If john is either not wise or not tall then someone is both patient and old.
Everyone who is either happy or not humble is not happy or curious and vice versa.
Paul is not humble.
Someone is wise or not wise.
Someone is either old or not humble.
Paul is not humble or not creative.
Someone is either not happy or strong.
Someone is either not brave or patient.
Fred is both tall and not wise. | John is not rich. | contradiction | (![X]:((~patient(X)&~quiet(X))=>(~tall(X)|~rich(X))))&
(![X]:((~calm(X)|old(X))<=>(brave(X)&tall(X))))&
(![X]:(kind(X)=>(~kind(X)&humble(X))))&
(![X]:((happy(X)|strong(X))=>kind(X)))&
(![X]:((happy(X)|funny(X))=>(~tall(X)&brave(X))))&
(![X]:(old(X)<=>(~patient(X)&patient(X))))&
(![X]:((patient(X)<~>~funny(X))=>patient(X)))&
((~tall(john))=>(?[X]:((~rich(X)<~>~happy(X)))))&
(((~kind(paul)<~>~brave(paul)))=>(?[X]:((~brave(X)<~>funny(X)))))&
((?[X]:(~quiet(X)))<=>((~kind(john)<~>~quiet(john))))&
(![X]:((generous(X)<~>happy(X))<=>(happy(X)|kind(X))))&
((?[X]:((humble(X)|~tall(X))))<=>((~kind(fred)&~wise(fred))))&
(![X]:(rich(X)<=>(~generous(X)<~>curious(X))))&
(![X]:((humble(X)|~rich(X))=>(rich(X)&calm(X))))&
(((~wise(john)<~>~tall(john)))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((happy(X)<~>~humble(X))<=>(~happy(X)|curious(X))))&
(~humble(paul))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((old(X)<~>~humble(X))))&
((~humble(paul)|~creative(paul)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((~brave(X)<~>patient(X))))&
((tall(fred)&~wise(fred))) | ~rich(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2169447622602098995481513
% SZS output start Proof for 2169447622602098995481513
14. ! [X0] : ((~rich(X0) | humble(X0)) => (calm(X0) & rich(X0))) [input p13]
24. ~rich(john) [input hypothesis]
34. ! [X0] : ((calm(X0) & rich(X0)) | (rich(X0) & ~humble(X0))) [ennf transformation 14]
120. rich(X0) | rich(X0) [cnf transformation 34]
143. ~rich(john) [cnf transformation 24]
146. rich(X0) [duplicate literal removal 120]
248. $false [subsumption resolution 143,146]
% SZS output end Proof for 2169447622602098995481513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and wise is both not strong and not quiet.
Everyone who is not generous is either funny or happy.
If paul is kind or curious then susan is either happy or tall.
Everyone who is either wise or creative is strong or not curious and vice versa.
If someone is either happy or generous then someone is both funny and not patient and vice versa.
Everyone who is both not brave and wise is tall or not old and vice versa.
Everyone who is not patient or old is not rich or not calm and vice versa.
If paul is not strong or not wise then alice is not calm or not kind and vice versa.
Everyone who is not creative or not calm is either not curious or not rich and vice versa.
Everyone who is not wise or not rich is both not rich and not funny.
Everyone who is not kind or not calm is not kind.
Everyone who is curious is either rich or humble.
Everyone who is either generous or not patient is either not funny or rich and vice versa.
If someone is both not humble and not quiet then someone is quiet and vice versa.
Everyone who is both not generous and rich is calm.
Everyone who is not calm or rich is both not quiet and not strong.
Susan is not brave or funny.
Fred is not kind.
Someone is creative or not brave.
Someone is both creative and not old.
Fred is either not funny or not curious.
Someone is both funny and creative.
Alice is either tall or not wise. | Fred is not wise. | neutral | (![X]:((~quiet(X)&wise(X))=>(~strong(X)&~quiet(X))))&
(![X]:(~generous(X)=>(funny(X)<~>happy(X))))&
(((kind(paul)|curious(paul)))=>((happy(susan)<~>tall(susan))))&
(![X]:((wise(X)<~>creative(X))<=>(strong(X)|~curious(X))))&
((?[X]:((happy(X)<~>generous(X))))<=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:((~brave(X)&wise(X))<=>(tall(X)|~old(X))))&
(![X]:((~patient(X)|old(X))<=>(~rich(X)|~calm(X))))&
(((~strong(paul)|~wise(paul)))<=>((~calm(alice)|~kind(alice))))&
(![X]:((~creative(X)|~calm(X))<=>(~curious(X)<~>~rich(X))))&
(![X]:((~wise(X)|~rich(X))=>(~rich(X)&~funny(X))))&
(![X]:((~kind(X)|~calm(X))=>~kind(X)))&
(![X]:(curious(X)=>(rich(X)<~>humble(X))))&
(![X]:((generous(X)<~>~patient(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((~humble(X)&~quiet(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~generous(X)&rich(X))=>calm(X)))&
(![X]:((~calm(X)|rich(X))=>(~quiet(X)&~strong(X))))&
((~brave(susan)|funny(susan)))&
(~kind(fred))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((creative(X)&~old(X))))&
((~funny(fred)<~>~curious(fred)))&
(?[X]:((funny(X)&creative(X))))&
((tall(alice)<~>~wise(alice))) | ~wise(fred) | [] | null | 0 |
If paul is wise then someone is either not kind or not funny and vice versa.
Everyone who is either not calm or funny is not creative or not curious and vice versa.
Everyone who is not curious or patient is either not creative or not funny.
If someone is both generous and funny then lucy is not calm.
If alice is both patient and curious then mary is happy or strong.
Everyone who is rich is either patient or wise and vice versa.
Everyone who is either wise or creative is calm or not old and vice versa.
Everyone who is not tall or not calm is either calm or not kind and vice versa.
If mary is not strong or not patient then alice is both not calm and not happy.
Everyone who is not funny is both creative and tall and vice versa.
If lucy is both patient and not kind then someone is either funny or curious and vice versa.
If someone is not creative then someone is either not patient or not quiet and vice versa.
If alice is tall or kind then paul is tall and vice versa.
Everyone who is both not generous and funny is both brave and not old.
Everyone who is not calm is not wise.
Everyone who is not happy or not old is either not generous or not tall.
Paul is tall or curious.
Someone is either rich or strong.
Someone is wise or curious.
Someone is brave or not rich.
Someone is not wise or generous.
Someone is both not funny and old. | Lucy is generous. | neutral | ((wise(paul))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
(![X]:((~calm(X)<~>funny(X))<=>(~creative(X)|~curious(X))))&
(![X]:((~curious(X)|patient(X))=>(~creative(X)<~>~funny(X))))&
((?[X]:((generous(X)&funny(X))))=>(~calm(lucy)))&
(((patient(alice)&curious(alice)))=>((happy(mary)|strong(mary))))&
(![X]:(rich(X)<=>(patient(X)<~>wise(X))))&
(![X]:((wise(X)<~>creative(X))<=>(calm(X)|~old(X))))&
(![X]:((~tall(X)|~calm(X))<=>(calm(X)<~>~kind(X))))&
(((~strong(mary)|~patient(mary)))=>((~calm(alice)&~happy(alice))))&
(![X]:(~funny(X)<=>(creative(X)&tall(X))))&
(((patient(lucy)&~kind(lucy)))<=>(?[X]:((funny(X)<~>curious(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(((tall(alice)|kind(alice)))<=>(tall(paul)))&
(![X]:((~generous(X)&funny(X))=>(brave(X)&~old(X))))&
(![X]:(~calm(X)=>~wise(X)))&
(![X]:((~happy(X)|~old(X))=>(~generous(X)<~>~tall(X))))&
((tall(paul)|curious(paul)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((wise(X)|curious(X))))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:((~funny(X)&old(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is happy or not quiet is either not patient or not kind. If someone is either not rich or not creative then paul is rich. Everyone who is not kind or humble is rich or generous. If mary is not tall then someone is both not old and wise and vice versa. Everyone who is quiet is not wise or not patient. Everyone who is not brave is either happy or not kind. Everyone who is both rich and not kind is kind or brave. Everyone who is either tall or not rich is not patient and vice versa. Everyone who is both not quiet and not curious is both strong and not strong and vice versa. If fred is not strong then susan is creative or wise. If fred is either rich or not generous then john is not creative and vice versa. Everyone who is patient is curious or not curious and vice versa. If john is either funny or not happy then someone is old or rich. If paul is brave then someone is either not kind or not quiet. Everyone who is not calm or not tall is not tall or not funny. Everyone who is not rich or creative is not patient or happy. Mary is either not wise or not humble. Alice is both rich and not strong. Alice is rich or not quiet. Someone is either not generous or creative. Someone is humble or not kind. Paul is not creative. Someone is both not calm and not kind. | Paul is not brave. | contradiction | (![X]:((happy(X)|~quiet(X))=>(~patient(X)<~>~kind(X))))&
((?[X]:((~rich(X)<~>~creative(X))))=>(rich(paul)))&
(![X]:((~kind(X)|humble(X))=>(rich(X)|generous(X))))&
((~tall(mary))<=>(?[X]:((~old(X)&wise(X)))))&
(![X]:(quiet(X)=>(~wise(X)|~patient(X))))&
(![X]:(~brave(X)=>(happy(X)<~>~kind(X))))&
(![X]:((rich(X)&~kind(X))=>(kind(X)|brave(X))))&
(![X]:((tall(X)<~>~rich(X))<=>~patient(X)))&
(![X]:((~quiet(X)&~curious(X))<=>(strong(X)&~strong(X))))&
((~strong(fred))=>((creative(susan)|wise(susan))))&
(((rich(fred)<~>~generous(fred)))<=>(~creative(john)))&
(![X]:(patient(X)<=>(curious(X)|~curious(X))))&
(((funny(john)<~>~happy(john)))=>(?[X]:((old(X)|rich(X)))))&
((brave(paul))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((~calm(X)|~tall(X))=>(~tall(X)|~funny(X))))&
(![X]:((~rich(X)|creative(X))=>(~patient(X)|happy(X))))&
((~wise(mary)<~>~humble(mary)))&
((rich(alice)&~strong(alice)))&
((rich(alice)|~quiet(alice)))&
(?[X]:((~generous(X)<~>creative(X))))&
(?[X]:((humble(X)|~kind(X))))&
(~creative(paul))&
(?[X]:((~calm(X)&~kind(X)))) | ~brave(paul) | [
"p0",
"p1",
"p5",
"p6",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3156389113033243545683236
% SZS output start Proof for 3156389113033243545683236
1. ! [X0] : ((~quiet(X0) | happy(X0)) => (~patient(X0) <~> ~kind(X0))) [input p0]
2. ? [X0] : (~rich(X0) <~> ~creative(X0)) => rich(paul) [input p1]
6. ! [X0] : (~brave(X0) => (happy(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : ((~kind(X0) & rich(X0)) => (brave(X0) | kind(X0))) [input p6]
12. ! [X0] : (patient(X0) <=> (~curious(X0) | curious(X0))) [input p11]
16. ! [X0] : ((creative(X0) | ~rich(X0)) => (happy(X0) | ~patient(X0))) [input p15]
24. ~brave(paul) [input hypothesis]
25. ! [X0] : ((~patient(X0) <~> ~kind(X0)) | (quiet(X0) & ~happy(X0))) [ennf transformation 1]
26. rich(paul) | ! [X0] : (~rich(X0) <=> ~creative(X0)) [ennf transformation 2]
31. ! [X0] : ((happy(X0) <~> ~kind(X0)) | brave(X0)) [ennf transformation 6]
32. ! [X0] : ((brave(X0) | kind(X0)) | (kind(X0) | ~rich(X0))) [ennf transformation 7]
33. ! [X0] : (brave(X0) | kind(X0) | kind(X0) | ~rich(X0)) [flattening 32]
40. ! [X0] : ((happy(X0) | ~patient(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 16]
41. ! [X0] : (happy(X0) | ~patient(X0) | (~creative(X0) & rich(X0))) [flattening 40]
42. ! [X0] : (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | (quiet(X0) & ~happy(X0))) [nnf transformation 25]
43. rich(paul) | ! [X0] : ((~rich(X0) | creative(X0)) & (~creative(X0) | rich(X0))) [nnf transformation 26]
48. ! [X0] : (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | brave(X0)) [nnf transformation 31]
53. ! [X0] : ((patient(X0) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | ~patient(X0))) [nnf transformation 12]
54. ! [X0] : ((patient(X0) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ~patient(X0))) [flattening 53]
69. ~kind(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 42]
74. rich(paul) | ~rich(X0) | creative(X0) [cnf transformation 43]
81. ~kind(X0) | happy(X0) | brave(X0) [cnf transformation 48]
82. ~happy(X0) | kind(X0) | brave(X0) [cnf transformation 48]
83. brave(X0) | kind(X0) | kind(X0) | ~rich(X0) [cnf transformation 33]
98. patient(X0) | ~curious(X0) [cnf transformation 54]
99. curious(X0) | patient(X0) [cnf transformation 54]
106. happy(X0) | ~patient(X0) | rich(X0) [cnf transformation 41]
107. happy(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 41]
119. ~brave(paul) [cnf transformation 24]
120. ~rich(X0) | kind(X0) | brave(X0) [duplicate literal removal 83]
122. 1 <=> ! [X0] : (~rich(X0) | creative(X0)) [avatar definition]
123. ~rich(X0) | creative(X0) <- (1) [avatar component clause 122]
125. 2 <=> rich(paul) [avatar definition]
127. rich(paul) <- (2) [avatar component clause 125]
128. 1 | 2 [avatar split clause 74,125,122]
181. patient(X0) [subsumption resolution 98,99]
201. 18 <=> brave(paul) [avatar definition]
203. ~brave(paul) <- (~18) [avatar component clause 201]
214. ~creative(X0) | happy(X0) [subsumption resolution 107,181]
215. rich(X0) | happy(X0) [subsumption resolution 106,181]
245. ~18 [avatar split clause 119,201]
347. kind(X0) | brave(X0) | happy(X0) [resolution 120,215]
348. kind(paul) | brave(paul) <- (2) [resolution 120,127]
352. brave(X0) | happy(X0) [subsumption resolution 347,81]
353. kind(paul) <- (2, ~18) [subsumption resolution 348,203]
372. ~patient(paul) | ~happy(paul) <- (2, ~18) [resolution 353,69]
374. ~happy(paul) <- (2, ~18) [subsumption resolution 372,181]
379. happy(paul) <- (~18) [resolution 352,203]
380. $false <- (2, ~18) [subsumption resolution 379,374]
381. ~2 | 18 [avatar contradiction clause 380]
383. creative(X0) | happy(X0) <- (1) [resolution 123,215]
387. happy(X0) <- (1) [subsumption resolution 383,214]
397. brave(X0) | kind(X0) <- (1) [resolution 387,82]
434. kind(paul) <- (1, ~18) [resolution 397,203]
439. ~patient(paul) | ~happy(paul) <- (1, ~18) [resolution 434,69]
441. ~happy(paul) <- (1, ~18) [subsumption resolution 439,181]
442. $false <- (1, ~18) [subsumption resolution 441,379]
443. ~1 | 18 [avatar contradiction clause 442]
444. $false [avatar sat refutation 128,245,381,443]
% SZS output end Proof for 3156389113033243545683236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not brave is not patient and vice versa.
Everyone who is either not patient or happy is kind or patient.
If alice is strong or generous then fred is either calm or tall and vice versa.
If someone is quiet then someone is curious or creative and vice versa.
Everyone who is not strong or not happy is either generous or creative.
If lucy is not kind then mary is either humble or not quiet.
If alice is rich or not curious then john is both not tall and not generous and vice versa.
Everyone who is creative is either curious or not humble and vice versa.
If someone is either old or funny then mary is either not old or not generous.
If someone is calm then john is not generous.
Everyone who is either calm or not quiet is old and vice versa.
If someone is not quiet or kind then fred is curious or not funny and vice versa.
Everyone who is not rich or rich is not old and vice versa.
If someone is not funny then someone is not tall or wise.
If someone is both not wise and generous then someone is wise.
Everyone who is both kind and curious is both humble and wise and vice versa.
Someone is brave.
John is not generous or generous.
Susan is creative.
Someone is patient.
Paul is either not brave or creative.
Susan is funny or not strong.
Paul is curious or tall.
Someone is either not creative or funny. | Fred is not old. | entailment | (![X]:((~rich(X)|~brave(X))<=>~patient(X)))&
(![X]:((~patient(X)<~>happy(X))=>(kind(X)|patient(X))))&
(((strong(alice)|generous(alice)))<=>((calm(fred)<~>tall(fred))))&
((?[X]:(quiet(X)))<=>(?[X]:((curious(X)|creative(X)))))&
(![X]:((~strong(X)|~happy(X))=>(generous(X)<~>creative(X))))&
((~kind(lucy))=>((humble(mary)<~>~quiet(mary))))&
(((rich(alice)|~curious(alice)))<=>((~tall(john)&~generous(john))))&
(![X]:(creative(X)<=>(curious(X)<~>~humble(X))))&
((?[X]:((old(X)<~>funny(X))))=>((~old(mary)<~>~generous(mary))))&
((?[X]:(calm(X)))=>(~generous(john)))&
(![X]:((calm(X)<~>~quiet(X))<=>old(X)))&
((?[X]:((~quiet(X)|kind(X))))<=>((curious(fred)|~funny(fred))))&
(![X]:((~rich(X)|rich(X))<=>~old(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~tall(X)|wise(X)))))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:(wise(X))))&
(![X]:((kind(X)&curious(X))<=>(humble(X)&wise(X))))&
(?[X]:(brave(X)))&
((~generous(john)|generous(john)))&
(creative(susan))&
(?[X]:(patient(X)))&
((~brave(paul)<~>creative(paul)))&
((funny(susan)|~strong(susan)))&
((curious(paul)|tall(paul)))&
(?[X]:((~creative(X)<~>funny(X)))) | ~old(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5713585158100120026237587
% SZS output start Proof for 5713585158100120026237587
13. ! [X0] : ((rich(X0) | ~rich(X0)) <=> ~old(X0)) [input p12]
25. old(fred) [input hypothesis]
59. ! [X0] : (((rich(X0) | ~rich(X0)) | old(X0)) & (~old(X0) | (~rich(X0) & rich(X0)))) [nnf transformation 13]
60. ! [X0] : ((rich(X0) | ~rich(X0) | old(X0)) & (~old(X0) | (~rich(X0) & rich(X0)))) [flattening 59]
119. ~old(X0) | rich(X0) [cnf transformation 60]
120. ~old(X0) | ~rich(X0) [cnf transformation 60]
138. old(fred) [cnf transformation 25]
269. ~old(X0) [subsumption resolution 119,120]
328. $false [subsumption resolution 138,269]
% SZS output end Proof for 5713585158100120026237587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either not tall or brave.
Everyone who is either calm or not happy is not curious and vice versa.
Everyone who is not tall is either not creative or not brave and vice versa.
Everyone who is both not creative and tall is not tall.
Everyone who is both not quiet and not patient is either not funny or old and vice versa.
Everyone who is both not rich and curious is not calm or humble.
Everyone who is both strong and brave is both patient and not tall.
If fred is not tall then lucy is either not brave or humble.
If susan is either happy or not tall then someone is both not wise and not creative and vice versa.
If fred is both calm and not strong then someone is either strong or not patient.
If fred is funny or not strong then alice is both not old and not funny.
Everyone who is either not funny or creative is not creative and vice versa.
If someone is generous or old then paul is either not calm or calm and vice versa.
Everyone who is both brave and not tall is either not curious or funny and vice versa.
Everyone who is both not calm and not happy is quiet or not kind and vice versa.
Everyone who is not brave is either not happy or not tall and vice versa.
Someone is curious or not patient.
Someone is either generous or creative.
Susan is not brave or humble.
Paul is both not brave and not quiet.
John is both patient and not calm.
Susan is both not calm and strong.
Someone is both happy and not generous.
Someone is either not strong or not quiet. | Paul is kind. | entailment | (![X]:(~funny(X)=>(~tall(X)<~>brave(X))))&
(![X]:((calm(X)<~>~happy(X))<=>~curious(X)))&
(![X]:(~tall(X)<=>(~creative(X)<~>~brave(X))))&
(![X]:((~creative(X)&tall(X))=>~tall(X)))&
(![X]:((~quiet(X)&~patient(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~rich(X)&curious(X))=>(~calm(X)|humble(X))))&
(![X]:((strong(X)&brave(X))=>(patient(X)&~tall(X))))&
((~tall(fred))=>((~brave(lucy)<~>humble(lucy))))&
(((happy(susan)<~>~tall(susan)))<=>(?[X]:((~wise(X)&~creative(X)))))&
(((calm(fred)&~strong(fred)))=>(?[X]:((strong(X)<~>~patient(X)))))&
(((funny(fred)|~strong(fred)))=>((~old(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
((?[X]:((generous(X)|old(X))))<=>((~calm(paul)<~>calm(paul))))&
(![X]:((brave(X)&~tall(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~calm(X)&~happy(X))<=>(quiet(X)|~kind(X))))&
(![X]:(~brave(X)<=>(~happy(X)<~>~tall(X))))&
(?[X]:((curious(X)|~patient(X))))&
(?[X]:((generous(X)<~>creative(X))))&
((~brave(susan)|humble(susan)))&
((~brave(paul)&~quiet(paul)))&
((patient(john)&~calm(john)))&
((~calm(susan)&strong(susan)))&
(?[X]:((happy(X)&~generous(X))))&
(?[X]:((~strong(X)<~>~quiet(X)))) | kind(paul) | [
"p1",
"p11",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1716831714799431163169603
% SZS output start Proof for 1716831714799431163169603
2. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> ~curious(X0)) [input p1]
12. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> ~creative(X0)) [input p11]
14. ! [X0] : ((~tall(X0) & brave(X0)) <=> (~curious(X0) <~> funny(X0))) [input p13]
15. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> (~kind(X0) | quiet(X0))) [input p14]
20. ~quiet(paul) & ~brave(paul) [input p19]
25. ~kind(paul) [input hypothesis]
37. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | curious(X0)) & (~curious(X0) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 2]
49. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | creative(X0)) & (~creative(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 12]
54. ! [X0] : (((~tall(X0) & brave(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (tall(X0) | ~brave(X0)))) [nnf transformation 14]
55. ! [X0] : (((~tall(X0) & brave(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | tall(X0) | ~brave(X0))) [flattening 54]
56. ! [X0] : (((~happy(X0) & ~calm(X0)) | (kind(X0) & ~quiet(X0))) & ((~kind(X0) | quiet(X0)) | (happy(X0) | calm(X0)))) [nnf transformation 15]
57. ! [X0] : (((~happy(X0) & ~calm(X0)) | (kind(X0) & ~quiet(X0))) & (~kind(X0) | quiet(X0) | happy(X0) | calm(X0))) [flattening 56]
72. ~curious(X0) | calm(X0) | happy(X0) [cnf transformation 37]
103. ~creative(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 49]
104. creative(X0) | ~funny(X0) | creative(X0) [cnf transformation 49]
114. brave(X0) | funny(X0) | curious(X0) [cnf transformation 55]
120. ~calm(X0) | kind(X0) [cnf transformation 57]
122. ~happy(X0) | kind(X0) [cnf transformation 57]
131. ~brave(paul) [cnf transformation 20]
141. ~kind(paul) [cnf transformation 25]
144. ~creative(X0) | ~funny(X0) [duplicate literal removal 103]
145. ~funny(X0) | creative(X0) [duplicate literal removal 104]
220. ~funny(X0) [subsumption resolution 144,145]
236. curious(X0) | brave(X0) [subsumption resolution 114,220]
277. happy(X0) | calm(X0) | brave(X0) [resolution 72,236]
388. calm(X4) | brave(X4) | kind(X4) [resolution 277,122]
392. kind(X4) | brave(X4) [subsumption resolution 388,120]
395. brave(paul) [resolution 392,141]
397. $false [subsumption resolution 395,131]
% SZS output end Proof for 1716831714799431163169603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or generous is either not brave or not happy and vice versa.
If someone is funny then lucy is generous.
Everyone who is not generous or creative is not funny and vice versa.
If susan is either brave or not strong then john is both patient and tall and vice versa.
If someone is generous or brave then someone is not brave.
Everyone who is both old and not strong is not funny or strong and vice versa.
Everyone who is both not old and wise is strong.
Everyone who is both tall and humble is either not curious or not brave and vice versa.
Everyone who is not happy or tall is not humble or not wise and vice versa.
Everyone who is both not tall and not calm is old and vice versa.
If paul is either not curious or not humble then john is not brave or quiet.
Everyone who is both not rich and not kind is both funny and kind and vice versa.
Everyone who is generous is either not strong or happy and vice versa.
Everyone who is patient is both curious and funny.
Everyone who is both not calm and old is quiet and vice versa.
Someone is either not patient or not happy.
Someone is tall.
Fred is either not humble or patient.
Someone is not brave or humble.
Someone is happy or not humble.
Lucy is not wise or not rich.
Someone is either quiet or generous.
Someone is patient. | Lucy is not curious. | neutral | (![X]:((kind(X)|generous(X))<=>(~brave(X)<~>~happy(X))))&
((?[X]:(funny(X)))=>(generous(lucy)))&
(![X]:((~generous(X)|creative(X))<=>~funny(X)))&
(((brave(susan)<~>~strong(susan)))<=>((patient(john)&tall(john))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:(~brave(X))))&
(![X]:((old(X)&~strong(X))<=>(~funny(X)|strong(X))))&
(![X]:((~old(X)&wise(X))=>strong(X)))&
(![X]:((tall(X)&humble(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((~happy(X)|tall(X))<=>(~humble(X)|~wise(X))))&
(![X]:((~tall(X)&~calm(X))<=>old(X)))&
(((~curious(paul)<~>~humble(paul)))=>((~brave(john)|quiet(john))))&
(![X]:((~rich(X)&~kind(X))<=>(funny(X)&kind(X))))&
(![X]:(generous(X)<=>(~strong(X)<~>happy(X))))&
(![X]:(patient(X)=>(curious(X)&funny(X))))&
(![X]:((~calm(X)&old(X))<=>quiet(X)))&
(?[X]:((~patient(X)<~>~happy(X))))&
(?[X]:(tall(X)))&
((~humble(fred)<~>patient(fred)))&
(?[X]:((~brave(X)|humble(X))))&
(?[X]:((happy(X)|~humble(X))))&
((~wise(lucy)|~rich(lucy)))&
(?[X]:((quiet(X)<~>generous(X))))&
(?[X]:(patient(X))) | ~curious(lucy) | [] | null | 0 |
If lucy is either tall or not rich then lucy is both not patient and not quiet and vice versa.
Everyone who is either not happy or not funny is both not calm and generous.
If someone is both rich and creative then lucy is either not strong or not calm.
Everyone who is curious or calm is either not kind or happy and vice versa.
If someone is not old then fred is either old or not humble and vice versa.
If fred is either happy or not brave then paul is not humble or creative and vice versa.
Everyone who is calm is curious or strong and vice versa.
If alice is both not humble and strong then john is curious or not strong and vice versa.
If someone is not patient then fred is both not old and generous and vice versa.
Everyone who is creative is both generous and quiet.
Everyone who is either not calm or not strong is either not old or not strong and vice versa.
Everyone who is either not brave or not humble is strong and vice versa.
If someone is not wise then someone is both not calm and not happy and vice versa.
Everyone who is not rich or not curious is not generous or not funny.
Everyone who is both brave and not humble is either rich or brave and vice versa.
If fred is both not brave and humble then someone is tall or not funny and vice versa.
Fred is not kind or not wise.
Mary is not quiet.
Lucy is not funny.
Someone is not tall.
Someone is not strong or tall.
Alice is patient or not creative.
Mary is both not curious and funny. | Fred is not brave. | entailment | (((tall(lucy)<~>~rich(lucy)))<=>((~patient(lucy)&~quiet(lucy))))&
(![X]:((~happy(X)<~>~funny(X))=>(~calm(X)&generous(X))))&
((?[X]:((rich(X)&creative(X))))=>((~strong(lucy)<~>~calm(lucy))))&
(![X]:((curious(X)|calm(X))<=>(~kind(X)<~>happy(X))))&
((?[X]:(~old(X)))<=>((old(fred)<~>~humble(fred))))&
(((happy(fred)<~>~brave(fred)))<=>((~humble(paul)|creative(paul))))&
(![X]:(calm(X)<=>(curious(X)|strong(X))))&
(((~humble(alice)&strong(alice)))<=>((curious(john)|~strong(john))))&
((?[X]:(~patient(X)))<=>((~old(fred)&generous(fred))))&
(![X]:(creative(X)=>(generous(X)&quiet(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>strong(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)&~happy(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)|~funny(X))))&
(![X]:((brave(X)&~humble(X))<=>(rich(X)<~>brave(X))))&
(((~brave(fred)&humble(fred)))<=>(?[X]:((tall(X)|~funny(X)))))&
((~kind(fred)|~wise(fred)))&
(~quiet(mary))&
(~funny(lucy))&
(?[X]:(~tall(X)))&
(?[X]:((~strong(X)|tall(X))))&
((patient(alice)|~creative(alice)))&
((~curious(mary)&funny(mary))) | ~brave(fred) | [
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5359555785145348559964415
% SZS output start Proof for 5359555785145348559964415
16. (humble(fred) & ~brave(fred)) <=> ? [X0] : (~funny(X0) | tall(X0)) [input p15]
19. ~funny(lucy) [input p18]
24. brave(fred) [input hypothesis]
61. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & (? [X0] : (~funny(X0) | tall(X0)) | (~humble(fred) | brave(fred))) [nnf transformation 16]
62. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & (? [X0] : (~funny(X0) | tall(X0)) | ~humble(fred) | brave(fred)) [flattening 61]
63. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & (? [X1] : (~funny(X1) | tall(X1)) | ~humble(fred) | brave(fred)) [rectify 62]
64. ? [X1] : (~funny(X1) | tall(X1)) => (~funny(sK4) | tall(sK4)) [choice axiom]
65. ((humble(fred) & ~brave(fred)) | ! [X0] : (funny(X0) & ~tall(X0))) & ((~funny(sK4) | tall(sK4)) | ~humble(fred) | brave(fred)) [skolemisation 63,64]
136. ~brave(fred) | funny(X0) [cnf transformation 65]
141. ~funny(lucy) [cnf transformation 19]
147. brave(fred) [cnf transformation 24]
217. 14 <=> brave(fred) [avatar definition]
291. 28 <=> ! [X0] : funny(X0) [avatar definition]
292. funny(X0) <- (28) [avatar component clause 291]
298. 28 | ~14 [avatar split clause 136,217,291]
336. 14 [avatar split clause 147,217]
337. $false <- (28) [resolution 292,141]
338. ~28 [avatar contradiction clause 337]
339. $false [avatar sat refutation 298,336,338]
% SZS output end Proof for 5359555785145348559964415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is curious and vice versa.
Everyone who is both not kind and patient is not funny.
If lucy is either not calm or quiet then fred is not kind or not creative and vice versa.
Everyone who is brave or patient is either not curious or patient and vice versa.
Everyone who is both strong and kind is not tall or not strong and vice versa.
Everyone who is funny or quiet is both brave and not curious.
If lucy is either not quiet or funny then alice is rich and vice versa.
Everyone who is either not old or generous is both kind and not tall and vice versa.
Everyone who is not happy is either not quiet or brave.
If someone is wise then someone is humble or brave and vice versa.
If someone is either not tall or curious then lucy is either not strong or not curious and vice versa.
If someone is either not rich or strong then john is both strong and not wise and vice versa.
If lucy is either curious or not wise then someone is not generous or brave.
Everyone who is either humble or happy is not calm or not humble and vice versa.
Everyone who is curious or not kind is curious and vice versa.
Everyone who is strong is not quiet or not creative and vice versa.
Paul is either not funny or patient.
Paul is not brave or not curious.
Paul is not kind or not generous.
Someone is not curious or not generous.
Someone is not old.
Someone is both patient and not calm.
Someone is either not kind or not rich.
Someone is either not curious or kind. | Lucy is not kind. | contradiction | (![X]:(old(X)<=>curious(X)))&
(![X]:((~kind(X)&patient(X))=>~funny(X)))&
(((~calm(lucy)<~>quiet(lucy)))<=>((~kind(fred)|~creative(fred))))&
(![X]:((brave(X)|patient(X))<=>(~curious(X)<~>patient(X))))&
(![X]:((strong(X)&kind(X))<=>(~tall(X)|~strong(X))))&
(![X]:((funny(X)|quiet(X))=>(brave(X)&~curious(X))))&
(((~quiet(lucy)<~>funny(lucy)))<=>(rich(alice)))&
(![X]:((~old(X)<~>generous(X))<=>(kind(X)&~tall(X))))&
(![X]:(~happy(X)=>(~quiet(X)<~>brave(X))))&
((?[X]:(wise(X)))<=>(?[X]:((humble(X)|brave(X)))))&
((?[X]:((~tall(X)<~>curious(X))))<=>((~strong(lucy)<~>~curious(lucy))))&
((?[X]:((~rich(X)<~>strong(X))))<=>((strong(john)&~wise(john))))&
(((curious(lucy)<~>~wise(lucy)))=>(?[X]:((~generous(X)|brave(X)))))&
(![X]:((humble(X)<~>happy(X))<=>(~calm(X)|~humble(X))))&
(![X]:((curious(X)|~kind(X))<=>curious(X)))&
(![X]:(strong(X)<=>(~quiet(X)|~creative(X))))&
((~funny(paul)<~>patient(paul)))&
((~brave(paul)|~curious(paul)))&
((~kind(paul)|~generous(paul)))&
(?[X]:((~curious(X)|~generous(X))))&
(?[X]:(~old(X)))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:((~curious(X)<~>kind(X)))) | ~kind(lucy) | [
"p4",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 469143991524807255258618
% SZS output start Proof for 469143991524807255258618
5. ! [X0] : ((kind(X0) & strong(X0)) <=> (~strong(X0) | ~tall(X0))) [input p4]
11. ? [X0] : (~tall(X0) <~> curious(X0)) <=> (~strong(lucy) <~> ~curious(lucy)) [input p10]
15. ! [X0] : ((~kind(X0) | curious(X0)) <=> curious(X0)) [input p14]
25. ~kind(lucy) [input hypothesis]
37. ! [X0] : (((kind(X0) & strong(X0)) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | (~kind(X0) | ~strong(X0)))) [nnf transformation 5]
38. ! [X0] : (((kind(X0) & strong(X0)) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | ~kind(X0) | ~strong(X0))) [flattening 37]
48. (? [X0] : ((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | ((~strong(lucy) | curious(lucy)) & (~curious(lucy) | strong(lucy)))) & (((curious(lucy) | strong(lucy)) & (~curious(lucy) | ~strong(lucy))) | ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0)))) [nnf transformation 11]
49. (? [X0] : ((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | ((~strong(lucy) | curious(lucy)) & (~curious(lucy) | strong(lucy)))) & (((curious(lucy) | strong(lucy)) & (~curious(lucy) | ~strong(lucy))) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1)))) [rectify 48]
50. ? [X0] : ((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) => ((~curious(sK2) | tall(sK2)) & (curious(sK2) | ~tall(sK2))) [choice axiom]
51. (((~curious(sK2) | tall(sK2)) & (curious(sK2) | ~tall(sK2))) | ((~strong(lucy) | curious(lucy)) & (~curious(lucy) | strong(lucy)))) & (((curious(lucy) | strong(lucy)) & (~curious(lucy) | ~strong(lucy))) | ! [X1] : ((~tall(X1) | ~curious(X1)) & (curious(X1) | tall(X1)))) [skolemisation 49,50]
62. ! [X0] : (((~kind(X0) | curious(X0)) | ~curious(X0)) & (curious(X0) | (kind(X0) & ~curious(X0)))) [nnf transformation 15]
63. ! [X0] : ((~kind(X0) | curious(X0) | ~curious(X0)) & (curious(X0) | (kind(X0) & ~curious(X0)))) [flattening 62]
96. strong(X0) | strong(X0) [cnf transformation 38]
97. tall(X0) | kind(X0) [cnf transformation 38]
119. ~curious(lucy) | ~strong(lucy) | ~tall(X1) | ~curious(X1) [cnf transformation 51]
141. kind(X0) | curious(X0) [cnf transformation 63]
158. ~kind(lucy) [cnf transformation 25]
162. strong(X0) [duplicate literal removal 96]
228. 13 <=> curious(lucy) [avatar definition]
242. ~curious(lucy) | ~tall(X1) | ~curious(X1) [subsumption resolution 119,162]
244. 16 <=> ! [X1] : (~tall(X1) | ~curious(X1)) [avatar definition]
245. ~tall(X1) | ~curious(X1) <- (16) [avatar component clause 244]
246. 16 | ~13 [avatar split clause 242,228,244]
344. curious(lucy) [resolution 141,158]
348. 13 [avatar split clause 344,228]
357. ~curious(X0) | kind(X0) <- (16) [resolution 245,97]
358. kind(X0) <- (16) [subsumption resolution 357,141]
359. $false <- (16) [resolution 358,158]
362. ~16 [avatar contradiction clause 359]
363. $false [avatar sat refutation 246,348,362]
% SZS output end Proof for 469143991524807255258618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and calm then alice is either creative or not happy and vice versa. Everyone who is both happy and quiet is not rich or not brave and vice versa. If someone is calm or curious then mary is either creative or humble. Everyone who is not humble or not wise is either humble or not quiet. If paul is both generous and tall then susan is both strong and not tall. If lucy is not funny then someone is both kind and not happy and vice versa. Everyone who is both not quiet and not humble is both tall and not calm and vice versa. If susan is both not generous and not rich then fred is not calm or kind. Everyone who is either not creative or creative is both brave and funny and vice versa. Everyone who is not brave or not strong is wise or not creative. Everyone who is either not quiet or not brave is wise and vice versa. Everyone who is not kind is either calm or not calm and vice versa. Everyone who is curious or strong is not funny or not kind and vice versa. Everyone who is both not generous and strong is both curious and wise and vice versa. If someone is both not creative and strong then fred is both old and not happy and vice versa. Everyone who is both not tall and happy is not kind and vice versa. Someone is not curious. Susan is both not calm and not kind. Someone is either not wise or curious. Fred is either not brave or humble. Someone is either creative or not generous. Lucy is either not brave or calm. Someone is not rich. | Mary is rich. | contradiction | ((?[X]:((wise(X)&calm(X))))<=>((creative(alice)<~>~happy(alice))))&
(![X]:((happy(X)&quiet(X))<=>(~rich(X)|~brave(X))))&
((?[X]:((calm(X)|curious(X))))=>((creative(mary)<~>humble(mary))))&
(![X]:((~humble(X)|~wise(X))=>(humble(X)<~>~quiet(X))))&
(((generous(paul)&tall(paul)))=>((strong(susan)&~tall(susan))))&
((~funny(lucy))<=>(?[X]:((kind(X)&~happy(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(tall(X)&~calm(X))))&
(((~generous(susan)&~rich(susan)))=>((~calm(fred)|kind(fred))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)&funny(X))))&
(![X]:((~brave(X)|~strong(X))=>(wise(X)|~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(calm(X)<~>~calm(X))))&
(![X]:((curious(X)|strong(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~generous(X)&strong(X))<=>(curious(X)&wise(X))))&
((?[X]:((~creative(X)&strong(X))))<=>((old(fred)&~happy(fred))))&
(![X]:((~tall(X)&happy(X))<=>~kind(X)))&
(?[X]:(~curious(X)))&
((~calm(susan)&~kind(susan)))&
(?[X]:((~wise(X)<~>curious(X))))&
((~brave(fred)<~>humble(fred)))&
(?[X]:((creative(X)<~>~generous(X))))&
((~brave(lucy)<~>calm(lucy)))&
(?[X]:(~rich(X))) | rich(mary) | [
"p1",
"p2",
"p3",
"p6",
"p8",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7187484679743876262318204
% SZS output start Proof for 7187484679743876262318204
2. ! [X0] : ((quiet(X0) & happy(X0)) <=> (~brave(X0) | ~rich(X0))) [input p1]
3. ? [X0] : (curious(X0) | calm(X0)) => (creative(mary) <~> humble(mary)) [input p2]
4. ! [X0] : ((~wise(X0) | ~humble(X0)) => (humble(X0) <~> ~quiet(X0))) [input p3]
7. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (~calm(X0) & tall(X0))) [input p6]
9. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (funny(X0) & brave(X0))) [input p8]
11. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) <=> wise(X0)) [input p10]
12. ! [X0] : (~kind(X0) <=> (calm(X0) <~> ~calm(X0))) [input p11]
13. ! [X0] : ((strong(X0) | curious(X0)) <=> (~kind(X0) | ~funny(X0))) [input p12]
14. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (wise(X0) & curious(X0))) [input p13]
15. ? [X0] : (strong(X0) & ~creative(X0)) <=> (~happy(fred) & old(fred)) [input p14]
16. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p15]
22. ~brave(lucy) <~> calm(lucy) [input p21]
24. rich(mary) [input hypothesis]
25. (creative(mary) <~> humble(mary)) | ! [X0] : (~curious(X0) & ~calm(X0)) [ennf transformation 3]
26. ! [X0] : ((humble(X0) <~> ~quiet(X0)) | (wise(X0) & humble(X0))) [ennf transformation 4]
37. ! [X0] : (((quiet(X0) & happy(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~quiet(X0) | ~happy(X0)))) [nnf transformation 2]
38. ! [X0] : (((quiet(X0) & happy(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~quiet(X0) | ~happy(X0))) [flattening 37]
39. ((~humble(mary) | ~creative(mary)) & (humble(mary) | creative(mary))) | ! [X0] : (~curious(X0) & ~calm(X0)) [nnf transformation 25]
40. ! [X0] : (((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (wise(X0) & humble(X0))) [nnf transformation 26]
45. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (calm(X0) | ~tall(X0))) & ((~calm(X0) & tall(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 7]
46. ! [X0] : (((~humble(X0) & ~quiet(X0)) | calm(X0) | ~tall(X0)) & ((~calm(X0) & tall(X0)) | humble(X0) | quiet(X0))) [flattening 45]
47. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 47]
49. ! [X0] : ((((brave(X0) | quiet(X0)) & (~brave(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0))))) [nnf transformation 11]
50. ! [X0] : ((~kind(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | kind(X0))) [nnf transformation 12]
51. ! [X0] : (((strong(X0) | curious(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (~strong(X0) & ~curious(X0)))) [nnf transformation 13]
52. ! [X0] : ((strong(X0) | curious(X0) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | (~strong(X0) & ~curious(X0)))) [flattening 51]
53. ! [X0] : (((strong(X0) & ~generous(X0)) | (~wise(X0) | ~curious(X0))) & ((wise(X0) & curious(X0)) | (~strong(X0) | generous(X0)))) [nnf transformation 14]
54. ! [X0] : (((strong(X0) & ~generous(X0)) | ~wise(X0) | ~curious(X0)) & ((wise(X0) & curious(X0)) | ~strong(X0) | generous(X0))) [flattening 53]
55. (? [X0] : (strong(X0) & ~creative(X0)) | (happy(fred) | ~old(fred))) & ((~happy(fred) & old(fred)) | ! [X0] : (~strong(X0) | creative(X0))) [nnf transformation 15]
56. (? [X0] : (strong(X0) & ~creative(X0)) | happy(fred) | ~old(fred)) & ((~happy(fred) & old(fred)) | ! [X0] : (~strong(X0) | creative(X0))) [flattening 55]
57. (? [X0] : (strong(X0) & ~creative(X0)) | happy(fred) | ~old(fred)) & ((~happy(fred) & old(fred)) | ! [X1] : (~strong(X1) | creative(X1))) [rectify 56]
58. ? [X0] : (strong(X0) & ~creative(X0)) => (strong(sK2) & ~creative(sK2)) [choice axiom]
59. ((strong(sK2) & ~creative(sK2)) | happy(fred) | ~old(fred)) & ((~happy(fred) & old(fred)) | ! [X1] : (~strong(X1) | creative(X1))) [skolemisation 57,58]
60. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 16]
61. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | tall(X0))) [flattening 60]
71. (~calm(lucy) | brave(lucy)) & (calm(lucy) | ~brave(lucy)) [nnf transformation 22]
80. ~brave(X0) | ~rich(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 38]
87. ~humble(mary) | ~creative(mary) | ~calm(X0) [cnf transformation 39]
89. ~quiet(X0) | humble(X0) | humble(X0) [cnf transformation 40]
98. tall(X0) | humble(X0) | quiet(X0) [cnf transformation 46]
103. brave(X0) | creative(X0) | creative(X0) [cnf transformation 48]
104. brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
111. wise(X0) | ~brave(X0) | quiet(X0) [cnf transformation 49]
117. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 50]
118. ~kind(X0) | calm(X0) | calm(X0) [cnf transformation 50]
122. strong(X0) | curious(X0) | kind(X0) [cnf transformation 52]
126. strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 54]
128. ~happy(fred) | ~strong(X1) | creative(X1) [cnf transformation 59]
132. ~tall(X0) | kind(X0) [cnf transformation 61]
133. happy(X0) | kind(X0) [cnf transformation 61]
143. calm(lucy) | ~brave(lucy) [cnf transformation 71]
146. rich(mary) [cnf transformation 24]
147. ~kind(X0) | ~calm(X0) [duplicate literal removal 117]
148. ~kind(X0) | calm(X0) [duplicate literal removal 118]
149. brave(X0) | creative(X0) [duplicate literal removal 103]
150. ~creative(X0) | brave(X0) [duplicate literal removal 104]
153. ~quiet(X0) | humble(X0) [duplicate literal removal 89]
183. 7 <=> creative(mary) [avatar definition]
187. 8 <=> humble(mary) [avatar definition]
189. ~humble(mary) <- (~8) [avatar component clause 187]
192. 9 <=> ! [X0] : ~calm(X0) [avatar definition]
193. ~calm(X0) <- (9) [avatar component clause 192]
194. 9 | ~7 | ~8 [avatar split clause 87,187,183,192]
234. tall(X0) | humble(X0) [subsumption resolution 98,153]
253. brave(X0) [subsumption resolution 149,150]
255. quiet(X0) | wise(X0) [subsumption resolution 111,253]
256. ~kind(X0) [subsumption resolution 147,148]
257. strong(X0) | curious(X0) [subsumption resolution 122,256]
258. ~wise(X0) | strong(X0) [subsumption resolution 126,257]
265. 23 <=> happy(fred) [avatar definition]
266. ~happy(fred) <- (~23) [avatar component clause 265]
279. 26 <=> ! [X1] : (~strong(X1) | creative(X1)) [avatar definition]
280. ~strong(X1) | creative(X1) <- (26) [avatar component clause 279]
281. 26 | ~23 [avatar split clause 128,265,279]
283. happy(X0) [subsumption resolution 133,256]
284. ~tall(X0) [subsumption resolution 132,256]
306. calm(lucy) [subsumption resolution 143,253]
307. $false <- (~23) [subsumption resolution 266,283]
308. 23 [avatar contradiction clause 307]
320. humble(X0) [resolution 234,284]
322. $false <- (~8) [resolution 320,189]
323. 8 [avatar contradiction clause 322]
375. ~rich(X2) | ~quiet(X2) | ~happy(X2) [resolution 80,253]
376. ~rich(X2) | ~quiet(X2) [subsumption resolution 375,283]
383. ~quiet(mary) [resolution 376,146]
386. wise(mary) [resolution 383,255]
401. strong(mary) [resolution 386,258]
405. creative(mary) <- (26) [resolution 401,280]
408. 7 | ~26 [avatar split clause 405,279,183]
418. $false <- (9) [resolution 193,306]
419. ~9 [avatar contradiction clause 418]
421. $false [avatar sat refutation 194,281,308,323,408,419]
% SZS output end Proof for 7187484679743876262318204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then paul is curious. Everyone who is both not curious and funny is not curious. Everyone who is both patient and not patient is kind or rich. Everyone who is both old and kind is quiet or not generous. If someone is both not old and old then someone is not creative or not wise. Everyone who is either not patient or not brave is either generous or kind. Everyone who is both not creative and not brave is both humble and not calm. If paul is not patient then someone is not wise and vice versa. If someone is both tall and not strong then mary is both generous and not creative and vice versa. Everyone who is either brave or quiet is either not wise or calm and vice versa. If someone is not kind then mary is funny or patient and vice versa. If someone is wise then someone is both not funny and humble. Everyone who is either curious or tall is either wise or not quiet. If lucy is wise then alice is curious and vice versa. Everyone who is either not tall or happy is either happy or curious and vice versa. If paul is both brave and not humble then someone is not humble or tall and vice versa. Someone is both not happy and patient. Someone is both brave and not old. Alice is calm. Someone is brave or not creative. Susan is not curious. Mary is either old or tall. Someone is not curious or humble. Someone is either not brave or not generous. | Mary is generous. | neutral | ((?[X]:(calm(X)))=>(curious(paul)))&
(![X]:((~curious(X)&funny(X))=>~curious(X)))&
(![X]:((patient(X)&~patient(X))=>(kind(X)|rich(X))))&
(![X]:((old(X)&kind(X))=>(quiet(X)|~generous(X))))&
((?[X]:((~old(X)&old(X))))=>(?[X]:((~creative(X)|~wise(X)))))&
(![X]:((~patient(X)<~>~brave(X))=>(generous(X)<~>kind(X))))&
(![X]:((~creative(X)&~brave(X))=>(humble(X)&~calm(X))))&
((~patient(paul))<=>(?[X]:(~wise(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((generous(mary)&~creative(mary))))&
(![X]:((brave(X)<~>quiet(X))<=>(~wise(X)<~>calm(X))))&
((?[X]:(~kind(X)))<=>((funny(mary)|patient(mary))))&
((?[X]:(wise(X)))=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((curious(X)<~>tall(X))=>(wise(X)<~>~quiet(X))))&
((wise(lucy))<=>(curious(alice)))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)<~>curious(X))))&
(((brave(paul)&~humble(paul)))<=>(?[X]:((~humble(X)|tall(X)))))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:((brave(X)&~old(X))))&
(calm(alice))&
(?[X]:((brave(X)|~creative(X))))&
(~curious(susan))&
((old(mary)<~>tall(mary)))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:((~brave(X)<~>~generous(X)))) | generous(mary) | [] | null | 0 |
Everyone who is funny or patient is either kind or quiet. Everyone who is either happy or not strong is both not calm and not kind and vice versa. If mary is not rich then alice is either strong or not curious. Everyone who is both humble and not funny is happy or creative. If paul is not kind or old then someone is not calm or not wise. If john is both not generous and kind then alice is brave and vice versa. If alice is either not creative or patient then someone is wise or not humble and vice versa. Everyone who is either not curious or old is either tall or not brave and vice versa. Everyone who is both rich and not humble is both not funny and not happy. If lucy is not generous then lucy is either humble or not curious and vice versa. Everyone who is both not wise and rich is both not curious and patient and vice versa. Everyone who is not patient or not humble is not curious or not wise. If someone is both curious and strong then mary is humble. Everyone who is either not creative or wise is humble and vice versa. If someone is not funny then paul is curious or creative and vice versa. If fred is not quiet or kind then someone is kind and vice versa. Alice is not creative. Someone is either old or happy. Lucy is not curious or wise. Fred is calm or creative. Someone is calm or not strong. Susan is both not creative and old. Paul is not wise. John is both not funny and not curious. | Fred is curious. | neutral | (![X]:((funny(X)|patient(X))=>(kind(X)<~>quiet(X))))&
(![X]:((happy(X)<~>~strong(X))<=>(~calm(X)&~kind(X))))&
((~rich(mary))=>((strong(alice)<~>~curious(alice))))&
(![X]:((humble(X)&~funny(X))=>(happy(X)|creative(X))))&
(((~kind(paul)|old(paul)))=>(?[X]:((~calm(X)|~wise(X)))))&
(((~generous(john)&kind(john)))<=>(brave(alice)))&
(((~creative(alice)<~>patient(alice)))<=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:((~curious(X)<~>old(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((rich(X)&~humble(X))=>(~funny(X)&~happy(X))))&
((~generous(lucy))<=>((humble(lucy)<~>~curious(lucy))))&
(![X]:((~wise(X)&rich(X))<=>(~curious(X)&patient(X))))&
(![X]:((~patient(X)|~humble(X))=>(~curious(X)|~wise(X))))&
((?[X]:((curious(X)&strong(X))))=>(humble(mary)))&
(![X]:((~creative(X)<~>wise(X))<=>humble(X)))&
((?[X]:(~funny(X)))<=>((curious(paul)|creative(paul))))&
(((~quiet(fred)|kind(fred)))<=>(?[X]:(kind(X))))&
(~creative(alice))&
(?[X]:((old(X)<~>happy(X))))&
((~curious(lucy)|wise(lucy)))&
((calm(fred)|creative(fred)))&
(?[X]:((calm(X)|~strong(X))))&
((~creative(susan)&old(susan)))&
(~wise(paul))&
((~funny(john)&~curious(john))) | curious(fred) | [] | null | 0 |
Everyone who is creative is humble.
Everyone who is either not humble or not calm is either curious or rich.
Everyone who is generous or strong is not wise.
Everyone who is both humble and not humble is not curious or not funny and vice versa.
Everyone who is either not quiet or not strong is not rich.
Everyone who is patient or humble is both tall and not happy and vice versa.
If susan is either not wise or not rich then susan is both not funny and patient.
If alice is not kind then someone is either kind or humble and vice versa.
Everyone who is either strong or not generous is not kind and vice versa.
If someone is not wise or quiet then someone is curious or not happy and vice versa.
Everyone who is both happy and strong is either curious or not strong.
Everyone who is not rich is either strong or not tall and vice versa.
If someone is not generous then lucy is not quiet or funny.
If paul is kind or not generous then alice is both not tall and not generous and vice versa.
Everyone who is brave or not rich is either quiet or not wise and vice versa.
If someone is rich then mary is not generous and vice versa.
Fred is not wise.
Someone is kind.
Paul is humble or tall.
Someone is humble.
Someone is not humble or happy.
Someone is not happy.
Fred is curious or happy. | Susan is not kind. | neutral | (![X]:(creative(X)=>humble(X)))&
(![X]:((~humble(X)<~>~calm(X))=>(curious(X)<~>rich(X))))&
(![X]:((generous(X)|strong(X))=>~wise(X)))&
(![X]:((humble(X)&~humble(X))<=>(~curious(X)|~funny(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>~rich(X)))&
(![X]:((patient(X)|humble(X))<=>(tall(X)&~happy(X))))&
(((~wise(susan)<~>~rich(susan)))=>((~funny(susan)&patient(susan))))&
((~kind(alice))<=>(?[X]:((kind(X)<~>humble(X)))))&
(![X]:((strong(X)<~>~generous(X))<=>~kind(X)))&
((?[X]:((~wise(X)|quiet(X))))<=>(?[X]:((curious(X)|~happy(X)))))&
(![X]:((happy(X)&strong(X))=>(curious(X)<~>~strong(X))))&
(![X]:(~rich(X)<=>(strong(X)<~>~tall(X))))&
((?[X]:(~generous(X)))=>((~quiet(lucy)|funny(lucy))))&
(((kind(paul)|~generous(paul)))<=>((~tall(alice)&~generous(alice))))&
(![X]:((brave(X)|~rich(X))<=>(quiet(X)<~>~wise(X))))&
((?[X]:(rich(X)))<=>(~generous(mary)))&
(~wise(fred))&
(?[X]:(kind(X)))&
((humble(paul)|tall(paul)))&
(?[X]:(humble(X)))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:(~happy(X)))&
((curious(fred)|happy(fred))) | ~kind(susan) | [] | null | 0 |
Everyone who is humble or happy is not old or not quiet and vice versa.
If lucy is both not funny and not kind then fred is either rich or humble and vice versa.
Everyone who is tall or kind is both not humble and not calm and vice versa.
Everyone who is either not generous or not strong is both not creative and not wise.
Everyone who is not wise is either quiet or not generous and vice versa.
If someone is both kind and not calm then someone is not tall or not wise and vice versa.
If paul is funny or not brave then someone is either not rich or not curious and vice versa.
If someone is not humble then mary is not tall and vice versa.
If someone is patient or not calm then fred is either old or not patient and vice versa.
Everyone who is either happy or wise is both not creative and creative and vice versa.
If someone is both not happy and not creative then someone is either quiet or not patient.
Everyone who is either not creative or humble is both quiet and not calm and vice versa.
If someone is tall or not curious then alice is either old or not rich and vice versa.
Everyone who is both tall and not brave is creative or not humble.
If fred is both not wise and generous then paul is not calm.
Everyone who is either not wise or not tall is either old or kind.
Paul is both old and not quiet.
John is either not old or not curious.
Mary is both not quiet and happy.
John is not strong or not kind.
Susan is both old and strong.
Someone is creative or kind.
Someone is either not quiet or happy. | Lucy is not happy. | neutral | (![X]:((humble(X)|happy(X))<=>(~old(X)|~quiet(X))))&
(((~funny(lucy)&~kind(lucy)))<=>((rich(fred)<~>humble(fred))))&
(![X]:((tall(X)|kind(X))<=>(~humble(X)&~calm(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(~creative(X)&~wise(X))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~generous(X))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
(((funny(paul)|~brave(paul)))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:(~humble(X)))<=>(~tall(mary)))&
((?[X]:((patient(X)|~calm(X))))<=>((old(fred)<~>~patient(fred))))&
(![X]:((happy(X)<~>wise(X))<=>(~creative(X)&creative(X))))&
((?[X]:((~happy(X)&~creative(X))))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)&~calm(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((old(alice)<~>~rich(alice))))&
(![X]:((tall(X)&~brave(X))=>(creative(X)|~humble(X))))&
(((~wise(fred)&generous(fred)))=>(~calm(paul)))&
(![X]:((~wise(X)<~>~tall(X))=>(old(X)<~>kind(X))))&
((old(paul)&~quiet(paul)))&
((~old(john)<~>~curious(john)))&
((~quiet(mary)&happy(mary)))&
((~strong(john)|~kind(john)))&
((old(susan)&strong(susan)))&
(?[X]:((creative(X)|kind(X))))&
(?[X]:((~quiet(X)<~>happy(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is calm is either kind or happy. If someone is both wise and creative then someone is patient or not calm. Everyone who is either wise or not rich is old or not funny and vice versa. If someone is not strong or not kind then mary is not wise and vice versa. Everyone who is funny or not strong is both not generous and brave and vice versa. Everyone who is both not kind and not happy is either not quiet or patient and vice versa. Everyone who is either old or not creative is both not calm and tall and vice versa. Everyone who is tall is not kind or happy and vice versa. Everyone who is not patient or patient is both not humble and not funny and vice versa. Everyone who is not old is both not funny and not calm and vice versa. Everyone who is either not kind or happy is either not brave or not generous. Everyone who is either not humble or not rich is either not tall or funny and vice versa. Everyone who is not old or patient is not creative. If someone is both not generous and funny then fred is both funny and not generous and vice versa. If someone is rich then someone is not quiet and vice versa. Everyone who is not old is both wise and strong and vice versa. Someone is either not happy or creative. Susan is not rich. Susan is not patient. John is either not strong or not calm. Someone is either not kind or not happy. Someone is brave or creative. | Mary is rich. | contradiction | (![X]:(calm(X)=>(kind(X)<~>happy(X))))&
((?[X]:((wise(X)&creative(X))))=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((wise(X)<~>~rich(X))<=>(old(X)|~funny(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>(~wise(mary)))&
(![X]:((funny(X)|~strong(X))<=>(~generous(X)&brave(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((old(X)<~>~creative(X))<=>(~calm(X)&tall(X))))&
(![X]:(tall(X)<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(~humble(X)&~funny(X))))&
(![X]:(~old(X)<=>(~funny(X)&~calm(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~old(X)|patient(X))=>~creative(X)))&
((?[X]:((~generous(X)&funny(X))))<=>((funny(fred)&~generous(fred))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
(![X]:(~old(X)<=>(wise(X)&strong(X))))&
(?[X]:((~happy(X)<~>creative(X))))&
(~rich(susan))&
(~patient(susan))&
((~strong(john)<~>~calm(john)))&
(?[X]:((~kind(X)<~>~happy(X))))&
(?[X]:((brave(X)|creative(X)))) | rich(mary) | [
"p2",
"p3",
"p6",
"p8",
"p9",
"p11",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6748483690733109404578045
% SZS output start Proof for 6748483690733109404578045
3. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (~funny(X0) | old(X0))) [input p2]
4. ? [X0] : (~kind(X0) | ~strong(X0)) <=> ~wise(mary) [input p3]
7. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (tall(X0) & ~calm(X0))) [input p6]
9. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~funny(X0) & ~humble(X0))) [input p8]
10. ! [X0] : (~old(X0) <=> (~calm(X0) & ~funny(X0))) [input p9]
12. ! [X0] : ((~humble(X0) <~> ~rich(X0)) <=> (~tall(X0) <~> funny(X0))) [input p11]
13. ! [X0] : ((patient(X0) | ~old(X0)) => ~creative(X0)) [input p12]
16. ! [X0] : (~old(X0) <=> (strong(X0) & wise(X0))) [input p15]
20. ~strong(john) <~> ~calm(john) [input p19]
23. rich(mary) [input hypothesis]
29. ! [X0] : (~creative(X0) | (~patient(X0) & old(X0))) [ennf transformation 13]
34. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 3]
35. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [flattening 34]
36. (? [X0] : (~kind(X0) | ~strong(X0)) | wise(mary)) & (~wise(mary) | ! [X0] : (kind(X0) & strong(X0))) [nnf transformation 4]
37. (? [X0] : (~kind(X0) | ~strong(X0)) | wise(mary)) & (~wise(mary) | ! [X1] : (kind(X1) & strong(X1))) [rectify 36]
38. ? [X0] : (~kind(X0) | ~strong(X0)) => (~kind(sK1) | ~strong(sK1)) [choice axiom]
39. ((~kind(sK1) | ~strong(sK1)) | wise(mary)) & (~wise(mary) | ! [X1] : (kind(X1) & strong(X1))) [skolemisation 37,38]
44. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (~tall(X0) | calm(X0))) & ((tall(X0) & ~calm(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 7]
45. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | ~tall(X0) | calm(X0)) & ((tall(X0) & ~calm(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 44]
48. ! [X0] : (((patient(X0) | ~patient(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 9]
49. ! [X0] : ((patient(X0) | ~patient(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [flattening 48]
50. ! [X0] : ((~old(X0) | (calm(X0) | funny(X0))) & ((~calm(X0) & ~funny(X0)) | old(X0))) [nnf transformation 10]
51. ! [X0] : ((~old(X0) | calm(X0) | funny(X0)) & ((~calm(X0) & ~funny(X0)) | old(X0))) [flattening 50]
53. ! [X0] : ((((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))))) [nnf transformation 12]
64. ! [X0] : ((~old(X0) | (~strong(X0) | ~wise(X0))) & ((strong(X0) & wise(X0)) | old(X0))) [nnf transformation 16]
65. ! [X0] : ((~old(X0) | ~strong(X0) | ~wise(X0)) & ((strong(X0) & wise(X0)) | old(X0))) [flattening 64]
69. (calm(john) | strong(john)) & (~calm(john) | ~strong(john)) [nnf transformation 20]
81. ~rich(X0) | wise(X0) | funny(X0) [cnf transformation 35]
83. ~wise(X0) | rich(X0) | funny(X0) [cnf transformation 35]
84. ~wise(mary) | strong(X1) [cnf transformation 39]
101. tall(X0) | old(X0) | creative(X0) [cnf transformation 45]
107. ~humble(X0) | patient(X0) [cnf transformation 49]
108. ~humble(X0) | ~patient(X0) [cnf transformation 49]
109. ~funny(X0) | patient(X0) [cnf transformation 49]
110. ~funny(X0) | ~patient(X0) [cnf transformation 49]
114. ~old(X0) | calm(X0) | funny(X0) [cnf transformation 51]
119. funny(X0) | ~tall(X0) | ~rich(X0) | humble(X0) [cnf transformation 53]
127. ~creative(X0) | old(X0) [cnf transformation 29]
135. old(X0) | wise(X0) [cnf transformation 65]
137. ~strong(X0) | ~old(X0) | ~wise(X0) [cnf transformation 65]
142. ~calm(john) | ~strong(john) [cnf transformation 69]
147. rich(mary) [cnf transformation 23]
161. 4 <=> wise(mary) [avatar definition]
178. 8 <=> ! [X1] : strong(X1) [avatar definition]
179. strong(X1) <- (8) [avatar component clause 178]
180. 8 | ~4 [avatar split clause 84,161,178]
181. ~funny(X0) [subsumption resolution 109,110]
182. ~humble(X0) [subsumption resolution 107,108]
183. ~old(X0) | calm(X0) [subsumption resolution 114,181]
186. ~tall(X0) | ~rich(X0) | humble(X0) [subsumption resolution 119,181]
187. ~tall(X0) | ~rich(X0) [subsumption resolution 186,182]
215. 15 <=> strong(john) [avatar definition]
216. ~strong(john) <- (~15) [avatar component clause 215]
217. strong(john) <- (15) [avatar component clause 215]
219. 16 <=> calm(john) [avatar definition]
223. ~15 | ~16 [avatar split clause 142,219,215]
245. wise(X0) | calm(X0) [resolution 183,135]
271. wise(mary) | funny(mary) [resolution 81,147]
277. wise(mary) [subsumption resolution 271,181]
278. 4 [avatar split clause 277,161]
317. old(X0) | creative(X0) | ~rich(X0) [resolution 101,187]
318. ~rich(X0) | old(X0) [subsumption resolution 317,127]
326. ~old(john) | ~wise(john) <- (15) [resolution 137,217]
330. 25 <=> wise(john) [avatar definition]
331. wise(john) <- (25) [avatar component clause 330]
332. ~wise(john) <- (~25) [avatar component clause 330]
334. 26 <=> old(john) [avatar definition]
336. ~old(john) <- (~26) [avatar component clause 334]
337. ~25 | ~26 | ~15 [avatar split clause 326,215,334,330]
338. calm(john) <- (~25) [resolution 332,245]
341. 16 | 25 [avatar split clause 338,330,219]
342. $false <- (8, ~15) [subsumption resolution 216,179]
343. ~8 | 15 [avatar contradiction clause 342]
344. rich(john) | funny(john) <- (25) [resolution 331,83]
345. rich(john) <- (25) [subsumption resolution 344,181]
362. old(john) <- (25) [resolution 318,345]
363. $false <- (25, ~26) [subsumption resolution 362,336]
364. ~25 | 26 [avatar contradiction clause 363]
365. $false [avatar sat refutation 180,223,278,337,341,343,364]
% SZS output end Proof for 6748483690733109404578045
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa. If susan is both not curious and not rich then someone is creative or not calm. Everyone who is both happy and not rich is funny or not creative and vice versa. Everyone who is either not tall or not curious is both humble and not funny and vice versa. Everyone who is either not funny or tall is not wise. If someone is both rich and old then someone is brave or humble. If lucy is tall or brave then someone is both patient and not patient. If mary is old then john is either not old or funny and vice versa. Everyone who is both funny and old is both not curious and not calm and vice versa. If someone is rich or funny then john is creative or not calm. Everyone who is humble is both not funny and not old. Everyone who is not old is not happy and vice versa. Everyone who is quiet is both not humble and wise and vice versa. Everyone who is either old or not wise is both not curious and not generous and vice versa. Everyone who is either not kind or tall is not wise and vice versa. If paul is both not wise and not happy then someone is kind or tall and vice versa. Someone is either humble or happy. Paul is both generous and not humble. Someone is tall or patient. Someone is not generous or generous. Someone is either not strong or not happy. Someone is happy or rich. Someone is not funny. | John is wise. | contradiction | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
(((~curious(susan)&~rich(susan)))=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((happy(X)&~rich(X))<=>(funny(X)|~creative(X))))&
(![X]:((~tall(X)<~>~curious(X))<=>(humble(X)&~funny(X))))&
(![X]:((~funny(X)<~>tall(X))=>~wise(X)))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((brave(X)|humble(X)))))&
(((tall(lucy)|brave(lucy)))=>(?[X]:((patient(X)&~patient(X)))))&
((old(mary))<=>((~old(john)<~>funny(john))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
(((~wise(paul)&~happy(paul)))<=>(?[X]:((kind(X)|tall(X)))))&
(?[X]:((humble(X)<~>happy(X))))&
((generous(paul)&~humble(paul)))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~generous(X)|generous(X))))&
(?[X]:((~strong(X)<~>~happy(X))))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(~funny(X))) | wise(john) | [
"p0",
"p2",
"p4",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 588125280719727068637571
% SZS output start Proof for 588125280719727068637571
1. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~happy(X0) <~> generous(X0))) [input p0]
3. ! [X0] : ((~rich(X0) & happy(X0)) <=> (~creative(X0) | funny(X0))) [input p2]
5. ! [X0] : ((~funny(X0) <~> tall(X0)) => ~wise(X0)) [input p4]
12. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p11]
14. ! [X0] : ((old(X0) <~> ~wise(X0)) <=> (~generous(X0) & ~curious(X0))) [input p13]
16. (~happy(paul) & ~wise(paul)) <=> ? [X0] : (tall(X0) | kind(X0)) [input p15]
18. ~humble(paul) & generous(paul) [input p17]
24. wise(john) [input hypothesis]
28. ! [X0] : (~wise(X0) | (~funny(X0) <=> tall(X0))) [ennf transformation 5]
34. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 1]
35. ! [X0] : ((funny(X0) | ~funny(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [flattening 34]
38. ! [X0] : (((~rich(X0) & happy(X0)) | (creative(X0) & ~funny(X0))) & ((~creative(X0) | funny(X0)) | (rich(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((~rich(X0) & happy(X0)) | (creative(X0) & ~funny(X0))) & (~creative(X0) | funny(X0) | rich(X0) | ~happy(X0))) [flattening 38]
42. ! [X0] : (~wise(X0) | ((~funny(X0) | ~tall(X0)) & (tall(X0) | funny(X0)))) [nnf transformation 28]
51. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 12]
52. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (generous(X0) | curious(X0))) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [nnf transformation 14]
53. ! [X0] : ((((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | generous(X0) | curious(X0)) & ((~generous(X0) & ~curious(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0))))) [flattening 52]
55. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X0] : (tall(X0) | kind(X0)) | (happy(paul) | wise(paul))) [nnf transformation 16]
56. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X0] : (tall(X0) | kind(X0)) | happy(paul) | wise(paul)) [flattening 55]
57. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & (? [X1] : (tall(X1) | kind(X1)) | happy(paul) | wise(paul)) [rectify 56]
58. ? [X1] : (tall(X1) | kind(X1)) => (tall(sK3) | kind(sK3)) [choice axiom]
59. ((~happy(paul) & ~wise(paul)) | ! [X0] : (~tall(X0) & ~kind(X0))) & ((tall(sK3) | kind(sK3)) | happy(paul) | wise(paul)) [skolemisation 57,58]
74. generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 35]
75. ~happy(X0) | generous(X0) | ~funny(X0) [cnf transformation 35]
76. ~generous(X0) | happy(X0) | funny(X0) [cnf transformation 35]
77. ~generous(X0) | happy(X0) | ~funny(X0) [cnf transformation 35]
82. ~funny(X0) | happy(X0) [cnf transformation 39]
92. ~wise(X0) | tall(X0) | funny(X0) [cnf transformation 42]
111. ~happy(X0) | old(X0) [cnf transformation 51]
112. ~old(X0) | happy(X0) [cnf transformation 51]
115. ~old(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 53]
127. ~happy(paul) | ~tall(X0) [cnf transformation 59]
130. generous(paul) [cnf transformation 18]
138. wise(john) [cnf transformation 24]
139. ~generous(X0) | happy(X0) [subsumption resolution 76,77]
140. ~happy(X0) | generous(X0) [subsumption resolution 74,75]
187. 11 <=> funny(john) [avatar definition]
188. funny(john) <- (11) [avatar component clause 187]
191. 12 <=> old(john) [avatar definition]
192. old(john) <- (12) [avatar component clause 191]
193. ~old(john) <- (~12) [avatar component clause 191]
219. 18 <=> ! [X0] : ~tall(X0) [avatar definition]
220. ~tall(X0) <- (18) [avatar component clause 219]
222. 19 <=> happy(paul) [avatar definition]
225. 18 | ~19 [avatar split clause 127,222,219]
287. happy(john) <- (11) [resolution 82,188]
290. old(john) <- (11) [resolution 111,287]
291. $false <- (11, ~12) [subsumption resolution 290,193]
292. ~11 | 12 [avatar contradiction clause 291]
294. happy(john) <- (12) [resolution 112,192]
297. happy(paul) [resolution 139,130]
300. 19 [avatar split clause 297,222]
304. generous(john) <- (12) [resolution 294,140]
320. tall(john) | funny(john) [resolution 92,138]
321. funny(john) <- (18) [subsumption resolution 320,220]
324. 11 | ~18 [avatar split clause 321,219,187]
430. ~wise(john) | ~generous(john) <- (12) [resolution 115,192]
435. ~generous(john) <- (12) [subsumption resolution 430,138]
436. $false <- (12) [subsumption resolution 435,304]
437. ~12 [avatar contradiction clause 436]
439. $false [avatar sat refutation 225,292,300,324,437]
% SZS output end Proof for 588125280719727068637571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not strong then someone is not funny or not kind. If susan is either kind or creative then fred is either happy or not quiet. If susan is both not generous and strong then mary is not tall and vice versa. Everyone who is not happy or patient is both curious and not creative. If john is not strong then lucy is not old or not generous. Everyone who is happy is either not strong or not funny and vice versa. Everyone who is curious or not old is curious. Everyone who is not happy or happy is strong. If someone is not strong or not quiet then someone is both not funny and patient. Everyone who is not tall or kind is curious and vice versa. Everyone who is both brave and not quiet is both quiet and not rich and vice versa. Everyone who is happy is not happy or not kind and vice versa. If someone is both kind and generous then someone is both wise and not tall and vice versa. Everyone who is not creative or not rich is wise or not happy. Everyone who is either not funny or humble is patient. If paul is either not tall or humble then someone is either happy or not humble. Someone is either not tall or not creative. Someone is both humble and creative. Someone is not calm or strong. Someone is both tall and happy. Someone is either not funny or old. Alice is brave or patient. Susan is both generous and not wise. Someone is either tall or creative. | Mary is not rich. | contradiction | ((?[X]:((kind(X)<~>~strong(X))))=>(?[X]:((~funny(X)|~kind(X)))))&
(((kind(susan)<~>creative(susan)))=>((happy(fred)<~>~quiet(fred))))&
(((~generous(susan)&strong(susan)))<=>(~tall(mary)))&
(![X]:((~happy(X)|patient(X))=>(curious(X)&~creative(X))))&
((~strong(john))=>((~old(lucy)|~generous(lucy))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((~funny(X)<~>old(X))))&
((brave(alice)|patient(alice)))&
((generous(susan)&~wise(susan)))&
(?[X]:((tall(X)<~>creative(X)))) | ~rich(mary) | [
"p3",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 14589684085951468133316
% SZS output start Proof for 14589684085951468133316
4. ! [X0] : ((patient(X0) | ~happy(X0)) => (~creative(X0) & curious(X0))) [input p3]
9. ? [X0] : (~quiet(X0) | ~strong(X0)) => ? [X0] : (patient(X0) & ~funny(X0)) [input p8]
10. ! [X0] : ((kind(X0) | ~tall(X0)) <=> curious(X0)) [input p9]
11. ! [X0] : ((~quiet(X0) & brave(X0)) <=> (~rich(X0) & quiet(X0))) [input p10]
12. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p11]
13. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X0] : (~tall(X0) & wise(X0)) [input p12]
14. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~happy(X0) | wise(X0))) [input p13]
25. ~rich(mary) [input hypothesis]
27. ? [X0] : (~quiet(X0) | ~strong(X0)) => ? [X1] : (patient(X1) & ~funny(X1)) [rectify 9]
28. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X1] : (~tall(X1) & wise(X1)) [rectify 13]
32. ! [X0] : ((~creative(X0) & curious(X0)) | (~patient(X0) & happy(X0))) [ennf transformation 4]
37. ? [X1] : (patient(X1) & ~funny(X1)) | ! [X0] : (quiet(X0) & strong(X0)) [ennf transformation 27]
38. ! [X0] : ((~happy(X0) | wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 14]
39. ! [X0] : (~happy(X0) | wise(X0) | (rich(X0) & creative(X0))) [flattening 38]
50. ? [X0] : (patient(X0) & ~funny(X0)) | ! [X1] : (quiet(X1) & strong(X1)) [rectify 37]
51. ? [X0] : (patient(X0) & ~funny(X0)) => (patient(sK1) & ~funny(sK1)) [choice axiom]
52. (patient(sK1) & ~funny(sK1)) | ! [X1] : (quiet(X1) & strong(X1)) [skolemisation 50,51]
53. ! [X0] : (((kind(X0) | ~tall(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [nnf transformation 10]
54. ! [X0] : ((kind(X0) | ~tall(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [flattening 53]
55. ! [X0] : (((~quiet(X0) & brave(X0)) | (rich(X0) | ~quiet(X0))) & ((~rich(X0) & quiet(X0)) | (quiet(X0) | ~brave(X0)))) [nnf transformation 11]
56. ! [X0] : (((~quiet(X0) & brave(X0)) | rich(X0) | ~quiet(X0)) & ((~rich(X0) & quiet(X0)) | quiet(X0) | ~brave(X0))) [flattening 55]
57. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 12]
58. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 57]
59. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X1] : (~tall(X1) & wise(X1)) | ! [X0] : (~generous(X0) | ~kind(X0))) [nnf transformation 28]
60. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X2] : (~tall(X2) & wise(X2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [rectify 59]
61. ? [X0] : (generous(X0) & kind(X0)) => (generous(sK2) & kind(sK2)) [choice axiom]
62. ? [X2] : (~tall(X2) & wise(X2)) => (~tall(sK3) & wise(sK3)) [choice axiom]
63. ((generous(sK2) & kind(sK2)) | ! [X1] : (tall(X1) | ~wise(X1))) & ((~tall(sK3) & wise(sK3)) | ! [X3] : (~generous(X3) | ~kind(X3))) [skolemisation 60,62,61]
91. ~patient(X0) | curious(X0) [cnf transformation 32]
93. ~patient(X0) | ~creative(X0) [cnf transformation 32]
106. patient(sK1) | quiet(X1) [cnf transformation 52]
109. ~curious(X0) | ~tall(X0) | kind(X0) [cnf transformation 54]
113. ~quiet(X0) | rich(X0) | ~quiet(X0) [cnf transformation 56]
114. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 58]
115. happy(X0) | happy(X0) [cnf transformation 58]
119. kind(sK2) | tall(X1) | ~wise(X1) [cnf transformation 63]
121. ~happy(X0) | wise(X0) | creative(X0) [cnf transformation 39]
142. ~rich(mary) [cnf transformation 25]
143. ~kind(X0) | ~happy(X0) [duplicate literal removal 114]
144. happy(X0) [duplicate literal removal 115]
146. ~quiet(X0) | rich(X0) [duplicate literal removal 113]
213. 15 <=> ! [X1] : quiet(X1) [avatar definition]
214. quiet(X1) <- (15) [avatar component clause 213]
216. 16 <=> patient(sK1) [avatar definition]
218. patient(sK1) <- (16) [avatar component clause 216]
219. 15 | 16 [avatar split clause 106,216,213]
225. ~kind(X0) [subsumption resolution 143,144]
227. 18 <=> ! [X1] : (tall(X1) | ~wise(X1)) [avatar definition]
228. ~wise(X1) | tall(X1) <- (18) [avatar component clause 227]
234. tall(X1) | ~wise(X1) [subsumption resolution 119,225]
235. 18 [avatar split clause 234,227]
237. wise(X0) | creative(X0) [subsumption resolution 121,144]
299. rich(X0) <- (15) [resolution 146,214]
300. $false <- (15) [resolution 299,142]
301. ~15 [avatar contradiction clause 300]
302. ~creative(sK1) <- (16) [resolution 218,93]
303. curious(sK1) <- (16) [resolution 218,91]
308. tall(X0) | creative(X0) <- (18) [resolution 237,228]
328. ~tall(sK1) | kind(sK1) <- (16) [resolution 109,303]
330. ~tall(sK1) <- (16) [subsumption resolution 328,225]
342. creative(sK1) <- (16, 18) [resolution 308,330]
343. $false <- (16, 18) [subsumption resolution 342,302]
344. ~16 | ~18 [avatar contradiction clause 343]
345. $false [avatar sat refutation 219,235,301,344]
% SZS output end Proof for 14589684085951468133316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or not brave then fred is both patient and not funny.
If someone is wise then lucy is both happy and not patient and vice versa.
Everyone who is creative or not humble is both funny and rich and vice versa.
Everyone who is strong or funny is both calm and funny and vice versa.
If fred is both brave and tall then someone is curious and vice versa.
If alice is brave then paul is curious and vice versa.
Everyone who is either not strong or patient is humble and vice versa.
Everyone who is not humble or not tall is not rich and vice versa.
If someone is humble then someone is both not quiet and not funny and vice versa.
Everyone who is not patient is both not tall and generous.
If someone is both not old and not funny then someone is not rich or not tall and vice versa.
Everyone who is either not happy or not calm is kind and vice versa.
If lucy is either humble or not tall then someone is patient and vice versa.
If fred is both not creative and not tall then john is both not patient and not wise.
If someone is either not happy or not wise then someone is either generous or not curious.
If someone is tall then john is either curious or not humble and vice versa.
Someone is not kind or not humble.
Fred is old.
Someone is both not quiet and generous.
Lucy is either kind or generous.
Someone is humble.
Someone is happy or patient.
Someone is both curious and not creative.
Someone is either not curious or funny. | Paul is wise. | contradiction | ((?[X]:((~calm(X)|~brave(X))))=>((patient(fred)&~funny(fred))))&
((?[X]:(wise(X)))<=>((happy(lucy)&~patient(lucy))))&
(![X]:((creative(X)|~humble(X))<=>(funny(X)&rich(X))))&
(![X]:((strong(X)|funny(X))<=>(calm(X)&funny(X))))&
(((brave(fred)&tall(fred)))<=>(?[X]:(curious(X))))&
((brave(alice))<=>(curious(paul)))&
(![X]:((~strong(X)<~>patient(X))<=>humble(X)))&
(![X]:((~humble(X)|~tall(X))<=>~rich(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:(~patient(X)=>(~tall(X)&generous(X))))&
((?[X]:((~old(X)&~funny(X))))<=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((~happy(X)<~>~calm(X))<=>kind(X)))&
(((humble(lucy)<~>~tall(lucy)))<=>(?[X]:(patient(X))))&
(((~creative(fred)&~tall(fred)))=>((~patient(john)&~wise(john))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:(tall(X)))<=>((curious(john)<~>~humble(john))))&
(?[X]:((~kind(X)|~humble(X))))&
(old(fred))&
(?[X]:((~quiet(X)&generous(X))))&
((kind(lucy)<~>generous(lucy)))&
(?[X]:(humble(X)))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:((~curious(X)<~>funny(X)))) | wise(paul) | [
"p1",
"p2",
"p4",
"p7",
"p9",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3429284206021290450733628
% SZS output start Proof for 3429284206021290450733628
2. ? [X0] : wise(X0) <=> (~patient(lucy) & happy(lucy)) [input p1]
3. ! [X0] : ((~humble(X0) | creative(X0)) <=> (rich(X0) & funny(X0))) [input p2]
5. (tall(fred) & brave(fred)) <=> ? [X0] : curious(X0) [input p4]
8. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> ~rich(X0)) [input p7]
10. ! [X0] : (~patient(X0) => (generous(X0) & ~tall(X0))) [input p9]
13. (humble(lucy) <~> ~tall(lucy)) <=> ? [X0] : patient(X0) [input p12]
23. ? [X0] : (~creative(X0) & curious(X0)) [input p22]
25. wise(paul) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~tall(X0)) | patient(X0)) [ennf transformation 10]
34. (? [X0] : wise(X0) | (patient(lucy) | ~happy(lucy))) & ((~patient(lucy) & happy(lucy)) | ! [X0] : ~wise(X0)) [nnf transformation 2]
35. (? [X0] : wise(X0) | patient(lucy) | ~happy(lucy)) & ((~patient(lucy) & happy(lucy)) | ! [X0] : ~wise(X0)) [flattening 34]
36. (? [X0] : wise(X0) | patient(lucy) | ~happy(lucy)) & ((~patient(lucy) & happy(lucy)) | ! [X1] : ~wise(X1)) [rectify 35]
37. ? [X0] : wise(X0) => wise(sK0) [choice axiom]
38. (wise(sK0) | patient(lucy) | ~happy(lucy)) & ((~patient(lucy) & happy(lucy)) | ! [X1] : ~wise(X1)) [skolemisation 36,37]
39. ! [X0] : (((~humble(X0) | creative(X0)) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | (humble(X0) & ~creative(X0)))) [nnf transformation 3]
40. ! [X0] : ((~humble(X0) | creative(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | (humble(X0) & ~creative(X0)))) [flattening 39]
43. ((tall(fred) & brave(fred)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~tall(fred) | ~brave(fred))) [nnf transformation 5]
44. ((tall(fred) & brave(fred)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ~tall(fred) | ~brave(fred)) [flattening 43]
45. ((tall(fred) & brave(fred)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ~tall(fred) | ~brave(fred)) [rectify 44]
46. ? [X1] : curious(X1) => curious(sK1) [choice axiom]
47. ((tall(fred) & brave(fred)) | ! [X0] : ~curious(X0)) & (curious(sK1) | ~tall(fred) | ~brave(fred)) [skolemisation 45,46]
50. ! [X0] : (((~tall(X0) | ~humble(X0)) | rich(X0)) & (~rich(X0) | (tall(X0) & humble(X0)))) [nnf transformation 8]
51. ! [X0] : ((~tall(X0) | ~humble(X0) | rich(X0)) & (~rich(X0) | (tall(X0) & humble(X0)))) [flattening 50]
63. (((tall(lucy) | ~humble(lucy)) & (~tall(lucy) | humble(lucy))) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | ((humble(lucy) | tall(lucy)) & (~tall(lucy) | ~humble(lucy)))) [nnf transformation 13]
64. (((tall(lucy) | ~humble(lucy)) & (~tall(lucy) | humble(lucy))) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | ((humble(lucy) | tall(lucy)) & (~tall(lucy) | ~humble(lucy)))) [rectify 63]
65. ? [X1] : patient(X1) => patient(sK6) [choice axiom]
66. (((tall(lucy) | ~humble(lucy)) & (~tall(lucy) | humble(lucy))) | ! [X0] : ~patient(X0)) & (patient(sK6) | ((humble(lucy) | tall(lucy)) & (~tall(lucy) | ~humble(lucy)))) [skolemisation 64,65]
84. ? [X0] : (~creative(X0) & curious(X0)) => (~creative(sK13) & curious(sK13)) [choice axiom]
85. ~creative(sK13) & curious(sK13) [skolemisation 23,84]
94. ~patient(lucy) | ~wise(X1) [cnf transformation 38]
99. rich(X0) | humble(X0) [cnf transformation 40]
108. tall(fred) | ~curious(X0) [cnf transformation 47]
115. ~rich(X0) | humble(X0) [cnf transformation 51]
121. ~tall(X0) | patient(X0) [cnf transformation 30]
135. tall(lucy) | ~humble(lucy) | ~patient(X0) [cnf transformation 66]
154. curious(sK13) [cnf transformation 85]
158. wise(paul) [cnf transformation 25]
172. 4 <=> patient(fred) [avatar definition]
174. patient(fred) <- (4) [avatar component clause 172]
182. 6 <=> patient(lucy) [avatar definition]
191. 8 <=> ! [X1] : ~wise(X1) [avatar definition]
192. ~wise(X1) <- (8) [avatar component clause 191]
193. 8 | ~6 [avatar split clause 94,182,191]
196. 9 <=> ! [X0] : ~curious(X0) [avatar definition]
197. ~curious(X0) <- (9) [avatar component clause 196]
199. 10 <=> tall(fred) [avatar definition]
201. tall(fred) <- (10) [avatar component clause 199]
202. 9 | 10 [avatar split clause 108,199,196]
224. humble(X0) [subsumption resolution 115,99]
254. tall(lucy) | ~patient(X0) [subsumption resolution 135,224]
256. 21 <=> ! [X0] : ~patient(X0) [avatar definition]
257. ~patient(X0) <- (21) [avatar component clause 256]
259. 22 <=> tall(lucy) [avatar definition]
261. tall(lucy) <- (22) [avatar component clause 259]
262. 21 | 22 [avatar split clause 254,259,256]
346. $false <- (4, 21) [subsumption resolution 174,257]
347. ~4 | ~21 [avatar contradiction clause 346]
348. $false <- (9) [resolution 197,154]
349. ~9 [avatar contradiction clause 348]
352. patient(fred) <- (10) [resolution 121,201]
353. patient(lucy) <- (22) [resolution 121,261]
357. 6 | ~22 [avatar split clause 353,259,182]
358. $false <- (8) [resolution 192,158]
361. ~8 [avatar contradiction clause 358]
362. 4 | ~10 [avatar split clause 352,199,172]
363. $false [avatar sat refutation 193,202,262,347,349,357,361,362]
% SZS output end Proof for 3429284206021290450733628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong then someone is not humble or calm. Everyone who is both curious and funny is either not quiet or patient. Everyone who is tall or not humble is either rich or funny. If someone is curious then susan is both kind and humble and vice versa. If mary is not strong then paul is either not happy or wise and vice versa. If someone is humble or not generous then someone is wise or not funny. Everyone who is not quiet is both creative and strong and vice versa. Everyone who is not rich or not brave is either not quiet or brave. Everyone who is both not humble and creative is both funny and strong and vice versa. Everyone who is either old or humble is either not kind or not creative and vice versa. Everyone who is either not tall or funny is either quiet or happy. Everyone who is either not old or not generous is kind or not generous. Everyone who is either old or humble is either quiet or not quiet and vice versa. If someone is either not curious or not old then lucy is both not old and not humble and vice versa. Everyone who is either not quiet or not strong is brave. If fred is both not quiet and strong then someone is both tall and not funny and vice versa. Someone is wise. Lucy is not strong. Someone is not old. Alice is rich or not brave. Alice is not humble. Someone is either strong or not old. Fred is not tall. | Alice is funny. | contradiction | ((?[X]:((tall(X)|~strong(X))))=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((curious(X)&funny(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((tall(X)|~humble(X))=>(rich(X)<~>funny(X))))&
((?[X]:(curious(X)))<=>((kind(susan)&humble(susan))))&
((~strong(mary))<=>((~happy(paul)<~>wise(paul))))&
((?[X]:((humble(X)|~generous(X))))=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&strong(X))))&
(![X]:((~rich(X)|~brave(X))=>(~quiet(X)<~>brave(X))))&
(![X]:((~humble(X)&creative(X))<=>(funny(X)&strong(X))))&
(![X]:((old(X)<~>humble(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((~tall(X)<~>funny(X))=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)<~>~generous(X))=>(kind(X)|~generous(X))))&
(![X]:((old(X)<~>humble(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~curious(X)<~>~old(X))))<=>((~old(lucy)&~humble(lucy))))&
(![X]:((~quiet(X)<~>~strong(X))=>brave(X)))&
(((~quiet(fred)&strong(fred)))<=>(?[X]:((tall(X)&~funny(X)))))&
(?[X]:(wise(X)))&
(~strong(lucy))&
(?[X]:(~old(X)))&
((rich(alice)|~brave(alice)))&
(~humble(alice))&
(?[X]:((strong(X)<~>~old(X))))&
(~tall(fred)) | funny(alice) | [
"p2",
"p6",
"p7",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4650754820255941092636840
% SZS output start Proof for 4650754820255941092636840
3. ! [X0] : ((~humble(X0) | tall(X0)) => (rich(X0) <~> funny(X0))) [input p2]
7. ! [X0] : (~quiet(X0) <=> (strong(X0) & creative(X0))) [input p6]
8. ! [X0] : ((~brave(X0) | ~rich(X0)) => (~quiet(X0) <~> brave(X0))) [input p7]
15. ! [X0] : ((~quiet(X0) <~> ~strong(X0)) => brave(X0)) [input p14]
20. ~brave(alice) | rich(alice) [input p19]
21. ~humble(alice) [input p20]
24. funny(alice) [input hypothesis]
30. ! [X0] : ((rich(X0) <~> funny(X0)) | (humble(X0) & ~tall(X0))) [ennf transformation 3]
32. ! [X0] : ((~quiet(X0) <~> brave(X0)) | (brave(X0) & rich(X0))) [ennf transformation 8]
36. ! [X0] : (brave(X0) | (~quiet(X0) <=> ~strong(X0))) [ennf transformation 15]
38. ! [X0] : (((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | (humble(X0) & ~tall(X0))) [nnf transformation 30]
48. ! [X0] : ((~quiet(X0) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | quiet(X0))) [nnf transformation 7]
49. ! [X0] : ((~quiet(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | quiet(X0))) [flattening 48]
50. ! [X0] : (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | (brave(X0) & rich(X0))) [nnf transformation 32]
62. ! [X0] : (brave(X0) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) [nnf transformation 36]
80. ~rich(X0) | ~funny(X0) | humble(X0) [cnf transformation 38]
91. quiet(X0) | strong(X0) [cnf transformation 49]
94. brave(X0) | ~quiet(X0) | brave(X0) [cnf transformation 50]
129. brave(X0) | ~strong(X0) | quiet(X0) [cnf transformation 62]
138. ~brave(alice) | rich(alice) [cnf transformation 20]
139. ~humble(alice) [cnf transformation 21]
143. funny(alice) [cnf transformation 24]
149. ~quiet(X0) | brave(X0) [duplicate literal removal 94]
220. brave(X0) | quiet(X0) [subsumption resolution 129,91]
221. brave(X0) [subsumption resolution 220,149]
247. rich(alice) [subsumption resolution 138,221]
284. ~funny(alice) | humble(alice) [resolution 80,247]
287. humble(alice) [subsumption resolution 284,143]
288. $false [subsumption resolution 287,139]
% SZS output end Proof for 4650754820255941092636840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not rich is calm or creative and vice versa. If alice is not brave then alice is both humble and strong. If susan is both rich and not old then alice is both not old and not calm and vice versa. Everyone who is generous or not creative is creative. Everyone who is happy or strong is either not calm or not tall and vice versa. Everyone who is both curious and strong is both tall and curious. If lucy is not quiet then susan is not generous or not rich and vice versa. If alice is not quiet or generous then mary is wise or kind and vice versa. Everyone who is curious or not calm is both not humble and tall. Everyone who is not funny or not brave is not humble. If someone is not kind or wise then someone is both brave and not tall and vice versa. If paul is both funny and not brave then someone is both not happy and old and vice versa. If fred is either strong or patient then lucy is both not tall and not rich and vice versa. If paul is either rich or not strong then paul is both wise and calm and vice versa. If someone is both rich and quiet then someone is not creative or not old. Everyone who is not quiet is either happy or not quiet. Someone is either not strong or not generous. Paul is generous. Someone is not quiet or not tall. Someone is not old or not curious. Mary is generous or not happy. Someone is not curious. John is either not old or not creative. | Alice is quiet. | neutral | (![X]:((strong(X)|~rich(X))<=>(calm(X)|creative(X))))&
((~brave(alice))=>((humble(alice)&strong(alice))))&
(((rich(susan)&~old(susan)))<=>((~old(alice)&~calm(alice))))&
(![X]:((generous(X)|~creative(X))=>creative(X)))&
(![X]:((happy(X)|strong(X))<=>(~calm(X)<~>~tall(X))))&
(![X]:((curious(X)&strong(X))=>(tall(X)&curious(X))))&
((~quiet(lucy))<=>((~generous(susan)|~rich(susan))))&
(((~quiet(alice)|generous(alice)))<=>((wise(mary)|kind(mary))))&
(![X]:((curious(X)|~calm(X))=>(~humble(X)&tall(X))))&
(![X]:((~funny(X)|~brave(X))=>~humble(X)))&
((?[X]:((~kind(X)|wise(X))))<=>(?[X]:((brave(X)&~tall(X)))))&
(((funny(paul)&~brave(paul)))<=>(?[X]:((~happy(X)&old(X)))))&
(((strong(fred)<~>patient(fred)))<=>((~tall(lucy)&~rich(lucy))))&
(((rich(paul)<~>~strong(paul)))<=>((wise(paul)&calm(paul))))&
((?[X]:((rich(X)&quiet(X))))=>(?[X]:((~creative(X)|~old(X)))))&
(![X]:(~quiet(X)=>(happy(X)<~>~quiet(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
(generous(paul))&
(?[X]:((~quiet(X)|~tall(X))))&
(?[X]:((~old(X)|~curious(X))))&
((generous(mary)|~happy(mary)))&
(?[X]:(~curious(X)))&
((~old(john)<~>~creative(john))) | quiet(alice) | [] | null | 0 |
If paul is not tall or not strong then fred is patient or curious and vice versa.
If someone is creative then someone is both wise and not funny.
Everyone who is not quiet is both happy and brave.
Everyone who is not rich is either generous or not rich.
Everyone who is not strong is patient or funny.
Everyone who is not kind or not tall is either happy or generous.
If fred is either not generous or quiet then someone is not calm or happy and vice versa.
If someone is either not curious or not tall then someone is both not patient and funny.
Everyone who is not patient is both not generous and not curious and vice versa.
Everyone who is not wise or not old is brave and vice versa.
Everyone who is strong is either patient or not generous and vice versa.
If john is not calm then someone is both happy and brave.
If john is both not brave and not funny then someone is generous and vice versa.
If someone is either quiet or not patient then mary is generous.
Everyone who is both not patient and not curious is not humble or not curious and vice versa.
Everyone who is quiet or tall is either not generous or patient and vice versa.
Someone is not old.
John is either brave or funny.
Lucy is either humble or not generous.
Someone is not tall.
Someone is humble or happy.
Lucy is either not quiet or happy.
Someone is either brave or curious.
Someone is either strong or not kind. | Fred is not strong. | entailment | (((~tall(paul)|~strong(paul)))<=>((patient(fred)|curious(fred))))&
((?[X]:(creative(X)))=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:(~quiet(X)=>(happy(X)&brave(X))))&
(![X]:(~rich(X)=>(generous(X)<~>~rich(X))))&
(![X]:(~strong(X)=>(patient(X)|funny(X))))&
(![X]:((~kind(X)|~tall(X))=>(happy(X)<~>generous(X))))&
(((~generous(fred)<~>quiet(fred)))<=>(?[X]:((~calm(X)|happy(X)))))&
((?[X]:((~curious(X)<~>~tall(X))))=>(?[X]:((~patient(X)&funny(X)))))&
(![X]:(~patient(X)<=>(~generous(X)&~curious(X))))&
(![X]:((~wise(X)|~old(X))<=>brave(X)))&
(![X]:(strong(X)<=>(patient(X)<~>~generous(X))))&
((~calm(john))=>(?[X]:((happy(X)&brave(X)))))&
(((~brave(john)&~funny(john)))<=>(?[X]:(generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))=>(generous(mary)))&
(![X]:((~patient(X)&~curious(X))<=>(~humble(X)|~curious(X))))&
(![X]:((quiet(X)|tall(X))<=>(~generous(X)<~>patient(X))))&
(?[X]:(~old(X)))&
((brave(john)<~>funny(john)))&
((humble(lucy)<~>~generous(lucy)))&
(?[X]:(~tall(X)))&
(?[X]:((humble(X)|happy(X))))&
((~quiet(lucy)<~>happy(lucy)))&
(?[X]:((brave(X)<~>curious(X))))&
(?[X]:((strong(X)<~>~kind(X)))) | ~strong(fred) | [
"p2",
"p6",
"p10",
"p12",
"p13",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4744135274567040978190577
% SZS output start Proof for 4744135274567040978190577
3. ! [X0] : (~quiet(X0) => (brave(X0) & happy(X0))) [input p2]
7. (~generous(fred) <~> quiet(fred)) <=> ? [X0] : (happy(X0) | ~calm(X0)) [input p6]
11. ! [X0] : (strong(X0) <=> (patient(X0) <~> ~generous(X0))) [input p10]
13. (~funny(john) & ~brave(john)) <=> ? [X0] : generous(X0) [input p12]
14. ? [X0] : (quiet(X0) <~> ~patient(X0)) => generous(mary) [input p13]
18. brave(john) <~> funny(john) [input p17]
22. ~quiet(lucy) <~> happy(lucy) [input p21]
25. strong(fred) [input hypothesis]
29. ! [X0] : ((brave(X0) & happy(X0)) | quiet(X0)) [ennf transformation 3]
36. generous(mary) | ! [X0] : (quiet(X0) <=> ~patient(X0)) [ennf transformation 14]
41. (((~quiet(fred) | generous(fred)) & (quiet(fred) | ~generous(fred))) | ! [X0] : (~happy(X0) & calm(X0))) & (? [X0] : (happy(X0) | ~calm(X0)) | ((~generous(fred) | ~quiet(fred)) & (quiet(fred) | generous(fred)))) [nnf transformation 7]
42. (((~quiet(fred) | generous(fred)) & (quiet(fred) | ~generous(fred))) | ! [X0] : (~happy(X0) & calm(X0))) & (? [X1] : (happy(X1) | ~calm(X1)) | ((~generous(fred) | ~quiet(fred)) & (quiet(fred) | generous(fred)))) [rectify 41]
43. ? [X1] : (happy(X1) | ~calm(X1)) => (happy(sK0) | ~calm(sK0)) [choice axiom]
44. (((~quiet(fred) | generous(fred)) & (quiet(fred) | ~generous(fred))) | ! [X0] : (~happy(X0) & calm(X0))) & ((happy(sK0) | ~calm(sK0)) | ((~generous(fred) | ~quiet(fred)) & (quiet(fred) | generous(fred)))) [skolemisation 42,43]
53. ! [X0] : ((strong(X0) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | ~strong(X0))) [nnf transformation 11]
56. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (funny(john) | brave(john))) [nnf transformation 13]
57. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | funny(john) | brave(john)) [flattening 56]
58. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | funny(john) | brave(john)) [rectify 57]
59. ? [X1] : generous(X1) => generous(sK3) [choice axiom]
60. ((~funny(john) & ~brave(john)) | ! [X0] : ~generous(X0)) & (generous(sK3) | funny(john) | brave(john)) [skolemisation 58,59]
61. generous(mary) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))) [nnf transformation 36]
68. (~funny(john) | ~brave(john)) & (funny(john) | brave(john)) [nnf transformation 18]
74. (~happy(lucy) | quiet(lucy)) & (happy(lucy) | ~quiet(lucy)) [nnf transformation 22]
85. happy(X0) | quiet(X0) [cnf transformation 29]
99. ~quiet(fred) | generous(fred) | ~happy(X0) [cnf transformation 44]
111. ~patient(X0) | generous(X0) | ~strong(X0) [cnf transformation 53]
117. ~brave(john) | ~generous(X0) [cnf transformation 60]
118. ~funny(john) | ~generous(X0) [cnf transformation 60]
120. generous(mary) | quiet(X0) | patient(X0) [cnf transformation 61]
133. funny(john) | brave(john) [cnf transformation 68]
139. happy(lucy) | ~quiet(lucy) [cnf transformation 74]
140. ~happy(lucy) | quiet(lucy) [cnf transformation 74]
145. strong(fred) [cnf transformation 25]
161. 4 <=> patient(fred) [avatar definition]
162. patient(fred) <- (4) [avatar component clause 161]
163. ~patient(fred) <- (~4) [avatar component clause 161]
168. 5 <=> ! [X0] : ~happy(X0) [avatar definition]
169. ~happy(X0) <- (5) [avatar component clause 168]
171. 6 <=> generous(fred) [avatar definition]
173. generous(fred) <- (6) [avatar component clause 171]
175. 7 <=> quiet(fred) [avatar definition]
177. ~quiet(fred) <- (~7) [avatar component clause 175]
178. 5 | 6 | ~7 [avatar split clause 99,175,171,168]
230. 18 <=> ! [X0] : ~generous(X0) [avatar definition]
231. ~generous(X0) <- (18) [avatar component clause 230]
233. 19 <=> funny(john) [avatar definition]
236. 18 | ~19 [avatar split clause 118,233,230]
238. 20 <=> brave(john) [avatar definition]
241. 18 | ~20 [avatar split clause 117,238,230]
248. 22 <=> ! [X0] : (quiet(X0) | patient(X0)) [avatar definition]
249. quiet(X0) | patient(X0) <- (22) [avatar component clause 248]
251. 23 <=> generous(mary) [avatar definition]
253. generous(mary) <- (23) [avatar component clause 251]
254. 22 | 23 [avatar split clause 120,251,248]
262. 20 | 19 [avatar split clause 133,233,238]
282. quiet(lucy) [subsumption resolution 140,85]
283. happy(lucy) [subsumption resolution 139,282]
304. $false <- (18, 23) [resolution 253,231]
305. ~18 | ~23 [avatar contradiction clause 304]
313. patient(fred) <- (~7, 22) [resolution 249,177]
314. $false <- (~4, ~7, 22) [subsumption resolution 313,163]
315. 4 | 7 | ~22 [avatar contradiction clause 314]
316. $false <- (6, 18) [subsumption resolution 173,231]
317. ~6 | ~18 [avatar contradiction clause 316]
318. $false <- (5) [resolution 169,283]
320. ~5 [avatar contradiction clause 318]
353. generous(fred) | ~strong(fred) <- (4) [resolution 111,162]
354. ~strong(fred) <- (4, 18) [subsumption resolution 353,231]
355. $false <- (4, 18) [subsumption resolution 354,145]
356. ~4 | ~18 [avatar contradiction clause 355]
357. $false [avatar sat refutation 178,236,241,254,262,305,315,317,320,356]
% SZS output end Proof for 4744135274567040978190577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not patient is both funny and wise and vice versa. Everyone who is not brave or happy is either not brave or funny. Everyone who is not curious is humble or creative and vice versa. Everyone who is either creative or kind is either patient or not brave and vice versa. Everyone who is either not tall or not old is not brave or not calm and vice versa. Everyone who is calm is generous. If someone is not creative then someone is both not kind and rich and vice versa. If mary is patient or kind then someone is both not wise and not tall and vice versa. Everyone who is humble is not rich or old. If john is not rich then someone is either not old or patient and vice versa. If mary is not rich or curious then alice is either not patient or not funny. Everyone who is either funny or strong is not patient or curious and vice versa. If fred is tall or not creative then mary is patient or strong. Everyone who is both not generous and tall is either quiet or calm and vice versa. Everyone who is either not funny or tall is both funny and kind. If someone is wise or not happy then alice is both not quiet and not wise. Someone is kind or generous. Someone is both happy and generous. Someone is not curious. Someone is either not happy or not rich. Someone is either not generous or not old. John is not calm. Someone is not calm or calm. Someone is creative. | Mary is happy. | entailment | (![X]:((~quiet(X)|~patient(X))<=>(funny(X)&wise(X))))&
(![X]:((~brave(X)|happy(X))=>(~brave(X)<~>funny(X))))&
(![X]:(~curious(X)<=>(humble(X)|creative(X))))&
(![X]:((creative(X)<~>kind(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((~tall(X)<~>~old(X))<=>(~brave(X)|~calm(X))))&
(![X]:(calm(X)=>generous(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~kind(X)&rich(X)))))&
(((patient(mary)|kind(mary)))<=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:(humble(X)=>(~rich(X)|old(X))))&
((~rich(john))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~rich(mary)|curious(mary)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(~patient(X)|curious(X))))&
(((tall(fred)|~creative(fred)))=>((patient(mary)|strong(mary))))&
(![X]:((~generous(X)&tall(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~funny(X)<~>tall(X))=>(funny(X)&kind(X))))&
((?[X]:((wise(X)|~happy(X))))=>((~quiet(alice)&~wise(alice))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((~generous(X)<~>~old(X))))&
(~calm(john))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:(creative(X))) | happy(mary) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8377296939808318125810982
% SZS output start Proof for 8377296939808318125810982
1. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (wise(X0) & funny(X0))) [input p0]
16. ? [X0] : (~happy(X0) | wise(X0)) => (~wise(alice) & ~quiet(alice)) [input p15]
25. ~happy(mary) [input hypothesis]
35. (~wise(alice) & ~quiet(alice)) | ! [X0] : (happy(X0) & ~wise(X0)) [ennf transformation 16]
36. ! [X0] : (((~patient(X0) | ~quiet(X0)) | (~wise(X0) | ~funny(X0))) & ((wise(X0) & funny(X0)) | (patient(X0) & quiet(X0)))) [nnf transformation 1]
37. ! [X0] : ((~patient(X0) | ~quiet(X0) | ~wise(X0) | ~funny(X0)) & ((wise(X0) & funny(X0)) | (patient(X0) & quiet(X0)))) [flattening 36]
82. wise(X0) | quiet(X0) [cnf transformation 37]
143. ~quiet(alice) | happy(X0) [cnf transformation 35]
144. ~wise(alice) | ~wise(X0) [cnf transformation 35]
157. ~happy(mary) [cnf transformation 25]
262. 22 <=> ! [X0] : happy(X0) [avatar definition]
263. happy(X0) <- (22) [avatar component clause 262]
265. 23 <=> wise(alice) [avatar definition]
266. wise(alice) <- (23) [avatar component clause 265]
267. ~wise(alice) <- (~23) [avatar component clause 265]
270. 24 <=> ! [X0] : ~wise(X0) [avatar definition]
271. ~wise(X0) <- (24) [avatar component clause 270]
272. 24 | ~23 [avatar split clause 144,265,270]
274. 25 <=> quiet(alice) [avatar definition]
276. ~quiet(alice) <- (~25) [avatar component clause 274]
277. 22 | ~25 [avatar split clause 143,274,262]
311. quiet(alice) <- (~23) [resolution 82,267]
312. $false <- (~23, ~25) [subsumption resolution 311,276]
313. 23 | 25 [avatar contradiction clause 312]
314. $false <- (23, 24) [subsumption resolution 266,271]
315. ~23 | ~24 [avatar contradiction clause 314]
316. $false <- (22) [resolution 263,157]
317. ~22 [avatar contradiction clause 316]
318. $false [avatar sat refutation 272,277,313,315,317]
% SZS output end Proof for 8377296939808318125810982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either brave or tall then someone is both not wise and not funny and vice versa. Everyone who is both quiet and not generous is both not kind and creative. If alice is both old and tall then someone is either curious or quiet and vice versa. Everyone who is generous or not happy is humble and vice versa. If mary is either not patient or not curious then someone is both creative and kind. If lucy is not humble then someone is brave or not curious and vice versa. If someone is both not generous and not patient then someone is either not generous or old and vice versa. If paul is both kind and curious then paul is either old or not generous and vice versa. Everyone who is not generous or not tall is both wise and not humble. If someone is funny then someone is not patient and vice versa. Everyone who is both happy and rich is either humble or generous and vice versa. Everyone who is not calm is either funny or not quiet and vice versa. If susan is happy or not calm then susan is both not humble and happy and vice versa. If lucy is either not funny or rich then someone is humble. If someone is both not calm and humble then someone is funny or not kind. If someone is not old then mary is patient or calm. Susan is both happy and brave. Lucy is both old and quiet. Mary is either old or not old. Someone is both not creative and wise. Susan is not old or not creative. Someone is both funny and not generous. Paul is rich. Mary is old. | Lucy is creative. | entailment | (((brave(susan)<~>tall(susan)))<=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:((quiet(X)&~generous(X))=>(~kind(X)&creative(X))))&
(((old(alice)&tall(alice)))<=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:((generous(X)|~happy(X))<=>humble(X)))&
(((~patient(mary)<~>~curious(mary)))=>(?[X]:((creative(X)&kind(X)))))&
((~humble(lucy))<=>(?[X]:((brave(X)|~curious(X)))))&
((?[X]:((~generous(X)&~patient(X))))<=>(?[X]:((~generous(X)<~>old(X)))))&
(((kind(paul)&curious(paul)))<=>((old(paul)<~>~generous(paul))))&
(![X]:((~generous(X)|~tall(X))=>(wise(X)&~humble(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~patient(X))))&
(![X]:((happy(X)&rich(X))<=>(humble(X)<~>generous(X))))&
(![X]:(~calm(X)<=>(funny(X)<~>~quiet(X))))&
(((happy(susan)|~calm(susan)))<=>((~humble(susan)&happy(susan))))&
(((~funny(lucy)<~>rich(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((~calm(X)&humble(X))))=>(?[X]:((funny(X)|~kind(X)))))&
((?[X]:(~old(X)))=>((patient(mary)|calm(mary))))&
((happy(susan)&brave(susan)))&
((old(lucy)&quiet(lucy)))&
((old(mary)<~>~old(mary)))&
(?[X]:((~creative(X)&wise(X))))&
((~old(susan)|~creative(susan)))&
(?[X]:((funny(X)&~generous(X))))&
(rich(paul))&
(old(mary)) | creative(lucy) | [
"p1",
"p3",
"p5",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4437554354788853546372344
% SZS output start Proof for 4437554354788853546372344
2. ! [X0] : ((~generous(X0) & quiet(X0)) => (creative(X0) & ~kind(X0))) [input p1]
4. ! [X0] : ((~happy(X0) | generous(X0)) <=> humble(X0)) [input p3]
6. ~humble(lucy) <=> ? [X0] : (~curious(X0) | brave(X0)) [input p5]
17. brave(susan) & happy(susan) [input p16]
18. quiet(lucy) & old(lucy) [input p17]
25. ~creative(lucy) [input hypothesis]
29. ! [X0] : ((creative(X0) & ~kind(X0)) | (generous(X0) | ~quiet(X0))) [ennf transformation 2]
30. ! [X0] : ((creative(X0) & ~kind(X0)) | generous(X0) | ~quiet(X0)) [flattening 29]
46. ! [X0] : (((~happy(X0) | generous(X0)) | ~humble(X0)) & (humble(X0) | (happy(X0) & ~generous(X0)))) [nnf transformation 4]
47. ! [X0] : ((~happy(X0) | generous(X0) | ~humble(X0)) & (humble(X0) | (happy(X0) & ~generous(X0)))) [flattening 46]
51. (~humble(lucy) | ! [X0] : (curious(X0) & ~brave(X0))) & (? [X0] : (~curious(X0) | brave(X0)) | humble(lucy)) [nnf transformation 6]
52. (~humble(lucy) | ! [X0] : (curious(X0) & ~brave(X0))) & (? [X1] : (~curious(X1) | brave(X1)) | humble(lucy)) [rectify 51]
53. ? [X1] : (~curious(X1) | brave(X1)) => (~curious(sK3) | brave(sK3)) [choice axiom]
54. (~humble(lucy) | ! [X0] : (curious(X0) & ~brave(X0))) & ((~curious(sK3) | brave(sK3)) | humble(lucy)) [skolemisation 52,53]
90. ~quiet(X0) | generous(X0) | creative(X0) [cnf transformation 30]
97. ~generous(X0) | humble(X0) [cnf transformation 47]
105. ~humble(lucy) | ~brave(X0) [cnf transformation 54]
145. brave(susan) [cnf transformation 17]
147. quiet(lucy) [cnf transformation 18]
157. ~creative(lucy) [cnf transformation 25]
162. 2 <=> brave(susan) [avatar definition]
163. brave(susan) <- (2) [avatar component clause 162]
235. 17 <=> humble(lucy) [avatar definition]
240. 18 <=> ! [X0] : ~brave(X0) [avatar definition]
241. ~brave(X0) <- (18) [avatar component clause 240]
242. 18 | ~17 [avatar split clause 105,235,240]
372. 2 [avatar split clause 145,162]
416. generous(lucy) | creative(lucy) [resolution 90,147]
431. generous(lucy) [subsumption resolution 416,157]
448. humble(lucy) [resolution 431,97]
451. 17 [avatar split clause 448,235]
462. $false <- (2, 18) [resolution 241,163]
463. ~2 | ~18 [avatar contradiction clause 462]
464. $false [avatar sat refutation 242,372,451,463]
% SZS output end Proof for 4437554354788853546372344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either wise or not funny then lucy is quiet or not happy and vice versa.
If paul is curious or brave then someone is humble.
Everyone who is both wise and not humble is both calm and wise.
Everyone who is both old and not funny is both funny and strong and vice versa.
Everyone who is kind is both funny and not strong.
Everyone who is both rich and not curious is both not creative and creative and vice versa.
Everyone who is both not tall and not happy is not kind and vice versa.
If someone is not patient or generous then someone is both not strong and not funny.
Everyone who is both not quiet and not humble is not rich or not calm and vice versa.
Everyone who is curious or patient is either not funny or not happy.
Everyone who is either rich or not strong is either not curious or tall.
Everyone who is either not rich or strong is either not funny or not rich and vice versa.
If lucy is strong or not brave then susan is either not strong or not happy.
If paul is both not kind and not calm then someone is creative and vice versa.
Everyone who is wise or generous is rich or creative and vice versa.
Everyone who is either not creative or not strong is either calm or not calm.
Lucy is either strong or brave.
Someone is not generous.
Fred is humble.
Someone is curious or not humble.
Fred is not curious or funny.
Someone is either not happy or not creative. | Susan is not happy. | entailment | (((wise(lucy)<~>~funny(lucy)))<=>((quiet(lucy)|~happy(lucy))))&
(((curious(paul)|brave(paul)))=>(?[X]:(humble(X))))&
(![X]:((wise(X)&~humble(X))=>(calm(X)&wise(X))))&
(![X]:((old(X)&~funny(X))<=>(funny(X)&strong(X))))&
(![X]:(kind(X)=>(funny(X)&~strong(X))))&
(![X]:((rich(X)&~curious(X))<=>(~creative(X)&creative(X))))&
(![X]:((~tall(X)&~happy(X))<=>~kind(X)))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((~strong(X)&~funny(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(~rich(X)|~calm(X))))&
(![X]:((curious(X)|patient(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((rich(X)<~>~strong(X))=>(~curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(~funny(X)<~>~rich(X))))&
(((strong(lucy)|~brave(lucy)))=>((~strong(susan)<~>~happy(susan))))&
(((~kind(paul)&~calm(paul)))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)|generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
((strong(lucy)<~>brave(lucy)))&
(?[X]:(~generous(X)))&
(humble(fred))&
(?[X]:((curious(X)|~humble(X))))&
((~curious(fred)|funny(fred)))&
(?[X]:((~happy(X)<~>~creative(X)))) | ~happy(susan) | [
"p4",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5115289277266629008142821
% SZS output start Proof for 5115289277266629008142821
5. ! [X0] : (kind(X0) => (~strong(X0) & funny(X0))) [input p4]
7. ! [X0] : ((~happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p6]
8. ? [X0] : (generous(X0) | ~patient(X0)) => ? [X0] : (~funny(X0) & ~strong(X0)) [input p7]
10. ! [X0] : ((patient(X0) | curious(X0)) => (~funny(X0) <~> ~happy(X0))) [input p9]
12. ! [X0] : ((~rich(X0) <~> strong(X0)) <=> (~funny(X0) <~> ~rich(X0))) [input p11]
23. happy(susan) [input hypothesis]
24. ? [X0] : (generous(X0) | ~patient(X0)) => ? [X1] : (~funny(X1) & ~strong(X1)) [rectify 8]
28. ! [X0] : ((~strong(X0) & funny(X0)) | ~kind(X0)) [ennf transformation 5]
29. ? [X1] : (~funny(X1) & ~strong(X1)) | ! [X0] : (~generous(X0) & patient(X0)) [ennf transformation 24]
30. ! [X0] : ((~funny(X0) <~> ~happy(X0)) | (~patient(X0) & ~curious(X0))) [ennf transformation 10]
42. ! [X0] : (((~happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (happy(X0) | tall(X0)))) [nnf transformation 7]
43. ! [X0] : (((~happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | happy(X0) | tall(X0))) [flattening 42]
44. ? [X0] : (~funny(X0) & ~strong(X0)) | ! [X1] : (~generous(X1) & patient(X1)) [rectify 29]
45. ? [X0] : (~funny(X0) & ~strong(X0)) => (~funny(sK1) & ~strong(sK1)) [choice axiom]
46. (~funny(sK1) & ~strong(sK1)) | ! [X1] : (~generous(X1) & patient(X1)) [skolemisation 44,45]
49. ! [X0] : (((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (~patient(X0) & ~curious(X0))) [nnf transformation 30]
51. ! [X0] : ((((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) & (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))))) [nnf transformation 12]
83. ~kind(X0) | funny(X0) [cnf transformation 28]
91. ~happy(X0) | kind(X0) [cnf transformation 43]
92. ~strong(sK1) | patient(X1) [cnf transformation 46]
94. ~funny(sK1) | patient(X1) [cnf transformation 46]
102. ~patient(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 49]
111. rich(X0) | funny(X0) | strong(X0) | rich(X0) [cnf transformation 51]
113. strong(X0) | ~rich(X0) | ~rich(X0) | funny(X0) [cnf transformation 51]
140. happy(susan) [cnf transformation 23]
142. rich(X0) | funny(X0) | strong(X0) [duplicate literal removal 111]
143. strong(X0) | ~rich(X0) | funny(X0) [duplicate literal removal 113]
188. 9 <=> funny(sK1) [avatar definition]
193. 10 <=> ! [X1] : patient(X1) [avatar definition]
194. patient(X1) <- (10) [avatar component clause 193]
195. 10 | ~9 [avatar split clause 94,188,193]
197. 11 <=> strong(sK1) [avatar definition]
199. ~strong(sK1) <- (~11) [avatar component clause 197]
201. 10 | ~11 [avatar split clause 92,197,193]
204. strong(X0) | funny(X0) [subsumption resolution 142,143]
214. 14 <=> happy(susan) [avatar definition]
216. happy(susan) <- (14) [avatar component clause 214]
273. 14 [avatar split clause 140,214]
274. kind(susan) <- (14) [resolution 91,216]
277. funny(susan) <- (14) [resolution 274,83]
290. funny(sK1) <- (~11) [resolution 204,199]
296. 9 | 11 [avatar split clause 290,197,188]
303. ~happy(X0) | ~funny(X0) <- (10) [resolution 102,194]
304. ~funny(susan) <- (10, 14) [resolution 303,216]
306. $false <- (10, 14) [subsumption resolution 304,277]
307. ~10 | ~14 [avatar contradiction clause 306]
310. $false [avatar sat refutation 195,201,273,296,307]
% SZS output end Proof for 5115289277266629008142821
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or humble is both not rich and not kind.
Everyone who is either quiet or wise is both not brave and not tall and vice versa.
If someone is either tall or not tall then fred is both not old and not brave.
If mary is both not creative and tall then someone is not strong.
Everyone who is both kind and not calm is not brave or patient and vice versa.
Everyone who is either not rich or not tall is strong or generous and vice versa.
Everyone who is either not tall or wise is both not quiet and not strong and vice versa.
If someone is not humble then susan is not rich.
Everyone who is either not wise or not curious is both rich and funny.
If someone is both not funny and not tall then john is creative and vice versa.
If john is either not rich or funny then someone is both wise and not rich.
Everyone who is not happy or old is creative.
If someone is not humble or brave then someone is quiet and vice versa.
If someone is both generous and not funny then paul is both not wise and brave.
Everyone who is either old or not calm is either not generous or generous and vice versa.
If someone is both creative and happy then fred is not wise.
Mary is both tall and calm.
Paul is curious or not quiet.
Lucy is either calm or wise.
Susan is calm.
Someone is old.
Someone is funny.
Someone is generous.
Susan is generous. | Mary is not strong. | contradiction | (![X]:((tall(X)<~>humble(X))=>(~rich(X)&~kind(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>((~old(fred)&~brave(fred))))&
(((~creative(mary)&tall(mary)))=>(?[X]:(~strong(X))))&
(![X]:((kind(X)&~calm(X))<=>(~brave(X)|patient(X))))&
(![X]:((~rich(X)<~>~tall(X))<=>(strong(X)|generous(X))))&
(![X]:((~tall(X)<~>wise(X))<=>(~quiet(X)&~strong(X))))&
((?[X]:(~humble(X)))=>(~rich(susan)))&
(![X]:((~wise(X)<~>~curious(X))=>(rich(X)&funny(X))))&
((?[X]:((~funny(X)&~tall(X))))<=>(creative(john)))&
(((~rich(john)<~>funny(john)))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~happy(X)|old(X))=>creative(X)))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((generous(X)&~funny(X))))=>((~wise(paul)&brave(paul))))&
(![X]:((old(X)<~>~calm(X))<=>(~generous(X)<~>generous(X))))&
((?[X]:((creative(X)&happy(X))))=>(~wise(fred)))&
((tall(mary)&calm(mary)))&
((curious(paul)|~quiet(paul)))&
((calm(lucy)<~>wise(lucy)))&
(calm(susan))&
(?[X]:(old(X)))&
(?[X]:(funny(X)))&
(?[X]:(generous(X)))&
(generous(susan)) | ~strong(mary) | [
"p1",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7785883420470707322578676
% SZS output start Proof for 7785883420470707322578676
2. ! [X0] : ((quiet(X0) <~> wise(X0)) <=> (~tall(X0) & ~brave(X0))) [input p1]
7. ! [X0] : ((~tall(X0) <~> wise(X0)) <=> (~strong(X0) & ~quiet(X0))) [input p6]
17. calm(mary) & tall(mary) [input p16]
25. ~strong(mary) [input hypothesis]
38. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [flattening 38]
47. ! [X0] : ((((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (strong(X0) | quiet(X0))) & ((~strong(X0) & ~quiet(X0)) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | strong(X0) | quiet(X0)) & ((~strong(X0) & ~quiet(X0)) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))))) [flattening 47]
76. ~quiet(X0) | wise(X0) | ~tall(X0) [cnf transformation 39]
77. ~wise(X0) | quiet(X0) | ~tall(X0) [cnf transformation 39]
96. ~quiet(X0) | wise(X0) | tall(X0) [cnf transformation 48]
97. ~quiet(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 48]
100. wise(X0) | ~tall(X0) | strong(X0) | quiet(X0) [cnf transformation 48]
101. ~wise(X0) | tall(X0) | strong(X0) | quiet(X0) [cnf transformation 48]
130. tall(mary) [cnf transformation 17]
140. ~strong(mary) [cnf transformation 25]
172. 6 <=> tall(mary) [avatar definition]
173. tall(mary) <- (6) [avatar component clause 172]
180. ~wise(X0) | strong(X0) | quiet(X0) [subsumption resolution 101,77]
181. ~tall(X0) | strong(X0) | quiet(X0) [subsumption resolution 100,180]
182. ~wise(X0) | ~tall(X0) [subsumption resolution 97,77]
183. ~quiet(X0) | wise(X0) [subsumption resolution 96,76]
274. 6 [avatar split clause 130,172]
351. 34 <=> wise(mary) [avatar definition]
352. wise(mary) <- (34) [avatar component clause 351]
355. 35 <=> quiet(mary) [avatar definition]
357. quiet(mary) <- (35) [avatar component clause 355]
414. strong(mary) | quiet(mary) <- (6) [resolution 181,173]
417. quiet(mary) <- (6) [subsumption resolution 414,140]
418. 35 | ~6 [avatar split clause 417,172,355]
533. wise(mary) <- (35) [resolution 357,183]
539. 34 | ~35 [avatar split clause 533,355,351]
548. ~tall(mary) <- (34) [resolution 352,182]
559. $false <- (6, 34) [subsumption resolution 548,173]
560. ~6 | ~34 [avatar contradiction clause 559]
561. $false [avatar sat refutation 274,418,539,560]
% SZS output end Proof for 7785883420470707322578676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not funny or brave then someone is both not brave and tall and vice versa. If alice is both strong and rich then lucy is both not curious and not quiet and vice versa. If fred is not calm then someone is not brave or not happy. If paul is creative or not rich then lucy is either not creative or not generous and vice versa. If alice is both not curious and not patient then susan is both kind and not creative and vice versa. Everyone who is kind or not quiet is either wise or generous and vice versa. Everyone who is not wise or not old is either not funny or happy and vice versa. If someone is not calm then paul is either not generous or wise. Everyone who is both wise and generous is not funny. Everyone who is generous or rich is not strong and vice versa. Everyone who is humble or not tall is not patient and vice versa. If lucy is both not strong and not tall then alice is either kind or not curious. If someone is not patient or not humble then lucy is either not calm or not old. Everyone who is either quiet or not strong is both calm and quiet and vice versa. Everyone who is either wise or humble is tall and vice versa. If someone is brave then someone is happy. Susan is both not brave and tall. Someone is not patient. Someone is strong or humble. Someone is not kind. Fred is happy or kind. Someone is happy or not rich. Lucy is either patient or calm. Paul is both strong and creative. | Susan is not creative. | neutral | (((~funny(paul)|brave(paul)))<=>(?[X]:((~brave(X)&tall(X)))))&
(((strong(alice)&rich(alice)))<=>((~curious(lucy)&~quiet(lucy))))&
((~calm(fred))=>(?[X]:((~brave(X)|~happy(X)))))&
(((creative(paul)|~rich(paul)))<=>((~creative(lucy)<~>~generous(lucy))))&
(((~curious(alice)&~patient(alice)))<=>((kind(susan)&~creative(susan))))&
(![X]:((kind(X)|~quiet(X))<=>(wise(X)<~>generous(X))))&
(![X]:((~wise(X)|~old(X))<=>(~funny(X)<~>happy(X))))&
((?[X]:(~calm(X)))=>((~generous(paul)<~>wise(paul))))&
(![X]:((wise(X)&generous(X))=>~funny(X)))&
(![X]:((generous(X)|rich(X))<=>~strong(X)))&
(![X]:((humble(X)|~tall(X))<=>~patient(X)))&
(((~strong(lucy)&~tall(lucy)))=>((kind(alice)<~>~curious(alice))))&
((?[X]:((~patient(X)|~humble(X))))=>((~calm(lucy)<~>~old(lucy))))&
(![X]:((quiet(X)<~>~strong(X))<=>(calm(X)&quiet(X))))&
(![X]:((wise(X)<~>humble(X))<=>tall(X)))&
((?[X]:(brave(X)))=>(?[X]:(happy(X))))&
((~brave(susan)&tall(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((strong(X)|humble(X))))&
(?[X]:(~kind(X)))&
((happy(fred)|kind(fred)))&
(?[X]:((happy(X)|~rich(X))))&
((patient(lucy)<~>calm(lucy)))&
((strong(paul)&creative(paul))) | ~creative(susan) | [] | null | 0 |
Everyone who is strong is not tall or not kind and vice versa.
If someone is not quiet then someone is either not creative or not quiet.
Everyone who is tall or not funny is both brave and not generous and vice versa.
If lucy is both not strong and not quiet then someone is not kind and vice versa.
If someone is not strong then someone is either funny or not brave and vice versa.
If mary is not funny then fred is both strong and tall.
Everyone who is patient or not patient is both not old and generous.
If susan is both strong and happy then alice is both kind and not strong and vice versa.
If someone is not happy or patient then someone is either not patient or rich and vice versa.
If someone is both tall and calm then someone is not calm or humble.
If mary is both brave and funny then someone is not funny or rich and vice versa.
Everyone who is both not old and patient is either not rich or strong.
If someone is both rich and tall then someone is either humble or rich.
If lucy is creative or not happy then someone is calm or happy and vice versa.
Someone is either not humble or happy.
Susan is either strong or not strong.
Someone is humble.
Alice is kind.
Paul is either not creative or quiet. | Mary is not generous. | contradiction | (![X]:(strong(X)<=>(~tall(X)|~kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((tall(X)|~funny(X))<=>(brave(X)&~generous(X))))&
(((~strong(lucy)&~quiet(lucy)))<=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
((~funny(mary))=>((strong(fred)&tall(fred))))&
(![X]:((patient(X)|~patient(X))=>(~old(X)&generous(X))))&
(((strong(susan)&happy(susan)))<=>((kind(alice)&~strong(alice))))&
((?[X]:((~happy(X)|patient(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((tall(X)&calm(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(((brave(mary)&funny(mary)))<=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((~old(X)&patient(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((humble(X)<~>rich(X)))))&
(((creative(lucy)|~happy(lucy)))<=>(?[X]:((calm(X)|happy(X)))))&
(?[X]:((~humble(X)<~>happy(X))))&
((strong(susan)<~>~strong(susan)))&
(?[X]:(humble(X)))&
(kind(alice))&
((~creative(paul)<~>quiet(paul))) | ~generous(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4247579315353124482818173
% SZS output start Proof for 4247579315353124482818173
7. ! [X0] : ((~patient(X0) | patient(X0)) => (generous(X0) & ~old(X0))) [input p6]
20. ~generous(mary) [input hypothesis]
28. ! [X0] : ((generous(X0) & ~old(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 7]
104. generous(X0) | ~patient(X0) [cnf transformation 28]
105. generous(X0) | patient(X0) [cnf transformation 28]
138. ~generous(mary) [cnf transformation 20]
207. generous(X0) [subsumption resolution 104,105]
362. $false [subsumption resolution 138,207]
% SZS output end Proof for 4247579315353124482818173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not funny and generous then susan is both not humble and not rich and vice versa.
Everyone who is not strong or funny is either not curious or not wise.
If someone is both not generous and humble then someone is either funny or not old and vice versa.
Everyone who is tall or not wise is quiet or not humble and vice versa.
Everyone who is either curious or wise is not funny and vice versa.
Everyone who is both patient and not tall is either not tall or not calm.
If someone is both not funny and funny then john is quiet and vice versa.
Everyone who is both not quiet and humble is not brave.
If lucy is both not kind and rich then someone is not generous or not old.
If someone is kind then alice is both not old and wise.
If paul is not strong then someone is humble.
If someone is creative or not creative then someone is both humble and calm and vice versa.
If alice is funny then paul is either quiet or not humble and vice versa.
Everyone who is both not strong and creative is both not tall and tall and vice versa.
Everyone who is both not strong and quiet is both not funny and tall and vice versa.
If fred is not kind or funny then someone is both curious and not kind and vice versa.
Someone is kind or funny.
Someone is both patient and creative.
Alice is both happy and kind.
Someone is either not old or rich.
Someone is not curious.
Fred is not generous or calm.
Someone is both not brave and not generous.
Someone is generous. | Alice is not curious. | entailment | (((~funny(susan)&generous(susan)))<=>((~humble(susan)&~rich(susan))))&
(![X]:((~strong(X)|funny(X))=>(~curious(X)<~>~wise(X))))&
((?[X]:((~generous(X)&humble(X))))<=>(?[X]:((funny(X)<~>~old(X)))))&
(![X]:((tall(X)|~wise(X))<=>(quiet(X)|~humble(X))))&
(![X]:((curious(X)<~>wise(X))<=>~funny(X)))&
(![X]:((patient(X)&~tall(X))=>(~tall(X)<~>~calm(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(quiet(john)))&
(![X]:((~quiet(X)&humble(X))=>~brave(X)))&
(((~kind(lucy)&rich(lucy)))=>(?[X]:((~generous(X)|~old(X)))))&
((?[X]:(kind(X)))=>((~old(alice)&wise(alice))))&
((~strong(paul))=>(?[X]:(humble(X))))&
((?[X]:((creative(X)|~creative(X))))<=>(?[X]:((humble(X)&calm(X)))))&
((funny(alice))<=>((quiet(paul)<~>~humble(paul))))&
(![X]:((~strong(X)&creative(X))<=>(~tall(X)&tall(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~funny(X)&tall(X))))&
(((~kind(fred)|funny(fred)))<=>(?[X]:((curious(X)&~kind(X)))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((patient(X)&creative(X))))&
((happy(alice)&kind(alice)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:(~curious(X)))&
((~generous(fred)|calm(fred)))&
(?[X]:((~brave(X)&~generous(X))))&
(?[X]:(generous(X))) | ~curious(alice) | [
"p1",
"p4",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7552589034074084477642002
% SZS output start Proof for 7552589034074084477642002
2. ! [X0] : ((funny(X0) | ~strong(X0)) => (~curious(X0) <~> ~wise(X0))) [input p1]
5. ! [X0] : ((curious(X0) <~> wise(X0)) <=> ~funny(X0)) [input p4]
10. ? [X0] : kind(X0) => (wise(alice) & ~old(alice)) [input p9]
19. kind(alice) & happy(alice) [input p18]
25. curious(alice) [input hypothesis]
28. kind(alice) [pure predicate removal 19]
31. ! [X0] : ((~curious(X0) <~> ~wise(X0)) | (~funny(X0) & strong(X0))) [ennf transformation 2]
36. (wise(alice) & ~old(alice)) | ! [X0] : ~kind(X0) [ennf transformation 10]
40. ! [X0] : (((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | (~funny(X0) & strong(X0))) [nnf transformation 31]
48. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | funny(X0)) & (~funny(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 5]
91. ~wise(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 40]
107. ~wise(X0) | ~curious(X0) | funny(X0) [cnf transformation 48]
115. wise(alice) | ~kind(X0) [cnf transformation 36]
142. kind(alice) [cnf transformation 28]
149. curious(alice) [cnf transformation 25]
202. ~wise(X0) | ~curious(X0) [subsumption resolution 107,91]
226. 16 <=> ! [X0] : ~kind(X0) [avatar definition]
227. ~kind(X0) <- (16) [avatar component clause 226]
229. 17 <=> wise(alice) [avatar definition]
231. wise(alice) <- (17) [avatar component clause 229]
232. 16 | 17 [avatar split clause 115,229,226]
321. $false <- (16) [resolution 227,142]
322. ~16 [avatar contradiction clause 321]
325. ~curious(alice) <- (17) [resolution 202,231]
326. $false <- (17) [subsumption resolution 325,149]
327. ~17 [avatar contradiction clause 326]
328. $false [avatar sat refutation 232,322,327]
% SZS output end Proof for 7552589034074084477642002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or patient then susan is not patient and vice versa.
Everyone who is either not strong or not patient is both rich and curious and vice versa.
Everyone who is both strong and not kind is funny and vice versa.
Everyone who is not curious is either not brave or not rich and vice versa.
Everyone who is both humble and brave is both generous and kind.
Everyone who is both not funny and generous is either wise or not curious.
If someone is calm then someone is not happy or tall.
If lucy is both happy and brave then fred is curious.
Everyone who is both quiet and kind is curious.
If fred is either kind or not curious then someone is either not kind or not humble.
If susan is not happy or not curious then someone is both not funny and not creative and vice versa.
If someone is either not brave or strong then someone is either generous or curious and vice versa.
Everyone who is not wise or not tall is tall and vice versa.
Everyone who is strong is either tall or generous and vice versa.
Everyone who is funny or not generous is not wise or quiet.
Everyone who is both kind and generous is not curious and vice versa.
Mary is not kind.
Someone is either humble or not wise.
Someone is not funny.
Alice is not kind.
Alice is quiet.
Susan is old. | Fred is not quiet. | neutral | ((?[X]:((brave(X)<~>patient(X))))<=>(~patient(susan)))&
(![X]:((~strong(X)<~>~patient(X))<=>(rich(X)&curious(X))))&
(![X]:((strong(X)&~kind(X))<=>funny(X)))&
(![X]:(~curious(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((humble(X)&brave(X))=>(generous(X)&kind(X))))&
(![X]:((~funny(X)&generous(X))=>(wise(X)<~>~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~happy(X)|tall(X)))))&
(((happy(lucy)&brave(lucy)))=>(curious(fred)))&
(![X]:((quiet(X)&kind(X))=>curious(X)))&
(((kind(fred)<~>~curious(fred)))=>(?[X]:((~kind(X)<~>~humble(X)))))&
(((~happy(susan)|~curious(susan)))<=>(?[X]:((~funny(X)&~creative(X)))))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~wise(X)|~tall(X))<=>tall(X)))&
(![X]:(strong(X)<=>(tall(X)<~>generous(X))))&
(![X]:((funny(X)|~generous(X))=>(~wise(X)|quiet(X))))&
(![X]:((kind(X)&generous(X))<=>~curious(X)))&
(~kind(mary))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:(~funny(X)))&
(~kind(alice))&
(quiet(alice))&
(old(susan)) | ~quiet(fred) | [] | null | 0 |
Everyone who is both funny and not creative is either tall or generous. If paul is either brave or not generous then john is not creative and vice versa. Everyone who is either not brave or not funny is not humble and vice versa. Everyone who is either curious or creative is both not quiet and curious and vice versa. Everyone who is not curious is not old or brave and vice versa. If someone is either quiet or creative then lucy is both not quiet and not generous. Everyone who is both not strong and tall is both not curious and funny. Everyone who is either generous or calm is both not calm and happy and vice versa. Everyone who is both tall and quiet is not patient or rich and vice versa. Everyone who is not kind is quiet or wise and vice versa. Everyone who is both not brave and not wise is either old or not generous and vice versa. Everyone who is not curious is old or not kind. Everyone who is both not old and not happy is both not old and not rich and vice versa. Everyone who is either curious or not humble is not generous and vice versa. If mary is both not creative and curious then mary is not happy. Everyone who is both curious and not kind is not funny. Someone is both not generous and brave. Paul is not kind. Someone is not strong. Fred is not curious or wise. Someone is either brave or not happy. Fred is patient or happy. Someone is humble. Someone is curious. | Lucy is tall. | neutral | (![X]:((funny(X)&~creative(X))=>(tall(X)<~>generous(X))))&
(((brave(paul)<~>~generous(paul)))<=>(~creative(john)))&
(![X]:((~brave(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~curious(X)<=>(~old(X)|brave(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>((~quiet(lucy)&~generous(lucy))))&
(![X]:((~strong(X)&tall(X))=>(~curious(X)&funny(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~calm(X)&happy(X))))&
(![X]:((tall(X)&quiet(X))<=>(~patient(X)|rich(X))))&
(![X]:(~kind(X)<=>(quiet(X)|wise(X))))&
(![X]:((~brave(X)&~wise(X))<=>(old(X)<~>~generous(X))))&
(![X]:(~curious(X)=>(old(X)|~kind(X))))&
(![X]:((~old(X)&~happy(X))<=>(~old(X)&~rich(X))))&
(![X]:((curious(X)<~>~humble(X))<=>~generous(X)))&
(((~creative(mary)&curious(mary)))=>(~happy(mary)))&
(![X]:((curious(X)&~kind(X))=>~funny(X)))&
(?[X]:((~generous(X)&brave(X))))&
(~kind(paul))&
(?[X]:(~strong(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(fred)|happy(fred)))&
(?[X]:(humble(X)))&
(?[X]:(curious(X))) | tall(lucy) | [] | null | 0 |
Everyone who is not rich is either not old or rich and vice versa. Everyone who is either patient or not old is not curious or old and vice versa. If someone is not strong then john is not rich and vice versa. Everyone who is not kind is either not quiet or not kind and vice versa. Everyone who is either generous or funny is both not brave and not rich. If alice is not rich then someone is either not tall or not humble. Everyone who is either funny or not curious is both happy and funny. If lucy is both strong and happy then lucy is not rich or not creative and vice versa. If someone is either curious or kind then someone is either not kind or happy and vice versa. Everyone who is either curious or calm is both not old and kind. If alice is either not humble or not strong then someone is patient. Everyone who is both not rich and not curious is not wise and vice versa. If someone is either creative or not patient then someone is not rich or not wise. If john is brave or not humble then mary is either not curious or not creative. If someone is both not curious and creative then someone is creative or not curious. Everyone who is both happy and not wise is quiet or not old and vice versa. Someone is either not tall or old. Mary is not old. Paul is not strong or not creative. John is not humble or generous. Alice is not funny or not tall. | John is brave. | neutral | (![X]:(~rich(X)<=>(~old(X)<~>rich(X))))&
(![X]:((patient(X)<~>~old(X))<=>(~curious(X)|old(X))))&
((?[X]:(~strong(X)))<=>(~rich(john)))&
(![X]:(~kind(X)<=>(~quiet(X)<~>~kind(X))))&
(![X]:((generous(X)<~>funny(X))=>(~brave(X)&~rich(X))))&
((~rich(alice))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((funny(X)<~>~curious(X))=>(happy(X)&funny(X))))&
(((strong(lucy)&happy(lucy)))<=>((~rich(lucy)|~creative(lucy))))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:((curious(X)<~>calm(X))=>(~old(X)&kind(X))))&
(((~humble(alice)<~>~strong(alice)))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&~curious(X))<=>~wise(X)))&
((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((~rich(X)|~wise(X)))))&
(((brave(john)|~humble(john)))=>((~curious(mary)<~>~creative(mary))))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((happy(X)&~wise(X))<=>(quiet(X)|~old(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(~old(mary))&
((~strong(paul)|~creative(paul)))&
((~humble(john)|generous(john)))&
((~funny(alice)|~tall(alice))) | brave(john) | [] | null | 0 |
If someone is quiet or old then someone is both wise and old and vice versa.
Everyone who is either curious or happy is kind or not humble.
If someone is both humble and not happy then someone is not tall and vice versa.
If john is either not happy or strong then john is curious or brave.
Everyone who is either not funny or not tall is happy.
Everyone who is either generous or not generous is not curious or creative and vice versa.
If someone is either brave or not funny then susan is not patient or generous.
Everyone who is both strong and old is kind and vice versa.
If someone is quiet then someone is both not creative and not generous and vice versa.
Everyone who is either not quiet or not generous is brave or creative.
Everyone who is not calm or wise is happy and vice versa.
If someone is wise then mary is not happy.
Everyone who is calm is not tall or creative and vice versa.
If mary is either not generous or not rich then susan is not curious or generous and vice versa.
Everyone who is not strong is not brave or generous and vice versa.
If someone is either generous or not creative then lucy is both not quiet and happy.
Someone is tall.
Mary is both not funny and not patient.
Mary is both not strong and not patient.
Someone is not curious or strong.
Someone is both humble and tall.
Someone is not calm or not patient.
Someone is both not quiet and kind.
Alice is patient. | Mary is calm. | entailment | ((?[X]:((quiet(X)|old(X))))<=>(?[X]:((wise(X)&old(X)))))&
(![X]:((curious(X)<~>happy(X))=>(kind(X)|~humble(X))))&
((?[X]:((humble(X)&~happy(X))))<=>(?[X]:(~tall(X))))&
(((~happy(john)<~>strong(john)))=>((curious(john)|brave(john))))&
(![X]:((~funny(X)<~>~tall(X))=>happy(X)))&
(![X]:((generous(X)<~>~generous(X))<=>(~curious(X)|creative(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>((~patient(susan)|generous(susan))))&
(![X]:((strong(X)&old(X))<=>kind(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((~quiet(X)<~>~generous(X))=>(brave(X)|creative(X))))&
(![X]:((~calm(X)|wise(X))<=>happy(X)))&
((?[X]:(wise(X)))=>(~happy(mary)))&
(![X]:(calm(X)<=>(~tall(X)|creative(X))))&
(((~generous(mary)<~>~rich(mary)))<=>((~curious(susan)|generous(susan))))&
(![X]:(~strong(X)<=>(~brave(X)|generous(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>((~quiet(lucy)&happy(lucy))))&
(?[X]:(tall(X)))&
((~funny(mary)&~patient(mary)))&
((~strong(mary)&~patient(mary)))&
(?[X]:((~curious(X)|strong(X))))&
(?[X]:((humble(X)&tall(X))))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((~quiet(X)&kind(X))))&
(patient(alice)) | calm(mary) | [
"p0",
"p7",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3483490109812512669761426
% SZS output start Proof for 3483490109812512669761426
1. ? [X0] : (old(X0) | quiet(X0)) <=> ? [X0] : (old(X0) & wise(X0)) [input p0]
8. ! [X0] : ((old(X0) & strong(X0)) <=> kind(X0)) [input p7]
11. ! [X0] : ((wise(X0) | ~calm(X0)) <=> happy(X0)) [input p10]
12. ? [X0] : wise(X0) => ~happy(mary) [input p11]
23. ? [X0] : (kind(X0) & ~quiet(X0)) [input p22]
25. ~calm(mary) [input hypothesis]
26. ? [X0] : (old(X0) | quiet(X0)) <=> ? [X1] : (old(X1) & wise(X1)) [rectify 1]
29. ! [X0] : (kind(X0) => (old(X0) & strong(X0))) [unused predicate definition removal 8]
37. ! [X0] : ((old(X0) & strong(X0)) | ~kind(X0)) [ennf transformation 29]
40. ~happy(mary) | ! [X0] : ~wise(X0) [ennf transformation 12]
42. (? [X0] : (old(X0) | quiet(X0)) | ! [X1] : (~old(X1) | ~wise(X1))) & (? [X1] : (old(X1) & wise(X1)) | ! [X0] : (~old(X0) & ~quiet(X0))) [nnf transformation 26]
43. (? [X0] : (old(X0) | quiet(X0)) | ! [X1] : (~old(X1) | ~wise(X1))) & (? [X2] : (old(X2) & wise(X2)) | ! [X3] : (~old(X3) & ~quiet(X3))) [rectify 42]
44. ? [X0] : (old(X0) | quiet(X0)) => (old(sK0) | quiet(sK0)) [choice axiom]
45. ? [X2] : (old(X2) & wise(X2)) => (old(sK1) & wise(sK1)) [choice axiom]
46. ((old(sK0) | quiet(sK0)) | ! [X1] : (~old(X1) | ~wise(X1))) & ((old(sK1) & wise(sK1)) | ! [X3] : (~old(X3) & ~quiet(X3))) [skolemisation 43,45,44]
64. ! [X0] : (((wise(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (~wise(X0) & calm(X0)))) [nnf transformation 11]
65. ! [X0] : ((wise(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (~wise(X0) & calm(X0)))) [flattening 64]
81. ? [X0] : (kind(X0) & ~quiet(X0)) => (kind(sK10) & ~quiet(sK10)) [choice axiom]
82. kind(sK10) & ~quiet(sK10) [skolemisation 23,81]
84. wise(sK1) | ~old(X3) [cnf transformation 46]
106. ~kind(X0) | old(X0) [cnf transformation 37]
112. calm(X0) | happy(X0) [cnf transformation 65]
115. ~happy(mary) | ~wise(X0) [cnf transformation 40]
142. kind(sK10) [cnf transformation 82]
144. ~calm(mary) [cnf transformation 25]
160. 4 <=> ! [X3] : ~old(X3) [avatar definition]
161. ~old(X3) <- (4) [avatar component clause 160]
172. 7 <=> wise(sK1) [avatar definition]
174. wise(sK1) <- (7) [avatar component clause 172]
175. 4 | 7 [avatar split clause 84,172,160]
252. 25 <=> ! [X0] : ~wise(X0) [avatar definition]
253. ~wise(X0) <- (25) [avatar component clause 252]
255. 26 <=> happy(mary) [avatar definition]
258. 25 | ~26 [avatar split clause 115,255,252]
317. old(sK10) [resolution 106,142]
318. happy(mary) [resolution 112,144]
321. 26 [avatar split clause 318,255]
322. $false <- (7, 25) [resolution 253,174]
323. ~7 | ~25 [avatar contradiction clause 322]
324. $false <- (4) [resolution 317,161]
325. ~4 [avatar contradiction clause 324]
326. $false [avatar sat refutation 175,258,321,323,325]
% SZS output end Proof for 3483490109812512669761426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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